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{"url":"http:\/\/geothermalresourcescouncil.blogspot.com\/2019\/04\/usa-california-geothermal_22.html","text":"Monday, April 22, 2019\n\nUSA, California: Testing Begins at Coso Closed-Loop Geothermal Power Generation Project\n\nGreenFire Energy Completes Construction of the First Field-Scale Demonstration of\u00a0 Closed-Loop Geothermal Power Generation\u00a0(News Release)\n\nTesting of the Demonstration Begins at the Coso, California, Geothermal Field\n\nGreenFire Energy Inc. today announced the completion of construction and the beginning of testing of the world\u2019s first field-scale demonstration of a closed-loop geothermal power system.\n\nThe project uses an inactive well in the Coso, California, geothermal field.\n\nAcceptance testing of key components is in process and active flow testing will begin in late April. A final report of testing results will be made available to the California Energy Commission and project participants later this year.","date":"2019-05-21 11:47:59","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\": 0.8367826342582703, \"perplexity\": 8309.356280653834}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-22\/segments\/1558232256314.52\/warc\/CC-MAIN-20190521102417-20190521124417-00332.warc.gz\"}"}	null	null
Q: AWS Canary Selenium User Agent String I am looking to set a custom user agent in AWS Selenium Canary, but somehow what I am trying to do is not working According to this documentation I should be able to change/append a string to the browser's user agent header... add_user_agent(user_agent_str) Appends the value of user_agent_str to the browser's user agent header. You must assign user_agent_str before creating the browser instance. Example: synthetics_webdriver.add_user_agent('MyApp-1.0') https://docs.aws.amazon.com/AmazonCloudWatch/latest/monitoring/CloudWatch_Synthetics_Canaries_Library_Python.html This is my sample code from selenium.webdriver.support.ui import WebDriverWait from selenium.webdriver.support import expected_conditions as EC from selenium.webdriver.common.by import By from selenium.webdriver.common.keys import Keys import selenium.common.exceptions from aws_synthetics.selenium import synthetics_webdriver from aws_synthetics.common import synthetics_logger as logger from aws_synthetics.common import synthetics_configuration async def main(): synthetics_configuration.set_config( { "screenshot_on_step_start": False, "screenshot_on_step_success": True, "screenshot_on_step_failure": True } ) synthetics_webdriver.add_user_agent('My User Agent String') driver = synthetics_webdriver.Chrome() driver.get('myurl.com') user_agent = driver.execute_script('return navigator.userAgent') # should be/contain 'My User Agent String' but instead looks like 'CloudWatchSynthetics-arn' logger.info('This is the user agent string: {}'.format(user_agent)) # selenium python tests async def handler(event, context): return await main() I've done a lot of debugging, making sure the method exists, moving the method to the top of a file, but I haven't had any luck getting it to work Any help would be greatly appreciated, Thanks in advance. A: From what I see, you need to create an object first to execute the add_user_agent method and save that state. I don't have the environment so please try this and let me know the result in the comment. syn_wdriver = synthetics_webdriver # syn_wdriver = synthetics_webdriver() # try this one if above does not work, i'm not sure about the syn_webdriver object syn_wdriver.add_user_agent('My User Agent String') driver = syn_wdriver.Chrome() Or: driver = synthetics_webdriver.add_user_agent('My User Agent String').Chrome() A: I just dove into my own code again and realize I was making a simple mistake this was my structure def myfunction(): # my selenium test myfunction() However, when I did this, the add_user_agent function for some reason does not inject the browser user agent header with the string when i changed the code to this def myfunction(): # selenium tests webdriver.execute_step('StepName', myfunction) it worked just fine...	{ "redpajama_set_name": "RedPajamaStackExchange" }	623
The Larsen C ice shelf collapse hammers home the reality of climate change NASA handout photo dated 10/11/16 showing a rift in the Larsen C Ice Shelf in Antarctica, as scientists have said that an iceberg a quarter the size of Wales is poised to break off from it. Photo: John Sonntag, PA, NASA Very soon, a large portion of an ice shelf in Antarctica will break off and collapse into the ocean. The name of the ice shelf is Larsen C; it is a major extension from of the West Antarctic ice sheet, and its health has implications for other ice in the region, and sea levels globally. [I]t is important for a number of reasons. First, when an ice shelf melts or collapses, it can unpin other ice that is sitting on land, which allows it to flow more quickly into the ocean. It is this secondary effect – the loss of ice resting on land – that changes the rate of sea level rise. Loss of a major ice shelf can also activate ice that rests on bedrock topography that makes it fundamentally unstable – ice that, once moving, will move faster and faster, until a large region is afloat. Perhaps a quotation from a seminal work on Antarctic ice sheets best sums up the situation. In a 1978 paper, John Mercer from the Institute of Polar studies concluded: One of the warning signs that a dangerous warming trend is under way in Antarctica will be the breakup of ice shelves on both coasts of the Antarctic Peninsula, starting with the northernmost and extending gradually southward. These ice shelves should be regularly monitored by LANDSAT imagery. Why is the ice shelf going to break off and collapse into the ocean? Since large calving events are so rare, and since our measurements in and around ice shelves don't go back in time far enough, it's hard to say whether this is a natural progression, variability, or a result of human activity (or more likely a mixture). A major reason may be human-caused warming, which has led to melting from both above and below in nearby areas. The Western Antarctic (the parts south of the U.S.) is warming quite quickly, faster than most of the planet. In addition, warmer waters can reach underneath the ice shelf and can melt it from below. That being said, there are vigorous discussions within the scientific community about how much, if any of this can be attributed to humans. Some scientists think there is strong connection; others are much less sure and see little or no evidence that humans are the cause. From my vantage point, part of this relates to our limited ability to measure what's going on, and part of this is a common sticking point of whether an absence of evidence is evidence of an absence. Antarctic Melt 1992 - Larsen C Ice Shelf Calving and Retreat 2017	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	9,489
# V. S. Naipaul A TURN IN THE SOUTH V. S. Naipaul was born in Trinidad in 1932. He went to England on a scholarship in 1950. After four years at Oxford he began to write, and since then he has followed no other profession. He is the author of more than twenty books of fiction and nonfiction and the recipient of numerous honors, including the Nobel Prize in 2001, the Booker Prize in 1971, and a knighthood for services to literature in 1990. He lives in Wiltshire, England. B OOKS BY V. S. NAIPAUL NONFICTION _The Writer and the World_ _Between Father and Son: Family Letters_ _Beyond Belief: Islamic Excursions Among the Converted Peoples_ _India: A Million Mutinies Now_ _A Turn in the South_ _Finding the Center_ _Among the Believers_ _The Return of Eva Perón_ (with _The Killings in Trinidad_ ) _India: A Wounded Civilization_ _The Overcrowded Barracoon_ _The Loss of El Dorado_ _An Area of Darkness_ _The Middle Passage_ FICTION _Half a Life_ _A Way in the World_ _The Enigma of Arrival_ _A Bend in the River_ _Guerrillas_ _In a Free State_ _A Flag on the Island_ * _The Mimic Men_ _Mr. Stone and the Knights Companion_ * _Miguel Street_ _A House for Mr. Biswas_ _The Suffrage of Elvira_ * _The Mystic Masseur_ *Published in an omnibus edition entitled _The Nightwatchman's Occurrence Book_ FIRST VINTAGE INTERNATIONAL EDITION, FEBRUARY 1990 _Copyright_ © _1989 by V. S. Naipaul_ All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by Vintage Books, a division of Random House, Inc., New York. Originally published, in hardcover, by Alfred A. Knopf, Inc., New York, in 1989. Library of Congress Cataloging-in-Publication Data Naipaul, V. S. (Vidiadhar Surajprasad), 1932– A turn in the South / V. S. Naipaul. —1st Vintage international ed. p. cm. —(Vintage international) "A portion of this work was originally published in the New Yorker"—T.p. verso. eISBN: 978-0-307-78928-0 1. Southern States—Civilization—20th century. 2. Southern States—Social life and customs—1865– 3. Naipaul, V. S. (Vidiadhar Surajprasad), 1932– —Journeys—Southern States. I. Title. [F216.2.N35 1990] 975—dc20 89-40108 A portion of this work was originally published in _The New Yorker_. Grateful acknowledgment is made to the following for permission to reprint previously published material: _Louisiana State University Press:_ Selections from the poetry of James Applewhite. Reprinted by permission. _The Songwriter Guild of America:_ Excerpt from "Late in the Day" by Timothy O'Brien. Copyright © 1987 by Pinspotter Music, Inc. Pursuant to secitons 304(c) and 401(b) of the U.S. Copyright Act. All rights administered by The Songwriters Guild of America. _Warner/Chappell Music Inc.:_ Excerpt from "Eighteen Wheels and a Dozen Roses" by Gene Nelson and Paul Nelson. Copyright © 1988 by Warner-Tamerlane Publishing Corp., Believus or Not Music, Screen Gems-EMI Music. All rights reserved. Used by permission. _Polygram International Publishing Companies:_ Excerpt from "Good Ole' Boys Like Me" by Bob McDill. Copyright © 1979 by Polygram International Publishing, Inc. International copyright secured. All rights reserved. Used by permission. v3.1 _There is a history in all men's lives Figuring the natures of the times deceased_. SEEPERSAD NAIPAUL 14 April 1906 3 October 1953 In ever renewed homage # CONTENTS _Cover_ _About the Author_ _Other Books by This Author_ _Title Page_ _Copyright_ _Epigraph_ [_Dedication_ ](Naip_9780307789280_epub_fm1_r1.htm) [Prologue DOWN HOME: A LANDSCAPE OF SMALL RUINS](Naip_9780307789280_epub_prl_r1.htm) [1 ATLANTA: TUNING IN](Naip_9780307789280_epub_c01_r1.htm) [2 CHARLESTON: THE RELIGION OF THE PAST](Naip_9780307789280_epub_c02_r1.htm) [3 TALLAHASSEE: THE TRUCE WITH IRRATIONALITY I](Naip_9780307789280_epub_c03_r1.htm) [4 TUSKEGEE: THE TRUCE WITH IRRATIONALITY II](Naip_9780307789280_epub_c04_r1.htm) [5 JACKSON, MISSISSIPPI: THE FRONTIER, THE HEARTLAND](Naip_9780307789280_epub_c05_r1.htm) [6 NASHVILLE: SANCTITIES](Naip_9780307789280_epub_c06_r1.htm) [7 CHAPEL HILL: SMOKE](Naip_9780307789280_epub_c07_r1.htm) # PROLOGUE # Down Home: A Landscape of Small Ruins JIMMY WORKED in New York as a designer and lettering artist. Howard was his assistant. Jimmy, who could become depressed at times, said to Howard one day, "Howard, if I had to give up, and you couldn't get another job, what would you do?" Howard, who was from the South, said, "I would go home to my mama." Jimmy was as struck by this as I was when Jimmy told me: that Howard had something neither Jimmy nor I had, a patch of the earth he thought of as home, absolutely his. And that was where—many months after I had heard this story—I thought I should begin this book about the South: with the home that Howard had. Howard arranged the visit. Jimmy decided to come with us. We went on the Easter weekend; the timing was pure chance. It was raining, had been raining in New York for two days. At La Guardia Howard said, "I hated the place when I was young, for the continuity." I thought he meant historical continuity, the past living on. But from other things he then said, I felt he meant only that it was a country place where little changed and little happened. I had this trouble with Howard's words sometimes; I was too ready to find in them meanings he didn't intend. Howard was six feet tall, but slender and light of movement. He was in his late twenties or early thirties. He was very much his own man. He lived alone, and he preferred not to live in Harlem. He was a serious reader of newspapers and magazines, and he had a special interest in foreign affairs. He liked to cook; and he kept himself fit by playing paddle ball on weekends. He was easy to be with, not spiky; and I put this down in part to the home he was so sure of and still close to. Howard said, "You see how the South begins. More black people here, on the plane." Most of the passengers were black, and they were not like an African or West Indian crowd. They were almost subdued, going home from the big city for Easter. We landed at Greensboro. It was a big airport; and then, just a few minutes away, proof of the scale of things here, there was another airport, just as big. We got off there. There were military people in the waiting areas. It was warmer than in New York; I changed into a lighter jacket. Soon we were on the highway. Howard said, "Look, the dogwood and the pines. It is what you see a lot of in the South." The dogwood was a small tree, and it was now in single-petaled white blossom. Not the dogwood of England, the water-loving red-stemmed shrub or small tree that made a bright autumn and winter show. And there were—Howard identified them for me—oaks and maples, in the freshest spring-green. The land was flat, like the pampas of Argentina or the llanos of Venezuela. But trees bordered the fields and gave a human scale to things. We passed tobacco barns, tallish, squarish, corrugated-iron structures, where in the old days tobacco was cured. They were in decay, the corrugated iron rusted dark red, the wood weathered gray. Against the green this corrugated-iron rust was a lovely color; it gave an extra beauty to the land. The highway looked like highways everywhere else in the United States: boards for motels and restaurants and gas stations. Tobacco was still a crop. We saw the seedlings being mechanically planted: one black man on the tractor, two men on the trolley behind dropping earth-rooted seedlings down a shafted dibble. All this used to be done by hand, Howard said. He picked tobacco in the school holidays. The resin from the green leaf stained his hands black and was hard to clean off. I never knew about this black-staining resin from the green leaf, but it was immediately comprehensible. It was for that resin, that tar, that people smoked the cured leaf. We had driven so fast on the highway that we were in Howard's area almost before I was ready for it. There was a small town center, a small rich white suburb attached to that town, and then outside that a black area. The differences were noticeable. But Howard, near his home now, appeared to claim both the white area and the black area. He had been excited all morning; he was more excited now. And then, entering another little town, we were seeing the places he had known as a boy. He had cut the grass and cleaned the swimming pool and mopped the porch of that house, the Bowen house, the house of the people who still more or less owned the little town that was called Bowen. And he had done the same job for people in that other house. That little green wooden house, now closed up, just beside the highway, had been his mother's house. He had grown up there. His mother lived in another house now; another house—bigger and newer—was home. We saw it from the highway. It was a concrete-block house set back from the road, behind some other houses: not the old, tree-embowered house I had had in my imagination. We didn't stop; we were going first to the motel, which was some way outside the town. The main building of the motel was a loghouse. In the sandy yard there were subsidiary little barracklike room-rows below trees and behind shrubs. A black boy was hosing down the veranda floor of the loghouse. He looked timid—for the first time that morning I had a feeling of racial constraint—and he said the office was inside. There was no apparent office. Only an empty low-ceilinged room with two or three close-set rows of little tables with red- or blue-checked tablecloths. The air conditioning had been turned off a long time before, and the air was dead and smelly. Howard called out, and after some time a young white man in shorts, with a yellow plastic apron and a large kitchen knife, came in from the back, through two doors. He was sallow, open-mouthed, and his movements were uncoordinated. A little while later a fat old white woman with a twisted face came in through the same two doors. I felt we had been wrong to disturb them, the old woman and the young man who was really a boy. Two rooms? Would we want two double rooms or two single rooms? I couldn't understand the old woman's questions. But then, putting down his knife, the boy with the shorts and the yellow plastic apron half beckoned to us, and we followed him—he walked with stamping, awkward steps—out of the dining room to the sandy yard below the pine trees, and then to a low building at the edge of the yard. The ground there was damp; and the small rooms that the boy opened up, one after the other, had the dampness of the ground, with a shut-in, old smell, and with stained cheap carpets. Better judgment was at work, however. And even while Jimmy and I were looking at the rooms with the silent boy in the yellow apron, Howard—who had not followed us—had heard from somebody in the motel (perhaps the old woman with the twisted face) that there was a more up-to-date motel in the next town, Peters. (Bowen, Peters: American places, big and small, are often named after people; and the ordinariness of the names can make some itineraries read like the muster of an army squad or a sports team.) To Peters, then, we went, through the highway landscape. And the Peters motel was an altogether bigger affair, with a number of two-story buildings in red brick. It even advertised a swimming pool (though something had happened to the filter, and the pool was green with algae). Howard, going up the steps ahead of us and entering the office through the two doors, turned to me and said mysteriously, with a touch of humor, "This is something for you." And what he meant by that was that the lady in the office was Indian, unmistakably, Indian from India, though she was not in a sari, and though there was an un-Indian confidence in her voice and manner. Her speech was American—to me. It let her down only once, when she said, in her brisk, undeferential way, that coffee and things like that were not available on the "pre-mises," making the word rhyme with "vices." That was Indian; that had a flavor of India. I heard later from Howard that in the last six years or so Indians from India had been buying the motels in the South from white people. (And this perhaps explained the big neon sign, AMERICAN OWNED, that I saw some time later on a motel in northwestern Georgia.) So there, in the place that was home to Howard: the white folk, who might have come out of a novel; and, not far away, people from the other side of the world who were already making themselves American, according to the special idea they would have had of the word. The motel lady's husband came into the office. He too was Indian. He wore a short-sleeved fawn-colored velour shirt, and he had a Texas accent—or so it seemed to me. His wife had said (and he now confirmed) that he had been in the oil business, as a petroleum engineer, in Houston. He had left oil and Houston six years before; and he thought (as his wife had said earlier, though admitting that Peters, North Carolina, was a very quiet place) he had made a good decision. HETTY'S HOUSE, Howard's new home, had been built in parts by Hetty herself, with her own hands. It was set back from the road, behind other houses in the settlement, and a drive led to it from the highway. The site had been well chosen. The house had a front portico with steps on either side, and a porch-garage at the end of the drive from the highway. At the back of the house was woodland. The fluffy, carpeted, upholstered sitting room was welcoming. In one corner was the kitchen, with a dining or serving counter. The bedrooms and general rooms were on either side of a central corridor that ran off from the sitting room. Hetty was a big but shapely woman. She was sixty, but her skin was still good. She wore glasses. She made a great deal of friendly noise welcoming Jimmy, whom she knew; and Howard acted out the role of the son returning home. He sat on a high stool in front of the kitchen counter, relaxed, his limbs elegantly arranged, one leg folded, one leg straight: in this house a son and now, in addition, half our host. On the wall beside the door that led to the porch-garage there were family photographs, including one of Howard in a graduation gown. We had lunch: fried fish, collard greens, sweet potatoes with the color of boiled carrots. Four of us sat at the dining table in the dining part of the front reception room. While we were sitting—I with my back to the front door, which opened out onto the portico with the steps on either side—there were great shouts. A party had arrived: Hetty's sister from Augusta, Dee-Anna (as I heard the name), and Dee-Anna's husband and son. Dee-Anna didn't look like Hetty. She was much bigger and more full of bulges than Hetty, and darker (Hetty was brown). She was more vivacious—acting up a little to her figure—but she had more searching eyes. She didn't have Hetty's serenity. Dee-Anna's son seemed sloppily dressed at first, but then I saw that his outfit had been assembled with care and was absolutely for show: a slate-blue jacket in the contemporary shapeless style, a shining, textured white shirt, tapered trousers with patches and exposed labels, and new shoes (new from the near-white appearance of the instep). Easter visitors; holiday dressing up. They talked for a while about a recent big boxing match. They all liked the winner. Howard said he was like a modern black man, smooth and educated; the other fellow was big and strong, but rougher. The young man with the contemporary clothes asked what I was doing in North Carolina. When I told him, he said, "What sort of book? Historical?" And when Howard and I explained, Dee-Anna said, with a knitting of her brows, "I hope you are not going to give us the gloom." Her son—his seriousness now seeming quite separate from his clothes—said, "We've had too much of the past." They were not interested in the past; they were interested in the present. IT HAD not occurred to me to ask whether Hetty did a job. Howard hadn't told me; and it was only after we had got to the house that I gathered that she worked part-time in the café side of a convenience store that was owned by the present head of the Bowen family. She took Jimmy and me to meet him after lunch. She said he was a good man. The convenience store was only one of Mr. Bowen's interests. We went to see him in his furniture factory. He said that he wasn't really a Bowen. He had only married into the family, but people spoke of him as a Bowen, and he had grown to accept the name. The first record of the name in the town of Bowen was a few years before the Declaration of Independence, but at that time the name of the town was Lawrence (which suggested some kind of dispossession during or after the War of Independence). History, though, wasn't what Mr. Bowen wanted to talk about. He was a big man in his early sixties, and he wanted Jimmy and me to see the furniture he made; he wanted to talk about business in Bowen; he wanted us to know that the little town was a go-ahead place, that, though it had only a few thousand people, there were very many millions deposited in the local banks. He was a Bowen man through and through; and while he gave us all the figures, walking Jimmy and me round the furniture factory, showing us the things he or his machines did with veneers, Hetty stood aside, in her full denim skirt, with something of Howard's elegance in her posture. Bowen—I had never heard of the name of the place until Howard had told me. And here it was everywhere, attached to every kind of local business, farm equipment and agricultural supplies, general store, video rentals, gas station, furniture, convenience store. He was a good man, Hetty said again, after we had left Mr. Bowen and the furniture factory. She had gone to him when she wanted $5,000 for her house. He had spoken that same day to the bank, and a loan had been arranged, and all that the bank had required as security was Hetty's car and some other small thing. And Mr. Bowen was a religious man, Hetty said. He had given land for the black cemetery. She had a family plot there, with carved headstones. We drove through suburban woodland to the cemetery. We drove up almost to the headstones. Hetty wanted us to see them, but she didn't encourage us to get out of the car. We stayed in the car and looked for a while. It was a small cemetery, not set apart by a fence or any kind of planting. Now, with all the spring growth, it was like part of the woodland. One of the headstones was of Hetty's father. When we were back in the house she told us something about him. He was a smart man; there had always been a lot of food in the house because of him. He worked on a farm for a white man—and I was beginning to understand how necessary it was for Hetty to define people in the way she did. The white man took no interest in his farm. Hetty's father did it all for him, the selling of the produce and everything. Now the farmhouse—where Hetty's father had lived and died—had deteriorated. It was still owned by the white family, but they didn't want to sell; they wanted to keep it for the memory. Where did this father of Hetty's come from? He had died in 1961. Had he perhaps been born around 1900? In 1894, Howard said. That was the year on the headstone in the black cemetery, on the land given by Mr. Bowen. And the story of the father was vague. He had been orphaned; he had run away from a difficult uncle and had found a job on the railroad and had then fetched up here, sharecropping for Mr. Smith, the white man, and ending successfully, being one of the first black men in the area to own a car. It was not possible to get more about this father, to push back further into time. Beyond that was vagueness, and the gloom Hetty's sister and the sister's son, and perhaps all black people, had had too much of. Later, after a nap—Jimmy in one of the bedrooms of Hetty's house, I in another—and after tea, we went out for a drive. Hetty knew the land well; she knew who owned what. It was like a chant from her, as we drove. "Black people there, black people there, white people there. Black people, black people, white people, black people. All this side black people, all this side white people. White people, white people, black people, white people." Sometimes she said, "Black people used to own this land." She didn't like that—that black people had lost land because they had been slack or because of family disputes. But blacks and whites appeared here to live quite close to one another, and Hetty herself had no racial complaints. White people had been good to her, she said. But then she said that that might have been only because she liked people. It was a landscape of small ruins. Houses and farmhouses and tobacco barns had simply been abandoned. The decay of each was individual, and they were all beautiful in the afternoon light. Some farmhouses had very wide eaves, going down low, the corrugated iron that once provided shelter now like a too-heavy weight, the corrugated-iron sheets sagging, fanning out in places. We went to see the house, now abandoned, where Hetty's father had lived when he had sharecropped for Mr. Smith. Bush grew right up against the open house. The pecan trees, still almost bare, just a few leaves now, were tall above the house and the tobacco barns. The colors were gray (tree trunks and weathered timber) and red (rusted corrugated iron) and green and the straw-gold of reeds. As we stood there Hetty told us of the death of her father in that house; the event was still vivid to her. Another house, even more beautiful, was where Hetty and her husband had lived for ten years. It was a farmhouse with a big green field, with forest trees bounding the distance on every side. Home was not for Howard just his mother's house, the little green house that was now closed up, or the new concrete-block house she had moved to. Home was what we had seen. And we had seen only a part: all about these country roads, within a few miles, were houses and fields connected with various members of Howard's family. It was a richer and more complicated past than I had imagined; and physically much more beautiful. The houses I was taken to were bigger than the houses many people in Trinidad or England might have lived in. But, stili, in the past there was that point where darkness fell, the historical darkness, even here, which was home. We went to dinner at the Seafood Bar-B-Q. It was really the only place possible. It was a roadhouse, a big dimly lit room with a silent jukebox and a few dressed-up white family groups. Beer couldn't be served. So we had the iced tea, which Howard said was very Southern. It was syrupy, the taste no doubt of the waitresses, who were white and young and friendly. One of them was very young, perhaps about twelve, and delighted to be dressed like a waitress, helping out a sister or a parent during the holiday weekend, serving goodies. I asked Hetty what she wanted for herself and her family. Her reply was strange and moving. For her family, she said, she wished that one of her sons had been cured of his drinking. And this was strange because it was a look backwards: the son she spoke of was dead. For herself, she said she would like, if it were possible, to get married. She didn't want to get married for the sake of getting married. She was old—she knew that—but that was why she would like to get married. She spent too much time alone; she wanted the companionship. Howard understood. But both he and Hetty didn't think it would be easy for her to find someone. Hetty said: "Men are scarce here. There are very few men here. Go to church and count the men. The good ones have gone away. And the ones who have stayed are no good. There may be a couple of good ones on the quiet, but..." What of the past, though? Had it been a reasonable sort of life? She said she had no regret for the past. Hadn't things got better for her? Hadn't things got better in the 1950s? She said, "I hardly think even about my own past." And Howard said, "I can hardly remember the past." The words were like the words spoken at lunchtime by Hetty's sister. But then Hetty said: "I didn't like the tobacco. It would make me sick at the end of one row, smell and all. When I was married we would get up early in the morning, when the dew was still on the tobacco leaves, and it didn't smell then. Even now tobacco makes me sick. When I was young I would be in a field and after two hours I would cry. That was when I was working with my father." And behind that was the unmentionable past. ON SATURDAY Hetty had talked with holiday excitement of the Easter Sunday sunrise service at five in the morning. She had said she might go to that. But when Jimmy and I checked out of the Peters Indian motel in the morning and went to the house for breakfast, we found Hetty there. The driving around the previous afternoon had tired her; she hadn't been able to make the sunrise service. She thought now she would go to the eleven o'clock service. Jimmy and I thought that we would go at eleven-thirty to hear the singing and at least the beginning of the sermon, which Hetty said would start at twelve. The problem about that was Jimmy's clothes. In New York Howard had said that Bowen was a very country sort of place and that casual clothes and sneakers would be enough for whatever we might have to do. The only warm-weather clothes Jimmy had was a Banana Republic safari outfit. Hetty said it would be all right; but she would at a certain stage have to stand up in church and ask the congregation's forgiveness for his clothes. On the television set in Hetty's sitting room there was constant religious excitement, with services from black churches and white churches, pastor and choir always stylishly dressed, each church having its own colors in clerical gowns, almost its own livery. One preacher, with a serious, hectoring manner, broke off from the matter in hand to give a puff for a new book about the Bible and the afterlife. The book answered the questions people asked, he said. "Will we be merry in heaven?" And before I could fully savor that "merry"—merry with wine, Merry Christmas, Old King Cole was a merry old soul—the other question the book answered was spoken: "Will there be progress in heaven?" This American heaven clearly being a replication of American earth, with black and white, and North and South, and Republicans and Democrats. Hetty, going into her room in her denim skirt, came out dressed for church in a bright-pink dress, quite overwhelming; and then she put on her flat dark-blue hat. The hat, and her glasses, gave her an executive appearance. She drove to church. Howard had allowed his driver's license to lapse; he couldn't drive Hetty and then come back for us. We walked. The church was about a mile away. Jimmy was in his Banana Republic clothes. Howard was casually dressed and in sneakers; he wasn't going to the service. He said he didn't like going to church; it was something he had had to do too often when he was a child. The road was wide. Cars went by one or two at a time. The grass was full of purple spring flowers; and from time to time, unexpectedly, there was black swamp (making one think of the primeval land, before the settlers came, and of the desolation the settlers must have felt sometimes). We walked past Mr. Alexander's house. He was an old black man, formally dressed for Sunday, with a jacket and tie and hat; and he was in the bare patch of ground at the side of his house, practicing putts, or at any rate holding a golf club. The area in front of his small house was choked with ornamental garden statuary and anything that could be put in a yard as an ornament. He said his grandfather had started the collection; and then, with his own quicksilver sense of time, he said, "Two hundred years." Some of the pieces came from Jamaica in the West Indies; Mr. Alexander pronounced it "Jee-maica." Howard said, as we walked on, "You can tell he's an oddball. Not only because of the golf club. But because he's not at church." A car stopped on the road beside us. There were three white men inside—the race and color of people being now what was very noticeable about them. They wanted to know where the country club golf course was. Howard said he couldn't help them; he was a visitor himself. And they drove on. The church was small and neat, in red brick, with a white spire and with the pediment of its portico resting on slender wooden columns. There were many cars in the yard at the side of the church. I said the cars made the town look rich. Howard said everybody had a car; cars meant nothing. As we went up the steps to the portico Howard said, "They're singing." He didn't go in with us. He said—very boyish now, very much the licensed son—that he would wait outside. A slender young brown woman welcomed Jimmy and me at the door and gave us an order of service. We sat at the back. And I remembered what Hetty had said: "Go to the church. Count the men." The men were fewer than the women. Some children were at the back, with their mothers. And everyone—as Hetty had hinted—was in his Sunday best. The church inside was as plain and neat as it was outside. It had newish blond hardwood pews and a fawn-colored carpet. At the end of the hall, on a dais, was the choir, with a pianist on either side. The men of the choir, in the back row, were in suits; the women and girls, in the three front rows, were in gold gowns. So that it was like a local and smaller version of what we had been seeing on the television in Hetty's sitting room. At the back of the choir, at the back of the girls in gold and the men in dark suits, was a large, oddly transparent-looking painting of the baptism of Christ: the water blue, the riverbanks green. The whiteness of Christ and the Baptist was a surprise. (As much a surprise as, the previous night, in the house of the old retired black teacher, the picture of Jesus Christ had been: a bearded figure, looking like General Custer in _Little Big Man_.) But perhaps the surprise or incongruity lay only in my eyes, the whiteness of Jesus being as much an iconographical element as the blueness of the gods in the Hindu pantheon, or the Indian-ness of the first Buddhist missionary, Daruma, in Japanese art. The singing ended. It was time for "Reports, Announcements, and Recognition of Visitors." The short black man in a dark suit who announced this—not the pastor—spoke the last word in an extraordinary way, breaking the word up into syllables and then, as though to extract the last bit of flavor from the word, giving a mighty stress to the final syllable, saying something like "vee-zee-TORRS." He spoke, and waited for declarations. One man got up and said he had come from Philadelphia; he had come back to see some of his family. Then Hetty stood up, in her flat blue hat and pink dress. She looked at us and then addressed the man in the dark suit. We were friends of her son, she said. He was outside somewhere. She explained Jimmy's tieless and jacketless appearance, and asked forgiveness for it. We got up then, I first, Jimmy after me, and announced ourselves as the man from Philadelphia had done. A pale woman in one of the front rows turned around and said to us that she too was from New York; she welcomed us as people from New York. It was like a binding together, I thought. And when, afterwards, the man in the dark suit spoke of brothers and sisters, the words seemed to have a more than formal meaning. The brass basin for the collection was passed up and down the pews. (The figure for the previous week's collection, a little over $350, was given in the order of service.) The pastor, a young man with a clear, educated voice, asked us to meditate on the miracle of Easter. To help us, he called on the choir. The leader of the choir, a big woman, adjusted the microphone. And after this small, delicate gesture, there was passion. The hymn was "What About Me?" There was hand-clapping from the choir, and swaying. One man stood up in the congregation—he was in a brown suit—and he clapped and sang. A woman in white, with a white hat, got up and sang. So I began to feel the pleasures of the religious meeting: the pleasures of brotherhood, union, formality, ritual, clothes, music, all combining to create a possibility of ecstasy. It was the formality—derived by these black people from so many sources—that was the surprise; and the idea of community. Someone else in a suit got up and spoke to the congregation after the black man in the dark suit had spoken. "This _is_ a great day," the new speaker said. "This is the day the Lord _rose_. He rose for everybody." There were constant subdued cries of "Amen!" from the congregation. The speaker said, "A lot of people better off than we are didn't have this privilege." Finally the educated young pastor in his elegant gown with two red crosses spoke. "Jesus had to pray. _We_ have to pray. Jesus had to cry. _We_ have to cry.... God has been so good to us. He has given us a second chance." Torture and tears, luck and grief: these were the motifs of this religion, this binding, this consoling union—union the unexpected, moving idea to me. And, as in Muslim countries, I understood the power a preacher might have. As Howard said afterwards, as he and Jimmy and I were walking back to the house, _"Everything_ happens in the church." We came upon another local oddball, to use the word Howard had used on the way out: this was the drinker of the black community. We were some way from the man's house when Howard spotted him looking out of a window. And Howard said, "Look down. Don't talk to him. Don't see him." It was one of the ways Howard had learned, both here and in New York, of avoiding trouble: avoiding "eye contact," which, he said, provoked the mugger, the beggar, the racial fanatic, the madman, the alcoholic. The drinking man, framed in his window, considered us as we walked towards his house. When we passed the house I glanced at him out of the corner of my eye. Standing at his window in his undershirt, isolated in his house, he was red-eyed, spiritually and mentally far away. I told Howard that the idea I had been given that morning of a black community with its own strict code was surprising to me. He said, "This community, or what you see, is going to disappear in twenty or twenty-five years." Segregation had preserved the black community. But now blacks and whites, especially of the younger generation, were doing more things together. This gave point to what Hetty (grieving for a son) had said the day before about black and white boys now "drinking together." And I wasn't sure whether Howard or Hetty wholly liked the new mixing and what it foreshadowed. I didn't think that Hetty could be as serene as she was, without her community. At lunch, when Hetty had come back from church, we talked for a little about the position of black people. We hadn't touched that subject the day before. Black people had lived through the bad times. Now, when things should have been easier for them, there were new racial elements in the country: Mexicans and Cubans and the other foreigners. The Mexicans were soon going to be politically powerful in the country. The Asians were not just buying motels; they were going into other kinds of business as well; and they had been here only a few years. In a hospital not far away, Hetty said, there were only two _American_ doctors. And soon Howard and Hetty were reminding each other of the way things were changing. In the old days trucks would come around to pick up blacks for the fruit-picking. The trucks didn't come now: the Mexicans did the fruit-picking. And Howard said the blacks had eased themselves out of Miami. The blacks hadn't wanted the hotel jobs; they thought those jobs demeaning. So the Cubans had taken over those jobs, and the blacks wouldn't be allowed to get in there again. In ways like that the blacks had allowed the Cubans to get control of the city. Spanish was now the language of Miami. Later, when we were going back to the airport, we saw a white congregation coming out of the other Baptist church in Bowen. It wasn't far from the black church where we had been. And it was only then that I realized that what I had been seeing was a segregated small town, with old segregated institutions. It gave a fuller meaning to Hetty's words, her chant, as we had driven through the countryside: "All this side white people, all that side black people. Black people, black people, white people, black people. Black people, white people." Reading the familiar land in her own way—where I saw only the colors of the spring, the purple flowers on the roadside, the sour weed, the pines and dogwood and oaks and maples, and the gray and green and dark-red colors of abandoned farmhouses and tobacco barns. Going back to the airport now, I saw the past a little more clearly. I saw a little more clearly what I had seen the day before. And I began to see how Howard, leaving his home and going to New York, could hold himself separate both from the past and from the rage of Harlem. I asked him why he didn't live in Harlem. "My rhythm is different. And they pick up on that. Rhythm? It's like your energy level. How shall I put it? I'm not angry. Most people in Harlem are angry." And, trying to explain more about himself, he said, "I'm different. I felt different at the high school. It's what you think and what you feel that makes you different. I always felt different. Which leads me to believe I was born in the wrong town. Like many people." TWO DAYS later, in New York (and just before I began my true Southern journey), I talked again with Howard, to make sure I had got certain things right. About the presence of Asians and Cubans and Mexicans he said, "I get very pro-American when I think about that." And that pro-American attitude extended to foreign affairs, which were his special interest. So, starting from the small Southern black community of Bowen, Howard had become a conservative. He said, "I think that when you come out of a Southern Baptist background that is the groundwork of being a conservative." I asked him about what he had said about the black community as we had walked back from the church. He had said that the community was going to disappear in twenty to twenty-five years; and he had seemed to talk neutrally about that. Was he really neutral? He didn't commit himself. He said that there would be less unity in the community, but that good would come of the change. Making a mystical leap, he said, "Change is like death. Good things can come out of it. It's like the Civil War, when a whole way of life ended." So at the end it turned out that his early comment, about the continuity of his home town, had had to do with history, as I had thought at the beginning. I had changed my mind because the word had then appeared to contain the idea of sameness and dullness: the same buildings, the ruins left standing in the fields, the dullness of the small-town life. He had meant that; but he had also meant the past living on. It was as though, talking to me, a stranger, he had had to find a way of talking about the unmentionable past. # 1 # ATLANTA # Tuning In IT WAS in New York that I planned my trip. One suggestion was that I should go to Tuskegee in Alabama, to have a look at the trades institute, now a university, that Booker T. Washington had founded more than a hundred years before for black people, then barely out of slavery. Tuskegee was a name I knew. It was half mythical for me, from my memories of the Booker T. Washington book _Up from Slavery_ , which I had been introduced to as a child in Trinidad. So far away: it was hard to think of this place with the strange name being there still, in the light of common day. I was given the name of a writer who had been educated at Tuskegee, Al Murray. He was, or had been, a protégé of Ralph Ellison's, and he lived in New York. He was friendly on the telephone, interested in my project, and ready to talk on. He wanted me to come to his apartment. It was in the heart of Harlem, he said; and he thought I should see Harlem. It would be part of my preparation for the journey. He lived on 132nd Street. He thought I should simply take the Madison Avenue bus. He made it sound feeble to do anything else, and it was my intention to take the bus; but at the last moment I faltered and waved down a taxi. In no time we were in Harlem. In no time, racing through the synchronized lights, we were in what looked like a caricature of the city lower down. It was like a jump ahead in time, a turning of the page: upper windows blown out and blackened in walls of warm brown stone or old red brick, houses surrendered, camped in, old craft and elegance surviving in stonework (as in some pillaged ancient Roman site), some house walls enclosing only earth, awaiting excavation one day: no apparent relation between the people and the place, the mixed population of the city lower down altered, the pavement bustle gone, the people now all black, not many women about, and the men often in postures of idleness, sitting on steps or standing on street corners. In the same light of fifteen minutes before, the same weather, in what was still Fifth Avenue. It should have stopped after a while; but it went on. At some lights a thin, expressionless boy ran to the car and said something to the driver. The driver, a fat black man, didn't reply. The lights changed; the thin-legged boy ran off again between the cars without another word. What had he wanted? The driver, from his accent a West Indian from one of the smaller islands, said, "He wanted to clean my windscreen." The driver gave a nervous laugh and—only now—turned up his window. Not far away was the apartment building where Al Murray lived. It was one of a set of three or four tall apartment buildings that must have been built on the site of old house-rows. In Al's building—set back from the sidewalk, and with a shallow curved drive to the glass-doored entrance—there was, unexpectedly, a uniformed doorman, and a notice that visitors had to be announced. His apartment was at the very end of a central, windowless corridor. It got warmer towards the end of the corridor; electric lights were on. When Al opened the door it was daylight again, and there was a glimpse, through the big glass window at the end of his sitting room, of the New York sky again. He was a brown man, and older than I had thought. I had expected a young man or a man in mid-career; and he had sounded young on the telephone. But Al had just turned seventy. His sitting room was full of books and records. A moment's looking showed that the books were a serious collection of twentieth-century American writing in first or very early editions: Al had been buying, or collecting, for more than forty years. His jazz records (worn sleeves standing upright, filling many shelves) were equally valuable. Jazz was one of his passions, and he was a noted writer on the subject. Among the first things he showed me were private photographs of Louis Armstrong—a small man, unexpectedly, Picasso-size, and, again unexpectedly, a careful dresser: everything about the great man noteworthy, almost an aspect of the talent, and to Al exciting. He was a man of enthusiasms, easy to be with, easy to listen to. His life seemed to have been a series of happy discoveries. Tuskegee—where he had studied fifty years before—had been one of those discoveries. He loved his school, and admired its founder. He showed photographs of the place: Georgian-style brick buildings built by the students themselves eighty or ninety years before. They were the first photographs I had seen of Tuskegee, and they made me want to go there. And Booker T. Washington, as Al spoke about him, became a little more real. He was born a slave in 1856, but that was only five years before the Civil War; so (whatever his memories) he hadn't been a slave for very long. And he would have grown up in the extraordinary period just after the Civil War, when freedmen asserted themselves here and there, and some of the gifted ones did well. He would have grown up with American ideas, the big ideas of the late nineteenth century. Booker Washington, Al said, had to be seen as an American of the late nineteenth century, in his energy and in his understanding of the way capitalist America worked. He would have been at one with the very rich and powerful men he successfully appealed to. Al Murray took down the two volumes of the Louis R. Harlan biography to show the photographs. They were moving: those long-held poses, Booker T. Washington with his family, with his dandified male secretary, all those clothes of turn-of-the-century respectability—and the great man's eyes always tired. And the Tuskegee students, men and women, doing as students the tasks so recently performed by slaves—raking hay, building brick walls—but doing those jobs now in respectable clothes, the men sometimes even in suits—clothes being important to people who, as slaves, hardly had any. Tuskegee was on the site of an old plantation, Al Murray said. The plantation mansion had for many years remained outside the school compound; but he had heard that it had been acquired recently and was now the residence of the school's president. Change, in the American way. And it might have been said that Al Murray, with his books and records, was a demonstration in himself of that change. He had been born in Alabama in the deepest South; had gone to Tuskegee; had served in the air force and retired as a major; and had then had a second career as an academic and a writer. It was at the end of his time with the air force that he had come to New York, to that apartment. Were his neighbors there middle-class, professional blacks? No; they were a mixed group. One neighbor, for instance, was a doorman at the midtown club of which Al was a member. "He's a doorman there. Here he's my neighbor." Al liked that. He also liked the apartment for its own sake. But there was the setting. When he took me out to his dizzying little balcony to show me the view, the elegance that the first builders of Harlem had intended, I saw from a height the streets that at ground level had so demoralized me. I also saw the ruins of the red-brick house-row to the south. There had been a fire six years before, Al said; the brick shells had simply been allowed to stand since then. A big tree (now with spring foliage) had grown within the walls of one house without damaging the walls. The scene was a little like the war ruins preserved in parts of East Berlin as a memorial—and certain ravaged streets of Harlem did make one think of war. But Al had lived for a long time with the burned-out houses on the next block. He seemed to have almost stopped seeing them; he saw the larger view. To the south, all Manhattan lay at our feet. If that tall building some blocks down wasn't in the way, Al said, we would have been seeing the Empire State Building from where we were. To the west was a multicolored row of buildings that a famous black artist, a friend of Al's, had made the subject of a picture. And when Al looked down at the street below he saw the two or three churches and the house of the local congressman: buildings standing for important aspects of local life. So, with Al's help, my eye changed. And where at first I had seen only Harlem and gloom, I began on the high balcony to see the comparative order of the area where Al lived. And the splendor of the original Harlem design: grander, in the intention of the planners, than anything farther south. But those first planners of Harlem had overbuilt. There were not enough people, in the 1890s, for the new houses of Harlem. Some businessmen had then begun to buy the houses, with the aim of renting to blacks from the South. They advertised; they tried to get the goodwill and participation of Booker T. Washington, at that time the best known black man in the United States. Washington didn't like the idea; he thought it too commercial. But Washington's secretary, Emmett Scott, one of the big three of Tuskegee (the big houses of Washington, his treasurer, and his secretary still stand side by side at Tuskegee), joined the business venture. So black Harlem began as it was to continue, in need and exploitation. And there was, ever so slightly, a Tuskegee connection. Al Murray took me walking in the neighborhood. He asked me to notice the very wide sidewalks: it was part of the elegance of the original Harlem plan. He took me to a bookshop with books about the black cause, and posters and leaflets about local events. I bought a paperback of _The Souls of Black Folk_ by Du Bois, a contemporary black critic of Washington (there was a very early edition of this book on Al's shelves); and we exchanged courtesies with the dedicated and cultured lady who ran the shop. He said, about the Harlem Hospital—the most important building in the neighborhood—that its standards were professional and that it was getting better. And then, my "disentangling" vision developing, we went to the Schomburg Center, a splendid new building devoted to black studies, with an extraordinary collection of books and documents, and with enthusiastic staff, black and white. The Center gave researchers a stipend to work in its library. The stipendiary or scholar I met was a handsome brown woman who had traveled much and was doing work on the cultural links between Brazil and West Africa. She spoke of her work with the excitement of a discoverer. For her the black cause, or this extension of it, was like a new country. I didn't take a taxi back. There were no taxis in the streets. Al waited a little while with me, talking of Ralph Ellison, until a bus came. And then, unwillingly, I saw again, and more slowly this time, stop by stop, what I had seen on the way out: a whole section of a great city in decay. IT WAS in Dallas in 1984, at the Republican convention, that the idea of traveling in the American South, or Southeast, came to me. I had never been in the South before; and though Dallas was not part of the Southeast I later chose to travel in, I had a sufficiently strong sense there of a region quite distinct from New York and New England, which were essentially all that I knew of the United States. I liked the new buildings, the shapes, the glossiness, the architectural playfulness, and the wealth that it implied. Architecture as pleasure—it was interesting to see it growing out of the drabness of the older, warehouse-style town. It was mid-August, and hot. I liked the contrast on the downtown streets of bright light and the deep shadows of tall buildings, and the strange feel of another, more temperate climate that those shadows gave. One constantly played with contrasts like that. The tinted glass of the hotel room softened the glare of the hot sky: the true color of the sky, outside, was always a surprise. Air conditioning in hotels, cars, and the convention center made the heat, in one's passages through it, stimulating. The heat was a revelation. It made one think of the old days. Together with the great distances, it gave another idea of the lives of the early settlers. But now the very weather of the South had been made to work the other way. The heat that should have debilitated had been turned into a source of pleasure, a sensual excitement, an attraction: a political convention could be held in Dallas in the middle of August. On the wall at the back of the podium in the convention center the flags of the states were laid flat, in alphabetical order. The flags of the older states were distinctive; they made me think of the British-colonial flag (and the British-given colonial motto, in Latin, from Virgil) I had known as a child in Trinidad. And for the first time it occurred to me that Trinidad, a former British colony (from 1797), and an agricultural slave colony (until 1833, when slavery was abolished in the British Empire), would have had more in common with the old slave states of the Southeast than with New England or the newer European-immigrant states of the North. That should have occurred to me a long time before, but it hadn't. What I had heard as a child about the racial demeanor of the South had been too shocking. It had tainted the United States, and had made me close my mind to the South. The convention center was very big. The eye could not take it all in at once. In that vast space the figures on the podium looked small. They could have been lost; but a big screen above them magnified their image, and scores of smaller screens all over the center repeated this living, filmed picture. It was hypnotic, that same face or gesture in close-up coming at one from so many angles. The aim might only have been communication and clarity; but no more grandiose statement could have been made about the primacy of men; nothing could have so attempted to stretch out the glory of the passing moment. And yet, almost as part of its political virtue, this convention dealt in piety and humility and heaven, and daily abased itself before God. A famous local Baptist pastor spoke the final benediction. His church organization was prodigious; its property in downtown Dallas was said by the newspapers to be worth very many millions. His service, on the Sunday after the convention, was to a packed congregation. It was also being carried on television; and it was a full, costumed production, with music and singing. But the hellfire sermon might have come from a simpler, rougher time, when perhaps for five or six months of the year people had no escape from the heat, when travel was hard, when people lived narrowly in the communities into which they had been born, and life was given meaning only by absolute religious certainties. I began to think of writing about the South. My first travel book—undertaken at the suggestion of Eric Williams, the first black prime minister of Trinidad—had been about some of the former slave colonies of the Caribbean and South America. I was twenty-eight then. It seemed to me fitting that my last travel book—travel on a theme—should be about the old slave states of the American Southeast. My thoughts—in Dallas, and then in New York, when I was planning the journey—were about the race issue. I didn't know then that that issue would quickly work itself out during the journey, and that my subject would become that other South—of order and faith, and music and melancholy—which I didn't know about, but of which I had been given an intimation in Dallas. FROM NEW YORK I went to Atlanta. I had been told that there was an old black elite there, a kind of black-American aristocracy; that there were many established black businessmen, and a number of black millionaires; and that blacks ran the city. I booked an airplane flight; in Atlanta stood in a line at the airport to hire a car; and then drove through the mighty roadworks of the city center to the hotel. And there I was, slightly astonished that the journey, so long in the planning, should begin in such a matter-of-fact way. And, as if answering my anxiety, all the little Atlanta arrangements I had made in New York came to nothing, one after the other, and very quickly. A newspaperman had gone to another town to cover a story; a black businessman said on the telephone that he was out of touch, had lived these last twenty years out of Atlanta. And the black man whose name had been given me by a filmmaker said that almost everything I had heard about Atlanta was wrong. The talk about a black aristocracy was exaggerated, this man said. By the standards of American wealth, blacks in Atlanta were not wealthy; in a list of the richest Atlantans, a black man might come in at number 201. Political power? "Political power without the other sort of power is meaningless." He sipped his wine, my informant, and seemed not at all displeased to have floored me. I actually believed what he said. I had felt that the grand new buildings of Atlanta one had seen in so many photographs had as little to do with blacks as the buildings of Nairobi, say, had to do with the financial or building skills of the Africans of Kenya. I had felt that the talk of black power and black aristocracy was a little too pat and sudden. I wanted to see for myself, though; and I was hoping to be put in touch with people. But there was no hint from this black man of that kind of help. I might see Andrew Young, the mayor, he said; but Andrew Young probably had about two hundred interviews lined up. (So I might be number 201—a popular number.) I felt about this black man, in fact, that—sipping his wine, looking at me over the top of his glass, enjoying my discomfiture, awaiting my questions and swatting them down—I felt he was being seized more and more by a spirit of contradiction and unhelpfulness and was about to grow quite wild: that soon I would be hearing, not only that there were no moneyed blacks in Atlanta, but that there had never been anything in Georgia, no plantations, no cotton, corn, or taters, that there was only himself in the wide vessel of the black Atlanta universe. From my room at the Ritz-Carlton, the view at night of the windows of the big Georgia Pacific building was like a big pop-art print. The windows, of equal size, were all lighted. Each level was like a filmstrip, or a strip of contact prints, of views almost the same. From my room the view changed, level by level. At the lower levels I looked down at the tops of desks and the floor of offices. At eye level I saw the desks silhouetted against the office wall. Level by level, then, the desks vanished. At the higher levels I saw only the lighted ceilings; and at the very top there was only light, a glow in the window. The offices were all empty; the men who sat in them during the day were in the suburbs somewhere. The paintings that hung on the walls of the offices of senior people were like arbitrary symbols of rank, mere rectangles at this distance, quite indistinct, even without color—the way great cities, from very high up, show as smudges below the earth's swirls. A formal society, private lives, a formal view: an introduction was needed to every one of those rooms, and the visitor didn't know on what door to knock. Where did the news happen? Was it only a production, on the television? BUT THEN I read in the newspaper about the affair of Forsyth County. Forsyth County was forty miles or so to the north of Atlanta. In that county in 1912 a young white girl was raped and beaten so badly that she died a few days later. A number of blacks were implicated. One was lynched; two others were tried and hanged. All the blacks of Forsyth were chased out of the county; and since then (so it was said) no blacks had been allowed to live in the county. This last fact, about blacks not being allowed to live in Forsyth, became a public issue earlier in the year, when someone organized a "Walk for Brotherhood" in Forsyth in the middle of January, to mark the anniversaries both of the assassination of Mahatma Gandhi and the birth of Martin Luther King. This march was attacked by some local people and Ku Klux Klan groups; it made the news. A second brotherhood march a week later—after all the publicity—was a much bigger affair. Twenty thousand people went to Forsyth to march, and there were about three thousand National Guardsmen and state and local police officers to keep the peace. There were protests nonetheless; fifty-six people, none of them marchers, were arrested. The man who had stage-managed the marches, or had made the issue as big as it had become, was a black Atlanta city councilor, Hosea Williams, called simply Hosea by everyone who spoke of him. He was sixty-one, and had been an associate of Martin Luther King's in the civil-rights movement. Hosea had since brought a lawsuit against some Klan groups for violating the civil rights of the people on the first brotherhood march; and he had also come up with the idea that some claim might be made against Forsyth County on behalf of the blacks who had lost land when they had been driven out in 1912. Tom Teepen, of the Atlanta _Constitution_ , with whom I had breakfast one day, spoke almost with affection of Hosea Williams. "A primary force, a rabble-rouser in the tradition of the Paris barricades, and canny." But I couldn't see Hosea that week. Tom said, "He's in jail." "Jail!" "It's all right. He's often in jail for some thing or the other. He'll be out in a few days." When I looked at some of Hosea Williams's own publicity material, and especially a _Who Is Hosea L. Williams?_ pamphlet, I saw that his jail record mattered to him. There was a photograph of him in a cell. "Rev. Hosea holds the civil rights arrest record for jailings.... He has gone to jail about as many times since Dr. King's death as during his life (a total of 105 times)." He was born in 1926. So for very many years his racial protests and battles would have been desperate affairs. But Hosea had won his war; and (though he was still a brave man: the first march at Forsyth had required courage) I felt that Hosea might now have become licensed, a star, a man on the news, someone existing in a special kind of electronic reality or unreality. And his political life required him to beat his own drum. In _The Dimensions of the Man—Dr. Hosea L. Williams—A Chronology_ , with a photograph of Hosea in an academic gown, apparently receiving an honorary degree from another black man, there was this: "Today he's not content to watch things happen, HE MAKES THINGS HAPPEN." THE NORTHERN suburbs of Atlanta almost touched Forsyth County. The freeways, which made Georgia look like Connecticut, enabled people to work in downtown Atlanta, where there were blacks in the streets, and then to drive twenty or thirty easy miles (in air-conditioned cars) to their houses in the suburbs, where there were few blacks—this part of Georgia had not been plantation country. There were branches of famous stores in the luxurious suburban shopping malls. The white suburbs could get by quite well without the black-run city center. There was a news item in the paper one day that some of these suburbs didn't want to be plugged into the Atlanta city-transit system, because they didn't want to be infiltrated by blacks. No Forsyth-like shouting, no Confederate flags, no white hoods and gowns—that wasn't the way of these new suburbs. A transit official said, "It's such a subliminal issue that it's extremely difficult to deal with." A lawyer I met said that, to understand, it was necessary to remember that 120 years or so ago there had been slavery. For poor white people race was their identity. Someone well off could walk away from that issue, could find another cause for self-esteem; but it wasn't that easy for the man with little money or education; without race he would lose his idea of who he was. I spoke about my weekend with Howard and Hetty. Hetty had a strong idea of her racial and family identity, and yet she also had a high regard for Mr. Bowen, whom she considered a good man. Did that mean anything? The lawyer thought not. Southern white people would do anything for black families with whom they had a relationship, but that attitude stopped there; it wasn't extended to blacks in general. We were lunching, the lawyer and I, in a big club in downtown Atlanta. The club had been started in the days when there had been a general movement out of Atlanta, and business people had felt the need for a place where they might meet in the middle of the day. It was part of the bubble in which the white professional people of Atlanta lived: the house, the air-conditioned car, the office (perhaps like an office in the Georgia Pacific building), the luncheon club. I asked the lawyer whether he personally felt threatened. He said the feeling was with him sometimes when he was out in the streets. He meant the fear of violence. But he also meant the larger fear of a world grown unstable: the more protective the bubble in which one lives, the more uncertain one's knowledge becomes of what lies out there. And this was why the lawyer thought it would be good if the black middle class could grow, if the blacks could become more active commercially. But—and like everyone talking about blacks now, he searched for words at once neutral and true—blacks (whatever their yearnings) didn't have the business sense, the business vocation. In a society that was economically driven, blacks didn't have the economic drive. But now there were immigrants of a new sort in the United States—Latin Americans, Asians. The lawyer thought that, when the blacks had a better understanding of what the presence of those immigrants meant to them, black racial sentiments might change. It was there, then, as Tom Teepen had told me, at the back of everything, however unspoken: the thought of race, the little neurosis, the legacy of slavery. The topic came up again when I went to see Anne Rivers Siddons, the novelist. She lived in North Atlanta: hilly plots, tall pines, dogwood, azaleas. The spring I had seen in Howard's home town was at its peak here, and the houses along the suburb's curving roads looked quite embowered. Anne Siddons had just published a novel, _Homeplace_ , and was doing promotional work on it, at some cost to herself: she had got started on a new book. She was a little withdrawn, living internally, holding on to her new book. She lived in such beauty now; but—as I saw when I looked at her previous book, _Fox's Earth_ —her thoughts (like those of many Southern people) went back easily to a poorer time. She said that Margaret Mead had made an important observation about the South: the relationship of the white man and the black servant woman, man and undemanding mistress, had left the white woman and the black man neutered. The black men, Anne Siddons said, were the disaffected ones. And the newspapers—the _Constitution_ and its sister paper, the _Journal_ ("Covers Dixie like the Dew" was the slogan on its editorial page and its delivery vans)—were full of racial items, interwoven with the running serials: Forsyth County, and the ramifying story of the private life of a black politician accused of using cocaine. One day there was this story. IBM sent a black executive to Columbia, South Carolina; but there was no room for the black man in the country club, no party invitations for his children. The next day there was this story: a black woman of thirty-one, a mother of two children aged five and two, took a revolver to work and shot herself in her office at Georgia Power. She felt she was being discriminated against by the company and passed over for promotion. She said in her suicide note that she wanted to give the managers and supervisors something to think about. Desperation; but there was also the kind of playfulness that a political cause attracts when it has become safe. There was news of a black arts festival. There was news of a mighty piece of sculpture for Atlanta by a New York sculptor, _Nelson Mandela Must Be Free to Lead His People and South Africa to Peace and Prosperity_. The rock sculpture weighed seven tons and was too heavy for its first site, which could take only a hundred pounds per cubic foot. So the sculpture was going to be moved to Woodruff Park in downtown Atlanta. (Woodruff was the great man of Coca-Cola, running the company for sixty years; Coca-Cola and _Gone with the Wind_ are the two fabulous success stories of post-Civil War Atlanta.) A twelve-foot iron fence, with a working gate, was to be welded into the rock. The gate was to be locked with a real key, and the key was to be given to the city of Atlanta, so that—assuming the key hadn't been mislaid—the gate could be opened when Mandela was freed. From Tom Teepen's column in the _Constitution:_ Metro Atlanta is a big city of 2.2 million; Atlanta is a medium city of 450,000; black Atlanta is a small city of 300,000. "The black leadership circle is a small town." A good journalist finds good clear ways of putting things. Tom Teepen also said this: white people in the United States don't have "leaders"; only black people have leaders. And I felt he had said that because (according to some other columnists in the paper) the current scandals about black politicians in a number of states were being used to run down black people generally. I liked the point about leaders. I thought it could be applied to many black or backward or revolutionary countries, where the leader is everything, and where journalists and others from outside, falling unwittingly into a version of the explorer's attitude ("Take me to your leader"), bestow on the leader alone the dignity that, in another kind of place, they would bestow more widely, on the country and the people. But then I began to wonder whether—since black politics in the United States were still racial and redemptive and simple—black people in the United States couldn't after all be said to have leaders, people they simply followed. And I wondered whether it was possible in these circumstances for black people to stand apart from their leaders, any more than it was possible for people of the Caribbean or Africa to stand apart from the racial or tribal chiefs whom they had created. I HEARD more about identity. Tom Teepen—shedding the suit and tie that he said was regulation office wear, and appearing instead in a many-pocketed vest or _gilet_ —took me one Saturday morning to a century-old Appalachian settlement in East Atlanta: a big old red-brick cotton mill, white frame houses, a cemetery on rising ground beyond a busy road. Mill wages at the beginning had been very low, 5¢ an hour, it was said; but for the mountain people the regularity of the wage had been a kind of security, and the community established around the mill had survived, though many people had gone away at various times, and the mill itself was now closed. We went to a community-and-craft center in the settlement. It was run by a woman with the beautiful name of Esther Lefever. She had come to the settlement many years before as a folksinger—a ten-year-old photograph in the Atlanta _Constitution_ showed her as a pretty woman with a guitar. But then, from being moved by the response to her singing—an old woman had got up and done a special dance, and other people had cried—she had become more deeply involved with the Appalachian community, and had even become a city councilor. She was small and slender, still attractive and clear-voiced. She was not herself from an Appalachian community, but she understood their closeness. She was a Mennonite from Pennsylvania, the eighth child of a preacher. She spoke of what it had meant to her to move from the strictness of her Mennonite background. She had felt alone, she said. What did it mean to be alone? She said she had the picture of being the last tree on the hillside: the other trees had all been cut down. It hadn't been easy for her even to give up the bonnet; all her life she had been taught to wear the bonnet out of respect for God and man. Even when she was in her twenties it made her nervous to be in the streets of Chicago. It wasn't a fear of black men so much as a dread of white men who (according to what she had been told) drank liquor and were gross. And then she had discovered the cruelty of the world outside, the cruelty of America. How had she discovered that? She told a story. One of her Appalachian women came to her one day and said she needed a job, "maid work." Esther Lefever took the woman to see someone, a woman with a lot of blonde hair combed back, a woman (Esther Lefever said) just a step or two above the woman looking for maid work. And the blonde woman said, "Why does she want to do maid work? That's for colored people." It was a simple incident, I thought; something that should have been passed over. The blonde woman herself (from the story) was as much a sufferer as everybody else. But the incident had many layers of meaning, and Esther Lefever had been upset and humiliated by it. She said, "They want to keep you in the slots they have fixed for you." Who were "they"? She thought, and said that they were the people who had arranged the system and wanted to keep everyone in his place. I asked her in what way identity was important, and whether there was some practical way in which it helped. She said that, if you moved to a new neighborhood or took a new job, and people were not too friendly, then it could be a help if you knew who you were; you could last out the hostility. If you didn't know who you were—if (and this was my extension) you were dependent on other people for your idea of your own worth—then you were in trouble. She was giving the view from below, the view of the poor people she was concerned about. And from what she said I got the impression that these people had raw sensibilities and lived on their nerves. I found that hard to imagine. (And yet, at another level, and with another, half-buried part of myself, I understood. Perhaps in a society of many groups or races everyone, unless he is absolutely secure, lives with a special kind of stress. Growing up in multiracial Trinidad as a member of the Indian community, people brought over in the late nineteenth and early twentieth centuries to work the land, I always knew how important it was not to fall into nonentity. In 1961, when I was traveling in the Caribbean for my first travel book, I remember my shock, my feeling of taint and spiritual annihilation, when I saw some of the Indians of Martinique, and began to understand that they had been swamped by Martinique, that I had no means of sharing the world view of these people whose history at some stage had been like mine, but who now, racially and in other ways, had become something other. And eight years or so later, in Belize in Central America, a similar feeling of the void broke through my other preoccupations when I saw the small, lost, half-Indian community of that wretched British colony, coastal timberland poached from what had been the Spanish Empire, peopled with slaves and servants, and then more or less abandoned: New World debris.) And I heard more about the ways of identity in the South from a religious scholar. Among the people he instructed were men and women studying for the ministry. I thought that people who wanted to be ministers might have been moved by some religious experience. But that attitude was a reflection of my own temperament and background, my own lack of a religious faith, and my thirty-five years and more in England, where formal religion had all but withered. In the United States, and especially in the South, religious faith was almost universal, and a religious vocation was as likely as any other. It was something a man could turn to for a number of reasons; and what I heard from this scholar was that some of the people he was in touch with (and he meant white people) had turned to the religious life in order to be confirmed in their identity: people from poor families who felt racially threatened by the new developments in the South, people who, in the booming new South, had gone into business and had then felt themselves drifting so far from the Southern world they had known that they had given up, to return to God and the life they felt more at ease in. I heard this talk about religion and identity far from Atlanta, at an open-air party on an estate in northwestern Georgia: hills, woods, long views, range beyond gentle range, blue upon blue. The party was in a rough, long-grassed field between woods, and in front of a gray, patched-up wooden hut on low pillars. The hut was said to be very old. It stood almost at the foot of a slope; and when you looked through the back door and window directly to the green of the land sloping up in the shade of pines, the site did have the feel of an ancient, protective solitude, quite different from any solitude one might arrange for oneself today. (Driving out from Atlanta, into the hills, aware of the fewness of blacks in the small towns I was passing through, I had felt I was driving into the wilderness. Some months later, when I was almost at the end of my journey, I was to approach Atlanta from the other way, from Nashville and Chattanooga, and this part of Georgia was to seem more used up and trodden over.) The party was "Southern" in its motifs. A Confederate flag fluttered in the sunlight in the rough field between the woods. A skinned pig, fixed in the posture of a hurdler, had been roasting all day, held on poles a little to one side of slow-burning hardwood logs. (On a table were more contemporary fast foods and dips and things in waxed paper.) And a band played bluegrass music from the wooden hut. Flag, pig, music: things from the past. The musical instruments were big, the music simple and repetitive. I was told that it was the words of the songs that mattered. The accents were not easy for me to follow; but the effect, especially from a little distance, of the unamplified music and singing in that enclosed green place was pleasant. Our hostess said, "Indians might have lived here." With that idea of being in the American wilderness, I felt a chill, thinking of them in this green land with its protective slopes, its shade, and rivers. Later I learned the ground was full of flint arrowheads. It was in this setting, with the bluegrass music coming from the wooden hut, that I heard about the religious faith and identity of the people who had come after the Indians. And I had a sense of the history here resting layer upon layer. The Indians, disappearing after centuries; the poor whites; the blacks; the war and all that had come after; and now the need everyone felt, black and white, poor and not so poor, everyone in his own way, to save his soul. The musicians were young and friendly; there was a girl among them. When they finished they put their big instruments in their pickup truck and went away. When the sun went down there was no wind; the flag drooped. It became cold very quickly; it was still only spring. THE Atlanta _Constitution_ 's file on the affairs of Forsyth County didn't come as a set of date-stamped newspaper clippings, but as computer printouts. The story of the events of 1912, as researched by one of the newspaper's writers, was terrible in every way. The white woman who had been dragged into woods, raped, and beaten—and died two to three days later—was the nineteen-year-old daughter of a well-known farmer. A hand mirror near the scene led police to a deformed eighteen-year-old black man. He confessed, and said that other blacks were also involved. Altogether, eleven blacks were arrested as suspects. Two days after the woman's death a crowd broke into the Forsyth County jail, shot and killed one of the suspects, beat the body with crowbars, and hung it on a telegraph pole. Three weeks later the deformed man and another black man were tried for the rape and murder and found guilty. The sister of the second man testified against him. Both men were publicly hanged a month after the trial, before a crowd of ten thousand. The few hundred blacks who lived in Forsyth were chased away. The destroyed young woman, the deformed black, the lynching at the jail and the hanging of the mangled body, the black woman giving evidence against her brother, the public hangings (ten thousand people turning up for that, in a county that fifty years later, before the Atlanta boom, had a population of under twenty thousand)—the story is unbearable in every detail. Yet what seemed to have survived in Forsyth above everything else was the knowledge, a cause for pride to some, that no black lived there. The man who had sought to challenge this pride was a white Californian, a karate teacher who had been living in Forsyth for five years. He called for a March of Brotherhood to mark the anniversaries of the death of Gandhi and the birth of Martin Luther King. He changed his mind after getting abusive telephone calls and threats. But the idea of the march had been taken up by another karate teacher, also white, from the next county. This was the march—about fifty people were expected to take part—that Hosea Williams had intervened in. This was the march that had been attacked by Klan groups and others, and had seeded, a week later, the big march of the twenty thousand, with the protection of three thousand National Guardsmen and state and local police officers. So that within a week what had been a brave and lonely cause had been turned by Hosea and a few others into a safe cause; and it had become safer and safer. A radio show had been taken to Forsyth. A very famous afternoon-television talk show with a witty black hostess had gone to Forsyth, and a program had been recorded in a local restaurant. Hosea, applying equal passion to the safe cause as he had to the brave one, had picketed this show, because only Forsyth residents were allowed to have a say, and they of course were all white. Hosea had managed to be arrested, to add to that record of his—105 jailings at the time his _Who Is Hosea L. Williams?_ pamphlet had gone to press. According to the Atlanta _Journal_ , Hosea had shouted as he was being put into the police van, "This is Forsyth County! This is what you see!" And Hosea's married daughter, who was with him, had shouted, "My daddy! I want to go with him!" And she too had been put in the van. Tom Teepen hadn't been able to arrange a meeting with Hosea when he had first told me about him, because Hosea at that time was in jail for a few days. And Tom couldn't find Hosea when he came out of jail. But then, late one morning, Tom telephoned me with the news that if I hurried to a certain building I might see Hosea. He was being arraigned on another charge at a federal court at eleven-thirty. It was almost that already, but Tom said that these affairs usually ran a little late. I took a taxi. It was driven by an African, a man from Ghana. It was a short run for him; in almost no time he had set me down again. An open paved forecourt, the big building set back; a security doorway; an elevator to the sixteenth floor. Hardwood doors, low ceilings, a brown-carpeted corridor, neat nameplates: formal, without drama, safe, even cozy. But the hearing was over. And in a room that was like a small lecture room or classroom there was a little group in one corner, like the subdued group that sometimes stays behind after a school examination to talk over the questions. In the little group I recognized Dick Gregory, gray-bearded and white-suited, a man grown old in the wars, and now really looking quite saintlike. And there was a squatter man with a bigger beard who could be none other than Hosea himself. Even in this moment of stillness in the courtroom his eyes suggested bustle—a man with many things to do and little time to spare. He had a toothbrush in his top pocket—a man ready to go to jail. He also had a press officer with him, a slender brown woman. She had a handout "for immediate release." And it seemed from what she said that my chances of meeting Hosea and having a heart-to-heart talk with him were not good. Hosea and Dick Gregory were going to fly to Washington that afternoon to picket the CIA. After that they were going straight off to Europe, to London and the Vatican, to do some work about apartheid. The handout from the press officer was about drugs: Hosea was saying that certain recent incidents were being used "to defame black leaders," and that the Mafia and the CIA were the ones most involved in the drug trade, which was "destroying our children and the future of our nation." That, in fact, was why Hosea and Dick Gregory were going to picket the CIA. And suddenly, before I could fully take in Hosea's eyes and beard and toothbrush, the little group had gone. Four or five minutes had passed since I had arrived, no more. And to add to the randomness of the occasion in Court No. I, there was my encounter with someone who, when the little group had gone away, had been left behind, like me. He was a reporter, quite young. He too had come too late for the arraignment. He too was new to Atlanta and didn't know a great deal about the affairs of the city. In the courtroom, in the brown-carpeted corridor, and in the elevator, we talked about his time in England. He had gone there to study the ancient Roman walls, Hadrian's Wall and the later Antonine wall. I had never seen those walls and was interested in what he had to say. We separated downstairs. When I was going out of the front door of the building I saw a small group around a bearded man. It looked so much like what I had seen upstairs that I thought the man was Hosea, giving an informal interview. It was only when I was almost in the group that I saw that the talker wasn't Hosea, was blacker, differently dressed, without the toothbrush, and that he only had the big stiff beard. THE CONVENTION business was important to Atlanta, and there were many big hotels in the center of the city quite close to one another. It was hard to think that these hotels could all be full at the same time. But it sometimes happened. A girl in the Ritz-Carlton dining room told me one day that an important convention was in town. What was this a convention of? Dry cleaners. And they were important because there were so many of them—as there had to be, if you considered how many dry cleaners there must have been all over the United States—that they had filled the Atlanta hotels. No hotel gave off such a company-holiday or convention feeling as the Marriott Marquis. And none was so overpowering. To enter it was like entering a gigantic, hollow, twisted cone. It had an atrium forty-seven stories high: gallery upon curving gallery, following the twist of the cone. That twist was unexpected; the eye was always led upwards. Great red streamers, like something from a Chinese festival, hung down the middle space. And all the time, like fairground conveyances, tall glass-walled elevators, their ribs picked out in lights, slid up and down the atrium wall. But the black man who worked for the Hilton (atrium-style there too, with the internal galleries, but not so sensational), with whom I had a talk one evening about the hotels of Atlanta, thought that I had done well by going to the Ritz. He said, "That's where the 'lite stay." As if in confirmation of this, I heard one day (with what truth I don't know) that Gloria Vanderbilt was staying in the Ritz and had been seen in one of the elevators. She was in Atlanta to do a promotion. Two weeks or so before, in New York, I had caught her on a talk show. She was talking about her life and about the way a woman is defined by the men whom she loves. And I assumed when I heard she was in town that she was here to promote her book. But there was much more to this promotion. "The Enchantment... The Heritage... The Prestige... MACY'S Proudly Introduces GLORIOUS by Gloria Vanderbilt.... Only a truly great fragrance has the power to stir our emotions. Glorious by Gloria Vanderbilt... Gloria Vanderbilt will autograph a complimentary photograph and any Glorious purchase." That was going on in Macy's, just across the road from the Ritz, on the morning Anne Siddons came to the hotel, to talk to me about growing up in the South. She was as intense and intelligent as I had expected; and though she was a little withdrawn (because of the book she was writing), and though the promotion she was doing for her publisher (on a different scale from Gloria Vanderbilt) was a further depletion, she spoke with a full heart, offering me a little of the experience that was her capital as a writer. She was Southern and Georgian, and almost Atlantan. She was born in Fairburn, twenty miles south of Atlanta. Fairburn was an agricultural and railroad town. Her father was a lawyer; though they were not rich, they were comfortably off. Her father was the first of his family to go to college. "We came down from Virginia around 1820. Our branch of the family farmed the same piece of land for seven generations. It makes me feel wonderfully rooted. But at the same time I feel it can be a yoke. I feel that we Southerners can be too deeply and narrowly focused into that land." I told her about my trip to Howard's home town and what I had seen there of black farming families. She said, "It's one thing Southern whites and blacks have shared. We have both been landowners since abolition." And she told me what Howard and his mother had told me: that land had been given or bequeathed to black people by the white men for whom they had worked. Some decades ago, she said, it had come out from a study of oral history that this giving of land had been seen by black and white as a benign aspect of the master-slave relationship. I asked, "In what way can the land be a yoke?" "We don't tend to lift our sights to get a broader vision." People settled too easily for staying on the land. They tended to say or feel, "Our sort don't go to college. We are farmers." Anne Siddons said: "I was a bright only child in a grammar-and-high school dominated by children from the surrounding farms. And everything I was naturally, I felt ashamed of. I spent twelve years trying to hide the fact that I was a bright child. Intellect has had no place here. The people who came to lead us obviously had intellect. But they had other things as well, to make it go down more easily. They had great charm, for instance." When we had first met she had said, "We are a colonial people." She made the point again. Southerners, she said, were uncertain of themselves. "I am talking about white people. At the time I was growing up, the white Southerner in the rural and small-town South felt threatened by the blacks. You don't hate what doesn't threaten you. As long as somebody was below you, you knew you had power. It was all about power, really. We were a conquered and occupied people, the only people in the United States to be like that. And this—our attitude to blacks—was the only way we could feel or exercise our power at all. We were a poor agricultural community, and we had bone-deep memories of real conquest and occupation and total humiliation. "We were untraveled people, the bulk of us uneducated. The only way we had of coping with change was by pretending it wasn't there. When the civil-rights movement was beginning, though it was just there, in Alabama, we could pretend it wasn't there. And when change did come it was brought to us right to our door by those black hands, which we hated and feared more than anything else in the world. These feelings are here still. What thoughtful Southerner couldn't know they are still there? This would be the background of a lot of thought." "Isn't it fatiguing for you, always to be with this idea of race?" "A lot of us find it almost too stifling to live in." That is why, she said, many Southern intellectuals had moved out of the South. I asked about racial protest. Hadn't it become formal, almost ritualized? There was the affair of the marches at Forsyth. It was clear, from the newspaper accounts, that only the very first protesters had risked anything. After that, the mood and tone of protest had changed. It had become the popular cause, the protected cause; some commentators had become self-righteous. "Of course the idiocy up in Forsyth needs to be dealt with. But the response can—and did—become banal." She had been shocked by the first news from Forsyth. But then she had had to acknowledge her own personal limitations as someone over fifty, someone who could now wake up in the mornings with the knowledge that death was going to come. "Active revolution is romantic for the young. The problem is: how do you deal with passion in middle age, when you must hoard passion? There can be no resolution of this problem, or at any rate not a neat one. And, aside from media notice and marches, I don't know how to deal with it. The form of the protest has got to be a cliché—Lord knows, Americans will protest anything." But race as an issue—it couldn't be avoided. "I deal with race in some form in every book I've written. It's my great war, I guess. I write to find out where I am now, what I think, to make order and simplicity in my own world. It's an impossible task. You can't simplify that. You can only clarify bits of it." I talked of the oddity of slavery in the New World, of the two far-removed races it had brought together, African, European. Now there was a common language and even a common religion. "I tend to think that they have enriched us more than we have enriched them. Perhaps we do on some deep level realize how very similar we are." She said a little later: "I feel very guilty about the civil-rights movement. I didn't march, back when marching would have been passionate and real and spontaneous. I was a young woman newly come to Atlanta and still deeply caught in that web of what is seemly and what is not." When was that real and passionate time? "I think the great marches in Selma were about 1965. Although I got into trouble for a column I wrote for our student paper. I was at a small college. This was when Autherine Lucy entered the University of Alabama. And there were cavalcades from all over the state going over to heckle those two poor blacks, heckle and worse. Nobody went from my college. It was because they were lackadaisical, really. I wrote a column praising the noninvolvement and made a few of those simplistic and sophomoric statements about race and about whatever—" " 'Whatever'?" "How we must keep calm, and this had to be a good thing. And I got hauled up before the dean of students, asking that I reconsider and not submit the column for publication. Which I would not do." I wondered how, coming from her background, she had arrived at that position. "I recall in high school a little epiphany. We were in something to do with black and white. It was an American-history class. I can't think what it might have been. But I remember feeling very strongly: this is _wrong_. I had never had that feeling before. And I blurted out, 'That is not right.' And one of the great big gangling country guys, who must have been twenty years old at that time, got up and called me a nigger-lover. Of course I had heard it all my life, but I had never been on the other side of it. I just remember the profound, simple shock of that moment. "My consciousness was raised a little. But not totally. I was still interested in fraternities and dances. You see, we were raised to be belles. "We all knew—nobody ever told us, but we knew with a deeper wisdom than words—that the highest we could aspire to was capturing a husband who would then provide for us. And we believed that. At fourteen I was constantly in love. Our mothers and grandmothers believed it was the best they could give us, the protection of a man. I have a theory that Southern madhouses are full of gifted women who were stifled." I said, "A pastoral or country society surviving in an industrial world?" "Yes, I think so." But I had interrupted. She went on: "In high school I did everything I thought I should. I was homecoming queen." "Homecoming queen?" "It's at a big football game. And when the alumni all come back there is a queen in her court, and she is given roses and presented to her court at half-time. And I was a cheerleader, and all the things you were supposed to be. I was a popular girl. And that was what we all thought we had to do, to get this man and to have a good life. "And most of us could learn to do that. But the other side of us that wanted to _learn_ —we were always ashamed of it. We never prized our minds. We never prized our individuality. It was all right to make good grades. It was all part of being a good little girl. But to be a great thinker, to have a great talent and pursue it, would cut you right out of the herd. And that was the thing we were most afraid of. It could send you walking alone. I mean it almost literally in some cases. "I knew a girl at college who was a wonderfully gifted painter—and, oh, she was good—and she spent all her working time in the art-department laboratory, painting. It was all she did. She was extremely reclusive. She was the only woman at that college allowed to have a room alone. The stigmas she bore were cruel." I wanted to know more about being "cut out of the herd." I remembered what Esther Lefever had said about leaving her Mennonite community and feeling "alone": feeling yourself the last tree on a hill, all the others having been cut down. Anne Siddons said, "The feeling you get is of being totally exposed, totally vulnerable to _chaos_. "I think that goes back to safety. I think I can tell you why Southern women teach their daughters that, or that they must have a man to protect them. After the Civil War those women had lost their entire worlds. Their homes were burnt, their slaves (if they had had them) were scattered, their men might have been killed. And I think they perceived that this had happened through the sheer folly and childishness of these men of theirs. That was a _silly_ war. It was quixotic, romantic in the extreme. It was foolhardy. We fought a ridiculous war that any reflection would have told us we couldn't win. "And these women who had lost everything determined to ensure that their daughters and granddaughters would never again hand their power over to men who would toss it away so lightly. Never again would they allow their men to throw their very lives away. And they determined then to control those men by guile and charm and feminine wiles, because those were the only weapons they had. "If we lived in the East—of the United States—we might have used our minds. In the West we might have exercised a physical initiative and bravery. But we were here, and many of us were trapped here economically. And you can't aspire to what you can't imagine. And so, to survive, we had to hook up with a man. My mother to this day would be happier if I had a teaching certificate and was married to a lawyer. 'You should get a teaching certificate. That way you'll always have something to fall back on.' " And Anne Siddons herself still had something of her old anxiety about chaos. "What I am most afraid of is a very real vulnerability to forces I can't control. This thing about control is important to me." She spoke again about the conventions of her adolescence. "The very things that could have enriched us and set us apart were the things that we learned, by omission, were wrong. We grew up without prizing what was real. The South is dreadfully hard on its women, and what we allow it to do to us... I suppose this is true of other regions as well, but I think it is more true of the South. It would be interesting to know _why_ we are so suspicious of eccentricity." "Did it affect your emotional life?" "I've only begun to know now how much it affected my emotional life. It kept me from examining myself. It terrified me. Consequently I came to that examination twenty years later than many people do. What I resent is the power that examination might have liberated earlier. In my writing and my life. "I am regretting the years of waste. I am trying to deal with anger against my parents for bringing me up as they did—though that anger comes out of the deep knowledge that they acted out of the highest love they had in them. "I am glad it happened to me. I might have become one of those beautiful tragic drunk women in the South, on a country-club terrace somewhere. There are many drunk women in the South." But there was the comfort of the land that the family had farmed for seven or eight generations, since the family had moved down from Virginia in 1820. "I'm glad I have those ties. The feeling of floating free is frightening to me. I go back almost every weekend. I have dinner with my parents." And now came the explanation of the "hoarding" of passion she had spoken about earlier: the need to spare feeling for private life, private ties, to divert at least some passion from public issues. "I've talked about this with two or three women friends. And we find that we are now irrationally angry with our parents. And I think that it's because we sense that the original contract—the contract between parent and child, the contract that says, 'I will always take care of you,' and is an impossible commitment—that contract is going to be broken now, and they are going to die soon. That is what I mean by our passions having to be focused." Still, what thought was there now, from her side, about the blacks, people equally obsessed? "If we, Southern women, feel strictured, I wonder how the Southern black, who has had so many more overt strictures, must feel about them. Though I suspect that I may have highly romanticized whatever they may feel about them—I have a tendency to do that." "Do you think protest is being so formalized that even black people are beginning to lose contact with what they feel, and often say what they think is expected of them?" "I think that rote and rhetoric have replaced outrage. The first thing that happened after the very real shock about the business in Forsyth County—the shock that _it_ , the Southern violence, wasn't dead—what swung into action then was the _perfect_ march. And we knew just exactly how to do it. As though some cosmic march chairman pulled all the switches—and, goodness, in a week we had the perfect march. "We had the right component of public-safety awareness, the right component of media awareness. The right crowd makeup, a nice balance of young blacks and old battle-scarred lions; and we had the right component of white liberals. You wouldn't have found an ex-president marching in that first civil-rights march. You know, the organization! The buses appeared, just like that. That's Hosea. Boy, can he stage a civil disobedience now!" Wasn't it good, though, that protest in the United States could be ritualized like this? "I don't want to sound pejorative. How else would I have it? I am so thankful no lives were lost in Forsyth County, no harm was done. What I miss are the howls of pure outrage that greeted the murder of the three civil-rights workers in Mississippi. In the 1960s. But it was the spilled blood that called out the outrage. And we must not have the blood." But there was this to the formalization of protest: there was an orthodoxy of thought about race and rights. Perhaps people would be censoring themselves sometimes, to appear to be saying the right thing. Anne Siddons said, "I guess that happens in all revolutions. They don't end. They just pass into caricature over the years. And therefore they lose their credibility. The civil-rights movement will lose its energy and peter out into a series of sporadic brush fires, as other things come up. The civil-rights movement began to die as the peace movement and the women's movement came to life in the sixties. As I said, Americans protest anything. We are protesters. But protest made the country. It's what we know how to do." We had talked for two hours. And across the road from the Ritz, on the ground floor at Macy's, smiling uniformed young men and women, like a kind of ceremonial designer-guard for Gloria Vanderbilt, walked lightly—lightly, like dancers—down a walkway between dark-red rope barriers, while a small band played and Gloria Vanderbilt herself—impossible to imagine that a real person possessed the name and actually was at the heart of the fame, the goods, the book, the talk show—Gloria Vanderbilt herself, dark eyes in pale, blooming skin, in the fluorescent light of the department store, the light matching the air conditioning, completing the bubble world, Gloria Vanderbilt sat and signed things for people waiting in line. TOM TEEPEN walked me over to the gold-domed Capitol building. In the big central hall, hung with portraits of people famous in the political life of Georgia, there was a display of flags from the Civil War. Tom Teepen said, "A lot of history here." And the lieutenant governor, Zell Miller, was in his wood-paneled office. He was from the northeast of the state, which he said was Indian territory, Cherokee territory, until the 1830s, when the Cherokees were sent to Oklahoma along the "Trail of Tears." Was that what the trail was called then? Possibly not; it was hard and painful to think about now. The settlers who took the Indian land were Scottish and Irish and some Germans, moving down from Carolina and Virginia. And the northeast of the state remained isolated—American history busy about other areas, leapfrogging or skipping over the hills of Appalachia and the communities in the "coves" and "hollows"—until the 1930s and 1940s. There were few blacks; that area was not a "racist society." But now, with the newcomers from other places, mainly from Florida, he said, there were prejudices among the local people. That was the lieutenant governor's background. His mother came to Atlanta in 1942, when he was ten years old, and she worked for two years at the Lockheed plant. She saved up and took the children once for lunch at the Biltmore Hotel. For two years they stayed in Atlanta, and then they went back to the mountains. And now the lieutenant governor was in the wood-paneled office. And to the paneled bar of the Ritz-Carlton later that evening came Atlanta City Council President Marvin Arrington, as concerned with his own past as the lieutenant governor was with his. But Marvin Arrington was black. He was heavy and strong, though with noticeable bowlegs. He was forty-six, by profession a lawyer. And his talk, open and unabashed, and fresh still, though he must have spoken the lines a hundred times, was about the difference between today and yesterday, between today, when honor was his, and yesterday, when Atlanta was so segregated that the only place where black people could use the lavatories was the bus station. So that his mother, when she brought the children to town, urged them to use the lavatories there if they didn't want to walk back the miles to it. The black bar attendants, women, were pleased to see Arrington. Smiles came to their faces, though he was not a glamorous man, and had a heavy, long face. He wore a pale-brown suit; he seemed to sit low in his chair. He told Tom Teepen he had lost twenty pounds. But his long day—he had come quite late for our meeting—had exhausted him; and though he had a cranberry juice only, he dipped his large hand into the nut bowl and drew out nuts by the handful. We talked about the rich blacks in Atlanta—were they real? He said (as in the reprint of an Atlanta _Constitution_ article I had read) that he earned a six-figure salary. But he didn't think there were all that many rich people among the blacks of Atlanta; and the figures he gave, of salaries and expenses, were really rather modest. He said he was sorry he couldn't talk more just then, but he would like to see me; and he gave me a two-hour appointment in his law office some days ahead. "CUT OUT of the herd." Anne Siddons had used the words to describe one of the anxieties of her Southern upbringing. And I heard almost the same words from a woman at a theology school, where I went to follow up the idea that had been given me in northwestern Georgia of religion and identity. The woman who spoke the words—"I didn't want to be not part of the herd. That's where my identity came from"—was, like Anne Siddons, from a long-established family, not in Georgia, but in Mississippi. Mississippi, this woman said, had a history of 250 years; her family had lived in the same house for nearly two hundred years. "The way my identity was formed was by my family and by who we were in Jackson and in Mississippi. In the Presbyterian church we had our own pew. And that was your identity. My aunt was shocked one day when she went to church and found a stranger in her pew." Didn't the idea of piety and correctness contain the idea of service? No, she said; that idea wasn't for her family. Other people had the idea of service; the idea was for other people. Yet she had spent much time in Atlanta serving the black community. "There is a noblesse oblige that separated you but imposed an obligation, but with no person-to-person connection. And I think the reason I've spent so much time in the black community in Atlanta is that I was _hungry."_ "For what?" "Hungry for..." She had trouble finding words. "For contact. With people who were living lives that were more real than mine was. We were real cold folks." She meant the decorum, the rigidity, the manners of the family. When she broke away she welcomed even the idea of tears. In the idea of service now, and in the dream of becoming a minister, she had found a new idea of community. "But remember," she said, talking of the identity that had been hers and probably still was, "this is a very specialized herd. White upper-class Mississippi people." And while she was reaching towards a new community, the old way of things she had known was changing. The family was now scattered all over the United States; and the old family house, the "plantation," was probably "going to disintegrate." "And my mother is distraught in a way I've never known her. Because a lot of her identity is going to go. That house has been the gathering place; many people can stay there. For my mother it's a sense of place. That house, those trees, that dirt. My aunts talked about the Civil War as though it was yesterday. And the people there show off the old houses, you know. It's part of the economy of the place. They put on the old costumes and show the houses." I said, "A kind of masque." She said, out of the security of her new idea of community, "It's more like religion." Identity as religion, religion as identity: it was the very theme of another theology student, a young man from a background quite different, a mountain community in northern Georgia. He said, "When I think of growing up, the two things are very much the same thing—family and church. The church was a small church, with about forty-five members, all related. Seven or eight generations ago the first member of our family moved into that area and bought four hundred acres, and we still live on that. It isn't a plantation. There might have been slaves early on, but that disappeared pretty soon. We were a family of small farmers. My grandfather had fifteen or sixteen brothers, and their descendants all live within three miles of one another. It is very rare that anybody moves away. When you go up there you know people, and you know them as relatives. "At the same time it is very easy for your own identity to get lost. But I have since grown to appreciate how wonderful that is: a warm, loving, open kind of family, not just father and mother and brothers and sisters, but cousins, aunts, and uncles. "The church is very much the same thing. Family members. The Holiness Church is a very emotional religion, and what struck me early on was how very different people were in church from what I knew of them at home. The emotion they expressed in church was different. There would be a lot of shouting. The preacher would try to work them up to the sinfulness of human nature. There would be moments during the service when people would get up and speak in tongues, and people would try to interpret what was being said. And there were times when people would get saved." "This religion was not a reaching out to the world?" "This religion was a calling away from the world, an excluding of the world. I still struggle to find how I relate to all that now. The first year in college I spent alone in my room. I was scared to go out. Then I became angry with some aspects of the faith that had such a rigid view of the world." But now (like the Mississippi plantation, and for the same, economic reason) the mountain world was changing. "A lot of the people have to go away to get work." They came back, it was true; they never lost touch. But: "The twentieth century is pouring over the mountain." Mountain family, old planter family: old ideas of community no longer served, and the descendants of those families were finding a new community in the ministry. But it hadn't been quite like this for Frank. He grew up in a blue-collar white urban neighborhood. It wasn't "ethnic," and it had no sense of community. It was Southern, but the Southern history and Southern past that were bred in the bones of the mountain boy and the plantation girl had had to be learned, studied, by the boy from the city. Because he had been born into a crowd, his early ambitions had been different. "I wanted to be an individual, a nonconformist, a person with his own rights, opinions. But at the same time I did want an identity. And I found that in the Democratic Party. It started at high school. I got into the Democratic group and quickly became a leader of the teen Democrats. It became my religion, because I evaluated everything according to the party's success or failure. When I left school I went straight into the party organization. The party became my community. But it wasn't a real community. It didn't have the caring that a Christian community should have. In the navy I had the sense of meeting Christ in reading the Scriptures, and I was touched by that. But it was isolated until I came here, which makes real on earth this relationship with God. I have found the real community here, in theology school." CITY POLITICS in Atlanta were mainly black politics, and Michael Lomax was one of the up-and-coming black politicians. He was only thirty-eight, but it was said that he would be running for mayor in 1989. He was not from Atlanta, but from Los Angeles, and he had style. He was tall and slender and well dressed and educated and softly spoken. He was of a pale complexion. He did not have a black man-of-the-people reputation; but service to the black cause was in his family tradition. His knowledge of black writing was considerable; his hero was the early black radical William Du Bois, the critic of Booker Washington. And he was a dedicated politician. Everything about him was considered. He had the politician's heightened sense of the self, as I was aware when, after our talk, we walked back together for a while in the city center, and on the Macy's side of Peachtree Street. He was known; people looked at him. He made a joke about it, but this kind of public response mattered to him. We met in the library, for which, as chairman of the Fulton County Commission, he was responsible. The people he greeted so affably in the forecourt were architects. He said grandly, but with a smile, "I like building things." And in the library council room upstairs there was tea: a silver service and white Wedgwood cups and a selection of pastries of small size, laid out for us by someone from the Commission, a white man, young, smiling, happy to serve his elegant chairman. Blacks had to look inwards, Michael Lomax said. The need now was not for marches so much as for an internal revolution. "The civil-rights movement distorted our conception of human relations. It made it completely adversarial. In an adversarial relationship there is a good person and a bad person, a victim and a victimizer. We were the good, we were the victim." None of the current black leaders talked of black responsibility, he said. And yet for him, with all that he had become, and all his future, there was still the burden of being black. He spoke of the burden in this way (and he might have spoken the words often before): "There's not a day, not a moment in my life when I don't have to think about the color of my skin. And being black is not just about what I see. It's about what I feel about myself. It's as much internal as external. "I think sometimes that an exorcism has got to happen for all of us, where you pull out all of those evil demons of race. They're still inside us, fighting with one another. "Ten years ago I went to Brazil. And I went to a place in northern Brazil called Salvador which has a very mixed population and where having skin the color of mine was nothing unusual. And I felt a tremendous sense of liberation and freedom. But I also felt a sense of loss because people weren't dealing with me negatively because of my skin. That was the freedom, but I had so many expectations inside me as a black person that I couldn't accept the ignoring of that person—it was another kind of invisibility. "You have to confront your own demons. For me it's confronting the fact that I am a black person and that every time a white person sees me I may be no different for him than seeing a drunk on the street. And that colors the way I think about myself. I have been angry about being black, saddened by it. And I cannot deal with the white person or the black person until I look in the mirror and accept the man I see there." IT WAS generally agreed that the correct behavior of the sheriff of Forsyth County had done much to take the poison out of the situation at the very beginning. When I spoke to him on the telephone I found him easy and businesslike; many people had been to see him. He told me how to get to his office. It was in the Forsyth County Jail, he said. And that made me think of any number of Western films. It was about an hour away from Atlanta. The holiday setting, of woods and well-kept roads and an enormous artificial lake created by the Army Corps of Engineers, was hard to associate with the blood tensions of 1912: the lynching of a man in the jail, the public hanging of two others, the roving crowds giving notice to the blacks. And the county town in the midst of these spring woods was very American: the fast-food places, the banks looking like churches, billboards—ordinary. A woman stepped out of her grocery shop to direct me to the sheriff's office. Across the main town road, past the cemetery, and then on to a low brick structure. And there, in the busy little red-brick town, it was: a new building, not the one of 1912, but still as flat and basic-looking as a sheriff's office in a Western film; assertively labeled (as in a film) FORSYTH COUNTY JAIL, but with a large asphalted forecourt full of parked cars—the jail and the sheriff's office, like the fast-food places, serving a motorized community. The United States flag and the Georgia flag hung side by side from flagpoles. Two sets of glass doors led into the reception area, where two elderly white people were sitting on low chairs. A secretary sat at a desk with papers. And at her back, on the concrete-block wall, was a seal-of-Georgia plaque: roughly rendered motifs of civility from 1776: an arch on two classical columns, a scroll hanging loose in the space between the columns, with the Georgia motto: WISDOM, JUSTICE, MODERATION. The sheriff was in a meeting, the secretary said. A man in blue jeans came in to talk about a parking ticket or something of that nature—giving an idea of the day-to-day business of a sheriff's office. The sheriff himself came out after a while, jacketless, a paisley-patterned tie on his white shirt. He said, "Be with y'all in just a moment." And soon I was called into his office, where, on an old-fashioned hat-rack, at the very top, was a black cowboy hat with the sheriff badge. The sheriff said he had worn the hat only once, on the day of the big Forsyth march. Also on the rack was the very clean pale-blue jacket of the sheriff. He was in his forties. He said he had been twenty years in the county. He had "taught school" for some time; he had been sheriff for eleven years. Years ago, he said, Forsyth County had been isolated, and the folks were very clannish. The same thing could be said of "the entire North Georgia area." "The liquor industry came along, and a few folks made moonshine here, because it was very isolated. And that was the only means of income." Later there came the Lockheed and General Motors plants; and there also came the poultry industry. "The poultry industry brought our community out of its low socioeconomic situation. You began to see better roads, a great influx." At the same time there was the Atlanta boom. "What we are attracting now is a lot of people." Land had tripled in price. In 1970 there were sixteen thousand people; in 1986 there must have been forty thousand. "We are becoming an affluent suburban county of Atlanta. So we are in a boom growth situation." So, though "folks threw rocks" at the first brotherhood march, the cause of the rock-throwers couldn't really succeed in the new Forsyth. The second march, of the twenty thousand, wasn't a racial occasion, the sheriff said. The marchers were white as well as black, and they were making clear that they didn't want to see violence. "The American public will not tolerate violence." About race as race, the sheriff said, there was nothing that could be done. "The real problem is social and economic.... There's nothing you can do, because people migrate where they feel comfortable. They migrate to their social-economic status." A black doctor who wanted to settle in Forsyth County might fit in. But it would be different for a lower-class black. People needed to feel comfortable with people. "If you have two sorry black folks and two sorry white folks they're gonna fight because they can't get along." About the big march itself, it had always been a media event, the sheriff said. A lot of people came to that march because it was the first march in twenty years. People who had missed out on the marches of the civil-rights movement in the old days wished to take part in one now. "It gave a lot of people an opportunity to take part in something they thought was going to be historical." So there were these two "volatile" groups—the marchers, and the people who were opposed to them. What sort of people were opposed? "A lot of the people I deal with on Saturdays. Law enforcement deals with ten percent of the population ninety percent of the time." This was how the sheriff talked: he was as much sociologist (and former teacher) as law-enforcement official. He made the affairs of Forsyth County seem much more manageable. And though he didn't say so, there came out from his talk the idea of two sets of people looking for attention. The civil-rights groups, their major battles and indeed their war won long ago, now squabbling, and looking for causes; and the white supremacists looking in almost the same way for publicity and patronage. The great Forsyth march, as the sheriff described it, was like a ritual conflict, played out before the cameras, and according to certain rules. Out of this formalizing, the issue had died. Overexposure was a very American aspect of this formalizing, I also felt. Everyone had been interviewed and interviewed; everyone, including the sheriff, had become a personality; everyone had now exhausted attention. So, as the sheriff said: "The issue is dead." And the sheriff made a further point. The marchers had won, but in the three months since then no black had moved into Forsyth. The county remained all white, proving the first point: that the issue now wasn't racial, but social and economic. He was impressive, Sheriff Walraven. He was an elected official, and he saw himself representing the will of the American people—who had turned their face against violence. And though he wasn't willing to play up this side of things, he was also doing his Christian duty, Christianity being a religion that taught love and peace. (Christianity, at one time, in this setting, stood for other things; the Christianity of the Ku Klux Klan still had to be taken into account. But the sheriff saw the events of 1912 as historical, seventy-five years old. He represented the current will of the American people. There was to be no violence; it was his duty to see that there was none.) Did he see a situation where that might change? He thought for a while and said, "If the system falls down." But then almost immediately he added, "The system can't fall down. Individuals might fall down." To meet this educated man with an almost philosophical idea of his duties was to see how far away from the center the Ku Klux Klan groups of Forsyth were. The point had in fact been made by the black mayor of Atlanta, Andrew Young. "I don't view the Klan action as just racist," the _Journal_ reported him as saying three days after the big march. "These are the desperate acts of people who find that history is leaving them behind. Basically what we need are some job training programs that help people get into the mainstream. What we are dealing with in Georgia now is a problem of the underclass—black and white. The black underclass gets caught up in drugs and crime. The white underclass gets caught up in drugs, crime and Klan. You can march until your feet drop, but you ain't going to change it that way." The point wasn't taken up. It wasn't made again; it was lost in the good, safe cause. A KIND of victory had been won. But little had changed. The message of Forsyth County was also the message of black Atlanta. It was of this special frustration that Marvin Arrington, president of the Atlanta City Council, spoke or appeared to speak. Our meeting was not a good one. I had telephoned his law office just before going over and he had said I was to come right away. But when I got there he wasn't in. He was said by his secretary—who gave me a Coca-Cola—to have stepped out. And he didn't return for half an hour. The offices of his firm were impressive. They were in a nicely refurbished old building in downtown Atlanta; an article in the _Constitution_ had said that the building had cost $1 million. When he came back he took me into his own office. It was sunny, overlooking the street, and warmer than the inner rooms. It had many diplomas and family photographs on the wall; and African statuary, tourist curios, on the windowsills. The failure of the occasion was partly my own fault, because when Arrington took off his jacket and urged me to begin, just like that, I could think of little to say. I had been hoping for a little chat beforehand; and hoping that during this chat I might see ideas or themes I might want to follow up. But this blunt request to get started filled my head only with what was most obvious. It didn't help that he was restless. He often got up and walked about; often spoke to his secretary through an open door; looked through papers on his desk. He said he did forty things at once. And all that came out of this unsatisfactory meeting was what might have been gathered from the _Constitution and Journal_ file and from his own publicity: a man of the inner city, growing up when all facilities were segregated, father a truck-driver, much of the ambition of the children being derived from their mother. "I broke out." An athletic scholarship helped him break out; he thought of all those who couldn't get such scholarships. And little had changed. Little economic power had come to black people with their political power; even the black business street, Auburn Avenue, was now neglected. Black people needed opportunity; opportunity could be provided only by the system. So that he seemed still to be laying responsibility on others. No thought here of the internal revolution Michael Lomax had spoken about. Still the rage. When I said that there had been movement for black people, he said, "Wait for another 350 years?" He smoked a big cigar; stubbed it out and created a cloud of aromatic smoke near where I was sitting. He apologized for that; there were, with his brusqueness, always these little moments of concern for me as a visitor. A colleague came in and was more interested in me than Arrington had been. His son came in, and Arrington momentarily softened at the sight of the big, confident boy, who told me he had been to England and had spent two and a half weeks there. After a time the boy went out. Arrington later referred to him. The world would be different for people like his son, he said. But that was the one touch of softness and optimism in his general spikiness. A spikiness about race. About the Atlanta newspaper that had tried to destroy him, he said—and he took me to an attached room to show me the attack on him in the Atlanta _Constitution:_ he had had it framed, together with a printed protest, signed by Martin Luther King's father among others, about the attitude of the press to black elected officials. And there was a spikiness, above all, about Michael Lomax, who was his opposite in so many ways: Arrington big, heavy, strong, brown-black, self-made; Lomax slender, light-complexioned, of an educated family, and conscious of his charm. Arrington had defeated Lomax for the Atlanta City Council presidency some six years before. And it was said that if Lomax ran for mayor in 1989, Arrington intended to run against him. He wanted me to read a profile of Lomax that had been written for an Atlanta paper. He spoke to someone in his office on the telephone and asked in an executive way for a copy of "the Lomax profile." Later again he spoke on the telephone to someone in his office, to ask for a copy of his own publicity pamphlet, _The Arrington Commitment_. Eight pages, sixteen photographs; professionally produced. He made other telephone calls. And once, while I was reading something on the wall—the past laid out in diplomas and photographs and newspaper columns—I heard him talking firmly to someone on the telephone, perhaps about the thing that had called him out of the office just after he had told me to come over. It was as though that day he had found many things to abrade him. He spoke again about his son. That softness led him to thoughts of London, where his son had been. But: there were riots, he said. And when he was there: "I didn't feel at ease in London." He added, "I went to the Shakespearean theatre. Didn't understand it, but I went for the culture." I would have liked to know more. But this was one of the many threads that were broken by his getting up and walking, his looking for papers, his smoking, his little bursts of courtesy. This trip to England—it would have been interesting to see the country through Arrington's eyes—was something we never got back to. I felt soon that there was nothing new for me to ask, that all the points I might raise would founder on the subject of black disadvantage. It was something I had worried about: that these figures of Atlanta, because they had been so often interviewed, and though they might appear new to the out-of-towner, might in fact have been reduced to a certain number of postures and attitudes, might have become their interviews. Like certain writers—Borges, to give a famous example, who had given so many interviews to journalists and others who, in the manner of interviewers, had wanted absolutely the set interview, the one in the file, had wanted to leave out nothing that had occurred in every other interview, that he, Borges, had finally become nothing more than his interview, a few stories, a few opinions, a potted autobiography, a pocket personality. Which was the way, I had been told, the media created two or three slogans for a politician and reduced him to those easily spoken words. I had worried about this, about not being able to get through the publicity; and with Arrington it had come to pass. I had not been able to go beyond the file. On the wall was a framed saying of Abraham Lincoln's: A lawyer's time and advice are part of his stock in trade. I got up to leave. He was courteous, and as a farewell offering he gave me a little tour of his firm's offices. The people I met were friendly and attractive; there was a white office manager. The quality and mood of people in an office or in any organization tell you immediately about the employer or management. So there would have been a much better side to Arrington than the side he had shown me that afternoon. Going down into the street, where the people were black, and Atlanta as a result appeared different from the areas I had so far seen, with a Caribbean, Latin American aspect to the crowd—and even to the city, since downtown Atlanta is not a city of solid, built-up blocks but, rather, a city of tall buildings and empty spaces, parking lots, so that it quickly acquires a semiderelict look—going down into the street, I was assailed by a very old feeling of constriction and gloom. I was taken back to some of the feelings of my childhood in Trinidad. There, though most of my teachers were Negroes (brown rather than black), and though for such people (as well as for policemen, Negroes again) I as a child had the utmost awe and respect, and though in my eyes people like teachers didn't really have racial attributes but were their professions alone, yet the minute I found myself in an out-of-school relationship with them I became aware—a child from an Indian family, full of rituals that couldn't be transferred outside the family house, rituals and attitudes that had day after day to be shed and reassumed, as one went to school and returned home—I became aware of the physical quality of Negroes, and of the difference and even, to me, the unreality of their domestic life. Something like that had happened in Arrington's office. His spikiness, his stress on race and the inner city ("Inner city is my ball game") and the strength he drew from the poor among blacks, had put up that old barrier around him. The spikiness was understandable; rage was understandable. But I also felt that rage and spikiness could make demands on other people that could never be met. He had said, "I'd like to be free. I cannot fly like the bird." Many people could say something like that; not everyone could make it a political statement. And I felt, especially in the Caribbean-seeming streets outside as I walked back to the hotel, that there were two world views here almost, two ways of seeing and feeling that could not be reconciled. And this was depressing. I had with a part of my mind been trying to find in the black politicians of Atlanta some of the lineaments of the black politicians of the Caribbean. In Arrington, for the first time, I thought I had found someone who might have been created by Caribbean circumstances. In the Caribbean such a person, proclaiming his origins in the people (like Bradshaw of St. Kitts or Gairy of Grenada) and claiming because of his early distress to understand the distress of his people, might have gone on to complete colonial power, might have overthrown an old system and set up in its place something he had fashioned himself. But here in Atlanta—though, as president of the City Council, Arrington had power of a sort, the power to say no—the power was circumscribed. And perhaps the very dignity that the politics of the city offered a black man made him more aware of the great encircling wealth and true power of white Atlanta. So that the politics of Atlanta might have seemed like a game, a drawing off of rage from black people. Just as civil-rights legislation gave rights without money or acceptance, so perhaps city politics gave position without strength, and stimulated another, unassuageable kind of rage. HOSEA WILLIAMS, after picketing the CIA in Washington about drugs, was to have gone to Europe to do some work about apartheid. Either he didn't go; or the trip was very short. Because a few days later Tom Teepen arranged a meeting for me with Hosea in Atlanta. The meeting was to be in East Atlanta, in one of the "neighborhoods," Tom said; and he drove me there to introduce me. The building we stopped at looked like a small factory or warehouse, and it stood next to a broken, three-walled shed. There was a central corridor, with people sitting at a desk. Stickers printed HOSEA were on walls and doors, and gave the place the feel of an election campaign headquarters. We were shown into an inner office, past a room with a secretary at a full desk. The walls of the inner office were hung with many big black-and-white photographs of the civil-rights marches: Hosea, much younger, in some of the photographs, with his amazingly young leader, Martin Luther King. There were photographs of arrests by police. But the most moving photographs were those that stressed simpler things: the overalls of the marchers, and the mule carts—the twin symbols of the movement, affecting, and inevitable, and right, like the Gandhi cap and homespun of India. Tom Teepen, looking at the photographs with me, said that when Martin Luther King was killed it was decided to carry his coffin on a mule cart; but the only one that could be found—and was commandeered—was in a museum or a fairground. Also on the wall were many shields and plaques given to Hosea for various things. And there was a poster with a Black Power twist on the Aunt Jemima theme. The big black woman didn't smile; she offered a big black fist; and the words were "No More" and "Net Weight 1000 lbs." Hosea (he had been busy somewhere in the building) finally came in, a man in his own place now, deferred to by the people there, and stiller than when I had seen him, in the federal courtroom. Tom Teepen introduced me; told him of my interest in Forsyth County. I saw in his eyes an immediate acceptance. And right away, even before Tom left us to go back to his paper, Hosea began to talk, began unaffectedly to act out the story, giving off energy, walking about, coming right up to me sometimes, while I sat at the long board table that was there in the big office in addition to the office desk. He took the story of Forsyth back to the beginning of the year, when the karate instructor from California had decided to have a Walk for Brotherhood to mark Martin Luther King Day in Forsyth. Hosea heard about that on television, and became interested. "He didn't know that violent and rabid racism existed up there. They came after him so vicious he began to realize, 'I mightn't get out of this town alive.' In places like that the major weapon is fire. Burn them out, burn down their houses. A martial-arts student from the next county came forward to help this fellow. The martial-arts fellow has the reputation of being a tough guy. He said to the Californian, 'We are white males. They can't do this to us.' He's a tough guy. But they not going to go after _him_. What they'll do is go after his family. So he began to reach out for black help. He became more shaky. "When I heard of this the first thing that hit me was this: 'Every movement we have ever been in, some whites came to our defense. Here are these white boys in trouble. If Dr. King was here, what position would he take?' I said, 'Hosea, pack your bag. We've got to go to Forsyth.' "I finally got the name of the martial-arts guy through a newspaper. I called the guy. 'My name is Hosea Williams. I offer you my help.' He was overwhelmed. He said, 'I know of you. Before I accept your help I want to talk face to face with you.' But I wouldn't drive to Forsyth that night. He said, 'I'll drive down to Atlanta.' I was afraid of him. I didn't know who he was. He might have been from the Klan. I staged a meeting in the lobby of a big hotel. He drove down that same night, he and his father-in-law. He said, 'I know you. I know your reputation. I know you're a tough man. But I tell you one thing. If you come to Forsyth and march with me you ain't gonna leave that place alive.' "I know how tough Forsyth is. But I thought he was being too pessimistic. I called a press conference. I announced that we are leaving from Dr. King's grave at nine o'clock and we are going to Forsyth. I didn't think nobody was going with me. Black people are afraid of Forsyth. They know the reputation. Black people don't even like stopping for gas at Forsyth. "Dean Carter, the martial-arts man, said: 'These people are ignorant. They are told to keep niggers out, don't care what it takes. They are taught from the cradle to the grave to keep those niggers out. You do whatever you have to do—you beat them, you kill them—to keep niggers out of the county. It's like their culture.' That's what Dean Carter said. 'It's like their _culture.'_ "I thought I knew how bad the place was. I didn't know how bad it really was. "The next morning there was about thirty-five to forty people. "I sensed, going up, that these people had a deep frustration. I got up and taught and talked and taught and talked and preached all the way up there. When we got there, there was about thirty or twenty people waiting to join us. One or two was the Ku Klux Klan waiting to infiltrate. But at the same time there were about fifteen hundred people all around—the papers say two hundred, but I say fifteen hundred—and they were having a Ku Klux Klan rally and they were shouting, 'Kill the niggers! Kill the niggers! Run the niggers back to the Atlanta watermelon field.' Fifteen hundred. All around. "The sheriff tried to discourage us getting off the bus. I said: 'We are Americans. Marching is a matter of free speech.' I wasn't going to let anybody stop us marching. "Those people all around were so souped up they were diving and running over four-foot fences like Olympic hurdlers, shouting, 'Kill the niggers! Kill the niggers!' " When I had seen him in the courtroom—doing nothing, saying little—he had seemed harassed, agitated. Yet now, though he was walking around my chair and acting out his story, stamping his feet, jabbing his fist down, he seemed lucid. His talk didn't seem exaggerated or quirky. And what increasingly came out was how practical he had been. Like the Indian mahatma, he knew how to organize things, how to use the institutions of the society: the law, the press. The opponents of the march had also organized. According to Hosea, they had laid by stores of missiles. Hosea said, "The press kept coming up to me"—odd, this description of a dangerous march, with the press on hand: how had he got them there?—"The press kept coming up to me and saying, 'Is this bad? Is this bad, Hosea?' And I said, acting, 'No, it ain't so bad.' And one of my own staff members came and said to me, 'Reverend, it's _bad.'_ And he was right. It was bad. "One man, one of the Forsyth crowd, was running up to the front of our bus and then to the rear of the bus—the bus that had brought us to Forsyth, the bus I had rented—running back and forth trying to get to me. I realized what he was doing. He seemed to be a leader, and I thought I would try to communicate with him through the eyes." (I remembered what Howard had told me: in moments of street danger avoid eye contact. It was Howard's rule for avoiding trouble generally; and I saw it practiced all the time by black waiters in Atlanta.) "And when he came back up to the front of the bus, I smiled at him. He went berserk. He started screaming: 'The nigger smiled at me! You gotta kill these niggers! I don't want these niggers march. But the nigger _smiled_ at me!' " The sheriff then asked Hosea to get his people back on the bus. "I got the people on the bus and take them down a lil ways, to give him a chance to contain the Ku Klux Klan." Hosea drew up the bottom of one trouser leg and showed the dark-red bruises on his pale-brown shin and calf. He said the bruises had been caused by a brick thrown during the march. That was the end of the march. On the bus going back to Atlanta a thought came to him, and he began to smile. His son asked why he was smiling, and Hosea said to him, "I feel like I've really celebrated Dr. King's birthday." It was his storyteller's way of rounding off the story, which had begun with his strictures on the false ways people, and black people among them, had begun to celebrate the birthday of "Dr. King"—which was the way Hosea invariably referred to Martin Luther King. Hosea said, "On the bus coming home I told my son, 'Them's some of the baddest white folks I've ever seen.' "I've faced mobs before. But they usually were older white males. If there was any women they was only one or two and they was quiet. But at Forsyth, oh God, they had a large number of women, many holding little babies in their arms, and screaming all kinds of vulgarity, especially hatred. 'Kill the niggers! The niggers get AIDS!' The number of young people, the teenagers! I thought: 'Oh my God, we got sixty more years of that kid standing over there.' " After that first march, Hosea said, some newspapers had reported that he had been run out of Forsyth County. That had encouraged him to organize the second march. Forty thousand people had marched then. The newspapers said twenty thousand, but he thought forty thousand. "Racism is coming back, man. Just like it did after the Civil War. They described that then as the ending of the Reconstruction. Well, we're now at the ending of the second Reconstruction." But the Forsyth issue was dead now, as the sheriff had said. Had anything been served? Hosea thought that, though no black had moved to Forsyth, a lot of good had come out of the affair. He offered a list of the good things. One: the good white people up in Forsyth had been able to stand up to the Klan. Two: the fragmented civil-rights groups had come together, in a way they hadn't been together since the death of Dr. King. "Three: Forsyth kind of forces so-called leaders to stop jiving and _lead_ , not to wait for things to happen naturally. Forces leaders to go out and initiate and provoke confrontation. Four: the greatest thing. It proved that Dr. King's strategies didn't become obsolete with his death, as other people say. They say to me, 'Hosea, you're just a battle-fatigued old general. It's time to stop demonstratin' and start negotiatin'.' They've taken the movement out of the street and into the suite. Out of the street and into the suite. That's what they spin around doing. But they have to come back to my position and admit that the street is where it's happening." "A primary force": that was how Tom Teepen had described Hosea. But I hadn't seen it like that. I had seen him more as a performer, acting up to the public character he had created for himself. I didn't think so now. The City Council politics he was engaged in required him to be a showman; but through his showmanship—now, in the privacy of his office—I was aware of his lucidity and goodness; and I felt that the mahatma himself—with all his own awkwardness—might have radiated something of that quality. As it happened, among the books on a bookshelf against the wall there was one with _Gandhi_ on the spine. And when Hosea had to go out of the office to talk to someone who had arrived, I went and looked at it. It was a paperback. It wasn't the mahatma's autobiography, as I had thought; it was the screenplay of the film _Gandhi_ , and on the fly leaf there was a dedication to Hosea from the writer, Jack Briley: a dedication that said it was (if I remember rightly) from a man who wrote words to a man who took the blows. The dedication, it seemed to me, did honor to both men, and hinted at one explanation (out of many) of the extraordinary power of that film. And the story Hosea had told (and I was an audience of only one), the energy he had given off, added a new meaning to the big photographs on the walls: the mule carts and overalls, and the young Martin Luther King, whom Hosea honored and adored. When he came back to the office a little of the energy that had come to him during his telling of the Forsyth story had gone away. In its place there was authority; he was now in my eyes absolutely lucid. I asked him about his recent campaign about drugs, and his picketing of the CIA. He said, "The drug thing, it's bad. Drugs are destroying our people more than anything—segregation, racism—since slavery. The fear of the drug-traffickers, the fear that results from the drug-trafficking, is worse than the drug. Nothing have they feared like those drug people. I was born in the streets; I was raised in the streets; I still live in the streets. And even I have just discovered how bad the drug business is." So there was logic in his behavior, as there had been in the mahatma's, the switching of reforming attention from public issues to private, from the external foe to the internal. And the impression he gave of being a very practical man was added to when I asked him about the building where we were. Was it his political headquarters in a "neighborhood," or what? He said it was his business place. He made chemicals. This was unexpected. I must have read about it somewhere, almost certainly; but it hadn't registered. He said, with as much gentleness as pride, "Come, I'll show you." We went out into the corridor and went past the desk where, ever since I had come, there had been two young people, a young woman and a young man, as still as students, serving some purpose in Hosea's affairs. At the end of the corridor Hosea pushed a door open, and there, attached to his office building, was a warehouse with barrels and on one side stacks of cardboard that would fold into cartons. "I make janitorial chemicals," Hosea said. "Floor-cleaners, window-cleaning fluid. Everything to do with janitorial cleaning. I had to make myself independent of those people downtown." He employed twenty people. The business was bigger than I thought; and in this business side of the man there was again, and more than ever, something of the Indian mahatma, who had started his professional life as a lawyer, was scrupulous about accounts, was careful about things like newspaper presses, and in South Africa in the 1900S, for this very purpose of independence and Ruskinian virtue, had started a farm. Strange fulfillment sixty years later of the mahatma's creed, and perhaps the achievement here had been bigger than the mahatma's in India: the winning of legal rights, against a background of slavery and violence, for a people long humiliated and disenfranchised. He took me outside, to wait for a taxi. There appeared to be none. He said, "I will stop someone I know and make him take you back." But no one he knew came along. In the end he asked two of his people, waiting in a shabby van, to drive me back. "Give them something for the gas," he said. And, driving back along Highway 20 to Atlanta, in the company of these followers of Hosea's, poor people, in their littered van (the radio turned on), I felt myself in another atmosphere, and felt the distance between the people Hosea led or spoke for and the setting, the towers of central Atlanta appearing in the distance above the freeways. FROM SCATTERED impressions (and really more from stories of Shango and Shouters in Trinidad and memories there of black street-corner preachers and beach baptisms) I had thought of black-American religion as the religion of ecstasy and trance. I was not prepared for its formality or its communal-social side, as in Howard's home town. I was not prepared for its purity, as in Hosea. Or, later, in Robert Waymer. He was a handsome man of forty-nine; formal clothes became him. He was on the Atlanta School Board. He came from a black South Carolina family. There was a family farm of fifty acres—not big, but it had maintained many of the family. And the family had been well known in South Carolina, in Orangeburg, for three generations. "Maybe four." I told him that family continuity like this had formed no part of my idea of black life in the American South. He said, "It was a secret." "Secret?" "You don't tell white people everything." And this was so strange from him, in the paneled lobby of the Ritz-Carlton, where he sat confidently, fitting the setting. He said: "They were hostile. People who understood their circumstances and took pride in doing something for themselves knew that if you were black you were living in a hostile environment." He told me about his extended family. "There was quite a resonance in the extended family. And from that resonance and cooperation my father's two eldest sisters married brothers who were tobacco farmers, cattle farmers, general truck farmers. It was from that beginning of farming we came. And we were quite ingenious people, I think. There were sixteen of us. My mother was the oldest daughter of an A.M.E. minister." He told me about the initials. African Methodist Episcopalian. The church had had its two hundredth anniversary that year, he said. African? Did it have something to do with Africa? No. It had been established by an ex-slave, Richard Allen, when he found that he was shut out of the white churches. And that was Bob Waymer's theme: the solidarity that had come to black people from being shut out, the necessity that had driven them to found their own institutions—and the breakdown that had occurred with the ending of segregation. His father was the eldest son of a farmer. So there was a tradition in his family. And yet there was a certain modesty. "We're really not leaders. Really not. You and other people haven't had an opportunity to learn about blacks the way they really are. My family doesn't consider themselves outstanding. We are good committed people, committed to helping each other. A kind of dedication that started with my grandfather and continued with my mother. "You got to know that you don't know anything about blacks. "The civil-rights movement was great for everybody. But it freed up whites more than it did blacks. We were a closed, segregated, persecuted group in America, and we knew that. Everything that we learned, my age group, we knew that we had to be good at what we did. We had to be curious. Patriotic. Better than the other guy. Educated. And religious. And _cautious_ too. We had to be cautious because we had to negotiate the hostile system in order to earn a living, to survive and exist with a feeling of well-being. We did well, as a general group of people. We established our institutions, educated our own. Public education is a relatively new concept. The first high school in Atlanta, the Booker T. Washington, was built in the 1940s." "Do you talk much about this now?" "No. Not much. There is nothing to say. If you said anything you were bragging about how well you were able to survive. Which is nothing. Or you would be boasting. Which among my family and other families like mine is tantamount to sin—it's vanity." I asked him about the place of the church. "The church is basic. And I'm not specially religious. The church is where I learned how to have respect for myself and others. And that's basic. And the Ten Commandments—that's the law. That's it. I used to think when I was a child they were my mother's laws, and I wondered how the other children had got to hear of the same things." He was calm. Yet there were others—I mentioned Marvin Arrington—who were not calm. He said that people like Arrington were "actors." He stressed the word, and then he explained it. Arrington was a lawyer. "There is a difference in the attitudes of black Americans who were educated solely in black institutions, and those who went to higher education in white institutions. "Everybody wants to be successful in what they do. Learning is a very painful changing of you and your mental attitudes. If you are going to be a success as a lawyer in America you are going to be successful only if you emulate or become a white lawyer. The profession—and this is not only for the legal profession—orients you in that direction. And you become an instrument of your own demise." Demise—death. That was a strong word. But he meant the death of the soul; and, as he saw it, it was the kind of death that had come to black people in some ways with desegregation and the consequent loss of community. This was the very subject that Howard—and it seemed now so long ago—had touched upon, as we were walking back from church to his mother's house. Bob Waymer said, "I mean demise. Let me tell you why. In the teaching profession and the legal profession and any other profession you learn certain things from white institutions about blacks. And they are ninety percent derogatory. Frederick Douglass—he is one of my heroes—and other people have said it—says that there is no planting without the tilling of the soil. For a while, because of the love and compassion which Dr. King was able to communicate to the rest of the world, there were many people all over the world who felt that something was askew, wrong, about the race question and the treatment of blacks. But these good people always knew that. They knew that already. What Dr. King did was to act as a catharsis for white people. He was a great mental-health cure for white Americans. What he did for blacks was to make their rights legal and to inspire tremendous numbers of blacks to take action for their people and themselves. "But once blacks got into white institutions they found that being in their own institutions was a lot better, and that being a white American wasn't all that great. We thought that once we had the same rights all our problems were over. What happened was that we retained eighty percent of the historical problem that we had, and that now we also had to deal with all of those things associated with being white. "Let me give you a comical example. If you were a domestic and you cooked dinner for a white family, you knew how much they would eat and you knew that if you cooked a little more you could always take that home with you. You always did that. It was part of the built-in economy, the hidden economy." And there were other examples, which were not so comical; were in fact humiliating to think about. In the days of segregation blacks could not stay in hotels or motels or be served in restaurants. Some places served blacks at the back window; and it often happened that when the cook knew his order was a back-window order he put on, if he were serving a hamburger, an extra piece of meat. This was the origin of the cheeseburger. And since there were no hotels for blacks there grew up, in certain black families or houses, the "tourist home," where blacks might stay. Local black people usually knew where these places were, and could direct the traveler. The "tourist home" was usually a room in someone's house; it provided a livelihood for some people. "The civil-rights movement made us equal. We didn't have to be resourceful any more. All we needed was a credit card and a good job. So, what's lost? Mrs. Smith, who operated her tourist home, can no longer earn a living. We went from four dollars a night for a family—which included breakfast and a sandwich to take with you, and communication—to fourteen dollars a night in a Holiday Inn room." Communication through the tourist homes: it was one of the unexpected fruits of segregation, and it was something Bob Waymer stressed. New dances, he said, traveled very fast between blacks because of this communication. In those days without television it was like magic: blacks from different parts of the country could always dance the same new dances when they met. With desegregation this was lost. "There was a tremendous boost for hotels like the Holiday Inn all across the United States. I remember people who weren't traveling anywhere who would go downtown and check into the Holiday Inn just because they had the right." RELIGION WAS like something in the air, a store of emotion on which people could draw according to their need. The religious vocation could come to many. For some the vocation contained the ideas of service and community. For others, with a stronger sense of self, who had gone out into the world with a will to win but had then withdrawn for various reasons, the vocation came as a wish to expound the word, to preach, to make an offering to God and men of the life that had been lived. The white former businessman I met, in a group of mature students in a religious school, had felt "humbled by God." It was only after he had made his religious decision that an offer had been made of the capital he had been looking for to keep his business going. That offer of capital had been a temptation; but he hadn't fallen. He was a handsome man, with arresting blue eyes; he couldn't have been unaware of his looks; he might have expected an easier passage through the world. The same could probably be said of the striking black woman from Alabama. She spoke of her beauty as of something to be taken for granted; and something still an asset. But her life after she had left the South had been one of poverty and disorder. And there was Danny, a musician. He too, like the former businessman, had felt humbled by God—he used the same words. Danny said, "I pictured my life as a shattered mirror—a piece here, a piece there." I was so taken by that—the kind of chaos Anne Siddons had talked about—and so interested by what he had to say about the development of his religious life, that I wanted to talk to him again. We fixed a time. He didn't come. I telephoned. He was eating; I could tell by the noises; he said he had had a lot more to do than he had thought. We fixed another time. And he came. He was black and stocky; in his short-sleeved open yellow shirt he looked very casual in the lounge of the Ritz, where that morning they were making a video about the hotel, with a male model, and they were shifting very bright lights about. This was the background to our talk of religion and the vanity of the world. I asked him about the feeling he had had of being humbled by God. And that was where his story began. "All my life I was such a winner, always seeking fame, even in high school. Everything I did I was number one. In music I have to be the leader. I was captain of the football team, the basketball team. I was the valedictorian of my class—I had got the highest grades of any graduating senior in my class. Even doing domestic work around the home, I would give it my very best because I knew my parents would praise me. I just loved people to brag on me. I thought I was something special in the world—I think it had a lot to do with grace and gifts that were naturally given, God-given, to me. "And also my parents were professional. My father was a minister and also a teacher, and my mother also. And, the small community we lived in, by both of them being professional was kind of unique. It made me proud, even as a small child. We lived in a little place in Texas. "I could even think we had indoor restrooms when most people in the community didn't. And though I would never brag about anything like that, it always had an effect on me. We were the first or second to get a TV set. My father was actually like the leader in the community. The first black to be on the school board after integration. "I was aware of the fact that being boastful and wearing pride—letting it show on the outside—would cause people to not like you or resent you. So throughout my life I always knew how to be modest. But the purpose was for praise. "I had a music scholarship, a football and a basketball scholarship. And I really didn't accept any of them because I didn't know what I wanted to do. I figured out eventually that music would be my best route. My mother taught me in the first and second grade, and my sister and I were always on program—always acting or singing solos—in the church. So music was always a way where people focused on me. It wasn't something I was thinking. It was something I just knew—that when you sang everyone sat down and listened to you, focused on you. I even used to go down to the grocery store and sing solos for the man, to get some candy. "When I went off to college I went and looked at the football players—and my decision was made about music. The guys on the football field were so large and brutal. It would have been a hard way to go. "There was a talent show at the college. I was walking through the dormitory and I heard someone playing a guitar downstairs, and so I went down to see what was going on. I went back to my room and got my clarinet and went down and started playing with this guy—songs. It drew crowds. People started coming down to listen. After that more musicians came. And we decided from that moment to perfect a couple of numbers for the talent show. We were successful that night. A nightclub owner was in the auditorium, and he asked us to come play in his club that night. We didn't play for money. We played for doughnuts. We loved it so much we didn't know but those two numbers. And that was when it started. And the group became the most popular group in the city. We got a manager. We toured the country. We made a reputation for ourselves. "I was making so much money and was so popular, and I was only nineteen, just a senior in college, and living in a fabulous apartment, I thought I was God's gift to women. Until all of a sudden school became unattractive. It actually seemed irrelevant, because I was already on my way to fame and fortune—and I put _fame_ before fortune. "So I left school, to concentrate on being a star. And after seventeen years of being with several recording companies touring the United States and Canada, Africa—my life became shattered." This was sudden, in the telling. But Danny's hidden point was that he had misread the music world, had misread his position in it. His position had always been subsidiary, supporting. He had been too quick to see himself as a star, had allowed himself to be deluded. "I began to sense that I wasn't in control of my life. Even that God was being unfair to me. Because I knew I had as much or more talent than anyone in the business. But I would always get exploited. They would take ideas from my songs and never release my material nationwide." "You mean you had no manager? In all those years?" And it turned out that the first manager he had had, while he had been in college, hadn't lasted. "One thing was that all my life everything had always been _me_. So I was everything. I figured I could be my own manager, everything. I wasn't submissive. My pride blinded me from the wisdom of what my very first manager said to me—he was offering to support me financially if I stayed with his group. But I wanted my own name up front. And so throughout the years we floated around. The record companies and promoters know that entertainers are addicted to one thing—entertaining. So they exploited us, and we allowed ourselves to be exploited. "I lost my group. That was the very point when the crisis came. I was in a club and I remember thinking, 'The time that I was most successful was the time when I was an apprentice.' That word came to me: _apprentice_. 'An _apprentice_ to someone that had connections and money.' "Reflecting back, I realize that the Lord was dealing with me then. I was being in a way humbled then—to even recognize that I need to be following someone, rather than being in direct control. But I was thinking strictly musically—maybe I need to join a group that's doing something, going somewhere, and be a follower rather than a leader. "Then a big opportunity came up. I remember I was in a recording studio, getting ready to do a song on an album for the company who had made the offer to me—it was like an auditioning. And I was _horrible_. I broke down in the recording studio and cried like a baby. "And I remember praying in the studio. I said, 'Lord, why are you letting this happen to me? How can I go to my family and tell them I have failed on my big break?' I had phoned people all over the United States and told people to look out for me, because this was it—I was going to be a big star at last. And even though my parents never agreed with what I was doing, I could even sense that they were hoping I would make it, my dreams would come true. The main thing I dreamed of was surprising my mother with a Rolls-Royce and a million-dollar home." "Why do you think you failed so badly in the studio?" "I just didn't seem to have it. I was embarrassed. I was depressed. Felt like my life was over. I felt like that was the last shot for me. It just shattered everything. To have your pride fed all your life and then to be denounced was like calling me counterfeit. Maybe I never was what I thought I was. "So it was during that time that I began to think of another way. And that was that all my life at the back of my mind I had always like heard a voice saying, 'If you would be a songwriter, first. Let other people record _your_ songs—that would be the best route for you.' I just sensed that. But I had too much pride. I didn't want to make it as a songwriter. I wanted to sing my own songs. But now I had reached the point where that was a last alternative. Because, even though I was at rock bottom, I never totally gave up. So this was a point of humility for me—that maybe I should try being a songwriter. So I gave one of my songs to a local musician, a tremendous vocalist, and I became his producer and manager. And we, on a local level, were successful. "It was at that time I met a man that told me about Christ. He was a minister. He was a black minister. In his early sixties. He was also a musician. I went to the office to meet my wife, and I met this man. And when I met him his countenance was like there were _lights_ coming from his eyes—just glowing. The smile just cut right through me. He looked at me with so much _love_. And at the same time I felt his countenance was drawing me to him. But inside I felt dirty and unclean and ashamed. And I wanted to go in another direction. All this was in the office of the insurance firm where he worked and my wife worked. "All he said was, 'I've been looking forward to meeting you. I've heard so much about you.' He was a saxophonist, but he told me he only played _hymns_ , and he asked if we could get together and play some hymns on the saxophone. Inside I had no desire, no intentions of doing that. But I told him yes. "Before he came, about a week later, he sent me a Bible. It was a Living Bible. Up front it had selected scriptures that addressed specific issues. And one was: What does the Bible say about success? It gave all the scriptures relating to success and what to do when you are distressed and frustrated. All those scriptures related to trust in the Lord. Trust, and He would do. The emphasis is on _He_. All my life the emphasis was on _I. I_ would do, or _I_ can do. Or _I_ have done." And at the thought of that _I_ having done, Danny laughed, as though he had made a joke. "When I got together with the old musician, I accepted Christ. He shared Christ with me. He opened the Scriptures up to me. "He came to my house a week after he had sent the Bible. My wife wasn't there at that particular time. He came with his saxophone. We played a little. And he really became interested in my singing. And he shared Christ with me. We had prayers. And I knew—but it was primarily reading the Bible for myself and seeing that where I had been carrying the burden of living, being successful, being happy, carrying that burden on my own shoulders—I knew, I saw through the Scriptures, that God, through Christ, offered everything I had been in pursuit of. "So I prayed and invited Christ to come into my life. I believe that God became human to take on our sins so that we could live in the righteousness of God. There was a scripture pertaining to that that really grabbed me. It was Galatians 5:22. The Living Bible put it this way: The Holy Spirit wants to produce fruit in you. 'Fruit.' Singular, but plural. Fruit, which are: love, joy, peace, patience, goodness, meekness, and self-control. That really grabbed me. To be successful is to have all of that living within me, because it wouldn't be my circumstances that would determine my happiness, but my relationship with God. So to be successful no longer depended upon personal achievements, but just simply having the peace and joy of knowing that God loves you. So much so that he would forgive me for all the things I have done. "That very night, after the prayers with the old musician in my house, I went to a jail with him and participated in a worship service. And this became a nightly thing—visiting the jails. He would preach and I would sing." "What did you think about the people in jail, the prisoners? How did they look upon you?" "I _loved_ them. I began to _see_ people. All my life all I had ever seen was myself. My love was a self-directed love. I began to see that people had a lot more to offer me than I had to offer them. In other words, I began to see people in the way that I saw God. "At this particular time I was still playing with a band at the weekend. But my songs changed. I started turning the secular words to songs about Jesus. I started preaching onstage." "How did people take that?" "As a joke." "Black audience or white audience?" "Mixed. I started having Bible studies on the way to the gig, as we called it. With the musicians. Bible studies during the breaks. And the group was becoming more popular than ever before. At the same time the gentleman who had led me to Christ was patiently—and lovingly—telling me that there would come a time when I would have to make a decision—to absolutely surrender to Christ. "And that's when I wrassled—I struggled. Because I told the Lord day after day, night after night, that I could be a witness in a nightclub, because people there don't go to church and don't want to go to church. But I kept reading scriptures, and hearing in my mind, 'Be you separate. Come ye from among them. What fellowship has light with darkness, or righteousness with unrighteousness?' "That's when, one night, my wife and I were at home. And I had a vision. I was in my home town in Texas. About two hundred yards from our house there is a pond. It is my favorite place, even now. Where I go to fish, to shoot my rifle, to swim. And I saw myself walking through the field going to the pond. When I heard a voice calling me Moses. And I looked up, upwards. And I recognized the voice. I knew that it was the voice of God, saying: 'You've gone as far as you can go.' Immediately I closed my eyes and lay down in the field. And suddenly another image that was transparent at first grew out of the image laying in the field. This image was muscular. I could see the intensity of the veins in my arms and muscles as it popped the shirt open. And on my face was self-determination, ambition, very powerfully prideful. And I continued walking towards the pond, each step growing more intense, ambitious, and confident. When suddenly again I heard a voice saying, 'Moses, this is as far as you can go.' This time I looked up with resentment. In my mind I was saying, 'No, you can't stop me now. I'm almost there. I can make it.' "The power that came from above suppressed me into the field, the power which all the time I was fighting. As I was on my knees, still fighting, my skin began to melt and my bones began to melt also, till finally I was a horrible-looking creature, like something in a scary movie. But I continued to resist until there was nothing but liquid—I was a liquid mess. And then another image, transparent at first, grew out of that image on the ground. This time I was peaceful—this image had peace on its face, my face, and there was love and joy in my heart. Submissive, willing to be obedient and to trust in the voice that was directing my path. "When I woke up I was—in the vision—touching my feet in the water. And my wife woke up as I was sitting in the bed with tears running down my face like water, chill bumps racing all up and down my body. And the power that was present woke my wife up as I was sitting up in the bed. My wife woke up in fear, and she was crying. 'Honey, what's wrong? Honey, what's wrong?' And I began to sing: 'Nothing is wrong. God is calling me.' And she immediately lay down and went back to sleep. "Shortly after that I surrendered totally and entered the ministry. Walked away from what was potentially a hit record. Knowing that the love of God and being submissive to God's will is success. "It was some time later, on my thirty-fourth birthday, that I promised the Lord that I would go where he sent me and do what he wanted me to do. And he led me to the Methodist church, where I became a candidate for ministry. Now, this church insists that one has to go to seminaries. The college I chose, in my home town, is very, very expensive. And I didn't have a dime. I went there. I was rejected. I was told I had to have money to come to that college. The person who rejected me was a minister on the council. He said, 'Sir, you have some nerve coming here. And you don't have a dime.' I said, 'The Lord sent me.' " Danny, telling this story of his rejection, laughed. I asked, "What did he actually say?" "He said something to this effect: 'Let the Lord give you some money, then come back.' " And Danny laughed again, as though he understood how tempting it had been, to someone in the minister's position, to reply like that. Danny said, "He was rough. That was on Friday. That Sunday I directed the choir and played a saxophone song in our church. The district superintendent came by that Sunday. He was impressed after hearing that I was a candidate for ministry. On Monday morning I received a call from the gentleman who had sent me away. He said, 'God must have sent you. We are going to get you in school.' And all my schooling was paid. Over twenty thousand dollars so far. That was three years ago." I asked about the old musician. "He is still my closest friend. I _love_ him. I call him my father, my brother, my friend. I tell this story, and would like it known, so that some people might be touched by Jesus." # 2 # CHARLESTON # The Religion of the Past THE INTERSTATE highway goes right into the Charleston peninsula. So you arrive quite easily in the historical area. And after Atlanta it was like arriving in Toytown. The people in the hotel lobby were in tourist clothes; their footsteps and voices ricocheted off the walls and the marble floor and hung in a roar above the extravagant chandelier, at which from time to time a new arrival aimed a camera, as though this too was part of tourist Charleston, together with the many shops of the hotel lobby; and the Slave Mart and the Confederate Museum in the eighteenth- and nineteenth-century streets outside; and the renovated old market with its many stalls and boutiques, and with grave black ladies sitting out on the pavement and weaving baskets. The tourist Charleston not only being the eighteenth-century town, and slavery and the Civil War, but also having something of the tourist Caribbean of today. In the historical area the horse-drawn tourist carriages moved up and down all the time, and the horses had "diapers," to catch the droppings. Other visitors walked about and looked. And others again—in curiously ritualistic postures, appearing to lean slightly backwards—pedaled themselves about, two at a time, in their pedal carriages, a new tourist style. The historical area is small. It doesn't seem possible that anything real can survive. But Charleston does have its pretty eighteenth-century streets and churches and graveyards; and in the historical area there are still people who carry the names commemorated in the names of the streets. ("What are they doing now?" a tourist asked his horse-carriage driver late one morning. He was asking—in his innocence still believing in the completeness of the world to which he had bought a tourist ticket—about the old families in the old houses they were passing. And the driver, living up to his role as a retailer of wonders, said, "Why, they haven't got up yet." The exchange, as it happened, was picked up in one of the houses. That was where I heard it—as an illustration of the little distance that can exist in downtown Charleston between the tourist and the thing toured.) It is in fact the tourist trade that keeps historical Charleston in working order, keeps the old families where they are; though it is possible in a foreseeable future that the tourist trade, by pushing up property values, might drive some away. The story in Charleston is that money has begun to come back to some of the old families; and money, it is said, has become a motive where once people were content with the antiquity of a name. Names—they are really what is celebrated in the plaques on some of the buildings. The events themselves are small, colonial, not memorable to a visitor. In this tourist Charleston the visitor soon stifles. But there is a larger town. There are the rich suburbs outside the peninsula. There is the Charleston of the naval station. And there are the various black areas. There is a large and pretty middle-class area, acquired and consolidated during a time of white panic. In the center, on what must have been the site of old houses, there are black housing projects, bald brick buildings going baldly down to scuffed earth, buildings that drive people out of doors and expose them and their children and their washing lines, so that the impression of slum, of many people living publicly in a small space, is as unavoidable as the impression of black faces. The east side of Charleston is also black. The houses there—some looked after, many not—are old, in the old Charleston style; but there are no tourists. So, after the Toytown aspect of the rest of old Charleston, the blacks seem like squatters, intruders at the Charleston ball. Yet they are as old as the old families. It is only when you cross over from peninsular Charleston to what were once the slave plantations, the town's vast hinterland, that the slave past becomes vivid—though there is now just forest for the most part. The land is flat and marshy, and it goes on for miles. The forest—oak, gum, maple, pine, sycamore, magnolia: tall forest—speaks of the fertility of the soil. The flatness and easiness and the extensiveness of the land make clear the need in the old days for abundant slave labor; and they also make painful the thought of that labor. Now all is peace. From time to time there is a gateway in the forest, indicating land acquired by a big company; there is an old church; and there are black settlements. These settlements have a history. Most of them are on the site of old plantations that were taken by the federal government after the Civil War and broken up into sixty-acre plots for former slaves. Old property now, historical, some of the houses good, some poor; but after 120 years of land being passed on without wills or deeds, most of the titles are impossible. I saw this coastal South Carolina forest on a Sunday morning. My guide was Jack Leland. He was a retired Charleston newspaperman, and he was of an old family. All this land and forest—so much the same to the visitor—was known to him in detail. This vegetation was the vegetation he had known as a child; it was still magical to him. Very few of the plantations now grew anything. Cattle were raised on some. Wealthy Yankees had bought others and turned them into hunting preserves. "This second Yankee invasion, as my father called it, began in the 1880s, and continued to the 1930s. And it was a good thing, because it preserved the old buildings and gave jobs to the local Negroes and added a lot to the economy." The land and the black people who worked on it, the memorializing of the past—these were still among Jack Leland's concerns, though his own family plantation had been alienated more than fifty years before. And our Sunday-morning excursion had a memorializing purpose. We were going to Middleburg Plantation. A chapel of ease there that was more than two hundred years old, and was in danger of being washed away, had had its foundations consolidated with the help of a federal grant. There was to be a service in the chapel that morning—a special spring service, but also one of thanksgiving. Middleburg Plantation had been in the possession of the Gibbs family until six years before; and old Mr. Gibbs, Jack Leland's father-in-law, had sent out invitations for the service to people who he thought would want to attend. Afterwards there was to be a picnic in the grounds of the plantation house. That house had been restored by the estate agent who had bought the property. The chapel of ease was at the end of a long lane in the forest. The lane was unpaved, soft; there were very bright spots of sunlight on the ground. It was cool in the forest shade; in the open sunlight the heat was immediate. The chapel was called Pompion Hill Chapel; in the flat coastal land of South Carolina a hill was anything a few feet high. The chapel stood beside a marsh where rice had once been cultivated. The surface of the water was in patches bright green. The original rice fields of this part of South Carolina had been created by Dutchmen who had learned about rice and dykes in the East Indies. Now the water level in the marsh had risen, because of some dam or hydraulic works some distance away; and it was this rise in the level of the water that had threatened the 1763 chapel of ease. With the grant from the federal government a rock revetment had been constructed around the "hill" at the water's edge. The cars bumped down the soft lane to the chapel. Old Mr. Gibbs, in a jacket with a big check pattern, welcomed each, and directed each to its parking place. The chapel was a single-chambered red-brick building, entered by the two side doors; whitewashed inside, undecorated; and, except for the baroque dome and pilasters at one end, without architectural flourish. The floor was tiled; paving tiles, Jack Leland said, were especially hard for colonials to make. The only notable furnishing was the pulpit, of local cedar, which was contemporary with the chapel and was the work of a Charleston cabinetmaker whose name was still known. IHS, the piety of the planter and slave-owner; now the sign of another kind of piety. And, indeed, after old Mr. Gibbs had been recognized and had shuffled up along the paving tiles and had spoken his thanks to everyone who had helped with the preservation, the theme of the sermon—a noisy motorboat racing about on the marsh from time to time, but its waves were now striking harmlessly against the gray rock revetment—the theme of the sermon was religion as a binding together of people. Community now with a special meaning, at once diminished and grander. Then we went on to the plantation house. Brick pillars, green gates, a gateway without a wall, led from the road to a very wide avenue of oaks. The oaks were 150 years old; and these oak trees of South Carolina had the shape and spread of the saman trees of Central America, which had been introduced in the Caribbean islands as a shade tree for certain crops—cacao and coffee—and had been taken on from there to places as far away as Malaysia; so that tropical plantations and colonies of the imperial time acquired a similar look, with the vegetation that had been brought together from different parts of the world. Here, in South Carolina, was something like the saman trees of Trinidad. And again the bright sunlight, coming through the foliage, fell in dazzling spots on the shaded ground. But then, after this long wide avenue, the restored plantation house was quite modest, a white-painted wooden building with three rooms upstairs and three rooms downstairs. This was upsetting to one's ideas about the grandeur of plantation life. Jack Leland said the house was small because the builder had been a Huguenot. English planters, when they did well, could become flamboyant; the Huguenots remained economical and austere, investing and reinvesting in land and slaves. (And the very first plantation house, according to the booklet about the restoration, had been even more modest, with a sitting room and a dining room alone on the ground floor, without a veranda or a back porch.) Separate from the main house was a "dependency," as an ancillary building was called; and this dependency, more or less in order, was a cookhouse with a brick chimney. Another dependency had burned down, and nothing remained now but its brick chimney. Black servants were careless, Jack Leland said. It was because of this carelessness that in Charleston there had been regulations forbidding the building of wooden dependencies. The main house could be of wood; the dependencies had to be of brick. There were other dependencies in the grounds of the Middleburg plantation house: stables at the end of an open field, and a commissary. Jack Leland thought I should go and have a look at the commissary. It was a two-floored building, wooden shingles on the upper floor, brick on the lower. Rice would have been stored on the upper floor. On the lower floor there were two cells with bars on the windows. These had been for slaves; not punishment cells, but "holding" cells, where difficult new slaves would have been broken in or reconciled, one at a time, to plantation life. The difficult slave would have been held in one cell. In the other there would have been an old slave, someone used to the ways of the plantation. The old slave—not locked in his cell, but free to come and go—would have talked to the new man and tried to calm him down; would have eaten food, shown how good it was, would have offered food; and the new slave's fears and resentments would have been soothed away. I walked across the bright field to the commissary. It was hot, stinging; not truly a spring field. On one side of the field were greenish ponds—like marshland breaking through the ground—and they were full of white water lilies. Lotuses, Jack Leland had said. But they were not the delicate red lotuses of India. These white lilies, which had naturalized so easily in South Carolina, had become like things of the marsh, growing thickly together, choking themselves out of the water. And, on the far side of the commissary building, were the two slave cells, separated by no more than a lattice partition, with the earth for floor, and with the small barred windows high up, too high to reach. They were really small spaces, tall boxes. It was easy to enter into the terror of the new man from Africa, the "new Negro," as he was called in the West Indies, who might have been snatched weeks or months before in the interior of Africa, marched or taken to the coast, held there in a dealer's stockade or compound in a place like Gorée Island off Dakar, and finally transferred to a ship for the passage across the Atlantic. Easy to enter into his terror, the terror of the man taken away stage by stage from what had been reality. Easy too to enter into the heart of the other man, the trusty slave on the other side of the partition, who sat with him and talked to him and tried to present the new life to him as one of ease and plenty, the only real life. Old Mrs. Gibbs wanted to know, at lunch, if I had seen the cells where the new slaves had been "acclimated." (I hadn't heard the word before; later I was to understand that the word was in general use in the South.) It was something that should be seen, she said; it showed the trouble planters went to, to make things easier for their slaves; that was a side of plantation life that wasn't generally known. The picnic was laid out on folding tables in the shade of trees. And all around, below the great oaks of the plantation avenue, there were picnic parties—the communion of the church service extending to this big picnic lunch, in the grounds of the restored plantation house. In the dining room of the house itself there was a spread for visitors on one table. On another table were photographs of the restoration work; photographs, too, of old black people who had worked in the house. There were no black people at the picnic; but these servants were remembered. And Mr. Hill—of the family who had bought the plantation from the Gibbses and had gone to so much trouble to restore it, as a gesture to the community and history and the land—Mr. Hill told me that among the house papers were documents that enabled you to trace the ancestors of many black people. He was in a blue-striped seersucker suit, a big, plumpish, friendly man, offering a formal welcome to the house. Many firms and many individuals had made gifts towards the restoration. The rooms themselves had been done up by different interior-decorating firms. This explained the puzzling description of the house in the advertisements I had seen: "Middleburg Plantation Designer House 1987." The nineteenth-century "State Room," for instance, had been done up by Lowcountry Decorators and Lowcountry Antiques. They had gone in for "dramatic upbeat fabrics on traditional upholstered pieces." As accessories they had chosen, among other things, "a beautiful oil painting of a black servant girl circa 1894," and "new silk trees and plants, the modern homemaker's answer to her 'too little time' problem." The rooms were, in effect, exhibition rooms aiming at a period feel; the restored house was for show. And for the visitors who were expected there had been incorporated, at one end of the back porch, a gift shop, and at the other end a kitchen. The restoration had been carefully done. No attempt had been made to make the house appear grander than it had been; and it was thought that what had been done would enable the house to live for a while. The magnificent grounds remained. Jack Leland's old father-in-law, who had lived in the house for some time, was greatly moved that the house would survive. And so was his daughter Anne, Jack Leland's wife. She had come to the house as a child to spend time "in the country." There was no electricity in those days, and she had had to go up to bed with an oil lamp. The land and the past were being honored, the plantation and the river at its back which had made for the rice paddies, as in the East Indies. But what was missing were the slave cabins. The plantation house, even with its surviving dependencies, was without what would have been its most important—and most notable—feature. Jack Leland told me that the slave cabins would have been set beside the oak avenue. The cabins were known as "the quarters" or "the village." They would never have been out of sight of the plantation house. And, considering the sanitation of those days, there would almost certainly have been a physically squalid side to the slave plantation. But now the plantation was cleansed of its cabins. There remained the wonderful oak avenue, ever growing. Hard, mentally, to set the cabins in that grandeur that spoke more of old European country houses. Only the heat of the marsh, and the light, assailing one whenever one moved out of the forest shade, brought to mind the idea of tropical crops growing fast: labor, sweat, people, squalor. The empty Sunday-afternoon road led through forest again, seen now with a slightly different eye; and led through the scattered black communities descended from the slaves who had, fleetingly, triumphed over their masters a full 120 years ago. Indigo, rice, cotton—all the big slave crops had collapsed here, just as, in the Caribbean, coconut had suffered from a kind of "rust," and cacao, which had once in some islands been "king," in planter language, had been all but wiped out by the blight known as witch broom. So that it appeared that certain crops, when planted beyond a certain human scale, became afflicted in some way, economically, or by some disease that redressed the balance; as plagues reduced human populations, and myxomatosis kept rabbits down when because of their numbers they ceased to be charming. Not far from where the country road met the highway, a black crowd was coming out of a big church. Suits; dresses; hats; cars. After the Middleburg picnic, an answering idea of community: the vanished slave cabins transformed into something quite different now, not only the old country communities in the forest, but also black settlements in Charleston itself, some middle-class, many more in projects, or in old houses on the east side, avoided by the holiday tourists in the horse carriages and pedal carriages. AN ELDERLY lady living in one of the houses of the historical town, when she heard that I had been born in Trinidad, said, "There is a story in my family that our Burke ancestors from Philadelphia had been left the island of Trinidad." We were sitting out in the small garden, drinking lemonade. The house next door, though of brick, looked extravagantly antique, small and crooked and quaint. I said, "The whole island?" "The whole island. That is the story. Southern people like to feel that, once upon a time at least, they were rich. But they died, the Burkes, in the Windward passage, when they were going to claim the land." I asked for a date. The lady went inside and then came out with a family tree, sketched out literally like a tree. Her mother had spent some time on that. And there on a lower left-hand branch was the inscription about the Burkes: "Died May 1795 when going out to claim land in Trinadad." _Trinadad_ —that was the inaccurate spelling in the family tree, indicating the romantic distance at which, in the family stories, Trinidad lay from Charleston and from Philadelphia. The story was interesting to me. Trinidad, for nearly three centuries after its discovery, had been an all but forgotten part of the Spanish Empire. Late in the eighteenth century, out of a wish to protect their South American possessions, the Spaniards had decided to open up the island to immigration, and to convert an island of bush into a slave sugar colony, on the pattern of Santo Domingo and Jamaica and Barbados. But the Spaniards couldn't provide the immigrants themselves. They didn't have the people; their empire was too big. To protect themselves as best they could, the Spanish authorities required immigrants to Trinidad to be Roman Catholic; in return they promised free land in proportion to the number of slaves a settler brought in. The people they had in mind, and the people who mainly went, were French, from the French West Indian islands, in turmoil after the French Revolution, and then the black revolution of Toussaint L'Ouverture in Santo Domingo, and all the upheavals and changes of flag that occurred in the Caribbean during the conquests and reconquests of the Napoleonic Wars. The story of people going out to Trinidad to "claim land" in 1795 was therefore not fanciful. It even in a way made sense to say that the whole island was to be claimed. What was news to me was that Irish people in Philadelphia—who couldn't have had many slaves and wouldn't have qualified for the free land—had thought of going. But the Burkes of this story didn't make it. They were drowned, and Trinidad became a myth of their great fortune. And, in the family chronicle, there was a sequel. The Burke family lawyer, the Charleston lady said, married the family nurse. Between them they did the Burke orphans out of their patrimony. Generations later the wickedness came to light. It happened one day that one of the lawyer's descendants was entertaining a descendant of one of the orphans. The lawyer's descendant showed some ancestral china plates. There were only eleven. The descendant of the orphan said, "I have the twelfth. It is one of my greatest treasures. The tradition in my family is that the other eleven were stolen." A Southern story: a story of old family, a dream of wealth in the past. But it interested me for another reason. One of the very first books written about the affairs of Trinidad was by a pamphleteer from Philadelphia. His name was Pierre Franc MacCallum. He was a man of radical, even revolutionary views; a hater of authority, in his own narrative. He went out to Trinidad in 1803, six years after the British conquest. He was hostile to the British governor, and hostile to British authority generally; so hostile, in fact, that he was eventually deported—taken from the very rough jail in Port of Spain to the harbor, and put on a ship for New York. MacCallum's French forenames suggest that he was partly of French origin. This may explain some of his radical or anti-British feeling. But what also comes out in his book is that, in his campaign against the British governor and British authority in Trinidad, he was driven more by rage about the way poor Scottish and Irish people had been dumped in the Carolinas. He had always been a mystery to me, this pamphleteer with the half-French name from Philadelphia. He was less so now. In this Charleston story of a family fortune lost two hundred years ago in Trinidad I thought I could see a story of remigration and fortune sought: some sort of movement of impoverished people from barren Philadelphia to just-opened-up Trinidad. There must always be certain things that drop out of history. Only the broadest movements and themes can be recorded. All the multifarious choppings and changings, all the individual hazards and venturesomeness, and failures, cannot be recorded. History is full of mysteries, even as family histories are full of gaps and embellishments. Certain things are lost, the way for me, the grandson of immigrants from India to Trinidad, ancestors as close as grandparents are mysterious, and some unknown, making it impossible to give a good answer, after just a hundred years, to a question like: "Where did your people come from?" What is not easily called to mind now is how close, in the slave days, the slave territories of the Caribbean and the South were. When the French planters of the West Indies were negotiating terms with the Spanish authorities for settling in Trinidad, one of the pressures they applied was a threat to take their slaves to the American South. That would be better for them as planters, they said, especially since after the war—the War of Independence—the United States seemed likely to be of some importance in the hemisphere (and therefore better able to protect people). And how rich and tempting the flat, well-watered lowlands of the Carolina coast must have appeared to people who knew only the islands! And how strange to reflect that the black people of Trinidad I grew up among might, with another twist, have been born in the Carolinas and might have had an entirely different history. The chief difference lies in the distance of the two societies from slavery. Slavery was abolished in the British colonies in 1834; and the Caribbean colonies were thereafter neglected. So 150 years separate the black people of the British Caribbean from slavery. American slavery ended with the Civil War. But it might be said that freedom came to the black man only in 1954; so American blacks have reached where they have reached in just thirty years. In those thirty years American blacks have grown to see opportunity; while the larger independent territories of the British Caribbean—Trinidad, Jamaica, Guyana—have in their various ways been plundered and undone. IT MIGHT have been that I was getting used to the Southern accent. But I felt from time to time that I was picking up something of the distinctive Barbadian enunciation—known to me from my childhood—in the speech of black people in Charleston. Strange—tiny Barbados finding an echo in grand South Carolina! But in the eighteenth century Barbados, sugar-rich and slave-rich, was the colonial land of opportunity. In Benjamin Franklin's _Autobiography_ it is the place to which people ran away to try their fortune as clerks or lawyers, Philadelphia itself being so poor that sometimes there wasn't even coin. And Barbados was the model for the South Carolina plantation colony. And Barbados was an element in the aristocracy of Jack Leland as an old Charlestonian. Two of his most valued possessions came from Barbados. They were sea chests, and they had been brought by an ancestor from Barbados in 1685, fifteen years after the founding of the South Carolina colony. The chests had been in Jack Leland's possession for forty years; they had been passed on to him by an aunt. He had talked to a historian about the chests, and he had been told that chests like those would have been made to measure for a voyage, to fit between the beams of a ship. They were carpenter's work or joiner's, not cabinetmaker's. They were high and undecorated, mortised at the corners, without extrusions, altogether plain; and they were prominent in his dining room. He lived in an old, very narrow "single house" in the center of old Charleston. The house was about fifteen feet wide; the plot was small; it was a house one would have passed by. To that extent, then, living in a very simple house in a narrow street, he was representative, almost emblematic, of the old Charlestonians, proud of family rather than money, proud of the land and his old connection with it. He carried its history with him. And one of the first things he did when I went to call on him after the Sunday at Middleburg was to show me a map of the district, made some years ago, with all the old plantations. There were many. The road along which we had traveled, though very much longer and straighter than any in Barbados, had shown only a fraction of what had existed. Each plantation had been an entity, each a little kingdom ruled by the planter; each had had a house, and quarters; and in each, according to Jack Leland, the quarters had been in the middle, to prevent communication between the slaves on different plantations. The map was on the landing of the staircase of his house. The staircase was in the center of the narrow house, separating the front room from the back room. The entrance to the house was on the side. That central side entrance and staircase was fundamental to the idea of a "single" Charleston house, a single house here not being, as I had thought, a small detached wooden house; but a house in which, for the sake of privacy, the entrance was not at the front but at the side, and in which there was a single room on either side of the entrance and staircase. A double house had two rooms on either side of the staircase. It was said that the idea of the single house had been imported, with the idea of the plantation slave colony, from Barbados and the West Indies generally. I hadn't seen anything like the Charleston houses in Trinidad. But Trinidad was a late West Indian foundation; and its origins were Spanish and French. The West Indian colonies to which Charleston looked were the older, British ones. It was always strange to me in Charleston, this harking back to the colonial British West Indies as to a mark of blood and ancestry. That idea, of a colonial aristocracy going back to the foundations, never really existed in Trinidad in my time; and doesn't exist in the former British West Indies now. The reason is simple: the British West Indian colonies more or less closed down in the 1830s, with the abolition of slavery, and became stagnant. The British Empire moved east; then moved into Africa. And there is no point in the former British West Indies now in claiming to have been among the first there. Perhaps there cannot truly be said to be an aristocracy in a place that came to nothing—they are just people (like Robinson Crusoe) who went to the wrong place. Whereas Charleston was claimed by the large events of a continental history, and its small-time beginnings are now indescribably romantic, when it was on a par with slave colonies like Antigua or Barbados or Jamaica, and looked to them for trade and support. The importance of a colony depends principally on its economic possibilities. The French exchanged Canada (or their idea of Canada) for the very small West Indian sugar island of Guadeloupe. The Dutch gave New York to the British in exchange for the South American coastal colony of Surinam in 1667. (When I was in Surinam in 1961 I was told by a Dutch woman teacher that in Dutch schools it was said that the Dutch had got the better bargain, because the British had lost New York, while the Dutch—in 1961—still had Surinam.) And without the United States at its back, post-plantation Charleston might have been like Surinam or Guyana in South America, or Belize in Central America, former continental slave colonies from which, after the money went, the slave-owners or their successors had finally to go, leaving the place to the slaves and the people who replaced the slaves. Whereas the Charleston that survives, the Charleston of the old families, the romance the tourist travels to, is a white town, where the black people (though they outnumber the white) appear as intruders. So, just a five-hour drive east and south from Atlanta (founded as a railway terminus in 1837), was a history quite different from Atlanta's. Though, as in Atlanta and northern Georgia, that history could be seen layer by layer: the tourist town, segregation, the Civil War, the plantations, the large slave population, the wealth, the eighteenth-century colony. IT WAS in indigo that early fortunes were made, Jack Leland said. "When the revolution started, Great Britain was paying a bounty on indigo. Indigo was a good dyestuff. India was not yet in the picture. The bulk of British indigo came from here. After the revolution there was no British market, and indigo faded out. No indigo was planted after 1800. The planters concentrated on rice and cotton. These were crops they already had, together with the indigo. "The rice-planters were at the top. The cotton-planters were just under them. The run-of-the-mill farmers were down at the bottom with the shopkeepers. It was like a caste system. You still hear people saying of somebody, but not so much nowadays, 'He's in trade.' And that means he's a little bit outside the pale. It's changing rapidly now. Money has become a big factor. Before, family was always more important than money." The social prejudices of England, reinforced by colonial wealth—it seemed from this account that (even apart from the fact of slavery) success, when it came to the Charleston plantations, began almost at once to undo itself. But the land was blessed: it was so fertile and well watered, so flat and easy. "After the loss of indigo this area became very prosperous. This strip of land which runs from North Carolina to Florida became probably the wealthiest agricultural area in the world. And these planters were the people who started Newport, Rhode Island. They built their summer residences there. "The Civil War was the first big blow. The war freed the slaves, and the planters had to pay them to work. And after the war the plantations fell apart, literally." That was easy now for me to imagine. I had only to think of the oak avenue at Middleburg, set slave cabins below the oaks, imagine a slave population on holiday or disaffected; imagine the rice growing in its water-logged fields, growing fast; think of the great distances, and the heat; the numbers of the blacks and the fewness of the whites. And it was easy to see how the little kingdoms that had created wealth for a few generations, had built houses in Charleston and summer houses in Rhode Island, could just collapse. "The final blows were the big hurricanes. There were three of them—1885, 1893, 1912. They broke the dykes, and there was no means of repairing them. At the same time rice began to be produced in Mississippi and Louisiana and Arkansas and East Texas. It was grown on high land, and it simply knocked these planters out of business. So by 1920 no more rice was being grown commercially here. We grew a little, but it was just for our own needs. "The boll weevil came in about 1915, and within three years it had killed the Sea Island cotton crop. Then the farmers went into truck-farming. That is, growing vegetables—potatoes, beans, tomatoes, squash—for New York and Eastern markets. That lasted until California came into the picture, after the irrigation of the desert. The desert soil is very rich, and all it needed was water." "So, after a certain stage, the plantation story is a story of bad luck and decline?" "It makes me very sad. My family owned slaves. I think they were very kind masters. Some years ago I interviewed some of the former slaves—they are all dead now—who had lived on my family's places. And they were very complimentary on the way they were treated. Slavery was wrong. I can't make any brief for that. But it existed. It was used to build the agrarian economy we had, and it was a fairly good, workable institution." "Was there a particular moment when you became aware of the plantation past?" "I grew up on a plantation where there were still twenty former slave cabins, and they were all occupied by Negroes. And right from the start I realized that these people had at one time actually belonged to my family. And we were friendly." "At this time the family fortune was already on the wane?" "Rice went, then cotton, then truck-farming. Then the Great Depression came. And my father had to sell it. And that was the end of that." This was also the time, as I heard later, when much of the furniture of old Charleston houses passed into the hands of dealers. Charleston furniture is now scattered over the United States and is very valuable, especially those pieces made by Charleston cabinetmakers (like the man who had made the pulpit for Pompion Hill). This story of loss reminded me of what Parkman had seen on the Oregon trail in the 1840s, when emigrants to the West, worn out by the dangers of the trail and the harshness of their travel, abandoned the precious pieces of furniture they had hoped to take to their new homes. Though this land had gone, Jack Leland was still romantic about it. "The land is not mine. But I feel it is my heritage." And this word, "heritage," I was to hear more than once from him, as though it was the word that explained much of his attitude to Charleston, his family and ancestors. "That particular plantation, the one on which I was born, was bought by my family in 1832. And my father lost it in 1935. So it was in my family for one hundred and three years. But there were other properties that had been in the family longer than that. "One of the unusual things about my family was that my Leland ancestors were really New Englanders. The first Leland in South Carolina was Aaron Whitney Leland"—Le was particular about all three names, repeating them slowly so that I could write them down—"and he was from Massachusetts. And he'd just graduated from Williams College in Massachusetts, and he'd come down here as a tutor in the Hibben family"—important again, the name of that family—"which at that time owned what is now Mount Pleasant, the eastern shore of the harbor. And I think that, being a sharp Yankee trader, he changed his religion and married one of the daughters. And that began the Leland family here. He changed his religion to Presbyterian from Unitarian, and he even became a Presbyterian minister. "But my mother and my father were members of families that had come in here at the beginning of the colony, in 1670." And it was from one of those early families that he had inherited the sea chests that were in the sitting room, on the other side of the central staircase. How had he become aware of the poverty of his family? "We had a very good life. There was plenty of food. And actually I didn't realize that we were poor. Of course, we were better off than the Negroes and what we call the backwoods whites. And I didn't realize that we were economically poor, that very little was coming in. "I had one year here at the College of Charleston. It was a private school then; my grandmother paid for it. Then she died. I was looking for a summer job, and I found this job on a Norwegian freighter which was hauling bananas from Cuba up to Charleston and Jacksonville, Florida. Then the captain, who owned two-thirds of the ship, got a cargo of coal to take to Argentina. And while we were in Argentina he got an offer to go to Australia. So I wound up in Australia, on a triangular run from Sydney to Singapore to Manila and back to Australia. In August 1939 we came back to this country and picked up a load of bananas in Honduras and came up to Mobile, Alabama. The day we came into port, Hitler invaded Norway. Which made the ship a belligerent-nation ship. The U.S. Border Patrol advised me to get off. I came home and went back to the College of Charleston. And of course the next year was the draft for World War II, and I was one of the first men to be drafted from Charleston." So he had missed some formal education. The years he might have spent at university had been spent as a seaman. Did he feel he had missed the company of his peers? "A lot of people on the ship spoke English English. British English. It was a tremendous education. The war was another educational experience. England, North Africa, Sicily, Italy. And having the background I had—my father and mother were great readers, and they had instilled in me the ability and desire to read and learn things. "I came back in 1945, and went back to college again. And I got a job with the local newspapers and stayed with the newspapers from then on." "You've seen Charleston rise again?" "I've seen it change too. When I was a boy there was no black district in Charleston, and no white district either. White people and black people lived side by side. The change began during the Depression, when a tremendous number of farms and plantations went out of business, and the Negroes who had worked on those places began moving into Charleston and also going north. And then World War II came along, and there was a tremendous economic thrust, because this was a major naval station, and they developed an airfield, and that drew a lot more of the Negroes from the rural areas into the city. "After the war the young men began coming back. The areas where most of the nineteenth-century immigrants had lived—Germans, Irish, and Italians and Greeks—these families were still living in what is now the black district. A middle- to low-income area. But the young men coming after the war couldn't get loans from the banks to buy old houses in the city. They had to build new houses in the subdivisions. And as they did that their parents' houses became vacant, and the blacks moved in. And today we have a tremendous black section. And the old Charleston, peninsular Charleston, is sixty percent black and forty percent white. The public schools are ninety-five percent black." "What a fate for a city that lived off the plantations!" "It really has been a tremendous upheaval. Consider this. This house, the house where I now live, was restored about seven years ago. The house was built in the 1840s by an Irish carpenter who had come over perhaps to escape the potato famine. The rooms are terribly small. The architect who opened it up was a good architect, and he utilized every bit of space. And right now we are the only white family on the block. I should say, on the street. The street is only two blocks long. All the rest are Negroes. "The house next door, now. You may or may not be interested in this. Some years ago my mother-in-law, Mrs. John E. Gibbs, discovered that some old Gibbs retainers—as she called them—were being taken advantage of. And she bought that house and restored it, made it into two apartments, with a little dependency in the back yard. And the old Gibbs servants now live there, and she only gets enough money out of them to pay the taxes and insurance. They are wonderful people to have. They look out for us. "We have, right down the street here, one of those low-cost housing projects. And those people are terrible. They're all black in that one. That project is a crime-producer. There is always something bad happening there or being done by people who live there." "Is it hard for you to live with Negroes without having authority over them?" "I've always lived with Negroes. Always done it. And they've helped me. We're good friends. But socially we are separate. There is no way to get around it. But last year, when my stepdaughter got married in Saint Philip's Episcopal Church, which is the mother church of the Anglican communion in the Southeastern United States—a big formal wedding, with a reception in the South Carolina Hall afterwards—the servants came to the wedding, and they were like part of the family. No getting around it. There's one old man who's the same age as my father-in-law—he's eighty-two. He grew up in a dependency of the Gibbs house on Logan Street. And he, the old servant, cannot read or write. He's legally blind. And my mother-in-law gets his food stamps and cashes his welfare checks. And he really thinks he's a Gibbs, one of the family. I feel very fortunate to have them." The old family servants, living in the restored house next door. "They look out for us." "When you think of the way the race issue has developed, do you feel sometimes that slavery was a calamity for the South?" "Slavery _was_ a calamity. The outcome was always inevitable. But you've got to remember that the people in New England also had slaves. They didn't have so many; they had small farms. The Southern economy depended on Negro slaves. The beginning of the end occurred shortly after 1800, when Great Britain outlawed the slave trade. And, then again, the United States passed a law against the importation of slaves." "So the end was visible even when the plantations were at the height of their prosperity?" "The great wealth was just building up." "Considering the effects now, do you see it as a weakening of the country?" "It is. The younger Negroes, the Negroes under sixty, have never been able to really associate with the way the white man lives." He meant that blacks of that age group lived in their own community, didn't serve in the houses of white people, as their parents and grandparents had done. "They stand on the outside and look in. And they don't adopt the white man's standards. "Now—just a matter of childbirth. As you probably know, the Negro woman keeps the family together. And they have a tremendous number of children. In South Carolina, at least, the number of illegitimate children born every year is predominantly black. And there's no stigma—of course, that's changing today in the white families as well. And these people are willing to live on welfare—or they _do_ live on welfare, I don't know how willingly. The Negro churches, which at one time were the center of the Negro communities, have never put any stigma on illegitimacy. They accept it. It's really a tragic situation, these young black girls having children when they are thirteen or fourteen years old, and no husband to provide money." I asked him about civil rights and postwar politics. "In 1947 a federal judge, Julius Waties Waring"—he stressed the three names, and he spelt the tricky middle one for me, and it was only later that I got to know how notorious this particular name was in Charleston—"Julius Waties Waring. And he was from a very old Charleston family. And he handed down a ruling that Negroes could no longer be excluded from the Democratic Party primaries. And his ruling was correct. Negroes shouldn't have been excluded. At that time, the Democratic Party primary was the real election in the state, because there wasn't any opposition. And by 1952 the Negroes were beginning to vote in large numbers. They are now a potent force in the election system. They've come a long way. Unfortunately, their leadership is sadly lacking. Their leaders tend to be negative, politicians with a lot of rhetoric but very little understanding of the true working of government." That was the point he stressed: the true working of government. Charleston had a "rabble-rouser," but among the black officials there were some good people. And, having lived through so much change, he was now philosophical. "I think we are coming along wonderfully." I wanted to know about the evolution of his thought on racial matters. "I grew up in a family where we were told we could be friends with Negroes, and had to respect them, and couldn't take advantage of them. But you couldn't elevate them to being social equals. I grew up believing strongly in that." Another day, when I was reflecting on what he had told me and I went back to this point, he said, "The Negroes had their own caste system. In Charleston there used to be a brick-mason contractor called Pinckney. He was a mulatto. He did a lot of the brickwork on the old houses in Charleston when they were being restored. But he knew that on his father's side he had come from a top-ranking family in South Carolina. And he would refer to his workers as 'my niggers.' This shocked me, because my father had told us never to use the word. "The Negro house servants looked down on the field hands. They referred to them in a derogatory way. 'A cornfield nigger.' The house servants started that word. The house people associated with themselves. "I was only seventeen when I went to work on that ship. At that age you don't have big ideas about anything. But, going into ports in the Caribbean and South America and Manila and Singapore, I began to change my mind a little about people of other races. Back here the Chinese were called Chinks. Over there in Singapore they ran the show. They were top of the heap. "Let me tell you this story. When I was in the Army Air Corps I went to Chanute Field, Illinois, to study meteorology. In my class there were four Negroes who had studied at Tuskegee, and they had a tremendous problem with mathematics. In the study of meteorology you study all sorts of things—the various forces of nature—and a lot of mathematics with it. And these young Negroes—it was incomprehensible to them. Most of the people in that school were Yankees. I was one of the few Southerners, and I realized the problem these Negroes had. I offered to help and I did help, and these Negroes were able to graduate. And I will never forget: I was getting ready to go to Florida, where I had been posted, and I had to catch the bus right there at Chanute Field, and these four Negroes showed up and brought me a bottle of whiskey as a farewell gift. The Yankees at that school would pal around with the Negroes, but they didn't see that the Negroes needed help and they didn't do anything to help them. But I had been brought up that you had to _help_ the Negroes. This was part of your duty, your heritage. "I guess it's just a part of your life. For instance, today, if I'm walking down the street and if some white man tries to panhandle, I ignore him. But if it's a black, I stop and talk with him, to see if he really needs help or if he's trying to get a drink. I think a lot of the blacks—the ones I know intimately—understand this about me. But to the other blacks I'm just a honkie, the enemy, the archdemon personified. And I'm perfectly willing to admit they have some reason for not liking whites. "It is really difficult to get a black person to sit down here." He gestured towards his settee, placed against the wall of his single house, next to the door, with, on the other side of the door, the two sea chests from Barbados, which had come into his family in 1685 and were the mark of his Charleston aristocracy, the mark of the colonial ancestor from Barbados. "Difficult to get a black person to sit down and talk to me. They don't say what they feel. They don't trust the white people. The Uncle Toms—there's no truth in them. In 1952 I was assigned to cover all the counties in the lower part of the state and find out how the Negroes were going to vote. The 1952 election was the first one in which Negroes were going to vote in some number. In Beaufort County, down the coast, I was amazed myself. The Republican Party was the party of Lincoln. But I found, after talking to about a hundred blacks, that they were all going to vote Democratic. I turned in a story to that effect, and my editor, who had a lot of Uncle Tom friends, refused to believe it." I asked Jack Leland whether he took an interest in the affairs of the Caribbean islands, and whether this to some extent affected his view of American blacks. He said, "Well, look what happened in Santo Domingo. That island was divided into two parts, Haiti on one side and the Dominican Republic on the other. In Haiti they killed all the white people. And when you go to Santo Domingo there is the difference between night and day. The Dominican Republic has a stable economy. The Haitians are starving. I had it tremendously impressed on me when I was on that ship—and we went to the Dominican Republic and we were loading bananas. I met some English people, and they took me over to Haiti. It was like the difference between night and day. I hate to think it's because there's no white connection in Haiti and there is in the Dominican Republic. But somewhere along the line something went wrong. And when I look at what's happening in Africa today—I don't think my point of view gets any hearing. The American people have closed their minds to thoughts like that. They think globally. They've turned their thoughts to one world, one people. It's unpractical, unfeasible. I don't think the way a native of Nigeria thinks, and he doesn't think the way I think. We are different people." I was aware the first day we had met that Jack Leland had a bad leg. The third or fourth time we met he seemed to be in especial discomfort, and I asked him about his leg. He said he had damaged both legs in North Africa, in February 1943. He had gone on a bombing run over Sicily, and the last bomb had stuck in the rack. Orders had been given to the returning crew to jump, and he had jumped; it was the first time he had ever used a parachute. He had landed on a rock and had torn the ligaments of both ankles; it had taken him two and a half months to recover. An irony was that the pilot who had given the orders to jump had managed to land the plane without accident. That was how the war had gone for him. Yet he had spoken of the war as a time of learning and adventure; he had never referred to this lasting damage until I had asked. It was like an aspect of his training, his fine manners, his "Sir?" when he hadn't quite caught what I had said: the manners that were part of the South's idea of itself. "IT'S MORE like religion," the upper-class woman from Mississippi had said, speaking of a certain attitude in her family (and other Mississippi families like hers) to the Civil War and the past; and the old family houses; and the dressing up in period costume on some days, when the houses were shown. Not a masque, not vanity: more like religion. And in Charleston too there came to one that idea of the past as religion. It wasn't only the old houses and the old families, the old names, the antiquarian side of provincial or state history. It was also the past as a wound: the past of which the dead or alienated plantations spoke, many of them still with physical mementoes of the old days, the houses, the dependencies, the oak avenues. The past of which the more-black-than-white city now spoke, the past of slavery and the Civil War. Not a day had passed since I had come to the South without my reading in the newspapers about General Sherman, or hearing about him on television. And—in that newspaper or television way, when a well-known name is to be stressed, ironically or otherwise—he was often given his full name, with the strange American Indian middle one: William Tecumseh Sherman. Charleston had survived the war. Columbia, the state capital, hadn't. It had been burned by Sherman in 1865. It was of that burning that the elderly lady, a guide to the cathedral near the State House in Columbia, spoke to me; and she spoke as though it had happened quite recently. And perhaps Hannibal had been remembered in Italy and Rome in a similar way a hundred years after he had passed. The cathedral was one of the few things in Columbia that hadn't been burned by Sherman, the lady said. And this might have been because he thought it was Roman Catholic; Sherman's wife was Catholic. And towards the end of the tour, when we were talking of the stained glass (so fragile in a city about to be razed), she broke off and said, as though offering thanks again, "It's a miracle the cathedral wasn't burned." I had read about the burning of Columbia. But the fact wasn't at the front of my mind that afternoon. And this talk of burning—from an elderly lady, in the cathedral—made a fearful impression. I hadn't been looking for the cathedral. I had gone in after noticing the graveyard. I was on my way to the State House grounds to look at the Confederate Memorial. I had been directed to that by a judge I had come to see. He had said that the inscription of the memorial was something that should be studied. It was poetic and contained much of the Souths idea of itself. On one side of the monument was engraved: _To South Carolina's dead of the Confederate Army 1861–1865_. On another side it said: _Erected by the Women of South Carolina. Unveiled May 13, 1879_. There was rhetoric in that reference to women; monuments of grief and revenge, or grief and piety, are most unsettling when they depict women bowed in grief. On the other side facing the busy road the monument read: _This monument perpetuates the memory of those who, true to the instincts of their birth, faithful to the teachings of their fathers, constant in their love for the state, died in the performance of their duty: who have glorified a fallen cause by the simple manhood of their lives, the patient endurance of suffering, and the heroism of death, and who, in the dark hours of imprisonment, in the hopelessness of the hospital, in the short, sharp agony of the field, found support and consolation in the belief that at home they would not be forgotten_. On the other side, facing the State House, and read with difficulty from an oblique angle if one didn't want to walk on the grass at the monument's back, there was this: _Let the stranger who may in future times read this inscription recognize that these were men whom power could not corrupt, whom death could not terrify, whom defeat could not dishonor, and let their virtues plead for just judgment of the cause in which they perished. Let the South Carolinians of another generation remember that the state taught them how to live and how to die. And that from her broken fortunes she preserved for her children the priceless treasure of their memories, teaching all who may claim the same birthright that truth, courage and patriotism endure forever_. On one side: birth, faith, duty, suffering, and death. On the other side: the nameless, undefined cause, ennobled by these virtues. The words are grand, nevertheless. The pain of defeat is something that can be shared by everyone, since everyone at some stage in his life knows defeat of some sort and hopes in his heart to undo it, or at least to have his cause correctly seen. But the pain of the Confederate Memorial is very great; the defeat it speaks of is complete. Defeat like this leads to religion. It can be religion: the crucifixion, as eternal a grief for Christians as, for the Shias of Islam, the death of Ali and his sons. Grief and the conviction of a just cause; defeat going against every idea of morality, every idea of the good story, the right story, the way it should have been: the tears of the Confederate Memorial are close to religion, the helpless grief and rage (such as the Shias know) about an injustice that cannot be rehearsed too often. And there was more of that in this central square of South Carolina, the state that had started the war: more pain, more humiliation, more exposing of a wrong that was one day to be undone. On the lower granite steps there was a life-size bronze statue of George Washington. This plaque had been affixed: _During the occupation of Columbia bySherman's army February 17–19, 1865, soldiers brickbatted this statue and broke off the lower part of the walking cane_. The cane had been left hanging in the air. On the pillar at the foot of the steps was another plaque: _Construction of this State House was begun in 1855 and continued uninterruptedly to February_ 71, 1865, when Sherman burned Columbia. Work was resumed in 1867 and carried on irregularly to 1900. The Confederate Memorial, the one erected by the women of South Carolina, had been put up in 1879; when the Northern occupation army had been removed and the state had been redeemed from Reconstruction. The State House plaque, with all its grief about Sherman and the burning, had been put up more than twenty years later, when the world had changed even more. There was evidence of this change right there: the other memorial in the paved forecourt of the State House was a jaunty one, a celebration of the Spanish-American War of 1898, with a Kiplingesque inscription. It was as though the grief of the Confederate Memorial had found its expiation in the jauntiness of the other memorial; as though the unmentioned Southern cause had lived on and found justification in the later imperialist war; as though the unmentioned racial anguish of the period after the Civil War, the later hardness towards blacks, had become incorporated into something a good deal less squalid than the slave cabins with the very black and ragged slaves of South Carolina, had become incorporated, as some Southerners had said, into the wider cause of white civilization, spreading to Africa, Australia, and the East Indies. But the true past of the South was the thing that had been lost: the world before the war, and then the war itself. That grief was special and was like religion; it would last beyond the decline of the nineteenth-century empires, beyond the idea of empire itself. And, now that the memorial about the Spanish-American War was embarrassing, the episode itself hardly remembered, what remained moving in the State House grounds, what could still be felt to come from the heart, were the words of the Confederate Memorial. And there was still that difficulty about the cause. How could such a cause be defended? In the library of my Oxford college, one day in 1952, I came across a small book, privately printed, a gift to the college from the author, possibly an old American member of the college. The book, which had been printed in the 1920s, was about slavery. The author wished to clear up the misunderstandings the rest of the world had about American slavery. That was what the author said. But the little memoir he had settled down to write in his old age was about his childhood and the pleasures of his childhood. Slavery had been part of his childhood; his childhood could not be imagined separate from the background of slavery, and its special rituals. White children, the writer said, were often given slave children of their own age to play with and knock about. The writer said that he too had had his "own negro boy." The fact that this had been so, that the writer had had his own slave boy, was offered as sufficient explanation of the practice. And something as simple and heartfelt as that was at the back of a beautiful, celebratory book, _A Carolina Rice Plantation of the Fifties_ , published in New York in 1936 by William Morrow. The fifties of the title were the 1850s, before the Civil War, when the slave-worked plantations were still going concerns. The historical core of the book was a short memoir of that time by D. E. Huger Smith (Huger one of the old Charleston names with a special Charleston pronunciation: "ewe-gee," just like the two letters "U" and "G"). To this had been added thirty water-color paintings—done seventy or eighty years later—by Alice R. Huger Smith; and a "Narrative"—really a historical essay—by Herbert Ravenel Sass (another old name, Sass a name of German origin, Ravenel pronounced in the French way and in Charleston in 1987 still a name seen on signboards). The water colors, of plantation scenes, were romantic: sometimes dealing with plantation work, black men in a work gang mending a broken embankment, women loading rice onto a flat plantation barge; sometimes atmospheric studies of water and forest; sometimes pure calendar (or "Soviet") art, the planter and his wife (like father and mother in an illustration in a children's book) moving white and gracious among the smiling blacks, with—in another picture—a little blonde girl receiving a bouquet from a black child. A big reproduction of the embankment-mending scene I was to see later in a Charleston restaurant, as something from the old days—and romantic, suitable for the tourist town. And the romance of the paintings was genuine. They hadn't come from the 1850s, the slave time. If they had they might have been different—more topographical and descriptive, and for that reason upsetting. The paintings had been done by someone who (as she said in the foreword) wished to record a world that was vanishing; and they had been done by someone who had been born towards the end of the Reconstruction period—in the 1870s—when the vast plantation world, the ordering of so many millions of acres, had been turned upside down. Shame and anger at the Reconstruction, grief for the defeat, nostalgia for the world as it had been, or an idea of the past: all of that mingled—in these water colors—with the delight in brush and color and paper, delight in the natural world, the painter's sense of her own delicacy. And there was something of that mood in Herbert Ravenel Sass's essay. He too dealt in romance: the oak avenues, the beauty of the river onto which the plantation houses fronted; the organization of the great plantations; the technical skills connected with the flooding and draining of a tidal plantation; the self-containedness of each plantation, each almost a little state with its own lord, who had certain legal punishing rights over his subjects. It was that idea of the plantation state that no doubt made the writer see the Rice Coast as "in essence an attempt to recreate in America the classic Greek ideal of democracy." And in a curiously written paragraph that makes no reference to Africans or slaves or black people, plantation slavery is incorporated into this Greek ideal as "the most complete 'economic security' " ever offered certain people in America. "For this security, covering the whole period of their lives from babyhood to old age, a price was paid." "A price"—that is the silent way in which, to preserve the idea of the classical world, slavery is referred to. And this "price," the writer adds, was "perhaps not wholly excessive," considering the people—again never mentioned—to whom this security was offered. But—when this Greek aspect was set aside—there was another way of talking about slavery. "For the South the slavery problem became the negro problem, and what in reality the Carolinian state strove against from 1831 to 1865 was a threatened 'solution' of the negro problem which would destroy them." The state required slaves; without slaves it couldn't get by; but the slaves threatened the state with extinction always. So the planter's special way of life in the ricelands of Carolina became "white civilization"; that was the thing that had to be preserved. There was a torment in this way of reasoning, this unwillingness of educated men and religious men—and sensitive men—ever to say that what they were defending was simply the world they had known. And there is always the silence—the lack of reference to Negroes, the slave cabins below the oaks—when the plantation world becomes something nobler than itself, becomes something like the Greek city-state. That had been the silence as well, fifty-seven years before, of the Confederate Memorial in Columbia; the virtues of the dead men ennobling the cause, the cause itself never defined. But how else, in 1879 or 1936, even at that time of high imperialism, could educated men defend slavery? I had come across the rice-plantation book in the collection of a lady with a famous name. She lived with unusual simplicity in an old house in Charleston, with a piazza (Charleston for "porch" or "veranda") looking out onto a green yard shaded by an old oak, a yard neither ordered nor overgrown. At the boundary of the plot (or beyond the fence) there was the windowless back of the neighboring house. This was the Charleston style, the piazza at the side, for privacy. But the house next door rocked with a radio; no protection against that. And it was there, on that piazza, where the furniture was simple, weather-hardened, with ingrained dust (the breeze in Charleston, Jack Leland told me, was from the south or the west, and that was where people placed their piazzas, to catch the breeze), it was there that, through the courtesy of the lady, I met the son of the man who had written the "Narrative" for the plantation book of fifty years before. Marion Sass was in his fifties, tall, thin, stooped, excessively wrapped up for this hot Charleston afternoon: a brown tweed jacket worn without stylishness over a pullover. He had small, sad blue eyes in a thin, gentle face. He didn't want to sit with his back to the breeze; he sat with his back to the wall of the house. The air was full of pollen. My own eyes were heavy; I felt a cough building up; and, like Marion Sass, I was wearing a jacket. And on the sagging floor of the piazza, facing the unkempt garden or yard, almost as on a stage set of a play about the South, and in the sound of the next-door radio, we talked. He was shy; he spoke softly; he looked down and away. As a Charlestonian he went right back, to Henry Woodward, who had explored and prospected the land for the foundation of 1670. I asked whether such an ancestry in Charleston wasn't a burden, whether it didn't constrict a man. He said it was a burden. His ancestry was one of the things that kept him in Charleston. There was a large part of him (in spite of his German surname) that would have liked to live in England; his late wife had been English. It was of England, and its curious effect on people—so many people, he said, seeing England for the first time, felt it to be their home—that he talked for some time; and it was of England, I felt, he would have preferred talking, if such a thing, so simple and free of complication, had been open to him. But there was the burden of the ancestry; and there was his Southernness. And it was to that, without my prompting just then, that he turned the talk. His father, Herbert Ravenel Sass, had been born in 1884 and had died in 1958. So his father was fifty-two when the rice-plantation book was published in 1936. Eighteen years later, when his father was seventy, the main civil-rights cause had been conceded. Marion Sass himself had been born in 1930. He would have shared some political defeats with his father; but the Southern cause, as he saw it, lived on in him. He told me that at the time the schools had been integrated his father had broken through the "paper curtain" the North had imposed on Southern views, and had published an article in the _Atlantic_ magazine suggesting that mixed schools would lead to a mixed race. That had been proved wrong, Marion Sass said; with integration the races had in fact kept more to themselves socially. But that didn't lessen the need for his political work, to which he now gave more time than to his law practice. This talk of political work, he said, might sound as though he were engaged in getting people elected to office. He had done that as well. But he was now more concerned with "resistance." Resistance to the conquest by the North and resistance to Americanization, which was really Northernization. Though it was ironical, he observed, that some of the most important "American" things—Coca-Cola, and country music, and even the idea of supermarkets—were Southern. (Just as there are Swedes who can recite the five—or six, or seven—industrial inventions that made Sweden rich, so Marion Sass appeared to have at his fingertips the Southern contributions to the idea of America.) There was no need to define Southern values. "Southern culture is not simply a matter of the agrarian culture versus the industrial, or the ideals of honor against the crass values of commerce. Southern identity is important because it is Southern. We are Southern. That's enough. It's like the Irish. But they—the Irish—don't have this terrible burden of an alien population in their midst." There, again, a full fifty years after his father's essay in the rice-plantation book, was the vagueness connected with "the problem." How did he deal with that—the question of race—as a thinker? He said, "Our way of dealing with that? I try to have as little as possible to do with the race problem. A lot of the white-supremacist cause is in the North and has nothing to do with the South. The Southern cause and the Southern problem are really different things. The North uses the blacks all the time against the South. They did it in 1860, and they've done it in this century." The North was now very concerned with all its minorities. It might have been thought that they would have considered the South a minority area. But they didn't. The official Northern view could be put like this: "The white Southerner is not a minority. He is a backward fellow American who oppresses a minority, the Negro." Had he looked at his father's book about the plantations recently? No, not recently. But he knew the book well, and he had some of the feeling for the old plantation life. I said, "But you can't feel nostalgia for what you don't know?" "Although I didn't grow up with any knowledge of the working life of the plantation, still, life on the plantations—when we went to visit them when I was a child—it was more like the old Southern countryside, even though we didn't have slavery. It was the old easygoing rural life, and relations between the races were much more what they had been. So I can feel nostalgia for a past." He was as concerned, even obsessed, as his father had been by the superficial destruction of the South—the highways, the fast-food chains—and pained by the alienation of some of the plantations to people and firms from outside. The past as a dream of purity, the past as cause for grief, the past as religion: it is the very prompting of the Shias of Islam to nobility and sacrifice, the dream of the good time of the Prophet and the first four caliphs, before greed and ambition destroyed the newly saved world. It was the very prompting of the Confederate Memorial in Columbia. And that very special Southern past, and cause, could be made pure only if it was removed from the squalor of the race issue. When—again as in a stage set—we got up from our chairs and went inside, for a salad provided by our hostess, I said I felt he was dealing in emotion without a program. He agreed; but then he said the program was being created. The talk became general. We looked at some of our hostess's old books about South Carolina. We looked at copies of her family letters—many of them plantation letters—that were almost two hundred years old: the letters had been typed out and bound in heavy folio volumes. When they—Marion Sass and our hostess—spoke the names of plantations, Fairfield, Oakland, Middleburg, Middleton, Hampton House, it was as though they were talking of country houses. But then I understood that they were also talking in an allusive way of the very many families to whom they were related. He drove me back to the hotel in his untidy old car. He was nagged by what I had said about emotion without a program; and the next morning he sent me a copy of a letter he had written to the local paper in 1983 and a copy of an advertisement announcing a Southern publishing program. These copies were left at the hotel in a very large, used envelope, with my name and his name in very small letters; the envelope carried the printed name of a health organization. And then he telephoned; and as he spoke I could visualize his thin, sensitive face. He hadn't done the publishing the advertisement had promised, he said; but the advertisement had drawn a response; he felt he had touched a chord. He told me that because of the developments of the 1950s his father had ended as a Southern separatist; and that was where he himself was now. The defeat of the South, the surrender of Lee, was for him an unappeasable sorrow, I felt. I asked him whether he knew the Confederate Memorial in Columbia. He said he had studied law in Columbia, and he liked the town, which some people didn't like. He knew the words of the Confederate Memorial very well; he spoke some of them on the telephone. He thought the words might have been written by W. J. Grayson, who in the 1850S had written an epic poem called _The Hireling and the Slave_ , a poem in rhyming couplets in the style of Pope. The theme of the poem was the superior condition of the slave in the South to the industrial worker in Massachusetts. He hadn't read the poem right through. His cause had come out of an unappeasable sorrow. And I felt it could lead only to further sorrow: he himself knew that there was now another, and perhaps more predominant, side to Southern thinking. I thought of what Anne Siddons had spoken in Atlanta: the need at a certain age to hoard emotion, to spare passion from public causes for one's own spiritual concerns, to make one's peace with age and the frailties of one's own human state. I spoke of that as best I could on the telephone. He said he understood; but still it worried him that at times he could so sink into himself that he could forget his cause. Then, courtesy returning, he said he would like to read some of the things I had written. But there was trouble with his eyes—those eyes whose sensitive rims and whose smallness had made an impression on me. He needed to have a cataract operation on both eyes. That was said to be a simple operation these days, but in the leaflet he had been sent (perhaps in that overlarge envelope in which he had sent me copies of his letter to the newspaper and his publishing advertisement) he had read of possible complications. And he wished to trust to his own lenses for as long as possible. ONE HOT morning—hot for May, everyone said, and without the rain that the gardens needed, the rain that could sometimes fall every afternoon—on such a morning Jack Leland took me through what he called his "territory." First we went to Mount Pleasant, on the east side of Charleston harbor. It had been the "summering place" of planters, and was now a rich-looking suburb with old trees, very shady. Not far below was the sea. We saw a trawler putting out. The Portuguese were the first to use those trawlers in Charleston, in the 1920s, Jack Leland said; he logged everything connected with his town. We had come to Mount Pleasant to see the Hibben house, the house of the family where Jack Leland's New England ancestor had come as a tutor and stayed to wed. It was at the end of a cul-de-sac, a two-hundred-year-old house with columns, the house of the people who had once owned all the land of this suburb—a story of ancestors given unexpected reality. On the road again, he pointed out where black communities had grown up on plots of ground that had been given them after the war, the Civil War. "They're not doing well. These Negroes up to World War II had land and they all had gardens. They raised a lot of their own food. Now you very rarely see a Negro family in the country that has a vegetable garden." We drove through one black village, and Jack Leland showed the houses of two of his black "friends." These friends were people he bought things from: his definition of black friends was South Carolinian. Some of the houses suggested that the owners were well off. I asked whether they were small businessmen. He said no; the blacks in those houses probably worked in the naval yard or had other federal jobs. The local black population had lost its most ambitious section with the migration to the cities in the North; almost every Negro of ambition had gone. "Does the name Stepin Fetchit mean anything to you?" It certainly did. Stepin Fetchit was adored in my childhood by the blacks of Trinidad. He was adored not only because he was funny and did wonderful things with his seemingly disjointed body and had a wonderful walk and a wonderful voice, and was given extravagant words to speak; he was adored by Trinidad black people because he appeared in films, at a time when Hollywood stood for an almost impossible glamour; and he was also adored—most importantly—because, at a time when the various races of Trinidad were socially separate and the world seemed fixed forever that way, with segregation to the north in the United States, with Africa ruled by Europe, with South Africa the way it was (and not at all a subject of local black concern), and Australia and New Zealand the way they were—at that time in Trinidad, Stepin Fetchit was seen on the screen in the company of white people. And to Trinidad blacks—who looked down at that time on Africans, and laughed and shouted and hooted in the cinema whenever Africans were shown dancing or with spears—the sight of Stepin Fetchit with white people was like a dream of a happier world. It wasn't of this adored figure that Jack Leland was speaking, though. He had another, matter-of-fact, local attitude. He said, "The ambitious people went north, and we were left with the Stepin Fetch-its." Now there was a movement back; not big, but noticeable. I said, a little later, that it was my impression that the blacks of South Carolina were very black people, not as mixed as black people in the Caribbean islands. He said there had been little mixing of the races. The planters thought it demeaning to have relations with a slave woman. There was a story that after the war the Union soldiers didn't have those scruples. But there were not many mixed people. Did that make for more difficult relations between the races? No; it made for easier relations. "Mulattoes and quadroons and those are the angry people." Later, some way up the highway, we turned off to have a look at a spectacular old oak avenue, partly in ruin: the kind of avenue with which Marion Sass's father had begun his nostalgic recall of plantation days. And when we drove on, the sea was on our right, hidden by forest; and the river was on our left. Salt and fresh: where the land was salt, cotton had grown in the old days; where the water was fresh, there had been rice. Now, along one stretch of road, there was a large kiwi-fruit plantation. We turned into a side road then, and suddenly, in overgrown ground, attached to a Presbyterian church of 1696, there was a little cemetery, where, Jack Leland said, some of the first settlers were buried. We were entering sacred territory. Beyond a certain creek the old plantation of Walnut Grove began. It was the ancestral property, acquired in 1832 and sold during the Depression, in 1935. Still with us, the roadside woodland. And, now, the black village where after the Civil War blacks had been given plots of plantation ground. "When the children were small," Jack Leland said, "and we crossed the creek, I stopped the car and made them get out and bow three times to the east. Sacred territory." "What did the children think of that?" He laughed. "They got a great charge out of it. They still do it when they come here. And I do it with them. People see us bowing. They probably think we're crazy. We probably are. But it's a nice craziness." And now, driving through his territory, memory overcoming him at certain spots, he filled out some of the things he had told me earlier. They had been poor, with little money coming in. But they had never been short of food. "Shrimps, crab, oysters. Clams. Fish. Venison. Wild turkey. Ducks, roes, partridges. There was just a wealth of wild food to be had. And, of course, my father had the farm where he grew the food." And when on a morning he, Jack Leland, went out with the shotgun, the birds he shot were for the table. The hunting life—it was important here (to blacks as well); and when you saw the land you understood. And the land concealed something else. There was a creek at some distance with very pure water. The creek was called "the branch"; visitors would be offered bourbon and branch. We turned off into a narrower road. We passed a house in a wooded garden. "That's a cracker house. Backwoods whites, poor white trash, as they say. And that's another cracker house, I would say. About seventy years old, perhaps. They're part of the picture. You can't leave them out." He had the local eye—just as in Malaysia the local people can distinguish a Chinese house from a Malay one, purely by the way the surrounding ground is used. The houses he had described as cracker houses had seemed to me attractive, with trees and shade and shrubs. He said, "They have a certain charm. But a lot of junk around. You can tell a cracker house by the trash, and the generally unkempt look of the place. Half a dozen defunct automobiles, say. That was very typical at one time." The crackers, like the blacks, had their own place in the local caste system. "When I was growing up we went to high school and grammar school with them. But we did not socialize. Our social lives were entirely different. Most of the crackers were Baptists, Methodists, or Pentecostal Holiness—that's the shouting religion. Whereas my family and the other families up here were Episcopalian mainly, and Presbyterian, and they were top of the heap. "I will tell you. At Walnut Grove we had a summer cottage, where my father's younger brothers and their friends stayed during the summer. A four-roomed house on the river. This was shortly after 1902—my father had just married and brought his bride back. He was the eldest of eleven children. "One day my father got up early in the morning, at six, for his usual cup of coffee. And he saw some of his horses standing by the gate, saddled but with their reins cut. After a while the younger brothers and their friends showed up, walking. They had been to a square dance out in the swamps, where the crackers lived. They hadn't found their horses afterwards, and they had had to walk back. And my father warned them not to go back. Because, he said, this—the cutting of the horses' reins—is the crackers' way of warning you not to meddle with their women. 'The next time they will take more drastic action.' "But they didn't listen. They went again. They were riding back through a trail in the swamps when the crackers dropped out of the tree limbs above them with knives. Like the Indians. One of the men with my uncle was killed. It was in the night. Nothing could be proved against anybody. Nobody was brought to justice. It was the law of the swamps. You just did not socialize with those people. My father always said he preferred having the Negroes living on his property, rather than those crackers." The blacks looked down on the crackers, and the crackers hated the blacks, because the blacks were in direct competition with them. But the crackers were as exploited as the blacks, Jack Leland said; and were probably treated worse by white employers because there was less feeling of responsibility towards them. "The crackers began to increase in number after the Civil War. Before the Civil War in this plantation area there were only planters and Negroes, and nobody in between except perhaps the overseers." There was a church that Jack Leland wanted to show me, the family church, the one connected with Walnut Grove—St. James, in Santee parish, Santee the name of the river. It lay along the King's Highway—the name coming down from colonial days, indicating a road made at the king's orders, at a time when most people traveled by water. The road was unpaved. If there had been the usual amount of May rain, it would have been difficult; but it was easy. And soon we were there: an old red-brick church with a portico. There was another portico at the back. The church was meant to serve French and English, but the portico for the French, at the back, was now blocked up. The red brick had the appearance of something neglected in a damp tropical climate. "Come," he said suddenly, moving briskly in spite of his bad ankles, leading me in through the fence. "Come, let me show you where I'm going to be buried." It was hot, no wind, and there was a hum of mosquitoes. All around, in the pines, were the cries of birds of various sorts. In the small churchyard, dry, full of brown leaves and fallen pine needles, were tombstones. "All these people are relatives." _Jonah Collins Born 1723 Died 1786_. "He's the son of the man who brought the sea chests from Barbados." _William Toomer 1866–1955_. "My mother's uncle. A lawyer and a judge." His sprightliness at being near the site of his burial place took me aback, then imposed reverence on me. "There." An ordinary, bare spot of earth, a little vacant space between the headstones. That was where he was going to be buried. "I want to be buried with a flat-topped marble tomb, right here by Jonah Collins. It will have my name, the date of my birth, the date of my death. And at the bottom there will be a line: _Have one on Jack_. And I'm leaving two thousand dollars to the church, so that every year at the spring service they can have wine, whiskey, or whatever. I think people will remember me because of that." The mosquitoes and other insects were a nuisance. He had expected them; he had come with a can of insect repellent. Without a breeze the heat was oppressive, scorching the head. But there was often a wind, he said. "There's no sound like the sound of the wind soughing through the pine trees. And that's where I want to be buried, so that I can listen to it forever." Inside, the church was very plain, with the mustiness and shut-up smell of a building not often used by people, without that warmth. The church had been built in 1763. (So the Pompion Hill chapel had been built in the same year.) It had a rough, tiled floor, and the building materials were brick and stucco and timber. There was no stone in these parts; and the windows had timber surrounds, dressed like stone: local work, local trees, slave work, perhaps. The pews were enclosed; a family in its pew would have been hidden, as if in a high-walled box, open at the top. Perhaps, Jack Leland said, the pews had been built like that to keep the children in, or perhaps in cold weather they were easier to heat, with the warm bricks that were used for that purpose. How had he got the idea of death and celebration? "There was a Professor Ogg of Oxford University in England. He came over twenty-five years ago. He told me a story I'd never heard of. There was a rice-planter's son, a Mr. Trapier, who was visiting Oxford in the 1830s. The son of a rice-planter from Georgetown, South Carolina—making the grand tour in the 1830s. He was being entertained by the dons"—Jack Leland spoke the word precisely—"of New College. I believe it was New College. And he asked for a mint julep. They'd never heard of a mint julep. So when he came back he had a sterling pitcher made and sent back to the college as a gift, with money for mint juleps." We went on to McClellanville, on the sea, the summer resort of the family. And it was still, literally, a family resort. There were cousins or relations in almost every house in the white part of the village. Most of the blacks lived outside the village proper. Jack Leland knew the history of every house. That magnolia tree had been planted by his father in 1892, in what had then been Jack Leland's grandmother's yard. His father had brought the seedling over from Walnut Grove in his saddle bag. And Jack Leland himself had planted a line of oaks on the street in front. He had done that in 1934, the year before his father had had to sell Walnut Grove. They were now very big trees. But that planting had been part of a federal program—and they contained a reminder of the poverty of those days. A woman ran the federal tree-planting program. She employed about fifteen high-school boys, and they were paid a dollar a day. We had lunch at a restaurant on the highway, not far from McClellanville. The very young waitress turned out to have the name of Leland; she was a cousin. I read him the words from the Confederate Memorial in Columbia. He was affected by them. He said, "I think it's great." Did he still have feelings about the Civil War? He did. "When I was a boy there was a story in my family about the burning of one of the family plantations after the war was over. The place belonged to one of the drafters of the ordinance of secession. That was in 1860. And that, of course, brought on the war. After the Civil War this whole area was under martial law, and the colonel in charge of the area of Christchurch parish was a Colonel Beecher, a brother of Harriet Beecher Stowe. They were great abolitionists from New England, and I think I can say that that book, _Uncle Tom's Cabin_ , did more than any other single thing to provoke the war. It irritated the South, where only thirteen percent of the people owned slaves, and it worked powerfully on people in the North. "The story is that the wife of Colonel Beecher went around in Christchurch parish burning plantation houses. I grew up thinking it was perhaps a folk story. But in recent years a diary has come to light of a Dr. Marcy, who was a Union Army surgeon. He was one of the people authorized to take books, art treasures, and what not out of the houses down here and ship them north. And my daughter—she is doing research out of Middleton Place: she is part Middleton—got a copy of this diary. In it she read of the burning of Laurel Hill. That's the house owned by the drafter of the ordinance of secession. There was proof there, in that diary. She burned perhaps twenty houses, Mrs. Beecher. Torching people's houses. The Beechers were Puritans. These people have a mentality that is very hard to understand. When they sent missionaries to Africa the first thing they did was to make the Africans wear clothes, cover up." Early afternoon. On the road again, we passed black church congregations dispersing, driving away in cars. I asked about blacks and cars, remembering that in Trinidad ownership of cars among blacks became widespread only after the second war. He said that for some years blacks weren't allowed to drive cars; they were thought to be reckless drivers. "And they were." And in the old days, he said, black churches had their Sunday services in the afternoon, because many of the black women would have been at work in the morning in white houses, cooking lunch. The green highway signs measured off our progress back to Charleston. There came a moment when Jack Leland stopped leaning forward, his hand on the back of my seat. He leaned back and said, "We are now out of my territory." IT WAS Alex Sanders, chief judge of the South Carolina Court of Appeals, who had directed me to the Confederate Memorial. I had had an introduction to him; and when we first met in Columbia he had given me lunch at the Faculty Club in the university. Our conversation had been general. I felt he had been puzzled by our inconclusive meeting. But it wasn't possible for me to tell him exactly what I wanted from him; for the simple reason that on this kind of journey one doesn't know what one wants from a man until one has spoken to him. He was a big man with a strong accent that could divert one from the precision and economy with which, as a lawyer, he could speak. He had sent me to the memorial, he said later, to enable me to understand something about the South. He himself, though he found the words moving, wasn't certain about the cause. "Lost causes are espoused or romanticized by the second generation." The memorial had been put up in 1879, 14 years after the end of the war. It was astonishing to him that people in 1879 had found the money to make the memorial, at a time when there wasn't enough to eat. He remembered talking to one or two veterans on the Confederate side. One of them said, "I gotten my arse shot off for other folks' niggers." "He didn't have any, you see. And the vast majority who fought in that war didn't have any. They were fodder for the aristocracy. Identity is more than just remembering the past. We have to be like museum curators. In the dynasty of Ming there was obviously a lot that was beautiful. But I am sure there was a lot that was junk. The job of the curator is to pick and choose." But didn't he, when he was growing up, have an attitude to the South? He didn't, any more than a fish has an attitude to the ocean in which he swims. "It was only after I'd grown up and left that I developed an attitude. And at first my attitude was that I was ashamed of it. But the older I get the more I realize that the transgressions of the South were the transgressions of mankind, and that there were certain things that were superior. There is a cultural attitude in the South that embraces respect for family and God and in some ways for country. Although patriotism is not among the highest virtues on my list, still, the patriot believes in something larger than himself, and it is therefore a virtue. There is an attitude in the South that there is more to life than the moment." "Honor? It's such a theme. So many people talk about it." "I was trained that way. To believe that truth is an ultimate virtue. The watchword for life was unselfishness." He stopped. "But I don't know that any of this is peculiar to the South. I am inclined to think, however, that the closer you get to the equator, life tends to be exaggerated." "Did you try to distance yourself from the South, after you'd become ashamed of it?" "Particularly when I was with people from the North. And even when I was in the South I spoke out against things I didn't like. That meant the racism." "It must create disturbance, turning against what you had grown up with." He said: "It produces a certain schizophrenia. But as I get older I get more tolerant. I become more tolerant of intolerance. If you find a Klansman to talk to you, and you ask him what the Ku Klux Klan stands for, he would say it stands for law and order, and love and friendship, and brotherhood. If you would ask him how he would set about achieving those things, he would say, 'Whatever it takes. Whether we have to blow up that building or attack that man.' He doesn't see how those two ideas are not in harmony with one another. You can't deal with that kind of schizophrenia." At our lunch he had spoken of the South's acceptance of civil rights as a kind of recognition by the South of the immorality of its earlier position. I wanted to know whether he could chart particular stages of that recognition. "I have a hard time explaining that to myself. It is a wondrous thing. If you had told me in the late fifties and early sixties that in the very near future we were going to have an integrated society, I wouldn't have believed you. I thought then that it might have been a hundred years in coming. It may even be divine, the change that has come about—I don't know. It's hard to understand. But people all of a sudden saw that it was wrong. And that is miraculous, for people to say that their own behavior had been morally defective. Nobody ever confesses on that scale. And here we have not only a somebody, an individual, saying that, but a whole society." And commercial pressures were now bringing about social change. There had been the recent uproar about a black IBM executive being denied membership of a club in Columbia. IBM as a result had dropped an idea about putting up a local plant. Neither IBM nor the executive had wished to talk about the matter or make race the issue; and it wasn't, therefore, easy for people to deal with. The consequence was that there had been no bluster on the part of the club; they had simply changed their policy and invited some blacks to join. Judge Sanders spoke as a lawyer. Through the law he had arrived at a larger identity. He said, "The common law is a majestic thing. It has a remarkable capacity to resolve disputes in a way which not only preserves civilization but enhances it. It is not unusual for me to find myself guided in a decision by a decision which a judge made a thousand years ago. I am aware I'm serving a larger civilization. And I know I'm _serving_ it." "So you don't have a problem of identity, no trouble between background and profession." "Not any more. I am more at peace with myself. Of course, that may be a matter of getting old and less judgmental and more understanding." His family had been in South Carolina "forever." An early ancestor on his mother's side had come out as a missionary to the Indians, and had then become a missionary to slaves. # 3 # TALLAHASSEE # The Truce with Irrationality—I PEOPLE IN Charleston had been complaining about the lack of their afternoon rain. As if to make up for this, on the day I left, and almost as soon as I had cleared the town and was going west, there was a fierce cloudburst. The tall trees tossed, the leaves showing their undersides, every big bough in separate convulsion. The rain slapped the windshield; nervous cars parked off the traffic lanes with their lights on. Not many miles away it became clearer, midafternoon again; though still from time to time approaching cars—when they had their headlights on—alerted one to the storms ahead. Tropical weather, of continental violence, matching the landscape: the swamp of South Carolina running into the marsh of northern Florida, reeds green and brown, patches of water silver or black, a landscape impressive by its great size. And soon enough, from this tropical swamp, Charleston—which one had begun to take for granted: so perfect a creation—began to seem far away. It was hard to think of that town being set down here—as it was hard to associate all this coastal land with African slavery, land so much of the New World, so unlike any other, land one wanted to contemplate, to enter a little into its wonder. The slavery of the British Caribbean islands began to seem small-scale, even domestic. Slavery in the British Caribbean was really an eighteenth-century institution; when slavery was abolished in the British Empire in 1834, England had become a manufacturing and trading country and could afford to write off both the plantations and the islands. Slavery in the Southern United States was most important in the first half of the nineteenth century—most important, that is, when slavery was on the point of becoming anachronistic, an absurdity in an industrializing country. But business people are concerned with the here and now (it is fearful to read of the slave-owners' wish to extend plantation slavery to the Western territories); and it took a war to do away with slavery in the South. The freed slaves remained, in inescapable numbers, no longer mere units of labor and wealth, a kind of currency; and it was they—for whose sake, one way or the other, the war had been fought—who bore the brunt of the South's anguish. A slave is a slave; a master need not think of humiliating or tormenting him. In the hundred years after the end of slavery the black man was tormented in the South in ways that I never knew about until I began to travel in the region. Jack Leland had told me that in the early days of the motorcar in South Carolina blacks hadn't been allowed to drive. In Tallahassee I heard that blacks were not allowed to try on clothes in stores; they had to buy anything they tried on. In Mississippi blacks could not be educated beyond a certain point; in South Carolina there was a time when attempts were made to deny blacks education altogether. And there was in the South something we never knew in the Caribbean of colonial days: violence, and the absence of law. How did a black family react to news of lynchings? What happened to the bodies? How were they buried? A man I met told me that when he was a child he was not allowed by his father to be a delivery boy. The father feared that a white woman might accuse the boy of being a Peeping Tom or of attempting rape. In the Caribbean the black man, after a hundred years of colonial neglect, a hundred years of separation from slavery, found himself in a majority on his own island, with the power of electing his own leaders and his own government. The black American, at about the same time, found himself just liberated but in a minority in the world's most advanced country, and among the most denuded in that country. His possibilities, as an American, were far greater than those of a West Indian. But there could be no easy movement forward for the mass; they had lived through too much; the irrationality of slavery and the years after slavery had made many irrational and self-destructive. It was in the news every day: drugs, crime, street life, "negative peer pressure" at school (blacks beating up those blacks who did well at school). In Atlanta, Anne Siddons had spoken of her need after a certain age to hoard emotion, to save parts of herself for herself. It seemed that blacks of all ages—living out their cause in their lives—felt a similar need. But in their more desperate condition this looking inward could separate them from their cause and often work against it. "Finally, I suppose, the most difficult (and most rewarding) thing in my life has been the fact that I was born a Negro and was forced, therefore, to effect some kind of truce with this reality." The words by James Baldwin (among the most elegant handlers of the language) had stayed with me since I had read them, nearly thirty years before. "Reality"—it was what I remembered and what I accepted; but now, in the South, in the middle of my own journey, I began to wonder whether the truce that every black man looked for hadn't in fact been with the irrationality of the world around him. And the achievement of certain people began to appear grander. THE REVEREND Bernyce Clausell lived in Tallahassee on Joe Louis Street. "Not in the project," she said on the telephone. "Tell the driver not in the project." And the white driver not only went straight to the house, but spotted the lady in her collar in the street, talking to a member of her congregation. Reverend Clausell was a Baptist pastor, and she had some reputation both as the only Baptist woman pastor in this part of Florida and as someone who did social work. She had been in the news for having sent a relief mission to Mississippi, to the town of Tunica, in a poor region with the name of Sugar Ditch. She had sent a truckload of supplies. Down the side of the truck there had been a professionally lettered banner: TALLAHASSEE TO TUNICA. There had been a copywriter's feeling there for effect, I thought. But the lady I saw in the street when the taxi-driver pointed had nothing forbidding or assertive about her. She was small and slender and mild-featured, academic-looking in her collar, someone suited to the quiet residential street, with its little houses and neat yards; definitely not a street in the "project." She said goodbye to the woman she was with, and greeted me. She said that the woman, who was of her congregation, had stopped her just as she was on her way to the church to turn the lights off. She asked me to go with her. It was a few house plots away, on the other side of the road: Calvary Baptist Church, a white building, with a board that gave the name of her late husband, the Reverend James Aaron Clausell. He had founded the church. The grass around the small church was as clipped and neat as the grass in the house yards. The light bulbs in the porch were burning wastefully away. Clausell—what sort of name was that? She said it was French. It came from Louisiana; it was the name of one of the important early settlers there. Her husband had been a light-skinned man, like many of his family. And there was a story about the founding of the church in that street. The Clausells had been holding prayer meetings in their house, and people were being saved and baptized. One day Reverend Clausell asked her, "What are we going to do with these people?" She said, "Let's start a church." He said, "I don't need a church. I pastor too many churches already." She said, "Well, honey, I wasn't thinking of what you needed. I was thinking of what the people needed." That was how the church had started. And when Reverend Clausell died, Bernyce, his wife, had become pastor, in response to the wishes of the congregation. The church, so white and plain outside, was full of things inside. It was clearly much used, and looked like a living room or a meeting place for the congregation. The main hall was about fifty feet long by thirty feet wide. It was full of flowers, and it had a piano and an organ. The carpet was green-blue; the pews were upholstered in a green fabric. At the end of the hall was a very big picture of Jesus and Mary Magdalen. It was at least fifteen feet wide and five feet high. The picture had been bought twenty-three years before from a printing house near Boston. The Christ was noticeably white, blond, long-haired, a little bit—as I had noticed in other places—like some paintings of General Custer. I asked Bernyce Clausell about the representation. She said, "It doesn't worry the congregation. I teach them that color is not important. A white Christ is better than no Christ at all. After all, Christ is colorless." But she also had a black Christ to show, a black Christ with black disciples. This picture was small, something she held in her hand. About the carpet and the pew upholstery she said, "Everything was given. We take what is given. That's why they don't match exactly." On the windows were stained-glass patterns on paper, strips of paper stuck on. The strips had been printed with a floral design. They had been ordered from Spencer Gifts, a mail-order business; and they had been chosen from a catalogue. The church door opened, and a woman's voice greeted the pastor. Reverend Bernyce knew the visitor. She excused herself and went to the woman. I didn't turn to look; I looked at the Boston mural. The woman who had turned up spoke in a low voice, and Reverend Bernyce's voice matched hers. Their words were not distinct. Only one sentence, of Reverend Bernyce's, came to me out of the burr-and-bumble. "You don't have to fall on the floor and jump to the ceiling." The consultation went on for a while: the second person that morning to have sought out the pastor with a spiritual problem. And when, after many goodbyes and thanks, the visitor left, Reverend Bernyce explained. "Her daughter came last week and accepted Christ. She's going to be baptized. The daughter is fourteen years old. But then somebody told the daughter that she wasn't ready—and they are really trying to keep her out of the church. Some denominations wouldn't let you join until you make some kind of emotional, physical reaction. That's why I told the mother that nowadays you don't have to jump to the ceiling." I asked her to explain a little more. She said, "You're born a Hindu. We are not born Christian. We are born black." That last thing seemed strange for the pastor to say. But perhaps she meant no more than that people had to choose Christ. "To become a Christian does not require lots of emotion. In our worship services we are emotional only if we are so moved." She led me to the room at the back of the main hall. It was an annex to the main building, and it was called the Clausell Fellowship Hall, in honor of her late husband. It was domestic-looking. There was a stove for cooking, and all about were clothes that had been collected for the church's charities, especially for Mission Outreach. The mild lady pastor spoke the slogan of the program with perfect seriousness: "It's our caring-sharing project." It was part of the "Tallahassee to Tunica" mission. There were clothes (covered with green cloths) on racks, in boxes, in sacks, and on tables. She said that her appeal for the poor of Tunica in Mississippi, some six hundred miles away, had touched a nerve in her congregation. All around in this annex, on walls and boards, were photographs of black Americans. "We keep black-American history in front of people, so they will know some of their heritage." There were portraits of Martin Luther King, Richard Allen (founder of the African Methodist Episcopal Church in Pennsylvania), Booker T. Washington, Harriet Tubman, Frederick Douglass, and black-American service heroes; and there was a photograph of the black-owned Atlanta Life Insurance Company. We left the annex and went back through the main church hall. On the wall next to the front door there were many color snapshots of Reverend Bernyce's European tour in 1972. This—and everything else—gave to the hall the feel of a devout person's scrapbook. But there was something more. This elderly black lady had been experiencing the larger world, the famous world, as a black person, and giving a little of the glamour of the experience back to her black congregation. Just as the honors that had been given to her were to be regarded as honors given to a black person, and honors therefore to all black people. In the church porch there were cutouts from magazines of black and white family groups. This was Reverend Bernyce's way of reminding her congregation of Mother's Day; and she had been careful to show both black and white family groups. She said, "We're a biracial country." The word was new to me; but then she qualified and extended it. "We are black, but the country isn't all black. We are many races. So in picturing families we have families of different colors." The air felt heavy with pollen. On the other side of the road, where her house was, the ground sloped away, so that the house was in a little dip; and the air was heavier. There was a car in a carport. And in her little sitting room, much smaller than one might have thought from the outside, there were many more photographs and mementoes and things. One wall was covered with framed diplomas and plaques. It was warm in the sitting room, even with the door open. She had been born in Georgia, and when she was nine months old had been taken away by her parents to Columbus, Ohio. "I don't know what my dad did. My dad was a laborer. He was a little feller. He couldn't do too much." And it was probably from her father that she had inherited her own smallness. "We stayed in Columbus a little while. Then my mother died and our auntie took us to New York. I loved my aunt. I was too young to know my mother. In New York we had everything all around us—reefers, murder, dope—but it didn't influence us, because of our church life." She broke off to talk about the accommodation black country people had to make when they went to the big city. "You lose all the ties to your family, your community, your church. But then there is the chance for you to gain new ties, even in a great metropolis like New York. You can get into a smaller group and be a viable person in that smaller group. Like, for instance, a church, a social club, a political group, or just a street group. Some young people, when they migrate from the South to the North, they still want a group to cling to. So unfortunately they become affiliated to a street group." How did she explain the strong religious instinct black people had? "I think it comes from slavery. And even from before slavery. From Africa. They just had a strong religious heritage. In slavery God was their deliverer. And they felt that some day God would work it out." Was it sometimes a form of escapism? "With some people it might be a form of escapism. I wouldn't deny it. But primarily Christianity is a way of life. I should say that the white churches that I know are similar to ours. They are doing great mission work. And more than we are, because they have the finances. Religion has had a great part in helping to break down segregation. "I have to speak personally. I did not experience any racial hostility until I left New York and went to live in Washington, D.C. This was in 1941, when I was twenty-five. I went to work for the government. And there was this experience that tore me up—the first day. The cafeteria in the War Department building was not open yet. So about four of our black girls went to a small sandwich shop to eat our lunch, and we bought sodas, and were about to sit down to eat, and the lady there said very harshly, 'Can't you people, can't you people find some place else to eat?' Of course we didn't have much appetite after that." "Did this shake your faith or your way of thinking?" "What it did, it made me wonder about my nation. Before that, I was a hundred percent patriotic. I loved America. But it began to shatter a little my patriotic fervor. It didn't shake my religion. In fact, because of my religious training I didn't hold any ill-feeling against the woman in the sandwich shop. Washington, D.C, was not integrated. And _that_ was mind-boggling to me, that the nation's capital wasn't integrated. "When we went to the large cafeteria in the War Department building, where we worked, whites would not want to sit at the same table with us. If we sat down with them they would move. We just began to know that this exists. It made me a fighter, all right. We joined a group there that was spearheaded by the Quakers, and our aim was to integrate some of the lunch counters in the city. We would meet—all the Quakers were white—and have prayers and decide where we were going. And we were being told not to show any reaction to any violence that would be shown to us. We had to be trained. You can't imagine the things that were said to us. People would spit in our faces. If we drank out of a glass they would take it up and throw it away. Christ said turn the other cheek. And finally Washington was integrated, a little later." The atmosphere was heavy, with the pollen and humidity of northern Florida. My eyes had begun to smart; and now, thinking of those prayer meetings, I began to cry. She said, "People have changed. And now some of those people wouldn't believe that they were that cruel back there." It was such a good way of putting it. She didn't offer a personal forgiveness. She spoke of a larger change of heart. It was immensely moving. She said, "These experiences helped to build me and give me more character and strength." But what of others? "Some people couldn't take it. They just gave up. They accepted. For those people it may have been the best thing to do. It's not for everyone to fight. The Bible says, Let the strong bear the infirmities of the weak." She, so frail and spare on her settee in her little sitting room, considered herself one of the strong. "It's still an issue. Not segregation, but racism. It's more subtle." I wanted to know her attitude to the past. But the past for her, as for nearly all black people I spoke to, stopped at a certain point. "I've never dug into my roots. I can go back as far as my grandfather and grandmother. Around 1900. And that's all." Now there were other problems beside those of racism. There were the problems of teenage pregnancies, drugs, dropouts, and the behavior of black students at schools who were reported to beat up those blacks who did well at their studies. "We didn't have that problem when the schools were all black. Now—I hate to say it—integration has damaged some of the black children. Because in the black schools we had to visit the parents' homes periodically. If we had problems we would go to the home, and the parents were very cooperative. We had religious activities at the schools. We had fifteen-minute morning devotions. In the integrated schools what happened was that some of the black children began to role-model some of the nonproductive white children. And parents didn't have that close tie with the schools. Those of us who are in this work have to work harder. You can't do too much in the schools now." She regarded herself as one of the strong. Her religion gave her some of her strength. Had there been any experiences that had confirmed her in her faith? She said, "Many. All the time. God speaks to people, just like he did in olden days. I knew when I was sixteen that I was going to preach. I told my church in New York. I don't know how it came. I just knew it. And I know that in 1971, when I became a minister, God had talked to me. They are words in your heart, when God speaks. But there have been occasions when God talked to me in words, when he called my name, and I looked around to see who was there who had called me, and there was nobody there. The first experience of God speaking audibly was when I was a child. He said, 'Get up and go join the church.' I didn't do it then. "But since I've been in the ministry God talks to me all the time. In words. He'll tell me to do something. And I'll reply to him out loud. Some of my congregation know about those experiences. One Sunday God spoke to me about a child in the congregation. I had just turned to go back to the pulpit, and God said, 'Pray for that child!' I turned around and saw this child sitting in somebody's lap. The command was urgent. And I said, 'Whose child is that? Bring that child here.' I prayed. People cried. A week later the child became ill, but the child did not die. Thank God!" She normally didn't speak of these experiences. The one time she did was when she appeared before the Ordaining Council, a group of black Baptists in New York City. "I had to justify my calling. I told how God spoke to me. When I told the Ordaining Council, they understood quite well." Her religion had helped her through the hard times in Washington in 1941 and later. "You see, it's the holy spirit that guides and protects us in these instances." "Did you ever feel abandoned?" "I never felt abandoned by God." "Did he tell you to be a fighter?" "I don't know. It was in me. And I felt I had done what I could do." She revered the memory of Martin Luther King. But the resistance she and the Quakers had undertaken in Washington was long before the civil-rights movement of the 1950s and 1960s. She was braver than she claimed. But she referred everything to her faith. "So many religious experiences, so many experiences of God." And she was pleased that both her daughters were religiously inclined, and one "totally dedicated to the church." To that extent she was passing on the torch as a woman pastor. "When I was a child in New York we had women preachers in our congregation, so to me it was nothing rare or different. When I married a minister I lost all thoughts of being a minister myself. My husband did not believe in women as ministers. But he knew I wanted to be a minister. He was a perceptive man. He was much older than I. He knew I wanted to be a minister because sometimes in church I would get up and talk. When the spirit moves, you move. He understood I was sincere. When God spoke to me in 1971, I couldn't help what my husband thought. I had to respond to the call this time. I had to hear God's voice and not my husband's voice." It was time for me to leave. She gave me a stapled photocopied booklet about herself, a souvenir of a celebration held in her honor six months before at the Florida Agricultural and Mechanical University. This booklet had copies of articles about her from the Tallahassee _Democrat;_ it listed her many awards and honors. The frontispiece was a full-page photograph of herself; and on the cover she was described as a "servant of Christ." She also gave me her card. On this card the Calvary Baptist Church was described—and again I thought of advertising copy—as "the friendly little church on the corner of Joe Louis and Arizona." At one time that would have seemed to me very "American." Now I understood a little more, and knew that churches like Reverend Bernyce's were more than places of worship, were community centers, social centers, and depended on the personality of the pastor. MAURICE CROCKETT, a big, upright, handsome brown man of fifty-six, was the Florida Parole Board commissioner. He had been represented to me as a local black success story. That made me want to see him. He had agreed to see me, but he hadn't understood what I was after. And when I was taken to his office early one afternoon—his desk was cleared, and he was resting his head on his crossed arms, but he was far from asleep—he was not immediately welcoming. He said, and it was like a prepared statement, "Most people from outside see us as ethnically deprived, semiliterate." There wouldn't have been much in the meeting if we had gone on like that; but when he understood that I had come to listen, his manner softened. Soon his natural graces took over; he talked easily, anxious to efface the first, unwelcoming impression. He said, "When I became a department head, over both blacks and whites, the whites were not happy, and I had to live with police protection for a couple of years." It seemed so unlikely now, in the general civility of his office. "It might have been an overreaction, but you never know. There were any number of threatening phone calls and innuendos. And a lot of the whites quit." The fight wasn't pleasant, but it was necessary. "Some people try to give the impression that when we were segregated the whites were happy and the blacks were happy. But it isn't true. I don't think any thinking person could be happy under those circumstances. I could never have _afforded_ to be happy. My choices were so limited. My son today has unlimited choices of career. I did not. When, in 1964, I thought I was due for a promotion, they came and drove me around in the car and explained that I was qualified but they weren't ready for a colored person to do that kind of job yet. I went home and, I'll tell you, I cried. And it still hurts. "My son, because of my job, has never experienced that kind of rejection. In my work here I've been surrounded mainly by whites, and that's the environment my son grew up in." His son went to white public schools, until his father put him in a black school affiliated with the local black university. "He couldn't take it. He had never been in an all-black situation. The music was different, the manners were different. Michael had been listening to white kids' music. In his scout troop he was the only black kid." Maurice Crockett had lived through a hard time, and had more than survived. But had some people broken under the strain? "Some people back away. And the way you do that is you involve yourself in your church, in things around the home. So to all practical purposes you isolate yourself from reality. The church is all black, and when you go there everybody is friendly, and you aren't threatened, and it's like being in the womb again." But he had had a special source of strength. "Most black kids have mainly a matriarchal system. But I grew up with a man. He was my stepfather. He was a role model and a guide for me. Mothers tend to be not as strict with boys. Boys need the kind of structure that a male provides. I think a lot of the black kids today would go to school if the basic family structure with the male was in place. But black males have a hard time establishing themselves, because of the lack of job opportunities." I asked him about his son, who had been taken out of white schools to be sent to black schools. Maurice Crockett said, "He's begun to be aware that he's black, and that everybody doesn't love him. He's starting his third year at Tuskegee. But Michael still has his basic cadre of white friends." Out of success now, out of his new security, Maurice Crockett was rediscovering, reasserting, his blackness. He needed religion, but he needed a black religion. "I'm not a shouter. But I like to be in a church where that kind of thing goes on. A lot of us want to emulate other standards, and we have to do that. But I still think that, like most ethnic groups, you shouldn't divorce yourself from your basic culture. Especially when I go to church. The church is my salvation. The church keeps me sane." Salvation, sanity—I hadn't heard the two run together. But in the job of Parole Board commissioner there were special needs. "Some days in this job the stress of trying to keep up sends you home with pain. One of the most stressful things we have to do is that we hold the final face-to-face interview with the prisoners on Death Row. We actually go to the prison and sit down with the inmate and his attorney. Our meeting is transcribed by a court reporter. And when the world gets too much for me, I go to church. The saving grace for us black Southerners is the church." "Do you feel successful now? Content?" "I'm not content. I'll go to my grave being not content. I'll constantly try to improve. People want to say we want to land from the trees and eat watermelon for the rest of our days. I want them to know that that kind of stereotyping is misplaced. I receive visitors a lot in my job. Most people from outside see us as ethnically deprived, nonverbal. I guess they see us as semiliterate people." That was where our conversation had begun. Now he had brought it back to that point, with an explanation. "But this is false. If you come to me like that, I will let you know that I am not the kind of person you can handle in that way." His own truce with irrationality—how had he managed it? What was it about the past that now, from this distance, most surprised him? "What I find hard to understand now is how I contained the anger. I suppose you have to learn that the anger doesn't solve your problems. You sometimes have to sit down and wrestle with yourself." He still occasionally wrestled. He lived in a white neighborhood. He took his dog for a walk. At whatever time of morning or afternoon he took the dog, there was always, in a house at one end of the street, an old white man who sat out on the porch and watched him. It would appear that the old man was waiting for Mr. Crockett to go past his house. "But what's the point?" I didn't understand the explanation Mr. Crockett gave. "He wants me to know that he is there. He wants me to know that I'm being watched." And Mr. Crockett made a gesture with his finger, drawing a horizontal line. "Does he say anything? Do you talk?" "We do. And I always have to think of something to say back. The last thing he said was, 'I don't know who's slower, you or the dog.' And I have to think of something to say, something foolish like, 'You're slower than both of us.' That kind of nonsense." But the neighbor would have been a religious man, perhaps a Baptist, a fundamentalist. Didn't that make for a certain kind of communication? Mr. Crockett rejected that. "White fundamentalism"—putting it in quite a different category from the black fundamentalism he liked in black churches and saw as part of his black culture—"it is their attempt to go back to the good old days. The white church now has a school attached to it. They call it a 'Christian school'; the main purpose is to keep it segregated. The white-fundamentalist church has consumed these people and consumed the issues. It's a half-baked attempt to establish a structure that has long since gone by the board." IT WAS the advice of a West Coast writer, someone originally from Tallahassee, that had sent me to Tallahassee. Northern Florida, I had been told, was quite different from southern Florida. Northern Florida, the panhandle part of the state, was part of the Deep South. But it had taken me a long time to find my way; it sometimes happens on this kind of journey. Tallahassee, the state capital, was an artificial administrative center midway between the extremities of the panhandle, midway between the towns of Pensacola and Jacksonville. And all that I had got to know of the countryside was the few miles between Tallahassee and the beach houses on the black creeks and white sandspits of the Gulf of Mexico: a holiday landscape of food shops, restaurants, mobile homes, gas stations, places offering live bait, and churches—disposable buildings in "redneck" country, where (I was told) in the old days blacks would have been burned out if they had tried to settle, and where there were still almost no blacks. But then, almost at the end of my time in Tallahassee, I saw something other than that holiday landscape. About an hour's drive away, and just behind the highway—American highways make one state look like another, and one part like another—I saw old dirt roads, forest where there had once been fields, houses that had been abandoned whole, barns and garages in overgrown yards. It was a little like being in an abandoned European town in Africa, in Zaire or Rwanda. There had been an old community here. Now it hardly existed. Farming could no longer support it; farming no longer paid. And here and there among the ruined houses—trees and shrubs and bush seeming to reach out towards them, darkening the open space of yards—were places in which people still lived, black and white, people not ready to go, holding on, people who it might be said were working out the quirks of their own character. The fat young man rocking on the low porch, for instance, was the son of a black farmer. That was the way he had chosen to spend his days; he had made that choice of solitude. I thought of the drinking man in Howard's village, framed in his window on a Sunday, looking out, but far from the life of his community. Here there was no longer a community; the fat young man rocked in the middle of bush. My guide was Granger. He was white, in his forties, and he worked in a hotel in a nearby town. He did that for the ready cash, to keep his own farm going. It was a small farm, 120 acres. But it was ancestral land. It had been homesteaded—Indian land, staked out and claimed from the federal government—in the decade before the Civil War. The local Baptist church had been established in 1856; Granger was a Baptist. The land had never been worked by slaves. "We feel like we were the first Americans," a relation of Granger's told me. And various ancestors had migrated to this part of Florida from South Carolina, Virginia, and Georgia. There were stories in some branches of the family of old wealth. There was a story that one ancestor had owned a third of a county in England. There was a later story, from a time after the calamities of the Civil War, of another ancestor who had made good in the China trade and had brought home a chest of gold coins, which, when emptied out onto the farmhouse floor, had sent up a cloud of pure gold dust. Now Granger worked in a hotel, two days on, two days off, and looked after what was left of the ancestral farm, doing so not for money but for the piety, the debt owed his ancestors, and doing so as well because farming was for him part of the beauty of the days. Farming meant being in these fields, these woods. We drove in his fields in his old, un-air-conditioned pickup truck. One of his cows had just calved. We stopped in the truck among the pine trees, in the thin, broken shade, among the cowpats and the pine litter, the cones, the needles, the brittle dead branches. He got out and, keeping his distance, spoke both to the mother and the birth-smeared calf struggling to its feet. He had been waiting for this event for some days. This was the kind of farming he did and liked. It had given him his gentleness. But development was coming. People with jobs in the towns were building houses in the villages. The old farms were under threat. A cycle that had begun when the Indian land was homesteaded was coming to an end. (The tomb of Osceola, the Seminole chief who had died at the age of thirty-eight in federal-government captivity, was not far from Charleston, and within sight of Fort Sumter.) Fifty miles or so away, still in the panhandle, building development and agricultural failure were putting an end to another kind of community, a community of black sharecroppers. Black people had lived on this land since the end of slavery. Once everyone was related; these fields bounded everyone's horizon. Now the roads had got there; the community, exposed, was breaking up; there were pine plantations in the old fields—young pines growing out of a lot of bush. But not everyone was ready to move to a town. The life on the land here was different from the life that Granger found on his 120 acres. There was a different idea here of ancestors, history, piety. For Barrett, the black man in his thirties who was showing me around, the agricultural life of this inbred black community was stultifying and shameful. Barrett was middle-class, with parents who were modest professional people. He came from a biggish town where there were few black people. Until he had come to Tallahassee he had thought that black people in the South were like his family; he was still unsettled and enraged by those aspects of black life in Tallahassee that didn't fit in with his old ideas. The idea of being in a minority was so much part of his upbringing, and so important to him, that he had had trouble, he told me, getting used to the sight of all-black streets. I liked him for saying that; not many people would have confessed to something so simple and undermining. And when his work had taken him to that old black agricultural community, he said, he had suffered from "culture shock." I didn't think that what he was showing me was all that bad. But, then, I didn't have his expectations. And, with anger building up in him again, and out of this anger wishing to see the worst again, and to show it to me, he drove me to a side road and said, "Look at that one. A house without windows." It was extraordinary, a much-patched-up and wretched old wooden house, standing by itself in a bare yard, with no trees around, and with bush in the field at the back. I thought I understood now what Maurice Crockett wished to save his son from: growing up "white" and then having, like Barrett, to make adjustments. Barrett didn't think as Maurice Crockett did about black religion. Barrett didn't think that the shouting religions were part of his own black culture. After he had got married, he said, he and his wife had talked about what church they should go to. They had talked very seriously, and they had decided to go to the Presbyterian church. He was twenty years younger than Maurice Crockett. He didn't have the older man's needs. At the start of our drive I had noticed his racial passion. He wished to blame someone first of all; but then his own words had led him away from that, to a more general irritation. I had asked him about his racial passion; it seemed to be so much his main subject. He had acknowledged my question, but not replied to it. Now, when we were almost back at the hotel, he returned to the question. He said, "You asked me about that. I've been thinking about it. I suppose I am angry because I am black. I don't know whether that's a good enough reason, but that's how it is." It was a good reply. It was part of his honesty. In the driveway of the hotel there was a black figure I had grown to recognize. He wore a black turban and a cream-colored Indian-style long shirt. He was reading aloud, chanting, from an Arabic book, perhaps a Koran. He paid no attention to the coming and going around him. He read aloud like a student; he held the fat book close to his face; he sat on a low wall; he could not be ignored. REVEREND Bernyce Clausell, Mr. Crockett, Barrett—they were all aspects of a developing black movement forward. And Jesse Jackson came to Tallahassee one day, looking for support for his presidential candidacy. Even if the man himself was not seen by many, his presence was felt. His entourage nearly filled the Golden Pheasant restaurant. Later that evening a limousine with its hood up waited outside a club where the candidate was meeting local people. Such style, such expense; and this was just one day, and not a very important one, in the calendar of a presidential candidate. It would have been historically satisfying, and simpler to manage intellectually, if this movement forward was, broadly, all; if black people, their legal rights won, were now becoming masters of their own destinies. But at the other end of this movement, and close enough to threaten this movement (in spite of the mighty presence in the Golden Pheasant restaurant of the men and women of the Jackson party), there was irrationality and self-destructiveness, and despair of a sort perhaps not known before. It is like the final cruelty of slavery: that now, at what should have been a time of possibility, a significant portion of black people should find themselves without the supports of faith and community evolved during the last hundred years or so. In the Caribbean islands, in the most settled days of slavery, the slaves played at night at having kingdoms of their own: a transference to the plantations of West African beliefs—still current in the Ivory Coast—that the real world begins when the sun goes down, and that at night men change or reverse their daytime roles. No fantasy even like this, no African millenarian dream, supports the new denuded black element. It is hard to enter into their vacancy. "I'm nothing. I'm just existing," a young black in a detention center said. "Your hands soft," another said, using words that seemed to me to come from a long time ago. "Your hands soft like cotton." His own hand was gentle. He had the intelligence and dangerous attractiveness of a kind of delinquent. But he was horribly lost; he couldn't be reached. Another man said, "It is very hard for a black man to make a very small step." They were all going to be released in a few months. But there was nothing for them in the world outside; they insisted on that. And they all spoke as though their lives had been predetermined, and were already over. "Nearly sixteen millions of hands will aid you in pulling the load upward, or they will pull against you the load downward. We shall constitute one-third and more of the ignorance and crime of the South, or one-third of its intelligence and progress; we shall contribute one-third to the business and industrial prosperity of the South, or we shall prove a veritable body of death, stagnating, depressing... the body politic." The words read like special pleading. And they were. They come from the speech Booker T. Washington made in Atlanta in 1895, when he was only thirty-nine: a famous speech that established him in his reputation, and in which he did two apparently irreconcilable things—calm Southern white people down, and offer hope to black people at a time of near hopelessness. Special pleading, overstated; but those words of the 1895 Atlanta speech now read like prophecy. # 4 # TUSKEGEE # The Truce with Irrationality—II I HAD got to know _Up from Slavery_ when I was a child. My father had read me a story from the book, and I believe I then read more of the book on my own. My father, born poor, and in spite of his ambition always poor, liked stories of self-help and of men rising from poverty. He suffered in Trinidad, and I would have known that _Up from Slavery_ had racial implications and could be related to the way things were on our own island. But I was too young to do anything with that kind of information. I received the Booker T. Washington story my father read me almost as a fairy story, and in the part of my consciousness where it lodged it was stripped both of race and historical time. Within the larger story of a man rising and making good, the story in question was the story of a test. The young boy, alone in the world, and just starting out in the world, had been asked to make up a bed (this was the way the story lived in my consciousness). And what was at stake, what depended on the correct making up of the bed, was the young boy's entire future. It was hard to forget that story (and every time I made up a bed it hovered in my consciousness): the fairy-tale test, the doing of a seemingly trivial or irrelevant thing supremely well. Like the story of a temptation to an honor-bound knight or a saint who had made a vow; like magical tests in other fairy stories: picking up the grains of rice, guessing the name of the dwarf, spinning straw into gold. But the story I carried in my consciousness was wrong in one detail. The ragged boy, born a slave, who had walked many days and nights to a particular school in order to be educated there, had been asked first of all not to make up a bed, but to sweep a room. The boy had swept the room four times. The woman who had set the test hadn't then simply said, "All right. You pass." She had run her fingers over the walls and floor, to check. The boy had judged rightly, after all. He had done the deceptively simple task very well; and in this way he had won over yet another potential tormentor, and turned her into an ally on his magical journey. There was a reason why, in my memory, the story had changed from sweeping a room to making up a bed. Beds were important to the slave boy. In the one-room slave cabin, also the farm cookhouse, where he had lived with his mother, the boy had slept in rags on the earth floor; and when, in his rise, he was first presented with a made-up bed, he didn't know how to use it. He didn't know whether he had to sleep on both sheets or between them or below both of them. (I would have been sympathetic to that predicament, having at the age of eighteen moved to temperate England from tropical Trinidad, where we made beds in our own way: one sheet spread on the bed, another sheet or blanket folded, to be used as a loose cover during the night if it was needed. I might even have transferred an early personal embarrassment to my memory of the book.) And in the school he had later established at Tuskegee in Alabama for people who, like him, were not far out of slavery, Booker T. Washington was concerned to teach his students how to use beds, and concerned in a more general way to teach good domestic manners as he had grown to understand them. A moving story, and a fabulous one: the boy who had slept on the floor of a slave cabin had become one of the most famous Americans of his day, had dined with the president, and had never ceased to serve the cause of his people. It is easy to see how _Up from Slavery_ could have worked on a self-made man like Andrew Carnegie and drawn great sums of money from him for the school at Tuskegee. At the same time the very fabulousness of the Booker T. Washington story had made it seem separate from the grimmer aspects of the Southern or American racial issue people wrote about in books and newspapers. What had the great fame of the man served? What had happened to the great achievement? And so the book had receded, leaving only a memory of the bed-making test (which in my mind ran together with the story of the middle-aged Tolstoy, in a peasant phase, wishing to make up his own bed). And then its very title had been undermined by the William Buckley parody title, _Up from Liberalism_. It was only when I began to plan this journey, and had been given the idea of Tuskegee, that the book became real again for me. It became especially real when I went to see Al Murray in his apartment in Harlem. Al Murray was the first person educated at Tuskegee whom I had met and spoken to about it. He it was who began to give me some idea of the grandeur and complexity (and anguishes) of Booker T. Washington; gave racial attributes to the neutral fairy-tale figure—the slave boy's father might have been a white man; and fitted him into historical time. When the school had begun in 1881, as a simple trades school, black men had the vote, and the school had been given some small subsidy by the state of Alabama. Twenty years later, when _Up from Slavery_ was published, black men had been virtually disenfranchised in the South. It was against this background, of increasing legal disabilities, that Booker T. Washington had built up his school. What would have been hard enough in a time of stability had been made much harder, with the walls of prejudice, segregation, and humiliation constantly shifting, closing in. Booker T. Washington did what he did, Al said, because he understood the way capitalist America worked; he knew how to present himself to that side of America. What was important to remember was that Booker T. Washington was a nineteenth-century American, the counterpart of the Carnegies and others whose wealth he tapped. Al Murray's admiration for his university and its founder made the old black-and-white photographs that he showed me, in the two volumes of Louis R. Harlan's biography, especially moving: the stately photographs of Booker T. Washington; the formally dressed young blacks, men and women, doing domestic work and agricultural work which, just a few years before, would have been slaves' work, but which was now (like their teacher's own room-sweeping test) a step to better things. It was to a special kind of romance, then, that I was traveling when I left Tallahassee and its drugged, asthma-inducing pollens, and made for Alabama and Tuskegee—going up through the plains of Georgia and then through the extensive flat neon confusion of the camp-following town of Columbus, Georgia: sex shows and pawnshops and fast food restaurants; crossing from that into quiet, rural, seemingly left-behind Alabama. Tuskegee became a name on the highway boards; became the name of a forest—speaking then of a pre-1830, preplantation, Indian past, giving another association to the unusual name; and then at last became the name of a town. I was expecting a town like some of those on the way. This was smaller, shabbier: small eating places, few of the great fast-food names (I missed the tall, bright, competitive signs, roadside commerce's equivalent of the joust and the pennants of chivalry), grimy garages, small grocery shops—a place still poor, hardly the setting for the great man's success story. But then came the campus, and it was grander than anything I, and I am sure my father, had imagined. My father, reading self-help books in Trinidad, no doubt compared himself to poor boys who had become engineers and bridge-builders in industrial England; and though my father might have found aspects of his own story in the beginnings of Booker T. Washington, a man's possibilities depend on the possibilities of the place where he finds himself. There was nothing slavelike or Trinidad-like about Tuskegee; nothing to be excused. However little one had known about it, it was real, and it was achievement on the American scale: scores and scores of dark-red Georgian brick buildings set about landscaped hilly grounds. "You should understand," a very old lady said to me some days later, and she had spent almost all her working life at Tuskegee, "that until the 1930s Negroes in the United States simply did not have money." And the effect on me of the first sight of the campus must have been like the effect on people who had seen it in the days of segregation, when it would have represented one of the few ways forward for a black person, and when to people who had little it would have appeared dreamlike. Al Murray had booked me into the university guest house. It was called Dorothy Hall. It had been built in 1901 as an industrial school for girls. It was almost at the center of the campus now, across the road from the big bronze statue of Booker T. Washington lifting the veil of ignorance from his people. It was a famous statue, and was the subject of Tuskegee postcards. I half knew it, but was nonetheless surprised by it. The sculptor had made concrete what was really only a turn of phrase, a metaphor. Booker T. Washington, in a three-piece suit, was shown literally lifting a sheet off a crouching, muscular young black who had an old-fashioned folio book on his knees: figures and properties so unexpected when taken together that they made one wonder how long the muscular black fellow, naked except for the sheet that was now being pulled off him, had been hiding with his big book below the sheet, and why he had stayed there, and why he had needed Booker T. Washington to display him like a conjuror. But a black man I had spoken to two or three weeks before had found the statue very affecting when he had been taken to Tuskegee as a schoolboy. "Perhaps you have to be black," he had said. And I was willing, at that moment of arrival, to see with his eyes of forty or so years before. Still, there it was, rhetorical and a little nagging, ever so slightly working against the romance. _I will let no man drag me down so low as to make me hate him_. The engraved words of another age, the philosophy of helplessness—as were these other words, also engraved at the base of the statue: _We shall prosper in proportion as we learn to dignify and glorify labor and put brains and skill into the common occupations of life_. The philosophy of a man working against the odds, combining uplift with a wish not to offend. Yet—it had resulted in a great achievement. I turned away from the statue and went to the entrance of Dorothy Hall. I saw that the windows were unrepaired and needed painting. One screen frame on an upper window was hanging loose. The beautiful dark-red brick of the old building was in need of repointing. These were bricks that the early students of Tuskegee had made with their own hands, after three heartbreaking failures with kilns. The building faced west. It was late afternoon and very hot. I asked whether there was an elevator, to help me with my luggage to the upper floor. I was told that the building was old and the elevator no longer worked. By the time I had taken my luggage up, making three trips up and down the hot steps and through the very hot upstairs hall to my room, my lungs were inflamed again. And the constriction there was to be with me all the time I was at Tuskegee. The colors in the hot paneled club upstairs were like the colors of a gentlemen's club. There was an oil portrait of a white military man; and on the landing wall there was a photograph of Teddy Roosevelt. Dorothy Hall had been built in 1901; _Up from Slavery_ had been published in 1901; and in that year Booker T. Washington had dined with Teddy Roosevelt at the White House. Old history, old dignities, old battles. And I was later told that many famous Americans had stayed at one time or another at Dorothy Hall. Almost at the end of my time there, I found out where the elevator was. The person who showed me was one of the oldest men on the campus. He was, or had been, a musician. He had come to Tuskegee as a boy of fourteen in 1913, when Booker T. Washington was still alive; and he had taken part in the funeral procession of Booker T. Washington in 1915. The old musician was very famous locally, and many people I met thought I should see him. He was out of town when I arrived, but he sent word he was going to come to see me at Dorothy Hall on a certain day at twelve o'clock; and he was there absolutely at the time he had given. He was proud of keeping time. It was part of the Booker T. Washington tradition, he said. And his stories—he started on them immediately—were of that old, romantic time. "It was like heaven when I got here in 1913. I'd never seen anything like it. I ran away from home and arrived here with a dollar and a half in my pocket. But Booker T. Washington didn't turn anybody away from this school." The old musician was dressed artistically: pink shirt, blue tie, light-green check jacket. He was tall and straight and proud, at eighty-eight, of the erectness of his carriage. That was another part of the Booker T. Washington training. Clean clothes, erect posture, firm strides: no old-time shambling. That was the way Booker T. Washington wanted it. Everything had to be just so; everything had to be clean. Every day Booker T. Washington walked around the campus dictating notes to a secretary about things that were wrong. The old musician came from a small town in Alabama, about 150 miles north of Tuskegee. "My father was a common laborer. My mother's family looked like white people and had some education." The old man opened his pink shirt to show the pale color of his skin. "Many white people up there referred to my mother's family as cousins. I came here just with my trousers and bag and no schooling. An old slave here, a Mr. Baker, he told me that if the people caught a slave learning how to write they would saw this"—the old man wiggled his right thumb—"they would saw that off, because if the slave could write he could write himself a pass to get off the plantation. Slaves weren't allowed to leave their plantation without permission. That was what Mr. Baker saw as a young man. "All that my father could teach me as his oldest child—there was nothing wrong with it, but it didn't go far enough. This was what he taught me. Don't talk back to old people. Don't be sassy. Stay out of bad company. And help Papa take care of the family. All that was good, but it didn't go far enough. My mother's brother went to Talladega College. White people started that—the American Missionary Society, organized by white people to start schools in the South for freedmen. Tuskegee was different. After emancipation we could vote here. Black people. Some local politician wanted our vote, and Mr. Adams told him that 'If you could help us get a school, I think I can get all the colored people to vote for you.' So people in this county voted for this white man, and the state gave two thousand dollars to start this school. "Up there in my hometown I paid a schoolteacher fifty cents a month to teach me reading and writing and arithmetic. Professor Moses had his school on the west side of town. Professor Carmichael had his school on the south side. I lived on the south side. My dad didn't know it, though—that I was paying fifty cents a month to Professor Carmichael. I was shining shoes. My father used to empty the coal out of the railroad train. Four o'clock in the morning. A dollar a day. "When I came here and saw all these buildings, and the dining hall, and the tablecloths, fourteen students to a table, girls on one side, boys on the other, it was like heaven—I'd never seen anything like it. The old chapel! We had grown people coming here. They would walk here, wanting to learn how to read and write. Booker T. would get jobs for these old people, jobs from white people in the town, to work in the day, so that they could study at night and pay their board." He loved the past, this dandified, good-natured man of eighty-eight. He was energetic and full of enthusiasm; he still drove his car. He drove me to see the site of the very first schoolhouse. "You mean no one has taken you to see that yet?" And then he was determined to get me back to Dorothy Hall at the time he had said. It was when we got back to Dorothy Hall that he showed me the little elevator there, and told me the story about it. Henry Ford had come to Tuskegee in 1941, when the George Washington Carver Museum was opened. Carver, the Tuskegee agricultural scientist, was then perhaps eighty. Henry Ford had been so shocked to see the old man tottering up the Dorothy Hall staircase that he had then and there made an offer of an elevator. Now the elevator was out of order and out of sight; and the old musician, older now than George Washington Carver had been in 1941, had to climb the difficult stairs. THAT MENTION of George Washington Carver dislodged old memories, memories akin to those I had of the Booker T. Washington bed-making test. Most of the teachers at the elementary school I went to in Trinidad were black. They were quiet people in the main, one or two fierce only with the whip; and at a time when the world offered them little they had their quiet ways of making racial gestures. A class question might be like this: Who is the world's greatest cricketer? If you said Bradman—the Australian—that might be wrong. A better answer, perhaps even the correct one, would have been Headley, the black Jamaican, or Constantine, the black Trinidadian. The name of George Washington Carver was associated in my mind with that elementary school, and the subterranean racial pride of the black teachers. I remember a little film that must have been shown one day during class hours: a frightened black family in a hut, white horsemen outside. I wasn't sure what the story was: the memory of the film is faint. With this film there was a lesson about George Washington Carver, a black scientific genius, who had done wonderful things with the common peanut, and found uses for every part except the shell or hull. The wonderful things he had done with the peanut I took on trust. But his inability to use the peanut shell had always interested me. Why—since bamboo pulp could be used for paper—hadn't the peanut shell been used for paper? It seemed to me to have the texture of bamboo pith (I was thinking of very rotten bamboo). And the question was there, the George Washington Carver association—why hadn't something been done with the shell?—every time I shelled a peanut. Just as the Booker T. Washington story was associated with the making up of beds. But—no doubt because of the path my studies had taken—I had never heard of George Washington Carver in the wider world. I had never heard of him outside that elementary school of mine; and I had grown to feel, not that he was a black fantasy figure, but that he was someone whose achievements had been exaggerated by local pride, just as the Trinidad _Guardian_ exaggerated the doings of local people in metropolitan places. I had never associated George Washington Carver with Booker T. Washington and Tuskegee. And now they were both there, both real, in a wonderful physical setting, with a whole museum named after George Washington Carver. It was in 1941 that the museum had been opened; in 1941 that Henry Ford had come and made the offer of the elevator; and that would almost certainly have been the year in which, in my elementary school in Trinidad, when I was eight or nine, I had seen the frightening film (probably provided by the American consul) about the black family in a hut and the white horsemen outside. All now cleared up, as I read the leaflets of the U.S. National Park Service, which had taken over both the Carver Museum and the Booker T. Washington house as historical sites. He had been born a slave, this George, and he had belonged to a man called Carver. He had been born in 1861, perhaps, during the Civil War; and he had been kidnapped, together with his mother, by people who kidnapped slaves in one state and sold them in another. George had been recovered from the kidnappers and returned to the Carvers, but George's mother was never found. George educated himself. In 1897 he came to Tuskegee, and there he stayed for the rest of his life. In addition to his agricultural research, he collected clays for paints; painted pictures; did needlework. He taught Sunday school. He had a high, feminine voice. In the museum there was a recording you could listen to of Carver reciting what was said to be his favorite poem: Figure it out for yourself, my lad. You've all that the greatest of men have had: Two arms, two hands, two legs, two eyes, And a brain to use if you would be wise. Photographs showed him to be tall and thin, spare-faced, handsome, unusual. Louis Harlan, in his biography of Booker T. Washington, has little to say about Carver, and that little is not always good. He was quarrelsome, according to Harlan, and deferential to white people. But perhaps the world picture of a not very masculine man, who had been kidnapped as a child and separated forever from his mother and had then had to depend on a kind and loving former owner, could only have been a slave's world picture. And perhaps, within that world picture, Tuskegee had been for him a kind of lifelong sanctuary. SANCTUARY IN Alabama—this was how after a while I had grown to think of Tuskegee in the days of segregation. So many of the people I met had been in Tuskegee for much of their lives. And though this might have been fortuitous, many of the old residents were light-skinned people, some of them almost white, courtly, polished people, who would have been dreadfully wounded by the indignities of the world outside, and even now, in their old age, didn't wish to drop their guard. But the idea of sanctuary—when I put it forward in connection with George Washington Carver—was rejected by an old campus man. He said that Booker T. Washington hadn't been concerned to offer anyone sanctuary. When he had asked Carver to come to Tuskegee, it was because, as always, he wanted the best for his school. Not a sanctuary; the word this man preferred was "oasis." "When I got here, in the twenties, there were no paved roads. The whole area, the Black Belt, is a poor area, and Tuskegee was really an oasis for blacks. In all kinds of ways. There was the academic atmosphere. The campus was pretty, comparatively. We weren't subjected to the sort of life black men were enduring in the rural areas, especially during the Depression. We had running water. We had food in the cafeteria. We had security. If I had been thrown out into the 'real world,' it might have been different. I might have become more aggressive—I can't tell what I may have done. "It wasn't a conscious thing in my mind to seek safety. It was just the way my life developed. Though this environment did provide a lot of protection to the person against a lot of things that a person was subjected to in those days—I mean blacks. In the outside world we didn't have the same protection under the law that whites had. The moment you stepped off this campus you were subjected to all of the indignities. Everything was segregated. "We were all aware of what the white attitude was, and we were unhappy about it. The most terrible thing was that you didn't know when it was ever going to end. But it wasn't something we dwelled on at the Institute." And the elderly man who drove me round the campus, to show me the extent of it and to explain the stage-by-stage development of the place, and then drove me round the modest town, all black now—this man told me that in the old days a black man, even in a car, wouldn't have been wise to hang around the Lake Tuskegee area. Indignity outside; within the campus, the erect posture, the military correctness. Yet always—and how the irrationality would have twisted people!—it was necessary to make signals to the people outside that you were not getting above yourself. Mrs. Guzman, who came to Tuskegee in 1923, and worked for many years on _The Negro Yearbook_ , recalled that the old school chapel was also a little cultural center for the town, with movies, concerts, speakers. "The white people in the town came. They were given the best sets in our chapel, the front seats. A lot of the students and faculty resented it. But that was the custom. Whites sat in front, and Negroes behind them. When a younger president came in and stopped that, the white people stopped coming." But what would have looked like old-fashioned servility in the 1920s and 1930s would have been simple prudence in the days of Booker T. Washington. And perhaps some intuitive wisdom, some kind of peace offering to the people outside, who might so easily have crushed the black institute, lay at the back of Washington's insistence that everyone should learn a trade. It encouraged a misunderstanding of the school outside (and perhaps that didn't do any harm). Some people thought of Tuskegee only as an industrial, vocational institute. (Louis Harlan says that white people sometimes wrote to ask for trained servants; one man wrote in for "a full negro," very black, to take to France. All these letters were acknowledged.) There was a good deal more to it, of course. Ruskinian or Tolstoyan ideas about manual skills, anti-industrial crafts, the training of the hands, were very much in the air in the latter part of the nineteenth century. Ruskin was certainly at the back of Gandhi's mind when, in South Africa in 1904, he established his Phoenix Farm (burned down by African rioters in 1986). And though the two men were so different—Washington the American with little time for Africans or Asiatics, Gandhi the spiritually adrift Hindu with little time for Africans—there was a remarkable coincidence in their aim and method: the inculcation of self-respect in a subject people through the idea of work and service. And, interestingly, a number of the old people I spoke to in Tuskegee seemed to have found some kind of beauty and content and human completeness in the trades they were taught. The old musician who had come to Tuskegee as a boy in 1913 learned shoemaking. (Tolstoy liked to do a little cobbling in his study sometimes.) The old man said, "I could sew on a pair of soles in twenty minutes by hand. A lot of people don't know I know that trade. They know me only as a musician." Mr. Louis Rabb—who did business administration at Tuskegee and then went on with Tuskegee grants to do personnel administration at Columbia and hospital administration at Northwestern, and afterwards had a long and distinguished career at Tuskegee—Mr. Rabb did tailoring for four years at the Tuskegee high school when he came there as a boy from Mississippi. His father chose that trade for him, and Mr. Rabb told me with a certain amount of quiet pride that he still sewed for himself. But outside the Tuskegee oasis the world was grim. On one rack in the library were the Booker T. Washington file boxes. On another rack were sixty-three file boxes labeled LYNCHING RECORDS. To take down the Washington files for part of 1903 was to feel even greater admiration for the man. So many letters from simple people—letters in pencil, some of them, letters on scraps of paper, letters shot through with need and hope—so well kept, so fresh, after more than eighty years. Every one had been read, acknowledged; and many of the carbon replies had the initials "BTW." I noted a schoolteacher's letter from the island of Jamaica, many pages long, in a neat schoolteacher's hand (clearly a "fair copy"); another letter from a black woman on the island of Tobago. Perhaps these letters in the Tuskegee files were the only relics now of these people. On narrow slips of pink paper there were initialed mauve carbon copies of Booker T. Washington's famous little notes to Tuskegee staff, dictated to his secretary during his walks about the campus or after his horse rides around the campus. And there were the more political letters to people in Washington, dealing with issues hard for the uninformed to understand. There are so many aspects to a life; so much gets lost. How had such method and punctiliousness come to a man who had started so late and with so little? Perhaps one of his secrets was an absence of sentimentality. The letters from simple black people had moved me. Booker T. Washington might have been more hardheaded. He knew that people just freed from slavery hardly had an idea of education and often saw it as a means of avoiding physical work. He knew that many black people who could barely read had turned to preaching, for the easy life it offered. He had often ridiculed such people. In _Up from Slavery_ he had had such a half-educated black say, "O Lawd, de cotton am so grassy, de work am so hard, and de sun am so hot dat I b'lieve dis darky am called to preach!" Extraordinary, this minstrel joke from the founder of Tuskegee. But the fact that he could make it, while never ceasing to fight for his cause, might have been part of his genius and toughness. And there in the library was the reminder of the setting: the sixty-three boxes of lynching records. I dreaded to look at them. I thought they might have contained unofficial investigations or statements and would have been full of unbearable things. I was relieved, when I took down a box, to find that the records were mainly newspaper cuttings. It was that kind of hostility that had given point to Tuskegee from its simplest beginnings. And as much as this hostility had frustrated some of the Institute's imaginative plans—for agricultural extension work among black farmers, for instance—so it had stimulated the Institute's growth, even after Booker T. Washington's death. Segregation and hostility, defining black needs, had also helped to define the Institute's goals, and given logic to the Institute's growth. When segregation went, there was nothing to pull against; the function of the Institute could no longer be what it had been. When black men could join the air force, there was no longer any need for them to learn to fly at Tuskegee. When black people could be admitted to the hospital at Montgomery, one of the best in the United States, there was no longer the same need for the hospital at Tuskegee. The town—where once black students had worn their Tuskegee uniform as a kind of protection—was now safe: when black people had won the vote, the white people of Tuskegee had moved away. So there had been a kind of victory here. But the town that had been taken over was small and poor, black-poor, with nothing of the life and money of the white university town of Auburn, just twenty miles away. And Tuskegee Institute, now Tuskegee University, which could be said to have contributed to that local victory, was in decay. The swiftly changing impressions I had had at the moment of arrival—the grandeur, the rhetoric, the decay—had endured and been amplified. President Reagan had visited the university not long before to inaugurate a new $18-million building for aerospace science and health education, named after General Daniel James, the first black four-star air-force general, who had graduated from Tuskegee in 1950. The campus roads of the presidential route had been asphalted for the occasion. But the roads elsewhere were not so good, and the broken glass globes of electric standards in other parts of the campus had remained broken. And no one I spoke to (though I spoke to no official) could assure me that the university could afford a faculty to match the splendor of its aerospace building. Decay was melancholy enough to me, a visitor, a man passing through. It wasn't a subject I felt I could raise with older people who had given their lives to Tuskegee, who had received so much in return, and to whom the Booker T. Washington spirit of service and self-help had mattered so much. And the subject didn't come up. Were there tennis courts? Yes, there were: just at the back of the library. But grass was growing through the asphalt surfacing of two (or three) of the courts. A kind of silence was imposed on the visitor, as in a private house; certain things were not to be seen. The subject of decay came up more easily in places where people felt more secure—in the veterinary department, for instance, which was said to be among the best in the country, and behaved as though it was. A department like that, successfully lobbying for federal funds (it had recently been granted 36 million for a new project), could survive on the basis of its own excellence. But for other departments it was not so easy. Now that good black students and faculty were in demand by universities all over the country, Tuskegee no longer had a special claim on government or foundation funds. The millionaire philanthropists of the North whom Booker T. Washington had charmed no longer existed; that way of doing things was over. But there were people who thought that Tuskegee still had its special cause to serve. Black students didn't score as well as others in the standardized university-entry tests. Tuskegee had always been ready to take in such students, and its record showed that it could train such people for the world of work. One retired official said, "Tuskegee will take a student as it finds him academically and socially, and through individualized attention and concern will bring that student in four to five years to his full realization." There was another, and perhaps more important reason why some people thought Tuskegee was still needed. Tuskegee was still in effect a black university, and it could provide a "black experience," which, with desegregation, more and more black people appeared to feel they needed. In Florida Mr. Crockett, the Parole Board commissioner, had told me how he had felt he had to take his son out of a too-white setting; he had sent the boy first to a black high school and then to Tuskegee. And I heard now, from a pretty woman of twenty-three who came from a distant state where there were few black people, and who would have made her way in any university, why she had come to Tuskegee. "The schools I went to in the other place were all-white. They don't concentrate on your being a black person. They give you some of your history, but not a lot. In the other place you try to push, thinking, 'If I can be like them I'd be all right.' You lose yourself a little bit. You're not really sure who you are." "What was your very first impression when you came here?" "My very first? 'Go back home.' After coming from a nice city, metropolitan, nice facilities, stores, shopping malls. After that, here, seeing little dirt roads—they're not _dirt_ roads, but some places they don't have sidewalks. At home I was used to being able to go downtown a lot, used to going places. Here there was no bus service. When I got here I realized, 'There is nothing to do. Oh my God, I'm trapped here and there's nothing to do. And it's hot and humid.' I think people here are real _country_. They're closed. They're friendly, but they have their little country ways." And the accommodation wasn't all that it could have been. "Some of the places are dangerous. There are things to be fixed, doors to be fixed. There are light switches upside down. I notice these things, being from where I come, a pretty place, where they do things prettily, nicely." But clearly there was a reason why she had stayed on. "It was _my_ idea to come here. My mother didn't want me to leave home. I wanted to be in an all-black town, to be not in a minority but a majority. And that is one thing I do like about being here. Sometimes in the other place you go into a place and you're the only black person there. But here, when you go into a business, the owner or the manager will be black, the workers will be black, and it helps you to feel you can progress after your goals and accomplish them. "Here you are in competition with your own kind. And they can be hard on you, because they're trying and you're also trying. At home I used to be a C-D student. Here I'm an A-B student. I get encouraged seeing other people doing things. And here that happened. I'm ready to leave now. I would probably like to go to another black college, maybe in Atlanta. But it doesn't have to be black any longer. Tuskegee has served a purpose." It was a version—a century on—of the Booker T. Washington idea. For this young woman (and there were others like her) the Tuskegee idea still held. Yet she said she had known almost nothing about Booker T. Washington before coming to Tuskegee. She had known only that he was a black man who had done something famous long ago. A month after she came she read _Up from Slavery_. "The teachers here encourage you to find out about the school, and you appreciate it." Tuskegee was still a going concern. It had a devoted community; and it still had heart. Its financial predicament was the predicament of black schools generally; and it was better off than some. Its physical condition was very far from that of Fisk University in Nashville, Tennessee, where in parts the campus looked ruined. There was a melancholy bronze statue there too, at Fisk, meant to set the seal on glory, but now seeming to watch over the ruins. The statue was of W. E. B. Du Bois, the rival and critic of Washington. Du Bois thought that Tuskegee's emphasis on vocational training was wrong; and that Washington's apparent acquiescence in segregation and black disenfranchisement could only lead to further humiliation. Was there an alternative, though? And mightn't it be said that Booker T. Washington's great achievement, his great service to black people at that time, was simply being very famous and admired? One can read books and documents, but it isn't easy imaginatively to reenter that bitter time, and to have a sense of the weight for black people of day-to-day life. The quarrel or debate between the two men, Du Bois and Washington, both mulattoes, is famous. Du Bois might seem closer to contemporary feeling. But his best-known book, _The Souls of Black Folk_ (1903), a collection of essays and articles, is a little mysterious. The very title of the book is strange, even whimsical. The lyrical, mystical tone (mixed up with social and economic facts, and sometimes a little romantic fiction) calls to mind some of the essays of the late-nineteenth-century English country writer Richard Jefferies (1848–87). (This is the lyrical Du Bois: "I have seen a land right merry with the sun, where children sing, and rolling hills lie like passioned women wanton with harvest. And there in the King's Highway sat and sits a figure veiled and bowed....") I even have the impression that Du Bois might have been trying to do for Southern blacks what Jefferies had done for farm people in the south of England. There is an uncertainty in both writers about their relationship with the people they are writing about. Jefferies, in spite of hints that he might be socially all right, was the son of a small farmer, and almost a laborer; Du Bois was a mulatto. The Jefferies model would explain Du Bois's occasional evasiveness and too-pretty ways with words (using the poetic conceit of "the veil," for instance, for segregation). If Booker T. Washington can make a darky joke, Du Bois can speak of "the joyous abandon and playfulness which we are wont to associate with the plantation Negro"; can say, "Even today the mass of the Negro laborers need stricter guardianship than Northern laborers"; and he can ask, "What did slavery mean to the African savage?" But we can read through both the Du Bois way of writing and the Booker T. Washington manliness to the facts of Negro life of the time, and see the difficulty both men would have had in defining themselves, and establishing their own dignity, against such an abject background. As if in resolution of that difficulty, Du Bois's book seems lyrical for the sake of the lyricism. It can appear to use blacks and ruined plantations as poetic properties. It deals in tears and rage; it offers no program. In this beginning of Du Bois there was also his end. He lived very long, and towards the end of his life—facing irrationality with irrationality—he left the United States and went to live in West Africa, in Ghana, a former British colony that had in independence very quickly become an African despotism, and was soon to revert to bush and poverty, exporting labor to its neighbors. At the very beginning of the century, in _Up from Slavery_ , Booker T. Washington, in his late-Victorian man-of-the-world style, had cautioned against just that kind of sentimentality about Africa. "In the House of Commons, which we visited several times, we met Sir Henry M. Stanley. I talked with him about Africa and its relation to the American Negro, and after my interview with him became more convinced than ever that there was no hope of the American Negro's improving his condition by emigrating to Africa." On this journey I read _Up from Slavery_ twice. On the second reading, after I had been nearly four months in the South, I found that the book had changed for me. It became more than the fabulous story of a disadvantaged man's rise. I began to see it as a painful coded work, making separate signals even in a single paragraph to Northerners, Southerners, and blacks. I also began to see the book as the work of a man constantly concerned to raise funds for his school. That should have been obvious to me always, but it hadn't been; that had been swept away by the power of the fable. Below that primary appeal, however, there were others: the man of the world appealing knowledgeably to the very rich on behalf of the wretched, representing himself as honorable and worthy and manly and educated; yet at the same time taking care to do the contrary thing, and making it clear that as a black man he knew his place. Hence his confident, socially knowing talk, like any solid late-nineteenth-century citizen, of the "best people" and the "vices" of "the lower class of people." But he is mortified when, on a train journey from Augusta to Atlanta in Georgia, in a Pullman car "full of Southern white men," two ladies from Boston, "ignorant, it seems, of the customs of the South," insist on inviting him to supper. The meal seems very long. As soon as he can, he breaks away from the ladies to go to the smoking room, where the men now are, "to see how the land lay." It is all right; the men know who he is and are anxious to introduce themselves to him. In England he develops a high regard for the aristocracy and the time and money they devote to philanthropic works. He is impressed by the deference of servants, who are content to be servants all their working life and, unlike American servants, use the words "master" and "mistress" without any constraint. In that ambiguous observation there are consoling messages both for blacks and Southern whites. He becomes friendly, he says, with the Duchess of Sutherland. She is a famous beauty. But as a black man he will be out of place to say so directly. He writes, "I may add that I believe the Duchess of Sutherland is said to be the most beautiful woman in England." So many snares; so many people to please; so many contradictions to resolve; so many possibilities of destruction. The achievement was great. But at what cost. He died at the age of fifty-nine. TO THE west, on the road to Mississippi, were shabby small settlements, like an extension of the poverty of the town of Tuskegee. I spent the night on a timber plantation on the border. There was still something like presettlement desolation there: cypress trees, half stripped of leaves, their bald knees rising out of muddy water like a kind of humped aquatic animal; shifting swamps, with forest litter at their margins; great damp heat. The land was not old. Tuskegee had been settled only in 1830. Two months later I entered Alabama again, but from the north, driving down from Nashville in Tennessee, down from the hills to the flat land around Huntsville. Huntsville was where space research and the industries it had attracted had created a whole new landscape in the South: wide boulevards, low, flat factories, spacious grounds meant only to please the eye. Huntsville was also near where, in 1873, the first State Normal and Industrial School for Negroes had been set up in Alabama. That past had been swallowed up—though cotton still grew at the very edge of the new industrial town. From the NASA museum—full of Asian visitors, Indians, Chinese ("coming to look at the place where they intend to work," as the Southern businessman with me said)—Tuskegee seemed to belong to another age, to exist in a melancholy time warp. It made one think of the prisons of the spirit men create for themselves and for others—so overpowering, so much part of the way things appear to have to be, and then, abruptly, with a little shift, so insubstantial. # 5 # JACKSON, MISSISSIPPI # The Frontier, The Heartland EVEN IN Alabama—the repeated vowel sound of which seems to be a mimicking of "ma mama" or "ma mammy" and (because of all the songs) carries suggestions of banjos and black men and plantations—even in Alabama I found that Mississippi had a reputation for poverty and racial hardness. But the black (really brown) pharmacist at Tuskegee also told me that my asthma would abate the farther west I got. And, true enough, after the heat and humidity of Tallahassee (made worse for me by the glass tower in which I had been staying, the western wall radiating heat from early afternoon), and after the enclosed hot air of the upper corridor of Dorothy Hall in Tuskegee (where at times, after climbing the steps, I felt the heat catch in my throat, and I couldn't breathe until I got to the comparative coolness of my room), I began to revive in the air-conditioned air of the Ramada Renaissance hotel in Jackson, Mississippi. The air-conditioning system was silent; the tinted glass of my window shut out glare as well as traffic noise. All around were great highways. To the east the city was green, trees hiding the better-off housing developments. To the northeast was a big new shopping area. Pleasing views: hardly the poverty I had been fearing. And I was grateful to the city for ridding me, as if by magic, of the constriction in my lungs. But, of course, there was another side to Jackson, there, in its very center. And on Sunday afternoon it was easy to see, in the streets without business traffic. The inner city was black. There were streets of "shotgun" houses. It was the first time I had ever heard the expressive word: narrow wooden houses (like mobile homes or old-fashioned railway carriages) with the front room opening into the back room and with the front door and back door aligned. On Sunday afternoon the people were out on the streets, so that the effect of crowd and slum and blackness was immediate: as though outdoor life, life outside the houses, was an aspect of poverty. At a street corner, on an open lot, in the hot midafternoon sun, there was a prayer meeting. It had no audience. Everyone there was a performer. The women were dressed for Sunday, and the men were in suits and ties, except for the pastor, who was in a white gown. This was the West Jackson Crusade of the Saint Paul Church of God in Christ. It was an occasion of music and dance. Many of the people in that dressed-up group were to have the chance to go to the pulpit or to hold the microphone and sing. The songs seemed to be variations on a single line. What would I do without Jesus? That was all that a middle-aged man in a brown suit was singing, leaning on the pulpit and bending over the microphone in a confiding manner, as though he had a large audience, instead of no one at all (save the people in our car). What would that man have done for a living? What would have been his true—or his other—occupation? The leader of the chorus was a big woman in a white dress. She stood a little way in front of the chorus. She was distinguished from them by the plain white of her dress, her size, and her voice. When her turn came to use the microphone she didn't go to the pulpit. She took the microphone on its cord and sang from where she stood: Don't let nobody turn you round! That was her line, and the variations on it seemed to come naturally. Don't let— Don't let nobody— Don't let nobody turn you round! And the group danced. Among the dancers were three small boys. One of them stood in front. He was very small, perhaps five or six, and he was in long trousers, with suspenders. The two other boys were bigger; they were at the back; and the dancing—all the intricate and inventive things they did with their legs—seemed to come to them in fits. At one moment they were like children at a grown-up occasion, indifferent and far away. And then suddenly they were possessed. The dance rippled through them. And then just as suddenly they came to the end of their dancing, even while the singing was going on, in the middle of a line of the song of the woman in white; and they returned to what they had been doing, their apparently childish concerns. The pastor, in his long white gown, danced while the woman sang, the disturbance of his gown, from his dancing on the spot, creating its own rhythm. They were not the only religious group active in West Jackson that afternoon. The bus of another group passed by, a bus painted white with thin red markings. And after that bus had passed, I saw, a few house plots away from the dancing evangelical group, another boy dancing, this time with a black neighborhood dog, the boy holding the front paws of the dog. When she had done with her singing, the young woman in white came across to where our car was. She was perspiring at the top of her forehead from her dancing in the afternoon heat, the heat added to here by its reflection from the streets and buildings. She asked, honey-voiced, whether we were witnessing the service, and she gave a tract. In the tract there was a photograph of the pastor, not in his white gown and with his cross, not in a pose suggesting the rhythm of his own dance, but in a jacket and tie, studious, looking past the photographer. He was the Elder Jesse Kelly. In addition to being pastor of his church he was "founder of the West Jackson Crusade, local announcer of WOAD, graduate of JSU," and "presently working towards a Masters of Divinity at Wesley Biblical Seminary." Some story—like that of Danny or that of Reverend Clausell in Tallahassee—might have been behind this religious call, which included (according to the tract the woman in white had given) a Sunday school, a nightclub ministry, a radio ministry, a street ministry, and tent services. The music and the singing held us; the dancing held us; we could marvel at the religious dedication. But we could only be witnesses; we couldn't participate. And the approach of the woman in white, in fact, made us think of leaving. At the side of my grandmother's house in central Trinidad there was a tall gate, of corrugated iron on a timber-plank frame. This was the main entrance to the house and yard. One of my earliest ideas—when I was six or seven—was that there were two worlds: the world within, the world without. To go out of that gate was to be in a world quite different from the one in the house; to go back through that gate at the end of the school day was to shed the ideas of the world outside. Everyone lives with ideas like these; everyone has different sets of behavior. But in a racially mixed society, especially one where race is a big issue, the different worlds have racial attributes or overtones. Distinctions and differences can have the force of taboos—things sensed rather than consciously worked out. In such a society participation is different from witness; they engage different sides of the person. And it was with—old—relief that I put an end to my pleasure in the singing and dancing of the West Jackson Crusade, and returned to the silent healing of the air-conditioned room of the Ramada Renaissance in the north of the city. IT WAS my wish, in Mississippi, to consider things from the white point of view, as far as that was possible for me. Someone in New York had told me that it wouldn't be easy. In Mississippi, though, I found that people were defensive about their reputation. This seemed to give me a start. But then I wasn't sure. How quickly, for example, I appeared to get to the limit of Ellen's ideas and memories! She was sixty, of a good family. She had liberal attitudes; and it seemed hard for her to go beyond a statement of those attitudes. She said: "I feel we've been through a revolution in Mississippi since the 1960s. It was like two separate societies here. Now black people have much better jobs than they had. Instead of everybody having to work in a home—I'm talking about women—now they're working in McDonald's or a bank or a store." And there we stayed for some time, Ellen—perhaps because I wasn't being acute enough, or because I hadn't yet learned to talk to Mississippi people—not appearing to say more than that. I even put away my notebook. She was gentle, welcoming, anxious to talk. But I couldn't find questions to put to her. Her optimism, her idea of progress and change, covered nearly everything I could think about. We got finally to talking about her childhood. And that was when I took my notebook out again. "I grew up in the Depression. But I didn't feel badly about myself. Everybody else was poor too. The reason I didn't feel badly was that I had a lot of aunts and uncles and cousins and all—a large extended family, but I didn't know you called it that. They loved me and had time for me. I would go out and spend summers with them. They always had time to talk to you and fix your favorite foods. They even made me dresses." That idea of a small community, where everyone knew everyone else and people were related—I had found that for many people it was part of the beauty of the ways of the past. I asked Ellen, "Where did those uncles and aunts live?" "They lived in the most conservative town in Mississippi." Happy summers in a small conservative town. What lay outside the family group? What did Ellen feel as a child about the rednecks? Was there really such a thing as a "redneck mentality"? There was. She acted it out. " 'Don't mess with me.' " She raised her slender arms in a boxing posture. "A fighting mentality." But she had been protected from that. "I had an aunt who read a lot to me. She had a lot of books. Actually, she was the postmistress. She encouraged me to be my best self. I guess this sounds snobbish, but she would say, 'Ellen dear, there are some things we just don't do.' There were some _people_ we just didn't go around." She returned to the topic of the love she had experienced in her childhood, the love that had partly made her. "It helped me to have a positive self-image—though that wasn't the way we talked about it then. I think people still have scars from the Depression here. It seemed to me like it was very bad here. There just weren't any jobs. My sister was older than I and she suffered more than I, but that was because she had had more to begin with. She had things that were lost. I just grew up poor. "I became more proud of being a Southerner when I got away from the South. My husband went to school in the East, and I worked. This was after World War II. At that time we had a politician, a senator called Bilbo. Bilbo was a racist, and he was advocating sending all the blacks back to Africa as a solution to the problem; and he was absolutely admired by the people of Mississippi, I guess. But he was absolutely hated by the people I worked with in Massachusetts. This was a psychology group I worked with. They were doing research in group dynamics—prejudice and so forth. "That was when I began to look for things that were positive about the South and Mississippi. I thought about the people. And I thought about the hardships we had been through—and you can't expect people to act perfect when you think of all the things they've gone through. The people in Massachusetts—in 1946—they could act surprised that someone from Mississippi could read and write and we 'wore shoes.' It's still true in some places. People have a very, very bad impression of Mississippi. But it's changing." "Is it because of the writers?" "The writing grew out of the dirt and this love of talk, talk." And, going back to her time in Massachusetts, Ellen said: "The people I worked with, they wanted to know if I would really do this. There was a black man visiting, and guess who they got to show him around? Well, I showed him around. He was a lovely person. I learned from him. I think they were surprised. They never did say it. I never gave them the opportunity. Do you see how far we've come?" But there was Mississippi's reputation for violence. "The rednecks to the south of the town were just mean. They had the reputation. They were very pugilistic. There were stories about them. Like, if a traveling salesman came through, they would hitch him to the plow and have him plow all night. I don't know if that was fact or fiction. They would get drunk on Saturday night and fight each other and kill each other off. That's really the worst part of Mississippi. It just had a bad reputation. But out of that group there grew some fine outstanding Mississippians, including some fine clergymen. It shows that there's hope, doesn't it?" And there was also the racial issue, never to be forgotten in Mississippi and the South. "I played with my cousins, and we played with black children, too. They were the children of the servants, the washerwomen and so on. That's why I think Southerners have a better feeling about black people than the Northerners. We called them Negroes—'black' is a new word. I've gotten used to it. We didn't use 'nigger' in my house." I didn't ask Ellen about the words, or prompt her; what she said came out naturally. "My relatives didn't call people niggers either. I guess they had a little more civility than that. Even though they lived out in the country." For the third or fourth or fifth time Ellen said, "I grew up in a loving environment." A memory came to her. She had been breaking off to say that our talk had begun to make her put things together, call up old things. "My daddy liked to fish. He took me fishing. I don't think I have as harsh attitudes"—and she meant racial attitudes—"as some people, because of that." She broke off again and smiled. "My summers in the country are important, aren't they?" "How many summers?" "It's more like the first twelve years of my life. I know I feel differently from some other people, but I just don't know why." "Religion?" "I do think my religion makes the difference, and the feeling that we are all made in God's image. Probably not as a child. I'd have to have more understanding to think that." Then she said, "And these stories about people doing mean things." Mean things, in a loving childhood? Ellen said—memory working, unrelated pieces of the past fitting together, as she said they had begun to do while she talked, answering questions that had never been put to her before—"My mother told me about hiding her maid from the Ku Klux Klan. It shows just how far we've progressed. My mother had a maid. Her name was Mollie Wheeler, I think. And the Ku Klux Klan was trying to get her. I don't know why. My mother didn't talk very much about it. I think the Klan wanted to give the maid a good beating and send her away for some reason. My mother said she hid her in a laundry basket in her house to protect her. Of course they wouldn't come into my mother's house. This was really before I was born. They—the Klan—they were probably young men, OK people in the town." "Didn't this frighten you?" "I don't think it frightened me. It gave me a great sense of disgust for something like the Klan." She added, "The rednecks—that story I told you, it probably happened before I was born." And I understood what Ellen was saying better than I said. No situation or circumstance is absolutely like any other; but in the Indian countryside of my childhood in Trinidad there were many murders and acts of violence, and these acts of violence gave the Trinidad Indians, already separated from the rest of the island by language, religion, and culture, a fearful reputation. But to us to whom the stories of murders and feuds were closer, other things were at stake. The family feuds or the village feuds often had to do with an idea of honor. Perhaps it was a peasant idea; perhaps this idea of honor is especially important to a society without recourse to law or without confidence in law. Imagine this scene in a Trinidad Indian village of the 1920s or 1930s. A village big man, say, is murdered. The next morning, after the legal formalities, the body is displayed in a coffin, which is perhaps set out on two chairs on the road outside his house. This is a statement of defiance by the family of the murdered man. Among the people coming to pay their respects is the killer. He has to come; he cannot stay away; and he is almost certainly known. And now two men's lives are spoiled: the killer's, and that of the relation of the dead man who will have to kill the killer. The code demands no less; it isn't open to a man who wishes to be at peace with himself to walk away. So deep, for me, was this idea of honor and the feud that the film of _Romeo and Juliet_ (with Basil Rathbone) was one of my earliest true theatrical experiences, the story to me being not so much a story of love as of the family feud. What fear, what horror at all that was to follow, when the blood darkened the shirt of Mercutio! Honor—that was what I understood, or saw, in some of the murders around us. Not the barbarism that, as I understood later, outsiders attributed to us. Some such way of feeling I attributed to Ellen, in her childhood in the small town where she had spent such happy summers with her extended family. Violence, where it existed, would not have appeared to her as naked as it would have done to absolute outsiders. Too many other things were attached. Violence then; and there was violence now. The violence of her childhood had been white. The violence people spoke of now was black, and was of the cities. She said: "I think it's just the frustration. So much of the violence is now in the black community. The black people don't like me to say this, but if you go to the penitentiaries you'll see it's true—a high population of young blacks." How had she arrived at her civility, her calmness, her wish to be fair—in a state with the reputation that Mississippi had? She said: "I went to college. I think that made an impression on me. I had a very good professor. They took a personal interest in you. And my father died when I was young. I was barely thirteen. That was when I started looking at myself and other people. I think I had to grow up too soon. I was living in a small town. My father didn't leave a lot of money for us to live on. And so my mother had to go to work. She was a nurse, and she went back to work. And I—I went back and lived with my aunts, to go to school, in that same little country town. My mother worked very hard to send me to college. She was very successful in her occupation. She was a strong woman, and she believed in fairness to all people. When she was in training she nursed everybody. She grew up with a great regard for all people." Abruptly, then, out of random memories that were coming to her, Ellen said: "This story really did impress me. I was talking about it to one of my relations not long ago. This really happened, and I was there. I was eight. I was visiting my aunt, and she had a wonderful maid; and several of my cousins were there. Myrtle—the maid—played the piano. She could play anything by ear. She kept all us children entertained with her music and everything. One time she had a little roadster car and she took us riding. And we really loved her. She was a black maid. Maybe one of her boyfriends gave her the car. She was quite a girl. She wore bright lipstick and she had a big gold tooth in front. "Anyway, she was missing one day. She lived in a house behind my aunt's house. And finally they went out to see about her. And they found her, and she was dead—in a wardrobe, upside down. She had been hit on the head with a pine knot. They called it a lighter knot—it was to start fires with. They thought it was one of her boyfriends, but we never knew. It was awful. I knew that was wrong. My aunt was grief-stricken. I think that if it had been a white woman killed like that, they would have found out who did it. But I think that's something I'm thinking now. I don't think I thought that when I was eight years old. To me Myrtle was Myrtle. I didn't think of her being black. She would snap her fingers and dance." And Ellen, remembering, sitting in her upholstered chair, made a gesture and snapped her fingers too. "She was just a lot of fun. She was the daughter of the woman who went from house to house doing the laundry. They did it in great big pots. This was before rural electrification, when they started having running water in most of the houses. My aunt had running water and a bathroom inside, because my daddy had built a water-tower when he had lived there—before I was born. "I went back to her house." Myrtle's mother's house, at the back of Ellen's aunt's house. "They had removed her body. But I saw where it was. That was just nosy. My aunt didn't want me to go see it. But I wanted to, and she let me." What a story, from a memory of twelve happy summers! And that story released another memory in Ellen. "My mother and father used to tell me about when they would hang people in the courthouse square. Legal hangings, not lynchings. That was when my father and mother were children. And my daddy was born in 1897. And that was just abhorrent to me—and it was to them. These were stories that people would tell you as you were growing up. I think we've come a long way. It seems like people are becoming more civilized, I hope." The stories told to Ellen as she was growing up were frontier stories; that was how I regarded them. They had echoes of any number of Western films; and it was remarkable to hear them from someone who had just turned sixty. In one lifetime, then, it seemed that she had moved from frontier culture, or the relics of a frontier culture, to late twentieth-century Jackson and the United States. It gave a new cast to my thoughts, and a new cast to my conversation with people. There are some film directors who prefer to work in natural light, the light that's available, the light they find. And travel of the sort I was doing, travel on a theme, depends on accidents: the books read on a journey, the people met. To travel in the way I was doing was like painting in acrylic or fresco; things set quickly. The whole shape of a section of the narrative can be determined by some chance meeting, some phrase heard or devised. If I had met someone else my thoughts might have worked differently; though I might at the end have arrived at the same general feeling about the place I was in. Ellen's thoughts, just before we separated, were of her father, who had died when she was thirteen. "My father told me you never got ahead by stepping on somebody's back. We all need to come up together." That had been the great discovery of my travels so far in the South. In no other part of the world had I found people so driven by the idea of good behavior and the good religious life. And that was true for black and white. MY THOUGHTS were running on the frontier, the life at the extremity of a culture. And I went early one afternoon to see Louise, nearly eighty and living alone in a big house in Jackson, in a garden too much for her now, and dry after many weeks without rain. In her old bookcase, American work from perhaps 1840, cherry-wood that had taken on a lovely deep color after nearly a century and a half, there were small, leather-bound volumes of an edition of _The Spectator_ —of Addison and Steele—issued by a Philadelphia firm in 1847. A reminder of the colonial past here, of an idea of civility and education so at odds with the world around. A reissue in 1847 of _The Spectator_ —American publishers having in those days the camp-following attitude to English books that English publishers today have to American books. _The Spectator_ , a hundred years out of date, at the time when Parkman was making his journey on the Oregon trail and coming across reminders, almost as terrible as bones, of the settlers who had passed that way: abandoned furniture, pieces perhaps of the early 1840s, like Louise's bookcase, which those settlers had loaded onto their carts and wagons, hoping to take them to the West. In a drawer of the cherrywood bookcase there were documents and copies of documents connected with Louise's family history. Her family went back to colonial times. Her husband's ancestor came from Pennsylvania. He came to Mississippi in about 1820. "All wilderness, you know." He was part of a group, families who had intermarried. They hadn't come directly to Mississippi. "They had traveled together in their migration through Georgia, Tennessee, and Alabama." She gave this idea of the kinship of the migrating group: "When the two young men"—her husband's ancestor, and another man in the group—"were of an age to marry, they went up to Oxford"—the Mississippi Oxford, in the hills to the east of the Delta, the flat alluvial river plain—"and married two Tankersley girls they had met." The Tankersleys were one of the families of the migrating group. "The land hadn't been cleared and travel was hard. And when they got there they stayed. "My grandfather was a sixteen-year-old boy when he went to the Civil War and fought at Shiloh in Tennessee. He survived it, and came back to northeast Alabama and started his family. Things were hard after the Civil War, and then my grandfather died. My father left home at the age of fifteen and came and stayed with an uncle in the Delta in Mississippi. He had some education, and he paid a Baptist minister to teach him bookkeeping, and he opened a little store and began buying land in the Delta. _And it was beautiful country_. Now it's one big cotton patch—all cleared and drained. But then it was like William Faulkner's 'Bear,' one of his finest pieces of writing. It was just wilderness country—great oaks that had not been harvested. This was before the plantations. It was just gorgeous. "It was a land of flowers, all kinds of wild iris and wild violets, water lilies and alligators. They were just beginning the plantations in the Delta. It was hard. You see, we had malaria. I had malaria every summer when I was a child. It took a little while to clear the Delta. It flooded every spring. "When I was a little girl—say in 1915—they were still clearing it. They would go and chop around these mighty oaks and they would let them die and then they would cut them. When they were going to clear out a field they would kill the trees. I never paid any attention to it. It was what they did. I took it for granted. I played in the woods. If you were not at home for meals you were punished, because you had gone too far away and they had to go out and look for you seriously. Everybody had so many children then, you know. There was no birth control. We had so many. And many families lost lots of children." Pioneer land, the Delta region of Mississippi. Yet Mississippi, for a frontier state, had the curious complication of slavery, from the days of the cotton plantations beside the river. The frontier, the pioneers, the solitude; but then, also, the cheap black labor. What did Louise think now? The black population was now very large in the country where as a child she had been delighted by the wildflowers and the big trees of the forest. She said, "There is not much reason for being in the Delta unless you were a big landowner. You could hardly have cleared it yourself. Parts of it were just canebrake." "I've read that word. What is it?" "A wild type of cane, not anything you cultivate. We had plenty of help, servants. After they were freed they just stayed where they were, you know. They lived and multiplied everywhere. As many of the whites grew up, they left. But the blacks stayed. And one reason they stayed—it's interesting to read the obituaries even now—is that they are very gregarious people. They don't bother too much about lines of marriage and that sort of thing, but they are very devoted families." And black people liked to come back to the place they considered home. That idea, about the importance of the family, I had heard about in West Africa, in the Ivory Coast. It overrode the other idea—if it existed at all among Africans—of marital fidelity. I had been told that in the Ivory Coast it would be considered frivolous to give infidelity as a cause for divorce. And that went with another, African idea: you didn't marry a person, you allied yourself to a family. Louise said, "I feel very concerned about the black thing, the black problem. My maid told me this morning that up and down their street they are out running and shooting guns in the air—these young blacks." A twisted version of the frontier, here in the city of Jackson. "I don't know how we are going to come out of it. Some of them are very intelligent and ambitious. Some are primitive. Some white people are too, but maybe not so many. We are not multiplying as fast as they do." She offered an unrelated memory, in which the ideas of the pioneer life and black people ran together. "When I was growing up in the Delta I had a nanny, I suppose. She even wet-nursed me. There were no formulas. Doctors didn't know anything about babies. In fact, they had only gotten a little beyond leeches, but not much further. They did not have much skill." The wonderful forests of the Delta, where a child could play among the wildflowers, had been cut down. And her father had created a plantation. What had happened to that plantation? "My father died when he was fifty. He sold about a thousand acres just before the Great Depression, and he had about seven hundred acres left." But forest no longer. "Mud in winter, dust in summer. My father bought a Chalmers automobile. This was even before the time of radio. It was a diversion." Sometimes they just sat in the Chalmers, for the pleasure, not going anywhere. "We lived quietly. If a town was five miles away, that was a long way." But later, when the roads improved and the cars improved, people in the Delta became famous in Mississippi for their willingness to travel long distances for dinner or other entertainment. And then Louise touched a topic that linked the Delta region to the Trinidad of my own Indian community. Chinese had been brought in to work the Delta; just as Chinese and Portuguese and, more enduringly, Indians from India had been brought into Trinidad and other colonies of the British Empire (including South Africa) to work the plantations, after the abolition of Negro slavery. Chinese here, beside the Mississippi! Louise said: "The Chinese lived strictly among themselves. And they still do. There was one at Vance, and the low-class whites would tease him unmercifully. My father looked after him if it got bad. After my father died the Chinese man left Vance too. They deviled him. The schoolchildren on their way home would pass his store and say: Chico Chinaman Eats dead rats. Chews them up Like ginger snaps. And he would come out—it may have been his sense of humor—and shake his fist, and they would laugh and run away." Still lodged in her memory, this meaningless children's rhyme, clearly from another country, and adapted to the Chinese of the Delta. As ineradicable as the rhyme lodged from childhood in my own head about Chinese in Trinidad, a rhyme sung by black children—and just as harmless: Chinee, Chinee, never die. Flat nose and chinkee-eye. Who was the originator? An adult—or a child, speaking verse naturally, as certain children can do? There must have been an originator, for my Chinese rhyme as well as for Louise's. It would have been pleasant to talk for a while about Mississippi children's rhymes. But Louise had other memories. She was getting tired now, and no longer as able to complete a train of thought as when we had started. She said: "The blacks were so oppressed during that time that it was a peaceful place. They didn't do the sort of things they do now. We had very little trouble. They went their way; we went ours. We were used to having help. During the Depression my sister had a maid. She had a daughter the same age—" But this story was never finished. Perhaps it was too painful to recall; perhaps Louise wished to keep it buried. It led to this thought, unexpectedly: "I have a great respect for what the blacks call poor white trash. I think they have suffered. They too need opportunities." Then Louise said wearily, as if with the weight now of her illness and age, "But the needs of the world are so great that they are overwhelming." The combination of thoughts about blacks, and poor white trash who needed help as much as anybody, and her sister and the Depression, led to the dredging up of this story: "During the depth of the Depression—we have not had anything ever in the class of that Great Depression—we lived not far from a penal farm." Thinking of the story she was about to tell, she said: "But it was something terrible. One of the trusties up there worked in the homes of employees of the penal farm. Ah, it was something that electrified the Delta! This daughter of one of the warders there—they said she was having an affair with one of these black prisoners. Unheard of. But, anyway, the prisoner killed her father. And then they set out to capture him, and there was a reward of two thousand dollars. A big sum then. And this young planter's son just walked into a barn loft to bring him down. And of course the prisoner shot him and killed him. Twenty-three or twenty-four, the handsomest man you ever saw, and a fine young man; but he just walked to his death. And then of course they took the black man and killed him. This happened about ten miles away from where we lived. And it just really upset everybody. But now we have rapes here all the time. It was a very, very rare thing then. Now they don't seem to make much of it. I was a young woman, about twenty. It affected me very deeply. It was very tragic. But there were occasional instances of violence like that." We talked about the Emmett Till murder in 1955. Emmett Till (how extraordinary the names of people become when they are associated with big and tragic events) was a black youth who had been accused of whistling at or molesting a white woman, and had been killed. It was something that had added to Mississippi's bad reputation. Louise said: "Parts of my family were still living there in the Delta. And he did more than whistle at her. My brother had a drugstore in Sumner, where they had that trial. We are not that kind of people." Louise was talking of the social distinctions of the Delta. Earlier, speaking of her family's position as planters, she had said, "There are class divisions everywhere." And she meant now that the woman who worked as a store clerk—like the woman Emmett Till had allegedly whistled at or molested—was of a different class. "My mother and sisters never worked in that commissary. We always had hired help." "Commissary," a plantation word, meaning the plantation store, where workers bought goods on trust, against their wages. "My father didn't think it was a suitable place for the women of his family to be. All kinds of people came in there—sometimes drinking." I had already been struck, in Ellen's account of her childhood, by the modest jobs that people of good family did. One of Ellen's aunts had been a postmistress; and now Louise was reporting that her brother ran a drugstore. It was as though, in the poverty of the South, class was something in the mind and consciousness of a family, related to an idea of good behavior and seemliness. Louise said, "The civil-rights movement altered everything. It's good and it's bad." She added, the thought seeming to come to her by association, "I wouldn't like to live anywhere where there are not any blacks. I've lived among them all my life and I like them. And right now"—and she meant in spite of the crime in Jackson, and although the city was moving towards a black majority and might soon even have a black mayor—"they are warmhearted and humorous. I would miss them. But—we have such a mass of them here in Jackson. And wherever they are they are in a mass, because they like their own kind of people, and they are not going to settle where there are not other black people—they're lonely. This woman was in Iowa, and she was earning much more, but she came back here because it was lonely for her there. But they are forming gangs now in Jackson. If they could be scattered about the country, it would be better. But we are not Russia. We can't do that." It was almost time for me to go. She half wanted to be free of the need to talk; but there was also a side of her that, having begun to talk, wished to go on. And once more she turned to her childhood in the Delta, when the land had been forest. "We fed ourselves, but we lived below what would now be called the poverty line. It was a privilege to live in the Delta. At night we would hear animals in the forest. A panther. It sounded like a woman crying." Close again to her now in old age, when she lived alone, was the loneliness of her childhood, the solitude of the Delta. "My stepmother used to tell the story of a lady called Miss Sunshine Easterling—Sunshine Easterling!—who wanted to go to a party. But there was no transportation except down the railroad track. So—away they went, down the track, with a handcar. Pumping it up and down, you know." I didn't know, really. I had seen the handcars she mentioned only in American serial-thriller films when I was a child in Trinidad. "And," Louise said, "they were wrecked by a freight train, and Miss Sunshine Easterling was crippled for life. That story was to prevent us from yearning too much for a social life. We certainly were isolated in the Delta in those days. "I remember one Christmas I got a most beautiful real beaver hat. It must have come from a store like Marshall Field, because there were no stores that had anything like that anywhere nearby. And there was nowhere for me to go with my beaver hat. So I put it on on Christmas afternoon and walked down the railroad track, hoping that someone would see me. But nobody did. I was twelve at the time." Sixty-seven years later, alone again, in a Jackson developed beyond her imagining, widowed, nearly all the adventures of her life in the past, she recalled that earlier memory of solitude. Outside, her overgrown garden, full of trees, the ground dry, yellow, waiting for rain. SOME DAYS later (when the rain had come) I went to call on Eudora Welty and mentioned this story of Louise's about the beaver hat. Miss Welty was only a year younger than Louise, and she knew the kind of hat Louise might have got for Christmas in 1920. "Those hats were called Madge Evans hats. They were named after a child actress. They were sold only in one store in Jackson. Many-years later I met the child actress. Of course she wasn't a child when I met her, but she had kept up with her acting career. I met her in New York. She was a little bit older than me. She said, 'I know your work, because in one story you had a Madge Evans hat. I'm Madge Evans.' She was a little girl like us when she wore the hat. The hat was wide-brimmed all around, with streamers that hung down your back as far as your waist. They were wonderful hats. And there were straw hats as well, for summer. In those days you wore hats all the time. You wore hats even to Sunday school." THERE WAS no longer the forest Louise had known in the Delta; and an embankment along the Mississippi now kept the flat land from flooding every year. The land was so flat that the trees looked low. And—from the car—the fields of young cotton plants created long, hypnotic perspective lines zipping by: the green of the cotton plants alternating with the yellow or dark brown of the earth. But agriculture had fallen on hard times; and though there were still splendid plantations like the one called Egypt, the Delta was no longer the "one big cotton patch" of Louise's description. Egypt, though, gave a glimpse of the past, and of the social graces and divisions of the plantation culture. At the back of the estate house and the plantation commissary was the Yazoo River, very muddy, down which the barges still go; the last river steamer called there in 1932. In the cool estate house, at lunch, there was a sense of space, of great distances separating one from one's neighbor. Books, the concern with history (Egypt had been in the possession of the same family for most of the century), and paintings (originals, mainly portraits, and reproductions), and even the small sculptured Negro head on the mantelpiece of the drawing room—all this suggested a culture far removed from the special Delta world of work. Even during the lunch the pest-control people had been busy outside. And just beyond the gardens of the house were the level fields on which it all depended. A million dollars' worth of equipment tilled and harvested and fertilized those fields. There would have been much less equipment in the old days; there would have been many more workers. In the flat land the single line of the widely spaced houses of the few black workers who were now needed stood out against the sky. In front of the houses, on the road—and seen very clearly, as though on a stage: the effect of the flatness of the land and the great height of the sky—the black children played, running about or cycling. In the estate house, at lunch, one might have been in Argentina, on an _estancia_. Outside, considering those workers' houses, one might have been in some country in Africa—Kenya perhaps, if there had been hills in the background. But cotton, though the prices had improved recently, was no longer absolutely king of the Delta. What the flatness of the land concealed from the highways was that many thousands of acres of Delta land were now given over to catfish-farming, as complicated and big and American-ingenious, and mechanized and risky, as any of the ventures of the Delta. I drove early one morning from Jackson to witness a "harvesting" of some catfish ponds. The "ponds"—each about fifteen to twenty acres—had been seined the previous evening. The seines were like the seines one knew. But the dragging had been done by two tractors, one on each embankment; and the embankments were strewn with dusty dead fish, now less like fish than like a kind of leathery material. There were snakes in the ponds sometimes; and goldfish, flashing red in the seine and in the wire-netted hopper that lifted the fish into the trucks from the pond. Goldfish, things of beauty when seen one or two at a time, had become "trash fish" here, to be separated from the catfish at the processing plant, and either thrown away with the other trash fish that a pond attracts (sometimes dropped by birds), or ground into fertilizer. Nature, manipulated, had gone slightly haywire. The goldfish had been introduced to eat the algae that had been giving a bad flavor to the catfish. But when the goldfish had flourished far too well—rather like the kudzu vine, the other great plague of Mississippi, which, introduced from Japan or China to prevent erosion in the hillier parts of the state, had so liked what it had found that it had overrun many square miles, racing up electric poles and pulling them down, killing trees, creating great festoons and swags everywhere, blanketing woodland with a thick, even growth of—almost literally—ineradicable vines (the kudzu had been introduced for that very reason, because its marvelous roots held so fast to the soil). Like the water hyacinth in the Congo River, the kudzu had become a strangler. Flavor—that was the great problem with catfish. And that had so far not been solved by all the research of the processing plant and the Catfish Institute. Catfish, especially in the summer, could develop strange flavors: mud, or burned wood, or something with a petroleum tang. So the processing plant carried out five or six flavor tests on fish that were ready to be harvested. The tail of a live fish was cut off, cooked, and tasted. The purchasing manager of the processing plant said, "We cut the fish with the skin still on. We don't want to adulterate it in any way. It's right off the truck, the tail is cut, and it's into the microwave. It isn't skinned or anything." The cooking and tasting was one man's job. "Our taster can easily do two hundred samples a day. It varies. I've known him do as many as 350 samples a day. He has his own kind of method of cleansing his palate. If a fish is very much off flavor he will turn on the fan in his kitchen—because the one that's off flavor will really smell up the test kitchen. Nowadays, in the summer, only two or three samples out of fifteen sent can be accepted. The rate of acceptance is higher in the winter." And the catfish farmer could only hope that the ponds with the rejected samples would become all right, and that the fish there would on a later occasion pass the flavor test. So the fish being loaded that morning into the processing-plant trucks had passed all but one of their tests. There was to be a very last one at the processing plant. For two days before their trip to the processing plant, the fish had not been fed, so that nothing might interfere with their flavor. Now, on flavor, and weighing from one to one and a half pounds, the fish were almost at the end of their eighteen-month farm cycle. In a hatchery, a small covered shed, they could be seen at the beginning: eggs in troughs, in water kept at a constant eighty degrees, an electrically driven paddle taking the place of the waving tail of the male catfish; without that disturbance of the water the eggs would die. In five days life—beginning as a black speck—comes to the eggs; and then the fingerlings are released into the ponds, to start their eighteen-month life. The ponds are aerated constantly, because without oxygen the fish will die. The oxygen content of the ponds is tested every two hours, day and night; a catfish farmer cannot stay away for too long from his fish. The food or grain fed to the catfish is regulated by computer. It is dropped at fixed times at the deep end of the pond. The fish swim to the deep end at feeding time. They are creatures of habit. They do not eat if they are fed irregularly or fed too much. If there are too few catfish in a pond the fish do not eat enough to put on marketable weight, because (as it appears) the lessening of competition makes the creatures as "laid back" as the wild fish that feed at the bottom of rivers. How much, then—how much experimentation and accident and loss—had gone into the rearing of those fish being loaded that early morning into the trucks of the processing plant! The plant was in the small town of Indianola. The workers from the processing rooms were sitting out in their lunch hour, in the broken shade of pine trees, across the paved road from the plant. They wore blood-stained white gowns and what looked like plastic shower caps. Most of these workers were black, and many of them were women. They sat on wooden stools at wooden tables and ate their lunch snacks. A number of them were eating hamburgers—workers in one food processing industry eating the products of another food-processing industry: the give-and-take of industrial society. When lunch was over the process resumed. The trucks of the processing plant released the fish they had brought—in well water, to keep the fish as clean as possible—into a metal cage. The fish were lifted in this cage and delivered into an electrical stunner, a box painted green. And they were passed down from there to the processing lines, inside the building, in a room noisy with machinery, to be de-headed, eviscerated, and skinned. De-headed, eviscerated, and skinned—the purchasing manager, who was showing us around, spoke the difficult words as easily as, in another age, people would have spoken of criminals being hanged, drawn, and quartered. Something of that process was involved here. But the emphasis in the fish plant was on speed, speed to preserve the freshness of the fish, which were to be kept alive to the very last moment, then de-headed, eviscerated, and skinned in a flat three and a half minutes, and immediately afterwards put (at least, the fillets or steaks or strips or nuggets) into very cold water mixed with ice. The ice was important at that stage: every detail in this process had been worked out. The ice, the purchasing manager said, rubbed up against the cut or filleted fish and acted as yet another cleansing agent. The fish were completely processed, ready for market, in thirty minutes. "And so," the purchasing manager said, "the customer can eat for dinner that evening a fish that was alive in the morning. This is a degree of freshness that cannot be equaled by any other aquaculture product. As far as seafood goes, forget it. Some of the seafood's been lying on a boat for four, five days before the boat gets back to dock." "De-heading"—the word was new to me. But it was absolutely right. A man can be beheaded; a man is not de-headed any more than a fish is beheaded; and "de-headed" suggested the industrial process involved. Part of the speed of the operation depended on the skill of the de-header or, as the purchasing manager said, the head-sawyer. A good head-sawyer could cut fifty-five heads a minute. But the fish had to be well stunned, and not wriggling about; the stunner in the green box had to work. Men and women both did the head-sawing job. The woman I studied for a while wore yellow gloves and slid the stunned fish at a great rate against a vertical bandsaw. The evisceration was done by suction, by a machine such as I had seen, nearly twenty years before, in what had remained of John Steinbeck's Cannery Row in Monterey, California. Outside, the entrails and other bloody matter of the processed fish poured down from two hoppers into red trucks, to be taken away somewhere, perhaps (but I didn't ask) to be turned into fertilizer. In the office building there was order and silence; and the girls were white. In the waiting room there was a photograph in color of two pretty white girls who were Miss Catfish 1985 and Miss Catfish 1986. In Cannery Row in 1969 I had been shown around silent, disused machinery by the man who had bought it and was hoping to sell it. He told me that machinery—even as involved and long-winded as the canning machinery appeared to be—wasn't difficult, once you "lived" it. And I felt that the president (and the purchasing manager) of this processing plant "lived" catfish in that way. But Cannery Row was a dead place, and Sam Hinote was building up a new industry. He was forty-five. He had been born in Alabama and had gone to Auburn University. The name brought back my evening drives to that town and to the nearby town of Opelika, for dinner, when I was staying at Tuskegee. And, remembering something I had been told at Tuskegee about the comparative merits of the veterinary departments of the two universities, I said, "Auburn. But that's the rival of Tuskegee, the black university." Sam Hinote smiled. I was a visitor; he was tolerant. He said, "Tuskegee is a black school. But Auburn is not its rival. Auburn's rival is Alabama State University." He had started his professional life as an economist, a market analyst dealing with grain prices and other commodity prices. Then, as director of economic research for a big company in Omaha, Nebraska, it became his job to find new ventures for that company. That was how he got into catfish. "We ended up in 1969 buying a small company that was involved in the catfish business. The company we bought had a hatchery and a processing plant. Their business was selling the baby fish to farmers, and buying back the market-size fish from farmers, and processing and selling the dressed fish. I thought it was very much like the early days of the chicken business." His analysis was right. The fish-farming cooperative he began to run in Indianola in 1981 with fifty employees now provided employment for fourteen hundred people, and indirectly for many more, many of them black people who until then could only get seasonal jobs on cotton plantations, "chopping cotton" in the spring, getting rid of weeds that couldn't be poisoned, and working in the cotton gin in the autumn. Many farmers had been saved from having to leave their farms. "A lot of farmers didn't want to be involved in catfish, but they had few alternatives. It's hard for a farmer once they've become a farmer to ever give up. It's a way of life for them." Sam Hinote had done a lot of useful advertising. "We're spending a lot of advertising dollars as a company and as an industry to upscale the image of catfish. We've hired professional chefs like this guy"—he held up a pamphlet with a photograph of a chef holding serious-looking dishes in both hands—"to help us change the image of catfish." Catfish, catfish—like the dedicated man he was, Sam Hinote appeared never to tire of speaking the word. The Catfish Institute, founded in 1986, had been publishing booklets. Sam Hinote gave me one: _Fishing for Compliments—Cooking with Catfish_. It had been an American-style campaign, and it had produced American results. The catfish business as a whole now had sales of $200 million; almost half of that came from the plant at Indianola. And Sam Hinote thought that within ten years the industry was going to have sales of $1 billion. And though men cannot absolutely control other living creatures—Cannery Row itself died because the sardine vanished from that coast—and no one can be absolutely certain what will happen to catfish—what mutations, what debilities—as a result of this intensive farming, it is nevertheless an astonishing thing to have happened in a place that Louise knew as wilderness, malarial, liable to floods, but beautiful with wildflowers, and where now, within hours of leaving their ponds, the red entrails of fish pour into red trucks, their life cycle over. THERE IS no landscape like the landscape of our childhood. For Louise, though her father had been a planter, the "big cotton patch" that the planters had created in the Delta was a disfiguring of the forest she had known as a child. And for Mary, born in the Delta forty years later, there would be no landscape like the flat, stripped land she had grown up in. She said, "I think there is nothing more beautiful than the flat, flat land and the big, big sky." She was showing me the small country town of Canton, fifteen miles or so north of Jackson, giving meaning to a shabbiness I had driven through once before without comprehension. I had taken in only the broken-down air of the main road through the town, and noticed the large number of black people in a town where there appeared to be little to do. All at once now, with Mary taking me through the streets around the main square, the layers of history became apparent, as they did in so many places in the South. The town had been established in the mid-1830s. But most of the buildings on the square had been put up in the twenty years from 1890 to 1910. The Civil War had intervened; and in a street not far from the main square was the first reminder. It was a street of pretty, old houses, but with black people. Some of them could be seen sitting on the porches. In the middle of this street was an open green space with a gray marble obelisk. It was inscribed on one side: _Erected by W. H. Howcott in memory of the good and loyal servants who followed the fortunes of Harvey Scouts during the Civil War_. On another side: _A tribute to my faithful Servant and Friend Willis Howcott, a Colored Boy of rare loyalty and faithfulness whose memory I cherish with deep gratitude. W. H. Howcott_. And on a third side: _Loyal, Faithful, True Were Each and All of Them_. The fourth side of the obelisk was bare. The slave, Willis, had taken the name of the master. Had the "colored boy" who had gone to the war with his master really been a boy, or had he been a man who had remained a boy even in death? True feeling was there, but how much of defiance had there also been, in this obelisk put up after the war to celebrate the loyalty of slaves? The obelisk was in a black street. The memorial to the Harvey Scouts was in the white cemetery, elsewhere. And the slave memorial was still tended. The grass around the gray obelisk was neatly cut; on the base there was a bouquet of artificial flowers. Black people sat on porches not far away. Black people walked past while we looked. Didn't they mind? They didn't. But, Mary said, it was something that hadn't been put to them. Perhaps they would mind if someone came one day and put certain things to them. In the white cemetery, some streets away, and centrally placed in it, was the memorial to the Harvey Scouts. It was also an obelisk, but not as plain as the one for the servants. It was carved with crossed flags, a star and crescent; and there was a metal plaque on the plinth. Some verse had also been carved: Long since has beat the last tattoo And peace Reigns now where Troopers Drew Their sabres Bright to Dare and Do Led Forward by Ad Harvey. It was unsettling, that flawed last line; it made one think that the first three lines had been borrowed. Yet there had been sacrifice: CAPT ADDISON HARVEY BORN JUNE 1837 KILLED APRIL 19 1865 _Just as the Country's Flag was Furled forever Death saved him the pain of defeat_. At the far end of the cemetery, not far from the corner with old Jewish graves, were small tombstones, in rows of five, running down the length of the cemetery, each stone marked UNKNOWN CONFEDERATE SOLDIER. It was shocking, in this small-town cemetery, the thought of all these unclaimed men. The bodies or the remains, Mary said, would have been gathered together some time after the war. The headstones might have been put up in the 1870s. The Harvey memorial, and the memorial to the black servants, would have been put up later. The cemetery was still in use. Other people, with heavier needs, were driving about the lanes, as we had been doing. There were two new graves, below green awnings marked with the undertaker's name, Breeland. And not far away was the undertaker's own family plot, with a large stone marked _Breeland_. Mary said, "Some people think it's advertising." Small as it was, Canton had its social and racial divisions. The railroad track divided the good side of the town from the bad. On the bad side, the black side, many of the houses were in disrepair; and many of them were shotgun houses, one room in front, one room at the back, the houses set close together. There were other, better black areas; but even new developments appeared to be going down. There didn't seem to be much doing in Canton. In an older part of the town were the settlements associated with the timber industry, when there had been one. Milltown was for the white workers. Next to it was the black area, with a designation that recalled the cabins of the slave plantations: Sawmill Quarters. There was still a furniture factory in Canton, and there were two or three other factories outside the town. But the industrial area was in a mess. It looked like tropical slum. It was hard to think, when we got to the area of the country club—with a membership of professional people from Canton and from Jackson—that both areas shared the same climate and vegetation. In one area the sun seemed part of the blight and torpor. In the other, among the tall trees and well-cut driveways, the sunlight was like part of the general privilege of the place. "Sun," "sunlight"—to me they had always been different words. "Sunlight" was a nice word. "Sun" was harsher; it was what the sunlight of early morning in Trinidad turned to at about eight, when it was time to go to school. The slogan on the label for Trinidad Grapefruit Juice, when I was a child, was "Fruit Ripened in Tropical Sunshine." I had always thought that the words were too pretty. "Fruit Ripened in Hot Sun" would have been truer to the climate I lived in; but then they might have been less of a slogan. "Tropical Sunshine"—they were tourist words, I always thought; and, indeed, they could have little meaning for someone who had known nothing else. Agricultural and industrial depression now; civil-rights movement twenty to thirty years before; the Great Depression before that; and Reconstruction; and the Civil War—it seemed, considering the layers of history whose memorials or remains one could see in a place like Canton, that the South had moved from crisis to crisis. And at the back of it all was the institution that had seeded most of the crises, or aggravated them: slavery, which had led to this present superfluity of black people, people no longer needed in a machine age. Mary said: "It's been frustrating to me because the enormity of the problem is something I know I'm not going to see solved. It's heartbreaking to see people living like that. And it will keep the area from progressing, economically and culturally. These people don't read books, or even newspapers. TV is the only thing. And in fact some of them probably can't read. Not in the way that you and I can read. They can read a sign, but not a thought or an idea." During our drive through the town she had shown me a red-brick high school that had been turned into a furniture store after the schools had been desegregated. "The enrollment in the public system made the building unnecessary." She meant that white people had withdrawn their children, and sent them instead to private and usually Christian academies. But now that was a financial strain on some people, and people were beginning to think again about the public system. "I've been encouraged recently because some of the people here who would not be considered liberal are realizing that so much of the future of the town is tied into the school system." "Is there still bitterness about desegregation?" "A lot of bitterness from the sixties has gone into the second generation. But now it's more of an economic resentment. People resent seeing the welfare programs like food stamps—and there is something that provides food and milk for babies. And of course people that have worked hard for their families are certainly going to resent seeing people being given for nothing the equivalent of what you've had to work hard to earn. Medicare is another thing. There are clinics for people who pay according to their income. Which means that they are supported by the federal government—that is, other people's income tax. "I'm not a bleeding heart racially, believing in universal brotherhood. People are too different. I believe in God, but I'm not religious. This is the Bible Belt. For some reason Southern people have a tremendous capacity for faith—black and white. When I go to a church service where people are extremely devout I feel I'm missing something. But it doesn't last. Religion is very social here—fellowship, church suppers, things like that. And I suppose I'm not a particularly social person." "When did you start thinking of yourself as a Southerner, somebody different?" "I've always felt it. We're so proud of it. We are permeated by the feeling that the South is special. My family were always interested in the literary aspects. We were very proud of our writers here." What about the other side? The bigotry, the violence? Was there one view that could hold it all? "I was aware of the other side. The violence, the deprivation. There was a very ugly incident when I was growing up. That was the Emmett Till murder. He was a young black boy from Chicago visiting the area. He was shot supposedly for whistling at a white woman who worked in a little store in a rural area. And this all happened close to Greenwood, where I was living. This was in 1955. I was eleven. I remember reading it in the newspaper first. I had a friend and she knew the people in the store. And I remember people at school saying it wasn't true, that he was still living in Chicago, and that people were trying to make Mississippi look bad. But even at eleven I knew that was a sad way of thinking, and that people who thought like that were of the same social class as the woman at the store." Here it was again, the emphasis on social distinctions. How did they operate in the Delta, where lives were so isolated and confined? Mary said, "My grandmother would say of some people that they were not folks. That was probably her favorite phrase. She was very conscious of who were and were not folks." "Who were folks?" "Generally, folks were people who weren't transient, who'd lived here for some time. You knew their families. And if they'd moved in, say, from Lafayette County, you would know their families." "But, apart from some people in Natchez, no one has been here for more than five generations." "No. It simply meant that you knew they were the same kind of people. They knew how to behave. They didn't say 'nigger.' Nor did they say 'ain't.' People who said 'ain't' and 'niggers' were not folks—that would definitely put you beyond the pale then and there. She was a stickler for manners. If you put your elbows on the table, she would pick up those heavy silver knives and she would hit your elbows, if there wasn't company—in those days people had the heavy silverware, not the stainless steel. I think we behaved like this because we genuinely thought that this—the South—was the best place in the world. To be technical about it, my grandmother came from Alabama. She had lived in Mississippi since she was married. I can remember my parents talking to me and trying to explain the racial problem. And since nobody really understood it—" I was interested in that idea. I said, "No one has put it like that to me." "I don't think they did. Understand the race problem. I still don't think they do. I know that people of, like, my grandmother's generation—her generation and black people of the same generation had a closeness that doesn't exist any more. In those days no one had any money. You know, the Depression and things. A lot of the jobs the black people had depended on the white people—in the houses and yards and things. But the white people depended on the black people too. I think that at that time there was a better respect between the races." "People outside didn't have that impression. There were the lynchings." "There were, exactly. But the people I was talking about—and I'm sure that people are much more capable of violence than I realize—the people who carried out the inhumanities were not typical of everyone." "What effect does the physical appearance of Canton have on you? The town you showed me." "That kind of question makes us defensive." "No, no. I don't want that." "What did I show you? Buildings and fields." "You showed me a lot that was run-down. It isn't worthy of the history." And I meant—though I didn't speak precisely—that if you took away the cemetery and the main square, there would be little in Canton that wasn't contemporary slum. The land and setting were hard to associate with a great and difficult history. How, in such a setting, did she support her sense of history? Mary said, "It may not be worthy. But I don't think poverty and deprivation are limited to the South. I think we are addressing the economic problems more than we have ever done. People are addressing the problems of black and white as of one group." "What do you like about the South?" "It's a very nourishing place to live. I like the people, even though I'm not close to them. If there was some sort of tragedy people would rally round, even though they were not my family. And the sense of the past can be satisfying—even though my family is not from this area. What did Faulkner say? The past is more real than the present? I can't remember the exact words. But it's that the past is something we all live with. Possibly in larger places they don't put the importance on the past. We're preoccupied with the past. Some people think that's because we lost the war." So we had circled back almost to where we had begun. I had asked, seeing some military-looking figure in a memorial in the cemetery, whether he was wearing a Confederate uniform. But the memorial wasn't what I had thought. And Mary had said, "There was no uniform. Towards the end they were lucky to have shoes." WILLIAM SAID: "People up north think they know better than we about problems and people down here. They think they know how the black man thinks and the white man thinks. They have missed miserably on the black man." The North had disrupted the more economically active South in 1860; and they had done it again after World War II. I wanted him to go beyond that. He said, "Let's talk through certain things first, before you make notes." I put away my notebook and we began to talk at random. He was a businessman, of a prominent Mississippi family. He was in his forties. He loved the outdoor life and was athletic and handsome. He appeared to be blessed in many ways. Yet what came out after a few minutes of conversation was that he was a man to whom religion was supremely important. His judgments, even the tough ones he had spoken at the beginning of our meeting, were contained within his idea of the religious life. And that was where we began again. We sat on rocking chairs in front of his desk: the tradition of the porch, transferred here to an air-conditioned office. William said, "The Bible says the Lord helps those who help themselves, and I really believe that. I feel there are not enough people trying to help themselves. And I don't think that the help these people need is a free check." I asked about the development of his faith. "Both sets of my grandparents were very strong workers in the Baptist church. My parents were and are strong members of the church. I don't remember us not praying or reading a Bible. I made my profession of faith when I was seven years old. I guess I went to my parents first—after hearing the Sunday-school teachers talk about Jesus and the Lord, and I believe that he did come out of heaven and walked among us and died for us, to give us an opportunity to be with him in heaven. And finally I said publicly, 'I want to accept Christ.' And they said, 'Fine, let's go to the preacher.' And he talked to me. And I guess they felt my feeling was strong enough, and I was baptized at seven. I grew up around it, I accepted it, and I made that profession of faith. "I had a dream around that time—but it didn't cross my mind until many years later. I was spending the night with my grandmother. I was sleeping on the porch. I remember sitting up in bed—waking up real fast—and I thought I saw Jesus Christ walking through the back door. The door had a little knocker, a wooden ball on a string, and I remember hearing that knocker, and the door opening. And I just had that vision of Jesus Christ walking through that door. And I remember sitting up all night to see if he was going out through the back door. But he never did. I never thought much about that dream until six or seven years ago. I was riding down the highway, and it just flashed back in my mind. At that point I really realized that it was Jesus Christ entering my heart. And the reason I didn't see him leave that back door was that he didn't leave us. I just haven't discussed that story with my family. But I remember that dream and that whole night as if it was yesterday. I feel that Jesus Christ entered my heart that day and he's never left." "Did it change your attitude to other people?" "I hope I have more patience with people. I hope I'm quicker to see the good than I am to see the shortcomings. I certainly try to have a short memory for bad experiences. I try to forgive and forget." "What about irreligious people? What do you think of them?" "I guess I feel that if I can set an example to them I can encourage them to be less irreligious. Nor do I think less of a person who has a different religion from mine." "Do you feel you are in a religious community?" "I think I am. I'm not sure that the religious part of the community is keeping up with the population growth. I'm not sure that the church _membership_ is keeping up. But I realize that there are many Christians. I was encouraged by the short patience people had with the Gary Hart–Donna Rice situation. I am certainly encouraged about Christianity in this country and the work of the Lord." "Why aren't you in the church?" He misunderstood the question. "I was there until nine last night." "No, no. I was asking why you aren't in the ministry." "I believe the Lord has a will for every one of us, a plan for us. He knows what he wants us to do. If we were all architects, we would all have pretty buildings, but we wouldn't have farmers to grow food. I think that his plan for creation is that it takes a lot of people to make up this world. And he needs workers in all of these areas." "Is this why you feel as you do about people who do no work?" "I have never expressed it like that. But I think that is why I feel the way I do." "Do you think men need to work?" "No question about that. The Lord created the Garden of Eden and he put Adam and Eve there, and when they sinned he put them out of the Garden of Eden and told them to go to work." "You feel that people are still working out that sin?" "I don't think I'm still working out their sin. But I think that all of us have sins. The human race is a sinful race—and this is where we are, and that's what we have to deal with now. I feel strongly that we are required to work for six days and rest on the seventh. The Lord talks about giving each individual talents, and the Lord told us to use them. I think that working is an important part of using those talents. Some people are writers, farmers, architects. These are talents that the Lord gave them. "Someone wrote to my father several months ago. In this letter he was saying: I enjoy my work; how does a successful businessman continue being a Christian? Should he stay with his business, or should he go back into the church? My father wrote a letter to explain why it's necessary for a Christian businessman to be in the world. Our own preacher here has said several times that with the TV pastors getting into such hot water and getting such bad attention, he's been seeing some doors closed against him; and the responsibility for leading people to Christianity is more on the shoulders of laymen." I said, "Some people are saying that it's the work of the devil, that those TV pastors are in trouble." William said, "When I fail at something I fail. I feel like I've got to take the consequences for my failure. I also know that I've got outside forces working against me. But I know that before I start. So I can't pass the buck. The devil might have made me do it, but it's still my problem, my responsibility. The ultimate accountability is mine." I asked him to talk about accountability. He sucked in his breath. "Whoo! It's difficult to go public about it. I guess it goes back to what I was taught by Mom and Dad: that if you have responsibility you have accountability. The more responsibility, the more people are affected. And I think the accountability to Christ is the ultimate responsibility I have. This also gives me a background to what Mom and Dad were teaching about responsibility and accountability. Perhaps the people dependent on me the most are my family. Then there are the people I'm tied into business with. They've given me a certain responsibility, and I've accountability. We are in business to serve customers. And that gives us another whole segment of people we're accountable to, people we'll never see. "You've told me about your trip to the catfish farms. Those catfish are going to go all over the world. And the farmer has got to see that the fish is on flavor—for that person who is going to eat that catfish, for where that catfish is going to end up. If we do it right they'll come back. If we do it wrong they won't come back." So the religious ideas of the God-given talent, work, and accountability coincided with sound business practice. It was true of other religious groups as well, this coincidence of religious devotion and business sense: one kind of dedication encouraging, and even becoming, another kind of dedication. It was true of certain Hindu caste groups and certain minority or heretical sects in Islam. But religions and cultures have their own identities. One isn't just like another. The idea of the God-given talent is contained in the Hindu idea of _dharma;_ but the Hindu religious-business dedication is different from the dedication William was talking about. However much his business practices appear to contain the idea of service, the Hindu businessman has a contract with God alone, and not with men. And it was of his contract with men that William went on to talk. He said: "To me, without religion there wouldn't be any purpose. It's religion that gives us purpose in being here. The purpose is to serve the Lord. And the only way we have of serving him is to serve mankind. We can't give him anything he doesn't already have. We can't touch that. Nothing he doesn't already have, unless it's our heart." William spent a certain amount of his spare time on church work. He gave "devotions" sometimes; he taught Sunday school sometimes; he worked with the boy scouts. Did he, so full of his church, judge people according to the degree of their faith? He read the question as half a political one, connected with "equal opportunity" and the racial issue. He said—puzzlingly, unless you understood the semipolitical question he felt he was answering—"I try not to judge an individual as an individual. I don't have the facts to judge on. But I try to judge and weigh his actions against the work that has to be done—to weigh his strengths and weaknesses as I can interpret them. Though that's what I used to be _told_ —that this person fits this particular job. Maybe they did, maybe they didn't. But what that does is that the individual knows intuitively: 'I'm here because you've been told to put me here. It doesn't matter about my job performance. Therefore it doesn't matter what I do here.' And at that point the person loses incentives and a proper motivation." But William talked about this wearily, as though he had talked about it many times before and had no faith now that the plain and obvious things he was saying would ever be heeded. Then, rocking, leaving the subject of equal opportunity aside, he said, "I have such a wholesome respect for the early-American natives. I really feel like they believed that the Lord lived in everything on earth, the rocks, the trees, the bush, the animals—the Lord lived in everything—and they were part of it. And what I think of the early-American natives is that they had an almost reverent respect for nature. For them the life of a blade of grass was as important as a great buffalo. They didn't make any distinction. And they probably realized, more than the greatest scientist on earth now, that everything on this earth is totally related. They understood the chain reaction that comes from getting one thing in nature out of balance with the others. And I think that, because of the reverence they had for all living things, they had a reverence for mankind that I'm not sure we'll ever see again." "How did you find out about the Indians?" "I've read a few books. I've made a few trips out west and talked with a few Indians by the roadside. And I was impressed with the minuteness of the attention to small details that they had. For every action there is a reaction. And what worries me the most now is that where I see a new highway or subdivision, where they're clearing land, there's a major destruction of plant life, animal life that can't be replaced. The thing that disturbs me about that is that it's not done with any consciousness or concern. It's only done with concern for the dollar. "Go down on your stomach on the ground. Look at a square foot of grass for about forty-five minutes. See the life, the insects. And magnify that to the size of a project." "But Mississippi needs investment." "I don't know how it can be worked out. The more concerns you have for these little things, and that side of life, the more concern you're going to have for your neighbor." The contract with other men, serving God by serving mankind—they were themes to which William returned. "I feel that man and nature have to go together. The Lord put us here to be caretaker of things. A lot of my thoughts are tied back with religion and the Lord's creation." It seemed to me that we could now go back to what he had said at the beginning, about the North's historical wish to disrupt the economy of the South. But he didn't want to go back just then to that side of things. He wanted to stay a little longer with his more mystical thoughts. I felt I had begun to understand how his fundamentalist faith—from the outside so constricting—was in fact complete and flexible. The mixture of the Old Testament and the New, the life of Jesus and the Book of Genesis, made a whole. The sanctity of the created world, the good life of conscience, the loving of one's neighbor as oneself—they ran together, and they appeared to fit the Mississippi character and history: the love of nature and the outdoor life, an admiration for the pantheism of the Indians, the love of family and community, the resentment of outside interference, which could feel almost like interference with a religious code. William said, of his religion, "I don't wear it on my sleeve. I hope I don't flash it around. It's just part of me. I don't want to be a goody-goody or better-than-thou, because I don't feel that way. I just want to be part of God's creation. His handiwork is in everything. And the more respect we have for his creation, the more respect we have for our fellow man." AFTER TALLAHASSEE and Tuskegee, I wanted in Mississippi to look at things from the white point of view, as far as that was possible. But it was put to me not long after I had arrived that, with the high percentage of black people in the state, and with the possibility that Jackson might soon have a black mayor, I should meet some black politicians. Andrew, a young Mississippian politician, put this to me at lunch one day, and he thought the man I should meet was Willard. Andrew himself was going to meet Willard for the first time that day, after lunch, and he thought I should come with him. "If the meeting goes well," Andrew said, "I can leave and you can talk to him. I can always talk to him some other time." Andrew was not looking for black votes. It was his ambition as a politician to rewrite the Mississippi state constitution of 1890, and to do that he needed all the political support he could get. For this first meeting with Willard he had dressed with some formality, in a pale-blue seersucker suit. The meeting was to take place in a hotel not far away. We left the cool of the restaurant and went down into the glare of the parking lot. The car was hot. The air conditioning, turned on to "high fan," roared; and it became hotter in the car than it had been outside. The air had just begun to cool when we arrived at the hotel and had to get out, into the glare of another parking lot. Always these reminders of the discomfort of earlier generations; and wonder at the energy they had shown; and more wonder that a great war should have been fought in temperatures like this. We sat in the lobby and waited for Willard. Conversation was easy up to the time at which Willard was due to come. After that it became awkward, with both of us waiting for Willard. Andrew said, "I've never met him." He said that two or three times. Once he got up and walked across the lobby to greet someone he knew: impeccable his manners, his charm unfailing, his politician's role now apparently second nature to him. And then, when we had given him up, fifteen minutes having passed beyond the appointed time, Willard came. He was in shirt and trousers; no tie; and he was unexpectedly ordinary, not at all the black leader or would-be leader I had imagined someone like Andrew treating with. I had expected a black man of disturbing charm. There was no charm to Willard. He was in his forties, plumpish, strong, no mark of physical hardship on him. He had prepared a serious face for the meeting. If one didn't know he was regarded as a politician one would have missed the rage in his eyes, or one might have read that deliberateness of gaze as sensuality. Willard was very much a local politician. In Mississippi, because of the 1890 constitution, the most modest of public offices are elected offices. This provision, intended to prevent any government from having too much power, and intended also to keep blacks out of even small jobs, now worked in favor of blacks, and politicized posts that elsewhere would have been purely professional or technical. Willard looked after the roads of a particular district of a particular county: a very small post indeed. I left almost as soon as I had met Willard. And, partly through Andrew's good offices (the meeting must have gone well), a meeting with Willard was arranged for me some days later. It was an early-morning meeting. I had assumed from the directions I had been given that the place was in Jackson. I hadn't asked what the distance was. But after twenty minutes or so on an interstate highway I began to feel that I was driving back to Alabama. At last, the time now past the time fixed for the meeting, the exit appeared. Only then did I realize that I had been given nothing like a house or office address, that I had driven all this way with only the number of a county district for destination. However, I pressed on, thinking I might make inquiries when I crossed the county border. I passed a board. It gave the name of the county and the number of the district. It was not the number I had been given, but I thought I would stop to ask at the building at the back. There were cars parked around it. When I got to the building I saw that among the parked cars there was a space, and the space was reserved for Willard. This was the address I had been meant to come to. But he wasn't there. I pushed the door open and found myself in a shed divided into offices. The shed was full of black people. In the front office or cubicle there was a black girl with a telephone, with other black people around her. This girl asked brightly for my name. I gave it. She said that she had been trying all morning, and Mr. Willard had been trying all the day before, to get to me, to tell me that Mr. Willard couldn't be at this address, but that he would be free to see me at an hour later than the one he had given, at Jackson. He would meet me in Jackson at my hotel. They had telephoned all the hotels in Jackson to locate me. But they hadn't succeeded. They had telephoned the Sheraton, the Holiday Inn. Where was I staying? I told her. She said that Mr. Willard would be there in an hour. How would she get a message to him? By the radio, she said; and I felt that the radio was important, a badge of office. I asked her to radio him while I was there, so that I would know he had got the message. She said I was not to worry. So I drove back to Jackson, along the route that had seemed so long and unlikely earlier that morning, and which towards the end had made me a little frantic because I had thought I was going to be late for Willard. When I got back to the Ramada Renaissance there was no Willard. Not then, and not in the afternoon. When I telephoned his office the girl said that Mr. Willard had spoken to her on the radio and that he intended to keep the appointment. He even knew my room number, she said. But Willard didn't come; and the next day there was no message from him or his office. Later I told Andrew of Willard's little—or big—joke. Andrew said, "I don't really know him. I met him for the first time that day with you." And when I asked whether the politics of cooperation such as he envisaged were really possible, Andrew said he had to be an optimist. The black problems were bad, and there were many blacks in Mississippi. If he wasn't optimistic, he said, it would be better for him to move to Oregon, where only 10 percent of the population was black. Andrew said, "It's been dawning on everybody that a disaster is occurring in the black community, and we do have to talk about it. The attitude of the polite press won't do any longer." Yet Andrew knew only what he knew. "I regurgitate more of what I've read about the society than what I've experienced. I get it from TV documentaries and specials. I haven't really experienced it. I haven't talked to black folks or rednecks. I've got to go over the top of some of these basic problems. If we can't get together we are lost." Optimism in the foreground; irrationality in the background. THE STORY about my adventure with Willard must have got around, because one day I had a telephone call from a man called Lewis. He said he was black and he wanted to introduce me to the real black culture. He worked in the stores section of a county department (like the one Willard oversaw). He began to give me directions to get to his house. But then he said he would come over to the hotel to pick me up. He said he would be there within the hour. He was as good as his word. I recognized him as soon as he came into the Ramada. He was easy, light, friendly. His manner was so easy that I was prepared for general or neutral conversation, at least in the beginning. But as soon as we were in the privacy of his car, and even before we drove out of the Ramada parking lot, he said that in the old days he wouldn't have been able to live where he now lived. He had helped "integrate" his neighborhood. It turned out to be a modest neighborhood. The houses were small and close together. The surprise, after what he had said, was his yard. It was overgrown, and noticeable among its better-kept neighbors. Inside, the house was cluttered, close, unaired. He made no reference to the clutter (even a few unwashed cups and plates in the sitting room), saying only that his wife had gone with the children to her mother's for a few days; and there was a kind of order below the clutter. On the sitting-room wall were framed enlargements of two old black-and-white studio photographs. They were of his grandparents. The period clothes, the choking up of the neck in collar and ruff, and the stare of the long-held expressions were oddly moving. In the enlargement or the printing the tones of the photographs had been bleached away, so that both the people looked white, with black eyes. The photographs carried the stamp of a studio in Memphis. Lewis said: "Mississippi people. They went to Memphis. Everybody went to Memphis. My father came back to Mississippi after the war. Do you know what they did? The people in the photographs. Do you want me to tell you? They were servants. Those two people made me. No hate developed in me because they taught me never to hate. The word was never used in their house. 'Be a good boy.' That was the motto. 'Treat everybody nice.' You heard it every day. I was taught that—to be good, and to be good to everybody." It was hot in the sitting room because the air-conditioning unit had broken down. I asked him if he could open a window. He said he couldn't; the insects would come in. So we sat in the high, warm, musty smell. He said, "When my grandfather died my grandmother sent some of my grandfather's clothes to my father. Servant clothes, suits. They were still good clothes, you see. Still some wear in them. And my father left one to me. I put it on one day. Just cloth, but I felt it burn my skin." "Do you still have that suit?" "I don't know where it is." "All this is such a long time ago, though." "But the past is always interesting. Knowing the past, I can do a better job. It's an awakening for me, to think of the past. Sometimes it's a rude awakening. To think of some of the things that happened—that I couldn't live where I'm living now, and didn't even think of it. That I sat at the back of the bus. That my grandmother washed clothes for white people at fifty cents a basket. Why didn't they pay her more? But I didn't question it when I heard. It's a rude awakening now. Still, they shielded me from the hate. It was there. I lived in my black section. They lived in their white section. That hatred was there, all around me, and I didn't feel it. They saved me from it, my grandparents, and my father after them. I'd hear about killing black men. But my father never allowed us to talk too much of it. And I'll tell you. Up to the day he died he said to whites, my father, 'Yes, sir!' 'No, sir!' No matter how young they were." "What do you think of that now?" "It doesn't bother me. He was my father. He did well for us, his family. So I didn't say to him, 'Don't say it.' " He went on, "I myself fight daily to be happy. Every day. It's the one thing I strive for. To be content, to be happy with myself." What did he mean by that? "I can't change my surroundings, but I can respect myself. I'll tell you a story. I went one time to my mother's sister's house. Black soldiers used to come to the house across the road, and they would be entertained by the young lady who lived there. One day one of the soldiers complained he had lost his billfold. The policeman who came to deal with this came to my mother's sister's house, because the young lady was sitting on the porch there when he came. He walked up to her and said, 'Gal, did you take that boy's billfold?' She said, 'No, sir.' He said, 'Get in the car.' And when she bent down to get in the car he kicked her hard on her behind. That never, _never_ got away from me." "What did you feel about that?" I wanted to know, because I was no longer certain of the point of some of the things he was saying, the memories he was playing with. It was getting dark, too, in the little choked house—he seemed as indifferent to this as to the airlessness and the clutter—and it was becoming harder to see the expression on his face when he spoke. He was running a number of ideas together. He wished to be happy, content; he had been shielded from pain; and threaded into this was something like admiration for the grandparents who had founded his line and taught him to keep out of trouble in an irrational world. "What do I think of the policeman and the woman? I don't know. I was so young. I didn't talk to anybody about it. I just saw it. It was cruel. But I don't know what I really felt about the cruelty. Every now and then the incident crosses my mind. Even today. I see it. But I don't know what I think about it." Wasn't it a little self-indulgent, living so much in the past, especially now that times had changed? "Yes. I'm enjoying the harvest now. But I don't think I've done much as a fighter, a marcher for freedom." "That worries you?" He didn't say anything. Then he laughed. "I don't know how I feel about it. I suppose I am in my own little world. And I suppose I'm selfish, being in my own world. I ought to be mad and angry and fighting. But I don't get mad." "Is this something from religion? Did your grandparents teach you that?" "I'm not religious. I'm not like many people who go to church every Sunday and want to be deacons." "Why do you look back at the past if you don't know what you think about it?" "I love to talk about the past." How far back did that past go? Did it go back to the days of slavery? It didn't, of course. The past he liked to talk about was the past he could remember, that curiously sheltered past. He said, "If my grandmother made fifty cents a day I ought to be happy with what I make now." What was it about his grandparents that he now especially remembered and liked? "Pride. Pride. My grandmother used to sit up in church with her corset on. Very proud, very cultured-like. Very classy lady. I don't know where she, and the others, got it from. Probably from the whites. Today I don't see it. They're nice people, but they don't have that something. I suppose I don't have it either. But you must know that I truly respect my past, be it segregated, be it filled with racism, be it whatever. Because I feel I have a place in the world, and I'm going to get it." The telephone rang. He took it up in the darkness. He listened more than he talked. He was being rebuked by someone he knew for not keeping an appointment. He said, when he put the phone down, "I'll drive you back to the Ramada." That was where he had told the man on the phone to meet him. "We'll talk again tomorrow. I'll come for you at six." It was a relief to be out of the house and in the open, warm though the air was. And now, driving to North Jackson, Lewis appeared to qualify some of the things he had said in his house. In the house he seemed not to have put together his thoughts about the civil-rights movement. Now he spoke with reverence of Martin Luther King. He said, "If he hadn't turned it the nonviolent way, they would have killed _every_ black in Mississippi. Every black in the South." I heard real panic in the words. I asked him again about his "little world." Had it really protected him? He said, "I suppose I was aware of everything outside. I was frightened of it—I suppose." And then, without prompting from me, he began to talk about God. In the house he had said he was not religious in the way most people were. Now he said that without God he would have done nothing; without God he would have been nothing; without God he didn't know how he would have endured. In the parking lot of the Ramada Renaissance he drove to the edge of one of the parking rows. There was a black man in a parked car. Lewis introduced me. The man in the car shrank from me. Lewis didn't come at six the next day, or at half past six. No one answered when I telephoned. About eight o'clock he answered. He sounded tired, distant. "I've been ill. I've been to the doctor. I didn't go to work today." "I telephoned very often and got no reply." "I was a long time at the doctor." He asked me to come to see him right away. I took a taxi. The ventilation in his house was better, but the clutter was as bad. He looked extraordinary. He was barefooted, with a dressing gown open over a bare chest and a black net over his hair. The getup was like a black version of the shower cap and white gown of the workers in the catfish plant. He said, "The net's to keep my hair curly." I began to say polite things about his illness. He brushed the subject aside. He walked barefoot about the sitting room. "I'll tell you about my grandfather. I think he was the kind of man who knew how to handle people, especially Southern whites. 'Yes, sir!' 'No, sir!' And tip your hat to them and grin. But he was successful, in his day. Regardless of how mediocre it might seem today or yesterday, it happened. And that's it." "It bothers you that you didn't do more for the civil-rights movement?" "The dogs never bit me. Does it bother me? I don't know. You must decide for me." The telephone rang. It was his friend again, the one of the night before. Lewis said into the phone, "He's here. We want your input." He laughed, and seemed to be getting out of control, laughing into the phone, stamping with his bare feet, and acting a little for me. He said, when he put the phone down, "My friend is scared of you." He laughed in his new way. "You must take off that jacket. Take off that jacket, and let me show you how the blacks really live. I will take you to certain places. You will get the smell of corruption." He made a gesture with his hand, like a cook suggesting an appealing aroma. And I understood then, putting things together, that he wasn't speaking metaphorically. The line of development that had begun with his grandfather was ending with him: his own little world, different now from the one he had grown up in. He began to dress to meet his friend. He said—and I'd hardly arrived—"I'll take you back to your hotel." He put on his trousers and shirt, and we went outside. He left the door unlatched. I pointed this out to him. He said, "I have to do something. I'll go back inside." I waited for him for some time. When he came out there was a white cream on his chin, the white glowing in the dusk and against his blackness. He said, "Blacks have kinky hair. Do you know about that? That hair grows under the skin. It is very hard to shave. This cream I've put on softens it. By the time I come back here I will be ready to shave, and I will get a very smooth shave." And that was how he drove me back to the alien white part of the city, with the net on his hair and the white cream on his chin and upper lip. He gave me another day to meet him. But he couldn't make it; I wasn't surprised. He sounded very tired and slow and far away when I telephoned. He asked me to telephone later in the evening. When I did there was no answer. JUST AS it is hard to comprehend American distances and the heat of the Southern summer until one has experienced them, so in Mississippi and in the city of Jackson it was hard to understand that people of seventy would have lived through many different worlds; that the childhoods of solid citizens would have left memories of frontier life, primitive conditions, and closed communities, things hard now to recapture. The town of Eupora, in the hills to the east of the Delta, is now on Highway 82. But someone like Judge Sugg, who was born in 1916 and retired from the state Supreme Court in 1983, carries memories from his childhood in Eupora of the time when the Big Black River had no bridge, only a ford. So that when the river was high there was no means of crossing it, and people stayed where they were, in their little communities, until the water subsided. "We had dirt roads. No electricity. I've seen all sorts of wonderful things happen in the world. I enjoy the luxury of modern civilization. Instant television, instant entertainment. Instant everything. I enjoy it all. Life was hard for us in the early days. At the end of the Civil War we were destitute. And the slaves who had been freed had no training. It has taken us a hundred years to rebuild our capital base. Our slaves had no capital. We were an agricultural state." Dates are relative. To me 1890, if I apply it to a place like Trinidad, and apply it therefore to the time when my Indian ancestors were just migrating to the New World—to me that date belongs to a period of darkness, something mythical, very far away. Apply it to England, and I think of the modern world: Oscar Wilde, the young Kipling, Gandhi (four years younger than Kipling) studying law in London. In the South dates became relative in this way. And I understood that many of the people of a certain age whom one saw had a special kind of success story to tell. Many of them had started with very little, had started in the wilderness perhaps with only an idea of civilization. (Many of them would have started with as little as my grandparents in Trinidad; but—a further relativity—they had found themselves in a place of greater potential.) "Everybody was poor. I was fortunate. My father was a merchant. He was also sheriff for one term. He ran a general merchandise store. Merchants lent to farmers. They furnished the merchandise to the farmers, and at the end of the year, when the farmers sold their crops, mainly cotton, they settled. If there was a bad year the merchants suffered with the farmers, because if the farmers couldn't pay the merchants couldn't collect. There was nothing in writing, no promissory notes or anything. The saying was, 'My word is my bond.' " A success story for the judge. But in the seventy or eighty years before his birth it had been a life with little movement forward for his ancestors. That too is worth contemplating. "My family on both sides came to Mississippi between 1830 and 1840. My Sugg grandfather lost his leg in the Civil War. He could barely read and write. When he came out he saw that a one-legged man couldn't make a living as a farmer. He went to school for three years, and then taught school for three years. Then he became treasurer of Calhoun County for four years and chancery clerk of Webster County for four years. He bought a farm. He had seven children who grew to adulthood, and some tenant families. The tenants were black, former slaves. I was up there about ten years ago, and I met some old people who were descendants of the tenants my grandfather had. When I left Webster County about a third of the people were black. I'm a country boy, you know. I haven't become accustomed to living in the city yet. "Once a year a tent would come. They called them 'chautauquas.' They would stay about a week in the town. They would have musical programs; sometimes a man would lecture; and you would have plays, dramas. That was our outside entertainment. They came in by train. That was the only way they could come. On Sunday afternoon a passenger train came through. We had four a day. But on Sunday at two-thirty we had a passenger train that went east. A third of the town would go down to the station to see the train, to see who was on the train and who was getting off, and who was leaving town. Everybody just had a big time—that was something to look forward to. "I remember when I was real young we received word that the Ringling Brothers Circus was going to come through some time after midnight. About half the town got up to get to see the circus train go through. You could see we were hurting for entertainment. It was over a hundred cars—that's what it seemed like at the time." Unlike the Delta, where there were rich and poor and caste or class distinctions, in the hills there were no social distinctions, except between black and white. "We didn't have private schools. Everybody went to church. We didn't have a society section. We didn't have a social register. We were just people. We had lots of illiterate whites. In the Depression we had only six months of school for one year; at other times we had eight months. There just wasn't the money to pay the teachers. Formal education suffered. But many of the older people were self-educated, like my father. He wrote a beautiful hand. He used good English. "I had a desire to look at the things I had read about. New York to me was just on the map. I just never dreamed I would go there. I knew that China was across the Pacific and Europe across the Atlantic. I never dreamed I would go to these places. Yes, I dreamed of it, but I didn't think it would become a reality. "But most people were content to remain where they were. We were a close-knit group of people. We had only about thirteen, fourteen hundred people in the town. The only way you could go anywhere was by rail, and you couldn't keep a secret in a place like that. "I believe that closeness is responsible for some of the Mississippi character. When you live that close to people you have to get on with them, or you'd be ostracized. You learn to accept people as they are. We had many eccentrics, rugged individualists. A friend of mine said the other day, 'We don't seem to produce characters like we used to.' I said, 'We're the characters now.' " The closeness of that community, deprived and ill-educated, led to violence. People mightn't feel the need for promissory notes, and mightn't lock their doors, mightn't even have keys for some of the doors. But tempers could be quick. There were homicides, crimes of passion. "They would just get angry, get into an argument, lose their temper. Some of them would be drunk. They would maybe be quarreling and have a fight, and somebody would get killed. They were slow to arouse, but when you get somebody like that angry somebody would get hurt. Otherwise, helpful people, lovely people." Self-reliance was another aspect of that Mississippi country character. "We had two and a half acres of land behind the house. To work that requires hard work. It makes you recognize the fact that anything you want you have to work for it. And it's tied into the religion, because we are taught in the churches that work was honorable and you were not to be lazy and you shouldn't be reliant on other people for a livelihood. In the Book of Proverbs there are many references to work and discipline and reward." So there again it was, the idea of religion threaded into the idea of the pioneer past. "I guess I was about the third or fourth generation from the pioneers. I guess some of it still remained. But I wasn't too conscious of it. When I think back to my childhood it reminds me of what I read about countries that are emerging. They are just beginning, some of them, to realize they can have a better life, but they will have to begin with what they have, and that takes education and training. This country was built on hard work. "The other day I went on a trip, my wife and I, to Arizona. I had been there before. The desert country has an appeal, with the openness of the space. We drove around for four days. And I got to thinking about the first people who went and settled Arizona, and the difficult times they had crossing canyons, rivers, finding water, and protecting themselves from the Indians who were unfriendly—not all were, but some were. And I'm just thankful that I live in a country that has a heritage of people who are willing to look beyond the horizon and catch a vision of opening up new country for others to enjoy a better life. "I think religion had a great part to play in the pioneer spirit. Because, in the pioneer spirit, at the back of the mind you know you are going to make things better for the generations to follow. Part of the motivation for that would come from religion. I think they are so closely intertwined you couldn't separate them." The frontier, nature, faith, work, the contract with other men—in Judge Sugg's world picture the ideas were as knitted together as they were in the world picture of William, the businessman. The Baptist faith made both men complete, each in his own way. But Judge Sugg had also been led by his faith and his past (the two things almost one) to an unlikely compassion—for black people, who had formed 30 percent of the population of his little home town. "I grew up with blacks that I knew intimately, played with—many blacks my own age. And I thought that they were for the most part a deeply spiritual people. After our church was over we used to go to the black churches on Sunday night and stand outside to listen to them sing, and also to see. We enjoyed hearing and seeing them. I remember an old black man we called Uncle Steve. I don't remember his last name. He played a tambourine. And many times it was the only accompaniment—but it was enough. They had rhythm. You could hardly stand still hearing the songs. Many of the songs they made up. Those songs have a great message." So it must make him unhappy, what had happened to the blacks in the cities, and in Jackson? He said: "Being black is not the reason. There are also many whites in that position. The reason is they don't have any spiritual values. Somebody asked Jesus one time what the greatest commandment was. The first one was: Love God. The second was: Love your neighbor as yourself. And that to me is the effect of Christian principles applied daily." Mississippi's reputation for violence towards blacks was deserved. "Especially in the 1960s, many people were unwilling to acknowledge that black people had the same rights and privileges as people of other colors. I think this was a holdover from the days of slavery, when the blacks were servants and were looked upon as property, not people. And we white people have got to recognize the fact that God loves _everybody."_ I told him about my conversation with Alex Sanders, the Court of Appeals judge in South Carolina. Judge Sanders had said that the change of heart in the South, the acceptance by white people of black people's rights, might have had a divine cause. Judge Sugg said: "I believe that God has to create a change of heart—from our adhering to the principles I have mentioned. He has set up the principles there, and I have to accept it. He didn't strike me with a bolt of lightning and say, 'Hey, son, love that black man.' Remember that I grew up in a society where black people were not permitted to enter your front door. They were servants. I had to do some soul-searching." "When did you start doing that?" "Early. Before the sixties. And I finally came to the conclusion that when he said love your neighbor as yourself—I came to the conclusion that the black man was your neighbor too. And I believe I've overcome 99.9 percent of the attitudes someone would have, growing up in a society of white supremists. "Well, here again I haven't had any bolt of lightning. It's been a slow, steady acceptance of the truth that's been with us since the world began. For example, I am now teaching a black man to read and write. He's thirty-nine years old. I count him as one of my friends. We go fishing together. He went to school through the eighth grade, but he lived in a rural community. His father was a farmer. So when school started in September he had to stay at home and pick cotton, gather the corn and other crops. So that by the time he finally entered the school in November all the books had been given out, and he just sat in class. From time to time he had to miss school to cut firewood. Had to drop out in the spring to prepare the land for planting. The result was he didn't go to school for half the school year. He could read a little, write a little, but not enough to function in our society. He is a good man; he has a good job; he works hard. He is deeply religious, married, with three children. Illiterate people are not dumb. Most of them have real good minds." This was how Judge Sugg touched on the work that had been occupying his retirement: the teaching of English to illiterate people and to "internationals." "I regard it as religious work. It gives me an opportunity to share my faith with the people I teach. The Christian faith is built on the great principle that we have to help our fellow man." When he was sixty, and while he was still a judge, he had taken a Baptist workshop in the teaching of English as a second language. He had done so with his wife's encouragement. "Two months after I took the workshop this young man appeared before me charged with burglary. He was fifteen years old. I sentenced him to the training school. The next day one of his sisters appeared and told me that he had got into trouble because his older brother led him to assist in the crime. The older brother was an ex-convict. The father and mother of the young man were both alcoholics, and he had gone to school for only part of one year—that was all the school he had gone to in his life. The sister told me that if I would give him a chance she would provide him with a home and get him a job. I told her that if she provided him with a home I would teach him to read and write. So I did. At the end of little more than a year he could read and write. His father was no longer an alcoholic. So I permitted him to return to Texas with his mother and father." There was a moving symmetry to the judge's career. The man who had grown up in an isolated, inward-looking community had now, in his busy retirement, found a mission. His faith had seen him through all the changes of his circumstances. At every moment his faith had been part of the completeness of his world. I HAD the vaguest idea of what a redneck was. Someone intolerant and uneducated—that was what the word suggested. And it fitted in with what I had been told in New York: that some motoring organizations gave their members maps of safe routes through the South, to steer them away from areas infested with rednecks. Then I also became aware that the word had been turned by some middle-class people into a romantic word; and that in this extension it stood for the unintellectual, physical, virile man, someone who (for instance) wouldn't mind saying "shit" in company. It wasn't until I met Campbell that I was given a full and beautiful and lyrical account, an account that ran it all together, by a man who half looked down on and half loved the redneck, and who, when he began to speak of redneck pleasures, was moved to confess that he was half a redneck himself. It wasn't for his redneck side, strictly speaking, that I had been introduced to Campbell. I had been told that he was the new kind of young conservative, with strong views on race and welfare. (Judge Sugg had told me that people of that type were still coming up, but that his own way, of understanding and help, was the way ahead and was the way most people would eventually go.) Campbell was also the man who represented the other side of the religious South: the authoritarian side. And it was of family and values and authority that we spoke, all quite predictably, until it occurred to me to ask, "Campbell, what do you understand by the word 'redneck'?" And—as though it had been prepared—a great Theophrastan "character," something almost in the style of the seventeenth-century character-writers, poured out of Campbell. It might have been an updated version of something from Elizabethan low-life writing, or John Earle's _Microcosmography_ , or something from Sir Thomas Overbury. (Sir Thomas Overbury, on the English country gentleman, 1616: "His travel is seldom farther than the next market town, and his inquisition is about the price of corn. When he travelleth, he will go ten mile out of the way to a cousin's house of his to save charges; and rewards the servants by taking them by the hand when he departs.") Campbell said, "A redneck is a lower blue-collar construction worker who definitely doesn't like blacks. He likes to drink beer. He's going to wear cowboy boots...." That was the concrete, lyrical way Campbell spoke. But it would be better at this point to go back and hear a little of what he said about himself. "My father was born in Alabama, and his family picked themselves up, left the farm they owned, 360 acres, left it and came to Mississippi to get an education. His father, my father's father, and his mother said, 'We got to get you guys over there to get you a good education.' They obviously had some money saved to do that, pick up and leave. They kept the farm. Daddy sold it all five or six years ago. And when they came to Mississippi all the brothers got jobs when they weren't in school. My father left Alabama in 1923-24. Graduated in 1928. Wound up having a garage and gas station. But they were happy. I never heard my father say a curse word in his life, and that's the truth. He worked all the damn time. We weren't ever real close. He didn't have time to be close. "My mother was a schoolteacher. I grew up in the Baptist church. I was pretty force-fed. We went to church as soon as the doors opened. We went there on Wednesdays for the prayer meeting. We would go for the big summer revivals. Go every night, bored to death." Then, without a pause, Campbell said: "In the long run it was the best thing I've ever had. My mom and dad gave me values that came back to me when I was twenty years old. But I'd rebelled out. Most of the children conformed. I really wanted to act crazy. I drank more, ran around more. I started working in a grocery store when I was twelve, and that's the damned truth. I loved it. You met all the characters. You got all the black trade. They sat on the feed bags; Mama came to town with four or five kids, and she had to nurse a couple. I liked working there. Always somebody coming in there. Hee-hawing all the time. You knew everybody who came in. It was a good store. This was Saturdays. I liked the money. When I started I made four dollars a day. When I left I was making about seven. "I cut right away. I drove a damn dumper in the summertime. They were constructing this interstate and they needed somebody who could read and write, to count the sacks of fertilizer that went into the airplane. They were fertilizing the sides of the road to get the grass to grow. It was boring as hell. These are days long gone. It's funny how you change and mature. I wanted to be crazy. I had a good time being crazy." "You wanted to be one of the boys?" "It's important in Northeast Jackson, as we call it, to be well liked, to be well thought of. But I wasn't relating to the church. I'd go with my mama at Christmastime, but I was bored to death. But the values of the church—do good, do right, don't drink, don't kill anybody, no stealing, the Ten Commandments, don't covet your neighbor's wife—I don't believe in some parts of this culture those values are being instilled. Those kids running up and down—I used to work in mobile-home parks, and we've got some unsavory characters there—they need their butts worn out, like I've gotten mine worn out. "I think the reason for that is the breakdown of the family. Where the father and mother are not both there doing their job. I bring up my children to respect me. And I think he fears me, and I think that's good, because he knows I'm not going to put up with everything. I hug him and kiss him every day. Some people say I'm right; some people say I'm wrong. I was afraid of my father. I was afraid I was going to get my behind worn out. I don't like it any other way. People saying 'Yah,' 'Nah'—smart-mouth children—I think they'd do so much better if they worked hard for just ten more minutes every day, and if they said 'Yes, sir,' 'No, sir,' and you whipped their ass until they said it right. "I think it all goes back to being brought up right. Get some values back in the homes. We're talking about blacks now. Get them to stay in the school, keep their damn butts quiet. I'd be a dictator and have this place shaped up. I'm just a law-and-order, blood-and-guts guy." Campbell was in his early forties or late thirties. He was short and chunky, a strong man. He wore bright colors. He talked like a man with a character to keep up, but there was no touch of humor in his voice or face. He had seen the black area of Jackson spread. And he had made money out of that, buying from fleeing whites and selling at a profit to the blacks moving in. There was one year when he had sold ten houses like that, and had made $60,000. "That wasn't bad. I was profiteering. I ought to be shot." I wasn't sure what was "character," and what was real. And then I said, "Campbell, what do you understand by the word 'redneck'?" And the man was transformed. He said: "A redneck is a lower blue-collar construction worker who definitely doesn't like blacks. He likes to drink beer. He's going to wear cowboy boots; he is not necessarily going to have a cowboy hat. He is going to live in a trailer someplace out in Rankin County, and he's going to smoke about two and a half packs of cigarettes a day and drink about ten cans of beer at night, and he's going to be mad as hell if he doesn't have some cornbread and peas and fried okra and some fried pork chops to eat—I've never seen one of those bitches yet who doesn't like fried pork chops. And he'll be late on his trailer payment. "He's been raised that way. His father was just like him. And the son of a bitch loves country music. They love to hunt and fish. They go out all night to the Pearl River. They put out a trot line—a long line running across the river, hooks on it every four or five feet. They bait them with damn old crawfish, and that line'll sink to the bottom, and they'll go to the bank and shit and drink all night long, and they'll get a big fire going. They'll check it two or three times in the night, to see if they're getting a catfish. It'll be good catfish. These redneck sons of bitches say that they'll rather have one of these river catfish than one of those pond catfish. They say it's got a better taste. "You know, I like those rednecks. They're so laid back. They don't give a shit. They don't give a shit." "Is that because they're descendants of pioneers?" "There's no question about it. They're descendants of pioneers. They're satisified to live in those mobile homes. I never knew how my father was so cultured. If you saw the place he came from—he came from the most absolute, the most desolate place in the woods on the Mississippi-Alabama border. The rednecks have the pioneer attitude, all right. They don't want to go to the damn country club and play golf. They ain't got fifteen damn cents, and they're just tickled to death. "They're Scotch-Irish in origin. A lot of them intermarried, interbred. I'm talking about the good old rednecks now. He's going to have an old eight-to-five job. But there's an upscale redneck, and he's going to want it cleaned up. Yard mowed, a little garden in the back. Old Mama, she's gonna wear designer jeans and they're gonna go to Shoney's to eat once every three weeks." I had seen any number of those restaurants beside the highways, but had never gone into one. Were they like McDonald's? Campbell said, "At Shoney's you'll get the gravy all over it. That's going to be a big deal. They'll love it. I know those sons of bitches. "If he or she moves to North Jackson, he'd be upscale. He wouldn't be having that twang so much. But the good old fellow, he's just going to work six or eight months a year. He's going to tell his old lady, 'I'm going to work.' And he ain't going. If it rains, he ain't going to work—shit, no. He's going to go to the crummiest dump he can find, and he's going to start drinking beer and shooting pool. When he gets home there'll be a little quarrel with his wife, and he'll be half drunk and eat a little cornbread and pass out, and that's the damn truth. And she'll understand, because she's so used to it. "She doesn't drink. It's normally the redneck guys who drink—whiskey or beer. She's got some little piddling job. She's probably the basis of the income. She's going to try to work every day. But he's always waiting for that big job at fifteen dollars an hour, which is never going to come around. One time he had a union job at twelve dollars an hour. And he thinks that's going to come back. He'll be waiting fifteen years for another twelve-dollar job. And he won't get it unless he gets off his ass and goes to Atlanta, Georgia, or Nashville—someplace that's hot. It's sure not hot around here. But he's so damn satisfied. The son of a bitch's so damn satisfied. When he gets the four-dollar job: 'No, I got something else to do.' I could give five guys a job today, minimum wage. Three-thirty-five an hour. But I wouldn't find five sons of bitches if I looked all damn day long. 'You want to work for three-thirty-five?' 'No. Not going to work for no three-thirty-five son of a bitch.' "So he's going to be making six dollars on an average, six to six and a half an hour. And just for six, eight months a year. You see, he doesn't want to work all day long. He's satisfied by getting by. They don't like to be told what to do. It's the independent spirit. It's the old pioneer attitude. 'I've got enough to eat, drink, and a little shelter. What more do I want?' "Religion? They'll go to church when the wife beats the hell out of him. But he's not going to put on a coat and tie or anything. He won't do it. He'll kick her ass. "They're not too sexual. They'd rather drink a bunch of old beer. And hang around with other males and go hunting, fishing. We're talking about the good old rednecks now. Not the upscale ones. They've got the dick still hard. That's damn true. "The rednecks are about sixty to sixty-five percent of the white population. I'm running the good old rednecks and the upscale rednecks and a whole bunch of lower-middle-class rednecks. They have the same old attitude as the black people. Daddy is home a little more often. But they're tickled pink that they ain't got nothing. You wouldn't believe." I asked about the dress, and especially the cowboy boots. Why were they so important? "It's the image they have to project. They'll have an old baseball hat with the bill turned down just so. They won't have the cowboy hat. They want that particular redneck style. They want people to know that they don't give a damn. They want people to know: 'I'm a redneck and proud of it.' "What you must put in, and make sure you do, is them sons of bitches _love_ country-and-Western music. It's down-home music. It's crying music. Somebody got killed in a truck. Or a train ran over somebody. Or somebody ran away with somebody's wife. "Presley is a redneck like you wouldn't believe. He's a double redneck. Some of the women here would whip your ass for saying it. I'm probably a redneck myself." And when he said that, Campbell won me over. He said, "I just dress differently. Polo shirt and Corbin slacks." I liked the concreteness of Campbell's details, the brand names, the revelation of a fashion code where I had just seen bright colors. Abruptly, then, he went off on another track. "If my father hadn't worked so hard—and I know that was important, to work hard and try to do good—" I got him back to the subject of redneck sex. "If they're young they got it hard. But the older they get they drink more, and then they don't care about it any more. And she's just there, getting some clothes washed down in the laundromat once a week. Sit down and watch it and smoke some cigarettes—that's right, that's what she will do. "I'll tell you. My son ain't gonna fool with a redneck girl in Rankin County. Can't hide it. Everybody knows everybody else. And I'll tell you something else. They talk different. And I want my children to stay in their social strata, and that's where they'll stay. I would say, 'Keith, you weren't brought up like that. You get your ass out of that. You're way above that, and we're going to stay way above that.' But Keith's all right. He wants to dress nice; he wants to look good; he wants to make money. We run in the Northeast Jackson crowd. That's supposed to be upscale." I said, "But beauty is beauty. A beautiful woman is going to win admirers anywhere." "Beauty is beauty. But when she opens her mouth and starts talking and says she lives in Rankin County— _uh-uh_ —that's the end of any charm. But that case will probably never happen with me. It will never happen with my son, because he already knows what a redneck is. You know what the word comes from? The back of the man's neck is red from the sun—" But something happened—somebody came into the room, someone asked a question—and Campbell didn't finish the thought. It was finished for me some days later when I heard from an old Mississippian that the word "redneck," when he was a child, was not a pejorative; was the opposite, in fact, and meant a man who lived by the sweat of his brow; and that it was only in the 1950s, when the frontier or pioneer life was changing, that the word began to have unflattering associations. Campbell said: "I admire them for their independence. But it's not right for the society now. No question about it. It was great a long time ago. But not now. You can't get business done in a modern city with that kind of mentality. We got to change that redneck society and that black society, or the wealth is going to be just in the few hands that it's always been in. As far as I'm concerned, I hope it stays like that. I ought to be shot." He came back from that political pitch. He said: "Rednecks like four-wheel-drives. Four-wheel drive pickup trucks. They can run down everywhere through the swamps. And some of them like an old beat-up van, half-painted. Half-painted, because he's going to fix this side but he's never going to get around to the other side. He'll drive that son of a bitch forever, until it falls apart or gets a flat tire, and he'll just leave it then. He won't have a spare, you see. And he'll come back that afternoon and get it fixed. He'll get one of his buddies to get an old tire, and they'll go and fix it. The sons of bitches can fix anything on a car. Them bastards can do anything. They can drag the car to the side of the highway and jack it up and fix it on the spot." The morning was over. Campbell had a business lunch. He was going just as he was, in his bright, horizontally striped green-and-yellow jersey, the stripes of varying width. But he had so enjoyed talking of redneck life; it had brought back so many memories of his own "crazy" youth, and prompted so many yearnings, that he wanted to talk a little more, and he promised to come again, in the afternoon, after his lunch and before a business trip to Florida. He telephoned after his lunch. I asked how it had gone. "I'm smelling like hell. A whole load of garlic at lunch. But made money. Unusual, a business lunch where I actually made money." We met later, in a hotel bar. He had been drinking to celebrate his deal. His eyes were moist, a little bloodshot. He had spoken deadpan in the morning; and he spoke deadpan now. But the drink had made his speech chaste. He spoke no swear word, no unnecessary or blaspheming intensive. I said I had been thinking over what he had said about the rednecks. From the way he had described them, I thought of them as a tribe, almost an Indian tribe, free spirits wandering freely over empty spaces. But weren't they now a little cramped, even in Mississippi? Campbell said: "It's a nice life, but it depends on a natural life being available. I would say that if those rednecks didn't have these natural surroundings in Mississippi—because the outdoor thing's their favorite pastime—they would be very bored. And hunting rights are becoming so valuable now, they're going to be forced out of the market within five years. We've got a lot of people coming up this far north now from Louisiana, because we have a lot of deer, big deer, and they're paying big prices for hunting rights. I bet you couldn't drive forty-five minutes out of Jackson without finding land that wasn't leased. It's going to have a 'Posted' sign: 'This land is leased by So-and-So Hunting Club. Don't Trespass.' One day there's going to be a killing about it, I tell you. They've already had a couple of killings in the state. Duck-hunting especially—it's so competitive in the Delta, so valuable, so expensive to get a lease up there. You've got to have a lot of money. It will cost you about three thousand dollars a year to hunt duck. Though duck-hunting is more of a gentleman's sport. Those rednecks are more meat-hunters. "Still, there's a lot of land in Mississippi. They'll poach on somebody. Otherwise they'll just be beer-drinkers and have no place to go and nothing to do. It's what's worrying me about rednecks. They're not adapting, and they're being left behind. As the population grows, it's going to be more and more expensive for them to go out hunting, and they're not going to be able to afford it. "At the moment they have some dog clubs. They get in real cheap somewhere and they'll do some deal, some deal with somebody's family—fifteen, twenty, thirty guys in a family deal; cousins, all of them on family land. All getting together ten or twelve times a year. And they'll have a ball." "What about the women? Do they go out on those trips?" "They just sit at home. They're worrying about where the next sack of potatoes is coming from. But they can live on a hundred dollars a week. Cheaper than you and I. And they're not skinny. Some of them are big and fat. What am I saying? They're _all_ big and fat. "After lunch, you know, I went back to the office. The secretary's a redneck woman. I told her about our talk this morning. About the rednecks and the frontier mentality. Telling her it's not so great these days, you know. Different times. And she said, 'You know, Mr. Campbell, at one time I used to be envious of you. I wanted what you had. But now I feel I'm just different. I'm just born into it. I ain't got nothing, and I know now I ain't going to have nothing.' I said, 'It's because you ain't got the right kind of husband. Why don't you kick your husband's ass?' And she said, 'Oh, Mr. Campbell, I can't do that. He's just an old redneck.' And her children are just like him. "Presley, he was the all-time neck. And that fellow there, that fellow at the desk with the long hair and beard." He was talking about a man with a red plaid shirt hanging out of his trousers. This man was walking delicately on the floor, as though nervous of slipping on it with the leather soles of his cowboy boots. Campbell said, "He's probably thinking, with that hair and beard, that he's God's gift to the world. But he's just a neck. He's as lost as a goose. He's never been on a tiled floor in his life. He's come in here thinking it was another motel. He doesn't know what to do. He's just moping around here: 'Oh shit, where am I?' " ART HALLOWS, creates, makes one see. And though other people said other things about rednecks—though one man said that the best way of dealing with them was to have nothing to do with them, that their tempers were too close to the surface, that they were too little educated to cope with what they saw as slights, too little educated to understand human behavior, or to understand people who were not like themselves; that their exaggerated sense of slight and honor could make them talk with you and smile even while they were planning to blow your head off—though this was the received wisdom, Campbell's description of their mode of living made me see pride and style and a fashion code where I had seen nothing, made me notice what so far I hadn't sufficiently noticed: the pickup trucks dashingly driven, the baseball caps marked with the name of some company. The next day, a Saturday, there was a crowd in the hotel and the restaurant across the parking area from the hotel. And, as if in fulfillment of Campbell's description of the redneck style, three men got out of a dented and dusty car and opened the trunk to take out their redneck boots. They had arrived in gym shoes. They took off their gym shoes and put on their cowboy boots before going into the hotel. One among them was opening a bottle of beer with his teeth. I felt now, after Campbell, that the man doing that very redneck thing perhaps needed a little courage. Perhaps, entering the hotel and walking on the tiled floor, he was going to feel "as lost as a goose." For some days Campbell's words and phrases sang in my head, and I spoke them to others. One afternoon I went to a farm just outside Jackson. Someone there, knowing of my new craze, came to me and said, "There are three of your rednecks fishing in the pond." And I hurried to see them, as I might have hurried to see an unusual bird or a deer. And there, indeed, they were, bare-backed, but with the wonderful baseball hats, in a boat among the reeds, on a weekday afternoon—people who, before Campbell had spoken, I might have seen flatly, but now saw as people with a certain past, living out a certain code, a threatened species. It gave a new poetry to what one saw on the highway: the baseball caps with the bill "turned down just so," the bandeaux or sweat bands on the forehead of women drivers of redneck-style pickup trucks. Even the advertisements in the newspapers for those trucks—and the price: about $8,000—had a new meaning. AND IT was of the redneck, the unlikely descendant of the frontiers-man, that I talked to Eudora Welty when I went to call on her. I had arrived early, and waited on the street below the dripping trees. She was ready early, and could clearly be seen through her uncurtained front window. But I was nervous of knocking too soon. So for a while we waited below the big, dripping trees in the gloom after rain, she behind her window at the end of her wet front garden, I in the car. And when I felt the time was suitable I walked up the wet path to her front door. On the door, in her strong writing, was a note asking people not to bring any more books for her to sign. She wanted to save as much of her energy as possible now for her work. I knocked; and she opened, like someone waiting to do just that. She was extraordinarily familiar from her photographs. The frontier was so much in her stories: a fact I had only just begun to appreciate. And she was willing to talk of the frontiersman character. "He's not a villain. But there's a whole side of him that's _cunning_. Sometimes it goes over the line and he becomes an outright scoundrel. The blacks never lived in that part of the state. They came over to work on the plantations. Most of the rednecks grew up without black people, and yet they hate them. That's where all the bad things originate—that's the appeal they make. Rednecks worked in sawmills and things like that. And they had small farms. They are all fiercely proud. They dictate the politics of the state. They take their excitement—in those small towns—when the politicians and evangelists come. Scare everybody, outwit everybody, beat everybody, kill everybody—that's the frontiersman's mentality." I told her the story Ellen had heard as a child about the rednecks to the south of the town where she had spent her summers: the story of traveling salesmen who had been roughed up and hitched to a plow and made to plow a field. Ellen had said that this story had come down from the past; and I had thought of it as a romantic story of the wickedness of times past, an exaggerated story about people living without law. But Eudora Welty took the story seriously. She said, "I can believe the story about the salesmen. I've heard about punishing people by making them plow farms." We talked about Mississippi and its reputation. "At the time of the troubles many people passed through and called on me. They wanted me to confirm what they thought. And all of them thought I lived in a state of terror. 'Aren't you scared of them all the time?' A young man came and said that he had been told that a Mr. So-and-So, who was a terrible racist, owned all of Jackson, all the banks and hotels, and that he was doing terrible things to black people. It was a fantasy. It wasn't true. The violence here is not nearly as frightening as the Northern—urban—brand." A frontier state, limited culturally—had that been hard for her as a writer, and as a woman writer? The richness of a writer depends to some extent on the society he or she writes about. She said: "There is a lot behind it, the life of the state. There is the great variety of the peoples who came and settled the different sections. There is a great awareness of that as you get older—you see what things have stemmed from. The great thing taught me here as a writer is a sense of continuity. In a. place that hasn't changed much you get to know the generations. You can see the whole narrative of a town's history or a family's history." I HAD been hearing more and more about the unusual constitution of the state of Mississippi, the constitution drafted in 1890, after the Civil War and Reconstruction. I had heard that this constitution was responsible for a good deal of what one saw still; and I went to see former Governor William Winter about it. He had a high reputation in the state, both as a governor and as a man knowledgeable about the state's history. Mr. Winter saw me in his office late one afternoon, at the end of a busy day; that morning he had flown to Little Rock, Arkansas. The former governor was now a partner in a Jackson law firm. He spoke precisely and legally; he had books and a map ready; and all the time we spoke he was looking up references in books. On the wall of his office—and among color photographs of his family—was a large, old map of the state. When he went to get me a cold diet-cola drink I got up and looked at it. It was linen-mounted and framed, and had been a gift to Mr. Winter. It was a French map, of 1830 perhaps. It showed only the southern counties of the state as settled. A large central area had been marked out for further white settlement. Though this area was almost as large as all the settled counties put together, on the map it was just called Hinds County (and part of that area was to become the Rankin County of which Campbell had spoken with so much feeling). The areas to the east and north were still, in 1830, Indian country: Choctaws and Chickasaws. Half the state Indian country in 1830; in 1860, the Civil War about to come; in 1890, after the Civil War and Reconstruction, a new constitution. History here seemed to come in thirty-year segments. Add the yellow-fever epidemics of 1873, 1874, 1878, 1903; add the Great Depression. There was nothing settled, stable. The former governor said: "The atmosphere in which the 1890 constitution was written was dominated by the need for whites to provide a means for the restoration of white control of the political processes of the state. The constitution of 1861 did not afford a vehicle for the elimination of black voters and black officeholders. There were many black officeholders when the 1890 constitution was written." There were two black senators, a black congressman, a black lieutenant governor, and a black superintendent of education. "The 1890 constitution of Mississippi became a model for other Southern states—in its resourceful provisions for the discouragement of black voting." Almost as important as the racial provisions were the antibusiness provisions. The people who wrote the constitution wanted the state to remain "a pastoral state, an agricultural state." They didn't want big business or the corporations coming in, encouraging "unfavorable competition for jobs with the agricultural community." "We threw various roadblocks in the path of corporate development. It had the effect of discouraging investment in industrial plants in the state. A major paper-manufacturing company, the Gaylord Corporation, desired to locate in Pearl River, Mississippi. Because of the constitutional limitations here, that plant located across the river, in Louisiana, within sight of Pearl River County, and virtually created a new town in Louisiana, Bogalusa. There was a limit in Mississippi on the amount of property a corporation could own, a limit on the capital structure of a corporation. Even in 1890 that constitution singled us out as being noncompetitive for capital. "There is an archaic tone to the whole document. We need the psychological benefit now of a late-twentieth-century document. And, the second thing, we need the restructuring of the manner in which we govern the state. We have to eliminate many of the processes designed to decentralize and fragment power. In 1890 there was a distrust of any concentration of power in any one individual. With the result that there's not a single law that's passed by the Mississippi legislature that is in strict accordance with the constitution of 1890." He handled a mighty law book and showed me Section 59 of the 1890 constitution. "Bills may originate in either house, and be amended or rejected in the other; and every bill shall be read on three different days in each house, unless two-thirds of the house where the same is pending shall dispense with the rule; and every bill shall be read in full immediately before the vote on its final passage; and every bill, having passed both houses, shall be signed by the president of the senate and the speaker of the house of representatives, in open session; but before either shall sign any bill, he shall give notice thereof, suspend business in the house over which he presides, have the bill read by its title, and, on the demand of any member, have it read in full; and all such proceedings shall be entered on the journal." There was a provision in the section for amendment, so that laws could be passed. But an awkward member could still cause delay. "I have seen it happen. I have seen one member stand up and demand that the bill be read." Was there an element of madness in the framers of the constitution? "It was an anti-government legislation. It was intended to make it as difficult as possible to pass legislation. The attitude being: The fewer bills we have, the better off we are going to be. The less government the better—that is a fair way to put it." "What sort of men were they in 1890?" "They represented the ultraconservative, planter, agricultural interests. Many of them were veterans of the Civil War. There was a strong racial bias which ran through the membership. They were committed to eliminating the black presence in the political process." "Do you think there was anything like a romantic feeling for the land?" "It was a feeling for the land of the landowner, not the worker. The yeoman farmer was not the dominant feature of the convention. The constitution spoke to the economic interests of those who drafted it. For instance, it spoke of the maintenance of a levee system along the Mississippi River—which really has no place in a constitution. "The story about that is like this. In the spring of 1890 the levees gave way and parts of the Delta were inundated. To cope with that, the constitution-framers later that year, 1890, wrote into the constitution a whole article designed to cope with such disasters. Article 11." He showed it to me. It ran to eight pages. It dealt in great detail, technical and fiscal, with the way the levees were to be maintained; it outlined taxation to meet the expenses; it mentioned the names of vanished railroad companies. "An article like this really has no place in the constitution of a state. But you can see the preoccupation of the drafters. They were looking after their farms up in the Delta." There might have been no romantic feeling for the land. But how did the former governor explain the anti-government tone of the constitution? "It reflected the basic frontier aspect of the state. They were saying: 'We're going to use government to solve those problems that appear to us important, but we're not going to use government to interfere with our lives.' As it was used, the constitution worked against the powerless in the state. But that is no longer a valid objection. Corrections have been made." And the constitution has left its mark. "The Carolinas and Georgia had tobacco-processing plants and textile plants. Alabama has a well-established industrial base going back to the nineteenth century. Mississippi never developed this kind of base." On the former governor's desk, and got out for our meeting, was a map of the United States showing, for 1984, the "economically competitive" counties and the "distressed" counties. The competitive counties were colored blue, the distressed counties pink. The map showed three concentrated areas of distressed counties: on the Mexican border; the Indian areas in the West; and, making almost one pink area, the Southern Black Belt of Alabama and almost all of Mississippi. Only the area around Jackson was colored blue. AND YET, though there was distress—comparatively speaking: American distress was not like the distress in other countries—and though many people would agree with what the former governor said about the archaic nature of the constitution, there was also in some people a nervousness about change. The frontier constitution had grown to represent something true about the state. Many people now grieved for the past which that constitution had secured, when life was "easier," more countrylike; when communities were small and everyone knew everyone else; when time was not money. In the 1830 map in the former governor's office Hinds County had been marked out for settlement by people whose descendants were to become the rednecks of Campbell's poetry. Now the rednecks, like the Indians before them, found their hunting grounds shrinking. IT HAD been a frontier state, but always with this contradictory component of slavery. It was of slavery that the old plantation land around Natchez, on the river, spoke. That land, as flat and warm and soft as the ricelands of South Carolina, spoke of wealth and the need for black men, by the thousands. But Natchez also had its plantation houses, nowadays the object twice a year of "pilgrimages": the old sentimentality of the South, the divided mind, the beauty and sorrow of the past containing the unmentionable, ragged, black thing of slavery. It was a wretched little town, steaming after rain on its "bluff"—not very high—beside the muddy river. Rain dripped from the heavy branches of the red and white crape-myrtle trees. It had had an oil boom. That boom, like so many other Southern booms, had abated. Louisiana lay across the river. I drove there, hoping to find some solid, real place—rather than something connected with the tourist trade—to have lunch in. It was flat, delta country. The air that came through the car's air conditioning smelled of onions. It was this high smell, as much as the flatness of the land and the apparent hopelessness of my quest—just fast-food places beside the highway: tall, beckoning signs above, simple structures below, bright colors against the flat green—that drove me back to Natchez. The Louisiana town was called Vidalia. Vidalia was also the name of a kind of onion. It must have been a delicacy in the South; in many places I had seen home-painted signs at the roadside offering Vidalia onions. So I smelled onions until I got back to Natchez, where I had the jungle-sewer smell, the smell of the river, which was almost exactly like the jungle-sewer smell of Manaus, on the Amazon, in Brazil. Just as the rusting corrugated-iron roofs and the relaxed black people sitting in old wooden houses or standing or rocking and staring gave a touch of the West Indies—as disturbing to one's sense of place as the overgrown tennis courts of Tuskegee had been: those courts one afternoon, with African students at play, had absolutely suggested Africa. And I was wrong about the Louisiana town of Vidalia. A woman in a souvenir shop with a little view of the river told me so. The Vidalia of the onions was in Georgia, however much I might have smelled onions in Vidalia, Louisiana. The woman, suffering—trade wasn't so good—said: "My husband loves Vidalia onions. On Sundays"—they lived on the other side of the river—"when we are going to the club, he will say, 'Susan, get a couple of Vidalia onions.' I will say, 'To take to the club? On Sunday?' And he will say, _'Bring_ me the onions.' He has a black girl up there in the club who spoils him. He loves bread, butter, ketchup, and slices and slices of Vidalia onions. She fixes it for him." There was a cloudburst. I looked over her stock. She was selling a big black mammy in a long red dress over a white blouse. She said, "The day I bought them I said to Pearlene—she's the cook—'Pearlene, do you know what I've done this morning? I've bought two of you.' It broke her up, and she said, 'Well, at least you could buy me the dress to go with it.' " It cleared up. But as soon as I went outside it began to rain again. I went back into the shop. I said, "I don't want to get a cold." She said, "The first year I ran this place I got bronchitis every day. If it wasn't for my husband, I wouldn't have stuck it out. But then somehow I developed an immunity. Silver tarnishes in three days in this kind of weather. Polishing silver every three days can't be good for the silver." The rain fell harder, big, splashing drops. She talked on, pleased to have the company, in the middle of her Natchez souvenirs. The Mississippi was hazed with mist and rain; the bridge was indistinct; the Louisiana bank couldn't be seen. And when I got back to Jackson—driving along the Indian Natchez Trace Parkway—I found that the rain, and the great heat, and my own ignorance of the beauties to look for, had kept me from the other wonder of Natchez. The river was altering its course; the bank at some place was being washed away; and some of the pretty old houses of planter days were collapsing into the river. And every gal on Natchez bluff Will cry as we go by, oh. They were lines brought back to me by the weather, and the heat, and the thought of plantation labor: lines, perhaps mangled by memory, from a long narrative poem about the Civil War by Stephen Vincent Benét, which I had looked at forty years before. # 6 # NASHVILLE # Sanctities DRIVING BACK one stormy afternoon in Mississippi from the Delta to Jackson, and excited by the dark sky, the rain, the lightning, the lights of cars and trucks, the spray that rose window-high from heavy wheels, I began to be aware of the great pleasure I had taken in traveling in the South. Romance, a glow of hopefulness and freedom, had already begun to touch the earlier stages of the journey: my arrival at Atlanta, the drive from there to Charleston. I had all but forgotten the writing anxieties I had had on both those occasions. And I thought that afternoon that it would have completed my pleasure if I didn't have to write anything; if I didn't have to worry about what to do next and who to see; if I could simply be with the experience. But if I wasn't writing, if I didn't have a purpose and at times a feeling of urgency, if the writing hadn't given me a schedule, places to go to, how would I have passed the days at the Ramada Renaissance hotel in Jackson, beside the freeways? Would I have even come to Mississippi? The land was big and varied, in parts wild. But it had nearly everywhere been made uniform and easy for the traveler. One result was that no travel book (unless the writer was writing about himself) could be only about the roads and the hotels. Such a book could have been written a hundred years ago. (Fanny Kemble's account of traveling in 1838 from Philadelphia to the Georgia Sea Islands, by rail and stagecoach, partly on a road covered with logs, is a proper adventure.) Such a book can still be written about certain countries in Africa, say. It is often enough for a traveler in that kind of country to say, more or less, "This is me here. This is me getting off the old native bus and being led by strange boys, making improper proposals, to some squalid lodging. This is me having a drink in a bar with some local characters. This is me getting lost later that night." This kind of traveler is not really a discoverer. He is more a man defining himself against a foreign background; and, depending on who he is, the book he writes can be attractive. A book like that can be written about the United States only if the writer, taking the reader into his confidence, sets himself up as alien or outlandish in some way. Generally, though, this approach cannot work in the United States. The place is not and cannot be alien in the simple way an African country is alien. It is too well known, too photographed, too written about; and, being more organized and less informal, it is not so open to casual inspection. I had been concerned, from the start of my own journey, to establish some lines of inquiry, to define a theme. The approach had its difficulties. At the back of my mind was always a worry that I would come to a place and all contacts would break down and I would not get beyond the uniformity of highway and chain hotel (the very romance I was surrendering to that afternoon in the Delta). If you travel on a theme, the theme has to develop with the travel. At the beginning your interests can be broad and scattered. But then they must be more focused; the different stages of a journey cannot simply be versions of one another. And, more than the other kind of travel, this traveling on a theme depended on luck. It depended on the people you met, the little illuminations you had. As with the next day's issue of a fast-moving daily newspaper, the shape of the chapter in hand was continually being changed by accidents on the way. Pure luck—our conversation had begun so tamely—had given me Campbell's lyrical account of the rednecks of Rankin County: the outdoor life, relic of frontier self-sufficiency, mixed up with a dislike of black people, and oddly meshed with the love of country music, "down-home music, crying music," and the cult of Elvis Presley. That meeting with Campbell (putting to flight ideas about Faulkner and Oxford, Mississippi) had suggested to me how I might move. Though I knew little about music; and the achievement of Presley, while he lived, had passed me by. PRESLEY'S BIRTHPLACE was in the small town of Tupelo in northern Mississippi. The businessman who was taking me there said, "He was the lowest of the low." He spoke gravely, without compassion; and with a very slight toss of the head. His distaste for the lowness he had in mind was touched with something like awe. I remembered Campbell's words, and quoted them: " 'The all-time neck'?" "Lower than that." In a magazine in the Jackson hotel I had seen a photograph of the narrow, two-roomed "shotgun" house, front porch opening into bedroom opening into back kitchen. I had expected, from the photograph, to find a preserved building in an urban wasteland. But Tupelo was a busy little town, one of the busier business places in Mississippi, and the area around the Presley birthplace had become suburban, with the house itself like somebody's ancillary cabin (or "dependency") in the shade of a tree, with lawn all around. On the front porch was a swing seat for two, hung on chains fixed to the ceiling. The front room was the bedroom. It was freshly papered, with a simple floral design; and on one wall was a framed printed copy of the "If" poem. I asked the woman in attendance whether the poem had been there in the Presley days—in the days of Presley's father, that is, who was said to have built the house. It was a foolish question; the woman didn't answer. The businessman said that the paper on the walls in the old days would have been newspaper. And of course the house had been made to look as pretty as possible, with the swing seat and the bedstead and the period stuff in the kitchen—like something from the Mississippi Agriculture and Forestry Museum in Jackson, where the artifacts, the household tools, of only a few years before had been put on reverential display because, though so recent, they were part of a special country past which many people had shared and which had now vanished. (In England the 1920s are within reach, like the day before yesterday. In Mississippi the 1920s are long ago, closer to the beginning of things.) In the Mississippi museum the past on display could be felt as a kind of religion, a bonding. And there was something of that feeling in the prettied-up little shotgun house. (Imagine people living in that cramped space, though: imagine the crush, the disorder.) The very lowness of the man's origins had made him that much more sacred, to the—fattish—people who sat on the swing seat and had their photographs taken. At the back of the house was a hall where cards and souvenirs and copies of Memphis newspapers printed the day after Presley's death in 1977 were on sale; and there was a new small chapel, with stained glass. At the side of the house was a park. Presley money had worked that magic. It was like the stories one heard—and these stories were always moving, the fulfillment of so many kinds of fantasies—of nurses in hospitals and other simple people whom Presley had surprised with the gift of a Cadillac. In the souvenir shop the businessman said, "Did you get that woman's accent? Listen." He spoke with the awe with which he had spoken of Presley's origins. But my ears didn't have the fine local tuning. They didn't pick up what the businessman heard. The businessman's attitude was historical. It had precedents almost as old as the state. Even Fanny Kemble, faced with the "pinelanders" of Georgia in 1839, is moved to rage and contempt, rejecting as unspeakable the people of her own race whom she sees as degenerate. One thinks of Fanny Kemble as gentle, hating injustice. But as a former actress, from a very great English acting family, she was also concerned with the way people looked. She hated slavery; but she didn't care for the physical appearance of the blacks on the American plantations (she thought the West Indian blacks were better-looking). And the passage about the pinelanders should be quoted in full. Its very repetitiveness catches the writer's confused emotion and shame: "These are the so-called pinelanders of Georgia, I suppose the most degraded race of human beings claiming an Anglo-Saxon origin that can be found on the face of the earth—filthy, lazy, ignorant, brutal, proud, penniless savages, without one of the nobler attributes which have been found occasionally allied to the vices of savage nature. They own no slaves, for they are almost without exception abjectly poor; they will not work, for that, as they conceive, would reduce them to an equality with the abhorred Negroes; they squat, and steal, and starve, on the outskirts of this lowest of all civilized societies, and their countenances bear witness to the squalor of their condition and the utter degradation of their natures. To the crime of slavery, though they have no profitable part or lot in it, they are fiercely accessory, because it is the barrier that divides the black and white races, at the foot of which they lie wallowing in unspeakable degradation, but immensely proud of the base freedom which still separates them from the lash-driven tillers of the soil." Georgia had been established in 1733 as a colony for free men. But within sixteen years the slave-owners had changed that; and communities of poor whites like the pinelanders, migrants from other states, had been created. There were no poor-white groups of comparable size in the West Indian slave colonies. There were only planters and slaves, in the main. So that after emancipation the islands became in effect black; and, without rednecks, there was on the islands no post-Reconstruction, "Southern"-style history. In the settling of the New World, and other new places in other continents, there were immense cruelties, not only to the local populations but also to the people transported. Long after any group can be held responsible, succeeding generations live on as victims or inheritors of old history. I began to get some new feeling about the Presley cult at Tupelo: the birthplace of the man of the people, the saint of the people, made pretty and suitable, a shrine. And I was half prepared for what I later saw in Charles Wilson's informal Presley collection when I went to the Center for the Study of Southern Culture at Oxford, Mississippi. The most striking item was a poster that showed a tight-trousered, full-bottomed Presley playing a guitar in the lower left-hand corner, with a staircase leading up to his mother and Graceland—the Presley house in Memphis—in the sky. Redneck fulfillment—socially pathetic at one level; at another, religious art of a kind, with Christian borrowings: the beatification of the central figure, with all his sexuality, Graceland like a version of the New Jerusalem in a medieval Doomsday painting. On the outskirts of Memphis was Graceland. Highway direction signs proclaimed the name. A public road separated the house and grounds from the Graceland parking lot, the ticket hall, and the place where the two Presley airplanes were now parked: emblems of majesty. The tours of the house and grounds were organized. Visitors couldn't wander around; they had to be taken from the ticket hall in special tour buses. On the afternoon I went the tours had been booked up an hour and a half ahead. So I didn't see the house, and had to be content with the stories of television sets everywhere, the decorations derived from the decorations of Las Vegas hotel rooms, the petty extravagances of a man whose pleasures and palate were simple, who didn't know how to spend the money he made and got into trouble when, thinking he owed himself more, he looked beyond the simple things he liked best. And it was easy in the busy ticket hall—Presley songs on the speakers, disturbingly alive: the saint's immortality—to sense the glamour, the magic of the voice, and the incomprehensible wealth it had brought. The wealth—spent in the way it was known to have been spent: simplicity magnified, and then magnified again—was like wealth for everyone, for all the fat people of the people who—acting on a similar Presley-like principle of expenditure, but restricting it to what was available to them, the fast foods they found eternally tempting, luxurious and within easy reach, like a real-life version of manna or a modern version of something in a classical legend—had turned fulfillment and the glory of abundance to personal fat, fat as a personal possession. Ever since the Charleston hotel (and especially after the busy business people of the hotel in Atlanta) I had been aware of very fat people, people who had risen (like dough) to special spheres of obesity. Not one or two; they were almost a class. Charleston was a resort town. They had appeared there, in the hotel, in gay holiday clothes that were on them doubly and trebly exaggerated; and they had, bizarrely, also appeared in couples. At one time there were at least four such couples in the hotel—gargantuan, corridor-blocking, and (no doubt the effect of numbers) not without aggression. I had noticed them in other places after that. But it was Campbell who first spoke to me about the fatness of redneck women, and made it appear a regional or group characteristic. It was at times a pleasure and an excitement to see them, to see the individual way each human frame organized or arranged its excess poundage: a swag here, a bag there, a slab there, a roll there. A kind of suicide, it might have seemed; but I also began to wonder—in the Graceland ticket hall, among all those proud and excited folk—whether for these descendants of frontier people and pinelanders there wasn't, in their fatness, some simple element of self-assertion. How was this adoration of the singer to be understood? These people had political leaders; they had sportsmen, film stars; they had any number of heroes. But these heroes were observed from a distance; this singer was a person like his admirers. He was a person his admirers felt they could live through: the singer experienced for them, on their behalf. In colonial days in the British West Indies—for about a hundred years after the abolition of slavery—the black people had no heroes. They began to get heroes very late, and these heroes were sportsmen, cricketers mainly. No other kind of hero was possible in that limited society. But then, when a political life developed, towards the end of the colonial period, West Indian blacks acquired leaders, union men in many cases, who then became political leaders and later, in independence, prime ministers. For these early leaders who were their very own, West Indian blacks had more than adulation. They wished these leaders to represent them, and more than in a parliamentary way. They wished their leaders (who had started as poor as everybody else) to be rich (by whatever means) and powerful and glorious. The glory of the black leader became the glory of his people. The leader lived (or lived it up) on behalf of his people; and the people lived through their leader. Ordinary ideas of morality and propriety didn't apply. A leader wasn't required to be modest and correct; those were the virtues of another world. A leader was invested as a black man with a responsibility: to be grand, larger than life, for the sake of all blacks. This idea of the leader—which has caused such havoc in the West Indies—has changed in recent times, but it is still there. Something like this black political adulation seemed to be at the back of the Presley cult. It was strange—to me—that music should have carried so much of a people's emotional needs. And when, in Nashville, Tennessee, I went to a performance of the "Grand Ole Opry," the long-running country-music radio program, I felt quite apart from what I was witnessing. It was like a tribal rite; it might all have been in a foreign language. How much talent was there on display? But did talent matter in this setting? It was enough for the famous and the greatly loved simply to show themselves to the audience. The auditorium was full; the aisles were full of people with cameras. The cowboy hats and overalls—working clothes—of some of the performers gave a clue: country music created a community, and was the expression of a community. Nashville was the center of the country-music industry. It was an industry, but the streets of the music area were full of tourists in holiday clothes. An elderly black man, driving me back to the hotel one day, said of the visitors, "They're all white. Do you see? Blacks hate country music. It's redneck music to them. It symbolizes all that oppressed them and all that they hate." I asked whether Presley had that attitude to blacks. The old man said, "To talk to Presley about blacks was like talking to Adolf Hitler about the Jews. You know what he said? 'All I want from blacks is for them to buy my records and shine my shoes.' That's in the record." WHEN I MENTIONED this to Allen Reynolds, a producer, he said, _"Oh no! Oh no!"_ Allen was from Arkansas. He was forty-nine, and I felt he might have been a little weary of defending the South against racial charges. He said, "I was at the Baptist Hospital in Memphis, and Elvis was there. Not as a patient perhaps—his wife may have been there. I was in a gathering near the elevator. Two black nurses came sailing by in a state of possession. They were saying, 'He's here, he's here.' Holding their hearts, and flying off to see Elvis. I tell this story because it makes me question that theory that blacks hated Elvis." Allen had been educated in Memphis. He loved the city, "musically and otherwise," until the killing of Martin Luther King in 1968. That killing spoiled relationships with black musicians and other black people. Nothing might have been said, but the killing was there, a barrier and an embarrassment, a cause for silence. (And I was aware, during my own time in Memphis, of the sourness of things there, with the black city an extensive, irretrievable desolation, and with the white people, under siege, living far to the east.) Allen still had friends in the music business in Memphis. "One of them is Sam Phillips, an independent label-creator. He's a kind of idol of mine. His achievements still impress me. He did Presley in the late 1950s. He grew up in Mississippi or Louisiana. A big influence on him when he was a boy was black music. We had this blending of music in Memphis. Sam loved black music and he was consciously looking for a white man with a black"—he searched for the word—"attitude. Black energy." I asked Allen what country music meant to him. "I grew up very close to country music, and I can't find anyone who can define country music. But to me it's real people's music, lyrically and melodically. And it's directly out of daily life. "My grandparents listened every Sunday night to the 'Grand Ole Opry.' My grandmother was one of fourteen children. And there was a guy called Little Jimmy Dickens who would sing a song called 'Sleeping at the Foot of the Bed.' And my grandmother would say, 'That's how it was.' When people would come visiting there would be no question of getting a new bed. The adults would sleep side by side, and the children would be placed at the foot of the bed. Country music at its best comes from the emotions of everyday life." In country music, the music itself was not important. What mattered were the words. But the words were few and simple, and the themes were so stylized. Was it hard to judge the quality of a song? Could one be taken in by trash? Allen said: "I can tell pretty quickly. For instance, I am now working on an album with a singer called Kathy Mattea. She's a new singer; this is only her fourth album. The way the business works is, there are a number of publishing companies with writers who make it their daily job to go into the office and write songs. I don't think that's always a very satisfactory system. It results in a lot of greeting-card stuff. When I announced that we were looking for material for this album of Kathy's, I got a huge volume of songs—almost all of which is not acceptable—from the publishers and the writers." That explained the typewritten notice I had seen on the front door, asking people just to drop their cassettes through the mail slot, and not to come in and talk. "I must listen to a grocery-bagful of cassettes every week. Nashville is like a Mecca for a lot of dreamers. But at the same time I keep on meeting publishers and writers, because I'm looking for material, and the real struggle is finding the real songs. So the sign on the front door is only partially operative." "Are you looking for a song, or for a writer?" "Both. I am always looking for the real writers. We have some who are very fine. Most of those I know are from simple backgrounds, rural backgrounds. It doesn't mean they are not educated. They are from all over the country. But generally they come from a background that is only partially urban. They have a good strong connection to the small towns and the people." I thought about other forms of stylized writing—Restoration comedy, the P.G. Wodehouse upper-class fantasy—where a witty manipulation of the form could be art enough. Allen said, "I know someone from the other end of the country. This person writes a wide variety of music. He has had some success in country with some pieces that I know are just imaginative, and based on the feel this person has for the stylized elements. And yet some of these pieces are very good pieces." "But you would say that some of the best work comes from true knowledge." "And originality." "Is that still possible?" "Yes. But the industry doesn't encourage originality much. As with other writing, there's ten percent that's original, and a lot that's quickly here and gone." We went up to listen to some of the tapes that had been sent in for the new Kathy Mattea album. In the listening room there were, literally, the grocery bags he had talked about. Allen said, "The first thing I notice in most of these tapes is how little originality there is in them. Even the titles can be the same. Any number of songs about the fire of love, the flames of love. Many titles like that. The fire of love that can't be quenched." The song we listened to was about love, sentimental, generalized, with no concrete detail to attach it to a setting or a person. Allen said, "It's a commercial ditty. Greeting card. Three writers worked on that one, and you can tell they had no purpose except to make some bucks. The music too. It's a hybrid. A little bit of pop, a little bit of country, a little bit of schmaltz. And not any soul. And back into the grocery bag it goes." There were tapes on the shelves of the listening room. And on top of the shelves were clown figures in china. We listened to one of the songs Allen was going to use in the album. "It's called 'Eighteen Wheels and a Dozen Roses.' He—the truck-driver—is on his last run home with a dozen roses for her. Now they're going to do a lot of catching up. It's not a heavy song. I'm humored by it. There've been a number of songs in country related to the trucking business. A lot of the country audience relates to cars and trucks." I picked up separate lines of the song, saw the play on the numbers in some of them: "Eighteen wheels and a dozen roses"; "A few more songs on the all-night radio"; "Ten more miles on his four-day run." Allen said, "Eighteen wheels. Everyone knows that's a big road rig." He played another song he had chosen. It was called "Late in the Day." He said, "It's reflective, sad. Dealing with lost affection, lost love." He quoted a line: " 'You don't know it's a good thing till it goes slipping through your fingers.' " And we listened again: Now I pour whiskey, break the ice, Put my feet up, close my eyes, And try hard to listen to what my heart might say, Try to find the rhyme to take me back in time, To be with you here, late in the day. Allen said, "I love that song, because the mood and imagery are evocative to me. And the melody alone is dear, is beautiful to my ears." We talked about his discovery of music. "In my life it has been a natural thing to have instruments in the house and to make music for your own entertainment and the entertainment of your friends. When I was a child—in Arkansas—neighbors would come over in the evening with guitars, fiddles, harmonicas, mandolins, and they would sit and sing for hours. They loved it. In my grandmother's day, during the summer they had teachers who would travel from community to community. They would have singing schools, and children and adults would go every day and learn singing and harmonies. And they would have 'a big all-day sing,' as they called it, at the end of that week. "Part of the attraction of the church in the South was the music. It was the music and the singing and the harmonizing that they enjoyed. For the whites and the blacks, the influence of the church and the gospel music is real apparent to me in the secular music. Some of Elvis's favorite songs—to sing—were for the church. He personifies the interrelation of secular and gospel, white and black." Kathy Mattea, whose new album Allen was producing, belonged to what Allen called "the folksy side" of country music. There was another side. "One of our great singers and writers is Loretta Lynn, and she is one of the real earthy writers, and a legend. Her music is more connected to barroom and domestic storms. She began singing when she had a house full of babies. It was a manifestation of something natural in her—a natural way of entertaining herself, expressing herself. And she was poor. All she had was a radio and a guitar. A hard life, a poor life." Although singers were for the most part religious people—religion a natural part of people of the South—and although audiences, equally religious, expected their singers to represent family values, there was at the same time a contrary current. Allen said, "Audiences see the singers struggling with their own _demons_. And they identify with the struggles." This made audiences humane and receptive and loyal, and gave an element of the passion play to the life and songs of some performers. Reverend K. C. Ptomey, the Presbyterian pastor of Westminster Church, in one of the more prosperous parts of Nashville, said of country music: "It's white soul music. It's comparable to the role that music played for slaves in the last century. It creates community among oppressed people. I like it. I listen to it because in the words I hear protest against the oppressive aspects of life as a poor white person experiences it." About the much-publicized religious faith of some of the singers, he said, "They're religious in a special way. Religion is to them a shared emotional experience rather than a shared doctrine." AND SOMETIMES the emotions could be extravagant. While I was in Nashville there was published a book called _Sunshine and Shadow_ , the autobiography of a "Grand Ole Opry" singer called Jan Howard. She was about to start on a sixteen-city promotional tour, and the Arts and Leisure section of the Nashville paper, _The Tennessean_ , carried a review of her book: "One of 11 children born into desperate poverty in rural Missouri, she was raped at age eight by one of her father's friends. At 15 she married. She bore three sons in four years, then became a battered wife who eventually collapsed in a nervous breakdown. "When her husband tried to kill her, she fled with 10 dollars in her pocket and her sons in tow. She knocked on the doors of strangers and begged for shelter. Her second husband, an Air Force sergeant, turned out to be a bigamist. Both of her children by him died." After this her luck changed for a while. She met a songwriter in California, married him, moved to Nashville, and became a star. Then the marriage ended, messily. "While she was recovering from the bitter divorce her oldest son Jimmy was killed in Vietnam. Soon after, actor/singer son David became a drug-induced suicide...." It was hard to believe that anyone could live through all that and come up singing. But there she was on the stage of the "Grand Ole Opry," a slender, slight figure, dressed up and smiling, although her terrible story had taken up much space in that morning's paper. And the Opry audience, running up the aisle to the stage with their cameras, were photographing her and willing her on, wishing her well. "Down-home music, crying music"—that was how Campbell had described it. But that was only the beginning. White soul music; the singer as star and victim, in both roles representing the community; and in and out of the simple music, through the echoes of ancient Scottish and Irish reels and jigs, there was a feeling of melancholy and loss, the melancholy of a transported people faintly remembering, or perhaps just having a community sense of, "old, unhappy, far-off things, and battles long ago." Inseparable from this were the fundamentalist frontier religions, which had preserved for these people the idea of a complete, created world and a complete, divinely sanctioned code. Jan Howard told _The Tennessean_ about the difficulties of writing her autobiography. "It was horrible reliving some of the bad parts. Sometimes I'd be sitting at the typewriter and find myself shaking so hard I literally couldn't touch the keys. Or I would cry. And sometimes I would literally pray for the strength to do it." Music and community, and tears and faith: I felt that I had been taken, through country music, to an understanding of a whole distinctive culture, something I had never imagined existing in the United States. THE MAGAZINE in my hotel room, mixing its metaphors, said that Nashville was "the buckle of the Bible Belt." Churches took up twelve pages of the Yellow Pages directory. _The Tennessean_ had a "religion news" editor, and there was a weekly page of "religion news," with many advertisements for churches (especially Church of Christ churches), some with a photograph of the stylish-looking pastor or preacher. Most of the Protestants in Nashville belonged to the fundamentalist frontier faiths; the predominant denomination was the Southern Baptist. The classier churches, the Presbyterian and the Episcopalian, looked at this Baptist predominance from a certain social distance, without rancor or competitiveness. Dr. Tom Ward, the Episcopalian pastor of Christ Church, said that the Southern Baptists who sometimes came to his church found it too quiet: " 'Y'all don't preach.' The Baptist ethos is the preached word. Which is the ethos of the Christian church in the South. Preaching meaning the emotional speech rather than the learned essay of the Church of England—preaching the word and counting the number of saved souls. But I have to say this. To say, 'I'm a Southern Baptist,' is another way of saying, 'I'm a Southerner.' What I mean is that that is the ethos, religiously. What is buried in their psyches is the fear of hellfire and damnation. My father was read out of the United Methodist Church in Meridian, Mississippi, in 1931—when he was seventeen—because he went to a dance. That's the Methodist Church. A lot of the Ku Klux Klan literature is Christian. Revivalism—why? To rekindle the spirit. What spirit? One bad step; many bad steps; and you have the Ku Klux Klan." The Presbyterian pastor of Westminster, K. C. Ptomey, agreed that the Southern Baptist identity was in part the Southern identity. "That's very accurate. You see, a Southern Baptist distinguishes himself from an American Baptist. American Baptists are much more open-minded; they are not so rigid. I would add about the Southern Baptists: it has to do with sharing biblical literalism; it has to do with morality. For example, to be a Southern Baptist is to be a teetotaler. Morality, dancing, drinking—it encompasses the whole of life." I asked him about the revivalism. "The revivalist mind-set is 'to get back to God.' You often hear the words used." " 'Back'?" " 'Lost' is the word they use. And what they mean by that is 'damned.' And therefore they need to be revived." THE SECOND-largest denomination in Nashville was the Church of Christ. It was also fundamentalist, and also originally a frontier faith. It had started (K. C. Ptomey told me) as a breakaway from the Presbyterians; and in some ways it aimed at a greater purity than the Baptists. "They have developed into a sect or denomination that believes they are the only true Christian denomination. The Baptists wouldn't say that. But the Church of Christ people would say, 'You are not a Christian. You have to be in the Church of Christ, because it is the only true church.' " There were more Church of Christ churches in Nashville than in any other city. Reverend James Vandiver, who was of the church, told me why. "The mid-South is at a pivotal point. It is so near the place of American origins. People came here from the seaboard, and they migrated from here to Texas, Oklahoma, and the prairies—and in all these places you will find the numerical strength of the Church of Christ. From a cultural and socioeconomic point of view, the people in this area have common value systems and basically an agrarian economy. And basically people of that niche tend to be a bit more religious." Reverend Vandiver gave me much of his time. He was happy to talk about his church and anxious to help with my inquiry. I found him absolutely fair. I wanted to meet someone from the church who had developed doubts about it. He promised to arrange that, and he did. Later he even put me in touch with someone who had left the church. He was the pastor of the Harpeth Hills Church of Christ, a good way to the south of downtown Nashville. When he was giving me directions on the telephone he referred to his church as a "facility." When I came to a certain boulevard or ring road I would turn left; a hundred yards on I would see "the facility." I liked the word. I had first heard it used in a comparable way in Grenada in 1983, at the time of the American invasion: at a morning briefing the military press officer had referred to the temporary barbed-wire compound for prisoners as a "facility." The Church of Christ facility at Harpeth Hills was of clean red brick: a prosperous church of a prosperous community. Reverend Van-diver was perhaps in his forties, sturdily built, with glasses. He asked me to call him James or Jim. "That informality suits me and suits our theology. We try in every way possible to erase the distinction between clergy and laity." Music was playing in the office. Jim said, "A soft-music station. I had it on while I was doing some work this afternoon. The younger generation would call it elevator music." He smiled. He was in shirtsleeves, but he was wearing a tie. He sat on a three-seater settee against the paneled wall. Above him was a painting of an arbor; to one side of the settee was a ficus tree. One whole wall was of bookshelves. Jim said: "Let me explain the Church of Christ in the simplest way historically. We are seeking to do two things in religion. One is to accept the Bible as our sole rule of faith and practice. We believe in the inerrancy of the Scriptures." The other thing the church was trying to do was to go back to the very earliest Christian faith. "Within three centuries of Christianity's foundation Romanism was predominant, until Luther, Calvin, and the great reformers, the people who said, 'Let's give the Bible to the common man, and reform the Roman church. Let's lay aside the abuses, the corruption that's developed.' "There's always a thread that looks back to the Scriptures and says, 'Let's duplicate.' In the early 1800s here, with the westward expansion, there arose these frontiersmen—as well as people of the seaboard—and I think the frontier spirit had a lot to do with it. These people represented a broad mainstream of Protestantism—especially the Methodists, the Baptists. The Church of Christ represented an abandoning of Protestantism, and did not represent a return to Rome, but to the very beginning of the faith, all the way back to Pentecost, the first Biblical dating of the Christian culture. "That was the frontier spirit. 'We're on the frontier now. Let's lay aside differences. Let's be brothers in Christ.' I'm not trying to be coy, but I think the church of which I'm a member was established in A.D. 30. I'm just saying that the restoration movement here is a historical tracking of that movement on American soil." "When was that?" "Early to mid-1800s. That was the period we refer to as the American restoration." "What was the need, you think?" "Every great religious renewal has been sparked by a return to the Scriptures." "You are so close to the Baptists. And yet you are so opposed to them." "We are close to the Baptists in many things. Bible, Trinity, a church, evangelism, personal conversion to Christ. But we are different in other things. We sing without music. We observe the Lord's Supper weekly. We teach that baptism is _essential_ to salvation. The Baptists teach baptism only as a requirement for admission to the church. And we're autonomous; every church is independent." But, important as the church was in Nashville, it was in decline. The church that had suited the needs of frontiersmen was less suited to city-dwellers. Jim was aware of the difficulties; he was clearsighted and frank. "We are in a time of great change, and that's a real challenge for us. Change? From agrarian to business and industry, from rural to urban, from blue-collar to white-collar, from lower to middle and upper class." In _The Tennessean_ I had read an item by the "religion news editor" that six Nashville Church of Christ churches were thinking of a merger, "to overcome high overhead... flagging membership and to rekindle enthusiasm for fellowship and missions." The six churches had a total membership of twelve hundred: six small churches, of an earlier, more rural time. Henry came into Jim's office. That had been the arrangement: that Jim and I would talk alone for a while, and that Henry would then join us. Henry was twenty-six. He was of middle size, with well-brushed-back hair, white jeans, and a short-sleeved blue Polo shirt. He had been a student all his life, and though his doctoral studies were in an inconclusive, suspended state, he still had academic ambitions. He had just been to Uganda on behalf of the church, prospecting that country for mission work. At the moment, for money, he was working as a carpenter, just breaking even on his S8.00 an hour. I asked what he thought about the church's chances in Uganda. He said, "Very good. But the situation could be evolving into a situation ripe for another coup." (And yet, within a few minutes, he was to make me understand that his ideas about Africa and mission work were not so straightforward.) In southeastern Uganda he had seen terrible things. He had seen hundreds of people tied up and sitting in circles. That had made an impression on him, but he didn't appear to know what to do with the knowledge and experience. I wanted to know about the development of his faith—this young man in jeans and a Polo shirt. Had he had some kind of spiritual illumination? Had he made a confession of faith? I had been told that it was necessary. He said, "There is a loophole. An irony. My parents were both pillars of the faith. There was a strong bonding between father, mother, and child. But—what this is to say—I knew what the necessary steps were to salvation in Christ. As early as five or six, I knew what those steps were. That's not uncommon at all." "It's like part of your identity." "Sure. I followed those steps of faith at the age of eight. I was baptized, fully covered in water, at the age of eight. But, going back to your question about spiritual experience, the answer is, candidly, no. In retrospect, I question whether those actions at the age of eight mean anything." He broke off and said, "I'm in a whirlwind at the moment. I've experienced a split with my family." I was surprised. Jim had promised to arrange a meeting with someone with doubts, but I had been expecting to meet that person on another day. Jim said, "As a mentor, let me say first of all I think Henry is typical of a person who grows up in a religious setting in which he makes a profession of faith." Henry said, "As a doctoral student I have come to question the objectivity—the rational processes—which the Church of Christ—" I had noticed at the beginning how he qualified his words. Now he appeared to be having trouble completing a train of thought: many new things were breaking into the original idea. He said, "I feel compelled to throw this. My African experience has reinforced a suspicion I've had that there might be something amiss—what I want to say—a Westerner's thought processes or thought form—I believe I can broaden this, and include not only the Church of Christ but other conservative Protestant churches as well—our misuse of reason—the Western mind—the conservative evangelicals—" I noticed that he was wearing an Yves Saint Laurent belt. Jim said, "I see you headed to the reduction of a lot of concepts." "I got to Africa and I was repulsed by what the missionaries had done. Instead of teaching the Africans first-century Christianity, they had taught them a Western, white-man's Christianity. Of all things—many of the young African ministers did not see themselves as carrying out their ministry in the most proper way without, for example, wearing a sports coat and tie, something that's totally un-African." That appeared to make a whole: the ideas of the Church of Christ fusing with a rejection of colonial mimicry. And Henry went on along that line. "Christianity was born out of an Eastern framework—" A thought, unexpressed, came to me: an Eastern religion for the Wild West? Had the early Church of Christ really been presented to its followers like that? Or was the Easternness of the religion a more recent idea? "—and we need to know when to separate the true essence of Christianity from Western cultural baggage." That made a whole, but then Henry said, "My parents' mentality is very exclusivistic, in terms of who is going to get to heaven. It's as basic as saying who are really—with a capital 'R'—Christians. The real tension began when I went to the university. They were not happy at all about that. I've been questioning parts of the body of church knowledge. And the idea seems to be that, if I don't have the same set of beliefs as my parents, I am rejecting the right belief." Abruptly he said, "I feel so desensitized to what's going on." He said that with relief, as though glad to give up the juggling with so many new and unrelated ideas. Jim said, "That's typical of questioning people of conservative churches." I said, "Somebody told me that I should study the Southern churches well. Because in fifteen years it's all going to change." Jim said, "I agree." Henry said, "I agree." He added, "The whole package of Christianity is bothering me. The point is, Jim, that is what is going on in my mind intellectually. But emotionally I have a very strong attachment to this _fellowship."_ An experience of Africa, the shock of a tribal civil war, a new vision of missionary effort, leading to a wider questioning: what had once been the complete, satisfying faith of a complete, clear, enclosed world no longer answered. And he was "in a whirlwind." BUT BEN—whom I met on another afternoon in Jim's office—was serene. He came from a Church of Christ family. His grandparents on both sides were of the church, and his father was a professional man. Ben was eighteen. He hadn't come from the country; he had been born in Nashville, but his faith was pure. He had preached for the first time when he was sixteen. He said, "The youth leader of the church encouraged us to get to know God—" I asked about the youth leader. Jim said, "He's a full-time staff person." Ben said, "The youth leader encouraged us to get to know God and to share him with others. He tried to instill in us a zeal and a fervor that would radiate. So naturally, when my knowledge of God grew, I wanted to share that." "Were there certain exercises that you were made to do?" "In worship and in church we would go to class and we would study and interact with each other. But then outside the church we would go and do things together—have a devotional at someone's house and eat together. And then, just being with the people you share the faith with, you would be uplifted. A lot of the time we would talk about what was going on in our lives. If you weren't getting on with your parents, for example, we would sit down and talk about that—both as a personal problem and a general issue or topic." Jim said to Ben, "A lesson in helping others." And to me, "A great amount of peer pressure which the adolescent faces. We believe that Christians live in the real world and should not withdraw from the real world." Ben said: "Occasionally we would—thirty or forty of us—go out of town, to a camp area, where we would be away from a lot of the distractions, the TV and radio, the outside influences, where we would all be together and break down into groups of four or five people. In the smaller groups you can always get more personal. It's easier to share with each other in the smaller group than in the group of thirty." I said, "Like the early Christians going into the desert." Jim said, "It's comparable." Ben said, "That re-creation of our spiritual lives—that's where the comparison with the early Christians holds good." "How long were those camps?" "Friday afternoon, all of Saturday, and much of Sunday. A weekend." "Fun? Or solemn?" "Not solemn," Ben said. "Meaningful." "Joyful occasions?" "Joyful. An inner joy, that we were re-creating, and growing. We knew that we were always stronger people, closer to God, and closer to the people around us as well as to ourselves, when we left. And that's the idea of the whole weekend." "How many weekends have you been on?" "I've been on eight." Jim said, "Twice a year." I asked him about his knowledge of God, and how that had come. "Oh, not miraculous. Nothing that happened last Wednesday or last Thursday. But all through the day I have a constant feeling of his presence and I know that he's with me. It's really developed in the last couple of years, when I have started to search the Scriptures. We're encouraged to search the Scriptures. You don't have to. It's a personal decision." "What of the future now?" "I hope to become a lawyer. I think it fits hand in hand. The type of religion that we have is a people religion. Just as Mr. Vandiver can be an influence from the pulpit, just as easily I can be a light in my community as a lawyer, and have people see me as a kindhearted, moral individual." "But the Church of Christ brotherhood is shrinking." "Numerically we might decrease. But the people who will be falling by the wayside will be those people who were halfhearted in their faith anyway." HENRY, in all his turmoil, had spoken—and Jim Vandiver had pointed it out to me—of his emotional attachment to the fellowship within the church. And Ben loved the idea of the brotherhood. But Melvin, who was in his early forties, and had drifted away from the Church of Christ in the last five years, made a face when I mentioned the subject of fellowship. He said, _"No, no_. The fellowship would _irritate_ me. I've never enjoyed the fellowship, _ever."_ And it was hard, indeed, to see someone so elegant and accomplished, playing down his profession and his skill in that profession-it was hard to see someone with those manners drawing sustenance from the kind of weekend Ben had described. He said, "It's boring." And at once the objection, so simple, appeared unanswerable. But Melvin had been in the church for much of his life. There was much knowledge behind that snappy word. "I don't think it was always boring. Going back seventy-five years, I think it would have been entertaining, a form of entertainment, the fellowship. Now I would agree that it's an extension of the evangelical movement. To keep you involved, to keep the numbers up. "The South was almost entirely agrarian. Tent revivals were an opportunity for almost the entire community to meet in one place—as well as Sunday services. You'll find that revivals played a very large part in the growth of the Church of Christ up till ten years ago—and they are _the_ most boring, dull experiences you can have." I said, "America being a fun civilization." "Agree. They're fighting a losing battle. And that's a very large factor, the fun civilization. Most of the people that attend these large evangelical events are young people. Eventually they don't go back. They get bored. And that's unfortunate. The church should never attempt to provide entertainment. It's boring when they try. It doesn't stimulate you emotionally or intellectually. All you have to do is to turn your TV on to be entertained. "I think I could defend this point easily. The whole American evangelical movement was based on these _shows_ , these circuses. The best example now is Oral Roberts. Those days are gone. There's movies, TV, traveling. But if all you did in the old days was sit on your farm, that provided a break in your life. "It will completely die, the church. Or let's say it will not exist in twenty-five years as it exists today. If it were to exist at all, it must go _back_ to its teachings. No, that's wrong. I think it probably was an error from the beginning. To keep it alive, it must offer answers of a redemptive nature. By which I mean that's really all it can do. It can only address people's questions about what life is. It's got to stop trying to be a judge, the entertainer, the meeting place. In the old days it was even the town hall. You didn't take your problem to a lawyer. You went to the church. The Church of Christ will tell you today that you shouldn't bring a lawsuit against anyone, that you should take your problems to the church and allow the church to arbitrate. This was a very efficient way of handling problems in a small agrarian community. Very effective. Though the church being judge and jury imposed on people moral guilt—they felt condemned by God for civil offenses." A rising professional man, he had grown to reject the completeness of the culture of his childhood. Religion, the frontier faith, had created this completeness; now it was a burden he could do without. In a new world, he wished religion to have its place, like everything else. Yet he knew that he was rejecting a part of his identity. "The Church of Christ does an excellent job in meshing traditional values with Christian principles, universal Christian principles. The result is that when one begins to doubt the traditions he is unable to separate his doubt about tradition from his belief in Christian principles. It becomes very confusing. The confusion is at times unbearable. I can understand why Henry has trouble finding words for certain things. There's guilt and alienation, the idea of abandoning your heritage. I went through a lot of guilt. Guilt is the most critical. The Church of Christ deliberately instills guilt in people. It is extremely judgmental. There is almost the circle-of-wagons sense that if you attack certain traditions it's blasphemy. I think I should tell you that I think of myself as a spiritual person. Actually, I think I am more spiritual now than I was. In a literal sense." And in Melvin there was something like grief at the necessary break with the South he had known. "The South is losing its identity, and that's a lamentable thing. Being Southern is a state of mind. I know that's a trite thing to say. It's a way of looking at your place in the world, a place that's more defined than many other places. Have you been to California? It's everything the South isn't. And an odd thing about that is that many business ideas begin in California. The fast food, the interstate highways, clothing styles. The reason is that creative people are stifled in the South. They move from the South and other places to California. Creative people have to get away from the South. It will be a very long time before that stifling will disappear. It will be my generation that will break the link. It's not something I say with any pride. Nor shame. No judgment. I say it purely as fact." Wasn't there the possibility of a new kind of intellectual life, a new kind of strength, from that breaking of the link? Melvin wasn't having any of that. He went back to his original point. "The link is broken by people of my generation because they don't want the boredom deal. As opposed to soul-searching experiencing. 'I just don't need this.' The church are genuinely perplexed by what's happening." There was confirmation of what Melvin had said from another distinguished man. This man told me that his neighbors, professional people, successful people, originally from small towns where they had been Baptist or Church of Christ, were now all Presbyterians. One reason (as Reverend Ptomey had hinted) was that the Presbyterian religion was more socially acceptable. The other reason was that it was more lenient, less demanding, less intrusive or encompassing. Religion now had to have its compartment, almost its social place. The frontier had ceased to exist. And the religions it had bred were beginning slowly to die. In the old days, when men, often of little education, had needed only to declare themselves ministers, people would have seen themselves reflected in the expounders of the Word. This quality of homespun would have made the religions appear creations of a community, personal and close and inviolable. Now a certain distance was needed. ONE OF the most successful country-music songwriters is Bob McDill. The South is his best subject: redneck celebration, against a background of the hard years middle-aged men have lived through and have spoken to their children about. McDill's best songs have the feel of folk songs. Cotton on the roadside, cotton in the ditch. We all picked the cotton, but we never got rich. He had an office in a music publisher's in Nashville, and he had a certain fame for going to his office every working day to write his songs. It was there that I went to see him. On his desk was a lined yellow pad with what looked like a fair copy in pencil of a finished song. There were no other papers on his desk. But there were curious ornaments: London mementoes—a toy red double-decker bus, a guardsman, beefeaters, a London taxi. He was forty-three. He was tall and slender. He liked the outdoor life, and went out duck-shooting. (That was the gentleman's sport here, as Campbell had told me; real rednecks were meat-hunters.) He had been born in East Texas, and had been writing songs since he was fifteen or sixteen. He had always been interested in poetry, music, guitars, drums, banjos, pianos. "Not that I play them all, or play them well." He said that the early songs he had written were self-indulgent. "I didn't learn to write commercially until I was in my late twenties." The professional attitude was necessary. The songwriter writes for singers, and has a special relationship with singers. He went to Memphis in 1967 and spent a year there. "In Memphis I tried to write songs for black artists, black singers. I was on the staff of a publisher as a writer, and was also working in a studio as an assistant engineer." That attempt to write black songs didn't work. "I could have succeeded if I had had time enough to learn that black mentality, that black approach to music. I was beginning to learn it when I left. You've got to say something that the singer wants to say and can identify with. It was the same thing when I moved here. I had to learn this mind-set. I learned this subculture, which wasn't my own. The vocabulary is very limited. You have to learn to do big things with little words. In both black music and country music, and more so in country music." It was such a special art, songwriting, so far from my own. I wanted to be taken into it a little way, and I asked him to talk about the problems he had had with a song. He chose "Somebody's Always Saying Goodbye." Railroad stations, midnight trains, Lonely airports in the rain, And somebody stands there with tears in their eyes. It's the same old scene, time after time. That's the trouble with all mankind. Somebody's always saying goodbye. Taxicabs that leave in the night, Greyhound buses with red taillights. Someone's leaving and someone's left behind. Well, I don't know how things got that way, But every place you look these days Somebody's always saying goodbye. Take two people like me and you. We could've made it. We just quit too soon. Oh, the two of us, we could've had it all, If we'd only tried. But that's the way love is, it seems. Just when you've got a real good thing, Somebody's always saying goodbye. Bob McDill said: "The bridge—between the images of the first two stanzas, the detachment, and the personal thing—that gave me a lot of trouble. Until I hit on the idea of just conversation. It eases the listener into it. There was another problem—I still hadn't defined the situation between the two people, the lover and the lost one. I had to do that in four lines. It seems so obvious now. But you know how long the obvious takes. I saw that there was no need to make a judgment on the behavior of either party. 'Somebody is always leaving.' It sounds almost as if it could be her, the singer. But, for whatever reason, she knows now it was a terrible thing—he threw away a great thing. Two verses of images, and then in seven lines you have to create all that personal thing. "I also had trouble with it musically. Two long pieces of melody that are complete once, twice. You need relief—and then I hit on the idea of repeating just the second half of the A-section melody." When he began to talk about the writing he stood up and looked away. "Sometimes you begin with an emotion, a feeling about something. Sometimes a title, sometimes a line of the lyric. But then the hard part comes. You take that little thing, that little bit of idea, and build on it and build on it. That's the tough part. The problem then is not to mess it. Your text is so small that every word has to count. From the very first word you are working towards that center. "You write line by line. The couple of parts we have to deal with which serious poets don't have to deal with is the tonality and also the singability. You can't do complex things and things that are hard to say. It has to be so easy to say and sing. It has to fall out of the singer's mouth." I asked him for an example of a line that had to be put right. He couldn't think of anything like that in his own work. "The computer in the brain is rejecting all the time. It rejects everything that is clumsy, hard to sing." And at the end there was no way of defining what a good song was going to be. It was all a matter of feeling. "If it feels good, if it does something to you, it's good." No amount of questioning, no amount of explaining, even from someone as willing to talk as Bob McDill was, could take one to the magic: the calling up and recognition of impulses that on the surface were simple, but which, put together with music, made rich with a chorus, seemed to catch undefined places in the heart and memory. Mama said, don't go near that river. Don't go hangin' round ole Catfish John. But come the mornin' I'd always be there Walkin' in his footsteps in the sweet delta dawn. Almost nothing at first. But then the images and the associations come: Mama, river, catfish, footsteps, delta, dawn. Bob McDill said he had had to learn the subculture. But the Southern images and words of his best songs are far from the stylized motifs of a good deal of country music. And though he makes much of writing in an office in a matter-of-fact, day-to-day way—and perhaps because he talks in a matter-of-fact way, since the mystery cannot be described—it is probably true that, when moved, he writes with that most private part of the self with which Proust said serious writers write. He says that his best song is "Good Ole Boys like Me." When I was a kid Uncle Remus he put me to bed, With a picture of Stonewall Jackson above my head. Then Daddy came in to kiss his little man With gin on his breath and a Bible in his hand. And he talked about honor and things I should know. Then he staggered a little as he went out the door.... I guess we're all gonna be what we're gonna be. So what do you do with good ole boys like me? Every detail there was considered. His aim, he said, was to get as much of the South as he could in a few lines. And the song has become very famous; many people I spoke to referred to it; the mood of the song spoke for them. A "good ole boy" (as I had gathered from Campbell in Jackson) was a redneck; but it was also a more general word for an old Southerner, someone made by the old ways. The song might seem ironical, then celebratory. But below that it is an elegy for the South, old history and myth, old community, old faith. THE SOUTHERN Baptist convention, meeting two weeks or so before in Saint Louis, had voted itself—over strong moderate opposition—into an extreme fundamentalist position. Baptist seminaries were to be purged of people who didn't believe in biblical literalism. Sunday-school literature was to reflect this new strictness. Reverend Tom Ward, the pastor of Christ Episcopal Church, said, "The more the Baptist religion is threatened, the more fervent it becomes." Reverend Ptomey, the Presbyterian, thought that the new moves represented the negative side of Baptist fervor. He said, "They've manipulated the political processes within their denomination to appoint people to the boards of their schools who share their perspective on biblical literalism." Reverend Will Campbell, more involved than either of these men, was outraged. Will Campbell was a famous local Baptist pastor or counselor. He had no church of his own. He operated informally, from his forty-acre farm just outside Nashville; the informality was part of his fame. In spite of the Thoreau-like setting and his frontiersman style, he had had a formal theological education, including three years at Yale Divinity School. He was in his early sixties. He had been to the convention. He said: "I cannot analyze why I came out with a near-clinical state of depression. I never was a steeple pastor—I walked away from that thirty years ago—but the Baptist notion historically is a glorious one. This little band of left-wingers, truly radicals, they believed in separation of church and state. No one believes in that any more. They would not go to war; they would not take an oath or serve on juries; they would not baptize their babies; they practiced community of goods. None of this holds good today. "Moderates and fundamentalists—neither party is historically Baptist. They claim to believe the Bible literally. No one believes the Bible literally. Ask the man who tells you he does, 'Shall we start dismantling the penitentiary?' "I never know if the true Baptist notion ever made it across the Atlantic Ocean. The frontier spirit, the culture, so dominated the religion that what you had was a civil religion, a cultural religion, a melding into one." I said, "But it served the people well." "It did indeed. But it betrayed the faith." Will Campbell had a special idea of the faith. "Religion should not be credal. The great church of Christ came into being by ignoring the life of Christ. What I heard in Saint Louis—what depressed me—was doctrine, doctrine, and its defense. I heard little about discipleship. The churches offer a theology of certainty. And that worries me. Jeremiah said, 'It is not good to be too sure of God.' And even Christ, when he was about to be crucified, cried in great agony, and the agony comes over in the translation, 'If it be possible, let this cup pass from me.' No great religion can give all the answers to everything. Jesus didn't tell people what to think. He didn't prescribe a confession of faith. Christ offered no creed or special theology." He seemed to be saying that faith was something that had to be constantly looked for and struggled towards. When I put that to him, he said it was fair. But Will Campbell's ideas were difficult; and I wasn't sure whether he wasn't being polite. It occurred to me afterwards that only a very devout man, and someone raised within the Southern Baptist church, could ask so much of people. His setting—the forty-acre farm, the log-cabin study where he met visitors—represented something about the man. He gave one an idea of the power of the frontier preacher, and the strength of the old faith. But it wasn't only for this that Will Campbell was famous and almost, as someone said, a Southern monument. He was famous for the political positions to which he had been led by his faith. He had done brave things in the civil-rights movement. But he hadn't stopped there. Religion and a wish to come to terms with Southern history had taken him beyond the black cause to the cause of the rednecks, the haters of the blacks. He had seen both these Southern groups as tragic. And something like a religious conversion (within his already fervent faith) had led him to offer spiritual succor to members of the Ku Klux Klan. The conversion had come about like this. A mocker had asked one day what the Christian message was. Will Campbell had said that the message was: "We are all bastards, but God loves us anyway." (It was a version of the illumination he had had at Yale—"God cares about the suffering of his people"—that had taken him beyond the rigidities of his upbringing and had led him to the civil-rights movement.) Some time later a Klansman shot and killed one of Will Campbell's friends. The mocker then asked Will Campbell, who was full of grief and raging about rednecks and Kluxers and crackers, "Which bastard does God love the most?" The bastard who had been killed, or the bastard who had done the killing and was alive? Will Campbell had no doubt about the answer: he had a mission to the living Klansman as well. The story of the conversion is told in Will Campbell's autobiography, _Brother to a Dragonfly_. Things are not always clear in that book. The main narrative is broken into by many little stories and is at times too fragmented. But it seems that with that conversion there came to Will Campbell a fuller and special comprehension of Southern history. The poor whites, many of them descendants of indentured servants, and to that extent sharing an ancestry of servitude with the blacks, were of no account in the South until the Civil War. Then, because they were needed to fight that war, they were evangelized and given their cause; and afterwards, as rednecks and Klansmen, still poor, still victims, they were held responsible and derided for what was really the racism of the entire society. The Klan religion, of piety and hate, derived from that war, Will Campbell compares to Old Testament Judaism. And he finds a resemblance to the 137th Psalm ("If I forget you, O Jerusalem") in a "spirited" Klan song like: You niggers listen now, I'm gonna tell you how To keep from getting tortured When the Klan is on the prowl. Stay at home at night, Lock your doors up tight. Don't go outside or you will find Them crosses a-burning bright. And he explains the resemblance to "If I forget you, O Jerusalem" by means of this paraphrase or transposition: "If I forget you, O Atlanta, Vicksburg, Oxford, Donelson, remember, O Lord, against the Yankees the night they drove old Dixie down! When Sherman said, 'Raze it, raze it, burn it down to the ground!' Happy shall he be who takes your little Yankee babies and slams them against Stone Mountain." Will Campbell didn't talk about the Klan when we met. He gave me a copy of an article he had written, "The World of the Redneck," which outlined his views and gave the text and analysis of the Klan song. He didn't refer me to his book, _Brother to a Dragonfly;_ that I turned to on my own. We talked of religion and the Southern Baptist convention; and the "liberal wilderness" he said he had walked in for many years. We talked, above all, of the immense Southern past, which—though born in 1924—he carried in himself, and which his setting—a log cabin at the back of his house on his farm—appeared to pay tribute to. He was from Mississippi. "I was a fourth-generation Mississippian. My family homesteaded in Mississippi about 1790, I'm thinking. In the frontier, Mississippi was a territory. It was part of the Louisiana Purchase. A territory, not a state. And citizens from states like Georgia could migrate there and stake a claim to a section of land if they intended to live there. The land belonged to the federal government. Pretty soon it was cotton. The whole economy in Mississippi was cotton for a long time. Six hundred and forty acres of land—that's a lot of land for a family. But say a family had ten children. You divided that. Sixty acres. Still, in the nineteenth century a family could make a living on that. But divide it again—that's how the families separated and scattered." Will Campbell was chewing tobacco while he spoke. It was something he was known for; and from time to time he spat into a spittoon. I had never actually seen anyone use a spittoon. In various places in the South I had seen big billboard advertisements for Granger Select chewing tobacco: "Meet Up with a Cleaner Chew." The Granger slogan had been puzzling until someone had told me it was really redneck language, "meet up with" meaning "get to know," "become friendly with." I asked to see Will Campbell's tobacco. It was Beech Nut, licorice-flavored: "Balanced and Better, Softer and Moister." In its pliable foil pouch, it was aromatic and tempting. "My family was a family of landowners in Georgia. One of the boys got in a fight with a friend in a barbershop and killed him. And the judge said to the father, 'Your only chance is to move to one of the territories.' So they packed up, the whole family, and moved with wagons until they got to this particular area in southwest Mississippi. They might have had a mind of going on further west. But in the morning, when they were starting to move on, they heard a rooster crow. So they knew there were some other settlers there. They went and talked to these people—if the Indians were hostile, and what the land was like, and what the winters were like, and what they grew. And to me the most interesting thing is that where they settled was precisely like where they had come from. If you close your eyes and then open them again you wouldn't know you had left Georgia. "By the time my parents were grown there was no room for us on the land. My family was rooted there, in that rural community, which made it illogical for some people to say—when I began to work for the civil-rights movement, as a troubleshooter for the National Council of Churches: some people said it was trouble _maker_ —that Mr. Lee Campbell's son, who is all mixed up in that nigger mess, is an outsider. Which in a sense made it more dangerous. I'm not trying to romanticize this—it didn't take much to make you a radical in those days. The only thing worse than an outsider is a traitor, and I was seen as a traitor—to the Campbell-Webb-Parker-McMillan family. My grandmother's family were Webbs. It was the Webb family who came and homesteaded there. "My grandmother, on the trek from Georgia to the Mississippi territory, remembered—when money ran out—seeing her father identify himself to a settler in Alabama as a Mason. They gave the secret Masonic grip, the secret Masonic passwords; and the settler gave some money. Ten dollars. Worth perhaps a thousand dollars today. My grandmother remembered that all her life." It was a beautiful and touching picture. I said so to Will Campbell. He said: "This oral tradition had an effect on the tenacity with which they hung on to all the old ways of doing things—and this meant segregation, among other things. 'Will, you weren't raised this way.' Which again makes you a traitor. To them segregation was a Christian way. God created races. And I couldn't explain to them that it wasn't God who created races. But God created people, and some of them would go to the Northern countries and lose the pigmentation of the skin, and some would go to the hot countries and develop the heavy pigmentation. To them God created white people—and Adam and Eve were white. And when he put the curse on Ham, the curse was to be black. But they were and are deeply religious people, and it was important to have a religious sanction for everything. "Let me say something which appears to negate what I've been saying. When I've been saying 'they' I am referring to the community at large. My immediate family had no vested interest in a segregated society, because they were not slaveholders. They were yeoman farmers. The further historical truth is that 'my people' also came to this country as indentured servants. An awful lot of the yeoman farmers came as indentured servants. And later we had black slaves. "I'm not denying that I had, and grew up with, racial prejudices. It wasn't something you discussed—black people didn't marry or date white people. They worked with them on farms. In the fields there was equality. We were even playmates. When we were small we played with black children. But at a certain point you knew that they were black—the time you started school. You accepted that." He said he had written a song about that. He took the guitar that was near and began to sing. I wasn't prepared for this. It took me by surprise; and the effect of the singing and the guitar, filling the small cabin, was hypnotic. I surrendered to the emotion of the singer and his absorption in his song. The song was long, a ballad, with much recitative. It was about a black boy and a white boy growing up together on a farm in the South, until they were separated according to the racial customs of the place. The black boy's father worked for the white boy's family. The black family lived in the smokehouse; the white family lived in the main house, which was not much bigger. When the Depression came the black worker was laid off, and he and his family went to Memphis. Then the white family lost the farm and they too had to go to Memphis. There one day the white boy, now a man, met the black boy, also a man, and they became friends again. Parts of the song were true, Will Campbell said; and parts were made up. His family didn't lose their farm; and they didn't migrate to Memphis. So what was sentimental about the song, what made it a fable, gave it a moral, was the made-up part. "The male members of my family were not bigots. Prejudiced, but not bigots. I remember one day in Campbelltown—all the Campbells lived in one place, within a mile of one another—and this thing happened. An elderly black man, John Walker—he lived in the neighborhood; he had recently been released from the state penitentiary for stealing some corn from his landlord—he came walking down the dirt road. And we were playing in the 'stomp.' Not the lawn. There would be the house, the yard, the picket fence; and beyond the picket fence would be a grassy area, like a meadow, and that was called the 'stomp.' It wasn't where crops were planted, or even pasture; it was more like a playground. Inside the yard there would be no grass. That would be swept down with a dogwood broom. If you had grass in your yard that was a trashy thing to do. And we were in the stomp, and this black man walked down the dirt road, and we taunted him: 'Hi, nigger! Hi, nigger!' To which he never responded. The local mores would not permit him to respond to white children. "And afterwards my grandfather called us all round him. And he was sitting there on this tree stump. He called us all 'hon.' And he said, 'Hon, there's not any niggers in the world.' And we said, 'Yes, Grandpa. John Walker is a nigger.' We could still see him disappearing down the dusty road. And he said, 'No, all the niggers are dead. Now there's only colored people.' And that was his way of explaining to us that the Civil War was over." (In _Brother to a Dragonfly_ there was another version of that story. The corn John Walker had stolen was "a sack of roasting ear corn." And he hadn't been to jail for stealing the corn. He had been beaten by some men, and he had told about the beating in a humorous way—which had partly encouraged the taunting from the younger boys. "Yessuh. Dey got me nekked as a jaybird. Took a gin belt to me. Whipped me till I almost shat." The story Will Campbell had told me in his cabin—with the black man silent and enduring—was more in line with contemporary sensibility. The version in the book, with the black man making a joke about the beating, and perhaps also about the theft, felt truer.) Will Campbell said: "My grandfather was a man only with a second-grade education. He could write his name and I suppose could read. But his use of the language! I always hoped that the preacher would call on him to lead us in prayer. We were Baptists. I remember the old man concluding one prayer, 'And when at last we kneel to drink from the bitter spring of life...' And by that, 'the bitter spring of life,' he meant death.... "So these were and are the dominant influences in the life of rural white Southerners—this sense of place, coming out of displacement, indentured servants, migrations, and the finding of this sense of place in the farms, the homesteads, the community. And this sense of place became sacred. "There was a threat to that sense of place by the racial changes that were taking place. And it _was_ a threat. To know suddenly that things you thought were stationary and would last forever would never again be the same. "And I used to try to explain to my colleagues—non-Southerners in the movement—that, when white people said that to desegregate the schools was to wreck the schools as they knew them, they were saying something that was fact. I used to use the example of Abraham and Isaac. People would say to me, 'You are asking me to sacrifice my children on the altar of integration built by the Supreme Court.' And my response was, and is, 'I'm only asking you to be faithful to the God you profess. As a Christian there is God beyond the idols we have built: place, community, public education—which indeed we may be sacrificing. Abraham was willing to sacrifice his child. We put our child on the altar of integration, we put the sticks of justice beneath. But the child was not sacrificed—by Abraham. Finally the child was saved.' " Will Campbell said, "Maybe that analogy breaks down. But it held for me at the time." He began to talk about his civil-rights work; and it was possible to detect the ways of thought that would later lead him, as a churchman, to resist being used politically. He said: "Our cue wasn't the Supreme Court decision of May 1954. Our cue was far more basic. Supreme Court justices change. It's already changed in our day. The motto of the liberal movement was law and order. But by the time Mr. Nixon and others discovered Middle America, the term 'law and order' became synonymous with 'nigger.' And then it was the other side that was saying, 'We must have law and order.' So that Martin Luther King, Jr. and others were seen as troublemakers, and consequently a threat to law and order." He talked of the paradoxes and ambiguities of the success of the movement. "I think that, the way I grew up, my chances of becoming free and open-minded about race were much greater than when my children grew up. Because when I was a child there were assumptions made that were never discussed. You didn't discuss whether black people would serve on juries or go to school with us or live with us. But every child born after May 1954 has heard black people discussed pejoratively. So now you have a generation of people who are full of hatred and in a position of being able to implement that. "I do think it is extremely dangerous, because you can never again have the kind of nonviolent resistance that you saw under the leadership of Dr. King and others." In the old days, he said, if you saw five thousand blacks marching around a courthouse, and you asked them why they were marching, they would say they were marching because they weren't being registered as voters. If you saw black people demonstrating at a lunch counter, they would tell you it was because they weren't allowed to eat at lunch counters. There was no trouble at all about the cause then. "Today, how would a nonviolent, passive resistance work? The issues are not as clear. Today, if you saw five thousand blacks marching, the only thing they can say is, 'We are marching around the courthouse because we are still niggers to you.' "I remember a song that was sung in our taverns: 'Move Them Niggers North.' Move them niggers north. Move them niggers north. If they don't like our Southern ways, Move them niggers north." Beginning with simply speaking the words, he was soon yielding to the lilting rhythm, and half singing. He said at the end, "I remember hearing it once in a recently desegregated roadside café in northern Alabama where I had stopped with a black friend. It was on a jukebox. This song was clearly directed at us. And when we left my friend said—my friend was hurt—'I guess there's no law against playing a jukebox.' And I said, 'Not yet. And I hope there will never be.' " He repeated the response he had made to his black friend. I missed the point Will Campbell was making here; and it was only later that I learned, from his own article, "The World of the Redneck," that the song was a Klan song. It was in this imprecise way that he introduced the subject of the Klan and redneck deprivation and tragedy, and his years in the "liberal wilderness." He was sitting on a stool at a high desk or table, with the spittoon at his feet. There was an old barber's chair in a corner of the log cabin, near the air-conditioning unit. There was also a rocking chair; a settee against one wall; a carpet on the floor; and a settee table with a polished or varnished tree-trunk slab as a top. A banjo or ukulele hung on a wall; and there were photographs and drawings and originals of cartoons. On a high ledge was an old tin advertisement: _Say Goo-Goo. A nourishing lunch for five cents. 5c._ Goo-Goo was the name of the candy that was still advertised on the "Grand Ole Opry" radio program. And it was that old tin advertisement that made me start seeing the apparently haphazard assemblage of objects in the log cabin as a collection of things of the people. Will Campbell said: "I went full circle. I grew up in a fundamentalist background—it wasn't called that then. Everyone was Baptist. In that world view to be a Christian meant don't smoke, don't drink, don't mess around on Saturday night." But he wanted more from religion; and his faith developed with his studies. "I was interested in ethical matters." This led in the South directly to the subject of race, and his civil-rights work. "I am still against wars and segregation and paying workers bad wages. But I began to see that I had traded one legalistic code for another. The liberalism of my middle life served me no better than the fundamentalism of my earlier life. The Christian message is that we are created free, and no one has the right to exact more of us than Jesus did. And Jesus had no creed or particular ideology. I found that the social liberal creed was as doctrinaire as the fundamentalist religious creed had been. Jesus asked us to be mindful of the one near at hand." And for Will Campbell this person was the—despised, as he saw it—redneck: the man like himself. He hated the word. He thought it should be used only by people like himself. "The tragedy of the redneck is that he chose the wrong enemy. I know a good song. 'Rednecks, White Socks, and Blue Ribbon Beer.' You want to hear it? I'm not a musician. But I like the songs of the people." He left the high stool and, taking his guitar, went and sat on the settee. A glossy black dog had come into the cabin. When Will Campbell began to play the guitar and sing, the dog sat up and sat still, fixing glittering eyes on the hand strumming the guitar, and listening to his master's voice. No, we don't fit in with that white-collar crowd. We're a little too rowdy and a little too loud. But there's no place that I'd rather be than right here, With my red neck, white socks, and Blue Ribbon beer. Will Campbell said, "That's the song of alienation. It says a lot: 'We're a little too rowdy,' 'a little too loud.' " I asked, "Who wrote it?" "Bob McDill. If you listen to it selectively you'll learn a lot." AND YET the history that so exercised Will Campbell could be by-passed, just as in some quarters the old, too-demanding faith had been bypassed. Twenty-five minutes away from downtown Nashville, in the little town of Smyrna, there was the very big Nissan truck-and-car assembly plant. It was three factories in one, on a site of eight hundred acres. The factory building was flat and straight-lined, gray and almost featureless on the flat land. From the outside it was hardly a disfiguring of the site or the surrounding landscape. But, inside, it was a world of its own: seventy-eight contiguous acres under a roof that seemed higher when you were below it than when you saw it against the sky. It was a plant run on Japanese lines, with the Southern work force, white and black and a few Asians, men and women, broken up into small military-style units, each with its own leader, goals, and loyalties. Thirty miles south of Nashville, in Spring Hill, an even bigger project was under way: the creation, on eleven hundred acres, of the Saturn plant of General Motors, a manufacturing plant (not an assembly plant like Nissan at Smyrna). It was going to cost $3.6 billion, and was going to be the largest industrial plant ever built in the United States. Even with its automation and robots, Saturn was going to employ some six thousand people. But nothing would show from the road. General Motors was landscaping the ground, banking up a low and not-too-noticeable hill, to hide the big plant. Crops would be grown on General Motors land beside the road. To the person driving by, the land would look like farmland. But Saturn, when it came, would physically and culturally alter the country for many miles around. General Motors thought that the "halo effect" would create fourteen to fifteen thousand new jobs in the middle-Tennessee area: new houses, new facilities, a new kind of working population. There was at the moment little to see. But the area was on the brink of an upheaval. Land values had risen. I had heard stories in Nashville of the "greed" of some local people, and of the readiness with which old Southern people, faced with the prospect of wealth, had alienated old farms and land and cut themselves off from the past that was, until the other day, so sacred to them. But Frank Bumstead, a Nashville businessman who knew the area well and drove me around it one morning, was less condemning. Frank was in his early forties, a self-made man, a Texan of Georgian ancestry; he had gone through university on a basketball scholarship. As a man with many business partnerships, he had an immense amount of local knowledge; and he had a precise, analytical mind. Frank said: "The fact of the matter is that in 1985, and today, an _efficient_ family farmer is fortunate if his farming covers his variable costs—seed, feed, fertilizer, chemicals, gasoline, etc., labor. If he has any debt on his land or equipment he is in serious financial trouble. Farmers cannot pay for their land or equipment. They can only hope to cover their variable costs. Why should people not sell? "A lot of the locals in fact were frozen like a frog who has a light shined in his eye at night. They saw the prices escalating and were scared to death to sell too cheap or too soon. That can be interpreted as greed. It can also be interpreted as someone intensely afraid that he is not going to sell a near and dear asset—to a farmer his land is next only to his wife and God—for enough money. Many of the people who sold had those farms in their families for several generations. "In many cases the people who sold used the money to pay off debts. I know one farmer who owned a piece of roughly 120 acres. It was not immediately adjacent to the site; it was about three miles away. He sold for $350,000. He paid the bank three hundred thousand. After the lawyers' fees he was probably left with twenty, twenty-five thousand." He talked of land values. "The Saturn project was announced by General Motors in 1985. Six months before the announcement farmland in Maury County, if you could sell it—and there was almost no market for it—sold for a low of four to five hundred an acre, up to a high of a thousand to fifteen hundred an acre, depending on the type of land, pasture being cheaper than cropland. A month after the Saturn announcement much of the land in northern Maury and southern Williamson, to the north, was selling for a low of twenty-five hundred an acre. Some land changed hands at prices up to ten thousand dollars an acre, 'raw' farmland. Some sales were reported in the twenty-to twenty-five-thousand area. In other words, it was insanity. A substantial amount of that speculation was done by Texas land-buyers who had experienced the land boom in Dallas and Houston and were in the midst of a downturn in those markets—'depression' is a better word. "There was a terrific amount of wealth created overnight in that area. I know someone who, having sold his radio station and his interest in a successful cable-TV system, bought three hundred acres less than half a mile south of southern Franklin City, on U.S. Highway 31. Lots of road frontage. He paid an average of three thousand dollars an acre six to nine months before the Saturn announcement. After the Saturn announcement he sold the land for seventeen thousand dollars an acre—and he owned it for less than eighteen months. He recognized that the land was far too valuable to raise horses on. He said he made more money on the farm than on the radio station. And he'd bought the farm to retire to. It just shows that it pays to be lucky rather than just smart." It was with Frank that on another morning I went to see the Nissan plant at Smyrna, moving from green Tennessee to, at first, office suites of gray and chrome, with noticeably thick, soft carpets. Many people were in uniform, dark-blue trousers, light-blue shirt, with NISSAN machine-embroidered above the left pocket of the shirt, and the person's first name above the other pocket. The public-relations woman with us said at one stage, in a corridor, "That was the president we just passed." He too had been in the Nissan uniform. In an open office area we saw a robot mail cart. It ran on a chemical strip laid into the gray carpet. The mail cart made the rounds of offices and halted at certain spots, not moving on again until someone pressed a strip at the top. If a person got in its way the cart beeped. The three-in-one assembly plant was E-shaped. The spine was more than a mile long: a lane, a road, flat and dead straight, disappearing at either end. Frank had seen places as big, and bigger; I hadn't. We rode about the great distances on an electric car, the public-relations woman driving and talking. There were no Japanese to be seen (there were only eleven among the thirty-five hundred staff); the people who looked Japanese were American Chinese or other American Orientals. In free areas in various parts of the plant there were basketball backboards and table-tennis tables. The table-tennis idea had been brought back by the workers who had trained in Japan before the opening of the plant. At many places there were television screens, giving constant production data and schedules and sometimes important items of national or international news. A real world, a complete world. But it was a relief to get outside and to see, in the distance, a relic of the old world: a corrugated-iron barn, against trees. Growing up in Trinidad, I had never wanted to be employed. I had always wanted to be a free man. This was partly the effect of my peasant Indian background and the colonial agricultural society of Trinidad. And though it had not been easy in the beginning, I had remained a free man. I had had as a result almost no experience of the twentieth-century world of work; and had few means of understanding the adjustments people made. Here at this Nissan plant people were treated well and paid well; there was freedom of a sort there, and dignity too. But it seemed to me that, for that, they lived in a very small space. Some days later I asked Frank, as a businessman and Southerner, to tell me what he thought we had seen. He said, "The first thing you saw there is the Nissan corporate culture. It's a superior corporate culture, that focuses on the participation of the worker in the process. It also focuses on the well-being of the worker. Their average work force is highly educated, extremely well paid, and nonunionized. The Japanese management idea is for the whole plant to be broken into little work groups, and these work groups have a specific responsibility. Within the group they elect a leader and assign responsibilities, and they are involved constantly in making their work more efficient and productive. Part of the culture is that the worker is encouraged to make the workplace a better, more efficient, safer, and happier place. You saw the table-tennis tables. "The corporate culture was adopted for several reasons. Wages are attractive. The plant is clean, modern, well cared for, and, as far as manufacturing facilities go, a very pleasant place to work in. Nissan provides many fringe benefits. 'Wellness'—that's one: a new word in our lexicon, a process of becoming and remaining well. And exercise facilities. And there's the team image. "The president walked by _in his uniform_ with his first name above his pocket. The uniforms are optional, but the vast majority were wearing their uniforms. Everyone is made to feel part of the team. And there are substantial incentives built into the Nissan corporate culture for excellent performers. These incentives are fair and evenly distributed across the work force and—more importantly—they are attainable. "You saw two components of the corporate culture that are worth mentioning. People with no experience of working side by side with robots find themselves working side by side with robots. These are Southerners, people whose roots are in the land and the farms. The second culture clash is that Nissan is a well-organized, very powerful, extremely large business, operating in the midst of a culture that had been largely agrarian, largely unorganized, and largely informal. "And what Nissan means to me is the cutting edge of a debate that is going to rage in the mid-sized metropolitan areas of the South for the next twenty years—Nashville, Lexington, Kentucky, Raleigh-Durham in North Carolina, Charlotte in North Carolina. This debate has quite simply to do with industrialization. Against the money, you have the sacrifice in life style. We've got a very high quality of life in the South, and even when we industrialize in a sensible way there are sacrifices. Increased traffic and the tensions that go with it; increased population and the tensions that go with that. Crime. And the increasing pressures brought on local governmental organizations to provide for growth. "Thirty-five percent of the Nissan assembly plant are women. In the South women didn't work. Woman's work was in the home. "Nissan had no effect on land prices. There was a lot of speculation, and most people lost. Because Nissan is an assembly plant, there was no halo effect. And Nissan had local people, people who were already here. Most of the General Motors workers are going to come from the upper Midwest. They will need homes. They're not Southerners. We know they're going to have an effect. They're unionized. Again, there's going to be a clash: standard of living versus quality of life. "My impression is that the upper-middle and middle class tend to resist growth and change, particularly if they have adequate jobs, a nice house, good schools. The upper class will profit from growth. The very wealthy support growth, because it's good for business. The poor become pawns in the game." IT WAS now getting towards the end of July. I went to stay in an estate in northwestern Georgia, seeing that area now differently from the way I had seen it almost at the beginning of my trip. Then I had traveled up from Atlanta and had seen it as a near-Indian wilderness. Now I came down from Chattanooga, an industrial town partly in decay. Not here the fast-food shops of the highways, with their tall standards and vivid liveries; just pawnshop after pawnshop, palmists and card-readers, little offices offering loans, and mobile-home sale lots sometimes strung with pennants. Outside Chattanooga I saw the mobile homes, tarnished and without bunting, in their home settings. I saw the small houses; the hoarded old-metal litter in some yards: Georgia of the crackers, with occasionally a small, disconcerting black figure in a yard, the figure intended to be what it looked like, an "artificial nigger," a local decorative feature, a reminder of the past. Fort Oglethorpe was my nearest town; James Oglethorpe was the founder of Georgia. There was a new way to Fort Oglethorpe, over the hills. There was another way, through the town of Lafayette (pronounced locally "Lafette") and then through the Chickamauga Battlefield Park—war as monuments and rhetoric and difficult strategy: Chickamauga the last big victory of the South over the North. My normal way to Fort Oglethorpe was over the hills; it was quicker. Driving on from there one day to Chattanooga, I saw from the slum around the Rossville Boulevard—saw and at first could scarcely believe—the patterns of white headstones in the battlefield cemetery: dotted white arcs, tidy and regular, on the low hills beyond the black and white slums, through which, as I drove, I continued to have glimpses of the cemetery. I didn't know the area; I wasn't expecting to see a cemetery there, and of such size, such patterns of dotted white lines; Chickamauga barely a name to me until I had come here, and now—the second day of that two-day battle perhaps the bloodiest day of the war, as I was to hear later in Memphis from Shelby Foote, the historian of the war—far more shocking than the cemetery at Canton in Mississippi. Important, that war, necessary; yet now it seemed past and dead, a waste. And seeing poor blacks and poor whites (with their jaunty baseball hats) in the decayed town—"pawns in the game"—I had a momentary vision of the world Will Campbell saw; and saw, again, the history of the place in easily seized layers: Indian land, blacks (artificial ones sometimes), war, industry, slum, with far away to the west, in Nashville, the beginning of a new order leading no one knew where. # 7 # CHAPEL HILL # Smoke IT HAD been hot from the beginning, from mid-April, that is, when I had gone south with Howard to see the place he thought of as home; and had been surprised by the colors of the Carolina spring, the new green of trees, the purple flowers in the roadside grass, the yellow-white dogwood blossoms; and had been further surprised by the beauty—in rust, wood-gray, faded green, and Indian red—of abandoned tobacco barns and derelict farmhouses and barns with peaked and spreading corrugated-iron roofs. The degree of heat or warmth I felt that Easter weekend I did not associate—after more than thirty-five years in England—with spring. And there was a morning in mid-May in South Carolina—still the Southern spring—that I found hard to bear: a steamy, stinging morning, in the ground of a great house on the bank of a muddy river, below a white sky, the air so full of biting spring insects that just to open the car door was to let in dozens. But then, after Tallahassee and Tuskegee, I had adjusted. Modern air-conditioning systems—not the single-room units, as debilitating by their noise and cold currents as the heat they pumped away—made that adjustment possible. The summer became something one had learned to live with. Until, in northwestern Georgia one day, about a week after I had arrived, there came, quite suddenly, the great heat, with thermometer temperatures of almost a hundred degrees. And that heat stayed in its first spell for three weeks. I wasn't aware the first day that the heat had come. The air conditioning of house and car and shops had set up an expectation of temperature contrasts. But then the ground heated up and the air heated up. Every exposed object radiated heat. To be in the open was to breathe in hot, humid air that irritated one's lungs. The house where I was staying was on the side of a hill and was set among fields and woodland. Outside the estate there were many small houses. From the road the area would have appeared to be pure cracker country. But from the estate itself the view—and it was an extensive one—showed no other house, showed nothing mean or disturbing. From the house and the pines around the house the hill sloped down, through rough open meadow, to an artificial pond and the branch-littered bank of a creek or river. Beyond, between massed trees, were glimpses of other fields and meadows; and in the distance were forested hills, blue fading into gray, line beyond line. There had been very few birds in the wood around the house. Now, in the heat, there appeared to be none. The crickets, though, started up as usual in the late afternoon, before the light changed, the cricket sound steady but with occasional, odd fadings-away. The meadows, the one in front of the house and the ones in the distance, browned after two or three days; the trees, both near and far, showed greener and darker. Then the leaves of some of the big trees around the house yellowed and fluttered down in masses for minutes at a time, as though it were autumn. The house dogs, importunate before for walks and human company, now became more private in daylight, raising a tail in greeting, letting it drop, and then going hunch-shouldered, head down, tail between legs, to the hollows they had dug themselves in the earth below the floor of the porch. In a pond beside the road on the way to Fort Oglethorpe cattle stood in muddy water up to their bellies—one might have been in India. The sky darkened in various places far away. But it seemed for many days that only other places were getting the rain. One day, though, it came, with wind. I saw it first on the water of the pool. Away from that, on the concrete edge of the pool, on the sandy ground, and on the wood shingles of the house roof, the rain dried almost as soon as it fell. But just as the first flakes of a snowfall can melt before the snow starts building up, so the rain now slowly soaked the roof shingles, and began to fall too fast on the pool edge to be evaporated away at once. Slowly the wet began to show. I opened the door to hear the rain and to smell it. There was the baked-earth smell—the first-rain smell that in India is re-created by some perfumers, using a kind of clay on a sandalwood-oil base, to make a monsoon scent. To this there was added a deep smell of pine, from the wet and cooling pine logs of the house. After the rain the dogs were everywhere active, running about the littered yards or ornamented gardens of small houses and mobile homes, or trotting intently at the sides of the road, as though they needed to be up and about in the cooler weather, after their long confinement, and as though they had been called out everywhere by the earth smells the rain had released. For a long time after the rain had fallen, the asphalted roads steamed. The thermometer fell twenty degrees in a few hours. But it was the merest remission in the heat, which soon returned: as imprisoning, while it lasted, as any spell of severe winter weather in the far North. It was hard to understand how people had made out here before air conditioning and screens. In the days before travel was easy, this kind of heat would have thrown people into themselves, as much as the winters of the Far North are said to throw Scandinavians into themselves. And perhaps this six-month summer weather, hot rising to hotter, was a factor in the still-visible degeneracy of a section of the local white population (the pinelanders whom Fanny Kemble observed would have left issue); and a factor as well in the almost Indian obsession of the South with religion, the idea of a life beyond the senses. TO THE west was Nashville or the area around it, awaiting the change that was going to come with the Saturn plant. To the east, in North Carolina, was the area known as the Research Triangle, bounded by the university campuses of Chapel Hill, Raleigh, and Durham, where over a period of almost thirty years a big industrial park of seventy-five hundred acres had been created: thirty thousand new jobs there, poor North Carolina pineland landscaped into the discreetest kind of industrial garden, many modern technological and pharmaceutical names represented by new buildings, long low lines of brick or concrete and glass, giving an impression of spaciousness and order and elegance, the land of rural poverty remade to suit its new function, the South seemingly abolished here, as it had been abolished at the space-research town of Huntsville in Alabama. At Huntsville the Southern businessman with me had pointed out a field of cotton—more than a crop: something from the past—literally across the road from a high-tech building: cotton, which, the businessman said, tore your hands and broke your back (because the plants were short and you had to bend all day to pick cotton). In some such way, at the edge of the Research Triangle Park in North Carolina, a small, well-tended field of tobacco was pointed out to me in late August: tobacco the famous old crop of North Carolina, the very names of some towns here more famous now as the names of cigarettes—Winston, Salem. When I had gone with Howard to his home town at Easter I had seen the tobacco seedlings being planted. I didn't know the plant and, though I must have seen tobacco in many places after that, I didn't know what I was looking at until now, when the bigness of the leaves was noticeable. I had been told that the great heat we had had in late July and the first half of August would have been good for cotton; and I thought that the same heat—which had yellowed the leaves of forest trees—had scorched the edges of the tobacco leaves lower down. But the tobacco leaves were ripening rather than drying. That was the way tobacco leaves ripened, from the bottom up. Tobacco leaves had to be picked or cropped only when they were ripe, so a row had to be worked many times. The lowest leaves on the plants we were looking at had already been cropped. Tobacco not only called for stoop labor; it had also to be harvested at the time of the greatest heat. The ridges and furrows of this tobacco field were as without weeds and as clean as a swept dirt yard. This little field, which one might have passed by without a second thought, spoke of a slow, detailed labor, as back-breaking as the cotton labor. The man who made me see all this was James Applewhite. He was from an old tobacco family in eastern North Carolina. He was fifty-two. He was a teacher at Duke University in Durham—the university founded and endowed by a tobacco fortune. He was also a poet. And though he was no longer part of the tobacco culture, and though he spoke of it as physically far away (though in fact it was reasonably close, two hours by car), that tobacco culture of eastern North Carolina was one of the subjects of his poetry, together with all that old semi-rural family life. I didn't know his poetry when I met him. But I began to be aware of his quality as a man when he stopped to show me the tobacco field: a poet's sensibility and a farmer's dedication, with an academic evenness of manner. He was a slender man, narrow-waisted, concerned about exercise. He took all my inquiries seriously, and spoke from the heart, without affectation, with a farmer's matter-of-factness, offering me at once, as soon as he saw that I was receptive, thoughts he would have spent some time arriving at. Durham was not his landscape, he said; he had only recently begun to make it the subject of his poetry. There was no landscape like the first that one knew. He elaborated on that, and he couldn't have known how directly he was speaking to me (the scarcely bearable idea of the beginning of things now existing only in my heart, no longer existing physically in the ravaged, repopulated Trinidad of today). I could understand how the past he meditated on, though physically so close and still existing in Wilson County, was in his mind quite far away. He took me by byways to his house. At a certain stage, after we had seen a man on a sit-down mowing machine in the garden of a house, he talked about the sweeping of the dirt yards in the old days. The soil would have been sandy; it would have been swept with brooms made of dogwood saplings. "And the marks of the sweeping would have been deliberately left in the yard to show that it had been swept and was clean." Would that sweeping have been done by a servant? No. "The mistress of the house did that with pride, as evidence of her good order." That touched something in me. But at the time all I could think of was the African huts and their clean yellow-brown yards on the banks of the Congo or Zaire River, seen from a river steamer twelve years ago. The yards were scraped like that, I had been told, to keep snakes away. Jim Applewhite thought there might have been something in that, even in the South. And that brought to mind Will Campbell's story about the "stomp" outside his bare, clean, family house yard near McComb, Mississippi. Something else remained, though. It came to me later: a memory, from some unplaceable time in my childhood, of the marks in dark sand of a _cocoye_ broom, a broom made from the hard central stems—rigid at the top, but thin and limber at the bottom—of the blades of a coconut branch or frond. Those marks in a corner of a Trinidad Indian yard that came back to me did stand for order and cleanliness, almost the piety of a house, its adherence to good old ways. There was a ritual about yard-sweeping in Indian or Hindu families like ours in Trinidad when I was a child. It had to be done first thing in the morning; it was part of the purification of a house before prayers. And there was something like a religious interdiction against sweeping after nightfall (no doubt because valuable things might have been swept away and lost). And perhaps, as well, some such idea of religion and piety lay at the back of the Japanese raked garden. Farmer, child, and poet came together in Jim Applewhite's contemplation of the physical circumstances of his childhood, and in his serious, generous talk. His house was in the countryside, in a dead end with a few other houses in a patch of woodland. It was a wooden house. The end wall of his sitting room was made up of old wide planks set diagonally. At the back was an unroofed platform looking onto woodland—a style of living that in other countries was open only to a few, but here in the United States was open to many. He gave me a copy of his new book, _Ode to a Chinaberry Tree_ , published in 1986 by Louisiana State University Press. While he got tea ready, I looked at "A Leaf of Tobacco." Is veined with mulatto hands Then the veins were seen as streams, "a river system draining a whole basin," collecting all the historical debris of the South. At the same time: Scented and sweetened with rum and molasses, Rolled into cigarettes or squared in a thick plug, Then inhaled or chewed, this history is like syrupy Moonshine distilled through a car radiator so the salts Strike you blind. Saliva starts in the body. We die for this leaf. The crop that required such labor, slave and free, the crop that gave the region a special calendar and culture, was a narcotic, dangerous to men. Commercially it was on the way out: another little disaster for the South. Jim Applewhite didn't smoke, had smoked only for a short while many years before. But the culture was so close to him that, almost in spite of himself, the tobacco product in the poem comes out as tempting. The idea of rum and molasses and tobacco, the sweet and the bitter, made me think of Will Campbell's aromatic, moist, licorice-sweetened Beech Nut chewing tobacco, and made me think of the cellophane or clear-plastic-wrapped squares of tobacco, as dark and rich as fruitcake, at the checkouts of Southern supermarkets. He liked tobacco as a culture, for the formalities that went with the growing and curing and selling of the crop. And when, later that evening, I read his poetry in my hotel room, I found it enriched by his talk and the sights I had seen, and already half familiar. In "For W. H. Applewhite" he wrote of his grandfather. (And in my imagination I saw the tobacco field he had shown me at the edge of the Research Triangle Park.) He dug grey marl near the swamp, set out Tobacco by hand, broke the suckers and tops Before they flowered, leaving some for seed. Cropped the broad sand lugs, bent double In air hot rank in his face from the rained-on Soil. "How to Fix a Pig," a celebration of a "pig-picking" at the end of the tobacco harvest, was also a celebration of the man who "fixed" or barbecued the pig, a man called Dee Grimes, who was—still—the sharecropper or tenant on the old Applewhite farm. It comes from down home, from When they cured tobacco with wood, and ears of corn Roasted in ashes in the flue. The pig was the last thing. The party At the looping shelter when the crop was all in. The fall was in its smell, Like red leaves and money. Agricultural communities are conditioned, given a calendar, by the crops they grow, and the origin or first purpose of the crop becomes unimportant: rice in Java, tobacco in North Carolina, sugarcane in Trinidad in the old days. The talk in that poem of celebration at the end of the crop—the hard crop, originally the slave crop—brought back very faint memories of something called "crop-over" in Trinidad, when the sugarcane had all been cut, and the horns of the black water buffaloes that drew the cane carts were decorated and there was something like music in the main road of the small country town where I lived, at the very edge of the sugarcane fields, acres upon acres, scene of bitter labor: memories like snapshots from very far back, when I was six or seven, memories seemingly spread over a long time, but perhaps in reality the memories of no more than a week or so. THE GREAT size of the land, the distance between places—this was one of the things that would have separated Jim Applewhite's comprehension of the world as a child from my own comprehension of things in Trinidad. Was it oppressive or frightening sometimes, in the old days? Did people feel lost? I asked him some days later, when we met at the hotel where I was staying. He said, "For my grandfather to go a buggy ride to Wilson, the county center and center of tobacco sales, ten miles there and ten miles back, was a day's journey." And even that was already familiar to me from the poetry: His memory held an earlier era: a steamboat To the New York fair, when soot spoiled his hat. Horse and buggy courting, when ten miles two ways Was a day. "Automobiles began to come into that area in the 1920s, and electric lights. Electrification tended to follow the roads. My wife's mother was reminiscing earlier this year, remembering when electrification got to the country. People did feel lost here. The sense of needing to form a life that had its own regularities, its own formalities—that was a reason that religion had the contour it had. That's why the formalities of tobacco-growing were so important." I asked him about the tobacco field he had shown me. I had seen that when I had just arrived in the area and was in a geographical haze. "We were on the boundary between Orange and Durham counties. The old road from Durham to Chapel Hill. There was a little soybean growing too, a little soybean nearby. What is happening in this area is that the rural agrarian economy is being replaced by another economy. Which made that farm unusual. It was five or six miles from Duke University campus." Then he spoke about the formalities of tobacco-growing. "Tobacco was associated with an older mode of living. Associated for me with my grandfather, with a kind of ritualized cyclical time order, where the cycle of the seasons was marked by sowing the plant bed, preparing the land in the spring, setting out the plants in early summer, harvesting in midsummer. You'd be finishing up curing and grading in August." Grading? "Grading involved separating the leaves from the different levels of cropping. And actually different levels of ripeness. So that the best tobacco was placed together, wrapped together, in these 'hands,' to bring the highest price at auction. There might be three or four tobacco companies, or five maybe—in flush times—bidding for the tobacco whose quality they liked. The buyers would travel to different markets. There would be a kind of marketing sequence. The market would begin south and go up north, following the pattern of tobacco ripening and harvesting, roughly. "I think that tobacco in its best incarnation was a sort of folk art. An art practiced by people who were extremely good at it but who might not be able to read and write. I remember when other areas, like Canada and Rhodesia, were trying to get into tobacco-growing, they would come to North Carolina to get to these folk experts—who might not be able to sign their own names, but who knew how to harvest, cure, and grade tobacco. "The artful thing about harvesting is knowing when the tobacco should be cropped. It won't cure properly if it's picked too soon or too late. You can't make a perfect leaf some seasons. That's why tobacco has a vintage, like wine." "Are you an expert?" "No, no. I just know what is involved. I saw this around me all my youth. Mostly, I think I was impressed by the aesthetic contour of the tobacco ritual. Planting had to be done at the right time, with hand care, individually. A handcrafted mode of agricultural production. It's much more mechanized now. But this handcrafted aspect of tobacco was predicated upon cheap labor in the South at a time when the South was economically disadvantaged. "Typically, the land would be owned by landlords who didn't any longer live precisely on the farm. Like my grandfather. People who had left the Civil War farmhouse homeplaces built by their grandparents or great-grandparents and had moved to town, to small hamlets, such as the one I was born in. And in those houses on the farm there would be living a sharecropper, the tenant farmer. He could be black or white. Typically in my experience, they were white. They farmed on shares. The farmer got half the proceeds on the crop. The owner furnished the supplies and the capital. Typically, there might be one or more black families living in smaller houses on the farm, living rent-free. They were not participants in the sharecrop deal, but worked as a kind of distanced retainer. They worked for money, and their large families provided the many hands required for housing tobacco." "Housing?" "The whole thing of getting the tobacco from the field into the curing barn and then the packhouse—where it was packed up and stored until brought to market. It was important to have a good tight packhouse that wasn't too humid and above all didn't leak—you couldn't afford to have your tobacco get wet after it had been cured. If it had too much moisture it would 'mold' and lose its value radically. "This housing involved whole teams of people with different ranks of hierarchical importance and responsibilities. The croppers, those who actually broke the leaves from the stalk, they were in a sense the most important. They had to do two difficult things. Hard physical labor, and they had to make the decision about which leaves to gather. And they had to work very fast. There would be two or three or four of them going through the field, breaking the leaves. It was most difficult when they were breaking the leaves at the bottom of the stalk. Then they would have to work bent double all day long in very hot temperatures. "Some of them would go along the row walking on their knees, to avoid bending over. But that is hard too. Following the croppers would be a mule-drawn or a tractor-drawn 'tobacco truck.' These tobacco trucks were really small wooden wagons with wooden wheels. They had stakes at the corners and burlap sides to hold the leaves in." I told him what Howard had said about the tobacco tar on his hands, and what Howard's mother, Hetty, had said about the tobacco smell making her sick. "Most of the workers complained about the way the gum got on their hands and arms. It usually wouldn't make anyone ill from the nicotine unless it was wet." Hetty had said the opposite. She had said that to avoid the smell she and her husband had gone to work in the tobacco fields in the early morning, when the dew was still on the leaves. "The other persons of most importance were the 'loopers.' They worked in the barns. They tied the tobacco leaves with cotton twine on to the sticks, which were then laid horizontally on racks in the barns, with the leaves hanging down from the sticks, stem ends up. Again, this had to be done rapidly. The loopers were always women—they might be the wife of the tenant farmer. And there would be 'handers.' They would hand the tobacco leaves from the tobacco trucks to the loopers. "Some people nowadays have even taken the whole tobacco truck with the wheels and made coffee tables out of them. An old-fashioned tobacco truck was only half again as large as a coffee table. They were made small to go down the rows. And possibly one truck packed up with about five feet of tobacco leaves was very heavy, enough for one person to manage. Tobacco, before it was cured, was heavy. "The looper would receive five or six tobacco leaves, stem end towards her, in her left hand, and with a few swift motions wrap and secure the stem ends together. And then she would flip the bundle"—he made a gesture, but the thing he was describing was not easy to follow—"so that it straddled the tobacco stick and hung there. It was very important that the leaves not fall off the stick, because if several leaves fell and landed on the galvanized steel flue beneath them they could start a fire, and the whole barn could be consumed in fifteen or twenty minutes." "Did that happen a lot?" "It was not unusual for a tobacco barn to burn. You would expect one or two barns to burn down in a growing season." He went back to talking of the various jobs in tobacco. Then he said, "A certain social stratification resulted. The sons and daughters of the owners became the town boys and girls. The sons and daughters of the tenant farmers were the country boys and girls. We went to school together. I really admired these country boys and girls, because they worked harder than I did." I asked about the effects of mechanization. His reply was unexpected. "The technological innovations that did away with much of the hard labor also did away with some of the quality of the tobacco. No 'hands' are tied now. Leaves are clamped together in bulk barns and cured." He spelled out the word "bulk" for me, as though the word itself contained some of the grossness of the new method. "Tobacco is no longer graded. The leaf is placed in canvas sheets and sold." A lot of the ambiguities of his attitude to tobacco came out in that expression of distaste for the new methods, which spared men but were bad for the tobacco. I put that to him. He didn't reject it. He said: "It's a mystery and a paradox. For me it has a certain resonance, the whole tobacco business, and it is close to the paradox of civilization itself. That this essentially poisonous substance formed the basis of a way of life that had so many attractive aspects—a formalized, seasonal cycle to it, which left the land combed into its even furrows after the stalks had been cut in the autumn. Which had the spectacle of the tobacco market, with the golden piles of aromatic leaf being sold for what were really considerable sums of money." Jim Applewhite's wife came from a tobacco family as well. They had been talking recently about tobacco, he said, and his wife had said that in the old days it was possible to tell, just from looking at a hand of tobacco leaves, who had tied the hand—so individual were the loopers' tying styles. "Tobacco was a product which allowed the South at a time of pretty serious economic disadvantage to bring in cash money from the whole country and even from abroad. No other crop brought in so much money per acre, and was so lucrative in return for effort expended. In a sense, as a poet who didn't know he was going to be a poet, the fact that the product was a folk art and nonutilitarian must have appealed to me. The final use of tobacco was as a social gesture. From production to consumption, it was a style-bearing medium. The life style has changed. I don't think the South absolutely needs to produce this poisonous substance any more. "I think of tobacco as an Old Testamentish aspect of a past way of life, a kind of traditional, conservative, fallen world, a world marked by original sin, of which tobacco was a kind of symbol." I asked whether members of his family smoked. "Father smoked a little. Not much. That's part of the paradox. The workers mostly smoked. Two of the sharecroppers who worked on the family farm during my teenage and adult years died of lung cancer." Those deaths worried him. He had spoken of them with feeling at our first meeting, almost while he was showing me the ripening tobacco field on the old road to Chapel Hill. But, as always in his talk, there was another side to the poison. "One can argue that any successful agrarian economy has most of the aspects of tobacco-farming. What it doesn't have is the handcrafted, graded, aromatic, sold-by-auction quality that tobacco has. The issue of quality, as determined by color, scent, and flavor, was central to tobacco. There's a region specificity to wine, and tobacco is in a sense analogous: there's a region specificity to tobacco as well." He said that there was something he had wanted to show me in his house, but he had forgotten. "The wallboards of a tobacco barn from my family farm are in my sitting room. And the ceiling beams were posts in the barn." But I had noticed the planks on the end wall, broad planks, set diagonally. He said they were of pinewood, and had been made so hard from the years of heat of the curing process that he had had to use an electric drill to get nails into them. "The industry changed in its desires when the filter tip came in. The classic cigarette was the unfiltered Lucky Strike or Chesterfield or Old Gold. That's the kind of cigarette the companies wanted the most beautiful tobacco for, the most beautiful, lemon-yellow, 'bright-leaf' tobacco. When the filter came in they wanted a heavier kind of tobacco, less bright, not as good a quality. So the premium for growing the most golden bright leaf lessened. The whole mode of production has been degraded by different kinds of demand and, most flagrantly, by altered growing practices. Chemicals are used to inhibit sucker growth and to artificially increase the bulk, the weight of the leaf. It's called MH 30. It was developed in North Carolina. And of course tobacco doesn't support as many people in its mechanized aspect. Formerly tobacco-growing would support whole countrysides of people. It was the chief cash source for the rural descendants of slaves, white Southern farmers who owned no land of their own, as well as for the landowners. Today there's simply so much more money, and the importance of tobacco is less." His past had been more or less abolished. But it was this past that gave him eyes for the landscape he now lived in—though there could be no landscape like the first. "I am now able to write about the landscape of Durham County.But I realize that that is in part the case because the landscape has been historicized for my imagination by the evidences I can still see there of an older agrarian economy, before the land was covered again with trees. "A Southern field, if you leave it alone, will grow up in broom sedge, and in a few years young pines will be bristling up, scattered through the broom sedge. After twenty or thirty years it's woodland again." Hardwood trees then grew up in the shelter of the pines; and then the hardwoods killed the pines. He lived in a landscape of second-growth timber, eighty to a hundred years old. "But in places the old farm rows are still there, like small waves in a bay frozen by time. They were the rows of the last crop planted by some farmer, in the last century perhaps, or the early part of this. And deep in the trees you see fallen chimneys, areas where in spring jonquils still come back where there had been family gardens. A few old tombstones in places. Some beech trees with names and dates still legible from being cut into the bark, in 1908 or 1911 or 1914. This is about the period when this change we've been talking about began—electrification, roads, motorcars." Every stage of history marked by small ruins, a landscape of small ruins—this had been my first impression of the South when I had come down at Easter with Howard, to see the place that to him was home, not very far from here. Jim Applewhite said: "The landscape of eastern North Carolina was always to me a kind of landscape of the past. There was this dichotomy in my own life between my father and my grandfather. My grandfather had been born in that Civil War-era farmhouse, and he was always associated in my mind with the agrarian economy. My father ran a service station and believed in progress and sold electrical appliances for a number of years. He was always in a hurry. My grandfather was never hurried. "It was in my grandfather's house—just across the road from our house—that we went for the ritual occasions that marked the farmer's year. My grandfather represented a kind of permanence for me. He had a packhouse—that's where they packed the meat. That's where they cured hams and shoulders. And they did lovely things like rendering lard, making sausages. Very hard work. But formalized, because people were in direct contact with the necessity that constrained them to do what they did. The hogs had to be killed on a very cold day in winter. Otherwise the meat would spoil. Corns and beans had to be canned when they were ripe, or they wouldn't last." Canning In kitchens with pots large as vats Wrinkled aprons and skin with the steam. Pigs were strung up from timbers in December. Their blood steamed like ghosts in the cold. "One has this romanticism, but when one goes and looks at it, it's not a fiction. It does exist. A quarter of a mile away from this farmhouse of my grandfather's is a graveyard, and there my grandfather's parents are buried with some other people." THE WORD "tobacco" is thought to have come from Tobago, the dependency or sister island of Trinidad. And before "Virginia" became the word in England for tobacco, tobacco was sometimes called "Trinidado," after the island of Trinidad, part of the Spanish Empire since its discovery by Columbus in 1498. Tobacco was a native Indian crop. But after the discovery and plunder of Mexico in 1519–20 and Peru fifteen years later, the Spaniards were interested only in gold and silver; they were not interested in tobacco. It was the English and the Dutch and the French who went to Trinidad to load up with tobacco. There were hardly ever more than fifty Spaniards at a time in Trinidad in the sixteenth and seventeenth centuries. The Gulf of Paria, between Trinidad and Venezuela, a vast safe harbor, was nearly always full of foreign ships. An English explorer and diplomatist, Sir Thomas Roe (who later went to the Mogul court at Agra in India as the representative of King James), came to the Gulf of Paria one year and saw fifteen English, French, and Dutch ships "freighting smoke." Another English official reported that the tobacco trade might in time be worth more than all the Spanish gold and silver from the Americas. The trade was illegal, however—even though crops were grown in Trinidad with the complicity of the Spanish governor. Under Spanish law only Spain could trade with a Spanish colony. Occasional sweeps were made by the Spanish navy against foreign interlopers in the Gulf of Paria; and foreign sea captains and sailors who were caught could be hanged on the spot. And the Indian tobacco fields—tobacco a crop requiring such great care, as I was to see in North Carolina—were flattened: part of the process by which in three hundred years both the native Indian population and tobacco were to be rooted out from Trinidad. The island that the British captured (without a shot) in 1797 was a sugarcane slave colony. And it was to work in the sugarcane estates that, thirty years or so after the abolition of slavery in the British Empire in 1834, Indians were brought over from India on indenture. It was sugarcane that gave a rhythm to the life of rural Indian communities. Tobacco was no longer a local crop. I would have been disbelieving, and delighted, to be told as a child that Trinidad had once been known for its tobacco. To me tobacco was glamorous, remote, from England (in absurdly luxurious airtight tins), or American (in soft, aromatic, cellophane-wrapped packets), something from an advertisement in _Life_. SHE HAD a name tag on her blouse: _Paula_ in white on black plastic, drawing attention to itself, and making you see that she was almost flat-chested. She was a waitress in a newish salad-and-quiche "gourmet" bar in one of the rich towns of the Research Triangle. She said, "Would you like a cocktail or a drink before your lunch?" It was a formality. As spoken by her, it held no invitation at all. There seemed to be as little zest in her for these restaurant refinements as there was in me, after months of restaurants and hotels. "Now, let me tell you about our specials." Mechanically, she recited the specials. At first on this trip, for the first month or so, during these recitals in restaurants, I used to smile: the recitals seemed ironic, to be a kind of joke between the waiter and the customer. But the recitals were always perfectly serious; the waiters were doing, often doggedly, what they had been told to do. Paula got through to the end of what she had to say. It was then, unexpectedly, that life came to her voice. She said, "I'm leaving today." "Leaving the restaurant?" "After this serving. Leaving here. Leaving the town. Going to Wilmington. Tomorrow." "Have you packed? You don't have much time now." "I'll just throw it all in the Chevy. One of those little subcompacts. Like a Pinto." "You won't take a U-Haul?" "I've been throwing away things for like a month. You throw away and throw away and then you find you still have things you want to throw away." "You really think it will all go in the Chevy?" It had become one of my own little anxieties about traveling and the hotel life: telephoning for the bellman, emptying the safe-deposit box, loading up, wondering whether it was all in, whether there was going to be a doorman at the other end, to help with the many bits and pieces: so many books and papers and files and notebooks now, so many little bags and sacks. She said, "Well, you see. My husband and I had like a fight about a month ago. And he took half the stuff, and I had, like, well, the other half. But God gave me the strength to see that through." "What are you going to do in Wilmington?" "Peter's there. I'm going to De with him." "Your husband?" "God worked the miracle. Let me bring you your salad." When she brought the salad I said, "The U-Haul people have a depot here. I saw it yesterday." "We have a lot of bills. I want to pay those off first. It'll all go in the Chevy." "Bills. I know." "It was one of the things we used to fight about. He'd pay some. And some he'd outright refuse to pay." "Why did he do that?" "Exactly. He said he was saved. Like me." "Are you saved?" Her voice trembled. "Oh yes. But he didn't, like, grow. Grow in Jesus, as they say." The last phrase, and its tone, suggested that she was slightly mocking what she was talking about, or keeping at a certain distance from it. But, as with the specials, she was speaking seriously. She wore cheap jeans, of a vivid, factory-fresh blue. The body below the heavy blue cloth was thin. There was a lot of Southern makeup on her face: rosy cheeks below big tinted glasses and above a thin white neck. A small, worn-away woman with a rustic accent: all the weakness and the fight, all the will to survive, contained in that little body. She brought the quiche, stale, soggy, dead-looking from its long exposure. She said, "We were always quarreling. Fighting every day. We would fight and he would want to go away, and then I would beg him not to leave." "Had you been married long?" "Three years." "You didn't think you would get someone else?" "I was frightened of being alone. But God gave me the strength this time. I didn't ask him to stay. I let him go. And then God worked the miracle in both our hearts." "How were you saved?" "I just got saved." "Did you have a pastor? Was there some preacher you were following?" "Nothing like that. I was feeling for some years that I had to do something. Feeling that if I didn't do something—" "You would be unhappy with yourself?" "Unhappi-er. But I felt that the God of the earth or the universe or whatever couldn't be interested in someone as unimportant as me. And I did nothing." "No one was advising you?" Many of the words she was using seemed to have been put in her mouth by someone who knew about the saving of souls. "There was a minister." She gave the name of a fundamentalist Protestant church. "And one day I don't know what came over me—I found myself walking to the altar during a service, and I said something, I don't know what, and I knew I was saved. I just felt the love of the Lord in me then. It was after that that I met Peter." "Was he already saved?" "He got saved after me. When I told him. But Satan was tempting me with an ex-boyfriend." "After you were married?" "After I was married. That was when Peter stopped paying bills and started to make trouble about the tithing. Started to make trouble generally. And we had these fights." "Did you fall when Satan tempted you?" "Only in my head." "Did you meet the ex-boyfriend?" "No, never. He wasn't interested in me. He never wanted me. That was the trouble." "What was it about the ex-boyfriend that was so attractive?" "I can't say. I don't know. It was just there. Satan's temptation." "I can see how your husband would get unhappy." "I'm not blaming Peter. But the tithing and the bills, and especially the tithing—that didn't have anything to do with anything. But God gave me the strength last month, when he left. I didn't fall before him and hold his knees and ask him not to leave. I just had the strength. I didn't know what I was going to do, what was going to happen to me. I just felt the strength God gave me. And now it's all right." "How often do you pray?" "Every morning. For about twenty minutes." "Do you speak to God in your head? Do you feel you have to make some physical gesture? Do you kneel?" "Sometimes I talk to God in my head. Sometimes I talk to him aloud." "You enjoy it?" "Most definitely. And the prayers are answered. Like the way Peter and I have come together again. That's prayer. That's God. But he answers prayers only when they're according to his wishes." "How do you know when they are according to his wishes?" "I used to pray to get my ex-boyfriend. But that wasn't according to God's wishes." "When did you pray to get your ex-boyfriend? After you were saved?" "After I was saved." She smiled at the boldness. "Do you love your husband now?" "That's why I'm going to him. I love him. I love him. God worked the miracle in both our hearts." "And your ex-boyfriend?" "I've forgiven him." Or she might have said she had forgotten him. Satan and God fighting for Paula's soul, Paula herself not responsible for the movements of her passion, helpless, capable only of choosing salvation and asking God to reveal his will: a medieval idea of chaos, and the solitude and helplessness of men, and the necessity for salvation. But this was not set in a medieval world of plague and disease and deprivation, the arbitrariness of the sovereign and the humility of the poor. We were in a town of the Research Triangle; and the theme of this culture was abundance and choice, the paramountcy of the individual (if only as consumer), with beauty and luxury and sensual satisfactions as imminent possibilities for all. Abundance and choice was the motif even of this little restaurant, where there were very big color photographs on the wall of loaves of bread and ears of wheat and unsmeared glasses of translucent red wine, and where even on her last day Paula dutifully recited the specials. "How old are you?" "Thirty-two." "I thought you were much younger." And that was true. The orange-colored thread zigzagging down the crotch of the blue jeans had come out less as an erotic device than a beginner's attempt at style, a signal of the inexperienced frailty of the body beneath—the body that was in fact the thirty-two-year-old woman's capital and liability. The big tinted glasses masked her eyes; and below the glasses the thick, flaring Southern makeup concealed the skin of her cheeks. She was like someone in disguise. She said, in the Southern way, _"Thank_ you! Thank you. When I was going through it I looked much older. I looked like nothing." I had asked Jim Applewhite whether in the old days people in the countryside hadn't felt lost. He had said, "People did feel lost here. The sense of needing to form a life that had its own regularities, its own formalities—that was a reason that religion had the contour it had." TO THE east it was a land of small farms, never absolute country, no big towns. The fields of corn (or maize) were tall and brown. The big thick leaves of tobacco, ripening fast now, were lime-yellow; and for me it was as though, having learned a little about the crop, I had learned to see its beauty: lime-yellow, gold, "bright leaf," against the brown and green of other fields: the green of potatoes or soybean, plants low to the ground, dotted with white and purple flowers that Jim Applewhite later told me would have been the flowers of the morning glory. There were old tobacco barns everywhere, tall, squarish, sealed structures, sometimes with green asphalted felting on the outer walls, the felting (originally intended to keep the barn as tight as possible, and now much torn) held down by closely spaced vertical battens. Battens and tattered felting sometimes suggested, from a distance, an old barn wearing down to its frames. Weeds and small trees grew right up against abandoned houses and farmhouses; vines covered chimneys; crape myrtle marked the site of drives and old gardens. Small fields, small houses, small ruins, churches, small towns, the freeways of the central part of the state giving way to crowded and dangerous two-lane roads—the land spoke of the nature of the people, independent small farmers, conservative or fundamentalist in religion, and conservative in politics. I had been told that the politics of the region were "tobacco politics," small-farmer politics, in which a promise of a continued subsidy for tobacco-growers could somehow also be read as containing a promise to keep blacks in their place. But Reverend James Abrahamson, pastor of the Chapel Hill Bible Church, thought that this ridiculing or underplaying of the conservatism of eastern North Carolina was foolish. He said, "The fundamentalist political impulse has always been there. From the 1930s it has been repressed, largely because it did not have the support of the universities. Ideologically, the universities pulled up their tent pegs and moved to another side. Ideologically, they moved from a world view which embraced a Christian God to a place where the only reality that was recognized was material, could be measured, scientifically defined. They are reappearing—the fundamentalists—largely because they have seen or felt the pressure of a secular society. "That eastern–North Carolina conservative side is viewed by many as being redneck and knee-jerk. Irresponsible—fanatical, almost. Unenlightened, lacking what I call the three 'I's—intelligence, information, and integrity. But they've got a stronger argument. They're easy to laugh at, and they'll never be popular. Our culture may self-destruct before they have a chance to articulate clearly the common sense they represent—for a culture that is based on more than self and materialism." Jim Abrahamson—it was the way he announced himself on the telephone—was from the Midwest. He was a fundamentalist himself, and he felt that his Bible Church was meeting a need in Chapel Hill. He had a number of Ph.D.'s in his congregation; and his church was expanding. Extensive construction work was going on when I went to see him. American society, he said, had been built on a religious base. It couldn't float free. A recent poll had found that one out of every three Americans was a born-again Christian. "That's a lot of people." But he had his quarrel with the fundamentalists of North Carolina. "I think there are powerful and legitimate and almost eternal principles that would recur again and again. But the people fighting for those principles are not able to articulate them palatably. The religious right appear not to understand the world view the left or the secular intelligentsia embrace. They tend to dismiss them as God-haters or infidels. And they have a difficulty about knowing how to translate religious ideals into a political policy." It was the Islamic problem too—since the Islamic state had never been defined by its founder—and it was the prompting to fundamentalism in many countries: how to know the truth and hold on to one's soul at a time of great change. It was strange that in a left-behind corner of the United States—perhaps the world motor of change—the same issue should come up, the same need for security. BUT NO one was more secure in his faith and in his politics than Barry McCarty. Politics and faith made with him a whole. He was only thirty-three, but he had already made some impression, and people who followed political affairs in the state saw him as one of the new generation of New Right leaders, someone whose time was going to come in ten or fifteen years. His training had been in theology and debate. (Like the training of many fundamentalist leaders in Muslim countries: again this curious convergence of two opposed cultures.) He had taken a first degree in Bible at Roanoke Bible College in 1975; had done a master's degree in speech and rhetoric at Abilene Christian University in 1977; and had got his Ph.D. in rhetoric and argumentation at the University of Pittsburgh in 1980. Since 1980 he had been professor of public speaking and debate at his old school. Roanoke Bible College was a Church of Christ institution. It was in Elizabeth City, a small town far to the east, on the coast, nearly two hundred miles away from Raleigh and the landscaped pinelands of the Research Triangle. Beyond the Chowan River the land, already without hill or accent, became flat, the land of a delta, with a high sky. Albemarle Sound (unknown to me, even as a name, until that moment) gave a great, continental sense of the North Carolina coast, making me half regret that I hadn't known of it before, and making me want to come again and be for a day in that openness. It was one of those places where it was easy to imagine the excitement of the early explorers, finding themselves in what was truly a new world. Barry McCarty's office was a small room on the upper floor of a turn-of-the-century wooden building. There were framed and autographed color photographs of President Reagan and Senator Jesse Helms on one wall. Below those photographs, and also framed, were Barry McCarty's various admission tickets as a delegate to the Republican convention in Dallas in 1984. A young politician's treasures. He also drew my attention to a flag laid flat on another wall: a flag with two red bars and a white bar, and seven stars in a circle on a blue field. He asked whether I knew the flag. He said the seven stars gave a clue. I didn't know the flag. He said it was the Stars and Bars, the first flag of the Confederacy. He was a small, stocky man, cool, self-possessed, pink-faced, with glasses. He looked very clean and neat in his collar and tie, as neat as his office, his bookshelves, his photographs, his files. He looked a middle-class professional man from a small town; not a politician, not a man anxious to stand out. He idolized Jesse Helms. On the telephone, trying to persuade me to make the two-hundred-mile run to Elizabeth City, he had said (as though it was going to be reward enough for me), "We're Jesse-crats here." I asked him what a Jesse-crat was. He said, "It describes a conservative North Carolina Democrat who votes for Jesse Helms and people like Jesse Helms. They represent the conservative values of the Old South. Faith in God. A belief in limited government. A belief in free enterprise. Individual liberty and individual responsibility—two ideas that go together." And within those principles were contained all his politics, all the conservative program. He showed me the text—typewritten or word-processed in capital letters, with emendations in handwriting—of a speech he had made in praise of Jesse Helms at a dinner for the senator. The speech began, "It is one of the greatest honors of my short life to be asked to present to you one of the greatest living Americans." And very quickly then, while offering praise to the senator and criticizing his enemies, the speech outlined the conservative program on taxes, welfare, government spending, education, communism; and fitted it together with freedom and religion. There was a story, in the speech, about the senator: "I was with him on one occasion as he checked into a hotel for an overnight stay. The woman behind the desk asked the senator if he had a credit card to charge his room to. He turned to her and said, 'Young lady, I'd just as soon carry a rattlesnake in my pocket.' And paid cash." Was it still true about the senator and the credit cards? Barry McCarty smiled. "He has one now. But that's the mind-set of someone prudent with his own finances." In 1985 the governor of North Carolina appointed Barry McCarty chairman of the state Social Services Commission for a four-year term. "We've been trying to introduce the 'workfare' idea instead of welfare. The basic idea of workfare is that welfare recipients who are able to work are required to work in order to continue to be able to receive their benefits. It's part of the Southern work ethic. "You must remember that the majority of the Founding Fathers of this country were Southerners. The first English-speaking colony on these shores were founded in 1584 by Sir Walter Raleigh—not sixty miles from where we are—at Roanoke Island. It is known as 'the lost colony,' because Walter Raleigh established the colony and the next time the provision ship came to find them they were lost." (But Sir Walter Raleigh also had other projects at that time. He became interested in the idea of El Dorado. In 1595 he raided the island of Trinidad with a large force. He killed the small, half-starved Spanish garrison and captured the Spanish governor, a crazed old soldier who had spent his fortune looking for El Dorado. Raleigh wanted Trinidad to be his base for El Dorado; he wanted the kidnapped Spanish governor to be his guide; and he wanted the Indians of Trinidad and Guiana—in the Orinoco Delta—to be his allies. He took Indians back to England, to prove to people where he had been; and in that same year, 1595, he wrote a book called _The Discovery of the Large, Rich and Beautiful Empire of Guiana_ , which suggested that he had discovered El Dorado and its gold mines without actually stating that he had. He talked of an English-Indian South American empire, Ralearía. But nothing happened. He had roused the local Indians against the Spaniards, but he could do nothing for them; they were ground down by the Spaniards. In 1617, as crazed now as the Spaniard he had dispossessed twenty-two years before, he was let out of the Tower of London to find the Guiana gold mines he had spoken about—which he had never seen, and which didn't exist. His son died in the fraudulent quest; Raleigh blamed a very old friend for the disaster and drove that friend to suicide. It is a squalid story. But Raleigh, because he is known mainly by his own writings, remains a romantic costume figure—and an exquisite tapestry of him in costume hangs in the Carolina Inn in Chapel Hill.) Barry McCarty said: "The country actually began here in the South. And when you look at the guiding minds of constitutional government in America you find that so many of them were Southerners—Jefferson, Washington, Patrick Henry, Randolph, the Madisons. "Slavery was not the real issue in the War Between the States. The real issue was the power of the federal government over the states. The same distrust of a central power, the same jealousy over individual rights that moved the Founding Fathers to demand the Bill of Rights, that same spirit is really what led the Southern states to resist the North in the issues that led to the War Between the States." Was that still of moment today? "Here is a man—Jesse Helms—who believes that the powers of the federal government ought to be strictly limited. The most important government to the individual should be the one closest to him. The more remote the government becomes, the less it should have to do with the life of the individual." "Where did you get your passion about politics? Was it through your father, your family?" "The first influence could be religious. The Bible teaches that governments are necessary in order to establish order and justice in human society." "Does the Bible teach that?" "Romans, chapter 13. Where the Apostle Paul teaches that governments have the authority of God." (Later, in my hotel, I read the chapter in the New International Version of the Bible. I thought it was full of repetitions and anxiety, the work of a man who had a very good idea of the power of the Roman Empire and didn't want his little group to be crushed. It was more than "Render unto Caesar the things that are Caesar's"; Paul appeared to be making up a theology to suit his purpose. "Everyone must submit himself to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. Consequently, he who rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves. For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and he will commend you. For he is God's servant to do you good. But if you do wrong, be afraid, for he does not bear the sword for nothing. He is God's servant, an agent of wrath to bring punishment on the wrongdoer. Therefore, it is necessary to submit to the authorities, not only because of possible punishment but also because of conscience. This is also why you should pay taxes...." The epistle could be used to defend anything. Barry McCarty's interpretation, which appeared to turn things inside out ["Governments are necessary in order to establish order and justice"], was the interpretation of a believer. Though that injunction about taxes seemed to go against some of his Jesse-crat political beliefs. The whole of that chapter, in fact, could be said to be contrary to his ideas about government. But I did my reading later. I couldn't at the time raise the points with Barry McCarty.) He said, continuing his thoughts about the 13th chapter of Romans, "That teaching suggests that the first function of government is to establish order, to punish the lawbreaker." He went on: "But nowhere in the Bible are such things as charity enjoined as duties of governments. They are definitely enjoined as the duties of individuals, but never of government. So I have a personal obligation to feed and house and clothe the poor." "You?" "Yes. The poor who it is in my power to help. There is another biblical belief that shapes my passion for strict constitutional government. The Bible teaches that we are fallen creatures, that men are by nature sinful. The way that constitutional government provides a remedy for that is that the collective power of men is checked and balanced. I believe that the basic difference between the liberals and the conservatives is that the liberals believe in the perfectibility of men, and conservatives do not. "Conservatives believe that human beings are fallen creatures whose collective power must be checked and balanced. Look at social spending in this country. Their belief—the liberals' belief—is that, if you give the right people enough money, they will eliminate poverty. I don't think that will ever happen. What will happen is that those people who have all the power and money become king, and because they are human, in some way sinful creatures, they will find a way to abuse that money and power. "I question the very morality of the federal welfare system. If you were hungry, and I take you home and feed you, that is benevolence, because I have chosen to show charity towards you. But when the federal government legally plunders me through taxation in order to give to you, I consider that immoral." He had so far not been interested in answering personal questions. He hadn't given a personal twist to any of his ideas. So I hadn't been granted any human understanding of his political drive. I tried again now. I knew that he had not been born in North Carolina, but had come there from Atlanta. I asked about his background. He didn't reply directly. He said he had got an up-to-date biographical sketch in his word processor. And, saying with a smile and a shake of the head how strange it was for someone like him to be using a word processor, he sat before the instrument, pressed various keys, and after a while presented me with a printed text. It was formal, an account of his education and his professional experience, his political life, and his career as a Church of Christ minister. I put the sheet with the other papers he had given, and asked what his father did. "My father was a fireman. He served in the U.S. Navy in World War II, and for the first eleven years of my life he worked as a firefighter in East Point, Georgia—a suburb of Atlanta. Then, until 1981, the year of his death, he was a safety engineer for an insurance company. "I was two weeks old the first time I was in church. I grew up in the Church of Christ. I happen to come from the branch of the church that uses music in its worship. Our people don't have the Calvinistic belief that you have to see some sort of miraculous sign to become a Christian. Our approach is more rational." "Did you have the weekend camps?" "I attended Christian-service camps as a boy." "Someone told me that he found those camps boring." "Some of my fondest memories and friendships of childhood come from my experiences in Christian camps." He came to Roanoke Bible College from Atlanta when he was eighteen. He was the first person in the history of his family to have a college education; and the course of study he had then started on was like an extension of his family faith. He was proud of his doctor's degree from the University of Pittsburgh. When I asked about the subjects he had taken for that degree—rhetoric and argumentation—he said, "I found I was attracted to the basic skills of thinking and speaking. These are two keys to just about any field of endeavor in life." I told him about what I had seen of the Church of Christ in Nashville. Had he had doubts, like two of the people I had met? "I have found that whenever I have questioned my faith I have always been able to find that evidence confirmed rather than denied my beliefs. I don't think I ever came to a place where I had any crisis. It has been a lifelong growing process. As I learned more and more about science I found the world to be a more and more complex and intricate phenomenon, which confirms my faith." Did he feel that the church made too many demands on people? "We live in a secular society, and a real commitment to Christianity becomes harder and harder. However, I don't think that that observation can be used to determine whether Christianity is true." I asked about the strength of the Church of Christ in the region. "The movement began in the early nineteenth century, through the efforts of a Scottish Presbyterian preacher, Alexander Campbell. Campbell said he wanted to be just a Christian. Campbell lived in West Virginia. From there the movement moved west and south." So it was fairly new in eastern North Carolina. The Church of Christ college had been founded in Elizabeth City in 1948. "To provide ministers and Christian leaders on the Eastern seaboard." It was an impressive set of buildings, occupying two residential blocks in what Barry McCarty said was the nicest part of the town. Most of the buildings were turn-of-the-century frame houses. The college had also bought eighteen acres across the road, beside the Pasquotank River. That was an Indian word, Barry McCarty said, meaning "where the current divides." The way he said that made me feel that he had some romantic feeling for the Indian past on this grand coast. But that wasn't so; he had got that fact about Pasquotank from _The North Carolina Manual_. Two dormitories, in brick, had recently been put up on the Pasquotank land. There were now 160 students at the college. In five years the college was hoping to have two hundred. All his professional life had been spent with religion and related matters, and he hadn't found it dull. "I find the Christian life an adventure. To know God and to share in making him known to others is the greatest quest upon which any human could set himself. I would say that my views are stricter than most. I will admit that." I asked him to describe the people of the region. "Most of the people here are very traditional and very conservative. They would be of basic European stock." "Scottish, mainly? That was what I was told." "Not Scottish. Most people can't remember that far back. They are very American. Southern. One of the phrases you might hear, or see on a bumper sticker, is, 'American by birth, Southern by the grace of God.' The people of this region are proud to be Americans and Southerners. They are small farmers, many of them with one or two hundred acres. Some of them are fishermen. Some work in the tourist trade. There isn't a lot of heavy industry. People are more tied to the land here than in Raleigh or Charlotte. I like the small-town atmosphere. The suburb where I grew up had very much of a small-town flavor, where you knew your neighbors and they knew you." "What do you feel is the difference between people here and people in towns?" "I probably qualify for membership in the yuppie society, as someone with a doctor-of-philosophy degree from a major American university. But I have a respect for the old values of Southern culture. Earning money is not the most important thing in my life. The people here have a devotion to principle over a love of profit. The basic difference from the towns is materialism. People in the towns are more devoted to things than ideas. The people here admire a statesman, a man of principle." "But they like people to look after their economic interests?" "Helms is interested in the right of the individual back home to earn a living for himself. The small farmer, the small entrepreneur." But how could the small farms last? Tobacco was on the way out. He agreed. He didn't himself like the idea of the tobacco subsidy, and he thought that most of the farmers accepted that tobacco was on the way out. "I know many people here in North Carolina who do not earn their sole livelihood through farming. You will find people who will be farmers and carpenters, farmers and mechanics, or farmers and other things. Or they will farm and log. I do not own a wood stove now. Before, I would buy firewood from a man who farmed in the summer and logged in the winter. The average person in eastern North Carolina—the colloquial phrase would be 'down east'—is not wealthy. They are working-class people." And the future for them? "I'm not in a position to predict the future of the small farm. But I would make two observations. One would be that simple, decent people have been working and making ends meet for centuries on this continent, here in the Americas. I see most of the folk of eastern North Carolina as being sons of pioneers. The people who carved this country out of the wilderness did so by simple, honest labor, and there wasn't a gigantic federal system to take care of everybody—the people on Roanoke Island and later at Jamestown. "The second observation is that these simple, honest people who are laboring down here are not so far behind the times as they appear. They watch the same TV programs as people in Chicago or New York or Atlanta. And many of them send their children to school in Chapel Hill or Vanderbilt or Raleigh. What I'm saying is that the conservatism and values that are held are held by choice, and not through ignorance of what the modern world has to offer. They are timeless values, enduring values. "And here in eastern North Carolina, when you talk of the future, you talk of something that only God knows for sure. And these folks know God pretty well." "How would you describe your opponents?" "People who believe that government has all the solutions." "And locally?" "It's hard to find any flaming liberals down here." "Describe the region." "It is one of the places where old Southern values still reign. It is a beautiful land, green, with much water. It is a place where people live close to the land, even those who don't live on farms. And you have many people who enjoy the water. There's fishing, hunting. The land is good here." The beauty of the land, the outdoor life—I had heard it before, from many kinds of people. Barry McCarty himself was a hunter. He hunted duck; he was looking forward to the opening of the dove-hunting season. And without any prompting from me, he spoke of his resentment of the federal regulations about guns. He possessed the conservative ideology complete, even down to this, its most puzzling aspect: the right to have guns. He said, "For the first time since talking to you, I find myself almost concerned how I present this attitude about guns." I liked that "almost concerned": it might have come from his training in speech or rhetoric. He went on: "Often Southerners are portrayed as gun-toting rednecks, racist, and it is said that a Southerner who really cares about his right to own a gun is really a member of the Ku Klux Klan. This connects with our discussion earlier about the Bill of Rights. Under Article 2 the right of the people to bear arms shall not be infringed. I think you will find among Southerners that since they are jealous of all their constitutional rights they are also jealous of their right to keep and bear arms. "I will live at peace with my neighbors. But I will not hesitate to protect myself and my wife and family against an intruder. A gun in such circumstances is the civilized man's last line of defense against an uncivilized man." I said I had been told in Mississippi that the hunting grounds of the common man were shrinking. Was the same thing happening here? "Not yet. The world constantly changes. We have to adapt. You have to be ready to defend your way of life. There are some values that never change." "But the physical world changes." "Yes. I used to write with a pen. Now I use a word processor and computer." How was he defending his way of life? He was going to pay for his children's education at a private Christian academy. It was going to cost S100 per boy a month. It was going to be expensive for three boys. "But we'll do it." And this led to his other point. "Excessive taxation is a threat to my way of life." I was moved by his passion and directness, and I read out to him what Jim Abrahamson of the Chapel Hill Bible Church had said to me about the Religious Right. They were people, he had said, who were easy to ridicule; but they represented a necessary common sense. Barry McCarty's eyes softened behind his glasses. He was surprised and pleased by what I had read out; he hadn't been expecting this degree of understanding. He became philosophical. "Up until the seventeenth century Western civilization basically was Christian. Within that world view the universe and everything in it, including human beings, had meaning and purpose. In the modern view the world is just one damned thing after another. A _horrible_ world view. Ultimately a world view human beings cannot live with. It cannot last. It will destroy itself. "When you look at the paintings of the Dutch masters and other artists whose work was informed by the Reformation in Northern Europe, the world view is of a world God made and God is in control of. A world in which individual people possessed freedom and dignity because they had been made in the image of God. That's why Rembrandt would bother to paint a picture of a woman cleaning a fish or slicing a loaf of bread. Because that woman had infinite value to God—she was made in the image of God." Easy to ridicule, conservatives like himself? But he had been to a major university, he said; he had studied philosophy; he knew the modern world. People knew that about him. He said, "That is why they feel that that man, the man who has looked at the new world and dismissed it, is to be feared." The eyes that a minute before had been soft grew hard. And I felt—quite suddenly—that within him, within the correctness of dress and manner, was a fire. When we had talked on the telephone to arrange our meeting, I had asked him to think of some educative or illuminating thing he might show me in Elizabeth City. He hadn't forgotten. At the end of our meeting he took me to see the Confederate Memorial in the Court Square. It had been put up in 1911 by the local chapter of the Daughters of the Confederacy, a chapter that, he said, perhaps no longer existed. He showed the memorial: the pillar (suggesting mass manufacture), the soldier at the top. He said nothing more about it; he said nothing while I looked. And then it was time to drive him back to the Bible College. I asked him about the blacks of Elizabeth City. He spoke with puzzlement and sorrow about them. Most of them had the Southern work ethic, he said; most of them, in their values and day-to-day life, were conservatives. But they didn't vote conservative; they voted for black candidates. It had been a long day, and it was a long drive back. About fifty miles from Elizabeth City, on the narrow, crowded road, there was a nasty-looking accident: one car smashed in, another overturned, people running to the spot, and then the sound of an approaching ambulance. My thoughts remained there for a while. And it was only a day or so later that I saw that Barry McCarty had opened our meeting by showing me the Stars and Bars in his office; and had closed it by showing me the Confederate Memorial. The past transformed, lifted above the actual history, and given an almost religious symbolism: political faith and religious faith running into one. I had been told that the conservatives of North Carolina spoke in code. The code could sometimes be transparent: "Tobacco Is a Way of Life" being the small farmer's plea for government money. But in this flat land of small fields and small ruins there were also certain emotions that were too deep for words. JIM APPLEWHITE took me one day to see his family farm in Wilson County, in what he said was the heart of the eastern-North Carolina tobacco country. We went first to Wilson, the main town of the county. It was ten miles from the farm—I knew that distance from the poems and from Jim's talk. Wilson was a more substantial town than I had expected. The residential part through which we drove looked rich and settled, with big houses set back in wooded gardens. In the old days money in Wilson came principally from the tobacco market. On the other, industrial side of the town (we drove through that side on the way back in the afternoon) there were the tobacco warehouses. We stopped at a supermarket to buy nuts and fruit for lunch. Ahead of me in the checkout lane was a drunken young black man with cans of beer. His speech, already Southern-slow, was made slower by drink, and he seemed to be making private sounds rather than words. The cashier, a white girl, was correct, appearing to notice nothing, speaking the supermarket's formula of thanks after she had taken money and given change. The forecourt, when we went out to it, looked less attractive: supermarket carts, litter, some lounging blacks. It wasn't a place to have a car snack in. Jim said, "We'll go to the farm." We crossed the railroad track. It had once divided the white town from the black. There was still an Amtrak station; and, on what would have been the white side of town, the old hotel. Like an arrangement of properties in a simple film set: station, rails, the small hotel. "Traveling salesmen would have stayed here," Jim said. "What a life." "Some of them would have liked it." Beyond the rails, and in what was still the black town, there were shotgun houses, as narrow as mobile homes, and set close together side by side. Already the Wilson of the big houses seemed far away. The ten miles to the farm went very quickly. There were old tobacco barns everywhere, three or four together sometimes in a field. And, before I was ready for the farm, we had turned off the road and parked in a clear space between an old two-story frame house and many galvanized-iron farm buildings. There were two oldish cars in the yard: part of the yard's metallic aspect. Across the road were fields connected with the farm. I had been told by Jim about the family house and farm, about the family move to the nearby small town of Stantonsburg, about the sharecropping family and the black hired hands. But I hadn't taken it all in. I was confused by all the things I had been told; and when we stopped in the yard I didn't absolutely know where I was. I thought that there would have been Jim's family in the old frame house; I thought of the sharecropper as a kind of employee. When Jim got out and went into the house, I opened my can of nuts and poured orange juice into a paper cup. Nuts in one hand, orange juice in another, with an elbow keeping the supermarket orange-juice carton upright beside me—that was how I was when a heavy pink-and-white man in his late forties, in dark-blue trousers and a check shirt, and with glasses, came out to the car, smiling. He said, with a certain confidence, "I'm Dee Grimes." I knew the name well. He was the man celebrated in the poem "How to Fix a Pig." His speech, his life in tobacco, had been turned into poetry. He waited for me to make a move out of the car—he had been told that I was coming. But I was encumbered. I couldn't open the car door just then, and couldn't find words to explain. He became abashed, said something I couldn't follow about "Mr. Jim," and took a step back. I said at last that I had read the poem about him. This pleased him. He said that someone else who had read the poem had wanted him to do some cooking. And it was only after some time that I understood—what in fact I had been told before—that Dee Grimes, the sharecropper, lived in the old Applewhite family house—one of Jim's sacred places. It stands today, upstairs porch railed in Before narrow windows, their antique glass Upright and open toward the cleanly furrows. Their hand-blown panes show lines imperfectly, As if miraging heat since the Civil War Had imprinted ripples. Between the main house and the kitchen, which was a separate building, there was a wide, covered passage, a "breezeway," with open screen walls. (There would have been no screens in the old days, Jim said.) It was there that we eventually sat, though Dee Grimes would have liked us to go inside to enjoy the air conditioning. His talk—not easy for me to follow: he sat on the other side of a table and at some distance from it—was about the drought. There had been no rain and no rain. He had tried to dig a well, but he had found no water. Some of his talk was also about Dan, a neighbor. Dan had an irrigation system; Dan had watered three times this summer. Dan also had a mechanical tobacco-cropper; it had cost him $35,000 some years ago. Dan was that very day "putting in" tobacco, using the mechanical cropper to pick the ripe leaf, and then getting his people to "put in" the leaf in the curing barns. He talked about the house; he had been told that I might be wanting to see that as well. He said that one of the most notable things about the house was that so much of it had been put together with wooden pegs, even the rafters of the breezeway. He took us inside. The house was more spacious than one would have thought from the outside. There was a solid feeling to the floor, no hollow sound in the wooden house, no resonance. The front rooms were of beautiful proportions, almost square, seventeen feet by eighteen, and high. When we were outside again, we considered the brick chimneys at the sides of the house, and the two railed porches facing the road and the fields across the road. Jim said: "It's a lovely old house. A noble house, in its plain vernacular fashion. I especially like the tall windows. Although I have never actually looked out across fields from the upper porch, it seems to me a vantage point." The bulk barns for curing tobacco were at the other side of the open yard. Three or four stood side by side and were like little mobile homes. The heat inside was electrically generated, and the air around the barns smelled of hot green leaf. When Dee opened the door of one barn the air that came out was very hot and the smell was a little cloying. The outer leaves on the racks, leaves already brown, were ragged. Dee said this was from the colder air striking them every time he opened the door to have a look; the leaves farther in would be better. In the packhouse—where the cured tobacco was stored, after it had been "ordered" (given moisture, that is) to prevent the cured leaves from going brittle and shredding away—we saw the poor crop of the year. In the large space there were just a few bundles of golden leaf in sacking. There was a warm, rich smell here, and the floorboards had a sheen from the resin of years. Without being asked, Dee prepared a couple of old-fashioned "hands": taking six leaves or so, holding them stem up, and then tying them tightly at the stem (on the principle first of the cummerbund and then of the loincloth) with a good-quality leaf folded two or three times. Dee's wife—she had been out somewhere, and had just got back—came into the packhouse. She stood silently with us, watching Dee tie the hands. The old mule barn was still whole, another of the metallic structures of the yard: a reminder of another labor of the past. There were no mules to look after now, but there were reminders of mules that had been there: the top boards of the stalls had been gnawed away in a wavy pattern. At the end of the yard was an amazing contraption. It was a tobacco-leaf harvester, with a canopy. There were low metal seats for four croppers, and the idea was that as the harvester was pulled along by a tractor the seated croppers would break off the ripe leaves from the tobacco stalks, without the strain of bending or walking on their knees. But, with the "handers" and others needed to transfer the picked leaf to the clamps, it took eleven people to keep the harvester going. Labor, labor in midsummer—and a little distance away, just the roof and upper walls visible, was the small one-story house where the black hired hands would have lived. Farmhouse, barns old and new, the house for the hired help at the back—there was as great a simplicity about this layout as about the railroad station, the railway track, and the small hotel at Wilson. But a poet had looked long at this yard; and everything in it was shot through with radiance for him. As I saw when, just before we left, Dee and his wife began to talk about the danger of branches falling off the oaks near the farmhouse. Dee and his wife wanted the trees to be lopped. Jim was concerned; he didn't want the trees to be lopped too hard, to lose their appearance. And for a while they talked, each side with its own interest. We left at last to go on to the small town of Stantonsburg. This was where Jim Applewhite's grandfather had moved after he had left the family farmhouse. It was there that Jim had been born. It wasn't far away. Jim said: "The Applewhites came from England, from Suffolk, and seem to have landed in Barbados. There are Applewhite or Apple-thwaite records in Barbados. The next records are in Virginia in the eighteenth century, and then in North Carolina. They were probably in Stantonsburg before the town was incorporated in 1818. "I've been told that at one time the Applewhites owned the land on both sides of the road between Stantonsburg and Saratoga, the next small town." There it was again, the recurring Southern story of great wealth in the past (the whole of the island of Trinidad, a third of an English county, a chest of gold that sent up a cloud of gold dust when it was emptied on to a floor). But there would have been some substance to this story: the Applewhites owned the Stantonsburg general store as well as a sawmill. The town was like Wilson in miniature. There was even a railroad track dividing the black town from the white, the side-by-side black shotgun houses from the frame houses and the lawns. We passed what had been the Applewhite store. It was a low white frame building with a shelter over the sidewalk. It now looked empty. Jim said: "It held everything you'd need to house a crop or carry on your life. In the old days these stores were essentially a company store. In other words, the farmer would get everything they needed on credit, paying back when they sold their crop. And when my grandfather owned a lot of land the tenant farmers would get their things there and pay him back." And it occurred to me just then, driving past the now empty store, that—without my having intended it—my journey was ending almost as it had begun. I had gone to the town of Bowen at Easter with Howard and seen his home district from the other side of the tracks, as it were. (I had such a clear memory still of the oddity I had felt on the Sunday morning when, as we were walking to the black church, three white men had stopped in a car to ask the way to the country club.) This town was like Bowen in its size and appearance; and the Applewhites (as I was to learn, but not from Jim) owned slaves, at one time forty. (And how odd it was that, as soon as you began to live with the idea of slaves, you developed this other way of reckoning wealth—in slaves.) Hetty, the daughter of a black sharecropper, had taken me to see Mr. Bowen, to pay my respects. She had then taken me to the black cemetery, where her father was buried. She had shown me the farmhouse, now in ruin, with small trees and vines growing right up against it, where her father had lived as a sharecropper. She had her special way of looking: her chant, as we had driven through the countryside, had been, "Black people, black people, white people, black people. All this side white people, all that side black people." She had said, but quite late, unwilling to go into the gloom of the past, that tobacco (which she had grown both with her father and her husband) had made her cry. At Bowen in the spring the flowers in the roadside grass had been purple. Now, in Stantonsburg, almost at the end of the summer, the flowers were yellow, little all-yellow daisies. And now, with Jim Applewhite, I was considering another kind of past: a past where the child had seen completeness, even in the stock—for tenants—of his grandfather's general store: mule collars, tobacco twine, ten-penny nails ("Probably they were ten for a penny"), bonnets, shoes for children. "I did feel there was a kind of complete world contained there. Partly because the houses here were built without architects, without trained builders, and I grew to feel that the capability of building those houses was contained in those objects in the store." The Applewhite house was in a residential street with two or three churches. Outside the Baptist church some black men and a white man were working. The street was full of children, many of them black, and for some reason they all had large ice-cream cones. Old Mr. Applewhite was in the sitting room watching football on a big television set. He was eighty, and a little proud of his age. He was much shorter than his son, and stouter, his physique suggesting a man who had been very strong. He explained about the children and the ice cream. A local shop was celebrating its seventy-fifth anniversary and selling ice creams for 5¢—which was what the shop had charged for an ice cream in 1912. On the table in the dining room was food for our visit. And the old man had got out a magazine for me, _The Flue Cured Tobacco Farmer_ , together with a booklet for tobacco farmers, _How to Grow It Ripe_. Jim ate. I talked to his father. He said, "Did my tenant show you some good stuff? This has been the sorriest tobacco crop for thirty-five years. There's been no rain for thirteen weeks." He told me that the farm was between 150 and 175 years old, and he showed me a framed certificate that said that the farmhouse was on the Register of Historical Places. He thought that Dee should have persevered with his well and gone down a further twenty feet; someone he knew had found water at 150 feet. Then he grew philosophical, religious. "We can't complain. The farm has done very well, up until this year. If you do right by your fellow man it will be all right. My father was in the best financial shape of anybody around. And he did like kind of what Social Security does now. He was blessed." Later, in a back room, with a view through a screen door of the shaded lawn and the neighboring house, Jim and I sat and talked and I took down his words. He had from the start spoken as though he had cut himself off from his past, made a far journey. But that past was here still, a couple of hours away from Durham—or as much of the past as a man of fifty-two might reasonably expect still to find. But a journey had been made; there had been a break. "I was put to bed when I was six with what was then said to be rheumatic fever. My mother read me the whole of _Huckleberry Finn_. I staved in bed for a year. I was protected more than my fellow students for a few years. It set me apart. Something like that always happens to the person who is going to be a writer. "I think I'm always conscious of the fact that I'm not truly of the world I've been showing you. I've not worked in tobacco. Dee Grimes is truly of that world. A real tobacco man, if you want to be colloquial. Educated in the school of hard knocks, educated by experience. I feel a kind of kinship and a kind of separation when I am with him." "Separation?" "Presumably it began with that separation when I was a child, when I was set apart from those who were unselfconsciously playing their part in this eastern-North Carolina world, which is a world of action, not of thinking." Separation, and kinship. The Applewhite name was no longer in the windows of the store. But for Jim the letters on the glass—they had been in gold, and set in an arc—still existed, "in a ghostly way." "I do remember occasions of visiting back during my early years of college and once again experiencing what I have now almost forgotten—and that is a sensation of being so utterly at home in, and a part of, a place, that one feels somehow coextensive with the place. "On the other hand, there is a sense of separateness in being in part of myself an observing stranger in my own native land. To the extent that at times I was fascinated by the idea of the pre-existence of the soul. Fascinated especially by the original Edgar Rice Burroughs book, _Tarzan of the Apes_ , the first and best of the Tarzan books. Because in that book the Tarzan-to-be was landed in the jungle by the crash of his parents' plane. There was something in that idea—of a person from another culture being deposited from the sky in a tropical environment—that was fascinating to me." It was extraordinary. Not only (as had happened more than once) did I find Jim Applewhite talking for me, expressing things I had felt as a child and an adolescent in Trinidad. He was also—though he was from the other side of the tracks—talking like Howard, Hetty's son. In New York, at the airport, Howard had said, of the place that was his home, "I hated the place when I was young, for the continuity." I had puzzled over that word "continuity." It had meant old things, old buildings (like tobacco barns and farmhouses) still standing, keeping a place physically dull. It had also meant, as came out later, old ways persisting. When we had returned to New York after our Southern weekend, Howard had said, "I'm different. I felt different at the high school. It's what you think and what you feel that makes you different. I always felt different. Which leads me to believe I was born in the wrong town. Like many people." Jim Applewhite said: "My feeling of duality at that time was being physically in the world I identified with, but which on the other hand completely left out a whole other side of my psyche or my soul. There was still a cultural transmission here—from something quite other—through the churches, the hymns, the words and the music, the poetry of the Psalms in the King James Bible, and through books. My uncle would stay with us in the summer. He was a bachelor. He was probably my first literary influence. When I was six years old he told me stories which I later realized were from the _Odyssey_. "There was a duality of worlds as a child and a young man that is probably not at all unique for a person of artistic inclinations, but which was given an exceptional tension by the intensity with which so many in this small-town world defied or opposed those values which were foreign to it—those cultural values that were transmitted from afar. There is a sense of self-subsistence about the South—that it is itself, knows itself, and needs nothing else. Because of this sense of beleaguered self-sufficiency it can be extremely pigheaded. It can cherish ignorance. It can cherish the unreasonable, the unreasoning. "And I was hungry to have things explained. I remember looking up at the constellations and not knowing the names of the constellations. Or not knowing the names of trees. I have my telescope now, which I didn't have then. "Finally, one wanted consciousness, the right to be aware, or to name in language, in harmonious language, or in music—to name things, or else simply to name. Art is a sort of divine uselessness. That's one of the reasons I'm also attracted to tobacco. It's not practical. It's not for any use that's good for anything." WE HAD heard much, from Dee Grimes and from Jim Applewhite's father, of Dan the neighbor, the lucky man with the irrigation system and the mechanical harvester, who was that day "putting in" tobacco. And when we left Stantonsburg we went to see Dan. He was a friendly, well-exercised middle-aged man with glasses, in pale-brown clothes and with a dark-brown baseball cap ("Pride in Tobacco")—through he himself didn't smoke. His hands were black with grease and also with tobacco tar, from the leaf he was "putting in"—the green-leaf tobacco tar I had first heard about from Howard. His harvester—with a black man at the controls—was at work, straddling many rows. It was fascinating to watch this large, awkward-looking, but delicate machine, which had done away with the brute labor of tobacco-cropping. The wheels of the harvester, and the driver's seat, moved along furrows; on either side two long rubber rollers with a little space between them caught the tobacco stalks and rolled off the leaves up to a certain height. The rolled-off leaves fell into bins and were taken up fast-moving bands to the leaf basket. The tobacco stalks with the uncropped upper leaves snapped back into their upright position; and at the end only an occasional yellow-green leaf remained on the ground to show that the harvester had just passed. In the shed outside Dan's bulk barns four black people, two men and two women (casual workers, to judge by their goodish clothes: no overalls), unpacked the leaves, fixed them into metal clamps, and slid the clamps along the racks in the bulk barns. To "put in" in a bulk barn was easier than in the tall old barns, where a man had to climb on a ladder to hang the sticks on the upper racks. Some years ago, Jim said, Dee Grimes had fallen off a top rack and fractured his hand. The racked leaves in the bulk barns looked like gigantic green salads. It was easier with the bulk barns. But some of the ritual of the old days that the boy had studied on the Applewhite farm had also gone—the many black women looping tobacco leaves on sticks, the heated barns tended all night, the sweet corn roasting in coals, the pig being barbecued. The field with the old Applewhite family graveyard no longer belonged to the family. But there is always a right of way to a graveyard, and a grass track led to it from the road. It was a small enclosure, about thirty feet by twenty. The iron rails were overgrown with weeds and orange trumpet vines. The oldest stone, very nearly indecipherable, had been put up in 1849. Small stones marked children's graves. There were two wooden markers. Jim said, "Probably heart of pine. What they call 'fat lightwood.' Possibly a slave. Sometimes slaves were buried with wooden markers." These markers looked scorched. I thought it might have been from age, but Jim said there might have been a fire in the field. The softer wood had worn away around the ridges of the harder grain. Across the grass track from the graveyard there was a field of tobacco, the veined, resilient, umbrellalike leaves drooping a little after the weeks of drought. These small fields and rusting old tobacco barns—picturesque when I had first seen them—spoke now of great, detailed labor. And in the graveyard in the center of the field it was easy to imagine how confining it would have been in the old days, before roads and motorcars and electricity, and how the country town of Wilson, ten miles away, made a day's journey. ... Closed in by miles Which sandy roads, pine barrens, swamps, made A limit to curiosity. The stars' light, The King James Bible and Wesley's hymns, Traveled equivalent distances, unquestioned. But now there was an easy road to Durham. OUT OF his intense contemplation of the physical world of his childhood—an act that made me feel close to him, though his world had not been at all like mine—and out of his separation from that first world of his, Jim Applewhite had gone beyond the religious faith of his father and grandfather and arrived at a feeling for "the sanctity of the smallest gestures." It was an imaginative, poetic resolution, quite different in its calm, its positiveness, and its import from Barry McCarty's feeling, as a politician and a Church of Christ minister, for the beauty of the simple life—which, with him, seemed also linked to the idea of a world threatening to get out of control. Such different men; yet they had certain important things in common. They had been made by the same history. And it was that sense of a special past, the past as a wound, that I missed almost as soon as I went north to Virginia, to Charlottesville. There was history there in quantity—Jefferson, Monticello, the University of Virginia. But that was history as celebration, the history of the resort, the history that was causing the subdivisions (or housing developments) to multiply in Virginia, and was even threatening the fox hunt (where already the hounds were trained to hunt foxes and foxes alone in special rented fox-compounds with deep-buried fences; and where the huntsman knew where all the foxes were in his "country" and inoculated all the cubs against rabies). I had been living until then—and this perhaps had made the people of the South or Southeast so congenial to me—with people coming to terms with a more desperate kind of New World history, and a poorer land reflecting this history—the history that, in his poem "Southern Voices," Jim Applewhite writes of as _"defeat,"_ putting the word in italics, the defeat that he hears in Southern speech: This colorless tone, like flour Patted onto the cheeks, is poor-white powder To disguise the minstrel syllables lower In our register, from a brownface river.	{ "redpajama_set_name": "RedPajamaBook" }	1,175
{"url":"https:\/\/www.gamedev.net\/forums\/topic\/137412-lets-make-a-game\/","text":"#### Archived\n\nThis topic is now archived and is closed to further replies.\n\n# Lets make a game...\n\nThis topic is 5496 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.\n\n## Recommended Posts\n\nWhat came to my mind, is maybe we can start making a game here? For example, we can post some useful code and how it''s going to be used in the engine, and then after all we can combine that code for ,say, next tutorial on game-making? Here''s my first addition to this topic - CVector class:\n\n\nclass CVector\n{\nprivate:\nvoid sub();\n\npublic:\nGLfloat\tx;\nGLfloat\ty;\nGLfloat\tz;\n\nVERTEX3fv data;\n\n\/\/ ructors\n\nCVector(GLfloat x=0, GLfloat y=0, GLfloat z=0) : x(x), y(y), z(z) { sub(); }\nCVector(CVector &V) : x(V.x), y(V.y), z(V.z) { sub();}\nCVector& operator = (CVector& V);\n\nGLfloat GetData();\n\n\/\/\tBoolean stuff\n\nbool operator == (CVector& Vector);\nbool operator != (CVector& Vector);\n\n\/\/\tAdd & Substract, Positive & Negative\n\nCVector operator + (CVector& Vector);\nCVector operator + ();\nCVector& operator += (CVector& Vector);\n\n\/\/ minus vector\n\nCVector operator - (CVector& Vector);\nCVector operator - ();\nCVector &operator -= (CVector& Vector);\n\n\/\/\tMultiply & Divide\n\nCVector operator (CVector& Vector);\nCVector& operator = (CVector& Vector);\nCVector operator (GLfloat d);\nCVector& operator = (GLfloat d);\nCVector operator \/ (CVector& Vector);\nCVector &operator \/= (CVector& Vector);\nCVector operator \/ (GLfloat d);\nCVector& operator \/= (GLfloat d);\n\nbool operator > (CVector& Vector);\nbool operator < (CVector& Vector);\n\/\/\tDot Product\n\nGLfloat operator % (CVector& Vector);\n\/\/\tCross Product\n\nCVector operator ^ (CVector& Vector);\nCVector& operator ^= (CVector& Vector);\n\n\/\/\tSet length (Normalize if 1) or Magnitude of vector\n\nGLfloat operator ! ();\nCVector operator \| (GLfloat dLength);\nCVector& operator \|= (GLfloat dLength);\n\nvoid Normalize();\n\nvoid SetNormal(CVector vTriangle0, CVector vTriangle1, CVector vTriangle2 );\n\n\/\/\tThe angle between two vectors in radians\n\nGLfloat Angle(CVector& Normal);\n\n\/\/\tReflect in Normal Vector\n\nCVector Reflection(CVector& PlaneNormal);\n\/\/\tRotate dAngle Degrees (radians) Around Normal\n\nCVector Rotate(GLfloat dAngle, CVector& Normal);\n\n\/\/\tMore Advanced Functions\n\nGLfloat PlaneDistance(CVector Normal, CVector Point);\n\n\/\/ Is Plane intersected?\n\nbool IntersectedPlane(CVector vTriangle[], CVector vLine[]);\n};\n\n\/\/ Source\n\n\/ --------------------------------- VECTOR IMPLEMENTATION -------------------------------\/\/\n\/\/----------------------------------------------------------------------------------------\/\nCVector& CVector::operator = (CVector& V)\n{\tx = V.x;\ny = V.y;\nz = V.z;\nsub();\nreturn this;\n}\n\n\/\/\tBoolean stuff\nbool CVector::operator == (CVector& Vector)\n{\treturn (x == Vector.x && y == Vector.y && z == Vector.z);\n}\nbool CVector::operator != (CVector& Vector)\n{\treturn !(this == Vector);\n}\n\n\/\/\tAdd & Substract, Positive & Negative\nCVector CVector::operator + (CVector& Vector)\n{\treturn CVector(x + Vector.x, y + Vector.y, z + Vector.z);\n}\nCVector CVector::operator + ()\n{\treturn CVector(this);\n}\nCVector& CVector::operator += (CVector& Vector)\n{\tx += Vector.x;\ny += Vector.y;\nz += Vector.z;\nsub();\nreturn this;\n}\n\/\/ minus vector\nCVector CVector::operator - (CVector& Vector)\n{\treturn CVector(x - Vector.x, y - Vector.y, z - Vector.z);\n}\nCVector CVector::operator - ()\n{\treturn CVector(-x, -y, -z);\n}\nCVector &CVector::operator -= (CVector& Vector)\n{\tx -= Vector.x;\ny -= Vector.y;\nz -= Vector.z;\nsub();\nreturn this;\n}\n\n\/\/\tMultiply & Divide\nCVector CVector::operator * (CVector& Vector)\n{\treturn CVector(x * Vector.x, y * Vector.y, z * Vector.z);\n}\nCVector &CVector::operator = (CVector& Vector)\n{\tx = Vector.x;\ny = Vector.y;\nz = Vector.z;\nsub();\nreturn this;\n}\nCVector CVector::operator (GLfloat d)\n{\treturn CVector(x * d, y * d, z * d);\n}\nCVector &CVector::operator = (GLfloat d)\n{\tx = d;\ny = d;\nz = d;\nsub();\nreturn this;\n}\nCVector CVector::operator \/ (CVector& Vector)\n{\treturn CVector(x \/ Vector.x, y \/ Vector.y, z \/ Vector.z);\n}\n\nCVector &CVector::operator \/= (CVector& Vector)\n{\tx \/= Vector.x;\ny \/= Vector.y;\nz \/= Vector.z;\nsub();\nreturn this;\n}\nCVector CVector::operator \/ (GLfloat d)\n{\tGLfloat _d = 1.0f \/ d;\nreturn CVector(x * _d, y * _d, z * _d);\n}\nCVector &CVector::operator \/= (GLfloat d)\n{\tGLfloat _d = 1.0f \/ d;\nx = _d;\ny = _d;\nz = _d;\nsub();\nreturn this;\n}\n\n\/\/\tDot Product\nGLfloat CVector::operator % (CVector& Vector)\n{\treturn xVector.x + yVector.y + zVector.z;\n}\n\/\/\tCross Product\nCVector CVector::operator ^ (CVector& Vector)\n{\treturn CVector(\ny Vector.z - Vector.y * z,\nz * Vector.x - Vector.z * x,\nx * Vector.y - Vector.x * y);\n}\nCVector &CVector::operator ^= (CVector& Vector)\n{\treturn this = this ^ Vector;\n}\n\nbool CVector::operator > (CVector& v)\n{\nreturn (x>v.x \|\| y>v.y \|\| z>v.z);\n}\n\nbool CVector::operator < (CVector& v)\n{\nreturn (x<v.x \|\| y<v.y \|\| z<v.z);\n}\n\n\/\/\tSet length (Normalize if 1) or Magnitude of vector\nGLfloat CVector::operator ! ()\n{\treturn sqrtf(xx + yy + zz);\n}\nCVector CVector::operator \| (GLfloat dLength)\n{\treturn this * (dLength \/ !this);\n}\nCVector &CVector::operator \|= (GLfloat dLength)\n{\treturn this = this \| dLength;\n}\n\nvoid CVector::Normalize()\n{\nGLfloat magnitude=!this;\nthis\/=magnitude;\n}\n\nvoid CVector::SetNormal(CVector vTriangle0, CVector vTriangle1, CVector vTriangle2 )\n{\nthis = (vTriangle2-vTriangle0)^(vTriangle1-vTriangle0);\t\t\t\t\/\/ Cross Product\nthis->Normalize();\t\t\t\t\t\t\/\/ Use our function we created to normalize the normal (Makes it a length of one)\n}\n\n\/\/\tThe angle between two vectors in radians\nGLfloat CVector::Angle(CVector& Normal)\n{\treturn acosf(this % Normal);\n}\n\/\/\tReflect in Normal Vector\nCVector CVector::Reflection(CVector& PlaneNormal)\n{\treturn (this - PlaneNormal * 2.0 * (this % PlaneNormal)) !this;\n}\n\/\/\tRotate dAngle Degrees (radians) Around Normal\nCVector CVector::Rotate(GLfloat dAngle, CVector& Normal)\n{\tGLfloat dCos = cosf(dAngle);\nGLfloat dSin = sinf(dAngle);\nreturn CVector(\nthis * dCos +\n((Normal * this) (1.0f - dCos)) * Normal +\n(this ^ Normal) dSin);\n}\n\nGLfloat CVector::GetData()\n{\treturn data; }\n\nvoid CVector::sub()\n{\ndata[0] = x;\ndata[1] = y;\ndata[2] = z;\n}\n\/ -------------------------------END VECTOR IMPLEMENTATION ------------------------------\/\/\n\/\/----------------------------------------------------------------------------------------\/\n\n\n\" Do we need us? \"\n\n##### Share on other sites\nOK, a forum is not the best place to start a project such as this one, we need a proper server and CVS. It could be a theme site, but it has to be properly commented and stepped through. Im up for it, i reckon i have stuff to offer, so feel free to sort out the proper details before we get started.\n\n##### Share on other sites\nHey man,\nI was talking about giving your code to public so they can use it in their projects.\nI don''t know about CVS (repository), but SourceForge offers it (although I don''t know how to use it)\nWould you like to start that kind of thing with me?\nI got HEAPS of useful code that I don''t really use for game creation, so I thought maybe someone else can make the game using this code? )\n\nThanks.\n\n\" Do we need us? \"\n\n##### Share on other sites\n\nOn my computer, 10000000 calls to sqrt() takes 1.98 seconds, where 10000000 calls to sqrtf() takes 3.08 seconds, a fairly large difference. conclusion: sqrt() is better.\n\nAlso, in your functions where you calculate the reciprocal, you''re not using the initial value again so you can avoid creating a new variable _d by just doing d = 1 \/ d; then multiplying by d.\n\nAnd you''d get another speed boost by getting rid of that sub() thing, I don''t see why you need the vars in array form =)\n\n##### Share on other sites\nThanks Hairybudda, I''ll consider changing that. As for sub(), its just that I didn''t knew about unions. E.g\n\n union{struct{float x;float y;float z;};float data[3];}Thanks.\n\n\" Do we need us? \"\n\n##### Share on other sites\nI'd like to make a couple of comments about the CVector class you've written (I'm not 'having a go', just passing on years of experience).\n\nFirstly, it's generally regarded as good practice not to redefine the meaning of operators. By this I mean not changing the 'XOR' operator into something else. The reason for this is that anyone not familiar with your implementation would expect 'a ^= b' to actually be 'a = a xor b' rather than a cross product. Worse still, you can't change the precedence of the operator - does a cross product have higher or lower precedence than the '+', or other, operator (mathematically speaking, it should be higher). So, for example, you might be tempted to do the following:\n\nCVector a,b,c;\n\/\/ assign values to a,b,c\nif (a > b ^ c)\n{\n\/\/ do stuff\n}\n\nThis will generate a compiler error, complaining that there is no definition of the '^' operator that takes the given arguments (in this case: bool, CVector).\n\nAll because you can do something in C++, doesn't mean it's a good idea.\n\nSecondly, member variables should be private. There's no reason here to expose them.\n\nThirdly, I'm assuming the 'source' bit would be in a '.cpp', otherwise you'd get multiple definitions of functions (in MSVC V6 at least). This will lead to inefficient code since none of it would be inlined, even with every inline option switched on it would never be inlined apart from the '.cpp' file containing the CVector source. This is because the translation unit processing a source file that includes the CVector class does not have the code in the implementation to hand to do the inlining (because it would be in another translation unit). And the linker wouldn't inline it since that would screw up all the relative jumps in the code. For a class this simple, put the code in the class declaration.\n\nFourth, I would personally have called the class CVector3D, so you can then have CVector2D and CVector4D. It would also eliminate any potential user confusion that the class may be implementing a custom 'std::vector' type. Also, using a single 'C' prefix could clash with the MFC classes (game objects defined as CObject?). Use a namespace or use a different prefix to avoid any potential problems (a problem prevented won't become a problem).\n\nLastly, I wrote a 3D vector class but declared it as a template so I could have vectors of floats, doubles, ints, bytes, etc.(bytes is useful to save disk space - quantize model data to 256 samples in x, y and z - saves 9 bytes per vertex!).\n\nSkizz\n\n[edited by - Skizz on February 3, 2003 6:17:52 AM]\n\n##### Share on other sites\nlol - so ... that''s fuced then.\n\n##### Share on other sites\nHello,\n\nIt''s not a nice thing to involve openGL specific types in a semi-generic vector class. I suggest you change them to floats instead.\n\nRegards,\nDeficte\n\n##### Share on other sites\nAnother criticism of your vector class is that the == and != operators won''t be very reliable since they''re comparing floating point values. Because of the way floating point values work (if you don''t know how they work I suggest you read up on them - check Google) comparing them directly is pretty foolish. A better approach for comparing two vectors would be to check the angle between them.\n\nAlso what''s the point of your operator + that takes no argument? It just seems to make a copy of a vector.\n\n##### Share on other sites\nrm3: sqrtf is EXACTLY the same as a sqrt, except it casts to a float for you. If you set a float = sqrt that many times, and a float = sqrtf that many times.. they should be the same speed, just one gives a warning, and the other doesn''t. If you are using doubles... stick with the sqrt obviously .\n\n##### Share on other sites\nlol remind me to never post code here you guys are brutal\n\n##### Share on other sites\nYou should welcome constructive criticism from others, it''s a significant aid to improving code (and many other things). In fact it''s probably the most significant aid since (in my experience) many people get stuck in coding ruts and, without someone else''s help, rarely uncover their own flaws.\n\n##### Share on other sites\nFurther to what Dobbs posted, in general, try to avoid the ''=='' and ''!='' operators when used in conjunction with floating point values. I always use this code to demonstrate why those operators are dangerous with floating point values:\n\n int main (int argc, char argv){\tfor (float value = 0.0f ; value < 2.0f ; value += 0.05f)\t{\t\tprintf (\"Does %.02f == 1? %s\\n\", value, value == 1.0f ? \"Yes\" : \"No\");\t}\treturn 0;}\n\nTry the above and see what happens. Then work out why.\n\nSkizz\n\n##### Share on other sites\nwhen we are talking about square roots you could use a large lookup table to get the values you want\n\nof course precision suffers a bit but who cares about precision\n\ntake a 2 mb chunk of your memory for the lookup table and you should be able to get squareroots from 0-2000 with a precision of 0.001\n\n##### Share on other sites\n2mb? You''d have to be nuts about your lookup table to use so much memory for it .\n\nThe way I see it\n\n(0-2000)\n100 2001 * 4 (float) \/ 1024 = ~781.25kb\n\nWhich still seems like quite a bit for a lookup table, it would probably be better to reduce precision by 10 to get it to 78.13kb\n\nAlthough that is still quite a bit, there are a number of ways to optimize the memory while inflicting a smaller calculation cost. (i.e. do you really need a float to store a number thats 0-2000?)\n\nSince we are all in a mood for constructive critism .\n\n-------\nHomepage: http:\/\/students.washington.edu\/andrey\n\n##### Share on other sites\nquote:\nOriginal post by Basiror\nwhen we are talking about square roots you could use a large lookup table to get the values you want\n\nof course precision suffers a bit but who cares about precision\n\ntake a 2 mb chunk of your memory for the lookup table and you should be able to get squareroots from 0-2000 with a precision of 0.001\n\n2MB lookup table? are you sane? Ever heard about caches ?\nWith intrinsic functions enabled sqrt() or sqrtf() will generate something like:\n\nfld var\nfsqrt\nfstp var\n\nwhich takes about 80 clock cycles on a Pentium 3\n\n##### Share on other sites\nThanks to everyone posting replies on this topic (and torring my code apart), I really appreciate that.\nAlthough that code was originally been written by Bas Kuenen (with some of my updates), I will try to consider all your thoughts and ideas.\nThanks again.\n\n\" Do we need us? \"\n\n\u2022 9\n\u2022 10\n\u2022 18\n\u2022 14\n\u2022 10","date":"2018-02-21 06:03:36","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2776543200016022, \"perplexity\": 11135.833004904352}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-09\/segments\/1518891813431.5\/warc\/CC-MAIN-20180221044156-20180221064156-00467.warc.gz\"}"}	null	null
Manuscript on parchment written in late Carolingian miniscule. Ms. note on f. 164r reads: Liber iste sancte marie de morimundo mediolani dyocesis. Purchased from H.P. Kraus, 1983. Flyleaves are from a 12th-century Italian homilary[?]. Binding: Fifteenth-century blind stamped leather over wooden boards, repaired and recovered. See Barcelona Catedral MS 64, which contains items c), d), e) and f). ff. i + i + 165 + i + i : parchment ; 314 x 209 (225 x 141) mm.	{ "redpajama_set_name": "RedPajamaC4" }	1,190
\section{Introduction} The origins of the celebrated quantum adiabatic theorem (QAT) date back to Einstein's ``Adiabatenhypothese'': ``If a system be affected in a reversible adiabatic way, allowed motions are transformed into allowed motions'' \cite{Einstein:adiabatic}. Ehrenfest was the first to appreciate the importance of adiabatic invariance, guessing---before the advent of a complete quantum theory--- that quantum laws would only allow motions which are invariant under adiabatic perturbations \cite{Ehrenfest:adiabatic}. The more familiar, modern version of the QAT was put forth by Born and Fock already in 1928 for the case of discrete spectra~\cite{born_beweis_1928}. Since then a series of increasingly sophisticated techniques have been developed in order to generalize the QAT to include degeneracy, unbounded models, continuous spectra, and exponential error estimates~\cite{kato_adiabatic_1950,Garrido:62,avron:87,nenciu_linear_1993,avron_adiabatic_1999,Hagedorn:2002kx,Jansen:07,lidar:102106}. This long history of adiabatic theorems is almost exclusively concerned with closed systems undergoing unitary evolution. Previous approaches to formulating an adiabatic condition for open quantum systems \cite{Breuer:book} have focused on a Jordan block decomposition of the dissipative generator \cite{PhysRevA.71.012331}, the weak coupling limit \cite{PhysRevA.72.022328,ABLZ:12-SI}, zero temperature \cite{Pekola:2010oj}, or on a noiseless subsystem decomposition \cite{oreshkov_adiabatic_2010,comment-SL-OC}. Here we prove that in analogy to the closed system case, where the system follows the instantaneous (pure) eigenstates of the Hamiltonian in the adiabatic limit of arbitrarily large total evolution time $T$, the open system follows the instantaneous steady state (ISS) of the Liouvillian. In doing so, we extend the seminal closed system result by Kato \cite{kato_adiabatic_1950} to infinite order in $1/T$. Rigorous extensions of the adiabatic theorem for generators of contractive semigroups, similar to ours, have also appeared in the mathematical literature \cite{springerlink:10.1007/BF01011696,joye_general_2007,salem_quasi-static_2007,Avron:2012tv}. Our focus is on estimating the adiabatic error in terms of the physical parameters of the theory, thus making the result more suitable for applications. We demonstrate that in the case of thermal baths satisfying the Kubo-Martin-Schwinger (KMS) condition \cite{KMS}, where the ISS is the instantaneous Gibbs state, a sufficient criterion for adiabaticity is $T\gg\Delta_{\min}^{-2}$, where $\Delta_{\min}$ is the smallest \emph{Liouvillian} gap in absolute value. Our QAT also allows for a finite number of level crossings in the Liouvillian spectrum, for which we demonstrate that the error scales asymptotically as $T^{-\eta}$ with a known exponent $\eta\in(0,1)$ related to the rate at which the gap closes. This setting is directly relevant to recent theoretical and experimental work on quantum annealing \cite{ABLZ:12-SI,q-sig,DWave-16q,Boixo:2014yu}, where the Liouvillian gap may close at the end of the evolution, and we verify this prediction using numerical simulations. \section{Instantaneous steady states} We assume that the evolution of a $d$-dimensional ($d<\infty$) quantum system with state $\rho(t)$ can be described by a linear, time-local master equation $d\rho/dt=\mathcal{L}_{T}(t)\rho$, where $T$ is the total evolution time. We also assume that $\mathcal{L}_{T}(sT)=\mathcal{L}(s)$ where $s=t/T\in[0,1]$ is a rescaled, dimensionless time coordinate, and $\mathcal{L}(s)$ is $T$-independent. Setting $\rho_{T}(s)=\mathcal{E}_{T}(s,0)\rho_{T}(0)$, the evolution operator $\mathcal{E}_{T}(s,s_{0})$ satisfies \begin{equation} \mathcal{E}_{T}'(s,s_{0})=T\mathcal{L}(s)\mathcal{E}_{T}(s,s_{0})\ ,\label{eq:ME} \end{equation} with $\mathcal{E}(s,s)=\openone$ {(}we drop the subscript $T$ from now on; we also write $\mathcal{E}(s)$ for $\mathcal{E}(s,0)$ for simplicity{)}, and where the prime denotes $\partial_s$. We are interested in the solutions of Eq.~(\ref{eq:ME}) for large $T$. We further assume that the Liouvillian $\mathcal{L}(s)$ can be written in Lindblad form for all $s$, i.e., $\mathcal{L}(s)\bullet=-i[H(s),\bullet]+\sum_{l} \left [ L_{l}(s)\bullet L_{l}^{\dagger}(s)-\frac{1}{2}\{L_{l}^{\dagger}(s)L_{l}(s),\bullet\} \right ]$, where $H(s)$ is the system Hamiltonian and $\{L_{l}(s)\}$ are the Lindblad operators. Equation~\eqref{eq:ME} then describes a Markovian master equation with a time-dependent Lindblad generator, and the corresponding evolution operator $\mathcal{E}(s_{2},s_{1})$ is a completely positive trace preserving (CPTP) map for any $s_{2}\ge s_{1}$ \cite{Wonderen:2000yi,Breuer:2004wq,ABLZ:12-SI}. We formulate our results in terms of Lindblad operators and CPTP maps, but in fact all our results are valid in the more general case where $\mathcal{L}(s)$ generates a contractive semigroup (i.e., $\parallel e^{t\mathcal{L}(s)} \parallel \le 1$ $\forall s$ and $t>0$). A special role is played by the ISSs, i.e., the states in the kernel of $\mathcal{L}(s)$. In the time-independent case [$\mathcal{L}(s)=\mathcal{L}$, $\forall s$], it follows from the CPTP property that any initial state evolves to $\mathrm{Ker}\mathcal{L}$ in the long time limit \cite{Alicki:87}. Let us denote by $P(s)$ the (instantaneous) spectral projection of $\mathcal{L}(s)$ with eigenvalue zero. The Lindblad form guarantees that zero is a semi-simple, possibly degenerate, eigenvalue of $\mathcal{L}(s)$ (see Appendix \ref{app:0} for a proof), and so there are no nilpotent terms in the zero sector, i.e., $\mathcal{L}(s)P(s)=P(s)\mathcal{L}(s)=0$. We are now ready to informally state the QAT for open systems: \emph{If a system is initialized at $s=0$ in $\mathrm{Ker}\mathcal{L}(0)$, the final state at $s=1$ will be close to $\mathrm{Ker}\mathcal{L}(1)$, provided the Lindbladian changes sufficiently slowly}. In principle one could formulate an open-system QAT considering other (non-zero) eigenvalues of $\mathcal{L}(s)$. However their corresponding invariant subspaces contain no physical states, so that the physical interest in such a generalization is questionable % \footnote{To see this, let $P_{0}$ be the projector onto the zero eigenvalue. Since it can be realized as the infinite time limit of a CPTP map, $P_{0}$ is itself a CPTP map, and in particular it is trace preserving. Let $P_{j}$ be the projector onto another invariant subspace, with $j\neq0$. Assume there is a state in its range, i.e., $\exists\, x\,\|$ $\rho=P_{j}x$ is a state. But $P_{0}P_{j}=0$ so $\mathrm{Tr}\left(\rho\right)=\mathrm{Tr}\left(P_{0}\rho\right)=0$ (where the first equality holds since $P_{0}$ is a CPTP map), a contradiction.% }. We proceed to rigorously establish the QAT and identify the timescales it entails. \section{Gapped case} We start by assuming that the zero eigenvalue is separated by a finite gap $\Delta_{\mathrm{min}}$ from the rest of the spectrum $\sigma(\mathcal{L}(s))$ for all $s\in[0,1]$, i.e.,~$\mathrm{dist}\left[\sigma(\mathcal{L}(s))\backslash\{0\},0\right] = \Delta (s) \ge \Delta_{\min} >0$, a condition we relax later. The ideal adiabatic evolution is represented by an operator $V(s)$ that satisfies the intertwining property: $V(s)P(0)=P(s)V(s)$. It is well known \cite{kato_adiabatic_1950} (see Appendix.~\ref{app:intertwiner}) that a possible choice for $V(s)$ is given by the solution of the differential equation $V'(s)=[P'(s),P(s)]V(s)$ with $V(0)=\openone$. We are interested in quantifying the deviation of the actual evolution, governed by the CPTP map $\mathcal{E}(s)$, from the ideal adiabatic evolution. However, $V(s)$ is not CPTP in general. Instead, we can prove that $W(s):=V(s)P(0)$ is a CPTP map, since it can be written as a product of projectors (CPTP maps): $W(s)=\lim_{N\to\infty}P(s)\cdots P(2s/N)P(s/N)P(0)$ (see Appendix \ref{app:positivity}) or Proposition 3 in \cite{Avron:2012tv}). Therefore, to state the QAT we wish to bound the deviation from the ideal adiabatic evolution projected to $\mathrm{Ker}\mathcal{L}$, $\\|\mathcal{E}(s)P(0)-V(s)P(0)\\|$, in the large $T$ limit \footnote{Unless explicitly noted otherwise, from hereon the norm is the induced trace norm, i.e., $\protect\\| A\protect\\|=\sup_{x\neq0}\protect\\|A(x)\protect\\|_{1}/\protect\\|x\protect\\|_{1}$, where $\protect\\| x\protect\\|_{1}$ denotes the trace norm, i.e., the sum of the singular values \cite{Bhatia:book}. For a discussion of the properties of the induced trace norm see, e.g., Ref.~\cite{PhysRevA.78.012308}, where it is denoted $\protect\\| \ \protect\\|_{\infty,1}$, or Ref.~\cite{Kretschmann:08}}. To proceed we introduce the reduced resolvent $S(s)=\lim_{z\to0}Q(s)(\mathcal{L}(s)-z)^{-1}Q(s)$, where $Q(s)=\openone-P(s)$ \cite{QAT-comment-smoothL}. We further assume that $\mathcal{L}$ is $m$ times differentiable, and let $X_{n+1}(s) =S(s) X_{n}'(s)$, with $X_{1}(s)=S(s)$. Under the additional simplifying assumption that the ISS is unique we then prove the following in Appendix \ref{sec:arb_order} using integration by parts: \begin{align} \label{eq:adia_final} &[\mathcal{E}(s)-V(s)]P(0) =\sum_{n=1}^{m}\frac{\Omega_{n}}{T^{n}} \\ & \qquad \qquad \qquad\qquad -\frac{1}{T^{m}}\int_{0}^{s}\!d\sigma\,\mathcal{E}(s,\sigma)X_{m}'(\sigma)W'(\sigma) \ ,\notag \\ &\Omega_{n} \!=\!\left.\mathcal{E}(s,\sigma)X_{n}(\sigma)W'(\sigma)\right\|_{0}^{s} -\int_{0}^{s}\!d\sigma \mathcal{E}(s,\sigma)X_{n}(\sigma)W''(\sigma) \ . \notag \end{align} The general result, valid also for degenerate kernels, is given in Appendix \ref{sec:degenerate_kernel}. It turns out that Eq.~\eqref{eq:adia_final} is valid in the $m=1$ case even without requiring that the ISS be unique, and as we show in Appendix \ref{sec:arb_order} we can bound the deviation from the ideal adiabatic evolution in general as \begin{equation} \\| \left[\mathcal{E}(s)-V(s)\right]P(0)\\| \le C/T\ . \label{eq:adia_bound} \end{equation} A similar result has been derived in \cite{Avron:2012tv} where, however, the constant $C$ is left undetermined. We show that the constant $C$, independent of $T$, can be taken to be \begin{multline} C=\\| S(s)\\| \\| P'(s)\\| +\\| S(0)\\| \\| P'(0)\\| \\ +\sup_{\sigma\in[0,s]}\\| [S'P'+SP''](\sigma)\\| \ . \label{eq:const_bound} \end{multline} Below we discuss how $C$ relates to the physical parameters of the model associated with $\mathcal{L}$. \emph{Inequality} \eqref{eq:adia_bound} \emph{states the QAT for open systems and implies the QAT in the standard form for states}. To see the latter let us initialize the system in a state $\tilde{\rho}(0)$ in $\mathrm{Ker}\mathcal{L}(0)$, i.e., $\tilde{\rho}(0)=P(0)\tilde{\rho}(0)$. Then $\tilde{\rho}(s):=V(s)\tilde{\rho}(0)$ is an instantaneous steady state at time $s$, since $\mathcal{L}(s)\tilde{\rho}(s)=\mathcal{L}(s)V(s)P(0)\tilde{\rho}(0)=\mathcal{L}(s)P(s)V(s)\tilde{\rho}(0)=0$, i.e., $\tilde{\rho}(s)\in\mathrm{Ker}\mathcal{L}(s)$. Under the actual evolution the state is mapped to $\rho(s)=\mathcal{E}(s)\tilde{\rho}(0)$ and one has $\\| \rho(s)-\tilde{\rho}(s)\\|_1 \le\\| \left[\mathcal{E}(s)-V(s)\right]P(0)\\| \\| \tilde{\rho}(0)\\|_1 \le C/T$. Namely, if $T\ge C/\epsilon$ ($\epsilon>0$) then the system is guaranteed to find itself $\epsilon$-close in norm to the instantaneous steady state, at the end of the evolution.% \section{The Closed System Limit} It is useful to comment on how our result relates to adiabatic theorems for closed systems, described by a system Hamiltonian $H(s)$ with eigenvalues $E_n$. First, if one is interested in initial states belonging to the $-i E_0$ level, one may simply set ${\cal L}(s) = -i [H(s)-E_0]$, as our formalism encompasses (with minor modifications) the case where ${\cal L}$ is anti-Hermitian. In this way one recovers the standard adiabatic theorem for closed system. The relevant gap is given by the eigenvalue closest to $E_0$ in modulus, i.e., $\|E_1 -E_0\|$. The bound we obtained for the constant $C$ in this case is similar to that given in Ref.~\cite{Jansen:07}, at least for what concerns the dependence on the gap. Another possibility is to write ${\cal L}(s)= {\cal K}(s)= -i[H(s),\bullet]$. The eigenvalues of ${\cal K}$ are $\{-i (E_n -E_m)\}$. There is a $\ge d$-fold degenerate zero eigenvalue arising from $E_n=E_m$ constituting ${\rm Ker} {\cal K}$. The relevant energy scale is determined by the next eigenvalue which is closest to zero in modulus. This is given by the smallest difference $\| E_{n} -E_{m} \|$ with $E_n\neq E_m$ (non-zero since we assume $d<\infty$ and hence discrete spectra). This is consistent with the previous result because in ${\rm Ker} {\cal K}$ one has the freedom to pick any state $\| n\rangle \langle n \|$ leading to a gap $\min_{m} \|E_{n} -E_{m}\| $. In this manner one obtains an adiabatic theorem for closed systems in the Liouvillian (superoperator) formalism. We discuss the closed system limit further in Appendix~\ref{app:closed}. \section{Thermal bath} It turns out that the open system version of the QAT can have additional structure that is absent in the closed system case. To demonstrate this we consider the important class of Lindbladians generated by the interaction of a system with a thermal bath, for which we can make the bounds above more specific. As a result of the KMS condition such Lindbladians satisfy the quantum detailed balance condition \cite{alicki_detailed_1976,Kossakowski:1977dk}. This fact has important consequences, namely, (i) the Gibbs state is an ISS, i.e., $\mathcal{L}(s)\rho_{G}(s)=0$ with $\rho_{G}(s)\equiv\exp\left[-\beta H(s)\right]/Z$, where $Z=\mathrm{Tr}\exp\left[-\beta H(s)\right]$ is the partition function; (ii) the generator $\mathcal{L}(s)$ is normal. Let us now show how we can relate $C$ to standard quantities such as the gap and $H'(s)$ using the assumption of a thermal bath. Assume for simplicity that $\rho_{G}(s)$ is the unique state in $\mathrm{Ker}\mathcal{L}(s)$. For such thermal baths the projector onto the ISS manifold is $P(s) = \|\rho_G (s) \rangle \langle \openone \|$ Then $P^{(n)}(s)=\|\rho_G^{(n)} (s) \rangle \langle \openone \|$, so that $\\|P^{(n)}(s)\\|=\\|\rho_{G}^{(n)}(s)\\|_{1}$. Thus, if $H(s)$ is bounded with bounded derivatives, $\\|P^{(n)}(s)\\|$ is bounded for all $s$, and hence $P'$ and $P''$ in the constant $C$ [Eq.~\eqref{eq:const_bound}] do not introduce any singularities. In addition, since $\mathcal{L}$ is normal, $\\| S \\| =c/\Delta $ where the constant $c$ depends only on the norm used \cite{kato_perturbation_1995}. Moreover, the identity $S'=S^2 \mathcal{L}' P + P \mathcal{L}' S^2 - S \mathcal{L}' S$ (Appendix \ref{app:identity}) implies that $\\|S'\\| \le 3 \\|S\\|^2 \\|\mathcal{L}'\\|$. \emph{Thus, from} Eq.~\eqref{eq:const_bound}, \emph{for thermal baths the dependence on the Liouvillian gap is} $C=O(\Delta_{\min}^{-2})$. Note that in the absence of the KMS condition one only has $C=O(\Delta_{\min}^{-3})$, implying $T=O(\Delta_{\min}^{-3})$ as a criterion for adiabaticity in accordance with the closed system result of Ref.~\cite{Jansen:07}. However, in particular cases the dependence can be even milder. For example, if $\mathcal{L}(s)$ is a unitary family, i.e., $\mathcal{L}(s)= e^{s \mathcal{K}} \mathcal{L}(0) e^{-s \mathcal{K}} $, with $ \mathcal{K}$ an anti-hermitian superoperator, one has (Appendix \ref{sec:gap_unitary}) $P' = \mathcal{K} P -P \mathcal{K} $, so neither $P'$ (nor $P''$) depends on $\Delta_{\min}$. Moreover $S' = \mathcal{K}S -S\mathcal{K}$ so that in this case $C=O(\Delta_{\min}^{-1})$, as also shown and extensively exploited in \cite{zanardi_coherent_2014,zanardi_geometry_2015}. In addition, for thermal baths the constants appearing in Eq.~\eqref{eq:const_bound} bear an explicit dependence on $H(s)$. E.g., one can show that $\\|\rho_{G}{'}(s)\\|_{1}\le 2\beta\sqrt{\langle[H'(s)]^{2}\rangle_{G}}$, where $\langle\bullet\rangle_{G}=\mathrm{Tr}[\rho_{G}\bullet]$ is the thermal average (see Appendix \ref{sec:bound_dP}). This fact has important consequences for adiabatic quantum computation where the complexity of a computation is encoded into $H(s)$ and depends on the system size $L$. In general we expect $\\| P^{(n)}(s)\\| $ to display a stronger divergence with $L$, for some $n$, e.g., at (positive temperature) phase transition points of $H(s)$ % \footnote{In general one can directly relate $\protect \\|P^{(n)}(s)\protect\\|$ to expectation values of powers of the Hamiltonian and its derivatives.}. When the gap $\Delta_{\min}$ is very small and is attained inside the interval $[0,s]$, the constant $C$ is dominated by the third term in Eq.~(\ref{eq:const_bound}), i.e., $C \simeq \sup_{\sigma} \\| S' (\sigma) P'(\sigma) \\|$. Using the above estimates for $S'$ and $P'$ we obtain $C \lesssim 6 c^2 \beta \\| \mathcal{L}' (\sigma)\\|_{\mathrm{max}}\sqrt{\langle[H'(\sigma)]^{2}\rangle_{G,\mathrm{max}}} \Delta_{\min}^{-2}$, where the subscript ``max'' means that the corresponding quantities must be maximized over $\sigma \in [0,s]$. In other words, taking $ T \gtrsim c^2 \beta \\| \mathcal{L}' (\sigma)\\|_{\mathrm{max}}\sqrt{\langle[H'(\sigma)]^{2}\rangle_{G,\mathrm{max}}} \Delta_{\min}^{-2} /\epsilon$ guarantees adiabaticity up to an error $O(\epsilon)$ in trace norm. \section{Case of level crossings} The gapped case is typical since a random Lindbladian will have a gap above zero with probability one for all values of $s$. However, symmetries may give rise to degeneracies, and so we would like to extend our result and consider the case where a finite number of level crossings with the zero eigenvalue may take place along the path \footnote{A generalization where the spectrum becomes continuous at some point (e.g., at a second order quantum phase transition) is possible in the unitary case \cite{avron_adiabatic_1999}. Such an extension is not considered here.% }. Since singularities are only algebraic in the finite dimensional case, it is reasonable to expect that, in the case of level crossing, one has $ \\| \left[\mathcal{E}(s)-V(s)\right]P(0)\\| \sim 1/T^{\eta}$ for large $T$, with a positive exponent $\eta<1$. We are interested in estimating $\eta$ for large $T$. For definiteness assume that at the level crossings the gap vanishes as $\Delta_{\min}(s) \simeq v_i (s-s_i^\ast)^{\alpha_i}$ with some positive exponents $\alpha_i$. The analysis is detailed in Appendix \ref{sec:level_crossing}. The final result is \begin{equation} \\| \left[\mathcal{E}(s)-V(s)\right]P(0)\\| \le\sum_{i=1}^{N}\frac{D_{i}}{T^{\eta_{i}}}\ , \qquad \eta_i = \frac{1}{1+\alpha_i}\ , \label{eq:eta_bound} \end{equation} where $D_i$ are positive constants. Clearly the asymptotic behavior of the right hand side is dictated by the smallest exponent $\eta_{i}$, i.e., by the largest $\alpha_{i}$, and hence the most divergent of the $N$ gaps. \begin{figure}[t] \subfigure[]{ \includegraphics[width=0.48\columnwidth]{Figure01a}\label{fig:1a}} \subfigure[]{ \includegraphics[width=0.48\columnwidth]{Figure01b}\label{fig:1b}} \caption{QAT for the gapped case using the model of Example 1. (a) Absolute values of the eigenvalues of the Lindbladian (zero is not shown). The eigenvalues show square-root singularities at $s\simeq0.88$ and $s\simeq0.94$. (b) Trace norm distance between the actual state and the ISS for increasing $T$. The blue line is given by $\left\Vert \rho(1)-\tilde{\rho}(1)\right\Vert \sim7.88/T$. Parameters: $m_{x}(s)=1-s$, $m_y(s) = 0$, $m_{z}(s)=s/150$, $\gamma=1/2$ arb. units Initial condition is $\tilde{\rho}(0)$ as given in Eq.~\eqref{eq:rhoISS1}.} \label{fig:amplitude_damping} \end{figure} \section{Examples} We now illustrate our results with a few examples. \subsection{Example 1} Let us first consider a time-dependent generalization of the amplitude damping master equation. The Lindbladian is $\mathcal{L}(s)=\mathcal{K}(s)+\mathcal{L}_{0}$ with $\mathcal{K}(s)=-i[H(s),\bullet]$, $H(s)=\boldsymbol{m}(s)\cdot\boldsymbol{\sigma}$ and $\mathcal{L}_{0}=2\gamma\left[\sigma^{-}\bullet\sigma^{+}-(1/2)\left\{ \sigma^{+}\sigma^{-},\bullet\right\} \right]$ ($\sigma^\alpha$ Pauli matrices and $\sigma^{\pm}=\sigma^x\pm i\sigma^y$). The steady state manifold is one-dimensional. The ISS is given by the solution of $\mathcal{L}(s)\tilde{\rho}(s)=0$ and is (in the $\sigma^z$ basis) \begin{equation} \tilde{\rho}=\frac{1}{c}\left(\begin{array}{cc} \boldsymbol{m}^{2}-m_{z}^{2} & -m_{-}(2m_{z}+i\gamma)\\ -m_{+}(2m_{z}-i\gamma) & \boldsymbol{m}^{2}+3m_{z}^{2}+\gamma^{2} \end{array}\right)\ , \label{eq:rhoISS1} \end{equation} where $c=2(\boldsymbol{m}^{2}+m_{z}^{2})+\gamma^{2}$ and $m_{\pm}=m_{x}\pm i m_y$. A plot of the absolute values of the Lindbladian's eigenvalues is shown in Fig.~\ref{fig:1a}. Parameters are chosen to illustrate a phenomenon which is not possible in the unitary case. Namely, the eigenvalues can have algebraic singularities of the form $(s-s^{\ast})^{r}$ with $r$ a non-integer rational number. Also shown, in Fig.~\ref{fig:1b}, is the expected scaling of $\\| \rho(1)-\tilde{\rho}(1)\\|_1$ as $C/T$. \subsection{Example 2} Consider a qubit with system Hamiltonian $H(s) = \boldsymbol{m}(s)\cdot\boldsymbol{\sigma}$ interacting with a heat bath at inverse temperature $\beta$, so that the total Hamiltonian is $H_{\mathrm{tot}}(t)=H(t)+H_{\mathrm{int}}+H_{\mathrm{B}}$, with $H_{\mathrm{int}}=A\otimes B$, where $A$ ($B$) is a system (bath) operator, and $H_{\mathrm{B}}$ is the bath Hamiltonian. {For $H(s)$ of the form of Landau-Zener driving, exact expressions for the transition probabilities for a particular zero-temperature bosonic bath have been obtained in Ref.~\cite{PhysRevLett.97.200404}. To treat the more general case we use the time-dependent Lindblad master equation approximation for a slowly varying system Hamiltonian \cite{ABLZ:12-SI}:} $\mathcal{L}_{\mathrm{tot}}(t)=\mathcal{K}(t)+\mathcal{L}(t)$, where $\mathcal{K}(t)=-i\left[H(t)+H_{\textrm{LS}}(t),\bullet\right]$. The dissipative part, specialized to the single qubit case, reads \begin{equation} \mathcal{L}(t)=\sum_{\omega}\gamma(\omega)\Big[A_{\omega}(t)\bullet A_{\omega}(t)^{\dagger}-\frac{1}{2}\left\{ A_{\omega}(t)^{\dagger}A_{\omega}(t),\bullet\right\} \Big], \end{equation} with rates $\gamma(\omega)=\int_{-\infty}^{\infty} d \tau e^{i\tau\omega}\langle e^{i\tau H_{\mathrm{B}}} Be^{-i\tau H_{\mathrm{B}}}B\rangle$. The Lindblad operators are given by the Fourier resolution $e^{i\tau H(t)}A e^{-i\tau H(t)} = \sum_{\omega}e^{i\omega\tau}A_{\omega}(t)$, where $\omega$ are the Bohr frequencies of $H(t)$. $H_{\textrm{LS}}(t)= \sum_{\omega}S(\omega)A_{\omega}(t)^{\dagger}A_{\omega}(t)$ is the Lamb shift Hamiltonian, with $S(\omega) = \int_{-\infty}^{\infty}d\omega'\gamma(\omega')\mathcal{P}\left(\frac{1}{\omega-\omega'}\right)$, where $\mathcal{P}$ denotes the principal value. Moreover, $\gamma_{\alpha}(-\omega)=e^{-\beta\omega}\gamma_{\alpha}(\omega)$ as a consequence of the KMS condition. This implies that the generator $\mathcal{L}(t)$ together with $\mathcal{K}(t)$ and $\mathcal{K}_{\mathrm{LS}}(t)=-i\left[H_{\mathrm{LS}}(t),\bullet\right]$ all commute at the same time. The corresponding Lindbladian has the following instantaneous eigenvalues (derived in Appendix \ref{app:ex2-deriv}): \begin{equation} \lambda = \left\{0, -\gamma(\delta)\left\|A_{01}\right\|^{2}(1+e^{-\beta\delta}), -\Gamma\pm i\mu\right\} \ , \label{eq:eigenvalues} \end{equation} with $2\Gamma=\gamma(0)(\left\|A_{00}\right\|^{2}+\left\|A_{11}\right\|^{2})+\gamma(\delta)\left\|A_{01}\right\|^{2}(1+e^{-\beta\delta})$ and $\mu=\delta-S(0)(\left\|A_{00}\right\|^{2}-\left\|A_{11}\right\|^{2})+\left\|A_{01}\right\|^{2}[S(\delta)-S(-\delta)]$, where $\delta=2\\| \boldsymbol{m}\\| $ is the instantaneous Hamiltonian gap, $A_{ab}=\bra{\epsilon_a}A\ket{\epsilon_b}$, and $\|\epsilon_a\rangle$, $a=\{0,1\}$ denotes the instantaneous eigenvectors of $H(s)$. We now illustrate the QAT for $H(s)=\omega_{x}(1-s)\sigma^{x}+\omega_{z}s\sigma^{z}$ and system operator $A=g\sigma^{y,z}$, where $g$ is a coupling constant. For $A=g\sigma^{y}$, there is always a gap in the Liouvillian spectrum above the zero eigenvalue. Correspondingly the decay is $T^{-1}$ as shown in Fig.~\ref{fig:3a}. For $A=g\sigma^{z}$ the system Hamiltonian commutes with $A$ when $s=s^\ast=1$, at which point the spectrum becomes degenerate. Indeed one can check that $\left\|A_{01}\right\|^{2}=\omega_{x}^{2}(1-s)^{2}/\\| \boldsymbol{m}(s)\\| ^{2}$ and, correspondingly, from Eq.~\eqref{eq:eigenvalues}, the second eigenvalue goes to zero quadratically in $s-s^\ast$: $\lambda_{2}(s)\simeq-\gamma(\delta_{})(\omega_{x}/\omega_{z})^{2}(1-s)^{2}(1+e^{-\beta\delta_{}})$. This corresponds to $\alpha=2$ and hence [recall Eq.~\eqref{eq:eta_bound}] an exponent $\eta=1/3$. Our numerical simulations are in agreement with this prediction, as seen in Fig.~\ref{fig:3b}. Note that the Hamiltonian gap $\delta$ enters only indirectly via $\lambda$. \begin{figure} \subfigure[]{ \includegraphics[width=0.48\columnwidth]{Figure02a}\label{fig:3a}} \subfigure[]{ \includegraphics[width=0.48\columnwidth]{Figure02b}\label{fig:3b}} \caption{Illustration of the QAT for a single qubit coupled to a thermal bath (Example 2). (a) Gapped case with $A=g\sigma^{y}$. The fit (blue line) gives $\\| \rho(1)-\tilde{\rho}(1)\\|_1 = 148.5/T^{0.9990}$. (b) Gapless case with $A=g\sigma^{z}$. Now the fit gives $\\| \rho(1)-\tilde{\rho}(1)\\|_1 = 1.910/T^{0.324}$. Fits are for $T\geq 10^{5.4}$. Parameters: $g = 10^{-2}$, $\omega_x = \omega_z = -1/2$ arb. units, $\beta = 1$ arb. units, $\gamma(\omega) = \frac{2 \pi \omega e^{-\|\omega\|/8\pi}}{1 - e^{- \beta \omega}}$.} \label{fig:tameem1} \end{figure} \section{Conclusions} Using a novel adiabatic expansion we have extended the adiabatic theorem of quantum mechanics to open systems described by a time-dependent master equation with generator $\mathcal{L}(t)$ in Lindblad form. The theorem, first proven using different methods in \cite{joye_general_2007,salem_quasi-static_2007,Avron:2012tv}, states that if one initializes the system in $\mathrm{Ker}\mathcal{L}(0)$ and a gap condition is satisfied, the evolution brings the system close to $\mathrm{Ker}\mathcal{L}(T)$ up to an error $C/T$, where $C$ is a constant and $T$ the total time. Our approach allowed us to extend the results of \cite{joye_general_2007,salem_quasi-static_2007,Avron:2012tv} in two directions particularly relevant for quantum state preparation and quantum annealing in open systems. On the one hand, we related the constant $C$ to the smallest (in absolute value) gap $\Delta_{\min}$ of the Liouvillian. For general Liouvillians we obtained $C=O(\Delta^{-3}_{\min})$, whereas for thermal baths satisfying the KMS condition we found an improved scaling $C=O(\Delta^{-2}_{\min})$. More precisely, we showed that taking $ T \gtrsim \beta \\| \mathcal{L}' (\sigma)\\|_{\mathrm{max}}\sqrt{\langle[H'(\sigma)]^{2}\rangle_{G,{\mathrm{max}}}} \Delta_{\min}^{-2} /\epsilon$, guarantees adiabaticity up to an error $O(\epsilon)$ in trace norm. On the other hand, we extended previous results to the case of level crossing, for which the error becomes $O(T^{-\eta})$ with an exponent $\eta$ that depends on the rate of the gap closing. Thus level crossings with the instantaneous steady state can slow convergence down. We provided several examples to illustrate our findings, which confirm the predicted scaling with $T$. An interesting open question is whether the growing body of techniques developed for bath engineering \cite{diehl_quantum_2008,verstraete_quantum_2009,zanardi_dissipative_2015} can be used to enact boundary cancellation methods and reduce the error to $O\left(T^{-n}\right)$ with controllable $n>1$, as in the closed system case \cite{lidar:102106,RPL:10,Wiebe:12,Ge:2015wo}. Our results have implications for adiabatic quantum computation and quantum annealing in the presence of dissipation, where the closed-system adiabatic theorem cannot be directly applied. \acknowledgments This work was supported under under ARO MURI Grant No. W911NF-11-1-0268 and ARO grant number W911NF-12-1-0523.	{ "redpajama_set_name": "RedPajamaArXiv" }	286
{"url":"https:\/\/www.physicsforums.com\/threads\/momentum-in-a-box-of-light.874152\/","text":"# Momentum in a Box of Light\n\n## Homework Equations\n\n<S>=c$\\epsilon$E2\/2\n\n$\\Delta P = A \\Delta t <S>\/c$\n\n## The Attempt at a Solution\n\nMy question is if we need the \"box height\"? This is my work which I'm assuming is wrong. :C\n\nIf there's another problem like this on here please put a link. I didn't see any, but my search terms may not have been ideal \"Pressure of light in a box\".","date":"2020-04-03 11:41:20","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\": 0.6671512126922607, \"perplexity\": 923.9260390674324}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585370510846.12\/warc\/CC-MAIN-20200403092656-20200403122656-00169.warc.gz\"}"}	null	null
.ui-tabs-header li .ui-icon-close { float: left; margin: 0.4em 0.2em 0 0; cursor: pointer; } .ui-panel-content {height:90%; padding:0.1em; position:relative; width:100%; display:inline-block;} .ui-panel-title {margin:0;padding:0.4em;text-align:center;} .ui-panel-footer {position:absolute;background-image:none;border-width:1px 0 0;bottom:0;display:block;margin:0.5em 0 0;text-align:left;width:99%;} .ui-panel-footer-content {padding:0.3em 1em 0.5em 0.4em;} .ui-panel-section {vertical-align:top;padding:0 0.5em 0.5em 0.4em} .ui-resizable-helper { border: 1px dotted gray; } .ui-selecting { background: #FECA40; } .ui-selected { background: #F39814; color: white; } .ui-layout-panel-section { display:inline-block; }	{ "redpajama_set_name": "RedPajamaGithub" }	4,704
Зиппел () — тауншип в округе Лейк-оф-те-Вудс, Миннесота, США. На 2000 год его население составило 140 человек. География По данным Бюро переписи населения США площадь тауншипа составляет 86,2 км², из которых 84,5 км² занимает суша, а 1,7 км² — вода (1,98 %). Демография По данным переписи населения 2000 года здесь находились 140 человек, 61 домохозяйство и 43 семьи. Плотность населения — 1,7 чел./км². На территории тауншипа расположено 142 построек со средней плотностью 1,7 построек на один квадратный километр. Расовый состав населения: 99,29 % белых и 0,71 % приходится на две или более других рас. Из 61 домохозяйства в 21,3 % воспитывались дети до 18 лет, в 65,6 % проживали супружеские пары и в 27,9 % домохозяйств проживали несемейные люди. 24,6 % домохозяйств состояли из одного человека, при том 8,2 % из — одиноких пожилых людей старше 65 лет. Средний размер домохозяйства — 2,30, а семьи — 2,75 человека. 18,6 % населения — младше 18 лет, 5,0 % — в возрасте от 18 до 24 лет, 26,4 % — от 25 до 44, 33,6 % — от 45 до 64, и 16,4 % — старше 65 лет. Средний возраст — 45 лет. На каждые 100 женщин приходилось 141,4 мужчин. На каждые 100 женщин старше 18 приходилось 128,0 мужчин. Средний годовой доход домохозяйства составлял 20 750 долларов, а средний годовой доход семьи — 32 500 долларов. Средний доход мужчин — 33 750 долларов, в то время как у женщин — 26 250. Доход на душу населения составил 22 272 доллара. За чертой бедности не находилась ни одна семья и 24,3 % всего населения тауншипа, из которых 33,3 % старше 65 лет. Примечания Тауншипы округа Лейк-оф-те-Вудс	{ "redpajama_set_name": "RedPajamaWikipedia" }	8,710
{"url":"https:\/\/codegolf.stackexchange.com\/questions\/123146\/vacancy-or-no-vacancy","text":"# Vacancy or no vacancy?\n\nWe've all seen the signs on motels telling us if there's a vacancy or not:\n\nTypically, these will permanently have the letters of VACANCY lit up, and have the letters of NO lit up if there isn't any room in the motel.\n\n# The challenge\n\nThe average motel in the U.S. has 200 rooms.\n\nYou will write a program\/function that takes an integer T (for taken rooms) as its only input.\nYour program will then display the words NO VACANCY. The letters of VACANCY will be printed in red.\nIf T \u2265 200, the letters of NO will also be printed in red.\n\nFor example, assuming a.out is your program and \"input\" = command line argument:\n\n(I typo'd and my system ignores case.)\n\n# The rules\n\n\u2022 Your program\/function must display (or, if lambda, return) the exact string NO VACANCY, including case.\n\u2022 Your program\/function may only set the text foreground color to red and not the background.\n\u2022 If you wish, you may use ANSI escape codes to print the red color - \\x1b[31m will work.\n\u2022 Your program\/function may not change the text color of your shell after it finishes.\n\u2022 Your program\/function must terminate normally.\n\u2022 Your program\/function must print only to standard output.\n\u2022 Your program\/function must use your shell\/terminal\/IDE's default background color. (If you choose to have graphical output you may choose whatever color you like, except red.)\n\u2022 If T \u2264 200, the letters of NO must be printed in your shell\/terminal\/IDE's default foreground color. (If you choose to have graphical output, once again you may choose whatever color you like)\n\u2022 If for some reason your shell\/terminal\/IDE's default foreground\/background color is red, you must print with a black background and a default white foreground.\n\u2022 If you choose to use graphical output, red may only be used when specified in the program (e.g. your background color or default text color may not be red).\n\n# The winner\n\nAs usual with , the shortest program wins! Brownie points for graphical output.\nI'll accept the shortest answer in a week. Happy golfing!\n\n# Leaderboard\n\nvar QUESTION_ID=123146,OVERRIDE_USER=61563;function answersUrl(e){return\"https:\/\/api.stackexchange.com\/2.2\/questions\/\"+QUESTION_ID+\"\/answers?page=\"+e+\"&pagesize=100&order=desc&sort=creation&site=codegolf&filter=\"+ANSWER_FILTER}function commentUrl(e,s){return\"https:\/\/api.stackexchange.com\/2.2\/answers\/\"+s.join(\";\")+\"\/comments?page=\"+e+\"&pagesize=100&order=desc&sort=creation&site=codegolf&filter=\"+COMMENT_FILTER}function getAnswers(){jQuery.ajax({url:answersUrl(answer_page++),method:\"get\",dataType:\"jsonp\",crossDomain:!0,success:function(e){answers.push.apply(answers,e.items),answers_hash=[],answer_ids=[],e.items.forEach(function(e){e.comments=[];var s=+e.share_link.match(\/\\d+\/);answer_ids.push(s),answers_hash[s]=e}),e.has_more\|\|(more_answers=!1),comment_page=1,getComments()}})}function getComments(){jQuery.ajax({url:commentUrl(comment_page++,answer_ids),method:\"get\",dataType:\"jsonp\",crossDomain:!0,success:function(e){e.items.forEach(function(e){e.owner.user_id===OVERRIDE_USER&&answers_hash[e.post_id].comments.push(e)}),e.has_more?getComments():more_answers?getAnswers():process()}})}function getAuthorName(e){return e.owner.display_name}function process(){var e=[];answers.forEach(function(s){var r=s.body;s.comments.forEach(function(e){OVERRIDE_REG.test(e.body)&&(r=\"<h1>\"+e.body.replace(OVERRIDE_REG,\"\")+\"<\/h1>\")});var a=r.match(SCORE_REG);a&&e.push({user:getAuthorName(s),size:+a[2],language:a[1],link:s.share_link})}),e.sort(function(e,s){var r=e.size,a=s.size;return r-a});var s={},r=1,a=null,n=1;e.forEach(function(e){e.size!=a&&(n=r),a=e.size,++r;var t=jQuery(\"#answer-template\").html();t=t.replace(\"{{PLACE}}\",n+\".\").replace(\"{{NAME}}\",e.user).replace(\"{{LANGUAGE}}\",e.language).replace(\"{{SIZE}}\",e.size).replace(\"{{LINK}}\",e.link),t=jQuery(t),jQuery(\"#answers\").append(t);var o=e.language;\/<a\/.test(o)&&(o=jQuery(o).text()),s[o]=s[o]\|\|{lang:e.language,user:e.user,size:e.size,link:e.link}});var t=[];for(var o in s)s.hasOwnProperty(o)&&t.push(s[o]);t.sort(function(e,s){return e.lang>s.lang?1:e.lang<s.lang?-1:0});for(var c=0;c<t.length;++c){var i=jQuery(\"#language-template\").html(),o=t[c];i=i.replace(\"{{LANGUAGE}}\",o.lang).replace(\"{{NAME}}\",o.user).replace(\"{{SIZE}}\",o.size).replace(\"{{LINK}}\",o.link),i=jQuery(i),jQuery(\"#languages\").append(i)}}var ANSWER_FILTER=\"!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe\",COMMENT_FILTER=\"!)Q2B_A2kjfAiU78X(md6BoYk\",answers=[],answers_hash,answer_ids,answer_page=1,more_answers=!0,comment_page;getAnswers();var SCORE_REG=\/<h\\d>\\s([^\\n,][^\\s,]),.?(\\d+)(?=[^\\n\\d<>](?:<(?:s>[^\\n<>]<\\\/s>\|[^\\n<>]+>)[^\\n\\d<>])<\\\/h\\d>)\/,OVERRIDE_REG=\/^Override\\sheader:\\s\/i;\nbody{text-align:left!important}#answer-list,#language-list{padding:10px;width:290px;float:left}table thead{font-weight:700}table td{padding:5px}\n<script src=\"https:\/\/ajax.googleapis.com\/ajax\/libs\/jquery\/2.1.1\/jquery.min.js\"><\/script> <link rel=\"stylesheet\" type=\"text\/css\" href=\"\/\/cdn.sstatic.net\/codegolf\/all.css?v=83c949450c8b\"> <div id=\"answer-list\"> <h2>Leaderboard<\/h2> <table class=\"answer-list\"> <thead> <tr><td><\/td><td>Author<\/td><td>Language<\/td><td>Size<\/td><\/tr><\/thead> <tbody id=\"answers\"> <\/tbody> <\/table> <\/div><div id=\"language-list\"> <h2>Winners by Language<\/h2> <table class=\"language-list\"> <thead> <tr><td>Language<\/td><td>User<\/td><td>Score<\/td><\/tr><\/thead> <tbody id=\"languages\"> <\/tbody> <\/table> <\/div><table style=\"display: none\"> <tbody id=\"answer-template\"> <tr><td>{{PLACE}}<\/td><td>{{NAME}}<\/td><td>{{LANGUAGE}}<\/td><td>{{SIZE}}<\/td><td><a href=\"{{LINK}}\">Link<\/a><\/td><\/tr><\/tbody> <\/table> <table style=\"display: none\"> <tbody id=\"language-template\"> <tr><td>{{LANGUAGE}}<\/td><td>{{NAME}}<\/td><td>{{SIZE}}<\/td><td><a href=\"{{LINK}}\">Link<\/a><\/td><\/tr><\/tbody> <\/table>\n\n\u2022 There is a conflicting rule: in and above the screenshot, it says to print NO in red \"If T \u2265 200\". Later, you say to print in the default color \"If T \u2264 200\" \u2013\u00a0Arc676 May 28 '17 at 6:28\n\u2022 @Arc676 Oops. Well, logically, if the hotel has 200 rooms then it must be the first description that is correct. \u2013\u00a0\u00d8rjan Johansen May 28 '17 at 7:27\n\u2022 For extra credit, do it for the Hilbert Hotel, which has an infinite number of rooms. \u2013\u00a0David Conrad May 29 '17 at 9:40\n\u2022 Are these outputs valid: i.imgur.com\/221Qxgj.png ? \u2013\u00a0sergiol Jun 16 '17 at 23:02\n\u2022 @sergiol Yes, that's fine. \u2013\u00a0MD XF Jun 16 '17 at 23:20\n\n# Jelly, 29 26 bytes\n\n<200o-\u201cNO\u201c\u025331m\u201dm\u201c=\u0224\u017b\u00bb\u0152u\u201c\u0253m\n\n\nThis uses <CSI> (0x9b), which is shorter than <ESC>[ (0x1b 0x5b).\n\nIt resets the foreground color with <CSI>m instead of <CSI>0m, as the 0 is implicit.\n\n### Verification\n\nNote that your terminal emulator (e.g., Konsole) must be set to ISO 8859-1 or similar.\n\n### How it works\n\n<200o-\u201cNO\u201c\u025331m\u201dm\u201c=\u0224\u017b\u00bb\u0152u\u201c\u0253m Main link. Argument: n (integer)\n\n<200 Compare with 200, yielding 1 if true, 0 if not.\no- Logical OR -1; map 0 to -1 (and 1 to 1).\n\u201cNO\u201c\u025331m\u201d Yield [\"NO\", \"\\x9b31m\"].\nm Take the list \"modulo\" 1 or -1, keeping it as is for 1,\nreversing it for -1.\n\u201c=\u0224\u017b\u00bb Implicitly print the previous result and yield the\nstring \" vacancy\". This is achieved by indexing into\nJelly's in-built dictionary.\n\u0152u Convert to uppercase.\n\u201c\u0253m Implicitly print the previous result and yield the\nstring \"\\x9bm\", which is printed on exit.\n\n\n# Javascript (ES6), 60 bytes\n\n(Open your browser's console while running the snippet to see the colored result.)\n\nf=\nn=>console.log((n>199?'%cNO':'NO%c')+' VACANCY','color:red')\n<input oninput=f(this.value)>\n\n\u2022 NO%c VACANCY color:red? \u2013\u00a0MD XF May 28 '17 at 2:45\n\u2022 @MDXF check your actual browser console. the snippet console emulator doesn't support it. \u2013\u00a0nderscore May 28 '17 at 2:48\n\u2022 Oh, good catch. +1 \u2013\u00a0MD XF May 28 '17 at 2:48\n\u2022 Standard JS rules allow you to shorten this greatly. Remove console.log() as the rules specify that returns are fine, you do not have to define the function as well. \u2013\u00a0MayorMonty May 29 '17 at 0:35\n\u2022 @MayorMonty this solution specifically takes advantage of console.log functionality to create the colored text, so I would feel weird not including it. \u2013\u00a0nderscore May 29 '17 at 6:44\n\n# Ruby (nix style terminal), 54484544 43 bytes\n\n1 byte saved thanks to Value Ink\n\n\u241b stands in for a literal esc byte (ASCII 27)\n\n->x{\"#{x>199?\"\u241b[31m\":p}NO\u241b[31m VACANCY\u241b[m\"}\n\n\nA port of my python answer, that is a byte several bytes shorter. I'm new to ruby golf but eager to learn so feedback is appreciated.\n\n\u2022 ->x{\"#{x>199?\"\u241b[31m\":p}NO\u241b[31m VACANCY\u241b[m\"} saves a byte. The trick is the fact that in string interpolation, \"#{nil}\" will evaluate to an empty string, and p can be used as a substitute for nil. \u2013\u00a0Value Ink Jun 17 '17 at 0:45\n\n# Python 3 (nix style terminal), 55 54 bytes\n\nlambda x:\"\\033[31m\"(x-199)+\"NO\\033[31m VACANCY\\033[m\"\n\n\nThis uses ANSI escape codes. \\033[31m Makes the terminal red, if x is less than 200 we will start with one making NO red, otherwise we will have one after NO making it red anyway. When we are done \\033[m clears the color from the terminal.\n\n\u2022 The multiplication of the color string instead of a condition is brilliant! \u2013\u00a0Hubert Grzeskowiak May 29 '17 at 15:17\n\n# HTML, 72 71 bytes\n\n<input min=200 type=number><x>NO <y>VACANCY<style>:valid+x,y{color:red}\n\n\u2022 You can save 1 byte by using the correct wording... \u2013\u00a0Neil May 28 '17 at 8:32\n\u2022 Oh my... I need a vacation. \u2013\u00a0GOTO 0 May 28 '17 at 14:12\n\u2022 One of the other answers defines CSS separately. If you do that too, you could save 7 chars with \"<style>\" (pun intended) \u2013\u00a0Hubert Grzeskowiak May 29 '17 at 15:27\n\n# Java (OpenJDK 9), 1028988 51 bytes\n\nYes, Java. :P This only works on nix terminals.\n\nx->(x>199?\"\\033[31m\":\"\")+\"NO\\033[31m VACANCY\\033[m\"\n\n\n# bash, 41 bytes\n\necho \u241b[$[($1>199)31]mNO \u241b[31mVACANCY\u241b[0m\n\n\nwhere \u241b represents a literal ESC character (ASCII \\033).\n\n\u2022 brilliant multiplication! \u2013\u00a0Ipor Sircer May 29 '17 at 9:45\n\n# Go, 82 81 bytes\n\nThis only works on nix terminals. I wonder how easy it would be to port this to Java... Done.\n\nfunc f(x int)string{v:=\"NO\\033[31m VACANCY\\033[m\";if(x>199){v=v[2:7]+v};return v}\n\n\u2022 I see a Java port coming. \u2013\u00a0MD XF May 28 '17 at 2:59\n\u2022 Ninja'd by 11 seconds. XD \u2013\u00a0totallyhuman May 28 '17 at 2:59\n\n## BASH \/ MKSH, 48 47 46 bytes\n\n(($1>199))&&a=^[[31m;echo$a^MNO ^[[31mVACANCY^[[m\n\n\nNote: ^[ means 1 byte wide ESC character: 0x1b or decimal 27.\n\n^M means 1 byte wide CR character: 0x0d, decimal 13.\n\n# Excel VBA, 76 73 72 Bytes\n\nAnonymous VBE immediate window function that takes input of expected type Integer from cell [A1] and outputs a (NO) VACANCY sign across cells A2:B2\n\n[A2]=\"NO\":[B2]=\"VACANCY\":Range([If(A1>199,\"A2:B2\",\"B2\")]).Font.Color=255\n\n\n-3 Bytes for changing rgbRed to 255\n\n\u2022 Sorry if this is incorrect, I'm not fluent with Excel. But did you mean to write iif, and does this return the correct value if the input is equal to 200? [A1]>200 makes me think otherwise. \u2013\u00a0MD XF May 28 '17 at 21:57\n\u2022 @MDXF Yes, I did mean to write iif (abbreviated from inline if) however, you are right that should be >199rather than >200 good catch! \u2013\u00a0Taylor Scott May 28 '17 at 23:11\n\n# HTML + CSS + JavaScript (ES6), 74 59 bytes\n\nTakes input as function argument of f, like f(100).\n\n### HTML\n\n<x id=n>NO <j id=r>VACANCY\n\n\n### CSS\n\n#r{color:red\n\n\n### JavaScript (ES6)\n\nf=a=>a>199?n.id=\"r\":0\n\n\n## Test Snippet\n\nf=a=>a>199?n.id=\"r\":0\n\nf(prompt(\"Enter a number\"))\n#r{color:red\n<x id=n>NO <j id=r>VACANCY\n\n\u2022 Gah that unclosed curly bracket is awful... \u2013\u00a0Beta Decay May 28 '17 at 8:34\n\u2022 @BetaDecay HAHA! LOL! :D \u2013\u00a0Arjun May 28 '17 at 9:06\n\u2022 @BetaDecay I feel with you.... It hurts deep down in your <s>heart<\/s> assembly level code... \u2013\u00a0Roman Gr\u00e4f May 28 '17 at 18:12\n\u2022 -1: f=a=>n.id=a>199&&\"r\" \u2013\u00a0nderscore May 28 '17 at 18:47\n\u2022 Get rid of second element's id and set the CSS rule selector to j,#r to save 3 bytes. \u2013\u00a0Hubert Grzeskowiak May 29 '17 at 15:36\n\n# Haskell, 54 53 bytes\n\nEDIT:\n\n\u2022 -1 byte: From @Dennis's Jelly answer, the 0 argument in the final escape sequence can be dropped.\n\nf takes an integer and returns a string. Use as putStrLn$f 200. f t\|t>199=\"\\27[31m\"++f 0\|0<1=\"NO \\27[31mVACANCY\\27[m\" Try it online! Alas, the colors don't show up in TIO, but you can see that the ANSI codes are correctly placed. Golfing seemed to peter out pretty quickly with this one - not even naming the escape strings seems to save anything. The cleverest bit is recursing with f 0 to use the other branch as a substring. Three different attempts at using list comprehensions all turned up one byte longer. Perhaps the nicest I found: f t=foldr drop\"\\27[31mNO \\27[31mVACANCY\\27[m\"[5\|t<200] \u2022 54 byte alternative: f t=concat[\"\\27[31m\"\|t>199]++\"NO \\27[31mVACANCY\\27[0m\". \u2013 Laikoni May 28 '17 at 7:07 \u2022 @Laikoni Oh! I was so close to that but somehow never noticed concat was shorter than id=<< because of the parentheses. \u2013 \u00d8rjan Johansen May 28 '17 at 7:15 \u2022 @Laikoni With Dennis's tip that's also 53 bytes. \u2013 \u00d8rjan Johansen May 28 '17 at 7:30 # Bash script, 60 bytes c=\"\\e[1;31m\";((199<$1))&&printf $c;printf \"NO$c VACANCY\\e[m\"\n\n\u2022 Just so you know, the downvote was cast automatically by the Community user when your answer was edited. I consider this a bug. \u2013\u00a0Dennis May 28 '17 at 3:57\n\u2022 @MDXF Input is via command-line arguments. \u2013\u00a0Dennis May 28 '17 at 3:59\n\u2022 @Dennis Ah, my bad. You may want to change the header to Bash script, 64 bytes. \u2013\u00a0MD XF May 28 '17 at 4:00\n\u2022 Unless you literally make hundred of edits, you can edit your answer every time you get an idea. Edits within the same 5-minute window get grouped into a single revision anyway. \u2013\u00a0Dennis May 28 '17 at 4:07\n\u2022 This doesn't reset the terminal color at the end, which is required. \u2013\u00a0Sriotchilism O'Zaic May 28 '17 at 20:22\n\n## Mathematica, 67 bytes\n\nPrint[s=Style[#,FontColor->Red]&;If[#>200,s,#&]@\"NO\",s@\" VACANCY\"]&\n\n\nor (60 bytes, but may be considered cheating)\nThis is actually Times[\"NO\",\"VACANCY\"], but appear to be correct.\n\n(s=Style[#,FontColor->Red]&;If[#>200,s,#&]@\"NO\")s@\"VACANCY\"&\n\n\nif(($1<200));then echo -n NO else echo -ne '\\033[31mNO\\033[0m' fi echo -e '\\033[31m VACANCY\\033[0m' This can be probably be golfed, but I'm low on time. I'll come back to this later. -5 bytes thanks to @R. Kap \u2022 Replacing if [$1 -le 200 ] with if(($1<200)) saves 5 bytes and fixes the bug of the output not appearing in all red with an input of 200. \u2013 R. Kap May 28 '17 at 3:56 \u2022 @R.Kap Thanks. OP requested default color for less than or equal to 200 though. \u2013 Arc676 May 28 '17 at 5:15 \u2022 No, OP asked for all red ouput for inputs more than or equal to 200. \u2013 R. Kap May 28 '17 at 5:54 # Mathematica, 47 bytes (If[#>199,Style[NO,Red],NO]Style[VACANCY,Red])& # C (nix style terminal), 505552 51 bytes -1 thanks to Wheat Wizard f(t){printf(\"\u241b[%dmNO \u241b[31mVACANCY\u241b[m\",t>199?31:0);} \u241b stands for the literal ESC byte, ASCII 27. Call with f(200), 200 being the number. Prints NO VACANCY colored to the spec. \u2022 In my terminal, that breaks your rule that it shouldn't change the text color of the shell. \u2013 \u00d8rjan Johansen May 28 '17 at 3:26 \u2022 @\u00d8rjanJohansen Fixed. I forgot that I run a custom shell which automatically sets the color. \u2013 MD XF May 28 '17 at 3:26 \u2022 You can change \u241b[0m to \u241b[m \u2013 Sriotchilism O'Zaic May 28 '17 at 11:35 # PHP, 41 bytes \u241b[<?=$argn<200?31:''?>mNO\u241b[31m VACANCY\u241b[m\n\n\n\u241b represents the Escape character.\n\n# shortC, 48 bytes\n\nf(t){R\"\u241b[%dmNO \u241b[31mVACANCY\u241b[m\",t>199?31:0\n\n\nWhere \u241b stands for ASCII 27, the ESCAPE byte.\n\n# GW-BASIC, 7874 65 bytes\n\n-12 thanks to Orjan Johansen\n\n1INPUT X:IF X>199THEN COLOR 4\n2?\"NO \";:COLOR 4:?\"VACANCY\":COLOR 7\n\n\nPrompts user for an integer. Output:\n\n\u2022 Hm can't find an online interpreter, but can't line 1 and 2 be joined with :? \u2013\u00a0\u00d8rjan Johansen May 30 '17 at 2:26\n\u2022 @\u00d8rjanJohansen Wow... can't believe I completely missed that. Thanks, and yeah, there are no online interpreters. However, you can use the first emulator on pcjs.org and type BASICA to get something close enough, although it may not have color. \u2013\u00a0MD XF May 30 '17 at 2:29\n\u2022 Assuming that emulator is good enough: You need a new line before the first PRINT. However, you don't need spaces after the line numbers, and PRINT can be abbreviated to ?. \u2013\u00a0\u00d8rjan Johansen May 30 '17 at 2:45\n\u2022 @\u00d8rjanJohansen NO WAY. I've used Microsoft BASIC for eight years and I never new about ?=PRINT. Updating... \u2013\u00a0MD XF May 30 '17 at 2:48\n\u2022 You missed the line number spaces, and seem to have a stray lower case x. \u2013\u00a0\u00d8rjan Johansen May 30 '17 at 2:50\n\n# Tcl\/Tk, 96 bytes\n\ngrid [label .n -text NO -fg [expr \\\\$argv>199?\"red\":\"tan\"]]\ngrid [label .v -text VACANCY -fg red]","date":"2019-07-20 00:59:20","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\": 0.2417299896478653, \"perplexity\": 10939.47686004136}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-30\/segments\/1563195526401.41\/warc\/CC-MAIN-20190720004131-20190720030131-00475.warc.gz\"}"}	null	null
Rebecca Stenn, dancer, choreographer, teacher, writer, founded Rebecca Stenn Company in 1996. The company has since performed to critical acclaim and sold out houses in over 50 cities in the US and internationally including such venues as The Edinburgh Festival, The Copenhagen Festival, The Joyce Theater, The Kitchen, Danspace Project, Dance Theater Workshop, Joyce SoHo, Symphony Space, Dance New Amsterdam and Jacob's Pillow Dance Festival among many others. Upcoming events include performances at the West End Theater in New York City, May 2011 and Artspace Theater in Capetown, South Africa, summer 2012. As a principal dancer with Momix Dance Theater from 1989 to 1996, Stenn performed in over 30 countries and throughout the U.S. and appeared as a featured performer in films for Italian, Spanish and French television. Stenn is a founding member of Pilobolus Too with whom she toured throughout the world from 1996 to 2002. Stenn has been has been a contributing editor at Dancemagazine and The Dance Insider. She is a teaching artist for The Joyce Theater and The Lincoln Center Open Stages Program, and is on faculty at The New School as Choreographer in Residence. Stenn is the Dance Mentor/Choreographer for the National Foundation for the Advancement of the Arts. She earned her BFA in dance from the Juilliard School and her MFA in dance from The University of Wisconsin Milwaukee. Stenn is the proud mother of two children, Jonah and Elie Weissman.	{ "redpajama_set_name": "RedPajamaC4" }	7,429
We Indians are a sentimental lot. And it is something we should be proud of too. When everything has become so fast paced, from cars to relations, it is nice to know that the idea of celebrating the closeness of siblings still hold appeal to everyone. Traditionally, the sister ties a rakhi on her brother's hand, giving him sweets and the brother reciprocates the love by showering her with gifts. In the case of younger brothers, the sisters give them gifts. Now, however, brothers, both elder and younger brothers want their share of gifts. And sisters are only too happy to dole them out what with the amazing array of rakhi gifts that one can buy in any price range. If you haven't yet decided what to buy for your siblings, make your shopping destination naaptol.com. With an endless range of gift items from mobiles to gift baskets to jewellery to clothes and accessories, naaptol.com has everything your sister or brother will wish for. You also can get up to 52% off on your purchases and avail other deals and free shipping offers too. Gadget guy, simple person, fashionable man, book worm…whoever your brother is, you will surely surprise him with a wonderful gift from naaptol.com. Buy or send Rakhi Thali sets with the ethnic thread, tikka, chocolates, sweets and greeting cards all in one box for as low as Rs. 289. You can also customize your thali and spend only for what you opt. For gadget loving brother, smart phones and PDAs are a great buy. Check the unbelievably slashed price at naaptol.com and you would surprise yourself in the spending department and surprise your brother with a thoughtful gift. A digital camera is another cool idea that your brother might appreciate for rakhi. If your brother has everything he wants for, then sending/buying a gift hamper is a good choice. Choose one from the different varieties of hampers containing thali sets with leather belt, or compass key chains, or chocolates, sweets, or home decors etc. Pens and pen stands, books, wallets, shorts and keepsakes are other ideas that will work for brothers. When it comes to buying for sisters, it's a piece of cake. Women love gifts. Period. So go for jewellery, phones, accessories, clothes, home decors, soft toys, perfumes and you will score right. If your sister is in college, she may love the ethnic hand embroidered mirror work shoulder bag that will come in handy to her at all times. A photo frame that captures memories of both of you growing together or a trophy that says she is the best sister can become a touching and a very beautiful gift. A married sister might appreciate home décor products like a vase or a picture frame to add beauty to her house or even a kitchen appliance that makes her life easy. So, whatever is your choice of gift, make naaptol.com your choice for shopping for this rakhi and take home great gifts for great price. Shop through pennyful.in and get discounts and cashback rebates of Rs. 100. No Replies to "Gift Ideas For Rakhi"	{ "redpajama_set_name": "RedPajamaC4" }	4,535
@interface HomeMenuViewController () @end @implementation HomeMenuViewController - (void)viewDidLoad { [super viewDidLoad]; // Do any additional setup after loading the view. } @end	{ "redpajama_set_name": "RedPajamaGithub" }	8,645
Q: Access static class of dynamic (not known at compile time) type? I want to access a static class of a name that I don't know at compile time - that's not a good description so let me elaborate. Imagine: 3 static classes that all inherit from an interface, Now a fourth class wants to access a function in that interface but for one of the 3 classes. And I don't know which of the 3 it's going to be at compile time. Some Research I've looked into, and in the past, used things like Activator.CreateInstance(); to solve this problem for non-static classes, but now I'd like to do it with static classes and I'm lost. I've also seen people storing references to the classes in a dictionary of <string, interface> and then accessing the classes by their name that way but this isn't ideal since it requires a lot of boilerplate. (I have quite a few more than 3 classes that are possibilities) A potential solution I could just create instances as I mentioned before but this seems wasteful which is why I've decided I want to use static classes. Perhaps this isn't as big of a problem as I thought and I should refer myself to the rules of optimisation...	{ "redpajama_set_name": "RedPajamaStackExchange" }	8,426
A housekeeper's work environment is full of many nasty things that need to be cleaned up, some seen and others unseen. It is the unseen ones I wish to address. Microbes are the bugs that a housekeeper cannot see and that need to be eradicated from the property as it is cleaned. Some of the microbes that need to be removed are: Salmonella, Escherichia Coli (E-Coli), Staphylococcus Aureus (Staph), and Multiple-Resistant Staphylococcus Aureus (MRSA). The primary way of killing the microbe is with a cleaning product. Some cleaning agents kill more microbes than others. To help illustrate this, below is table that lists different cleaning products across the top. As you move down the chart you can see the effectiveness (what it kills), dwell time (how long it takes to kill the microbes), and health effects to the housekeeper. As the chart illustrates, different cleaning products kill differet microbes and at different speeds. It is extremely important to know what microbes your product will kill. If you purchase your products from a janitorial supply company, they can provide this information to you. If, however, you purchase your products from a retail store, you will need to reach out to the manufacture listed on the bottle. A list of what microbes the product will kill. How long it takes the product to kill the microbes (dwell time). Whether the product is a spray and wipe. In other words, do I have to rinse the product off the surface I am cleaning? If the product has to be rinsed, that means more work and more time to clean. One last item to consider about cleaning solutions: what does section 8 of the Safety Data Sheet say? This section tells the user what personal protective equipment is needed when using the cleaning product. Read carefully as some products recommend face shields and chemical resistant impervious gloves. If these items are present that means the product is very corrosive, and I would stop using it immediately!	{ "redpajama_set_name": "RedPajamaC4" }	1,623
I had thought that Center Parcs would be the place where my youngest learns to ride her bike, allowing me a few sprint sessions as I chase down to where she has fallen or given up for some reason. If it took several sessions to get her up and pedaling, that's fine, good training for me. Turns out, after the first night – we picked up the bikes and were cycling back to our 'chalet', very slowly with lots of stop starts, me parking my bike, going to help her, trotting back to get my bike, catching up, repeat, repeat, repeat – that she was a natural. So instead of sprint sessions, we did loops of the holiday village, about 2 miles a loop, so not bad going for a brand new cyclist. It was here, though, that my training fell off a little. We did do lots of cycling, around things to do and "Please can we do another loop?" which was the catchphrase of the week, I didn't make as many opportunities to run. I tried to sneak off early to run, I was heard and how could I refuse the, "Can I come?" from a new cycling convert? Oh, and there was the odd bottle of wine and a pint or two. Still, I managed to do a couple of loops alone once, and it was good to get the feel of a hill again, my poor old injury ravaged calves get very nervous at the hint of a slope, and my left Achilles seems to brace itself, but all held out and I enjoyed the foresty feel of the Parc, lots of sun filtering through the trees and twisty paths over rivers. Still, I can't say that I did more than 4.5 miles over the week and was really worried that I'd set my 10k progress back. Back home, Monday night, I had an opportunity to run and went for it. Garmin ran out of battery after 1.5miles – I'd forgotten you have to charge it, it's usually plugged into the computer, but being away, it hadn't happened – so I just winged it. It felt good, winging it, but I was shocked by the dark, I haven't run in the evening for a long time and the lack of street lighting surprised me. Even if there were plenty of street lamps, the trees seemed to absorb all the light and I couldn't see what was in front of me, it was just darkness. I felt nervous about hitting a broken paving slab or an unexpected bin bag, but I ran a decent distance in my local area and enjoyed it. I ran the same route the next night (Garmin now fully charged) and was reassured to discover I'd run 6.1 miles. I'm happy that I seem to have kept my fitness up so far. Only two weeks now till I join the Write This Run team at the Women's Running 10k, looking forward to being part of something that supports sport for women and girls. I'm going to make every effort to improve my training over the next two weeks.	{ "redpajama_set_name": "RedPajamaC4" }	8,113
\section{Introduction} In this paper, we investigate the wave front set of the solutions to the following Schr\"odinger equations with time-dependent variable coefficients: \begin{align} \label{CP1} &\begin{cases} i\partial_tu+ \displaystyle\frac{1}{2}\sum_{j,k=1}^{n} \partial_{x_j} a_{j,k}(t,x)\partial_{x_k}u -V(t,x)u= 0, \quad &(t,x)\in\mathbb{R}\times\mathbb{R}^{n},\\ u(0,x)=u_0(x),\hspace{100pt} &x\in\mathbb{R}^n, \end{cases} \end{align} where the coefficients $a_{j,k}(t,x)$ and the potential $V(t,x)$ satisfy the following assumptions:\\ \begin{Assu}\label{assu} For $i,j\geq1$, $a_{j,k}=a_{k,j}$, $a_{j,k}(t,x)$ and $V(t,x)$ are in $C^{\infty}(\mathbb{R}\times\mathbb{R}^n;\mathbb{R})$ and there exist $\rho>1$ and $C_\alpha>0$ for each $\alpha\in\mathbb{Z}_+^n$ such that \begin{align} \label{as1} \|\partial_x^\alpha(a_{j,k}(t,x)-\delta_{j,k})\|\leq C_\alpha(1+\|x\|)^{-\rho-\|\alpha\|},\quad (t,x)\in\mathbb{R}\times\mathbb{R}^n,\\ \label{as2} \|\partial_x^\alpha V(t,x)\|\leq C_\alpha(1+\|x\|)^{2-\rho-\|\alpha\|},\quad (t,x)\in\mathbb{R}\times\mathbb{R}^n, \end{align} where $\delta_{j,k}$ is the Kronecker delta. \end{Assu} In addition, we assume the existence of the propagater of $\eqref{CP1}$. \begin{Assu}\label{assu2} There exists a family of unitary operators $(U(t,\tau))_{(t,\tau)\in\mathbb{R}^2}$ in $L^2(\mathbb{R}^n)$ satisfying the following conditions. \noindent(i) For $f\in L^2(\mathbb{R}^n)$, $U(t,\tau)f$ is strongly continuous function with respect to $t$ and satisfies \[ U(t,\tau')U(\tau',\tau)=U(t,\tau),\,U(t,t)=I\quad\mbox{for all }t,\tau',\tau\in\mathbb{R}, \] where $I$ is the identity operator on $L^2(\mathbb{R}^n)$.\\ (ii) For $u_0\in L^2(\mathbb{R}^{n})$, $u(t)=U(t,0)u_0$ is strongly continuously differentiable in $L^2(\mathbb{R}^n)$ with respect to $t$ and satisfies $\eqref{CP1}$. \end{Assu} In this paper, we write $\mathcal{S}(\mathbb{R}^n)$ and $\mathcal{S}'(\mathbb{R}^n)$ as the Schwartz space and the set of the temperd distributions, respectively. \begin{Def}[$C^\infty$-type wave front set]\label{wave-front-set} Let $f\in \mathcal{S}'(\mathbb{R}^n)$ and $(x_0,\xi_0)\in\mathbb{R}^n\times( {\mathbb{R}^n\setminus\{0\})}$. Then we say that $(x_0,\xi_0)\notin WF(f)$ if and only if there exist $\chi\in C_0^{\infty}(\mathbb{R}^n)$ with $\chi (x_0) \not= 0$ and a conic neighborhood $\Gamma$ of $\xi_0$ ({\rm i.e.,} $\xi\in\Gamma$ and $c>0$ implies $c\xi\in\Gamma$) satisfying that for $N\in\mathbb{N}$ there exists $C_N>0$ such that $$\|\widehat{\chi f}(\xi)\| \leq C_N(1+\|\xi\|)^{-N}$$ for any $\xi\in\Gamma$, where $\hat{f}(\xi)=\mathcal{F} [f](\xi)\equiv(2\pi)^{-n/2}\int_{\mathbb{R}^n}f(x)e^{-ix\cdot\xi}dx$ denotes the Fourier transform of $f$. \end{Def} This wave front set is introduced by L. H\"ormander \cite{Hor}, which is one of the main tools of microlocal analysis in $C^\infty$ category. G. B. Folland \cite {Fo} introduced the characterization of the wave front set in terms of wave packet transform which is introduced by A. C\'ordoba--C. Fefferman \cite{CF}. \begin{Def}[Wave packet transform]\label{wpt-def} Let $\varphi\in\mathcal{S}(\mathbb{R}^n)\setminus\left\{ 0\right\}$, $f\in\mathcal{S}'(\mathbb{R}^{n})$ and $F(y,\xi)$ be a function on $\mathbb{R}^{n}\times\mathbb{R}^{n}$. We define the wave packet transform $W_\varphi f(x,\xi)$ of $f$ with the wave packet generated by a window $\varphi$ as follows: \[ W_\varphi f(x,\xi)=\int_{\mathbb{R}^{n}}\overline{\varphi(y-x)}f(y)e^{-iy\xi}dy \quad\mbox{for } (x,\xi)\in\mathbb{R}^{n}\times\mathbb{R}^{n}. \] \end{Def} The main statement of this paper is following. \begin{Th}\label{main-theorem} Suppose that Assumption $(A)$ and $(B)$ are satisfied. Let $u_0\in L^2(\mathbb{R}^n)$, $u(t)=U(t,0)u_0$, $\varphi_0(x)=e^{-\|x\|^2/2}$ and \begin{align}\label{w-l} \varphi_\lambda(t,x) =e^{it\Delta/2}\lambda^{n/4}\varphi_0(\lambda^{1/2} x) =\mathcal{F}^{-1}[e^{-it\|\xi\|^2/2}\lambda^{n/4}\mathcal{F}[\varphi_0(\lambda^{1/2} \cdot)](\xi)](x). \end{align} Then $(x_0,\xi_0)\notin WF(u(t,\cdot))$ if and only if there exist a neighborhood $K$ of $x_0$ and a conic neighborhood $\Gamma$ of $\xi_0$ such that for all $N\in\mathbb{N}$, $a\geq1$ and $\varphi_0\in \mathcal{S}(\mathbb{R}^n)\setminus\{0\}$, there exists $C_{N,a,\varphi_0}>0$ satisfying \begin{align}\label{m-th} \|W_{\varphi_{\lambda}{(-t)}}u_0 (x(0,t,x,\lambda\xi), \xi(0,t,x,\lambda\xi))\|\leq C_{N,a,\varphi_0}\lambda^{-N} \end{align} for $\lambda\geq1$ and $(x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$. Here $x(s)=x(s;t,x,\xi)$ and $\xi(s)=\xi(s;t,x,\xi)$ are the solutions of \begin{align} \label{h-eq} \begin{cases} \dfrac{d}{ds} x(s)=\dfrac{\partial H}{\partial \xi}(s,x(s),\xi(s)),\ x(t)=x, \\[3mm] \dfrac{d}{ds} \xi(s)=-\dfrac{\partial H}{\partial x}(s,x(s),\xi(s)),\ \xi(t)=\xi,\\ \end{cases} \end{align} where $H(t,x,\xi)=-(1/2)\sum_{j,k=1}^{n}a_{j,k}(t,x)\xi_j\xi_k+V(t,x)$. \end{Th} Using the properties of the classical orbits, we obtain the following corollary. \begin{Cor}\label{Cor2} Under the same assumpton and notation in Theorem \ref{main-theorem}. Then $(x_0,\xi_0)\notin WF(u(t,\cdot))$ if and only if there exist a neighborhood $K$ of $x_0$ and a conic neighborhood $\Gamma$ of $\xi_0$ such that for all $N\in\mathbb{N}$, $a\geq1$ and $\varphi_0\in \mathcal{S}(\mathbb{R}^n)\setminus\{0\}$, there exists $C_{N,a,\varphi_0}>0$ satisfying \begin{align}\label{m-th-c} \|W_{\varphi_{\lambda}(-t)}u_0 (x-t\lambda\xi,\lambda\xi)\|\leq C_{N,a,\varphi_0}\lambda^{-N} \end{align} for $\lambda\geq1$ and $(x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$. \end{Cor} \begin{Rem} In \cite{KaI}, the similar corollary was proven. However, there is insufficiency of the argument in the proof. In this paper, we make up for the insufficiency in Section 4. \end{Rem} In the previous studies of the wave front set, G. B. Folland used the basic wave packet as a window. T. \=Okaji \cite{Oo} obtained the same conclusion with a general window under some conditions. After that, K. Kato--K. Kobayashi--S. Ito \cite{KKI} removed some restriction of window completely. The following results of wave front sets for the solutions of the Schr\"odinger equation without time-dependent variable coefficients are well-kwown. A. Hassell--J. Wunsch \cite{HW} and S. Nakamura \cite{Na} has studied the wave front set for the time-independent case i.e., $a_{j,k}(t,x)=a_{j,k}(x)$ and $V(t,x)=V(x)$. A. Hassell--J. Wunsch investigated the quadratic scattering wave front set which is introduced by Melrose \cite{Me}. S. Nakamura used the semi-classical way with the pseudo-differential operators. On the other hand, K. Kato--S. Ito \cite{KaI} has treated the case $a_{j,k}(t,x)=\delta_{j,k}$ with time-dependent sub-quadratic potentials by using the wave packet transform instead of the pseudo-differential operators, however, this method cannnot be applied directly for the solution to the equation with general coefficients $a_{j,k}(t,x)$. Thus we use the series function $\Phi(t)$ defined in \eqref{def-ph} and apply the Gronwall inequality for $\Phi(t)$ and thereby we get the caracterization of the wave front set for the solution to the equation with general coefficients $a_{j,k}(t,x)$. Our result is different from the previous results by including time-dependent variable coefficients. In \cite{KaI}, time-dependent potentials are treated but the principal part does not depend on time. In order to treat time-dependent case, we use the phase space analysis, in particular, we use the wave packet transform. The idea of the proofs of the main theorems is as follows. Splitting the part $(1/2)\sum\partial_{x_j} a_{j,k}(t,x)\partial_{x_k}u -V(t,x)u$ into $((1/2)\sum\partial_{x_j} (a_{j,k}-\delta_{j,k})(t,x)\partial_{x_k}u)+((1/2)\Delta u-V(t,x)u)$ and estimating the each term by using the wave packet transform, we prove the decay estimate with respect to $\lambda$. The latter part can be estimated by the similar way in \cite{KaI}. However, the estimate of the former part cannot be applied to the method introduced in \cite{KaI}. Hence the key of our proof is to estimate the former part. In order to prove this, we need to estimate the term like $\lambda^2\sum_{\|\alpha\|=2}\xi^\alpha W_\varphi[(a_{j,k}(t)-\delta_{j,k})u(t)](x,\lambda \xi)$, which does not appear in \cite{KaI}. Thus we introduce the series $\Phi(t)$ defined in $\eqref{def-ph}$ and take a window like $\eqref{w-l}$. This idea can solve the difficulties. In the proof of Corollary \ref{Cor2}, the new method is used. Introducing the inverse function of $(x(s),\xi(s))$, we prove the smallness between $(x(s),\xi(s))$ and $(x-t\xi,\xi)$ and find suitable neighborhoods of $x$ and $\xi$. \begin{Rem} Assumption $\mathrm{(B)}$ is satisfied by the Stone theorem under Assumption $\mathrm{(A)}$ if $a_{j,k}$ and $V$ do not depend on $t$ and $\det(a_{j,k})> 0$ for any $x\in\mathbb{R}^n$. \end{Rem} In this paper, we use the following notaitons. $i=\sqrt{-1}$, $n\in\mathbb{N}$, $\partial_{x_j}=\partial/\partial_{x_j}$, $\partial_t=\partial/\partial t$, $\Delta=\sum_{j=1}^{n}\partial x_j^2$ and $\int =\int_{\mathbb{R}^n}$. We denote $B_r(x)$ as a open ball $\{y\in\mathbb{R}^n\,\|\,\|y-x\|<r\}$. We often write $W_\varphi u(t,x,\xi)$ as $W_\varphi [u(t)](x,\xi)$. $e_j=(0,\ldots,0,\overset{j}{\check{1}},0,\ldots,0)$. For a vector $x\in\mathbb{R}^n$, $\langle x\rangle=\sqrt{1+\|x\|^2}$. For a multi-index $\alpha=(\alpha_1, \cdots, \alpha_n),\,\beta\in\mathbb{Z}_+^n$, $\|\alpha\|=\alpha_1+\cdots+\alpha_n$, $x^{\alpha}=x_1^{\alpha_1}\cdots x_n^{\alpha_n}$, $\partial_{x}^{\alpha}=\partial_{x_1}^{\alpha_1}\cdots\partial_{x_n}^{\alpha_n}$ and $p^{(\alpha)}_{(\beta)}(x)=x^\beta\partial_x^\alpha p(x)$ for $p\in C^\infty(\mathbb{R}^n)$. The plan of the paper is as follows. In section 2, we shall study the properties of the classical orbits. In section 3, we give a proof of Theorem \ref{main-theorem}. In section 4, we give a proof of Corollary \ref{Cor2}. \section{Property of classical orbits}\label{co} In this section, we study the property of the classical orbits which are solutions to $\eqref{h-eq}$. The following property is used in the proof of the Theorem \ref{main-theorem}. \begin{Prop}\label{c-o-prop} Suppose that Assumption $(A)$ is satisfied. Then the solutions $x(s)=x(s;t_0,x,\xi)$ and $\xi(s)=\xi(s;t_0,x,\xi)$ of $\eqref{h-eq}$ exist uniquely and are $C^\infty$ class in term of $(x,\xi)$ and their derivatives are $C^1$ class in term of $s$. Moreover, there exists a constant $\lambda_0\geq1$ such that \begin{align}\label{c-o-p-1} \frac{1}{2}\lambda\langle s-t_0 \rangle\|\xi\|\leq1+\|x(s;t_0,x,\lambda\xi)\|\leq 2 \lambda \langle s-t_0 \rangle\|\xi\|, \end{align} and \begin{align}\label{c-o-p-2} \frac{1}{2}\lambda\|\xi\|\leq\|\xi(s;t_0,x,\lambda\xi)\|\leq 2\lambda\|\xi\|. \end{align} for $\lambda\geq\lambda_0$, $\|s-t_0\|\leq\|t_0\|$ and $(x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$. \end{Prop} \begin{proof We define $x_N(s)$ and $\xi_N(s)$ as follows: \begin{align} \begin{cases} x_0(s)=x+\lambda(s-t_0)\xi,\\ \xi_0(s)=\lambda\xi \end{cases} \end{align} and for $N\geq1$ \begin{align} \begin{cases} x_N(s)=x+\dint_{t_0}^s\xi_N(\theta)d\theta+\dint_{t_0}^s(A(\theta,x_{N-1}(\theta))-E)\xi_{N-1}(\theta)d\theta,\\ \xi_{N}(s)=\lambda\xi-\displaystyle\frac{1}{2}\sum_{j,k=1}^n\dint_{t_0}^s\nabla_x a_{j,k}(\theta,x_{N-1}(\theta))\xi^j_{N-1}(\theta)\xi^k_{N-1,}(\theta)d\theta +\dint_{t_0}^s\nabla_x V(\theta,x_{N-1}(\theta))d\theta, \end{cases} \end{align} where $A(t,x)=(a_{j,k}(t,x))$, $E$ denotes the $n\times n$ identity matrix and $\xi_N(s)={}^t(\xi^1_N,\ldots,\xi^n_N)$. The existence of the solutions of $\eqref{h-eq}$ follows from the Picard iteration method. Thus $x(s)$ and $\xi(s)$ are obtained by $\lim_{N\to\infty}x_N(s)=x(s), \lim_{N\to\infty}\xi_N(s)=\xi(s)$. We only show (\ref{c-o-p-1}) and (\ref{c-o-p-2}) with $x(s)=x_N(s)$ and $\xi(s)=\xi_N(s)$ by induction. Clearly, (\ref{c-o-p-1}) and (\ref{c-o-p-2}) hold for $N=0$. Assuming that (\ref{c-o-p-1}) and (\ref{c-o-p-2}) hold with $x(s)=x_l(s)$ and $\xi(s)=\xi_l(s)$, we have \begin{align} \left\|\xi_{l+1}(s)\right\|&\leq\lambda\|\xi\| +\dfrac{1}{2}\sum_{j,k=1}^n\left\|\dint_{t_0}^s\nabla_x a_{j,k}(\theta,x_{l}(\theta))\xi^j_{l}(\theta)\xi^k_{l}(\theta)d\theta\right\| +\left\|\dint_{t_0}^s\nabla_x V(\theta,x_{l}(\theta))d\theta\right\|\\ &\leq\lambda\|\xi\| +\dfrac{1}{2}\sum_{j,k=1}^n\dint_s^{t_0}C(1+\|x_l(\theta)\|)^{-\rho-1}\|\xi^j_{l}(\theta)\|\|\xi^k_{l}(\theta)\|d\theta +\dint_s^{t_0} C(1+\|x_{l}(\theta)\|)^{-\rho+1}d\theta\\ &\leq\lambda\|\xi\| + C\dint_s^{t_0}(1+\|x_l(\theta)\|)^{-\rho-1}\left(\frac{1+\|x_l(\theta)\|}{\langle \theta-t_0 \rangle}\right)^2d\theta +C\times \|t_0\|\\ &\leq \lambda\|\xi\|\left(1+\frac{C''}{\lambda\|\xi\|}\right). \end{align} Here we use $\langle s-t_0 \rangle\|\xi_l(s)\|\leq 2\langle s-t_0 \rangle\lambda\|\xi\|\leq 4(\|x_l(s)\|+1)$. Hence, taking $\lambda_0$ sufficiently large, we have $\|\xi_{l+1}(s)\|\leq 2\lambda\|\xi\|$ for $\lambda\geq\lambda_0$. $\|\xi_{l+1}(s)\| \geq \lambda\|\xi\|/2$ can be shown in the same way. On the other hand, we have \begin{align} 1+\|x_{l+1}(s)\|&=1+\left\|x+\dint_{t_0}^s\xi_{l+1}(\theta)d\theta+\dint_{t_0}^s(A(\theta,x_{l}(\theta))-E)\xi_{l}(\theta)d\theta\right\|\\ &\geq1+\left\|\dint_{t_0}^s\xi_{l+1}(\theta)d\theta\right\| -\|x\|-\left\|\dint_{t_0}^s(A(\theta,x_{l}(\theta))-E)\xi_{l}(\theta)d\theta\right\|\\ &\geq1+\lambda\|s-t_0\|\|\xi\|-\|x\|-\displaystyle\frac{1}{2} \sum_{j,k=1}^n\left\|\dint_{t_0}^s\dint_{t_0}^{s_1}\nabla_x a_{j,k}(\theta,x_l(\theta))\xi^j_{l}(\theta)\xi^k_{l}(\theta)d\theta ds_1\right\|\\ &\quad-\displaystyle\left\|\dint_{t_0}^s\nabla_x V(\theta,x_{l}(\theta))d\theta\right\| -\left\|\dint_{t_0}^s(A(\theta,x_{l}(\theta))-E)\xi_{l}(\theta)d\theta\right\|\\ &\geq1+\lambda\|s-t_0\|\|\xi\|-\|x\|-C(s-t_0)^2-C\|s-t_0\|\\ &\geq \lambda\langle s-t_0 \rangle\|\xi\|\Big(1-\frac{C}{\lambda}\Big). \end{align} Thus we have $\|x_{l+1}(s)\|\geq \lambda\langle s-t_0 \rangle\|\xi\|/2$ for large $\lambda$. Similarly, $\|x_{l+1}(s)\|\leq 2\lambda\langle s-t_0 \rangle\|\xi\|$ holds. Hence (\ref{c-o-p-1}), (\ref{c-o-p-2}) are obtained with $x(s)=x_{l+1}(s)$ and $\xi(s)=\xi_{l+1}(s)$. \end{proof} We can obtain the following proposition by the similar way in the proof of Proposition \ref{c-o-prop}. \begin{Prop}\label{c-l-1} Suppose that Assumption $(A)$ is satisfied. Then the solutions $y(s)=y(s;t,y,\eta)$ and $\eta(s)=\eta(s;t,y,\eta)$ of \begin{align}\label{h-eq2} \begin{cases} \dfrac{d}{ds} y(s)=\dfrac{\partial H}{\partial \xi}(s,y(s),\eta(s)),\ y(0)=y-t\eta, \\[3mm] \dfrac{d}{ds} \eta(s)=-\dfrac{\partial H}{\partial x}(s,y(s),\eta(s)),\ \eta(0)=\eta.\\ \end{cases} \end{align} exist uniquely and are $C^\infty$ class in term of $(x,\xi)$ and their derivatives are $C^1$ class in term of $s$. Moreover, there exists a constant $C>0$ such that \begin{align}\label{l-decay} \|y(t;t,y,\lambda\eta) -y\|&\leq C\lambda^{-\rho+1}\\ \|\eta(t;t,y,\lambda\eta) -\lambda\eta\|&\leq C\lambda^{-\rho+1} \end{align} for $\lambda\geq1$, $\|s-t_0\|\leq\|t_0\|$ and $(x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$. \end{Prop} The relation between $(x(s),\xi(s))$ and $(y(s),\eta(s))$ is following. \begin{Lem}\label{c-l-2} Suppose that Assumption $(A)$ is satisfied. Let $(x(s),\xi(s))$ and $(y(s),\eta(s))$ be solutions to $\eqref{h-eq}$ and $\eqref{h-eq2}$, respectively. Then the following identities hold: \begin{align}\label{l-decay} \begin{cases} x(0;t,y(t;t,y,\eta),\eta(t;t,y,\eta))&=y-t\eta\\ \eta(0;t,y(t;t,y,\eta),\eta(t;t,y,\eta))&= \eta \end{cases} \end{align} for $\lambda\geq1$, $\|s-t_0\|\leq\|t_0\|$ and $(x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$. \end{Lem} \begin{proof} By the uniqueness of the solutions, we have for $s\leq t$ and $(x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$ \begin{align} \begin{cases} x(s;t,y(t;t,y,\eta),\eta(t;t,y,\eta))=y(s;t,y,\eta),\\ \xi(s;t,y(t;t,y,\eta),\eta(t;t,y,\eta))=\eta(s;t,y,\eta), \end{cases} \end{align} which implies $\eqref{l-decay}$. \end{proof} \section{Proof of Theorem\ref{main-theorem}} In this section, we give a proof of Theorem \ref{main-theorem}. We devide the proof into two steps. The former part is to get the representation of the solution to (\ref{CP1}) by the wave packet transform. In the latter part, we estimate the each term in the representation generated in the former part and prove Theorem \ref{main-theorem} by using the lemma in \cite{KKI}. Let $t_0\in\mathbb{R}^n$ and $\varphi_0\in\mathcal{S}(\mathbb{R}^n)\setminus\{0\}$ be fixed. The Cauchy problem (\ref{CP1}) is transformed by the wave packet transform with $\varphi(t,x)=e^{it\Delta/2}\varphi_0$ (defined in $\eqref{w-l}$) to \begin{align} \label{wpt-CP1} \begin{cases} \Big[i\partial_t+iA(t,x)\xi\cdot\nabla_x -i\displaystyle\Big(\frac{1}{2}\sum_{j,k=1}^n\nabla a_{j,k}(t,x)\xi_j\xi_k+\nabla_x V(t,x)\Big)\cdot\nabla_\xi\\ \hspace{6cm}+f(t,x,\xi)\Big]W_{\varphi(t)}u(t, x, \xi) = Ru(t, x, \xi), \\ W_{\varphi(0)}u(0, x, \xi)=W_{\varphi_0}u_0(x, \xi), \end{cases} \end{align} where \begin{align} f(t;x,\xi)=-\displaystyle\frac{1}{2}\sum_{j,k=1}^n(a_{j,k}(t,x)-x \cdot \nabla_{x}a_{j,k}(t,x))\xi_{j}\xi_{k} +V(t,x)-x \cdot \nabla_x V(t,x) \end{align} and \begin{align} &Ru(t,x,\xi;\varphi_0)\\ &=\frac{1}{2}\sum_{j,k=1}^n\Bigg[(a_{j,k}(t,x)-\delta_{j,k})W_{\varphi^{(e_{j,k})}(t)}u(t,x,\xi)+\partial_{x_k}a_{j,k} (t,x)W_{\varphi^{(e_j)}(t)}u(t,x,\xi)\\ &+\sum_{l=1}^n\left(\partial_{x_l} a_{j,k}(t,x)W_{\varphi^{(e_{j,k})}_{(e_l)}(t)}u(t,x,\xi)-2i\partial_{x_l} a_{j,k}(t,x)\xi_jW_{\varphi^{(e_{k})}_{(e_l)}(t)}u(t,x,\xi)\right)\\ &-i\partial_{x_k}a_{j,k}(t,x)\xi_jW_{\varphi(t)}u(t,x,\xi)+\dint u(t,y) (\partial_{y_k}\mathcal{A}^{j,k}_{M})(t,x,y)\partial_{y_j}(\overline{\varphi(y-x)}e^{-iy\xi})dy\\ &+\dint u(t,y)\mathcal{A}^{j,k}_{M}(t,x,y)\partial_{y_k}\partial_{y_j}(\overline{\varphi(y-x)}e^{-iy\xi})dy+\dint \overline{\varphi(t,y-x)}\mathcal{V}_{M}(t,x,y)u(t,y)e^{-iy\xi}dy \Bigg], \end{align} where $e_{j,k}=e_j+e_k$, $\mathcal{A}_M^{j,k}=\mathcal{A}_1^{j,k}+\mathcal{A}_2^{j,k}$, $\mathcal{V}_M=\mathcal{V}_1+\mathcal{V}_2$, \begin{align} \mathcal{A}_1^{j,k}(t,x,y)&=\sum_{2\leq\|\alpha\|\leq M-1}\frac{1}{\alpha!}(\partial_x^\alpha a_{j,k})(t,x)(y-x)^\alpha,\\ \mathcal{A}_2^{j,k}(t,x,y)&=\sum_{\|\alpha\|=M}(M/\alpha!)\int_0^1(1-\theta)^{M-1}\partial_x^\alpha a_{j,k}(t,x+\theta(y-x))d\theta (y-x)^\alpha,\\ \mathcal{V}_1(t,x,y)&=\sum_{2\leq\|\alpha\|\leq M-1}\frac{1}{\alpha!}(\partial_x^\alpha V)(t,x)(y-x)^\alpha \end{align} and \begin{align} \mathcal{V}_2(t,x,y)=\sum_{\|\alpha\|=M}({M}/\alpha!)\int_0^1(1-\theta)^{M-1}\partial_x^\alpha V(t,x+\theta(y-x))d\theta (y-x)^\alpha. \end{align} Here we use the Taylor expansion for $M\geq2$ as follows: \begin{align} a_{j,k}(t,y) =&a_{j,k}(t,x)+\nabla_x a_{j,k}(t,x)\cdot(y-x)+\mathcal{A}_M^{j,k}(t,x,y)\\ V(t,y) =&V(t,x)+\nabla_x V(t,x)\cdot(y-x)+\mathcal{V}_M(t,x,y). \end{align} Let $x(s;t_0,x,\xi)$ and $\xi(s;t_0,x,\xi)$ be solutions of $\eqref{h-eq}$. Then we have by the method of characteristic curve \begin{align}\label{rep-by-wpt} &W_{\varphi(t)}u(t,x(t;t_0,x,\xi),\xi(t;t_0,x,\xi))\\ \nonumber&=e^{i\int_0^tf(s)ds}W_{\varphi_0}u(0,x(0;t_0,x,\xi),\xi(0;t_0,x,\xi))\\ \nonumber&\hspace{3cm}-i\dint_0^te^{i\int_s^tf(\theta)d\theta}Ru(s,x(s;t_0,x,\xi),\xi(s;t_0,x,\xi);\varphi_0)ds \end{align} Substituting $\varphi_\lambda(-t_0)$ and $\lambda\xi$ for $\varphi_0$ and $\xi$ in (\ref{rep-by-wpt}), we obtain the following representation of solution to (\ref{CP1}). \begin{align}\label{wpt of CP1} &W_{\varphi_\lambda(t-t_0)}u(t,x(t;t_0,x,\lambda\xi),\xi(t;t_0,x,\lambda\xi))\\ \nonumber&=e^{i\int_0^tf(s)ds}W_{\varphi_\lambda(-t_0)}u(0,x(0;t_0,x,\lambda\xi),\xi(0;t_0,x,\lambda\xi))\\ \nonumber&\hspace{3cm}-i\dint_0^te^{i\int_s^tf(\theta)d\theta}R u(s,x(s;t_0,x,\lambda\xi),\xi(s;t_0,x,\lambda\xi);\varphi_\lambda(-t_0))ds. \end{align} In order to complete the proof, we use the following proposition. \begin{Prop}[\cite{KKI}] Let $u_0\in L^2(\mathbb{R}^n)$, $\varphi_0=e^{-\|x\|^2/2}$ and $\varphi_\lambda(t)$ be satisfying $\eqref{w-l}$. Then $(x_0,\xi_0)\notin WF(u_0)$ if and only if there exist a neighborhood $K$ of $x_0$ and a conic neighborhood $\Gamma$ of $\xi_0$ such that for all $N\in\mathbb{N}$, $a\geq1$ and $\varphi_0\in \mathcal{S}(\mathbb{R}^n)\setminus\{0\}$, there exists $C_{N,a,\varphi_0}>0$ satisfying \begin{align* \|W_{\varphi_{\lambda}}u_0 (x, \lambda\xi)\|\leq C_{N,a,\varphi_0}\lambda^{-N} \end{align} for $\lambda\geq1$ and $(x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$. \end{Prop} We show only sufficiency. The other case can be shown in the same way. We fix $a\geq1$. Let $K$ be a neighborhood of $x_0$ and $\Gamma$ be a conicneighborhood of $\xi_0$ satisfying (\ref{m-th}) for $t=t_0,\ \lambda\geq1,\ (x,\xi)\in K\times\Gamma$\ with\ $a^{-1}\leq\|\xi\|\leq a$. Then we show the following claim\ $P(N,\varphi_0)$:\\ "There exists a constant $C_{N,a,\varphi_0}>0$ such that \begin{align} \label{ind-1} \|W_{\varphi_\lambda(t-t_0)}u(t,x(t;t_0,x,\lambda\xi),\xi(t;t_0,x,\lambda\xi))\|\leq C_{N,a,\varphi} \lambda^{-N/2} \end{align} for $\lambda\geq1,\ (x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$, $0\leq t\leq t_0$". We show that claim\ $P(N,\varphi_0)$ holds for all $N\in\mathbb{N}\cup\{0\}$ and $\varphi_0\in \mathcal{S}(\mathbb{R}^n)\setminus\{0\}$ by induction with respect to $N$. First, we show $P(0,\varphi_0)$. For fixed $\varphi_0\in\mathcal{S}(\mathbb{R}^n)\setminus\{0\}$, we have \begin{align} &\|W_{\varphi_{\lambda}(t-t_0)}u(t, x(t; t_0, x, \lambda\xi), \xi(t; t_0, x, \lambda\xi))\|\\ &\leq\dint\|\varphi_\lambda(t-t_0, y-x)\|\|u(t,y)\|dy\\ &\leq\\|\varphi_\lambda(t-t_0,\cdot)\\|_{L^2}\\|u(t,\cdot)\\|_{L^2}\\ &=\\|\varphi_0\\|_{L^2}\\|u_0\\|_{L^2}. \end{align} Hence, $P(0,\varphi_0)$ holds $N=0$ for all $\varphi_0\in\mathcal{S}(\mathbb{R}^n)\setminus\{0\}$. Next, we fix $\varphi_0\in \mathcal{S}(\mathbb{R}^n)\setminus\{0\}$. We show $P(N+1, \varphi_0)$ assuming $P(N, \varphi_0)$ for all $\varphi_0\in \mathcal{S}(\mathbb{R}^n)\setminus\{0\}$. Then it suffices to prove the following statement:\\ ``There exists a constant $C_{N,a,\varphi_0}>0$\ such that $$\|Ru(s, x(s; t_0, x, \lambda\xi), \xi(s; t_0, x, \lambda\xi);\varphi_\lambda(-t))\|\leq C_{N,a,\varphi_0}\lambda^{-(N+1)/2}$$ for $\lambda\geq1,\ (x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a,\ 0\leq s\leq t_0$,'' since the first term of the right hand side of $\eqref{wpt of CP1}$ is estimated by $\lambda^{-(N+1)/2}$ because of the condition of $u_0$. We classify the term of $Ru$ as follows: \begin{align} R_1(t,x,\xi;\varphi_0)=\frac12\sum_{j,k=1}^n\Bigg[&(a_{j,k}(t,x)-\delta_{j,k})W_{\varphi^{e_{j,k}}(t)}u(t,x,\xi) -i\partial_{x_k}a_{j,k}\xi_jW_{\varphi(t)}u(t,x,\xi)\\ &-2i\sum_{l=1}^n\partial_{x_l}a_{j,k}(t,x)\xi_jW_{e^{it\Delta/2}(x_{l}\partial_{x_k}\varphi_0)}u(t,x,\xi)\\ &+\sum_{\|\alpha\|=2}\partial_{x}^\alpha a_{j,k}(t,x)\xi_j\xi_kW_{e^{it\Delta/2}(x^\alpha\varphi_0)}u(t,x,\xi)\Bigg] \end{align} and \begin{align} R_2(t,x,\xi;\varphi_0)&=Ru(t,x,\xi;\varphi_0)-R_1(t,x,\xi;\varphi_0). \end{align} $R_2(t,x,\lambda\xi;\varphi_\lambda(-t))$ can be estimated in the same way in \cite{KaI} by using the equality \begin{align x^\beta\partial_x^\alpha(\varphi_\lambda(t,x)) =\lambda^{\|\alpha\|/2}((\lambda^{-1/2}x+it\lambda^{1/2}\nabla)^\beta(\partial_x^{\alpha}\varphi_0))_{\lambda}(t,x,\xi), \end{align} where $(x_j\varphi_0)_{\lambda}(t,x)$ and $(\partial_{x_j}\varphi_0)_{\lambda}(t,x)$ are denoted by $\eqref{w-l}$ with $\varphi_0\rightarrow x_j\varphi_0$ and $\varphi_0\rightarrow \partial_{x_j}\varphi_0$ for $j=1,\ldots,n$, respectively. Next, we shall estimate $R_1(t,x,\lambda\xi;\varphi_\lambda(-t))$. By Proposition \ref{c-o-prop}, we have $\|\nabla_x a_{j,k}(s,x(s))\|\leq C(1+\lambda\|s-t_0\|)^{-\rho-1}$ and $\|\xi_j(s)\|\leq C\lambda$ for large $\lambda$ and $j,k=1,\ldots,n$, which yields that \begin{align} &\Big\|\dint_0^t \partial_{x_l} a_{j,k}(s,x(s)) \xi_j(s)W_{(y_l\partial_{y_k}\varphi)_\lambda(s-t_0)}u(s,x(s;t_0,x,\lambda\xi),\xi(s;t_0,x,\lambda\xi))ds\Big\|\\ &\leq C\lambda\dint_0^\infty (1+\lambda\|s-t_0\|)^{-\rho-1} ds\times \displaystyle \sup_{\substack{0\leq t\leq t_0,x\in K,\\ \xi\in\Gamma,a^{-1}\leq\|\xi\|\leq a}} \|W_{(y_l\partial_{y_k}\varphi)_\lambda(t-t_0)}u(s,x(t),\xi(t))\|\\ &\leq C\displaystyle \sup_{t,x,\xi} \|W_{(y_l\partial_{y_k}\varphi)_\lambda(t-t_0)}u(s,x(t),\xi(t))\| \end{align} for $l=1,\ldots,n$. Let $b>0$ be fixed, take $\kappa$ and $m$ satisfying $(\rho-1)^{-1}<\kappa<m-1$ and define $\Phi(t)$ as follows: \begin{align}\label{def-ph} \Phi(t)=\Phi(t;\lambda,x,\xi)\equiv\displaystyle\sum_{l=0}^\infty\frac{{C_m(t)}^{l+1}}{l!}\sum_{\|\alpha+\beta\|=2l}\Big\langle W_{e^{\frac{i}{2}t\Delta}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x, \xi)\Big\rangle_{N,\lambda}, \end{align} where $\langle\cdot\rangle_{N,\lambda}=\sqrt{\lambda^{-Nb}+\|\cdot\|^2}$ and $C_m(t)=e^{\kappa(1+\lambda t)^{-\rho+1}-m}$. If $\varphi_0(x)=\sum_{\gamma}C_{\gamma}x^{\gamma}e^{-\|x\|^2}$, the above sum converges absolutely and uniformly with respect to $t$. Indeed, for $\varphi_0=e^{-\|x\|^2}$, we get $\|x^\alpha\partial_x^\beta\varphi_0\|\leq 2^{2l}\max\{1,\|x\|^{2l}\}\varphi_0\leq2^{2l}(l+1)!(1+x^2)^{-1}$ for any $\alpha,\, \beta\in \mathbb{Z}_+^n$ with $\|\alpha+\beta\|=2l$ by the inequality $e^{x^2}\geq (1+x^{2l+2})/(l+1)!$. Thus there exists the positive constant $M$ independent of $l$ such that $\langle W_{e^{\frac{i}{2}t\Delta}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x, \xi)\rangle_{N,\lambda}\leq M2^{l}(l+1)!$, which implies the convergence of the above sum for large $\lambda$. The case for general $\varphi_0$ can be proven similarly. For $l\in\mathbb{N}\cup\{0\}$ and $\alpha, \beta\in \mathbb{Z}_+^n$ with $\|\alpha+\beta\|=2l$, the inequality $$\|W_{e^{it\Delta/2}(y^\alpha\partial_y^\beta\varphi_0)_\lambda} u(t, x(t), \xi(t))\|\leq C\Phi(t;\lambda,x(t),\xi(t))$$ holds for any $t\in[0,t_0]$ and $(x,\xi)\in K\times\Gamma$ with $a^{-1}\leq\|\xi\|\leq a$, where $C$ depends only on $n$, $t_0>0$, $M$ and $N$. Thus it suffices to estimate $\Phi(t)$. Since $(d/dt)\langle z(t)\rangle\leq\|(d/dt)z(t)\|$ holds for complex-valued function $z(t)$, we have \begin{align} \displaystyle\frac{d}{dt}\Big\langle W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}&u(t, x(t), \xi(t))\Big\rangle_{N,\lambda} =\frac{d}{dt}\Big\langle e^{i\int_0^tf(s)ds}W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x(t), \xi(t))\Big\rangle_{N,\lambda}\\ &\leq\left\|\frac{d}{dt}(e^{i\int_0^tf(s)ds}W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x(t), \xi(t)))\right\|\\ &=\left\|e^{i\int_0^tf(s)ds}\Big(i\partial_t+ix(t)\cdot\nabla_x+i\xi(t)\cdot\nabla_\xi +f(t,x,\xi)\Big)W_{\varphi(t)}u(t, x, \xi) )\right\|\\ &=\|Ru(t, x(t), \xi(t))\|, \end{align} which and the equality that \begin{align} \Phi^{'}(t) &=\displaystyle\sum_{l=0}^\infty\frac{(l+1){C_m(t)}^{l}C'_m(t)}{l!}\sum_{\|\alpha+\beta\|=2l}\Big\langle W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x(t), \xi(t))\Big\rangle_{N,\lambda}\\ &+\displaystyle\sum_{l=0}^\infty\frac{{C_m(t)}^{l+1}}{l!}\sum_{\|\alpha+\beta\|=2l}\frac{d}{dt}\Big\langle W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x(t), \xi(t))\Big\rangle_{N,\lambda} \end{align} yield that \begin{align} \Phi'(t)&\leq\displaystyle\sum_{l=0}^\infty\frac{(l+1){C_m(t)}^{l}C'_m(t)}{l!}\sum_{\|\alpha+\beta\|=2l}\Big\langle W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x(t), \xi(t))\Big\rangle_{N,\lambda}\\ &+\displaystyle\sum_{l=0}^\infty\frac{{C_m(t)}^{l+1}}{l!}\sum_{\|\alpha+\beta\|=2l}\|Ru(t, x(t), \xi(t))\|\\ &\leq \lambda\kappa (1+\lambda t)^{-\rho}(1-\rho)\sum_{l=0}^\infty\frac{(l+1){C_m(t)}^{l}C_m(t)}{(l+1)!}\sum_{\|\alpha+\beta\|=2l}\Big\langle W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x(t), \xi(t))\Big\rangle_{N,\lambda}\\ &+\Big(C\lambda(1+\lambda t)^{-\rho}\sum_{l=0}^\infty\frac{{C_m(t)}^{l}}{l!}\sum_{\|\alpha+\beta\|=2l}\Big\langle W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x(t), \xi(t))\Big\rangle_{N,\lambda}\Big)+C\lambda^{-(N+1)/2}\\ &=C(1-(\rho-1)\kappa)\frac{\lambda}{(1+\lambda t)^{\rho}}\sum_{l=0}^\infty\frac{{C_m(t)}^{l}}{l!}\sum_{\|\alpha+\beta\|=2l}\Big\langle W_{e^{it\Delta/2}(x^\alpha\partial_x^\beta\varphi_0)_\lambda}u(t, x(t), \xi(t))\Big\rangle_{N,\lambda}\\ &+C\lambda^{-(N+1)/2}\\ \end{align} The choice of $\kappa$ implies that $\Phi'(t)\leq C\lambda^{-(N+1)/2}$. Hence, we have $\Phi(t)\leq \Phi(0)+tC^{'}\lambda^{-(N+1)/2}\leq \Phi(0)+t_0 C^{'}\lambda^{-(N+1)/2}$. In particular, we have $\Phi(0)\leq C\lambda^{-(N+1)/2}$. The other terms in $R_1(t,x,\lambda\xi;\varphi_\lambda(-t))$ can be estimated similarly. Therefore, we complete the proof of Theorem \ref{main-theorem}. \section{Proof of Collorary \ref{Cor2}} In this section, we give a proof of Collorary \ref{Cor2}. The differences between $x(0;t,x,\lambda\xi)$ and $x-t\lambda\xi$ between and $\xi(0;t,x,\lambda\xi)$ and $\lambda\xi$ is small for large $\lambda$. Using this property, we prove Collorary \ref{Cor2}. \begin{proof}[Proof of Corollary \ref{Cor2}] In order to complete the proof, it suffices to prove that for any neighborhood $K_0$ of $x_0$ and conic neighborhood $\Gamma_0$ of $\xi_0$, there exist neighborhoods ${K}_1$, ${K}_2$ of $x_0$ and conic neighborhoods ${\Gamma}_1$, ${\Gamma}_2$ of $\xi_0$ such that for large $\lambda$ \begin{align} \label{subs} \left\{(x-t\lambda\xi,\lambda\xi)\,\middle\|\,(x,\xi)\in{K}_1\times{\Gamma}_1\right\} \subset \left\{(x(0;t,x,\lambda\xi),\xi(0;t,x,\lambda\xi))\,\middle\|\,(x,\xi)\in{K}_0\times{\Gamma}_0\right\} \end{align} and \begin{align} \label{sups} \left\{(x(0;t,x,\lambda\xi),\xi(0;t,x,\lambda\xi))\,\middle\|\,(x,\xi)\in{K}_2\times{\Gamma}_2\right\} \subset \left\{(x-t\lambda\xi,\lambda\xi)\,\middle\|\,(x,\xi)\in{K}_0\times{\Gamma}_0\right\}. \end{align} Indeed, $\eqref{subs}$ implies \begin{align} \label{subs1} \sup_{(x,\xi)\in V_1}\|W_{\varphi_{\lambda}{(-t)}}u_0 (x-t\lambda\xi,\lambda\xi)\| \leq\sup_{(x,\xi)\in V_0}\|W_{\varphi_{\lambda}{(-t)}}u_0 (x(0,t,x,\lambda\xi), \xi(0,t,x,\lambda\xi))\| \end{align} and $\eqref{sups}$ implies \begin{align} \label{sups1} \sup_{(x,\xi)\in V_2}\|W_{\varphi_{\lambda}{(-t)}}u_0 (x(0,t,x,\lambda\xi),\xi(0,t,x,\lambda\xi))\| \leq\sup_{(x,\xi)\in V_0}\|W_{\varphi_{\lambda}{(-t)}}u_0 (x-t\lambda\xi, \lambda\xi)\|, \end{align} which yields that Collorary \ref{Cor2} follows from Theorem \ref{main-theorem}, where $V_j=\{(x,\xi)\|x\in K_j,\xi\in \Gamma_j,a^{-1}\leq\|\xi\|\leq a\}$ for $j=0,1,2$. Without loss of generality, we have $K_0=B_r(x_0)$ and $\Gamma_0=\{\xi\in\mathbb{R}^n\,\|\,(\xi\cdot\xi_0)/\|\xi\|\|\xi_0\|>1-\gamma\}$ for some $r>0$ and $0<\gamma<1$. We shall only prove $\eqref{subs}$ since $\eqref{sups}$ can be proven similarly. Then there exists $\lambda_1\geq1$ such that \begin{align} \delta_1(\lambda)\equiv\|x(0;t,x,\lambda\xi)-(x-t\lambda\xi)\|\leq r/2 \end{align} and \begin{align} \delta_2(\lambda)\equiv\|\xi(0;t,x,\lambda\xi)-\lambda\xi\|\leq \|\xi_0\|\sqrt{\gamma/2} \end{align*} for any $(x,\xi)\in V_0$ and $\lambda\geq\lambda_1$, since $\delta_1(\lambda),\delta_2(\lambda)=\mathcal{O}(\lambda^{-\rho+1})$ by Lemma \ref{c-l-2}. Taking $K_1=B_{r/2}(x_0)$ and $\Gamma_1=\{\xi\in\mathbb{R}^n\,\|\,\|\xi\cdot\xi_0\|/\|\xi\|\|\xi_0\|>\sqrt{(2-\gamma)/2}\}$, we have \begin{align} \label{subs2} \left\{(x-t\lambda\xi,\lambda\xi)\,\middle\|\,(x,\xi)\in{K}_1\times{\Gamma}_1\right\} \subset \left\{(x+\delta_1(\lambda),\xi+\delta_2(\lambda))\,\middle\|\,(x,\xi)\in{K}_0\times{\Gamma}_0\right\} \end{align} for $\lambda\geq\lambda_1$. Since $\Gamma_1\subset \Gamma_0$, $\eqref{subs2}$ shows $\eqref{subs}$. \end{proof}	{ "redpajama_set_name": "RedPajamaArXiv" }	850
Perelandra sau Voyage to Venus este un roman științifico-fantastic din 1943 scris de C. S. Lewis, al doilea din The Space Trilogy (Trilogia Spațiului) Cosmic Trilogy sau Ransom Trilogy, care mai conține romanele Out of the Silent Planet (1938) și That Hideous Strength (1945) . Trilogia a fost inspirată și influențată de romanul lui David Lindsay din 1920, A Voyage to Arcturus. În cel de-al doilea volum din serie, Elwin Ransom, un filolog, erou modelat după trăsăturile lui J. R. R. Tolkien, călătorește spre planeta Venus în care primii humanoizi abia au apărut. Iată o lume neatinsă de păcatul originiar. Note Legături externe Quotations & Allusions in Perelandra Perelandra the Opera Donald Swann's opera, based on Lewis' book Vezi și 1943 în științifico-fantastic Opere de C. S. Lewis Romane științifico-fantastice Romane din 1943 Cărți din 1943 The Space Trilogy 1943 în științifico-fantastic	{ "redpajama_set_name": "RedPajamaWikipedia" }	1,183
{"url":"https:\/\/math.stackexchange.com\/questions\/3015653\/group-actions-and-orbits","text":"# Group actions and orbits\n\nLet $$X=\\{\\{1,2\\},\\{1,3\\},\\{1,4\\},\\{2,3\\},\\{2,4\\},\\{3,4\\}\\}$$ and $$G=S_4$$\n\n(a) Show that $$\\phi \\{x_1,x_2\\}=\\{\\phi (x_1),\\phi (x_2)\\}$$ determines an action of $$S_4$$ on $$X$$, where $$\\phi \\in G$$\n\n(b) Determine the number of orbits of this action.\n\n(a) I\u2019m not really sure how to explain this but it comes as an intuitive action that if you act $$\\phi$$ on $$x_1$$, it is just mapping $$x_1$$ to $$\\phi (x_1)$$, which essentially is just mapping 1 to $$\\phi (1)$$. But I\u2019m not sure how to present this formally.\n\n(b) Any hints on how I can do this? I\u2019m not sure if I should write out all 24 elements in $$S_4$$ and use Burnside\u2019s Theorem to find the number of orbits. But if I do so it might be too tedious. What happens when the it becomes larger? i.e $$S_5$$ acting on $$X$$; I don\u2019t think I can write out all 120 elements.\n\nWondering if anyone can help with this?\n\n\u2022 What are $x_1$ and $x_2$ denoting? I guess they range over $\\{1,2,3,4\\}$. \u2013\u00a0Berci Nov 27 '18 at 11:10\n\u2022 @Berci Yes. OP is acting on a graph. \u2013\u00a0Pedro Tamaroff Nov 27 '18 at 11:16\n\u2022 If we take $g=(1,2) \\in S_4$ then $g$ reverses the co-ordinates of each member of $X$ (I am assuming that the members of $X$ are ordered tuples rather than unordered sets). But $\\{2,1\\}, \\{3,1\\}$ etc, are not in $X$. So I am puzzled as to how the operation specified is an action on $X$ if $X$ only consists of the six points listed. Am I missing something ? \u2013\u00a0gandalf61 Nov 27 '18 at 11:20\n\u2022 @gandalf61 Yes it\u2019s supposed to be an unordered set \u2013\u00a0Icycarus Nov 27 '18 at 11:34\n\u2022 @Icycarus But in that case each member of $G$ simply maps each member of $X$ to itself, so this is a very uninteresting action ! Is it possible that the operation that is intended is $\\phi\\{x_1,x_2\\} = \\{\\phi(x_1), \\phi(x_2)\\}$ ? \u2013\u00a0gandalf61 Nov 27 '18 at 11:51\n\na) Note that $$X$$ contains all 2 elements subsets of $$\\{1,2,3,4\\}$$, so $$X$$ is indeed closed under the given map and that map satisfies the condition of being a group action.\n\nb) Start with an element of $$X$$ and find its orbit. If there's any element left off, find its orbit too, and so on..\n\na) To formally show that $$\\phi\\{x_1,x_2\\}=\\{\\phi(x_1),\\phi(x_2)\\}$$ is an action, you need to show two things:\n\n1) $$e\\{x_1,x_2\\}=\\{x_1,x_2\\} \\space \\forall \\{x_1,x_2\\} \\in X$$ where $$e$$ is the identity in $$G$$.\n\n2) $$\\phi_1(\\phi_2\\{x_1,x_2\\}) = (\\phi_1 \\phi_2)\\{x_1,x_2\\} \\space \\forall \\{x_1,x_2\\} \\in X \\space \\forall \\phi_1, \\phi_2 \\in G$$\n\nThese are both straightforward.\n\nb) Given two elements of $$X$$, think about how you can find a member of $$G$$ that maps one to the other (in fact, there is more than one as user25959 hints at above). This shows that $$G$$ acts transitively on $$X$$, so there is only one orbit.\n\n\u2022 i) the identity element is (1)(2)(3)(4) so applying $e\\{x_1,x_2\\}=\\{x_1,x_2\\}$ so it\u2019s straightforward. How about (ii)? How do we go about showing it? \u2013\u00a0Icycarus Nov 27 '18 at 20:17\n\u2022 @Icycarus For (ii) here is an example. To find a permutation in $g \\in G$ that maps $\\{1.2\\}$ to $\\{3,4\\}$, you could start by requiring $g$ to map $1$ to $3$ and $2$ to $4$. Now $3$ can either map to $1$, which gives $g=(13)(24)$, or $3$ can map to $2$ which gives $g=(1324)$. Note that $3$ cannot map to $4$ because $2$ already maps to $4$. Alternatively, you can require $g$ to map $1$ to $4$ and $2$ to $3$, which gives $g=(14)(23)$ or $g=(1423)$. So there are four possibilities for $g$. \u2013\u00a0gandalf61 Nov 28 '18 at 8:54\n\nThe stabilizer of $$\\{i,j\\}$$ consists of the permutations $$e, (ij), (kl)$$, and $$(ij)(kl)$$ where $$k,l$$ are the \"other two\" elements of $$\\{1,2,3,4\\}$$. So by the orbit-stabilizer theorem, $$\|Orb_{\\{i,j\\}}\|\\cdot 4 = \|S_4\|= 24$$.","date":"2019-10-16 14:02:57","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\": 33, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8679666519165039, \"perplexity\": 136.16333862712878}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570986668994.39\/warc\/CC-MAIN-20191016135759-20191016163259-00178.warc.gz\"}"}	null	null
Q: What are the viable non-anthropic explanations for the tininess of the cosmological constant? The cosmological constant is 10-120 times its natural value, but it is yet nonzero. Even TeV-scale supersymmetry breaking can't save it. The renormalization group would seem to imply it ought to be at the Planck scale, assuming naturalness, and no fine-tuning. The anthropic principle explains the size of the cosmological constant nicely, but are there any other explanations? Dynamical mechanisms run into problems with the renormalization group. The mechanism has to act in the infrared, but any ultraviolet definition will be modified by the renormalization group. A: At this moment, there are no widely known explanations that are as "ready to be used" as the anthropic would-be explanation. There are of course vague ideas how the problem could be solved but no full framework how to incorporate particle physics and predict a tiny C.C. has been proposed. The partial proposals include: The supersymmetric cancellations Low-scale supersymmetry reduces the natural prediction of the C.C. from $O(1)$ to $O(10^{-60})$ in Planck units which seems progress but it's still very far from the required $O(10^{-123})$. Despite the fact that SUSY seems to "solve" one half of the problem on the log scale, in some sense, it makes the problem qualitatively worse because one can be "more certain" than the $O(10^{-60})$ piece which is still way too large survives. No-scale supergravity is a framework to guarantee that the leading term to the cosmological constant cancels. In general, spontaneously broken supersymmetry hasn't been able to explain the smallness of the C.C. Mirror matter There are various highly speculative articles suggesting that there exists a "mirror world" whose zero-point energies cancel against those in our world. Such worlds are probably unstable and suffer from many other problems. Link to the neutrino masses The C.C. expressed as a vacuum energy density is comparable to the fourth power of the neutrino masses and the neutrinos are the lightest massive particles we know. It could be that there is something wrong about the ways how we apply - or fail to apply - the Renormalization Group on the running of the C.C. It may be that there is some mechanism that makes a theory inconsistent if the C.C. at the neutrino scale - which is also the C.C. at zero energies - is much larger than the neutrino scale. Seesaw mechanisms It just happens that the C.C. is approximately $m_{TeV}^8 / m_{Planck}^4$, which is linked to the formula for the neutrino masses. So on the log scale, the C.C. is on the opposite side from the natural TeV-scale energy density (e.g. predicted by broken SUSY) than the Planck density on the other side. There exist highly speculative proposals how to derive this seesaw formula from a deeper mechanism, for example, from some mixing between different vacua, tunneling, and so on. Others and appraisal There also exist various papers on self-adjusting cosmological constants that don't work, as far as I know. If one looks at what is known, it's fair to say that the anthropic explanation of the C.C. is the only available game in town. However, in this particular case, it's totally plausible that a much better explanation will be found in the future. In this case, there's no real evidence that all the alternative explanations have been mapped or ruled out.	{ "redpajama_set_name": "RedPajamaStackExchange" }	5,798
\section{Introduction} As cars get more intelligent and their functionalities develop exponentially, the need for a natural form of interaction increases. There are several advantages to using hand gestures, eye gaze, head movements and speech over traditional touch-based interaction methods, such as increased simplicity and naturalness when interacting with a relatively complicated machine like a modern car, in addition to a reduction in distraction during the primary task (i.e. driving)~\cite{pickering2007research,Garber2013,feld2016combine,Roider2017}. Thus, researchers have tried to incorporate these modalities to control various components inside the vehicle~\cite{molchanov2015hand, molchanov2015multi, ohn2014hand,zobl2003real,roider2018see,sezgin2009multimodal}. Furthermore, the advances in gesture recognition and computer vision domains allow for real-time interaction with the car's surrounding environment, especially for referencing landmarks and buildings outside the vehicle using hand pointing and eye gaze gestures~\cite{rumelin2013free,fujimura2013driver,kang2015you}. Despite these major advances and their application in the automotive domain, existing methods often rely on single modality solutions~\cite{vora2017generalizing,vasli2016driver,ohn2014hand} or only partially use the second modality (i.e. as a control channel only)~\cite{nickel20043d,poitschke2011gaze}, which is insufficient for accurate referencing. Although the use of multimodal fusion could outperform single modality approaches, fusion still suffers from multiple challenges~\cite{baltruvsaitis2018multimodal,atrey2010multimodal} such as representation (e.g. exploiting complementarity and redundancy), alignment (e.g. time synchronization), translation (e.g. transforming coordinate systems) and co-learning (e.g. knowledge transfer) which are addressed within our approach. There have been several attempts for modality fusion between eye gaze and symbolic hand gestures. However, to the best of our knowledge, neither multimodal referencing of objects outside a moving vehicle using eye gaze and deictic pointing gestures nor the interaction between them has been studied before. Besides, since pointing and gaze behaviour when referencing objects differ greatly among users~\cite{brown2016exploring,nickel20043d}, a global solution which fits all users is not feasible~\cite{brown2014performance} and a person-specific approach would perform better. This paper makes the following contributions: In a medium fidelity driving simulation, we investigated the multimodal behaviour for the secondary task of referencing objects outside a moving vehicle. Through a quantitative and qualitative analysis, we studied pointing and gazing differences in behaviour when performing this secondary task under several conditions (e.g. when the object was near or far from the driver). Furthermore, we analysed individual differences among users to increase understanding of personal pointing and gazing behaviour. Finally, our approach better adheres to the dynamic and safety aspects of the driving process, as it is tested with a long driving scenario. \section{Related Work} Pointing and eye gaze gestures have been studied rigorously in multiple applications. Nickel et al.~\cite{nickel20043d} laid the foundation for pointing gestures in a human-robot interaction environment, Jing et al.~\cite{jing2013human} used pointing gestures in selecting objects on large displays and Kehl et al.~\cite{kehl2004real} studied pointing using both arms. Similarly, Vidal et al.~\cite{vidal2012detection,vidal2013pursuits} studied eye gaze interaction with moving targets on a large display, while Cheng et al.~\cite{cheng2018smooth} studied across devices eye gaze interaction. However, these methods studied pointing and eye gaze in a stationary, standing environment that is not applicable in a driving scenario. Furthermore, Roider et al.~\cite{Roider2017} and Nesselrath et al.~\cite{feld2016combine} studied the selection of objects inside the vehicle using hand gestures, eye gaze or speech commands separately. Similarly, Poitschke et al.~\cite{poitschke2011gaze} studied referencing objects inside the vehicle using eye gaze gestures while Sezgin et al.~\cite{sezgin2009multimodal} studied selection using speech commands and facial recognition. Recently, Roider et al.~\cite{roider2018see} also assessed the combination of pointing and passive eye gaze to reference objects inside the vehicle. However, the use cases of these approaches were simple two-to four-object classification ones that are hard to extend to a generic outside-the-vehicle referencing approach like the one presented in this work. Moreover, referencing objects outside the vehicle has been investigated using different approaches and modalities. Rümelin et al.~\cite{rumelin2013free} used free-hand pointing gestures, Fujimura et al.~\cite{fujimura2013driver} used hand-constrained pointing gestures, Kang et al.~\cite{kang2015you} used eye gaze gestures, while Kim et al.~\cite{kim2014identification} and Misu et al.\cite{misu2014situated} used speech-triggered head pose trajectories. However, these studies focused on single-modality approaches that were lacking in performance. For example, eye gaze suffered from the Midas touch problem and sporadic involuntary eye movements that hindered accurate tracking~\cite{young1975survey,rayner2009eye,land2009looking,Moniri_2018} while pointing gestures suffered from performance inconsistency among users~\cite{brown2016exploring,brown2014performance,nickel20043d}. Although these studies are not directly comparable with our approach due to previously mentioned differences, they still presented insights into differences in pointing and gazing behaviour among users that were used in our analysis. For example, Rümelin et al.~\cite{rumelin2013free} and Nickel et al.~\cite{nickel20043d} reported an average pointing time of 1.8 seconds. Furthermore, Rümelin et al. defined three phases for driver's gazing (i.e. glancing) behaviour during this pointing time as follows: \begin{itemize} \item \textbf{Information Glance:} Users look at the object to select \item \textbf{Pointing Position:} Users point at the object and quickly draw their eyes back to the road while keeping their hands pointed at the object \item \textbf{Control Glance:} Users look again at the object to maintain the pointing position; then the pointing gesture ends and they move their arms back \end{itemize} They also observed different behaviour for different users during the last control glance phase, wherein for 57\% of the gestures, users looked again (making two control glances) to further maintain the pointing position, while other users did not take the control glance at all in 8\% of the gestures. Moreover, they reported that free-hand pointing does not increase the cognitive load of the driver in terms of constant driving speed during gestures performance, which was later confirmed by Roider et al.~\cite{Roider2017} as well. In conclusion, previous multimodal referencing methods mostly focused on in-car interaction, unlike this work, which focuses on interaction with the environment outside the car. Additionally, both in-car and outside-the-car existing methods either focused on a stationary car scenario where performing the referencing gestures was the primary task, or they had a short driving route, unlike our approach, which focuses on driving as the primary task and performing the referencing gestures as the secondary task in a long driving route. \section{Method} A within-subject counterbalanced experiment was designed in a medium fidelity driving simulator~\cite{math2013opends}. We chose a driving simulator instead of a real car scenario for better control over the study and safety aspects. A driving simulator might have some influence on participant's behaviour in comparison to a real car scenario as it is a more relaxed environment. However, we hypothesize that drivers tend to reference objects outside a moving vehicle only in relaxed and easy driving situations (i.e. drivers prioritize the primary task of driving~\cite{rumelin2013free}). Therefore, a simulated driving scenario matches the real experience to a great extent for this task. \autoref{fig:implementationarchitecture} shows an architecture overview of the desired system. Users' pointing and gaze along with their driving route were tracked for the referencing task. Each of the data channels was processed separately to reach a common data format (i.e. common coordinate system) among them while synchronising their internal clocks. Finally, modalities' interactions were investigated and fusion approaches were attempted to identify the referenced objects. \begin{figure}[!t] \begin{center} \includegraphics[width=0.85\linewidth]{images/Implemntation_architecture_overview.pdf} \end{center} \caption{Overview of system architecture} \label{fig:implementationarchitecture} \end{figure} \subsection{Design and Procedure} \begin{table}[b] \centering \caption{Driving conditions} \resizebox{0.75\linewidth}{!}{\begin{tabular}{c c c c} \hline\hline Condition & Autonomous Driving & Distance & Density \\ \hline 1 & No & Near & Dense \\ 2 & No & Far & Dense \\ 3 & No & Near & Non-Dense \\ 4 & No & Far & Non-Dense \\ 5 & Yes & Far & Dense \\ \hline \end{tabular}} \label{table:conditions} \end{table} The experiment consisted of a driving task in a driving simulator. A pilot study was conducted before the main experiment to enhance the design and ensure feasibility. Each participant drove for 40 minutes on the right of a two-lane road with no traffic at a maximum speed of 60 km/hour while performing a secondary task of referencing (i.e. pointing and looking at) objects (i.e. buildings) which will be called \textit{Point Of Interest} (PoI) hereafter. Participants were informed which PoI they had to point at in real time by displaying the targets on a small tablet and signalled with an auditory cue. The driving route was designed as a star shape containing five corners (i.e. sections). To ensure that there is no confounding influence of the angled parts, target buildings and distractors were only presented while driving straight. Each corner of the star corresponded to different conditions with respect to environmental parameters and driving mode. The environmental parameters were the PoI distance from the road and number of distractors in the environment as seen in~\autoref{table:conditions}. The first and second condition had near and far PoIs respectively in a dense environment (i.e. many distractors around the PoI) while the environment was less dense in the third and fourth condition (i.e. few to no distractors around the PoI). The last condition was the same as the second in terms of density and distance, but the vehicle drove autonomously. An online \textit{pre-study} was conducted to determine the optimal values for distance and density levels. Another goal for the pre-study was to choose the visual appearance of the PoIs (i.e. their shape and color), to determine the salience of the PoI (i.e. target) against the distractor buildings. A medium-salient PoI is required to keep moderate discoverability, to avoid confounding factors \sugg{(i.e hard enough not to spot with peripheral view but easy enough to find it eventually)}. Seventeen participants (59\% male) with a mean age of 31.12 years (SD = 15.47) completed this online pre-study. Participants performed the referencing task 24 times per condition in a counterbalanced manner. Two-thirds of the PoIs were located on the right side of the road, since the hand tracking only captures right-handed pointing, which could affect pointing at left-oriented PoIs (i.e. PoIs located on the left side of the road). Between two consecutive PoI notifications, there was a time gap of 10 to 20 seconds, giving participants enough time for visual search and referencing while maintaining the primary driving task. The road had no traffic to accommodate this relatively small time gap. \subsection{Apparatus} \begin{figure}[t] \begin{center} \includegraphics[width=0.9\linewidth]{images/SetupOverview.pdf} \end{center} \caption{Driving simulator setup overview. The PoI notification tablet is highlighted in green, the hand pointing camera in red, the GoPro camera in yellow and a sample of the ArUco markers highlighted in blue.} \label{fig:setup2} \end{figure} The driving simulator (\autoref{fig:setup2}) was situated in an enclosed room to ensure minimum disturbance. It consisted of three 55-inch LCD screens with a steering wheel, pedals and two left and right speakers. ArUco~\cite{Aruco1,Aruco2} markers were attached to fixed known locations at the edges of the LCD screens which were used in eye gaze vector mapping. The PoI image was presented on a tablet next to the steering wheel and was preceded by a sound notification. The hand tracking camera and the experiment recording camera (a GoPro camera) were situated to the right of the participant. The hand tracking camera was a state-of-the-art non-commercial prototype especially designed for in-vehicle control. The eye gaze tracker used was a pair of \textit{SMI Eye Tracking Glasses}\footnote{\url{https://imotions.com/hardware/smi-eye-tracking-glasses/}}. \subsection{Participants} In total, 73 participants were recruited for the study. However, 34 participants were excluded for the following reasons: technical problems in pointing and gaze trackers such as severe frame drops and failure to save data (30 participants), premature termination due to motion sickness (2 participants) or improper task execution (2 participants). The data of the remaining 39 participants were manually verified to ensure correct synchronization with no technical problems. The remaining participants (46\% male) with a mean age of 25.87 years (SD = 6.26) completed the entire driving route while referencing objects using their right hand as instructed, to stay within the pointing tracker range. 83\% of the participants were right-handed. 14\% were left-handed and 3\% reported ambidexterity. \subsection{Coordinate System and Features Extraction} Each of the pointing and gaze tracking systems had their own coordinate systems which needed to be mapped to the simulation environment. We only considered horizontal angle in our approach, similar to Kang et al.~\cite{kang2015you}, as there is no overlap in the PoI vertical position. Thus, we used a 1D cylindrical coordinate system as a common coordinate system (see~\autoref{fig:implementationoverview}).~\autoref{fig:coordinatesystem} shows an example of the coordinate system at a given time instance where $\theta$ is the angle between the vehicle's centre line and the line connecting the vehicle with the PoI. It was considered as the ground truth (GT) angle which is calculated at all time frames. However, this GT angle was further relaxed with the addition of the PoI's angle span (i.e. the relative angle corresponding to building's width) since users could point at the edge of the PoI instead of the centre. ~\autoref{fig:preprocess_angle_extract} illustrates the process of mapping the tracking systems to the simulation system and extracting the 1D horizontal angles. \begin{figure}[b] \begin{center} \includegraphics[width=0.45\linewidth]{images/coordinate_system.pdf} \end{center} \caption{An example of the angular coordinate value at a given time instance.} \label{fig:coordinatesystem} \end{figure} \begin{figure}[t] \begin{center} \includegraphics[width=\linewidth]{images/Preprocessing_angles_extraction.pdf} \end{center} \caption{Overview of our approach showing the analysis process for each system and highlighting the input (raw data) and output (horizontal angles) formats.} \label{fig:preprocess_angle_extract} \end{figure} \paragraph{Ground Truth Preprocessing and Angle Extraction} For each time instance, the GT angle ($\theta$ in~\autoref{fig:coordinatesystem}) was calculated in multiple stages as seen in~\autoref{fig:preprocess_angle_extract}. First, the car's virtual 2D location and orientation along with the PoI's virtual 2D location were mapped into the world 3D Cartesian coordinate system through linear transformation. Next, the 3D coordinate system was transformed into a 1D cylindrical coordinate system where the horizontal ground truth was extracted with a 0.1 degree resolution. Since the user was allowed to point anywhere at the PoI building, the building width was added as a margin to the ground truth angle in further calculations. \sugg{The advantage of the previously mentioned approach is that it is only time-dependent and not speed-or distance-dependent, because it takes the car location information from each participant data file (and not from a hard-coded driving path which is usually the case for GT calculation). This allowed for a personalized analysis of the data, as each participant had his own GT based on his driving speed and behaviour.} \paragraph{Gaze Preprocessing and Angle Extraction} The gaze tracker outputs gaze pixel location inside the recorded surroundings. These 2D gaze pixel (x,y) coordinates were mapped to a reference coordinate system using translation transformation as seen in~\autoref{eqn:mapping}: \begin{equation} \label{eqn:mapping} \begin{split} (x,y)_{gaze\:new} & = (x,y)_{gaze\:image} \\- & [(x,y)_{ArUco\:image}-(x,y)_{ArUco\:reference}] \end{split} \end{equation} where $(x,y)_{gaze\:new}$ is the gaze coordinates in the new common coordinate system, $(x,y)_{gaze\:image}$ is the one calculated from the frames and $(x,y)_{ArUco\:image}$, $(x,y)_{ArUco\:reference}$ are the ArUco marker's coordinates calculated from the frames and set in the common coordinate system, respectively. The horizontal angle was calculated by linear transformation from x-coordinates (ranging from -1280 to 1280) to angle coordinates (ranging from -90 to 90). However, this linear transformation had a scale of one for the middle screen only (range from -45 to 45) and scale of half for the left and right screens (range from -90 to -45 and 45 to 90, respectively). This is due to the 45 degree inclination of the side screens (see ~\autoref{fig:implementationoverview}). The final horizontal angle was scaled per participant to adjust for different seating positions. Average x-coordinate difference between two predefined ArUco markers was calculated per participant and divided by the x-coordinate difference between the same two markers in the common coordinate system; then, the resultant was multiplied with the previously calculated horizontal angle as seen in~\autoref{eqn:mapping_scaling}: \begin{equation} \label{eqn:mapping_scaling} \theta_{new} = \theta_{old} * \frac{(x_{ArUco1} - x_{ArUco2})_{participant}}{(x_{ArUco1} - x_{ArUco2})_{reference}} \end{equation} The final gaze angle had a resolution of 0.01 degrees; however, there was an error margin of $\pm 3$ degrees due to rounding approximations. \paragraph{Pointing Preprocessing and Angle Extraction} For each time instance, the hand tracker gave the position of the fingertip and the vector of pointing in the 3D real world coordinate system referenced to the tracker position. The tracker also classified the hand gesture type (i.e. pointing, sliding right, sliding left, etc.). This classification was used to mask only pointing gestures and passed the fingertip position and the pointing vector as input to next stages (as seen in~\autoref{fig:preprocess_angle_extract}). To calculate the angle of pointing, the LCD screens' 3D planes were calculated with respect to the camera, then intersected with the pointing vector to get the intersection point coordinates in the 3D world Cartesian system with respect to the participants (instead of the camera). Similar to gaze and GT, the 3D Cartesian coordinates were transformed into 1D cylindrical coordinates and the final horizontal pointing angle was obtained. It had a resolution of 1 degree and an error margin of $\pm 4$ degrees. \subsection{Performance Metrics} To study the referencing behaviour systematically, a behavioural model was constructed from the related work and observations on our task of referencing predetermined PoIs while driving.~\autoref{fig:performancemeasurement} shows a simplified representation of this model for a right-oriented PoI. The predetermined PoIs appeared at a certain angle which slowly increased until the PoI disappeared to the far right. Participants gazed at it several times to compare it to the given image of the PoI and to confirm accurate referencing. Users pointed at the PoI only once as instructed. The same model represents left-oriented PoI but with negatively increasing angle values. Task performance was assessed by analysing the effect of several independent variables on multiple dependent ones which were used in related work for assessing multimodal gesture recognition systems. \subsubsection{Independent Variables (IVs)} The previously mentioned conditions are the main independent variable. They were further subdivided to several IVs based on distance, density and PoI orientation. Furthermore, the personalized behaviour of participants was considered among these conditions. \begin{figure}[b] \begin{center} \includegraphics[width=\linewidth]{images/Example_performance_calculations.pdf} \end{center} \caption{A representation of our behavioural model for pointing and gaze angles vs. the ground truth \textbf{for a single trigger} with (simplified) horizontal angle on the y-axis and time on the x-axis. Where $t_{1}$ and $t_{7}$ are the start and end times of the ground truth calculation (i.e. start of PoI target being displayed on the tablet). $t_{2}$ is the start time of the first gaze at the target PoI. $t_{3}$ and $t_{5}$ are the start and end times of the pointing gesture, respectively. $t_{4}$ is the start time of the first gaze that occurs after the start of the pointing gesture and $t_{6}$ is the start time of the first gaze that occurs after the end of the pointing gesture.} \label{fig:performancemeasurement} \end{figure} \subsubsection{Dependent Variables (DVs)} The dependent variables are divided into two main categories as follows. They were calculated as a mean value per independent variable. For example, pointing accuracy is calculated per participant, density, distance and PoI orientation for each participant. \paragraph{Performance-related DVs (i.e. Accuracy)} For each trigger, the pointing gesture was considered accurate if the pointing angle was in the range of the PoI angular width plus a fixed tolerance angle span of 10 degrees for 400 milliseconds or more~\cite{mcleod1987visual}. \textit{Pointing accuracy DV} was then calculated per independent variable by dividing the sum of \textit{accurate pointing} triggers by the sum of \textit{pointed at} triggers (as seen in~\autoref{eqn:pointingaccuracy}). For example, condition one for each participant contained 24 triggers; a participant only pointed at 21 triggers (due to losing focus or similar issues); if he accurately pointed at only 17 triggers, then the accuracy of pointing in condition one for this participant was 17 divided by 21. \begin{equation} \label{eqn:pointingaccuracy} (Pointing\_Accuracy)_{per\,IV} = (\frac{\sum Accurate\_Pointing}{\sum Pointing})_{per\,IV} \end{equation} Similarly, \textit{gaze accuracy DV} is calculated as the sum of \textit{accurate gaze} triggers divided by the sum of \textit{pointed at} triggers (as seen in~\autoref{eqn:gazeaccuracy}). However, \textit{accurate gaze} had an extra time condition where gaze should only be considered during the pointing time window with a tolerance of 500 milliseconds before and after (i.e. \textit{accurate gaze} is only considered in the time from $(t_{3} - 500ms)$ to $(t_{5} + 500ms)$ in~\autoref{fig:performancemeasurement}). \textit{Accurate gaze} is also considered if all previous conditions are met for 400 milliseconds or more~\cite{mcleod1987visual}. \begin{equation} \label{eqn:gazeaccuracy} (Gaze\_Accuracy)_{per\,IV} = (\frac{\sum Accurate\_Gaze}{\sum Pointing})_{per\,IV} \end{equation} \paragraph{Timing-related DVs} Four dependent variables were calculated from our model as follows: \begin{itemize} \item \textit{Detection Time} describes the time that passed between the presentation of the target building on the tablet and the time when the building was first gazed at (discovered) by the participant ($t_{2} - t_{1}$ in~\autoref{fig:performancemeasurement}). \item \textit{Pointing Time (Reaction Time)} describes the time interval between the presentation of the building on the tablet and the onset of the pointing gesture towards the PoI ($t_{3} - t_{1}$ in~\autoref{fig:performancemeasurement}). It could also be described as reaction time (i.e. the time it takes for the participant to react to a given PoI). \item \textit{Modality Delta Time (Action Time)} is the time interval between the onset of the gaze on the PoI and the onset of the pointing gesture ($t_{3} - t_{2}$ in~\autoref{fig:performancemeasurement}). This showed whether pointing gesture usually follows the gaze or vice versa and how much participants wait to start pointing. If the first gaze occurred after the pointing, this value would be negative. \item \textit{Confirmation Time} describes any confirmation gazes that the participant made back at the PoI to confirm if it had truly been the correct building ($t_{6} - t_{5}$ in~\autoref{fig:performancemeasurement}). \end{itemize} Additionally, dependent variables relating to duration and frequency of pointing and gaze gestures were calculated as follows: \begin{itemize} \item \textit{Pointing Duration} was calculated for each trigger ($t_{5} - t_{3}$ in~\autoref{fig:performancemeasurement}) and averaged per independent variable. \item \textit{Gaze Duration}: three aspects of gazing behaviour were identified in the analysis. During a visual inspection of the data and similar to~\cite{rumelin2013free}, it became apparent that gazes towards a PoI could be divided into three categories (as seen in green in~\autoref{fig:performancemeasurement}) as follows: \begin{enumerate} \item \textit{Gaze Begin} describes gazes towards the PoI before the pointing gesture. \item \textit{Gaze Middle} describes gazes towards the PoI during the pointing gesture. \item \textit{Gaze Confirmation} is identified as one or several gazes back towards the PoI, after the pointing has ended (possibly to confirm the correctness of the targeted PoI). \end{enumerate} \item \textit{Gaze Frequency}: Similarly, the frequency of occurrence of gaze was calculated separately for each gaze gesture type. As an example in~\autoref{fig:performancemeasurement}, \textit{Gaze Begin Frequency} is one, \textit{Gaze Middle Frequency} is two and \textit{Gaze Confirmation Frequency} is one as well. \end{itemize} \subsection{Auxiliary Hypotheses} Five auxiliary hypotheses were developed specifically for the performance metrics for interpretation based on literature findings. Better performance in these hypotheses means higher pointing and gaze accuracy and lower reaction time: \begin{itemize} \item \textbf{Hypothesis 1}: A high density of buildings in the scenery leads to a higher mental load, since there are more stimuli that require processing and comparison. Therefore, performance should be better in the non-dense condition. \item \textbf{Hypothesis 2}: A high distance between the target building and the road leads to lower detection performance. Therefore, performance should be better in the near condition. \item \textbf{Hypothesis 3}: Overall performance should be better in the autonomous driving than in the normal driving condition, since participants have to perform two tasks when driving normally, which is more difficult. \item \textbf{Hypothesis 4}: Performance should be better for targets on the right side of the road. There were more PoIs on the right side, which could lead to a higher learning effect. \item \textbf{Hypothesis 5}: During a multimodal referencing task, accuracy of gaze should be better than accuracy of pointing. \end{itemize} \section{Results} \begin{table}[b] \centering \caption{Descriptive statistics and Intraclass correlation result per DV} \resizebox{\linewidth}{!}{\begin{tabular}{c c c} \hline \hline Dependent Variable & Mean (Std Dev.) & ICC in percentage \\ \hline Pointing Accuracy & 68.97\% (17.15) & - \\ Gaze Accuracy & 83.48\% (10.22) & - \\ Detection Time & 1.81 sec. (0.48) & 3.5\% \\ Pointing Time & 3.69 sec. (2.58) & 53.7\% \\ Modality Delta Time & 1.91 sec. (2.54) & 38.4\% \\ Confirmation Time & 2.43 sec. (0.44) & 1.6\% \\ Pointing Duration & 1.88 sec. (1.09) & 41.5 \% \\ Total Gaze Duration & 5.04 sec. (0.72) & 4.7\% \\ Gaze Begin Duration & 1.83 sec. (0.99) & 21.7\% \\ Gaze Middle Duration & 0.67 sec. (0.41) & 12.7\% \\ Gaze Confirmation Duration & 2.54 sec. (0.72) & 7.8\% \\ \hline \end{tabular}} \label{table:descrstatistics} \end{table} The results section is divided into two main parts. The first part is the statistical analysis of the data, while the second part explains the results of several clustering approaches. \subsection{Statistical Results} In this section, results from the descriptive statistics, several intraclass correlation (ICC)~\cite{Johnson2011} analyses and inferential statistical analyses are described \subsubsection{Descriptive statistics} \autoref{table:descrstatistics} shows the means and standard deviations for all dependent variables. Average gaze accuracy was better than average pointing accuracy during the multimodal interaction. Average pointing time (3.69 seconds) was relatively short compared to the time gap (10 to 20 seconds) between two consecutive PoI appearance which suggests swift pointing behaviour. Further investigation shows that the average GT angle at the middle of the pointing frame was found to be $\pm 9.8$ degrees (i.e. 9.8 degrees on the right or the left) which confirms this finding. Moreover, average duration of gaze during pointing (0.67 seconds) was quite short compared to the average pointing duration (1.88 seconds) which suggests that participants don't keep their eyes on the PoI during the entire pointing interaction duration. \autoref{table:freqstatistics} shows the average frequency of gazes for the three defined gaze types per participant and sum frequency of gazes per trigger. \begin{table}[t] \centering \caption{Average gaze frequency percentage per participants and number of triggers for each gaze category} \setlength{\tabcolsep}{3pt} \renewcommand{\arraystretch}{1.25} \resizebox{\linewidth}{!}{\begin{tabular}{c\|cc\|cc\|cc} \hline\hline \multirow{2}{*}{Frequency~} & \multicolumn{2}{\|c}{Gaze Begin} & \multicolumn{2}{\|c}{Gaze Middle} & \multicolumn{2}{\|c}{Gaze Confirmation} \\ \cline{2-7} & \% Partic. & \% Trig. & \% Partic. & \% Trig. & \% Partic. & \% Trig. \\ \hline 0 & - & 25.2\% & 46.0\% & 52.1\% & - & 17.0\% \\ 1 & 56.8\% & 35.7\% & 51.3\% & 35.9\% & 13.5\% & 18.3\% \\ 2 & 27.0\% & 20.7\% & 2.7\% & 8.0\% & 27.0\% & 18.0\% \\ 3 & 13.5\% & 8.2\% & - & 2.4\% & 51.4\% & 16.7\% \\ 4 & 2.7\% & 4.9\% & - & 1.0\% & 8.1\% & 12.6\% \\ $\geq 5$ & - & 5.3\% & - & 0.6\% & - & 17.4\% \\ \hline \end{tabular}} \label{table:freqstatistics} \end{table} \subsubsection{Intraclass correlations results} \autoref{table:descrstatistics} also shows intraclass correlations (ICCs) for all timing-related dependent variables. The average ICC across all variables was 20.62\% which confirms the person-specific behaviour of participants during the referencing task~\cite{brown2016exploring,brown2014performance,rumelin2013free}. \subsubsection{Statistical inference} Several multivariate analyses of variance~\cite{smith1962multivariate} (MANOVA) were chosen for its suitability to assess the auxiliary hypotheses for multiple dependent variables. Statistical significance is compared against an alpha level of 5\% (i.e. p-value < 0.05). The statistical preconditions for a MANOVA were met. Performance was measured by \textit{pointing accuracy}, \textit{gaze accuracy} and \textit{pointing time} dependent variables. \paragraph{Distance and density} A 2x2 within-subject MANOVA was conducted to measure the effects of density and distance on the defined performance DVs. There was a significant effect in performance for density (Pillai trace=.72, F(3,32)=27.62, p<.001, $\eta_p^2$=.72). This difference is significant for all three performance variables (pointing accuracy: F(1,34)=34.94, p<.001, $\eta_p^2$=.51; gaze accuracy: F(1,34)=52.79, p<.001, $\eta_p^2$=.60; pointing time: F(1,34)=56.31, p<.001, $\eta_p^2$=.62). Pointing and gaze accuracy were higher and pointing time was faster for the non-dense conditions. There was no significant overall effect on performance measurements for distance levels (p=.254) and no significant interaction of distance and density (p=.155). \paragraph{Autonomous vs. normal driving} A within-subject MANOVA was conducted to compare conditions two and five. There was a significant difference between the conditions for the defined performance variables (Pillai trace=.49, F(3,32)=10.91, p<.001, $\eta_p^2$=.49). However, this difference is only significant for gaze accuracy (F(1,34)=21.46, p<.001, $\eta_p^2$=.39) where it was higher in the autonomous drive condition (i.e. condition five). There was no significant difference for pointing accuracy (p=.456) and pointing time (p=.116). \paragraph{Left vs. right PoI orientation} A within-subject MANOVA was conducted to compare left and right PoI orientation for the defined performance variables. There was a significant difference in performance for PoI orientation (Pillai trace=.54, F(3,32)=12.48, p<.001, $\eta_p^2$=.54). This difference can be found significantly in gaze accuracy (F(1,34)=16.72, p<.001, $\eta_p^2$=.33) and pointing time (F(1,34)=8.61, p=.006, $\eta_p^2$=.20). PoI oriented on the right side were pointed at faster and gazed at more accurately. There was no significant difference for pointing accuracy (p=.965). \paragraph{Pointing vs. gaze accuracy} Lastly, a within-subject MANOVA was conducted to compare pointing and gaze accuracy. Gaze accuracy was significantly higher compared to pointing accuracy (Pillai trace=.42, F(1,37)=26.77, p<.001, $\eta_p^2$=.42). \subsection{Clustering Results} Cluster analysis was used to find patterns in participants' behaviour beyond their individuality for possible fusion approaches that fits these clusters. In this section, clustering the participants based on their behaviour was attempted, using the previously mentioned metrics as features. Two clustering approaches were attempted: k-means non-hierarchical clustering and agglomerative hierarchical clustering. Both approaches yielded similar results. Therefore, only the results of k-means clustering are presented here. Clustering was done using participants' performance-related dependent variables and time-related dependent variables as features. An elbow curve was used to determine the best value for \textit{k}. \subsubsection{Clustering using \textit{performance-related} dependent variables} \begin{figure}[b] \begin{center} \includegraphics[width=0.45\linewidth]{images/kmeans_cluster_accuracies.pdf} \includegraphics[width=0.45\linewidth]{images/kmeans_cluster_timedv.pdf} \end{center} \caption{K-means clustering using performance-related features (left, with K=11) and timing-related features (right, with K=6)} \label{fig:kmeansclusteraccuracy} \end{figure} \autoref{fig:kmeansclusteraccuracy} shows k-means clustering output using gaze and pointing accuracy as features. To get rid of specific condition influence on the total average value, clustering pointing and gaze accuracy per each independent variable was investigated; all analyses showed similar results to the statistical inference analysis. Typical clustering algorithms did not yield meaningful clusters since both pointing accuracy and gaze accuracy dependent variables are normally distributed with similar standard deviations and only shifted means. Instead, heuristic clustering was done on the participant's distribution by dividing the participants into four quadrants in terms of accuracy (see~\autoref{fig:distraccuracywithquadrants}), which could be used for modality switching based on tracking performance. \begin{figure}[t] \begin{center} \includegraphics[width=0.75\linewidth]{images/Moadlityswitchingdistr.pdf} \end{center} \caption{Participants' distribution across pointing accuracy (y-axis) and gaze accuracy (x-axis) with four quadrants clustering at a threshold of 80\%} \label{fig:distraccuracywithquadrants} \end{figure} \subsubsection{Clustering using \textit{time-related} dependent variables} Similar to clustering using performance-related dependent variables, k-means clustering was done using all time-related dependent variables as features. To visualize the clustering output, principal component analysis (PCA) was applied to the 11D features to reduce them to 2D.~\autoref{fig:kmeansclusteraccuracy} shows the clustering output. \section{Discussion and Limitations} This section is divided into two parts. The first part describes our interpretation of the results and how can it be utilized in multimodal referencing, while the second part explains the limitations of our approach. \subsection{Discussion} \subsubsection{Descriptive statistics} Descriptive statistics shows that on average, gaze accuracy was better than pointing accuracy during the multimodal interaction. However, as previously mentioned, the gaze accuracy calculation already included pointing modality timing so it was not a stand-alone modality. It also shows that pointing time was relatively short, which means that users did not wait for the PoI to come closer before pointing, but rather pointed quickly at distant PoIs. The average ground truth angle confirms this finding as it was $\pm 9.8$ degrees, while a close PoI ground truth angle was in the range of 30 to 40 (right-oriented PoI) or -30 to -40 (left-oriented PoI) degrees. Regarding gaze type frequency analyses, `gaze begin' shows that half of the participants looked at the target (i.e. PoI) two to four times before pointing, while half of the participants looked only once. For `gaze middle', almost all participants did not look at the target while pointing, or looked only once, which suggests that users don't get visually distracted by the referencing task during driving. For `gaze confirmation', all participants looked at the target at least once while half of them had three confirmation gazes, which shows that confirmation gazes were very common. These differences in behaviour can be utilized in multimodal referencing in several ways. For example, pointing can be used as the main modality and could be tracked at all times, while gaze could be tracked only for a short time window before and after pointing. This is because almost all participants did not gaze during pointing at all or only gazed once. The mean modality delta time and confirmation time (1.91 and 2.43 seconds, respectively) can be used to determine this time frame for gaze tracking. \subsubsection{Intraclass correlations} Since users point at objects in a unique way generally~\cite{brown2016exploring,brown2014performance} and while driving~\cite{rumelin2013free}, intraclass correlations (ICCs) were calculated to assess the variance in the data originating from participants' differences. A fifth of the data variance originates from participants. Some variables such as \textit{pointing duration}, \textit{pointing time} or \textit{modality delta time} had especially high ICCs. This indicates that individual differences influenced how long participants pointed at a building, how long it took to find the building and how long it took to start pointing. Other variables (e.g. \textit{detection time}, \textit{confirmation time} and \textit{gaze confirmation duration}) had a relatively low ICC, indicating a low influence of inter-individual differences and homogeneous variations across participants. This could also be utilized in the referencing and tracking process. For example, the threshold for pointing detection could be lowered for users with shorter pointing duration, which would lead to better pointing accuracy. \subsubsection{Statistical inference} Inferential statistical analysis shows that the first hypothesis was supported. Participants performed better (i.e. pointed and gazed more accurately and pointed faster) in non-dense conditions compared to dense conditions with a large effect size. There was no significant difference in distance, as well as no significant interaction between density and distance in terms of performance. Thus, hypothesis two was not supported, which could be attributed to the fact that most participants already pointed when the PoI was still far away, as previously mentioned. Hypothesis three was partially supported since only gaze accuracy was significantly better during autonomous driving. Moreover, there was a significant difference for PoI orientation. PoIs on the right side of the road were gazed at more accurately and pointed at faster compared to buildings on the left side, which supports hypothesis four. However, this could be due to a learning effect (since more buildings were on the right side). Other possible reasons could be that most of the participants were right-handed or mainly drove on the right side of the road. Thus, they might have an attentional focus bias towards the right side. Furthermore, participants were instructed to point with their right hand even when pointing left, to make sure that their gesture was not out of range for the camera. This instruction might have negatively influenced pointing performance for left-side PoIs. Hypothesis five was supported by both the descriptive statistics and the statistical inference where gaze accuracy was significantly better than pointing accuracy. However, this finding needs to be interpreted with caution, since gaze accuracy calculation in this approach still depended on the pointing modality and therefore cannot be considered as an independent modality. The results for these hypotheses would determine the way each modality is tracked and fused. For example, the results for hypothesis four could be utilized by the system through tracking both pointing and gaze modalities for a right-oriented PoI, while tracking only the pointing modality for a left-oriented PoI. \subsubsection{Clustering} Another approach for utilizing behavioural differences in fusion is clustering the participants. Clustering can be done using performance-related dependent variables and time-related dependent variables as features. Clustering using performance-related dependent variables shows that there are too many clusters and it is hard to cluster participants based on pointing and gaze accuracy alone. However, a possible fusion approach would be modality switching (see~\autoref{fig:distraccuracywithquadrants}), where the system tracks pointing modality alone for users with high pointing accuracy and low gaze accuracy while it tracks gaze modality alone for users with low pointing accuracy and high gaze accuracy. As for time-related dependent variables, the clustering output looks more separable than that of the performance-related one; however, it is harder to interpret and apply to actual use cases since it depended on multiple dependent variables. An alternative approach is to heuristically cluster participants based on each dependent variable separately to enhance the pointing and gaze gestures tracking. For example, users that usually point for a short amount of time (i.e. \textit{pointing time} is small) should have a lesser time threshold for accurate pointing detection than users who point for a longer time, and so on. \subsection{Limitations} Finally, there are several limitations for the current work that we will address in future studies. First, the traditional feature extraction approach used in our approach involved several assumptions and transformation steps that propagated small rounding errors. This led to an error margin of $\pm 4$ degrees in pointing modality and $\pm 3$ degrees in gaze modality. Secondly, although the driving route was long to assure safety-critical and dynamic criteria, it was simple and easy by design to increase internal validity, which could lead to a lower external validity. Lastly, from a technical side, the eye gaze tracker lacked a real-time communication feature and did not allow for online synchronisation with other devices. This led to the use of an offline synchronisation approach which resulted in a timing error margin of $\pm 300$ milliseconds. Besides, both the eye gaze and pointing gesture trackers had several hardware and software limitations that led to 40\% of the recorded data being unusable. \section{Conclusion and Future work} In conclusion, person-specific behaviour can be exploited to enhance the referencing task performance using several different approaches such as: triggering gaze tracking based on the pointing starting time; adjusting pointing tracking threshold based on user's pointing duration; changing tracking methodology based on target orientation; switching between the pointing and gaze tracking system based on users' clusters to maximize the overall referencing performance. To overcome this work's limitations in future studies, we plan to use a deep learning approach for feature extraction, which would significantly reduce the traditional method's error margin. However, it would significantly reduce the explainability of the extracted feature as well, and the right hyperparameters for such an approach could be hard to find. Moreover, we plan to use more complicated and harder driving routes in further studies to increase the external validity. However, a more challenging driving task could slightly alter the user's behaviour. Finally, more reliable hardware that also supports online synchronisation could be used to avoid offline synchronization problems and output more reliable data. However, such devices can be significantly more expensive. \begin{acks} This work is partially funded by the German Ministry of Education and Research (project TRACTAT: Transfer of Control between Autonomous Agents; grant number 01IW17004). \end{acks} \bibliographystyle{ACM-Reference-Format} \balance	{ "redpajama_set_name": "RedPajamaArXiv" }	3,284
Q: Variation in critical point of a function Consider a smooth function of the form $f(\alpha, x, y)$. Write the function as $f_{\alpha}(x,y)$. Assume $x$ and $y$ are parameters over which we'd like to optimize $f_{\alpha}$ for each fixed $\alpha$. For each fixed $\alpha$, critical points $(x^, y^)$ are defined by the vanishing of $\partial_x f_{\alpha} (x^, y^) $ and $\partial_y f_{\alpha} (x^, y^) $. The question is: how can we compute the partial derivative $\partial_{\alpha} x^$. Presumably, I think the question is how does $x^$ vary as $\alpha$ is allowed to vary. I don't quite understand the question, though. Any suggestions/hints? A: Denote the partial derivatives of $f_{a}(x,y)$ wrt to x and y by $P(x,y; a)$ and $Q(x,y;a)$ respectively. Setting $P$ and $Q$ equal to zero (to define critical points) gives you two equations in three variables. Visualize this as two surfaces in 3D space, whose intersection (typically) carves out a smooth curve $C$ in space whose parametrized description is $C=<x(a), y(a), a>$. This parametrizes the critical point as a function of the pseudo-constant $a$. The derivative $\frac{dC}{da}= <x'(a), y'(a), 1>$ contains the answer you seek. On the other hand, from multivariable calculus, you learn that the cross product of the 3D gradient vectors $\vec T=\nabla P \times \nabla Q$ is also a tangent vector to this curve. If you rescale $\vec T$ so that its last component equals $1$, then this modified $T$ equals $\frac{dC}{da}$.	{ "redpajama_set_name": "RedPajamaStackExchange" }	8,791
Ю́рий Петро́вич Щекочи́хин (9 июня 1950, Кировабад Азербайджанской ССР — 3 июля 2003, Москва) — российский журналист, писатель и драматург, сценарист, телеведущий, депутат Государственной думы. Известен громкими журналистскими расследованиями. Биография Родился 9 июня 1950 года в Кировабаде (ныне Гянджа, Азербайджанская Республика). Окончил факультет журналистики МГУ имени М. В. Ломоносова (1975). Журналистскую карьеру начал в 17 лет (первая публикация — в «Московском комсомольце»). В 1972—1980 годах вёл рубрику «Алый парус» в газете «Комсомольская правда», где занимался подростковыми проблемами. С 1980 по июль 1996 года состоял редактором отдела расследований в «Литературной газете», «специалистом по организованной преступности», как определял его Фёдор Раззаков. В 1995 году Юрий Щекочихин — автор и ведущий программы («журналистского расследования») «Специальная бригада» (программа была снята с эфира как «дестабилизующая обстановку в стране»). С 1996 года работал заместителем главного редактора и редактором отдела расследований в «Новой газете». В числе основных тем публикаций Щекочихина в 1990-е годы — состояние российской армии, освобождение пленных и заложников в Чечне, коррупция в органах государственной власти, социальные проблемы. Политическая деятельность Политическую деятельность Щекочихин начал в 1990 году, когда был избран народным депутатом СССР от одного из избирательных округов Луганской области. В 1995 году стал депутатом Государственной думы второго созыва от фракции «Яблоко», в 1999 году вошёл в Государственную думу третьего созыва (по списку «Яблока»). Щекочихин входил в состав Комитета по безопасности Госдумы (занимал должность заместителя председателя Комитета в Госдуме третьего созыва) и Комиссии по борьбе с коррупцией в органах государственной власти. Рассматривал проблемы организованной преступности (в том числе подростковой преступности), был автором ряда острых публикаций на эту тему. Был экспертом ООН по вопросам организованной преступности. Был президентом Международного фонда в поддержку молодой творческой интеллигенции (1993—2003). В последние годы жизни Щекочихин расследовал Дело «Трёх китов» и сопутствовавший конфликт между силовыми органами. Требовал возобновления этого остановленного дела в Генеральной прокуратуре. В 2002—2003 годах получал анонимные звонки с угрозами. В 2003 году Юрий Щекочихин не смог добиться от российских спецслужб и Генпрокуратуры внятных ответов на свои многочисленные вопросы. Тогда он обратился за информацией в ФБР США. До своей внезапной смерти Щекочихин должен был посетить Вашингтон, чтобы обменяться документами с представителями американских правоохранительных органов (к тому времени следственные действия проводились в США, Германии и Италии). Сергей Соколов писал, что расследования Щекочихина, подобные делу министра Адамова, делу об отмывании денег через «Бэнк оф Нью-Йорк», делу «Трёх китов» и десятку других, «затрагивали интересы коррупционеров высочайшего уровня». Незадолго до своей смерти, в 2002—2003 годах, Юрий Щекочихин был членом «Общественной комиссии по расследованию обстоятельств взрывов домов в городах Москве и Волгодонске и проведения учений в городе Рязани в сентябре 1999 года» под руководством Сергея Ковалёва. Писатель и журналист Юрий Щекочихин был одной из ключевых фигур «Комсомольской правды» 1970-х годов, где он вёл рубрику «Алый парус», ставшей стартовой площадкой для любителей-журналистов. Щекочихин — автор пьес, киносценариев, прозаических произведений. Одним из направлений его творчества была подростковая преступность. Автор книги «Рабы ГБ. XX век. Религия предательства», 1999 год. Работал журналистом «Новой газеты». В одной из статей 2001 года отмечал, как месяц участия в операции в Чечне в 1995 году ожесточал мировоззрение борцов с профессиональной преступностью, которые выполняли приказы руководства. Смерть и расследование Скончался в возрасте 53 лет после скоротечной болезни 3 июля 2003 года в Москве. По утверждениям заместителя главного редактора «Новой газеты» Сергея Соколова, Щекочихин «за две недели превратился в глубокого старика, волосы выпадали клоками, с тела сошла кожа, практически вся, один за другим отказывали внутренние органы». При похоронах милиция оцепила место погребения никого туда не подпуская. Олег Калугин предполагает, что Щекочихин был отравлен как и Александр Литвиненко. Согласно заключению судебно-медицинской экспертизы, причина смерти — тяжёлая общая интоксикация, выразившаяся в синдроме Лайелла. Заведующий отделением анестезиологии и реанимации В. П. Фоминых писал в объяснении, что исследование в двух лабораториях обнаружило в биологическом материале «фармацевтические ингредиенты» фенол и лидокаин, которые не должны были находиться в организме человека. Фоминых заключил, что присутствие лидокаина объясняется его применением для местного обезболивания, а присутствие фенола — распадом белка в терминальной стадии заболевания. Редакция «Новой газеты» не смогла найти результатов повторного анализа крови, взятого 3 июля по «договорённости с начальником Медицинского Управления МВД Кругловым А. Г.», среди медицинских документов. В октябре 2007 года Следственный комитет при прокуратуре Российской Федерации (СК РФ) возобновил, по настоянию «Новой газеты», расследование обстоятельств смерти Юрия Щекочихина. В начале апреля 2008 года представитель СК РФ заявил: «Планируется провести целый комплекс следственно-оперативных мероприятий, в том числе, ряд сложных комплексных экспертиз с привлечением зарубежных специалистов из экспертных учреждений». 4 апреля 2008 по факту смерти Юрия Щекочихина было возбуждено уголовное дело по статье «убийство». В сентябре 2008 была проведена эксгумация тела Юрия Щекочихина и назначена экспертиза по факту его смерти. 4 апреля 2009 года уголовное дело по факту смерти Юрия Щекочихина было прекращено «за отсутствием события преступления». 16 сентября 2010 года СК РФ возобновил расследование уголовного дела по факту смерти Юрия Щекочихина «в связи с поступившими в распоряжение следствия новыми данными, требующими проведения дополнительных следственных действий». Однако расследование было прекращено в связи с «отсутствием события преступления». Коллектив «Новой Газеты» не согласился с официальной версией смерти Юрия Щекочихина. В июле 2013 года в газете была опубликована статья, в которой описаны результаты параллельного расследования; также «Новая газета» объявила премию за существенную информацию, которая поможет расследовать смерть Юрия Петровича Щекочихина. Память Похоронен на Переделкинском кладбище. Могила находится в нижней части кладбища около оврага, участок 15, недалеко от могилы Роберта Рождественского. Награды Медаль «Защитнику свободной России» (1993) Медаль «В память 850-летия Москвы» Медаль Памяти 13 января (9 января 1992, Литва) Примечания Литература С любовью: произведения Ю. Щекочихина; воспоминания и очерки о нём. СПб.: ИНАПРЕСС; Новая газета, 2004. — 288 с., илл. — ISBN 5-87135-156-5. Ссылки Биография, публикации Биография. Публикации Юрий Щекочихин. Рабы ГБ. XX век. Религия предательства, М., 1999. Персональный сайт Юрия Щекочихина Юрий Щекочихин. Зачем я был нужен КГБ // журнал «Столица» № 4, 1991 Информация о смерти и расследовании Последнее дело Юрия Щекочихина // Новая газета № 45, 19 июня 2006 Отказ прокуратуры в возбуждении уголовного дела по поводу смерти Щекочихина // Новая газета № 2, 15 января 2007 года. Следственные органы в третий раз отказались возбудить уголовное дело по факту убийства заместителя главного редактора «Новой» Юрия Щекочихина // Новая газета № 20, 24 марта 2008 Народные депутаты СССР от округов Украинской ССР Журналисты газеты «Комсомольская правда» Журналисты газеты «Московский комсомолец» Журналисты «Новой газеты» Депутаты Государственной думы Российской Федерации II созыва Депутаты Государственной думы Российской Федерации III созыва Похороненные на Переделкинском кладбище Выпускники факультета журналистики МГУ Члены партии «Яблоко» Ведущие радиостанции «Радио России» Журналисты-расследователи России Умершие от отравления Журналисты, освещавшие войну в Чечне Журналисты «Литературной газеты»	{ "redpajama_set_name": "RedPajamaWikipedia" }	7,348
Q: LibGdx java Preference confusion So im trying to figure out preferences for a game im creating, however im getting dumbfounded by it. So my preferences file right now reads <?xml version="1.0" encoding="UTF-8" standalone="no"?> <!DOCTYPE properties SYSTEM "http://java.sun.com/dtd/properties.dtd"> <properties> <entry key="Level_Default">Default</entry> </properties> However for my code to get certain levels and what not looks like this. if (!(PreferenceManager.getPreferences("Zero").equals("Zero"))) { game.batch.draw(levelOneButtonLocked, BUTTON_WIDTH * 2 / GravitySpikes.PPM, ROW_ONE_BUTTON_Y / GravitySpikes.PPM, BUTTON_WIDTH / GravitySpikes.PPM, BUTTON_HEIGHT / GravitySpikes.PPM); } else if (PreferenceManager.getPreferences("Zero").equals("Zero")) { if (Gdx.input.getX() / GravitySpikes.PPM < (levelOneX + BUTTON_WIDTH) / GravitySpikes.PPM && Gdx.input.getX() / GravitySpikes.PPM > levelOneX / GravitySpikes.PPM && (GravitySpikes.HEIGHT - Gdx.input.getY()) / GravitySpikes.PPM < (ROW_ONE_BUTTON_Y + BUTTON_HEIGHT) / GravitySpikes.PPM && (GravitySpikes.HEIGHT - Gdx.input.getY()) / GravitySpikes.PPM > ROW_ONE_BUTTON_Y / GravitySpikes.PPM) { game.batch.draw(levelOneButtonActive, BUTTON_WIDTH * 2 / GravitySpikes.PPM, ROW_ONE_BUTTON_Y / GravitySpikes.PPM, BUTTON_WIDTH / GravitySpikes.PPM, BUTTON_HEIGHT / GravitySpikes.PPM); if (Gdx.input.isTouched()) { game.setScreen(new LevelOneGameScreen(game)); } } else { game.batch.draw(levelOneButtonInactive, BUTTON_WIDTH * 2 / GravitySpikes.PPM, ROW_ONE_BUTTON_Y / GravitySpikes.PPM, BUTTON_WIDTH / GravitySpikes.PPM, BUTTON_HEIGHT / GravitySpikes.PPM); } } I'm not an expert at programming, just starting to use libgdx and what not, but the problem is why is the first if not working and the else if is executing when that entry isn't even in my preferences? I tried deleting the preference file and it still does the same thing even though that preference is not even there. I feel like i missed something very simple. Also another note: Whenever i do beat my game and go to the next level it does add the entry normally. Okay i solved my own problem, it had to do with my getPreferences. before it was return getPreferenceFile().getString("Level_" + level, level); but i changed it to this and it seems to work fine now. return getPreferenceFile().getString("Level_" + level);	{ "redpajama_set_name": "RedPajamaStackExchange" }	7,601
Zinaida Michajłowna Tusnołobowa-Marczenko , (ur. 23 listopada 1920 w chutorze Szewcowo, gubernia witebska, zm. 20 maja 1980 w Połocku) – radziecka pielęgniarka, sanitariuszka w okresie II wojny światowej, wyróżniona tytułem Bohatera Związku Radzieckiego (1957). Życiorys Urodziła się 23 listopada 1920 roku we wsi Szaucowa pod Połockiem w guberni witebskiej (obecnie w rejonie rossońskim obwodu witebskiego na Białorusi) w rodzinie chłopskiej. W 1941 roku poznała i poślubiła Iosifa Marczenkę. Od 1942 roku mieszkała w Lenińsku Kuźnieckim, biorąc udział w kursie dla pielęgniarek. Od kwietnia 1942 roku służyła jako sanitariuszka w 303-dywizji piechoty 60. armii ZSRR na froncie woroneskim. W ciągu 8 miesięcy służby frontowej wyniosła z pola walki 123 rannych. Została wówczas odznaczona Orderem Czerwonej Gwiazdy. W lutym 1943 roku została ranna w trakcie walk. Odnaleziono ją ranną w zamarźniętym błocie. W wyniku odmrożeń i gangreny, lekarze ze szpitala polowego amputowali jej obydwie ręce i nogi. Po kuracji udzielała się propagandowo występując w radzieckich w fabrykach i radio-rozgłośniach. Po wojnie osiadła wraz z mężem w Połocku. 6 grudnia 1957 roku została wyróżniona tytułem Bohatera Związku Radzieckiego. Zinaidę Tusnołobową-Marczenko wyróżniono również Orderem Lenina, a w 1965 roku Międzynarodowy Komitet Czerwonego Krzyża, przyznał jej jako trzeciej radzieckiej pielęgniarce w historii – Medal Florence Nightingale. Zmarła 20 maja 1980 roku i została pochowana w Połocku. Przypisy Radzieccy żołnierze II wojny światowej Radzieckie sanitariuszki Rosyjscy Bohaterowie Związku Radzieckiego Odznaczeni Orderem Czerwonej Gwiazdy Odznaczeni Orderem Lenina Odznaczeni Medalem Florence Nightingale Kobiety – radzieccy wojskowi Starszyny Sił Zbrojnych ZSRR Urodzeni w 1920 Zmarli w 1980	{ "redpajama_set_name": "RedPajamaWikipedia" }	8,574
# ALSO BY KEVIN KWAN _Crazy Rich Asians_ _China Rich Girlfriend_ This novel is a work of fiction. Names, characters, businesses, organizations, places, events, and incidents either are the products of the author's imagination or are used fictitiously. Any resemblance to actual persons, living or dead, events, or locales is entirely coincidental. Copyright © 2017 by Tyersall Park Ltd. All rights reserved. Published in the United States by Doubleday, a division of Penguin Random House LLC, New York. www.doubleday.com DOUBLEDAY and the portrayal of an anchor with a dolphin are registered trademarks of Penguin Random House LLC. _Cover design and illustration by Joan Wong_ Library of Congress Control Number: 2017930108 ISBN 9780385542234 (hardcover) ISBN 9780385542241 (ebook) v4.1 ep # Contents Cover Also by Kevin Kwan Title Page Copyright Dedication Genealogy Prologue Part One Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Chapter Six Chapter Seven Chapter Eight Chapter Nine Chapter Ten Chapter Eleven Chapter Twelve Chapter Thirteen Chapter Fourteen Part Two Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Chapter Six Chapter Seven Chapter Eight Chapter Nine Chapter Ten Chapter Eleven Chapter Twelve Chapter Thirteen Chapter Fourteen Chapter Fifteen Part Three Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Chapter Six Chapter Seven Chapter Eight Chapter Nine Chapter Ten Chapter Eleven Chapter Twelve Chapter Thirteen Chapter Fourteen Chapter Fifteen Chapter Sixteen Chapter Seventeen Part Four Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Chapter Six Chapter Seven Chapter Eight Chapter Nine Chapter Ten Epilogue Acknowledgments A Note About the Author For my grandparents, and for Mary Kwan Detail left Detail right # PROBLEM NO. 1 _Your regular table at the fabulous restaurant on the exclusive island where you own a beach house is unavailable._ # HARBOUR ISLAND, THE BAHAMAS, JANUARY 21, 2015 Bettina Ortiz y Meña was not accustomed to waiting. A former Miss Venezuela (and Miss Universe runner-up, of course), the exceedingly bronzed strawberry blonde was these days the wife of the Miami auto-parts tycoon Herman Ortiz y Meña, and at every restaurant she chose to grace with her presence, she was always greeted with reverence and whisked to the exact table she desired. Today she wanted the corner table on the terrace at Sip Sip, her favorite lunch spot on Harbour Island. She wanted to sit on one of the comfy orange canvas director's chairs and stare out at the gently lapping turquoise waters while eating her kale Caesar salad, but there was a large, noisy group taking up the entire terrace and they didn't seem in much hurry to leave. Bettina fumed as she glared at the tourists happily savoring their lunch in the sun. Look how tacky they were...the women overly tanned, wrinkled, and saggy, none of them properly lifted or Botoxed. She felt like walking up to their table and handing out her dermatologist's business cards. And the men were even worse! All dressed in old rumpled shirts and shorts, wearing those cheap straw hats sold at the trinket shop on Dunmore Street. Why did such people have to come here? This three-and-a-half-mile-long paradise with its pristine pink-sand beaches was one of the best-kept secrets in the Caribbean, a haven for the very very rich filled with quaint little wood houses painted in shades of sherbet, charming boutiques, chic oceanfront mansions turned into inns, and five-star restaurants to rival St. Barths. Tourists should have to take a style exam before being allowed to set foot on the island! Feeling like she had been patient long enough, Bettina stormed into the kitchen, the fringe on her crocheted Pucci caftan top shaking furiously as she made a beeline for the woman with a shock of pixie-cut blond hair manning the main stove. "Julie, honey, what's the dealio? I've waited more than _fifteen minutes_ for my table!" Bettina sighed to the owner of the restaurant. "Sorry, Bettina, it's been one of those days. The party of twelve on the terrace showed up just before you did," Julie replied as she handed off a bowl of spicy conch chili to a waiting server. "But the terrace is your prime spot! Why on earth did you let those _tourists_ take up all that space?" "Well, that _tourist_ in the red fishing cap is the Duke of Glencora. His party just boated over from Windermere—that's his _Royal Huisman_ you see moored off the coast. Isn't it the most handsome sailboat you've ever seen?" "I'm not impressed by big boats," Bettina huffed, although secretly she was rather impressed by people with big titles. From the kitchen window, she surveyed the party assembled on the terrace with new eyes. These aristo British types were such a strange breed. Sure, they had their Savile Row suits and their heirloom tiaras, but when they traveled, they looked so painfully frumpy. It was only then that Bettina noticed three tan, well-built men in fitted white T-shirts and black Kevlar pants sitting at the adjacent table. The guys weren't eating but sat watchfully, sipping glasses of seltzer water. "I assume that's the duke's security detail? They couldn't be more obvious! Don't they know that we're all billionaires here on Briland, and this isn't how we roll?"1 Bettina tut-tutted. "Actually, those bodyguards belong to the duke's special guest. They did a whole sweep of the restaurant before the party arrived. They even searched my walk-in freezer. See that Chinese fellow seated at the end of the table?" Bettina squinted through her Dior Extase sunglasses at the portly, balding, seventy-something Asian man dressed in a nondescript white short-sleeved golf shirt and gray trousers. "Oh, I didn't even notice him! Am I supposed to know who he is?" "That's _Alfred Shang_ ," Julie said in a hushed tone. Bettina giggled. "He looks like their chauffeur. Doesn't he look like that guy that used to drive Jane Wyman around in _Falcon Crest_?" Julie, who was trying to focus on searing a cut of tuna to perfection, shook her head with a tight-lipped smile. "From what I hear, that chauffeur is the most powerful man in Asia." "What's his name again?" "Alfred Shang. He's Singaporean but lives mostly in England on an estate that's half the size of Scotland, so I'm told." "Well I've never seen his name on any of the rich lists," Bettina sniffed. "Bettina, I'm sure you know that there are people on this planet who are far too rich and powerful to ever appear on those lists!" # PROBLEM NO. 2 _The twenty-four-hour on-call personal physician that you have on a million-dollar annual retainer is busy attending to another patient._ Sitting on the terrace overlooking Harbour Island's legendary beach, Alfred Shang marveled at the spectacular sight before him. _It's true—the sand really is pink!_ "Alfred, your lobster quesadillas are going to get cold!" the Duke of Glencora piped up, interrupting his reverie. "So this is the reason you dragged me all the way here?" Alfred said, staring dubiously at the triangular wedges placed artfully before him. He didn't really care much for Mexican food, except when the chef of his good friend Slim in Mexico City was doing the cooking. "Try it before you judge it." Alfred took a careful bite, saying nothing, as the combination of semi-crisp tortilla, lobster, and guacamole worked its magic. "Marvelous, isn't it? I've been trying to convince the chef at Wilton's to replicate this for years," the duke said. "They haven't changed a thing at Wilton's in half a century—I don't think there's much of a likelihood they would ever put this on their menu." Alfred laughed, picking up a stray lobster chunk that had fallen onto the table with his fingers and popping it into his mouth. His phone began to vibrate in his trouser pocket. He took it out and stared at the screen in annoyance. Everyone knew that he was not to be disturbed on his annual fishing trip with the duke. The screen read: TYERSALL UPSTAIRS SECURE. This was his elder sister, Su Yi, the only person whose calls he would take no matter the hour. He picked up immediately, and an unexpected voice said in Cantonese, "Mr. Shang, this is Ah Ling." It took him a few seconds to register that it was the housekeeper at Tyersall Park. "Oh...Ling Jeh!"2 "I was instructed by my lady to call you. She was feeling very unwell tonight and has just been taken to the hospital. We think it's a heart attack." "What do you mean _you think_? Did she have a heart attack or didn't she?" Alfred's plummy Queen's English suddenly shifting into Cantonese in alarm. "She...she didn't have any chest pains, but she was sweating profusely, and then she vomited. She said she could feel her heart racing," Ah Ling stuttered nervously. "And did Prof Oon come over?" Alfred asked. "I tried to reach the doctor on his cell phone, but it went straight to voice mail. Then I called his house and someone there said he was in Australia." "Why are _you_ doing all the calling? Isn't Victoria at home?" "Mr. Shang, isn't Victoria in England?" _Alamak_. He had completely forgotten that his niece—Su Yi's daughter, who lived at Tyersall Park—was at this moment at his house in Surrey, no doubt embroiled in some inane gossipfest with his wife and daughter. "How about Felicity? Didn't she come over?" Alfred inquired about Su Yi's eldest daughter, whose house was nearby on Nassim Road. "Mrs. Leong could not be reached tonight. Her maid said she was in church, and she always turns off her mobile phone when she's in the house of God." _Bloody useless, all of them!_ "Well, did you call an ambulance?" "No, she didn't want an ambulance. Vikram drove her to the hospital in the Daimler, accompanied by her lady's maids and two Gurkhas. But before she left, she said you would know how to contact Professor Oon." "Okay, okay. I'll take care of it," Alfred said in a huff, hanging up the phone. Everyone at the table was staring at him expectantly. "Oh my, that did sound rather serious," the duke said, pursing his lips worriedly. "I'll just be a moment...please carry on," Alfred said, getting up from his chair. The bodyguards trailed after him as he strode through the restaurant and out the door to the garden. Alfred hit another number on his speed dial: PROF OON HOME. A woman picked up the phone. "Is this Olivia? Alfred Shang here." "Oh, Alfred! Are you looking for Francis?" "Yes. I'm told he's in Australia?" _Why the bloody hell did they have this doctor on a million-dollar retainer if he was never available?_ "He just left an hour ago for Sydney. He's doing a triple bypass tomorrow on that actor who won an Oscar for—" "So he's on a plane right now?" Alfred cut her off. "Yes, but he'll be arriving in a few hours if you need to—" "Just give me his flight number," Alfred snapped. He turned to one of his bodyguards and asked, "Who has the Singapore phone? Somebody get Istana3 on the line right now." Turning to another bodyguard, he said, "And please order me another of those lobster quesadillas." # PROBLEM NO. 3 _Your airplane is forced to land before you can finish drinking your Dom Pérignon._ # EAST JAVA, INDONESIA The silk sheets had just been turned down in the first-class suites, the enormous double-decked Airbus A380-800 had reached a comfortable cruising altitude of thirty-eight thousand feet, and most of the passengers were comfortably ensconced in their seats, scanning through the latest movie offerings. Moments later, the pilots of Singapore Airlines Flight 231 bound for Sydney received the most unusual instructions from Jakarta air traffic control as they flew over Indonesian airspace: AIR TRAFFIC CONTROLLER: singapore two thirty one super jakarta. PILOT: singapore two thirty one super go ahead. ATC: I have been instructed to have you turn around immediately and return to Singapore Changi Airport. PILOT: Jakarta, you want us to return to Singapore Changi? ATC: Yes. Turn the plane around and return immediately to Singapore. I have the amended route advise ready to copy. PILOT: Jakarta, what is the reason for the course change? ATC: I don't have that information, but this is a direct order from the Directorate General of Civil Aviation. The pilots looked at each other in disbelief. "Should we really be doing this?" the captain wondered aloud. "We'll have to dump a quarter-million liters of fuel before we can land!" Just then, the aircraft's selective-calling radio system lit up with an incoming message. The co-pilot read the message quickly and gave the captain an incredulous look. " _Wah lan!_ It's from the minister of fricking defense! He says to get back to Singapore pronto!" When the airplane made an unexpected landing at Changi Airport just three hours after it had departed, the passengers were disoriented and startled by the strange turn of events. An announcement was made over the intercom: "Ladies and gentlemen, due to an unexpected event, we have made an emergency diversion back to Singapore. Please remain in your seats with your seat belts fastened, as our flight to Sydney will resume immediately after refueling." Two men in discreet dark suits came aboard and approached the man seated in suite 3A—Professor Francis Oon, Singapore's leading cardiologist. "Professor Oon? I'm Lieutenant Ryan Chen from SID.4 Please come with us." "We're leaving the plane?" Professor Oon asked, utterly baffled. One minute he was in the middle of watching _Gone Girl_ , and the next minute the plane had landed back in Singapore. He hadn't even recovered from the film's jaw-dropping plot twist. Lieutenant Chen nodded curtly. "Yes. Please gather up all your belongings—you won't be returning to this flight." "But...but...what did I do?" Professor Oon asked, suddenly feeling uneasy. "Don't worry, you didn't do anything. But we need to get you off this plane now." "Am I the only one leaving?" "Yes, you are. We are escorting you directly to Mount Elizabeth Hospital. You have been requested to attend to a VVIP patient." At that moment, Professor Oon knew something must have happened to Shang Su Yi. Only the Shangs had the kind of influence to turn around a Singapore Airlines flight with four hundred forty passengers onboard. * * * 1 A slight exaggeration, but this island—known affectionately as "Briland" to the locals—is home to twelve billionaires (at last count, and depending on who's counting). 2 Cantonese for "elder sister," often used as a term of familiarity for household help in the way that "boy" is sometimes used, as in Sonny Boy or Johnny Boy. 3 Malay for "palace." In this instance, Alfred is referring to Istana in Singapore, the official residence of the president. 4 The Security and Intelligence Division, Singapore's equivalent of America's CIA or Britain's MI5, is so secretive that most people don't even know it exists. But yes, that man eating fish ball on a stick outside NTUC FairPrice could be the Singaporean James Bond, and you wouldn't even know it. # PART ONE > The only thing I like about rich people is their money. > > —NANCY ASTOR, VISCOUNTESS ASTOR # CHAPTER ONE DAVOS, SWITZERLAND Edison Cheng stared up at the soaring honeycomb-structured ceiling in the vast white auditorium, feeling on top of the world. _I'm here. I'm finally here!_ After years of Olympic-level networking, Eddie had at long last made it—he had been invited to attend the annual meeting of the World Economic Forum in Davos. Strictly by invitation only,1 this prestigious event was the most elite schmoozefest on the planet. Every January, the world's most important heads of state, politicians, philanthropists, CEOs, tech leaders, thought leaders, social activists, social entrepreneurs, and, of course, movie stars2 would descend upon this secluded ski resort high in the Swiss Alps in their private jets, check in to their luxurious hotels, put on their $5,000 ski jackets and ski boots, and engage in meaningful dialogues about such urgent issues as global warming and rising inequality. And now Eddie was part of this ultraexclusive club. As the recently appointed senior executive vice chairman of Private Banking (Global) for the Liechtenburg Group, he now found himself standing in the middle of the futuristic auditorium at the Congress Centre, breathing in the rarefied air and catching slivers of his own reflection in the thin chrome leg of an auditorium chair. He was wearing his new bespoke Sartoria Ripense suit, which had been outfitted with an inner lining of ten-ply cashmere so that he never had to wear a ski jacket over it. His new Corthay squirrel suede chukkas had special rubber soles, so he would never slip on the slick Alpine streets. On his wrist was his newest horological acquisition—a rose gold A. Lange & Söhne Richard Lange "Pour le Mérite," peeking out the precise amount from his sleeve cuff so other watchophiles would see what he was wearing. But most important of all was what he wore over this sartorial splendor—a black lanyard at the end of which was attached a white plastic badge with his name printed in the middle: _Edison Cheng_. Eddie fondled the slick plastic badge as if it were a jewel-encrusted amulet, personally bestowed on him by the God of Davos. This badge distinguished him from all the pee-ons at the conference. He wasn't some PR hack, journalist, or one of the common attendees. This white plastic badge with the blue line at the bottom meant that he was an _official delegate_. Eddie glanced around the room at all the clusters of people in hushed conversations, trying to see which dictator, despot, or director he could recognize and connect with. Out of the corner of his eye, he spotted a tall Chinese man wearing a bright orange ski parka peeking in through the auditorium's side door, seemingly a little lost. _Wait a minute, I know that guy. Isn't that Charlie Wu?_ "Oy—Charlie!" Eddie yelled, a little too loudly, as he rushed over toward Charlie. _Wait till he sees my official delegate badge!_ Charlie beamed at him in recognition. "Eddie Cheng! Did you just get in from Hong Kong?" "I came from Milan, actually. I was at the men's fall fashion shows—front-row seat at Etro." "Wow. I guess being one of _Hong Kong Tattle_ 's Best Dressed Men is serious work, isn't it?" Charlie quipped. "Actually, I made it into the Best Dressed Hall of Fame last year," Eddie replied earnestly. He gave Charlie a quick once-over, noticing that he was wearing khaki pants with cargo pockets and a navy blue pullover under his bright orange parka. _What a pity—he used to be so fashionable when he was younger, and now he's dressed like every other tech-geek nobody._ "Where's your badge, Charlie?" Eddie asked, flashing his own proudly. "Oh yes, we're supposed to wear them at all times, aren't we? Thanks for reminding me—it's somewhere buried in my messenger bag." Charlie dug around for a few seconds before fishing out his badge, and Eddie glanced at it, his curiosity morphing into shocked dismay. Charlie was holding an all-white badge affixed with a shiny holographic sticker. _Fucky fuck, this was the most coveted badge! The one they only gave to world leaders! The only other person he had seen so far wearing that badge was Bill Clinton! How the fuck did Charlie get one? All he did was run Asia's biggest tech company!_ Trying to mask his envy, Eddie blurted, "Hey, are you attending my panel—Apocalypse Asia: How to Secure Your Assets When the China Bubble _Really_ Bursts?" "I'm actually on my way to give a talk to IGWEL.3 What time do you go on?" "Two o'clock. What's your talk about?" Eddie asked, thinking that he could somehow tag along with Charlie. "I don't have anything prepared, really. I think Angela Merkel and some of the Scandinavians just wanted to pick my brain." Just then, Charlie's executive assistant, Alice, walked up to join them. "Alice, look who I found! I knew we'd bump into someone from back home sooner or later," Charlie said. "Mr. Cheng, so nice to see you here. Charlie—could I have a quick word?" "Sure." Alice glanced at Eddie, who looked only too eager for her to continue while he was standing right there. "Er...would you mind coming with me for a moment?" she said diplomatically, guiding Charlie into a side reception room furnished with several lounge chairs and glass-cube coffee tables. "What's up? Are you still trying to recover from sitting at the same breakfast table with Pharrell?" Charlie teased. Alice smiled tensely. "There's been a developing situation all morning, and we didn't want to disturb you until we knew more." "Well, spit it out." Alice took a deep breath before beginning. "I just got the latest update from our head of security in Hong Kong. I don't quite know how to tell you this, but Chloe and Delphine are missing." "What do you mean _missing_?" Charlie was stunned—his daughters were under round-the-clock surveillance, and their pickups and drop-offs were handled with military precision by his SAS-trained security team. _Missing_ was not a variable in their lives. "Team Chungking was scheduled to pick them up outside Diocesan at 3:50 p.m., but the girls couldn't be located at the school." "Couldn't be located..." Charlie mumbled in shock. Alice continued, "Chloe didn't respond to any of her texts, and Delphine never showed up for choir at two. They thought maybe she sneaked off with her classmate Kathryn Chan to that frozen yogurt shop like she did last time, but then Kathryn turned up at choir practice and Delphine didn't." "Did either of them activate their panic codes?" Charlie asked, trying to remain calm. "No, they didn't. Their phones both appear to have been deactivated, so we can't trace them. Team 2046 has already spoken with Commander Kwok—the Hong Kong police have been placed on high alert. We also have four of our own teams searching everywhere for them, and the school is now reviewing all their security-camera footage with Mr. Tin." "I'm assuming someone's talked to their mother?" Charlie's wife—from whom he was estranged—lived in their house on The Peak, and the children spent every other week with her. "Isabel can't be reached. She told the housekeeper that she was meeting her mother for lunch at the Kowloon Cricket Club, but her mother reports that they haven't spoken all week." Just then, the cell phone rang again and Alice quickly answered. She listened in silence, nodding her head every now and then. Charlie looked at her pensively. _This couldn't be happening. This couldn't be happening. Ten years ago his brother Rob had been kidnapped by the Eleven Finger Triad. It was like déjà vu all over again._ "Okay. _Tor jeh, tor jeh_ ,"4 Alice said, hanging up. Looking at Charlie, she reported, "That was the leader of Team Angels. They now think that Isabel might have left the country. They spoke to the upstairs maid, and Isabel's passport is missing. But for some reason she didn't take any suitcases." "Isn't she in the middle of some new treatment?" "Yes, but apparently she didn't show up at her psychiatrist appointment this week." Charlie let out a deep sigh. This wasn't a good sign. * * * 1 And if you happen to get invited, just know you're still obliged to pay the $20,000 attendance fee unless you are one of the people listed in the next footnote. (Beautiful people never have to pay for anything.) 2 Leo, Brad, Angelina, and Bono have all attended. 3 The acronym for Informal Gathering of World Economic Leaders, the most exclusive inner sanctum of the conference, so secretive that their meetings take place at an undisclosed location deep within the Congress Centre. 4 Cantonese for "Thank you, thank you." # CHAPTER TWO FULLERTON HOTEL, SINGAPORE Every month, Rosalind Fung, the property heiress, hosted a Christian Fellowship Banquet for three hundred of her closest girlfriends in the opulent ballroom of the Fullerton Hotel. An invitation to this occasion was highly coveted by a certain segment of Singapore society regardless of their religious affiliation as it was a seal of approval from the old guard (there wasn't a single Chindo or Mainlander in sight), and also because the food was _heavenly_ —Rosalind brought in her personal chefs, who took over the hotel's kitchens for one day and prepared an enormous buffet feast consisting of the most mouthwatering Singaporean dishes. Most important—this biblical bacchanal was completely _free of charge_ thanks to Rosalind's generosity, although guests were asked to contribute something to the offering basket immediately following the closing prayer.1 Having strategically chosen a table closest to the buffet area, Daisy Foo sighed as she watched Araminta Lee standing in line at the noodle station dishing out some _mee siam._ " _Aiyah_ —that Araminta! _Bein kar ani laau!_ "2 "She doesn't look old. She just doesn't have any makeup on, that's all. Those supermodel types look like nothing on earth without makeup," Nadine Shaw said as she tucked into her steaming bowl of _mee rebus_ noodles. Dousing her _mee goreng_ with more chili oil, Eleanor Young commented, "It has nothing to do with that. I used to see her swim at the Churchill Club, and even when she was coming out of the pool dripping wet, she looked beautiful without a stitch of makeup on. Her face has just taken a turn, that's all. She has one of those faces that I always knew would age badly. What is she...twenty-seven, twenty-eight now? It's all over for her, _lah_." At that moment, Lorena Lim and Carol Tai arrived at the table with plates piled dangerously high with food. "Wait, wait...who's aging badly?" Lorena inquired eagerly. "Araminta Lee. Over at that table with all the Khoo women. Doesn't she look haggard?" Nadine said. " _Alamak_ , bite your tongue, Nadine! Didn't you know she just had a miscarriage?" Carol whispered. The ladies all stared at Carol, mouths agape. "Again? Are you joking? Who told you, _lah_?" Daisy demanded, still chewing on her _mee pok_. "Who else? Kitty, _lor_. Kitty and Araminta are the best of friends now, and ever since this latest miscarriage, she's been spending a lot of time at Kitty's house playing with Gisele. She's completely heartbroken." "How often do you see Kitty and Gisele?" Lorena asked, marveling that Carol could be so forgiving of her ex-daughter-in-law—the same woman who had cheated on her son, Bernard, with a man Kitty met at the funeral of Carol's late husband and who subsequently dragged Bernard through a particularly acrimonious divorce and custody battle. (Of course, it didn't hurt that Carol abhorred her son's new lifestyle of yoga and "that ridiculous Jurassic diet," both of which she considered to be satanic.) "I go over to Kitty's at least once a week, and Gisele comes to church with me every Sunday," Carol proudly reported. "Is it healthy for Araminta to be playing with your granddaughter when she just lost her own baby?" Nadine wondered out loud. " _Aiyah_ , I'm sure old Mrs. Khoo must be giving Araminta _soooo_ much pressure to produce a grandson! It's been five years since she married Colin! My Nicky and Rachel have been married for two years now, and they still won't give me a grandchild!" Eleanor complained. "But Araminta is still young. She has plenty of time, _lah_ ," Nadine argued. "With all of Dorothy Khoo's side disinherited, Puan's side good-for-nothings, and Nigel Khoo running off and marrying that _Russian cabaret singer_ , who is obviously too old to _seh kiah_ ,3 Colin and Araminta are the last hope to carry on the Khoo name," Daisy commented. Having been born a Wong, of the tin-mining Wongs, Daisy had an encyclopedic knowledge of Singapore's social history. The ladies all shook their heads, casting pitiful glances at Araminta, who to anyone else but these women's hypercritical eyes looked perfectly gorgeous and lovely in her yellow striped minidress from Jacquemus. "Well, Eleanor, your niece Astrid just arrived. There's one girl who never seems to age," Carol observed. All the women turned to look as Astrid descended the sweeping curved staircase with her mother, Felicity Leong; the society queen Mrs. Lee Yong Chien; and another elderly lady decked out in a cobalt blue sequined hijab. "Who is that Malay woman wearing that _ginormous_ ruby choker? If that center stone looks as big as it does from here, it must be the size of a lychee up close!" Lorena exclaimed. Having been married into the L'Orient Jewelry family for more than three decades, she definitely knew her rocks. "Oh that's the Dowager Sultana of Perawak. She's staying with the Leongs, of course," Eleanor reported. " _Alamak_ , having royalty as houseguests is such a nuisance!" Daisy complained. Lorena, like most of the other women in the ballroom, scrutinized Astrid from head to toe as she walked to her table wearing what appeared to be a crisp men's button-down shirt tucked into exquisitely cut navy-and-white gingham cigarette trousers. "It's true, Astrid actually looks younger and younger every time I see her. Isn't she in her late thirties by now? She looks like an MGS4 girl coming off the school bus! I bet you she must be sneaking off somewhere and getting things done." "I can tell you she hasn't had _a thing_ done. She's not the type," Eleanor said. "It's how she puts it all together. The other girls her age are dressed up like Christmas trees but just look at Astrid...hair in a sleek ponytail, ballet flats, not a drop of jewelry except that cross...is it turquoise? And _that outfit!_ She looks like Audrey Hepburn on the way to a screen test," Daisy said approvingly as she fished around in her new Céline handbag for a toothpick. "Blah-dee-hell! See what my snobby daughter-in-law forces me to carry? She gave me this fancy handbag for my birthday because she's embarrassed of being seen next to me when I'm carrying my no-name purse, but I can't ever find anything in here! It's so damn deep, and there are so many damn pockets!" "Daisy, will you please stop swearing? We are in the Lord's presence tonight, you know," Carol admonished. As if on cue, the Christian Fellowship Banquet's hostess, Rosalind Fung, got up from her table and walked onto the stage. A short, plumpish woman in her mid-sixties with a frizzy spiral perm, Rosalind was dressed in what seemed to be the regulation uniform of every middle-aged old-money Singaporean heiress—a sleeveless floral blouse, probably purchased from the clearance rack at John Little, taupe elastic-waist pants, and orthopedic open-toe sandals. She smiled happily from the podium at her gathered friends. "Ladies, thank you all for coming tonight to join in fellowship with Christ. A quick warning to everyone before we start: I'm told that the _laksa_ 5 is dangerously spicy tonight. I don't know what happened, but even Mary Lau, who everyone knows has to have extra chili with everything, told me that she _buey tahan_ 6 the _laksa_. Now, before we continue to nourish our stomachs and our souls, Bishop See Bei Sien will begin our program with a blessing." As the bishop started one of his notoriously tedious prayers, bizarre noises could be heard coming from behind one of the ballroom's side doors. It sounded as if there was a heated argument going on outside, followed by a series of muffled bangs and scrapes. Suddenly the door burst open. "NO, I SAID YOU CANNOT GO IN!" a female attendant shouted forcefully, breaking the silence. Something could be heard running along the side of the ballroom, wailing intermittently like an animal. Daisy prodded the woman at the next table who had stood up to get a better view. "What can you see?" she asked anxiously. "Dunno, _lah_ —it looks like...like some crazy homeless person," came the reply. "What do you mean 'homeless'? There is no such thing as a homeless person in Singapore!" Eleanor exclaimed. Astrid, who was seated at the far end beside the stage, wasn't fully aware of what was happening until a woman with extremely disheveled hair wearing stained yoga sweats suddenly appeared at her table, dragging two young girls in school uniforms behind her. Mrs. Lee Yong Chien let out a gasp and clutched her purse tightly to her chest, as Astrid realized in astonishment that the two girls were Chloe and Delphine, Charlie Wu's daughters. And the deranged-looking woman was none other than Charlie's estranged wife, Isabel! The last time Astrid had seen Isabel, she had been exquisitely attired in Dior couture at the Venice Biennale. Now she was completely unrecognizable. What were they doing here in Singapore? Before Astrid could properly react, Isabel Wu took her eldest daughter by the shoulders and turned her toward Astrid. "Here she is!" she screamed, spit forming at the corners of her mouth. "I want you to see her with your own eyes! I want you to see the whore that spreads her legs for your daddy!" Everyone at the table gasped, and Rosalind Fung immediately made the sign of the cross, as if it would somehow protect her ears from absorbing the obscenity. The hotel's security guards came rushing up, but before Isabel could be properly restrained, she grabbed the nearest bowl of _laksa_ and hurled it at Astrid. Astrid backed away reflexively, and the bowl ricocheted off the edge of the table, splashing scalding extra-spicy soup all over Felicity Leong, Mrs. Lee Yong Chien, and the Dowager Sultana of Perawak. * * * 1 Most of the guests left five or ten dollars each, except Mrs. Lee Yong Chien, who never left anything. "I do all my giving through the Lee Family Foundation" was what she always said. 2 Hokkien for "Gotten so old!" 3 Hokkien for "bear a child." 4 Methodist Girls' School, which we Anglo-Chinese School (ACS) boys used to call Monkey Girls' School. 5 A spicy noodle soup dish served with cockles, fish cake, and thick rice noodles. 6 Singlish for "cannot endure it." # CHAPTER THREE RADIO CITY MUSIC HALL, NEW YORK Patti Smith was in the middle of belting out "Because the Night" when Nicholas Young's cell phone began lighting up like a firecracker in his jeans pocket. Nick ignored the call, but when the lights came up after the concert's final encore, he glanced at the screen and was surprised to find one voice mail from his cousin Astrid, another from his best friend Colin Khoo, and five text messages from his mother. His mother never texted. He didn't think she even _knew_ how to text. The messages read: ELEANOR YOUNG: 4?Z Nicky# ELEANOR YOUNG: p lease cakk me at once! Where are y ELEANOR YOUNG: oy? Why don't you answered any of your phines? ELEANOR YOUNG: Ah Ma had a massive heat attack! ELEANOR YOUNG: C allhome now! Nick handed the phone to his wife, Rachel, and sank into his seat. After the euphoric high of the concert, he felt like someone had suddenly knocked all the wind out of him. Rachel read the text messages quickly and looked up at Nick in alarm. "Don't you think you'd better call?" "Yeah, I guess I should," Nick replied. "Let's get out of here first, though. I need some air." — As the two of them exited Radio City Music Hall, they hurried across Sixth Avenue to avoid the crowds still milling under the famous marquee. Nick paced around the plaza outside the Time & Life Building to make his call. There was that familiar dead pause for a few seconds, usually followed by the distinctive Singapore ringtone, but today, his mother's voice abruptly came onto the line before he was ready for it. "NICKY? Nicky, ah? Is that you?" "Yes, Mum, it's me. Can you hear me?" " _Aiyah_ , why did you take so long to call back? Where are you?" "I was at a concert when you called." "A concert? Did you go to Lincoln Center?" "No, it was a rock concert at Radio City Music Hall." "What? You went to see those Rockette girls with the kicking legs?" "No, Mum, it was a ROCK CONCERT, not the Rockettes." "A ROCK CONCERT! _Alamak_ , I hope you wore earplugs. I read that people are losing their hearing younger and younger now because they keep going to those rock-and-roll concerts. All those heepees with long hair are going stone-deaf. Serves them right." "The volume was fine, Mum—Radio City has some of the best acoustics in the world. Where are you?" "I just left Mount E. Ahmad is driving me to Carol Tai's—she's having a chili crab party. I had to get out of that hospital ward because it was getting too chaotic. Felicity is being her usual bossy mother hen—she said I couldn't go in to see Ah Ma because too many people had been to see her already and they had to start restricting the number of visitors. So I just sat outside for a while and nibbled away on the buffet with your cousin Astrid. I wanted to show my face so no one would dare say I didn't do my duty as the wife of the eldest son." "Well, how _is_ Ah Ma?" Nick didn't want to admit it to himself, but he was rather anxious to know whether his grandmother was dead or alive. "They managed to stabilize her, so she's okay for now." Nick looked up at Rachel and mouthed, "She's okay," as Eleanor continued her update: "They put her on a morphine drip so she's sedated at the moment in the Royal Suite. But Prof Oon's wife told me that it's not looking good." "Prof Oon's wife is a doctor?" Nick asked, confused. "No, _lah_! But she's his wife—she heard it straight from the horse's mouth that Ah Ma's not going to last long. _Alamak_ , what do you expect? She has congestive heart failure and she's ninety-six years old—it's not like they can operate at this point." Nick shook his head derisively—patient confidentiality was obviously not high on Francis Oon's list. "What is Mrs. Oon even doing there?" "Don't you know Mrs. Oon is the niece of Singapore's First Lady? She brought along the First Lady, Great-aunt Rosemary T'sien, and Lillian May Tan. The entire floor at Mount E has been sealed off to the public—it's become a restricted VVIP floor because of Ah Ma, Mrs. Lee Yong Chien, and the Dowager Sultana of Perawak. There was a bit of a fuss over who would be put in the Royal Suite,1 as the Malay ambassador insisted that the Dowager Sultana had to get it, but then the First Lady intervened and told the hospital's chief officer, 'This isn't even up for discussion. _Of course_ Shang Su Yi must have the Royal Suite.' " "Wait a minute, Mrs. Lee and the Sultana of Perawak? I'm not following you..." " _Aiyoh_ , you didn't hear what happened? Isabel Wu had a psychotic breakdown and kidnapped her children from school and flew them to Singapore and barged into Rosalind Fung's Christian Fellowship Banquet and threw a bowl of extra-hot _laksa_ at Astrid but missed and it landed all over the ladies but thank God Felicity was wearing one of her _pasar malam_ 2 polyester dresses from that tailor of hers in Tiong Bahru so the soup did NOTHING to her and slid right off like Teflon but poor Mrs. Lee and the Dowager Sultana got drenched and are recovering from first-degree burns." "Okay, you've completely lost me there." Nick shook his head in exasperation, as Rachel gave him a questioning look. "I thought of all people you'd know. Isabel Wu accused Astrid of spreading her legs...I mean, having an affair with her husband, Charlie! Right in front of Bishop See Bei Sien and everyone in the banquet hall! _Aiyoh_ , it's so shameful—now it's out in the open and all of Singapore is talking about it! Is it true? Is Astrid Charlie's mistress?" "She's not his mistress, Mum. That much I can tell you," Nick said carefully. "You and your cousin—always keeping secrets from me! Poor Astrid looked completely shell-shocked at the hospital, but she was still trying to play the gracious hostess to all the visitors. Anyway, when are you coming home?" Nick paused for a moment, before saying decisively, "I'm not coming back." "Nicky, don't talk nonsense! You _must_ come home! Everyone is coming back—your father is already on his way from Sydney, Uncle Alfred arrives in a few days, Auntie Alix and Uncle Malcolm are flying in from Hong Kong, and even Auntie Cat is coming down from Bangkok. And get this—supposedly all your Thai cousins are coming too! Can you believe that? Those high-and-mighty royal cousins of yours _never_ deign to come down to Singapore, but I'm telling you"—Eleanor paused, glancing at her driver before cupping her hands over the cell phone and whispering rather indiscreetly—" _they all sense that this is the end_. And they want to show their faces at Ah Ma's bedside just to make sure they're in the will!" Nick rolled his eyes. "Only you would say something like that. I'm sure that's the last thing on anyone's mind." Eleanor laughed derisively. "Oh my goodness, don't be so naïve. I guarantee you that's the only thing going through _everyone's_ mind! The vultures are all circling like mad, so get yourself on the next flight! This is your last chance to make up with your grandmother"—she lowered her voice again—" _and if you play your cards right, you still might get Tyersall Park!_ " "I think that ship has sailed. Trust me, I don't think I'll be welcomed." Eleanor sighed in frustration. "You're wrong about that, Nicky. I know Ah Ma won't close her eyes until she sees you one last time." — Nick ended the call and quickly updated Rachel on his grandmother's condition and the Isabel Wu hot-soup incident. Then he perched on the edge of the plaza's reflecting pool, suddenly feeling drained. Rachel sat beside him and put her arm around his shoulder, not saying anything. She knew how complicated things were between him and his grandmother. They had once been extremely close—Nick being the adored only grandson who bore the Young surname and the only grandchild who had lived at Tyersall Park—but it had now been more than four years since they had last seen or spoken to each other. And it was all because of her. Su Yi had ambushed them during what was supposed to be a romantic getaway in the Cameron Highlands of Malaysia, commanding Nick to end his relationship with Rachel. But Nick had not only refused; he had uncharacteristically insulted his grandmother in front of everyone—something that had probably never happened to this revered woman in her entire life. Over the past few years, the gulf had only widened as Nick defiantly married Rachel in California, leaving his grandmother and the majority of his large family off the wedding invitation list. _This girl does not come from a proper family!_ Rachel still vividly remembered Su Yi's condemnation, and for a moment, a slight chill went down her spine. But here in New York, Shang Su Yi's shadow didn't loom as large, and for the past two years, she and Nick had been blissfully enjoying married life far away from any family interference. Rachel had occasionally tried to see if anything could be done to mend the fences between Nick and his grandmother, but he had stubbornly refused to talk about it. She knew Nick wouldn't react so angrily if he didn't care about his grandmother so much. Rachel looked Nick squarely in the face. "You know, as much as it pains me to admit it, I think your mother's right—you should go home." "New York is my home," Nick replied flatly. "You know what I mean. Your grandmother's situation sounds really precarious." Nick stared up at the windows of Rockefeller Center, still lit at this late hour, avoiding Rachel's eyes. "Look, I'm starving. Where should we go for a late supper? Buvette? Blue Ribbon Bakery?" Rachel realized it was pointless to push him any further. "Let's do Buvette. I think their coq au vin is just what we need right now." Nick paused for a moment. "Maybe we ought to avoid any place with hot soup tonight!" * * * 1 The Royal Suite at Mount Elizabeth Hospital was originally built by the royal family of Brunei for their private use, but is now open to other VVIP patients. 2 Literally "night market" in Malay, the _pasar malam_ is a traveling outdoor street market where many bargains are sold. In this instance, Eleanor is implying that Felicity Young's custom-tailored outfit looks like a cheap schmatta from an outdoor street market. # CHAPTER FOUR MOUNT ELIZABETH HOSPITAL, SINGAPORE After five hours at the hospital's intensive care unit, alternately sitting beside her grandmother, managing the visiting dignitaries, managing her mother's nerves, and managing the caterers from Min Jiang that had set up a buffet1 in the VIP visitors' lounge, Astrid needed a break and some fresh air. She took the elevator down to the lobby and walked out to the little grove of palm trees adjacent to the side entrance off Jalan Elok and began texting with Charlie on WhatsApp. ASTRID LEONG TEO: Sorry I couldn't talk earlier. No phones allowed in the ICU. CHARLES WU: No worries. How's your Ah Ma? ALT: Resting comfortably at the moment, but the prognosis isn't good. CW: So sorry to hear that. ALT: Are Isabel and the kids all right? CW: Yes. Their plane landed a couple of hours ago, and thankfully Isabel's mother managed to keep her calm during the flight. She's been admitted to Hong Kong Sanatorium and her doctors are attending to her. The kids are okay. Bit shaken up. Chloe's glued to her phone as usual, and I'm lying here next to Delphine while she sleeps. ALT: I have to tell you—they were such angels through it all. I could tell they were trying to stay composed during the whole ordeal. Delphine dashed to the side of Mrs. Lee Yong Chien while Chloe tried to help calm Isabel down as she was being restrained. CW: I am SO SORRY for this. ALT: Come on, it wasn't your fault. CW: It IS my fault. Should have seen this coming. She was supposed to sign off on the divorce settlement this week, and my lawyers were pressuring her. That's why she snapped. And my security team totally screwed up. ALT: Wasn't it the school that screwed up? Letting Isabel walk in and take them out of class in the middle of the school day? CW: She apparently put on an Oscar-worthy performance. With the way she looked, they really thought there was a family emergency. This is what happens when you donate too much money to a school—they don't ever question you. ALT: I don't think anyone could have anticipated this. CW: Well, my security team should have! This was an epic fuckup. They never even saw Isabel and the kids exiting—they only had the front entrance under surveillance. Since Izzie went to Diocesan too, she knew all the secret ways to sneak out. ALT: OMG I didn't think of that! CW: She took them out through the laundry-room door and they hopped on the MTR straight to the airport. BTW, we discovered how she knew where to find you. Rosalind Fung tagged you in a Facebook pic from last month's Christian Fellowship event. ALT: Really? I'm never on FB. Look at it about once a year. CW: Isabel's mum is FB friends with Rosalind. She messaged her three days ago asking if you would be at this event, and Rosalind said yes and even told her you'd be seated at the table of honor! ALT: So THAT'S how she knew how to find me in that crowd! I was so shocked when she started screaming at me. CW: I guess the cat's out of the bag. Everyone must be talking about us now. ALT: I have no idea. Probably. CW: What did your mother say? Did she go ballistic when she found out about us? ALT: Mum's said nothing so far. I'm not sure she even connected all the dots. When it happened she was too busy dabbing tissues on Mrs. Lee and the Sultana. And then in the midst of all that, Araminta Lee rushed up to us and said, "Haven't you heard? Your grandmother had a heart attack!" CW: You've really had the day from hell. ALT: Not compared to your kids. I'm sorry they had to go through this. Seeing their mother in that state... CW: They've seen it before. It's just never been this bad. ALT: I wanted to hug them. I wanted to get them out of there and fly them back to you myself but it was total chaos with everything happening all at once. CW: YOU need a hug. ALT: Mmm...would be so nice. CW: I don't know how you put up with me and all the shit that keeps happening. ALT: I could say the same myself. CW: Your shit ain't half as crazy as mine. ALT: Just you wait. With Ah Ma in the condition she's in, I don't know what's going to happen anymore. There's going to be a family invasion this week, and it's not going to be pretty. CW: Is it going to be like "Modern Family"? ALT: More like "Game of Thrones." The Red Wedding scene. CW: Oh boy. Speaking of weddings, does anyone know about our plans? ALT: Not yet. But I think this might be the perfect opportunity to start prepping my family...letting some of my closer relatives know that I'm divorcing Michael, and there's a new man in my life... CW: Is there a new man in your life? ALT: Yes, his name is Jon Snow. CW: Hate to break it to you, but Jon Snow is dead.2 ALT: No he's not. You'll see. :-) CW: Seriously, I'm here if you need me. Do you want me to come down? ALT: No, it's fine. Chloe and Delphine need you. CW: I need you. I can send the plane anytime. ALT: Let's see how this week goes with my family and then we can really begin making some plans... CW: I'll be counting the minutes... ALT: Me too...xoxoxo * * * 1 Yes, you can be sure Min Jiang's legendary wood-fired Beijing duck—with a first serving of crispy duck skin dipped in fine granulated sugar, wrapped in homemade pancakes with sweet sauce, shredded leeks, and cucumbers, followed by a second serving of the sliced duck in fried noodles—was part of the impromptu ICU buffet organized by Felicity Leong. 2 In 2015, the world was most preoccupied about figuring out if the economy would continue to recover, how to keep the Ebola outbreak in Africa from becoming a global pandemic, where ISIS terrorists would strike next after the horrendous Paris attacks, how to help Nepal after its devastating earthquakes, who would be the front-runners in the next U.S. presidential campaign, and whether Jon Snow, Lord Commander of the Night's Watch and one of the heroes in George R. R. Martin's _Game of Thrones_ television series, really died in the season finale. # CHAPTER FIVE RUE BOISSY D'ANGLAS, PARIS She stood on a raised mirrored platform in the middle of Giambattista Valli's elegantly appointed atelier, staring up at the glittering chandelier, trying to hold still as two seamstresses meticulously pinned up the hem of the delicate tulle skirt that she was modeling. Looking out the window, she could see a little boy holding a red balloon walking down the cobblestone street, and she wondered where he was heading. The man with the string of baroque pearls around his neck smiled at her. " _Bambolina_ , could you please turn for me?" She twirled around once, and the women surrounding her all oohed and aahed. " _J'adore!_ " Georgina swooned. "Oh Giamba, you were right! Just two inches shorter and look how the skirt comes alive. It's like a flower blooming right before our eyes!" Wandi cooed. "Like a pink peony!" Tatiana gushed. "I think for this dress, I was inspired by the ranunculus," the designer stated. "I don't know that flower. But Giamba, you're a genius! An absolute genius!" Tatiana praised. Georgina walked around the platform, scrutinizing the dress from every angle. "When Kitty first told me that this couture dress would cost €175,000, I have to confess I was a little surprised, but now I think it's worth every cent!" "Yes, I think so too," Kitty murmured softly, assessing the tea-length gown from its reflection in the rococo mirror leaning against the wall. "Gisele, do you like it?" "Yes, Mommy," the five-year-old said. She was getting tired of standing there in the dress with the hot spotlight on her, and she wondered when she could get her reward. Mommy had promised her a big ice-cream sundae if she would stand very still during her fitting. "Okay then," Kitty said, looking at Giambattista Valli's assistant. "We will need three of these." "Three?" The tall, gangly assistant looked at Kitty in surprise. "Of course. I buy everything in threes for myself and Gisele—we need one for each of our closets in Singapore, Shanghai, and Beverly Hills. But this one has to be ready for her birthday party in Singapore on March first—" "Of course, Signora Bing," Giambattista cut in. "Now, ladies, I hope you don't mind if I leave Luka to show you the new collection. I have to rush off to an appointment with the fashion director of Saks." The women exchanged air kisses with the departing designer, Gisele was sent off with her nanny around the corner to Angelina for ice cream, and as more Veuve Clicquot and café crèmes were brought into the showroom, Kitty stretched out on the elegant chaise lounge with a contented sigh. It was only their second day here, and already she was having the time of her life. She had come on this Parisian shopping spree with her Singaporean BFFs—Wandi Meggaharto Widjawa, Tatiana Savarin, and Georgina Ting—and somehow, things were so different on this trip. From the moment she stepped off _Trenta_ , the Boeing 747-81 VIP she had recently refurbished to look exactly like the Shanghai bordello in a Wong Kar-wai movie,1 she was experiencing heretofore unprecedented levels of sucking up. When their motorcade of Rolls-Royces arrived at the Peninsula Paris, all of the hotel management stood in a perfect line to greet her at the entrance, and the general manager escorted her up to the impressive Peninsula Suite. When they went to dinner at Ledoyen, the waiters were bowing and scraping so frantically that she thought they were going to break into somersaults. And then during her Chanel couture fittings at rue Cambon yesterday, none other than _Karl Lagerfeld's personal assistant came downstairs with a handwritten note from the great man himself!_ Kitty knew that all this royal treatment was because she had arrived in Paris this time as MRS. JACK BING. She wasn't just the wife of some random billionaire anymore, she was the new wife of China's second-richest man,2 one of the ten richest men in the world. To think that Pong Li Li, the daughter of sanitation workers in Qinghai, had achieved such great heights at the relatively young age of thirty-four (although she told everyone she was thirty). Not that any of this had been easy—she had worked nonstop her entire life to get to this place. Her mother had come from an educated middle-class family, but she had been banished with her family to the countryside during Mao's Great Leap Forward campaign. But she had instilled in Kitty that getting an education was the only way out. All through her youth, Kitty studied extra hard to always be the top in her class, top in her school, top in her state exams, only to see her one chance at a higher education get snatched away when some boy with all the right connections was awarded the only slot to university in their entire district—the slot that was rightfully meant to be hers. But Kitty didn't give up, she kept on fighting, moving first to Shenzhen to work at a KTV bar where she had to do unspeakable things, and then to Hong Kong, landing a bit part in a local soap opera, transforming it into a recurring role after becoming the director's mistress, dating a series of rather inconsequential men until she met Alistair Cheng, that cute, clueless boy who was much too sweet for his own good, going with him to the Khoo wedding and meeting Bernard Tai, running off to Vegas with Bernard to get married, meeting Jack Bing at Bernard's father's funeral, divorcing Bernard, and finally, at long last, marrying Jack, a man who was truly worthy of all her efforts. And now that she had provided him with his first son (Harvard Bing, born in 2013), she could do anything she damn well pleased. She could fly to Paris on her own private jumbo jet with one French translator, two children, three fabulous girlfriends (all as toned and polished and expensively dressed as she was, and all wives of rich expats in Shanghai, Hong Kong, and Singapore), four nannies, five personal maids, and six bodyguards and rent out the entire top floor of the Peninsula Hotel (which she did). She could order the entire Chanel Automne-Hiver couture collection and have every piece made in triplicate (which she did). She could take a personal guided tour of Versailles with the chief curator followed by a special al fresco lunch prepared by Yannick Alléno at Marie Antoinette's hamlet (which was happening tomorrow, thanks to Oliver T'sien, who set it all up). If someone wrote a book about her, no one would believe it. Kitty sipped her champagne and glanced at the ball gowns that were being paraded before her, feeling a little bored. Yes, it was so beautiful, but after the tenth dress, it was all beginning to look the same. Was it possible to overdose on too much beauty? She could buy up the whole collection in her sleep and forget she ever owned any of it. She needed something more. She needed to get out of here and look at some Zambian emeralds, maybe. Luka recognized the look on Kitty's face. It was the same expression he had seen all too often in some of his most privileged clients—these women who had constant, unlimited access to everything that their hearts ever desired—the heiresses, celebrities, and princesses that had sat in this very spot. He knew he needed to change direction, to shift the energy in the room in order to reinspire his high-spending client. "Ladies, let me show you something very special that Giamba has been toiling away at for weeks. Come with me." He pressed against one panel of the boiserie walls, revealing Giambattista's inner sanctum—a hidden workroom that contained only one gown displayed on a mannequin in the middle of the pristine space. "This dress was inspired by Gustav Klimt's _Adele Bloch-Bauer I_. Do you know the painting? It was purchased for $135 million by Ronald Lauder and hangs in the Neue Galerie in New York." The ladies stared in disbelief at the artistry of the off-the-shoulder ball gown that transformed from ivory tulle at the bodice and into a shimmering gold column, with a cascading train-length skirt embroidered with thousands of gold chips, lapis lazuli, and precious gemstones, painstakingly scattered into a swirling mosaic pattern. It truly looked like a Klimt painting come to life. "Oh my God! It's unbelievable!" Georgina squealed, running one of her long manicured nails over the gem-encrusted bodice. " _Ravissement!_ " Tatiana commented, mistakenly trying to show off her secondary-school French. " _Combien?_ " "We don't have a price on it yet. It's a special commission that's taken four full-time embroiderers three months to assemble so far, and we still have weeks of work to go. I would say that this dress, with all the rose-gold disks and precious stones, will end up costing more than two and a half million euros." Kitty stared at it, her heart suddenly beginning to pound in that delicious way it did whenever she saw something that aroused her. "I want it." "Oh, Madame Bing, I'm so sorry, but this dress is already spoken for." Luka smiled at her apologetically. "Well, make me another one. I mean another three, of course." "I'm afraid we cannot make you this exact dress." Kitty looked at him, not quite comprehending. "Oh, I'm sure you can." "Madame, I hope you will understand...Giamba would be happy to collaborate with you on another dress, in the same spirit, but we cannot replicate this one. This is a one-of-a-kind piece made for a special client of ours. She is from China also—" "I'm not from China, I'm from Singapore," Kitty declared.3 "Who is this 'special client'?" Wandi demanded, her thick mane of Beyoncé-bronzed hair shaking indignantly. "She's a friend of Giamba's, so I only know her by her first name: Colette." The ladies suddenly fell silent, not daring to ask what they wanted to ask. Wandi finally piped up. "Er...are you referring to Colette Bing?" "I'm not sure if that is her surname. Let me check the spec sheet." He turned over a leaf of paper. "Ah yes, it _is_ Bing. _Une telle coïncidence!_ Is she related to you, Madame Bing?" Luka asked. Kitty looked like a deer caught in headlights. Was Luka kidding? Surely he must know that Colette was her husband's daughter from his first marriage. Tatiana quickly jumped in. "No, she's not. But we know of her." "Do we ever." Wandi sniffed, wondering whether she should tell Luka how Colette's bitch-from-hell video tirade had gone viral in China, logging more than thirty-six million views on WeChat alone, making her such a notorious poster child of _fuerdai_ 4 bad behavior that she was forced to flee to London in disgrace. Wandi decided that it was better not to bring it up now. "So this dress is for Colette," Kitty said, fondling one of the gossamer-like organdy sleeves. "Yes, it's going to be her wedding dress." Luka smiled. Kitty looked up at him, stunned. "Colette is getting married?" "Oh yes, madame, it's the talk of the town. She's marrying Lucien Montagu-Scott." "Montagu-Scott? What does his family do?" Wandi asked, since everything in her universe revolved around being part of an incredibly rich Indonesian family. "I don't know anything about his _famille_ , but I believe he's a lawyer?" Luka said. Tatiana immediately began googling his name, and read aloud from the first link that popped up: "Lucien Montagu-Scott is one of Britain's new generation of environmental lawyers. A graduate of the Magdalen College—" "It's pronounced 'Maudlin,' " Georgina corrected. "Maudlin College, Oxford, Lucien sailed across the Pacific on a catamaran made out of 12,500 reclaimed plastic bottles with his friend David Mayer de Rothschild to highlight the problem of global marine pollution. More recently, he has been involved in publicizing the environmental crisis in Indonesia and Borneo—" "I think I'm going to fall asleep," Tatiana scoffed. "He's a charming gentleman—comes with her to every fitting," Luka remarked. "I can't imagine why Colette Bing of all people would end up settling for this guy. He's not even an M&A lawyer—his annual salary probably wouldn't even pay for one of her dresses! I guess she must be desperate to have mixed-race babies," Georgina said, glancing covertly at Kitty, hoping she wasn't too upset by the news. Kitty just stood staring at the dress, her expression inscrutable. "Oooh...I want to have a beautiful mixed-race baby too! Luka, do you know any hot single French counts?" Wandi asked. "I'm sorry, mademoiselle. The only _comte_ I know is married." "Married is fine...I'm married too, but I would dump my boring hubby if I could get a beautiful half-French baby!" Wandi giggled. "Wandi, careful what you wish for. You never know what sort of baby you'll get," Tatiana said. "No, if you have a baby with a Caucasian man, you're almost guaranteed it will be attractive. There's a ninety-nine percent chance it will look like Keanu Reeves. That's why so many Asian women are desperate to find white husbands." "First of all, Keanu isn't half white. He's like three-quarters—his mother is only part Hawaiian and his father is American.5 And not to burst your bubble, but I have seen some rather unfortunate-looking mixed-raced babies," Georgina insisted. "Yes, but it's very rare. And soooo tragic when that happens! OMG—did you hear about that man in China who sued his wife because all their children came out looking so ugly? He had purposely married this beautiful woman, but it turns out she'd had tons of plastic surgery before she met him! So the children all looked like her before the surgery!" Wandi giggled. "That story was a lie!" Tatiana insisted. "I remember when it went viral, but it turned out the newspaper made up the whole thing and did a fake photo shoot with two models posing with a bunch of ugly kids." Finding the topic of unattractive children to be appallingly distasteful, Luka tried to steer the conversation in another direction. "I think Monsieur Lucas and Mademoiselle Colette will have beautiful children. She's so pretty, and he's very handsome, you know." "Well, good for them," Kitty said in a merry tone. "Now, all this baby talk has made me want to look at some daytime outfits for Gisele. Can we do that? And do you have anything fun and unisex I can dress Harvard in?" " _Oui,_ _madame._ " As he headed back into the main showroom, Georgina took him by the arm. "Tell me, Luka, do you live on the second floor?" Without missing a beat, Luka replied with a grin, "Yes, mademoiselle, I think you've seen me before." Wandi and Tatiana stood by the doorway watching as Kitty lingered for a moment longer by the dress. As she turned to leave, she grabbed the back of the precious Klimt-inspired skirt and gave it one quick, forceful tug—ripping it clear down the middle. * * 1 See Wong Kar-wai's _The Grandmaster_. I much prefer Wong's _In the Mood for Love_ to this film, but the set design was amazing. 2 Or third or fourth or seventh richest, depending on which financial tabloid you trust. 3 Kitty has only lived part-time in Singapore for two years, but like so many other immigrants from Mainland China has taken to referring to it as home. 4 Mandarin for "second-generation rich," this label is akin to "trust-fund kids" and carries all the scorn and envy it implies. 5 Actually, Keanu Reeves was born in Beirut, Lebanon, to an English mother and a father of Hawaiian, Chinese, and English ancestry. # CHAPTER SIX 11 NASSIM ROAD, SINGAPORE Winding through the heart of Bukit Timah, Nassim Road was one of the few long, picturesque streets in Singapore that still retained a feel of graceful, Old World exclusivity with its parade of historic mansions converted into embassies, tropical modern bungalows on crisp manicured lawns, and stately Black and White houses left over from the colonial era. Number 11 Nassim Road was a particularly fine example of Black and White architecture, as it had only changed hands once since it had been built a century ago. Originally commissioned by Boustead and Company, it had been purchased by S. K. Leong in 1918, and every original detail had been preserved and lovingly maintained since then by three generations of Leongs. As Astrid pulled up the long driveway lined with Italian cypresses to the home where she had grown up, the front door opened, and Liat, the majordomo, gestured for Astrid to come down. Astrid frowned—she was picking up her mother to visit Ah Ma at the hospital, and they were already running late for the morning briefing with Professor Oon. Astrid left her dark blue Acura in the arched porte cochere and entered the foyer, bumping into her sister-in-law Cathleen, who was seated on a rosewood stool lacing up her walking shoes. "Morning, Cat," Astrid greeted. Cathleen looked up at her with a strange expression. "They're still eating. Sure you want to show your face today?" Astrid figured that Cathleen was referring to the Isabel Wu fiasco the other evening. With all the attention focused on her grandmother, the incident had gone unmentioned by her parents, but she knew that wouldn't last long. "It's now or never, I guess," Astrid said, bracing herself as she walked toward the breakfast room. "Godspeed," Cathleen said, grabbing her battered Jones the Grocer shopping bag as she went out the door. Breakfast at Nassim Road was always served in the glassed-in summer porch adjacent to the drawing room. Boasting a circular marble-top teak table from the Dutch Indies, wicker chairs cushioned in whimsical monkey-print chintz, and a profusion of hanging ferns from the Tyersall Park greenhouses, it was one of the loveliest rooms in the house. As Astrid entered, her elder brother, Henry, gave her a dirty look and got up from the table to leave. He muttered something under his breath as he passed by, but Astrid couldn't make out what he said. She glanced first at her father, who was sitting in his usual wicker chair methodically slathering a piece of toast with gooey Marmite, and then at her mother, who sat in front of an untouched bowl of porridge, clenching a wadded-up ball of tissue in her hand, her face red and puffy from crying. "My God, did something happen to Ah Ma?" Astrid asked in alarm. "Hnh! I think the question should be: 'Will you finish your grandmother off with another heart attack when she reads _this_?' " Felicity chucked a sheet of paper onto the marble-top table in disgust. Astrid grabbed the sheet and stared at it in dismay. It was a printout from Asia's most popular online gossip column: > # DAILY DISH FROM LEONARDO LAI > > ## THE BEWITCHING HEIRESS AT THE CENTER OF THE ISABEL WU SOUPGATE INCIDENT! > > For those of you who have been following the scalding _scandale_ involving tech billionaire Charlie Wu's wife Isabel that almost caused an international incident between Malaysia and Hong Kong, fasten your seat belts, because boy do I have some shockers for you! We all know that Charlie and Isabel announced their separation in 2013, and informers tell me they've been privately negotiating the terms of their divorce ever since. At stake is a share of the Wu family fortune, their heritage mansion on Peak Road, and custodial rights of their two daughters. But a close friend of Isabel tells me, "It's been terribly hard for Isabel. She suffered her recent breakdown because of the emotional stress of the divorce and _that other woman_ involved." > > Yep, you heard that right. SHOCKER NUMBER ONE: Daily Dish can now confirm that _that other woman_ is none other than Astrid Leong Teo , the model-pretty wife of hunkalicious Singaporean Venture Capitalist Michael Teo (who I think missed his calling as a Calvin Klein underwear model) and mother to a seven-year-old boy, Cassius. Yes, Charlie and Astrid have been having a torrid, secret affair for the past five years, and in fact, SHOCKER NUMBER TWO: that incredible Tom Kundig –designed house currently under construction in Shek O that everyone thought was Leo Ming's new private museum is actually going to be Charlie and Astrid's love pad once they can legally shack up! (Astrid and Michael Teo are apparently headed to divorce court too.) > > The stunning seductress Astrid may be an unfamiliar name to Hong Kong readers, but she has an extraordinary backstory: According to my trusted Singapore insider, Astrid is the only daughter of Harry Leong , who officially is the chairman emeritus of the Institute of ASEAN Affairs. Unofficially, he's one of Singapore's most influential political power brokers who—my sources tell me—also happens to head S. K. Leong Holdings Pte Ltd, the secretive corporate behemoth that is rumored to own the Bank of Borneo, Selangor Mining, _New Malaysia Post_ _,_ and Palmcore Berhad, one of the world's largest commodity traders. And that's not all—Astrid's mother, Felicity Young , hails from one of Singapore's most pedigreed families. "The Youngs are in their own stratosphere. Cousins to the T'siens, the Tans, and the Shangs—they are related to practically everybody who's anybody, and Felicity's mother, Shang Su Yi , owns Tyersall Park, the largest private estate in Singapore," my insider reports. > > Schooled in London and Paris, Astrid moves in the most rarefied circles and counts among her friends deposed European royals, A-list fashion designers, and celebrity artists. "How can Isabel compete with that? Izzie isn't some filthy-rich heiress—she has an important career as a legal advocate for Hong Kong's poor and downtrodden and is busy raising her two daughters, not jet-setting around the world, sitting in the front rows of fashion shows. No wonder she would suffer a breakdown! Of course Charlie would be swept up by the ultra-glamorous life of Astrid—he was seduced by her once before." > > Which leads us to SHOCKER NUMBER THREE: Back in their college days, Astrid and Charlie _were actually engaged_ , but the union was broken off by her family because the Hong Kong Wus weren't deemed worthy enough by those snooty Singaporeans! It seems like the star-crossed lovers have never gotten over each other, which has led to this big ugly mess. Stay tuned to Daily Dish for more shockers to come! Astrid sank into a chair, trying to collect herself after reading the incendiary column. She was so upset, she didn't even know where to begin. "Who sent you this?" "What does it matter who sent it? The news is everywhere now. Everyone knows your marriage is on the rocks, and that you are at fault!" Felicity moaned. "Come on, Mum. You know it wasn't my fault. You know how careful and discreet I've been for the past couple of years as we've been working out the divorce. This article is nothing but a stream of inaccuracies and lies. When have I ever sat in the front row of any fashion shows? I'm always backstage helping out. Look, they even got Cassian's name wrong." Her mother looked at her accusingly. "So you're denying everything? You're not having an affair with Charlie Wu?" Astrid let out a deep sigh. "Not for the past five years! Charlie and I have only been together for about a year and a half—and this was _after_ I left Michael and Charlie filed for divorce from Isabel." "Then it is true! _That's_ why Isabel Wu would go berserk and try to attack you! You broke up her marriage...you broke up her family!" Felicity muttered through her tears. "Mum, Isabel Wu's marriage to Charlie has never been a happy one. I had nothing to do with their breakup. If you want to know the truth, _she_ has been cheating on him for many years, with numerous men—" "That still doesn't give you any excuse to be Anna Karenina! You're still being unfaithful! You're both still married to other people under the eyes of the law and God! Goodness me, what will Bishop See think when he gets wind of all this?" Astrid rolled her eyes. She didn't give a rat's ass what Bishop See thought. "So now what? You're going to move in to that 'love pad' with Charlie after the divorce and live in sin?" "That's the other lie...it's _not_ our love pad. Charlie started building that house long before we ever got together. He bought the land after his first separation from Isabel—four years ago!" Astrid took in a deep breath and steeled herself—it was the time to come completely clean with her parents. "But I suppose you should know that Charlie and I _do_ intend to get married when our divorces are finalized, and I will likely be spending more of my time in Hong Kong." Felicity looked at her husband in horror, waiting for him to react. "You _suppose_ we should know? You're planning to get married this year and you only tell us now? I cannot believe you would actually marry Charlie after all this. Disgraceful...so disgraceful!" "I really don't see what's so disgraceful about this, Mum. Charlie and I are in love. We've both acted entirely honorably throughout a very difficult time. It's just unfortunate that Isabel had another breakdown, that's all." "That breakdown! Those obscene things she said about you in front of the whole world—I have never felt so humiliated in all my life! And those poor ladies! How can I ever look the Sultan of Perawak in the face again? We almost killed his poor mother." "Auntie Zarah is just fine, Mum. You saw it yourself—her hijab was so encrusted with diamonds, hardly anything got through. She was more in shock because the _laksa_ wasn't halal." "That Charlie Wu—this is all his fault that our names are being dragged through the mud!" Felicity continued to rage. Astrid sighed in frustration. "I know you've never liked Charlie or his family—that's why you broke us up in the first place all those years ago. But things have changed now, Mum. No one cares about their lineage and all that nonsense anymore. The Wus are no longer considered nouveau riche. They are an establishment family now." "Establishment my foot! Wu Hao Lian's father used to sell soy sauce on a bicycle!" "That may be how they started out, but they've come a long way since Charlie's grandfather's time. Charlie has created one of the most admired companies in the world. Look at your new phone—the screen, the casing, I'm sure at least half the components are manufactured by Wu Microsystems!" "I _detest_ this phone! I never know how to use this stupid thing! I swipe and swipe and instead of making a phone call, some silly video of an Indian granny singing 'Twinkle, Twinkle Little Star' keeps appearing on my screen. I have to ask Lakshmi or Padme to make every damn call for me!" Felicity was seething. "Well, I'm sorry you still don't know how to use your smartphone. But that has nothing to do with how the Wus are perceived these days. Look how much money Mrs. Wu gives to that church on Barker Road—" "Those Wus are frightfully common, and they prove it all the more by giving an obscene amount of money to that church. They think their dirty money can buy their way into heaven!" Astrid just shook her head. "Stop being unreasonable, Mum—" "Your mother is _not_ being unreasonable," Astrid's father cut in, speaking up for the first time that morning. "Look at what's happened. Until today our family was able to enjoy the privileges of total privacy and anonymity. The Leong name has never appeared in the gossip columns, much less something as silly as this...this...I don't even know what to call this idiotic Internet thing." "And you're blaming Charlie for this?" Astrid shook her head, not seeing her father's logic. "No. I am blaming _you_. Your actions, however unconsciously, have led to this. If you had never gotten entangled with these people, our lives would not now be under the spotlight." "Come on, Dad, you're making a mountain out of a mole—" "SHUT YOUR MOUTH AND DON'T INTERRUPT ME WHEN I'M TALKING!" Harry banged his fist on the table, startling both Astrid and her mother. Neither of them could recall the last time he had raised his voice like this. "You have completely exposed yourself! And you have exposed and compromised your family! For more than two hundred years our business interests have never been scrutinized, but now they will be. Don't you see how this affects you? I don't think you truly realize how much damage has been done, not just to us but to your mother's side. The Shangs were mentioned. Tyersall Park was mentioned. And all at the most inopportune time possible, when your grandmother is so ill. Tell me how you plan to face Uncle Alfred when he arrives this afternoon?" Astrid was momentarily dumbfounded. She hadn't thought about the repercussions of this gossip site, but she finally said, "I will face Uncle Alfred myself if that's what you want me to do. I'll explain everything that happened." "Well, you can thank your lucky stars you won't have to. This column and this whole ridiculous website have been taken down." Astrid looked at her father, momentarily surprised. "This article is really gone?" "Erased from the face of this planet! Although enough damage has been done—there's no telling how many people must have read this rubbish before it was taken down." "Well, hopefully the exposure will be minimal. Thanks, Dad—thank you for doing this," Astrid muttered in relief. "Oh I had nothing to do with this—thank your husband." " _Michael_ had it taken down?" "Yes. He bought the company that owns this infernal website and put an end to all of the nonsense. It's probably the first useful thing Michael has ever done to protect you. Which is far more than I can say for Charlie Wu!" Astrid sat back in her chair, feeling her face flush with anger. This was all Michael's doing. He must have alerted her parents to this gossip column in the first place, and of course he was only too happy to alert them that he'd saved the day. Hell, he was probably Leonardo Lai's "Singapore insider," relishing his chance to sabotage Charlie, to sabotage her. * * * * Cathleen Kah Leong, the wife of Harry and Felicity Leong's eldest son, Henry, takes great pride in her thrift. A partner at Singapore's most esteemed law firm, she takes the public bus to work every day. A granddaughter of the late banking tycoon Kah Chin Kee, she uses a plastic bag from the local neighborhood gourmet grocers to transport her legal briefs when she could well afford to buy Goyard. (Not a nice Goyard leather tote bag—I mean Goyard, the company.) # CHAPTER SEVEN 19 WEST FOURTH STREET, NEW YORK Rachel was in her office suite at New York University, splitting a piece of German chocolate cake from Amy's Bread with her suitemate, Sylvia Wong-Swartz, when her mother called. "Hey, Mom! How's Panama?" Rachel answered in Mandarin. Her mother was on a Chu family reunion cruise through the Panama Canal. "I don't know. I haven't left the ship," Kerry Chu replied. "You guys have been cruising for four days now and you haven't docked once?" "No, no, the ship has docked but we've never gotten off. No one wants to leave the boat. Auntie Jin and Auntie Flora want to get their money's worth, so they just sit and stuff their mouths at the all-you-can-eat buffet all day long, and of course Uncle Ray and Uncle Walt aren't speaking to each other again. So they're both at the casino, but at opposite ends. Walt is at the blackjack tables, and supposedly Ray is losing his shirt at baccarat but won't stop playing." "Well, Uncle Ray can afford it." Rachel chuckled. She was so glad she decided to skip this family reunion. "Ha! Yes. You should see that wife of his! She changes outfits four times a day, and every night it's a different ball gown and different jewelry. I don't know where she thinks she is—this is a cruise ship, not the Oscars." "Auntie Belinda is just doing what she loves, Mom." "She's trying to rub it in all our faces, that's what she's doing! And of course, your cousin Vivian has to ask her what she's wearing every time, and Belinda always says something like, 'Oh, this one I bought in Toronto at Holt Renfrew, or this is a Liberace—I bought it on sale. It was $7,500, marked down to $3,000.' " "Liberace? I don't think he ever designed clothes, Mom." "You know that Italian designer, the one that got shot in Miami." "Oh, you mean _Versace_." "Hiyah, Liberace, Versace, it's all the same to me. If it's not on sale at Ross Dress for Less, I don't care what the brand is." "Well, I'm sure Auntie Belinda appreciates Vivian's attention. She's _clearly_ the only person on the cruise Auntie Belinda can talk to about high fashion." Rachel took a bite from her share of the cake. "You and Nick should have come. All your cousins would have enjoyed spending time with you. You know this is the first holiday Vivian's taken since Ollie was born?" "I would have loved to see everyone, Mom, but the dates just didn't work with my teaching schedule. I couldn't imagine Nick on a cruise ship, though—I think he'd jump overboard before the ship even left port." "Hahaha. Your husband only likes those private yachts!" "No, no—you got it all wrong. He'd much rather rough it than be on some luxury cruise—I could see him on some sort of expedition frigate going to Antarctica or on a fishing boat in Nova Scotia, but not on any kind of floating palace." "A fishing boat! All these rich kids who grew up with everything just want to live like they are poor. How is Nick anyway?" "He's fine. But you know what, his grandmother had a heart attack last week." "Oh really? Is he going to go back to Singapore?" "I don't know, Mom. You know how sensitive he gets about anything having to do with his grandmother." "Nick should go back. You should convince him to go back—this might be his last chance to see the old lady." Rachel's radar suddenly went off. "Wait a minute...you've been talking to Nick's mom, haven't you?" Kerry Chu paused for a moment too long, before saying, "Noooo. We haven't spoken in ages." "Don't lie to me, Mom. Only Eleanor calls Nick's grandmother the 'old lady'!" "Hiyah, I can't lie to you, you know me too well! Yes, Eleanor called. She's called a few times now and won't leave me alone. She thinks only you can convince Nick to go home." "I can't talk Nick into doing anything he doesn't want to do." "Did you know that Nick was supposed to inherit that house?" "Yes, Mom— _I know_. I'm the whole reason she cut him out of her will. So don't you see I'm the last person to tell him to go back?" "But his grandmother only has a few weeks to live. If he plays his cards right, he could still get the house." "Jesus, Mom, stop parroting Eleanor Young!" "Hiyah, no Eleanor! I'm speaking as your mother—I am thinking of _you_! Think about how this house could benefit your life." "Mom, we live in New York. That house has no benefit to us except as one gigantic cleaning nightmare!" "I'm not suggesting you should live there. You would sell it. Think of the windfall you'd have." Rachel rolled her eyes. "Mom, we're already so fortunate compared to the rest of the planet." "I know, I know. But imagine how your life could change _right now_ if Nick inherits that house. It's worth _hundreds of millions_ , so I'm told. That's like winning the Powerball lottery. This is crazy money, life-changing money, enough money so your poor mother doesn't have to work so hard anymore." "Mom—you know you could have retired years ago, but you love what you do. You've been the top property agent in Cupertino three years running." "I know, but I just wanted you to think about what it would be like to have that kind of fortune at your fingertips. I want to see all the good things that you and Nick can do with that money. Like that Chinese girl who's married to that Facebook fellow—they've given away billions. Think of how proud her parents must be of her!" Rachel looked over at Sylvia, who was leaning back in her chair precariously as she stretched to reach for the cake on the coffee table. "I can't talk about this now, Mom. Sylvia's about to fall over and break her neck." "Call me back! We need to—" Rachel hung up on her mother just as her friend had scraped a nice bit of chocolate-and-coconut frosting off with her finger and comfortably returned to her usual seated position. "Way to go. Using me as an excuse to get off the phone with your mom." Sylvia cackled as she licked her finger clean. Rachel smiled. "Sometimes I forget you can speak Mandarin." "A lot better than you, banana girl! Sounds like she was in turbo nagging mode." "Yeah, she was fixating on something and wouldn't let it go." "If she's anything like my mom, she's going to call you back tonight and try the guilt angle." "You're probably right. Which is why I need to see what Nick is up to for lunch." — A few hours later, Rachel and Nick were seated at their favorite window table at Tea & Sympathy. Nicky Perry, the owner, had been by to share a funny video of Cuthbert, her bulldog, and their lunches had just been placed on the table. It was a snowy January afternoon and the windows had fogged up inside the cozy restaurant, creating an even more inviting atmosphere for Rachel to enjoy the chicken-and-leek pie in front of her. "This was the perfect idea. How did you know I was craving T&S for lunch?" Nick asked as he tucked into his usual English bacon, avocado, and tomato sandwich. Taking advantage of his good mood, Rachel got right to the point. "So I spoke to my mom a little earlier. Apparently, our mothers have been talking—" "Oh God, not the grandchildren talk again!" "No, this time it was all about you." "Let me guess...my mother has enlisted her help to convince me to return to Singapore." "You're psychic." Nick rolled his eyes. "My mother is so predictable. You know, I don't think she really cares about my grandmother dying—she's just fixated on me getting Tyersall Park. It's her entire raison d'être." Rachel broke the thick golden pastry crust of her chicken pie with a fork and let some of the steam escape. She took her first tentative bite of the piping-hot creamy sauce before speaking again. "What I've never really understood is why everyone thinks the house is supposed to go to you. What about your father, or your aunts? Don't they have more right to the house?" Nick sighed. "Ah Ma, as you know, is an old-fashioned Chinese woman. She has always favored her son over her daughters—they were all just supposed to marry and be taken care of by their husband's families, while my father got Tyersall Park. It's this warped mash-up of archaic Chinese customs and the British rules of primogeniture." "But that's so unfair," Rachel muttered. "I know, but that's the way things are and my aunts grew up always knowing they would get the short end of the stick. Mind you, each of them is still going to inherit from Ah Ma's financial holdings—so no one's going to be hurting for cash here." "So then how is it that you suddenly got to be first in line to inherit Tyersall Park?" Nick leaned back in his chair. "Do you remember when Jacqueline Ling came to New York a couple of years ago and summoned me to lunch aboard her yacht?" "Oh yeah, she had two Swedish blondes kidnap you in the middle of a lecture!" Rachel laughed. "Yes. Jacqueline is Ah Ma's goddaughter, and they've always been extremely close. Jacqueline revealed to me that back in the early nineties, when my father decided to move to Australia pretty much full-time, it so angered my grandmother that she decided to change her will and disinherit him from Tyersall Park. She skipped a generation and made me the heir to the property. But then after I married you, she supposedly changed her will again." "Who do you think is currently in her favor to get Tyersall Park?" "I honestly have no idea. Maybe Eddie, maybe one of my cousins in Thailand, maybe she's going to leave it all to her beloved guava trees. The point is, Ah Ma uses her fortune to control the family. She's always changing her will according to her latest whim. No one really knows what she's going to do, and at this point, I've stopped caring." Rachel looked Nick straight in the face. "Here's the thing. I know that you don't care what happens to your grandmother's fortune, but you can't pretend that you don't still care for her. And that's the only reason why I think you should go back now." Nick stared out of the fogged-up window for a moment, avoiding her eyes. "I dunno...I think part of me is still so angry at her for how she treated you." "Nick, please don't hold on to this because of me. I forgave your grandmother long ago." Nick looked at her skeptically. Rachel put her hand on his. "I have. Truly. I realized it was a waste of time to be mad at her, because she never really got to know me. She never gave me a chance—I was this girl who came out of left field and stole her grandson's heart. But the more time passes, I find myself actually feeling grateful toward her now." "Grateful?" "Think about it, Nick. If your grandmother hadn't been so resistant to us being together, if she hadn't supported your mom in all her crazy shenanigans, I would never have found my real father. I would have never met Carlton. Can you imagine what my life would be like if I hadn't met them?" Nick softened for a moment at the mention of Rachel's half brother. "Well, I can imagine what Carlton's life would be like if he'd never met you—he probably would have wrecked a dozen more sports cars by now." "Oh God, don't even say that! The point I'm trying to make is, I think you need to find some way to forgive your grandmother. Because it's clearly an issue for you, and it's going to keep eating you up inside if you don't. Remember what that radio host Delilah always says? 'Forgiveness is a gift we give ourselves.' If you think you're able to let things go without ever seeing her again, more power to you. I'm not going to force you to get on a plane. But I think you need to see her in person, and I'm guessing she probably really wants to see you too but—like you—she's too damn proud to admit it." Nick looked down at his cup of tea. The saucer was emblazoned with an image of Queen Elizabeth II, and seeing the gold patterning at the edge of the porcelain suddenly took him back to a memory of Tyersall Park, of sitting in the ornate eighteenth-century French pavilion overlooking the lotus pond with his grandmother when he was six years old, being taught how to properly pour a cup of tea for a lady. He could remember how heavy the Longquan celadon teapot felt in his hands, as he carefully lifted it toward the teacup. _If the butler doesn't notice that her cup needs to be refilled, you must do it for her. But never lift the cup away from the saucer when pouring, and be sure the spout is turned away from her_ , his grandmother had instructed. Emerging from the memory, Nick said, "We can't both take off for Singapore at the beginning of the semester." "I wasn't saying we should both go—I think this is a trip you should make on your own. You're on sabbatical right now, and we both know you haven't made much progress on that book you were going to write." Nick swept his tousled hair off his forehead with both hands with a sigh. "Everything's so perfect in our life right now, do you really want me to go back to Singapore and open another Pandora's box?" Rachel shook her head in exasperation. "Nick, look around you. The box has been opened! It's been smashed open and gaping at you for the last four years! You need to go back and repair that box. Before it's too late." # CHAPTER EIGHT BOMBAY, INDIA His nails were like onyx. They were perfectly formed and lightly buffed so that there was just a hint of sheen. Su Yi had never before seen such beautifully manicured nails on a man, and couldn't help but stare as his fingers counted out rupees for the woman manning a cart piled high with brightly colored candles and strange wax figures, some in the shape of babies, some in the shape of houses, and others resembling arms and legs. "What are these wax sculptures for?" Su Yi asked. "People burn them as favors, in the hopes that their prayers will be answered. The babies are for people hoping for a child, the houses are for those that want a new home, and the sick choose a body part that corresponds to their ailment. So if you are looking to heal a broken arm, this is the one you'd get," he said, holding up a wax form of an arm with a clenched fist. "I bought two candles in pale red and blue—they were the closest colors I could find to represent the British flag." "You must tell me what to do," she said hesitantly. "It's very simple. We just place them in the shrine, light them, and say a little prayer." As they walked up the hill with the lovely views of the Arabian Sea, Su Yi glanced at the imposing Gothic façade of Mount Mary Church. "Are you sure they'll allow me to enter? I'm not Catholic." "Of course. I'm not Catholic either, but everyone is welcome. If anyone asks us what we're doing, we can tell them that we're lighting candles for Singapore. Everyone is aware of what's happening there right now." Stretching out his arm, he gestured gallantly at the arched front doors. Su Yi stepped into the church sanctuary, feeling self-conscious as her high-heeled shoes echoed against the black-and-white marble floor. It was her first time inside a Catholic church, and she stared in fascination at the vibrant frescos on the walls and the words painted in gold script against the majestic arch: _All Generations Shall Call Me Blessed_. The main altar reminded her of those in a Chinese temple, except that instead of a statue of Buddha, there was a beautiful small wooden one of the Virgin Mary dressed in gold-and-blue robes, holding an even smaller wooden baby Jesus.* "I didn't know there were so many Catholics in India," she whispered to him, noticing the worshippers filling up the first four to five rows of pews, some kneeling in silent prayer. "Bombay was a Portuguese colony during the sixteenth century, and they converted many Indians. This whole area—Bandra—is the main Catholic neighborhood." Su Yi was impressed. "You've only been here a few months, but you've come to know the city rather well, haven't you?" "I like to explore different areas. Mostly I wander around the city out of sheer boredom." "Has life been that boring?" "Before you arrived, everything was boring," he said, gazing at her face intently. Su Yi lowered her eyes, feeling her face begin to flush. They walked along the transept until they arrived at a side chapel where hundreds of burning candles flickered. He handed her the red candle and gently guided her hand as she placed its wick onto a flame. The whole ritual seemed strangely romantic. "There. Now just find an empty slot for your candle. Anywhere you like," he said in a hushed voice. She placed hers on the lowest rack, next to one that was almost burned out. As Su Yi watched the flame begin to brighten, she thought of the island she had been forced to flee. She still wished she could have defied her father and stayed on. She knew she should be feeling grateful rather than angry at her father, especially in light of the latest news. The Jurong-Kranji defense line had finally been breached yesterday morning, and invading Japanese soldiers were probably all over Bukit Timah now, swarming her neighborhood as they made their way to the city center. She wondered what was happening at Tyersall Park, if it had sustained any bomb damage, or whether the troops had discovered and pillaged the place. Su Yi closed her eyes and chanted a little prayer for everyone who remained at Tyersall Park and for her cousins, her aunties and uncles, and her friends—everyone who couldn't get off the island in time. When she opened her eyes, James was standing right in front of her, so close she could feel his warm breath. "My goodness, you startled me!" she gasped. "Do you wish to confess?" he said, leading her toward a wooden booth. "I'm not sure...should I?" Su Yi asked, her heart beginning to race. She wasn't sure she wanted to go into the dark box. "I think it's time." He opened the latticework screen door for her. She stepped inside the confession booth hesitantly, surprised by how comfortable the cushion on the seat was as she sat down. It was plush velvet, and it felt all of a sudden like she was seated in the Hispano-Suiza that her father had given to her for her sixteenth birthday. Every time she was driven into town, clusters of people would run after the car in excitement. The Anglos would look in curiously, wondering which dignitary was inside the grand automobile, and she loved seeing their stunned expressions when they realized it was a Chinese girl. Children would try to grab on to the car, while young suitors would attempt to throw roses through the window in the hopes of winning her attention. The window to the confession booth slid open, and she could see that James was sitting on the other side, playing at being the priest. "Tell me, my child, have you sinned?" he asked. She didn't want to say anything, but suddenly, she felt her lips moving uncontrollably. "Yes I have." "I can't hear you—" "I have sinned. I have sinned against you." Again the words just pouring out even as she tried to keep her mouth closed. "Speak up, dear. Can you hear me?" "Of course I can hear you. You're sitting one foot away from me," Su Yi said, annoyed, as a bright flash of light coming through the latticework screen suddenly glared into her eyes. "Can you hear me?" The voice sounded garbled as it morphed from English into Hokkien. Suddenly it was all terribly bright, and she was no longer in the confession booth of Mount Mary in Bombay. She was in a hospital room, and her cardiologist was staring down at her. "Mrs. Young, can you hear me?" "Yes," she murmured weakly. "Good, good," Professor Oon said. "Do you know where you are?" "Hospital." "Yes, you're at Mount Elizabeth. You had a cardiac episode, but we've managed to stabilize you and I'm very happy with the progress you're making. Do you feel any pain?" "Not really." "Good, you shouldn't. We have you on a constant dose of hydrocodone, so you should not have to feel any discomfort at all. Now, I'm going to send Felicity in. She's very eager to see you." Felicity entered and tiptoed rather awkwardly to her mother's bedside. "Oh Mummy! You're finally awake. They've had you sedated for the past two days so that your heart could rest. How are you feeling? You gave us quite a scare!" "Where are Madri and Patravadee?" "Oh, your lady's maids are right outside. They've been with you all this time, but you haven't known it. Francis only allows one of us in at a time." "I'm very thirsty." "Yes, yes. It's this medication they have you on, and the oxygen tube in your nose. It really dries out your throat. Let's get you some water." Felicity looked around and found a water jug on a side table. "Hmm. I wonder if this is filtered or from the tap. Oh dear, they only have plastic cups. Do you mind? I'll have some proper glasses brought up as soon as possible. I don't understand why there are only plastic cups in here. I don't know if you can tell, but you're in the Royal Suite, built for the Brunei royals. We had it specially arranged for you. But dear me, they need proper cups." "I don't care," Su Yi said impatiently. Felicity poured some water into the cup and brought it over to her mother. She held the cup up to her mother's lips and began to tilt it forward, noticing that her hands were beginning to shake. "Oh, silly me, we need a straw. We wouldn't want to spill any of this on you." Su Yi let out a sigh. Even in her delirious state, Su Yi noticed that her eldest daughter always brought along a certain frenetic energy. She was so eager to please, but in a cloying, obsequious way that Su Yi found so irritating. She had been like this even as a child. Where did she get it from? Felicity found a cluster of straws on the side table and hastily jabbed one into the cup. "Here, that's much better." As she placed the straw up to her mother's lips, she glanced at the heart monitor and saw the numbers slowly begin to rise: 95...105...110. She knew she was agitating her mother, and her hands started shaking again. A few drops of water splashed onto her mother's chin. "Hold still!" Su Yi hissed. Felicity grasped the cup tightly, suddenly feeling like she was ten years old again, perched on the ottoman in her mother's bedroom as one of the Thai maids arranged her hair into an intricate braid. She would shift a little, and her mother would groan in annoyance. "Hold still! Siri is doing very delicate work here, and if you make one false move, you're going to mess it all up! Do you want to be the only girl at Countess Mountbatten's tea party with bad hair? Everyone will be looking at you because you're my daughter. Do you want to disgrace me by looking unkempt?" Felicity could feel the veins in her neck beginning to throb at the memory. Where were her blood-pressure pills? She couldn't deal with Mummy like this. She hated even seeing her like this, dressed in a hospital gown with her hair out of place. Mummy must never look unkempt. Now that she was conscious, they must send over some of her own clothes and have Simon set her hair properly. And some jewelry. Where was the jade amulet she always wore against her chest? She stared at the heart monitor anxiously: 112...115...120. Oh dear oh dear. She didn't want to be responsible for causing another heart attack. She needed to leave the room now. "You know, Astrid's been dying to see you," Felicity blurted out, appalled at her own choice of words. She pulled the cup away from her mother and fled out the door. A few moments later, Astrid entered, the bright light from the doorway silhouetting her, and making her glow like an angel. Su Yi smiled at her. Her favorite granddaughter always looked so calm and collected, no matter the occasion. Today she was wearing a pale lilac dress with a low-waisted sash and delicate knife pleats all along the skirt. Her long hair was gathered into a loose bun at the nape of her neck, and the delicate locks on the side framed her face like Botticelli's Venus. " _Aiyah_ , how wonderful you look!" Su Yi said in Cantonese, the dialect she preferred to use with most of her grandchildren. "Don't you recognize the dress? It's one of your Poirets, from the 1920s," Astrid said, sitting in the chair beside her bed and taking her hand. "Ah yes, of course. It was my mother's actually. I thought it was terribly old-fashioned by the time she gave it to me, but it looks perfect on you." "I wish I could have met great-grandma." "You would have appreciated her. She was very beautiful, like you. She always told me that it was unfortunate that I took after my father." "Oh but Ah Ma, you're so beautiful! Weren't you the leading debutante of your day?" "I wasn't ugly, but I didn't come close to my mother in looks. My older brother looked more like her." Su Yi sighed for a moment. "If only you could have met him." "Great-uncle Alexander?" "I always called him by his Chinese name, Ah Jit. He was so strikingly handsome and so kind." "You've always said that." "He died much too young." "Cholera, wasn't it?" Su Yi paused for a moment, before saying, "Yes, there was an epidemic in Batavia, where father had sent him to manage our businesses. You know, things would have been so different for all of us had he lived." "What do you mean?" "He wouldn't have behaved like Alfred, for one thing." Astrid wasn't sure what her grandmother meant, but she didn't wish to upset her by prodding any further. "Great-uncle Alfred is coming home, you know? He's due in on Thursday. Auntie Cat and Auntie Alix are on their way as well." "Why is everyone coming down? Do they think I'm dying?" "Oh, no, no. Everyone just wants to see you." Astrid laughed lightly. "Hmm. Well, if that's the case, I want to be at home. Please tell Francis that I want to go home today." "I don't think you can go home just yet, Ah Ma. You need to get a bit better first." "Nonsense! Where is Francis now?" Astrid pushed the button beside the bed, and within a few moments Francis Oon arrived in the room accompanied by his usual entourage of nurses. "Is everything okay?" he asked, looking a bit flustered. He always got flustered around her. Astrid noticed a spot of chili sauce at the edge of his mouth and tried to ignore it. She addressed him in English. "My grandmother wishes to be discharged." Professor Oon leaned toward his patient and spoke in Hokkien. "Mrs. Young, we can't allow you to go home just yet. You need to get stronger first." "I feel fine." "Well, we want you to feel _even better_ before we release you—" Astrid cut in. "Professor Oon, I think my grandmother would be so much more comfortable at home. Can't we just have things set up for her at Tyersall Park?" "Er, it's not that simple. Step outside with me for a moment, will you?" the doctor said a little uneasily. Astrid followed him out of the room, slightly annoyed by the ungracious way he had handled that. Now of course her grandmother would know they were discussing her condition. Professor Oon found himself staring at Astrid. This woman was so blindingly pretty, it made him nervous just to be around her. He felt like he could lose control at any moment and say something inappropriate. "Er, Astrid, I must be very...um, blunt with you. Your grandmother's condition is extremely...touch and go...at the moment. There's been a tremendous amount of scarring on the heart, and her erection...I mean, her ejection fraction is up to twenty-seven percent. I know it looks like she's getting better, but you need to know that we are making monumental efforts to keep her alive. All those machines she's hooked up to...she needs them, and she requires nonstop care." "How long does she really have?" "Hard to say, but it's a matter of weeks. Her heart muscle is irreparably damaged, and her condition is worsening day by day. She could go at any moment, really." Astrid let out a long exhale. "Well, it's even more essential that we get her home then. I know my grandmother would not want to spend her last days here. Why can't we simply move all the machines? Let's set up a medical suite just like this one for her at home. We can have you and the rest of her medical team stationed there." "Something like that has never been done before. To set up a mobile cardiac intensive care unit in a private home with all the equipment we would need and round-the-clock doctors and nurses—it's a huge undertaking, and it would be extremely cost prohibitive." Astrid cocked her head, giving him a subtly eviscerating look that said: _Really? Do we really need to go there?_ "Professor Oon, I think I can speak for my entire family. The cost is not an issue. Let's just make it happen, shall we?" "Okay, I'll get to work on that," Professor Oon replied, his face flushing red. Astrid reentered the Royal Suite, and Su Yi smiled at her. "All taken care of, Ah Ma. They will move you home as soon as possible. They just have to set up the medical equipment for you first." "Thank you. You are much more efficient than your mother." "Hnh! Don't let her hear you say that. Anyway, you shouldn't be talking so much. You should rest." "Oh, I feel like I've rested enough. Before I woke up, I had a dream about your grandfather. Ah Yeh." "Do you dream about Ah Yeh often?" "Rarely. But this dream was very strange. Part of it felt so real, because it was a memory of something that really happened during the war, when I had been evacuated to Bombay." "But Ah Yeh wasn't in Bombay, was he? Didn't you only meet him when you returned to Singapore?" "Yes, when I went home." Su Yi closed her eyes and was silent for a few moments, and Astrid thought she had drifted back to sleep. Suddenly she opened her eyes wide. "I need you to help me." Astrid sat up in her chair. "Yes, of course. What do you want me to do?" "There are some things you must do for me at once. Very important things..." * * * * Called Moti Mauli, or "Pearl Mother" in Marathi, legend has it that the statue was brought to India in the sixteenth century by the Jesuits from Portugal but was stolen by pirates. One day, a fisherman had a dream in which he saw the statue floating in the sea, and this is how it was rediscovered. # CHAPTER NINE TYERSALL PARK, SINGAPORE The lid on the enamel kettle started rattling, and Ah Ling, the head housekeeper, reached for the kettle on the hot plate and poured some boiling water into her tea mug. She relaxed into her armchair and breathed in the earthy, musky scent of the _ying de hong cha_ before taking her first sip. For the past two decades, her younger brother had been sending her a parcel of this tea every year from China, wrapped in layers of brown paper and sealed with old-fashioned yellow Scotch tape. These tea leaves were grown in the hills above her village, and drinking it remained one of her last connections to the place where she had been born. Like so many girls of her generation, Lee Ah Ling left her tiny village on the outskirts of Ying Tak when she was just sixteen, taking a boat from Canton to an island far away in the Nanyang, the Southern Seas. She remembered how most of the other girls who were crammed into that stifling little cabin had wept bitterly every night on their voyage, and Ah Ling wondered if she was a bad person to be feeling not sadness but a sense of excitement. She had always dreamed of seeing the world beyond her village, and she didn't care if it meant leaving her family. She was leaving a difficult home—a father who died when she was twelve and a mother who seemed to have resented her since the day she was born. Now at least she could do something to quell that resentment—in exchange for a modest sum of money that would enable her brother to go to school, she would go abroad, take the vow of celibacy that every black-and-white amah was asked to, and be tied to serve an unknown family in a strange new land for the rest of her life. In Singapore, she had been brokered to work for a family called the Tays. They were a couple in their late thirties with two sons and a daughter living in a mansion more lavish and luxurious than she had ever dreamed was possible. Actually, it was a rather unspectacular bungalow off Serangoon Road, but to Ah Ling's untrained eyes, it might as well have been Buckingham Palace. There were three other black-and-white amahs like her in the household, but they had been there for years. Ah Ling was the new girl, and for the next six months she was assiduously taught the finer details of the domestic arts, which for her meant learning how to properly clean varnished wood and silver. One day, the most senior maid announced, "Mrs. Tay thinks you're ready. Pack your belongings—we're sending you to the Youngs." It was only then that Ah Ling realized that her time at the Tay household had been a training ground, and she had passed some sort of unspecified test. Ah Lan, the junior maid who had been there ten years, said to her, "You are very lucky. You were born with a pretty face, and you've proven yourself good at polishing silver. So you get to work at the big house now. But don't let your head get too big over this!" Ah Ling had no idea what she meant—she couldn't imagine a bigger mansion than the one she was already in. She soon found herself in the passenger seat of the Austin-Healey, with Mr. Tay at the wheel and Mrs. Tay in the backseat, and she would never forget that drive. They had entered what seemed like a jungle road, and at a clearing they pulled up to a grand wrought-iron gate painted light gray. She thought she was dreaming, to suddenly come upon this strange ornate gate in the middle of nowhere. A fierce-looking Indian _jaga_ 1 wearing a crisp olive uniform and a bright yellow turban emerged from the sentry house and scrutinized them closely through the car window before ceremoniously waving them through the gates. Then they drove up a long winding gravel lane that had been cut through the thick trees, giving way to an avenue lined with majestic palm trees, until suddenly the most magnificent building she had ever seen came into sight. "What is this place?" she had asked, suddenly becoming afraid. "This is Tyersall Park, the home of Sir James Young. You will be working here from now on," Mrs. Tay informed her. "Is he the governor of Singapore?" Ah Ling asked in awe. She never knew a house could be this immense...it was like one of the grand old buildings on the Shanghai waterfront she had once seen on a postcard. "No, but the Youngs are far more important than the governor." "What does Mister...Sir James do?" "He's a doctor." "I never knew doctors could be so rich." "He is a wealthy man, but this house actually belongs to his wife, Su Yi." "A _lady_ owns this house?" Ah Ling had never heard of such a thing. "Yes, she grew up here. It was her grandfather's house." "He was my grandfather too." Mr. Tay turned to Ah Ling with a smile. "This is your grandfather's house? Why are you not living here, then?" Ah Ling asked, puzzled. " _Aiyah_ , stop asking so many questions!" Mrs. Tay scolded. "You will learn more about the family in due course—I'm sure the other servants will fill you in on all the gossip very fast. You will quickly see that it is Su Yi who rules over everything. Just work very hard and be sure that you never do anything to upset her and you'll do fine." Ah Ling had done more than fine. Over the next sixty-three years, she rose from being one of twelve junior maids to become one of the Young family's most trusted nannies—having helped raise Su Yi's youngest children, Victoria and Alix, and then in the next generation, Nick. Now she was the head housekeeper, overseeing a staff that at its peak reached fifty-eight but for the past decade had remained at thirty-two. Today, as she sat in her quarters drinking tea and eating a few Jacob's Cream Crackers smeared with peanut butter and Wilkin & Sons red currant jam—one of the strange Western habits she had picked up from Philip Young—a round, smiling face suddenly appeared at her window. "Ah Tock! My God, I was just sitting here thinking of your grandmother, and suddenly you appear!" Ah Ling gasped. "Ling Jeh, didn't you know I had no choice but to come this afternoon? Her Imperial Highness summoned me," Ah Tock reminded her in Cantonese. "I had forgotten. My head is jumbled with a million things today." "I can only imagine! Hey, I hate to make your life more difficult, but do you mind?" Ah Tock held up a Metro shopping bag full of clothing. "These are Mama's dresses—" "Of course, of course," Ah Ling said, taking the bag. Ah Tock was a cousin of the Youngs through Su Yi's side,2 and Ah Ling had known his mother, Bernice Tay, since she was a girl—she was the daughter of the couple who first took Ah Ling in "for training" when she arrived in Singapore. Bernice regularly smuggled some of her finer clothes to be cleaned at Tyersall Park, knowing there was a full team of launderers that washed every piece by hand, air dried them in the sun, and ironed them with lavender-scented water. There wasn't a finer laundering service on the entire island. "Mama wanted me to show you this _sam fu_...the fastening hook came off." "Don't worry, we'll have it sewn back for her. I know this vintage _sam fu_ —Su Yi gave it to her years ago." Out of another bag, Ah Tock produced a bottle of Chinese rum. "Here, from Mama." "Hiyah, tell your mother she shouldn't have bothered! I still haven't finished the bottle she gave me a year ago. When do I have time to enjoy this?" "If I had to run this place like you do, I'd be drinking every night!" Ah Tock said with a chuckle. "Should we go up now?" Ah Ling gestured, getting out of her chair. "Sure. How is Her Imperial Highness today?" "Irritable, as always." "Hopefully I can help fix that," Ah Tock replied cheerily. Ah Tock was a frequent presence at Tyersall Park, not because he was a beloved relation but because of his expertise in catering to the needs of his more privileged cousins. Over the past two decades, Ah Tock had smartly leveraged his family connections and founded FiveStarLobang.com, an exclusive luxury concierge service that serviced the most spoiled Singaporeans—from procuring that Beluga black Bentley Bentayga months before it hit the market to arranging covert Brazilian butt-lifts for bored mistresses. Crossing the quadrangle that separated the servants' wing from the main house, they passed the kitchen garden, which was meticulously planted with rows of fresh herbs and vegetables. "Oh my. Look at those little red chilli padis—I'm sure they must be extra hot!" Ah Tock exclaimed. "Yes. Burn-your-mouth hot. Let's not forget to pluck some for your mother. We also have too much basil right now—it's just gone wild. Do you want some of that too?" "I'm not sure what Mama would do with that. Isn't it an _ang mor_ 3 herb?" "We use it here for the Thai dishes. The Thais use basil a lot in their cooking. And also sometimes Her Imperial Highness demands fancy _ang mor_ food. She likes this disgusting sauce called 'pesto.' It takes so many of these basil leaves just to make one little batch of pesto sauce, and then she eats one tiny plate of linguine with pesto and the rest gets thrown out." A young maid walked past them, and switching to Mandarin, Ah Ling ordered, "Lan Lan, can you pluck a big packet of the chilli padis for Mr. Tay to take home?" "Yes, ma'am," the girl replied shyly before darting off. "Very cute. She's new?" Ah Tock asked. "Yes, and she's not going to last long. Spends too much time staring into her phone when she knows she's not allowed. All these young China girls don't have the same work ethic as my generation did," Ah Ling complained, as she led Ah Tock through the kitchen, where half a dozen cooks sat around the enormous wooden worktable, deep in concentration as they meticulously folded little bits of pastry. " _Shiok!_ 4 You're making pineapple tarts!" Ah Tock said. "Yes—we always make a huge batch whenever Alfred Shang comes to town." "But didn't I hear that Alfred brought over his own Singaporean chef to England? Some Hainanese hotshot?" "Yes, but Alfred still prefers our pineapple tarts. He complains that it's not the same when Marcus tries to make it in England...something about the flour and water being different." _Crazy rich bastard_ , Ah Tock thought to himself. Even though he had been coming here for as long as he could remember, he never ceased to be awed by Tyersall Park. He had of course been into many homes of the high and mighty, but nothing else came close to this. Even the kitchen was impressive beyond belief—a series of cavernous spaces with vaulted ceilings, walls covered in beautiful majolica tiles, and rows of shimmering copper pans and perfectly seasoned woks hanging over the gigantic Aga stoves. It looked like the kitchen of some historic resort hotel in the south of France. Ah Tock remembered a story his father had told him: _Back in the old days before the war, Gong Gong_ 5 _loved entertaining—there used to be parties for three hundred people every month at Tyersall Park, and we lesser children weren't allowed to attend, so we used to peer down at the guests from the upstairs balcony in our pajamas._ Taking a service staircase to the second floor, they walked down another hallway leading into the east wing. There, Ah Tock found his cousin Victoria Young on the sofa of the study room adjoining her bedroom, going through stacks of old papers with one of her personal maids. Victoria was the only one of Su Yi's children who still lived at Tyersall Park, and in many ways she was even more imperious than her mother, hence "Her Imperial Highness," the nickname Ah Tock and Ah Ling used behind her back. Ah Tock stood in the room for several minutes, seemingly ignored. By now, he should be used to this kind of dismissive treatment, since his entire family had for three generations basically served as glorified help to these cousins, but he nevertheless felt a bit insulted. "Lincoln, you're early." Victoria finally looked up for a moment to acknowledge his presence, calling Ah Tock by his English name as she riffled through a set of blue aerogram letters. "These can be shredded," she said, handing them off to the maid, who immediately fed them into the paper shredder. Victoria's severe chin-length bobbed hair was looking frizzier and grayer than ever. Ah Tock wondered if she had ever heard of hair conditioner. She was wearing a white lab coat stained with paint marks over a polyester leopard-print blouse and what appeared to be white silk pajama pants. _If she wasn't born a Young, everyone would think she's an escapee from Woodbridge._ 6 Fed up with waiting, Ah Tock tried to break the silence. "That looks like a ton of paperwork!" "Mummy's personal papers. She wants everything destroyed." "Er...are you sure you should be doing this? Wouldn't some historians be interested in Great-auntie Su Yi's letters?" Victoria frowned at Ah Tock. "Precisely why I'm going through all of them. Some we'll save for the National Archives or the museums if there's anything relevant. But anything personal Mummy wants gone before she dies." Ah Tock was taken aback by how matter-of-factly Victoria put it. He tried to change the subject to more pleasant matters. "You'll be pleased...everything is on schedule to be delivered. The seafood supplier is sending a big truck tomorrow. They promised me the very best lobsters, jumbo prawns, and Dungeness crabs. They've never gotten such a large private order before." "Good." Victoria nodded. Ah Tock was pleased with the huge kickback he was getting from the seafood supplier, but he still found it hard to believe that the two Thai daughters-in-law of his cousin Catherine Young Aakara—Su Yi's second-eldest child—subsisted on a diet of shellfish and nothing else. "And I managed to track down that mineral-water bottler in Adelboden," Ah Tock said. "So they can have all the water here in time?" "Well, it's coming from Switzerland, so it will take about a week—" "Cat and her family arrive on Thursday. Can't you have it airfreighted?" "It _is_ being airfreighted." "Well Lincoln, get them to put a rush on it. Or have some courier service do it if these people can't get it here fast enough." "It's going to cost a fortune to have five hundred gallons of bottled water flown overnight!" Ah Tock exclaimed. Victoria gave him a look that said: _Do I look like I give a damn how much it costs?_ In moments like these, Ah Tock couldn't believe he was actually related to these people. For the life of him, he could not imagine why the Aakaras needed to have special mineral water from some obscure spring in the Bernese Oberland flown in just for them. Wasn't Singapore tap water—rated one of the best in the world—good enough for these people? Or Perrier, for fuck's sake? Were these delicate Thai royals going to drop dead if they had to drink Perrier? "How are things coming along with the room?" Victoria asked. "The team will be here to install everything tomorrow morning. I've also rented two mobile-home units, which we can park behind the French walled garden. This is where the doctors and nurses can be based, since you don't want them in the house," Ah Tock reported. "It's not that we don't want them in the house, but between Alix and Malcolm coming in from Hong Kong and the Aakaras bringing all their maids, there's just no room." Ah Tock was incredulous. This was the biggest private house in Singapore—he had never been able to count how many bedrooms there actually were—and they couldn't even find space for the dedicated medical team that would be moving in to care for their dying mother? "How many maids is Auntie Cat bringing?" "She usually brings three of her own, five when Taksin joins her, but with all her sons and their wives coming, goodness knows how many of them will show up." Victoria sighed. "The team from Mount E came earlier today to do their assessment, and they think that the best place to set up the cardiac care unit is in the conservatory," he said, trying to reason with his cousin. Victoria shook her head irritatedly. "No, that won't do. Mummy will want to be upstairs in her own bedroom." At this point, Ah Ling felt like she had to interject. "But Victoria, the conservatory is perfect. They won't have to transport her upstairs, not to mention all the machines and generators. It's secluded from any noise in the service wing, and they can set up all the machines in the adjoining dining room and have the wiring brought in right through the conservatory doors." "It's no use arguing. Years ago when I suggested to Mummy that she move her bedroom downstairs so that she didn't have to keep climbing the stairs, she said to me, 'I will never sleep downstairs. The servants sleep downstairs. And the only members of my family who have ever slept downstairs have done so in their coffins.' Trust me, she will expect everything to be set up in her bedroom." Ah Tock had to resist rolling his eyes. Even from her deathbed, Great-auntie Su Yi was still trying to control the whole world. And a little gratitude from Her Imperial Highness would have been nice—he had worked nonstop to make all this happen in record time, and Victoria hadn't uttered "thank you" even once. Just then, a maid knocked softly on the open door and peered in. "What is it?" Victoria asked. "I have a message for Ah Ling," the maid said in a very soft voice. "Well, come in here and tell it to her. Don't just stand there skulking by the door!" Victoria scolded. "Sorry, ma'am," the maid said, glancing at Ah Ling nervously. "Um, the guardhouse called. Mrs. Alexandra Cheng and family are arriving." "What do you mean arriving?" Ah Ling asked. "They are pulling up to the house now." "Now? But they aren't supposed to be here until Thursday like everyone else!" Ah Ling groaned. "Oh for heaven's sake—did they give us the wrong dates?" Victoria fumed. Ah Ling looked out the window and saw that it wasn't just Alix and her husband, Malcolm, getting out of the car. There were six cars, and the whole damn family was pouring out of them—Alistair Cheng; Cecilia Cheng Moncur and her husband, Tony, with their son, Jake; and who was that stepping out of the car in a white linen suit? Oh dear God. It couldn't be. She looked at Victoria in a panic and blurted out, " _Eddie_ is here!" Victoria groaned. "Alix didn't say he was coming! Where are we going to put him?" "It's not just him...Fiona and the children are here too." "Good God! He's going to kick up a fuss and demand the Pearl Suite again. And that's reserved for Catherine and Taksin when they arrive on Thursday." Ah Ling shook her head. "Actually, Catherine's lady's maid in Bangkok called me to say that Adam and his wife should have the Pearl Suite." "But Adam is their youngest son. Why on earth should he get the Pearl Suite?" "Apparently Adam's wife is the daughter of some prince who ranks higher than Taksin. So they must have the Pearl Suite." "Oh yes, I forgot about all that protocol nonsense. Well, Ah Ling, it will be your job to deliver the news to Eddie." Victoria smiled wryly. * * * 1 Hindi for "watchman," the term is used for any sort of security guard. The _jagas_ at Tyersall Park were, of course, highly trained Gurkhas that could disembowel another man with just two strokes from their daggers. 2 Ah Tock is a great-great-grandson of Shang Zhao Hui, the grandfather of Shang Su Yi, but because he was descended from the second wife of the patriarch's five official wives, none of the children from her branch inherited any substantial fortune from the Shang empire and were considered lesser, "distant cousins" when they were in fact not so distant at all. 3 The literal meaning in Hokkien is "red hair," but it's a derogatory colloquial term used to describe anything of Western origin, since to many of Singapore's older-generation Chinese, all Western people are considered _ang mor kow sai_ —"redhaired dog shit." 4 Singlish slang that's equivalent to "cool" or "fantastic" or "amazing" in Malay. 5 Cantonese for "grandfather." 6 Officially known as the Institute of Mental Health, Singapore's first psychiatric hospital was founded in 1841 on the corner of Bras Basah Road and Bencoolen Street. It was first known as the Insane Hospital but was renamed the Lunatic Asylum in 1861 when it moved to a site near the old Kandang Kerbau Maternity Hospital. In 1928, a new building was built along Yio Chu Kang Road and after several more name changes—the New Lunatic Asylum and the Mental Hospital among them—it was renamed Woodbridge Hospital in an effort to shake off some of the stigma associated with its previous names. Yet for generations of Singaporeans, Woodbridge only means one thing: You've gone bat-shit crazy. # CHAPTER TEN PORTO FINO ELITE ESTATES, SHANGHAI Lined up in perfect military precision on the steps of the monolithic granite-and-concrete structure were six attendants. Back in the days when Colette Bing was the mistress of the house—thanks to her indulgent father, Jack—the staff had been clad in chic black T-shirts and black jeans from James Perse. But ever since Kitty Pong Tai Bing had taken over the grand residence at the heart of Porto Fino Elite Estates, she had outfitted the men in black-tie butler's uniforms and the women in classic black-and-white French maid outfits. As the convoy of black Audi SUVs pulled up to the house, Kitty, her daughter, Gisele, her infant son, Harvard, and the children's nannies alighted from the car and the line of staffers bowed in unison before scurrying around to gather all the luggage. "Oooh! It's good to be home!" Kitty squealed, kicking off her red Aquazzura suede fringe-and-tassel sandals as she entered the great hall, which was now reduced to a construction site with scaffolding against the walls, plastic tarp on all the furniture, and exposed wiring hanging from the ceiling. In an effort to remove every last reminder of Colette's taste, Kitty had spent the past year "collaborating" with Thierry Catroux—the celebrated interior designer who worked only with billionaires—to redesign every last square inch of the estate. "Where is my husband?" Kitty asked Laurent, the estate manager she had poached from some tech mogul's estate in Kona to replace Wolseley, Colette's British butler, who had once worked for Princess Michael of Kent at Kensington Palace. "Mr. Bing is having his daily massage, madame." Kitty headed over to the spa pavilion and descended the steps to the subterranean swimming pool encircled with carved marble pillars. As she walked down the lacquered-cinnabar passageway leading to the treatment rooms, she smiled at the thought of all this coming down too—Colette's hammam-inspired Turkish spa was going to be transformed into a futuristic Egyptian fantasy spa inspired by the movie _Stargate_. It was her own idea! Kitty entered the treatment room illuminated by scented candles and found Jack lying facedown on the massage bed. The scent of frankincense permeated the air, as Céline Dion played softly in the background. One of the female therapists* was doing reflexology on Jack's feet, while another walked precariously along his spine as if she were on a tightrope, grasping an elaborate lattice of poles affixed to the ceiling in order to ensure the precise amount of body weight on his aching muscles. "Waaah! That's it! That's the spot!" Jack groaned through his face cradle, as the woman standing on his back dug the ball of her left foot into a muscle below his shoulder blades. "Looks like someone's having a good time!" Kitty declared. "Yea...aahh! Yessss! You're home!" "I thought I'd find you waiting to welcome me!" "When I heard the plane was delayed coming in, I thought I'd...oooooh...get my massage first!" "Those stupid French officials delayed our takeoff for two hours because of some idiotic bomb scare. They wouldn't even let me onto our plane, so I was stuck in that ghastly terminal with _the public_." Kitty pouted, as she stretched out on the plush chaise lounge next to Jack. "I'm so sorry you had to be with the public, babylove. Did you have a good time in Paris?" "I sure did! Do you know what happy news I heard while I was there?" "Owwahhh! Gentle, gentle there! What?" "You'll be pleased to know that your daughter is finally getting married," Kitty said, her voice dripping with sarcasm. Jack let out a slow grunt. "Ummm...really?" "Yes. And to an _Englishman_. But of course you already knew?" "How would I? Colette hasn't spoken to me in almost two years—not since our wedding." "You just don't seem overly surprised." "Why should I be surprised? She was bound to get married at some point." "But to an Englishman?" "Well, Carlton Bao stopped talking to her, and Richie Yang wouldn't have her, so I think her options in China became quite limited. What is this fellow's story?" "He's a nobody. Some nonprofit lawyer who's trying to save the planet. I suppose your ex-wife will have to support the both of them forever. Do you know what else I heard? Colette's wedding gown costs two million dollars." "That's absurd. Is it made of gold?" "Actually, there are gold chips sewn into it, and it's encrusted with precious stones. It's totally outrageous," Kitty said, as she sniffed a glass container of body lotion placed on the side table and began rubbing some on her arms. "Well, I suppose she can do whatever she wants with her money." "But I thought you cut her off completely?" Jack went silent for a minute, then suddenly groaned. "AWWWWW! Why does that hurt so much?" The therapist kneaded a point on his foot with her thumb and forefinger and sternly pronounced, "Sir, this is your gallbladder—it's totally inflamed. I think you must have consumed too much cognac and oily foods last night. Did you have those fried oysters and abalone noodles again when I told you not to?" "Aww! Aww! Let go! Let go!" Jack screamed. "Jack, answer me. What did you mean by _her money_?" Kitty pressed on, oblivious to his pain. Jack sighed in relief as the therapist finally released his foot. "Colette receives income from a trust fund. It was part of my divorce settlement with Lai Di." "Why is this the first time I'm hearing of it?" "Well, I didn't want to bore you with the details of my divorce." "I thought Lai Di only got two billion?" "She did, but as a condition of her walking away and not making any more noise, I had to set up a trust fund for Colette." "Oh really? And how much is that trust fund worth?" Jack murmured something in a muffled tone. "Speak up, honey, I can't hear you...you said what in U.S. currency?" "About five billion." "YOU GAVE YOUR DAUGHTER FIVE BILLION DOLLARS?" Kitty bolted upright on the chaise lounge. "I didn't _give_ her five billion. She gets the income from a trust worth about five billion. It's all tied to shares in my companies, anyway, so her income fluctuates every year depending on the dividend yields. And it's only for her lifetime." "And what happens _after_ her lifetime?" "It will go to any children she has." Suddenly visions of Colette and her future half-white children began flooding into Kitty's mind. She could see Colette in a white summer dress, running barefoot through a field in the English countryside with laughing golden-haired kids. She began to seethe quietly as she calculated the figures in her head. Even if the trust was getting a measly one percent interest on five billion, this meant that Colette—who she always presumed was being supported by her poor mother who only had two billion dollars—would get at least _fifty million dollars in pure income every year!_ And her unnaturally photogenic children, who wouldn't even know their Chinese grandfather, would also benefit from this! "So where does this leave us?" Kitty said in a grave tone. "What do you mean?" "If you've set aside so much money for your darling daughter, who by the way won't even speak to you anymore, and her half-breed children, that haven't even been born yet, what are you doing for your other children and your poor wife?" "I don't understand your question. What do _I_ do for you? I work my balls off for you, and you have a fantastic life and get everything your heart desires. Didn't you just spend ten million dollars in Paris?" "It was only nine point five—I'm a Chanel Privé preferred client, and they gave me a special discount. But say something happens to you? What happens to me?" Kitty demanded. "Nothing's going to happen to me. But don't worry, you'll be well taken care of." "What do you mean by 'well taken care of'?" "You'll also get a two-billion-dollar trust." _So, I'm not worth as much as your daughter_ , Kitty thought to herself, feeling her anger boil up. "And how much is Harvard getting?" "Harvard is my son. He will get everything else of course, and let me remind you that's a great deal more than five billion dollars." "And Gisele?" "I don't see why I need to leave Gisele anything. She is going to inherit all the Tai billions one day." Kitty stood up from the chaise lounge and walked toward the door. "It is _so interesting_ to know all this. I can see where your true priorities lie now." "What's that supposed to mean?" "You're not really thinking of me...or our children," Kitty said, her voice shaking with emotion. "Of course I am!" "No, you're not! You're not thinking of us at all." "Babylove, don't be unreasonable...ooohhwwhhh...not so hard there!" Jack yelled at the therapist who had climbed up on the massage table and was now kneading his ass with the full weight of her bare feet. "Sir, you spend too much time sitting—that is why your buttocks hurt so much. I am barely stepping on them," the woman said in a soothing tone. "I cannot believe you would give your daughter five billion dollars just like that! After all she's done to you!" Kitty cried. "Ouch...aww...Kitty, you're not making any sense! Colette is my only daughter—why should it matter if she gets five billion, when I give you everything you want? Aii-yowwww!" Jack moaned. "Stomp harder on his ass! And stomp on his saggy balls while you're at it!" Kitty shouted, fleeing the room in tears. * * * * Kitty also had the attractive eastern European therapists that Colette kept on staff replaced with middle-aged Chinese women who resembled Madame Mao. # CHAPTER ELEVEN HONG KONG Chloe had finally fallen asleep after he had rubbed her back for half an hour, and Charlie tiptoed quietly up to his bedroom. He sat leaning against the foot of the bed, facing the floor-to-ceiling window with its panoramic view of Victoria Harbour and dialed Astrid's private line in Singapore. It rang a few times, and just as Charlie began to think he was calling too late, a sleepy-sounding Astrid picked up. "Sorry, did I wake you up?" Charlie half whispered. "No, I was reading. Did you just get home?" "I've been in all night, but I was putting out a few fires." "Isabel again?" Charlie sighed. "No, nothing to do with her this time. Chloe had been bugging me for weeks to let her watch this movie, and I stupidly allowed her and Delphine to see it tonight... _The Fault in Our Stars_." "I don't know it." "I thought it was for kids, but trust me, it's not. It's sort of like a modern-day retelling of _Love Story_." "Oh no. Young love, tragic ending?" "You have no idea. When I began to realize where it was headed, I tried turning the movie off, but the girls screamed bloody murder, so I let them keep watching. Chloe's obsessed with the guy in the film, this goofy blond kid. But then in the end...oh God." "In the end you had two weeping girls?" "Sobbing uncontrollably. I think Delphine's traumatized for life." "Charlie Wu! She's eight years old! What on earth were you thinking?" Astrid scolded. "I know, I know. I was lazy, I saw the DVD cover and read the first two lines on the back. It looked harmless." "You might as well have put on _A Clockwork Orange_ for them." "I'm a bad father, Astrid. That's why I need you in my life. The girls need you. They need a good, sensible influence around." "Ha! I don't think my mum would agree with that statement." "They're going to love you, Astrid. I just know it. And they're going to love Cassian too." "We're going to be the Asian Brady Bunch, minus a few kids." "I can't wait. By the way, I had a really good meeting with Isabel's lawyers yesterday. They don't have any more objections, thank God. You know, in a strange way the stunt Isabel pulled in Singapore has worked to our advantage. Her lawyers were so afraid that I'd try to get full custody of the girls that they've withdrawn most of their demands and are willing to settle now." "That's the best news I've heard all week," Astrid said, closing her eyes for a moment. Slowly but surely, she was beginning to see her life with Charlie come into focus. She pictured herself cuddled up next to him on their new bed in their beautiful new house in Shek O, far from the crowds of Hong Kong or Singapore, bathed in moonlight and listening to the waves crashing against the rocks on the cliffs far below. She could picture Chloe and Delphine watching an age-appropriate movie in the media room with their new stepbrother, Cassian, passing a big pint of gelato amongst themselves. Charlie's voice suddenly jarred her out of her daydream. "Hey, I'm going to India tomorrow. Visiting our new factories in Bangalore, and then I have to attend this charity polo match in Jodhpur that we're sponsoring. Why don't you come for the weekend?" "This weekend?" "Yeah. We can stay at the Umaid Bhawan Palace. Have you ever been there? It's one of the most gorgeous palaces in the world, and the Taj group now runs it as a very exclusive hotel. Shivraj, the future maharaja, is a good friend, and I'm sure we'll be treated like royalty," Charlie said. "Sounds tempting, but there's no way I can leave Singapore right now with Ah Ma so sick." "Isn't she feeling a bit better? And didn't you say that a million relatives have descended on Tyersall Park? They're not going to miss you for two or three days." "It's precisely because so many relatives are in town that they'll need me. It's my duty to help entertain everyone." "Sorry, I realize I'm being extremely selfish. You're a total saint for your family. I just miss you so much." "I miss you too. I can't believe it's been more than a month since we've seen each other! But between my grandmother and everything going on with Isabel and Michael and our lovely legal teams, don't you think it's better for us to lay low and not to be seen together right now?" "Who's going to know we're in India? I'm flying into Mumbai, you can fly straight to Jodhpur, and we'll be totally secluded at the hotel. In fact, if things go according to my plan, we're not going to ever leave our room the entire weekend." "If things go according to your plan? Whatever do you mean, Mr. Grey?" Astrid teased. "I'm not going to tell you, but it will involve chocolate mousse, peacock feathers, and a good stopwatch." "Mmmm. I do love a good stopwatch." "Come on. It'll be fun." Astrid mulled it over. "Well, Michael's got Cassian this weekend, and I am supposed to represent my family at this royal wedding in Malaysia on Friday. I could maybe fly from KL after the big banquet—" "I'll have the plane ready and waiting for you." "Khaleeda, the bride, is a good friend. I know she'll cover for me. I could say I had no choice but to stay all weekend for the festivities. I was roped in." "And I'm at the end of my rope. I _need_ to see you," Charlie pleaded. "You're such a corruptor. Even back when we lived in London during our uni days, you've always made me do bad things." "That's because I've always known deep down you want to be a bad girl. Admit it, you want me to fly you to India, shower you with gemstones, and make love to you all weekend in a palace." "Well, since you put it that way..." # CHAPTER TWELVE CHANGI AIRPORT, SINGAPORE As Nick pushed his luggage cart into the arrival hall of Terminal 3, he saw a familiar face holding up a sign that read PROFESSOR NICHOLAS YOUNG, ESQ, PHD. Most people at the airport would have figured the guy with the sign—clad in a faded yellow ACS tank top, navy blue Adidas jogging pants, and flip-flops—as some surfer bum hired to be a substitute driver and not the heir to one of Singapore's biggest fortunes. "What are you doing here?" Nick said, hugging his best friend Colin Khoo. "You haven't been back since 2010. I wasn't going to let you arrive without a proper greeting party," Colin said cheerily. "Look at you! Tan as ever and rockin' that man bun! What does your father think of this look?" Colin grinned. "He detests it. He says I look like an opium addict, and if this was the 1970s and I arrived at Changi Airport, Lee Kuan Yew would personally come down to Immigration, grab me by the ear, drag me to the nearest Indian barbershop, and have me shaved _botak_!"1 They took the glass elevators down to Level B2, where Colin's car was parked. "What are you driving these days? Is this a Porsche Cayenne?" Nick asked as Colin helped him to load his luggage into the back of the SUV. "No, this is the new 2016 Macan. It's not actually out yet until March, but they let me have this special test driver." "Sweet," Nick said, opening the passenger-side door. There was a cashmere wrap on the seat. "Oh, just throw that in the back. That's Minty's. She freezes whenever she rides up front. She sends her love, by the way—she's in Bhutan at her mother's resort, doing a meditation retreat." "Sounds nice. You didn't want to join her?" "Nah, you know how my brain works. I'm totally ADHD—can't meditate for the life of me. My form of meditation these days is Muay Thai boxing," Colin said as he backed out of the parking spot at what felt like sixty miles per hour. Trying not to flinch, Nick asked, "So it sounds like Araminta's been feeling better?" "Um...getting there," Colin said haltingly. "Glad to hear that. I know things have been rough lately." "Yeah, you know how it is—depression comes in waves. And this miscarriage really pulled her under for a while. She's trying to be good to herself, doing all these retreats, and she's cut back on work. She's seeing a really great psychologist now, even though her parents aren't thrilled about that." "Still?" "Yeah, Minty's dad made her doctor sign this gigantic stack of NDAs, even though you know all psychologists are already bound by a confidentiality code. But Peter Lee needed assurance that the doctor would never even admit that Minty is a client of his, or that she would ever need something as shameful as therapy." Nick shook his head. "It amazes me that there's still such a huge stigma about mental illness here." " 'Stigma' implies that something exists but society is prejudiced against it. Here, everyone's in denial that it even exists!" "Well, that explains why you're not locked up," Nick deadpanned. Colin punched Nick playfully. "It's so great to see you, to be able to say this stuff out loud!" "Surely there are other people you can talk to?" "Nobody wants to hear that Colin Khoo and Araminta Lee have any kind of problems. We're too rich to have problems. We're the golden couple, right?" "You _are_ the golden couple. And I've seen the pictures to prove it!" Colin scoffed, remembering the infamous fashion shoot for _Elle_ _Singapore_ where he dressed up like James Bond and Araminta was painted in gold from head to toe. "Biggest mistake of my life was doing that photo shoot! I'm never going to live that down. You know, I was taking a piss at the bathroom at Paragon the other day when the guy at the next urinal suddenly looked at me and said, ' _Wah lao!_ Aren't you that Golden God?' " Nick burst out laughing. "So did you give him your number?" "Fuck you!" Colin replied. "Strangely enough, guess who's been a good friend to Minty lately? Kitty Pong!" "Kitty! Really?" "Yes, she was the one who connected Minty to her psychologist. I think it's because Kitty's not a local—she doesn't have the same sort of baggage that we have, and Araminta feels like she can speak frankly with her because she's completely removed from our tight little circle. She didn't go to Raffles, MGS, or SCGS,2 and she's not a Churchill Club member. She hangs with that foreign billionaire crowd." "It's only fitting. She's Mrs. Jack Bing now." "Yeah, I feel a bit sorry for Bernard Tai. As much of an idiot as he used to be, he did become a good father, from what I hear. But he totally got burned by Kitty. I don't think he ever saw that Jack Bing thing coming. Hey, what ever happened to that daughter of his?" "Colette? Hell if I know. After she had Rachel poisoned, we made sure to steer clear of her. I wanted to press charges against her, you know? But Rachel wouldn't hear of it." "Hmm...Rachel sure is a forgiving person." "That she is. And that's why I'm here. I'm under specific orders to come back and make peace with Ah Ma." "And is that what you want to do?" Nick paused for a moment. "I'm not sure, quite honestly. Part of me feels like all this happened a lifetime ago. Our daily lives are so removed from everything going on here. On the one hand, I can't ever forget the way Rachel was treated and how my grandmother couldn't trust me, but on the other hand, her acceptance is kind of irrelevant now." "Everything ends up seeming irrelevant in the face of loss," Colin said as he sped onto East Coast Parkway. "So am I taking you straight to the house, or do you want to grab a bite first?" "You know what, it's so late, I probably should go straight to the house. I'm sure there will be food for us there. With everyone in town, I think Ah Ching's kitchen staff must be churning out food nonstop." "No problem. Tyersall Park, coming right up! I'm just going to visualize a hundred sticks of satay awaiting me there. You know, not to push you in any way, but I like your grandmother. She's always been good to me. Remember how I ran away from home after my stepmonster threatened to ship me off to boarding school in Tasmania, and your grandma let us hide out in the tree house at Tyersall Park?" "Yeah! And every morning, she would make the cook send a big basket full of breakfast goodies up to the tree," Nick added. "That's what I mean! All my associations with your grandma revolve around food. I'll never forget the _chee cheong fun_ and _char siew baos_ delivered on those bamboo trays, and the freshly baked _roti prata_! We were feasting like kings up there! When I finally got sent home, I wanted to find any excuse I could to run away to that little tree house again. Our cook was nothing compared to yours!" "Haha! I remember you ran away from home so many times." "Yep. My stepmonster made life so miserable. You only ran away once, if I remember correctly." Nick nodded as the memory began to unfurl in his mind, taking him back to when he was eight years old... _They had been in the middle of dinner, just the three of them. His father, mother, and him, eating in the breakfast room off the kitchen, as they did when his parents weren't entertaining guests in the formal dining room. He could even remember what they ate that night._ Bak ku teh. _He had poured too much of the rich, aromatic broth over his rice, making it too watery for his liking, but his mother had insisted he finish his bowl before she would let him redo it. She was more irritable than usual—it seemed like both his parents had been so tense for days now._ _Someone came speeding up the driveway, too fast, and instead of parking by the front porch like all the guests would, the car kept going until it reached the back of the house, stopping just behind the garage. Nick looked out the window and saw Auntie Audrey, his parents' good friend, emerging from her Honda Prelude. He liked Auntie Audrey, she always made the most delicious_ nyonya kuey _. Was she bringing something yummy for dessert tonight? She came bursting through the back door, and Nick saw immediately that Auntie Audrey's face was puffy and bruised, her lip bleeding. The sleeve from her blouse was torn, and she looked totally dazed._ _"_ Alamak _, Audrey! What happened?" His mother gasped, as several maids came rushing into the room._ _Audrey ignored her, staring instead at his father, Philip. "Look what my husband did to me! I wanted you to see what the monster did to me!"_ _His mother rushed to Auntie Audrey's side. "Desmond did this? Oh my dear!"_ _"Don't touch me!" Audrey cried out as she crumpled to the floor._ _His father stood up from the table. "Nicky, upstairs now!"_ _"But Dad—"_ _"_ NOW _!" his father shouted._ _Ling Jeh rushed to Nick's side and steered him out of the dining room._ _"What is happening? Is Auntie Audrey okay?" Nick asked worriedly._ _"Don't worry about her, let's go to your room. I'll play dominoes with you," his nanny replied in her soothing Cantonese as she rushed him up the stairs._ _They sat there in his bedroom for about fifteen minutes. Ling Jeh had laid out the dominoes, but he was too distracted by the sounds coming from downstairs. He could hear muffled shouts and a woman weeping. Was it his mum or Auntie Audrey? He ran out to the landing and overheard Auntie Audrey shouting, "Just because you are Youngs, you think you can go around fucking anyone you want?"_ _He couldn't believe his ears. He had never heard an adult use the f word like that. What did this mean?_ _"Nicky, come back into the room at once!" Ling Jeh yelled, pulling him back into his bedroom. She shut the door tightly and began rushing around, hurriedly shutting the jalousie windows and turning on the air conditioner. Suddenly the familiar_ tock, tock _sound of an old taxi could be heard laboring up the steep driveway. Nick rushed to the veranda and leaning out he could see that it was Uncle Desmond—Auntie Audrey's husband—stumbling out of the taxi. His father came outside, and he could hear the both of them arguing in the dark, Uncle Desmond pleading, "She's lying! It's all lies, I'm telling you!" while his father murmured something and then suddenly, forcefully, raised his voice. "Not in my house._ NOT IN MY HOUSE _!"_ _At some point he must have fallen asleep. He woke up, not knowing what time it was. Ling Jeh had left the room, and the air conditioner had been turned off but the jalousie windows were still closed. It felt stiflingly hot. He cracked open the door carefully and saw across the hallway the line of light underneath the door to his parents' bedroom. Did he dare leave his room? Or would they be shouting at each other again? He didn't want to hear them fighting—he knew he wasn't supposed to hear them. He was feeling thirsty, so he walked out to the landing where there was a refrigerator that was always stocked with ice and a jug of water. As he opened the fridge and stood in front of it, feeling the cool draft against his body, he heard sobs coming from his parents' bedroom. Creeping over to their door, he could hear his mother suddenly scream, "Don't you dare! Don't you dare! You'll see your name splashed over the front pages tomorrow."_ _"Lower your voice!" his father shouted back angrily._ _"I'm going to ruin your precious name, I tell you! What I've had to put up with all these years from your family! I'm going to run. I'll run off with Nicky to America and you'll never see him again!"_ _"I'll kill you if you take my son!"_ _Nicky could feel his heart pounding. He had never heard his parents this angry before. He rushed into his bedroom, stripped off his pajamas, and threw on a T-shirt and his soccer shorts. He took out all the_ ang pow _money he had saved in his little metal safe box—$790—and grabbed his silver flashlight, tucking it into the waistband of his shorts. He went out the door leading onto the veranda, where a large guava tree arched over the second floor. He grasped hold of one of the thick branches, swung onto the tree trunk, and quickly shimmied down to the ground, as he had done hundreds of times._ _Jumping onto his ten-speed bicycle, he raced out of the garage and down Tudor Close. He could hear the Alsatians at his neighbor's house begin to bark, and it made him cycle even faster. He sped down the long slope of Harlyn Road until he reached Berrima Road. At the second house on the right, he stopped in front of the tall steel electronic gate and looked around. The concrete fence had glass spikes at the top, but he wondered whether he could still climb it, holding on to the edges and propelling himself quickly enough that he wouldn't get cut. He was still out of breath from his escape. A Malay guard came out of the sentry box next to the gate, astonished to see a boy standing there at two in the morning._ _"What do you want, boy?"_ _It was the night guard who didn't know him. "I need to see Colin. Can you tell him Nicky is here?"_ _The guard looked momentarily perplexed, but then he went into his sentry box and got on the phone. A few minutes later, Nick could see lights come on in the house, and the metal gate began to slide open with a quiet clang. As Nick walked down the driveway toward the house, the porch lights came on and the front door opened. Colin's British grandmother, Winifred Khoo, who always reminded him of a plumper version of Margaret Thatcher, stood at the doorway in a quilted peach silk robe._ _"Nicholas Young! Is everything all right?"_ _He ran up to her and breathlessly blurted out, "My parents are fighting! They want to kill each other, and my mother wants to take me away!"_ _"Calm down, calm down. No one is going to take you away," Mrs. Khoo said soothingly, putting her arms around him. The tension that had been bottled up all evening came out, and he began sobbing uncontrollably._ _Half an hour later, as he sat on a barstool in the upstairs library, enjoying a vanilla root beer float with Colin, Philip and Eleanor Young arrived at the Khoo residence. He could hear their polite tones as they talked to Winifred Khoo in the drawing room downstairs._ _"Naturally, our boy overreacted. I think his imagination got away with him." He could hear his mother laughing, speaking in that English accent of hers that she put on whenever she was talking to Westerners._ _"All the same, I think he should probably just spend the night here," Winifred Khoo said._ _Just then, another car could be heard pulling up the front driveway. Colin turned on the television, which flickered a security-camera screen that revealed a stately black Mercedes 600 Pullman limousine arriving at the front door. A tall uniformed Gurkha jumped out and opened the passenger door._ _"It's your Ah Ma!" Colin said excitedly, as the boys rushed to the banister to peek at what was going on downstairs._ _Su Yi entered the house, with two Thai lady's maids trailing behind her, and Nick's nanny, Ling Jeh, suddenly also appeared, clutching three big boxes of mooncakes. Nick figured that Ling Jeh must have alerted his grandmother to what had happened at his house. Even though she now worked for his parents, her ultimate loyalty was always to Su Yi._ _Su Yi, wearing her trademark tinted glasses, was dressed in a chic rose-colored linen pantsuit with a ruffled high-necked blouse, looking as if she had just come from addressing the UN General Assembly. "I must apologize for inconveniencing you like this," he heard his grandmother say to Winifred Khoo in perfect English. Nick had no idea his grandmother could speak English so well. He saw his parents standing off to the side with stunned, chastened looks on their faces._ _Ling Jeh handed Winifred the towering stack of square tin boxes._ _"My goodness, the famous mooncakes from Tyersall Park! This is much too generous of you!" Winifred said._ _"Not at all. I am so appreciative of your calling me. Now, where's Nicky?" his grandmother asked. Nick and Colin ran back into the library, pretending they had heard nothing until they were summoned downstairs by Colin's nanny._ _"Nicky, there you are!" his grandmother said. She put her hand on his shoulder and said, "Now, say thank you to Mrs. Khoo."_ _"Thanks, Mrs. Khoo. Good night, Colin," he said with a grin, as his grandmother guided him out the front door and into the Mercedes. She climbed in after him, and Ling Jeh also got in, sitting on the folding seat in the middle row of the stretch limousine with the Thai lady's maids. As the car door was about to shut, his father came rushing out. "Mummy, are you taking Nicky to—"_ "Wah mai chup!"3 _Su Yi said sharply in Hokkien, turning away from her son as the guard shut the door firmly._ _As the car pulled out of the Khoo residence, he asked his grandmother in Cantonese, "Are we going to your house?"_ _"Yes, I am taking you to Tyersall Park."_ _"How long can I stay there?"_ _"For as long as you want."_ _"Will Dad and Mum come to see me?"_ _"Only if they can learn to behave themselves," Su Yi replied. His grandmother reached her arm out, drawing him closer, and he remembered being surprised by the gesture, by the softness of her body as he leaned against her while the car rocked gently back and forth as it navigated down the dark leafy lanes._ And now in a flash Nick found himself on that same dark lane again, more than two decades later, with Colin at the wheel of his Porsche. As the car wound along Tyersall Avenue, Nick felt like he knew every curve and bump of the road—the sudden dip that put them eye level with the gnarled ancient tree trunks, the dense overhang of foliage that kept it cool even on the hottest day. He must have walked or cycled down this narrow lane a thousand times as a kid. He realized for the first time that he was excited to be home again, and that the hurt he had felt over the past few years was fading. Without quite realizing it, he had already forgiven his grandmother. The car pulled up to the familiar gates of Tyersall Park, and Colin breezily announced to the approaching guard, "I'm delivering Nicholas Young." The yellow-turbaned Gurkha peered in the front window of the car at the both of them and said, "I'm sorry, but we're not expecting any more visitors tonight." "We're not visitors. This is Nicholas Young right here. This is his grandmother's house," Colin insisted. Nick leaned toward the driver's seat, trying to get a better look at the guard. He didn't recognize the man—he must have started working for Tyersall Park after his last visit. "Hey, I don't think we've met before. I'm Nick—they are expecting my arrival up at the house." The guard turned around and went back into the guardhouse for a moment. He returned with a brown paper log and began flipping through the pages. Colin turned to Nick and snickered in disbelief. "Can you believe this?" "I'm sorry, but I don't see either of your names here, and we are under high alert at the moment. I'm afraid I'm going to have to ask you to turn around." "Look, is Vikram here? Can you please call Vikram?" Nick asked, beginning to lose his patience. Vikram, who headed the guard unit for the past two decades, would quickly put an end to this absurdity. "Captain Ghale is off duty right now. He returns at eight tomorrow morning." "Well, call him, or call whoever the on-duty supervisor is." "That would be Sergeant Gurung," the guard said, getting out his walkie-talkie. He began talking in Nepali into the device, and a few minutes later, an officer emerged from the darkness, having come from the main guardhouse up the road. Nick recognized him immediately. "Hey, Joey, it's me, Nick! Will you tell your friend here to let us through?" The burly guard in the starched olive fatigues walked up to the passenger-side window with a big smile. "Nicky Young! It's so good to see you! What has it been? Four, five years now?" "I was last back in 2010. That's why your compadre over here doesn't know me." Sergeant Gurung leaned against the car window. "Listen, we are under specific orders here. I don't quite know how to put this, but we're not allowed to let you enter." * * 1 Malay for "bald-headed." For some reason, the word has also become popular as a nickname for little boys with crew cuts. 2 Singapore Chinese Girls' School, which we ACS boys used to call Sucking Co—uh, never mind. 3 Hokkien for "I couldn't give a damn." # CHAPTER THIRTEEN TYERSALL PARK, SINGAPORE # TWENTY-FOUR HOURS EARLIER... "Three, four, five," Eddie counted as he stood by the window in the upstairs foyer, looking down the driveway. There were five cars in the motorcade—four, really, if you didn't count the minivan transporting all the maids bringing up the rear. Auntie Catherine and her family had just flown in from Bangkok, and Eddie was surprised there were so few cars in their convoy. In the lead was a white Mercedes S-Class with diplomatic license plates, obviously provided by the Thai embassy, but the other cars were a random assortment: a BMW X5 SUV behind the Benz, an Audi that looked at least five years old, and that last car, he didn't even have a clue what it was—it was some non-European four-door sedan, something that didn't register on his list of acceptable vehicles to be seen in. Yesterday, when he had arrived with his family from Hong Kong, his executive assistant, Stella, had arranged a fleet of six matching Carpathian Grey Range Rovers, making for an impressive entrance as the Cheng _famille_ pulled up to the front door of Tyersall Park. Today he felt almost embarrassed for Auntie Catherine and her clan. Her husband, M.C. Taksin Aakara,1 was one of the descendants of King Mongkut, and Eddie remembered every detail of his last visit to Thailand when he was nineteen as if it was yesterday: The sprawling compound of historic villas set in a garden paradise on the banks of the Chao Phraya River; the way his cousins James, Matt, and Adam had three servants _each_ that would prostrate at their feet as if they were little gods, ready to attend to their every whim; the fleet of forest green BMWs idling in the front courtyard ready to take them to the polo club, the tennis club, or any of Sukhumvit's hottest dance clubs; and Jessieanne, that sexy cousin of theirs who went down on him in the upstairs toilet of a pizza parlor in Hua Hin one night. So why were the Aakaras pulling up in such a ragtag bunch of cars? And wait a minute—what the hell was happening outside? Sanjit the butler and the entire household staff—including the Gurkha guards—were all dressed in their crisp uniforms and assembling along the front driveway! And Ah Ling and Auntie Victoria were also part of the greeting party! Fucky fuck, why hadn't they done this for his family when they arrived yesterday? Eddie was annoyed to see that his parents had gone outside too, and he was determined that he would under no circumstances join them. Thank goodness Fiona had taken the kids to the zoo, otherwise they would surely want to be part of this idiocy and make the Aakaras feel like they were truly hot shit. He ducked out of view and hid in the service hallway, waiting for everyone to come upstairs, knowing it was always the custom at Tyersall Park for guests to be served iced longan tea in the drawing room when they first arrived. Two waiters passed by rolling cocktail trolleys filled with glassware and large silver samovars of tea, mystified by Eddie lurking in the hallway. He glared at them and hissed, "You didn't see me! I'm not here!" When Eddie began to hear voices coming up the stairs, he ambled into the drawing room with his hands nonchalantly tucked into the pockets of his salmon-colored Rubinacci trousers. Auntie Cat was the first to arrive at the top of the grand staircase, chattering away excitedly with his mother in that distinctive convent-schoolgirl lilt of hers.2 "What a surprise to see you and Malcolm out front! I thought you weren't arriving until this evening?" "That was the plan, but Eddie managed to fly all of us down on a private jet yesterday." " _Wah, gum ho maeng!_ "3 Catherine remarked, as a waiter approached them bearing a silver tray filled with tall glasses of iced longan tea. Eddie studied his aunt for a moment as she sat down on a divan next to his mother, marveling at how different the sisters looked. Auntie Cat's stocky, athletic physique was enviable for a woman in her seventies, and in such contrast to his other aunties with their bony, aristocratically malnourished frames. Unfortunately, she _did_ take after her sisters in her fashion sense—on a charitable day, Eddie might have politely described her style as "eccentric." Today, she just looked god-awful in that boxy purple silk pantsuit, obviously tailor-made and obviously several decades old, mud-colored Clarks open-toed walking sandals, and the same pair of Sophia Loren bluish-tinted bifocals he had seen her wear for decades. Catching sight of him, Catherine exclaimed, "My goodness, Eddie, I hardly recognized you. You look like you've lost a bit of weight!" "Thank you for noticing, Auntie Cat! Yes, I've lost about twenty pounds in the past year." "Good for you! And your mother tells me you flew the whole family down yesterday?" "Well, I was attending the World Economic Forum in Davos as an official delegate and my client Mikhail Kordochevsky—you know, one of Russia's richest men—insisted that I borrow his Boeing Business Jet when he heard about Ah Ma's heart attack. And you know, it's such a huge plane, I thought it was a pity that I was the only passenger. So instead of flying straight to Singapore, we made a detour to Hong Kong so I could pick up the whole family." Catherine turned to her sister. "You see, Alix, I don't know what you keep complaining about—your son is so thoughtful!" "Yes, very thoughtful," Alix added, trying to block out the memory of Eddie screaming at her over the phone yesterday: _You have two hours to get everyone to Hong Kong airport or I'm leaving without you! My special friend is doing us a very special favor by lending us his very special plane, you know! And for God's sake please pack some decent clothes and jewelry this time! I don't want you to be mistaken for a Mainland tourist when I'm with you in Singapore! Last time we got such bad service at Crystal Jade Palace because of the way you looked!_ "How did you all fly down?" Eddie asked, wondering what kind of private jet the Aakaras had these days. "Well, Thai Airways was running a special just for today. If you buy three economy tickets, the fourth person flies for free. So it was quite a savings for our whole lot. But then when we got to the airport and they realized it was your uncle Taksin, they upgraded us to first class." Eddie couldn't believe his ears. The Aakaras never flew commercial—not since Uncle Taksin had become a special attaché to the Thai Air Force back in the 1970s. Just then, Eddie spied his uncle entering the drawing room alongside his father. It had been years since he had last seen his uncle, but he appeared not to have aged one bit—he was older than his father but looked about a decade younger. His perpetually tan face was wrinkle-free, and he still had that ramrod-straight posture and robust gait of a man accustomed to seeing and being seen. If only his dad wasn't getting so stooped, and if only he dressed more like Uncle Taksin! Eddie had always admired his uncle's dapper style, and on visits to Bangkok during his teens, he made a point of sneaking into his uncle's closet and checking out all the labels on his clothes—no small feat when there were so many pesky servants lurking everywhere. Today Uncle Taksin was decked out in an impeccably tailored pale orange dress shirt—judging from the Sea Island cotton it was most likely Ede & Ravenscroft—worn with a pair of navy blue chinos and a highly polished pair of monk strap loafers. Were they Gaziano & Girling or Edward Green? He would have to ask him later. And most important, what watch was Uncle Taksin sporting today? He glanced at his sleeve cuff, expecting to see a Patek, Vacheron, or Breguet, but was horrified to see an Apple Watch strapped to his wrist. Dear God, how the mighty had fallen! Behind Taksin came his son Adam, whom Eddie didn't know all that well because he was more than a decade younger. The baby of the family, Adam was slightly built and had delicately chiseled, almost feline features. He looked like one of those Thai pop idols, and seemed to dress the part in his skinny jeans and a vintage Hawaiian shirt. Eddie was not impressed. But wait a minute, who was this sexy thing that he would definitely swipe right for? Sauntering up the stairs was a girl with alabaster skin and waist-length black hair. Here at last was someone with style—the girl was wearing a sleeveless ice-blue Emilia Wickstead jumpsuit, blue suede ankle boots, and casually slung on her shoulder was the sort of handbag that Eddie was sure had a three-year waiting list. This must be Adam's new wife, Princess Piya, whom his mother couldn't stop gushing about after she attended their wedding last year.4 "Uncle Taksin! So good to see you! And Adam—long time no see!" Eddie patted his cousin on the back enthusiastically. Adam turned to his wife and said, "This is Auntie Alix's eldest son, Eddie, who also lives in Hong Kong." "Princess Piya, it is an honor to meet you!" Bending forward, Eddie grasped her hand and bowed to give it a kiss. Adam snorted almost imperceptibly, while Piya burst into giggles at Eddie's ridiculously overblown gesture. "Please, it's just Piya. Only the children and grandchildren of the king use any sort of formal titles. I'm just a distant relation." "I do believe you're being very modest. I mean, you've been given the Pearl Suite!" "What's that?" Piya asked. Before Eddie could answer, Adam cut in, "It's this bedroom where all the walls are inlaid with mother-of-pearl. Really remarkable." "Yes, it's this vast suite of rooms, perfect for families, really. My wife and three children usually stay in there when we visit," Eddie couldn't help adding. "Which room are you in now?" Adam asked. "We're in the Yellow Room. It's very...cozy." Piya's brow furrowed. "Adam, this doesn't sound right to me. We must move in to another bedroom so Eddie and his family can have this larger suite." "But you're our honored royal guest! You must have the Pearl Suite. I didn't mean to imply anything with my comment. Constantine, Augustine, and Kalliste are having loads of fun sharing the same bed, and Fiona even managed to get three hours of sleep last night." "Oh dear, I wouldn't feel comfortable in the Pearl Suite knowing that. Adam, could you take care of this?" Piya insisted. "Of course. I'll have a word with Ah Ling the minute I see her," Adam replied. Eddie smiled graciously. "You are both too kind. Now, where are your brothers? I thought the whole family was coming today. There's an eighteen-wheeler full of seafood awaiting them." Adam gave him a puzzled look. "Piya and I were the only ones who came down with Mum and Dad. Jimmy, as you know, is a doctor, so he can't get away from work so easily, and Mattie is on a skiing trip with his family in Verbier." "Ah. I was just in Switzerland too! I was at Davos, as an official delegate at the World Economic Forum." "Oh, I was at Davos two years ago," Piya said. "Really? What were you doing there?" "I was giving a talk to IGWEL." Eddie looked momentarily stunned as Adam proudly explained, "Piya's a virologist based at WHO5 in Bangkok—she specializes in mosquito-borne viruses like malaria and dengue fever, and she's become one of the leading authorities on tropical diseases." Piya smiled bashfully. "Oh, Adam's exaggerating, I'm no authority—I'm just part of the team. Now that man over there looks like he's an authority." Eddie turned to see Professor Oon, still in his surgical scrubs, enter the drawing room. Catherine got up from her divan and rushed up to him. "Francis! So good to see you. How is Mummy today?" "Her vitals are stable at the moment." "Can we go in and see her now?" "She's in and out of consciousness. I will let four visitors in, but two at a time and only for five minutes each." Alix looked at her sister. "Go on. Take Taksin, Adam, and Piya with you. I've already spent time with her this morning—" "I haven't seen Ah Ma yet today," Eddie cut in. "Dr. Oon, surely one more visitor won't make any difference?" "Okay, I'll let you go in for a few minutes after the rest have come out, but only for a few minutes. We don't want to add any more strain to her today," the doctor said. "Of course. I won't say a word." "Eddie, will you say a little prayer for Ah Ma when you're in the room with her?" Auntie Victoria suddenly asked. "Em, sure, I can do that," Eddie promised. The five of them headed down the corridor to Su Yi's private quarters. The sitting room adjoining her bedroom had been transformed into a cardiac care unit, with half the room turned into a clinical prep area and the other half filled with various medical machines. Several doctors and nurses huddled over a bank of computer screens, analyzing every blip in their VVIP patient's vital signs, while Su Yi's Thai lady's maids hovered just by the doorway, ready to spring into action should their mistress bat an eyelash. The minute they saw Prince Taksin approach, they dropped to the floor, prostrating themselves. Eddie felt his gut tighten in a mixture of awe and envy as he noticed that his aunt and uncle walked right past the ladies, not even noticing the gesture. _Fucky fuck, why couldn't he have been born into that family?_ While Catherine and Taksin went into Su Yi's bedroom, Eddie waited in the hallway with Adam and Piya. Taking the seat next to Piya on a velvet Ruhlmann settee, he whispered, "So, I take it you had an IGWEL badge?" Piya was momentarily confused. "I'm sorry, are your referring to Davos?" "Yes. When you were at Davos two years ago, what kind of badge did they give you? The white one with the blue line at the bottom, or the plain white one with the hologram sticker?" "I'm afraid I can't remember what it looked like." "What did you do with it?" "I wore it," Piya replied patiently, wondering why on earth her husband's cousin was so weirdly fixated on this badge. "I mean, what did you do with your badge after the conference?" "Er...I must have either thrown it away or left it in the hotel room." Eddie stared at her in disbelief. His Davos badge was folded and placed in a special pouch along with his prized Roger W. Smith6 watch and his precious sapphire-and-platinum cuff links. He couldn't wait to get it framed the minute he returned to Hong Kong. He was quiet for a few moments before turning his attention to Adam. "So what are you up to these days? Do you work or do you just live a life of leisure?" Adam felt like grimacing, but he was too well brought up to show any reaction. Why did so many people assume that just because he had a royal title, he didn't have to work for a living? "I'm in F&B.7 I have a restaurant at Central Embassy, which is the newest mall in town, and I also have a few gourmet food trucks that serve authentic Austrian _Würstelstand_ snacks like bratwurst, currywurst, and Käsekrainer. You know, those Austrian sausages filled with cheese?" "A sausage truck! You actually make a profit from that?" Eddie asked. "We do quite well. We park the trucks in all the nightlife spots around the city. People love to get a snack late at night after they leave the bars and clubs." "The sausages help to soak up the alcohol," Piya added. "Hmm. Drunk-people snacks. How lucrative," Eddie said with a not-so-subtle hint of condescension. He sat waiting for Adam or Piya to ask him what he did for a living when his aunt and uncle came out of the bedroom. "She's asleep, but you can go in," Catherine said to her son. Catherine sank down on the settee next to Eddie, suddenly looking totally deflated. "How is she today?" Eddie asked. "Hard to tell. Francis said that with the morphine drip, she wasn't in any pain. I've just never seen her look so...so frail," Catherine said, her voice cracking a little. Taksin placed a comforting hand on her shoulder as she continued to talk. "I should have come down in November like I meant to. And the boys. Why didn't we make them come down more often?" "Auntie Cat, you should go to your room and rest for a little while," Eddie suggested in a gentle tone. He became uncomfortable whenever women got emotional around him. "Yes, I think that's a good idea," Catherine said, getting up from the settee. "I'm going to call Jimmy and Mattie. We'll get them to fly over immediately. There's not a moment to waste," Taksin said to her as they walked off. _Not a moment to waste_ , Eddie thought to himself. But Auntie Cat had done nothing but waste her time. She had spent so many decades away, and his cousins hardly knew their grandmother. And now that Ah Ma was dying, they were finally going to show their faces? It was too little, too late! Or could there be another motive behind all this? Were the Aakaras tight on money these days? Was this why they came down on a commercial flight? He couldn't imagine the humiliation. A Thai prince, flying in economy class! And they only brought five maids with them this time. And Adam had to run these pathetic little hot-dog trucks. It was all beginning to make sense. Was Uncle Taksin urgently summoning all his sons to Singapore so they get their hands on Tyersall Park? Everyone knew that Nicky had been disinherited, and that Ah Ma would never leave any of the Leong cousins Tyersall Park when they already owned most of Malaysia. The only contenders left were the Aakara boys; his brother, Alistair; and _him_. Ah Ma had never thought much of Alistair, especially after he tried to bring Kitty Pong home, but the Aakaras, she always had a soft spot for them because they were half Thai. She loved her Thai food and her Thai silks and her creepy Thai maids—everything from that goddamn country! But he wasn't going to let those Aakaras win. They lived their lavish snotty royal lives and only deigned to come for short visits every three or four years, while _he_ made a point of visiting his grandmother at least once a year. Yes, he was the only one who deserved the deed to Tyersall Park! Adam and Piya emerged from the bedroom, and Eddie immediately went in—there wasn't a moment of _his time_ to waste. Su Yi's canopied bed with its ornately carved art nouveau headboard had been replaced by one of those state-of-the-art hospital beds with an electronic mattress that constantly shifted the patient's body weight to prevent bedsores. Aside from the oxygen tube at her nose and a few tubes coming out of various veins on her arms, she looked so serene lying there under her sumptuous lotus silk bedsheets. A heart monitor on a stand pulsed quietly by her side, its screen displaying her ever changing heart rate. Eddie stood at the foot of the bed, wondering whether he should say a little prayer or something. It seemed slightly absurd, since he didn't really believe in God, but he did promise Auntie Victoria. He kneeled down beside his grandmother, folded his hands, and just as he closed his eyes, he heard a sharp voice say in Cantonese, " _Nay zhou mut yeah?_ " What on earth are you doing? Eddie opened his eyes and saw his grandmother staring at him. "Fucky fuh...I mean, Ah Ma! You're finally awake! I was about to say a prayer for you." " _Nay chyee seen ah!_ 8 Don't you start on me. I'm so sick of all these people trying to pray for me. Victoria kept sending that Bishop See Bei Sien to drone his idiotic prayers every morning when I was at the hospital, and I was too weak to chase him out at the time." Eddie laughed. "If you want, I can make sure Bishop See isn't allowed to see you ever again." "Please!" "Were you awake when Adam and Piya came in?" "No. Adam is here?" "Yes, and he brought his wife. She's pretty, in that Thai sort of way." "How about his brothers?" "No, they aren't here. I'm told Jimmy is much too busy working to come down. I guess since he's a plastic surgeon, there are too many urgent face-lifts and nose jobs that require his attention right now." Su Yi smiled slightly at Eddie's comment. "And do you know what Mattie is doing?" "Tell me." "He's on holiday with his family. _Skiing in Switzerland!_ Can you imagine? I happened to be in Switzerland too, attending a very important conference with the world's most important businessmen, political leaders, and Pharrell, but I dropped _everything_ and flew straight to Singapore the minute I heard you were ill!" Eddie looked up at her heart monitor and saw that it was accelerating from 80 to 95 beats per minute. Su Yi let out a brief sigh. "Who else is here?" "Our whole family came down from Hong Kong. Even Cecilia and Alistair." "Where are they?" "Everyone's at the zoo right now. Fiona, Constantine, Augustine, Kalliste, Cecilia, and Jake. Ah Tock got them special VIP tickets for that River Safari thing, but they will be back by tea time. Uncle Alfred gets in later tonight, and...um, I'm told that Nicky is arriving tomorrow." "Nicky? Coming from New York?" Su Yi muttered. "Yes. That's what I hear." Su Yi remained silent, and Eddie observed that the heart rate number on her monitor was rising rapidly: 100, 105, 110 beats per minute. "You don't want to see him, do you?" Eddie asked. Su Yi simply closed her eyes, a lone tear streaming down the side of her face. Eddie glanced uneasily at the monitor: 120, 130. "I don't blame you, Ah Ma. Showing up here like this now, after all he's done to betray your wishes—" "No, no," Su Yi finally said. Her heart rate suddenly jumped to 145 beats per minute, and Eddie looked at her in alarm. When the number hit 150, the heart monitor began emitting a high-pitched beep, and Professor Oon rushed into the room along with another doctor. "She's elevating too rapidly!" one of the doctors said in alarm. "Should we defibrillate?" "No, no, I'm going to give her a slow bolus of digoxin. Eddie, please clear the room," Professor Oon ordered, as two nurses rushed in to assist. Eddie backed out just as his aunt Victoria entered the sitting room. "Is everything okay?" "Don't go in now. I think Ah Ma's having another heart attack! I mentioned Nicky and she began to freak out." Victoria moaned. "Why on earth did you mention Nicky?" "She wanted to know who was here and who was coming. I can tell you one thing, though—Ah Ma does not wish to see Nicky. She does not even want him to set foot in this house! It was the last thing she told me." * * 1 M.C. is an abbreviation for Mom Chao, which translates to Serene Highness and is the title reserved for the grandchildren of the King of Thailand. Since King Chulalongkorn (1853–1910) had ninety-seven children by thirty-six wives and King Mongkut (1804–1868) had eighty-two children by thirty-nine wives, there are several hundred people still alive who can use the title of Mom Chao. 2 Catherine Young Aakara, like many of the girls of her generation and social standing, attended the Convent of the Holy Infant Jesus Girls' School in Singapore, where they were taught by British nuns and developed the curious distinctive accents that made them all sound like extras in BBC period dramas. 3 Cantonese for "Wow, what a good life." 4 To his eternal chagrin, Eddie had not been invited to his cousin's wedding to M.R. Piyarasmi Apitchatpongse. Only his parents had been invited to the small, intimate destination wedding held at a private villa in the Similan Islands. 5 The World Health Organization is a specialized agency of the United Nations that deals with international public health issues. The South-East Asia Regional Office is located in Bangkok. 6 One of the most sought-after bespoke watches in the world, each Roger W. Smith watch is made by hand, takes eleven months to complete, and there's a four-year waiting list for one (probably five years after this is published). 7 An abbreviation for food and beverage, currently one of the hottest industries in Asia. All the CRAs that used to work in M&A want to get in to F&B these days. 8 Cantonese for "Have you lost your mind?" # CHAPTER FOURTEEN JODHPUR, INDIA Astrid stood on the balcony, breathing in the luxuriant scent that wafted up from the rose gardens below. From her vantage point at the Umaid Bhawan Palace Hotel, she had a sweeping view of the city. To the east, an impossibly romantic-looking fort perched on a mountaintop, while in the distance the tight clusters of vibrant blue buildings that made up the medieval city of Jodhpur gleamed in the early-morning light. _The Blue City_ , Astrid thought to herself. She had heard somewhere that all the houses here were painted this shade of cobalt because it was believed to ward off evil spirits. The color reminded her of Yves Saint Laurent and Pierre Bergé's estate in Marrakech—the Majorelle Gardens—much of which was also painted a distinctive shade of blue, the only house in an entire city of rose ochre allowed by decree of the king to be painted a different color. Astrid stretched out on the chaise lounge and poured herself another cup of chai from the silver art deco teapot. This monumental palace had been commissioned by the present maharaja's grandfather in 1929 to give work to all the people during a great famine, so every detail retained its original art deco style—from the pink sandstone pillars in the rotunda to the blue mosaic tiles in the underground swimming pool built so that the maharani could swim in complete privacy. The place reminded her a bit of Tyersall Park, and for a moment, Astrid felt an intense pang of guilt. Her grandmother lay in bed attended by a team of doctors while she was here, enjoying a secret weekend rendezvous at a palace. Her guilt faded slightly as she caught sight of Charlie padding out onto the balcony clad only in his drawstring pajama trousers. When did he become so built? Back in their university days in London Charlie had been positively scrawny, but now his lanky torso took on that distinctive V-shape and his abs looked more ripped than she had ever remembered. He stood behind her as she lay on the chaise lounge, bending over and kissing that tender spot on her neck. "Morning, gorgeous." "Good morning. Did you sleep well?" "Now I don't recall getting any sleep last night, but I'm sure glad _you_ did," Charlie teased as he poured a cup of coffee from the samovar set up on the chrome-and-glass trolley. He took his first sip and murmured in satisfaction, "Mmm. How great is this coffee?" Astrid smiled placidly. "Actually, I'm sure their coffee is great, but I brought these beans. I know how much you love your first cup, so I had them ground for you this morning. It's Ethiopian Yirgacheffe from Verve Coffee in LA." Charlie gazed at her in appreciation. "That's it. I'm kidnapping you and not letting you go back to Singapore. I'm never going to let you leave my side for...well, the rest of eternity." "Kidnap me all you want, but you'll have to contend with my family. I'm sure my dad will send out a SWAT team if I don't turn up for breakfast at Nassim Road on Monday morning." "Don't worry, I'll get you back in time, and you can even show up with a big tray of these parathas for breakfast," Charlie said, taking a bite out of the buttery, still-warm Indian layered bread. Astrid giggled. "No, no, it has to be something Malay, otherwise they'll suspect. It feels like I'm playing hooky, but I'm so glad you convinced me to do this—I really needed it." "You've been spending so much time at your grandmother's bedside, dealing with the family circus, I thought you could use a break." Charlie perched on the balcony's edge, looking down at an ornately turbaned man sitting on a pile of pillows in the middle of the grand terrace, playing a soft melody on his bansuri while a flock of peacocks wandered behind him on the great lawn. "Astrid, you need to come check this out. There's a flute player on the terrace, surrounded by peacocks." "I saw him. He's been out there all morning. It's absolute heaven here, isn't it?" Astrid closed her eyes for a moment, listening to the enchanting melody as she savored the warmth of the sun on her face. "Well, just wait. We haven't even toured the city yet," Charlie said with a sly gleam in his eyes. Astrid smiled to herself, enjoying his impish little-boy expression. What was Charlie up to? He looked just like Cassian did whenever he was trying to hide a secret. After they had enjoyed a classic Indian breakfast of akuri-spiced scrambled eggs on laccha paratha, chicken samosas, and fresh mango pudding on their private balcony, Charlie and Astrid walked to the front entrance to the palace. As they waited for the maharaja's Rolls-Royce Phantom II to pull up to the front steps, the guards started showering compliments on Astrid. "Ma'am, we've never seen anyone look so beautiful in jodhpurs," they praised. Astrid smiled bashfully—she was wearing a white linen tunic tucked into the new pair of white jodhpurs that had just been tailored for her. But instead of a belt, she had wound a long hand-beaded Scott Diffrient turquoise necklace through the belt loops. They were driven in the vintage convertible to the Mehrangarh Fort, an imposing red sandstone fortress perched on a dramatic cliff four hundred feet above the skyline of Jodhpur. At the foot of the hill, they transferred into a small jeep that sped them up the steep road to the main entrance, a beautiful arched gateway flanked by ancient frescos known as Jai Pol, the Gate of Victory. Soon they were strolling hand in hand through the interconnected network of palaces and museums that made up the fort complex, marveling at the intricately carved walls and expansive courtyards that afforded commanding views of the city. "This is incredible," Astrid said in a hushed voice as they entered an elaborate chamber where the walls and ceilings were made entirely of mirrored glass mosaic tiles. "Well, they don't call this the most beautiful fort in Rajasthan for nothing," Charlie said. As they strolled through a reception hall where every surface—from the walls to the ceilings to the floors—was painted in dizzyingly colorful floral patterns, Astrid couldn't help but comment, "It's so empty. Where are all the tourists?" "The fort's actually closed today, but Shivraj had the place opened just for us." "How sweet of him. So this fort belongs to his family?" "Since the fifteenth century. It's one of the only forts in India that's still controlled by the original ruling family that built it." "Am I going to get the chance to thank Shivraj in person?" "Oh, I forgot to tell you—we've been invited to the private residence at Umaid Bhawan for dinner tonight with his family." "Great. I wonder if they are related to the Singhs—you know, Gayatri Singh, our family friend who throws those fabulous parties where she displays all her jewels? Her father was a maharaja of one of the Indian states...though I can't recall which one at the moment." "Maybe. I think many of the royal families of India intermarried," Charlie replied a little distractedly. "Are you okay?" Astrid asked, noticing his change of mood. "Yeah, yeah, I'm fine. There's this amazing room that I'm trying to find for you—I know you'll love it. I think it's up these stairs." Charlie led her up a steep staircase that wound around in a teardrop shape, and at the top of the stairwell they arrived at a long narrow room flanked by arched windows along every wall. In the middle of the room was a collection of golden baby cradles, each more ornate than the other. "Is this the nursery?" Astrid asked. "No, this is actually part of the _zenana_ , where the ladies of the palace were cloistered. This building is called the Peeping Palace, because the ladies would come here and peep down on the activities of the courtyard below." "Oh, that's right. The royal wives and concubines could never be seen by the public, could they?" Astrid leaned out a window framed by a distinctive Bengali-style eave, peeking through the little star-patterned holes in the screened window. Then she opened the shutters completely, taking in the view below of the grand marbled courtyard surrounded on three sides by palace balconies. "Hey, do you want to get your hands painted with henna?" Charlie asked. "Ooh. I'd love to!" "The concierge at the hotel told me there's a henna artist here who does the most incredible work. I think she's in the museum gift shop. Let me go get her." "I'll come with you." "No, no, stay here and enjoy the incredible view. I'll get her and be right back." "Oh, okay," Astrid said, a little puzzled as Charlie rushed off. She sat on a bench in the room, contemplating what it would have been like to be married to a maharaja back in the time when they were absolute rulers of their kingdoms. It would have been a life of unfathomable luxury, but she wasn't sure she wanted to be part of a harem with dozens of queens and concubines. How could she ever share the man she loved with someone else? And were the women ever allowed to wander beyond the palace walls, or even to step onto the elegant courtyard below? Astrid heard some laughter in the distance, and she spied several women emerging through an arched doorway in the courtyard. How pretty they looked in their red-and-white lehenga cholis. They were followed by another row of women in the same tightly cropped blouses and flowing embroidered skirts, and soon there were about a dozen of them in the courtyard. The women walked single file in a circle as the sound of drumming began to emanate from deep within the fort. Suddenly the women formed a straight line right below where Astrid was standing. They flung their hands in the air, jerked their heads up at her, and began stomping their feet in rhythm to the drumming. From the archways on the lower floor beneath where Astrid was standing, a dozen men in white came running out between the women to the far side of the courtyard. A Hindi pop song began blasting through the air, and the men and women danced opposite each other in a seductive face-off. They were soon joined by another dozen female dancers in vibrant blue-and-purple saris, streaming in from the north and south gates of the courtyard, as the music got louder and louder. Suddenly the song stopped abruptly, and the window shutters on the opposite side of the courtyard flung open, revealing a man in a gold embroidered sherwani. He extended his arms toward Astrid, singing a cappella in Hindi. Then the music resumed as the dancers continued to stomp and twirl. Astrid burst out laughing, delighted at the Bollywood spectacle unfolding before her. _Charlie must be behind all this! No wonder he's been acting weird ever since we got here_ , she thought. The man disappeared from the turret, only to appear moments later in the courtyard leading a band of musicians. The entire troupe danced to the beat of the music, moving in perfect formation. She looked down at the handsome lead singer outfitted in gold, realizing with a shock that it was none other than Shah Rukh Khan, one of India's biggest stars. Before she could even react properly, the sound of trumpets filled the air, followed by a strange roaring sound. Turning to the main archway into the courtyard, Astrid's eyes widened in surprise. Coming through the gate was an elephant festooned with gemstones and vibrant pink-and-yellow patterns painted onto its head, being led by two mahouts dressed in the full regalia of the royal court of Jodhpur. On the elephant's back was an ornate silver howdah, and perched majestically on one of its seats, dressed in a midnight blue paisley sherwani with matching trousers and turban, was Charlie. Astrid's jaw dropped, and she ran out of the room onto the open veranda. "Charlie! What's all this?" The elephant strode over to her veranda, and she was almost at eye level with Charlie as he sat on top of the elephant. The mahouts guided the elephant so that it stood alongside the balcony, and Charlie leapt off the howdah onto the terrace where Astrid stood. "I wanted this to be a surprise. I haven't wanted to tell you until now, but Isabel signed our divorce papers last week." Astrid let out a little gasp. "Yes, I am a free man. Completely free! And I realized that in all the craziness of the past few years, we've just talked about getting married as though it was a done deal, but you know, I never properly proposed to you." Charlie suddenly got down on one knee and stared up at her. "Astrid, you are and have always been the love of my life—my angel, my savior. I don't know what I'd do without you. My dearest sweet love, will you marry me?" Before she could answer, the elephant let out another roar, and then curled his trunk upward to grab something from Charlie's hand. The animal then extended its trunk toward Astrid, waving a red leather box in front of her face. Astrid took the box gingerly and opened it. Sparkling inside was a five-carat canary diamond solitaire, encircled in a delicate floral scrollwork of white gold. It was an unusual setting, unlike anything that a contemporary jeweler might design. "Wait a minute...this...this looks like my grandmother's engagement ring!" "It _is_ your grandmother's engagement ring." "But how?" Astrid asked, utterly confused. "I flew down to Singapore last month and had a secret date with your grandmother. I know how important she is to you, so I wanted to be sure we had her blessing." Astrid shook her head in disbelief as she stared at the precious heirloom ring, covering her mouth with her right hand as tears began streaming down her face. "So how about it? Are you going to marry me?" Charlie looked at her plaintively. "Yes! Yes! Oh my God, yes!" Astrid cried. Charlie got up and embraced her tightly, as the crowd of dancers and musicians cheered. The two of them walked downstairs into the courtyard, and Shah Rukh Khan bounded toward them to be the first to offer his congratulations. "Were you surprised?" he asked. "My goodness, I'm still in shock. I didn't think I could still be surprised at this point in my life, but Charlie really pulled it off!" In the euphoria of the moment, no one noticed the series of bright flashes coming from the highest turret on the southern end of the fort. It came from the sunlight glinting off the telephoto lens of a Canon EOS 7D, the camera favored by paparazzi and private detectives. And it was pointed straight at Astrid and Charlie. # PART TWO > I made my money the old-fashioned way. I was very nice to a wealthy relative right before he died. > > _—_ MALCOLM FORBES # CHAPTER ONE LONDON, ENGLAND Wandi Meggaharto Widjawa was in London with her mother, Adeline Salim Meggaharto, supposedly to watch her nephew Kristian compete in a fencing tournament, but secretly they were both there for their triannual visits to the clinic of Dr. Ben Stork on Harley Street, who was considered by the most discerning filler addicts to be the Michelangelo of Botox. So deft were his hands at plunging needles into fine lines, fragile cheekbones, and delicate nasolabial folds, even his patients with the thinnest skins never bruised, and so subtle was his artistry that every patient visiting his clinic departed with the guarantee that they would be able to close both eyelids completely should they ever choose to blink.1 As Wandi sat in the elegant Hollywood Regency–style waiting room of the clinic in her floral embroidered Simone Rocha dress, waiting for her mother to get her usual combo of Botox®, Juvéderm Voluma®, Belotero Balance®, Restylane Lyft®, and Juvéderm Volbella® injections, she paged through the latest issue of _British Tattle_. She always flipped to the back of the magazine first to look at the Spectator section, which featured party pictures from the only parties that mattered throughout the realm. She loved scrutinizing all the English socialites from head to toe—the women looked like either chic swans or unmade beds (there was no middle ground). This month's Spectator section was quite disappointing—nothing but photos from the twenty-first birthday bash of yet another kid named Hugo, the launch party for yet another Simon Sebag Montefiore book, and some boring country wedding. She could never understand why all these aristocrats loved getting married in decrepit little English country churches when they could have the most lavish nuptials at Westminster Abbey or St. Paul's Cathedral.2 Suddenly Wandi's eyes zeroed in on the obligatory photo of the bride and groom. As was the custom with all the wedding shots in _British Tattle_ , the couple was pictured posing underneath the stone archway of the modest rectory festooned with a few anemic sprigs of roses, sporting painful grins as rice was being pelted at them. But the thing that stood out to Wandi was that the bride was _Asian_ , and this immediately triggered an alert. Wandi was part of a particular breed of Chindocrat3 that had been raised in a very specific manner—the only daughter of an Indonesian Chinese oligarch, she was a typical third-culture kid who had grown up all over the world. Born in Honolulu (for the American passport), her early childhood was divided between her family's hospital-wing-size house in Singapore and the historic family _joglo_ in Jakarta, where she attended kindergarten at the exclusive Jakarta International School (JIS). In the second grade, she was sent to the elite Singapore American School (SAS) before an unfortunate fake-Prada-backpack-trafficking incident in eighth grade led to her expulsion and swift enrollment into Aiglon, the boarding school of choice for privileged rebels in Chesières-Villars, Switzerland. After Aiglon, Wandi spent two years majoring in marketing at the University of California at Santa Barbara before dropping out and marrying the son of another Indonesian Chinese oligarch, shuttling between homes in Singapore and Jakarta, having her baby at Kapiolani Medical Center in Honolulu, and going through the existential crisis of trying to decide whether to send her firstborn son to JIS, SAS, or ACS.4 Like most of the women who made up Asia's jet set, Wandi had an innate radar for OAWS—Other Asians in Western Settings. Whenever she was traveling outside of Asia and happened to be, say, lunching at Tetsuya's in Sydney, attending the International Red Cross Ball in Monaco, or hanging out at 5 Hertford Street in London, and another person of Asian descent happened to enter the room, Wandi would notice that Asian well before any non-Asian did, and their face would immediately be run through the ten-point social-placement scanner in her brain: 1. What kind of Asian is this? In descending order of importance: Chindo, Singaporean, Hong Konger, Malaysian Chinese, Eurasian, Asian American living in New York or Los Angeles, Asian American working in private equity in Connecticut, Canadian Asian from Vancouver or Toronto, Australian Chinese from Sydney or Melbourne, Thai, Filipino from Forbes Park, American-Born Chinese, Taiwanese, Korean, Mainland Chinese, common Indonesian.5 2. Do I know this OAWS? Specifically, is this a famous actor/pop singer/politician/social figure/social media star/doctor/celebrity without portfolio/billionaire/magazine editor. Add 50 points if royalty or Joe Taslim. If Joe Taslim, have bodyguard slip him my room key. 3. Do I know any members of this OAWS's family? Have I met/attended school/socialized/shopped/co-chaired a gala/blown/backstabbed anyone related to this person? 4. How much is this OAWS or his/her family worth? Evaluate actual net worth against published net worth. Add 25 points if they have a family office, 50 points if they have a family foundation, 75 points if they have a family museum. 5. Have there been any juicy scandals in this OAWS or their family's past? Add 100 points if it involved bringing down an elected official, political party, or BFF at the Olivier Café in the Grand Indonesia Mall. 6. Does this OAWS or their family happen to own some fabulous hotel/airline/spa resort/luxury brand/restaurant/bar/nightclub that I could potentially benefit from? Add 25 points if family owns a private island, 500 points for a major movie studio. 7. How attractive and stylish is this OAWS in relation to me? Body-scan assessment in this order: _For Ladies:_ face, skin whiteness, physique, jewelry, watch, handbag, shoes, outfit, hairstyle, makeup. Subtract 50 points if any gauche brands are visible, or for an obvious cosmetic procedure. _For Gentlemen:_ hair density, watch, shoes, physique, rest of outfit. Subtract 100 points if wearing an Hermès "H" buckle belt, which only looks good on French or Italian men with deep tans and/or titles. 8. How attractive, well-dressed, important, or famous are the white people that this OAWS is with? Subtract 20 points if it's a business occasion with Americans in corporate attire, add 25 points if European, add 50 points if French or Italian with deep tans and/or titles. 9. How many bodyguards in this OAWS security detail? Evaluate intimidation level of bodyguards, factoring in muscle mass, uniforms, any visible weaponry, quality of earpieces, type of sunglasses, and how noticeable they are in the current space. The more they look like trigger-happy brick shithouses ready to unleash their Sig Sauers on the dinner crowd at Nobu Malibu, the better. 10. When was this OAWS or their family last profiled in their local edition of _Tattle_ , _Pinnacle_ , or _Town & Country_? Add 100 points if they've never appeared in any magazines but you _still_ recognize them. At this point in her life, Wandi's social-placement test was so finely calibrated, it could evaluate a new Asian face in a matter of nanoseconds, thus determining to what degree Wandi felt prettier, richer, or more important than this OAWS, and what appropriate overture she felt comfortable making—whether it be stealth eye contact, a nod of recognition, the slight smile, or actually greeting the person in close physical proximity. Of course at the present moment the OAWS in question only appeared in a rectangular two-by-three-inch photograph _,_ but it was so highly unusual for an Asian face to appear in this setting—an English country wedding worthy of being featured in the Spectator section of _British Tattle_ —that Wandi couldn't help but take notice. The text block in the middle of the page simply read: > # WINTER WEDDING WONDERLAND > > The unexpected snowfall didn't deter England's grandest from dusting off their furs and braving the icy roads for the wedding of Lucien Montagu-Scott* at St Mary's, Chipping Norton. Naturally, the Glencoras were out in full force along with the Devonshires , the Buccleuches , and a smattering of Rothschilds and Rochambords from both sides of the channel. Many a girl mourned that Lucien aka #TallDrinkofWater was off the market, but no one could fault the bride, Colette Bing , whose porcelain-doll complexion and ravishing smile could warm all the frigid chapels in the Home Counties put together. Wandi couldn't believe her eyes as she stared at the picture of the couple again. There was no way the bride in the simple, almost monastic high-necked wedding gown was the same Colette Bing she had seen splashed over all of Asia's tabloids. What happened to the signature swath of black eyeliner and her matador-red lipstick? This girl's face bore no evident traces of makeup, her lips ghostly pale. Where was the spectacular gold Giambattista Valli dress that she had commissioned for her wedding? And most important, why wasn't she wearing some glittering tiara? Wandi dug into her Mark Cross white python handbag for her phone, quickly snapped a photo of the page, and sent it via WhatsApp to Georgina Ting, who was at that very moment lounging poolside at the American Club in Singapore, not watching her daughter splash around in the deep end of the pool. WANDI MEGGAHARTO WIDJAWA: Check this out!!! GEORGINA TING: Badly dressed Brits? WMW: No, check out the bride!!!! GT: OMFG!!! Where did you find this??? WMW: British Tattle! GT: Colette's wedding was in BRITISH TATTLE?!? Wow, she really hit the Holy Grail! Did you send to Kitty? WMW: No!!! I didn't want to be the one to upset her. GT: Good thinking. Messenger always gets blamed. You don't want to risk losing your spa privileges on her plane. WMW: At least with me what you see is what you get—if I'm being a bitch, you know it's because I hate you. Kitty is so unpredictable! You remember what happened at Giambattista Valli's atelier in Paris—she was so calm and collected and then suddenly she attacked Colette's wedding dress! GT: Yeah. No wonder she didn't wear it—they probably couldn't repair it in time. WMW: Still, I can't believe the dress she chose instead. What the hell? She looks like Fräulein Maria at the convent. She's unrecognizable! Do you think she had her face rearranged in Seoul or Buenos Aires or London? GT: I think that's just how she looks with no makeup. I know that style...she's going for the posh Brit look now. They all want to look like freshly exfoliated virgins on their wedding day. WMW: This guy she married looks like a true blueblood. GT: I thought he was some science nerd? WMW: No, lawyer. GT: Didn't you google him when we were all in Paris? WMW: Tatiana did. GT: Has Tatiana seen this? WMW: Not yet. GT: Gimme a sec... Georgina forwarded the photo on to Tatiana Savarin, and then started doing a bit of googling on her own. A few moments later, Tatiana, who was holidaying on the island of Mustique, answered back. TATIANA SAVARIN: THAT'S who Colette Bing married?!?! WMW: Can you believe it? TS: Hottie McHotpocket! Doesn't look like a boring suit at all! GT: Tatiana, you suck as a private eye. I just did some googling, and look what I found. Check out this link, ladies... > From RANKMYPEER.CO.UK > > Lord Lucien Plantagenet Montagu-Scott, Earl of Palliser, is the eldest son of the Duke of Glencora. In 2013, Tattle listed him as one of the ten most eligible bachelors in Britain. According to the Sunday Times Rich List, the Duke of Glencora is the fifth-largest landowner in England, with holdings in Northamptonshire, Suffolk, and Scotland. But the crown jewels of their portfolio are vast property holdings in Central London. Next to the Dukes of Westminster and Portland, the Glencoras are London's leading landlords, owning huge swaths of prime Bloomsbury and Chelsea. Furthermore, Lucien's mother, Liliane, hails from the French Rochambords. C'est formidable! TS: This must be new! It didn't pop up when I did a search on him! WMW: Holy fuck! GT: Colette the future Duchess of Glencora! Kitty's going to shit gold bricks if she finds out about this. TS: What do you mean IF? I just sent everything to her. GT: You what?!? Suddenly, all three women's phones started buzzing as a group call was being initiated from a Shanghai number. WMW: That's Kitty calling! TS: Should we pick up? She can see that we're all on a group chat. "Tatiana, you silly bitch," Georgina muttered under her breath as she swiped her phone to initiate the group call. "Hi Kitty!" Wandi said in an overly cheery pitch. "Hi everyone. What's this you sent me?" Kitty asked. "Um, did you look at the picture or look at the link I just sent? Check out the photo. Don't bother looking at the other links," Tatiana piped in urgently. There was a brief pause while Kitty scrutinized the picture on the screen of her phone. "What am I supposed to be looking at? There's a bunch of gray-haired women with yellow teeth." "You don't see the bride?" Wandi asked. "No—" Georgina cut in. "Kitty, scroll down to the bottom of the page. Do you see the image of the bride and groom?" There was silence for a few moments, as the girls all held their breath, not knowing how Kitty would react. "How interesting," Kitty finally said in a frighteningly neutral tone. "Colette looks awful, doesn't she? Without her usual makeup and jewelry, she's such a plain Jane—her common features really come out." Wandi sniggered. "She looks like she's fallen on hard times," Tatiana remarked. Kitty let out a little laugh. "I can assure you Colette hasn't fallen on hard times. She's just trying to appear modest to impress her new relatives. They look like the sort of people Corinna Ko-Tung is always trying to introduce me to. Well, good luck to her and her new English life." Georgina was relieved that Kitty was taking it all so well. She was crossing her fingers, hoping to God that Kitty had completely missed the articles about the bridegroom when Kitty suddenly asked, "So do we know anything about the Rochambords?" _Damn, she's read everything_ , Wandi said to herself. "I've never heard of them." Georgina sniffed. "Hey, I'm at this house party on Mustique right now, and there's a girl here who might know," Tatiana offered, adding rather unnecessarily, "She comes from a high-society family in France, from what I'm told." Tatiana padded out onto the terrace of the Balinese-style villa, where the girlfriend of her husband's business partner sat sipping black coffee out of a bowl. "Lucie, I'm on the phone with some friends. Have you ever heard of a family in France called the Rochambords?" "Which branch?" Lucie asked. "Um...I don't know. We know someone who married a guy whose mother is a Rochambord. Here, let me put you on speakerphone..." "The mother's name is Liliane Rochambord," Georgina offered. Lucie's eyes widened. " _Liliane de Rochambord_? Are you talking about the mother of Lucien Montagu-Scott?" "Yes! Do you know him?" Tatiana asked excitedly. Lucie shook her head with a sigh. "I don't know him personally, but my God, every girl in France was madly in love with him. I mean, he's a future _duc_ , and his mother is one of the _Bretagne_ Rochambords, not the Paris branch that are the poorer cousins." "But who are the Rochambords?" Georgina pressed on. "Oh, they are an _ancienne famille de la noblesse_...how do you say...an ancient noble family that intermarried with the Bourbons, and their line goes back to Louis XIII. The Paris branch has all the vineyards—you know, Château de Rochambord—but the Bretagne Rochambords own one of the biggest military defense companies in France. They make all the submarines and ships for the French navy. So who's your friend that married Lucien?" "Colette Bing. But she's not our friend exactly," Tatiana said awkwardly. "She's a socialite and fashion blogger from Shanghai that—" Wandi began. "She's a spoiled little cunt!" Kitty suddenly blurted out. Everyone was too shocked to speak at first, but Georgina tried to turn it into a joke. "Haha, yes, she's famous for that spoiled rant that went viral, isn't she, Kitty?" The line went silent for a few moments. "Uh...I think Kitty hung up," Tatiana said. * * * 1 Smiling, laughing, frowning, or arching of eyebrows is highly discouraged, though. 2 What Wandi doesn't know is that the only people who can be married in Westminster Abbey are members of the British royal family, Order of the Bath members and their children, or anyone living in the Abbey's precincts. St. Paul's only allows weddings for members of the Order of Saint Michael and Saint George, the Order of the British Empire, holders of the British Empire Medal, and members of the Imperial Society of Knights Bachelor and their children (but not their grandchildren). 3 Chinese + Indonesian × Aristocrat = Chindocrat 4 She knew by age three that Hugo was too dumb to get in to Raffles. 5 If they happened to be Japanese, Vietnamese, or any other type of Asian not mentioned on this list, abort scanner function. Totally inconsequential. # CHAPTER TWO RANAKPUR, INDIA Su Yi placed her hand on the white marble pillar and with her fingers traced the intricate carving of a goddess, feeling every undulating curve of the figure, so cool to the touch. The entire pillar was carved with figures of dancing damsels from the ground all the way up to the soaring dome. Su Yi looked around the space and saw that she was surrounded in every direction by thousands of white pillars, so many of them that it was impossible to count.1 And every one of them had been sculpted with deities, animals, love scenes, war scenes—each one so painstakingly carved it looked more like lacework than stone. She could hardly believe how exquisite it was. Su Yi felt so grateful that the maharani had arranged this trip for her to the Adinatha Temple, hidden in the remote Aravalli Range between Jodhpur and Udaipur. As she followed the marble passageway, she felt as though she were walking into a dream, and around another corner of the temple she came upon a beautiful tree growing in the middle of a serene stone courtyard. Underneath the tree was a young man in a simple saffron-colored robe, picking up stray leaves. He glanced up for a moment and smiled at her. Su Yi smiled shyly back at him before walking into yet another breathtakingly carved vestibule, this one depicting a deity entwined with hundreds of snakes. "Excuse me, do you speak English?" a voice behind her suddenly asked. Su Yi turned around and saw that it was the young man. This time, she could see a faint gold dot painted in the middle of his forehead. "I do," she replied. "Are you from China?" "No, I am from the island of Singapore. It is in the Straits Settlements—" "Ah, yes, on the tip of Malaya. There are a few Jains in Singapore. Please allow me to introduce myself: My name is Jai, and I am a priest here. My grandfather is the high priest of this temple, and one day my father shall be high priest, and then it will pass on to me. But not for a long time." "You are very fortunate. This is the most beautiful temple I have ever been to," Su Yi said. "May I offer you a blessing?" "I would be honored." The priest guided her along to a quiet corner of the temple that was open to the view. They sat on the steps of a marble altar and looked out at the undulating hills as a cool breeze blew into the chamber. The monk smiled at her again. "We do not often get visitors from Singapore at the temple. I noticed you when you first entered the temple with your chaperone, because you were so beautifully dressed, but when you smiled at me, I sensed a great sadness in you." Su Yi nodded, lowering her eyes. "I am away from my family, and my island is at war." "Yes, I have heard about the war spreading through southern Asia. I do not understand this war. But I sense that your sadness comes from a deeper place..." He gazed intently at her, and Su Yi noticed for the first time that his irises had an almost bluish gray tint to them. Suddenly she found her eyes welling uncontrollably with tears. "My brother," Su Yi said almost inaudibly, her throat choking up. "My elder brother has been missing for some time." She had told no one about this, and she wasn't sure why she was telling him now. She was about to reach into her purse for her handkerchief when the monk produced one, seemingly out of nowhere. It was a silk scarf with a deep-blue-and-purple paisley pattern, and it seemed incongruous with the rest of his austere appearance. Su Yi wiped away her tears and looked up at the priest, who suddenly appeared to be wearing wire-frame glasses just like the ones her brother wore. "Yes, your brother Alexander wants to tell you something. Would you like to hear his message?" Su Yi looked at him, not comprehending what he meant at first. Before she could answer, the priest began to unleash a torrent of Hokkien: _Seven. Eight. Nine. Coming ashore. Bloody hell, there's too many of them. This won't work. This won't work at all._ A chill ran down her spine. This was her brother's voice coming out of the priest's mouth, and he was muttering the same nonsensical things he had said when he had been deliriously ill. "What won't work? Ah Jit, tell me, what won't work?" Su Yi asked urgently. "I can't take that many. It's too dangerous. We have to move very quickly, and we can't fight back?" "Ah Jit, slow down, who's fighting back?" Su Yi wrung her hands in frustration, feeling them get sticky. When she looked down at the silk paisley handkerchief, she saw that it was covered in a strange weblike mucus mixed with blood. Suddenly her brother stopped his incoherent ranting and spoke to her in a clear, lucid tone. "I think you know what to do now, Su Yi. Trust your instincts. This is the only way we can atone for all that our ancestors have done. You can never tell anyone, especially not Father." In an instant, she knew what her brother meant. "How am I going to do all this by myself?" "I have no doubt in you, sister. You are the last hope now...are you awake? Mummy, are you awake?" Su Yi felt a hand on her shoulder, and suddenly she was no longer in that exquisite temple in Ranakpur, and the priest with the bluish eyes was gone. She found herself waking up in her bedroom at Tyersall Park, the morning sun glaring into her eyes. "Mummy, are you awake? I've brought Bishop See to see you," Victoria said chirpily. Su Yi let out a low groan. "I think she may be in pain," Bishop See said. Su Yi groaned again. _This irritating daughter just interrupted me from one of the most vivid moments in my life. Ah Jit was speaking to me, Ah Jit was trying to tell me something, and now he's gone._ "Let me call in the nurse," Victoria said in a worried tone. "She's pumped so full of hydrocodone, she really shouldn't be feeling anything. They said there might be hallucinations, that's all." "I'm not in pain, you just woke me up so suddenly," Su Yi muttered in frustration. "Well, Bishop See is here to say a prayer for you—" "Please, some water..." Su Yi said, her throat as usual feeling so parched in the morning. "Oh yes, water. Now, let me see. Bishop See, could you do me a favor and go into my mother's dressing room? There are some Venetian glasses on a tray beside her dressing table, lovely handblown glasses with dolphin stems from a wonderful shop near the Danieli. Just bring me one of those." " _Aiyah_ , there's a plastic cup right here." Su Yi gestured to the bedside table. "Oh, silly me, I didn't see that. Ah, Bishop See, do you see a water carafe by that table behind you? There should be an insulated silver carafe, with an art nouveau motif of stephanotis flowers carved along the handle." "Just get me the goddamn cup," Su Yi said. "Oh dear, Mummy, _language_. Bishop See is in the room," Victoria said, trying to hand over the cup. "Do you not see that my hands are tangled up in tubes? You need to help me sip the water from the straw!" Su Yi said in frustration. "Here, do allow me." The bishop stepped in and took the cup from a frazzled Victoria. "Thank you," Su Yi said gratefully after she had taken a few precious sips. "Now Mummy, Bishop See and I were speaking earlier over breakfast, and I was reminded that you've never been baptized. The bishop has kindly brought with him a little vessel of holy water from the River Jordan, and I'm wondering if we might do a ritual baptism right here in this room." "No, I don't want to be baptized," Su Yi said flatly. "But Mummy, do you not realize that until you are baptized, you can never enter the kingdom of heaven?" "How many times do I have to tell you I am not a Christian?" "Don't be silly, Mummy, of course you are. If you're not a Christian, you won't be able to go to heaven. Don't you want to be with Daddy...and _all of us_ in the future that is eternity?" Su Yi could not think of a worse fate than to be trapped with her _eem zheem_ 2 daughter throughout all of eternity. She simply sighed, tired of having this conversation again. "Er, Mrs. Young...if I might ask," the bishop began gingerly, "if you aren't a Christian, what do you consider yourself to be?" "I respect every god," she replied softly. Victoria rolled her eyes derisively. "My grandfather Shang Loong Ma's people were Buddhists, Taoists, Quan Yin worshippers, all that mishmash of religions...you know, in that old-fashioned _Chinese_ sort of way." The bishop adjusted his collar, looking slightly uncomfortable. "Well, Victoria, we really can't force your mother to be baptized, but perhaps we can pray that she will allow Jesus Christ into her heart. We have to let Jesus come into her softly, gently." "I don't need Jesus to come into me," Su Yi said agitatedly. "I am not Christian. If I'm anything, I'm a Jain." "Mummy, what on earth are you talking about? What is a Jane? Are you confused and talking about your friend Jane Wrightsman?" Victoria asked, looking up at the IV machine to make sure her mother wasn't being overdosed with some crazy opiate. "Jainism is an ancient religion that is an offshoot of Hinduism—"3 Bishop See began to explain. Victoria stared at her mother in horror. "Hinduism? You can't possibly be Hindu. My goodness, _our laundry maids are Hindu!_ Don't say you are a Hindu, Mummy—it would absolutely break my heart!" Su Yi shook her head wearily and pressed the buzzer in her right hand. Moments later, her lady's maids entered the room. "Madri, Patravadee, please show Victoria out," she ordered. "Victoria, come, we can say a prayer together outside," the bishop urged, glancing up at Su Yi's heart rate monitor nervously. "Mother, you can't just order me out of your room like this. Your soul is in peril!" Victoria shrieked, as Alix entered the bedroom amid all the commotion. Su Yi glanced up at Alix pleadingly. "Please tell Victoria to leave. She is irritating me to death!" "All right then," Victoria said in a quiet voice, as she turned swiftly and stormed out of the bedroom. Patravadee turned to Su Yi with an attentive smile. "Madame, your usual porridge this morning?" "Yes. And tell them to put an egg in it today," Su Yi instructed. As soon as her lady's maids left, Su Yi let out a long sigh. "She means well, Mummy," Alix said diplomatically. "Why does she always have to be such a nuisance? And I can't stand that fat little _lan jiau bin_ 4 See Bei Sien. You know he only wants money for his cathedral building fund. Victoria writes him so many checks every month her account is always going into overdraft." "Victoria may have her irritating ways, but she has a good heart. She is the most generous person out of anyone I know." Su Yi smiled at Alix. "And you are always the peacemaker. Even when you were a little girl, you were always the one to heal the rifts between your sisters. Will you be sure to keep the peace after I'm gone?" "Of course, Mummy. But don't worry—Prof Oon assures me your heart is improving every day. Even Malcolm said he's so pleased with your progress." "That may be the case, but I know I can't live forever." Alix didn't know what to say. She simply busied herself by straightening her mother's bedsheets and smoothing them out. "Alix, you don't have to be afraid for me. I have no fear of death—you have no idea how many times I've stared it in the face. I just don't wish to be in any pain, that's all." "Prof Oon is making sure of that," Alix said matter-of-factly. "Alix, will you do me a favor? Will you call Freddie Tan and tell him to come over?" "Er...Freddie Tan, your lawyer?" Alix asked, unnerved by the request. "Yes. It's very important that I see him as soon as possible. His number is in the address book on my dressing table." "Of course. I'll go and call him right now," Alix said. Su Yi closed her eyes, attempting to relax for a moment. She was still trying to forget the look of hurt she had seen on Victoria's face after she had snapped at her. _Stupid girl!_ The words came echoing back to her, from a memory far back in time... _"You stupid, stupid girl!"_ _Her father had snarled angrily when Su Yi had appeared in the basement of the shop house at Telok Ayer Street. "Do you know the fortune I spent, the number of favors I had to call in, just to get you safely out of Singapore? Why are you here?"_ _"Did you think I could just sit in the Taj Mahal Palace Hotel while I got news every day about all the terrible things that were happening back here? All the bombings, all the people being tortured and killed?"_ _"Which is exactly why I got you out of Singapore! On the last frigate out!"_ _"I didn't know what was happening here, Pa. I got news about everyone else—Tan Kah Kee, Uncle SQ, Uncle Tsai Kuen, but there was never any news of you. When Chin Tuan came to India, he said he hadn't heard any news about you. That's when I thought you had been captured or maybe even killed somewhere!"_ _"I told you you weren't going to hear from me. I told you I would be fine!"_ _"Fine? Look at you—hiding in a hole in the ground, dressed in rags!" Su Yi said, tears in her eyes as she looked at her father in his stained singlet and trousers full of cigar ash. She had never seen her father out of his three-piece suit before. With his head shaved and his face smeared with dirt, he looked almost unrecognizable._ _"Silly girl! Don't you see I'm dressed like this on purpose? The only way to survive is to be invisible. I made myself look like an illiterate dockworker. The Japanese soldiers don't even bother to spit in my direction! Now how the hell did you get back into the country without getting yourself raped or killed?"_ _Su Yi gestured at the Thai silk dress she was wearing. "I crossed from India to Burma on the train, and then came down through Bangkok as part of the Thai ambassador's entourage—I'm disguised as a lady's maid to Princess Narisara Bhanubhakdi."_ _Shang Loong Ma let out a phlegmy laugh as he looked over his daughter. On the one hand, he was furious at her for coming back to a war-ravaged island, but on the other hand, he had to admire her resourcefulness. She knew how to be invisible too, and she had proved herself braver than her brothers. "What are we going to do with you, now that you're back? It's too dangerous for you to go to Tyersall Park, you know." He sighed._ _"I'm going back to Tyersall Park whether you like it or not! I'm going to stay there and do everything I can to help anyone who is suffering and in danger."_ _Su Yi's father scoffed. "The Japanese control everything now. Where on earth did you get such an idea that you could actually be of help?"_ _"A priest told me, Pa. A young priest at the most beautiful temple on earth."_ * * 1 Actually, there are 1,444 pillars in the temple, which also boasts 29 halls and 80 domes in a 48,000-square-foot area. Built by a wealthy Jain businessman named Dharma Shah, construction of the temple began in 1446 and took more than fifty years to complete. If you are ever in Jodhpur, please do yourself a favor and head to this amazing place instead of wasting your time and money buying cashmere throws from charming merchants who claim they were "handwoven exclusively for Hermès" (or Etro, or Kenzo) "in a nearby village that employs 800 women." They really weren't, and Richard Gere wasn't just there last week buying a hundred scarves either. 2 Cantonese for "difficult, persnickety." 3 Actually, Bishop See is wrong about that. While Jains and Hindus agree on the concept of karma, the cycle of life and death, and some other aspects of emancipation, liberation, and release, they are two distinct and separate religions. 4 Hokkien for "dick face." # CHAPTER THREE SINGAPORE In all his years of working for the Young family as the head of security, Captain Vikram Ghale never had to deal with a situation quite like the one he now faced. Standing before him at the gates of Tyersall Park was Philip Young, the only son of Shang Su Yi. This was the man who had interviewed and hired him for the job thirty-two years ago, and this was the man who should have been his future boss had he not foolishly incurred his mother's wrath two decades ago by inexplicably moving to Australia and losing his rightful inheritance of the house he had grown up in. Normally, Philip Young's hunter-green Jaguar Vanden Plas would have been waved through the gates without any hesitation, but the problem was the man sitting in the front passenger seat—Nicholas Young, whom Vikram had known since he was a little boy. Until about five years ago, Nicky was his grandmother's favorite and the presumptive heir of Tyersall Park. He was, for all intents and purposes, the young lord of the manor. But now Vikram was under the strictest of orders not to allow entry to Nicky. Vikram knew he had to handle the situation as diplomatically as possible. Knowing how mercurial his mistress, Shang Su Yi, could be, there was still a chance that she could change her mind at the last minute and reinstate Nicky or Philip as heir to the estate. For heaven's sake, Philip's initials formed the shape of the elaborate boxwood labyrinth in the gardens, and Nicky's bedroom was still left unoccupied and untouched—exactly as it had been the last time he stayed there. Either of these men could very soon be his boss, and he mustn't offend. "I'm so sorry, Mr. Young. You must see how my hands are tied. Please don't take this personally," Vikram said earnestly, casting an embarrassed smile at Nick. "I understand. Tell me, who gave the orders?" Philip's tone was polite, but his irritation was apparent. Eleanor flung the car door open and climbed out angrily. "Vikram, what is all this nonsense? Don't tell me we can't go in!" "Mrs. Young, as I was just explaining to Mr. Young, you are both more than welcome to enter. But I am under strict orders not to allow entry to Nicky. I checked again after he first arrived the other night while I was off duty. They said no, absolutely not." "Who are _they_? Who gave you the orders? Su Yi is a living vegetable right now—she couldn't have said a thing to you!" "Beg your pardon, Mrs. Young, but Mrs. Young is not a living vegetable!" Vikram sputtered. Nick rolled down the window. "Mum, Dad, why don't you both just go in and I'll—" "Shut up, _lah_!" Eleanor waved her hand in front of Nick's face dismissively. "Vikram, how much money have you made on my stock tips over the years? Sino Land, Keppel Corp, Silverlake Axis. Hnh! I swear to God I am never going to give you a single tip again. I made you a rich man, and this is how you repay us? _Mangkali kow sai!_ "1 Vikram sighed, as he tried to find a way out of this quagmire. "Why don't I call up to the house again, and perhaps you can speak to Miss Victoria directly?" Philip had reached the end of his patience. "No, Vikram, I've had enough of this. This is my house too, and I will not take orders from my little sister! If my mother does not want to see Nicky, she can tell me herself. He won't go into her room unless he's asked for. But I will not have my son waiting by the gates like some sort of beggar. Call up to the house if you want to, but we are _all_ going in." Philip returned to the driver's seat and revved the engine. Vikram stood in front of the gray wrought-iron gates with his arms crossed, as Philip inched the sedan slowly toward the gates until the front bumper was almost touching the imposing guard's knees. The other guards stood by, not sure what to do. _Five, four, three, two, one._ Vikram counted in his head. Have I let this go on long enough? Philip was a decent fellow, and he knew he wouldn't get in trouble with him. As far as he was concerned, there was no real security risk to letting the three of them in. It was just a family quarrel, and now that he had done his duty and put on a good show, he was going to get out of the way. He sidestepped the car in one easy stride and ordered his men, "Open the gates!" Philip jammed his foot on the pedal angrily and zoomed up the gravel driveway at top speed. As the road curved toward the main approach to the house, the most curious sight unfolded before them. Assembled on the front lawn were several rows of wrought-iron chairs shaded by colorful silk parasols. Most of the family members staying at Tyersall Park—Victoria Young, the Aakaras, and the Chengs—were seated watching a doubles badminton match along with a few invited guests like Bishop See Bei Sien, Rosemary T'sien, and the Thai ambassador. Behind the seats, an elaborate ice-cream bar had been set up alongside a table dominated by an immense crystal punch bowl brimming with icy fruit punch. Eleanor shook her head disparagingly. "So shameful! Your mother lies on her deathbed while everyone is outside having a garden party!" "What are they supposed to do? Kneel all day by her bedside and chant prayers?" Philip asked. "Well, the bishop is here! At the very least he should be inside praying for her instead of eating an ice-cream sundae." "Mummy detests that man. The only reason he's here is because Victoria is still infatuated with him. She's been like this since their NUS2 days." "Oh my God...how come I never knew this? This explains why she's always so bitchy toward Mrs. See." "Mum, haven't you noticed that Auntie Victoria is a bitch to anyone who doesn't have a doctorate in divinity?" Nick chuckled. As the Jaguar pulled up to the circular driveway in front of the house, Nick could see Eddie Cheng and his brother, Alistair, battling it out with Uncle Taksin and Adam Aakara. Taksin, Adam, and Alistair were casually dressed in shorts and polo tees, but Eddie was dressed completely in white—from his long-sleeved white linen shirt and white linen pleated trousers to his white lace-up wing tips. Nick chuckled as he noticed that Eddie's wife, Fiona, and their three children were also sweating away under the afternoon sun in white linen outfits with beige cashmere sweaters tied around their shoulders, no doubt at Eddie's behest. As Philip, Eleanor, and Nick emerged from their car, the match came to an abrupt halt as the group assembled on the lawn stared at the new arrivals. For a moment, Nick wondered if his relatives were going to treat him differently now that he had been officially banished from Tyersall Park. His cousin Alistair dropped his racket and bounded over immediately. "So glad you're here, man," he said, giving Nick a big hug. Nick smiled in relief—he could always count on good ol' Alistair. Following behind him came Catherine. Of the four Young sisters, she was the one who had always been closest to Nick's father, since they were barely two years apart in age and had been sent away to boarding school in England together. " _Gor Gor_ ,"3 she said warmly, giving Philip a quick peck on the cheek. "Did you just get in?" "Hi, Cat! I arrived earlier this morning. Is the whole family here?" "Just Tak, Adam, and Piya for the time being. The other boys are making plans to come down." "I see it's Thailand versus Hong Kong. What's the score?" "Five to two. Advantage Thailand. Eddie suggested the match, but he's not carrying his own weight. Alistair's admirably trying to hold up his end, but I don't think he realizes that Tak used to play on the Thai Olympic team." "Bloody hell! No wonder he's kicking my ass!" Alistair groaned. Catherine gave Eleanor a kiss before glancing over at Nick. "It's good to see you, Nicky. Been far too long. Is Rachel not here with you? I can't believe I still haven't met her." "No, it's just me," Nick said, giving his aunt a hug. Catherine looked into his eyes, wanting to say something, but Victoria marched up to their little cluster before she could continue. " _Gor Gor_." Victoria nodded curtly at her brother while fanning herself furiously with a carved wooden fan. Then she glanced at Nick and said, "I'm afraid you can't come into the house. Please don't take this personally." "How am I supposed to take it, then?" Nick said with a wry smile. Eleanor spoke up. "This is ridiculous! Why can't Nicky go into the house? He just wants a chance to say he's sorry to Mummy." Victoria winced visibly. Even after four decades, she had never gotten used to her sister-in-law calling her mother _Mummy._ "Eleanor, tell me what I'm supposed to do? You of all people should know what my mother is like. I'm just following her wishes." Philip looked at his sister skeptically. "Mum _specifically_ told you she didn't want to see Nick?" "Actually, she told Eddie." "Eddie! My goodness! You actually believe him? Eddie has been jealous of Nicky since they were children!" Eleanor scoffed. Hearing his name come up among the chatter, Eddie sauntered over to the group. "Uncle Philip, Auntie Elle, let me be very frank. Three days ago, when I was with Ah Ma in her bedroom, I told her that Nicky was on his way home. I thought it would soothe her to know that he was coming to make amends, but instead she got so upset that she went into cardiac arrest. Auntie Victoria was right there when it happened. We almost lost her that day." "Well, that was three days ago. I'm going up to see my mother now. She can tell me to my face if she doesn't wish to see Nicky," Philip insisted. "You're _really_ going to put Ah Ma's life at risk again?" Eddie said. Philip stared contemptuously at his nephew, who was drenched in sweat, his clammy skin showing through in large blotches on the most unflattering areas of his white outfit. What a ridiculous boy he was, all dressed up like he was playing in a cricket match at Lord's. He didn't trust him for one second. "Eddie, let me worry about my mother. Perhaps you should be more concerned about your own children at the moment." "What do you mean?" Eddie swung around and saw his children standing by the ice-cream bar with their cousin Jake Moncur. Constantine, Augustine, and Kalliste were happily licking away at cones topped with double scoops of ice cream, oblivious to the ice cream melting down their hands and dripping all over their white linen outfits. Eddie broke into a sprint toward them as he began screaming, "FI! FIONA! LOOK WHAT THE KIDS ARE DOING! I TOLD THEM NO ICE CREAM IN THEIR BRUNELLO CUCINELLI LINENS!" Fiona Tung-Cheng, who was huddled in conversation with Piya Aakara and Cecilia Cheng Moncur, looked up for a brief moment. She rolled her eyes and went right back to talking with the ladies. With Eddie urgently marching his three children off in search of Ah Ling and the head laundress, Nick took his place in the badminton game while his parents went into the house with Victoria. "She's really not supposed to have any more visitors today," Victoria muttered as she led Philip and Eleanor down the corridor toward Su Yi's bedroom-cum-hospital suite. "I'm not a visitor—I'm her son," Philip shot back in annoyance. Victoria fumed silently to herself. _Yes, I know you are her son. Her only son. Mummy's made this abundantly clear to me my entire life. Her precious only son gets special bird's nest soup prepared for him every week all through his childhood while we girls only get it on our birthdays. Her only son has all his clothes tailor-made on Savile Row while we have to sew our own dresses. Her only son gets his own Jaguar convertible the minute he returns from university while the girls have to share one miserable Morris Minor. Her only son gets to marry whomever he wants no matter how common she is while every man I ever bring home is deemed "unsuitable." Her only son abandons her to live out his Crocodile Dundee fantasies in Australia while I'm forced to stay here and take care of her in her old age. Her precious only son._ When they arrived at her mother's sitting room, Victoria started interrogating the nurses while Philip and Eleanor went into the bedroom. Alix was sitting in the armchair by her mother's bedside when they entered. "Oh, _Gor Gor_ , you're here. Mummy's just fallen asleep. Her blood pressure was fluctuating too wildly, so they gave her a sedative." Philip looked down at his mother, suddenly shocked by her appearance. When he had last seen her at Christmas, barely five weeks ago, she was still climbing on the ladder to the top of her star-fruit trees. But now she seemed so small in the hospital bed, so lost in the tangle of tubes and machines surrounding her. All his life, she had seemed so strong, so invincible, he couldn't even begin to fathom the possibility of her not being around. "I think I'll spend the night here with Mum," he said in a quiet voice. "There's really no point. She's going to sleep right through the night, and besides, her lady's maids take turns to be with her all night long in case she wakes up. The nurses also come in to check on her every half hour. Come back tomorrow. She's usually conscious for a few hours in the morning," Alix said. "It doesn't matter if she's asleep. I'll stay with her," Philip tried to insist. "Are you sure? You look like you could use a little sleep yourself—" Alix began. Eleanor agreed. "Yah, _lah_ , you didn't sleep much on your flight, did you? You look so run-down—I can see all the bags under your eyes. Let's go home and come back early tomorrow." Philip finally relented. "Okay. But Alix, can you do me a favor? If Mummy wakes up anytime soon, will you tell her I was here?" "Of course." Alix smiled. "And will you tell her Nicky was here too?" Philip pressed her. Alix hesitated for a moment. She was concerned that any mention of Nicky would upset her mother again, but she also felt that her mother needed to mend her rift with him. It was the only way she would truly close her eyes in peace. "Let's see. I'll try my best, _Gor Gor_." * * 1 Hokkien for "Bengali dog shit." However, Eleanor is technically wrong in her swearing, since Vikram—being a Gurkha—is Nepali, not Bengali. But to her, there are only two types of Indians: rich ones, like her friends the Singhs, and poor ones, like everybody else. 2 National University of Singapore. 3 Cantonese for "brother." # CHAPTER FOUR SURREY, ENGLAND _Anyone lucky enough to be a guest at Harlinscourt should wake in time to watch the sun rise above the gardens_ , Jacqueline Ling thought as she sipped the orange pekoe tea that had just been brought to her bedside on an exquisite bamboo tray. Propped up against four layers of goose-down pillows, she had the perfect view onto the pure symmetry of the box parterres, the majestic yew hedges beyond, and the morning mist rising over the Surrey Downs. It was these quiet moments before everyone began to assemble downstairs for breakfast that Jacqueline relished most during her frequent visits at the Shangs'. In the rarefied stratosphere inhabited by Asia's most elite families, it was said that the Shangs had abandoned Singapore. "They've become so grand they think they're British" was the common refrain. Though it was true that Alfred Shang enjoyed a lifestyle that surpassed many a marquess at his six-thousand-hectare estate in Surrey, Jacqueline knew it would be a mistake to assume that he had transferred all his allegiances to queen and country. The simple truth was that over the decades, his three sons (all Oxbridge educated, naturally) had one by one taken English wives (all from appropriately aristocratic families, of course) and chosen to make their lives in England. So beginning in the early eighties, Alfred and his wife, Mabel, were compelled to spend greater parts of the year there—it was the only way they would get to see their children and grandchildren regularly. Mabel, being the daughter of T'sien Tsai Tay and Rosemary Young T'sien, was far more Chinese in her ways than her husband, who was an Anglophile even before his Oxford days in the late 1950s. At Harlinscourt, Mabel set about creating a decadent domain that indulged her favorite aspects of East and West. To restore the nineteenth-century Venetian revival–style house built by Gabriel-Hippolyte Destailleur, Mabel coaxed the great Chinese decorative-arts historian Huang Pao Fan out of retirement to work alongside the legendary British decorator David Hicks.1 The result was a ravishingly bold mix of modern European furnishings with some of the finest Chinese antiquities held in private hands. Harlinscourt soon became one of those great houses that everyone talked about. At first, many of the Burke's Peerage crowd talked about how terribly vulgar it was for a Singaporean to buy one of the finest houses in Britain and try to run it "in the old way" with its mind-numbing number of staff and all the trimmings. But the landed gentry accepted their invitations anyway and after their visits grudgingly had to admit that the Shangs hadn't mucked it up. The restoration was splendid, the grounds were even more splendid, and the food—well, that was utter heaven. In the decades that followed, guests the world over began to covet their invitations because word got out that Harlinscourt's chef Marcus Sim—a Hong Kong–born prodigy who had trained with Frédy Girardet—was a genius in both classic French and Chinese cuisine. And it was the thought of breakfast this morning that made Jacqueline reluctantly get out of bed. She walked into the dressing room adjoining her bedroom and discovered a fire already burning in the fireplace, a vase of freshly cut Juliet roses arranged on the dressing table, and the outfit she had selected for the morning already hanging against the copper warming rack. Jacqueline slipped on her figure-hugging cream fit-and-flare sleeveless dress with iconic pointelle knit trim, marveling at how it had been warmed to the perfect temperature. She thought of weekends at other English estates, where the bedrooms felt like iceboxes in the morning and her clothes felt just as frozen when she put them on. _I don't even think that the queen lives this well_ , Jacqueline thought, recalling that before Alfred and Mabel had moved in, her godmother, Su Yi, had sent a team over from Tyersall Park to help train the British staff properly. Asian hospitality standards were fused with English manor-house traditions, and even her boyfriend Victor had been impressed the last time he visited. Holding up his Aubercy dress shoes one evening as they dressed for dinner, he said in astonishment, "Honey, they fucking ironed my shoelaces!" This morning, it was the chef's eggs that most astonished Jacqueline as she sat at one end of the immense dining table in the Grade II Heritage-listed breakfast room. "Ummmm. How is it that only Marcus can make scrambled eggs like this?" She sighed to Mabel as she savored another forkful. "Doesn't your chef do good eggs?" Mabel asked. "Sven's omelets are fabulous, and he can poach perfectly. But there is something about these scrambled eggs that are absolutely _divine_. Fluffy, creamy, and just the right amount of runny. I look forward to every visit because of them. What is the secret?" "No idea—I never touch the eggs. But you must try some of this _yu zhook_.2 It's made with Dover sole that was caught just this morning," Mabel said. "It's the cream. Marcus uses the top cream made from our Guernsey cows in the scrambled eggs," twelve-year-old Lucia Shang piped up from the far end of the table. "At last— _she speaks!_ That's the first peep I've heard out of you all morning, Lucia. Now, what's this book you're so engrossed in? You're not still reading those _Hunger Games_ vampire novels, are you?" Jacqueline asked. " _The Hunger Games_ isn't about vampires. And I stopped reading them ages ago. I'm reading _Siddhartha_ now." "Ah, Hesse. He's quite good." "It sounds Indian," Mabel said, scrunching up her nose at her granddaughter. "It's about the Buddha." " _Aiyah_ , Lucia, what are you doing reading about Buddha? You're a Christian, and don't forget that we come from a very distinguished long line of Methodists." "Yes, Lucia, on your great-grandmother Rosemary's side—the Youngs—your ancestors were actually the first Christians in southern China," Jacqueline agreed. Lucia rolled her eyes. "Actually, if it wasn't for missionaries running amok in China after England won the Opium Wars, we'd all be Buddhists." "Shut up, _lah_! Don't talk back to Auntie Jacqueline!" Mabel admonished. "It's fine, Mabel. Lucia's just speaking her mind." Mabel wouldn't let it go, muttering to Jacqueline, " _Neh gor zhap zhong syun neui; zhan hai suey toh say!_ "3 "Ah Ma, I understand every word you're saying!" Lucia said indignantly. "No you don't. Shut up and read your book!" Cassandra Shang, Mabel's daughter (and better known by those in her circle as "Radio One Asia"), entered the room, cheeks still flush from her morning ride. Jacqueline did a double take. Cassandra's hair, normally parted down the middle and pulled into a tight coil at the nape of her neck Frida Kahlo–style, was rather uncharacteristically braided intricately along the sides but flowing free down her back. "Cass, I haven't seen your hair down like this in ages! This is a throwback to your Slade days. Looks marvelous!" Mabel peered at her daughter through her bifocals. " _Chyee seen, ah!_ 4 You're not a young girl anymore—it looks ridiculous." Cassandra felt tempted to tell her mother that you could begin to see the face-lift scars through the thinning hair in her scalp, but she resisted. Instead, she chose to acknowledge Jacqueline's compliment. "Thanks, Jac. And you look ridiculously perfect as always. New dress?" "No, _lah_! I've had this old rag for ages," Jacqueline said deprecatingly. Cassandra smiled, knowing full well Jacqueline was wearing a one-of-a-kind Azzedine Alaïa. Not that it even mattered what she wore—Jacqueline had the sort of beauty that made anything she put on look drop-dead chic. Cassandra headed to the sideboard, where she helped herself to a single toast point, a dollop of Marmite, and some fresh prunes. As she took her seat opposite Jacqueline, a footman approached, deftly placing her morning cappuccino (made with small-batch, single-origin beans) and iPad next to her. "Thank you, Paul," Cassandra said, switching on the device and noticing that her e-mail in-box was unusually full for this early in the morning. The first message came from her cousin Oliver in London: OTSIEN@CHRISTIES.COM: Have you seen the photos yet? Oy vey! I can already imagine what your mother must be saying... CASSERASERA@GMAIL.COM: Which photos? While she waited for his response, an instant message came in from her sister-in-law India Heskeith Shang. Cassandra looked up from her iPad and announced to everyone, "India just messaged me—apparently Casimir has an opening for his photography at Central Saint Martins tonight and he didn't tell anyone. She's wondering if we want to go and surprise him? Lucia, your mother wants to know if you want to go up to London to see your brother's latest photos?" "If it's going to be more pictures of his friends vomiting curry outside of pubs, I'm not interested," Lucia replied. " _Aiyah_ , don't talk like that! It's fine art. Casimir won an award for his photography last year," Mabel told Jacqueline, in defense of her favorite grandson. Cassandra realized that Oliver must be talking about Casimir's photographs. "Well, I think these photos are going to be quite...daring. I just got an e-mail from Oliver, and apparently he's already seen them." "Oh. Oliver's back in London? Is he going to come to the show too?" Mabel asked. "I'm not sure, but India is now saying that Leonard can pick us up in the helicopter on his way from Southampton. We can all go to the opening together and then dinner at Clarke's." " _Alamak_ , another tasteless English dinner." Mabel groaned. Cassandra checked her Facebook wall and let out a sudden gasp. " _Oh. My. God._ " She clasped her hands over her mouth, staring at the photos that flashed through on her iPad. Oliver wasn't talking about Casimir's silly little exhibit after all. _These_ were the photos he was talking about. "What are you looking at now? Another piece of dirty gossip from one of your unreliable _kang taos_?"5 her mother asked derisively. "Jacqueline, you need to see this!" Cassandra said, handing her the iPad. Jacqueline peered at the screen and saw an image of Astrid standing on a turret next to an elephant. "I don't get it. What's the big deal?" Jacqueline asked. "Oh, you're on the last photo. Scroll up. There's a whole series of photos." Jacqueline waved her hand over the screen, her eyes widening as she scrutinized the images. "Are these real?" "Looks pretty real to me," Cassandra chuckled. "Dear me..." "What is it?" Mabel asked. Jacqueline held up the iPad, and from across the table, Mabel could see the blaring headline: > # EXCLUSIVE PICS OF TECH TITAN CHARLES WU'S LAVISH PROPOSAL TO GIRLFRIEND ASTRID LEONG—BUT SHE'S STILL MARRIED! " _Alamak!_ Let me see! Let me see!" Mabel demanded excitedly. A footman wordlessly appeared at Jacqueline's side. She handed the iPad to him and he dutifully walked it over to the other side of the table where Mabel was seated. Lucia, clearly not as engrossed in _Siddhartha_ as she pretended to be, rushed over to peer at the pictures with her grandmother, reading aloud: > "The ink hasn't even dried on Hong Kong tech titan Charles Wu's divorce papers yet, but this apparently didn't stop him from orchestrating an over-the-top marriage proposal to his gorgeous girlfriend Astrid Leong. The million-dollar proposal involved renting out the fairy-tale Mehrangarh Fort in Jodhpur, hiring more than a hundred musicians and dancers, and having Bollywood superstar Shah Rukh Khan serenade them while an elephant helped to deliver the ginormous diamond ring. Looking at the pictures, Astrid has obviously said yes, but there's one small problem—as far as we know, this high-born beauty is STILL MARRIED to Charlie's arch rival, the Singapore tech wünderkind Michael Teo." Mabel squinted at the picture. " _Aiyah, hou sau ga!_ 6 When were these taken?" "Last weekend, it looks like," Jacqueline said. "Last weekend? But isn't Astrid in Singapore with the rest of the family?" "Obviously she snuck out of town with Charlie. My God, can you imagine how furious Felicity and Harry are going to be when they see this?" Cassandra said, shaking her head. "Not only that, but this is a disaster for her divorce case. Michael's going to have so much new ammunition now. Poor Astrid!" Jacqueline sighed. Mabel huffed, "Poor Astrid my foot! She should be at her grandmother's bedside instead of splashed all over the news! How dare that Charlie Wu propose to her again! The cheek of him...still trying to invade _our family_! I thought Felicity got rid of him years ago!" "Oh Mother, those two have been in love since day one. If Felicity had let it happen the first time around, the whole Michael Teo disaster would never have happened!" Cassandra said. "Felicity was right to put a full stop to that nonsense. Those Wus were completely unacceptable! That ghastly vulgar mother of his—I'll never forget what she did to me!" "What did Irene Wu do to you?" Jacqueline asked. Cassandra rolled her eyes. "That's ancient history, Mum. Please don't bring it up again!" "That! Woman! Tried! To! Steal! My! Seamstress! I found this girl, Minnie Pock, who did the most wonderful tailoring. She had a little shop next to Fitzpatrick's on Dunearn Road, soooo convenient, and she could replicate all the Nina Ricci, Scherrer, and Féraud dresses I loved so perfectly." "My goodness, Mabel, those Louis Férauds were fakes? They looked like they came straight from his Paris boutique!" Jacqueline lied. Mabel nodded indignantly. "Yes, I had everyone fooled. But then that Irene Wu came along and tried to hire the girl to work in their tacky 'mansion' full-time! So then I had to go and hire her full-time!" "So you won?" Jacqueline asked. "Yes, but it should never have happened. I had to pay Minnie Pock _almost fifteen percent_ over what Irene offered to pay her!" "It was 1987, Mum. Time to get over it," Cassandra said. "People like the Wus...they never know when to stop. And now look what's happened? Once again they are dragging our family name into the mud. Who sent this article to you anyway?" "Mrs. Lee Yong Chien posted it to her Facebook page," Cassandra replied. " _Mrs. Lee Yong Chien is on Facebook?_ I don't believe it! The old lady can't even draw her own eyebrows!" Mabel exclaimed. "Rosie, that adopted daughter she treats like a slave, does everything for her! Ever since Mrs. Lee discovered Facebook, she's been posting like a fiend. Every other day there's either annoying photos of her grandchildren winning some award or pictures of some funeral she's attending." " _Aiyah_ , if Mrs. Lee knows about this, then the whole of Singapore will soon know. All her mah-jongg _kakis_ 7 will find out about this!" Mabel surmised. "Ah Ma, I don't think you understand—this is on _Facebook_. The whole world can already see this," Lucia informed her. Mabel tut-tutted sadly. "Then I truly feel sorry for Su Yi! This is happening at the worst time. I thought Astrid was her last hope, but one by one all her grandchildren have disgraced her. How is she ever going to close her eyes in peace? No wonder she changed her will yet again!" " _Really?_ " Jacqueline and Cassandra gasped in unison. Jacqueline sat bolt upright in her chair. "Is this why Alfred rushed back to Singapore?" Mabel looked a bit flustered. " _Aiyah_ , I'm not supposed to say anything." "Say what? What did Dad tell you?" Cassandra prodded, leaning forward in anticipation. "Nothing, nothing!" Mabel insisted. "Mum, you are so bad at lying. You clearly know something. Come on, spit it out!" Mabel stared down at her bowl of porridge, looking conflicted. "Oh well, there's no use trying to force her. After all these years, your mother still doesn't trust us. So sad." Jacqueline sighed, giving Mabel her seductive, sideways stare. "See what you've done? You've insulted Jacqueline!" Cassandra scolded her mother. "Hiyah! You two! I know you are both such big mouths. If I tell you, you must promise not to say anything, okay?" The two ladies nodded in unison like obedient schoolgirls. Mabel, who had grown up surrounded by staff and usually spoke in her unfiltered manner with no thought to their presence, did the rare thing of making eye contact with George, the head footman, who immediately recognized her signal for privacy. George gestured quickly to the four other footmen, and they made a discreet exit from the morning room. As soon as the door closed, Mabel said in a hushed tone, "I know your father had a big meeting with all the lawyers from Tan and Tan two days ago. Very hush hush. And then Freddie Tan went off to see Su Yi. _By himself._ " "Hmmm," Jacqueline said, digesting this intriguing new tidbit. Cassandra winked at Jacqueline. "Don't worry—I'm sure you're still in the will!" Jacqueline laughed lightly. "Come on, I am the _last_ person to expect to be in Su Yi's will. She's already been so generous to me over the years." "I wonder what she did this time?" Cassandra mulled. "Well, until these pictures leaked, I actually thought Astrid might have a chance at inheriting Tyersall Park," Jacqueline theorized. "Astrid? Never, _lah_! Su Yi is so old-fashioned, she would never leave that house to _a girl_! She might just as well leave it to her own daughters!" Mabel insisted. "Then if it's just the boys, my bet is on Eddie. I hear that he's _really_ been working overtime to be the number-one grandson. He apparently won't leave her side!" Cassandra reported. "I'm not sure it will be Eddie. Su Yi told me herself that she can't take him seriously," Jacqueline said. "Well then she's running out of contenders. No way she would ever let one of the Leong boys get ahold of the house, but maybe one of the Aakaras?" Mabel wondered. Cassandra snorted. "That would be too ironic for words! Would she really spite Philip and Nicky—the only true Youngs left—in favor of those foreign grandsons getting Tyersall Park? I think not." "Maybe she's had a change of heart, then. Don't you think Nicky might have been reinstated?" Jacqueline said. "Definitely not. He's still banned from the house! My sources tell me that he goes over there every day groveling on his knees, hoping to see her, but he still can't get in. Why would she suddenly give him Tyersall Park now?" Cassandra argued. Mabel scrunched her face. "That stupid boy. Giving everything up for that ugly girl." "Come on _lah_ , Mabel, she's not ugly. She's quite pretty, actually. She's just...not the kind of beauty one would have expected for Nicky," Jacqueline remarked diplomatically. "I know what you mean. Rachel is pretty, but in a very conventional way. Her lack of style doesn't do her any favors, either," Cassandra said. Jacqueline smiled. "I wish I could tell her that she needs to grow out her hair by another four inches. That medium-long length is just so _American_." Cassandra nodded in agreement. "And her nose is a bit too rounded. Her eyes could be a bit bigger too." "And have you seen the way she sits? So frightfully common." Mabel sniffed. "Uggh! I can't bear to listen to any more of this!" Lucia shrieked in anger, pushing her chair back dramatically. "You're all talking about Rachel as if she was some kind of show dog! What does it even matter what she looks like, as long as they love each other? Uncle Nicky gave up everything to be with her. I think that's sooooo romantic! I can't wait to meet her. And you're all wrong—I know what's going to happen to Tyersall Park, and it's certainly not what any of you think!" "Shut up, Lucia! Stop making up stories!" Mabel scolded. "Ah Ma, you and Auntie Cassie just chatter on and on about so much rubbish but none of you have a clue what's really going on! Do you ever listen to what Grandpa and Daddy talk about?" With that, Lucia stormed out of the breakfast room, the ladies staring openmouthed after her. "What utter nonsense!" Cassandra scoffed. Mabel shook her head gravely. "Can you believe how rude that girl has become? I knew Bedales would be all wrong for her—those teachers do nothing but keep encouraging her confidence! My goodness, back in my day at the Convent,8 if I had talked like that, the nuns would have beat me blue black with a wooden ruler! _Neh kor suey neui moh yong, gae!_ "9 Jacqueline's eyes narrowed. "On the contrary, Mabel—I don't think she's useless at all. I think you have a very smart little girl on your hands. Smarter than I ever realized..." * * * 1 The interiors were given a marvelous face-lift in the mid-1990s by David Mlinaric, coinciding with Mabel's own (much less marvelous) face-lift. 2 Cantonese for "fish porridge." 3 Cantonese for "This half-breed granddaughter will be the death of me." 4 Cantonese for "so crazy." 5 Hokkien slang for "contacts" or "connections." 6 Cantonese for "so shameful." 7 Malay slang for "mates" or "buddies." Although, should you really be calling the cheating scoundrels who try to screw you at every mah-jongg game your buddies? 8 Mabel, like many other well-born women of her generation, attended Singapore's venerable Convent of the Holy Infant Jesus. These days, the nuns have long since retired, and by most accounts, corporal punishment is no longer practiced. 9 Cantonese for "This lousy girl is useless." (A refrain heard by Cantonese daughters since the beginning of time.) # CHAPTER FIVE PULAU CLUB, SINGAPORE Godfrey Loh, the esteemed Supreme Court justice, could not believe what he was hearing in the stall next to his in the men's room of the Pulau Club. "Yeah, that's so hot. Fucky fuck! I need a close-up. Send me a close-up, pleeeease." _What in God's name was happening?_ "Wait a minute. The pic is still downloading—Wi-Fi's terrible in here. Oh my God...I'm looking at it now. _Phwoar!_ So...fucking...sexy!" _Someone is looking at dirty pictures on his phone right next to me! But who is it? Sounds like a Hong Kong accent. No wonder, all the men in Hong Kong are perverts. That's what you get from a country when you can buy filthy magazines right in the airport!_ "Looks like it's dripping wet. It's so beautiful I want to lick it all over! Come on, come on, I'm ready for it now!" _Is this creep actually engaging in phone sex in the next stall?_ Godfrey had heard enough. He emerged from the cubicle hurriedly and went over to the sink, washing his hands furiously with twice the amount of soap he would normally use. He felt dirty all over just listening to that heavy breather in the stall. "I want to slip my whole foot inside." _He wants to do_ WHAT _with his foot? This man should be arrested._ Godfrey banged his fist against the stall door and said loudly, "You are a degenerate! A complete disgrace to this esteemed club! Take your dirty business elsewhere! Not in our toilets!" Inside the cubicle, Eddie looked up from his phone, completely mystified. "Sorry, I have no idea what that was about. Some ranting weirdo—Singapore's full of them. Anyway, when will this last coat dry? Stop teasing me, Carlo. I need these shoes now!" "Just a few more days. We are waiting for this latest coat of varnish to dry, and then we're going to add one more. Once the patina is perfect, we can overnight them to you in Singapore," Carlo replied. "My uncle Taksin—you know, he's a Thai prince—I can't wait for him to see me in these. Taksin started wearing bespoke Lobbs when he was five years old. Nobody else will appreciate them like he would," Eddie said as he gazed longingly at the picture of his new custom-made Marini shoes. These tasseled loafers were glazed a deep lapis blue, a process that took up to four weeks to achieve in Marini's Rome atelier, and the shoemaker, Carlo, had been sending him teaser photos of the progress all through the month. "You will have them by this weekend," Carlo promised. Eddie ended his call, pulled up his pants, flushed the toilet, and walked back to the Lookout—the casual eatery with sweeping views of the nature reserve where Singapore's oldest and most exclusive country club was situated. Returning to the table where members of his extended family had gathered for a luncheon hosted by his aunt Felicity, he asked his wife, Fiona, "Did you order me the beef satay and the chicken rice?" "No one's ordered yet," Fiona replied, giving him a strange frown. It was then that Eddie noticed that no one at the table was talking, but all eyes were on Felicity. Her eyes were red and swollen with tears, and his mother, Alix, was busily fanning her with a menu. "What happened? Is it Ah Ma?" Eddie whispered to Fiona. "Hiyah! Ah Ma's fine, but Auntie Felicity just received some news that's quite upsetting." "What news?" Eddie asked, irritated that he had only been in the toilet for barely ten minutes and somehow missed the whole first act. His auntie Cat was now speaking in a low, soothing tone to Felicity. "If you ask me, this is all much ado about nothing. It's a slow news week, and the press just had to pounce on something." "Just watch, Felicity, this will all blow over in a few days," Taksin agreed. Eddie, who was seated in the middle of the long table, cleared his throat loudly. "Will someone please tell me what's going on?" Alistair handed a cell phone over to him, and Eddie eagerly scrolled through the paparazzi pictures of Astrid and Charlie Wu in India, feeling his pulse begin to race. Oh boy oh boy oh boy. His always perfect, goody-goody cousin had really stepped in shit at long last! What would Ah Ma think when she found out? One by one, all his cousins were falling from grace, and he was the last man standing. He stared at the hundreds of comments left by viewers of the leaked photos: > Wah! So beautiful. This is my dream engagement!—AngMohKioPrincess > > What a fucking waste! Outrageous that CRAs spend this much on one day when 75 million Indians still don't have access to clean water! —clement_desylva > > Astrid is babelicious. Charlie Wu is the man of the hour!—shoikshoik69 Suddenly, those words sparked something in Eddie's mind that hadn't quite occurred to him until this moment. _Man of the hour._ Earlier in the week, his grandmother's lawyer, Freddie Tan, a senior partner at Singapore's most prestigious law firm Tan and Tan, had paid an unexpected visit to Tyersall Park. Aside from Bishop See, he had been the only nonfamily member allowed into the private sanctum of his grandmother's bedroom, and the distinguished white-haired gentleman had arrived with a smart-looking Dunhill briefcase and spent a rather long time behind closed doors with Su Yi. At some point during their meeting, Professor Oon and his associate doctor were summoned into the bedroom. Could they have been witnesses to the signing of a new will? Eddie naturally hovered around outside her bedroom like a dog eager for scraps, and when Freddie Tan emerged, he studied Eddie from cravat to wing tips and said, "You're Alix Young's eldest boy, right? I haven't seen you since you were a teenager, and now look at you—man of the hour!" Freddie then proceeded to spend the next ten minutes chatting with Eddie, asking after his wife and which schools his children attended. At the time, it didn't occur to Eddie why a man who had never paid him any attention before was suddenly chatting him up like he was his biggest client. But now it dawned on him...did his grandmother make him the heir to Tyersall Park? Was this why Freddie was calling him the _man of the hour_? As this epiphany was still settling in Eddie's brain, he suddenly heard Alistair saying, "You know, you really can't blame Astrid for this. How would she know that the paparazzi would be there? I'm sure she meant for this to be a very private moment." _Fucky fuck!_ Eddie thought irritatedly. What the hell was Alistair doing defending Astrid? Didn't he realize that they all needed to play this to their advantage, especially now when he stood to inherit the whole kit and caboodle. Eddie quickly cut in, drowning out his brother. "Auntie Felicity, I am so sorry you had to be put through this horrible scandal. What a disgrace!" Alix scowled at her son, as if to say, _Don't make this any worse than it is!_ Victoria spoke up. "Actually, I rather agree with Eddie. This is a complete disgrace. I can't believe Astrid would be so careless." Felicity pulled another piece of tissue out of her Jim Thompson silk pouch and sniffed into it dramatically. "My hopeless daughter! We have spent all our lives protecting her from the press, spent so much money protecting her from unwanted attention. And now look how she's repaid us!" At the other end of the table, Piya Aakara whispered into her husband's ear, "I don't understand what the big deal is. Her daughter just got engaged, and the pictures look wonderful. Shouldn't she be happy for her?" "I don't think Auntie Felicity approves of this fellow. And my family just doesn't like to see themselves in the press—ever," Adam explained. "Not even _Tattle_?" Overhearing Piya's comments, Victoria suddenly piped up, "Especially not _Tattle_. My God, that ghastly magazine! You know, I wrote a few pieces for them back in the 1970s. But then one day the editor said my stories were too 'cultural'—yes, I believe that's the word he used. He said to me, and I'll never forget it, 'We don't need any more stories on emerging Chinese artists. We thought you were going to write about your relatives. That's why we hired you.' And that's when I gave my notice!" Eddie continued to fan the flames. "It's one thing to be in _Tattle_ or _Town & Country_—I'm featured in those magazines all the time. Full disclosure, Piya—Fiona and I have been on the cover of _Hong Kong Tattle_ once, and I alone have been on the cover three times. But it's another thing to see Astrid's photos popping up on these _cheap gossip_ _websites_. As if she's some actress or, even worse, a porno star. Like that Kitty Pong girl Alistair dated for half a minute." Alistair was indignant. "For the millionth time, Kitty was not a porn star! It was some other girl who just looked like her!" Eddie ignored his brother and kept on talking. "The thing I can't believe is that Astrid would dare to leave Singapore when Ah Ma is so sick. I mean, here we all are, spending every precious moment we have with her." "She was supposed to be in Malaysia, representing us at Prince Ismail's wedding. I can't believe she deceived us like this! Running off to India, of all places. Getting engaged on an elephant! Who on earth does Charlie Wu think he is? A maharaja?" Felicity sniffed angrily. "So vulgar. Those Wus are all the same—they haven't changed in all these years." Victoria tut-tutted, shaking her head. "Did you know that that horrid Wu woman tried to steal Mabel Shang's seamstress? Imagine the cheek! Thank goodness Mabel rescued that talented girl from her clutches! She made me several nice silk jacquard blouses, perfectly copying the style of this Liz Claiborne blouse Lillian May Tan brought back for me from America. I gave one to Mummy, which she loves, and didn't I give you one too, Cat, when I came to visit you in 1992?" Catherine looked like a deer caught in headlights for a moment. "Oh yes, that's right...lovely!" she said, remembering that she had immediately passed on the hideous blouse to one of her maids. Eddie furrowed his brow and tried to sound terribly concerned. "I saw Charlie Wu at Davos. You know, he didn't even have the decency to wear a proper suit and tie to the most important conference in the world! My God, what if Astrid and Charlie are on their way back to Singapore now? What if she wants him to meet Ah Ma? Or worse, to introduce his mother to Ah Ma? Can we risk upsetting Ah Ma when her condition is so fragile?" "She wouldn't dare bring that man to Tyersall Park! Or her seamstress-snatching mother!" Victoria sniffed. "She's not going to have the chance. I'm going to make sure that girl doesn't show her face anywhere near Tyersall Park!" Felicity angrily decreed. Eddie tried to hide his satisfied smirk by looking at the view of the golf course for a moment. Nicky was banned from Tyersall Park, and now his biggest ally Astrid was banished as well. Things could not be working out any better if he had planned it himself. And let's not forget, his sexy-as-fuck bespoke Marinis were on their way too. * * * * If you assumed that Eddie did not wash his hands, you would be correct. # CHAPTER SIX PORTO FINO ELITE ESTATES, SHANGHAI The fountain-blue Bentley Mulsanne pulled up by the front steps and a bodyguard jumped out of the passenger side to open the back door. As Araminta Lee Khoo emerged from the car in a sculptural ballerina-pink silk strapless Delpozo dress with a contrasting oversize yellow bow and pink sequined miniskirt, the paparazzi began clicking away furiously at her showstopping look. "Araminta! Araminta! Look over here!" "Can we have a fashion pose, please, Araminta?" Araminta paused for a moment, pivoted expertly toward the photographer with one hand on her hip, her other hand showing off her exquisite Neil Felipp Suzy Wong minaudière, before proceeding up the red-carpeted steps. Waiting at the freshly lacquered front doors of their mansion were Kitty and Jack. Kitty wore an explosion of powder-blue feathers courtesy of Armani Privé, and chose this occasion to debut her new diamond and antique Burmese cabochon sapphire earrings from Chaumet. Jack squirmed uncomfortably beside her in skinny black jeans and a shawl-collared white tuxedo jacket by Balmain that was made-to-measure but looked two sizes too small. "Minty! You made it!" Kitty leaned over and gave her an air kiss, as another set of photographers stationed by the front doors clicked away. "My yoga retreat is practically right next door to you in Moganshan, so I thought it could do no harm to sneak away for just one night!" Araminta replied. "I'm so glad you did. And now you finally get to meet my husband. Jack, this is my best friend from Singapore—Araminta Lee, er, I mean Khoo." "Thank you for coming," Jack said stiffly. "Fabulous to meet you! I feel like I know you already!" Araminta tried to give Jack an air kiss, but he tilted back reflexively as he saw the glossy red lips coming at him. Kitty prodded him sharply with an elbow and he quickly straightened up just in time to collide heads with Araminta. " _Aiyoh!_ " Jack groaned. Araminta appeared to see stars for a second, but quickly recovered and laughed it off. "Please forgive my husband. He's just excited to meet you—he gets excited whenever he's around famous supermodels," Kitty gushed apologetically. Araminta moved along into the house, while Kitty shot daggers at her husband with her eyes. "Don't you know how to do a perfect Euro-fashionista triple-cheeked air kiss? You almost gave her a concussion!" Jack muttered under his breath, "Tell me why we're doing this again?" "Honey, we were specially chosen by _Vogue China_ to host the most exclusive party of Shanghai Fashion Week! This is the party all the most important _lao wais_ 1 are attending! Do you know how many people would sell their servants' organs for this opportunity? Please stop complaining." "What a waste of time..." Jack muttered under his breath. "Waste of time? Do you even know who my friend is?" "Some silly model." "She's not just a model—she's the wife of Colin Khoo." "No idea who that is." "Oh come on, he's the heir to the Khoo empire of Singapore. And besides, Araminta is also the only daughter of Peter Lee. I'm sure you know who that is—he was the first Chinese billionaire in U.S. dollars." "Peter Lee's old news. I'm worth exponentially more than him." "You may have more money, but the Lees have more influence. Don't you realize I'm introducing you to the most influential people in the world?" "These people make clothes. How are they influential?" "You have no idea. These people control the world. And the cream of Shanghai society wants to be around them. Just think of who has showed up so far—Adele Deng, Stephanie Shi. And now the First Lady is about to arrive—" "And it looks like Mozart came with her." "Oh my God, that's not Mozart, that's Karl Lagerfeld. He's a very, very, _very_ important man! He's the Kaiser of fashion." "What the fuck does that even mean?" "He is so powerful, he could simply flare one of his nostrils and have me banned from Chanel forever and I might as well be dead. Please, _please_ be polite." Jack snorted. "I'll try not to fart in his general direction." After all the VVIP _lao wais_ had been greeted, Kitty made her grand entrance into the house while Jack fled to his screening room until it was time for dinner. ("As long as you show up for my toast and tell Peng Liyuan how much you adore her singing at some point during the banquet, I don't care what else you do," Kitty had told him.) The whole party was actually an excuse for Kitty to show off the redesign of the house, and she stood on the top step of the former great hall—which she had renamed the Salon Grande—surveying the scene. Gone was Colette's Zen-like Puli Hotel–inspired decor, and in its place, Thierry Catroux had created a look he called "Ming emperor meets Louis-Napoléon at Studio 54." Ming dynasty urns mingled with rare Aubusson carpets against sixties-mod Italian leather-and-Lucite furniture, while the monochromatic Shikumen gray brick walls were now covered in Tibetan yak hair dyed in shimmering shades of persimmon. The eighty-foot-long east wall had been covered with purple-and-crimson latticework screens—in homage to the Hall of Dispelling Clouds at the Summer Palace in Beijing. Colette's prized collection of black-and-white Wu Boli calligraphy scrolls had been banished to the museum wing, and in its place were enormous paintings of vibrantly colored canvases by Andy Warhol, Jean-Michel Basquiat, and Keith Haring in antique rococo gilt frames. Kitty's guests flocked to her side, gushing about the radical transformation. "It's unbelievable, Kitty," Pan TingTing praised. "So...original, Kitty," Adele Deng demurred. "You've _really_ put your stamp on the house," Stephanie Shi said and smiled. "It's such a trip, all that's missing are the quaaludes!" Michael Kors2 said. At some point during the social swirl, Araminta appeared at her side with a glass of champagne. "I thought you could use this. I can see you've been circulating nonstop." "Oh thank you. Yes, everyone has been soooo nice, except for that awful Englishman over there talking to Hung Huang." "Philip? But he's usually so charming!" Araminta furrowed her brow in surprise. "Charming? Do you know what that snob said to me? When I asked him what he did, he actually dared to say, 'I'm a millionaire!' " Araminta clutched Kitty's arm and doubled over in laughter. Trying to catch her breath, she said, "No, no, you're mistaken!" Kitty continued her tirade, "So I said to him, 'Well, I'm a _billionaire_!' " Wiping the tears of laughter away from her eyes, Araminta explained. "Kitty, that man is Philip Treacy. He's not a millionaire, he's a _milliner_ —a hat designer. I'm sure that's what he told you. He's one of the best milliners there is—Perrineum Wang is wearing one of his hats right over there." Kitty gazed at the young Shanghai socialite, who was sporting a gigantic flesh-colored disk with a bejeweled starfish of pink rubies in the middle that covered eighty percent of her face. "No wonder he gave me a strange look." "Oh Kitty, you can always crack me up!" Araminta was still laughing when a pair of hands reached out from behind her and covered her eyes. "Oh, who's this?" Araminta giggled. "Three guesses," a man whispered into her ear in an extremely affected French accent. "Bernard?" " _Non._ " "Er...Antoine?" " _Non._ " "Surely it can't be Delphine? I give up!" Araminta whipped around and saw a patrician-looking Chinese man in a three-piece suit and small round tortoiseshell glasses grinning back at her. "Oliver T'sien, you rascal! You had me fooled with that ridiculous accent." Araminta giggled. "Oliver, have you met the chatelaine of this...er...magnificent estate, Kitty Bing?" "I was hoping you'd introduce me," Oliver purred. "Kitty, this is Oliver T'sien. He's an old friend from Singapore...and...aren't we somehow related now through Colin? Oliver is related to practically everyone who's anyone in Asia, and he's also the consultant at large for Christie's." Kitty shook his hand politely. "It's a pleasure to meet you. You work for Christie's, the auction house?" "Indeed I do." "Oliver is one of the top specialists in Asian art and antiquities," Araminta continued. "Hmm...there's a little horse sculpture in the library I would love to show you. My husband is convinced it's from the Tang dynasty, but I think it's a fake. His ex-wife bought it," Kitty said derisively. "I am at your service, madame," Oliver said, extending an arm. They walked into the library, and Kitty led him to a magnificent Macassar and Gabon Boulle armoire in one corner. She pressed against the tortoiseshell-and-gilt-bronze marquetry doors, which opened to reveal a hidden entryway into Jack Bing's private cigar lounge. "Well, this is quite splendid!" Oliver exclaimed, looking around the decadently upholstered room. As soon as the doors closed behind them, Kitty sank into one of the tasseled velvet Louis-Napoléon smoking chairs and breathed a sigh of relief. "I'm so glad we're finally alone! How do you think it's going?" Unbeknownst to any of her guests, and especially to friends like Araminta, Kitty knew Oliver rather well—he had been secretly advising her for the past couple of years and had been instrumental in helping her acquire _The Palace of Eighteen Perfections_ , a set of prized Chinese scrolls that had broken auction records two years ago to become the most expensive Chinese artwork ever sold. "You have nothing to worry about. Everyone is most impressed. Did you notice that Anna actually took her sunglasses off for a moment to scrutinize your Qianlong dragon vessel?" "No, I missed that!" Kitty said excitedly. "It happened so quickly, but it happened. I also spoke to Karl and—fingers crossed—I think you're getting front row at next season's show in Paris." "Oliver, you're a miracle worker! You'd think spending nine million dollars a year at Chanel would be enough to get you a front-row seat at the damn fashion show." "You'll be front row dead center next season! See? You have nothing to worry about. We should head back to the party before anyone suspects anything. We've been gone too long to look at one Tang horse. Which, by the way, is not fake but is frightfully common. Every drawing room on Park Avenue has at least one collecting dust on top of a stack of coffee-table books. Just throw it away, or give it to Sotheby's to auction off—some philistine will buy it." As Oliver and Kitty were about to emerge from the hidden cigar lounge, a trio of ladies entered the library. Oliver peeked through the crack in the armoire door and whispered to Kitty, "It's Adele Deng, Stephanie Shi, and Perrineum Wang!" Stephanie could be heard saying, "Well, Kitty has certainly succeeded in removing every trace of Colette from the house. What do you think of this Picasso over the desk?" "I'm so sick of seeing Picassos—every starter billionaire in Beijing has one. You know that in the last two decades of his life, the man was doing four paintings a day like some desperate whore? The market is flooded with mediocre Picassos. Give me a good Gauguin any day—like the one in my father's museum," Adele Deng said with a sniff. "Colette's vision for this house was utter perfection, and now it's been ruined," Stephanie lamented. "I don't care what anyone says—to me this will always be Colette's house," Perrineum chimed in. Adele walked up to the Boulle armoire, tracing over the marquetry with her fingers. "This is actually a nice piece, but what the hell is it doing here in the corner? If you ask me, Kitty's trying so desperately to impress. Every single object in this house is a museum showpiece. Everything is screaming, 'Look at me! Look at me!' Kitty wouldn't understand the meaning of subtlety if it hit her on those fake breasts. As Marella Agnelli might say, 'It will take her another lifetime to understand wicker.' " "Hiyah, what do you expect from a porn star? She will never have Colette's taste—you have to be born with it," Perrineum decreed, readjusting her gigantic hat for the millionth time. "I wonder if we can sneak over to her bedroom wing. I want to see what she did with the space," Stephanie suggested. "She probably put mirrors on the ceiling," Perrineum cracked. "Louis XIV mirrors. Stolen from Versailles!" Adele cackled, as she followed the ladies out the door. Perched in the corner of the cigar lounge, Kitty couldn't hide her look of devastation. "My breasts are _not_ fake!" she cried. "Don't listen to them, Kitty." "Adele Deng told me the house was 'so original.' Why would she lie to my face like that?" Oliver paused for a moment, thinking that Adele was right on one score—Kitty certainly didn't pick up on the subtler cues. "They're just jealous of all the attention you're getting. Ignore them." "You know, it's not so easy to ignore those ladies. Adele Deng and Stephanie Shi—they rule the scene here. If this is what they're really thinking, I'll never be able to compete." "Kitty, look—you've already conquered the world stage. These women aren't your competition anymore, don't you see?" "I realize that, but I also realize something else. No matter what I do, this will always be known as Colette's house. And this will always be Colette's town, even though she's gone. She was born here—these are her people. I will always be an outsider in Shanghai, no matter what I do. Why did I even bother spending two years redecorating this house? I should be where people appreciate me." "I couldn't agree more. You have houses all over the world, you can be anywhere you want to be, creating your own social universe. Honestly, I don't know why you don't live in Hong Kong full-time. It's my favorite city in Asia." "Corinna Ko-Tung tells me it will take at least one generation for me to break into Hong Kong society—Harvard might have a chance if I enroll him in the right kindergarten, but it's already too late for Gisele. You know, the only place where Chinese people have ever treated me well is Singapore. Look how nice Araminta Lee has been. And my friends Wandi, Tatiana, and Georgina live there part-time too." Oliver didn't want to remind Kitty that Araminta was actually born in Mainland China, and that neither Wandi, Tatiana, nor Georgina were native Singaporeans, but he began to see a new opportunity arise. "You know, you already own one of the most historic houses on one of the best streets in Singapore. I had assumed you'd spend more time there after you acquired it." "I thought I would. But then I got pregnant with Harvard and Jack insisted that I give birth in the United States. And after that we just somehow spent more time in Shanghai because I needed to redo this house." "But your poor Frank Brewer estate in Singapore is completely neglected. It's only half decorated. Think of what you could accomplish there if you focused your attention on it. Think of all the accolades you would receive from architectural preservationists if you truly restored it to its former glory. My God, I'm sure my friend Rupert would insist on doing a feature story for _The_ _World of Interiors_." The wheels in Kitty's head began turning. "Yes, yes. I could transform that little house. Make it even more spectacular than this cursed place! And it will be _one hundred percent mine_! Will you help me?" "Of course. But you know, aside from the house, I do think it's time for _you_ to undergo another radical transformation as well. You need a new look that will launch you into Singapore society properly. My God, the _Tattle_ crowd will love you. Let's get you a photo shoot and feature story. Hell, I'm sure I can wrangle you the cover." "You really think so?" "Absolutely. I can see it already...we'll get Bruce Weber to shoot it. You, Gisele, and Harvard, romping through your historic heritage property in Singapore surrounded by a dozen golden retrievers. All wearing Chanel! Even the dogs!" "Um...can we get Nigel Barker to shoot it instead? He's soooooo dreamy!" "Of course, dear. Whoever you want." Kitty's eyes lit up. * * * 1 A derogatory term for Caucasians; in Mandarin it translates as "foreign/white/Caucasian." 2 Michael, _Project Runway_ just hasn't been the same without you. Pleeeeeeeeease come back. # CHAPTER SEVEN RESIDENCES AT ONE CAIRNHILL, SINGAPORE The cook had brought home the most scrumptious Singaporean breakfast delicacies from the market. There was _chwee kueh_ —delicately steamed rice-flour cakes topped with salty radish pickle and chili sauce; freshly grilled _roti prata_ —crisp, buttery Indian bread served with a curry dipping sauce; _chai tow kuay_ —daikon radish cakes pan-fried with egg, shrimp, and spring onions; and _char siew bao_ —sweet barbecued-pork buns. As Eleanor and Philip gleefully unwrapped the brown waxed-paper packets of food, Nick entered the white Calacatta-marble-clad kitchen and padded toward the elegant diner-style banquette that had been glassed in so Eleanor's guests could enjoy a "chef's table" experience without having to worry about getting any of the smoky aromas on their expensive outfits or in their perfect coiffures. "Oh good, you're up. Come, come, eat while it's still hot," Eleanor said, dipping a piece of her _roti prata_ into the spicy coconut chicken curry. Nick stood at the table, not saying anything. Eleanor looked up at him and saw the grimace on his face. "What's wrong? Are you constipated? I know we shouldn't have gone to that Italian restaurant last night. So overrated, and so awful." "I rather enjoyed my linguine with white truffles," Philip commented. " _Aiyah_ , nothing special, _lah_. I could open a can of Campbell's Cream of Mushroom Soup and pour it over some noodles and you wouldn't even know the difference! Not worth the money, even if Colin did pay, and all that cheese always clogs up the system." "I just can't believe you sometimes." Nick pulled out a chair and sat down at the banquette. "What don't you believe? Eat a ripe banana, or I have some Metamucil if that doesn't work." "I'm not constipated, Mum, I'm annoyed. I just got off the phone with Rachel." "Oh, how is she?" Eleanor asked in a merry tone, as she spooned a heaping portion of _chai tow kuay_ onto her Astier de Villatte plate. "You know exactly how she is. You spoke to her yesterday." "Oh, she told you?" "She's my wife—she tells me everything, Mum. I can't believe you actually asked her what kind of birth control we use!" "What's wrong with that?" Eleanor asked. "Have you gone completely mental? She's not some Singaporean girl you can interrogate about every bodily function. _She's American._ They don't discuss things like that with just anyone!" "I am not just anyone. I am her mother-in-law. I have a right to know when she's ovulating!" Eleanor snapped. "No you don't! She was so appalled and embarrassed, she didn't even know what to say." "No wonder she hung up so quickly." Eleanor giggled. "This whole grandchildren business has to stop, Mum. We won't be pressured into having kids just because you want us to." Eleanor banged down her chopsticks irritatedly. "You think I'm pressuring you? Hiyah, you don't know the meaning of pressure! When your father and I came back from our honeymoon, your darling Ah Ma commanded her maids to ransack our luggage! When she found our French letters,* she got so upset, she said that if I wasn't pregnant within six weeks, she would throw me out of the house! Do you really want to know what it took for me to get pregnant? Your father and I had to—" "Stop, stop! Boundaries, please! I don't need to know any of this!" Nick groaned, waving his hand in front of his mother's face frantically. "Believe me, I'm not trying to pressure you to have a child. I'm only trying to help you!" "Help me how? By trying to ruin my marriage again?" "Don't you see? I thought if we caught Rachel at the right time in her cycle, we could just fly her to Singapore. Auntie Carol already offered to loan her new Gulfstream G650—it's very fast and Rachel can be here in eighteen hours. She can even come this weekend. And my _kang tao_ at Capella Resort can get me a nice ocean-view suite." "And then what?" " _Aiyah_ , you do your job and get her pregnant, and we can announce it immediately. And then maybe, just maybe, Ah Ma will agree to see you!" Nick looked at his father incredulously. "Can you believe this?" Philip simply put a _char siew bao_ on Nick's plate in a silent show of commiseration. "Believe what? I am trying to do anything I can to get you into that damn house! Your best chance now is to get Rachel pregnant. We need to prove to Su Yi that you can actually produce the next heir to Tyersall Park." Nick sighed. "I don't think that's going to matter at this point, Mum." "Hnh! You don't know your grandmother—she's so old-fashioned. Of course it will matter to her! It will restore you into her good graces. She will have no choice but to see you!" "Listen to me, Mum. Rachel is _not_ going to get pregnant just so I can see Ah Ma. That's the most ridiculous plan I've ever heard. You should stop all your ploys trying to get me into Tyersall Park. It's only going to make things worse. I've actually made my peace with the whole situation. I came to Singapore, I offered to visit Ah Ma. If she doesn't want to see me, I'll get over it. At least I tried." Eleanor wasn't listening to him. Instead, her eyes narrowed as a new thought entered her head. "Don't tell me...hmm...Nicky, are you...how do they say it...robbing banks?" Nick furrowed his brow in confusion. "Robbing banks? What do you mean? I do all my banking online these days, Mum." " _Aiyah_ , when was the last time you went to see the doctor? Do you have a good urologist in New York?" Eleanor demanded. Philip chuckled, realizing what his wife was talking about. "She means _shooting blanks_ , Nicky." "Yes, yes, shooting blanks! Have you ever checked your sperm count? You used to play around with so many girls when you were younger, maybe you used all your good sperm up." "Oh my God, Mum. Oh my God." Nick put his hand to his forehead and shook his head, completely mortified. "Don't 'oh my God' me. I'm dead serious," Eleanor said indignantly as she chewed. Nick got up from the table in a huff. "I'm not going to answer any more of these questions. It's so weird and inappropriate! And don't you dare bring any of this up with Rachel either. Have some respect for our privacy!" "Okay _lah_ , okay _lah_. Don't be so sensitive. I wish we hadn't sent you to school in England, I don't know what kind of man they turned you into over there. Everything is so private-private with you, even medical issues. You're my son—I've watched your nannies change your diapers, you know! Now, aren't you going to eat any of the food we bought? The _chwee kueh_ is extra good today," Eleanor said. "Not only have I completely lost my appetite but I'm going to meet Astrid for breakfast." " _Aiyah_ , that poor girl. Did you read the latest gossip this morning?" "No, Mum. I don't pay attention to silly gossip," Nick replied as he stormed out. * * * * Women of Eleanor's generation—especially God-fearing MGS girls like Eleanor—were brought up using this quaint term for condoms. # CHAPTER EIGHT EMERALD HILL, SINGAPORE Since separating from Michael, Astrid had moved in to one of the heritage shop houses on Emerald Hill Road that she had inherited from her great-aunt Mathilda Leong. As Nick strolled down the street toward her place, he couldn't help but stop along the way and admire some of the ornamental friezes, timber-framed windows, and elaborate entrance gates on the beautifully restored Peranakan-style terrace homes that made this street so unique.1 No two façades were alike—each one blended different elements of Chinese baroque, late-Victorian, and art deco details. When Nick was a child, many of these shop houses where old Peranakan families lived and worked had fallen into neglect and the street had an air of faded grandeur, but now that real estate prices had shot up to absurd levels and the neighborhood had been designated a conservation area, these houses had become highly coveted properties going for tens of millions. Many of them had been turned into hip bars or sidewalk cafés, leading some of Nick's snootier relatives to derisively refer to Emerald Hill Road as "that street where all the _ang mor kow sai_ go to _leem tzhiu_ ,"2 but Nick found it all rather charming. Arriving at a handsome white shop house with smoky gray shutters, he stopped and rang the doorbell. A blond girl in her early twenties peered over the _pintu pagar_ —an ornately carved wooden half door that was a typical feature of such houses—and asked in a heavy French accent, "Are you Nicolas?" Nick nodded, and she slid the lock open to allow him to enter. "I'm Ludivine, Cassian's au pair," she said. " _Salut, Ludivine. Ça va?_ " Nick said with a smile. " _Comme ci comme ça_ ," Ludivine replied coquettishly, wondering why she'd never met madame's hottie French-speaking cousin before. Stepping into the front foyer, Nick could see that the room had been painstakingly restored to its original style. The floor was an elaborate mosaic of ceramic tiles painted in a William Morris–esque floral pattern, and intricately carved gilt wood screens created a partition between the front room and the rest of the house beyond. The centerpiece of a typical Peranakan front room was the ancestral shrine, and Astrid had honored the tradition by installing an elaborate Victorian altarpiece against the back wall. But instead of placing pictures of dead relatives or porcelain gods within the altar, she had cheekily hung a small Egon Schiele drawing of a nude male figure inside. Ludivine led Nick from the front foyer through a darkened antechamber into the _chimchay_ —the open courtyard exposed to the sky that provided the natural ventilation and lighting essential to these long, narrow shop houses. Here, Astrid had departed from tradition and completely transformed the space: The roof had been glassed in and the entire space air-conditioned, while the usual concrete floor was now covered in obsidian black tiles, making it shimmer like a pool of black ink. But the pièce de résistance was the east wall of the courtyard, where Astrid had worked with the pioneering French landscape architect Patrick Blanc to install a vertical garden that soared three stories high. Creepers, ferns, and other exotic palms seemed to grow out of the wall, defying gravity. Against this dramatic fresco of flora was a sleek arrangement of sculpted bronze divans covered in soft pillows of blindingly white linen. There was a verdant, monastic stillness to the space, and in the midst of it all, Astrid perched cross-legged on a divan, nestling a cup of tea on her lap, Zenly attired in a black tank top and a voluminous black skirt.3 Astrid stood up and gave Nick a tight hug. "I've missed you!" "Same here! So this is where you've been slumming it." "Yeah, you like it?" "It's incredible! I remember coming here as a kid for one of your great-aunt's _nyonya_ feasts—I can't believe what you've done with it!" "I moved in here thinking it would just be temporary, but I ended up falling in love with the place so I figured I'd do some work on it. I can feel my great-aunt all around me here." Astrid gestured for Nick to take a seat next to her on the divan, and she began to pour him some tea out of a cast-iron teapot. "This is a Nilgiri from the Dunsandle Tea Estate in South India...I hope you like it." Nick took a sip of the tea, savoring its delicate smokiness. "Hmmm...fantastic." He gazed in wonder at the ocular-patterned skylight far above. "You've really outdone yourself with this space!" "Thanks, but I can't take any credit for it—Studio KO, this amazing Parisian duo, designed everything." "Well, I'm sure you inspired them much more than you let on. I don't think I've ever been in a house quite like this—it feels like Marrakech two hundred years from now." Astrid smiled and gave a little sigh. "I wish I could be in Marrakech two hundred years from now." "Yeah? I get the feeling it hasn't been all that great a morning. What's this latest gossip I hear?" Nick asked, sinking down into the plush sofa. "Oh, you haven't seen it?" Nick shook his head. "Well, I'm _very_ famous now," Astrid said self-mockingly as she handed him the newspapers. It was the _South China Morning Post_ , and on the front page, the headline screamed: > # MICHAEL TEO SEEKS RECORD $5 BILLION DIVORCE SETTLEMENT FROM HEIRESS ASTRID LEONG > > SINGAPORE—For the past two years, billionaire venture capitalist Michael Teo, 36, has been mired in divorce proceedings with Singapore heiress Astrid Leong. What was supposed to be an amicable divorce has taken a new twist, as Mr. Teo's legal team is now demanding a $5 billion settlement in light of recent developments. > > Last week, pictures of Ms. Leong, 37, went viral on international gossip sites. The images purport to show Ms. Leong being proposed to by Hong Kong tech tycoon Charles Wu, 37, at the Mehrangarh Fort in Jodhpur, India. Surrounding them were 100 classical Indian dancers, 20 Sitar players, two elephants and Bollywood superstar Shah Rukh Khan, who reportedly serenaded the couple with a Hindi version of the Jason Mraz love ballad "I'm Yours." > > Mr. Teo is now accusing Ms. Leong of "intolerable cruelty and adultery" in his latest divorce filings. He claims to have incontrovertible evidence that his wife has been having an affair with Mr. Wu "since as early as 2010." It is a sad ending to what was once a romantic Cinderella story in reverse: Mr. Teo, the son of two schoolteachers, grew up in middle-income housing in Toa Payoh, met Ms. Teo, an heiress to one of Asia's largest fortunes, at the birthday party of one of his army friends. After a whirlwind courtship and wedding, the ridiculously photogenic couple married in 2006. > > It was a union that took many in Asia's society circles by surprise. Ms. Leong is the only daughter of Henry Leong, the president of S. K. Leong Holdings Pte Ltd, the secretive conglomerate said to be the world's leading supplier of palm oil. Before she married Mr. Teo, she had previously been engaged to Charles Wu and also linked to a Muslim prince and several members of European nobility. Like her family, Ms. Leong is an exceedingly private individual who has never granted an interview and has no social media presence. The Heron Wealth Report has ranked the Leong family number three on a list of Asia's richest families, and estimates Ms. Leong's personal fortune to be "in excess of $10 billion." > > Now, half of Ms. Leong's fortune is at stake, along with custody of their seven-year-old son, Cassian. "My client is a self-made-billionaire—this is not about the money," claims Mr. Teo's lawyer Jackson Lee of the esteemed firm Gladwell and Malcolm. "This is about the principle of it all. Michael Teo, a loyal and devoted husband, has been humiliated on the world stage. Imagine how you would feel if the woman you were still married to was proposed to by another man, in such a public and disgustingly showy manner." > > Singapore legal experts feel that Mr. Teo's legal maneuvers are unlikely to succeed, due to Ms. Leong's assets being tied up in the labyrinthine S. K. Leong Trusts. But this latest filing has already done its damage. An insider to Singapore's social scene comments, "The Leongs do not ever like being in the news. This is a huge embarrassment for them." "Bloody hell," Nick said, throwing the newspaper on the floor in disgust. Astrid smiled at him wanly. "How does the _Post_ get away with publishing this? I've never read so much bullshit in all my life." "You're telling me. Self-made billionaire my ass." "And if you're really worth ten billion, there's this David Bowie limited-edition box set I want for my birthday. It's $89.95 on Amazon." Astrid laughed for a moment, and then shook her head. "All my life, I've done everything to avoid being in any newspapers, but it seems like these days, the harder I try, the more I end up becoming front-page news. My parents are apoplectic with rage. They were angry enough when the pictures first leaked, but this just put them over the edge. My mother has taken to her bed and is mainlining Xanax, and I've never heard my father scream so loud as he did this morning when he came by with the newspaper. The blood vessels were bulging out of his temples so hard, I thought he was going to have a stroke." "But can't they see that none of this is your fault? I mean, surely they know that Michael set this all up?" "It seems pretty obvious to me, but of course, it doesn't matter to them. I'm the naughty girl who snuck off to India. I mean, I'm a thirty-seven-year-old mother, and I still need to ask my parents' permission to go away for the weekend. It's all my fault. I'm the one who's 'exposed' the family, I'm the one who's disgraced the family name for a thousand generations." Nick shook his head in commiseration, cracking his knuckles as something else came to his mind. "You gotta give Michael some credit...he _knew_ that the Singapore papers wouldn't touch this story, so he purposely had it leaked to the _South China Morning Post_ in Hong Kong." "It was a well-played move. He's trying to do maximum damage to Charlie and to our future life there." "I'll bet you anything he's behind those paparazzi pictures too." "Charlie seems to think so. He's got his whole security team trying to figure out how Michael's had me under surveillance." "I know this is going into Jason Bourne territory, but is there any way Michael could have put some sort of tracking device on you before you went on your trip? I mean, he _did_ hack your cell phone once upon a time." Astrid shook her head. "I haven't seen Michael in almost a year. We only communicate through our lawyers now—and that's his doing, not mine. Ever since he hired this Jackson Lee fellow, who I'm told is a mad legal genius, things have gotten more and more acrimonious." "How often does Michael see Cassian?" "Technically, he gets him three days a week, but Michael rarely lives up to his end of the deal. He takes Cassian for a meal once a week or so, but sometimes he goes two or three weeks before he sees him. It's like he's forgotten he even has a son," Astrid said sadly. A maid entered the courtyard and set a breakfast tray down on the coffee table. "Kaya toast!" Nick exclaimed happily at the sight of the perfectly toasted triangles of bread smeared with a thick layer of kaya coconut jam. "How did you know I was craving that this morning?" Astrid smiled. "Don't you know I can read your mind? This is Ah Ching's homemade kaya from Tyersall Park, of course." "Brilliant!" Nick said. Astrid noticed the glint of sadness that played across his eyes as he took his first bite of the crisp yet fluffy white bread. "Listen, I heard about how you've been banned from Tyersall Park. It's so ridiculous. I'm sorry I haven't been able to help, but now that I'm back, I'm going to try to figure something out." "Come on, Astrid, you've had so much to deal with. Don't worry about it. Do you know the stunt my mother's been trying to pull? She wants me to get Rachel pregnant, pronto, and then she'll announce the news to Ah Ma in the hopes that she will want to see me." "You can't be serious!" "She called Rachel and demanded to know where she was in her cycle. She had Carol Tai's plane all lined up to whisk her to Singapore this weekend specifically so that I could impregnate her. She even had a honeymoon suite ready at her friend's resort in Sentosa." Astrid clasped her mouth in laughter. "Jesus! And I thought I had a crazy mother!" "No one is crazier than Eleanor Young." "Well, at least she's still trying to look out for you. She'll do anything for you to get back in Ah Ma's good graces." "For my mother, everything's about the house. But you know I just want to see Ah Ma. It's taken me a while to get there, but I realize I do owe her an apology." "That's big of you, Nicky. I mean, she was pretty horrendous to you and Rachel." "I know, but I still shouldn't have said the things I said. I know how much it hurt her." Astrid reflected on this, staring into her teacup for a moment before looking up at her cousin. "I just don't understand why Ah Ma suddenly doesn't want to see you. I sat by her bedside for a whole week while she was at Mount E. She knew you were on your way back, and she never mentioned a thing about not wishing to see you. Something's up. I think Auntie Victoria or Eddie or somebody's been influencing her while I've been out of the picture." Nick looked at Astrid hopefully. "Maybe you can find a way to bring it up with her...delicately. You've always had a way with her that no one else has." "Oh, didn't you know? I'm persona non grata at Tyersall Park too. My parents don't want me to show my face at the house, or anywhere in public for that matter, until this scandal blows over a bit." Nick couldn't help but laugh at the whole situation. "So we've both been excommunicated, as if we were the devil's spawn." "Yep. We're the friggin' Children of the Corn. But what can we do? Mum doesn't want anything at all to risk upsetting Ah Ma right now." "I think Ah Ma would be more upset that you're not there by her bedside," Nick said indignantly. Astrid's eyes brimmed with tears. "We're losing precious time with her, Nicky. Every day, she's fading away more and more." * * 1 Originally an area of orchards and nutmeg plantations during the colonial era, Emerald Hill was developed into a residential neighborhood for Peranakan families in the early twentieth century. These Peranakans—or Straits Chinese, the term that was used for them in the era—were English educated (many of them at Oxford and Cambridge) and intensely loyal to the British colonial government. Serving as the middlemen between the British and Chinese, they grew rich and powerful as a result, as was clearly evidenced in the opulent shop houses they built. 2 Although the Hokkien phrase literally translates to "redhaired dog shit go to drink alcohol," it can be interpreted as "that street where the Eurotrash go to get drunk." 3 Deceptively simple, as it turns out—Astrid was wearing a perfectly constructed ribbed jersey tank from The Row over a vintage Jasper Conran black silk skirt in a festive tiered rah-rah design. # CHAPTER NINE TYERSALL PARK, SINGAPORE Eddie walked down the east corridor on the way to his grandmother's bedroom, admiring the cluster of old photographs that had been hung salon-style over a damask-covered settee. In the center was a framed oversize print of his great-grandfather Shang Loong Ma posing next to several enormous elephant tusks and a jewel-turbaned maharaja after a safari in India. Next to that hung a studio portrait of his grandfather Sir James Young in the late thirties, looking every inch the matinee idol in his houndstooth jacket and white fedora, and improbably clutching a Norwich terrier in his arms. _How dapper he looked! Who made that blazer for him? Could it be Huntsman, or Davies & Son?_ Eddie wondered. _I wish I had known him back then. Of all his grandsons, I'm obviously the only one who inherited his style._ Lower down on the wall was a long, rectangular photo of his grandmother Su Yi wearing a tea dress, sprawled elegantly on a picnic blanket in what looked like the Jardin du Luxembourg. Next to her were two French ladies, and each of them clutched intricate lace parasols that appeared to be straining against a gust of wind. The two ladies were laughing, but Su Yi stared straight into the camera, perfectly composed. How beautiful she had been in her youth. Eddie scrutinized the signature that had been scrawled at the bottom of the print: J. H. Lartigue. _Holy fuckballs, did the great French photographer Jacques Henri Lartigue really take this picture of Ah Ma? Jesus, this is priceless. I must have it for my office. It could go right next to my Cartier-Bresson print of the boy holding the wine bottles. No one else would appreciate this photograph like I would. If I took this photo and replaced it with one of the others hanging on the other wall, would anyone notice?_ Eddie looked around the corner to see if any of the maids were skulking nearby. There were so many goddamn maids everywhere, no one had any privacy to steal a thing in this house. That's when he heard the slow, deep moan. _Ooaahhh!!! Ooooaaaahhh!_ It was coming from a door halfway down the hallway that had been left slightly ajar. Eddie quickly realized it was the suite where his cousin Adam and Piya Aakara were staying. He knew that Thais could be kinky, but would they really leave the door ajar like this while they were having their morning nooky? Anyone coming down this corridor could hear them. Then again, if that sexy Piya was his wife, he'd ride her into next week and not give a damn if the whole house could hear. Eddie crept closer to the door, and a woman's voice could be heard giggling. Suddenly, another guttural voice could be heard moaning over the first one. _Gwaahhh! Gwaahhh!_ Wait a minute, there were _two guys_ in the room. And then the second male voice moaned, _Oh yeah, right there! Go deeper! Gwaaaaahhh!_ Eddie's eyes widened as he recognized that voice. It was his brother, Alistair. What the fucky fuck was happening? Was Alistair having a ménage à trois with his Thai cousins _right under his grandmother's roof, while she lay dying_? The sacrilege! Whenever he came to visit his grandmother, he always had the common decency of checking his latest mistress in to the Shangri-La Hotel nearby. He would _never think_ of sleeping with anyone that wasn't his wife in his dear Ah Ma's house. Eddie barged into the room in a self-righteous fit. "WHAT IN GOD'S NAME DO YOU THINK YOU'RE DO—" he began, and then he stopped in surprise. Piya was seated on the chaise lounge sipping her morning cappuccino, coolly elegant in a sleeveless kelly green silk faille top with matching faille pencil pants from Rosie Assoulin. Eddie swung around and discovered the most curious sight. Sitting at the foot of the silver-enameled four-poster bed was Alistair, stripped to the waist, and leaning over him was Uncle Taksin, digging his elbows deep into Alistair's shoulders. Adam lay facedown naked on the bed while his mother straddled his thighs, massaging his lower back with coconut oil. "Ooaahhh!" Adam groaned, as Piya continued to giggle. "I told you boys to do some stretches before your badminton match, but you didn't listen, did you?" Catherine chided, as she rubbed Adam's lower back vigorously. "Duuude, Uncle Taksin is giving me the best Thai massage on the planet! You really should try it," Alistair said. Eddie stared at the scene in disbelief. He couldn't believe that the Thai prince was giving his brother a massage. "Um, shouldn't your maids be doing this?" "No...Mummy's the best." Adam sighed through his pillow. Piya laughed. "All the Aakara boys have been spoiled by their parents giving them massages since they were little. Adam doesn't even like it when I try to massage him—only Mummy will do." Catherine looked up at Eddie, her chin smeared with a drop of coconut oil as she kneaded her fingers deep into Adam's butt muscles. "Do you want a massage? I'm almost done here." "Er...no, I'm fine, thanks. I'm not sore—I...I...only played the first set, remember?" Eddie stuttered, uncomfortable at seeing his auntie touch her own son _down there_. "You don't know what you're missing." Alistair sighed contentedly. "I'm just on my way to see Ah Ma," Eddie said, backing out of the room as fast as he could. Those Aakaras were such strange people. Imagine, giving their children massages when they had a posse of prostrating servants at their beck and call! He could hardly believe that Auntie Cat and his mother were sisters—they were such polar opposites. His mother was always so poised and ladylike, while Cat was this no-nonsense woman with tomboyish ways. Her arms, her face—practically the whole front of her body was smeared with coconut oil as she gave her son a massage. His mother didn't even like putting moisturizer on her own hands. How the hell did Cat ever manage to snag a prince? Of all the sisters, his mother had clearly made the worst match, not including old maid Auntie Victoria, of course. He entered his grandmother's private study and saw his father huddled in conversation with Professor Oon. Malcolm Cheng was one of Asia's most respected heart surgeons, and had only recently retired as the chief of the Cardiology Centre at Hong Kong Sanatorium. Professor Oon was one of his protégés, and he was obviously keeping close tabs on Su Yi's condition. "How's the patient doing today?" Eddie said cheerily. "Don't interrupt when I'm talking!" His father scowled at him, turning back to Professor Oon. "And I'm really not happy with the fluid buildup in her lungs." "I know, Malcolm," Professor Oon murmured worriedly. Eddie went into the bedroom, where he found his mother rearranging the vases of flowers that had been sent to Su Yi. Every day, several dozen new arrangements were delivered to the house, along with cases upon cases of Brand's Essence of Chicken. "Mummy hates hydrangeas. Who sent them?" Alix said, opening the creamy thick envelope to look at the card. "Oh God, it's from the Shears. Well, I suppose we have to keep the flowers here until Mummy wakes up to see them. She was so close to Benjamin. He was the doctor who delivered me, you know?" "Oh look, I think she's awake now!" Eddie said excitedly, as he ran over and crouched beside her. "Dear Ah Ma, how are you feeling today?" Su Yi's throat was too dry to talk, but she managed to mutter, "Water..." "Yes, yes of course. Mother, Ah Ma needs some water now!" Alix looked around and grabbed the nearest pitcher. "Tsk, why is this empty?" she said irritatedly, as she ran into the bathroom to refill it. She came back out and started to pour some of the water into the plastic cup with the sippy straw attached. "Is that tap water? Are you trying to kill Ah Ma?" Eddie snapped at his mother. "What do you mean? Singapore tap water is perfectly safe!" Alix argued. "Ah Ma should only drink sterilized water in her condition. Where's that damn Swiss water that the Aakaras have been guzzling nonstop? Why isn't any of it in here? And where are her goddamn lady's maids when you need them?" "I sent them to prepare her breakfast." "Well, call down and get them to bring up some of the Swiss water too," Eddie ordered. Su Yi sighed, shaking her head in annoyance. Why were all her children so incapable of fulfilling this simple request? Alix could see the look of frustration on her mother's face and quickly decided to override her son. "Step aside Eddie, let me give her this water now." "No, no, let me," Eddie insisted, grabbing the cup from her hands and leaning down at his grandmother while mustering his best Florence Nightingale expression. When Su Yi was hydrated and feeling more revived, she gazed around her bedroom, as if searching for something. "Where's Astrid?" she asked. "Er...Astrid isn't here at the moment," Alix said, not wanting to mention anything about the unfolding scandal surrounding her niece. She made eye contact with Eddie, silently warning him not to say anything. "Astrid went to India," Eddie announced with a smirk. Alix glared at her son in dismay. Why was he trying to agitate his grandmother like this? "Oh good. She went," Su Yi said. Eddie couldn't hide his surprise. "You knew about this? You know about Charlie Wu's proposal?" Su Yi said nothing. She closed her eyes, her lips curling into a slight smile. Suddenly she opened her eyes again and looked questioningly at Alix. "And Nicky?" "Um, what about Nicky?" Alix asked carefully. "Isn't he supposed to be back by now?" "Do you mean you want to see Nicky?" Alix asked, trying to clarify. "Of course. Where is he?" Su Yi said. Before Alix could answer, Eddie cut in. "Ah Ma, Nicky unfortunately had to cancel his trip at the last minute. Something came up with work, and he couldn't make it back just yet. You know how important that history professor job is to him. He had to deliver a lecture on the Intergalactic Wars." "Oh," Su Yi said simply. Alix stared at her son, amazed by his bold-faced lie. She was about to say something when Su Yi's lady's maids entered with the breakfast trays. "Mummy—" Alix began, when she suddenly felt Eddie grab her arm forcefully from behind and pull her into Su Yi's dressing room. From there, he took his mother onto the balcony and shut the glass door firmly behind them. "Eddie, I don't know what's gotten into you. What was that nonsense about Nicky? What kind of game are you playing this time?" Alix demanded, squinting at him under the glare of the morning sun. "I'm not playing any games, Mother. I'm just letting nature take its course." Alix stared her son in the eye. "Eddie, I want the truth: Did Ah Ma _really_ tell you that she didn't want Nicky in the house?" "She...she almost went into cardiac arrest when I mentioned his name!" Eddie sputtered. "Then tell me why she just asked for him?" Eddie paced around the balcony, looking for a shady spot to stand. "Can't you see that Nicky only wants to see Ah Ma so that he can beg for her forgiveness?" "Yes, and I'm all for it. Why shouldn't he be allowed to patch things up with her?" "Are you crazy or what? Do I really need to spell it out for you? I'm fighting for what's rightfully mine!" Alix threw up her hands in exasperation. "You're delusional, Eddie. Do you really think my mother is going to change her will and leave _you_ Tyersall Park?" "She already has, Mother! Didn't you see how Freddie Tan acted the other day after he came to visit Ah Ma?" "He seemed his usual friendly self to me." "Maybe he's always been friendly to you, but to me, he behaved in a way that he never has. The man has hardly exchanged two words with me over the past thirty years, but the other day, he spoke to me as if I was his biggest client. He told me I was the 'man of the hour.' And then he spent an inordinate amount of time talking to me about my watch collection. What does that tell you?" "Only that Freddie Tan is a watch lunatic like you." "No, Mother, Freddie Tan was trying to give me a hint about being the _man of the hour_ in Ah Ma's new will! He's already sucking up to us, can't you see? Now, do you want to ruin all that and see Ah Ma give Nicky this house? The house you grew up in?" Alix gave a weary sigh. "Eddie, this house is already supposed to be his. We have all known since the day Nicky was born that it was meant for him. He's a _Young_." "That's right, he's a Young, he's a Young! All my bloody life people have been telling me he's a Young and I'm just a Cheng. This is all your fault!" "My fault? I don't understand you half the time—" "Why the hell did you have to marry Dad, a complete nobody from Hong Kong? Why couldn't you marry someone else, like an Aakara or a Leong? Someone with a respectable surname? Didn't you think of how it would affect your children? Didn't you realize how it has fucked up my whole life?" Eddie seethed. Alix looked at her son's petulant expression and for a moment felt the urge to slap him. Instead, she took a deep breath, sat down on one of the wrought-iron chairs, and said through gritted teeth, "I'm glad I married your father. He may not have inherited an empire or been born a prince, but for me he is far more impressive. He built himself up from nothing to become one of the world's leading cardiologists, and his hard work has sent you to the best schools and given us a lovely home." Eddie laughed mockingly. "A lovely home? Oh my God, Mum, your flat is a disgrace!" "I think ninety-five percent of the population of Hong Kong would beg to differ. And don't forget, we even bought you your first flat when you graduated from university to help you get started—" "Ha! Leo Ming was given a hundred-million-dollar tech company when he graduated." "And where has that gotten him, Eddie? I don't see that Leo has accomplished much in his life except expand his number of ex-wives. We gave you the support to become successful on your own terms. I can't believe you fail to see all the advantages your father and I tried to give you. How did we manage to raise you to be so ungrateful? I don't hear Cecilia or Alistair complaining about their lives or their surname." "They're both underachieving losers! Cecilia is so obsessed with her horses, you should have named her Catherine the Great! And Alistair and his film-production bullshit—who in Hong Kong has ever seen any of those strange art-house movies that his director friend makes? _Fallen Angels_? It should have been called 'Fallen Asleep'! I'm the only one of your children who has ever accomplished a damn thing! Do you really want to know what having the surname Cheng has done for me? It meant that I didn't get to go to Robbie Ko-Tung's birthday party at Ocean Park when we were in Primary Two. It meant that I didn't get picked for the debate team at Diocesan. It meant that I didn't get asked to be a groomsman at Andrew Ladoorie's wedding. It meant that I knew I would never get a cushy no-show job at one of the Hong Kong banks and had to spend half my life licking the balls of everyone at Liechtenburg Group in order to claw my way to the top!" "I never realized you felt this way." Alix shook her head sadly. "That's because you never bothered to get to know your own children! You've never really had time to care about our needs!" Alix got up from her chair, finally losing her patience. "I'm not going to sit here in the hot sun and listen to you whine about being a neglected child, when you jet around the world and hardly ever make time for your own kids!" "Well, that's fitting, isn't it? Dad spent most of my childhood flying to medical conferences in Sweden or Swaziland while you were always off buying up properties in Vancouver. You've never listened to me! You've never once asked me what I truly wanted! YOU'VE NEVER EVEN GIVEN ME A BUTT MASSAGE!" Eddie wailed, as he collapsed onto one of the balcony chairs, his body suddenly wracked with sobs. Alix stared at her son, thinking that he must have temporarily gone mad. Eddie wiped away his tears and glared at his mother. "If you truly care about your children, if you truly love us as you say you do, you will say NOTHING to Ah Ma about Nicky. Don't you see what a perfect opportunity this is for us? We need to make sure he never gets to see her, and we need to keep reinforcing to Auntie Felicity that Astrid is still not welcome here! We can tell Uncle Philip that Ah Ma is too weak to see anyone. I will plant myself outside Ah Ma's bedroom at all times—nobody is going to get in or out without my approval!" "This is insane, Eddie. You can't restrict other family members from seeing Ah Ma like this." "This is not insane!" Eddie screamed. "YOU'RE insane if you allow us to lose this opportunity. This could be our only chance to get Tyersall Park. Yes—OUR. You see, I'm always thinking of what's best for our family! I'm not doing this just for me, but for Alistair and Cecilia and all your precious grandchildren. If we are the new owners of Tyersall Park, no one can ever say that the Chengs aren't as great as the Youngs or the Shangs. Please don't ruin everything for us now!" # CHAPTER TEN TYERSALL PARK, SINGAPORE "Which bottle?" Jiayi asked in Cantonese as she stood on the third-highest step of the wooden rolling ladder. "Um...look for any bottle from before 1950," Ah Ling instructed. The maid squinted her eyes at the ancient yellowing labels affixed to the front of the large glass canisters, looking at the dates. She remembered going to a fancy herbal shop in Shenzhen when she was a teenager and seeing one precious golden tin of _yen woh_ in a locked glass cabinet in the pride of place behind the cash register. Her mother had explained that the container was full of edible bird's nest—one of the most expensive delicacies in China. Now she was looking at an entire shelving unit lined with them. "I can't believe that all these bottles are filled with _yen woh_. It must be worth a fortune!" "That is why we keep this larder under lock and key," Ah Ling said. "All of these bottles came from Mrs. Young's father. Mr. Shang owned a company that supplied the finest _yen woh_ in Asia, taken from the most prized caves in Borneo." "Is this how they became so rich?" "Hiyah, you can't build a fortune like the Shangs' on _yen woh_ alone. This was just one of the many companies Mr. Shang owned." The maid climbed down from the ladder hugging a huge bottle almost as big as her entire torso. She stared through the musty glass at what looked like dried white husks, marveling at the precious treasure inside. "Have you ever tried it?" "Of course. Mrs. Young always has a bowl prepared for me on my birthday." "What does it taste like?" "I can't quite describe it...it's like nothing you've ever had. It's more about the texture...it's sort of like snow fungus, but much more delicate. But here, Ah Ching makes it into a dessert soup. She cooks it in a double boiler with dried longan and rock sugar for forty-eight hours, and then puts shaved ice over it. It's marvelous. Now, third rack from the bottom on that shelf over there. Get me three cups of dried longan," Ah Ling instructed, as she carefully marked the amount of bird's nest she had taken out of the canister in a ledger book. "Whose birthday is it now?" Jiayi asked. "Nobody's. But Mrs. Young's brother Alfred Shang is coming over for Friday-night dinner. And we know how much he likes _yen woh_." "So he gets to have it whenever he wants?" "Of course! This used to be his house too, you know." "Life is so unfair..." Jiayi muttered as she strained to open the lid of the bottle of dried longans. There was a knock on the door, and Vikram, the head of security, poked his head in and smiled at Ah Ling. "There you are! Ah Tock said you were down in the larder, but he didn't say which one. I searched two other larders before finding you!" "I only ever come to the dried-goods larder, because only I have the key. The other larders I never bother with. What do you need?" Vikram eyed the young maid scooping out the dried longans into a bowl and said to the housekeeper, "May I have a few minutes of your time after you're done with this?" Ah Ling looked over at Jiayi. "Take everything up to Ah Ching now. And maybe if you are very nice to her, she will let you have a little taste of the _yen woh_ on Friday." As soon as the maid had left the room, Ah Ling asked in a slightly weary tone, "What is the problem today?" "Well, I've been going through something in my mind for the last couple of days," Vikram began. "You know how Joey's been out on leave since his mother's surgery? Well, I took over his patrol schedule myself, and the other day while I was on the roof, I overheard something rather interesting coming from Mrs. Young's balcony." Ah Ling's ears perked up. "What was so interesting?" "It was Eddie Cheng talking to his mother. From what I could gather, it sounds like Mrs. Young never said she didn't want to see Nicky. I think Eddie made it all up." Ah Ling cracked a smile. "I suspected this all along. Su Yi has never banned anyone from the house before, and surely not Nicky of all people." "I felt it was wrong too, but what could I say? Clearly Eddie has an agenda of his own, and he's the one who has instigated this ban on Nicky. And Victoria has fallen for his ploy." "What did Alix have to say? I'm surprised she's going along with it—mother and son are usually at loggerheads." "She didn't say much. He was so busy screaming at her, the poor woman could hardly get a word in. Apparently Eddie has held a grudge against his mother for a very long time because she won't massage his buttocks." "Whaaaat?" Ah Ling made a face. Vikram couldn't help but chuckle a bit. "Yes, I know, strange family. What can you expect—they're Hong Kongers. Anyway, Alix tried to reason with Eddie, but he's determined to make sure Nicky doesn't get to see Mrs. Young at all. He's gotten it into his fat head that he alone will inherit Tyersall Park—that's why he's been planting himself outside her bedroom for the past two days like a Doberman. He's not letting anyone in who will ruin his plan!" " _Sek si gau!_ " Ah Ling muttered angrily. Vikram peeked out of the larder door for a moment to see if there was anyone within earshot before continuing in a lower voice. "Now, from what I understand, Mrs. Young thinks that Nicky had to cancel his trip because of the Intergalactic Wars. She has been kept completely in the dark, and has no idea he's even back on the island. Astrid is being kept away too, and you know none of those daughters are going to tell her anything. We need to do something about this!" Ah Ling let out a long sigh. "I don't know if we can interfere. This is a family matter. I don't like to get mixed up in their quarrels. And I especially don't want either of us to get in trouble for this...after Su Yi is gone." "Mrs. Young isn't...going anywhere!" Vikram sputtered. "Vikram, we both have to face it...I don't think Su Yi is going to last much longer. I see her waning day by day. And we have no idea who's going to get control of Tyersall Park. God forbid, it could be Eddie. We need to be extra careful, especially now. I've seen what has happened before in this family. You weren't around when T'sien Tsai Tay passed away. My God, the drama!" "I think there's going to be drama no matter what. But you practically raised Nicky—don't you want to see him get the house?" Ah Ling gestured for Vikram to follow her to the back of the larder. "Of course I do," she whispered. "We both know it would be ideal if Nicky is the new master of Tyersall Park. He is our best hope to keep things just the way they are. That's why we have to do what we can to make sure he gets to see Mrs. Young." "But what can we do? How are we going to get Nicky into the house and into her bedroom without the whole family knowing about it? Without losing our jobs?" Vikram felt a lump in his throat, but he continued to speak. "Ah Ling, I swore an oath—a Gurkha's oath—to protect and serve Mrs. Young with my life. I feel like I would be betraying her if I didn't see that her wishes are followed. You just confirmed that she wants to see Nicky, right?" Ah Ling nodded. "I have a feeling she's hanging on to see him." "Well, it's my duty to make sure that happens. Even if I lose my job." "You are an honorable man," Ah Ling said as she sat down on a wooden stool, momentarily lost in a thought. She gazed up at the rows and rows of glass bottles containing the world's rarest foods—wild mountain ginseng, preserved abalone, caterpillar fungus—precious herbs that had been stored here since before World War II, suddenly remembering one afternoon back in the early eighties... _Su Yi had taken out a leather box from the vault filled with old medals that she wanted Ah Ling to polish with extra care. Most of them were honors given over the years to Su Yi's husband—his Order of the British Empire badge, a medal from the Knights of Saint John of Jerusalem, various decorations from Malay royals—but one medal stood out: an eight-point Maltese cross made of pewter, and at its center was a large amethyst._ _"What did Dr. Young receive this medal for?" Ah Ling asked, holding up the translucent gemstone to the light._ _"Oh, that wasn't his. This was given to me after the war by the queen. Don't bother to polish that," Su Yi answered._ _"How come I never knew you were honored by the queen?"_ _Su Yi huffed dismissively. "It wasn't very significant to me. Why would I care what the Queen of England thinks? The British abandoned us during World War II. Instead of sending more troops to defend the colony that helped to make them rich, they retreated like cowards and wouldn't even leave us with real weapons. So many young men—my cousins, my half brothers—died trying to hold back the Japanese."_ _Ah Ling nodded her head gravely. "So what did you get this medal for?"_ _Su Yi gave her a wry smile. "One night during the height of the occupation, I got careless. I was in the Botanic Gardens with a small group of friends, and none of us should have been there. The island was under curfew, and the gardens were locked up in the evenings—they were especially out of bounds. A patrol of Kempeitai—the vicious Japanese military police—came out of nowhere and surprised us. Now, a few of my friends couldn't risk getting caught by the Japanese—they were already on the wanted list—so I let them flee and allowed myself to be caught. I had protection papers, you see. Our family friend Lim Boon Keng had gotten me a special badge that was marked 'Overseas Chinese Liaison Officer,' and this meant that I could go about the island unmolested by the soldiers._ _"But these soldiers didn't buy my story—I told them that we were all just good friends out on a lark, but they still arrested me and took me to their commanding officer. When I saw I was being taken to a certain house on Dalvey Estate, I remember getting very anxious—this colonel was known for his brutality. He once shot a young boy on the street just because the boy didn't salute him in the correct manner. And here I was about to face him after committing a big offense._ _"When we got to the front door, some soldiers were coming out carrying a body that was covered by a bloody sheet. I thought it was all over for me then, that I was about to be raped or shot, or maybe both. My heart was racing a mile a minute. They dragged me into this sitting room, where I came upon the most unexpected sight. The colonel was this tall, elegant man sitting at the grand piano playing Beethoven. I stood there just watching him perform the entire piece, and when he had finished, for some reason I decided to speak first, something you were never supposed to do. I said to him, 'The Piano Concerto No. 5 in E-flat major is one of my favorites.'_ _"The colonel turned and gave me this piercing stare and said in perfect English, 'You're familiar with this piece? You know the piano? Play something for me.'_ _"He got up from the stool, and I sat down at the piano absolutely petrified, knowing what I chose to play could mean the difference between life and death. So I took a deep breath and thought, if I'm about to die, this is what I want to play. Debussy's 'Clair de Lune.'_ _"I played my heart out, and when I finished, I looked up from the piano and saw that there were tears in his eyes. It turns out that before the war, he had been in the diplomatic corps in Paris. Debussy was his favorite. He let me go, and twice a week for the next year, he made me come over to his house and play the piano for him."_ _Ah Ling shook her head incredulously at the story. "You were very lucky to get away like that. How did you and your friends get in to the Botanic Gardens in the first place?"_ _Su Yi gave her a sphinxlike smile, as if she was trying to decide whether or not to let her in on something. And then she shared her secret._ — Emerging from the memory of Su Yi's story, an idea began to form in Ah Ling's mind. She looked up at Vikram and said, "There is a secret about this house that even you don't know. Something from the war times." Vikram looked at her in surprise. Ah Ling continued, "Now, don't you have connections in the Khoo household?" "Sure, I know their head of security very well." "This is what I need you to do..." ··· Nick and Colin were spending the afternoon hanging out at Red Point Record Warehouse on Playfair Road, where they had spent countless hours listening to obscure records back when they were teenagers. As Nick flipped through the meticulously organized bins, he called out to Colin, "Did you know that the Cocteau Twins collaborated with Faye Wong?" "No way!" "Take a look at this," Nick said, handing him a record. While Colin read the liner notes to a rare EP recorded by the Hong Kong diva titled _The Amusement Park_ , his phone buzzed with a text message. He glanced at the screen and read a message from Aloysius Pang—the head of his family's security team—summoning him to his father's house to pick up a package ASAP. Colin wondered what this was all about, as it was highly uncharacteristic of Aloysius to summon him like this. "Hey Nick, I need to run over to my dad's place to pick up something that's apparently quite urgent. Do you want to stay here or come with?" "I'll come along. If I stay any longer I'll just end up buying the whole store," Nick replied. The two of them sped over to Colin's father's house on Leedon Road, a stately Georgian mansion that looked like it had been transported straight out of Bel Air, California. "Jeez, it's been years since I've been here," Nick remarked as they entered the house through the front door. A grandfather clock ticked loudly in the circular foyer, and all the curtains in the formal living room had been closed to block out the afternoon sun. "Is anyone home?" "My dad and stepmom are on a safari in Kenya at the moment," Colin answered, as a Filipino maid appeared from the corridor. "Is Aloysius here?" "No, but there's a package for you, Sir Colin," the woman replied. She went into the kitchen and returned moments later with a large padded envelope that didn't bear the markings of any courier service. "Who dropped this off?" Colin asked. "Sir, Mr. Pang, sir." He ripped open the envelope, and inside was a smaller manila envelope that was stamped PRIVATE & CONFIDENTIAL. There was a Post-it affixed to the front of it. Colin looked up at Nick in surprise. "This package isn't for me—it's for you!" "Really?" Taking the package, Nick saw that the Post-it note read: > Please give this letter by hand to your friend Nicholas Young. > > It is imperative that he receives it by tonight. "Well this is convenient! I guess whoever sent this knows I'm crashing at your place," Nick said as he began tearing into the sealed envelope. "Wait! Wait! Are you sure you want to do that?" Colin said. "Why not?" Colin glanced suspiciously at the package. "I dunno...what if there's anthrax or something in there?" "I don't think my life is as exciting as that. But here, why don't you open it?" "Fuck no." Nick laughed as he continued to open the envelope. "Has anyone told you that you have an overactive imagination?" "Dude, I'm not the one getting mysterious packages delivered to my best friend's house!" Colin said, taking a few steps back. * * * * Cantonese for "shit-eating bastard." # CHAPTER ELEVEN 28 CLUNY PARK ROAD, SINGAPORE Nigel Barker had photographed some of the most famous and beautiful women in the world, from Iman to Taylor Swift. But he'd never had a subject fly him halfway around the world in their personal Boeing 747-81 VIP before, and he had never gotten a lymphatic drainage massage and a seaweed exfoliating body wrap in a private spa on a private jet. Naturally, when he arrived at Kitty Bing's gracious heritage bungalow on 28 Cluny Park Road with his team of four photo assistants, there was yet another never-before-witnessed drama unfolding. A Chinese man wearing a deconstructed black Moroccan djellaba was standing on the front driveway, screaming, "CHUAAAAAAAAAAN! Where the fuck did you put the Oscar de la Renta? If you didn't pack it, I'm going to fucking skin you alive! CHUAAAAAAAAAN!" As he yelled, he bounced several inches off the ground, looking like a deranged Jedi. Twenty feet from the main house, a huge tent had been set up, and Nigel could see dozens of fashion assistants in white lab coats rushing from the house to the tent with various bits of clothing, while another set of assistants within the tent were going through the rolling racks filled with hundreds of ball gowns straight from the Paris catwalks. A guy in a white denim zip-up jumpsuit came running out of the tent. "We're still steaming it! It just arrived from New York thirty minutes ago!" " _Ka ni nah!_ I need the dress now, you good-for-nothing _goondu_!"* Nigel approached the ranting Jedi warily. "I'm assuming this is the location for the _Tattle_ photo shoot?" " _Wah laooooo!_ " The man gasped, putting his hands to his mouth. He suddenly stood ramrod straight, his face went from manic to Zen in a nanosecond, and his speech took on a pseudo-English-meets-Eurotrash accent. "Nigel Barker, it's really you! _Merde!_ You are even more dashing in person! How is that possible? I'm _Patric_ , the couture consultant. I'm styling the shoot today." "Pleasure to meet you," Nigel replied in a real English accent. Patric kept staring Nigel up and down. "It's an honor to be working with you! I've worked with Mert and Marcus, Ines and Vinoodh, Bruce and Nan, Alexis and Tico, I've worked with them all! Now come with me. We're having a minicrisis at the moment, but I think your presence will help calm things down!" They entered the house, which was filled with more staffers rushing around frantically at full speed. "As you know, Mrs. Bing has spared no expense on this shoot. Oliver T'sien flew in the top hairstylist from New York, the top makeup artist from London, and the top set designers from Italy for this shoot. Everyone's a top, and we're having to compete for space with all these tops. It's not how I usually like to work," Patric said with an arched eyebrow. Climbing up the beautiful Arts and Crafts–style wooden staircase, he led Nigel to the door of the library. "Brace yourself," Patric warned as he cracked open the door slowly. Inside, Nigel could see a woman seated in a hairdresser's chair in front of a bank of lighted mirrors, her face streaked in tears, surrounded by half a dozen stylists. "Kitty...Kitty...I have a little treat for you..." Patric cooed. Kitty looked in the mirror and saw them approaching. "Nigel! Nigel Barker! Oh no, this isn't how I wanted you to meet me for the first time. Look at my hair! Look what they've done! It looks terrible, doesn't it?" Nigel glanced at the floor quickly and saw that they had lopped off about ninety percent of her hair. Kitty now had a pixie hairstyle that actually looked incredibly chic. "Kitty, it's a pleasure to meet you, and I think you look wonderful." "See? We wanted a radical change, and this is a terrific look for you. It's very gamine," Oliver tried to reassure her in a calm voice. "You look like Emma Watson. Wait till we do the color," Jo the hairstylist said. "No, no, I'm not desirable anymore. I look like... _a mother_! Nigel, what do you think? Would you ever want to make love to me looking like this?" Kitty swiveled her chair around dramatically and gave him a piercing stare. Nigel hesitated for a moment. "Now, don't make things awkward for Nigel! He's a married man," said a blond woman with a British accent. "Hello, Charlotte, I didn't know you'd be here," Nigel said, giving the makeup artist a quick hug. Patric continued to reassure her. "Kitty, by the time Jo Blackwell-Preston is done with your hair color, Charlotte Tilbury is done with your makeup, I'm done pouring you into an amazing gown, and Nigel works his magic, you will look like the very definition of MILF! All the husbands and teenage boys who see you in these photos will want to take the magazine into the bathroom with them, trust me." "Kitty, remember what we discussed," Oliver said. "The entire point of this photo shoot is to reposition your image. You're not supposed to look like a high-fashion temptress anymore. You're going to look like a supremely elegant hostess who's not trying too hard to impress. A cultural force and a rising civic leader. Charlotte, think of those photos by Skrebneski of Jacqueline de Ribes in her Paris apartment. Or C. Z. Guest bending down to pet her poodle. Or Marina Rust on her wedding day. We want young, regal, comme il faut." "Ollie, we're going to comme-il-faut the hell out of her! Kitty, dry your tears. We need to give your face one of my emergency hyaluronic acid boosters right now, before it gets too puffy," Charlotte commanded. "And then we're going to add the subtlest sun-kissed highlights to your hair. You'll look like you just came back from a summer in the Seychelles!" Jo proclaimed. Two hours later, Kitty was posed on a Regency settee in front of _The Palace of Eighteen Perfections_ , the magnificent Chinese scroll painting she had purchased two years ago for a record-breaking $195 million. She was dressed in a pale pink Oscar de la Renta off-the-shoulder ball gown, the billowing duchesse satin skirt pooling gloriously around her, and on her head was a delicate Edwardian pearl headband. Gisele, in an adorable Mischka Aoki cornflower blue dress with feathers and cascading ruffles was positioned lying on the settee, one leg dangling and her head resting on her mother's lap. Harvard stood on the other side of his mother with his arms around her neck, looking precious in a white sailor suit with navy blue piping from Bonpoint and white socks that went up to his knees. At the foot of the settee lay a gleaming pair of Irish setters. Nigel had imagined Kitty's cover shot as a sort of modern-day re-creation of a Watteau portrait, and to achieve this he had brought all the way from New York the enormous Polaroid 20 x 24 camera. There were only six of these unique handmade cameras in the entire world, and so precious were the prints that every frame Nigel shot would cost $500. But the camera was somehow able to achieve an indescribable alchemy, creating images that were remarkably crisp and yet otherworldly. To go along with this concept, Nigel had confected an extraordinary blend of natural light fused with massive studio lights to create the sort of dappled, late-afternoon northern light straight out of an eighteenth-century atelier. "Gisele, you have the prettiest smile," Nigel remarked as he stared into his viewfinder. Harvard was distracted by the dogs and kept reaching down to try to pet them. "Harvard, give your mommy a kiss!" Nigel encouraged, and then at the precise moment, just as Gisele was relaxing into her smile, Harvard was planting kisses on his mother's cheek, and the sunlight was hitting the painting at just the right angle, Nigel asked, "Kitty, what are you thinking?" Her expression suddenly took on a faraway look, and Nigel clicked the shutter, knowing he had just captured the defining shot. Minutes later, the giant Polaroid was ready, and Toby, the first assistant, carefully placed the print on a special easel at the back of the room for all to see. "Oh that's the shot! It looks like a Sir Joshua Reynolds come to life! Isn't this the most perfect tableau you've ever seen?" Oliver said to Patric. "If only Nigel could join them in the photo. And take his shirt off. Then it would be perfect," Patric whispered back. "I'm speechless! It's sooooo gorgeous I can hardly believe it. Nigel, this is going to be our best cover ever!" gushed Violet Poon, the editor in chief of _Singapore Tattle_. "Oliver, I'll admit I thought you were out of your mind when you said you wanted to cut all her hair off. But it was a stroke of genius! Kitty looks so soigné! Like Emma Stone! She's positively regal now. I can already see the headline on the cover: _Princess Kitty!_ I'm going to take a picture of this glorious print for my friend Yolanda, since she so kindly allowed us to borrow her Irish setters for the shoot!" Violet snapped a picture on her phone and immediately sent it out in a text. Minutes later, she excitedly reported, "Yolanda is absolutely crazy about the photo!" "Would this be Yolanda Amanjiwo you're referring to?" Oliver asked. "The one and only!" "This is the woman who's so pretentious, she put a Picasso in her powder room right above the toilet so everyone has no choice but to notice it while they pee?" "She's really not like that, Oliver. Haven't the two of you met?" "I'm not sure she'd ever deign to meet me, since I don't have a title or my own plane." "Oh come on, Oliver. You know Yolanda would love to meet you. She's throwing one of her famous dinners tonight. I'll see if you can come," Violet said as she continued to text at warp speed. A few moments later, she looked up at Oliver. "Guess what? Yolanda wants to invite everyone to her dinner. You, Nigel, and especially Kitty." "No doubt she's heard about Kitty's three planes," Oliver quipped. "Oliver T'sien, don't be like that!" Violet scolded. Oliver approached Kitty, who was now posing languidly Madame Récamier–style in a vintage emerald-green-and-white-striped Anouska Hempel ball gown as Nigel and his team rearranged the lighting for a more dramatic evening look. "Do you think this pose works?" Kitty asked. "It's gorgeous. So, guess what they are going to put on the cover of _Tattle_ as a headline to your photo? 'Princess Kitty.' " Kitty's eyes widened. "Oh my God I love it!" "Annnnd...guess who has just invited you to dinner tonight? Yolanda Amanjiwo." Kitty couldn't believe her ears. "This is that lady _Tattle_ calls the Empress of Entertaining?" "The very one," Violet said excitedly. "I sent her a pic from your photo shoot and she's absolutely bonkers to meet you. See, your photo shoot isn't even out yet, and already you're the toast of the town, Princess Kitty! Please say you'll come tonight!" "Of course. I'll change my plans," Kitty said. She had planned a moonlight dinner cruise alone with Nigel, but this, she felt, was more important. "Splendid! Eight o'clock sharp, white tie." "White tie? In _Singapore_?" Oliver frowned. "Oh yes. You'll see. Yolanda does things on a grand scale. She entertains like no one else I know." — Several hours later, Oliver, Nigel, and Kitty found themselves in Yolanda Amanjiwo's drawing room, a vast space with black travertine floors that felt more like the lobby of a resort hotel than a home. Half the room was comprised of a reflecting pool that extended outdoors into an even larger pool, and from the middle of the pool rose an immense Jeff Koons gold _Balloon Dog_. Yolanda and her husband, Joey, stood at the far end of the room in front of a wide marble block that displayed a collection of ancient Apulian vases. As Kitty was led to the receiving line, she knew she had made the right choice by wearing a black off-the-shoulder vintage Givenchy gown with white satin gloves and her not overly flashy necklace of graduated diamonds ending in a teardrop canary diamond of forty carats. As she approached her hosts, flanked by her debonair escorts in their white-tie tuxedos, a butler announced in a high, nasal tone, "The Honorable Oliver T'sien, Mr. Nigel Barker, and Mrs. Jack Bing." Yolanda was a tall, thin woman with a gravity-defying bouffant hairdo, clad in a dramatic strapless scarlet column gown that Kitty recognized to be Christian Dior couture. She had obviously chosen her plastic surgeon with meticulous care, since she possessed one of those faces that looked perfectly taut and sculpted, but not a single muscle moved when she spoke. Which was a pity, since she spoke in an exceedingly warm, rapid-fire Indonesian accent. "Oliver T'sien we meet at last I am such an admirer of your family and of course your grandfather was such a great man so revered Nigel Barker how lovely to meet you my God what a beauuuuuuutiful set of pictures you took today can I commission you to please do a portrait of my Irish setters?" "Actually, I did take some pictures of just the two of them. I'm having them printed as a gift to you." "Oh my goodness Joey did you hear that Nigel Barker did a portrait of Liam and Niall and we didn't even have to pay him a million bucks!" Yolanda prodded her husband frantically, who looked like he was in the midst of waking from a long coma. "Ummm" was all the short, paunchy man said, his eyelids heavy. "And you must be the divine Kitty Bing I have heard so much about you and my God what a divine dress it must be a classic Givenchy and that party you threw during Shanghai Fashion Week ooh la la I wish I had been there Karl Lagerfeld told me your new villa is to die for and your plane the big one has a spa in it my God what a genius idea I must visit I absolutely must!" "Thank you. Of course you'll have to visit my spa—we call it the mile-high spa." "Hahahehe mile-high spa you're too funny oh my goodness Kitty I know we are going to be dear dear friends." As the Amanjiwos continued to greet the arriving guests, Kitty broke into a big smile as she spotted Wandi Meggaharto Widjawa arriving. "Kitty!" Wandi screamed from across the room, as the two ladies ran to hug as though they hadn't just seen each other yesterday. "What are you doing here?" Kitty asked excitedly. "Joey's my cousin. I always get invited to these dinners because Yolanda needs me to sit beside him to keep him awake. Look at you! I love the new hairstyle. You look like Emma Thompson! How did the shoot go today?" "It was fantastic. I couldn't be happier." "Well I'm so happy to see you here! We're going to have such a good time! You know, Joan Roca i Fontané is the celebrity chef tonight. He has the top restaurant in the world right now—El Celler de Can Roca. It's so hard to get a reservation, you have to murder someone to get on the list. I wonder who else Yolanda invited? Oh look who's here—it's the First Lady of Singapore!" Kitty looked over and saw Oliver greeting the First Lady as if they were both embarrassed to be seeing each other at the party. "You are among the crème de la crème of Singapore now, Kitty. These parties are so exclusive that no photographers are ever allowed," Wandi said, just as a roving photographer dressed in a black tuxedo flashed his camera at them. "That's Yolanda's personal documentarian. It's not for the public," Wandi quickly explained. "Oh look, here come the footmen—this means we are adjourning to the dining room!" A set of grand double doors were opened, and as Kitty walked through the arched doors, her eyes widened in wonder. She felt as if she had been transported back to a royal banquet in eighteenth-century France. The room was a mirrored chamber decorated with baroque gold boiseries, gilt bronze mirrors stretching from floor to ceiling, and dozens of candlelit crystal chandeliers. An immense dining table that seated thirty stretched along the middle of the room, heaving with Meissen china, gilt silverware, and towering gold birdcage centerpieces filled with white doves. The room sparkled under the light of thousands of candles, and footmen with powdered white wigs and dressed in black-and-gold livery stood behind every Amiens tapestry-covered chair. "Hashtag madamedefuckingpompadour!" Oliver muttered under his breath. "Yolanda had this dining room rescued from an old crumbling palace in Hungary and transported here piece by piece. It took three years to restore it to its former glory," Wandi proudly announced. "Can we do this at my house? Find an old palace and transport the dining room over?" Kitty whispered to Oliver. Oliver cast Kitty a disapproving look. "Absolutely not! Alexis de Redé would be projectile vomiting in his grave if he saw this travesty." Kitty didn't have a clue what he meant, but she was only too thrilled to be shown to her seat by a handsome footman, where her place card was a small antique gilt mirror with her name etched in glass. As she was about to sit down, the man beside her grabbed her arm. "Madame, not yet. We don't sit until the First Lady has been seated. Yolanda follows the official court protocols here," he said in a Scandinavian accent. "Oh, sorry, I had no idea," Kitty said. She stood by her seat, watching everyone stand at their places. Finally, the butler standing by the double doors announced, "The Honorable First Lady of the Republic of Singapore!" The First Lady entered and was shown to her seat. Kitty's five-inch Gianvito Rossi heels were beginning to kill her and she couldn't wait to sit down, but the First Lady perplexingly remained standing by her seat near the head of the table. Why the fuck was everyone still standing? The butler entered the room again and called out in a booming voice, "The Earl and Countess of Palliser!" Kitty's eyes widened in shock as a tall blond man entered the room, dressed casually in a button-down shirt, khaki chinos, and a rumpled navy blazer. By his side was Colette, dressed in a long white cotton eyelet dress with her hair pulled into a casual ponytail. She didn't appear to be wearing any makeup, and her only jewelry was a pair of pearl-and-coral drop earrings. After reacting to the shock of seeing her nemesis in Singapore, Kitty wanted to laugh out loud at how inappropriately Colette was dressed. This stepdaughter of hers was a complete disgrace. Did Colette even know where she was? And then, to Kitty's horror, the First Lady of Singapore performed a deep curtsy. Yolanda Amanjiwo and all the other guests in the room quickly followed suit—the men bowing low and the women dropping curtsies as the Earl and Countess of Palliser were led to the place of honor. * * * * Don't quote me on this, but I believe a _goondu_ is the Malay cousin of a _goondusamy_ (India), which is in turn distantly related to a _goombah_ (Jersey Shore and certain suburbs of Long Island). # CHAPTER TWELVE BOTANIC GARDENS, SINGAPORE It was still dark when Colin and Nick entered the grounds of the Botanic Gardens.1 They followed to a tee the instructions in the mysterious letter that Nick had received—parking in the Gleneagles Hospital parking lot and crossing Cluny Road to enter the gardens through a little-known side gate. Just as the letter had said, the gate had been left unlocked. As they walked down the tree-lined pathway, monkeys could be heard chattering and leaping through the bushes, no doubt alarmed by the sudden presence of humans in this secluded part of the garden. "God, it's been years since I've been here," Nick commented. "Why would you come here? You had your own private botanic gardens right next door!" Colin said. "Sometimes my dad and I would go on walks here, just for a change, and I only wanted to go to the lake with the two islands in the middle. I called it my 'secret island.' Wait a minute, let's check the instructions again," Nick said, unfolding the map that had been placed inside the envelope. Colin held his iPhone up to provide some lighting, while Nick peered at the map intently. "Okay, the animal topiaries are over on the right, so I think we're supposed to cut through this grove of trees right here." "There isn't any path," Colin said. "I know, but the arrow points down this way." Lit only by the light of their phones, they ventured into the thick of the forest, Colin feeling a little creeped out. "It's pitch-black in here. Why do I feel like I'm suddenly in _The Blair Witch Project_?" "Maybe we'll run in to a _pontianak_ ,"2 Nick joked. "Don't joke—a lot of people say that parts of the Botanic Gardens are haunted, you know. I mean, the Japanese tortured and killed people all over the island." "Good thing we're not Japanese," Nick said. Soon the trees gave way to a trail, and after following it for a few minutes, they came upon a small concrete hut under an enormous casuarina tree. "I think this is it. It's some sort of pump room," Nick said, trying to peer in through the darkened windows. Suddenly a dark figure darted out from behind the tree. " _Pontianak!_ " Colin yelled, dropping his iPhone in panic. "Sorry, it's just me," a female voice said. Nick flashed his iPhone in the direction of the figure and suddenly before them, illuminated in the white blue light, appeared Astrid in an audaciously large Vetements hoodie with super-long sleeves and tight camouflage pants. "Jesus, Astrid! I almost shit myself!" Colin exclaimed. "Sorry! I was scared for a moment when you first walked up, and then I realized it was you guys," Astrid said. Nick smiled in relief. "I'm assuming you got the same note I did about seeing Ah Ma?" "Yes! It was all rather mysterious. I was at my parents' watching Cassian swim in the pool. I must have dozed off in my deck chair for a moment, because when I got up, there was a tray of iced tea and pandan cake by my side, and the envelope was under the cake. Cassian swears he didn't see who put it there." "How curious. Are you okay?" Nick asked. "I'm fine. It didn't really spook me." Just as Astrid said this, a light came on inside the pump room and the three of them jumped a little in shock. The steel door could be heard being unlocked from the inside, and as it opened with a loud rusty creak, a turbaned silhouette could be seen peeking out. "Vikram!" Nick said excitedly. "Come quickly," Vikram instructed, ushering them all in. "What is this place?" Astrid asked. "This is the pump room that controls the intake for the two ponds," Vikram said as he led them toward the back of the space, which was cramped with machinery. Behind a large round pipe going into the ground, a barely discernable panel opened to reveal a dark gaping void. "This is where we're going. Each of you take turns—there are ladder rungs against the inner wall of this pipe." "Is this what I think it is?" Nick said in astonishment. Vikram smiled. "Come on, Nicky, you go first." Nick hauled himself into the small crawl space and climbed down what seemed like a dozen or so rungs. After landing on solid ground, he helped Astrid find her footing as she descended the steps. When the four of them finally made it down, they found themselves in a small steel-walled vestibule. An old sign nailed against one wall read in English, Chinese, and Malay: > DANGER! NO OUTLET! > > CHAMBER WILL FLOOD DURING VALVE RELEASE! Vikram pushed against one of the wall panels, and it opened to reveal a well-lit tunnel. Nick, Astrid, and Colin entered with mouths agape, stunned by the existence of such a space. "No. Fucking. Way!" Colin exclaimed. "This tunnel leads to Tyersall Park, doesn't it?" Nick asked excitedly. "It goes right under Adam Road and puts us within the grounds of the house. Let's go, we don't have much time," Vikram said. As they made their way through the tunnel, Nick looked around in wonderment. There were spots of mold along some of the concrete walls and the ground was caked in a layer of dirt, but overall the tunnel was remarkably well preserved. "When I was a little kid, my father used to tell me stories about how there were secret passages in Tyersall Park, and I just thought he was pulling my leg. I begged him to show me one, but he never would." "Did you always know this was here?" Astrid asked. "Not until yesterday," Vikram said. "Ah Ling told me about it. Apparently this tunnel was used during the war by your great-grandfather Shang Loong Ma. That's how he got in and out of the property and was never once caught by the Japanese." "I've heard there are tunnels similar to this. There's supposedly one that leads from Uncle Kuan Yew's house on Oxley Road to the Istana," Astrid commented. "I just never imagined Tyersall Park would have one too." "Incredible! I can't believe this whole elaborate plan—just to see your grandmother!" Colin remarked to Nick. "Yes, apologies for all the cloak-and-dagger. Ah Ling and I needed to devise a way to get messages to the both of you without incriminating ourselves. Tyersall Park has been on complete lockdown for the past few days, as you are well aware," Vikram said with a grin. "I'm so grateful, Vikram." Nick smiled back at him. They arrived at the end of the tunnel and faced another set of rungs. Nick went first, and when he was out of the shaft, he looked down at Astrid as she climbed up. "You'll never believe where we are!" Astrid climbed out of the shaft and found herself standing in the middle of hanging orchid plants. They were in their grandmother's orchid conservatory, and the large round stone table carved with griffins at its base in the middle of the conservatory rolled to the side to reveal the entrance into the tunnel. "I've spent countless hours sitting at this table, having afternoon tea with Ah Ma!" Astrid exclaimed. Standing on lookout at the door of the conservatory was Ah Ling. "Come, come, let's get in before it gets light and people start waking up." When they were all safely ensconced inside Ah Ling's room in the servants' quarters, she wasted no time in explaining her plan. "Colin, you should stay here in my room, out of sight. I will take Astrid and Nicky up to Su Yi's bedroom. I know a special route that will let us enter from the balcony outside her dressing room, and Astrid, you should go in alone first and be with her when she awakes. She will usually wake up after you draw the curtains open. She'll be pleased to see you, and then you can tell her that Nicky is outside waiting to see her. This way she won't get a shock if she wakes up and sees Nicky standing right there." "Good thinking," Nick said. "Madri and Patravadee know about the plan. They are stationed right outside her door in the sitting room. Usually the nurses will check on her every fifteen minutes, but today they will block the nurses from entering. Professor Oon usually does his first check-in at seven thirty. Now, Astrid, I am counting on you to be outside Su Yi's bedroom at seven thirty to intercept him. I've seen how he defers to you." Astrid nodded. "Don't worry, I'll deal with Professor Oon." "The other thing is Eddie. These days he likes to be the first to visit Su Yi in the morning. But I got Ah Ching to make his favorite crepes with Lyle's Golden Syrup this morning, so I will tell him he needs to eat them while they are hot. I'll try to keep him at breakfast as long as possible." "Maybe you can slip a sedative into his crepe batter," Nick suggested. "Or something to give him explosive diarrhea," Colin said. They all laughed for a moment, and then Ah Ling got up from her chair. "Okay, everyone ready?" Nick and Astrid proceeded up the servants' staircase to the second floor, following quietly behind Ah Ling as she expertly guided them through the service hallways until they found themselves on the balcony outside Su Yi's dressing room. Astrid opened the door as quietly as she could and tiptoed in. The cool, mosaic-tiled space adjoining Su Yi's bedroom smelled of jasmine and lavender water. She stood by the doorway, peeked into her grandmother's bedroom, and saw Su Yi's lady's maids silently prepping the room for the morning. Madri was spritzing a beautiful pot of orchids with water, while Patravadee was tidying up the nurses' station. The minute they saw Astrid, they nodded at her and pulled the curtains open. Then the two ladies slipped out of the bedroom, closed the door behind them, and stood guard diligently outside. A nurse could be heard behind the door asking, "Is Mrs. Young awake yet? Are you getting her breakfast?" One of the lady's maids replied, "She wants to sleep a little longer today. We will send for her breakfast after eight." Astrid headed first to the side table, opened a bottle of Adelboden water, and refilled one of the cups. Then she took it over to Su Yi's bedside and sat down in the chair beside her. Su Yi's eyelids fluttered open, her eyes hazily registering Astrid beside her. "Good morning, Ah Ma," Astrid said cheerily. "Here, drink some water." Su Yi accepted the water gratefully, and after satiating her parched throat, she looked around the room and asked, "What day is it today?" "It's Thursday." "Did you just return from India?" "Yes, Ah Ma," Astrid fibbed, not wanting to cause her grandmother any undue concern. "Let me see your ring," Su Yi said. Astrid held her hand up to show her grandmother her engagement ring. Su Yi studied it carefully. "I knew it would look perfect on you." "I don't know how to thank you for this, Ah Ma." "Did everything go according to plan? Did Charlie manage to surprise you?" "Yes, I was so stunned!" "Were there elephants? I told Charlie he needed to arrive on an elephant. That's how my friend the Maharaja of Bikaner proposed to his queen." "Yes, there was an elephant." Astrid laughed, realizing just how involved her grandmother had been in helping to plan the whole affair. "Are there any pictures?" "No, we didn't take any...oh, wait a minute." Astrid took out her phone and did a quick google search for the paparazzi photos that had been leaked of her private moment. She never imagined how useful they would be until this moment. As she showed a few of the snapshots to her eager grandmother, she thought how ironic it was that the rest of her family was so upset by what was one of the happiest moments in her life. Su Yi sighed. "It looks beautiful, I wish I could have been there. Charlie looks so handsome in his outfit. Tell me, is he in Singapore now?" "Actually, he'll be coming to town tomorrow. He comes to visit his mother every month." "He's a good boy, that one. I knew from the moment I met him that he will always take good care of you." Su Yi stared at the grainy shot of Charlie putting the ring on Astrid's finger. "You know, of all the jewelry I own, this ring is the most special to me." "I know, Ah Ma." "I never got the chance to ask your grandfather if he bought it." "What do you mean? Who would have bought this engagement ring, if not him?" "Your grandfather did not have that much money when I first met him. He was just a recent medical graduate. How on earth would he have been able to afford this canary diamond?" "You're right. It would have cost a fortune at the time," Astrid said. "I always suspected that Uncle T'sien Tsai Tay was the one who bought it, since he helped to broker the marriage. The quality of the stone isn't perfect, but when I wore it, it always reminded me of how life can surprise you. Sometimes, the thing that at first appears flawed can end up being the most perfect thing in the world for you." Su Yi was silent for a few moments, and then she looked at her granddaughter with a sudden intensity. "Astrid, I want you to promise me something." "Yes, Ah Ma?" "If I die before your wedding day, please don't go into all that mourning nonsense for me. I want you to have your wedding just as you planned in March. Will you promise me you'll do that?" "Oh Ah Ma, nothing's going to happen. You're go...going to be sitting in the front row of my wedding," Astrid stammered. "I'm planning on it, but I wanted to say this just in case." Astrid looked away, trying to hold back her tears. She sat there holding her grandmother's hand for a few quiet moments, before she said, "Ah Ma, you know who's back in Singapore to see you? Nicky." "Nicky's home?" "Yes, he's here. In fact he's right outside. Do you want to see him now?" "Send him in. I thought he was going to be here last week." Astrid got up from her chair and was about to head for the dressing room when her grandmother said, "Wait a minute." Astrid stopped in her tracks and turned around. "Yes?" "Is his wife here as well?" Su Yi asked. "No, it's just him." Astrid paused for a second, anticipating another question from her grandmother. But Su Yi was now fidgeting with the bed controls, raising the incline of her bed to the exact angle she wanted. Astrid proceeded to the balcony, where she found Nick sitting pensively at the wrought-iron table. "Is she awake?" he asked. "Yes." "How is she?" "She's okay. A lot better than I was expecting, actually. Come on, your turn." "Um...she really wants to see me?" Nick asked trepidatiously. Astrid smiled at her cousin. For a moment he looked like he was six years old again. "Don't be ridiculous. Of course. She's ready for you now." * * * 1 Declared a UNESCO World Heritage Site in 2015, the Singapore Botanic Gardens is cherished by locals in the same way Central Park is by New Yorkers or Hyde Park is by Londoners. A verdant oasis in the middle of the island filled with amazing botanical specimens, colonial-era pavilions, and one of the most amazing orchid collections on the planet, it's no wonder that so many Singaporeans want to have a tiny bit of their ashes scattered here. In secret, of course, since it's highly illegal. (No one escapes the law in Singapore, not even the dead.) 2 If you read _China Rich Girlfriend_ , you'd already know what a _pontianak_ is. But just in case you haven't (and why the hell haven't you?), allow Dr. Sandi Tan, the world's foremost pontianakologist, to elucidate you: "A tropical female vampire-slash-dryad combo, often assuming the form of a comely, sarong-draped maiden, who inhabits the darker corners of the Southeast Asian jungle. Her metamorphosis into her true form will reveal: putrefying gray flesh, mucho teeth, many claws, accompanying unpleasant odors. Her traditional prey is the unborn fetus of a pregnant woman, consumed in situ, though during severe hunger pangs, any living person—even flatulent, stringy grandpas—would suffice. She can be summoned by tying a white string between two adjacent banana trees and intoning a chant of your own choosing, but she is more than capable of being an independent operator. Must not be confused with her inelegant country cousins, also female bloodsuckers, the _penanggalan_ (bodiless flying she-demon with long, unwashed hair and a meaty chandelier of entrails) and the _pelesit_ (an all-purpose slave, horrendously and pathetically devoted to her conjuror, with no agency of her own)." # CHAPTER THIRTEEN CHANGI AIRPORT, SINGAPORE Oliver had just boarded his flight to London and was in the process of stealing an extra pillow from the seat behind him when Kitty called. "Morning, Kitty," he said cheerily, steeling himself for the barrage he knew was about to come. "Did you sleep well?" "Are you fucking kidding me? That was the worst night of my entire life!" "I know several billion people who would have happily traded places with you, Kitty. You got to attend one of Yolanda Amanjiwo's legendary dinners. The world's most acclaimed chef prepared a twelve-course tasting menu for you. Did you not enjoy that? I thought the langoustines were superb—" "Ugh! That so-called genius chef from that de la cellar place should be locked in his own cellar and they should throw away the key!" "Come on, aren't you being a bit harsh? Just because you don't appreciate deconstructed surrealist Catalan fusion cuisine doesn't mean you should sentence him to the gallows. I could have eaten ten more plates of that _jamón ibérico_ flash-frozen fried rice." "How could I possibly appreciate the food when I was being tortured? I've never been more humiliated in my life!" Kitty seethed. "I don't know what you mean, Kitty," Oliver said lightly as he took the stack of in-flight magazines out of the seat pocket and shoved them into the pocket adjacent to him before the passenger arrived. Anything for the extra legroom. "Everybody at the dinner curtsied to Colette! That snotty Swedish ambassador guy next to me glared at me when I didn't move, but I'll be damned if I curtsy to my own stepdaughter!" "Well, Thorsten obviously did not know who you were. And Kitty, that whole curtsying thing was a complete farce. I don't know which edition of _Debrett's_ Yolanda Amanjiwo is reading, but she was absolutely incorrect. A British earl does _not_ have precedence over the First Lady of the country where he is nothing more than a visitor. They should have been bowing to _her_. But these Singaporeans are so awed by any _ang mor_ with a two-bit title that they just bow and scrape away like subservient little toadies. I remember a time when the Countess of Mountbatten came to visit Tyersall Park, and Su Yi wouldn't even come downstairs to receive her!" "You're missing the point. Everyone treated Colette like royalty all through the dinner. They were dressed like peasants and the people were still sucking up! That idiot on my right wouldn't even lift his fork until Colette lifted her fork. And then the minute she was done with her dinner, we all had to stop. That Carolina Herrera–perfumed flan was the first thing I was actually enjoying, but then dinner abruptly ended and the royal couple was off." "The last thing I thought I'd ever wanted to eat was a dessert that tasted like Carolina Herrera, but it was superb, wasn't it? Well, aren't you at least glad the dinner passed with no incident? Colette didn't try to insult you or cause a scene." "No, what she did was worse—she didn't even acknowledge my presence! And I'm married to her father! The man who pays all her bills even though she won't talk to him anymore! Do you know how hurt he feels? That ungrateful, spoiled little beast!" "Kitty, I wouldn't take it so personally if I were you. There were thirty of us in that ghastly room, sixty if you count the ridiculous footmen, and Yolanda was dominating every minute of Lucien and Colette's time. Trust me, I was right opposite from them. You were on the other end of the table hidden behind those ridiculous birdcage centerpieces—I honestly don't think she even saw you." "Colette saw me, I can assure you. She doesn't miss a thing. Why was she even in Singapore anyway?" "Lucien is an environmentalist, and they are going to be based in Singapore for the next month, that's all. They're on their way to Sumatra to observe the orangutan situation." "What orangutan situation?" "Oh, it's quite a tragedy. Thousands of orangutans are dying because of deforestation in their natural habitats. Colette's become quite involved in orangutan orphan rescue." "That's what you talked about? There was no mention of me? Of her father?" "Kitty, I can assure you that the only people that were mentioned by name happened to be orangutans." "So she doesn't know you and I have a connection?" "She doesn't. But what would it matter anyway? Why didn't you just come over and say hi? Be the bigger person and welcome her to Singapore? That would have been the smart move," Oliver said as he struggled to tuck his leather valise under the seat next to him. "Hnh! I am her stepmother! She should introduce herself to _me_ , not the other way around!" "Wait a minute...are you saying you've never met Colette?" Oliver was genuinely shocked. "Of course not! I told you, she hasn't seen her father since she found out about our affair. And she wouldn't come to the wedding. She hasn't set foot in China in more than two years. She told him that he...that he was marrying a whore." Oliver could hear the tears in her voice, and he began to see the situation in a whole new light. No wonder Kitty had been traumatized when Colette made her grand entrance last night. In China, Kitty had been eclipsed by Colette in absentia, and here in Singapore, she had been eclipsed again in an even more dramatic fashion. A flight attendant gestured to Oliver. "Kitty, my flight to London is about to take off now, so I have to put away my phone." "Oh really? I thought no one cared if you use your phone in first class." "Well, you don't know this, but I'm one of those aviation geeks that actually likes to watch the safety demonstration." "I didn't know you were off to London again. You should have told me—I would have lent you one of my planes." "That's very kind of you. Kitty, I'm going to spend the next fourteen hours on this flight coming up with a plan. I promise you, Colette will never humiliate you again." "You promise?" "Absolutely. And look on the brighter side...you have so much to look forward to. Your _Tattle_ cover is coming out next month. You will be an absolute sensation, I tell you! And you're besties with Yolanda Amanjiwo now. This is just the beginning for you, Kitty. Colette has to head back to some drafty old manor in England, while we are designing you the most spectacular house Singapore has ever seen." Kitty sighed. Oliver was right. There was so much to look forward to. She put down her phone and looked in the small gilt mirror that was given to her as a party favor last night. She did look a bit like Emma Watson, that actress who played Hermione Granger. And Oliver with his big round spectacles looked a bit like Harry Potter. Oliver really was a kind of wizard. And now he was going to wave his wand and bring even more magic into her life. On the SQ 909 flight to London, Oliver turned off his phone and tucked it into the seat pocket. A flight attendant suddenly leaned into his row. "Excuse me? Is that an extra pillow I see? I'm afraid I'm going to need that," she said with an apologetic smile. "I'm sorry, I didn't even see it," Oliver lied. "And is that your leather bag? I'm also going to have to ask you to tuck it under your own seat. Make sure the straps are tucked in completely. We have a very full cabin here in economy class today," the stewardess said. "Oh, of course," Oliver said, as he bent down to retrieve his bag, cursing silently. It was going to be a very long flight. # CHAPTER FOURTEEN TYERSALL PARK, SINGAPORE The morning light filtering through the windows made the mahogany art deco furniture in Su Yi's bedroom glow like amber, and Nick was shocked for a moment to see how tiny and frail his grandmother looked in the middle of her hospital bed, the machines clustered around her like an army of invading robots. It had been almost five years since he had seen her, and now a tremendous sense of remorse descended over him. How had he let so much time pass? He had lost five precious years because of a quarrel, because of his pride. As Nick approached her bed, he was temporarily at a loss for words. Astrid stood by Nick's side for a moment, and then she announced in a gentle voice, "Ah Ma, here's Nicky." Su Yi opened her eyes and gazed up at her grandson. _Tien, ah. He looks more and more like his grandfather every day_ , she thought to herself. "You look even handsomer than before. I'm glad you haven't put on any weight. Most men put on weight after they get married—look how bloated Eddie has become." Nick and Astrid both laughed a little, breaking the tension in the room. "I'll be back in a while," Astrid said, quietly slipping out through the bedroom door. No sooner had she closed the door behind her than Professor Oon entered Su Yi's sitting room. "Good morning, Professor Oon," Astrid said cheerily, blocking his way. The doctor was momentarily taken aback. It had been more than a week since he had seen Astrid, and he couldn't believe how she was dressed today. Holy Annabel Chong! She looked even sexier than he could have possibly imagined in this skater punk outfit and those bootylicious camouflage pants. It was better than any Japanese-schoolgirl porn site. Was she wearing a sports bra under that big hoodie? Her body was a work of God. Recovering himself, Professor Oon put on his blasé, clinical tone. "Ah, Astrid. Welcome back. I was just about to run the morning vitals on your grandmother." "Oh, don't you think that can wait for a moment? Why don't you give me an update first, since I've been away? Ah Ma seems rather well this morning. Could her condition be improving?" Professor Oon frowned. "It's possible. We put her on a new cocktail of beta-blockers, and she's benefited from a sustained period of rest." "I'm soooo grateful for all you've done," Astrid said warmly. "Um, yah. After I look at her latest EKG, I'll be able to give you a more accurate prognosis." "Tell me, doctor, have you heard of a specialist at St. Luke's Medical Center in Houston named David Scott? Dr. Scott has developed an experimental new treatment for congestive heart disease," Astrid continued, not letting him off the hook. _Wow, beauty and brains. A woman who can talk so seductively about heart disease_ , Professor Oon thought. That damn Charlie Wu was one lucky prick. If only Astrid came from another family, if only she wasn't so bloody rich, she could be his mistress. He would set her up at his secret apartment at The Marq and watch her do laps, naked, in the pool all day. — Inside the bedroom, Nick was wondering what precisely to say to his grandmother. " _Nay ho ma?_ "1 he said, and then immediately wondered why he had asked her such a stupid question. "I haven't been too well. But today I'm feeling better than I have in many weeks." "I'm so glad to hear that." Nick crouched beside Su Yi and looked her squarely in the face. He knew that the moment had come for him to deliver his apology. As much as he had been hurt by her, and as much as he felt that she had wronged Rachel, he knew that it was his duty to ask for her forgiveness. He cleared his throat and began, "Ah Ma, I'm so sorry for the way I behaved. I hope that you can find it in your heart to forgive me." Su Yi looked away from her grandson and let out a long slow exhale. Nicky was home. Her dutiful grandson was by her side again, kneeling at her feet and asking for redemption. If only he knew how she truly felt. She was quiet for a few moments, and then she turned to face him again. "Are you comfortable in your bedroom?" "My bedroom?" Nick asked, momentarily confused by her question. "Yes, has it been made up nicely for you?" "Um, I haven't been staying here. I've been at Colin's." "On Berrima Road?" "No, Colin's family sold that house a few years ago. He's living in Sentosa Cove now." "Why on earth are you staying there and not here?" It dawned on Nick at that moment that his grandmother didn't have a clue that he'd been back for over a week. She obviously had nothing to do with banning him from Tyersall Park! He wasn't sure what to say at first, but then quickly recovered himself. "There are so many people visiting at the moment, I didn't think there would be room for me." "Nonsense. No one is supposed to be in your bedroom." Su Yi pushed a button beside her, and within a few seconds Madri and Patravadee were by her bedside. "Please tell Ah Ling to have Nicky's rooms made up. I have no idea why he is staying at some godforsaken place instead of here," Su Yi instructed her lady's maids. "Of course, ma'am," Madri replied. At that moment, Nick realized that this was his grandmother's tacit manner of forgiving him. He felt suddenly lighter, as if a gigantic boulder had been lifted off his back. As Su Yi's lady's maids stepped out of the bedroom, Adam and Piya walked into the sitting room and for a few seconds before the bedroom door closed saw their cousin Nick crouched by his grandmother's side. Astrid waved from the settee where she was seated talking with Professor Oon. "Adam! It's so good to see you!" "Oh Astrid, I'm sorry, I didn't see you over there. Piya, this is my cousin Astrid. She's Auntie Felicity's daughter." "I've heard so much about you," Piya said with a smile. "Was that Nicholas I saw in there with Ah Ma? We were just going to have a quick look-in before breakfast," Adam said. "Nicholas Young?" Professor Oon said in alarm. "He's in the bedroom? But we are under strict orders not to—" "Francis, hold that thought for one minute," Astrid said, placing her hand on his lap, her fingers almost grazing his inner thigh. The doctor trembled at her unexpected touch and immediately went mute. Astrid turned to Adam and Piya and said, "I'm sure Ah Ma would love to see you in a little while. She's doing much better this morning. Why don't you head down to breakfast first? I hear that Ah Ching is making her famous crepes." "Ooh, I do love a good crepe," Piya said. "Me too. And Ah Ching makes a special sauce of Belgian chocolate and Lyle's Golden Syrup to drizzle over them. Professor Oon, have you ever had chocolate-infused golden syrup drizzled over your crepes?" "Er, no," the doctor said, sweat beginning to bead around his temples. "Well you must. In fact why don't you join us right now? Let's all go down for some crepes. I'm sure the whole family would love to have an update from you about Ah Ma," Astrid said, getting up from the settee. The three of them stood there, waiting for the doctor. "Um, give me a minute," Professor Oon said sheepishly. He knew that there was no way he could stand up at that moment. — Back in the bedroom, Su Yi had instructed Nick to go to the top drawer of her bureau and fetch something for her. "Do you see the pale blue box?" "Yes." "At the bottom of the box are some silk pouches. Please bring me the yellow one." Nick unfastened the metal clasp on the blue embossed leather box and flipped open the lid. Inside was an assortment of objects and curiosities. Vintage tortoiseshell combs and coins of varying currencies mixed in with letters and faded old photographs. He came upon a small stack wrapped with a piece of ribbon and realized that it was every picture he had ever sent to her from his boarding-school days in England. At the bottom of the box were several jewelry pouches, the kind made of padded silk that one saw in Chinatown trinket shops all over the world. He found a small yellow pouch and returned to his grandmother's bedside. Su Yi unzipped the pouch, took out a pair of earrings, and placed them in the palm of Nick's hand. "I want you to have these. For your wife." Nick felt a lump in his throat as he realized the enormous significance of her gift. His grandmother was acknowledging Rachel as his wife for the very first time. He glanced at the earrings in his palm. They were simple pearl studs set on old-fashioned gold posts, but the luminosity of each pearl was stunning—they seemed to glow from within. "Thank you, Ah Ma. I know Rachel will love these." Su Yi looked her grandson in the eye. "My father gave these to me when I escaped Singapore before the war, when the Japanese soldiers had finally reached Johor and we knew all was lost. They are very special. Please look after them carefully." "We will cherish them, Ah Ma." "Now, I think it's time for my morning pills. Will you call Madri and Patravadee in?" — In the breakfast room, Ah Ching had set up a cooking station at the end of the long dining table. Rather unusually, she eschewed the use of a crepe pan to make her beloved recipe. Instead, she cooked them on her trusty wok, expertly tilting and twisting the large black wok to create the perfect round thin pancakes. Eddie had woken up Fiona and the kids for this special treat, and his mother, Victoria, Catherine, and Taksin were assembled in the room as well, eagerly awaiting their custom-made crepes. "Can I have mine with some ham and cheese?" Taksin asked. "I prefer savory ones to sweet ones, especially in the morning." "Uncle Taksin, you're missing out if you don't try the fabulous sauce that Ah Ching makes," Eddie said. "I want mine with ice cream," young Augustine said. "Augie, you will eat them exactly as I instruct you to!" Eddie barked at his son. Catherine exchanged glances with Alix, who simply rolled her eyes and shook her head. As the family began tucking into the first round of crepes, Astrid entered the dining room with Adam, Piya, and Professor Oon. "What are you doing here?" Eddie said, startled by his cousin's sudden appearance at the house. He thought she had been ordered to stay away by her parents since the India engagement scandal. "I'm having crepes, just like you," Astrid replied breezily. "Well, I suppose _some of us_ don't have any shame," Eddie muttered under his breath. Astrid chose to ignore her cousin and went over to greet her aunties with pecks on their cheeks. Victoria stiffened visibly as Astrid kissed her and asked, "How is your mother? I hear she's been bedridden for the past two days." Implicit in her disapproving tone was that Astrid was the one responsible for making her mother sick. "Considering the fact that she managed to play bridge for five hours yesterday with Mrs. Lee Yong Chien, Diana Yu, and Rosemary Yeh, I think she's doing just fine," Astrid replied. Alix wondered what the doctor was doing at their breakfast table, but ever well mannered, she smiled graciously at her old classmate and said, "Francis, how good of you to join us." "Er, Astrid insisted I try some of Ah Ching's famous pancakes." "You've been upstairs already?" Eddie said in alarm, wondering if she had told Ah Ma that Nicky was in town. Astrid looked him straight in the eye. "Yes, I've spent a little time with Ah Ma. She wanted to see photos of my engagement, since she helped to plan it. Such a wonderful stroke of luck that there was someone there to capture the occasion." Eddie looked at her openmouthed. "Congratulations on your engagement, Astrid," Fiona said. "Yes, congratulations," Catherine and Alix both chimed merrily. Victoria was the only aunt not to offer any wishes, turning instead to Professor Oon. "How is my mother faring this morning?" "Well, I haven't had the chance to look in on her yet, as Nicholas is with her at the moment." "WHAAAAT? Are you telling me that Nicky is upstairs with my grandmother?" Eddie exclaimed loudly. "Calm down, Eddie," Fiona chided. Astrid smiled sweetly at her cousin. "Precisely what is your issue with Nicky seeing Ah Ma? When did you become her bouncer?" "He's been banned from the house!" Eddie said. "Who banned him, exactly? Because if you ask me, Ah Ma was certainly quite overjoyed to see him a few minutes ago," Astrid said, calmly pouring some of the chocolate golden syrup onto her crepe. "Are you sure about that?" Victoria said indignantly. "Yes, I was in the room when Ah Ma specifically requested to see him." Eddie shook his head angrily, bolting up from his chair. "If nobody is going to do anything about this, I am! Nicky's going to give her another heart attack!" "Give _who_ a heart attack?" Eddie spun around to see his grandmother sitting in a wheelchair as Nick pushed her into the breakfast room. Trailing them were her oxygen tank and several other medical devices, dutifully being guided along by her Thai lady's maids. Behind them followed a cluster of nurses and the on-duty associate cardiologist. "Mummy! What are you doing down here?" Victoria shrieked. "What do you mean? I wanted to have breakfast in my own breakfast room. Nicky told me that Ah Ching was making her delicious crepes." The young associate looked at Professor Oon rather helplessly, but handed his boss several computer printouts. "Prof, she insisted on coming downstairs, but I managed to run some diagnostics first." Professor Oon scanned the morning's reports, his eyes widening. "My goodness...Bravo, Mrs. Young—I am amazed you are feeling so well this morning!" Su Yi ignored the doctor, her eyes instead focusing on Eddie. "What an interesting place for you to sit," she said mischievously. "Oh, sorry," Eddie said, getting flustered as he hastily got up from his chair at the head of the table, while Nick dutifully rolled Su Yi's chair into place. "Come, sit next to me," Su Yi said to Nick, patting the table. One of the maids swiftly produced a chair, and as Nick took his seat beside his grandmother at the head of the table, he couldn't help but grin from ear to ear. For the first time since he had arrived in Singapore, he felt like he was home again. Ah Ling entered the breakfast room and placed a cup and saucer in front of Su Yi. "Here's your favorite _da hong pao_ 2 tea." "Splendid. I feel like I haven't tasted tea in ages. Ah Ling, did you get my message to see that Nicky's room is made up? For some reason he's been staying in Sentosa, of all places!" "Yes, Nicky's bedroom is all ready for him," Ah Ling announced, trying to suppress a giggle as she noticed the veins in Eddie's neck beginning to twitch. "Is my little brother coming over tomorrow for Friday-night dinner?" Su Yi asked. "Yes. We're making Mr. Shang his favorite _yen woh_." "Ah, good. Astrid, be sure to invite Charlie tomorrow night." Astrid's heart soared. "I'm sure he would love to come, Ah Ma." "Has everyone seen Astrid's engagement ring?" Su Yi asked. Catherine, Alix, and Victoria craned their necks to study the diamond on Astrid's finger, realizing with a start that they were staring at their mother's old engagement ring. Alix, who had absolutely no interest in jewelry, quickly went back to devouring her crepe, but Victoria couldn't hide her look of disappointment—she always thought that this ring would be hers one day. "Astrid, it looks lovely on you," Catherine offered, before adding, "Are you planning on having an engagement party?" Su Yi cut in enthusiastically, "What a good idea. Ah Ling, will you call the T'siens and the Tans to come over tomorrow night? Let's have a party!" "Of course," Ah Ling said. "Mummy, I don't think you should have so much excitement when you're just beginning to feel better. You should rest," Victoria said officiously. "Nonsense, I'll rest when I'm dead. Tomorrow, I want to see everyone. Let's celebrate Astrid's engagement and Nicky's homecoming!" Su Yi decreed. Fiona noticed that Eddie was turning purple. Elbowing him in the ribs, she said, "Eddie, loosen your ascot so the air can get in. And breathe, darling. Breathe deeply." * * * 1 Cantonese for "How are you?" 2 Grown in the Wuyi Mountains of China's Fujian Province, _da hong pao_ —which translates to "big red robe"—is one of the world's rarest teas. It's priced at $1,400 per gram, which makes the tea worth thirty times its weight in gold. # CHAPTER FIFTEEN WU MANSIONS, SINGAPORE "Your IC, please," the security guard said sternly as Astrid rolled down the window of her car. Astrid dug into her purse for her wallet, took out her Singapore Identity Card, and handed it to the guard. He held the card up to his eye level to compare the semi-pixilated photograph to her face, squinting at every detail. "It was a bad-hair day," Astrid joked. The guard didn't crack a smile, but took her IC into the guardhouse and began to scan it through his computer system. Astrid had to resist rolling her eyes. This particular Mainland Chinese guard already knew her—how many times had she been here in the past few months? It made her understand how the Wus came to develop a particular reputation among Singapore's establishment when Charlie's father, Wu Hao Lian, first made his fortune in the early 1980s. The Wus did seem pretentious—there was no avoiding that fact. At a time when the moneyed crowd preferred to populate elegant bungalows tucked away in the leafy enclaves of Districts 9, 10, and 11, Wu Hao Lian had bought a large parcel of land off one of Singapore's busiest thoroughfares and built a sprawling family compound right there for all the world to see. He had erected a tall white stucco wall around the property, and at the top of the wall, sharp red-glazed tiles undulated up and down like the scaley curves on a dragon's back, ending at the main gates with twin carved dragon heads in bronze. Rectangular gold plaques placed in niches at thirty-foot intervals around the wall were engraved in an ornate calligraphy script with the words: > To ordinary Singaporeans—the ninety percent who lived in public-housing apartments—it seemed like the Wus were the richest family in the land. The family was seen being driven around in a fleet of ever-changing Rolls-Royces, always accompanied by security guards in a Mercedes wherever they went. They were one of the first families on the island to flaunt their private jet, and spent all their holidays touring Europe, where Irene Wu and her daughters developed a voracious appetite for haute couture and haute jewelry. Whenever Irene appeared in public, she was always clad in the most ornately festooned frocks and laden with so much jewelry that all the other socialites nicknamed her "Christmas Tree" behind her back. _But all this was so long ago_ , Astrid thought as the tall steel gate embossed with the ornate W seal began to slide to one side and she sped up the short driveway to the Palladian-style house with a white columned portico covered in bougainvillea. The Wus had receded into the background, especially after Charlie's father passed away and a new generation of brash billionaires burst onto the scene in the early 2000s, building even more ostentatious pleasure domes and vying for visibility in the society pages. Only Charlie's mother remained in Singapore these days, reluctant to give up her house. Astrid pulled up behind a gray Mercedes SUV already parked underneath the portico. She saw Lincoln Tay, her distant cousin, emerge from the driver's seat and walk around to the trunk of the car. "Ah Tock! Fancy seeing you here," Astrid said as she got out of her car. "What can I tell you? You're always hanging around the rich and famous, and I just work for them," he joked. "Now Astrid, tell me why are you still driving that old Acura? Does it even pass inspection anymore?" "This is the most reliable car I've ever owned. I'm going to drive it until I'm forced to scrap it." "Come on _lah_ , you are so loaded, at the very least you should upgrade to the ILX. Or maybe Charlie can buy Acura the company for you and have them design you a car from scratch." "Ha-ha, very funny," Astrid said. It occurred to her that every time she saw this distant cousin, he would make some sort of reference to her money. "Hey, come and see something very special," Ah Tock said, as he opened the trunk of the SUV. A large Igloo cooler was strapped to one side of the spacious rear, and Ah Tock carefully lifted out a large plastic bag that had been inflated with oxygen. Inside was a dragon-like fish about two feet in length. "Oh, it's an arowana," Astrid said. "Not just any arowana. This is Valentino, Mrs. Wu's prized super red arowana. It was worth at least $175,000 and now it will be worth $250,000, minimum." "Why's that?" "I just took Valentino to his plastic surgeon. He was beginning to develop a droopy eye, so we gave him an eye lift. And he even got a very slight chin job. See how handsome he looks now?" "There's a plastic surgeon for _fish_?" Astrid asked incredulously. "The best in the world, right here in Singapore! He specializes in arowanas."1 Before Astrid could properly soak in this fabulous bit of trivia, the front door opened and Irene Wu came running out. A round-faced woman in her early seventies, she was dressed in a bright orange Moroccan-style tunic top embroidered with tiny mirrored glass pieces and sequins, white capri pants, and fluffy white bedroom slippers embroidered with the Four Seasons Hotel logo. On her fingers sparkled an emerald ring; another ring consisting of three interlaced bands of diamonds set in white, yellow, and rose gold; and a pear-cut diamond ring that was nearly as big as the real fruit itself. "How is he? How's my baby Valentino?" Irene asked breathlessly, rushing toward Ah Tock and the plastic bag. "Mrs. Wu, he's doing very well. The surgery was a success, but he's still a bit sluggish at the moment from being drugged. Let's get him acclimated back in his tank." "Yes, yes! _Aiyah_ , Astrid, I didn't even see you. Come in, come in. Sorry-ah, I am so _kan jyeong_ 2 today because of Valentino's procedure. My goodness, don't you look lovely. Who are you wearing today?" Irene asked, admiring Astrid's floral kimono-inspired wrap dress. "Oh, this is a dress that Romeo Gigli made for me years ago, Auntie Irene," Astrid said, leaning in to give her a peck on the cheek. "Of course it is. So pretty! And don't you think it's high time you started calling me Mama instead of Auntie Irene?" "Come on, Mum, lay off Astrid!" Charlie said, standing at the front door. Astrid beamed at the sight of him and rushed up the steps to give him a tight hug. " _Aiyah_ , I'm going to tear up and ruin my mascara. Look at my two lovebirds!" Irene sighed happily. As the group entered the house, Charlie steered Astrid towards the sweeping _Gone with the Wind_ –style double staircase instead of the living room. "Where are you two going?" Irene asked. "I'm just taking her upstairs for a little while, Mum," Charlie said in a slightly exasperated tone. "But Gracie has spent all day making so many types of _nyonya kueh._ You must come and have tea and _nyonya kueh_ with me in a little while, okay?" "Of course we will," Astrid said. As they climbed the stairs, Charlie said in a low voice, "My mum is getting more and more needy every time I see her." "She just misses you. It must get rather lonely for her now that none of you are around in Singapore." "She's surrounded all day by her staff of twenty." "It's not the same and you know it." "Well, she has a house in Hong Kong—she could spend all her time there if she wants, but she insists on staying here," Charlie argued. "This is where most of her memories are. Just like yours," Astrid said as she entered Charlie's bedroom. The space had been redecorated several years ago in cool, masculine tones with shagreen-covered walls and custom-designed contemporary wood furnishings from BDDW in New York, but Charlie had kept one reminder of his childhood in the bedroom: The entire ceiling had been installed with a mechanized mural depicting all the constellations in the sky, and as a kid, Charlie would go to sleep every night staring at the glowing ceiling of stars as they rotated daily according to the zodiac. Today, he wasted no time in pulling Astrid onto the bed and smothering her with kisses. "You have no idea how much I've missed you," Charlie said, kissing the tender area right above her collarbone. "Me too," Astrid sighed, as she put her arms around him, feeling the ripple of muscles down his back. After spending some time making out, they lay entwined in each other's arms, staring up at the sparkling night sky together. "I feel like a teenager again." Astrid giggled. "Remember how you used to sneak me up here after MYF3 on Saturdays?" "Yeah. I still feel like I'm doing something naughty having you in here right now." "The door's wide open, Charlie. We haven't done anything R-rated," Astrid said with a laugh. "I'm so happy to see you in such a good mood," Charlie said, running his fingers through her hair. "I feel like the storm's finally lifted. You have no idea how amazing it felt to be in the breakfast room yesterday when my grandmother came downstairs." "I can only imagine." "She made everyone look at my engagement ring. It's like she was daring the rest of the family to challenge us." "Your grandmother is one cool lady. I'm looking forward to seeing her tonight. She invited my mum too, you know?" "Really?" Astrid looked at him in surprise. "Yeah, an engraved invitation was delivered this morning. My mother could hardly believe it. She never thought the day would come that she would be invited to Tyersall Park. I think she's going to frame the card." "Well, it's going to be quite a party. I can't wait to see the looks on certain faces when I walk into the drawing room with your mother!" "Which ones?" "Oh, you know, one or two of my aunties are snottier than others. And there's one cousin in particular who's going to lose his shit!" "Rico Suave, the Best Dressed Man in Hong Kong?" Charlie teased. "Best Dressed Hall of Fame, he'll tell you." Astrid laughed. "Come on, let's go back downstairs before your mother thinks we're doing something nasty up here." "I _want_ her to think I'm doing something nasty." They got out of bed reluctantly, straightened their clothes, and strolled down the gracious curving stairway hand in hand. Passing through the archway underneath the staircase, they entered the grand living room, which was handsomely decorated in French Empire style intermingled with museum-quality Chinese antiques. In the middle of the cavernous space was a large free-form pond, where a grove of tropical trees grew out of the water, reaching almost to the top of a glass-domed cupola. Big koi swam in the gurgling pond, but the focal point of the living room was the main wall, which featured a two-hundred-gallon fish tank painted pitch-black that was recessed into the wall. "Valentino looks happy to be home!" Charlie said excitedly as the two of them went up to look at him. Inside the tank, Irene's precious super red arowana undulated happily all alone, the pink fiber-optic light making his body glow an even brighter iridescent red. Astrid looked down at the coffee table, which was groaning with a colorful array of _nyonya_ dessert cakes on navy-and-gold-rimmed Limoges plates. " _Kueh lapis_ , my favorite!" Charlie said, plopping down on the plush gold-brocade sofa and picking up one of the buttery pieces of cake with his fingers. "Don't you think we should wait for your mum?" "Oh, she'll be out in a minute, I'm sure. Let's get started. You don't ever have to stand on ceremony here—you know how down-to-earth my mother is." Astrid began to pour tea into Charlie's cup from the silver tea service. "That's what I've always loved about your mother. She doesn't put on any airs—she's such a warm and simple lady." "Yeah, tell that to the folks at Bulgari," Charlie snorted, as Ah Tock entered the living room. "Lincoln! Are you going to join us for some tea? Where's my mum?" "Um, she's in her bedroom. She went to lie down," Lincoln said as he fidgeted with his cell phone. "Why is she lying down?" Charlie asked. Astrid looked up from pouring her tea. "Is she not feeling well?" "Er, no..." Ah Tock stood there with a funny look on his face. "Astrid, I think you better call home." "Why?" "Um...your grandma just passed away." * * 1 The Asian arowana is the world's most expensive aquarium fish, especially coveted by collectors in Asia who will pay hundreds of thousands for a fine specimen. Known in Chinese as _lóng yú_ —dragon fish—this long fish plated with large shimmering scales and with whiskers jutting from its chin resembles the mythological Chinese dragon. Aficionados believe that the fish brings good luck and fortune, and there have even been tales of arowanas sacrificing their lives by leaping out of their tanks in order to warn their owners of imminent danger or bad business deals. No wonder lovers of this fish are willing to shell out thousands to get their precious pets eye lifts, fin tucks, or chin jobs. No word on arowana Botox yet, but that can't be far behind. 2 Cantonese for "panicky, anxious." 3 Methodist Youth Fellowship. # PART THREE > The man who dies rich, dies disgraced. > > —ANDREW CARNEGIE, 1889 # CHAPTER ONE TYERSALL PARK, SINGAPORE # MADRI VISUDHAROMN ## Lady's Maid to Su Yi Since _1999_ Madame usually has a bowl of congee in the morning, sometimes with a fresh raw egg cracked into the steaming-hot congee, sometimes with just a few _ikan bilis_. Today she asked for Hokkien _ma mee_ , which was a highly unusual request for breakfast. The noodles Ah Ching prepares for her are done in a very specific way, using a hand-pulled flat yellow noodle, which she likes stir-fried in a thick oyster sauce gravy with a dash of brandy. For lunch, madame just wanted me to bring her some fresh star fruits and guavas from her trees. She asked for the whole fruit—she didn't want them sliced or anything, and sat up in her bed, staring at her fruits and holding them in her hands but not eating anything. That's the moment I realized that something was terribly wrong. # PHILIP YOUNG ## Only Son I saw Mummy after breakfast. For the first time in as long as I can remember, she wanted to know how I spent my days in Sydney. I told her about how I drive down to my favorite café in Rose Bay every morning for my flat white, and then there are always errands to run, something in the house that needs fixing, or I'll have lunch in the city at one of my clubs or play a round of tennis with a friend. In the late afternoons I like to sit at the end of my dock and do a spot of fishing...that's when the fish are always biting. For dinner I often eat whatever I've caught. Mickey our chef will always do something terrific with the fish—grilled and served over risotto, made into a tartare, or steamed Chinese-style with rice or noodles. Sometimes I'll just go down to the local and have a pub dinner. (Mummy shook her head in a mixture of sadness and disbelief—the thought of me sitting in a pub eating a burger by myself like a common laborer is too much for her to fathom.) But I love eating very simply when Eleanor isn't around. If she's in town, Eleanor keeps Mickey very busy cooking twelve to fourteen courses for her dinners. Then Mummy said something rather surprising. She asked me if I had forgiven Eleanor. I was a bit shocked for a moment; in all these years, Mummy had never brought it up. I told her that I had forgiven my wife a very long time ago. Mummy seemed happy about this. She looked at me for a long time and said, "You are just like your father after all." I told her I was going to meet up with a few of my ACS old boys for drinks at the Men's Bar in the Cricket Club, but I would be back before our dinner guests arrived. As I left her bedroom, there was a part of me that sensed she didn't want me to leave. I wondered for a moment if I should cancel the meet-up and stay by her bedside, but then I thought, Philip, you're being ridiculous. You'll be back in two hours. # LEE AH LING ## Head Housekeeper At around 4:30 p.m., I went upstairs to give Su Yi a final update on tonight's menu for the party. When I went into the bedroom, Catherine was sitting by her bedside and I noticed that someone had opened all the windows and curtains. Su Yi usually prefers the curtains drawn in the afternoons, to protect her antique furniture from the setting sun, so I began to close them. "Leave them," Catherine said. I looked over at her and began to ask why, and that's when I realized that Su Yi was gone. You could just see that her spirit had left her body. I was so shocked, I panicked at first and asked, "Where are the doctors? Why didn't the alarms go off?" "They did. The doctors came in and I sent them all away," Catherine said in an unnaturally calm voice. "I wanted to be alone with my mother one last time." # PROFESSOR FRANCIS OON, MBBS, MRCP (U.K.), MMED (INT MED), FRCP (LONDON), FAMS, FRCP (EDIN), FACC (USA) ## Personal Cardiologist I had been entertaining Debra Aronson, the publisher of Poseidon Books, at home in my wine cellar when the call came. You see, I collect contemporary Chinese art, and Poseidon has been trying to woo me into doing a coffee-table book on my collection. When my associate Dr. Chia called with the urgent news from Tyersall Park, I immediately said, "Do _not_ resuscitate." I knew it would be hopeless. There's been so much scarring to her heart, it would be pointless to try and revive her. It's her time to go. None of this came as a surprise to me. In fact, after looking at her stats the previous morning during that fabulous crepe breakfast, I was surprised that she was even able to get out of bed. Her heart rate, her blood pressure, her ejection fraction—everything was off the charts. But you know, I've seen this happen time and again. In the day or two before a patient passes, they can experience a sudden spurt of energy. The body rallies, as if it knows that this will be the last hurrah. The minute I saw Su Yi appear at the breakfast table, I surmised that this was happening. After all this time, with all the medical advances we've made, the human body is still an unfathomable mystery to us. The heart most of all. # ALEXANDRA "ALIX" YOUNG CHENG ## Youngest Daughter I was in the library with Fiona and Kalliste, showing Kalliste my Enid Blyton first editions, when the dogs started howling. It must have been around half past three in the afternoon. It wasn't just our pack of Alsatians that patrol the grounds, but it seemed like every dog within a two-mile radius was making restless, high-pitched yelps. I gave Fiona a look and she knew exactly what I was thinking. She left the library without a word and went upstairs to check on Mummy. By now the howling had stopped, but I remember feeling enveloped by a sense of dread. My heart was beating a mile a minute, and I kept staring at the door. I was somehow willing Fiona to not come back through those doors. I didn't want to hear any bad news. I was trying to focus on Kalliste, who wanted to know if she could have the entire Malory Towers series—they were her favorites too when she was younger. Then Fiona came back in and I just froze until she smiled. "All's well. Auntie Cat is with her," she whispered to me. I was so relieved, and we went back to the stacks. About an hour later, Ah Ling came rushing into the library to tell me to get upstairs. The look on her face told me everything. You see, the dogs knew all along. They could sense it coming. # CASSANDRA SHANG ## Niece I was in bed at Harlinscourt, reading the latest Jilly Cooper novel when my phone began to vibrate on silent mode. I recognized the number immediately—it was Deep Throat, my spy at Tyersall Park. (Of course you knew I had an inside source at that house. It would be so foolish of me not to.) At first, Deep Throat simply said, " _Boh liao_." I said, "What do you mean _boh liao_?" Deep Throat was overly excited, but she managed to get it out: "Su Yi just died. Big fight upstairs right now. I must go." So of course the first thing I did was call my father. I said, "Are you at Tyersall Park?" He said, "Er, no." I think I caught him at his mistress's apartment—he was very out of breath. So I said, "You better head over there now. Something just happened to your sister." # LINCOLN "AH TOCK" TAY ## Distant Cousin Great-uncle Alfred called me. I think he was on his way to Tyersall Park. He said to tell everyone on my side of the family that Su Yi had just passed. But he didn't want any of us at the house tonight. "Tell your father to stay home, and I'll let you all know when to come. Tonight is just for the family." As if we're not part of the family, fucking bastard! Then he said, "Better start ordering the tents and folding chairs. We're going to need a lot of them." I was still at Irene Wu's house trying to acclimate the damn fish back into the tank, so I told her the news and she started to lose it. "Oh no! _Alamak!_ How to face Astrid?" she cried, fleeing to her bedroom. I went back into the living room and when I saw Astrid sitting there pouring tea like Princess Diana, I realized the spoiled bitch didn't have a clue that her grandma had just kicked the bucket. _Kan ni na_ , I had to be the one to tell her. Of course she was in total shock, but I don't feel sorry for her one bit. She's now instantly a million times richer than she already is. # VICTORIA YOUNG ## Third Daughter The first thing that came into my mind when I saw her lying there with Eddie crying over her body hysterically was: _Thank you Jesus, thank you Jesus, thank you Jesus. She has been released, and so have I. I'm free at last. Finally free._ I numbly put my hand on Alix's back, and tried to rub it soothingly while she stood looking at Mummy. I thought I might cry, but I didn't. I looked over at Cat, who was sitting in the armchair still holding Mummy's hand, and she wasn't crying either. She was just staring out the window with a rather odd look on her face. I suppose we must have all looked rather odd that day. I started to consider the curtains—Mummy's curtains with the _point d'Alençon_ lace trim, and I began to imagine how they would look in the front windows of the town house I would buy in London. I could really see myself moving to one of those lovely town houses in Kensington, perhaps on Egerton Crescent or Thurloe Square, just a stone's throw from the Victoria and Albert. I would use the V&A's glorious library every day, and go for afternoon tea at the Capital Hotel or the Goring. I'd attend All Souls Church every Sunday, and maybe even start my own Bible-study fellowship. I could endow a chair in theology at Trinity College, Oxford. Maybe I could even convert an old rectory in some charming town in the Cotswolds. Someplace with a particularly smart and handsome clergyman like that Sidney Chambers in _Grantchester_. Goodness me, one look at him in that stiff clerical collar and I go weak in the knees! # MRS. LEE YONG CHIEN ## Chairwoman Emeritus of the Lee Philanthropic Foundation, Su Yi's Mah-jongg Kaki I was at my Friday-afternoon mah-jongg game at Istana with the First Lady, Felicity Leong, and Daisy Foo when Felicity got the call. She didn't say anything to us at first—she just started rummaging through her Launer handbag, saying she needed to find her blood-pressure pills. Only after she had swallowed her pills did she say, "Ladies, I'm terribly sorry to leave like this in the middle of a game, but I must go. My mother has just passed." My goodness, the First Lady became so overcome I thought she was going to faint right there at the table! After Felicity left, the First Lady said she should go upstairs to the office to tell the president the news, and Daisy said, " _Alamak_ , I should call Eleanor! She didn't call me, so I bet you she doesn't know yet!" When the ladies all returned, we decided to toast Su Yi. After all, she was a mah-jongg maven par excellence. We all knew never to bet serious money when Su Yi was at the table. Now that she has left us, my money market account won't feel the loss, but I know her family will. Su Yi was the glue that held them all together. Those children of hers are a disgrace. Philip is a simpleton, Alix is a useless Hong Kong _tai tai_ , Victoria is a spinster, and the one that married the Thai prince, I never really knew her, but I always heard she was very stuck up, like most Thais I've met. They think just because they've never been invaded they are the best. Only Felicity has any sense _,_ because she was the eldest. But all those grandchildren are also good-for-nothings. This is what happens when too much money falls on people who are too attractive. That Astrid, so pretty, but her only talent is spending more than the GDP of Cambodia on her clothes. Look at my grandsons. Four of them are doctors, three are lawyers—one is the youngest judge ever to be appointed to the Court of Appeal, and one is an award-winning architect. (Let's not mention the grandson living in Toronto who is a hairdresser.) So sad for Su Yi, she can't brag about any of her descendants. Just you watch, everything is going to go down the toilet now. # NICHOLAS YOUNG ## Grandson I had only just arrived at Tyersall Park and was unpacking my suitcases when I heard the commotion outside my bedroom. Maids were running down the corridors everywhere like a fire alarm had gone off. "What's going on?" I asked. "Your Ah Ma!" one of them shouted frantically as she passed me. I immediately ran up the back stairs to Ah Ma's bedroom. When I got there, I couldn't see anything. There were too many people blocking the way, and someone was wailing uncontrollably. Victoria, Alix, Adam, and Piya were hovering around the bed while Uncle Taksin was embracing Auntie Cat, who was still sitting in the armchair beside Ah Ma. Ah Ling was closest to me by the door, and she turned toward me, her face swollen with tears. As Adam and Piya moved aside to make room for me, I could see that Eddie was lying in bed with Ah Ma, holding her body, shaking violently as he whimpered like a tortured animal. He caught my eye and suddenly, he leapt out of bed and started screaming, "You killed her! You killed her!" Before I knew what was happening, he's on top of me and we're both on the ground. # HER SERENE HIGHNESS _MOM RAJAWONGSE_ PIYARASMI AAKARA ## Granddaughter-in-law What an odd family I've married into. Adam's aunties are like characters straight out of a Merchant Ivory film. They go rattling around this huge palace, dressed like underpaid civil servants, but then they start speaking and they all sound like Maggie Smith. Auntie Felicity clucks about like a mother hen, criticizing everyone, while Auntie Victoria seems to be an expert on everything even though she hasn't worked a day in her life. She even tried to challenge me on the origin of the hantavirus! Then there are the Hong Kong cousins—Alistair Cheng, who is very sweet but...how do I put it politely...not the sharpest tool in the box, and his sister, Cecilia, and Fiona Tung-Cheng, both perfectly polite but soooooooo stuck up. Why do all Hong Kong girls think the sun shines out of their asses? They just chatter away to each other in Cantonese and go off on foodie adventures every day with their kids. I suspect they only came to Singapore to eat. Every time they are around I feel like they are assessing me from head to toe. I don't think Cecilia approves of Balmain. And then there's Eddie. What a crazy fuck. Grandma has just died, and all her daughters stand there staring at her body without a single tear in their eyes. The only people who seem to be crying are the maids, the Sikh guard, and Eddie. OMFG I have never seen a grown man sob like that. Crawling into bed and cradling his dead grandmother. Dressed in a velvet smoking jacket! And then Nick—the only halfway normal person in the whole house—enters the room and Eddie lunges at him. The aunties start to scream but really, it's a pretty pathetic fight, because Eddie hits like a girl and Nick simply rolls him off and pins him to the ground. "Calm the fuck down!" Nick says, but Eddie's screaming, kicking, thrusting, and finally Nick has no choice but to sock him right in the nose, and blood just goes EVERYWHERE. Especially all over my brand-new Rick Owens toad-skin boots. And now I'm told we have to spend at least another week with these people. Kill me now. # CAPTAIN VIKRAM GHALE ## Head of Security, Tyersall Park Ah Ling called me in a panic. " _Aiyah_ , come quick! They are fighting! Eddie is trying to kill Nicky!" I rushed upstairs with two Gurkhas but by the time I got to the room, it was all over. Eddie was sitting at the foot of the bed, blood all over his face. He kept saying, "You broke my nose! You are going to fucking pay for my nose job!" Nicky just stood there, looking stunned. Alix smiled at me as if nothing had happened and said, in the calmest voice ever, "Ah, Vikram, you're here. I'm not sure what the procedure is. Who do we call? Do we call the police now?" I was confused at first and said, "You want to report this fight?" She said, "Oh no, not that. My mother has passed away. What are we supposed to do now?" In all the confusion, I hadn't even noticed that Mrs. Young was dead. I couldn't help myself—I burst into tears right there in front of everyone. # FELICITY LEONG ## Eldest Daughter No matter how old you are, no matter how ready you think you are, nothing quite prepares you for the loss of a parent. My father passed away years ago, and I still haven't quite recovered. People have been saying to me all week long, "At least your mother lived to this ripe old age, and you got to spend all these years with her." And I just want to spit in their faces. I want to scream at them, _Shut up, all of you!_ My mother died. Please don't tell me how lucky or fortunate I am that she lived this long. She has been here on this earth my entire life and now suddenly in the blink of an eye she's gone. Gone, gone, gone. And I am an orphan now. And even though she was a difficult woman, even though she drove me crazy half the time and I was never ever quite good enough for her exacting standards, my heart is broken. I will miss her every day and every hour for the rest of my life. My only regret was that I wasn't there with her at the moment of her passing. Cat was the only one in the room with her, and I kept asking her what happened. But Cat seems too distraught to speak. She won't tell me a thing. — A small, discreet, one-column death notice was published in the obituary section of _The Straits Times_ : > SHANG SU YI, Mrs. James Young > > (1919–2015) > > Beloved wife and mother > > _Son_ —Philip Young > > _Daughters_ —Felicity Young, Catherine Young, Victoria Young, Alexandra Young > > _Sons-in-law_ —Tan Sri Henry Leong, M.C. Taksin Aakara, Dr. Malcolm Cheng > > _Daughter-in-Law_ —Eleanor Sung > > _Grandchildren and Their Spouses—_ Henry Leong Jr. (m. Cathleen Kah), Dr. Peter Leong (m. Dr. Gladys Tan), Alexander Leong, Astrid Leong, M.R. James Aakara (m. M.R. Lynn Chakrabongse), M.R. Matthew Aakara (m. Fabiana Ruspoli), M.R. Adam Aakara (m. M.R. Piyarasmi Apitchatpongse), Nicholas Young (m. Rachel Chu), Edison Cheng (m. Fiona Tung), Cecilia Cheng (m. Tony Moncur), Alistair Cheng > > _Great-grandchildren_ —Henry Leong III, James Leong, Penelope Leong, Anwar Leong, Yasmine Leong, Constantine Cheng, Kalliste Cheng, Augustine Cheng, Jake Moncur, Cassian Teo > > _Brother_ —Alfred Shang (m. Mabel T'sien) > > _Visitations begin tonight at Tyersall Park by invitation only._ > > _Funeral at St. Andrew's Cathedral, Saturday at_ _2_ _:_ _00_ _p.m. by invitation only._ > > _No flowers please. Donations may be made to the St. John's Ambulance Association._ * * * * Hokkien for "No more." # CHAPTER TWO TYERSALL ROAD, SINGAPORE Goh Peik Lin turned to Rachel from the driver's seat of her Aston Martin Rapide. "How do you feel?" "Well, I didn't manage to sleep a wink on the plane, so it's 7:30 a.m. New York time for me right now and I'm about to crash the funeral of a woman who didn't approve of me marrying her grandson and meet all of her possibly hostile relatives that I haven't seen in five years. I feel _great_." "You're not crashing the funeral, Rachel. You're part of the family and you're here to support your husband. You're doing the proper thing," Peik Lin tried to assure her. Peik Lin was her closest friend from their Stanford days and had always been such a pillar of support. Sitting beside Rachel in the backseat of the sports sedan, Carlton squeezed her hand in a show of support. Rachel leaned her head against her brother's shoulder and said, "Thanks for flying down from Shanghai. You really didn't have to do this, you know." Carlton made a face. "Don't be daft. If you were going to be anywhere in this hemisphere, did you think I could stay away?" Rachel smiled. "Well, I'm glad I get to spend a few moments with you both before I get sucked into the matrix. Thanks so much for picking me up, Peik Lin." "Don't even mention it. Poor Nick, I know he wanted to come get you but he's totally trapped at the night visit," Peik Lin said. "So what is this night-visit thing, exactly?" Rachel asked. "Night visits are like sitting Shiva, Singapore-style. It's officially for family and close friends to come to the house to pay their last respects, but really, it's a chance for all the _kaypohs_ 1 to get in on the family gossip and start scheming. I guarantee you everyone at Tyersall Park is furiously speculating about what's going to happen to the house now that Shang Su Yi has dearly departed, and there are plenty of shenanigans going on in every corner." "Unfortunately I think you may be right," Rachel said with a slight grimace. "Of course I'm right. When my grandfather died, all my uncles and aunties came out of the woodwork and crept around his house during the night visit, putting stickers with their names behind paintings and under antique vases so they could claim that he had given it to them!" Peik Lin said with a chuckle. Soon they found themselves in bumper-to-bumper traffic as the line of cars snaking up Tyersall Road to the estate's gates were stopped at a security checkpoint. Glancing at the policemen peering into the cars ahead of them, Rachel felt her stomach begin to knot up. "There's so much security—I think the president or prime minister must be here," Peik Lin noted. After passing through all the checkpoints, the car sped up the long driveway, and as they rounded the last curve, Tyersall Park finally came into view. "Bloody hell," Carlton said, impressed by the scene before him. The great house was ablaze in lights, the front driveway resembled a parking lot lined with fancy cars, many with diplomatic plates. Uniformed Gurkhas and policemen were stationed everywhere, trying to manage the traffic flow. As the three of them got out of the car, a large black military helicopter swooped into sight over the house and descended gracefully onto the manicured lawn. The doors slid open, and a portly Chinese man in his early eighties dressed in a black suit with a deep purple tie was the first to get out. A woman in a black cocktail dress with art deco patterned jet beading followed behind him. Rachel turned to Peik Lin. "Is that the president and First Lady?" "No. I have no idea who they are." Then a middle-aged man in a black suit emerged, and Carlton exclaimed, "Well that's the president of China!" Peik Lin looked awestruck. "Oh my God, Rachel, the _president of China_ has come to pay his respects!" Much to their surprise, the next person to emerge was a tall, lanky college-age kid with long, messy shoulder-length brown hair, dressed in tight black jeans, steel-tipped black boots, and a black tuxedo jacket. A Chinese man in a pinstripe suit and a blond middle-aged lady in a black dress with a pale green shawl draped around her shoulders emerged next, followed by a cute fair-haired girl of about twelve. "Stranger and stranger," Peik Lin said. A small crowd had clustered outside the house to observe the arriving dignitaries, and as Rachel walked up, she saw Nick's cousin Alistair waving at her. Alistair greeted Rachel with a big bear hug before excitedly hugging Carlton and Peik Lin as well. "Peik Lin, I haven't seen you since Rachel's wedding! I love your new red hair! I'm so glad you guys are finally here—it's been soooo lame inside...all anyone wants to talk about is 'Who's getting the house?' And now things are about to get _even_ stuffier," he said, gesturing to the arriving VIPs. "Who _are_ those people with the president of China?" Rachel asked. Alistair looked momentarily surprised. "Oh, you haven't met them yet? Those people are the Imperial Shangs. The old farts are my uncle Alfred and auntie Mabel. The younger farts are my cousin Leonard and his very posh wife, India, who's apparently descended from Mary Queen of Scots or something like that, and those are his kids, Casimir and Lucia. Doesn't Cass look like Harry Styles from One Direction?" Everyone laughed. "I think Harry's shorter," Peik Lin quipped. "So they all just came from China?" Rachel asked, still confused. "No, the Shangs just had dinner with the president at the Chinese embassy. The president's only here because of Uncle Alfred. He never knew Ah Ma, of course." "I believe my father knows him," Rachel remarked. "They've been good friends since their university days, and Dad serves on his standing committee," Carlton chimed in. "Of course, I keep forgetting your father is Bao Gaoliang," Alistair said. "One last question...who is _that girl_?" Carlton asked. Stepping out last from the helicopter was an astonishing Eurasian beauty in her early twenties. She had waist-length, sun-streaked hair and wore a long, sleeveless black linen Rochas dress and gold sandals from Da Costanzo, looking like she had just stepped in from a beach party on Majorca. "I think I've just met my future wife," Carlton declared as he watched the girl's hair billow around her sensationally under the draft of the helicopter rotors. "Best of luck, mate! That's my cousin Scheherazade Shang. She's working on her dissertation at the Sorbonne. Brains _and_ beauty. You know, I've heard there's another dude that's been trying to get her number for years with absolutely no success. His name's Prince Harry." ··· As the Shangs retreated into the house with the president of China, Rachel, Carlton, and Peik Lin followed a few paces behind. In the grand foyer, they ran into Oliver T'sien staring disapprovingly as hordes of people passed through, navigating past the hundreds of floral wreaths—some bigger than Michelin tires—that now invaded the space. "Rachel! Wonderful to see you! Isn't this awful?" Oliver whispered in her ear. "Singaporeans just love sending these ghastly funeral wreaths." Rachel glanced at the card on the nearest wreath: GREAT EASTERN LIFE ASSURANCE OFFERS CONDOLENCES ON THE DEATH OF MADAM SHANG SU YI. As they continued past the dining room where an enormous dinner buffet had been set up, Rachel could see guests standing in a long queue that snaked out the terrace doors, waiting to devour the delicacies at the various food stations. A little boy dashed past Rachel, shouting, "Auntie Doreen wants more chili craaaaab!" "Whoa!" Rachel said, narrowly dodging the boy who was precariously clutching a heaping platter of crustaceans. "Not what you were expecting?" Peik Lin said with a laugh. "Not quite. It's all so...festive," Rachel remarked. "It's the funeral of the year!" Oliver quipped. "Don't you know everyone who's anyone wants to be here? A little earlier, a rather pushy young socialite named Serena Tang tried to take a selfie with Su Yi's coffin. She got thrown out, of course. Here, let's take a shortcut." He directed them through a side door and the atmosphere changed completely. They found themselves in the magnificent Andalusian Cloister, an enclosed courtyard surrounded by carved columns open to the sky. Rows of chairs with white slipcases had been arranged around the reflecting pool in the center of the courtyard, and the guests who gathered here murmured quietly amid the sound of the trickling water. Antique silk lamps had been placed in each of the arched alcoves surrounding the courtyard, the flickering candles within each lamp adding to the monastic stillness of the space. At the far end of the courtyard, in front of the carved lotus blossom fountain, Su Yi's simple black teakwood casket rested on a marble dais surrounded by orchids. In a nearby alcove, Nick, his parents, and many members of the extended Young clan stood in an informal receiving line. Nick was dressed in a white button-down shirt with black trousers, and Rachel noticed that all the men present—Nick's father, Alistair Cheng, and a few other men she didn't recognize—were dressed in the same manner. "Rachel, why don't you go to Nick first. We don't want to disrupt your reunion," Peik Lin suggested. Rachel nodded and descended the few steps into the courtyard toward the receiving line, feeling her stomach tense up in a sudden wave of anxiety. Nick was hugging Lucia Shang and was just about to be introduced to the president of China when he saw her approach. He quickly stepped out of the receiving line and dashed to her. "Darling!" he said, sweeping her into an embrace. "Oh my, did you just dis the president of China?" Rachel asked. "Did I? Oh well, who cares? You're far more important." Nick laughed, and taking Rachel by the hand, led her to the receiving line and announced proudly, "Everyone—my wife has arrived!" Rachel immediately felt every eye in the room turn to take her in. Philip and Eleanor welcomed Rachel and the avalanche of introductions began. Nick's uncles, aunts, and cousins from all the various branches greeted her far more warmly than she had expected, and suddenly Rachel found herself face-to-face with the president of China. Before she could say anything, Nick stepped forward and announced in Mandarin, "This is my wife. I believe her father, Bao Gaoliang, serves on your standing committee?" The president looked momentarily startled, and then he broke into a wide grin. "You're Gaoliang's daughter? The economics professor from New York? It's a pleasure to meet you at last. My God, you look just like your brother, Carlton." "He's right over there," Rachel replied in perfect Mandarin, waving her brother over. "Carlton Bao, you seem to be everywhere these days! Didn't I just see you at my daughter's birthday dinner two nights ago? I hope you're flying on air miles," the president said in mock seriousness. "Of course, sir," Carlton replied. He beamed at the gathered group, making sure to catch Scheherazade's eye. Alfred Shang, who had observed the whole scene silently, looked at Rachel and Carlton with a newfound curiosity. Rachel turned to Nick and said in a quiet voice, "Can I pay my respects to your grandmother?" "Of course," he said. They walked up to the casket, which was surrounded by exquisite orchids in delicate celadon pots. "My grandmother was most proud of her prizewinning orchids. I don't think I ever saw her happier than the day the National Orchid Society named one of her hybrids after her." Rachel peered into the casket a little hesitantly, but she was surprised by how splendid Su Yi looked. She lay majestically swathed in a robe of shimmering yellow silk intricately embroidered with flowers, and her hair was crowned by the most spectacular Peranakan headpiece made of gold and pearls. Rachel bowed her head for a moment, and when she looked up at Nick, she saw that his eyes were brimming with tears. Placing her arm around his waist, she said, "I'm so glad you got to see her before she passed. She looks very peaceful." "Yes, she does," Nick said, sniffing quietly. Rachel noticed something glistening between Su Yi's teeth. "Um, what's that in her mouth?" "It's a black pearl. It's an old Chinese custom...the pearl ensures a smooth transition into the afterlife," Nick explained. "And do you see the Fabergé case beside her?" "Yeah?" Rachel noticed a small rectangular bejeweled box next to the pillow. "Those are her glasses, so she can have perfect vision in her next life." Before Rachel could make another comment, a strange, whimpering sound could be heard echoing from one of the alcoves. They turned to see Alistair and his father, Malcolm, holding up a frail man as he limped toward them slowly. Rachel realized with a start that the man was Nick's cousin Eddie, and behind him walked his wife, Fiona, and their three children, all dressed in matching black linen and silk bespoke outfits. "Kaiser Wilhelm has arrived," Oliver pronounced, rolling his eyes. Eddie collapsed into a heap dramatically at the foot of the casket and began to convulse and emit deep, hacking sobs. "Ah Ma! Ah Ma! What will I do without you now?" he wailed, flailing his arms wildly, almost knocking over one of the orchid pots. Felicity Leong whispered to her sister Alix, "He better not break any of those vases! They're worth a fortune!" "What a devoted grandson!" the president of China observed. Hearing this, Eddie cried out even more bitterly, "How can I go on living, Ah Ma? How will I survive?" Tears poured down his face, mixing with lines of dangling snot as he continued to prostrate himself beside his grandmother's casket. Eddie's two younger children, Augustine and Kalliste, knelt on either side of their father and began to rub his back soothingly. He elbowed the kids quickly, and they started to cry on cue. Standing at a distance, Alistair whispered to Peik Lin, "I guess we didn't need to hire any professional mourners."2 "Well, your brother can certainly do this professionally! The kids are doing a great job too." "I'm sure they were forced to rehearse a million times," Alistair said. Eddie suddenly turned around and glared at his other son. "Constantine, my firstborn! Come! Give your great-grandma a kiss!" "No fucking way, Dad! I don't care how much you say you'll pay me, I'm not going to kiss a dead body!" Eddie's nostrils flared in rage, but since everyone was staring at them he simply gave his son a big you're-gonna-get-your-ass-wupped-later smile and sprang up from the ground. He smoothed out his Mandarin-collared linen suit and announced, "Everyone, I have a surprise in honor of Ah Ma. Please follow me." He led the group of relatives out to the walled rose garden that bordered the east wing of the house. "Kaspar, we're ready!" he shouted. Suddenly, a bank of floodlights illuminated the darkened garden, and everyone gasped. In front of them was a three-story structure made out of wood and paper. It was an intricately constructed scale model of Tyersall Park, with every pillar, eave, and awning painstakingly replicated down to the last detail. "Kaspar von Morgenlatte, my personal decorator, had a whole team of artisans working on this for weeks," Eddie proudly announced, bowing to the crowd that had by now gathered in front of the house replica. "I am not a decoratur! I am an interieur arkitect und art konsultant!" declared a tall, exceedingly thin man with slicked-back white-blond hair, dressed in a white turtleneck sweater and high-waisted white linen trousers. "Ladies und gentlemen, pleazzze pay attention! The interieur of this maknificent schloss opens up..." Four equally blond assistants scurried out from the shadows. They unfastened a few hinges along the side columns, allowing the entire front façade of the house to open and reveal interior rooms that had been decorated to excruciating detail, but unfortunately _did not_ replicate the real interiors of Tyersall Park. "The walls are twenty-four-carat gold leaf, the fabrics are all Pierre Frey, the crystal chandeliers are Swarovski, und the furnishings are hand-krafted by the same people that did the set designs for Wes Anderson's _Graaand Hotel Budapeshhhhhhhht_ ," Kaspar continued. "Good God, what an insult to Wes. This looks more like a Ukrainian bordello," Oliver whispered to Rachel. "Thank God it's about to be set on fire." Rachel laughed. "I know you don't care for it, but don't you think that's a bit extreme?" "Rachel—Oliver's not joking," Nick cut in. "This is a paper tomb offering. People burn these at funerals as gifts for the deceased to 'enjoy' in the afterlife. It's an ancient ritual." "It's more of a... _working_ -class custom," Oliver continued. "The families buy paper objects and accessories that represent aspirational things the deceased couldn't afford in this life. Paper mansions, Ferraris, iPads, Gucci bags.3 But the paper mansions are usually quite small—like dollhouses. Eddie, of course, has to do everything to the extreme," Oliver noted as Eddie walked around the three-story house excitedly showing off all the objects he had commissioned. "Check out her closet—I had some little dresses made in her favorite lotus silk. And I even had them make exact replicas of Hermès Birkin bags, so Ah Ma will have a good selection of handbags to use in heaven!" The family members stared at the structure in stunned silence. Finally, Eddie's mother said, "Mummy would never use an Hermès handbag. She never carried a handbag—her lady's maids held everything for her." Eddie glared at his mother angrily. "Ugh! You just don't get it, do you? I know she wouldn't normally carry an Hermès. I'm trying to give Ah Ma the best of everything, that's all." "It's very impressive, Eddie. Mummy would have been touched," Catherine said, trying to be diplomatic. Victoria suddenly piped up. "No, no, this is all wrong. It's incredibly tasteless, and what's more, it's extremely un-Christian." "Auntie Victoria, this is a Chinese tradition—it has nothing to do with religion," Eddie argued. Victoria shook her head in fury. "I don't want to hear any more of this nonsense! We Christians do not require worldly things in the kingdom of heaven! Remove this monstrosity at once!" "Do you know how much I spent on this mansion? This cost me over a quarter of a million dollars! We are burning it, and we are burning it now!" Eddie shouted back as he gave Kaspar the signal. "Wolfgang! Juergen! Helmut! Schatzi! _Entzündet das Feuer!_ " Kaspar commanded. The Aryan minions dashed around the structure, dousing it with kerosene, and Eddie theatrically flicked a long matchstick and held it high for all to see. "Don't you dare! Don't you dare burn it on this property! It's satanic, I tell you!" Victoria screamed, as she ran up to Eddie and began trying to wrestle the burning matchstick out of his hand. Eddie lobbed the match onto the structure and it ignited instantly, the force of the flames billowing outward suddenly and almost singeing both their heads. As the enormous replica of Tyersall Park began to be consumed by the fire, all the guests streamed out of the house and surrounded it like a bonfire, taking out their phones and snapping photos. Eddie stared in triumphant silence at the burning house, while Victoria sobbed on the shoulder of the president of China. Cassian, Jake, Augustine, and Kalliste ran around the structure gleefully. "It's actually rather beautiful, isn't it?" Rachel said as Nick came up behind her, wrapping her in his arms as they stared at the fire together. "It is. I have to agree with Eddie this time—I think Ah Ma would have enjoyed this. And why shouldn't she have a Birkin bag in heaven?" Carlton glanced at Scheherazade, marveling at how her hair seemed to glow the most spectacular shades of gold against the rising flames. He took a deep breath, straightened his jacket, and strolled over to where she was standing. " _Je m'appelle Carlton. Je suis le frère de Rachel. Ça va?_ " " _Ça va bien_ ," Scheherazade replied, impressed by his perfect French accent. Breaking into English, Carlton said, "They don't have anything quite like this in Paris, do they?" "No, they sure don't," she answered with a smile. As the paper house and all the paper luxury accoutrements smoldered into black ashes, the crowd began to make their way back into the house. Walking through the rose garden, Mrs. Lee Yong Chien shook her head and leaned over to Lillian May Tan's ear. "What did I tell you? Su Yi's body isn't even cold yet, and the family is already up in smoke!" "This is nothing. Things are going to get far worse when they find out who will get the house," Lillian May said, her eyes flashing in anticipation. "I think they are in for the shock of their lives," Mrs. Lee whispered back. — A humongous, full-page color notice appeared in the obituary section of _The Straits Times_ for five consecutive days: * * 1 Hokkien slang for "busybody." 2 If you're looking to make some extra cash, many families in Singapore will hire you to cry at the funerals of their loved ones. Because the more mourners there are at a funeral, the more impressive it looks. Professional mourners usually come in groups, and they offer a variety of packages (i.e., normal crying, moaning hysterically, foaming at the mouth, and collapsing in front of the coffin). 3 In 2016, Gucci sent out warning letters about trademark infringement to several mom-and-pop shops in Hong Kong that were selling paper Gucci tomb offerings. After a backlash from Chinese shoppers and an avalanche of bad publicity, Gucci issued an apology. # CHAPTER THREE THE CLAYMORE, SINGAPORE Oliver T'sien was in the middle of his morning shave in his condo when Kitty rang, so he put her on speaker. "I'm going to see you today! I'm going to Alistair Cheng's grandmother's funeral this afternoon," Kitty chirped. "You received an invitation?" Oliver tried to mask the astonishment in his voice. "I thought since Alistair is my ex-boyfriend, and I _did_ meet his grandmother once, it would only be appropriate to convey my condolences in person. It will be so nice to see his family again." "Where did you even hear about the funeral?" Oliver asked, as he arched his neck toward the mirror and focused his razor on the stray hairs under his chin. "Everyone was talking about it at Wandi Meggaharto Widjawa's party last night. Apparently, Wandi knows a few of the people from Jakarta flying in for the funeral. She said it was going to be the society funeral of the century." "I bet she did. But I'm afraid the funeral is really by invitation only." "Well, you'll be able to get me an invitation, won't you?" Implicit in Kitty's coquettish tone was, _since you're on my payroll_. Oliver rinsed off his shaving cream. "Kitty, I'm afraid that this is one time where I really don't have the power to help you." "What if I get dressed up in a very conservative black Roland Mouret dress and wear a nice hat? I'll even use the Bentley instead of the Rolls and bring a few bodyguards along. Surely they won't turn me away?" "Kitty, you need to trust me on this. This is one funeral you _don't_ want to crash. It would be a faux pas of epic proportions. This is a funeral for family and very close friends only. I assure you there will be no one you know, and it really won't matter if you're not there." "Can you assure me that _Colette_ won't be there?" "Kitty, I can assure you she has probably never even _heard_ of my family." "But that doesn't necessarily mean she won't be there. I heard she got back to Singapore two days ago. It was mentioned in Honey Chai's gossip blog: 'Countess of Palliser is staying at the Raffles Hotel.' Did she leave her orangutans to come to the funeral?" Oliver rolled his eyes in exasperation. "There is no way Colette or Lady Mary or whatever she calls herself these days will be anywhere near that funeral. I promise." "I guess I'll go spend the day on Tatiana Saverin's new yacht then. She says it was designed by the same guy that did Giorgio Armani's boat." "Yes, it is a beautiful day for sailing. Why don't you slip on your sexiest Eres bikini, put on your sailing diamonds, and spend the day sipping Aperol spritzes on a yacht? Stop wasting your precious time thinking about this dreary funeral that I _wish_ I didn't have to attend!" (Oliver lied. As much as he adored Su Yi, he had to admit that today was truly going to be the social event of the century.) "Okay, okay." Kitty laughed and hung up. Oliver leaned against his bathroom sink, methodically patting some Floris aftershave on his cheeks and throat. The phone rang again. "Hello, Kitty." "What are sailing diamonds? Do I need to get some?" "It's just an expression, Kitty. I made it up." "But do you think I should wear a diamond necklace with my bikini? I could put on my Chanel Joaillier diamonds, the one in the sunburst floral pattern. Diamonds are waterproof, aren't they?" "Of course. Go for it. I have to run now, Kitty, or I'm going to be late for the funeral." Two seconds after hanging up, Oliver's mother, Bernadette, walked into the bathroom. "Mother, I'm not dressed!" Oliver groaned, tightening the towel around his waist. "Hiyah, what do you have that I haven't already seen? Tell me, is this okay?" Oliver scrutinized his sixty-nine-year-old mother, slightly annoyed by the graying roots that were showing on the top of her head. Her Beijing hairdresser really wasn't doing a good job maintaining her color. Bernadette, who was born a Ling, came from a family where all the women were renowned for their beauty. Unlike her sisters or her cousins—Jacqueline Ling being the prime example, who appeared preternaturally preserved—Bernadette looked her age. Actually, in the tailored dark blue silk brocade suit with the ribbon tie at the collar, she looked older. _This is what happens when you spend twenty-five years toiling away in China_ , Oliver thought to himself. "Is this the only dark dress you brought with you?" "No, I brought three dresses, but I already wore the other two during the night visits." "Then I suppose this one will have to do. Did your tailor in Beijing make this one for you?" " _Aiyah_ , this one was very pricey compared to my Beijing tailor! Mabel Shang's girl in Singapore made this for me more than thirty years ago. It's a copy of some famous Paris designer. Pierre Cardin, I think." Oliver exploded in laughter. "Mother, no one would copy a Pierre Cardin. It's probably one of those 1980s designers Mabel used to love. Scherrer, Féraud, or Lanvin back when Maryll was in charge. Well, at least you can say it still fits. You didn't bring one of your little cloche hats, did you?" "No, I didn't. I packed for Singapore weather. But Oliver, what do you think of this?" Bernadette asked, fingering the impressive jade-and-ruby butterfly brooch pinned to her lapel. "Oh, it's fabulous." "You sure no one will be able to tell? Heaven forbid I get seated next to your grandmother and she notices," Bernadette fretted. "With grandma's glaucoma, I don't think she can even see that you have the brooch on. Trust me, I had the best jeweler I know in London replicate it." "I should never have let the real thing go." Bernadette sighed. "We didn't really have a choice, did we? Just forget it ever happened. You still have the brooch, right here. The jade looks flawless, the rubies look real, the diamonds are sparkling like they came straight out of Laurence Graff's hands. If I can't tell, no one will be able to tell." "If you say so. Now, do you have a tie Dad can borrow? The only one he brought got all stained with chocolate cake last night. So sad, once Tyersall Park goes, I'm going to miss that chocolate cake." "Of course. Go to my closet and pick out anything you'd like for him. One of the Borrellis might be nice. Actually, give me a second and I'll do it." As his mother left the bathroom, Oliver thought to himself, _I've learned my lesson. Next time I'm going to put them up at a hotel, even if they kick and scream._ _This flat is just too small for three people._ * * * * Asian parents visiting their adult children who live in other cities ALWAYS INSIST on staying with them, no matter if the child lives in a studio apartment or the house is already bursting at the seams with too many hormonal teenagers, and even if the parents could afford to buy out a whole floor of the Ritz-Carlton. And of course, even if you're forty-six years old, suffering from sleep apnea and chronic sciatica, you're still expected to give up your master bedroom to your parents and sleep on the inflatable mattress in the living room. Because that's just how it is. # CHAPTER FOUR ST. ANDREW'S CATHEDRAL, SINGAPORE Inside the lead Mercedes escorting the funeral cortege from Tyersall Park to the cathedral, Harry Leong was staring out the window, trying to ignore the incessant chatter that came from his wife, Felicity, arguing over last-minute details with her sister Victoria. "No, we _have_ to let the president of Singapore speak first. That follows official protocol," Victoria said. "But then the Sultan of Borneo will be terribly insulted. Royalty should always come before elected officials," Felicity argued back. "Rubbish, this is _our_ country, and o _ur_ president has precedence. You only care about the sultan because of all the Leong plantations in Borneo." "I care about him not urinating all over the pulpit at St. Andrew's. His Majesty is an elderly diabetic with a weak bladder. He should get to have the first word. Besides, he knew Mummy even before the president was born." "Reverend Bo Lor Yong is going to have the first word. He's going to read the blessing." "WHAT? You invited Bo Lor Yong too? How many pastors are going to be at this funeral?" Felicity asked incredulously. "Only three. Reverend Bo will deliver the blessing, Bishop See will give the sermon, and Pastor Tony Chi will say the closing prayer." "What a pity. Is it too late to ask Tony to deliver the sermon? He's so much better than that See Bei Sien," Felicity scoffed. Harry Leong groaned. "Can you speak softer? You two are giving me a migraine. If I knew you were going to argue all the way, I would have ridden in Astrid's car." "You know your security won't let you ride with her. She doesn't have bulletproof windows," Felicity said. — In the Jaguar XJL (which was not bulletproof) following behind them, Eleanor Young sat scrutinizing her son's face intently. "I think next week I should make an appointment for you to see my dermatologist. Those puffy lines under your eyes...I'm not happy with them. Dr. Teo can do wonders with his laser." "Mum, it's fine. I just didn't get much sleep last night," Nick said. "He was up all night writing his tribute to Ah Ma," Rachel explained. "Why did it take all night?" Eleanor asked. "It was the hardest thing I've ever had to write, Mum. You try condensing Ah Ma's entire life into a thousand words." Rachel squeezed Nick's hand encouragingly. She knew how much he had struggled over his speech, working on it until the wee hours and getting out of bed several times after that to make a change or add another anecdote. Eleanor kept prodding. "Why should there be a word limit?" "Auntie Victoria insisted that I only have five minutes for my speech. And that's about a thousand words." "Five minutes? What nonsense! You were her closest grandson, and the only _Young_. You should be allowed to speak as long as you wish!" "Apparently there are going to be a lot of speeches, so I'm just toeing the party line," Nick said. "It's fine, Mum. I'm very happy with my speech now." "Oh my. Who is that woman in the car beside us?" Rachel suddenly asked. Everyone turned to look into the Rolls that was trying to overtake them, where there was a woman wearing a black hat with a dramatic black veil draped over her face. "Looks like Marlene Dietrich," Philip chuckled as he drove. " _Aiyah_ , Philip! Pay attention to the road!" Eleanor yelled. "Actually, it _does_ look like Marlene Dietrich. I wonder which sultan's wife that could be?" Peering over, Nick laughed. "That's no sultana. That's Fiona Tung behind that getup." — In the backseat of the Rolls-Royce Phantom—the only Rolls in the stately procession of cars—Fiona fidgeted with her hat uncomfortably. "I don't know why you made me wear this ridiculous veil. I can't see out of it, and I can hardly breathe." Eddie snorted. "I don't know what you're talking about. Kalliste can breathe just fine in hers, can't you?" Eddie's tween daughter was wearing a hat and veil identical to her mother's, and she stared straight ahead, not answering her father. "Kalliste, I SAID: CAN YOU BREATHE?" "She's got headphones on, Dad. She can't see or hear a thing. She's like Helen Keller right now," Augustine said. "At least Helen Keller could speak!" Eddie said in annoyance. "Um, actually, she couldn't, Pa. She was mute," Constantine responded from the front passenger seat. Eddie reached over and tugged his daughter's veil aside. "Get those headphones off! Don't you dare wear them into the church!" "What difference does it make? No one will be able to see me under this thing. Can't I just listen to Shawn Mendes while I'm in the church? I promise you his songs will make me cry buckets like you want me to." "No Shawn Mendez! And no Mario Lopez, Rosie Perez, or Lola Montez either! Kids, you are all going to sit in the church with ramrod-straight posture, singing all the hymns and crying pitifully. Cry as if I've cut off your allowance!" "That's really going to work, Dad. _Boo hoo hoo, what am I going to do without my twenty dollars this week?_ " Constantine said sarcastically. "Okay, you've just lost your allowance for the rest of the year! And if I don't see you crying until your eyes bleed, especially while I'm singing my song—" "Eddie, ENOUGH! What is the point of trying to force the kids to cry when they don't wish to cry?" Fiona snapped. "How many times do I have to tell you...we need to be the chief mourners at this funeral. We need to show everyone how much we care, because all eyes will be on us! Everyone knows that we are going to be benefiting the most!" "And how would they know that?" "Fiona, have you been in dreamland all week? Ah Ma died before she could make any changes to her will! We're going to be the ones getting the lion's share! In a few days, we're going to become bona fide members of the three-comma club!1 So we have to really go all out to display our grief!" Fiona shook her head in disgust. At this moment, her husband truly made her feel like crying. ··· "Lorena, Lorena, over here! I _choped_ 2 this seat for you!" Daisy shouted, waving from her strategically chosen aisle seat. Lorena made a beeline for Daisy and saw the packet of tissues she had placed next to her on the wooden pew. "Thanks for saving me this seat! I thought I was going to have to sit with my in-laws. Is Q.T. still parking?" " _Aiyah_ , you know my husband doesn't do funerals. Just the sight of a coffin will give him diarrhea." Just then, there was a loud buzzing from Daisy's handbag. "Wait ah, I'm going to take out my iPad. Nadine wanted me to FaceTime her from the funeral. She's beside herself that she didn't get invited." "What? Ronnie and her didn't get invitations?" "No, Old Man Shaw got the invitation, and of course he brought the new wife. They are two rows in front of us." Lorena craned her neck to look at Nadine's father-in-law, the eighty-five-year-old stroke survivor Sir Ronald Shaw and his brand-new twenty-nine-year-old wife from Shenzhen. "I must say she's very pretty, but I'm still surprised that Sir Ronald isn't, you know, _chee cheong fun_." " _Aiyah_ , these days with Viagra, even _chee cheong fun_ can become _you char kway_."3 Daisy giggled as she activated the FaceTime function. Nadine's dramatically made-up face popped up on screen. " _Alamak_ , Daisy, I've been waiting and waiting! Who's arrived? Who do you see?" "Well, your father-in-law is here with your new...er...mother-in-law." "Oh, who gives a damn about them! How does Eleanor look? And what's Astrid wearing?" Nadine asked. "Eleanor of course looks great—I think she's wearing that black Akris suit with notched lapels she bought when we all went to the Harrods sale a couple of years ago. Astrid hasn't arrived yet, or at least I don't see her anywhere. _Oh my goodness!_ Who's this? The Bride of Frankenstein just walked in!" "What? Who? Hold up your iPad, let me see!" Nadine said excitedly. Daisy covertly pointed her iPad toward the central aisle. " _Alamak_ , it's Eddie Cheng's wife, the long-suffering Tung girl. She's dressed up like Queen Victoria in full mourning garb with a big black hat covered by a floor-length black veil. And oh look, their daughter is dressed just like her! And the sons are wearing black brocade Nehru jackets. Good grief, they look like they are in some suicide cult!" — Rachel went along with Nick's parents to the beautifully polished wooden pews reserved for the family, marveling at the beautiful neo-Gothic features of Singapore's oldest cathedral as she walked up the central aisle. Nick meanwhile headed to the chapel behind the altar to confer with his aunt Victoria, who was in the midst of coordinating all the speakers. He shook the president's hand and waited patiently for his marching orders. Victoria finally noticed him. "Oh Nicky, good, you're here. Listen, I hope you don't mind, but we've had to cut your speech from the program. We simply don't have the time, with everyone needing to speak." Nick stared at her in dismay. "You're not serious?" "I'm afraid I am. Please understand, we're already running overtime. We have three pastors speaking, the Sultan of Borneo, and the president. And then the Thai ambassador has a special message to deliver, and we also have to fit in Eddie's song—" " _Eddie's going to sing?_ " Nick was incredulous. "Oh yes. He's been rehearsing a special hymn all week with a very special guest musician who's just flown in." "So let me understand this: We have six people giving speeches, but _no one_ from the family will actually get a chance to speak about Ah Ma?" "Well, there's also been a last-minute addition. Henry Leong Jr. has decided to give a speech." "Henry Junior? But he barely knows Ah Ma. He's spent most of his life in Malaysia being doted on by his Leong grandparents!" Victoria smiled embarrassedly at the president, who was watching the whole exchange with piqued interest. "Nicky, may I remind you that your cousin Henry is the eldest grandson. He has every right to give a speech. And besides," Victoria lowered her voice, " _he's running for a seat in parliament this year. Felicity said we_ HAVE _to let him speak. And of course the president wants him to!_ " Nick stared at his aunt for a moment. Without another word, he turned around and headed back to his pew. — Michael Teo—Astrid's estranged husband—came striding up the central aisle of St. Andrew's Cathedral, dressed in a brand-new Rubinacci suit with shiny black John Lobb wing tips. He looked around for where Leong family members might be seated, and just as he caught sight of Astrid fussing over Cassian's Windsor knot in the second pew from the front, two men in dark suits suddenly appeared, blocking his path. "I'm sorry, Mr. Teo. _Family only on this side_ ," the man with the earpiece said. Michael opened his mouth, about to say something, but as he knew that all eyes were on him, he nodded, smiled politely, and took the nearest empty seat in another pew. Sitting in the pew opposite from Michael were members of the T'sien family. "Did you just see that? That was _brutal_ ," Oliver whispered to his aunt Nancy. "Hnh! Serves him right. I don't know how he even got an invitation," Nancy huffed, as she thought to herself, _That man was wasted on Astrid. The things I could do with that body..._ Nancy turned to face Oliver's mother. "Bernadette, how nice you look in that...frock." _Ghastly. I can smell the mothballs._ "Thank you. You look so fashionable, as always," Bernadette replied, eyeing Nancy's Gaultier couture dress. _Wasting my brother-in-law's money. No matter how expensive that dress is, you still look like mutton dressed as lamb._ "It's always nice to see the T'sien jade come out for an airing." Nancy eyed the brooch Bernadette had on. _This should have been mine. What a travesty to see it pinned on that horrific schmatta she calls a dress._ The heirloom jewel had been passed down from T'sien Tsai Tay's mother to Bernadette—her favorite granddaughter-in-law—and was said to have belonged to the Empress Dowager Ci'an. Nancy leaned over and said to her mother-in-law, "Do you see Bernadette's brooch...doesn't the carved jade butterfly look more translucent and vibrant than ever?" Rosemary smiled. "It's imperial jade. It always looks better the more it's worn." _I'm so glad we gave it to Bernadette. This is the gift that keeps on giving—just seeing how jealous Nancy still is after all these years._ Bernadette smiled nervously at the two women and tried desperately to deflect attention from herself. " _Aiyah_ , Nancy, this is nothing. I don't have much compared to you. Look at your pearls! My goodness, I've never seen so many worn at the same time." _She looks like a madwoman who just robbed Mikimoto._ Nancy fingered the enormous Sri Lankan sapphire-and-diamond clasp on her eight-strand pearl necklace. "Oh these? I've had them for ages. I think Dickie bought these for me when we were invited to Prince Abdullah of Jordan's wedding to the beautiful Rania. Of course, this was long before he knew he was going to be king." Overhearing the exchange, Oliver added, "I don't think Abdullah ever expected it. His uncle was supposed to be the next king, but Hussein bypassed him on his deathbed and anointed his son the successor. It was a shock to everyone." Nancy sat back in her seat, wondering what shocks lay in store for her Young relatives. What would become of all of Su Yi's jewelry? Her collection was said to be unparalleled in all of Asia, so there was surely going to be a battle royal over her treasures. — Sitting in the middle of her row, Astrid heard an urgent little ping from her cell phone. She got out her phone discreetly and read the text message: MICHAEL TEO: First u exclude my name from the Straits Times death notice, and now u bar me from sitting next to my own son! Yur gonna pay for this. Astrid began texting back furiously. ASTRID LEONG: What are you talking about? My mother and uncle arranged the notice. I didn't even know you were coming. MT: I'm not a monster. I liked your Ah Ma, ok? AL: So where are you now? You're going to be late! MT: Already here. I'm sitting one row behind and across from u. Astrid swiveled around and saw Michael seated across the aisle. AL: Why are you over there? MT: Don't pretend u don't know. Your father's fucking bodyguards wouldn't let me into your row! AL: I promise you I had nothing to do with that. Come join us now. Michael stood up, but before he could leave his pew, a cluster of guests walking up the aisle blocked him from moving. Instead, they were being directed into his row, and a lady wearing a chic dark gray silk shantung dress with a silver gray frayed bouclé topper coat and black gloves was ushered into the seat next to him. Astrid's jaw dropped. She spun around and faced Oliver, who was seated just behind her. "Am I hallucinating, or is that who I think it is over there in head-to-toe Chanel couture?" Oliver turned and saw the lady who had just taken the seat on the aisle opposite from him. "Holy Anita Sarawak!" he muttered under his breath. It was Colette, sitting with her husband, the Earl of Palliser, and the British ambassador. How stupid of him—of course the earl would attend. His father, the Duke of Glencora, was great friends with Alfred Shang. Eagle-eyed Nancy T'sien leaned over and whispered to Oliver, "Who is that girl over there?" "Which girl?" Oliver asked, feigning ignorance. "The pretty Chinese girl sitting with all those _ang mors._ " As the two of them looked at Colette, she suddenly swept her hair aside, revealing an enormous jade butterfly brooch pinned to her left shoulder. Oliver turned white as a sheet. Nancy almost gasped, but she stopped herself. Instead, she said, "What an exquisite brooch. Mummy, do you see that lady's lovely jade brooch?" She tugged furiously at Rosemary T'sien's elbow. "Oh. Yes," Rosemary paused for a moment in recognition. "How lovely it is." Just then, Reverend Bo Lor Yong approached the pulpit and spoke too close to the microphone. His voice came out booming: "Your Majesties, Highnesses, Excellencies, Mr. President, ladies and gentlemen, may I present Shang Su Yi's dearest grandson, Edison Cheng, accompanied by the one and only...Lang Lang!" The crowd murmured excitedly at the announcement of the celebrated pianist, and all eyes were on the main altar as Lang Lang walked to the grand piano and began to play the opening chords of a curiously familiar melody. The doors of the cathedral swung open, and eight Gurkha guards from Tyersall Park stood silhouetted in the dramatic arched entrance, bearing Su Yi's casket on their shoulders. Captain Vikram Ghale was the lead pallbearer, and as they slowly began to enter the nave of the cathedral, Eddie emerged from the shadows of the transept and took his place in front of the piano, a lone spotlight on him. As the guests in the church stood up respectfully, the casket made its way up the central aisle as Eddie began to sing in a quivering tenor: > " _It must have been cold there in my shadowwwwww,_ > > _to never have sunlight on your faaaaaaace..._ " "You've got to be fucking kidding me," Nick muttered, burying his face in his hands. "They cut your speech for _this_?" Rachel was furious and yet trying desperately not to laugh. " _Did I ever tell you you're my heeeeeeeeeeeero..._ " Eddie belted out, not quite hitting the right pitch. Victoria turned to Felicity with a frown. "What on earth?" Felicity whispered to Astrid, "Do you know this hymn?" "It's not a hymn, Mum. It's 'Wind Beneath My Wings' by Bette Midler." "Bet who?" "Exactly. She's a singer Ah Ma would never have heard of either." As the guards proceeded up the aisle, everyone in the cathedral suddenly went quiet as they caught sight of Su Yi's two devoted Thai lady's maids. Swathed in dark gray silk dresses with a single black orchid pinned above their breasts, they walked five paces behind her casket, tears running down their faces. * * 1 Just count the commas and you'll understand what Eddie means: $1,000,000,000. 2 A Singlish term meaning "to reserve." Singaporeans _chope_ seats at concerts, hawker centers, and other public venues by placing a packet of tissue paper on the seat. 3 _Chee cheong fun:_ a long, limp, rice noodle roll. _You char kway:_ a long, stiff, deep-fried breadstick. # CHAPTER FIVE ST. ANDREW'S CATHEDRAL, SINGAPORE After the memorial service, guests were invited to a white tent that had been erected next to the cathedral, where everyone could mingle over an elaborate afternoon-tea buffet. The tent was decorated to replicate Su Yi's conservatory at Tyersall Park. Hundreds of pots of orchids in full bloom hung from the ceiling, while towering topiaries composed of roses from Su Yi's rose garden commanded each of the tables covered in Battenberg lace. A battalion of waitstaff rolled around antique silver carts arrayed with steaming cups of Darjeeling tea and ice-cold flutes of Lillet champagne, while chefs in white toques manned the tables filled with afternoon-tea standards like finger sandwiches, scones with clotted cream, and _nyonya_ cakes. Nick, Rachel, and Astrid sat in a quiet corner reminiscing with cousins Alistair, Scheherazade, and Lucia. "You know, I used to be deathly afraid of Ah Ma when I was little," Alistair confessed. "I think it's maybe because all the adults seemed to fear her, I just picked up on that." "Really? She always seemed like a fairy godmother to me," Scheherazade said. "I remember one summer hols many years ago, I was wandering around Tyersall Park by myself when I came upon Great-auntie Su Yi. She was standing at the edge of that pond with those enormous lily pads, and when she saw me, she said, 'Zhi Yi, come'—she always called me by my Chinese name. She looked up at the sky and made this clicking sound with her tongue. Out of nowhere these two swans swooped down and landed right on the pond! Su Yi reached into the pocket of that blue gardening coat she always wore and pulled out little sardines. The swans glided up to her and gently ate the sardines out of her hand. I was absolutely mesmerized." "Yes, those swans were the same pair that were always at the lake in the Botanic Gardens. Ah Ma used to say, 'Everyone thinks these swans live there, but actually this is their pond, and they just visit the Botanic Gardens because they've gotten fat and spoiled by all the tourists that feed them!' " Nick remembered. "It's not fair, I feel like you got to know Great-auntie Su Yi much better than I did, Scheherazade!" Lucia said with a little pout. Rachel shot Lucia a smile, and then noticed Carlton strolling nonchalantly toward them. "Carlton! How did you get through Fort Knox?" "I may or may not have been slipped an invitation by someone," Carlton said with a wink, as Scheherazade blushed. "Astrid, mind if I have a quick word?" Carlton said. "Me?" Astrid looked up in surprise. "Yes." Astrid got up from her chair and Carlton took her over to a corner. "I have a message from a friend. Go to the chapel behind the north transept of the cathedral right now. Trust me." "Oh. Okay," Astrid said, her brow furrowed at Carlton's mysterious message. She walked out of the tent and headed into the church through a side door, making her way to the north transept. As she entered the small alcove chapel within the cathedral, her eyes took a moment to adjust to the darkened room. A figure emerged from behind a pillar. "Charlie! Oh my God! What are you doing here?" Astrid exclaimed as she rushed to embrace him. "I just couldn't let you be alone today." Charlie hugged her tight, kissing her forehead repeatedly. "How are you?" "I'm okay, I guess." "I know this is the last thing on your mind, but you look stunning today," Charlie said, marveling at her knee-length black dress with a white Greek key motif piping on the skirt and collar. "This was my grandmother's, from the 1930s." "Was the service beautiful?" "I wouldn't really call it that. It was grand, and it was strange. The Sultan of Borneo talked about the war and how my great-grandfather helped to save his family. He spoke in Malay, so everything had to be translated by this very perky woman. Then my brother spoke, and he was so weird and stilted he sounded like the Manchurian Candidate. The most emotional moment came when my grandmother's casket first entered the church. When I saw Madri and Patravadee walking behind the casket, I just lost it." "I know it's been a very sad day. I brought something for you...I was debating at first whether or not to show it to you today, but I think it might actually cheer you up." Charlie took a small envelope out of his pocket and handed it to Astrid. She opened it up and unfolded a handwritten note: > Dear Astrid, > > I hope you don't mind the intrusion, but I want to express how sorry I am to hear of your grandmother's passing. She was a great lady, and I know she meant so much to you. I was very close to my Ah Ma as well, so I can imagine what you must be feeling right now. > > I also want to apologize for my actions several months ago in Singapore. I am so terribly sorry for any pain or embarrassment I might have caused to you and your family. As I'm sure you're aware, I was not myself that day. I have made a complete recovery since then, and I can only hope and pray that you will accept my heartfelt apology now. > > In the last few months, I've had the luxury of time. Time to heal and recover, time to reassess my life. I know now that I do not ever wish to come between what you and Charlie have together, and I want to give you my blessing, not that you in any way need it. Charlie has been so decent to me throughout the years, and I only want what's best for him now. As we are all only too painfully aware, life is precious, and much too fleeting, so I want to wish the both of you everlasting happiness. > > Yours truly, > > Isabel Wu "How sweet of her!" Astrid said, looking up from the note. "I'm glad she's doing so much better." "I am too. She gave me the note when I went to drop off the girls last night. She was worried that you wouldn't want to read it." "Why wouldn't I? I'm so happy you showed it to me. It's the best thing that's happened today. It feels like one more burden has been lifted. You know, all through the service, I was thinking of my grandmother's last conversation with me. She really wanted me to be happy. She wanted us to ignore all the rules of mourning and get married as soon as we possibly could." "We will, Astrid, I promise." "I never thought Michael would be the one to hold things up," Astrid said with a sigh. "We'll get through this. I have a plan," Charlie said. They were suddenly interrupted by voices echoing through the north transept. Astrid peeked out the door for a moment. "It's my mother," she mouthed to Charlie. Victoria, Felicity, and Alix skulked through the transept and entered the chapel on the opposite side. In the middle of the room was Su Yi's coffin. "I'm telling you, her dentures were crooked," Felicity said. "They didn't look crooked to me," Victoria argued. "You'll see. Whoever the stupid mortician was that worked on her didn't place them properly." "This is such a bad idea—" Alix began to protest. "No, we must do this for Mummy. I won't be able to sleep if I let Mummy be cremated with crooked teeth." Felicity began to unfasten the lid of the casket. "Here, help me with this." The three women lifted the lid of the casket slowly. Looking down at their mother cocooned in her golden robe, the sisters, normally such pillars of discipline and resolve, began to sob quietly. Felicity reached over to embrace Victoria, and the two of them began to cry even harder. "We must be strong. We're all that's left now." Felicity sniffed as she began to collect herself. "It's funny how lovely she looks. Her complexion is smoother than it's ever been." "While we're here, do we really want to let this Fabergé spectacle case be cremated? What a waste," Victoria said, sniffing. "Those were her funerary instructions. We must honor them," Alix insisted. Victoria scoffed at her little sister. "I don't think Mummy really considered the implications when she wrote that. Surely she would have wanted us to remove the Fabergé case after the funeral? Just like we removed the gold tiara? You know how she hated waste." "All right, all right, just take the glasses out and place them beside her pillow. Now, someone help me open her mouth." Felicity leaned into the coffin and tugged at her mother's stiff jaw. Suddenly she let out a shriek. "What happened, what happened?" Victoria gasped. Felicity cried, "The pearl! The Tahitian black pearl! I opened her mouth and it rolled down her throat!" # CHAPTER SIX EMERALD HILL, SINGAPORE It was eleven thirty on Sunday night, and Cassian was finally down for the count. Astrid padded back to her bedroom, sinking wearily into bed. It had been a long weekend after a very long week, what with her grandmother's funeral, and she thought that Cassian spending a day with his father would give her a chance to recoup a little. Instead, her son had returned home and had spent the better part of the evening attempting to launch an insurrection. Astrid fired off a text to Michael: ASTRID LEONG: Simple request—when Cassian spends the day w/ you, could you please refrain from letting him play 7 straight hours of Warcraft? He comes back a total zombie and is just impossible. Thought we were in agreement about the gaming. A few minutes later, Michael replied: MICHAEL TEO: Stop exaggerating. He didn't play for 7 hrs. AL: 7 hours, 6 hours, it was clearly too much. Tomorrow is a school day and he's still up. MT: Not sure what yr prob is. He always sleeps fine @ my house. AL: Because you let him go to bed whenever! His schedule is all messed up when he comes back. You have no idea—I have to deal with him all week. MT: U wanted it this way. He should be at Gordonstoun. AL: Boarding school in Scotland is not the answer. Not going to argue with you over this again. I just don't understand why you bother having him when you don't even want to spend time with him. MT: To get him away from your corrupting influence. Astrid sighed in frustration. She knew Michael was trying to bait her again, and she wasn't going to fall for it. He was just getting back at her for how he perceived he had been treated at her grandmother's funeral. She was about to switch off her phone when his next message popped up: MT: Anyway, this will be over soon. I'm getting full custody of Cassian. AL: You're delusional. MT: No, yur a lying cheating whore. Astrid's text message app froze for a moment, and then a high-resolution file came through. It was a photograph of Astrid and Charlie lounging together on pillows on the deck of a vintage Chinese junk that had been cruising the South China Sea. Astrid's head was resting intimately against Charlie's chest. Astrid recognized the photo from five years ago, when Charlie had attempted to cheer her up after Michael had dropped a bombshell on her in Hong Kong, begging to end their marriage. Michael's follow-up text read: MT: No judge is going to give u custody now. AL: This photo proves nothing. Charlie was only consoling me after you left. MT: "Consoling." Did this include blow jobs? AL: Why do you need to be so crass? You know I never cheated on you. You were the one who fake cheated, wanting out of our marriage at that time, and I was so destroyed. Charlie was just being a good friend. MT: Friends with benefits. I got tons more pics. U have no idea. AL: I don't know what else you could possibly have. I've done nothing wrong. MT: Yes, jury will really believe you. Wait till they see what I've got. Astrid stared at his words, her face going hot with fury. She immediately speed-dialed him, but it went straight to voice mail. _Hi, you've reached Michael Teo._ _This is my private line, so you must be damn important. Leave a message and I will get back to you if it's important enough. Heh Heh Heh._ At the sound of the beep, Astrid spoke: "Michael, this isn't funny anymore. I don't know what sort of advice that lawyer of yours has been giving you, but these tactics are only going to end up harming you. Please just stop, and let's try to come to a reasonable agreement. For the good of Cassian." Astrid hung up the phone, placed it on the side table, and turned off her bedside lamp. She lay in bed in the darkness, furious at Michael, but even more furious with herself because she knew she'd played right into his trap. She should never have texted him in the first place. Michael just wanted to agitate her. That's all he wanted to do in every interaction they had these days. Her phone beeped again, and she knew it would be another incendiary text from Michael. She was determined not to look at any more of his texts. She needed to get some sleep, because tomorrow was going to be another big day—the reading of her grandmother's will was taking place at 10:00 a.m. sharp. Her phone buzzed again with another text message notice. And then another. Astrid turned to face away from her phone, clenching her eyes closed. Suddenly it occurred to her... _What if it wasn't Michael? What if it was Charlie, who had just returned to Hong Kong?_ Sighing, she reached for her phone and turned it on. There were three text messages, and surprise, surprise, they were from Michael. The first one simply read: For the good of Cassian. The second text was a file that was still in the process of downloading, but the third text read: $5 billion or you lose him forever. A few seconds later, the download was complete, and Astrid tapped on the icon before she could stop herself. It was a thirty-second video clip, a grainy, night-vision shot, and as Astrid squinted at the glowing screen in the dark, she could make out the figure of a naked girl with her back to the camera, straddling a man lying on a bed. The couple was unmistakably in the midst of sex, and as the woman's body thrust and swayed, her head shifted for a moment, and Astrid could clearly recognize that the man on the bed was Charlie. It was only at that moment that she realized, in absolute horror, that _she_ was the girl in the video. Astrid gasped out loud and dropped her phone as if it had burned her hands. "Ohmygodohmygodohmygod!" she whispered to herself before picking up the phone and attempting to dial Charlie's number. Her trembling fingers somehow couldn't swipe to the correct menu on her phone, and instead made the video play again. Finally, she got to her contacts screen and hit CW1, his private mobile. After several rings, Charlie picked up. "Baby, I was just thinking about you." "Oh God Charlie—" "Are you okay? What is it?" "Oh God, I don't even know what to say—" "Just take your time. I'm right here," Charlie said, trying to sound calm. He could hear the terror in her voice. "Michael just sent me a video. It's of the two of us." "What kind of video?" "He texted it to me. It's a video of us...having sex." Charlie almost jumped out of his chair. "What? Where?" "I don't know. I didn't look too hard. The minute I saw your face, I just freaked out." "Send it to me right now!" "Um, is it safe to text it to you?" "Fuck if I know. Send it via WhatsApp. I think that's supposed to be more secure." "Okay, hold on." Astrid found the video clip and forwarded it to Charlie. He went silent for a few interminable minutes, and she knew he had to be scrutinizing it. Finally, his voice came back on, sounding preternaturally calm. "Michael just sent this to you?" "Yes. We were in the middle of a texting argument. Over Cassian, of course. Charlie, is it really us?" "It is." Charlie sounded grim. "Where was it taken? How—" "It's taken right here in my bedroom in Hong Kong." "So it must have been taken within the last year. Because I didn't start sleeping over at your place until three months after my formal separation with Michael." Charlie suddenly groaned. "Fuck, I could still be under surveillance right now! Let me get outta here and call you back." Astrid paced her bedroom, waiting for Charlie to call her back. She felt herself suddenly becoming paranoid. Michael used to be a high-level security expert for the Ministry of Defense. Had he somehow managed to plant a hidden camera in this bedroom too? Grabbing her phone, she fled her bedroom and went downstairs into her courtyard sitting room. Maybe being in a tranquil space would calm her down. As she sank into the sleek white sofa, it occurred to her that the whole house could be bugged. She didn't feel safe here anymore. She slipped on her sandals and walked out of the house. It was midnight, and a few of the nearby outdoor cafés on Emerald Hill Road were still buzzing with people chatting away and having drinks. She began strolling up the street when Charlie called again. "Charlie! Are you okay?" "I'm fine. I'm downstairs now, talking from my car. Sorry it took so long. I just needed to get my security team on the case. They are doing a full sweep of the flat now." "Did you wake Chloe and Delphine?" "They are both at a sleepover party tonight." "Thank God they're out of the house." "What the fuck is Michael trying to pull? Does he realize how illegal this is?" Charlie fumed. "He's been in a black mood all weekend, ever since the funeral when my father's bodyguards tried to stop him from sitting in the family row. He wants his full settlement—$5 billion—or he's threatening to leak this video. He's sure I'll lose custody of Cassian, and he knows that's the last thing I want." "I can't believe the fucker is trying to use his own son as a bargaining chip!" "What should we do, Charlie? I think my house is bugged now." "I'll fly my security team down to Singapore tomorrow and they will take care of it. We'll get to the bottom of this. You should go home. You'll be fine. Even if your house is bugged, at least we know who's watching. It's not some gang of thieves trying to rob you or anything." "It's only one asshole trying to rob me of $5 billion," Astrid sighed. "You know what? I think we should assign a security detail to you. I'll get the top team in the world." "You sound like my father now. He's always trying to do this to me. I don't want to live in a cage, Charlie. You know how invisible I try to be. If I can't feel safe in my own house, in my hometown, I don't know what point there is in living here." "You're right, you're right. I'm just paranoid right now, I guess." "Well, I'm wandering the streets of Singapore in nothing but a little linen shift and bedroom sandals, and no one's even noticing me." "I bet you're wrong. I bet every guy on the street is thinking, who is that half-naked babe?" Astrid laughed. "Oh Charlie, I love you. Even in the midst of all this craziness, you can make me laugh." "It's important to laugh. Otherwise, we're letting the fucker win." Astrid had circled back to her terrace house, and now she sat down on the little step that extended just a foot beyond her front gate. "Win, lose, how did this even become a battle? All I ever wanted was for us to be able to find happiness." Charlie sighed. "Well, it's clear to me that Michael doesn't want to be happy. Ever. He just wants to be in a constant state of war with you. That's why he's been stalking us at every turn and dragging his heels with the divorce negotiations." "You're right, Charlie. He sent that video tonight because he wanted to scare us and drive us out of our own homes." "And he damn near succeeded. But you know what? We don't scare so easily. We're both going to go back into our homes now. We're both going to lock our doors, and we're never going to let him in again!" # CHAPTER SEVEN THE LAW OFFICES OF TAN AND TAN, SINGAPORE The OCBC Centre at 65 Chulia Street was nicknamed "the calculator" because of its flat shape and windows that resemble button pads. The architect I. M. Pei had intended for the hulking gray tower to be a symbol of strength and permanence, since it was the headquarters of the Oversea-Chinese Banking Corporation, the island's oldest bank. Unbeknownst to most people, the thirty-eighth floor of the tower was home to Tan and Tan, a small law firm that kept an exceedingly low profile but was undoubtedly one of the most influential legal powerhouses in the country. The firm almost exclusively represented Singapore's establishment families and did not take on new clients—one had to be specially recommended. Today, the glowing mahogany-and-glass reception counter had been given an extra polish, fresh-cut roses bloomed in the guest toilets, and every member of the staff had been told to dress in their smartest outfits. At around fifteen minutes to ten, the elevator doors began to work overtime as the descendants of Shang Su Yi started to arrive en masse. The Leongs showed up first—Harry, Felicity, Henry Jr., Peter, and Astrid1 were joined by Victoria Young and the Aakaras. At 9:55 a.m., Philip, Eleanor, and Nick joined the others in the discreet reception room with its imitation Le Corbusier leather couches. Sitting down next to Astrid, Nick asked, "You okay?" He could always sense whenever things weren't right with his cousin. Astrid smiled, trying to reassure him. "I'm fine. I just didn't get enough sleep last night, that's all." "I haven't been sleeping much either. Rachel thinks my body's just catching up to the grief, but it all still feels like some bizarre dream," Nick said. As he made that comment, the grandfather clock in the lobby began to chime ten, and Alix Young Cheng entered with her husband, Malcolm, and Eddie, Cecilia, and Alistair. Eddie cleared his throat as if he were going to make a speech, but he was interrupted by Cathleen Kah,2 who came out into the reception area to greet the family. Cathleen shepherded everyone down the corridor and through the double doors into the main conference room. A massive dark oak table dominated the room, placed in front of the bank of windows framing a panoramic view of the bay. Sitting at one end of the table was Freddie Tan, Su Yi's longtime lawyer, having coffee with Alfred Shang, Leonard Shang, and Oliver T'sien. _I knew Uncle Alfred would be part of this, but what the hell are Leonard and Oliver doing here?_ Eddie thought to himself. "Good morning, everyone," Freddie said jovially. "Please make yourselves comfortable." Everyone took their seats around the table, clustered more or less in their family units, except for Eddie, who positioned himself at the head of the table. "That was quite the send-off yesterday, wasn't it? Eddie, I never knew you could sing like that," Freddie remarked. "Thank you, Freddie. Shall we begin?" Eddie eagerly suggested. "Relax, kiddo. We're just waiting for one more person," Freddie said. "Who else is coming?" Eddie asked, suddenly alarmed. At that moment, the sound of expensive designer heels making soft clicks against marble could be heard in the corridor outside, and the receptionist opened the conference room doors. "This way, ma'am." Jacqueline Ling breezed into the room in a deep purple wrap dress, her Res Rei sunglasses still on and a Mitford blue Yves Saint Laurent couture overcoat flung across her shoulders. "So sorry to keep you all waiting! Would you believe my driver took me to the wrong place? He thought we were going to the Singapore Land Tower for some reason." "No need to apologize. It's just a few minutes past ten, so you're fashionably late, haha," Freddie joked. Jacqueline took a seat next to Nick, who leaned over and gave her a friendly peck on the cheek. Freddie looked around at the anxiously assembled group and decided it was time to put them out of their misery. "Well, we all know why we're here, so let's get on with it." Eleanor smiled pensively, while Philip leaned back in his chair. Alfred peered down at the sumptuously lacquered wood grain, wondering whether the table had been made by David Linley. Nick winked at Astrid seated across from him, and Astrid smiled back. Freddie pressed a button on the telephone next to him. "Tuan, you can bring it in now." An assistant, nattily dressed in a red sweater vest and striped tie, entered the room, ceremoniously holding an oversize parchment envelope folder. The assistant placed the folder on the table next to Freddie, and then handed him a horn-handled letter opener. Everyone could see Su Yi's personal wax seal on the envelope flap. Freddie took the letter opener and dramatically flicked the blade underneath the bloodred wax. Eddie inhaled audibly. Freddie carefully slid out a legal-size document from the envelope, held it up to the room so everyone could clearly see what it was, and then he began to read: > ### > > I, Shang Su Yi of Tyersall Park, Tyersall Avenue, Singapore, revoke all former wills and testamentary dispositions heretofore made by me and declare this to be my last Will. 1. Appointment of Executors. I appoint my nephew Sir Leonard SHANG and my great-nephew Oliver T'SIEN to be the Co-Executors of my Will. (Eddie darted his eyes over at his cousins, a little dismayed. _Why in the world would Ah Ma choose them as the executors? Oliver I can handle but, ugh, now I have to suck up to that pretentious Leonard!_ ) 2. Specific Cash Legacies. I direct my Residuary Estate to execute payment on the following legacies: a. $3,000,000 to my housekeeper LEE Ah Ling, who has served my family with excellence and devotion since she was a teenager. (Victoria smiled. _Oh good, she deserves it._ ) b. $2,000,000 to my personal chef LIM Ah Ching, who has nourished my family with her fine culinary talents since 1965. (Victoria, shaking her head: _Ah Ching's going to throw a fit when she realizes she got less than Ah Ling. Better not eat the soup tonight!_ ) c. $1,000,000 to my head gardener Jacob THESEIRA, who has maintained the grounds of Tyersall Park with such loving care. I further bequeath to him all the rights and future royalties related to the orchid hybrids we developed together over the course of five decades. d. $1,000,000 to each of my dear lady's maids Madri VISUDHAROMN and Patravadee VAROPRAKORN along with the antique Peranakan gold-and-diamond bracelets labeled for them in the Tyersall Park vault. e. $500,000 to my head of security Captain Vikram GHALE, who has diligently protected me since 1983. I further bequeath to him the Type 14 Nambu pistol given to me by Count Hisaichi Terauchi preceding his departure from Singapore in 1944. (Eleanor: _Wah, so generous! I wonder if Old Lady knew that he made a fortune with his day trading?_ ) f. $250,000 to my chauffeur Ahmad BIN YOUSSEF. I further bequeath to him the 1935 Hispano-Suiza Type 68 J12 Cabriolet3 that was given to me by my father on my sixteenth birthday. (Alfred: _Damn, I wanted the Hispano! I guess I can buy it off him._ ) g. I bequeath every remaining employee of Tyersall Park not mentioned here the amount of $50,000 each. 3. Specific Legacies of Personal Property. a. I direct that my jewelry collection be given and distributed according to the detailed list in Appendix A of this my Last Will and Testament, and as labeled in my vault at Tyersall Park. (Cecilia Cheng Moncur: _I wonder why she bothered. Everyone knows Astrid already got all the good shit._ ) b. I direct that all artwork, antiques, and other household goods not specifically gifted by my Will be distributed equally among my surviving children by my executors in as nearly equal portions as may be practicable, with the exception of the following: i. To my daughter Felicity YOUNG LEONG, I bequeath my collection of Celadon porcelain, which I know she will cherish and keep immaculately spotless for all eternity. (Alix: _Hahaha! Felicity and her_ OCD _. Mummy sure had a sense of humor when she wrote her will!_ ) ii. To my daughter Victoria YOUNG, I bequeath a small painting of a woman by her bedroom window by Édouard Vuillard. I know she has always detested this painting, so I trust she will divest of it immediately and use the proceeds to buy that dream house in England that she keeps talking about. (Victoria: _Criticize me from the grave all you want, but I've already been town-house shopping on Sothebysrealty.com._ ) iii. To my son Philip YOUNG, I bequeath all objects in Tyersall Park belonging to his father, Sir James Young. (Philip: _Did I remember to program the_ DVR _to record the new season of_ Arrow _? Can't wait to get back to Sydney. This is such a colossal waste of time!_ ) iv. To my daughter Alexandra YOUNG CHENG, I bequeath my collection of carved ivory-and-jade name seals, since she is the only one of my children who actually knows Mandarin. v. To my daughter-in-law Eleanor SUNG, I bequeath a box of Santa Maria Novella Almond Soap. (All the women in the room gasped audibly, while Eleanor simply broke out in laughter. Nick glanced at his mother, not understanding. Jacqueline whispered to Nick, "She's letting everyone know she thinks your mother was a dirty woman.") vi. To my cherished granddaughter Astrid LEONG, who in every way takes after my mother's style, I bequeath my collection of cheongsams, ceremonial robes, vintage textiles, hats, and accessories. vii. To my dear granddaughter Cecilia CHENG MONCUR, champion equestrienne, I bequeath a Chinese scroll painting of a galloping herd of horses from the Northern Song period by Li Gonglin. viii. To my loyal and always amusing grand-nephew Oliver T'SIEN, I give and bequeath the pair of Émile-Jacques Ruhlmann table lamps from my dressing room and my signed first edition of W. Somerset Maugham's _Far Eastern Tales_. (Oliver: _Niiiiiice._ ) ix. To my devoted grandson Edison CHENG, I bequeath a pair of Asprey sapphire-and-platinum cuff links, gifted to my husband Sir James Young on our golden anniversary by the Sultan of Perawak. James was far too modest to wear the cuff links, but I know Edison will not be so bashful. (Eddie: _Phwoar! But enough with this piddly shit—can we just get on to the main event?_ ) x. I have made no specific bequests or provisions for my grandchildren Henry LEONG Jr. and Peter LEONG, for whom I have great affection, because they were left generous legacies in my late-husband Sir James Young's Will, and because I know they have been amply provided for by the Leong Family Trusts. (Henry Leong Jr.: _What generous legacy? Gong Gong only left me $1 million, and I was just a little kid!_ ) 4. Legacy of Historical Archives, Photographs, Documents, Personal Letters, and Ephemera. I bequeath ownership and all copyrights and intellectual property rights of my personal archive at Tyersall Park, including all family photographs, letters, journals, and documents to my dearest grandson, Nicholas YOUNG, the noted historian of our family. 5. Legacy of Shares. I bequeath my 1,000,000 Ling Holdings Pte Ltd Preference Shares—which Ling Yin Chao lost to me during an epic mah-jongg battle in 1954—to my beloved goddaughter Jacqueline LING. If she does not survive me, I bequeath the shares to her daughter Amanda LING. It is my hope that this will correct the imbalance of power within the Ling clan. (Jacqueline's cool, collected visage hid what she was feeling inside: _Dear, dear Su Yi, you've liberated me! My God, I wish I could hug you right now!_ Felicity and her sisters frowned a little, not quite understanding what all this meant, but Eleanor, who was on top of the market, immediately started doing the math in her head: _One million shares, and Ling Holdings is around $145 per share today. Jesus, Jacqueline is getting a huge windfall!_ ) 6. Residue of My Estate. The residue of my estate consists of: Cash and other financial instruments held at my banks (OCBC in Singapore, HSBC in Hong Kong, Bangkok Bank in Thailand, C. Hoare & Co. in London, Landolt & Cie in Switzerland). I direct all the monies held in these institutions to be used toward payment of the legacies specified in Clause 2. At the fulfillment of all the specific legacies, I ask that any remaining monies be used to fund a new charitable foundation to be named THE YOUNG FOUNDATION, in memory of my husband Sir James Young. I appoint Astrid Leong and Nicholas Young as co-executors of the foundation. 7. Legacies of Real Property. a. I give and bequeath my property in CAMERON HIGHLANDS, Malaysia, and all the contents within this eighty-acre estate to my dear grandson Alexander LEONG. If he does not survive me, I give the property to his wife Salimah LEONG and my great-grandchildren James, Anwar, and Yasmine LEONG, who I most unfortunately have never been able to meet, in equal shares. (Harry Leong was stunned. This was such a slap to his face! Felicity didn't dare look at her husband, but Astrid couldn't help but smile: _I can't wait to Skype Alex. I want to see the look on his face when he finds out that Ah Ma left the incredible heritage estate in Malaysia to_ HIM _—the son who's been disowned by his father for marrying a native Malay girl._ ) b. I give and bequeath my property in CHIANG MAI, Thailand, and all the contents within this three-hundred-acre estate to my beloved daughter Catherine YOUNG AAKARA. If she does not survive me, I give the property to her children James, Matthew, and Adam AAKARA in equal shares. (Catherine started to sob, while Felicity, Victoria, and Alix all bolted up in their seats, staring at her in shock. _What estate in Chiang Mai?_ ) Freddie Tan paused for a moment, and without a hint of fanfare, read the final clause of the will. c. I give and bequeath my house in SINGAPORE to the following family members in the portions indicated below: My only son, PHILIP YOUNG: 30 percent My eldest daughter, FELICITY YOUNG: 12.5 percent My second daughter, CATHERINE YOUNG AAKARA: 12.5 percent My third daughter, VICTORIA YOUNG: 12.5 percent My youngest daughter, ALEXANDRA YOUNG CHENG: 12.5 percent My grandson, NICHOLAS YOUNG: 10 percent My grandson, ALISTAIR CHENG: 10 percent > SIGNED by SHANG SU YI — Freddie put the document down and looked up at everyone. Felicity, Victoria, and Alix were still trying to digest the surprising news that their mother had owned a secret estate in Thailand. "Go on!" Eddie said impatiently. "I'm finished," Freddie answered. "What do you mean you're finished? What about Tyersall Park?" "I just read you that clause." "What do you mean? You didn't mention Tyersall Park at all!" Eddie insisted. Freddie sighed and began to recite the final clause again. When he was finally done, the room was completely silent for a moment, and then things erupted as everyone started talking at once. "We _all_ have a share in Tyersall Park?" Felicity asked, utterly confused. "Yes, you specifically have a 12.5 percent share in the property," Freddie explained. "Twelve point five percent...what does this even mean?" Victoria grumbled. Eleanor smiled triumphantly at Nick, and then she whispered in Philip's ear, "Your mother can insult me all she wants, but at the end of the day you and Nicky got the majority share and that's what counts!" Nick glanced across the table at his cousin Alistair, who shook his head in disbelief. "I can't believe Ah Ma actually left me something in her will." "More than a little something," Nick said with a grin. Witnessing Nick's exchange with his brother, Eddie grew more livid by the moment. Suddenly he jumped out of his chair, shouting, "THIS IS TOTAL BULLSHIT! Where's my share in Tyersall Park? Let me see that will! Are you sure this is even the latest version?" Freddie looked at him calmly. "I can assure you this is your grandmother's Last Will and Testament. I was present when she signed it." Eddie snatched the document from his hands and flipped through to the last page. There, on the bottom of the page, was the notarized seal, accompanied by the following words: > Signed in the presence of FIONA TUNG CHENG and ALFRED SHANG > > on this the Ninth day of June 2009 Eddie's eyes almost bulged out of his head. "Fucky fuck, _my wife_ was a witness?" "Indeed she was," Freddie replied. "That bitch never told me! And the will was signed in _2009_? How is this possible?" Eddie said, almost shrieking. "Stop asking stupid questions, you _goblok_!4 She took a pen and signed it!" Alfred scolded him, getting fed up. Eddie ignored his great-uncle. "But this means she never changed her will? Not even when Nicky married Rachel?" Nick realized his cousin was right. After all the endless speculation about being disinherited, it turned out his grandmother never once waivered from her original plan. She left a majority stake of Tyersall Park to his father, knowing one day it would be passed down to him. Suddenly he felt an enormous wave of guilt wash over him. Why did he waste so many years being mad at Ah Ma? But Eddie wasn't done with his tirade. He stormed over to Freddie Tan's chair and looked him in the eye accusingly. "The other day when you came to see my grandma, you _told me_ I was going to be the main beneficiary!" Freddie looked startled. "I have no idea what you're talking about. I said no such thing." "You told me I was the 'man of the hour'!" Freddie almost began to laugh, but seeing the look on Eddie's face, he tried to soften the blow. "Eddie, I was making a pun about the Patek Philippe you were wearing. You had on the 150th-anniversary Jump Hour Reference 3969 watch. One of my favorite models." Eddie glared at him incredulously before crumbling into his chair in embarrassment. Alix gave her son a pitiful look, and then turned to the lawyer. "Freddie, I'm not clear about how my mother's financial holdings are going to be divvied up. What about her other stocks and her share of Shang Enterprises?" Freddie looked very uncomfortable and swiveled his chair in Alfred's direction. "Your mother had no other stocks, aside from Ling Holdings," Alfred said. "But Mummy had a huge stock portfolio—she told me she had every blue-chip counter! Wasn't she the biggest private shareholder in Keppel Land, Robinson's, Singapore Press Holdings?" Felicity argued. Alfred shook his head. "No, I am." "But doesn't she share all that with you? As co-owner of Shang Enterprises?" Alfred leaned back in his chair and looked at Felicity. "You need to understand something...Shang Enterprises—the shipping company, the trading firm, all our various business interests around the world—are controlled by the Shang Loong Ma Trust. Your mother was a beneficiary of the Trust, but never a co-owner." "So who owns Shang Enterprises?" Alix asked. "Once again, the Trust owns Shang Enterprises, and I am the chief custodian of the Trust. Your grandfather's will stipulated that the Trust would be passed down through the male line. Only the Shang men could inherit. He was extremely old-fashioned, as you know." "So how did my mummy get all her income?" Alix asked. "She had no income, but the Trust paid for all her expenses. My father's wording in his will was very specific. He stipulated that 'Su Yi's every need, desire, and whim is to be taken care of in her lifetime by the Trust.' So we did." "The Trust paid for everything?" Felicity was incredulous. Alfred sighed. " _Everything._ As you well know, your mother did not have any concept of money. She was born to live like a princess, and she continued to live this way for nine decades. Supporting all of you, maintaining her lifestyle at Tyersall Park, in Cameron Highlands, everywhere she traveled. How much do you think it costs to keep a staff of seventy for so many years? To throw grand parties every Friday night? Believe me, your mother blew through a vast amount." "What will the Trust pay for now?" Victoria asked. Alfred leaned back in his chair. "Well...nothing. The Trust has met all its fiduciary duties to your mother." Victoria looked at her uncle, almost afraid to ask the next question. "So are you telling us that we are inheriting _nothing_ from the Shang Trust?" Alfred shook his head solemnly. The room went silent for a moment as everyone soaked in this bombshell. Felicity was silent, the enormity of her uncle's words slowly sinking in. All this time she thought her mother the great heiress had been co-owner of an empire worth hundreds of billions, and now it turns out she had never even been part of the equation. This meant in turn that _she_ would inherit nothing from Shang Enterprises. She was not a great heiress to anything. She had only been left 12.5 percent of the house, just like the rest of her sisters. But this wasn't right. She was the eldest child. How could Mummy do this to her? Collecting herself, Felicity steeled herself and looked Alfred in the eye with a question. "How much does Mummy have in her bank accounts?" "Not much, really. Some of her accounts are absolutely ancient. Hoare's only has about three million pounds—she inherited that account from my mother, and that was Mum's shopping account when she ordered things from Harrods. Landolt & Cie in Switzerland holds her gold bullion, and that was really just in case the world went to absolute hell. I'd say she has about forty-five, fifty million total." Freddie chimed in, "But that money will automatically go toward paying for all the legacies she left—to Ah Ching, Ah Ling, and so forth." Victoria frowned at Freddie accusingly. "I don't believe this! I don't believe that all this time Mummy had so little money!" Freddie sighed. "Well, she did have one major income-producing asset, and that was her Ling Holdings Preference Shares. She had one million shares that paid a considerable dividend, but she reinvested it all in buying more shares. Her shares are valued at about half a billion dollars today, but as you all know, that's spoken for now." The sisters stared at Jacqueline in absolute horror. Su Yi's beautiful goddaughter had automatically inherited more money from their mother's estate than they did. "So you're telling me the only thing of any income-generating value we're inheriting from our mother is Tyersall Park?" Felicity said slowly, as if not quite believing her own words. "Well, that isn't exactly chopped liver. Tyersall Park is worth about a billion dollars today if you sold it," Freddie remarked. "Two billion," Alfred piped up. Victoria shook her head vehemently. "But we could never sell Tyersall Park! It has to stay in the family. Where does that leave us? We get nothing! Am I supposed to live off the proceeds of one miserable Vuillard?" Felicity looked at her husband with tears in her eyes and said in a quivering voice, "If we are forced to sell Tyersall Park I only get a few hundred million. I'm going to be _a nobody_ now!" Harry squeezed her hand encouragingly. "Darling, you're my wife. You're _Puan Sri_ Harry Leong and we have our own money. You'll never be a nobody." Philip got up from the table abruptly and spoke for the first time. "This was obviously Mum's plan all along. If she wanted one of us to get Tyersall Park, she would have left it to that person outright. But the way she divided it up, she knew there would be only one thing we could do. She wanted us to sell the damned house!" * * 1 The Leongs' third son, Alexander, who married a Malay woman and has three children with her, lives in Brentwood, California. He has neither returned to Singapore nor spoken to his father in eleven years. 2 None of the grandchildren's spouses were invited to this meeting, with the exception of Henry Leong's wife, Cathleen Kah. The fact that she is a senior partner at Tan and Tan and is descended from the distinguished family that provides the firm with forty percent of its billable hours might have had something to do with it. 3 For comparison, a 1936 Hispano-Suiza Type 68 J12 Cabriolet sold at 2010 auction in Scottsdale, Arizona, for $1,400,000. 4 Indonesian slang for someone that is stupid or retarded. # CHAPTER EIGHT DEMPSEY HILL, SINGAPORE PS.Café was an oasis nestled in the parklands of the former Dempsey Hill barracks, and the moment Nick entered the tranquil space with Astrid he felt like he could breathe easier. As if echoing his thoughts, Astrid said, "I'm so glad we managed to make our escape." "Two hours with the family in the lawyers' office...I think it's going to take me a year to recover!" Nick laughed, looking around to see if Rachel and Carlton had arrived. "Ah, they're hiding over in the corner." "So you have a hot date tomorrow night?" Rachel teased her brother as they sat at a table bathed in sunlight filtering through the giant plate-glass windows. "I'm _hoping_ it will be a hot date! You know, sometimes an actual date just screws things up," Carlton said, taking a sip of his lychee-and-lime soda. "Scheherazade and you have been inseparable for the past week. I don't see how you could possibly screw it up at this point." Rachel looked up and saw Nick and Astrid navigating between the crowded tables toward them. "Here they come. Let's ask Astrid—" "Noooo!" Carlton said bashfully. "Ask me what?" Astrid asked as she leaned over to give Rachel a peck on the cheek. "In your expert opinion, do you think it's a bad idea for Carlton to take your cousin on a date?" "What, a real date? I figured they were already halfway to Vegas to get married!" Astrid teased. "Stop it, I'm not sure she's that into me," Carlton said. "Carlton, if she wasn't into you, you wouldn't even be able to get close." "Really?" Carlton seemed dubious. Astrid sat down next to him. "First of all, her parents are pathologically protective of her. You've seen her security detail. I'm told that in Paris, she has undercover agents trailing her everywhere she goes, and even she doesn't know who they are. But aside from that, Scheherazade has left a trail of carnage since she was a teenager. I've never seen so many love-sick puppies get their hearts stomped on. But you, Mr. Dimples, have gotten through the Praetorian Guard." "So where are you taking her on your hot date?" Nick prodded. "I thought I'd keep things really casual...maybe a walk followed by drinks at LeVeL33?" Astrid made a little face. "You might want to rethink that." "You're going to have to up your game, Carlton. Scheherazade Shang does not impress easily," Nick warned. "Okay, duly noted." Carlton laughed. Rachel, meanwhile, was on the edge of her seat wanting to know what happened at the reading of the will. "Anyway, enough about Carlton's love life. How are you guys? Did everything...um...go okay?" Nick stared out the window. From where he was sitting, it seemed as though the entire café was a glass tree house, and he just wanted to dive out the window and be enveloped by the foliage. "I'm not sure, my brain is totally fried. How do you think it went, Astrid?" Astrid leaned back in her chair and let out a sigh. "I've never been in a room that was filled with that much tension. There were many surprises, and I think everyone's in shock at the moment. Eddie especially." "Why Eddie?" Rachel asked. Nick gave a little laugh. "The poor sod thought he was going to inherit Tyersall Park." Knowing the big question on Rachel's mind, he continued, "It's not going to me either. I have a small share, but Tyersall Park is being divided up like a big wheel of cheese among my father, his sisters...and Alistair, as it turns out." Rachel's jaw dropped. "Alistair? Jeez, no wonder Eddie's in shock!" "Shock today, fratricide tomorrow," Astrid quipped. "How about you, Astrid? Are you surprised that you didn't get a share of the house?" Rachel asked. "I never imagined I would. I'm happy enough that Ah Ma left me a few things she knows I'll cherish." Astrid's phone began to ring, and seeing that it was Charlie, she quickly got up from the table and said, "Back in a moment. If the waitress comes, can I get a peach-and-lychee fizz?" After Astrid had left the table, Rachel asked, "So if the house is being divided up among so many people, how's that going to work?" Nick shrugged. "I guess that's what they're trying to figure out now. The rest of the family is back at the house having a big powwow over lunch." Rachel reached across the table and gave Nick's hand a squeeze. She could only imagine how difficult it must have been for him, to sit there in that office and find out how his grandmother's entire life was going to be dismantled and dispersed. Changing the topic, she said cheerily, "Well, let's order. I'm starving, and I hear the Tiger beer-battered fish-and-chips are amazing." — Standing in the patio outside the café, Astrid listened worriedly as Charlie tried to explain the situation. "My security team did a full sweep. They searched every last inch of my apartment but they couldn't find a thing. No hidden cameras, no surveillance devices, nothing. And I just heard back from the Singapore team—they couldn't find anything in your house either." Astrid frowned. "What does this mean?" "I'm not sure. It's pretty damn alarming that there's video footage of us in my bed, but no one has any idea how it was recorded." "Could it have been done from a drone?" Astrid wondered. "No, it's the wrong angle. We studied every frame of the footage, and it had to have been shot from the foot of my bed, not out the window. Whatever device was in my bedroom is now gone." "Oh that's reassuring," Astrid said mordantly. "So whoever planted the device came back to remove it." "That would appear to be the case. Listen, I'm flying in more security experts from Israel to do another assessment. I want them to go over everything with an even finer comb. And then I'll send them to Singapore to do another sweep of your house. Until then, I don't think you should go back to your place until we figure this out." Astrid leaned against a pillar, sighing in frustration. "I can't believe this is happening. I feel so violated, like nowhere I go is safe anymore. I feel like Michael has eyes everywhere in this town." "Why don't you come to Hong Kong? I'm holed up at the Peninsula now, in their Peninsula Suite. This is where all the heads of state stay. It's really the most secure place you can be at the moment." "I feel like if I leave now, it's admitting defeat. Michael will know he's managed to intimidate us." "Astrid, listen to me. What did we say last night? We're not going to let Michael win. We're not going to let him dictate the rules here. You're not fleeing town. You're coming to Hong Kong to see me, to have a good time, to start looking into options for our wedding. Your grandma's funeral is over, and we're getting on with our lives," Charlie said reassuringly. "You're absolutely right. I have to come to Hong Kong. We have a wedding to plan!" Astrid proclaimed, the fire returning to her voice. # CHAPTER NINE TYERSALL PARK, SINGAPORE Even from the service wing downstairs, Eddie's yelling could be heard. Ah Ling, Ah Ching, and a dozen maids craned their necks by the kitchen window, mesmerized by noises wafting down to them from the bedroom where Eddie and Fiona were staying. "Fucky fuck! You knew all along what was in my grandmother's will, and you didn't tell me a thing!" Eddie shouted. "I keep telling you I didn't know anything! I was only a witness to the signing, don't you understand? I wasn't going to sit there and read her will!" Fiona argued back. "Why the hell didn't you?" "Lower your voice, Eddie! Everyone can hear us!" "I give precisely zero fucks who can hear us! I want the whole world to know what an idiot you are! You had a chance to read my grandmother's will and you didn't!" "I have respect for your grandmother's privacy!" "Respect my ass! What about me? Why don't I get the respect I fucking deserve?" Eddie continued to yell. "I'm not going to sit here and take this abuse anymore! Take an Effexor and calm the hell down." Fiona got up from the settee and tried to leave, but Eddie grabbed her forcefully. "Don't you get it? You've ruined your children's lives and you've ruined my life!" he screamed, taking hold of Fiona by the shoulders and shaking her. "Let go of me, Eddie!" Fiona shrieked. " _Aiyoh!_ That Eddie is too much," Ah Ching said, shaking her head as she heard his ranting. "It sounds to me like he didn't get the house, did he? Oh thank all the gods!" "He's an utter fool if he thought Su Yi would leave this place to him!" Ah Ling chimed in. Just then, the muffled sound of something hitting the marquetry floor could be heard. Jiayi, the young Chinese scullery maid, flinched in terror. "Oh my God! Did he just hit her? It sounds like she landed on the floor! Someone do something! Ah Ling, what should we do?" Ah Ling just sighed. "We should stay out of it! Remember, Jiayi, we don't see anything and we don't hear anything. That's what we do. Now, let's get the first five courses out to the dining room. Quickly! The animals are hungry." As the rest of the kitchen maids sprang into action, Jiayi instead made a dash up to Eddie's bedroom. Fiona had been so sweet to her, she wasn't going to let anyone hurt her. She crept up the stairs to the hallway where the guest bedrooms were, and as she came to their bedroom, she could hear someone moaning in anguish. Jiayi opened the door slowly and whispered, "Ma'am, are you okay?" She looked in and saw Eddie lying on the floor in a fetal position, his head in Fiona's lap. Fiona sat on the floor, calm as a pietà, stroking his hair as he sobbed uncontrollably like a little boy. She looked up at Jiayi, and the maid quickly closed the door. — In the family dining room of Tyersall Park, everyone had gathered around the massive round mahogany dining table designed by the great Shanghai artist Huang Pao Fan. Anticipating that this was going to be a contentious meal, Ah Ling and Ah Ching devised a lunch that consisted of the favorite dishes of the Young siblings when they were children—pumpkin and prawn noodle soup (Catherine's favorite), fried rice with _lap cheong_ 1 and extra eggs (Philip's favorite), steamed pomfret in ginger sauce (Felicity's favorite), _lor mai kai_ 2 (Alix's favorite), and Yorkshire pudding (Victoria's favorite). If it made for a slightly schizophrenic menu, no one noticed except the in-laws. Victoria threw out the opening salvo as she savored her first forkful of pudding. "Philip, surely you weren't serious when you said we should sell Tyersall Park?" "I don't see any other choice," Philip answered. "Why don't you buy us all out? You have the majority stake, and we'll sell you our shares at a family discount. This way we all can keep our rooms, and Tyersall Park can be like our private family hotel." Alix looked up from her aromatic chicken rice. What on earth was Victoria suggesting? She had no intention of selling her share at a discount. Philip shook his head as he swallowed a mouthful of fried rice. "First of all, I can't afford to buy you all out, but that's beside the point. What would I do with this house? I live in Sydney most of the year—I can't be bothered to maintain this white elephant." "Cat, wouldn't you like to have Tyersall Park? You can afford it, can't you?" Victoria asked her sister hopefully. "Everything about this place reminds me of Mummy, and I'd be too sad," Catherine mused, picking at her noodles without much of an appetite. Alix spoke up. "Cat's right. This house just isn't the same now that Mummy's gone. Look, Mummy clearly wanted us to sell it. She knew none of us would really want to take it on." Victoria looked distressed. "Then what happens to me? Am I supposed to move in to _a flat_? Goodness gracious, I'd feel like I'm suddenly part of the 'new poor'!" "Victoria, no one cares anymore," Alix argued. "Look at all our friends, our cousins—the T'siens, the Tans, the Shangs. No one we know still lives in their original houses. Buitenzorg, Eu Villa, 38 Newton Road, the House of Jade. All the great estates are long gone. Even Command House is now part of bloody UBS. I've lived in a three-bedroom condo for decades and I love it." Harry nodded in agreement. "I _dream_ of the luxury of living someplace small, like one of those HDB flats! Why, I hear that most of them even have elevators these days!"3 Alix looked around the table at each of her siblings. "A property of this size has not come on the market in almost a century—this is like Central Park going up for sale in New York. In this neighborhood, the going rate is $1,000 per square foot. We have more than 2.8 _million_ square feet here, and that adds up to $2.8 billion. But I think developers would pay even more, and there's going to be a bidding war. Trust me, I've been flipping properties in Hong Kong for years. We have to orchestrate this very methodically, because this is our one chance to make an absolute killing." Victoria gave a dramatic sigh, although secretly she was already thinking of the cute topiaries she would put on the doorstep of her town house in London. "Okay, so let's sell the house. But we can't appear to want to sell it anytime soon. That would be unseemly." "I think we should wait at least six months. We wouldn't want to look like greedy pigs," Felicity stated as she sucked on a fish bone. Philip took a sip of his coffee and winced. "All right then, I'm heading back to Sydney tonight—I can't stand another day without a proper flat white. I'll be back in six months and we can officially put the house on the market." Just then, Ah Ling entered the dining room with an announcement: "Something just arrived that I think you all should see." Two Gurkha guards wheeled a large flatbed dolly into the room. Piled on it was a mountain of colorful ribboned boxes, all from Ladurée in Paris. There were boxes upon boxes of chocolates and truffles, macaroons and cakes—all manner of delicious confections from the legendary dessert maker. Crowning this elaborate display was a _croquembouche_ , with a large embossed gold card affixed to the front. Ah Ling took the card and handed it to Philip. He tore it open and began to laugh. "What is it?" Eleanor asked excitedly. Philip read the card aloud. "Bright Star Properties wishes the Young family prosperity and good tidings in the coming Year of the Goat. May we respectfully extend an all-cash tender offer of $1.88 billion for the purchase of Tyersall Park." Felicity gasped, while Alix turned to Victoria with a smirk. "I don't think we have to worry about looking like greedy pigs." * * 1 Chinese sausage. 2 Steamed glutinous rice with chicken in a lotus leaf wrap, my dim sum favorite. 3 Harry Leong has obviously never set foot in a Housing and Development Board flat in his entire life, but like so many oblivious one-percenters is always fantasizing about downsizing and moving in to an HDB flat "since I am entitled to one." # CHAPTER TEN 28 CLUNY PARK ROAD, SINGAPORE Kitty was floating on an inflatable lounger in the middle of her pool in an alluring one-shoulder cutout Araks swimsuit when she heard the car returning to the house. She had been waiting impatiently for the past hour, after sending a maid to the bookstore to buy a whole stack of the new issue of _Tattle_ , which had just been released this morning. Kitty paddled her lounger over to the edge of the pool as the maid came rushing down the stone steps with a stack of magazines in her arms, followed by the driver, who was also carrying a big stack. "What took you so long?" Kitty asked. "I'm sorry, ma'am. We got there before the bookstore opened, but they had to unpack the magazines from the boxes and scan them into the computer first. But here, we bought all forty copies," she said, handing Kitty the top copy from her stack. It was wrapped in plastic, with a big gold panel over the cover and words that screamed: "OUR WILDEST ISSUE EVER!" Kitty felt her heart race as she tried to tear into the plastic, desperate to get to the magazine. She couldn't wait to see her photo on the cover under the headline "Princess Kitty." The lounger wobbled, and her wet fingers kept slipping against the plastic. "Here, let me help you!" the maid said, sensing her mistress's excitement. She ripped through the plastic, slipped the glossy magazine out of its sleeve, and handed it to Kitty. Kitty stared at the cover, her face changing from anticipation to absolute horror. Staring back at her on the cover of _Tattle_ was a photograph of Colette and her husband, Lucien, seated at a breakfast table with a huge orangutan. "Aaaahhh! What is this? This is the wrong issue!" Kitty screamed from her reclining position. "No ma'am, this is the new issue. Brand-new. I saw them take it out of the boxes." Kitty scrutinized the cover, where the headline read: LORDS OF THE JUNGLE: THE EARL AND COUNTESS OF PALLISER. "No! No! No! This can't be real," Kitty sat up on the lounger, tearing through the magazine maniacally and getting the pages wet as she searched for her story. What happened to her beautiful photo shoot with Nigel Barker? The photos of Harvard kissing her? They were nowhere to be found. Instead, the feature article was a ten-page spread dedicated to pictures of Colette and Lucien's visit to a conservation center in Indonesia. There were photos of Colette hosting a tea party for a family of orangutans at a wrought-iron table by the edge of a river, Colette trekking through the rain forest with a group of primatologists, and Colette cradling a baby orangutan. By this point, Kitty's lounger had drifted to the middle of the pool, and she screeched at the maid, "Get me my phone!" Kitty jabbed at her phone angrily, calling Oliver T'sien. It rang a few times before he picked up. "Ollie's Psychic Hotline," he answered jokingly. "Have you seen the latest _Tattle_ yet?" Kitty said, her voice shaking with fury. "No. Did it come out today? I'm in Hong Kong this week, so I haven't seen it yet. Congratulations! How does it look?" "Congratulations? Go look at the magazine and tell me how I fucking look on the cover!" Kitty screamed, before hanging up. _God, what now?_ Oliver thought to himself. Did they end up going with a photo that was slightly less flattering to her surgically sculpted nose? There was no way he would find a copy of the magazine in Hong Kong, but maybe the issue was already online. He went to his browser and logged on to Tattle.com.sg. Within seconds, the page loaded, and the cover of _Tattle_ popped up. "Oh for fuck's sake!" Oliver cursed, as he began to scan through the story. > # ECO WARRIOR PRINCESS: AN EXCLUSIVE INTERVIEW WITH COLETTE, THE COUNTESS OF PALLISER > > The Countess of Palliser enters the garden of the British embassy in Singapore with no pomp or circumstance, no personal assistant or PR handler in sight. She shakes my hand and immediately starts fretting that I'm seated in the sun. Am I too hot? Would I like to swap seats? Has no one brought me a drink? > > This was not the woman I was expecting to meet. The former Colette Bing, once China's most influential fashion blogger—with over 55 million followers—is today sitting before me in a simple yet lovely floral dress with not a dab of makeup on her face or any jewelry except for a simple wedding band of Welsh gold. I ask her who designed her dress and she laughs. "This is a Laura Ashley dress that I got out of a bin at an Oxfam thrift shop in the village near where I live." > > It's the first hint that as ordinary as the Countess's life seems to be, things are not all that ordinary. The village she is referring to is Barchester, perhaps one of the most charming in all of England, and home for the Countess and her husband, Lucien Montagu-Scott, the Earl of Palliser, is a charming old vicarage with 10 bedrooms tucked away at Gatherum Castle, the 35,000-acre Barsetshire estate of her father-in-law, the Duke of Glencora. > > I've heard rumors that the interior designer Henrietta Spencer-Churchill, of the Blenheim Palace Spencer-Churchills, has been busy transforming the cottage into an elysian paradise, but when I try to ask the Countess about it, she simply says that the house is being refurbished and redirects me to the matter at hand. "My life is not that interesting. Let's talk about Indonesia," she says with an effervescent smile. > > Indonesia is the reason the Earl and Countess have been spending so much time in these parts of late. The Earl, a renowned environmental activist, and the Countess actually met there. "I was a bit adrift, traveling to various spa resorts on my own for a few months," the Countess admits. "By chance I met Lucien in Bali, and he told me that he was on the way to a remote part of North Sumatra. I decided on a whim to follow him." > > It was a decision that changed her life forever. "Lucien brought me to an orangutan rescue center, and it was my first exposure to the terrible environmental tragedy that's been unfolding here. Sumatran orangutans are classified as 'critically endangered,' and the population is being decimated, along with scores of other species, because of deforestation and illegal poaching. Infant orangutans are being sold to the pet trade, and the way they do this is by killing the mother first. For every baby orangutan sold, it's estimated that six to eight adult orangutans die in the process of capturing them. Can you imagine?" the Countess says, her normally pearl-white complexion flushed with fury. > > What she witnessed those first weeks in Sumatra has given the Countess a singular mission in life: to spread awareness of this environmental tragedy and to advocate for change. "People talk about the Amazon, but it's horrific what's being done in this part of Southeast Asia. The main culprit is the palm oil industry. _Everyone_ should stop consuming products that contain palm oil! In the quest for more land to create more palm oil plantations, ancient forests are being burned down, destroyed completely, and we are losing so many species that will never be seen again. Orangutans, one of our planet's most precious animals, could be extinct in the wild within 25 years," the Countess says with tears in her eyes. > > "And beyond this, look at what the massive bushfires and deforestation have done environmentally to the region—look what it's doing to the air quality right here in Singapore. You can feel the effects of these forest fires right now if you just take a deep breath!" > > At this point in the interview, the Countess's husband walks out onto the terrace to join us. He is a tall, blindingly handsome blond fellow who immediately reminds me of Westley from _The Princess Bride_. I'm surprised by how down-to-earth the Earl is, and when he talks about his new wife, his face lights up like a lovestruck teen. "Colette's dedication to the orangutan babies—how she handled them, how she wasn't afraid to get her hands dirty and really just give her all to the cause—really surprised me. It one hundred percent made me fall in love with her. I knew I had found my eco-warrior princess, and after our time together at the camp, I never wanted to let her go." > > "Our mission is just beginning. There's just so much to do, and that's why we've decided to move to Singapore for the next few years," the Countess reveals. "This will be an excellent base for our work all over the region," the Earl chimes in. > > Are the Earl and Countess going to commandeer one of Singapore's toniest properties? "I don't know if we'll actually be here all that much, so I think we'll just lease a little flat someplace very central," the Countess says. In case you are misled into thinking that the Pallisers have completely hidden away their ermine robes and tiaras in favor of cargo pants and Tevas, Colette reveals that she is in the midst of organizing an event that will no doubt send every reader of this article scrambling for their best jewels. > > "I'm going to host a fund-raising ball in aid of orangutan rescue with my friends the Duchess of Oxbridge and Cornelia Guest. Both of them are dedicated conservationists doing such amazing rescue work with animals—Alice with endangered sea turtles, and Cornelia with miniature horses. Hopefully we'll have friends from all over the world jetting in for a ball that will be inspired by Marie-Hélène de Rothschild's legendary Proust Ball at Château Ferrières." > > If history is to be repeated again, the enchanted evening promises to be the most highly anticipated gala of the spring charity season, and hopefully, it's the start of many good things to come from this gorgeous, aristocratic, and _conscious_ couple. When he was done reading, Oliver immediately called Violet Poon at _Tattle_. "Can you please explain why there's a fucking monkey on the cover of your magazine this month instead of Kitty Bing?" "Oh Oliver, I was going to call you! It was a last-minute mandate that came from my boss. They're running this cover story on every edition of _Tattle_ around the world this month. It's such an important story." "So what happens to Kitty's important story?" "Well, since Colette was on the cover this month, we felt like a little, ahem, diplomacy was in order. Of course we couldn't put Kitty's story in the same issue. I mean, she _is_ her stepmother. We wouldn't want to offend either of them. But you know I adore Kitty's cover! Those Nigel pictures are just beyond! We're going to save it for later in the year. It'll actually be much better in the fall, don't you think? Wouldn't it be a fabulous cover for the September issue?" Oliver went silent for a moment, trying to figure out how he was going to explain all this to Kitty. "I hope Kitty won't be upset about this? We will give her the star treatment, I promise. We'll throw a cover launch party at some boutique." "Upset? Violet, I don't think you have any clue what you've done. You've just started World War III." "Oh dear..." "I have to go. I need to see if I can disarm the nuclear warhead now." Oliver hung up with Violet, took a deep breath, and called Kitty's number. He found her eerily composed when he explained the whole situation to her. "I actually think this is going to be much better for you, Kitty. Landing a fall cover is more prestigious. Think of the September issue of _Vogue_. That's always the biggest issue of the year. You'll get so much more exposure. Far less people will see the March issue of _Tattle_ , and to be honest, it's a ghastly cover. Look at that mother orangutan and her saggy brown nipples." "Did you read the article?" Kitty said quietly. "I did." "So you know that Colette is moving to Singapore with her husband. The royal couple!" "Kitty, they aren't royal." "Oh yeah? So tell me why they were getting the royal treatment at your great-aunt's funeral? Don't try to deny it, I saw the pictures of Colette with the Dowager Sultana of Perawak on the official royal Instagram! You lied to me! You _promised_ me she wouldn't be there!" "Kitty, I had no clue that her husband's family knew my great-uncle Alfred's family. This isn't some conspiracy." "It's not? Then why does it feel like she's doing everything she can to outshine me? She gets invited to the funeral of the century, she steals my _Tattle_ cover, and now she's throwing this big charity ball in Singapore to raise money for her damn monkeys!" "Those orangutans need all the help they can get, Kitty." "That's not the point. Colette is hosting this huge ball so that all of Singapore society can come out and curtsy at her feet, like she's the Queen of fucking Sheba! You know she's doing all this as revenge, don't you? She's just trying to insult me over and over again!" Oliver sighed in exasperation. "Kitty, don't you think you're blowing this out of proportion? You haven't even met Colette. You have no idea what's going through her mind! I really don't think this girl has any interest in insulting you." "Of course she's insulted me, and she's insulted my husband. Did you notice that she didn't mention Jack once? Who do you think is funding all her monkey business?" "Kitty, you're just building all this up in your head and sending yourself into a tailspin." "No, I'm sending _you_ into a tailspin. I want you to get me a title. I want a proper royal title that's higher-ranking than Colette's." Oliver sighed. "Kitty, getting you any sort of title is going to take time. Living in Singapore, you could aim for an honorific from one of the Malay royal families. But you'd have to do an obscene amount of sucking up. Best-case scenario if you play your cards right, you may be able to receive a title within a few years." "No, I'm not waiting that long. I don't care what you have to do, how much you have to spend. I want a title and I want it before Colette's stupid monkey ball." "That's just not realistic, Kitty. I mean, I do know a few bisexual Italian princes that might be willing—in exchange for certain financial incentives—to marry you, but you'll have to divorce Jack." Kitty scoffed. "What are you talking about? I'm not divorcing my husband!" "Then I'm afraid there's really no way to get you a royal title within a month." "Well then, you're out of a job! I'm not going to pay your retainer anymore. In fact, I'm stopping payment on everything right now. The Nigel Barker photo-shoot fees, all the money you've spent decorating my house, _everything_." "Kitty, stop being unreasonable. That's close to a hundred million dollars. You know I'll be on the hook for all those bills if you don't pay them," Oliver sputtered in alarm. "Exactly. So get me that title! What's higher-ranking than a countess? A duchess? A princess? An empress? I don't care if you need to bribe Prince Bibimbap of Korea, I just want Colette to have to curtsy to me the next time I encounter her. I want to wipe the floor with her face!" Kitty screamed. "Kitty, please calm down. Kitty?" Oliver realized she had hung up on him. A wave of fear suddenly passed through his body. Kitty was one client he could not risk losing. His monthly retainer from her was the one thing that kept the wolves at bay. Unbeknownst to the Youngs, the Shangs, or the rest of the world, Oliver's family had fallen on hard times, ever since Barings went bust in 1995. Most of the T'sien portfolio had been invested with the storied investment firm in London that were bankers to Britain's most aristocratic families, including the queen. But after the firm went bankrupt—ironically due to a rogue trader based in Singapore—the T'siens along with every Barings investor had been wiped out. What remained in the other T'sien accounts was a pittance, about ten million, and all that went into maintaining his grandmother Rosemary's lifestyle. It was her money rightfully, and she was entitled to live out her last years in comfort, but it meant that there would be barely anything left for her five children. The T'siens had been one of Singapore's largest landowners in the 1900s, but there was only one property left now—his grandmother's sprawling bungalow on Dalvey Road that was maybe worth thirty-five million, forty if the market ever recovered. Split five ways between her children, that meant his father would only inherit six or seven million at the most if the house was ever sold. Far, far less than what his parents were now in debt for. For years, they had taken out loan after loan, and Oliver had spent his youth living the life of a rich man's son, sent abroad to the best schools money could buy—from Le Rosey to Oxford. But after the Barings crash, he found himself in the unthinkable position of having to work for a living. Oliver had always existed among the world's point-one percent crowd, and very few people understood the special hell of having to live in a world where every single person around you was staggeringly rich but you were not. No one knew the degrees of subterfuge he took to keep up appearances for the sake of his family and career. There were the ballooning interest payments on all their bank loans. There were ten credit cards that he had to play Russian roulette with month after month. There were the mortgages on his parents' _hutong_ in Beijing, his flat in London, and the condo in Singapore. Last year had been the worst, when his mother had been forced to sell off the legendary T'sien jade brooch along with other family heirlooms in order to pay for unexpected medical expenses. The bills kept coming, and they were endless. And now Kitty was threatening to renege on her gargantuan decorating bills—bills he had signed off on. If he couldn't work a miracle and get Kitty her title, he knew his whole life, his family, his career, his reputation—all would come crashing down. # CHAPTER ELEVEN TYERSALL PARK, SINGAPORE Walking in to lunch the next day, Nick and Rachel found that the dining room had been transformed into a makeshift situation room. Rolling bulletin boards had been placed around the room, and the dining table was lined with stacks of documents and various brochures, and seven or eight young staffers huddled over spreadsheets on their laptops. Ah Ling entered with another package that had just arrived and noticed the baffled couple. "Oh, Nicky, lunch is being served on the terrace today." "Um...who are these people?" Nick whispered. "They're from Uncle Harry's office. They're helping out with all the house offers," Ah Ling responded, giving Nick a look that clearly registered her disapproval. Nick and Rachel went out to the terrace to find a much smaller gathering of relatives. The Aakaras had flown back to Bangkok earlier in the morning, while most of the Chengs had left the day before. The only out-of-town guests that remained were Alix and Alistair, since they were both shareholders in the property. While Nick and Rachel stood by the buffet table arrayed with different dishes, Victoria spoke up as she looked over a prospectus. "This offer from the Far East people is an insult! Two point five billion, paid out over five years. Do they think we fell off the turnip truck yesterday?" "Let's not even bother responding," Alix declared. She looked up as Nick and Rachel sat down at the wrought-iron table with their lunch plates. "Nicky, do you have any idea what time your father will be here? We have so much to go over with him." "Dad's back in Sydney." "What? When did he leave?" "Last night. Didn't he tell you he was heading home?" "Yes, but we assumed he would have changed his plans now that the offers are flooding in. Ugggh! That irresponsible boy! We're in the midst of a bidding war, and he _knows_ we can't make any moves without him," Felicity huffed. "Dad's become quite set in his ways, and he really missed the coffee from this café he goes to every morning in Rose Bay," Nick tried explaining. "There are billions of dollars at stake here and he's complaining about the coffee? As if Folgers Crystals here aren't good enough for him!" Victoria scoffed. Rachel jumped into the conversation. "Some people really can't function without their coffee. In New York, I have to grab my usual cup at Joe Coffee on the way to work or I won't be able to get through the morning." "I'll never understand you coffee people." Victoria tut-tutted as she carefully stirred her cup of tea made from GFBOP Orthodox leaves she had flown in every month from a special reserve estate in Tanzania. "Call your father. Tell him we're in the middle of a heated bidding war and the house could be sold before the end of the week," Felicity ordered. Nick looked at his aunts in surprise. "Are you all really intending on selling Tyersall Park that quickly?" "We need to close the deal while the wok is sizzling! It's almost Chinese New Year, and everyone is feeling particularly prosperous and bold right now. Do you know that our top bid now exceeds three billion?" Alix excitedly reported. Nick raised his eyebrows. "Who is it from, and how will they ensure that they will preserve the house?" Felicity laughed. "Come on, Nicky, no one is going to preserve this house. The developers are only interested in the land—they are going to tear it all down." Nick looked at Felicity in horror. "Wait a minute—how can they tear down the house? Isn't this a protected heritage property?" Victoria shook her head. "If this was a Peranakan-style house, or a colonial Black and White, maybe it would have heritage protection, but this house is such a mishmash of styles. It was built by some Dutch architect that the sultan who originally owned the place brought in from Malaysia. It's an architectural folly." "But of course, this is also what makes it so valuable. This is a freehold property with absolutely no heritage or zoning regulations. It's every developer's dream! Here, look at the leading proposal," Alix said, handing Nick a glossy brochure. > # _Zion Estates_ > > ## A LUXURY CHRISTIAN COMMUNITY > > _Imagine an exclusive gated community for high-net-worth families who share in the blessings of the Holy Spirit._ > > _Ninety-nine splendid villas, inspired by the Hanging Gardens of Babylon, ranging from 5,000 to 15,000 square feet on half-acre lots will surround Galilee, a glorious artificial lagoon complete with the world's tallest man-made waterfall supplied only with water imported from the River Jordan. At the heart of the community lies the Twelve Apostles, a unique twelve-hole golf course designed by our faithful brother Tiger Woods, and an exquisite clubhouse—the King David—which will boast a trinity of world-class restaurants operated by Michelin-starred chefs, along with Jericho, sure to become Singapore's most decadent spa and state-of-the-art health club._ > > _Come to Zion—live abundantly and be saved._ Nick looked up from the brochure in disbelief. "Are you seriously telling me that these people are the front-runners? _A luxury Christian community?_ " "Isn't it inspired? It's Rosalind Fung's company—your mother goes to her Christian Fellowship Banquets at the Fullerton. They've offered us $3.3 billion, and they will throw in a villa for each of us!" Victoria said breathlessly. Nick was barely able to hide his disgust. "Auntie Victoria, in case you've forgotten, Jesus served the poor." "Of course he did. What's your point?" Felicity chimed in. "Jesus said, 'To grow rich is glorious.' " "Actually, Deng Xiaoping, the late Communist leader of China, said that!" Nick shot back. He got up from the table abruptly and said to Rachel, "Let's get out of here." As they got into Nick's father's vintage Jaguar XKE convertible and sped down the driveway, Nick turned to Rachel. "Sorry, I lost my appetite sitting there with my aunts. I just couldn't stand listening to them one minute longer." "Trust me, I get it. Where are we going?" "I thought I'd take you to my favorite restaurant for a proper lunch—Sun Yik Noodles. It's a little café that's been around since the 1930s." "Fantastic! I was just starting to get hungry." Within fifteen minutes they had arrived in the Chinatown neighborhood, and after parking the car, they strolled down Club Street with its picturesque old shop houses toward Ann Siang Road as Nick began to fill Rachel in on the place. "It's a total hole-in-the-wall, and they haven't even changed the Formica tables since the fifties, I bet. But they have the best noodles in Singapore, and so everyone comes here. The former chief justice of the Supreme Court used to eat lunch here every day, because the noodles were so addictive. You're gonna die when you taste these noodles. They are hand-pulled egg noodles, and they have this incredible, perfectly chewy texture to them. And they serve it with braised chicken that's been simmering for hours in this garlicky gravy. Oh man, the gravy! I wanna see if you think you can possibly replicate it. We're here after lunch rush, so we probably won't have to wait too long for a ta—" Nick stopped dead in his tracks, staring at a façade across the road that had been covered by a metal construction fence. "What's wrong?" "This is it! Sun Yik Noodles! But where is it?" They crossed the street and came to a small sign that was glued to the metal sheeting. It read: > TORY BURCH > > Opening Summer 2015 Nick ran in to the shop next door, and Rachel could see him gesturing frantically to the baffled salesman inside. A few moments later, he came outside, his face registering nothing but shock. "It's gone, Rachel. No more Sun Yik. This area has become so trendy, the original owner's son apparently sold the building for an insane amount of money and decided to retire. And now it's going to be a friggin' Tory Burch boutique." "I'm so sorry, Nick." "What the fuck!" Nick yelled, kicking the metal sheeting angrily. He sank down onto the pavement and covered his face with his hands despondently. Rachel had never seen him look quite so upset before. She sat down next to him on the pavement and put her arm around his shoulder. Nick sat there for a few minutes, staring off into space. After a while, he finally spoke. "Everything I love about Singapore is gone. Or it's disappearing fast. Every time I'm back, more and more of my favorite haunts have closed or been torn down. Restaurants, shops, buildings, cemeteries, nothing is sacred anymore. The whole character of the island I knew growing up is almost completely obliterated." Rachel simply nodded. "Sun Yik was such an institution, I thought it would always be safe. I mean, I swear to God, _they had the best noodles in the whole world_. Everyone loved it. But now it's gone forever, and we can never ever get that back." "I don't think people ever realize what they've lost until it's too late," Rachel said. Nick looked into her eyes with a sudden intensity. "Rachel, I have to save Tyersall Park. I can't let it be torn down and turned into some grotesque gated community that only allows in millionaire Christians." "I've been thinking the same thing." "I thought for a while that I would be okay with everything. I thought I wouldn't care if I didn't inherit the estate as long as someone in the family got it and maintained it properly. But now I know I'm not." "You know, I've been wondering all along if you were really okay with losing the house," Rachel observed. Nick considered what she'd said for a moment. "I think part of me always resented Tyersall Park in a subconscious way, because everyone always associated me with the house, and I could never detach from it when I was younger. I think that's why Colin and I became such good friends...I was always 'the Tyersall Park Boy' and he was always 'that Khoo Enterprises Boy.' But we were just _boys_." "It was like a curse in a way, wasn't it? It's amazing how you both managed not to let it define you," Rachel remarked. "Well, at some point I made my peace with it, and getting away also helped me appreciate it in a new light. I realized how much the place nurtured me, how I found my adventurous side climbing trees and building forts, and how spending all those hours in the library reading all my grandfather's old books—Winston Churchill's memoirs, Sun Yat-sen's letters—got me fascinated with history. But now it feels like I'm seeing my entire childhood sold off to the highest bidder." "I know, Nick. It's been so painful even for me to watch on the sidelines. I just can't believe how it's happening so quick, and how your aunts who also grew up in the house don't seem to care about letting it go." "Even though my grandmother's will clearly states what it does, I don't think she would have wanted Tyersall Park to be demolished and forgotten like this. To me, there are so many things that just don't add up with my grandmother's will and everything." "That's been my suspicion all along too, but I didn't feel like it was my place to say anything," Rachel said with a frown. "I wish I had more time to dig deeper, and figure out why my grandmother wanted the house sold off like this. But things are moving so fast with my aunties." "Wait a minute—your aunties can move as fast as they want, but you heard them yourself, nothing is going to happen without your father. And as far as I know, he's somewhere in Sydney sipping a well-made cappuccino. And how about Alistair? He's got a stake in all this too." "Hmm...come to think of it, Alistair hasn't been around the house much over the past few days, has he?" Nick said. "If your father, Alistair, and you join forces, the three of you have enough votes to block any sale." Nick kissed Rachel excitedly and leapt up from the pavement. "You're brilliant, you know that?" "I'm not sure that required much brilliance." "No, you're a genius, and you just gave me the best idea! Let's go call my dad!" * * * * Any good tea sommelier will tell you that GFBOP stands for Golden Flowery Broken Orange Pekoe tea leaves, but of course. # CHAPTER TWELVE THE HELENA MAY, HONG KONG Astrid walked into the dining room at the Helena May, Hong Kong's historic private ladies' club, and Isabel Wu waved to her from her table by the window. She strolled toward Charlie's ex-wife a little trepidatiously. It was only the third time they were meeting, and the last time in Singapore hadn't gone so well. "Astrid. Thank you so much for agreeing to meet with me for lunch. I know it's your last day in Hong Kong, and you must be so busy," Isabel said, getting up from her chair and giving Astrid a peck on the cheek. "Thank you for inviting me. I love coming here." "Yes, it's such a special place, isn't it? There are very few places like this anymore." Astrid took a moment to look around at the other smartly dressed ladies having lunch together. The dining room with its Queen Anne furniture and botanical prints covering the walls was a throwback to another era, when Hong Kong was a British Crown Colony and this was the exclusive bastion for all the wives of high-ranking officials and expatriates. It was all so civilized. Astrid was relieved by such a warm welcome from Charlie's ex-wife, and glad to see Isabel looking so well, and so chic in white jeans, a rose-colored cashmere sweater with a quilted vest thrown over it. She looked the epitome of Hong Kong old money. "What have you been doing since you got here?" Astrid hesitated for a moment. She didn't think it would be a good idea to tell Isabel that she'd spent most of the week planning her upcoming Hong Kong wedding, and yesterday, Charlie had taken her to see the breathtaking new house he had built for them in Shek O. "Not much really, I've just been decompressing. It's good to be away from Singapore, you know?" "Yes, the past few weeks must have been very hard on you. I'm so sorry about your grandmother's passing. She was a great lady, from everything I know." "Thank you." "As I told you in my note, I was very close to my Ah Ma. In fact, she used to bring me here for afternoon tea once a month. So this place holds many memories for me." "My grandmother used to take me to afternoon tea as well. One of my earliest memories, I think, is of having tea with her at the Raffles in Singapore. But soon after that, she stopped going out." "So she became a recluse?" Isabel asked. "Yes, and no. She didn't go out much, but that's because she felt that the standards had slipped everywhere. She had very exacting standards, and she didn't much care for restaurant food. So she only went to friends' houses—the ones that she knew had good chefs—or she entertained at home. She liked to have people over all the time, and she was very social up until the end of her life." "Sounds like quite a character. All the women of her generation, like my grandmother, were characters. My grandmother was known as the hat lady. She had the most incredible collection of hats, and she never left the house without one." The waitress came over and took their orders. After Astrid ordered the cream of asparagus soup, Isabel looked across the table at her with an almost embarrassed look. "You know, I have to confess I've been so nervous all morning about this lunch. I am still so mortified over what I did when I was in Singapore." "It's fine, really. I'm just happy to see you so well again." "Those women whom I scalded. Was one of them a nun or something? Is she okay? I have such a strange memory of that day. Because I remember everything, you know, but I just had no control over my actions." "A nun?" Astrid didn't know what she was referring to. "I remember the look on her face when I threw that soup. Her eyes got so huge, and she had Tammy Faye levels of mascara on. She was wearing a nun's habit." "Oh! You're talking about the Dowager Sultana of Perawak—she was wearing a hijab. She was fine, the soup hardly touched her. Don't worry, it was probably the most thrilling thing that's happened to her in decades." "Well, I appreciate your understanding, and I really must thank you for taking such good care of my daughters during that difficult time." "Don't mention it. Chloe and Delphine are lovely girls." Isabel paused for a moment and looked out the window at the view of the hillside park. It was apparent to Astrid that she was going through a spectrum of emotions. "Soon, you will be their stepmother. You'll be spending much more time with them, and I'm...I'm actually glad they will have you in their lives. Not just their crazy mother." Astrid reached out and put her hand over Isabel's. "Don't say that. You've done such a great job raising them. You're their mother, and I'm not going to try to be any sort of substitute mother. I only hope that in time they will come to see me as a friend." Isabel smiled. "Astrid, I'm so glad we are having lunch together. I feel like I finally know who you are now." — After lunch, as the two of them stood at the entrance of the Helena May on Garden Road bidding farewell to each other, Isabel asked, "What are you going to do now? Some shopping in Central? Can my driver drop you off anywhere?" "Well, I'm leaving for Singapore in a few hours, but I'm going to meet with Charlie first. I think he's at the house, waiting for me to make some decisions about the decor." "The new house in Shek O? I'd love to see it sometime. After all, Chloe and Delphine are going to be spending half their lives there." "Of course. Actually, if you're free, why don't you come with me right now?" "Oh...well...I wouldn't want to intrude..." Isabel said hesitantly. "No, no, I'm sure it will be fine. Let me just text Charlie." Astrid quickly shot off a text: ASTRID LEONG: Hey! Just finishing up with Isabel. It went GREAT. CHARLIE WU: I'm so glad. AL: Isabel would like to see the house. Ok if I bring her? CW: Sure, if you don't mind. AL: Of course not. See you soon. "Let's go!" Astrid said, looking up from her phone. The two of them jumped into the back of Isabel's chauffeured Range Rover and sped off. As they made their way around the south side of Hong Kong Island, the landscape began to change dramatically as the dense skyscrapers that cascaded down the mountainside gave way to picturesque bays and ocean vistas. The winding highway took them through Repulse Bay and its crescent-shaped beaches, hugging the coastline as they passed Deep Water Bay and the village of Stanley. Finally, they arrived in Shek O, a historic fishing village on the southeast corner of Hong Kong Island, which was also home to one of the world's most exclusive neighborhoods. "Charlie's always longed to live here, but I would never let him. I prefer being closer to town. I could never live way out here in the middle of nowhere—I'm too much of a city girl," Isabel remarked as they pulled up in front of an imposing metal gate with an attached gatehouse. "There's no one there," the chauffeur said. "Oh, we don't have it staffed yet. Just enter 110011 into the keypad," Astrid said, glancing at the instructions Charlie had texted her. The gate slid open silently, and they proceeded down the long driveway to the house. Rounding the corner, the oceanfront villa cantilevered on a rocky cliff came into view. "This place is so Charlie." Isabel laughed as they drove up to the imposing series of contemporary structures designed by Tom Kundig clad in steel, limestone, and glass. "Your house on The Peak is more traditional, isn't it?" Astrid inquired. "I'm not sure where you heard that, but it's classical Palladian, built in the twenties. I have it done in a French provincial style. I wanted it to feel like a manor in Provence. You must come over the next time you're back." "I've heard that it's one of the most elegant houses in Hong Kong," Astrid said. They stepped out of the car and entered a large courtyard dominated by a reflecting pool. Here the walls of the main villa were made entirely of glass, allowing for a seamless transition between the inside and outdoors. Entering the house, Astrid was once again taken aback by the spectacular ocean views from every vantage point in the house. In the great hall, an immense window perfectly framed a tiny island just beyond the coastline, and stepping into the living room, a wall of windows opened onto the terrace, where an infinity pool ran along the entire side of the house, its horizon line melding into the South China Sea. As Charlie came around the corner to greet them, Isabel graciously offered, "Charlie, you've outdone yourself. You finally have your dream house by the sea." "I'm glad you approve, Izzie. We're still quite a way from being done and we've just received the first big pieces of furniture, but here, let me show you Chloe and Delphine's private wing." After giving Isabel a tour of her daughters' rooms, the three of them entered the dining room, where an immense vintage George Nakashima dining table had just been delivered. Standing around the free-form structure that resembled an immense piece of driftwood, Charlie looked at Astrid. "What do you think? Is it too Pacific Northwest?" Astrid considered the piece for several moments. "I love it—it goes great under the Lindsey Adelman chandelier." "Phew, I'm so relieved!" Charlie said with a chuckle. Isabel stared up at the bronze light fixture that resembled blown-glass bubbles budding from the stems of an intricate tree branch, saying nothing. In her former life as Mrs. Charles Wu, she would have vetoed all of this, but now as the three of them headed for the front door, she simply said, "I do think Chloe and Delphine will love it here." "Well, you will always be welcome," Astrid said, her heart soaring that Isabel was being so agreeable about everything. It had been such an unexpectedly lovely day. As they stepped outside into the courtyard, Astrid's phone pinged, and she saw four text messages suddenly pop up: LUDIVINE DOLAN: I went to pick up Cassian after school but found out that his father already got him. .... FELICITY LEONG: WHERE ARE YOU? WHAT TIME YOU GETTING BACK TONIGHT? COME STRAIGHT TO TYERSALL PK! SO MUCH HAPPENING WITH THE HOUSE! WE NEED YOU! .... OLIVER T'SIEN: Aren't you friends with Prince Alois of Liechtenstein? And that Poet Prince Fazza of Dubai? Can you connect us? Call me, will explain. .... LUDIVINE DOLAN: Just spoke to Mr. Teo and asked if he needed me to help with Cassian but he wants me to take the rest of the day off. No idea what's happening. Astrid put her phone back into her purse, suddenly feeling a bit sick to her stomach. Why the hell did she have to go back to Singapore? # CHAPTER THIRTEEN BONDI BEACH, SYDNEY "Are you fishing on your dock?" Nick asked when his father picked up the phone. He could hear the crashing waves along the seashore. "No, I'm doing the cliff walk from Bondi to Coogee right now." "I love that hike." "Yeah, it's a good day for it. You know your mother invited Daisy, Nadine, Lorena, and Carol to Sydney? The whole gin gang's here, and it's such a toilet-seat-down invasion, I needed to get out of the house. The ladies are busy hatching some kind of plot...I think involving Tyersall Park." "That's the reason I was calling, Dad. It looks like things are moving far too quickly with the house. Your sisters seem really primed to sell it to the highest bidder, and I don't even want to tell you what those developers have planned." "Does it even matter? Once we sell it, the new owners can do whatever they want." "But I feel like everyone's losing sight of the big picture," Nick argued. "Tyersall Park is a unique property, and we need to make sure that it's preserved. I mean, I'm at the house right now, and even just looking out the window onto the gardens—the rambutan trees are bearing fruit, and they are flaming red. There's nothing quite like it." "I think you're being too sentimental," Philip said. "Maybe I am, but I'm just surprised that no one else cares about this house in the way that I do. Everyone's just seeing dollar signs while I see something so rare that needs to be protected." Philip sighed. "Nicky, I know for you this house was like some never-never land, but for the rest of us, it was a bit of a prison. Living in a palace was no fun as a kid. I grew up with nothing but rules. There were so many rooms I wasn't even allowed to enter, chairs I couldn't sit in because they were too valuable. You have no idea, because by the time you came along, my mother was a very different person." "Yes, I've heard the stories. But surely you must have some good memories?" "To me, it's just one gigantic headache. Don't forget, I was shipped off to boarding school practically as soon as I could walk, so it never truly felt like home to me. Now, even the thought of having to come back to Singapore to deal with all these property folks fills me with dread. Do you know how many ACS old boys have called me up out of the blue to invite me to lunch, to golf, all that nonsense? People I haven't seen in eons are suddenly behaving like my best friend because they can smell the money." "I'm sorry that's happening, Dad. But let me ask you something." Nick took a deep breath as he prepared to make his pitch. "If I can somehow raise the money, would you consider leveraging your thirty percent stake and joining me and possibly Alistair to buy everyone else out? If you give me a little time, I know I can find a way to make it financially worthwhile for us to own the estate." The line went silent for a moment, and Nick wasn't sure if his father was upset or if he was just on a particularly arduous stretch of the hike. Suddenly he spoke up again. "If you care that much about Tyersall Park, why don't you handle this whole house sale? Do what you think is best. I'll give you permission to act as my proxy, power of attorney, whatever they call it. In fact, I'll sign over my thirty percent stake to you right now." "Really?" Nick said, not quite believing what he was hearing. "Sure. I mean, it's all going be yours one day anyway." "I don't even know what to say." "Do whatever you want with the house, just keep me out of it," Philip said, climbing along the edge of a beautiful cliff-side cemetery overlooking the South Pacific. "Nicky, I'm up at that cemetery by Bronte now. Will you make sure—" "Yes, Dad, you've told me many times before. You want to be buried there. You want to have a view of the humpback whales doing backflips for all of eternity." "And if they run out of lots, you'll find another ocean-side spot? New Zealand, Tasmania, anyplace but Singapore." "Of course." Nick laughed. He hung up the phone and found Rachel staring at him curiously. "That sounded weird, from what I heard." "Yeah, it was one of the weirdest calls I've ever made. I think my father just gave me his share of Tyersall Park." "WHAAT?" Rachel's eyes got huge. "He told me he'd sign over his stake, and I can do whatever I want as long as I leave him out of it." "What's the catch?" "There's no catch. My dad has never been interested in financial matters at all. He really would rather not be bothered with it." "I guess when you've been born with it..." Rachel shrugged. "Precisely! I still can't believe how easy it was to convince him, though. I thought I was going to have to fly down to Sydney and grovel on my knees." "With your father's share in your hands, you're the biggest stakeholder now!" Rachel said excitedly. "No, _we are_. And this gives us the leverage to stall the bidding war and buy some time." "Do you want to go downstairs and break the news to your aunties?" Nick grinned. "No time like the present." They left their bedroom and walked over to the drawing room where Felicity, Victoria, and Alix were all sitting, unusually silent. "I have an announcement to make," Nick said boldly. Felicity had a peculiar look on her face. "Nicky, we just got off the phone. It seems we have a new offer on the table." "I have an offer to propose as well." "Well, this is a very unusual offer...it comes from someone who wants to preserve the house entirely and not build a single new structure on the estate," Alix said. Nick and Rachel exchanged looks of surprise. "Really? And they are offering more than those Zion people?" Rachel asked dubiously. "A great deal more. The offer is for ten billion dollars." Nick was incredulous. "Ten BILLION? Who on earth would want to pay so much money and _not_ develop the property?" "It's some fellow from China. He wants to come and see the house tomorrow." "China? What's his name?" Rachel asked. Felicity frowned. "If I recall correctly, I think Oliver said his name was Jack something. Jack Ting? Jack Ping?" Nick put his hand on his forehead in dismay. "Oh God—Jack Bing." # TWENTY-FOUR HOURS EARLIER... KUALA LUMPUR, MALAYSIA "So, she is the queen?" "No, Kitty, she is the mother of the current Sultan of Perawak, so she's the Queen Mother but she's called the Dowager Sultana," Oliver explained through his headset microphone as they rode together in the helicopter. "Ah. So I have to curtsy to her?" "You certainly do. She's as royal as it gets. And remember, only speak when you are spoken to." "What do you mean?" "I mean, you're not allowed to speak to her. The sultana initiates the conversation and gets to do all the talking—you simply keep your pretty mouth shut until she asks you a question. And if you have to leave the room for any reason—which you really shouldn't before she does—but if you feel the sudden urge to vomit, make sure to walk out of the room _facing_ her. The sultana must never see your ass, so you are never to turn your back on her, understood?" Kitty nodded diligently. "I understand—no talking, no vomiting, no ass-backing." "Now, as I said, I don't want you to expect too much today. This is just an introduction, and a chance for Her Majesty to become acquainted with you." "So you're saying she isn't going to give me a knighthood today?" "Kitty, women don't get knighted in Malaysia. There is a whole different system of honors here. The sultana can bestow a title whenever she pleases, but don't get your hopes up that it's going to happen today." "You sound angry at me," Kitty said with a little pout. "I am not angry, Kitty. I'm just speaking over the chopper noise." Truth be told, Oliver had been on the verge of a nervous breakdown ever since Kitty had delivered her ultimatum, and he was anxious for everything to go as planned today. He had way too much to lose if it didn't. Trying to placate her a bit, he continued, "I'm just trying to make you understand that these titles given by royals like the sultana are _real_ honors. They honor truly deserving people who have done a tremendous amount of good for Malaysia over a lifetime. People who build hospitals and schools, who start companies that support entire towns and provide work to thousands of locals. These honors mean a great deal more than Colette's title. All she ever did was spread her legs for some posh dimwit." The helicopter swooped over the Kuala Lumpur skyline, passing the iconic Petronas Towers as it started to descend. "So this is where the sultana lives?" Kitty asked as she peered out at the exclusive leafy neighborhood of Bukit Tunku. "This is just her little crash pad in KL for when she comes to the capital. She has residences all over the world—a house on Kensington Palace Gardens, a villa overlooking Lake Geneva, and of course, the gigantic palace in Perawak," Oliver informed her as the chopper touched down on the great lawn. The two of them jumped out of the chopper, and a uniformed officer awaited them on the lawn. "Welcome to the Istana al Noor," he said as he led them toward a humongous white palace that resembled a wedding cake. Entering through the front doors, Oliver and Kitty found themselves in a vast reception hall with nine gigantic pyramidal chandeliers that descended from the coffered gold-leafed ceiling like upside-down versions of the Rockefeller Center Christmas tree. "This is her _little_ crash pad?" Kitty remarked. "Oh, you have no idea, Kitty. Her home in Perawak is twice the size of Buckingham Palace." They were shown into the drawing room, which had dramatic black marble floors and walls painted in a shimmering crimson hue. The space was filled with priceless Peranakan gilded wood antiques mixed with fantastical Claude Lalanne bronze furniture. Facing them was a vibrant pink-and-yellow triptych of Andy Warhol paintings depicting the Dowager Sultana in her younger days. "Wow, this was not what I was expecting," Kitty said, clearly in awe of her surroundings. "Yes, the Dowager Sultana was definitely a hell-raiser back in the seventies," Oliver noted as they both sat down on a backless velvet settee. Next to the settee was a round Lalanne table laden with gold-framed photographs of the sultana posing with famous personages. Kitty peered at the pictures, recognizing the Queen of England, Pope John Paul II, Barack and Michelle Obama, Indira Gandhi, and a woman with an enormous pile of blond hair. "Who is that blond woman? She looks so familiar. Is she some queen?" Kitty asked. Oliver squinted at the picture and then let out a quick laugh. "No, but she is adored by many queens. That's Dolly Parton." "Ah," Kitty said. Suddenly the double doors opened, and two honor guards in full-dress uniform entered. Flanking the doorway, they clicked their heels at attention and tapped the base of their long bayonets on the marble floor twice in unison. "We need to stand, Kitty," Oliver suggested. Kitty quickly stood up, smoothing out the wrinkles on the front of her ankle-length Roksanda skirt and then adjusting her posture. The guard on the right side shouted sternly, " _Sama-sama, maju kehadapan! Pandai cari pelajaran!_ " They tapped their bayonets on the floor again, as the sultana swept into the room in a flaming violet silk kebaya, followed by four attendants. Her head was covered in a matching violet, blue, and white headscarf, and she resembled Queen Mary, covered in precious jewels from the waist up. Pinned in the middle of her hijab right above her forehead was an enormous sunburst diamond brooch with a forty-five-carat pink diamond in the center. On her ears were a pair of diamond-and-pearl girandole earrings, and around her neck were what appeared to be ten or twelve heaping necklaces of nothing but diamonds, diamonds, and more diamonds. Kitty's jaw hung open at the sight of this Queen Mother ablaze in diamonds and she dropped to a curtsy so deep, Oliver thought she was doing the limbo. Oliver bowed smartly. "Oliver T'sien, what a pleasure!" "The pleasure is all mine, ma'am. May I humbly present Mrs. Kitty Bing of Shanghai, Los Angeles, and Singapore." "It's an honor to be in your beautiful country, Your Majesty," Kitty blurted out nervously, before remembering that she wasn't supposed to speak first. The Dowager Sultana pursed her lips and stared at Kitty for a brief moment, saying nothing. She sat down on a throne-like Bergère chair, and Oliver and Kitty took their seats again. An army of maids entered the room bearing gold-lacquered platters filled with Malay desserts and steaming pots of tea. As the maids began serving tea to everyone, the Dowager Sultana smiled at Oliver. "Come, don't be shy! I know how much you love _ondeh ondeh_." "You know me too well," Oliver said, helping himself to one of the bright green rice-cake balls stuffed with palm sugar and rolled in grated coconut. "Now, what brings you to this neck of the woods today?" "Well, Kitty has recently become enchanted with Malaysia, so since we were in town, I thought it only fitting that she meet this country's greatest living legend." The Dowager Sultana beamed. "Oh Oliver, you make me sound like a fossil! Tell me, child, what do you like about my country?" Kitty stared at the sultana blankly. Until today, she had never set foot on Malay soil and didn't know a thing about the country. "Er...well...I love the people most of all, Your Majesty. So warm and...hardworking," Kitty said, thinking of the half a dozen or so Malay maids that worked at Cluny Park Road. The Dowager Sultana pursed her lips again. "Really? I was not expecting to hear that at all. Most people tell me how much they love our beaches and our satay. So do you intend to put down some roots here?" "Well, if I can find a palace as beautiful as yours, I'd be very tempted." "Why thank you, but this is no palace. This is just a house." "Kitty's husband, Jack Bing, is one of China's premier industrialists. So they are highly interested in investing in Malaysia." "Well we do have such a wonderful relationship with China. And I do adore that First Lady of yours," the Dowager Sultana said, picking up a piece of _ondeh ondeh_ with her fingers and chewing on it slowly. "Oh, you've met her?" Kitty said excitedly, forgetting royal protocol again. "Why yes. I gave her an audience at my palace in Perawak. What an accomplished woman, and what a voice! Now, tell me, Oliver, how has your dear grandmama been since I last saw her?" "Her health is excellent, ma'am. But I must confess her spirits have been rather low lately. As you know, my great-aunt Su Yi's passing has affected her greatly." Kitty, feeling bored, began to zone out on the photo of the sultana with Michelle Obama. She was trying to identify the designer of Michelle's red dress. Was it Isabel Toledo or Jason Wu? She felt sorry for the First Lady—that poor woman was obligated to only wear American designers. The sultana continued to speak. "Ah yes, it was such a beautiful funeral. Did you not enjoy my son's eulogy to Su Yi?" "It was remarkable. I did not know that the sultan spent a year living at Tyersall Park." "Yes, when he was doing a special course at the National University of Singapore, Su Yi was kind enough to host him. I'm afraid he found the Malay embassy accommodations to be lacking, and he was much more at home at Tyersall. You do know his great-grandfather was the sultan who originally built it?" "Forgive me, ma'am, I had forgotten. No wonder he would feel a kinship to the place. If I might venture to ask, was Su Yi ever conferred with a title?" Kitty's ears suddenly pricked up. "To my knowledge, she wasn't. I believe in the 1970s the Agong—whoever it was back then, I've lost track—tried to honor her, but she graciously turned it down. She was already Lady Young, and never even used that title. _Alamak_ , what would Su Yi need a title for? There was never any doubt of her position. I mean, she already had Tyersall Park. What more do you need?" "That's quite true." Oliver nodded, stirring his tea. "Tell me, Oliver, what is going to happen to that spectacular palace now?" the sultana asked, her brow furrowing. "Oh it's anyone's guess. My cousins are entertaining an avalanche of offers. Every day I hear there's someone new coming in with an even higher bid. We're in the billions now." "I'm not surprised at all. If I was younger, I might have considered it as a home in Singapore myself. Of course, it will never be the same without Su Yi, but whoever ends up living there will be tremendously fortunate." Oliver sighed dramatically. "Sadly, though, I don't think that will happen. The house will surely be torn down." "Oh my goodness, how can that be?" The sultana placed her hand to her chest in shock, showing off her fifty-eight-carat blue diamond ring. Kitty's eyes followed the solitaire like a cat distracted by a shiny toy. "The land is far too valuable. All the developers that have put in bids have ambitious plans for Tyersall Park, and I don't believe that would include the old house." "But what a travesty that would be! Tyersall Park is one of the most elegant estates in Southeast Asia. That rose garden, and the grand salon—such sophistication! Someone needs to rescue it from the greedy developers!" "I couldn't agree more," Oliver said. Kitty listened to them with fascination. This was the first time she had heard anything about this old house. "Well, Oliver, surely you know someone who will want to buy the estate and maintain it to the same standards as Su Yi did? What about that new Chinese duchess whatshername who's moving to Singapore to save the chimpanzees? I met her at the funeral." Kitty looked up from her tea in alarm. "Um, you're referring to the Countess of Palliser?" Oliver said, glancing at Kitty uncomfortably. "Yes, that one. Do you know her? She should buy the house. Then she would become the undisputed queen of Singapore!" the Dowager Sultana declared, popping another sweet coconut ball in her mouth. — After their audience with the sultana, Kitty remained silent during the helicopter ride back to Singapore. As she alighted from the chopper, she turned to Oliver and said, "This house the sultana was referring to, how much are we talking about?" "Kitty, I know you heard what you heard, but the Dowager Sultana lives in a bit of a fantasy land. Colette would never buy Tyersall Park." "And why not?" "I know my cousins—they would never sell the house to her." "Oh really? You said Colette would never be at your auntie's funeral, and yet there she was. You said Colette wasn't a threat, but then she bumped me off the cover of _Tattle_. I don't think I can believe anything you say anymore." "All right, I'll admit, I'm not the Oracle of Delphi. But there are some things that even Colette could not make happen. For one thing, there is no way she can afford that house." "Really? How much is it?" "Well, I'm told the highest bid right now is four billion. And I know Colette doesn't have that kind of money on her own." Kitty frowned. "She doesn't, but she has a trust fund worth five billion. She can borrow against that trust if she really wants this house. And something tells me she does. She wants so desperately to be the queen of Singapore, queen of the fucking universe!" "Look, Kitty, if it will stop you from losing your mind from this ridiculous rivalry, go ahead, try to buy the house. I'll even go to my cousins with your offer for you. But just so you know, in order for the Youngs to regard your offer as serious, you've got to come in with a bid that wipes everything else off the table clean." "So we offer them five billion." "That's not going to work. You have to realize something, Kitty: You are a _Mainlander_ who's married to a mogul with a very big but very new fortune. You haven't yet gained the degree of respectability that these people value. If you want to steal Singapore's most prized estate away from its snottiest family, you've got to do it in a big way. You need to shock and awe them with your money." "How much will that take?" "Ten billion." Kitty inhaled deeply. "Okay then, offer them ten billion." Oliver was taken aback by how quickly she responded. "Are you serious? Don't you need to talk to Jack first?" "I'll worry about my husband. You worry about getting me that house and you better get it before that little snake Colette comes around with her tongue out. If she steals this house from under my nose, I will never ever forgive you. And you know what that means," Kitty warned, as she got in to her waiting car. After waving her off, Oliver took out his cell phone and punched a number on his speed dial. "Hallooooo?" a voice answered. "It worked. It bloody worked." Oliver sighed in relief. "That Kitty girl is going to buy the house?" "You better believe it. Auntie Zarah, I could kiss your feet." "I can't believe it was that easy," the Dowager Sultana of Perawak said. "The minute you started talking about Tyersall Park, she forgot all about the stupid title. You were absolutely brilliant!" "Was I?" "I had no idea you could act like that!" The Dowager Sultana giggled like a schoolgirl. "Oh my goodness, I haven't had this much fun in a long time! That ridiculously formal way you were speaking to me—' _If I might venture to ask'_ —hahahaha, you sounded like you were in a Jane Austen novel! I was biting my lip to stop from laughing. And oh, and I have a horrible neck ache now from wearing all those damn necklaces! I thought I was going to be strangled by diamonds, heeheeheeheehee!" "If you hadn't been dressed like that, Kitty would not have been in such awe of you. She's been spoiled with jewels herself, so we really had to lay on the shock and awe." "Shock and awe indeed! Did you like what I had my guards chant before I made my grand entrance into the room?" "Oh my God, I almost peed in my pants! I was thinking, why are they chanting the Singapore Children's Day song?" "Heeheehee! Remember when your mummy made you sing it to me one day when you came home from school? You were so proud to sing a song in Malay. Now, did you like my mention of China's First Lady?" "I did, I did. Very appropriate, Auntie Zarah." "I've never even met her, heeheeheehee!" "You deserve an Oscar, Auntie Zarah. I owe you big-time." "Just send me a jar of those pineapple tarts that your cook makes, and we'll call it even." "Auntie Zarah, you're going to get a whole crate of those pineapple tarts." " _Alamak_ , no! Please don't! I'm on a diet! I was so nervous during my performance, I ate too many of those coconut puffs today, heeheeheehee. I have to force myself to go to my granddaughter's zoomba class in the ballroom now!" * * * The Yang di-Pertuan Agong, or Agong for short, is the monarch of Malaysia. The Nine Malay states each have their own hereditary rulers and royal families, and the Agong is elected from among these rulers every five years. # CHAPTER FOURTEEN MACRITCHIE RESERVOIR, SINGAPORE It had been a long, hot, mosquito-ridden hike, and as Carlton pounded his way up another sloping hill, he wondered what the hell he had been thinking when he suggested this plan to Scheherazade. His shirt was drenched in sweat, and he was certain that no amount of Serge Lutens cologne could mask how he smelled at this point. He turned around to check on Scheherazade and saw that she was crouched on the ground, staring at something. At a discreet distance, three of her bodyguards in jogging clothes stood watching them. "Look! It's a monitor lizard!" She pointed. "He's a pretty big fella," Carlton said as he caught sight of the three-foot-long reptile resting under a clump of bushes. "It's a she, I believe," Scheherazade corrected. "We had quite a big menagerie of pets when I was growing up. Reptiles were my thing." "This was in Surrey?" "Actually, this was when we were in Bali. My family lived there for about three years when I was a little girl. I was a bit of a wild child then, going barefoot everywhere around the island." "That explains why you're not even breaking a sweat right now," Carlton said, trying his best not to stare too hard at her goddess-like physique shown off to perfection in her mesh paneled leggings and stretch knit sports bra. "You know it's funny—I never sweat. Ever. I'm told that Queen Elizabeth doesn't either." "Well, you're in good company," Carlton remarked, as they finally arrived at the TreeTop Walk, a 250-meter suspension bridge that stretches from Bukit Peirce to Bukit Kalang, the two highest points of the preserve. As they traversed the narrow bridge, it began to sway slightly, but then the view opened up and suddenly it felt as though they were floating above the trees. They reached the middle of the bridge and stood in silence for a while, taking in the remarkable view. The tropical-forest canopy stretched all around them as far as the eye could see, and the sounds of cackling birds echoed through the breeze. "Unbelievable! Thanks for bringing me here," Scheherazade said. "It doesn't feel like we're in Singapore anymore, does it?" "Sure doesn't. This is the first place I've been to in a long while that's reminded me of my childhood. I mean, it's quite a relief to see that all this nature still exists here." Scheherazade stared at the calm reservoir in the distance, the water glinting in the late-afternoon sun. "Has the island changed that much? I only started coming here about five years ago." "Carlton, you can't even imagine. Every time I'm back I hardly recognize it anymore. So much of the old atmosphere has just been wiped clean." "I guess that's why you like living in Paris?" "Partly. Paris is great because every street you walk down is like an unfolding novel. I actually love it because even though there's history everywhere, it's not _my_ history. Does that make any sense?" "Sure. Shanghai is my hometown, but it doesn't feel like home anymore. Whenever I'm back it feels I can never escape my past. Everyone remembers everything about you—your family history, your mistakes," Carlton said, his face clouding for a moment before he turned back to her. "But that's not what you meant, was it?" "Not really. For me, Paris is like neutral territory because it's neither Singapore nor England. You know, even though I was born in Singapore and lived here until I was ten, I never felt like I truly belonged. Maybe it was because of how I looked—my hair was almost blond back then—it seemed like most people just assumed I was _ang mor._ And my mum inadvertently reinforced this by pretty much raising me as though I was British. Aside from my Chinese cousins, everyone else we knew was part of the British set. I don't blame her at all—she felt awfully homesick and was overwhelmed at first by my father's family. So we sort of existed in this English expat bubble, and for the first ten years of my life I went along thinking of myself as completely English." Carlton gave her a knowing smile. "Bit of a shock when you actually got to England, wasn't it?" "Uh-huh. When we finally moved to Surrey, I realized that the English didn't really see me as I saw myself. I was this exotic, half-Chinese girl to them. So I felt like I was just absolutely screwed on both ends—I wasn't Singaporean enough, but neither was I English enough." Carlton nodded in agreement. "I was sent away to school in England for most of my life, and now I can't really relate to the Chinese back home. In Shanghai, I'm seen as too Westernized. Here in Singapore, I'm seen as an uncivilized Mainlander. But in London, even though I'm clearly an outsider, I feel like I can just be myself and no one's judging my every move. I guess that's what Paris does for you. You feel liberated." "Exactly!" Scheherazade said, flashing Carlton a smile so alluring, he had to stop himself from staring. A group of men entered the bridge from the other end, and as they came closer Scheherazade couldn't help but notice that they all looked Italian and were impeccably dressed in white jackets and bow ties. "Looks like we're being joined by extras from a Fellini movie," Scheherazade joked. "Yes, _La Dolce Vita_. And right on time," Carlton said. The men began setting up an elaborate bar right in front of them, taking out a mixture of spirits, cocktail implements, and glassware. "Did you arrange this?" Scheherazade asked wide-eyed. "Well, I couldn't take you on a sweltering sunset hike and not provide you with sunset drinks." Three of the men whipped out a bass, a saxophone, and a small drum set and began to play a Miles Davis tune. "Can I offer you a Negroni, signora?" the bartender said, handing Scheherazade a highball glass filled with Campari, gin, and red vermouth over ice with an orange peel elaborately curled over the rim. " _Grazie mille,_ " Scheherazade replied. " _Salute!_ " Carlton said, clinking her glass with his Negroni. "How in the world did you know this was my favorite drink?" Scheherazade asked as she sipped her aperitif. "Um...I might have done some Instagram stalking." "But my Instagram account is locked." "Um...I might have been on Nick's Instagram," Carlton confessed. Scheherazade laughed, utterly charmed. Carlton looked in her eyes, and then glanced over her shoulder at her security guards loitering at the end of the bridge. "Would it be crazy if I kissed you? I mean, would your guards have me on the ground in under two seconds?" "It would be crazy if you didn't," Scheherazade said, leaning in to kiss him. After a long, lingering kiss, the two of them stood wrapped in each other's arms in the middle of the bridge, watching as the setting sun glimmered over the treetops, casting a glow of flaming amber over the horizon. — It was almost seven thirty by the time Carlton pulled up to the driveway of Scheherazade's home. He didn't want to drop her off just yet, and wished he could whisk her off to dinner and spend the whole evening with her. But his sense of decorum took over, and he wanted her to set the pace of how things should go. Scheherazade smiled at him, and it was obvious that she didn't want their date to end just yet either. "Why don't you come up? My parents usually have drinks around this time." "Are you sure? I wouldn't want to intrude." "Not at all. I think they'd like to meet you properly. They've been rather curious about you." "Well, if you don't think I'm unpresentable right now in my soiled hiking gear." "Oh, you're fine. It's all very casual." Carlton handed off the keys to his vintage 1975 Toyota Land Cruiser to the valet in the driveway and they strolled through the elegant lobby of the sleek glass tower. For a family that arguably controlled the majority of the country's GDP, the Shangs lived modestly when they were in Singapore. Alfred had long ago divested all of his landed properties on the island, but he had built this exceedingly discreet private apartment tower on Grange Road, where each of his children had been given several floors. "Good evening, Miss Shang," the guards at the reception desk said in unison. One of them escorted them to the elevators, reaching inside to enter a security code into a keypad. They zoomed up to the penthouse, and when the doors opened, Carlton could hear the murmur of voices just off the entrance foyer. The two of them strolled into a circular, atrium-like sunken living room, and then Carlton stopped dead in his tracks. Standing in the middle of the room in a shimmering peacock blue cocktail dress was his ex-girlfriend Colette. He had not spoken to or seen her in almost two years, not since he discovered that she was responsible for poisoning Rachel. "Oh hello. Looks like we have more guests than I thought," Scheherazade said. Her father turned to them and said, "Ah, at last, the prodigal daughter returns! Scheherazade, come meet Lucien and Colette, the Earl and Countess of Palliser." Scheherazade strolled over to greet them and then she proceeded to introduce Carlton to everyone. Still in shock, Carlton shook hands numbly with Leonard and India Shang, who were dressed to the nines and gave Carlton's hiking attire a rather disapproving once-over. Then the unavoidable moment came when he was face-to-face with Lucien and Colette. She looked different. Her hair was pulled into an elegant ballerina's knot at the nape of her neck and she wore far less makeup than he remembered, but he was surprised at how all his anger toward her suddenly came flooding back. The last time they had seen each other, he had accused her of trying to poison his sister. "Hello, Carlton," Colette said, perfectly composed. "Colette," Carlton murmured back, trying valiantly to stay calm. "Oh, you two know each other?" India Shang said in surprise. "But of course, you lived in Shanghai for a period." "For a period," Colette said. "Well then, you must stay for dinner," India insisted. "Yes, do stay," Colette said sweetly. Carlton forced a smile at his hostess. "It would be a pleasure to join you for dinner, Mrs. Shang." Soon they were all seated around the table in a dining room enjoying a twelve-course tasting menu prepared by Marcus Sim, the Shangs' personal chef. Carlton looked around at the exquisite minimalist paintings surrounding them and commented, "Are these works by Agnes Martin?" "Indeed they are," Leonard Shang replied, impressed that Carlton recognized the artist. "Do you collect?" India asked. "Not really, no," Carlton replied. "Carlton collects cars," Colette said, with a gleam in her eye. "Oh really? What sort? I'm restoring an MG Midget at the moment," Lucien said. "I do love MGs, but I actually have a car import business in China. We specialize in exotics like McLarens, Bugattis, and Koenigseggs." "My goodness, those are awfully fast cars, aren't they?" India commented. "They are incredibly engineered automobiles—works of art, really—and yes, they are built for speed," Carlton answered calmly. "Carlton likes to go _very_ fast. He used to race." Colette took a bite of her grilled octopus and gave him an innocent look across the table. Scheherazade glanced at Carlton, noticing the tension on his face. "Oh dear. Have you ever been in an accident?" India asked, making up her mind right then that Scheherazade should never ride in this young man's car again. "Actually, I have," Carlton replied. "What happened? Hope you didn't wreck one of those million-dollar sports cars." Lucien laughed. "It was a very unfortunate accident. But it taught me to be extremely careful. I don't race anymore," Carlton said. "I'm glad you're okay," Scheherazade said with a little smile. "Well," Colette interjected with a glint in her eye, "when you kill one girl and paralyze another from the waist down, it's probably best not to, isn't it?" While Leonard Shang choked on his chardonnay and his wife froze as if she had just been turned into a pillar of salt, Colette flashed a smile at Carlton. It was a smile he knew only too well, and at that moment he realized that Colette Bing might call herself the Countess of Palliser these days, but she hadn't changed one fucking bit. # CHAPTER FIFTEEN THE PEAK, HONG KONG Chloe made the call from her bathroom, with the shower turned on full blast. "Dad, you said to call...you know...if Mum was ever acting weird again." Charlie felt his gut tighten. "What happened? Are you and Delphine okay?" "Um, we're fine. But maybe you should come over." Charlie looked at his watch. It was just past eleven at night. "I'm leaving my office right this second. Be there in fifteen minutes! Do me a favor, honey. Stay with your mother?" "Um, okay." Charlie could hear the fear in her voice. He raced to the house in his Porsche 911, the sports car careening dangerously along the hairpin curves and steep hills all the way up to The Peak. He speed-dialed Isabel's lead security officer, Jonny Fung, from his Bluetooth but it went straight to voice mail. All the while, his heart was beating a mile a minute as he dreaded what he would find when he arrived at the house. Isabel had been doing so well. Was this really another breakdown, or did she stop taking her meds again? A few blocks from the house, Charlie got caught in a traffic jam as cars waited bumper to bumper. He leaned on his horn anxiously, and then decided, fuck it, he would cut onto the oncoming traffic lane. He raced past the line of cars and discovered that they were all trying to go to the same place—Isabel's house. There was a cluster of people in front of the gates as Charlie pulled up. He jumped out of the car and approached the security guards stationed by the gate. "What the hell is happening?" "Private party," one of the guards said in Cantonese. "Party? _Tonight?_ I'm going in." "Wait a second, are you on the list? What's your name?" the baby-faced guard asked, holding an iPad with a list of names glowing on the screen. "My name? Jesus, get out of my face!" Charlie seethed, pushing past him and running down the driveway. Just as he reached the porte cochere of the house, three bodyguards in black suits suddenly appeared out of nowhere and jumped on top of him. "Got the crasher!" One of the guards said into his earpiece as he pinned Charlie's face to the ground. "Get off me! This is my house!" Charlie grunted as one of the guards held him in a knee-lock. "Yeah right," the guards laughed mockingly. "Get Mr. Fung out here now! I'm Charlie Wu and this is my house! I sign all your paychecks!" At the mention of their boss's name, one of the guards started talking urgently into his earpiece. Moments later, the head of security came out of the house and began shouting, "That's Mr. Wu! Get off him, you fucking morons!" Charlie got up from the ground and brushed the dirt off his face. "Jonny, what the fuck is going on here? Why aren't you picking up your phone?" "Sorry, I was inside, and it's very loud in there," Jonny apologized. "Mrs. Wu decided to have the party just this afternoon. It's a benefit for the earthquake victims in Yunnan Province." "You've got to be fucking kidding me," Charlie muttered as he entered the house. There were at least fifty people crowded in the foyer, and a man suddenly grabbed him from behind and gave him a full-on bear hug. "Charlie! You're here!" It was Pascal Pang, his face inexplicably powdered white, with rouge on his cheeks. "I was just telling Tilda that I've never seen _such_ a pleasant divorce as you and Isabel had. Look, he even comes to her parties! My ex-wives won't even take my calls, hahaha." Charlie was bewildered as a pale, thin woman with uniquely androgynous features dressed in a silver jumpsuit smiled at him sweetly. "So you're Charlie! Astrid's told me so much about you," she said in a lilting British accent. "Has she? Excuse me, I just need to find someone." Charlie squeezed through the crowded foyer and into the sprawling formal room, which had been utterly transformed into a dark, funereal space. All of Isabel's pretty French furniture had been covered in black fabric, and even the walls were draped in black. Guests sat at little black bistro tables lit with red votive candles, and a woman dressed in a long deep red velvet dress lay on top of the grand piano with a microphone in her hand. As the pianist tickled the keys, she sang in a deep, throaty voice, " _Fawwwwwwl-ling in love again, never wanted to,_ _what am I to do, I can't help it..._ " Charlie spotted Isabel at one of the front tables, dressed in a man's tuxedo with her hair slicked back, sitting on the lap of a male model who looked to be no older than twenty-five. Chloe and Delphine stood behind her, dressed in matching outfits of black vests, black shorts with garter belts, and black bowler hats, looking extremely uncomfortable. Chloe's face lit up in relief the moment she saw her father. Charlie marched up to Isabel's table and demanded, "Can we talk?" "Shh! Ute Lemper's singing!" Isabel said, waving him off. "We really need to talk _now_ ," Charlie said as calmly as possible, grabbing her arm and leading her to the back of the room. "What is your problem? We have one of the greatest chanteuses in the world right here, and you're interrupting!" Isabel's breath reeked of vodka, and Charlie looked into her eyes, trying to figure out if she was just drunk or having a manic episode. "Isabel, it's Thursday night. Why are you hosting a party for two hundred people right now, and what on earth did you make the girls put on?" "Don't you get it? This is the Weimar Republic. It's 1931 Berlin and we're at the Kit Kat Club. Chloe and Delphine are both dressed like Sally Bowles!" Sighing deeply, he said, "I'm going to take them home with me right now. It's past midnight on a school night and they can hardly keep their eyes open." "What are you talking about? The girls are having the time of their lives! I especially invited Hao Yun Xiang to the party because Chloe's got a crush on him!" Isabel gestured to the strapping male model whose lap she had been keeping warm. "You're just jealous, aren't you? Don't worry, I think you've got a bigger cock." At that moment, Charlie knew she was out of her mind. Isabel could do some outrageous things, but she was never profane. "I'm not jealous—" he began calmly. "Well then, stop spoiling all the fun for the rest of us!" Isabel declared, going back to her chair. She straddled her male model this time and began swaying to the music. It was obvious to Charlie that Isabel was in the midst of a manic high, and sooner or later she was going to come crashing down, and who knows what she would do. It was useless to argue with her like this. He grabbed Chloe and Delphine by their hands and marched them toward the exit. At the front door, he whispered to Jonny Fung, "You don't let Isabel out of your sight, you hear me? And don't let her leave the house until I come back tomorrow morning with her doctors." "Of course," the head of security nodded. — At 3:00 a.m., Charlie was woken up by a phone call. Seeing it was Isabel, he rolled over onto his back with a sigh and answered. "Where are my girls?" Isabel said, sounding preternaturally calm. "They're here with me. Fast asleep." "Why did you drag them off like that?" "I didn't drag them off. They were only too happy to leave the freak show and come home with me." "You know, you deprived them of seeing Ute's full performance. She sang three encores. She sang 'Non, Je Ne Regrette Rien.' And I wanted Chloe to meet Tilda Swinton. When will she ever get a chance like this again?" "I'm sorry, Isabel. I'm sorry Chloe didn't get a chance to meet Tilda. But apparently she's friends with Astrid, so maybe she'll have another chance—" "I don't give a flying fuck about Astrid! Don't you see that there are people suffering in the world? Do you know we raised two million dollars tonight for the earthquake victims? Think of all the children we are helping!" Charlie gave an exasperated laugh. He knew it was pointless to argue with her when she was having one of these episodes, but he couldn't help himself. "You could start with your own children." "So you think I'm a bad mother," Isabel said, suddenly sounding very sad. "I don't think that. I think you're a wonderful mother, but you're just having a bad night." "I am NOT having a bad night! I am having a _fantabulous_ evening! I am a charity fund-raiser par extraordinaire, and I am trying to help our children." Isabel began to sing in a slow, soulful voice: " _I believe the children are our future. Teach them well and leeeeeet them lead the way..._ " "Izzie, it's three in the morning. Can we stop with the Whitney Houston?" Charlie said wearily. "I'll never stop! Those bastards crushed Whitney's spirit, but they will never crush mine, do you hear me?" "Izzie, I'm going to sleep now. I will see you tomorrow morning first thing. I'll bring the girls home before school so they can change into their uniforms." "Don't you dare hang up on me, Charlie Wu!" Isabel demanded. But it was too late. Charlie had hung up. He had hung up on her in the way that he never used to. Isabel's mind went into a roller-coaster dip as she stared out the window onto the crashing waves of the ocean. Unbeknownst to Charlie, she had been sitting in the bedroom of his new house in Shek O during the entire call. Foiling her security crew, she had swapped outfits with Ute Lemper after her second encore and slipped unnoticed out of her own party in a deep red velvet dress. She had taken the first car in the valet line and driven in a manic rage all the way to Charlie's house. She had punched in the code she remembered: 110011. And now she was wandering through the empty Tom Kundig–designed house, spiraling into greater and greater rage. _So this is what it's going to be like now. This is how it is now that you have your new life in this perfect glass house by the sea. This boring bourgeois_ Architectural Digest _fantasy, with all your boring mid-century furniture and that boring little decorative object you wake up next to every morning. Because that's what she is. That Astrid Leong and her sham aesthetics. Just because she wears Alexis Mabille to lunch she thinks she's hot shit, she thinks she's an original. She's nothing but a perfectly bred decorative doll with no substance and no grit. Everyone thinks she's soooo exquisite and soooo elegant, but I know the truth. I know what kind of woman she really is._ Isabel leaned against the dining table, took out her cell phone, and swiped around the screen furiously until she found what she was looking for. It was a video clip she had saved in a locked folder. It was the video of Charlie and Astrid making love, and as she played the video, the sound of their moans echoed through the vast, empty house. _Look at her. She's no better than a whore. Look at the way she straddles him, commanding his invading prick like she's riding one of her Thoroughbreds. This isn't a woman who will just settle for being "friends" with Chloe and Delphine. This is a woman who wants it all. And because of all her money she thinks she can buy whatever she wants. She bought Charlie and now she wants to buy my children and buy their love and turn them into little carbon copies of herself, with long ballerina necks and perfect couture outfits. She wants to sit in this perfect house and look out at the perfect view of the sea with my daughters and stroke their hair in the golden sunlight and twirl them around the garden like they are all in some goddamn Terrence Malick movie and convince them that this is the only life they should ever want. "You'll always be welcome here," she says. Like hell I will. The day after her wedding she's going to shut me out forever. I just know it. She thinks she's going to erase me from their lives, but I will never let this happen. Never never never!_ With trembling fingers, Isabel jammed out a message on the gossip columnist Honey Chai's WeChat message board: > Astrid Leong has stolen my life. She is a cheating, husband-stealing whore. Just look at her whoring herself in this video. She is nothing but a vapid rich girl, an heiress to an evil fortune that destroys our planet. I curse her! I curse Charlie Wu! I curse this house built on deceit and sin! For the rest of eternity, there will never ever be any peace in this house! Isabel attached the video clip and hit "post," as the video streamed out to millions of WeChat users all over the world. Then she climbed up on the wooden Nakashima dining table as if it was a giant surfboard, took off her long velvet gown, rolled it into a tight long rope and threw one end around the Lindsey Adelman chandelier. She fastened the other end taut over the white, tender part of her neck and inched to the edge of the table slowly, step by step, gazing out the window at the moonlit sea. And then she jumped. # CHAPTER SIXTEEN TYERSALL PARK, SINGAPORE "It was an epic fail, a disaster of titanic proportions," Carlton sighed over the phone to his sister as he recounted his date with Scheherazade. "I'm so sorry, Carlton—it sounds traumatic," Rachel said. "So what happened after Colette dropped her bombshell?" "Well, it basically killed the dinner for everyone. Scheherazade didn't eat a thing after that, and I bolted right after dessert was served. It became apparent to me that Scheherazade's parents were going to file a restraining order against me if I stuck around one minute longer." "I'm sure it wasn't that bad." "No, actually, it probably got worse. Everyone went into the drawing room for drinks and coffee, and I _just know_ Colette was itching to get into all the details of exactly what happened in London. I'm sure she went on a no-holds-barred campaign to tell the Shangs what a murderous monster I am. Scheherazade walked me down to my car, and I tried to tell her the whole story but it just all came out wrong. I was rushing and nervous, and I think she was too in shock to process anything." "It's a lot of story for a first date, Carlton. Give her a little time to recover," Rachel said gently. "She'll have all the time in the world—I heard she left for Paris first thing this morning. Game over." "It's not game over. Maybe her leaving had nothing to do with you." "Uh-uh, I don't think so. She hasn't responded to any of my texts in the past twenty-four hours." Rachel rolled her eyes. "Jesus, you millennials! If you really want to win her back, fly to Paris, send her a thousand roses, take her to dinner at some romantic rooftop in the Marais, _just do something other than text her!_ " "It's not so simple. She's surrounded by bodyguards 24/7. If she's not going to respond to my texts, I don't want to be some creepy stalker who shows up at her doorstep." "Carlton, even if you tried, you would never come across as a creepy stalker. Scheherazade's obviously freaked out because she's been fed a line of bullshit from Colette. So you need to show her who you really are. She's waiting for you to do that, don't you see?" "I think she's back in Paris living her life, probably dating some French count with three-week-old stubble by now." Rachel sighed. "You know what it is, Carlton? You're just spoiled. You had the fortune, or maybe the misfortune, of being born good-looking, and girls have been throwing themselves at you all your life. You've never had to lift a finger. Scheherazade is the first girl who's challenging you, who's making you work for it. You've met your match. So are you gonna step up?" Carlton was quiet for a moment. "So what's my next move, Rachel?" "You need to figure that out. I'm not going to give you a cheat sheet! You need to win her back with a wildly romantic gesture. Look, I need to go. There's a potential buyer coming to tour Tyersall Park this morning, and you _don't_ want to know who it is." "Why not?" Carlton asked. "Because it's Jack Bing." "Bollocks! You're pulling my leg!" "I wish I was. He's offering an insane amount of money for the house." "Bloody hell, between Colette and her father, the Bings are clearly out for blood in Singapore. Don't sell it to him." Rachel sighed. "I wish it were up to me. Nick and I are actually trying to avoid him, and I think I hear people arriving." "Okay, call me later." ··· Jack Bing stood in the middle of the Andalusian Cloister, puffing away on his cigar as he stared at the ornately carved columns. "This is incredible. I've never seen a house like this in my whole life," he said in Mandarin. "I love this inner courtyard! We can take out this reflecting pool and put in a _real_ swimming pool," Kitty suggested in English. Felicity, Victoria, and Alix winced but said nothing. Oliver stepped in diplomatically. "Kitty, this reflecting pool was brought over tile by tile from Córdoba, Spain. Do you see these blue-and-coral Moorish tiles lining the pool? They're extraordinarily rare, from the thirteenth century." "Oh, I had no idea. Of course we must keep them, then," Kitty said. Jack stared at the lotus-shaped rose quartz in the middle of the fountain that was bubbling a slow, hypnotic trickle of water. "No, we mustn't change a thing. This house may not be as grand as our place in Shanghai, but it has amazing feng shui. I can feel the chi flowing through everywhere. No wonder your family prospered here," Jack told the assembled ladies. The Young sisters nodded politely, as none of them spoke Mandarin and only understood about thirty percent of what he said. Jack looked at the three frumpily dressed sisters, thinking to himself, _Only women who grew up in a place like this can get away with looking like that._ _And they can't even speak a word of Mandarin. They are like dodo birds, a useless species. No wonder they are losing their house._ The group proceeded through the arcade into the library. Jack looked around at all the old books lining the double-height bookcases and the sleek Indian rosewood desk. "I love this kind of furniture. Art deco, isn't it?" "Actually, this was Sir James's library, and he had all the furniture custom designed by Pierre Jeanneret in the late 1940s," Oliver informed him. "Well, it reminds me a bit of the old Shanghai clubs where my grandfather used to play," Jack remarked. Turning to the ladies, he said, "My grandfather worked in a water-boiler factory, but he was also a trumpet player. Every night for extra money, he would play in a jazz band that performed in all of the clubs frequented by Westerners. When I was a little boy, it was my duty to shine his trumpet for him every night. I would spit and spit at the trumpet to clean it, in order to make the polish go farther." Felicity backed away nervously, afraid that he might actually perform one of his spitting demonstrations near her. "How much for the furniture?" Jack asked. "Er...which pieces did you have in mind? Some of them are...things...that we could never part with," Victoria said in the rudimentary Mandarin she used with her servants. "Oliver, how do you say 'heirloom' in Mandarin?" "Ah, that's ' _chuan jia bao_ ,' " Oliver told her. "Oh, I love the tables, the chairs, this purple-and-blue rug, especially." Jack pointed at the floor. Felicity stared down at the purple silk rug and a story her aunt Rosemary T'sien had once told her suddenly came flooding back... _You know your mother once stared a Japanese general in the eye and dared him to shoot her? It happened right here in this library, where Su Yi was hosting a card party for some high-ranking officers. They were always forcing her to do things like this during the occupation, host these horrible debauched parties for them. My husband—your uncle Tsai Tay—had just been arrested for some ridiculous offense, and when the general lost a game of gin rummy to your mother, she demanded that in return he free Tsai Tay. Of course the general was outraged by her boldness, and immediately took out his pistol and held it to her temple. I was sitting right next to her, and I thought she was a gone case._ _Su Yi remained completely calm and said in that imperious way of hers, "General, you are going to ruin Rosemary's beautiful cheongsam if you shoot me right now. My brains will be all over it, not to mention this beautiful art deco carpet from Paris. Do you know how much this carpet is worth? It's designed by a very famous French artist named Christian Bérard, and would make such a beautiful present for your wife, if only it wasn't stained with my blood. Now, you wouldn't want to disappoint your wife, would you?" The general was silent for a moment, but then he burst into laughter. And then he put down his gun, took the rug with him, and the next day, they released my husband from prison. Tsai Tay would never forget what Su Yi did for him._ _Hiyah, there are so many stories I can tell you about the war years, but Su Yi wouldn't want me to. But you know, she saved the lives of so many people, and most of them didn't even realize she was the one responsible. She wanted it that way. After the war was over, we heard that the general was executed for war crimes during the war tribunals in Manila. One day, your mother called me up and said, "You'll never guess what just arrived in a long box. That purple art deco rug that the general took back to Japan. I suppose his wife never approved of it."_ Felicity snapped out of her reverie and said decisively, "Mr. Bing, this rug isn't for sale. But there are some items that we could offer with the house." "All right then. Oliver, could you make an assessment of how much everything is worth? I'll take whatever _chuan jia biao_ these nice ladies will let me have," Jack said, turning to the Young sisters with a little smile. "Of course," Oliver said. "Ladies, I approve of this house, and I think my family will be very happy using it whenever we visit Singapore. Thank you for showing us around this morning, and please, this is a standing offer, so take your time to decide. I know this must not be an easy decision for all of you," Jack said. He then strolled out the front doors, flicked his cigar onto the gravel driveway, and got into the back of the first black Audi SUV. Kitty climbed in after him, the bodyguards got into their SUVs, and the convoy of cars zoomed off. — "Well _that_ was excruciating," Victoria said as they sank into the sofas in the drawing room. "Oliver, where on earth did you ever dig up these people?" Felicity asked contemptuously. "Believe it or not, they're far from the worst. Jack has become quite an astute art collector—they have one of the top private museums in Shanghai—and Kitty's taste has actually matured. Plus, she's willing to learn. Don't worry, they won't do anything to the house without my approval." Victoria looked up in surprise to see Nick and Rachel entering the drawing room. "I didn't realize you two were home! Why didn't you come out and meet these people? Rachel, we could have used another Chinese translator!" Nick plopped down on one of the art deco club chairs. "Oh I've met them before—I met Jack in Shanghai a couple of years ago and had hoped never to meet him again, and his wife we all met when she came for Colin's wedding." "Wait a minute...that woman was at Colin Khoo's wedding?" Felicity looked taken aback. "Auntie Felicity, _she was at your house_. She used to be Alistair's girlfriend," Nick said irritatedly. "Good grief, _that was_ _her_? The one with the big brown cow nipples? Pussy Ping or whatever her name was?" Alix blurted out. "Her name is Kitty Pong," Rachel said. "Dear me, I didn't recognize her at all. She has a completely new face! No wonder Alistair suddenly flew back to Hong Kong first thing this morning! But I thought she was married to that ghastly boy, Carol Tai's good-for-nothing son? The one that butchered his face with plastic surgery too?" Alix said. "That was ages ago, Auntie Alix. Kitty's traded up." "She most certainly has. I actually quite liked her pretty floral dress today. Why, she didn't look very vulgar at all," Victoria noted. "It's _impossible_ to look vulgar in Dries Van Noten," Oliver declared. "So you really want to sell the house to them?" Nick asked gruffly. "Nicky, you tell me how we can say no to _ten billion dollars_? That's three times more than our top offer. It would be pure stupidity to refuse this kind of money!" Felicity reasoned. Oliver nodded. "It would be looking a gift horse in the mouth." Nick glanced over at Oliver in annoyance. "That's easy for you to say. You didn't grow up in this house. For some of us, it's not just about the money." Oliver sighed. "Look, Nicky, I know you're upset with me, but I really didn't mean for any of this to hurt you. I loved your grandmother and I love this house more than you can possibly imagine. I thought you _wanted_ to preserve Tyersall Park, and when I heard that the Bings were on the lookout for a new place in Singapore, I just put two and two together. These people love the house, and they're committed to maintaining its architectural integrity. And they actually have the kind of money it takes to restore the house and keep the estate in tip-top condition for generations to come." Rachel spoke up. "Do those generations include Colette Bing?" Oliver's face flushed red, while Felicity asked, "Who's Colette Bing?" "Colette Bing is Jack's daughter. Two years ago, her personal assistant, Roxanne, tried to poison Rachel, on Colette's behalf," Nick answered sharply. "WHAAAT?" Felicity and Victoria shrieked in horror. "Oh my goodness, I had completely forgotten that this was _that family_." Alix moaned, putting her hands to her face. "Rachel, that was such an unfortunate incident, but you should know that Jack and Kitty have absolutely _nothing_ to do with Colette anymore," Oliver said. Nick's face flashed with anger. "It wasn't an unfortunate incident. My wife almost died! Just how much do you stand to make on this deal, Oliver? Aside from your commission on the sale, which will be in the millions, how much will you and that auction house of yours be making selling new stuff to these eager Bings?" Oliver got up from the divan and smiled apologetically. "You know, I think I will leave you all now. I can see that I've frayed a few nerves. The offer's on the table, and I look forward to hearing your response." As soon as Oliver had left the room, Victoria spoke up. "You know, I've been thinking...there is something to all this that's just been so serendipitous, so impossible to believe, this has to be a sign. Nicky, this incredible offer from the Bings, I think part of it is because they are atoning for what happened to Rachel. I think this is all Mummy's work. She is looking out for us from heaven." Nick rolled his eyes in frustration. "It is hard to believe that anyone would pay this much over the market value for Tyersall Park—" Alix began. "Mummy had it planned all along. She knew we wouldn't be getting any money from the Shang Trust, and so she wanted us all to get the most money possible out of Tyersall Park. That's why she split it up like she did, and now she's working a miracle for us." Victoria's voice brimmed with conviction. Nick suddenly stood up and looked at his aunties. "Look, you can tell yourself any story you want if it helps you to sleep at night. Personally, I can't stand the idea of this house going to the family that almost killed my wife! I don't think we can trust them to keep their word about preserving the house—I can tell that Kitty's just waiting to get her claws into redesigning it from top to bottom. But if I can match Jack's offer, will you sell it to me?" Rachel looked at him in surprise, while Alix answered, "Nicky, don't be silly. It would be absurd for you to buy this house at that price! We couldn't let you do that!" "You didn't answer my question. If I can get us ten billion, do we have a deal?" The aunties looked at one another. "Okay, we will give you one month," Felicity finally relented. # CHAPTER SEVENTEEN SENTOSA ISLAND, SINGAPORE Twice a year, the acquisitions board of the Singapore Museum of Modern Art convened to go over potential new purchases for the permanent collection. The exclusive board was composed of the city's young elite collectors, mostly descended from the country's most powerful families. As with most entitled scions, it simply wouldn't do for them to actually have to perform their duties at the museum's perfectly nice but rather ordinary offices, so some new fabulous location with celebrity-chef-prepared cuisine was always selected for the acquisitions board meetings. Today, the meeting took place over breakfast at the Capella on Sentosa, the island playground off Singapore's southern coast. When the museum's curator Felipe Hsu arrived at the gorgeous reception room overlooking a beautiful tiered infinity pool, he found the atmosphere positively buzzing among the dozen or so members that had already assembled. "I couldn't believe it! Absolutely couldn't believe it!" Lauren Lee Liang (the wife of Roderick Liang of the Liang Finance Liangs, and a granddaughter of Mrs. Lee Yong Chien) whispered in a corner to Sarita Singh (former Bollywood actress and daughter-in-law of Gayatri Singh). "How can you possibly recover from something like that?" Sarita shook her head as she fingered the mother-of-pearl medallions on her Van Cleef and Arpels necklace as if they were rosary beads. "Well, the one consolation is that her tits did look great. I wonder if she's had them lifted?" Lauren said as she shielded her mouth with her VBH clutch. Felipe strolled over to the buffet to help himself to two soft-boiled eggs and some toast points. Patricia Lim (of the Lim Rubber Lims), who was standing next to him trying to decide between eggs Benedict or eggs Norwegian, gave him a look. "What a morning, huh?" "Yes, it seems like everyone's caffeinated and ready to go! Good, good, we have quite a long agenda today." "Are you thinking of making any sort of announcement, or do you plan to maintain a dignified silence?" "I'm not sure what you're referring to, Pat." The curator frowned. "Don't play dumb with me, Felipe! Oh dear lord...SHE'S ACTUALLY HERE!" The room went dead silent as Astrid entered. She said hi to her cousin Sophie Khoo (of the Khoo Enterprises Khoos),* grabbed a pain au chocolat from the buffet and sat down at the head of the long marble table as everyone took their places. Then she stood up abruptly. "Good morning, everyone. Before we dive headlong into our agenda, I have a confession to make." Most of the board members gasped audibly as they stared wide-eyed at Astrid. "When it comes to Anish Kapoor, I am totally biased. I have loved his work for many years now, and as you probably know I own several of his pieces and yes, I was the anonymous donor who helped to fund the new installation in Antwerp. So we will be examining two new artworks from him for possible acquisition, and I will recuse myself from that vote." Astrid smiled at everyone and sat down again. "Un fucking believable..." Lauren Lee muttered under her breath. Sarita Singh tapped on her coffee mug with her spoon, and everyone looked at her as she spoke up in a righteous tone. "I was expecting our chairwoman to humbly announce her resignation, but since she has shown no intention of doing that, I'd like to start a motion for Astrid Leong's immediate removal from the acquisitions board." Astrid stared at Sarita in shock. "I second that motion," Lauren Lee immediately said. "What the hell?" Felipe blurted out, his mouth still full of soft-boiled egg as the room erupted in commotion. "Sarita, why are you suddenly suggesting this motion?" Astrid asked. "Astrid, let's be perfectly honest here. We're going to lose funding now because of your actions. The entire museum's reputation is going to be affected because of you. I can't even believe you dared to show up here this morning." "I'm really not following...is this because of my divorce?" Astrid asked, trying to remain gracious and calm. From the other end of the table, Sophie Khoo stood up and ran over to Astrid's side. "Come with me now," she whispered, taking hold of her arm. Astrid stood up and followed Sophie out of the room. "What is going on in there?" she asked, absolutely bewildered. "Astrid, it just became apparent to me that you don't even know yet." "Know what?" Sophie closed her eyes for a moment and inhaled. "There is a video of you that leaked late last night. It's gone viral." "A video?" Astrid still didn't catch on. "Yes, of you...with Charlie Wu." All the color drained from Astrid's face. "Oh my God." "I'm so sorry..." Sophie began. Astrid stood stock-still for a moment, and then she snapped into crisis-management mode. "I need to go. I need to get Cassian out of school. Please tell them I needed to go," Astrid said, as she made a run for her car. As Astrid sped along the Sentosa Gateway heading back to Singapore, she found herself unusually calm and collected. She tried ringing Charlie from her Bluetooth but his cell kept going straight to voice mail. Finally, she left a message: "Charlie, I suspect you've already heard about the video leak since you're not answering. I just found out minutes ago. I'm fine, don't worry, I'm on my way to ACS now to get Cassian. I would suggest doing the same for Chloe and Delphine. If they haven't found out already, it's better coming from us than from some classmate. You know how kids can be. I'll talk to you soon." The minute Astrid ended the call, her phone started ringing again. "Charlie?" There was a brief silence on the other end, and then a screeching voice filled her car. "Oh my God, you are still talking to that horrible pervert! I can't believe you!" It was her mother. "Mum, please calm down." "A sex tape! Ohmygod, in my worst nightmare I never imagined I would ever hear those words uttered about one of my children! I just got home from showing Tyersall Park to some dreadful Chinese people, and now I hear this news from Cassandra Shang? Your father is so angry, I'm worried he's going to drop dead of a heart attack!" Felicity cried. Astrid couldn't help but notice how her mother always managed to sob hysterically, scold, and guilt-trip her simultaneously. "Mother, we did nothing wrong! Michael secretly videotaped us in the privacy of Charlie's home, and now he's leaked the video everywhere. This is a crime, Mum." "The crime is you sleeping with Charlie in the first place!" "How is that a crime?" "You're a harlot! Your reputation has gone down the toilet, and you're branded for life now!" "Did you even see the video? It's ten seconds of grainy footage—" "Ohmygod, if I were to actually see the video I think I would instantly go blind! How could you have slept with that man when you're not even married to him? This is God punishing you!" "I'm sorry, I've had sex before marriage, okay, and I've had sex with Charlie, who, by the way, I was having sex with the first time he was my fiancé over a decade ago!" "The two of you have brought nothing but disgrace onto us. You have disgraced your father and me and you have disgraced your family for generations! And you have ruined poor Cassian's life! How will he ever show his face at ACS again?" "I'm on my way to get Cassian now." "We already got him. Ludivine just collected him from school and is bringing him over here." "Oh good, I'll be there in ten minutes." "Absolutely not! What are you thinking? We don't want you anywhere near this house!" "Stop being ridiculous, Mum—" "Ridiculous? I don't know how I'm ever going to recover from this! You need to leave Singapore and not come back until things blow over! Don't you realize what this scandal has done to your father's reputation? Good grief, this might affect the next election! This might throw the sale of Tyersall Park into jeopardy! My God, the price might come tumbling down! I can feel my blood pressure skyrocketing now. Oh my goodness I need my pills. Sunali, where are my pills?" Felicity shrieked to one of her maids. "Calm down, Mum, I don't see how this has anything to do with Tyersall Park!" "How can you not see it? You have tainted the family legacy! Do not come over to Nassim Road, do you understand? Your father does not want to see your face! He says you are dead to him!" Astrid felt winded for a few moments, overwhelmed by her mother's attack. Thankfully, her phone beeped and Charlie's number flashed on the screen. "Okay, Mum, don't worry, I'm not coming over. I'm not going to shame you for one moment longer," she said, switching over to Charlie. There was a short pause, and then Charlie's voice came through. "Astrid, are you okay?" "Yes, thank God it's you!" Astrid said with a heavy sigh. "Are you driving?" "Yes, I was on the way to get Cassian out of school, but—" "Can you find someplace to pull over?" Charlie's voice sounded strange. "Sure, I just got to Tanglin Road. Let me pull over into this Esso right here." Astrid parked in the gas station and relaxed into her seat. "Okay, I'm parked." "Good, good. First of all, are you okay?" Charlie asked. "Well, my mum just screamed at me in a way I've never heard before and ordered me to leave the country. Otherwise, life is peachy. How has your day been so far?" "I'm not sure how to tell you this, Astrid," Charlie said in a shaky voice. "Let me guess, you found out why Michael leaked the video?" "Actually, Michael didn't leak it." "He didn't?" "No. It was Isabel." "ISABEL? How did she even get the video?" "We're not sure...we're still trying to piece it all together, but the video came from her phone. She posted it to the gossip blog." "Why on earth would she do that?" "She had another psychotic episode, Astrid. And this time, she tried to hang herself." "She _what_?" Astrid found herself going numb. "She tried hanging herself in our new house, on the dining-room chandelier. She wanted to curse the house and curse our marriage forever." "So what happened?" Astrid barely got the words out. "The chandelier broke, and that saved her. But now she's on life support. She's in a coma, and they don't know if she'll ever come out of it," Charlie said, his voice cracking in grief. "No. No, no, no, no, no," Astrid cried, breaking down into uncontrollable sobs. * * * * Sophie is the sister of Colin Khoo, and they are cousins to Astrid through their late mother, who was Harry Leong's sister. Yes, Singapore is a very small world, and even smaller within the high-net-worth crowd. # PART FOUR > I often think how unfairly life's good fortune is sometimes distributed. > > —LEO TOLSTOY, _WAR AND PEACE_ > > What's a soup kitchen? > > —PARIS HILTON Four days after Isabel's suicide attempt, an exclusive story broke in _The Daily Post_ : > # HEIRESS DRIVES RIVAL TO SUICIDE ATTEMPT AFTER SEX VIDEO LEAK! > > The gorgeous Singaporean heiress Astrid Leong's sensational $5 billion divorce from venture capitalist Michael Teo continues to pile up collateral damage. The latest victim is Isabel Wu , the ex-wife of Astrid's current boyfriend, tech billionaire Charles Wu. > > Apparently, an explicit video of Ms. Leong in bed with Mr. Wu sent Mrs. Wu into an emotional tailspin, and after leaking the video to a popular Chinese gossip blog, Mrs. Wu tried to hang herself at the spectacular new Tom Kundig–designed mansion that her ex-husband has been building in Shek O. > > Isabel has been in a coma at Hong Kong Sanatorium for over a week, where sources say there had been a concerted attempt by Mr. Wu to keep the tragedy under wraps. But Isabel's mother, The Hon. Madam Justice Deirdre Lai, demands a further investigation into her daughter's suicide attempt. "Charlie and Astrid are responsible, and I want the world to know what they have done to my daughter!" sobbed the Hong Kong High Court Judge. > > The scandal has become the talk of Asia, splitting Hong Kong society as friends and family take opposing sides. An insider on Team Charlie says, "Isabel has been suffering from mental health issues for over two decades. The footage in question was secretly recorded long after Isabel and Charlie's marriage fell apart, and Isabel leaked it while she was suffering from a manic episode. Charlie and Astrid are the real victims here." > > "Nonsense!" counters an insider from Team Isabel. "Izzie was devastated by this video. It was recorded while Isabel and Charlie were happily married, and it really put her over the edge to learn just how long their affair had been going on." > > Deirdre Lai says, "My poor granddaughters Chloe and Delphine! First they have a porn star for a father, and now they might lose their mother! Can you believe that after all this, that dirty woman dared to show up at the hospital where my poor daughter lies in a coma?" > > _The Daily Post_ tried to contact Ms. Leong for a comment, but since her appearance at Hong Kong Sanatorium, Ms. Leong has seemingly vanished. When we contacted her family's company, Leong Holdings, for comment, spokeswoman Zoe Quan said, "Astrid Leong has no functioning role in this company, and we have no comment." When we inquired as to Astrid's whereabouts, Ms. Quan hurriedly barked, "No idea, _lah_! She is out of the country for an indefinite period." # CHAPTER ONE PLACE DE FURSTENBERG, PARIS Scheherazade padded into the gleaming, state-of-the-art kitchen of her apartment in Saint-Germain, lifted the lid from her frying pan, and put a finger on the crust. Not ready yet. She put the lid over the pan again, went back into her dressing room, and took off her sheer ruffled Delpozo blouse. She had just returned from a party at the loft of a fashion photography couple, where the former pastry chef at Noma had cooked up the most elaborate feast ever, but all through the dinner, Scheherazade only dreamed of getting back to her place, heating up some two-day-old pizza in her frying pan,* opening a bottle of red wine, and catching up on _The Walking Dead_. Changing into her pajamas, she brought the plate of pizza into her living room, sank down into her gray suede sofa, turned on her television, and selected the latest episode. As her favorite show began to play, the dialogue was suddenly drowned out by the sound of muffled music outside her window. Scheherazade turned up the volume on her TV, hoping to drown out the noise, but it only got louder. Cars started honking on the street and a neighbor could be heard screaming out his window. Getting annoyed, Scheherazade paused the show, walked over to her balcony, and opened the glass-paned doors. Suddenly the full force of the music flooded her ears, and as Scheherazade peered over her railing, she saw the most curious sight. Carlton Bao was standing on the roof of a Range Rover parked outside her building, holding up a boom box that was blasting Peter Gabriel's "In Your Eyes." "Carlton! What the hell are you doing?" Scheherazade shouted down at him, absolutely mortified. "I'm trying to get your attention!" Carlton shouted back. "What do you want?" "I want you to listen to me. I want you to know that I'm not some reckless killer! The only thing I'm guilty of is falling—" "What? Turn down the music! I can't hear you!" Carlton refused to turn down the music, but yelled louder, "I said the only thing I'm guilty of is falling in love with yo—" At that moment, four bodyguards dressed in civilian clothes suddenly grabbed him by the legs, yanked him off the car, and body tackled him onto the ground. "Oh fuck!" Scheherazade started giggling. She ran out the door, down four flights of stairs, and out the front door. "Get off him!" she told the security guards that were now standing over Carlton. "Miss Shang, are you sure?" "Yes, I'm sure! He's fine. He's with me," Scheherazade insisted. The beefiest guard reluctantly released his knee from Carlton's back, and when Carlton got off the ground, Scheherazade saw that the left side of his face was all cut up from the asphalt. "Oh no. Come upstairs—let's get some disinfectant on that," Scheherazade said. As they entered her building and rode up in the ornate wrought-iron elevator, she looked him over again. "What did you think you were doing?" "That was my wildly romantic gesture!" Scheherazade frowned. "That was supposed to be romantic?" "I was doing my best John Cusack impersonation." "Who?" "You know, _Say Anything_." "Say what?" "You haven't seen the movie, have you?" Carlton said, suddenly crestfallen. "No, but you did look cute standing on top of that car," Scheherazade said, pulling him in for a kiss. ··· At the other end of Paris, Charlie was walking back to the Hotel George V after a very frustrating dinner with Astrid's old friend Grégoire L'Herme-Pierre. Grégoire had been more charming than usual, and Charlie suspected that he knew far more about Astrid's whereabouts than he let on. She had been in Paris for probably three days, Grégoire surmised, and then she was gone. _No, she hadn't seemed distraught—I just assumed she was making her usual semiannual trip to the city for her couture fittings._ Over the past two weeks, Charlie had crisscrossed the globe frantically searching for Astrid. Mad with worry, he had started in Singapore, then Paris and London, going to all their familiar haunts and speaking with all her friends. He then headed down to Venice to see if she was hiding out in her friend Domiella Finzi-Contini's palazzo, but Domi, like so many of Astrid's friends, remained as silent as the Sphinx. _I haven't heard a peep from Astrid, but then I've been in Ferrara for the past month. We always spend the winter in Ferrara. No, I didn't hear about the scandal at all._ Now he was back in Paris, trying to retrace her steps, trying to understand how she could have abandoned her entire life, and how her family didn't seem to care that she had been missing for the past month. Entering the hotel, he went to the reception desk to see if there had been any messages. _No, monsieur, nothing for you tonight._ Charlie went up to his suite and opened the doors to the balcony, letting in some fresh cold air. The cold air kept him on his toes, helped him to think clearly. Paris had been a dud. She had been here, but she clearly wasn't coming back. He should try Los Angeles next. Even though her brother Alex had assured him she wasn't there, he was still suspicious. His entire security team and all the private investigators he had hired had been poring over everything since day one. Astrid had been meticulous. She hadn't left any sort of paper trail, no bank transfers, no credit card charges in more than five weeks. Someone had to be helping her. Someone close. He stepped out onto the balcony and leaned against the railing, gazing at the soft golden glow that always seemed to hover over Paris at night. The city, breathtakingly lovely as always, suddenly seemed so lonely. He should never have let her come to Hong Kong. She had insisted on coming, wanting to help him through his crisis, but when she saw Isabel in the ICU, hooked up to all those machines...he knew she was trying to be strong for him, for the girls, but he could see that it just devastated her. And then when Isabel's mother saw Astrid at the hospital, she went berserk, and that's when she gave the whole story to _The Daily Post_ , breaking the scandal wide open. It was all his fault. His stupid damn fault. Charlie went back into the suite and sat down on the bed. He opened the drawer beside the bed and took out a small brown padded envelope. It was an envelope that had been mailed to him in Hong Kong from this very hotel a few weeks ago, and inside was a box containing the engagement ring he had given Astrid, along with a handwritten note that he had now read hundreds of times: > Dear Charlie, > > I've been doing a great deal of thinking over the past days. Ever since I came back into your life five years ago, I've only caused you heartache. I dragged you into my problems with Michael, I dragged you into my horrendous divorce, and now I have dragged you and your daughters into an unthinkable tragedy. Chloe and Delphine almost lost their mother, and I am the only one to blame. I feel like no matter how hard I try, nothing I do ever leads to anything good, and so the best I can think to do is to simply go away so that no more damage can be done. I don't think I will ever be fit to be your wife, and I can only hope and pray that you and your family will in time be able to find happiness and peace again. > > Yours truly, > > Astrid > > P.S. Please give this ring to my cousin Nicky when you next have the chance. He should have it for Rachel. Charlie put down the note and reclined on the bed, staring up at the ceiling. Astrid had been lying on this very bed, probably staring at the same view. It was her favorite suite at the George V and he had been the one to introduce her to it the first time he brought her to Paris back in their university days. It seemed like a lifetime ago, and he wished he could just go back to that time and do everything differently. Charlie rolled over and buried his face in the pillow, inhaling deeply. He thought that if he breathed deep enough, maybe her scent would return. * * * * Truly the best way to heat up two-day-old pizza. The crust gets crispy and the cheese gets cheesy if you leave a lid on for a minute at the end. # CHAPTER TWO TYERSALL PARK, SINGAPORE Rachel was walking through the rose garden, looking at the fresh new blooms and inhaling their deep, intoxicating scent when Nick returned. He had been to see Alfred Shang in the hope of raising enough money to buy Tyersall Park from his aunts. "How did it go?" she asked as he entered the garden, although from the look on his face she already knew the answer. "I walked him through the entire proposal, thinking he would at least throw me some kind of bone since Tyersall Park had been his father's estate. Do you know what he told me? He thinks that we are in the midst of another financial bubble waiting to burst, and when that implodes all of the property markets in Asia will collapse. He said, 'If this idiot really wants to give you ten billion for Tyersall Park, you would be an even bigger idiot not to take it. Take his money and go buy some gold. It's the only asset worth keeping in the long run.' " Nick leaned into one of the rosebushes and said, "This is maybe the third time I've actually stood here and smelled the roses. It's funny how one takes things for granted when they've always been around." "We'll plant our own rose garden," Rachel said encouragingly. "I think we can afford a little country house now, don't you think? Maybe in Vermont, or even in Maine. I hear North Haven is beautiful." "I dunno, Rachel. With four billion dollars, it's going to be tough finding something out there," Nick deadpanned. Rachel smiled. It was still impossible for her to fathom that kind of money coming into her life, especially since Nick had just spent the past month desperately trying to raise funds and not getting anywhere close to what he needed. Now that the deadline was up, and his last-ditch effort with Uncle Alfred had failed, Nick had no choice but to give in to his aunts' demands. Picking a beautiful blossom that was dangling from a half-broken stem, Rachel looked up at Nick. "Shall we go in?" "Yes, let's do this." Nick took her hand and they walked up the stone steps into the house, where Nick's aunts sat pensively around a table in the library. Alix looked up at him. "Are we ready to make the call?" Nick nodded, and Felicity picked up the telephone in the middle of the table and dialed Oliver's number. "Hiyah! It's his international cell phone. Now we'll have to pay the long-distance rates," Felicity grumbled. The phone rang a number of times before Oliver picked up. "Oliver, can you hear us? We have you on speakerphone here," Alix shouted into the phone. "Yes, yes, you can lower your voice. I can hear you just fine." "Where are you right now, Oliver?" "I'm back in London at the moment." "Ah, how lovely. How's the weather today?" _"Hiyah,_ _gum cheong hay!_ 1 Let's just get on with it, Alix!" Victoria scolded. "Oh, okay...um, I'll let Nicky speak, since he is technically the majority shareholder," Alix said. "Hi Oliver. Yes, I just wanted to inform you that we've reached a consensus." Nick paused for a moment, took a breath, and then continued. "We're ready to take Jack Bing's offer of ten billion dollars for Tyersall Park." "Okay. And I am accepting on their behalf. We have a deal!" Oliver replied. Felicity leaned in. "And Oliver, we'd like your expertise on valuing the furniture. We'll sell him most of the furniture and objects in the house, with the exception of a few things that we wish to keep." "He's not getting Mummy's Battenberg lace doilies, that's for sure," Victoria muttered under her breath. "Super. The Bings will be thrilled, and I know it hasn't been easy for all of you to reach this decision, but I can tell you that you have made a superb deal. This is a record-breaking amount for real estate, and I don't think you would have realized a price like this from anyone else on the planet. Great-aunt Su Yi would have been pleased." Nick rolled his eyes, while Victoria and Alix nodded. "You'll let them know, Oliver?" Felicity asked. "Of course. I will call Jack right after we get off the phone, and then I'll e-mail Freddie Tan to begin drawing up the contract." "Okay then, goodbye." Nick turned off the speakerphone. The ladies sighed collectively. "It's done," Felicity muttered, as though she had just drowned a litter of puppies. "It was the right thing to do. Ten billion dollars! Mummy would be so proud of us," Alix said, dabbing her eyes with a rolled-up tissue. Felicity looked at her sister, wondering if what she said was true. Would her mother ever be proud of her? Nick got up from the table and walked out the French doors into the garden again. Rachel was about to go after him when Alix placed a hand on her arm. "He'll be fine," she said to Rachel. "I know he will," Rachel said softly. ··· _I just put four billion dollars into his pocket and that fucker didn't even thank me_ , Oliver thought after Nick had abruptly hung up. Then he picked up his phone again and called Kitty's cell phone. "Kitty? It's done. The Youngs have accepted the offer...Yes, really...No, no, you can't move in next week, it's going to take a few months at the very least to get the deal done...Yes, they will sell some of the furnishings...Of course I will tell you what's worth acquiring, don't worry...I don't think we can pay them more to move out tomorrow. This has been a home to the family for more than a century, Kitty. They need some time to get things sorted and dismantle the estate. The silver lining is that you'll have time to plan the new interiors...Henrietta Spencer-Churchill? Yes, I do know her, but Kitty, why would you want the same designer who's already doing Colette's new house?...I know she's related to Princess Diana, but I have an even better idea...I can think of only one person in the whole world I would trust with a redo of Tyersall Park. Can you meet me in Europe next week?...No, not Paris. We're going to Antwerp, Kitty...No, it's not in Austria. Antwerp is a city in Belgium...Oh, you'll swing by London to pick me up? How awfully kind of you...Perfect. Look forward to it." Oliver hung up the phone and stared into his computer screen for a few minutes. Then he clicked on iTunes and scrolled through his albums until he found a song. He clicked play, and Puccini's "Nessun Dorma" came blasting on.2 Oliver sat in his chair and listened to the first few verses of the aria. As it reached the crescendo, Oliver suddenly leapt out of his chair and started dancing madly around his flat. It was a wild, Dionysian release, and then he collapsed on the floor and started sobbing. He was safe. Safe at last. With the commission earned on the sale of Tyersall Park, the long nightmare of the past two decades was finally over. His 1.5 percent commission on the Tyersall Park sale would garner $150 million, enough to pay off all his student loans and his parents' crushing debts. They wouldn't be rich, but at least they would have enough to survive. His family could be restored to a proper level of respectability again. He would never, ever have to fly economy again. As Oliver lay on the carpet of his London flat, staring up at the cracked plasterwork on the ceiling that had needed fixing ten years ago, he cried out in joy, " _All'alba vincerò! Vincerò, vinceròòòòòòò!_ " * * * 1 Cantonese for "so long-winded." 2 The Pavarotti version, of course. # CHAPTER THREE THE PENINSULA HOTEL, LOS ANGELES "It's as baffling to me as it is to you," Alex Leong said, stirring the ice cubes in his scotch glass with his finger. "Astrid's never left Cassian for this long a period before. I can't imagine what's going through her mind." From his chair on the rooftop bar, Charlie gazed out at the palm trees that seemed to line every street in Beverly Hills. He didn't know if Astrid's brother was truly sincere or putting on a performance, especially since he knew that Alex—long estranged from his parents—was especially close to Astrid. Trying a different tactic, Charlie said, "I'm worried Astrid's had some sort of breakdown and she's unable to get help. She's been MIA for _five weeks_ now. You'd think your parents would be the least bit concerned." Alex jerked his head indignantly, his Persol sunglasses reflecting against the setting sun. "I am the last person to answer this question, since I haven't spoken to my father in years." "But surely you know them well enough to know how they might react?" Charlie pressed on. "I was always the black sheep of the family, so I suppose I was more prepared when my parents took out the knives. But Astrid has always been the darling princess. She's been raised her whole life to be absolutely perfect, to never put a wrong foot forward, so it must have really hit her hard when things didn't go so perfectly. Astrid's scandal makes me look like a saint at this point—I can't begin to imagine how they must have reacted, the things they must have said." "She did tell me that her parents ordered her to go into hiding. But if they adore Astrid as much as I know they do, I don't understand how they could be so coldhearted. I mean, she's done absolutely nothing wrong! None of this was her fault," Charlie tried to reason. Alex leaned back in his chair and grabbed a fistful of wasabi peas from the little bowl on the table. "The thing you have to understand about my parents is that the only thing that matters to them is their reputation. They care about appearances more than anything else in life. My father has spent his whole life crafting his legacy—being the elder statesman and all that shit, and my mum just cares that she's the queen bee of the establishment crowd. So everything in their world has to be according to their exacting standards. They excommunicated me for defying their wishes and marrying a girl whose skin tone was just one shade too dark for them." "I still can't believe they disowned you for marrying Salimah. She's a Cambridge-educated pediatrician, for God's sake!" Charlie exclaimed. "How accomplished she was didn't matter to them one bit. I'll never forget what my father said to me when I told him I was marrying her with or without his blessing. He said, 'If you don't care about your own future, think of the children you will have with that woman. For eleven generations, the blood will never be pure.' And that's the last conversation I ever had with my father." "Unbelievable!" Charlie shook his head. "Were you surprised that he harbored those feelings?" "Not really. My parents have always been racist and elitist to the extreme, like so many in their crowd. Peel away the veneer of wealth and sophistication and you'll find extremely provincial, narrow-minded people. The problem is that they all have too much money, and it's come so easily to them that they think they're bloody geniuses and so they are always right." Charlie laughed as he took a swig of his beer. "I'm lucky, I guess—my father always told me I was an idiot who was wrong about everything." "By sheer dumb luck, my father was born in the right place at the right moment in time—when the whole region was going through enormous, unprecedented growth. And oh yeah, he also inherited an empire that had already been set up four generations before him. I think he looks down on people like your father—people who are self-made—because at the heart of it he is a deeply insecure individual. He knows he did absolutely nothing to deserve his fortune, and so the only thing he can do is disparage others who have the audacity to _make their own money_. His friends are all the same—they are frightened of the new money that's rolling in, and that's why they cluster in their little enclaves. I'm so glad I got away from all those people." "If Astrid ever comes back to me, she'll never have to put up with her parents if she doesn't wish to. I want to build a whole new life for us, and I want her to live anywhere in the world she wants to live," Charlie said, his voice thick with emotion. Alex raised his glass to Charlie. "You know, I always thought it was a pity the two of you didn't get married the first time around. You and Astrid let my parents scare you off too easily then. I swear to you, if I knew where Astrid was, you'd be the first person to know. But my sister is a smart girl. She knows how to disappear, and she knows where everyone's likely to be looking for her. If I were you, I'd be looking in all the unlikeliest places, rather than all her old haunts or cities where her best friends are." After seeing Alex off, Charlie went back to his suite and found that the butler had already performed the turndown service. The shades were drawn, and the television was set on the channel with New Age music playing softly. He threw off his shoes, unbuttoned his shirt, and sank into the bed. After dialing room service to order a hamburger, he reached into his pocket and took out the letter that Astrid wrote to him from Paris, reading it yet again. As Charlie stared at the words, the glow coming from the flat-screen TV at the foot of the bed shined through the piece of paper, and Charlie saw for the first time something on the heavy stationery that he'd never noticed before. Near the bottom-right corner was a faint watermark with a distinctive, ornate monogram pattern: > It suddenly occurred to Charlie that while the envelope had been from the Hotel George V in Paris, the letter itself was written on someone else's expensive custom stationery. Who in the world was DSA? On a lark, Charlie decided to call his friend Janice in Hong Kong, who was one of those people who seemed to know everybody on the planet. "Charlie, I can't believe it's you. It's been ages!" Janice purred into the phone. "Yes, it's been much too long. Listen, I'm trying to solve a little mystery here." "Ooh, I love a good mystery!" "I have a piece of monogrammed stationery, and I'm trying to figure out who it belongs to. I was wondering if you might be able to help." "Can you send me a snapshot? I'll circulate it to everyone I know." "Well, this needs to be kept private, if you don't mind." "Okay, not everyone then. Just a few key people." Janice laughed. "I'll take a picture and send it to you right now," Charlie said. He hung up his phone, got out of bed, and threw open the window shades. The setting sun streamed into the room, almost blinding him for a moment as he held the letter against the windowpane. He took a few pictures and sent the sharpest image to Janice. Just then, the doorbell rang. Charlie went to the door and looked out the peephole. It was room service with his burger. As he opened the door to let the uniformed waiter in with his trolley, his phone began to ring again. He saw that it was Janice calling and rushed to pick it up. "Charlie? This is your lucky day. I thought I would have to send your picture around, but I recognized that monogram from a mile away. I know those initials well." "Really? Who is it?" "There is only one DSA in the whole world that matters, and that's Diego San Antonio." "Who is Diego San Antonio?" "He's one of the leading social figures in the Philippines. He's the host with the most in Manila." Charlie turned to the waiter just as he was lifting the silver dome to reveal a delicious, juicy burger. "Actually, I'm going to need that to go." # CHAPTER FOUR TYERSALL PARK, SINGAPORE Rachel and her best friend Peik Lin stood on the veranda, looking at the figure of Nick in the distance as he disappeared into a wooded part of the garden. "He's been like this for the past week. Going off for walks on his own in the afternoons. I think he's saying goodbye to the place, in his own way," Rachel said. "Is there nothing more that can be done?" Peik Lin asked. Rachel shook her head sadly. "No, we already agreed to sell yesterday. I know it makes no sense, since we've just come into a huge windfall, but my heart still hurts for Nick. It's like I'm in sync with his every emotion." "I wish I could find someone I could be in sync with like that," Peik Lin sighed. "I thought there was some secret new Mr. Perfect you promised to tell me about 'when the time was right'?" "Yeah, I thought so too. I thought I'd finally met a guy who wasn't intimidated by me, but like all the other losers, he disappeared with no explanation." "I'm sorry." Peik Lin leaned on the veranda railing and squinted into the afternoon sun. "Sometimes I feel like it would be far easier not to tell guys that I went to Stanford, that I run a huge property development company, that I actually love what I do." "Peik Lin, that's total bullshit and you know it. If a guy can't handle exactly who you are, then he clearly doesn't deserve you!" Rachel scoffed. "Damn right he doesn't! Now, let's go get smashed. Where do they keep the vodka around here?" Peik Lin asked. Rachel led Peik Lin back into her bedroom and showed her a small button by the bedside wall. "Now, here's one thing I'm really going to miss about Tyersall Park. You press this button and a bell rings downstairs somewhere. And before you can even count to ten—" Suddenly there was a soft knock on the door, and a young maid entered the room with a curtsy. "Yes, Mrs. Young?" "Hi, Jiayi. We'd like some drinks. Can we have two vodka martinis on the rocks?" "Extra olives, please," Peik Lin added. — Nick walked down the pathway past the lily pond, entering the deepest part of the woods in the northwest section of the property. When he was a boy, this was the area of the estate he never dared to venture into, probably because one of the old Malay servants from ages past had told him this was where all the tree spirits lived, and they should be left undisturbed. A bird high in one of the trees made a strange, piercing call that Nick had never heard before, and he looked up into the thick foliage, trying to spot what it was. Suddenly a blur of white flickered past his eyes, startling him for a second. Collecting himself, he saw it again, something white and shiny on the other side of a grove of trees. He crept slowly toward the trees, and as the bushes cleared, he saw the figure of Ah Ling facing a large tembusu tree, clutching a few joss sticks. As she prayed and bowed from the waist repeatedly, the smoke from the joss sticks wafted around her, and her white blouse would shimmer as it caught the rays of sunlight filtering through the low-hanging branches. When Ah Ling was finished with her prayers, she took the joss sticks and stuck them inside an old Milo can that had been placed in the hollow of the bark. She turned around and smiled when she caught sight of Nick. "I didn't know you came out here to pray. I always thought you did your prayers in the garden behind the service wing," Nick said. "I go to different places to pray. This is my special tree, when I really want my prayers to be answered," Ah Ling said in Cantonese. "If you don't mind me asking, who do you pray to here?" "Sometimes to ancestors, sometimes to the Monkey God, and sometimes to my mother." It occurred to Nick that Ah Ling had seen her mother less than a dozen times since she had moved to Singapore as a teenager. Suddenly the memory of one day from his childhood came rushing back. He remembered going into Ah Ling's bedroom and seeing her stuff a suitcase full of things—McVitie's Digestive Biscuits, Rowntree's sweets, packs of Lux soap, a few cheap plastic toys—and when he asked her what these were for, Ah Ling told him they were gifts for her family. She was going back to China for a month to visit them. Nick had thrown a tantrum, not wanting her to go. Decades had passed since that day, but now Nick stood in the middle of a forest with his nanny overwhelmed with guilt. This was a woman who had dedicated nearly her entire life to serving his family, leaving her own parents and siblings behind in China and only seeing them once every few years when she had saved up enough to go back. Ah Ling, Ah Ching the head chef, Jacob the gardener, Ahmad the chauffeur, all these people had served his family for most of their lives. This was their home, and now they were about to lose it too. Now he was letting them all down. As if reading his mind, Ah Ling came over and put her hand on his face. "Don't look so sad, Nicky. It's not the end of the world." Suddenly, tears began to spring from his eyes uncontrollably. Ah Ling embraced him, in the way she had so many times when he cried as a child, stroking the back of his head as he wept quietly against her shoulder. Nick hadn't shed a single tear during the entire week of his grandmother's funeral, and now he was letting it all out. After he had recovered himself, Nick walked quietly next to Ah Ling along the wooded pathway. When they reached the lily pond, they sat on the stone bench at the water's edge, watching a lone egret as it stepped gingerly among the shallow marshes looking for little minnows. Nick asked, "Do you think you'll stay in Singapore?" "I think I will go back to China, for a year at least. I want to build a house in my old village, and spend a little time with my family. My brothers are getting older, I have so many new grandnephews and grandnieces who I have never met. Now I can finally be the rich old auntie who spoils them." Nick chuckled at the thought. "I'm so glad Ah Ma provided for you in her will." "Your Ah Ma was very generous to me, and I will always be grateful to her. For the first few decades I worked here, she frightened me to death. She was not the easiest woman to please, but I think in the last twenty years or so, she came to see me as a friend and not just a servant. Did I ever tell you that a few years ago she invited me to take a room in the big house? She thought I was getting a bit old to be trudging back and forth from the servants' wing to the house. But I turned her down. I wouldn't feel comfortable in one of those grand bedrooms." Nick smiled, remaining silent. "You know, Nicky, I really don't think your grandmother wanted this house to go on after she was gone. That's why she prepared things the way she did. She wouldn't have taken care of me and Ah Ching and everyone else like she did. She thought of every detail." "She may have thought of every detail, but for me, so many questions remain unanswered. I keep beating myself up about how stubborn I was, refusing to come back to make peace with her until the very end. I wasted so much time," Nick lamented. "We never know how much time any of us have. Your Ah Ma could have gone on living for many more months, or even years, you never know. Don't regret anything. You are lucky you were back in time to say goodbye," Ah Ling said soothingly. "I know. I just wish I could talk to her again, to understand what she truly wanted," Nick said. Ah Ling suddenly sat up on the bench. " _Alamak!_ I'm getting so absentminded, I almost forgot that I have a few things for you from your Ah Ma. Come, come to my room with me." Nick followed Ah Ling to her quarters, where she produced an old imitation Samsonite suitcase from the back of her closet. He recognized it as the suitcase she used when she had gone back to China all those decades ago. Ah Ling opened the suitcase on the floor, and Nick saw that it contained stacks and stacks of different-colored fabrics, the kind she used to make the beautiful silk patchwork quilts that hung at the foot of the bed in every guest room. At the bottom of the suitcase was a bundle tied in dark blue satin fabric. "When your Ah Ma was in the hospital, she asked Astrid to gather a few things from the vault and various hiding places she had. Astrid brought these down to me, to be kept for you. I don't think your Ah Ma wanted any of your aunties getting their hands on these," Ah Ling said, handing Nick the bundle. He undid the knotted satin and found a small rectangular leather box. Inside was a vintage pocket watch on a gold chain signed Patek, Philippe & Cie, a silk coin purse full of gold sovereigns, and a small stack of old letters tied in yellowed ribbon. At the bottom of the box lay a newer, crisper envelope with "Nicky" on the front in his grandmother's elegant handwriting. Nick tore open the letter and began reading it immediately: > Dear Nicky, > > I feel that time is running short and I don't know whether I will see you again. There are so many things I had wished to tell you, but never found the chance or the courage. Here are some things I am entrusting to you. They do not belong to me, but to a gentleman named Jirasit Sirisindhu. Please return these things to him on my behalf. He lives in Thailand, and your auntie Cat will know how to find him. I am also entrusting you with this mission because you will want to meet Jirasit in person. When I am no longer here, he will be able to provide you with the resources that you will need. I know I can count on him to be of great help to you. > > Love, > > Your Ah Ma "Thank you for safeguarding these things for me!" Nick said, kissing Ah Ling on the cheek as he left her room. He walked across the courtyard to the main house and went up the stairs to his bedroom, where he found Rachel working on her laptop. "Good walk?" Rachel looked up. "You'll never believe this, but something rather remarkable just landed in my hands!" Nick waved the letter at her excitedly. Nick sat on the edge of the bed and quickly read the letter to her. Rachel's brow furrowed as she listened to the cryptic letter. "I wonder what it all means? Do you know this guy? Jirasit?" "I've never once heard my grandmother utter his name." "Let's google him quickly," Rachel said. She typed in the name and it popped up immediately. "M.C. Jirasit Sirisindhu is a grandson of King Chulalongkorn of Thailand. He is an exceedingly reclusive figure but is said to be one of the wealthiest individuals in the world, with interests in banking, real estate, agriculture, fisheries, and—" Nick's eyes suddenly lit up. "Oh my God, don't you see? 'He will be able to provide you with the resources you need.' He's one of the richest men in the world—I think this man holds the key in helping us get Tyersall Park!" "I'm not sure if I would read so much into this letter," Rachel cautioned. "No, no, you don't know my grandmother like I do. She doesn't do anything without precision. She wants me to go to Thailand and meet this man—it says right here that Auntie Cat in Bangkok will know how to find him. Rachel, this is the plan she had all along!" "But what about the deal we've made with the Bings?" "It's only been a day, and we haven't signed any contracts yet. It's still not too late to rescind the deal, especially if this man can help us! We should catch the next flight to Thailand!" "Actually, maybe _you_ should catch the next flight out, and I should stay here to put the brakes on anything that comes up. We wouldn't want your aunts signing anything until you're back," Rachel suggested. "You're absolutely right! Honey, you're an angel—I'm not sure what I'd do without you!" Nick said breathlessly, grabbing his travel duffel from the cupboard. # CHAPTER FIVE CHIANG MAI, THAILAND After landing in Chiang Mai, the ancient Thai city known as the "rose of the north," Nick was driven by Jeep to an estate nestled in the foothills of Doi Inthanon. Like so many of the great houses hidden in these parts, the walled compound was tucked away up a long, steep road and virtually invisible from the outside. But past the tall, fortresslike gate, Nick found himself in a sybaritic paradise that defied description. The residence was comprised of eight wood-and-stone pavilions built in the traditional Royal Lanna Thai style around an artificial lake, all interconnected by a series of bridges and walkways. As Nick was led through the lush gardens and onto a wooden walkway that floated on the lake, a thin layer of mist hovered over the still waters, adding to the feeling that he had stepped back in time. At an open pavilion overlooking the center of a lake, an elderly man nattily dressed in tweed trousers, a maroon cardigan, and a peak cap was sitting at a beautiful wooden table, cleaning the inside of an old Leica camera with a tiny brush. On the table rested three or four other old cameras in various states of repair. The man looked up as Nick approached and grinned widely. Nick could see that the hair under his cap was snow-white, and though he must have been in his early nineties, his face still retained its handsome features. He put down the camera and got up with an agility that surprised Nick. "Nicholas Young, what a pleasure! Did you have a good journey?" the man said in English tinged with the slightest British accent. "Yes, Your Highness, thank you." "Please call me Jirasit. I hope I didn't rouse you too early?" "Not at all—it was great to get an early start, and your plane landed just as the sun was rising." "I had your aunt Catherine arrange it for you this way. I think the mountains are at their most beautiful right at dawn, and I must confess, I am a very early bird. At my age, I'm up by five and quite useless by midafternoon." Nick simply smiled, and Jirasit clasped Nick's hands in his own. "I am glad we are meeting. I've heard so much about you over the years!" "Really?" "Yes, your grandmother was inordinately proud of you. She talked about you all the time. Come, sit, sit. Do you take tea or coffee?" Jirasit asked as a flurry of servants appeared with trays of refreshments and food. "Coffee would be great." Jirasit uttered a few words in Thai as the servants began setting up an elaborate breakfast on the wide stone ledge of the pavilion. "You'll have to excuse the mess, I have been indulging in my favorite pastime," Jirasit said, as he moved his cameras to one side of the table to make room for the coffee service. "That's quite a collection you have there," Nick said. "Oh, they're all rather obsolete at this point. I prefer shooting with my digital Canon EOS these days, but I do enjoy cleaning these old cameras. It's very meditative." "So you were in quite frequent contact with my grandmother, then?" Nick asked. "Off and on, over the years. You know how old friends are...we would skip a year here and there, but we did try to stay in touch." Jirasit paused for a moment, staring at an old Rolleiflex twin lens on the table. "That Su Yi...I shall miss her." Nick took a sip of his coffee. "How did you two become acquainted?" "We met in Bombay in 1941, when we both worked at the British India Office." Nick sat forward in his chair, surprised. "Wait a minute, is this the Indian branch of the War Office? My grandmother worked there?" "Oh yes. She never told you? Your grandmother started out in the code-breaking office, and I was in the cartography department, helping to create a detailed map of Thailand. The cartographers didn't really know Thailand well, especially in these remote northern parts near the border, and we needed accurate maps in the event of an invasion." "How fascinating. I always pictured her luxuriating away in some maharaja's palace during the Japanese occupation." "Well, she did that too, but the British, you see, enlisted her to do some...sensitive diplomatic work as soon as they realized what she was capable of." "I had no idea..." "Your grandmother had a certain allure that's hard to put your finger on. She was never one of those typical beauties, but men just fell at her feet. It came in very useful during the war. She was good at influencing those rajahs in certain directions." Nick reached into his satchel and took out the leather box that Su Yi had entrusted to him, placing it on the table. "Well, the reason I'm here is because my grandmother wanted me to return these to you." "Ah, my old Dunhill case! I never thought I'd be reunited with it after all these years," Jirasit said like an excited child. "You know, your grandmother was a very stubborn woman. When she insisted on returning to Singapore during the height of the war—complete madness, I tell you—I gave her a few of my most valuable possessions. My father's Patek and these gold sovereigns, and a few other things, I can't remember what. I thought she would need them to bribe her way into Singapore. But see, she hardly needed them after all." Jirasit began winding the pocket watch, and then he held it up to his ear. "Listen? Still ticking perfectly after all these years! I'm going to have to tell my friend Philippe Stern about this!" Jirasit picked up the packet of old envelopes tied in ribbon and studied them for a moment. "What's this?" "I have no idea. I assumed they were yours, so I didn't open them," Nick said. Jirasit untied the ribbon and began sifting through the letters. "My goodness! These were my letters to her after the war. She saved every last one of them!" His pale gray eyes clouded over with tears, which he flicked away quickly. Nick had brought with him a prospectus of his Tyersall Park buyback scheme, and he was about to take it out of his satchel to show Jirasit when the man abruptly stood up and announced, "Come, let us attend to the matter at hand!" Nick had no idea what he was talking about, but he followed Jirasit as he strolled swiftly toward a pavilion on the other side of the lake, marveling at his pace. "Jirasit, I hope I'll be as agile as you are when I'm your age!" "Yes, I hope so too. You seem quite slow for your age. Do keep up! I picked up yoga when I lived in India, and I've never stopped my daily practice. Also, it's important to keep your body alkaline, young man. Do you eat chicken?" "I love chicken." "Well, stop loving it. Chickens reabsorb their own urine—and so their meat is extremely acidic," the man said as he quickened his pace. When they reached the glass-walled pavilion, Nick noticed two guards flanking the entrance. "This is my private office," Jirasit explained. They entered the room, which contained nothing but an ancient gold statue of Buddha inset into a niche on one wall and a beautiful black-and-gilt desk facing a window onto the lake. Jirasit went to a door against the back wall, and placed his hand on the security scanning pad. A few seconds later, the deadbolt unlocked automatically and he gestured for Nick to follow him into the room. Inside, Nick found a space that resembled a walk-in vault with built-in cabinets along every wall. At the corner was an old antique Wells Fargo safe that had been bolted into the floor. Jirasit turned to Nick and said, "Here we are. The combination please?" "I'm sorry, you want _me_ to give you the combination?" "Of course. This is your grandmother's safe from Singapore." "Um, I have no idea what it is," Nick said, surprised by this turn of events. "Well, unless you're good at safe-cracking, you're going to need the combination. Let's see, why don't we call Catherine in Bangkok and see if she knows what it is?" Jirasit took out his phone and moments later had Catherine on the line. The two of them spoke animatedly in Thai for a few moments, and then Jirasit glanced up at Nick. "Did you bring the earrings?" "What earrings?" "Your grandmother's pearl earrings. The combination is on them." "Oh my God! The earrings! Let me call my wife!" Nick said in astonishment. He quickly called Rachel's cell phone, and moments later she answered in a sleepy voice. "Honey, sorry to wake you. Yes, I'm in Chiang Mai now. Remember those earrings I gave you? The pearl earrings from my grandmother?" Rachel crawled out of bed, went over to the dressing table and opened the drawer where she kept her jewelry. "What am I looking for exactly?" she asked, still half asleep. "Do you see any numbers carved on the pearls?" Rachel held a pearl stud up to the window light. "Nothing, Nick. It's totally smooth and luminous." "Really? Can you look again?" Rachel closed one eye and squinted at each pearl as closely as she could. "I'm sorry, Nick, I see nothing. Are you sure we're talking about these earrings? They are so tiny, I can't imagine where someone would hide any information, unless it's _inside_ the pearl." Nick thought back to what his Ah Ma told him when she had handed them over. _My father gave these to me when I escaped Singapore before the war, when the Japanese soldiers had finally reached Johor and we knew all was lost. They are very special. Please look after them carefully._ The words took on a whole new significance now. He stared at the safe, wondering what it could possibly hold. Would there be gold bullion bars, stacks of old bonds or some other type of financial documents that would help him secure Tyersall Park? What was in there that was so valuable to his grandmother that she would go to such great lengths to protect it? "Rachel, I'm sure those are the earrings. Maybe we do need to crack them open. Or maybe the numbers appear if you put them in water? I dunno, try anything," Nick said in frustration. "Well, before we destroy these lovely pearls, let me try the water thing." Rachel went into the bathroom and turned on the tap to fill the sink. She looked at the earrings again—they were simple pearl studs on gold posts, each with a little gold disk as backing. Before dipping one of the earrings into the water, she decided to pry the backing off the stud. Suddenly she gasped. There, on the underside of the backing were tiny Chinese characters carved into the gold. "Nick, I never thought I'd ever get to say these words, but...EUREKA, I'VE FOUND IT! There are Chinese characters carved into the backing of the earrings!" Rachel quickly deciphered the numbers: "9, 32, 11, 17, 8." Nick turned the dial to the corresponding numbers, his heart pounding as each of the locks seemed to click into place one by one. When he finally turned the lever to open the safe, he held his breath, wondering what he would find inside. The safe door creaked open, and when Nick peered inside, all he saw were small red leather-bound books, neatly arranged in stacks. He took one of them out and began flipping through its pages. Every page was written in Chinese, and Nick realized he was looking at his grandmother's private diaries, beginning from the time she was a child to her adulthood. "Why are these here?" Nick was completely mystified. Jirasit gave Nick a serene smile. "Your grandmother was a very private person, and I think she felt that this was the only place she could leave them for safekeeping, without the risk of anyone seeing them or censoring them after she was gone. She never wanted them kept in Singapore, and she never wanted them to leave this compound. You are the historian, from what I'm told, so she wanted you to have access to them. She told me you would one day come." "Is this all there is? These diaries?" Nick asked, bending down to peer more closely into the dark safe. "I believe so. Was there something else you were looking for?" "I don't know. I guess I had imagined that she would have some other valuable treasures stored away in here," Nick said a little disappointedly. Jirasit frowned. "Well you should read them, Nicholas. You may find a great many unexpected treasures within those pages. I'll leave you be, and perhaps we can meet up again for lunch at noon?" Nick nodded, as he took a stack of journals out to the desk. Deciding that the best thing to do was read the journals chronologically, he reached to the bottom of the pile for the oldest journal. As he opened the cover gently, the leather binding cracking after decades of stillness, he began to hear his grandmother's young voice in her handwritten words. > # March _1_ , _1943_ > > It feels like we have been riding for a week, but Keng tells me it has only been three days. Whenever we reach a new outpost I ask him if we are still on the estate and he sighs frustratedly. Yes, we are. Apparently, my mother's family is the largest landowner in West Sumatra, and it would take a full week on horseback to traverse the estate. The highlands are glorious—rugged with a strange wildness to everything. On another trip, it might have even seemed romantic. If I had only known we would be spending so many days riding just to get to my brother's house, I would have brought my own saddle! > > # March _2_ , _1943_ > > Finally arrived. They take me upstairs to see Ah Jit, and at first I don't understand what is going on. My brother lies unconscious, his handsome face so swollen and purple I can hardly recognize him. There is a deep, bloody gash on his right jaw that they are trying to keep from being infected. I asked what was going on? I thought the cholera was under control? "We didn't want to tell you till you got here. It's not cholera. He's bleeding internally. He was tortured by Japanese agents. They were trying to get him to give up the locations of some key people. They broke his body, but they couldn't break him." > > # March _5_ , _1943_ > > Ah Jit died yesterday. He was awake for a while, and I know he was happy to see me. He tried to talk, but I stopped him. I held him in my arms and kept whispering into his ear, "I know, I know. Don't worry. All is well." But all is not well. My darling brother is gone now and I have no idea what is to be done. This morning I walked outside into the garden and saw that all the rhododendron trees have bloomed overnight. Suddenly they are bursting with flowers, in shades of pink I never knew could exist. Blooms so thick, they brushed against my face as I walked through the garden weeping uncontrollably. Ah Jit knew how much I loved these flowers. He did this for me. I know he did. Nick stared at the journal, feeling utterly confused. None of this made any sense. His great-uncle Ah Jit was tortured by the Japanese, and his grandmother was there? But wasn't she supposed to be in India during the war? He leafed through a few more pages, and a loose letter fell out. As Nick glanced over the crisp but yellowing letter, a chill ran down his spine. He couldn't believe his eyes. # CHAPTER SIX THE STAR TREK HOUSE, SINGAPORE Eleanor paced around the room restlessly. "She's late. Maybe she changed her mind." " _Aiyah_ , Eleanor, don't be so _kan jyeong_. She's not late. It's only two minutes past one. Don't worry, I'm sure she'll turn up," Lorena tried to assure her as she lounged on one of the plush white sofas in Carol's enormous poolside bedroom. "Traffic was hideous today! My driver had to take two detours just to get here! I don't know what is wrong. It seems like traffic is getting worse and worse these days. What is the whole point of all these ERPs1 when everywhere is so damn congested? I'm going to have Ronnie call our local MP and complain!" Nadine tut-tutted. Daisy went over the plan again like a battalion leader. "When she does come, everyone knows the plan, right? We'll serve the champagne first, and then I'll just speed through a very short Bible verse, something from Proverbs. Then we get interrupted for lunch. I had my cook put _extra_ chicken fat into the rice today, so hopefully between the champagne, the chicken rice, and all the _nyonya kueys_ , she'll get very full, tipsy, and drowsy. The perfect combination! Then while we're all eating, Nadine, you know what to do." Nadine gave a conspiring grin. "Yes, yes, I just sent the nanny very specific instructions." "Ladies, I'm going to say it again. I think this is a very bad idea," Carol warned, grasping her hands nervously. "No, _lah_! This is serendipity! How lucky are we that my niece Jackie just happened to be visiting from Brisbane this week? We might never have an opportunity like this again!" Eleanor rubbed her hands together excitedly as her niece reentered the bedroom. "Is it okay? They promised me that everything would be state of the art." "Don't worry, Auntie Elle, everything is all set up and ready to go," Jackie said. "Jackie, this won't be breaking the Hypocritical code, will it?" Lorena asked delicately. "You mean the Hippocratic oath? No, not at all. As long as the person doesn't object, there is no issue," Jackie replied. Nadine flipped through the latest issue of _Tattle_ idly. "Hey, are you all going to go to this costume ball being thrown by this Countess Colette? It seems like _everyone_ from _everywhere_ is coming to town for the big event." "Who is everyone?" Lorena asked. "All these socialites from Europe and America, Hollywood celebrities, and the environmentalists. It says here that all the world's top designers are going insane trying to keep up with all the orders for costumes for the ball. Apparently everyone is going to dress up like Prowst." "Hahaha, I highly doubt everyone's going to dress up like Proust—he was a small, pasty little man. They are dressing up like characters from his books!" Lorena corrected. "I've never read any of his books. Did he write that _Da Vinci Code_ one? I saw the movie and didn't understand a thing!" Nadine said. "Anyway, there's a rumor that some British princess will be the surprise guest of honor! I heard that Yolanda Amanjiwo bought five tables—cost her half a mil." "That Amanjiwo woman can stand in her shower and tear up hundred-dollar bills all day for all I care, I wouldn't pay a cent to go to any costume ball!" Daisy huffed. Nadine gave Daisy a pleading look. "But it's for the orangutans. Don't you care about the plight of the cute orangutans?" "Ey, Nadine, when Ah Meng died, did you cry?" Daisy asked.2 "Er...no." "I didn't either. So why on earth would I want to pay ten thousand dollars just to sit in a room full of _ang mors_ eating _ang_ _mor_ food to save a bunch of Ah Mengs?" Daisy argued. "Daisy, you just don't have the heart for animals like I do. Beyoncé and Rihanna, my two Pomeranians, bring me so much joy you have no idea," Nadine said. Just then, a maid showed Rachel into Carol Tai's bedroom. "Rachel, you came!" the ladies all said excitedly. "Of course I came! Nick's told me so many stories about your Thursday Bible study, I've always been curious to attend! Sorry I'm late. I drove myself and got a bit lost trying to find the neighborhood. Google Maps didn't anticipate all the detours." " _Alamak_ , why didn't you have Ahmad drive you? He's so free shaking legs all day at Tyersall Park now that the old lady is gone," Eleanor remarked. "Oh, I didn't even think of it!" Rachel said. "Well, Rachel, come meet my niece Jackie. She's a doctor that lives in Brisbane," Eleanor continued. "Hello. It's a pleasure!" Rachel said, shaking hands with the pretty thirtysomething woman and sitting down beside her on the chaise lounge. A maid immediately thrust an oversize flute of champagne into her hands. "Ooh, I didn't know you ladies drank during Bible study!" Rachel said in surprise. "Of course we do! After all, Jesus turned water into wine," Eleanor said. "Rachel, this is very expensive champagne from the _Dato_ 's wine cellar. You mustn't waste a drop—drink it all up!" "Twist my arm," Rachel said merrily, as Carol handed her a Bible. "Sister Daisy is going to lead us in the Scripture reading today," Carol began, as the ladies quickly flipped their Bibles open to Proverbs. "Yes, okay, Proverbs 31:10: 'A wife of noble character who can find? She is worth far more than rubies.' What does this mean to you all?" Daisy asked. "The only thing that is worth more than rubies are good Bolivian emeralds," Lorena remarked. "Well, you haven't seen my new ruby earrings from Carnet! They are drop-dead, and worth far more than my emeralds," Nadine interjected. "Nadine, are you still buying jewelry at your age? Don't you have enough at this point?" Daisy chastised. Nadine gave her a sharp look. "Pardon me, what do you mean by 'enough'?" Just then, an army of maids entered the room, each carrying a lacquer tray containing a bento box filled with Hainanese chicken rice. " _Aiyah_ , they're too quick with lunch today. I told my butler we wouldn't be ready to eat until one thirty at the earliest!" Carol pretended to complain. "Well, we mustn't let the food get cold!" Lorena commented. "Okay!" the ladies said, throwing their Bibles aside and digging in to their individual bento boxes with gusto. "Wait, that's it?" Rachel figured that Bible study with these ladies probably wasn't going to feature any probing theological discussions, but she was surprised it was over this quickly. "You're very lucky, Rachel. Auntie Daisy heard you were going to come to Bible study today, so she _personally_ had her cook Swee Kee make her famous Hainanese chicken rice," Eleanor explained, as she quickly shoveled a tender, juicy piece of sliced chicken into her mouth. "Oh wow, thank you, Auntie Daisy. I've become addicted to chicken rice ever since Nick first introduced me to it! I wish we could find authentic chicken rice in New York," Rachel remarked. Right on cue, Nadine's iPad started buzzing. " _Alamak_ , I totally forgot! It's time for my daily good-night call with my grandson in London." She took her iPad out of her large Bottega Veneta Hobo bag and turned on FaceTime. "Joshie, Joshie, is that you?" A moon-faced blond girl appeared on the screen. "Mrs. Shaw, I just got your urgent e-mail. You wanted me to put—" Nadine quickly interrupted. "Yes, yes, Svetlana, you don't have to mention anything in the e-mail! Just put Joshua on the screen." "But we're in the middle of his bath now." "It doesn't matter, put him on, _lah_!" Nadine insisted. The nanny tilted her phone and a little naked toddler appeared on the screen, sitting in shallow water in the middle of an enormous marble bathtub. " _Alamak_ , what a cutie he is!" the ladies all gushed in unison. "There's my little Joshie!" Nadine cooed. "He's not that little. Don't you think he has an _enormous_ coo-coo for his age? My boys were never that big," Daisy whispered to Lorena. "Isn't the father Arab? Arab men are supposed to be hung like camels," Lorena whispered back. "The father's not Arab. He's a Syrian Jew. And we shouldn't be talking about such things at Bible study!" Carol glared at the women distastefully. " _Aiyah_ , what's the big deal? The Bible is filled with penises! There are so many scriptures about circumcising your boys and all that nonsense!" Daisy said. "You know, in Australia we don't customarily circumcise boys anymore," Jackie interjected. "It's seen as an outdated practice, and a human rights issue. Boys should be given the right to make a decision about their own foreskins." Rachel had been enjoying her lunch immensely, but all this foreskin talk was suddenly making the glistening bits of chicken skin on her dish look particularly unappetizing. After the ladies had taken turns passing around the iPad and oohing and aahing over the chubby little toddler, Nadine ended the call as the maids brought in trays filled with sinfully delicious _nyonya kueys_. Daisy spoke up as she ate a piece of _kuey dadar_.3 "That grandson of yours is just tooooo cute! I look at him and I want to pinch those fat cheeks!" "Next to Beyoncé and Rihanna, he is the greatest joy of my life," Nadine said. Rachel glanced at Nadine curiously, wondering if she had heard her correctly. "Really, Nadine, you should be in London enjoying your grandson. He's at the most adorable age right now!" Carol suggested. "I loved my grandkids when they were at that age. After they were potty trained, but before they started getting potty mouths!" Daisy laughed. "How about you, Rachel? When are you going to make Eleanor a proud grandmother?" Lorena asked point-blank. Rachel saw that all eyes in the room were suddenly glued on her. "Nick and I do hope to have children someday." Lorena cocked her head. "And when might that someday be?" Rachel noticed that Eleanor was staring at her intently but staying absolutely silent, so she chose her words carefully. "Well, the last few years have been...so eventful...we're just waiting for the right time." "Trust me, there's never going to be a right time. You just have to do it! I had three sons in three consecutive years. Got them out of the way in one go, _lah_!" Daisy said breezily. "It's a lot more challenging to have kids these days than during your time, Auntie Daisy. Especially raising children in New York, you really have to—" "So have your baby in Singapore. You can have your pick of nannies here—Filipino, Indonesian, Sri Lankan—or even splurge on an eastern European," Lorena chimed in. "And all of us will gladly help to babysit!" Nadine volunteered. Rachel was quietly aghast at the thought—Nadine couldn't even babysit her own shopping bags. She smiled at the ladies and said diplomatically, "Thank you for all your advice, aunties. I really will take it to heart and discuss this with my husband." "Is it Nicky who's stopping you from having a baby?" Daisy inquired. "Um, no, not exactly..." Rachel said awkwardly. "Then is it you? Are you concerned about being not able to bear a child at your age?" Daisy prodded. "No, that's not a concern." Rachel took a deep breath, trying not to get annoyed by all this probing. " _Aiyah_ , aunties, stop putting so much pressure on poor Rachel!" Jackie suddenly spoke up. "A woman's decision to have a child is the most important decision she can make." "Okay _lah_ , okay _lah_ , we are just so eager for Eleanor to join us in the grandmas' club!" Daisy laughed, breaking the tension in the room. Rachel shot Jackie a grateful look. Jackie stood up and said to Rachel, "Here, come with me. Let's get a little fresh air." Rachel put her tray aside and followed Jackie out of the bedroom. Jackie made a quick turn around the corner and opened the door to what was Carol's private prayer room. "Let's go in here." Rachel entered and the first thing she saw was a medical examination table in the middle of the room, the kind with raised footrests found in gynecological clinics. "You know, Rachel, I'm an ob-gyn in Brisbane, and if you have any medical concerns at all about your reproductive system, we can address them right now," Jackie suggested, flipping on a switch. The room was suddenly flooded with harsh white fluorescent light. Rachel stared at her for a few seconds, too stunned to speak. Jackie smiled as she handed Rachel a pale green patient gown. "Here, why don't you put this on and get on the table, and I'll perform a quick pelvic exam?" "Um, I'm quite all right, thanks." Rachel began backing away from her. Reaching into her pocket, Jackie pulled out a pair of surgical gloves and began to put them on. "This will just take a few minutes. Auntie Elle just wants to know how those ovaries of yours are doing." "Get away from me!" Rachel cringed as she turned toward the door. She ran into Carol Tai's bedroom and grabbed her purse without a word. " _Aiyah_ , so fast?" Nadine commented. "Is everything okay?" Carol asked sweetly. Rachel turned to Eleanor, her face red with fury. "Just when I thought you might be a semi-normal mother-in-law, you go and pull this stunt?" "What are you talking about?" Eleanor said innocently. "You had an entire friggin' examination room set up next door! You planned this entire bullshit ambush, didn't you? Just because Nick and I haven't had any babies yet, you think _I have some medical problem_?" "Well, you can't blame her for thinking that. We all know this isn't Nicky's problem—he's got great genes," Lorena said. "What is wrong with you people?" Rachel seethed. Eleanor suddenly stood up and began shouting. "What is wrong? Look at my hands, Rachel. They are empty!" She thrust her open palms out. "Why am I not getting to cradle a baby? It's been more than two years now, five if you count how long you've been sleeping with my son! So where's my grandchild? How much longer are these hands going to be cold and empty?" "Eleanor, THIS ISN'T ABOUT YOU! Nick and I will have a child when we are good and ready!" Rachel yelled back. Daisy spoke up in defense of her friend. "Don't be so selfish, Rachel! You and Nicky have had your fun! It's time to do your duty and give Eleanor a grandchild now! How many more years do she and Philip have to enjoy their grandchildren? The next time I see you in Singapore, I want you to be holding a big bouncy baby!" Rachel was outraged. "Do you think it's that easy? I just snap my fingers and a baby will magically appear?" "Of course! It's soooo easy to have babies these days!" Nadine exclaimed. "I mean, my Francesca didn't even have to get pregnant herself. She was so scared of getting stretch marks, she hired a pretty girl from Tibet to carry the baby. The day after Joshie was born she was already off to some party in Rio!" Carol tried to step in. "Ladies, let's not get too worked up. I think we should all say a prayer together—" "You want a prayer? I'll give you a prayer. Dear Lord, thank you for getting me the fuck out of here. Amen!" Rachel said, storming out of the room. * * 1 Singapore's impressive Electronic Road Pricing system (ERP), used to manage road congestion, has also led to impressive levels of bitching from citizens. 2 Ah Meng was an irrepressible orangutan that was for many years in the 1980s the star attraction of the Singapore Zoo. 3 A sweet rolled pancake filled with coconut palm sugar that, because of the way the pancake is folded at the ends, just happens to resemble a small uncircumcised penis. # CHAPTER SEVEN MANILA, PHILIPPINES From Tommy Yip's daily gossip column: > Titas were atwitter last night over what happened in the middle of the spectacularly elegant party at China Cruz* 's divine mansion in Dasmariñas. Apparently, while Chris-Emmanuelle Yam (clad in a curvy Chloé confection) was belting out the Captain and Tennille's "Love Will Keep Us Together" accompanied by a full orchestra, a tremendous crashing noise sent the couture-clad guests rushing out of the ballroom to the grand foyer. There they found debonair Diego San Antonio wrestling on the marble floor with an intruder. > > "It was this Chinese man, rather handsome, but obviously quite deranged. He had Diego by the collar and he kept shouting, 'Tell me where she is!' " social dynamo Doris Hoh (enchanting in an emerald Elie Saab) breathlessly told me. "It was surreal. Here were two men rolling around on the floor, with purple glass everywhere and a huge roasted pig right next to them!" Apparently the fight began upstairs, where Diego first encountered the intruder in China's library. A tussle began and they ended up rolling down the dramatic curving _Gone with the Wind_ –style double staircase, toppling over the buffet table where a huge _lechon_* was just about to be carved, and smashing into a Ramon Orlina glass sculpture. > > "That sculpture was of my breasts. It was a beautiful masterpiece that got destroyed!" China (sheathed in a showstopping strapless Saint Laurent) lamented. "What a waste! I was so looking forward to the _lechon_. I heard it was a special pig that had only eaten truffles its entire life and was flown in from Spain," Josie Natori (draped in a dress of her own design, of course) said with a sigh. Thankfully, before the intruder could do much damage to Diego's fabulous Brioni blazer, Brunomars —China's 250-pound Tibetan mastiff—leapt onto the intruder and according to onlookers "bit him in the ass." > > But the intrepid journalist Karen Davila (astonishingly alluring in Armani) quashed that story. "Tommy, do your fact-checking, please! Brunomars _did not_ bite him in the ass! He is still a puppy, and he leapt onto the men on the floor because he was trying to get a taste of the _lechon_! He bit the _lechon_ on the ass!" Whoever's ass it was, Brunomars saved the day, because the intruder suddenly calmed down when he saw all the guests clustered around like they were watching Manny Pacquiao in the boxing ring. (Manny was actually at the party too, but he was in the basement having an intense chess match with China's son.) He ran out the front door without another word, jumped into a waiting black Toyota Alphard, and sped off before any of China's guards could stop him. ··· Charlie leaned against the bathroom sink in his suite at the Raffles Makati, holding a towel full of ice to his face to soothe the swelling. How in the world had he let things devolve to this point? He had snuck unnoticed into China Cruz's party, and managed to get Diego's attention when the singing began. Diego had suggested that they go upstairs to the library to talk things over, but things became heated when Diego had refused to reveal Astrid's whereabouts. "I can assure you, Mr. Wu, that you can search every corner of Manila and all seven thousand islands of the Philippines, but you'll never find her. If she wanted you to know where she was, she would have told you," Diego had said rather nonchalantly. "You don't understand! If she knew what was really happening, she'd come out of hiding. The situation has changed, and there's some vitally important information she needs to know!" he had pleaded. "Well, who put her in this situation in the first place? As far as I'm concerned, everything bad that's happened to Astrid in the past few months has had something to do with your involvement in her life. The leaked paparazzi photos. The leaked video. Your ex-wife. I'm sorry, but my only duty here is to protect Astrid _from you_." And that's when things got out of control. He knew he shouldn't have lunged at Diego, but some visceral force just overtook his body. And now he had caused yet another scandal, this time among the most elite circles of Manila high society. And these people were sure to talk. The news would be all over town, all over Asia, and into Astrid's ears in no time. And this might make her go even deeper into hiding. Goddamnit, he had really screwed things up again. Charlie dumped the ice from his towel into the sink and splashed some cold water on his face. Turning off the running faucet, he suddenly heard a soft knock on the door. He walked out of the bathroom and peered through the peephole. He saw a petite Filipino girl in a gold lamé cocktail dress standing in the hallway. "Who is it?" "My name is Angel. I have a message for you." Charlie opened the door and stared at the girl. She looked to be in her early twenties, with shoulder-length hair and a friendly, open face. "Sir Charlie, I have some instructions for you from my boss. Go to the ITI Private Terminal on Andrews Avenue in Pasay City tomorrow morning and take the seven-thirty flight. Your name will be on the list." "Wait a minute, how do you know me?" "I was at China's party tonight. I recognized you immediately." "Who's your boss? How does he know I was staying here?" "My boss knows everything," Angel said with an enigmatic smile, before turning to leave. — The next morning, Charlie followed the instructions that had been provided by the mysterious girl and went to the private terminal in Pasay City, where he discovered in the hospitality lounge that this was a charter plane bound for different resorts on the Philippines' southwest coast. He boarded the twin-propeller plane, which was filled with tourists eager to get their beach vacations started. The plane took off and flew low over the coast, landing forty-five minutes later at a small desolate airstrip on the edge of the sea. It was gray and raining when Charlie got off the plane. All the passengers were guided onto a colorfully painted bus, and they were driven down a muddy track to a series of open-air wooden huts. EL NIDO AIRPORT, a charming painted wooden sign announced. A row of Filipino women stood in the rain at the edge of the hut, singing a welcome song. Charlie got off the bus and was about to follow the tourists into the hut when an athletic young Filipino dressed in a white polo tee and crisp navy cargo pants approached him, holding a large white golf umbrella. "Sir Charlie? My name is Marco. If you'll come with me please," the man said in an American accent. Charlie followed the man down a pathway to a private dock, where an elegant Riva speedboat awaited. They hopped into the boat, and Marco turned on the engine. "It's been a wet morning. There's a raincoat under that seat for you," Marco said, as he expertly turned the boat around and sped off onto the open sea. "I'm fine, I enjoy the rain. Where are we going?" Charlie yelled over the roar of the wind and the splashing waves. "We're heading twenty-five nautical miles southwest." "How did you recognize me?" "Oh, my boss showed me your picture. You're easy to spot in a crowd of American tourists." "Sounds like you spent some time in America yourself," Charlie said. "I went to UC Santa Cruz." "I don't suppose you'll tell me who your boss is?" "You'll find out soon enough," Marco said with a little nod. After about thirty minutes, the gray clouds gave way to open sky and puffy white clouds, turning the color of the ocean into a deep sapphire. As the speedboat continued to zoom along the Sulu Sea, Charlie stared out to the horizon as fantastical rock formations rose up from the water like apparitions. Soon they were surrounded by what seemed like hundreds of tiny islands floating on the blindingly azure waters. Each island resembled a monolithic rock carved in some otherworldly shape, bursting with lush tropical vegetation and sugary white beaches. "Welcome to Palawan," Marco announced. Charlie took in the mystical landscape in awe. "I feel like I'm dreaming. These islands look like they don't belong on this earth—they look like they rose out of Atlantis." "They are more than fourteen million years old," Marco said, as they sped past a towering rock face that gleamed in the late-morning sun. "It's all part of a marine reserve park." "Are most of them deserted?" Charlie asked as they passed an island with a particularly pristine crescent-shaped beach. "Some, but not all. That one we just passed has a great little beach bar that only opens after sunset. They make the best margaritas," Marco said with a big grin. The Riva sped past a few other small islands before coming to one of the larger ones. "Did you bring any swimming trunks?" Marco asked. Charlie shook his head. "I had no idea where I would be going." "There's a pair in that cabinet under your seat that should fit you. You're going to need them." As they rounded the other side of the island, Charlie hastily threw on the pair of blue-and-white-striped Parke & Ronen swimming trunks that happened to fit him perfectly. Marco anchored the boat by a rocky cove and handed Charlie a mask and snorkel. "The tide is a bit high right now, so we're going to be underwater just for a little while. You're okay with a bit of ocean swimming?" Charlie nodded. "Where are we going? Or let me guess, I'll find out soon enough." Marco flashed his pearly whites again. "This is the only way you're gonna meet the boss." He stripped off his clothes to reveal a red Speedo underneath and dove into the water. Charlie dove in after him, and as they floated together by the side of the speedboat, Marco said, "These rocks are really treacherous whenever the waves crash onto them. Once you dive underwater, you'll see a cave opening under the rocks. We're going to swim through the opening, and you'll only need to hold your breath for fifteen, twenty seconds max." "We're going now?" "Wait for my signal. We'll go after this next big wave has passed. Otherwise we get smashed against the rocks. Understand?" Charlie nodded, putting on his mask and snorkel. "Okay, now!" Marco dove under the water and Charlie followed. They swam along the side of the jagged cliffs and suddenly the rocks opened up to reveal a large cave entrance. Marco swam freestyle without a mask, guiding Charlie along as they swam through the underwater passage. Within a few moments, they emerged to the surface again. Charlie caught his breath and when he ripped his mask off, what he saw almost took his breath away again. He was in the middle of a calm lagoon completely encircled by towering limestone cliffs. The only entrance to this secret place was through the underwater cavern. The shallow, crystal-clear turquoise waters teemed with colorful fish, coral rock, and sea anemones, and along one side of the lagoon was the perfect hidden beach of sparkling white sand shaded by overhanging branches of palm trees. Charlie was awestruck by the unbelievable beauty surrounding him, and he floated in silence for a few moments, looking around like a newborn child who had just entered a completely different world. Marco caught his eye and said with a nod, "Over there. My boss." Charlie turned toward the hidden beach and there, emerging from behind a cluster of palm trees, stood Astrid. * * * * A traditional roast pig and one of the hallmarks of Filipino cuisine. # CHAPTER EIGHT TYERSALL PARK, SINGAPORE Before Rachel was even fully awake, she could smell the coffee. The aroma of the Homacho Waeno beans she loved so much roasted, ground, and poured into a French press with boiling water. But wait a minute—she was still in Singapore, and the one thing that wasn't absolute perfection at Tyersall Park was the coffee. Rachel opened her eyes and saw her usual breakfast tray placed on the ottoman next to the tartan-covered armchair, the beautiful silver curves of the Mappin & Webb teapot glinting against the morning light, and gorgeous Nick sitting in the armchair smiling at her. "Nick! What are you doing here?" Rachel sat up with a start. "Um, last time I checked this was our bedroom." Nick laughed as he got up and gave her a kiss. "But when did you get back from Thailand?" "An hour ago on Prince Jirasit's plane. Guess what type of coffee they had on board?" "Oh my God—I think I smelled it in my dreams!" Rachel exclaimed as Nick handed her a cup and sat cross-legged on the bed next to her. "Mmmmm!" Rachel sighed in contentment after taking her first sip. "I love seeing you so satisfied." Nick beamed. "I thought you were going to stay in Chiang Mai until the end of the week?" "You know, I went to Chiang Mai expecting to meet a guy who would lend me a few billion dollars. But what I discovered there were treasures far beyond my imagination, things you can't place a monetary value on. I was reading Ah Ma's diaries, and what I found in them was so important that it couldn't wait another day. I needed to share them with you." Rachel sat up against her pillows. She hadn't seen Nick this excited about anything in a long time. "What did you find?" "There's so much to tell you, I don't even know where to begin. I think the first revelation was that Prince Jirasit was my grandmother's first love. They met in India, where she had escaped to just before the Japanese invaded Singapore during World War II. She was twenty-two, and they had a passionate wartime affair and traveled through India together." "That's not too surprising. I mean, she did entrust him with her most private journals," Rachel commented. "Yes, but here's a surprise: At the height of the Japanese occupation of Singapore, my grandmother actually managed to sneak back onto the island with Jirasit's help. It was pure madness, because the Japanese were on a torturous rampage, but she did it anyway. And when she was reunited with her father, she found out he had arranged for her to be married to a man she had never even met." Rachel nodded, recalling a story Su Yi had told her. "When we had tea five years ago, your Ah Ma told me that her father had specially chosen James for her, and that she was grateful for his actions." "Well, she was actually dragged kicking and screaming to the altar by her father, and for the first few years, she resented my grandfather and treated him abominably. After the war, she reunited with Jirasit in Bangkok and although both of them were married to other people by this point, they couldn't resist resuming their relationship." Rachel's eyes widened. "Really?" "Yes, but that's not even the real shocker. She found that she was pregnant in the midst of her affair." "Noooo!" Rachel gasped, almost spilling her coffee. "Who's the baby?" "My aunt Catherine." "Oh my God, it all makes sense now. That's how Auntie Cat knows Prince Jirasit, and that's why she was left the estate in Chiang Mai! Are you the only one besides her who knows?" Nick nodded. "I actually flew back to Bangkok last night and had a very interesting conversation with her. We sat in her garden overlooking the Chao Phraya River and she told me the whole story. My grandmother was in a terrible bind, of course, when she found out she was pregnant. Jirasit couldn't leave his wife—he was a prince and too bound to all the family politics, and they also had two young children—so my grandmother was faced with a choice: She could either divorce my grandfather and live as a single woman alone with an illegitimate child, cast out by society, or she could tell him the truth and beg him to take her back." "I can't even imagine how hard it must have been for her in those days, especially for a woman of her background," Rachel mused, suddenly feeling sorry for Su Yi. "Well, I always knew my grandfather was a saint, but I didn't realize quite how much. Not only did he take Ah Ma back, he apparently never once gave her any grief over the affair. He knew going in to this marriage that she wasn't in love with him, but he was determined to win her over. And that he did. Being the good Christian man that he was, he forgave her completely and he treated Auntie Cat exactly as he did his other children. In fact, I always thought she was his favorite." "So you think your grandmother grew to love him then?" Rachel asked. "According to Auntie Cat, my grandmother fell in love with him—truly, deeply—when she saw the kind of man he really was. You know, before I left her last night, Auntie Cat told me something else she's never told anyone—what happened the day that Ah Ma died. She was the only one in the bedroom with her when she passed." Nick's voice became a little choked up as he recounted his aunt's words: _When I first got to Singapore, your grandmother told me that the spirits had been visiting her. She said that her older brother, Ah Jit, had come, her father had been in the room. Of course, I thought that all the morphine she was on was giving her hallucinations. Then on the afternoon she died, I was sitting at her bedside when her breathing started becoming more and more labored. I watched the monitors, but everything seemed fine and I didn't want to raise the alarm just yet. Then suddenly Mummy opened her eyes and gripped my hand. "Be a good girl, give up your chair for him," she said. "Who?" I asked, and then I saw this look on her face, this look of pure love. "James!" she said in this joyous tone, and that was her last breath. I swear to you, Nicky, I felt him. I could feel my father's presence in the room, sitting on that chair, and I could feel them leave together._ Rachel sat on the edge of her bed, blinking away the tears. "Wow. I'm getting chills. It's starting to make sense now...why your grandmother was so opposed to our marrying." "She felt that her father had been right to choose my grandfather for her, and she should have obeyed his wishes all along. _That's_ why she was so adamant that I obey her!" Nick said. Rachel nodded slowly. "Yes, and think about how she found out that my mother had an affair with a man out of wedlock, and that I came from that relationship. It must have brought back all her own fears and her guilt over her affair." Nick sighed. "It was so misguided, but she thought she was protecting me. Let me show you something. It fell out of one of her diaries." Nick took out a small folded letter and handed it to Rachel. Embossed in red below an ornate coat of arms were the words: > WINDSOR CASTLE > > My Dear Su Yi, > > I cannot begin to express my debt of gratitude for all you and your brother Alexander did during the darkest days of the war. Allowing Tyersall Park to be a safe haven for some of our most essential British and Australian officers played no small role in saving countless lives. Your acts of heroism, too many to recount here, will never be forgotten. > > Sincerely, > > George R.I. "George R.I...." Rachel looked at Nick incredulously. "Yep, Queen Elizabeth's father. He was the king during the war. Rachel, you won't believe some of the stories in my grandmother's diaries. You know, growing up I was told so many stories of how my grandfather was a war hero, how he saved countless lives as a surgeon. But it turns out my grandmother and her brother were also instrumental in saving so many lives. Right as the occupation was beginning, Alexander was in Indonesia officially to oversee my great-grandfather's business interests, but secretly he was helping get important people out of the country. He helped hide some of Singapore's most crucial anti-Japanese activists—people like Tan Kah Kee and Ng Aik Huan—in Sumatra. In the end, he was tortured to death by a Japanese agent trying to find out his secrets." "Oh no!" Rachel gasped, putting her hands over her mouth. "Yes, but as it turns out my grandmother had secretly returned to Singapore at the height of the Japanese occupation. And she had made a daring trip to see Alexander in Indonesia right before he died. She absolutely adored him, and this tragedy is what galvanized her to continue his fight. Tyersall Park became a sort of Underground Railroad for all the operatives passing from Malaysia through Singapore, trying to get to safety in Indonesia and Australia. It became a place for secret high-level meetings and a safe house for some of the key people who were being hunted down by the Japanese." "How amazing! I would have thought that this house would be too conspicuous a place," Rachel remarked. "Well, it would have been, but the leader of the occupying Japanese forces, Count Hisaichi Terauchi, commandeered Tyersall Park and took over the main house. So my grandmother and all the servants were made to live in the back wing, and that's how she managed to hide so many people right under the nose of the general. She disguised them as part of the staff—because there were so many of them everywhere, the Japanese troops never noticed. And then she managed to get them in and out through the secret passage from the conservatory to the Botanic Gardens." "The one you used to sneak into the house!" Rachel exclaimed. Nick held the letter up to Rachel. "This is not just about me anymore and losing my childhood home or my connection to the past. It's much bigger than that. This house should be a historic landmark, a heritage site for _all_ Singaporeans. It's far too important to be altered in any way, and I believe conservationists would argue it urgently needs to be preserved." "Does this mean you can block the sale to the Bings?" "That's what I'm trying to figure out. Knowing Jack Bing, I'm sure he'll put up a fight." "And so will your aunties. They're going to want their money from the sale. What would happen if you deprived them of what they see as their rightful inheritance?" "What if there was another way where no one had to be deprived? I've been thinking it over for the past few days, and I think I have a plan that can save this historical landmark _and_ transform it into something viable for the future." "Really?" "Yeah, but we're going to need people with really deep pockets to believe in us." Rachel's mind began to race. "I think I may know just the people we need to talk to." # CHAPTER NINE MATINLOC ISLAND, PALAWAN Charlie and Astrid stood on the beach of the lagoon, locked in an embrace. "I'm never going to let you go again!" Charlie sighed happily, as Astrid simply smiled up at him. They sat down on the sand, dipping their toes into the gently lapping waters, staring out at the incredible view of the towering rocks encircling this hidden place, holding hands and not saying anything. Astrid spoke first. "I didn't mean to worry you. I hadn't realized quite how concerned you would be until I heard about the fight at China's from Diego. How's your jaw? It looks a little purple." "It's fine," Charlie said, rubbing his jaw absentmindedly. "I haven't even thought about it once, to be honest. How could you not know I was worried? I mean, you've been missing for close to six weeks!" "I haven't been missing. I've been on FaceTime with Cassian every other day and my family knows I'm fine. But I guess my mother never mentioned anything to you, did she?" "No, she didn't! The last time I spoke to her over the phone, she said she hadn't heard from you and she didn't much care to. And then she banged down the phone," Charlie huffed. "Figures." Astrid smiled, shaking her head. "I've been fine, Charlie. More than fine, actually. I needed to take some time out for myself. You know, being here, I realized I haven't ever done that. Any trip I've ever taken has involved family, or it's been a work trip, wedding, or some other social obligation. I've never actually gone anywhere alone just for _myself_." "I understand, I knew you needed the time alone. But I also was scared that your mind was spiraling out of control, not knowing all that's been happening back home." "I haven't wanted to know, Charlie. And I'm not sure I even want to know now. That's the whole point. I needed to get to someplace where I could really escape and unplug from everything just so I could make sense of what was going on in my own head." Charlie gazed at the calm waters, bluing in intensity as the late-morning sun continued to rise. "How did you ever find this place?" "I've owned a little island here for many years. Not this one, mind you, this is Matinloc, and it belongs to the state. But I have a little spit of land not too far away. Great-aunt Matilda Leong left it to me, but in secret. You know she was a bit of an eccentric...she was a conspiracy theorist and she really thought the world was going to be wiped out in a nuclear war one day. So she bought a little island in Palawan and built a house. 'The ultimate safe haven,' she called it, and she wanted me to have this as a refuge of last resort. I'd never actually visited until now, and I can't believe I've waited this long." "It's paradise here. Any minute, I expect to see a naked Brooke Shields coming out of the water!" "You wish!" "Actually, I have an even better vision right in front of me," Charlie said, admiring the hints of Astrid's beautiful tan body showing through her gauzy white cover-up. As if reading his mind, Astrid stood up. "Have you ever swum naked in a hidden lagoon before?" she asked, as she removed the linen cover-up. "Um, won't Marco be back soon?" Charlie asked, a little alarmed. "Marco's not coming back for a couple of hours," Astrid said as she slipped off her white string bikini and dove into the lagoon. Charlie reflexively looked around for a moment to make sure they were alone, took off his swimming trunks, and dove in after her. They glided through the crystal-clear water for a while, peering at all the colorful fish darting about the coral reef, the sea anemones waving their fingers Zen-like in the current, the giant clams embedded in the sand that would open for a split second to suck in water before shutting again forcefully. They floated on their backs in the middle of the lagoon, staring up at the passing clouds, and then Charlie took Astrid in his arms, lifted her out of the water, and made love to her on the smooth glistening sand, their moans of ecstasy echoing in the lagoon as they became one with nature, with the sea and sky. Afterward, Charlie lay on his back against the pillowy sand. He was beginning to doze off in the sun, slightly hypnotized by the palm fronds undulating in the breeze over him. Suddenly the sound of chattering voices began to fill the air. "What's that?" Charlie asked lazily. "Tourists, probably," Astrid replied. "Tourists? What?" Charlie bolted up and saw a gaggle of people in bright yellow T-shirts entering the lagoon through the cave, which was only partially submerged now that the tide had gone down. "Fuck! Where are my swim trunks?" Charlie scrambled around, trying to find them. "You didn't tell me there could be tourists." "Of course—this is one of the most popular attractions in Palawan!" Astrid giggled at the sight of Charlie rushing around naked on the beach, trying to find his trunks. "Oy, mate! You looking for these?" an Aussie surfer shouted from the other side of the lagoon, holding up Charlie's blue-and-white trunks. "Yes, thanks!" Astrid shouted back. She turned to Charlie, who was hiding behind a palm tree, still laughing. "Oh, come on out! You have nothing to be ashamed of!" ··· "You really _have_ changed. I don't know if the Astrid I knew would ever want to make love spontaneously in a lagoon or walk around naked on a beach in front of a bunch of Australian tourists," Charlie said as they sat having lunch on the terrace of Astrid's spectacular white villa perched on the hilltop of her private island. "You know, it might sound cliché, but getting away from it all has been a transformative experience for me. I've realized that so many of my fears aren't really my own. They're the fears of my mother, my father, my grandparents. I've just unconsciously internalized them, and I've let these fears affect every decision I make. So a few people see me naked on a secluded beach in one of the remotest places on earth. Who cares? I'm proud of my body, I have nothing to hide. But of course, some voice in my head would automatically say, 'Astrid, put some clothes on. It's not proper. You're a Leong, and you're going to disgrace the family.' And I realize that most of the time it's my mother's disapproving voice I hear." "Your mother has always driven you half crazy," Charlie said as he piled another big helping of _guinataang sugpo_ over his garlic rice.* "I know, and it's not all her fault. She said some terrible things to me, but I've already forgiven her. She's damaged herself—look, this was a woman that was born during World War II, in the midst of the most unimaginable horrors occurring in Singapore. How could she not have internalized all the experiences of my grandparents? My grandfather was imprisoned by the Japanese and barely escaped the firing squad, my grandmother was covertly helping to organize resistance efforts while being a new mother and trying not to get killed herself." Charlie nodded. "My mother's entire childhood was spent at the Endau concentration camp in Malaysia. Her family was forced to grow all their own food, and they almost starved to death. I'm sure that's why my mother is the way she is now. She makes her cook save money by buying the discounted, three-day-old bread from the supermarket, but she'll spend $30,000 on plastic surgery for her pet fish. It's completely irrational." Astrid looked out onto the view of the peaceful cove below the terrace. "Scientists talk about how we inherit health issues from our parents through our genes, but we also inherit this entire lineage of fear and pain—generations of it. I can acknowledge whenever my mother is reacting out of this fear, but the most powerful thing I've realized is that _I'm not responsible for her pain_. I won't make her fears mine any longer and I don't want to pass them on to my son!" Charlie stared at Astrid, pondering her words. "I like everything you're saying, but I gotta ask— _who are you_? It's like you're speaking in a whole new language." Astrid smiled enigmatically. "I have to confess, I've been here for the past five weeks but I haven't been here alone. When I left Singapore, I went to Paris first and saw my friend Grégoire. He told me about a friend of his who was living in Palawan. That's really why I came here. I had no intention of being anywhere near Asia—I was on my way to Morocco, to a place I know in the Atlas Mountains. But Grégoire really encouraged me to see his friend." "Who is this person?" "Her name is Simone-Christine de Ayala." "Is she related to Pedro Paulo and Evangeline in Hong Kong?" "Turns out they are cousins—it's a big family. Anyway, I'm not quite sure how to describe her. Some people call her an energy worker or a healer. To me she's just a very wise soul, and she has a beautiful home on a neighboring island. We've met up almost every day since I got here and had these amazing talks. She's led me through these guided meditations that have led to some incredible breakthroughs." "Like what?" Charlie asked, suddenly getting worried that Astrid was under the influence of some quack guru. "Well, the biggest one is realizing that I've lived my entire life trying to anticipate the fears of my parents—trying to be that perfect daughter at all costs, never putting a wrong foot forward, never speaking to the press. And look where that's gotten me? By trying to hide behind that façade of perfection, by trying to always keep my personal life and my relationships so goddamn private, I've actually done far more damage than if I'd just lived my life the way I wanted to in the first place!" Charlie nodded, a little relieved. "I couldn't agree more, actually. To me, it's always seemed like you've lived your whole life in the shadows. You're so much smarter and more talented than anyone's ever given you credit for, and I've always thought you were in the perfect position to be doing so much more." "Do you know how many things I've wanted to do that have been shot down by my parents? When I graduated from college and got that great job offer from Yves Saint Laurent in Paris, they told me to come home. Then they wouldn't let me start my own fashion business—it was just too common for them. Then when I wanted to work for certain very _unfashionable_ causes, like the horrific problem of human trafficking and child prostitution in Southeast Asia, they wouldn't hear of it. The only acceptable thing for Astrid Leong to do is serve on the board of certain well-vetted institutions, and even those had to be on one of the super-private committees, nothing that would put me in the public eye. It's like my family has lived for generations so frightened of their own wealth, of the fact that someone might accuse us of being rich, of being vulgar and showy. To me, it's our wealth that puts us in the fortunate position of being able to do an enormous amount of good in the world, not hide from the world!" Charlie clapped his hands excitedly. "So come back, Astrid. Come back with me and we can do this together. I know you were in a completely different head space when you wrote me that letter, so I'm going to forget you ever wrote it. I want us to be together. I want you to be my wife, to live your life and be exactly the woman you want to be." Astrid looked away for a moment, staring up at the beautiful white villa gleaming in the sun. "It's not that simple...I don't know if I'm ready to return yet. I think I need to repair myself for a while longer before I can face the world I left behind." "Astrid! The world you left behind has changed so much. Can I please tell you what's been happening? I think it will help," Charlie pleaded. Astrid took a deep breath. "Okay, tell me what you want to tell me." "Well first of all, Isabel is out of her coma, and it looks like she's on her way to a great recovery. She's suffered quite a bit of memory loss, and she has no clue what happened to her that night, but she's going to be okay." "Thank God," Astrid muttered, closing her eyes. "The other big thing that you need to know is that Michael has signed your divorce papers with no contest." "What?" Astrid sat up in her chair, completely shocked. "How did this happen?" "Well, it's quite a tangled story, but let's start with the leaked video. It turns out that Isabel was the one who had the video first, not Michael. She had us under surveillance all along. The paparazzi tailing us in India, the video of us in my bedroom, that was all her doing." Astrid shook her head in disbelief. "How did she do all this?" Charlie smiled. "You're never going to believe it. You know that raggy old stuffed giraffe that Delphine has?" "Yes! The one she can't sleep without every night?" "It was a gift from Isabel, and it turns out there was a very sophisticated camera and recording device implanted inside." "Oh my God..." "Delphine would drag the damn stuffed animal with her between both houses, so Isabel always knew my every move. And she got the footage of us completely by accident, because Delphine had slept in my room the night before you came over and left the giraffe on the chest at the foot of my bed." "No wonder the footage was shot from such a weird angle!" Astrid said with a little laugh. "But how in the world did she get this sophisticated nanny cam made?" "Michael helped her. They were in cahoots all along. It came out after Isabel's suicide attempt, and the police got involved investigating the source of the video clip on her phone." Astrid shook her head sadly. "So they ganged up...the two bitter ex-spouses." "Yep. But their little partnership is also the silver lining in all this. I flew to Singapore a few weeks ago and had a nice long chat with Michael. I told him he could withdraw the lawsuit, sign the divorce papers, and go on enjoying his life as a billionaire bachelor, or he could do the following: First, he could go to jail for aiding and abetting Isabel in her illegal surveillance. Second, he could go to jail for extortion, since he stupidly sent you the video with that text message demanding $5 billion. And third, he could go to jail for being linked to the malicious leak of the video. By the time the Singapore court system is done with all the charges that I would bring against him, he could very well spend the rest of his life in Changi Prison, or worse, he could be extradited to Hong Kong and then sent to a prison camp in Northeast China, near the Russian border, where guys that look as pretty as he does end up having a very _sore_ time." Astrid leaned back into her chair, taking it all in. Charlie grinned. "Michael has promised to never be of any trouble to you or Cassian. Ever again. So the minute you put your name on those divorce papers, you'll be a free woman." "A free woman," Astrid said the words softly to herself. "Charlie, I love you, and I'm so grateful for everything you've done for me over the past few weeks. If I'm being true to myself—to the new me—and if I'm being completely honest with you, I just don't know if I really want to get married again right now. I'm not sure I'm ready to return to Singapore yet. I've been exploring these islands quite a bit, getting to know the locals, and I am really connecting to this place. I think there's a great deal I could do right here to help the indigenous people. I could really use more time here, and what I really want is to send for Cassian. I've seen how happy the kids are in these islands...their lives are so integrated with nature, they're so free and adventurous. They run along the narrow little prows of wooden boats like sailors, they climb the trees like acrobats and knock down all the ripe coconuts. They laugh and they laugh. It reminds me a little of the kind of childhood I had at Tyersall Park. Cassian's whole life these days is about homework and exams and Chinese lessons and tennis lessons and piano competitions, and then when he's not doing that he's just glued to his computer screen playing those violent games. I can't remember the last time I saw him laugh. If I'm going to live a new life of true freedom, I want the same freedom for him too." Charlie peered deep into Astrid's eyes. "Listen, I want you to have exactly the kind of life you've dreamed about, for yourself and for Cassian. My only question to you is: In this new life, is there a place for me?" Astrid looked at Charlie, not sure what to say. * * * * Fresh caught jumbo prawns in coconut milk, a Palawan delicacy. # CHAPTER TEN ANTWERP, BELGIUM Kitty stood in the middle of the space, staring at the exquisite alchemy of furnishings, _objets_ , nature, and light. There was an elegant purity to the way everything was arranged, and the room emanated a calm and quietly invigorating energy. "This is what I want! This is how I want Tyersall Park to be," she told Oliver. They were in the midst of wandering through Kanaal, a nineteenth-century complex of industrial spaces next to a former grain silo on the Albert Canal that had been breathtakingly transformed into the atelier and private showroom of Axel Vervoordt, one of the world's most esteemed interior designers. "We're already halfway there, Kitty. Tyersall Park has amazing bones, and it's got that perfect patina of age that no amount of money can buy. We wouldn't have to import any new floors or create new walls that look like they came from the seventeenth century. But look how this bronze ax from the Neolithic period changes the whole vibe of the room. And these simple ferns wilting beautifully on this refectory table. It's all about _placement_ , and Axel is the master of all this." "I want to meet him right now!" Kitty said. "Don't worry, he'll be here very soon. Didn't you hear what his assistant said? _He's having lunch with Queen Mathilde of Belgium right now_ ," Oliver whispered. "Oh, I couldn't understand his accent. I thought he said he was in the middle of reading _Matilda_. I was thinking, why is this man reading a children's book when I've flown all the way here to meet him?" "Axel's work is held in such high esteem, his clients include many of the world's crowned heads," Oliver informed Kitty as they wandered into a dramatically lit chamber that was, coincidentally enough, filled with nothing but ancient Buddha heads carved out of stone. "Can we do this somewhere in the garden? I think it would be so cool to wander through the forest and just find a bunch of Buddha heads everywhere," Kitty suggested. Oliver chuckled to himself, trying to imagine how Victoria Young might react to the sight of dozens of Buddhas scattered around Tyersall Park. Still, Kitty's idea wasn't half bad. Maybe the way to really launch Kitty into the social stratosphere would be to style her as Singapore's answer to Peggy Guggenheim, and have the grounds of Tyersall Park become a venue for contemporary art like Storm King in New York or the Chinati Foundation in Marfa. They could have the world's greatest artists in residence to create site-specific installations. Christo could wrap the entire house in silver fabric, James Turrell could create a light projection in the conservatory, and maybe Ai Weiwei could do something controversial with the lily pond. In the midst of his reverie, there was a sudden flurry of activity as Axel Vervoordt entered the room, impeccably dressed in a gray suit with a black turtleneck, and surrounded by a monastic entourage of assistants. "Oliver T'sien, what a pleasure to see you again!" the legendary antiquarian said. "Axel, the pleasure is all mine. May I introduce Mrs. Jack Bing." "Welcome to Kanaal," Axel said, giving Kitty a courtly bow. "Thank you. Axel, I am in awe of your creations! I've never seen anything quite like this before, and I feel like I just want to move in here right now," Kitty effused. "Thank you. Mrs. Bing, if you enjoy what you see here, perhaps I can invite you to visit me at my private residence Kasteel van's-Gravenwezel while you are with us in Antwerp." "You won't want to miss this, Kitty. Kasteel van's-Gravenwezel is one of the most beautiful castles in the world," Oliver explained. Kitty batted her eyelashes at Axel. "I'd love to!" "If I had known earlier that the two of you were coming today, I would have invited you to lunch. Her Majesty the Queen honored us with her presence today, and she brought along a most delightful couple." "I hope you had a lovely time," Oliver said. "We did, we did. This young couple have just acquired the most magnificent property in Singapour. It is apparently the largest private estate on the island." Kitty's face went pale. Axel continued. "Wait a minute—it completely escaped my mind. You're from Singapour, aren't you, Oliver?" "Indeed I am," Oliver said, forcing a smile. "Have you heard of this property? Apparently it's quite an architectural folly—a mixture of styles and periods, but set on sixty-four acres. Tivoli Park, I think it is called." Axel cocked his head. Kitty calmly walked out onto the balcony of the showroom and could be seen jabbing her iPhone screen frantically. "Actually, I believe you mean Tyersall Park," Oliver corrected him. "Yes, that's the place! Apparently, the lady's father has given her the property as a wedding present, and she wants me to help her with the redo. It will be quite the commission." Oliver looked out the window, where Kitty was screaming in Mandarin and gesticulating wildly into her phone. "I know you never discuss your clients, but I'm going to guess that the couple were an English lord and his Chinese wife?" Axel smiled. "Nothing escapes you, does it? I haven't attempted anything on this scale before in Asia, and I do believe I'm going to be calling on you for some help." "Congratulations, Axel. It would be a pleasure," Oliver managed to utter as he felt like he was going to throw up. "Now, what can I do for you and Mrs. Bing?" Oliver watched Kitty fling her cell phone off the balcony into the canal far below. "Oh we were just in the neighborhood. I'm about to take her to meet Dries at Het Modepaleis, so I figured we should stop by." ··· "He said Colette was a new woman. That she had transformed her life and he was proud of her for wanting to do something good in the world. That's why she needed a proper house in Singapore. How gullible can you be?" Kitty cried. "Yes, let it out. Let it all out," a soothing voice above her said. "He said that Colette had made a secret trip to see him in Shanghai. She had prostrated herself at his feet and begged for his forgiveness. Can you fucking believe it?" Kitty was lying on the massage table, her head in the face cradle, as her massage therapist Elenya placed a row of hot stones along her spine. "Good, good. As I place this stone on your lower back, I want you to really feel it burn into your second chakra, and I want you to go deeper into your anger and release it," Elenya encouraged. "He said, 'Do not make me choose between you and my daughter, because you will lose. I only have one daughter, and I can always get another wife.' I hate him I hate him I hate him!" Kitty screamed, tears flowing freely and dripping on the tatami-matted floor. Suddenly the floor trembled violently, and a couple of the stones rolled off her back onto the side of the table. Oliver, sitting in an armchair next to the massage table, pulled his seat belt tighter. "That wasn't turbulence, Kitty. That was your anger releasing into the universe. How does it feel?" Elenya asked, as she began to rub Kitty's feet with a steaming hot towel. "It feels fucking great! I want to tell the pilots to steer this plane and crash it right into his fucking face!" Kitty screamed again, before breaking into loud heaving sobs. Oliver sighed as he looked out the window of the spa on the second floor of Kitty's Boeing 747-81 VIP. They were over the English Channel now, and soon they would be landing in London. "I don't know if a quick revenge is the answer, Kitty. I think you need to be playing a long game here. Look at the life Jack has given you. You've got three airplanes at your disposal, wonderful Elenya here to give you hot-stone massage treatments when you need it most, and all your other beautiful homes around the world. And let's not forget about Harvard. You've given Jack a son, and as he grows up, he will begin to eclipse Colette in importance. Kitty, do you know the story of the Empress Dowager Cixi?" "She was the old lady that died in the opening scene of that _Last Emperor_ movie, wasn't she?" Kitty said in a quiet voice. "Yes, the Empress Dowager Cixi was one of the concubines of Emperor Xianfeng, and after he died she launched a palace coup and became the true force of power in China. Cixi had a greater impact than possibly any other emperor in the country's history—she transformed it from a medieval empire into a modern nation, opened the country up to the West, and abolished foot-binding for girls. And she did all this, Kitty, even though she technically had no power at all because she was a woman." "So how did she do it?" Kitty asked. "She ruled indirectly through her five-year-old son, who succeeded to the throne as emperor. And after he died as a teenager, she adopted another boy and put him on the throne so she could rule through him. As the Empress Dowager, court etiquette decreed that she wasn't even allowed to be seen by men, so she took all her meetings with her ministers from behind a silk screen. You could learn a great deal from Cixi, you know. You need to bide your time and solidify your position by being the best mother to Harvard that you can possibly be. You need to be the most influential person in his life, and in time, he'll come to rule the Bing empire and you will be the power behind the throne. Throughout history, Kitty, the people who wielded the most power weren't always the ones who were in the spotlight. Dowager Empress Cixi, Cardinal Richelieu, Cosimo de' Medici. These are the people who flew under the radar in their own time, but they amassed all the power and influence through patience, intelligence, and stealth." "Patience, intelligence, and stealth," Kitty repeated. Suddenly she rolled over and sat up on the massage bed, the hot stones rolling off her back and scattering onto the floor as Elenya scurried to pick them up. "Has the contract to buy Tyersall Park been signed yet?" "I think the lawyers are still drafting the agreement." "So it's not a done deal?" "No. There's a gentleman's agreement, but it won't be official until the contracts are actually signed." Oliver wondered where she was going with all this. "Didn't you tell me that there were other interested parties in Tyersall Park before Jack bought it?" "Well yes, my cousin Nick was trying to buy it, but he never managed to scrape up enough money to match Jack's offer." "How much did he need?" "I think he was short about four billion dollars." Kitty's eyes gleamed. "What if I became a secret investor in the house? What if I put in the money and stole this house away from Jack?" Oliver stared at her in surprise. "Kitty, do you have that kind of money on your own?" "I got two billion in my divorce settlement from Bernard, and I invested all that money in Amazon. Do you know how much those shares have gone up in the past year? I have more than five billion dollars, and it's just all sitting there in an account managed by the Liechtenburg Group," Kitty proudly announced. Oliver leaned forward in his armchair. "You'd really be willing to invest all that money in a deal with my cousin?" "You'd still get your commission either way, wouldn't you?" "I would, but I'd just be concerned about you putting so much of your own money into one venture." Kitty went quiet for a moment, touched that Oliver cared for her beyond her money. "It will be worth every last cent just to know that Colette doesn't get her hands on that house!" "Well, let me make a few calls." Oliver unbuckled his seat belt and left the spa cabin. Five minutes later, he returned with a smirk on his face. "Kitty, there's been the most interesting development. I just spoke to my cousin Nicky. It turns out that Tyersall Park has been deemed a national historic landmark, and he and a group of partners are putting together a radical new proposal to challenge Jack Bing's offer." "Does this mean Colette won't get it either?" "Well, that's very likely. However, they are desperate for one more investor. They're short three billion dollars." "Only three billion? Sounds like a deal." "Should I call the cockpit and get them to turn this plane around?" "Why not?" Oliver picked up the phone by the console. "There's been a change of plans. We need to get to Singapore, and fast." "Not too fast. I want to get back to my hot-stone massage," Kitty purred, as she stretched languidly onto her massage bed again. # EPILOGUE TYERSALL PARK, SINGAPORE # ONE YEAR LATER... "I can't wait to see the bride. I wonder which designer she chose to do her gown?" Jacqueline Ling said to Oliver T'sien at the reception before the intimate wedding ceremony. Two hundred guests invited by the happy couple's families milled about the Andalusian Cloister, enjoying cocktails and canapés while admiring the mesmerizing light installation created by artist James Turrell in the columned arcades surrounding the courtyard. "Let's make a bet," Oliver ventured. "The way you're rolling in money these days, I'm not sure if I want to bet against you. Congratulations on your new commission in Abu Dhabi, by the way." "Thank you. It's just one palace for now. The princess was so impressed by what we did here that she's put me on an embarrassingly large retainer. Anyway, let's make the bet for lunch at Daphne's the next time we're both in London, and my money's on Giambattista Valli," Oliver said. "Okay, lunch at Daphne's. Well, I wager that the bride's gown will be designed by Alexis Mabille. I know how much she adores his work." The string quartet that had been playing suddenly stopped as the door at the far end of the courtyard opened to reveal a dashing young fellow in a tuxedo holding a violin to his chin. "Oh look, it's Charlie Siem! He's popping up everywhere these days, isn't he?" Oliver commented as the absurdly handsome virtuoso strolled along the arcade playing Elgar's "Salut d'amour." The doors at the other end of the arcade opened slowly, and Charlie strolled through, turning around to beckon the guests to follow him as he continued to play. Outside, a pathway lit with thousands of votive candles led from the rose garden past the stunning new saltwater swimming pool lined with thirteenth-century Moorish tiles into the wooded area of the estate. Following the musician as he ambled along merrily playing his violin, the guests oohed and aahed when they reached the lily pond, where black wooden chairs had been arranged in a crescent along one side of the pond. Hundreds of pale pink lanterns hung from the trees, cascading down branches and mixing with thousands of hanging vines that had been festooned with white dendrobium orchids, peonies, and white jasmine. A beautiful arched bridge built just for the wedding extended from one side of the pond to the other, covered entirely in different-hued roses, making the whole bridge appear as if it had been painted with impressionistic brushstrokes like one of Monet's bridges at Giverny. After the guests had settled into their seats, four cellists placed in the direction of the four winds began to play Bach's Cello Suite No. 1 in G major as the wedding procession began. An adorable little flower girl dressed in a gossamer white Marie-Chantal gown scattered rose petals along the central aisle, followed by Cassian Teo, who ambled up the aisle in a white linen suit (but barefoot), focused intently on not dropping the velvet pillow bearing the wedding rings. Next came Nick and Rachel walking arm in arm. Eleanor swelled up with pride as she watched Nick, dashing in his midnight blue Henry Poole tuxedo, escort Rachel, who Eleanor had to admit looked glowingly beautiful in a sublimely simple eggshell pink silk crepe gown designed by Narciso Rodriguez. " _Aiyah_ , it's like their wedding all over again," Eleanor sniffed to her husband, dabbing away a few tears. "Minus your crazy helicopter invasion," Philip quipped. "It wasn't crazy! I saved their marriage, those ungrateful kids!" Nick and Rachel parted at the end of the aisle as they took their places as best man and matron of honor on opposite sides of the bridge. Suddenly, a grand piano became illuminated behind the bridge, giving the effect of floating in the middle of the pond. Sitting at the piano was a young man with slightly disheveled strawberry blond hair. Irene Wu gasped out loud, " _Alamak_ , it's that Ed Saranwrap! I love his music!" As Ed Sheeran began singing his wildly popular love ballad "Thinking Out Loud," the groom, looking sharp in a bespoke tuxedo from Gieves and Hawkes, walked up to the middle of the bridge with the American pastor from Hong Kong's Stratosphere Church. And then as a full band assembled at the far end of the pond emerged to accompany Ed in his song, the bride made her grand entrance at the foot of the pathway. The guests rose from their seats in unison as the proud father of the bride, Goh Wye Mun, nervously escorted his daughter Peik Lin up the aisle. The bride wore a strapless gown with a fitted white bodice and a long train skirt of ruffles appliquéd with pale pink silk roses. Her hair was swept up into an elaborate braided bun and crowned with a vintage pearl-and-diamond tiara from G.Collins & Sons. Jacqueline and Oliver looked at each other and said in unison, "McQueen!" As Peik Lin glided past them, Jacqueline nodded approvingly. "Sublime. Sarah Burton does it again!" "We both lose, but we can still have lunch at Daphne's. Of course, you're treating, Jac—you've got more fuck-you money than I do," Oliver said with a wink. Peik Lin walked up to the middle of the bridge, where she was met by the pastor, who looked a little too disturbingly like Chris Hemsworth, and the man she was about to marry—Alistair Cheng. Nick and Rachel beamed joyously as the couple exchanged their handwritten vows, while Neena Goh, dressed in a gold-sequined Guo Pei gown with a plunging neckline, wept noisily. The Young sisters—Felicity, Catherine, Victoria, and Alix—glared at the mother of the bride with varying degrees of disapproval while shedding their own discreet tears. "I can't believe my baby Alistair is getting married," Alix sniffed to her sisters. "It seemed like only yesterday he was crawling into my bed, too afraid to asleep in the dark, and look at him now." "Well, the boy was smart enough to marry a woman as capable as Peik Lin! I must admit I am quite impressed with what she and Alistair have done with Tyersall Park," Felicity said. "I'm impressed by what they _all_ did!" Catherine interjected. After all, it was she who cast the tiebreaking vote between the sisters one year ago when Nick had come to them with a radical new proposal hours before they were about to sign the sales contract with Jack Bing. The result of Nick's proposal had now come to life as the just completed Tyersall Park Hotel and Museum, which preserved the main house as a historic landmark while breathing new life into it as an incomparably elegant new boutique hotel run by Colin Khoo and Araminta Lee. Set among nineteen acres of lush gardens in the immediate vicinity of the main house were forty guest villas exquisitely designed by Oliver T'sien in partnership with Axel Vervoordt. Beyond this rose Tyersall Village, a forty-five-acre community of sustainable housing specifically designed for artists and middle-income families, built by Goh Developments—the construction company owned by Peik Lin's family. "I think Father would be proud of Nicky. I don't think he was ever truly comfortable coming home every night to this decadent palace, when he spent the whole day being a doctor to the poorest people on the island," Alix said approvingly. From the row behind the sisters, Cassandra Shang leaned in and whispered, "I'm told every single house in Tyersall Village sold on the first day of offering, because for so long no one with less than ten million dollars has been able to afford a house with a garden in Singapore! But apparently the people living in those big houses along Gallop Road are furious that the hoi polloi are now moving in to this tony neighborhood!" "I don't mind what they did with Tyersall Village, but all those Buddha heads in the garden have got to go!" Victoria huffed. "I wonder if Peik Lin had anything to do with that. Those parents of hers look like they could be Buddhist." Felicity shook her head. "I don't think Peik Lin was involved. I think the Buddhas belong to the secret investor who chipped three billion in to Nick's venture. I just wish I knew who it was!" When the ceremony had concluded, the guests proceeded to the wedding banquet at Alexander's, the ravishing new restaurant in what was formerly the conservatory managed by Araminta Lee's Sublime Hospitality Group. Su Yi's prizewinning orchid hybrids commanded the space, but now they sprang out of handblown glass vessels suspended from the ceiling. Lit by candlelight, the hundreds of orchids seemed to dance in the air like celestial creatures over the long wooden seventeenth-century refectory tables. Eddie was the first to clink his wineglass and propose a toast to the newly married couple. "Peik Lin, I want to officially welcome you to the Cheng family, even though you know that you've already been welcomed into our hearts. And Alistair, my baby brother, I've never been more proud of you than I am today, and I just wanted to tell you how much I appreciate you and cherish you! I love you, brother!" Eddie said, crushing Alistair into a tight bear hug as he began sobbing into his collar. Sitting at the family table, Astrid turned to Fiona. "Is Eddie okay?" Fiona smiled. "He's fine. After Ah Ma died, I forced him to go see a therapist. I gave him an ultimatum—either he went, or I would leave him. At first he was very resistant, but now it's completely changed his life. And ours too. He's given up all his mistresses, he's become totally devoted to me and the kids, and he's really learning to process his feelings in a healthier way." "Well, it's been more than a year since I've seen him, so it does seem like quite a transformation," Astrid noted, watching as Eddie continued to soak Alistair's shoulder with tears. "You know my Eddie. Whenever he does anything, he goes all out. Anyway, how have you been? I see that island life suits you well—you look amazing!" Fiona remarked, as she admired Astrid's golden tan, naturally sun-streaked hair, and new style, which seemed like a perfect fusion of laid-back beach chic with imperial splendor. Astrid wore a simple indigo-dyed sarong-wrap dress with an incredible pearl choker that was comprised of crisscrossing vertical ropes of pearls starting from just underneath her chin and cascading down to the middle of her chest. "Thank you." "The choker is just _beyond_! Is that one of Ah Ma's pieces?" "No, it's from Chantecler Capri—a birthday present from Charlie." "I have to ask where you got that dress. It looks so refined, and yet somehow so relaxed!" Astrid gave an almost bashful smile. "Actually, I made this dress." "You're joking? I thought you were going to say this was Yves Saint Laurent from some obscure resort collection in the eighties." "Nope, it's Astrid Leong Resort Wear 2016. I've learned to sew, and I'm also creating my own fabrics. This is actually a bamboo cotton, hand-dyed in ocean water." "My God, Astrid, it's amazing! Can I buy a dress from you?" Astrid laughed. "Of course, I'll make you a dress if you like." "I guess you aren't bored in paradise?" "Not at all. I'm absolutely in love with my life in Palawan, and every day's an adventure. Charlie and I have also started a school, partnered with this wonderful arts-focused school in Brooklyn called Saint Ann's. Charlie's discovered a new passion—teaching! He's leading all the math and science classes, and Cassian's one of the students. The boy's never been happier being in a classroom with no walls and a constant ocean breeze. You really should bring the kids for a visit sometime." Charlie came strolling up with two flutes of champagne for the ladies. "Thanks, Charlie. So are tonight's nuptials inspiring you two?" Fiona teased. "Haha. A little bit, maybe. But right now I just enjoy living in sin with my gorgeous lover. Plus, it infuriates my parents to no end," Astrid said, giving Charlie a long, tender kiss just as her mother glanced over in their direction. — After the banquet, the bride stood on the top steps of the rose garden with her back to a gaggle of excited women ready to catch her bouquet. Peik Lin threw it up in the air with gusto, and the bouquet of lilies of the valley made an almost perfect arch, landing right in Scheherazade Shang's hands. The crowd cheered wildly as Scheherazade blushed. Catching Carlton's startled expression, Nick said teasingly, "The pressure's on now!" "No shit." Carlton nodded grimly, before breaking into a huge grin. An ornate outdoor ballroom had been created on the great lawn, complete with marquetry floors and enormous standing baroque mirrors placed strategically around the perimeter so that the dancers could feel as though they were whirling through the ballroom at Peterhof Palace. As the band went into full swing and the guests took to the dance floor, Nick, Rachel, and Kitty stood off to the side admiring Colin and Araminta's two-month-old son, Auberon. "He's sooooo cute!" Kitty cooed at the wriggling infant. "Look, Harvard, you were just like this not too long ago." "Was I ever that little?" Kitty's three-year-old boy asked. "Of course you were, darling! You were my little pea pod!" "I think we should probably get Auberon home. He's getting a bit fussy, and he'll never go back to sleep with the music," Araminta said a little anxiously to Colin. "Okay, okay. Hate to dash off so early, guys, but Mummy calls the shots now." Colin looked around apologetically. "But hey, this evening marks an auspicious start to our venture, don't you think? Two of our partners got married in grand style, and everything went off without a hitch! Tyersall Park Hotel and Museum is going to be the premier event space in Singapore!" "No, it will be the premier event space in all of Asia!" Kitty insisted. "Oh, I forgot to mention—I've just received an inquiry from a certain European prince who wants to buy out the entire hotel for a week to throw a huge birthday bash!" Araminta said. "We're attracting royalty already! Maybe the Countess of Palliser will hire it out for her next big gala," Rachel said with a slightly naughty smile. "How is she doing, by the way?" Araminta asked Kitty. Everyone knew that Colette had been the victim of a horrendous freak accident at her Save the Orangutans Proust Ball last year at the historic Goodwood Park Hotel. Colette had insisted on re-creating the space to look exactly like the French château where the original Proust Ball took place in 1971, complete with authentic 1971 lighting. In the middle of her speech, the electrical wiring on the 1970s lamp at her podium had short-circuited, and it would have been fine if Colette hadn't been wearing her multimillion-dollar Giambattista Valli gown plated with eight hundred eighteen-carat rose gold disks. "From what her father tells me, she's getting better every day. She's still in that wonderful facility in England, and she can speak without dribbling now, but it will be some time before she can make it to Sumatra again," Kitty said sweetly. Harvard tugged at her sleeve. "Mother, I'm getting hungry." "Okay honey," Kitty said. She walked with him to a quiet corner of the woods, undid the specially designed bodice on her strapless black Raf Simons jumpsuit, and took out her left breast. Kitty had become a staunch believer in attachment parenting, and as her son sucked happily on her nipple, she admired all the hauntingly lit ancient Buddha heads staring back at her, feeling extremely pleased with her one decorating suggestion. All these Buddhas would surely bring this place good karma. On the other side of the garden, Nick and Rachel were taking a walk to see how the new development was coming along. "It's unbelievable how fast they've worked," Nick remarked as he peeked into one of the bungalows. "Yeah, when we were back last Christmas, this was all one giant construction site, and now these beautiful little villas have appeared, looking like they've been here forever!" Rachel said admiringly as she fondled the ivy creeping along one of the reclaimed stone walls. "You know, none of this would have happened without you. You're the one who came up with the idea of putting Peik Lin, Alistair, Colin, and Araminta together to create this dream team, and look what they've achieved. In one year, they've created this whole eco-village _and_ Araminta even had time to have a baby! Isn't Auberon a cutie?" "He's adorable." Rachel paused for a moment, as if deciding whether to say something. "I'm so happy she had her baby now...because he's going to be the perfect playmate for ours." Nick looked at his wife with eyes huge as saucers. "Are you saying what I think you're saying?" Rachel nodded, with a smile. Nick hugged her excitedly. "When? Why didn't you tell me?" "I was waiting for the right moment. I took the test a couple of days ago—I'm about six weeks along." "Six weeks!" Nick sank down on a carved stone bench outside the villa. "Jesus, my head is spinning!" "Are you going to be okay?" Rachel asked. "Totally! I'm just overwhelmed with joy!" Nick said. Suddenly he looked up at Rachel with a jolt. "Listen, we _cannot_ mention this to my mother." "Oh, hell no!" Nick got up and took Rachel by the hand as they strolled down the pathway back to the wedding festivities. "Maybe if Mum behaves herself, she can meet our baby at age eighteen." Rachel thought about it for a moment. "We should probably wait till twenty-one." Nick escorted Rachel onto the dance floor just as the band struck up a ballad. As he held her body tight against his, he closed his eyes for a moment, thinking he could almost feel the heartbeat of his child. He opened his eyes again, gazing at his beautiful wife, gazing across the dance floor at Astrid and Charlie in their blissful embrace, and gazing at last toward the great house with all the lights in its windows ablaze, alive, reborn. # ACKNOWLEDGMENTS SPECIAL THANKS I am deeply grateful to the following guardian angels for so graciously sharing their expertise, talent, advice, inspiration, and support during the writing of this book: Nigel Barker Ryan Chan John Chia Cleo Davis-Urman Todd Doughty David Elliott Richard Eu Grant Gers Simone Gers Cornelia Guest Doris Magsaysay Ho George Hu Jenny Jackson Judy Jacoby Wah Guan Lim Lydia Look Alicia Lubowski Alexandra Machinist Julia Nickson Anton San Diego David Sangalli Alexander Sanger Jeannette Watson Sanger Shane Suvikapakornkul Nellie Svasti Sandi Tan Jami Tarris Lynn Visudharomn Eric Wind Jackie Zirkman # A NOTE ABOUT THE AUTHOR Kevin Kwan is the author of the international bestsellers _Crazy Rich Asians,_ soon to be a major motion picture, and _China Rich Girlfriend._ Born in Singapore, he has called New York's West Village home since 1995. For the latest news and information, please visit www.kevinkwanbooks.com. # _What's next on your reading list?_ [Discover your next great read!](http://links.penguinrandomhouse.com/type/prhebooklanding/isbn/9780385542241/display/1) * * * Get personalized book picks and up-to-date news about this author. Sign up now. 1. Cover 2. Other Titles 3. Title Page 4. Copyright 5. Contents 6. Dedication 7. Genealogy 8. Prologue 9. Part One 1. Chapter One 2. Chapter Two 3. Chapter Three 4. Chapter Four 5. Chapter Five 6. Chapter Six 7. Chapter Seven 8. Chapter Eight 9. Chapter Nine 10. Chapter Ten 11. Chapter Eleven 12. Chapter Twelve 13. Chapter Thirteen 14. Chapter Fourteen 10. Part Two 1. Chapter One 2. Chapter Two 3. Chapter Three 4. Chapter Four 5. Chapter Five 6. Chapter Six 7. Chapter Seven 8. Chapter Eight 9. Chapter Nine 10. Chapter Ten 11. Chapter Eleven 12. Chapter Twelve 13. Chapter Thirteen 14. Chapter Fourteen 15. Chapter Fifteen 11. Part Three 1. Chapter One 2. Chapter Two 3. Chapter Three 4. Chapter Four 5. Chapter Five 6. Chapter Six 7. Chapter Seven 8. Chapter Eight 9. Chapter Nine 10. Chapter Ten 11. Chapter Eleven 12. Chapter Twelve 13. Chapter Thirteen 14. Chapter Fourteen 15. Chapter Fifteen 16. Chapter Sixteen 17. Chapter Seventeen 12. Part Four 1. Chapter One 2. Chapter Two 3. Chapter Three 4. Chapter Four 5. Chapter Five 6. Chapter Six 7. Chapter Seven 8. Chapter Eight 9. Chapter Nine 10. Chapter Ten 13. Epilogue 14. Acknowledgments 15. A Note About the Author 1. Cover 2. Cover 3. Title Page 4. Contents 5. Start 1. iii 2. v 3. vi 4. vii 5. PB 6. viii 7. ix 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215. 216. 217. 218. 219. 220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242. 243. 244. 245. 246. 247. 248. 249. 250. 251. 252. 253. 254. 255. 256. 257. 258. 259. 260. 261. 262. 263. 264. 265. 266. 267. 268. 269. 270. 271. 272. 273. 274. 275. 276. 277. 278. 279. 280. 281. 282. 283. 284. 285. 286. 287. 288. 289. 290. 291. 292. 293. 294. 295. 296. 297. 298. 299. 300. 301. 302. 303. 304. 305. 306. 307. 308. 309. 310. 311. 312. 313. 314. 315. 316. 317. 318. 319. 320. 321. 322. 323. 324. 325. 326. 327. 328. 329. 330. 331. 332. 333. 334. 335. 336. 337. 338. 339. 340. 341. 342. 343. 344. 345. 346. 347. 348. 349. 350. 351. 352. 353. 354. 355. 356. 357. 358. 359. 360. 361. 362. 363. 364. 365. 366. 367. 368. 369. 370. 371. 372. 373. 374. 375. 376. 377. 378. 379. 380. 381. 382. 383. 384. 385. 386. 387. 388. 389. 390. 391. 392. 393. 394. 395. 396. 397. 398. 399. 400.	{ "redpajama_set_name": "RedPajamaBook" }	4,604
{"url":"https:\/\/publikationen.bibliothek.kit.edu\/1000049598","text":"# Search for vector-like T quarks decaying to top quarks and Higgs bosons in the all-hadronic channel using jet substructure\n\nThe CMS Collaboration; Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Bergauer, T.; Dragicevic, M.; Er\u00f6, J.; Friedl, M.; Fr\u00fchwirth, R.; Ghete, V.M.; Hartl, C.; H\u00f6rmann, N.; Hrubec, J.; Jeitler, M.; Kiesenhofer, W.; Kn\u00fcnz, V.; Krammer, M.; Kr\u00e4tschmer, I.; Liko, D.; ... mehr\n\nAbstract:\nA search is performed for a vector-like heavy T quark that is produced in pairs and that decays to a top quark and a Higgs boson. The data analysed correspond to an integrated luminosity of 19.7 fb-1 collected with the CMS detector in proton-proton collisions at root s=8TeV. For T quarks with large mass values the top quarks and Higgs bosons can have significant Lorentz boosts, so that their individual decay products often overlap and merge. Methods are applied to resolve the substructure of such merged jets. Upper limits on the production cross section of a T quark with mass between 500 and 1000 GeV\/c2 are derived. If the T quark decays exclusively to tH, the observed (expected) lower limit on the mass of the T quark is 745 (773) GeV\/c2 at 95% confidence level. For the first time an algorithm is used for tagging boosted Higgs bosons that is based on a combination of jet substructure information and b tagging.\n\n Zugeh\u00f6rige Institution(en) am KIT Institut f\u00fcr Experimentelle Kernphysik (IEKP) Publikationstyp Zeitschriftenaufsatz Jahr 2015 Sprache Englisch Identifikator ISSN: 1126-6708KITopen ID: 1000049598 Erschienen in Journal of High Energy Physics Band 2015 Heft 6 Seiten 80 Bemerkung zur Ver\u00f6ffentlichung Gef\u00f6rdert durch SCOAP3\nKIT \u2013 Die Forschungsuniversit\u00e4t in der Helmholtz-Gemeinschaft KITopen Landing Page","date":"2018-04-21 11:55:18","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\": 0.8148142695426941, \"perplexity\": 11056.600048927601}, \"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-2018-17\/segments\/1524125945143.71\/warc\/CC-MAIN-20180421110245-20180421130245-00123.warc.gz\"}"}	null	null
EOS was the cryptocurrency market's top performer on Wednesday and has now recovered more than a third of its recent low, a sign that investor confidence was slowly returning. The value of EOS surged 14.6% to $6.17, the highest in three weeks. According to CoinMarketCap, the digital currency has a total market capitalization of $5.6 billion. With the gain, EOS has managed to pare its monthly loss down to 13%. It was down by as much as 40% through the middle of the month. EOS trade volumes amounted to $741 million, up 40% from last week's levels. Exchanges with the highest EOS turnover include OKEx, Binance and Huobi. EOS' gains far outpaced the broader market. The combined value of cryptocurrencies rose 2.9% on Wednesday to $232.1 billion, the highest since. Aug. 7. Trade volumes are up 11% over the previous day's levels. Decentralized applications (DApps) are widely considered to be the future of internet technology, but a recent analysis of EOS and Ethereum DApp users show limited uptake of these new protocols. According to Kevin Rooke, a Canadian cryptocurrency researcher, Ethereum and EOS have only eight DApps that are actively utilized. To be considered "active," a decentralized application needs to have more than 300 daily users, according to Rooke. A further breakdown reveals that, among the eight, only three are hosted on EOS. The most popular EOS decentralized application is EOS Bet with weekly transaction volume of $18.1 million. By comparison, Ethereum's IDEX (the most popular on the platform) sees more than $7 million in weekly transaction volume. Dubbed the "Ethereum Killer" by some, EOS officially launched its network back in June to a myriad of issues. However, much of its functionality remains in development, including a governance process that will allow token holders to vote in referenda based on the number of tokens in their possession. This is vital because EOS currently has $35 million in a savings account to fund future initiatives. That figure is expected to rise to more than $20 million after 12 months, assuming the current price point of $6.17. Without a voting process in place, there's no way to actually allocate the funds.	{ "redpajama_set_name": "RedPajamaC4" }	1,360
package modules import ( "os" "path/filepath" "strings" xml "github.com/andaru/flexml" "github.com/openconfig/goyang/pkg/yang" "github.com/pkg/errors" ) // Package modules provides a YANG module (schema) collection // Collection is a YANG module collection type Collection struct { ms yang.Modules processed bool } // SetYANGPath sets the YANG import path. Each path in paths is a // directory to search when importing YANG modules either directly or // when referenced by other modules during import. This must be // called prior to NewCollection. func SetYANGPath(paths ...string) { yang.Path = paths } // NewCollection returns a new YANG module collection. Prior to // creating a collection, YANG paths must have been set using // SetYANGPath. func NewCollection() Collection { return &Collection{ms: yang.NewModules()} } func (c Collection) Raw() yang.Modules { return c.ms } func (c Collection) GetSchemaNode(schemaNodeID string) (e yang.Entry) { if match := c.IterLatest(func(m yang.Module) error { if mod := yang.ToEntry(m); mod != nil && mod.Find(schemaNodeID) != nil { return errors.New("match") } return nil }); match != nil { return e } return nil } // Import imports a module by its module name. Process must be called // before calls to ModuleEntry after this returns. func (c Collection) Import(moduleName string) error { if len(yang.Path) == 0 { return errors.New("no module paths to search for YANG modules, use SetYANGPath") } if c.ms.Modules[moduleName] != nil { return nil } if strings.HasSuffix(moduleName, ".yang") \|\| strings.Contains(moduleName, string(os.PathSeparator)) { return errors.Errorf("received invalid module name %s", moduleName) } err := c.ms.Read(moduleName) if err == nil { c.processed = false } return err } func (c Collection) ReadString(moduleName string, data string) error { if c.ms.Modules[moduleName] != nil { return nil } if strings.HasSuffix(moduleName, ".yang") \|\| strings.Contains(moduleName, string(os.PathSeparator)) { return errors.Errorf("received invalid module name %s", moduleName) } err := c.ms.Parse(data, moduleName) if err == nil { c.processed = false } return err } // ImportAll reads all YANG files found in the YANG path(s), returning // any import errors. Process must be called before calls to // ModuleEntry after this returns. func (c Collection) ImportAll() []error { var errs []error for _, root := range expandYANGPath(yang.Path) { _ = filepath.Walk(root, func(path string, info os.FileInfo, err error) error { if err != nil { errs = append(errs, importError{path, err.Error()}) return nil } if info.Mode().IsRegular() && strings.HasSuffix(path, ".yang") { if err := c.ms.Read(path); err != nil { errs = append(errs, importError{path, err.Error()}) } else { // clear the processed flag as we've imported a // module potentially unforseen c.processed = false } } return nil }) } return errs } // Process processes all modules previous read by Import or ImportAll, // and must be called before collection accessors, to ensure the // schema Entry tree including all augmentations is built. func (c Collection) Process() []error { errs := c.ms.Process() c.processed = len(errs) == 0 return errs } // ModulesLen returns the number of unique module names in the // collection, excluding sub-modules. func (c Collection) ModulesLen() (length int) { for name := range c.ms.Modules { if !strings.Contains(name, "@") { length++ } } return } // ModuleEntry returns the YANG schema node entry for the given YANG module // name, if it exists in the collection. An error is returned if no // such module exists in the collection or the collection is not ready // to be read. func (c Collection) ModuleEntry(name string) (yang.Entry, error) { if !c.processed { return nil, errors.New("must call Process first") } if mod := c.ms.Modules[name]; mod != nil { return yang.ToEntry(mod), nil } return nil, errors.New("not found") } // RootEntry scans the latest version of the module matching the // name's Space field for child entries matching the name's Local // field. If no such module is found, or no such child is found within // the module, an error is returned. func (c Collection) RootEntry(name xml.Name) (yang.Entry, error) { if !c.processed { return nil, errors.New("must call Process first") } var entry yang.Entry if stopped := c.IterLatest(func(mod yang.Module) error { // only search modules with a matching namespace if mod.Namespace == nil \|\| mod.Namespace.Name != name.Space { return nil } for local, e := range yang.ToEntry(mod).Dir { if name.Local == local { entry = e return errors.New("stop") } } return nil }); stopped != nil { return entry, nil } return nil, errors.New("not found") } // IterLatest iterates oves the latest version of all YANG modules in // the underlying module collection. func (c Collection) IterLatest(f func(yang.Module) error) error { for name, mod := range c.ms.Modules { // only consider "latest" versions, those without a '@' char. if !strings.Contains(name, "@") { if err := f(mod); err != nil { return err } } } return nil } func expandYANGPath(paths []string) []string { var result []string var roots []string for _, path := range paths { if "..." == filepath.Base(path) { roots = append(roots, filepath.Dir(path)) } else { result = append(result, path) } } for _, root := range roots { _ = filepath.Walk(root, func(path string, info os.FileInfo, err error) error { if err != nil \|\| strings.Contains(path, "/.git/") \|\| strings.Contains(path, "/.hg/") \|\| !info.IsDir() \|\| (len(info.Name()) > 0 && info.Name()[0] == '_') { return nil } result = append(result, path) return nil }) } return result } type importError struct { path string msg string } func (e importError) Error() string { if e.path != "" { return e.path + ": " + e.msg } return e.msg }	{ "redpajama_set_name": "RedPajamaGithub" }	6,237
{"url":"https:\/\/www.physicsoverflow.org\/36837\/about-boltzmann-h-theorem","text":"+ 4 like - 0 dislike\n847 views\n\nWhat is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize eventually? Does it apply for many-body localized states?\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user Mr. Gentleman\nCould you specifically reference the derivation you mention. The assumptions should be in there. But just out of the top of my head, you're going to have to assume some specific initial conditions (they have to be \"typical\"). The way Boltzmann did it was with the Stosszahlansatz. But more modern derivations use more explicit assumptions on the initial conditions.\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user Raskolnikov\nBoltzmann's H-theorem is not for unitary quantum mechanics, but for classical (nearly ideal) gases. For the quantum mechanical H-theorem, see von Neumann's work from 1929. For an English translation, see arxiv.org\/abs\/1003.2133\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user Zoltan Zimboras\n\n+ 6 like - 0 dislike\n\nI would like to share my thoughts and questions on the issue. The Boltzmann H theorem based on classical mechanics is well discussed in various literatures, the irreversibility comes from his assumption of molecular chaos, which cannot be justified from the underlying dynamical equation. Here I will try to say something on quantum H theorem, the point I want to make is that, although seemingly H theorem can be derived from unitarity, the true entropy increase in fact comes from the non-unitary part of quantum mechanics. Let me first recap the derivation using unitarity $^{1,2}$.\n\nH theorem as a consequence of unitarity\n\nDenote by $P_k$ the probability of a particle appearing on the state $\|k\\rangle$, $A_{kl}$ the transition rate from state $\|k\\rangle$ to state $\|l\\rangle$, then by the master equation\n\n$${\\frac {dP_{k}}{dt}}=\\sum _{l}(A_{{kl }}P_{l }-A_{{l k}}P_{k})=\\sum _{{l\\neq k}}(A_{{kl }}P_{l }-A_{{l k}}P_{k})\\cdots\\cdots(1).$$ Then we take the derivative of entropy\n\n$$S=-\\sum_k P_k\\ln P_k\\cdots\\cdots(2),$$\n\nwe obtain\n\n$$\\frac{dS}{dt}=-\\sum_k\\frac{dP_k}{dt}\\left(1+\\ln P_k\\right)\\cdots\\cdots(3).$$ Together with (1) we have $$\\frac{dS}{dt}=-\\sum_{kl}\\left\\{(1+\\ln P_k)A_{{kl }}P_{l }-(1+\\ln P_k)A_{{l k}}P_{k}\\right\\}\\cdots(4).$$ For the seond second term let us interchange the dummy indices $k$ and $l$, we get $$\\frac{dS}{dt}=\\sum_{kl}(\\ln P_l-\\ln P_k)A_{kl}P_l\\cdots\\cdots(5)$$ Now use the mathematical identity $(\\ln P_l-\\ln P_k)P_l\\geq P_l- P_k$, we obtain\n\n$$\\frac{dS}{dt}\\geq \\sum_{kl}(P_l-P_k)A_{kl}= \\sum_{kl}P_l(A_{kl}-A_{lk})\\\\=\\sum_{l}P_l\\big\\{\\sum_{k}(A_{kl}-A_{lk})\\big\\}\\cdots\\cdots(6)$$\n\nNow unitarity ensures $\\sum_{k}A_{kl}$ and $\\sum_{k}A_{lk}$ are both 0, because as transition rates, $$\\sum_{k}A_{kl}=\\frac{d}{dt}\\sum_{k}\|\\langle l\|S\|k\\rangle\|^2=\\frac{d}{dt}\\sum_{k}\\langle l\|S\|k\\rangle\\langle k\|S^{\\dagger}\|l\\rangle\\\\=\\frac{d}{dt}\\langle l\|SS^{\\dagger}\|l\\rangle=\\frac{d}{dt}\\langle l\|l\\rangle=0\\cdots\\cdots(7),$$ where $S$ is the unitary time evolution operator describing the system. This is nothing but saying the total transition probability from one state to all states must be 1. It is clear (6) and (7) imply the H theorem: $$\\frac{dS}{dt}\\geq 0.$$ Where does the irreversibility come from?\n\nNow we are in a position to question ourselves with Loschmidt's paradox, analogously to its classical version: There are many unitary and time-reversible quantum mechanical systems, if we have just derived H theorem using unitarity alone, how can it be reconciled with time-reversibility of the underlying dynamics?\n\nWhat sneaked into the above derivation?\n\nThe crucial thing to notice is that, in the quantum regime, the definition of entropy using equation (2) is inherently an impossible one: the value of the entropy in (2) depends on the basis we choose to describe the system!\n\nConsider a two-level system with two choices of orthogonal basis $\\{\|1\\rangle, \|2\\rangle\\}$ and $\\{\|a\\rangle, \|b\\rangle\\}$ related by $$\|1\\rangle=\\frac{1}{\\sqrt2}(\|a\\rangle+\|b\\rangle),\\\\\|2\\rangle=\\frac{1}{\\sqrt2}(\|a\\rangle-\|b\\rangle).$$ Suppose the system is in the state $\|1\\rangle$, then the entropy formula gives $S=0$ in the first choice of basis since it has 100% chance to appear in $\|1\\rangle$, while in the other basis $S=\\ln2$ since it has 50%-50% chance to appear in either $\|a\\rangle$ or $\|b\\rangle$.\n\nNow we may argue, it is one thing that to say the system is in $\\frac{1}{\\sqrt2}(\|a\\rangle+\|b\\rangle)$ and have the potential 50%-50% chance to transit into $\|a\\rangle$ and $\|b\\rangle$ after a measurement, but a different thing to say the transition has been realized by some measurement. Two situations must be described differently. If we look back to our derivation, it is not hard to see what we really did was, after a basis state evolves to a new state which is a superposition of the basis states, we assumed transitions to original basis states have happened instead of just staying in that superposition state, and in fact the original definition of entropy is not capable of describing such situation, as explained just now.\n\nA plausible definition of quantum entropy is the Von Neumann entropy, which is a basis-independent definition of entropy, and in this description, the entropy of a unitarily evolving system is constant in time, while a (projective) measurement can increase the entropy.\n\nBased on the above comparison, we see the irreversibility really comes as an assumption, the assumption that a measurement\/decoherence has happened, and as we know, a (projective) measurement is a non-unitary, irreversible process, no paradox anymore.\n\nMy own question on the issue is, what to make of the fact that von Neumann entropy is constant in time? Does it mean it is incapable of describing a closed system evolving from non-equilibrium to equilibrium, or should we just reverse the argument and say any non-equilibrium to equilibrium evolution must be described by some non-unitary process?\n\n1.Rephrased from section 3.6 of The Quantum Theory of Fields, Vol1, S. Weinberg\n\n2.If I remember correctly(which I'm not quite confident on), such derivation was first given by Pauli, and he correctly spotted the origin of irreversibility, which he called the \"random phase assumption\".\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user Jia Yiyang\nanswered Feb 8, 2014 by (2,640 points)\nThe von Neumann entropy is not the same thing as thermodynamic entropy, for the same reason the information entropy $\\int -\\rho\\ln \\rho\\, dq\\,dp$ is not thermodynamic entropy in classical statistical physics. Both von Neumann and information entropy are constant for isolated Hamiltonian systems. Thermodynamic ( Clausius ) entropy has to be derived from statistical physics differently - it is proportional to logarithm of the accessible phase space(classical statistical physics) or logarithm of the number of accessible microstates (quantum statistical physics).\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user J\u00e1n Lalinsk\u00fd\nThe latter entropies are defined only for equilibrium states. There is no law saying that the entropy has to be defined for non-equilibrium states or that it has to increase in time.\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user J\u00e1n Lalinsk\u00fd\n@J\u00e1nLalinsk\u00fd: thanks for pointing out my misunderstanding. So in the quantum case what would be the proper definition of thermodynamic entropy? Or what would be a basis-independent way of counting microstates?\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user Jia Yiyang\nI am not sure about this, but the closest thing is this: let the system be isolated with energy somewhere in $\\langle E,E+\\Delta E\\rangle$ (the interval is large enough to contain zillion of Hamiltonian eigenstates). Define statistical entropy as $S = k_B \\ln ( D(E)\\Delta E )$ where $D(E)$ is density of the Hamiltonian eigenfunctions on the energy line. This is statistical entropy for microcanonical ensemble and for macro-systems (such ideal gas with many particles) can be treated as quantity similar to thermodynamic entropy.\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user J\u00e1n Lalinsk\u00fd\n@J\u00e1nLalinsk\u00fd: ok, I'll try to look into this, thanks.\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user Jia Yiyang\n@JiaYiyang: Thank you for your sharing your thoughts and thank you for filling up the derivation, which is indeed what I meant. I agree with you that the derivation missed the basis dependence, and your argument is quite good. Another point on Boltzmann entropy (proportional to the logarithm of numbers of microscopic states), however, my opinion is that this is the quantity that is maximized in thermal equilibrium, and when equilibrium is reached, ergodicity indicates the entropy can also be written as $-tr(\\rho\\ln\\rho)$.\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user Mr. Gentleman\n+ 0 like - 0 dislike\n\nThat calculation has restrictions, but, one in particular should be mentioned, that master equation is supposed to be connected to this entropy, but is not necessarily, the master equation can be connected to general entropic form, and that is a fundamental idea for a more complete proff.\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user Maike Afs\nanswered Jul 13, 2016 by (0 points)\nWouldn't that be better as a comment?\n\nThis post imported from StackExchange Physics at 2016-08-04 12:34 (UTC), posted by SE-user MAFIA36790\n\n Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the \"link\" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)\u00a0\u00a0 Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\\varnothing$ in the following word:p$\\hbar$ysi$\\varnothing$sOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.","date":"2021-04-12 00:48:52","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\": 0.8710881471633911, \"perplexity\": 671.6241907328055}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-17\/segments\/1618038065903.7\/warc\/CC-MAIN-20210411233715-20210412023715-00374.warc.gz\"}"}	null	null
include(FindPackageHandleStandardArgs) include(Findosg_functions) OSG_FIND_PATH (OSGQT osgQt/) OSG_FIND_LIBRARY(OSGQT osgQt) FIND_PACKAGE_HANDLE_STANDARD_ARGS(osgQt DEFAULT_MSG OSGQT_LIBRARY OSGQT_INCLUDE_DIR)	{ "redpajama_set_name": "RedPajamaGithub" }	7,163
Q: J/Connector fails to connect to Sphinx server via SphinxQL I have a server running the latest version of Sphinx (2.0.1-id64-beta) and am trying to access its SphinxQL interface via a Java application using the latest J/Connector JDBC driver (5.1.18). Whenever a connection is attempted to be established the process will block indefinitely on a socket read. The call stack looks like the following: (StackExchange informs me to that I am not permitted to post images directly due to my reputation level.) Image: http://dunkelhaft.dyndns-server.com/tmp/callstack.png It looks like the JDBC driver is waiting for the Sphinx server to supply it with some message that never arrives. It's worth noting that if I use something like the MySQL command-line client or Sequel Pro or a simple PHP script, the MySQL interface works without issue, leading me to suspect that the issue is some sort of protocol discrepancy between the Sphinx server and the JDBC protocol. Any ideas? A: you're not the only one with that problem. i don't have a direct solution, just some dirty workarounds to get things working - look here [in short - you'll have to use older connector/j and will need to make small change in the sphinx 2.0.3 code]. there's also a bug report to the sphinx devs: #959. edit. it seems that adding mysql_version_string = 5.0.37 to the sphinx.conf should solve the problem.	{ "redpajama_set_name": "RedPajamaStackExchange" }	2,119
{"url":"https:\/\/www.gktoday.in\/question\/a-certain-sum-of-money-amounts-to-756-rs-in-2-year","text":"A certain sum of money amounts to 756 Rs. in 2 years and to 873 Rs. in $3\\frac{1}{2}$ years at a certain rate of simple interest. The rate of interest per annum is :\n[A] 10%\n[B] 11%\n[C] 12%\n[D] 13%","date":"2018-05-24 02:10:43","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 5, \"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\": 0.8755801320075989, \"perplexity\": 702.1010271791705}, \"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-2018-22\/segments\/1526794865884.49\/warc\/CC-MAIN-20180524014502-20180524034502-00534.warc.gz\"}"}	null	null
package camera import ( "errors" "io" ) func capture( device string, format Format, resolution *Resolution, ) (io.ReadCloser, error) { return nil, errors.New("camera: capture not implemented") }	{ "redpajama_set_name": "RedPajamaGithub" }	5,910
{"url":"https:\/\/indico.cern.ch\/event\/895086\/contributions\/4727312\/","text":"# QM 2022\n\nApr 4 \u2013 10, 2022\nAuditorium Maximum UJ\nEurope\/Warsaw timezone\nProceedings submission deadline extended to August 15, 2022\n\n## Ratio of photon anisotropic flow\n\nApr 6, 2022, 7:22 PM\n4m\nPoster Electroweak probes\n\nPingal Dasgupta\n\n### Description\n\nThe anisotropic flow of direct photons produced in relativistic heavy ion collisions is known to be dominated by the thermal radiations. The non-thermal contributions dilute the photon anisotropic flow by adding extra weight factor in the $v_n$ calculation. The discrepancy between experimental photon anisotropic flow data and results from theoretical model calculations is not well understood even after significant developments in the model calculations as well as in the experimental analysis methods.\n\nWe show that the ratio of photon $v_n$ can be a potential observable in this regard by minimizing the non-thermal contributions and the ratio along with the individual flow parameters could be valuable to constrain the initial state as well as to understand the photon anisotropic flow from heavy ion collisions better [1].\n\nThe photon $v_2\/v_3$ is found to be larger for peripheral collisions than for central collisions and the $p_T$ dependent behavior of the ratio is found to be different from the individual flow parameters. The ratio is found to be sensitive to the initial conditions of the model calculation at different $p_T$ regions compared to the individual anisotropic flow parameters.\n\nThe $v_1\/v_2$ ( and $v_1\/v_3$ ) shows a completely different $p_T$ dependent nature compared to $v_2\/v_3$ of photons. An experimental determination of photon $v_1\/v_n$ is expected to confirm the range of thermal contribution. In addition, the $v_1\/v_n$ is found to be less sensitive to the initial formation time compared to $v_2\/v_3$. However, $v_1\/v_n$ is expected to be much more sensitive to the final freeze-out temperature as photon $v_1$ does not depend strongly on the value of $T_f$ .\n\n[1] R. Chatterjee and P. Dasgupta, arXiv: arXiv:2106.15922\n\n### Primary author\n\nDr Rupa Chatterjee (Variable Energy Cyclotron Centre)","date":"2022-08-17 08:26:29","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\": 0.8491556644439697, \"perplexity\": 938.2336142356558}, \"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\/1659882572870.85\/warc\/CC-MAIN-20220817062258-20220817092258-00781.warc.gz\"}"}	null	null
Welcome to the Yale Club of San Francisco - Meklit Hadero (CC '02) at SFJAZZ Center Meklit Hadero (CC '02) at SFJAZZ Center Discounted tickets available to the Yale community. Date: Friday July 12 Location: SFJAZZ Center, Miner Auditorium Cost: 20% off with discount code Yale20 Tickets and more information available at the SFJAZZ event page. Meklit Hadero's music is imbued with poetry and multiplicity, from hybridized sounds of Tizita (haunting and nostalgic music) drawing from her Ethiopian heritage, to the annals of jazz, folk songs, hip-hop and art rock. Drawing from the concept of the "inbetween", Meklit's music transports us to the post-national space of Africa and the Americas, inspiring us to bridge the frontiers between language, tribes and disciplines. Her songs celebrate the newness of life and the hyphens that bring us together. Meklit has released three studio albums, served as an artist-in-residence at NYU, and completed musical commissions for the San Francisco Arts Commission, the Fund for Artists, the Brava Theater, and the De Young Museum. In 2011, Meklit co-founded the Nile Project with Egyptian Ethnomusicologist Mina Girgis, the initiative's Executive Director and creative instigator. She is the founder of the Arba Minch Collective, former Co-Director of the Red Poppy Art House, and a TED Senior Fellow, with the Nile Project as her main fellowship focus. She graduated from Yale University in 2002 with a BA in Political Science.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	2,075
\section{Introduction} So far the observed elementary particles in nature have spin $s=0,1/2,1$. In principle, we could have elementary particles of arbitrary integer or half-integer spin. In particular, in the spectrum of superstring theories, there are massive particles of arbitrarily high spin. As we increase the spin we need higher rank tensors for a Lorentz covariant description. The higher the rank, the more redundant fields are introduced which must be eliminated afterwards in order to achieve the correct counting of degrees of freedom, namely, $2s+1$ in the massive case and $2$ for massless particles which corresponds to the helicities $+s$ and $-s$. Some of the fields are called auxiliary fields. They have no physical content but their equations of motion lead to nontrivial constraints required for the reduction of degrees of freedom. From the theoretical point of view, the main difficult in describing higher spin particles lies in the fact that some of the auxiliary fields may stop being purely auxiliary due to interactions. They acquire a nontrivial dynamics and we end up with an incorrect number of degrees of freedom, some of them become ghosts. In $D=2+1$ dimensions it is possible to trade auxiliary fields into local symmetries by going to dual models of higher order in derivatives which acquire more symmetries as the number of derivatives is increased. Since it is easier to control local symmetries (gauge symmetries) than the dynamics of auxiliary fields it is of interest to investigate this trading procedure. In particular, in $D=2+1$ we can define the so called self-dual models which are parity singlets of spin-s and of order $j$ in derivatives, henceforth $SD_j^{(s)}$. They describe massive particles of a given helicity $+s$ or $-s$ in a local way. By means of a Noether gauge embedding (NGE) procedure one can go from $SD_j^{(s)}$ to $SD_{j+1}^{(s)}$. This has done in \cite{clovis}, \cite{mls} and \cite{SD_4} respectively for spin $s=1,3/2$ and $s=2$. In all those cases $j$ runs from $1$ until the top value $2s$. In the spin-3 case, further examined here, we have partially succeeded \cite{nge} in going from $j=1$ until $j=4$ along the $NGE$ approach. Here we show in section 2 how to go from the model $SD_5^{(3)}$ of \cite{ddhigher} to the top model $SD_6^{(3)}$ of \cite{bhth}. We still have a gap between $SD_4^{(3)}$ and $SD_5^{(3)}$. Moreover, the $NGE$ also works for parity doublets containing both helicities $+s$ and $-s$. In \cite{SD_4} we have obtained the fourth order linearized ``New Massive Gravity'' of \cite{bht} from the usual second order Fierz-Pauli (FP) \cite{fp} theory which describes massive spin-2 particles. Here we derive in section 3 a fourth and sixth order spin-3 doublet model from the second order spin-3 Singh-Hagen model \cite{sh}. We conjecture that there is chain of parity doublet models of order $2,4,6,\cdots, 2s$ for arbitrary spin-s. \section{Higher derivative singlet models} Here the spin-3 field is described in terms of a totally symmetric rank-3 tensor $h_{\mu\nu\alpha}$. There are some ``geometrical'' objects similar to those we know from general relativity like the Einstein and Schouten tensors which are given by: \begin{eqnarray} \mathbb{G}_{\mu\nu\alpha}=\mathbb{R}_{\mu\nu\alpha}-\frac{1}{2}\eta_{(\mu\nu}\mathbb{R}_{\alpha)}\quad,\quad\mathbb{S}_{\mu\nu\alpha}=\mathbb{R}_{\mu\nu\alpha}-\frac{1}{8}\eta_{(\mu\nu}\mathbb{R}_{\alpha)}\end{eqnarray} \noindent where the spin-3 Ricci tensor and its vector contraction have been introduced in \cite{deserdamour}, namely: \begin{eqnarray} \mathbb{R}_{\mu\nu\alpha}&=&\square{h}_{\mu\nu\alpha}-\partial^{\beta}\partial_{(\mu}h_{\beta\nu\alpha)}+\partial_{(\mu}\partial_{\nu}h_{\alpha)}\\ \mathbb{R}_{\alpha}&=&\eta^{\mu\nu}\mathbb{R}_{\mu\nu\alpha}=2\square{h}_{\alpha}-2\partial^{\beta}\partial^{\lambda}h_{\beta\lambda\alpha}+\partial_{\alpha}\partial^{\beta}h_{\beta}.\end{eqnarray} \noindent Along this work we use the mostly plus metric $(-,+,+)$ and unnormalized symmetrization: $(\alpha\beta\gamma)=\alpha\beta\gamma+\beta\gamma\alpha+\gamma\alpha\beta$. It is also often the use of the anti-symmetric operator $E_{\mu\nu}=\epsilon_{\mu\nu\alpha}\partial^{\alpha}$ where $(Eh)_{\mu\nu\alpha}\equiv(2/3)E_{(\mu}^{\;\;\;\beta}h_{\beta\nu\alpha)}$. Given another totally symmetric tensor $j_{\mu\nu\alpha}$, the operators $\mathbb{G}_{\mu\nu\alpha}$ and $\mathbb{S}_{\mu\nu\alpha}$ are hermitian in the sense that: \begin{equation} \mathbb{G}_{\mu\nu\alpha}[\mathbb{S}(h)]j^{\mu\nu\alpha}=\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(j)=\mathbb{S}_{\mu\nu\alpha}(j)\mathbb{G}^{\mu\nu\alpha}(h)=h_{\mu\nu\alpha}\mathbb{G}^{\mu\nu\alpha}[\mathbb{S}(j)]\end{equation} A great advantage of the higher order self-dual models introduced in \cite{ddhigher}, is the absence of auxiliary fields, this is a key issue when we add interactions since auxiliary fields may become dynamic and destroy the correct counting of degrees of freedom. Here we revisit the equivalence of those models under the point of view of the $NGE$ approach, which reveals the role of the symmetries. The fifth order self-dual model ($SD_5^{(3)}$) for the massive spin-3 particle is given by: \begin{eqnarray} S_{SD_5^{(3)}}=\int{d^{3}x}\Big[-\frac{1}{2m^{2}}\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(h)+\frac{1}{4m^{3}}\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(E\,h)\Big]\label{SD_5}\end{eqnarray} \noindent The whole action $S_{SD_5^{(3)}}$ is invariant under the gauge transformation \begin{equation} \delta_{\tilde{\xi},\psi^{T}}{h}_{\mu\nu\alpha}=\partial_{(\mu}\tilde{\xi}_{\nu\alpha)}+\eta_{(\mu\nu}\psi^{T}_{\alpha)}\label{Tr-4},\end{equation} where the parameter $\tilde{\xi}_{\nu\alpha}$ is symmetric and traceless while the the vector parameter $\psi_{\alpha}^T$ of the Weyl transformation is transverse ($\partial^{\alpha}\psi_{\alpha}^T=0$). Besides, the fifth order term has an additional symmetry, \begin{equation} \delta_{\xi,\psi}{h}_{\mu\nu\alpha}=\partial_{(\mu}\tilde{\xi}_{\nu\alpha)}+\eta_{(\mu\nu}\psi^T_{\alpha)}+ \eta_{(\mu\nu}\partial_{\alpha)} \phi=\partial_{(\mu}{\xi}_{\nu\alpha)}+\eta_{(\mu\nu}\psi_{\alpha)} \label{Tr-5}\end{equation} \noindent where the parameter $\xi_{\nu\alpha}$ is symmetric while $\psi_{\alpha}$ is an ordinary vector. Once the additional symmetry, the longitudinal Weyl transformation, of the fifth order term is broken by the fourth order one, we would like to impose such symmetry to the model (\ref{SD_5}) in order to obtain a sixth order model ($SD_6^{(3)}$), which is invariant under (\ref{Tr-5}) but with the same particle content of the $SD_5^{(3)}$. We begin by adding a source term $j^{\mu\nu\alpha}$ coupled to a totally symmetric dual field $\tau^{\ast}_{\mu\nu\alpha}$: \begin{eqnarray} S_{SD_5^{(3)}}[j]=\int{d^{3}x}\Big[-\frac{1}{2m^{2}}\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(h)+\frac{1}{4m^{3}}\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(E\,h)+\tau^{\ast}_{\mu\nu\alpha}j^{\mu\nu\alpha}\Big]\label{sd5j}\end{eqnarray} Notice that the dual field is chosen in such a way that it preserves the gauge invariance under (\ref{Tr-4}), then we have the fourth order dual field: $\tau^{\ast}_{\mu\nu\alpha}=(1/m^{4})\mathbb{G}_{\mu\nu\alpha}(\mathbb{S}(h))$. From (\ref{sd5j}) we now take the Euler tensor: \begin{eqnarray} K^{\mu\nu\alpha} \equiv \frac{\delta S_{SD_5^{(3)}}}{\delta h_{\mu\nu\alpha}}=-\frac{1}{m^{2}}\mathbb{G}^{\mu\nu\alpha}[\mathbb{S}(h)]+\frac{1}{2m^{3}}\mathbb{G}^{\mu\nu\alpha}[\mathbb{S}(Eh)]+\frac{1}{m^{4}}\mathbb{G}^{\mu\nu\alpha}[\mathbb{S}(j)],\label{Euler-SD_5}\end{eqnarray} \noindent in order to implement a first iteration which is given by \begin{eqnarray} S_{1}=S_{SD_5^{(3)}}+\int{d^{3}x}\,\,K^{\mu\nu\alpha}a_{\mu\nu\alpha}\end{eqnarray} \noindent where $a_{\mu\nu\alpha}$ is an auxiliary field. By taking the gauge variation of $S_1$ with respect to (\ref{Tr-5}) and choosing $\delta{a}_{\mu\nu\alpha}=-\delta{h}_{\mu\nu\alpha}$, we obtain: \begin{equation} \delta_{\xi,\psi}S_{1}=\int{d^{3}x}\;a_{\mu\nu\alpha}\delta_{\xi,\psi}{K}^{\mu\nu\alpha}.\end{equation} \noindent By calculating the variation of the Euler tensor we have then \begin{eqnarray} \delta_{\xi,\psi}{S}_{1}=\int{d^{3}x}\;\delta_{\xi,\psi}\left[\frac{1}{2m^{2}}\mathbb{S}_{\mu\nu\alpha}(a)\mathbb{G}^{\mu\nu\alpha}(a)\right],\end{eqnarray} \noindent which automatically takes us to the second iteration, which is gauge invariant by construction and given by: \begin{eqnarray} S_{2}&=&S_{1}-\int{d^{3}x}\frac{m}{2}\mathbb{S}_{\mu\nu\alpha}(a)\mathbb{G}^{\mu\nu\alpha}(a)\nonumber\\ &=&\int{d^{3}x}\Big[{\mathcal{L}}_{SD_5^{(3)}}(h)-\frac{1}{m^{2}}\mathbb{S}_{\mu\nu\alpha}(a)\mathbb{G}^{\mu\nu\alpha}(h)+\frac{1}{2m^{3}}\mathbb{S}_{\mu\nu\alpha}(a)\mathbb{G}^{\mu\nu\alpha}(Eh)-\frac{1}{2m^{2}}\mathbb{S}_{\mu\nu\alpha}(a)\mathbb{G}^{\mu\nu\alpha}(a)\nonumber\\ &&\qquad+\frac{1}{m^{4}}\mathbb{S}_{\mu\nu\alpha}(a)\mathbb{G}^{\mu\nu\alpha}(j)+\tau^{\ast}_{\mu\nu\alpha}j^{\mu\nu\alpha}\Big].\end{eqnarray} \noindent Integrating over the auxiliary fields $a_{\mu\nu\alpha}$ we have: \begin{eqnarray} S_{2}&=&\int{d^{3}x}\Bigg[-\frac{1}{4m^{3}}\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(Eh)+\frac{1}{8m^{4}}\mathbb{S}_{\mu\nu\alpha}(Eh)\mathbb{G}^{\mu\nu\alpha}(Eh)\nonumber\\ &&\qquad\quad+\frac{1}{2m^{5}}\mathbb{S}_{\mu\nu\alpha}(Eh)\mathbb{G}^{\mu\nu\alpha}(j)+\frac{1}{2m^{6}}\mathbb{S}_{\mu\nu\alpha}(j)\mathbb{G}^{\mu\nu\alpha}(j)\nonumber\\ &&\qquad\quad-\frac{1}{2m^{2}}\mathbb{S}_{\mu\nu\alpha}\Big(a+h-\frac{Eh}{2m}-\frac{j}{m^{2}}\Big)\mathbb{G}^{\mu\nu\alpha}\Big(a+h-\frac{Eh}{2m}-\frac{j}{m^{2}}\Big)\Bigg].\end{eqnarray} \noindent Notice that by shifting the auxiliary fields in such a way that $a_{\mu\nu\alpha}\rightarrow{a}_{\mu\nu\alpha}-h_{\mu\nu\alpha}+(1/2m)(Eh)_{\mu\nu\alpha}+(1/m^{2})j_{\mu\nu\alpha}$ we get a completely decoupled term depending on $a_{\mu\nu\alpha}$ which is free of particle content, see \cite{deserdamour}, and will be neglected henceforth. This allow us to obtain the sixth order self-dual model \footnote{We have used the following properties: $\mathbb{S}_{\mu\nu\alpha}(Eh)\mathbb{G}^{\mu\nu\alpha}(Eh)=\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(E^{2}h)$.}: \begin{eqnarray} S_{SD_6^{(3)}}=\int{d^{3}x}\Big[-\frac{1}{4m^{3}}\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(Eh)+\frac{1}{8m^{4}}\mathbb{S}_{\mu\nu\alpha}(h)\mathbb{G}^{\mu\nu\alpha}(E^{2}h)+h^{\ast}_{\mu\nu\alpha}j^{\mu\nu\alpha}+\mathcal{O}(j^{2})\Big]\label{SD_6}\end{eqnarray} \noindent with the fifth order dual field \begin{equation} h^{\ast}_{\mu\nu\alpha}\equiv\frac{1}{2m^{5}}\mathbb{G}_{\mu\nu\alpha}[\mathbb{S}(Eh)].\end{equation} The sixth order self-dual model obtained here, is precisely the one first found in \cite{bhth} and investigated by some of us in \cite{ddhigher}. It is invariant under a large set of gauge symmetries in the sense that $\tilde{\xi}_{\mu\nu}\to \xi_{\mu\nu}$ and $\psi_{\alpha}^T\to \psi_{\alpha}$. Once again we stress that such self-dual descriptions do not need auxiliary fields, differently of the doublet models we are going to address in the next section. Finally, we can verify the classical equivalence between the $SD_5^{(3)}$ and the $SD_6^{(3)}$ models at the level of the equations of motion. From (\ref{SD_5}), we have: \begin{eqnarray} -\frac{1}{m^{2}}\mathbb{G}_{\mu\nu\alpha}(\mathbb{S}(h))+\frac{1}{6m^{3}}E_{(\mu}^{\;\;\;\beta}\mathbb{G}_{\beta\nu\alpha)}(\mathbb{S}(h))=0\; ;\end{eqnarray} \noindent which in terms of the dual fields $\tau^{\ast}_{\mu\nu\alpha}$ give us: \begin{eqnarray} -m^2\tau^{\ast}_{\mu\nu\alpha}+\frac{m}{6}E_{(\mu}^{\;\;\;\beta}\tau^{\ast}_{\beta\nu\alpha)}=0\label{eom-SD_5}\;.\end{eqnarray} In the other hand, the equations of motion from (\ref{SD_6}) with $j^{\mu\nu\alpha}=0$ are given by: \begin{eqnarray} -\frac{1}{2m^{3}}\mathbb{G}_{\mu\nu\alpha}(\mathbb{S}(Eh))+\frac{1}{12m^{4}}E_{(\mu}^{\;\;\;\beta}\mathbb{G}_{\beta\nu\alpha)}(\mathbb{S}(Eh))=0\;.\end{eqnarray} \noindent Again, rewritten it in terms of the dual field $h^{\ast}_{\beta\nu\alpha}$ we have: \begin{eqnarray} -m^2h^{\ast}_{\mu\nu\alpha}+\frac{m}{6}E_{(\mu}^{\;\;\;\beta}h^{\ast}_{\beta\nu\alpha)}=0\label{eom-SD_6}\;.\end{eqnarray} \noindent Then, we have showed that the $SD_5^{(3)}$ equations of motion (\ref{eom-SD_5}) can be taken to the $SD_6^{(3)}$ equations through the dual map $\tau^_{\beta\nu\alpha} \to h^_{\beta\nu\alpha}$ once they have the same form. \section{Higher derivative doublet models} Here we complement some previous discussions that we have made in \cite{hds3} where we have suggested master actions interpolating among three equivalent doublet models describing massive spin $3$ particles in $D=2+1$ dimensions. We have verified that the Singh-Hagen model is in fact dual to a fourth order model, which is analogue to the spin-2 New Massive Gravity model \cite{bht} . However in the spin-3 case differently of the spin-2 case one can obtain a sixth order model which has no analogue in the spin-2 context. After revisiting this issue under the point of view of symmetries some other analogies arise. In order to understand the role of symmetries when we are mapping such dual descriptions we start with the massive second order Singh-Hagen model. The model requires a totally symmetric field $\phi_{\mu\nu\alpha}$ and auxiliary fields which may be either a vector or a scalar field. Here to keep the similarities with our previous work, we choose scalar fields $W$: \begin{eqnarray} S_{SH} &=& \int d^3x \left[\frac{1}{2}\phi_{\mu\nu\lambda} {\mathbb G}_{\mu\nu\lambda}(\phi)-\frac{m^{2}}{2}(\phi_{\mu\nu\lambda}\phi^{\mu\nu\lambda}-3\phi_{\mu}\phi^{\mu}) -m\, \phi_{\mu}\partial^{\mu}W\right]+S_1[W].\label{master}\end{eqnarray} \noindent The auxiliary action $S_1[W]$, is given by: \begin{equation} S_1[W]=\int d^3x \left(9m^2W^{2}-\frac{4}{3}W\Box W\right).\end{equation} \noindent With respect to the symmetries one can easily verify that the second order rank-3 term is invariant under traceless reparametrizations $\delta_{\tilde{\xi}}\phi_{\mu\nu\lambda}=\partial_{(\mu}\tilde{\xi}_{\nu\lambda)}$ . From the equations of motion with respect the rank-3 field, we have the Euler tensor: \begin{equation} K^{\mu\nu\lambda}={\mathbb G}^{\mu\nu\lambda}(\psi)-m^2(\phi^{\mu\nu\lambda}-\eta^{(\mu\nu}\phi^{\lambda)})-\frac{m}{3}\eta^{(\mu\nu}\partial^{\lambda)}W.\label{M}\end{equation} \noindent It is also convenient to keep in hand the trace of (\ref{M}) which is given by: \begin{equation} K^{\lambda}=\mathbb{G}^{\lambda}(\phi)+4m^2\phi^{\lambda}-\frac{5m}{3}\partial^{\mu}W.\end{equation} Introducing an extra auxiliary field $a_{\mu\nu\lambda}$ with the specific gauge symmetry $\delta_{\tilde{\xi}}a_{\mu\nu\lambda}=-\delta_{\tilde{\xi}}\phi_{\mu\nu\lambda}$ we have the first iteration: \begin{equation} S_1=S_{SH}+\int d^3x\,\, a_{\mu\nu\lambda}K^{\mu\nu\lambda}.\label{fi}\end{equation} In (\ref{fi}) we now perform the $\tilde{\xi}$-gauge variation wich after some calculation take us to the following result: \begin{equation}\delta_{\tilde{\xi}} S_1=\int \,\,d^3x\, \delta_{\tilde{\xi}}\left\lbrack \frac{m^2}{2}(a_{\mu\nu\lambda}a^{\mu\nu\lambda}-3a_{\mu}a^{\mu})\right\rbrack,\end{equation} \noindent which by construction allows us to determine the second iterate action automatically $\tilde{\xi}$-gauge invariant given by: \begin{equation} S_2= S_{SH}+\int\,\,d^3x\,\left\lbrack a_{\mu\nu\lambda}K^{\mu\nu\lambda}-\frac{m^2}{2}(a_{\mu\nu\lambda}a^{\mu\nu\lambda}-3a_{\mu}a^{\mu})\right\rbrack\end{equation} \noindent solving the equations of motion for the auxiliary fields $a_{\mu\nu\lambda}$, one can invert it in terms of the Euler tensors, which then give us: \begin{equation} S_2=S_{SH}+\frac{1}{2m^2}\int\,\,d^3x\,\left(K_{\mu\nu\lambda}K^{\mu\nu\lambda}-\frac{3}{4}K_{\mu}K^{mu}\right),\label{S2}\end{equation} \noindent by substituting back the Euler tensor in the expression (\ref{S2}), we finally have the fourth order model: \begin{eqnarray} S_4&=&\int d^3x \, \left[-\frac{1}{2}\phi_{\mu\nu\lambda}{\mathbb G}^{\mu\nu\lambda}(\phi)+\frac{1}{2m^2} {\mathbb S}_{\mu\nu\lambda}(\phi){\mathbb G}^{\mu\nu\lambda}(\phi)+\frac{1}{12m}\phi_{\mu\nu\lambda}{\mathbb G}^{\mu\nu\lambda}(\eta\partial W)\right]+S_2[W].\nonumber\\ \label{fourth}\end{eqnarray} \noindent Where $\eta\partial W$ stands for the fully symmetric tensor $\eta_{(\mu\nu}\partial_{\rho)}W = \eta_{\mu\nu}\partial_{\rho}W + \eta_{\nu\rho}\partial_{\mu} W + \eta_{\rho\mu} \partial_{\nu} W $, while \begin{equation} S_2[W]=\int d^3x \left(9m^2W^{2}-\frac{9}{8}W\Box W\right). \label{s2w}\end{equation} \noindent The fourth order model that we have obtained in (\ref{fourth}) is precisely the one we have found in \cite{hds3}. There we have also added source terms in order to verify the dual map with the equations of motion of the Singh-Haggen model. One also notices that the auxiliary action as well as the linking term between $\phi_{\mu\nu\alpha}$ and the auxiliary fields $W$, have been automatically corrected during the process, which is a fundamental step in order to get rid of the lower spin propagation modes, which in this case is a spin-0 mode. \section{From the fourth to the sixth order model } The action (\ref{fourth}) is invariant under the traceless reparametrization $\delta_{\tilde{\xi}}\phi_{\mu\nu\lambda}$, but once the fourth order term is indeed the same one we have in the fifth order self-dual model (\ref{SD_5}), we know that it is invariant under an additional gauge symmetry given by transverse Weyl transformation $\delta_{\psi^T}\phi_{\mu\nu\lambda}=\eta_{(\mu\nu}\psi_{\lambda)}^T$. Such symmetry is broken by the first term of the Singh-Hagen action, which indicates that there is another round of $NGE$ in order. To implement this symmetry we start by calculating the Euler tensor from (\ref{fourth}) which is given by: \begin{equation} K^{\mu\nu\lambda}=-{\mathbb {G}}^{\mu\nu\lambda}(\phi)+\frac{1}{m^2}{\mathbb {G}}^{\mu\nu\lambda}\left[S(\phi)\right]+\frac{1}{12m}{\mathbb {G}}^{\mu\nu\lambda}(\eta\partial W)\label{eu}.\end{equation} \noindent Again, an auxiliary field is suggested in a first iterated action: \begin{equation} S_1=S_{SH}-\int d^3x\,\, a_{\mu\nu\lambda}K^{\mu\nu\lambda}.\label{fi2}\end{equation} When we take the $\psi_{\lambda}^T$ gauge-transformation on $S_1$ we end up with the following result, after some calculation: \begin{equation} \delta_{\psi^T}S_1=\int \,\,d^3x\,\delta_{\psi^T}\left[\frac{a_{\mu\nu\lambda}\mathbb{G}^{\mu\nu\lambda}(a)}{2}\right].\end{equation} \noindent As we have seen before, now we have a gauge invariant action given by: \begin{equation} S_2=S_4-\int\,d^3x\,\,\left[a_{\mu\nu\lambda}K^{\mu\nu\lambda}+\frac{a_{\mu\nu\lambda}\mathbb{G}^{\mu\nu\lambda}(a)}{2}\right]\end{equation} \noindent One can notice that the Euler tensor given at (\ref{eu}) can be rewritten in such a way that $K_{\mu\nu\lambda}=\mathbb{G}^{\mu\nu\lambda}(b)$ where \begin{equation} b^{\mu\nu\lambda}=-\phi^{\mu\nu\lambda}+\frac{1}{m^2}\mathbb{S}^{\mu\nu\lambda}(\phi)+\frac{1}{12m}\eta^{(\mu\nu}\partial^{\lambda)}W\end{equation} \noindent which allows us to rewrite the action $S_2$ as: \begin{equation} S_2=S_4-\int\,d^3x\,\, \left[\frac{1}{2}(a_{\mu\nu\lambda}+b_{\mu\nu\lambda})\mathbb{G}^{\mu\nu\lambda}(a+b)-\frac{1}{2}b_{\mu\nu\lambda}\mathbb{G}^{\mu\nu\lambda}(b)\right]\label{s6d}\end{equation} \noindent shifting the auxiliary field $a_{\mu\nu\lambda}\to a_{\mu\nu\lambda}-b_{\mu\nu\lambda}$ we get a completely decoupled second order term, which is free of particle content, see \cite{deserdamour}. After substituting back $b_{\mu\nu\lambda}$ in (\ref{s6d}) we have after some rearrangements a sixth order action invariant under the gauge transformations (\ref{Tr-4}). \begin{eqnarray} S_6&=&\int d^3x\,\left[- \frac{1}{2m^2}{\mathbb S}_{\mu\nu\lambda}(\phi){\mathbb G}^{\mu\nu\lambda}(\phi)+\frac{1}{2m^4}{\mathbb S}_{\mu\nu\lambda}(\phi){\mathbb G}^{\mu\nu\lambda}[{\mathbb S}(\phi)]+\frac{1}{12m^3}{\mathbb S}_{\mu\nu\lambda}(\phi){\mathbb G}^{\mu\nu\lambda}(\eta\partial W)\right].\nonumber\\ &+& S_3[W]\label{HD}\end{eqnarray} \noindent Notice that the auxiliary action $S_3[W]$ has now an extra higher derivative term : \begin{equation} S_3[W]=\int d^3x \left(9m^2W^{2}-\frac{9}{8}W\Box W+\frac{9}{64m^2}W\Box^2 W\right).\end{equation} The sixth order spin-3 model \cite{hds3} and the fifth order self-dual model $SD_5^{(3)}$ (\ref{SD_5}) share the same symmetries (\ref{Tr-4}). This is similar to the spin-2 case where the $NMG$ ($4th$ order) and the Topologically Massive Gravity $TMG$ \cite {DJT}, ($3rd$ self-dual model $SD_3^{(2)}$) have the same symmetries. \section{Conclusion} In the works \cite{clovis}, \cite{mls}, and \cite{SD_4} one has shown respectively, that the spin-1, spin-3/2 and spin-2 self-dual models of j-th order in derivatives can be obtained from the models of previous (j-1)-th order via a Noether gauge embedding (NGE) procedure, where j runs from $2$ until the top value $2s$. Regarding the spin-3 case we have shown in \cite{nge} that such procedure only works until the fourth order, i.e., j$=2,3,4$. Explicitly, the models and the symmetries\footnote{The field $\omega_{\mu (\alpha\beta)}$ satisfies $\omega_{\mu (\alpha\beta)}=\omega_{\mu (\beta\alpha)}$ and $\eta^{\alpha\beta}\omega_{\mu (\alpha\beta)}=0$.} used in the NGE procedure are sketeched below \begin{center} \begin{tikzpicture}[>=latex',node distance = 5.25cm] \node (S1) {$SD_1^{(3)}$}; \node [right of = S1] (S2) {$SD_2^{(3)}$}; \node [right of = S2] (S3) {$SD_3^{(3)}$}; \node [right of = S3] (S4) {$SD_4^{(3)}$}; \draw [->,thick] (S1) to [ left=50] node[below] {$\delta\omega_{\mu(\nu\alpha)}=\partial_{\mu}\tilde{\xi}_{\nu\alpha}$} (S2); \draw [->,thick] (S2) to [ right=50] node[below] {$ \delta\omega_{\mu(\beta\gamma)}=\epsilon_{\mu\beta\rho}\Phi^{\rho}_{\,\,\gamma}+\epsilon_{\mu\gamma\rho}\Phi^{\rho}_{\,\,\beta}$} (S3); \draw [->,thick] (S3) to [ left=50] node[below] {$\delta\phi_{\mu\beta\gamma}=\partial_{(\mu}\xi_{\beta\gamma)}$} (S4); \end{tikzpicture} \end{center} \noindent In particular, we had not been able to derive any fifth order spin-3 model via NGE. Consequently, the top 6th-order spin-3 model $SD_6^{(3)}$ of \cite{bhth} could not be reached from the fourth order model $SD_4^{(3)}$ of \cite{nge}. Usually, a self-dual model of order j contains a j-th and a (j-1)-th order term. The j-th term has more symmetries in general as compared to the rest of the Lagrangian. The exceeding symmetry is the one we use in the NGE approach. It turns out that both fourth and third order terms inside the $SD_4^{(3)}$ model defined in \cite{nge} are invariant under the same set of transformations ($\delta h_{\mu\nu\rho} = \partial_{(\mu}\xi_{\nu\rho )}$) . So no difference is left over to be implemented in the NGE approach. Recently however, we have found \cite{ddhigher}, by other means, the missing spin-3 fifth order self-dual model $SD_5^{(3)}$. Here we have shown that it is now possible to arrive at the $SD_6^{(3)}$ via NGE of longitudinal Weyl transformations which is the symmetry of the fifth order term of $SD_5^{(3)}$, not present in the fourth order term, namely \begin{center} \begin{tikzpicture}[>=latex',node distance = 7.0cm] \node (S1) {$SD_5^{(3)}$}; \node [right of = S1] (S2) {$SD_6^{(3)}$}; \draw [->,thick] (S1) to [ left=50] node[below] {$\delta\phi_{\mu\beta\gamma}=\eta_{(\mu\nu}\partial_{\alpha)}\Phi$} (S2); \end{tikzpicture} \end{center} \noindent We still do not know how to fill up the gap between $SD_4^{(3)}$ and $SD_5^{(3)}$. We believe that there might be another fourth order self-dual model whose embedding would lead us to $SD_5^{(3)}$. Unfortunately we do no know how to go downstairs in derivatives systematically. This is still under investigation. The NGE procedure also works for parity doublets, we have shown in \cite{SD_4} that the fourth order spin-2 ``New Massive Gravity'' of \cite{bht}, in its linearized form, can be derived from the usual (second order) Fierz-Pauli theory \cite{fp} via NGE of linearized reparametrizations $\delta h_{\mu\nu}=\partial_{\mu}\xi_{\nu} + \partial_{\nu}\xi_{\mu}$. Here we have generalized \cite{SD_4} for spin-3 doublets. From the usual massive second order Singh-Hagen model we have derived a fourth and a sixth order dual doublet model with helicities $+3$ and $-3$. Namely, \begin{center} \begin{tikzpicture}[>=latex',node distance = 5.0cm] \node (S1) {$S_{SH}$}; \node [right of = S1] (S2) {$S_4$}; \node [right of = S2] (S3) {$S_6$}; \draw [->,thick] (S1) to [ left=50] node[below] {$\delta\phi_{\mu\beta\gamma}=\partial_{(\mu}\tilde{\xi}_{\nu\lambda)}$} (S2); \draw [->,thick] (S2) to [ right=50] node[below] {$\delta\phi_{\mu\beta\gamma}=\eta_{(\mu\nu}\psi_{\lambda)}^T$} (S3); \end{tikzpicture} \end{center} \noindent We believe that there is a chain of $s$ dual doublet models of spin-s and order $j=2,4,6, \cdots ,2s$. Differently of the spin-2 case, where the top fourth $(2s)$ order term (K-term) of the top doublet model (linearized NMG) coincides with the fourth order term of the top (4th order) spin-2 self-dual model, the sixth order term of the top doublet model $S_6^{(3)}$ does not coincide with the sixth order term of the top singlet model $SD_6^{(3)}$. We are currently investigating the soldering of two $SD_6^{(3)}$ models of opposite helicities in order to produce a doublet model without auxiliary fields, contrary to $S_6$ which contains an auxiliary scalar field. There is no doublet spin-3 model without auxiliary fields even in $D=2+1$, to the best we know. If the soldering procedure can be successfully implemented we will be able to build up massive higher spin Lagrangians systematically in $D=2+1$ and in $D=3+1$ (doublet models) since the doublet models have the same form in $D=2+1$ and in $D=3+1$. \section{Acknowledgements} The work of D.D. is partially supported by CNPq (grant 306380/2017-0). A.L.R.dos S. is supported by a CNPq-PDJ (grant 150524/2018-8).	{ "redpajama_set_name": "RedPajamaArXiv" }	5,379
{"url":"https:\/\/gamedev.stackexchange.com\/questions\/172843\/how-to-set-the-first-color-of-the-list-in-the-sprite","text":"# how to set the first color of the list in the sprite\n\npublic List<SpriteRenderer> spritebox = new List<SpriteRenderer>();\npublic List<Color> colorbox = new List<Color>();\n\nvoid Start() {\nvar renderer = GetComponent<SpriteRenderer>();\ncolorbox.Add(renderer.color);\/\/I did so, except that it sends the color of the sprite to the list and in the last slot\n\nspritebox = GetComponent<SpriteRenderer>();\ncolorbox = spritebox.color;\/\/I did that too but it did not work\n\n}\n\n\nI'm trying to make the first color of the list in case the element 0 send the color to the sprite,would have any tips to help me?\n\nIn arrays and C# lists (which are wrappers for arrays that allow dynamic resizing) you should access elements by index in square brackets.\n\nExamples:\n\nThis will get the first color from colorbox and store it in variable color:\nColor color = colorbox[0];\n\nThis will assign color color to the first SpriteRenderer from spritebox:\nspritebox[0].color = color;\n\nYou can put a variable or an expression inside brackets.\n\n\u2022 Thank you it worked perfectly \u2013\u00a0Rangel Jun 13 '19 at 20:57","date":"2021-01-24 22:41:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.21488231420516968, \"perplexity\": 2578.121602667532}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703557462.87\/warc\/CC-MAIN-20210124204052-20210124234052-00255.warc.gz\"}"}	null	null
package com.rackspacecloud.blueflood.outputs; import com.netflix.astyanax.connectionpool.exceptions.ConnectionException; import com.rackspacecloud.blueflood.exceptions.GranularityException; import com.rackspacecloud.blueflood.io.astyanax.AstyanaxReader; import com.rackspacecloud.blueflood.io.astyanax.AstyanaxWriter; import com.rackspacecloud.blueflood.io.CassandraModel; import com.rackspacecloud.blueflood.io.IntegrationTestBase; import com.rackspacecloud.blueflood.outputs.formats.MetricData; import com.rackspacecloud.blueflood.outputs.handlers.RollupHandler; import com.rackspacecloud.blueflood.rollup.Granularity; import com.rackspacecloud.blueflood.service.SingleRollupWriteContext; import com.rackspacecloud.blueflood.types.; import org.junit.Assert; import org.junit.Before; import org.junit.Test; import java.util.; /** * This class writes FULL data for a 48 hour period and then rolls up only a 5 hour portion from the middle of the 48 hours. * * Then the following conditions are tested, for both Single Plot and Multi Plot: * <li> Where the front part of a requested range needs to be rolled-up-on-read and the back half is already rolled up. * <li> Where the back part of a requested range needs to be rolled-up-on-read and the front half is already rolled up. * <li> Where the entire range needs to be rolled up. * * These tests verify that the correct timestamp keys are generated as well as that the total average of all FULL values * and the returned rolled up values are within 5%. * * NOTE: * <li> The MPLOT tests depend upon CoreConfig.TURN_OFF_RR_MPLOT == false, which is currently the default setting. * / public class RollupHandlerIntegrationTest extends IntegrationTestBase { RollupHandler rollupHandler = new RollupHandler(); private String acctId = "rollupIntegrationTest" + IntegrationTestBase.randString(8); private List<String> metricList = new ArrayList<String>( Arrays.asList( "rollupHandlerIntegrationTest1," + randString( 8 ), "rollupHandlerIntegrationTest2," + randString( 8 ), "rollupHandlerIntegrationTest3," + randString( 8 ) )); private List<Locator> locatorList = new ArrayList<Locator>(); private long hours = 48; private long startMS = 1432147283000L; // some point during 20 May 2015. private long endMS = startMS + (1000 60 * 60 * hours); // 48 hours of data private long startRollupMS = startMS + (1000 * 60 * 60 * (hours/2 - 5)); private long endRollupMS = startMS + (1000 * 60 * 60 * (hours/2)); @Before public void initData() throws Exception { for( String metric : metricList ) { locatorList.add( Locator.createLocatorFromPathComponents( acctId, metric ) ); } AstyanaxWriter writer = AstyanaxWriter.getInstance(); AstyanaxReader reader = AstyanaxReader.getInstance(); writeFullData( writer ); writeRollups( reader, writer ); } private void writeRollups( AstyanaxReader reader, AstyanaxWriter writer ) throws GranularityException, java.io.IOException, ConnectionException { for( Locator locator : locatorList ) { ArrayList<SingleRollupWriteContext> writes = new ArrayList<SingleRollupWriteContext>(); for ( Range range : Range.getRangesToRollup( Granularity.FULL, startRollupMS, endRollupMS ) ) { // each range should produce one average Points<SimpleNumber> input = reader.getDataToRoll( SimpleNumber.class, locator, range, CassandraModel.CF_METRICS_FULL ); BasicRollup basicRollup = BasicRollup.buildRollupFromRawSamples( input ); writes.add( new SingleRollupWriteContext( basicRollup, locator, Granularity.FULL.coarser(), CassandraModel.getColumnFamily( BasicRollup.class, Granularity.FULL.coarser() ), range.start ) ); } writer.insertRollups( writes ); } } private void writeFullData( AstyanaxWriter writer ) throws Exception { // insert something every minute for 48h for ( Locator locator : locatorList ) { for ( int i = 0; i < 60 * hours; i++ ) { final long curMillis = startMS + i * 60000; List<Metric> metrics = new ArrayList<Metric>(); metrics.add( getRandomIntMetricMaxValue( locator, curMillis, 100 ) ); writer.insertFull( metrics ); } } } @Test public void testSplotRollupsOnReadGenerationLeft() throws Exception { List<String> metric = new ArrayList<String>(); metric.add( metricList.get( 0 ) ); Locator locator = locatorList.get( 0 ); Map<Locator, MetricData> metricDataMap = rollupHandler.getRollupByGranularity(acctId, metric, startMS, endRollupMS, Granularity.MIN_5); Map<Long, Points.Point<BasicRollup>> points = metricDataMap.get(locator).getData().getPoints(); // test keys Iterator<Range> repairedRanges = Range.getRangesToRollup(Granularity.FULL, startMS, endRollupMS).iterator(); for (Long timestamp : points.keySet() ) { Assert.assertEquals( repairedRanges.next().getStart(), timestamp.longValue() ); } /* TODO: Fix with CMD-1001 // test value double fullMean = fullPointsMean( metric, locator, startMS, endRollupMS ); double rollMean = meanOfPointCollectionRoll( points.values() ); Assert.assertEquals( rollMean, fullMean, getEpsilon( fullMean, rollMean ) ); / } @Test public void testSplotRollupsOnReadGenerationRight() throws Exception { List<String> metric = new ArrayList<String>(); metric.add( metricList.get( 0 ) ); Locator locator = locatorList.get( 0 ); Map<Locator, MetricData> metricDataMap = rollupHandler.getRollupByGranularity(acctId, metric, startRollupMS, endMS, Granularity.MIN_5); Map<Long, Points.Point<BasicRollup>> points = metricDataMap.get(locator).getData().getPoints(); // test keys Iterator<Range> repairedRanges = Range.getRangesToRollup(Granularity.FULL, startRollupMS, endMS).iterator(); for (Long timestamp : points.keySet() ) { Assert.assertEquals( repairedRanges.next().getStart(), timestamp.longValue() ); } / TODO: Fix with CMD-1001 // test value double fullMean = fullPointsMean( metric, locator, startRollupMS, endMS ); double rollMean = meanOfPointCollectionRoll( points.values() ); Assert.assertEquals( rollMean, fullMean, getEpsilon( fullMean, rollMean ) ); / } @Test public void testSplotRollupsOnReadGenerationEntireRange() throws Exception { List<String> metric = new ArrayList<String>(); metric.add( metricList.get( 0 ) ); Locator locator = locatorList.get( 0 ); // start 1 hour after rollups ended long start = endRollupMS + 1000 60 * 60; // test keys Map<Locator, MetricData> metricDataMap = rollupHandler.getRollupByGranularity(acctId, metric, start, endMS, Granularity.MIN_5); Map<Long, Points.Point<BasicRollup>> points = metricDataMap.get(locator).getData().getPoints(); Iterator<Range> repairedRanges = Range.getRangesToRollup(Granularity.FULL, start, endMS).iterator(); for (Long timestamp : points.keySet()) { Assert.assertEquals(repairedRanges.next().getStart(), timestamp.longValue() ); } /* TODO: Fix with CMD-1001 // test value double fullMean = fullPointsMean( metric, locator, start, endMS ); double rollMean = meanOfPointCollectionRoll( points.values() ); Assert.assertEquals( rollMean, fullMean, getEpsilon( fullMean, rollMean ) ); / } @Test public void testMplotRollupsOnReadGenerationLeft() throws Exception { Map<Locator, MetricData> metricDataMap = rollupHandler.getRollupByGranularity(acctId, metricList, startMS, endRollupMS, Granularity.MIN_5); for( int i = 0; i < locatorList.size(); i++ ) { Locator locator = locatorList.get( i ); List<String> metric = new ArrayList<String>(); metric.add( metricList.get( i ) ); // test keys Map<Long, Points.Point<BasicRollup>> points = metricDataMap.get( locator ).getData().getPoints(); Iterator<Range> repairedRanges = Range.getRangesToRollup( Granularity.FULL, startMS, endRollupMS ).iterator(); for ( Long timestamp : points.keySet() ) { Assert.assertEquals( repairedRanges.next().getStart(), timestamp.longValue() ); } / TODO: Fix with CMD-1001 // test value double fullMean = fullPointsMean( metric, locator, startMS, endRollupMS ); double rollMean = meanOfPointCollectionRoll( points.values() ); Assert.assertEquals( rollMean, fullMean, getEpsilon( fullMean, rollMean ) ); / } } @Test public void testMplotRollupsOnReadGenerationRight() throws Exception { Map<Locator, MetricData> metricDataMap = rollupHandler.getRollupByGranularity(acctId, metricList, startRollupMS, endMS, Granularity.MIN_5); for( int i = 0; i < locatorList.size(); i++ ) { Locator locator = locatorList.get( i ); List<String> metric = new ArrayList<String>(); metric.add( metricList.get( i ) ); // test keys Map<Long, Points.Point<BasicRollup>> points = metricDataMap.get( locator ).getData().getPoints(); Iterator<Range> repairedRanges = Range.getRangesToRollup( Granularity.FULL, startRollupMS, endMS ).iterator(); for ( Long timestamp : points.keySet() ) { Assert.assertEquals( repairedRanges.next().getStart(), timestamp.longValue() ); } / TODO: Fix with CMD-1001 // test value double fullMean = fullPointsMean( metric, locator, startMS, endRollupMS ); double rollMean = meanOfPointCollectionRoll( points.values() ); Assert.assertEquals( rollMean, fullMean, getEpsilon( fullMean, rollMean ) ); / } } @Test public void testMplotRollupsOnReadGenerationEntireRange() throws Exception { // start 1 hour after rollups ended long start = endRollupMS + 1000 60 * 60; Map<Locator, MetricData> metricDataMap = rollupHandler.getRollupByGranularity( acctId, metricList, start, endMS, Granularity.MIN_5 ); for( int i = 0; i < locatorList.size(); i++ ) { Locator locator = locatorList.get( i ); List<String> metric = new ArrayList<String>(); metric.add( metricList.get( i ) ); // test keys Map<Long, Points.Point<BasicRollup>> points = metricDataMap.get( locator ).getData().getPoints(); Iterator<Range> repairedRanges = Range.getRangesToRollup( Granularity.FULL, start, endMS ).iterator(); for ( Long timestamp : points.keySet() ) { Assert.assertEquals( repairedRanges.next().getStart(), timestamp.longValue() ); } /* TODO: Fix with CMD-1001 // test value double fullMean = fullPointsMean( metric, locator, start, endMS ); double rollMean = meanOfPointCollectionRoll( points.values() ); Assert.assertEquals( rollMean, fullMean, getEpsilon( fullMean, rollMean ) ); / } } private double meanOfPointCollectionFull( Collection<Points.Point<SimpleNumber>> fullPoints ) { double sum = 0; for( Points.Point<SimpleNumber> p : fullPoints ) { sum += p.getData().getValue().intValue(); } return sum / fullPoints.size(); } private double meanOfPointCollectionRoll( Collection<Points.Point<BasicRollup>> fullPoints ) { long sum = 0; for( Points.Point<BasicRollup> p : fullPoints ) { sum += p.getData().getAverage().toLong(); } return sum / fullPoints.size(); } private double fullPointsMean( List<String> metric, Locator locator, long start, long end ) { Collection<Points.Point<SimpleNumber>> fullPoints = rollupHandler.getRollupByGranularity( acctId, metric, start, end, Granularity.FULL ) .get( locator ).getData().getPoints().values(); return meanOfPointCollectionFull( fullPoints ); } private double getEpsilon( double fullMean, double rollMean ) { return Math.abs( Math.max(fullMean, rollMean) .05 ); } }	{ "redpajama_set_name": "RedPajamaGithub" }	6,567
Kidane Kale (dosł. "Początek, Słowo") znany lepiej jako Abije (ur. ? – zm. około 1745) – władca Szeua w latach 1718-1744 lub 1745. Nosił tytuł meridazmacza i był ważnym amharskim możnowładcą osiemnastowiecznej Etiopii. Był synem poprzedniego władcy szeuańskiego o imieniu Sebestianos. Żoną Abije była ueizero Tagunestija, córka zarządcy Mamameder. Nie jest do końca pewne ile lat rządził Abije w Szeua. Według Mordechaia Abira okres jego rządów trwał dwadzieścia pięć lat, zaś wedle angielskiego podróżnika Williama Cornwallisa Harrisa piętnaście lat. Życiorys Początek rządów Abije odziedziczył tron Szeua po śmierci swojego ojca i początkowo ustanowił swoją stolicę w Har Amba. Według Donalda Levine'a Sebestianos zmarł wskutek osobliwego wypadku. Otóż Abije odbudowywał niektóre z kościołów zniszczonych przez muzułmańską inwazję imama Grania, która miała miejsce w XVI wieku. Jeden z odnawionych przez Abije kościołów znajdował się w Dokakit i był pod wezwaniem świętego Michała. Część ceremonii związanej z nowo odbudowaną świątynią wymagała tabotu z kościoła w Ajne, gdzie mieszkał jego ojciec. Tabot został potajemnie usunięty z Ajne i przeniesiony do Dokakit przez Abije. Sebestianos potraktował to jako akt buntu i postanowił schwytać oraz zdyscyplinować swego syna. W wynikłej później walce, jeden ze sług Abije przypadkowo zabił meridazmacza Sebestianosa. Konflikt z cesarzem Ponieważ Sebestianos odmówił złożenia hołdu cesarzowi Etiopii, krótko po dojściu do władzy Abije miał do czynienia z atakiem armii etiopskiego cesarza Jozuego II Kuareńczyka. Mimo iż zaatakowany przeżył zagrożenie bez szwanku, źródła różnią się co do szczegółów cesarskiej wyprawy. Mordechai Abir podał wersję, według której pośrednicy obu stron umówili się, że w zamian za ofiarowanie daniny Abije oficjalnie uzyska tytuł meridazmacza. Harold Marcus uważał, iż Jozue II był bardziej skupiony na walkach z plemieniem Uello Oromo, znajdującym się bliżej jego ośrodka władzy w stolicy Gonderze. Z kolei Donald Levine postawił tezę zakładającą, że Abije spotkał się z Kuareńczykiem i pokonał go w walce. Późniejsze lata Abije kontynuował wojskową konsolidację chrześcijańskich księstw zlokalizowanych dookoła Szeua i toczył walki z Oromami, najeżdżającymi Etiopię od XVI wieku. Według relacji niemieckiego misjonarza Johanna Ludwiga Krapfa, Abije pokonał władcę miasta Menz zwanego Gole, a następnie przyłączył ten region do Sheua. Abije zmarł w walce z Karaju Oromo, na południe od Jifat i został pochowany w swojej stolicy Dokakit. Następcą Abije został jego syn znany jako Amhajes Sprawiedliwy. Zobacz też Etiopistyka Abba Sjeru Guangul Aligaz z Jedżu Sahle Syllasje Mikael Syul Uwagi Przypisy Bibliografia Andrzej Bartnicki, Joanna Mantel-Niećko, Historia Etiopii, Wrocław, Zakład Narodowy im. Ossolińskich – Wydaw., 1987. Harold G.Marcus, The Life and Times of Menelik II: Ethiopia 1844-1913, Lawrenceville: Red Sea Press, 1995, . Mordechai Abir, Ethiopia: The Era of the Princes; The Challenge of Islam and the Re-unification of the Christian Empire (1769-1855), London: Longmans, 1968. Historia Etiopii Zmarli w 1745 Władcy Szeua	{ "redpajama_set_name": "RedPajamaWikipedia" }	9,351
Robert Crudup, Executive Vice President & CIO, SEI Chad Sheridan, CIO, USDA Martin P.Rose, CIO, Pinellas County Tom Duncan, Executive Director, CBRE Marc Priolo, VP, City National Bank Brent Preator, VP, Data Governance, Global Accounts, JLL Leandro Pinter, Head of Software Engineering, Tyro Payments Ranjan Singh, Vice President, Product Management, IPC Systems Proven Opportunities of DevSecOps in Security Management By CIO Applications Europe\| Tuesday, December 11, 2018 DevOps is nothing new to the current technology market, particularly in the security industry; businesses are in need for automation and orchestration abilities which are considered to be the basic requirement for the deployment and development of technology applications. As a new approach to this scenario, DevOps or the DevSecOps changes the security management in many ways. Although there are several reasons for the adoption of DevSecOps; one of the most significant is the attacks by hackers. Today, organizations cannot think about a situation where their businesses are hacked. Implementation of DevSecOps' automated functions enables organizations to scan source code and all libraries completely within the business. The recent changes or shifts in DevOps help organizations to manage security threats far better than how they have managed them before. DevSecOps changes the security management function of an organization with the help of its several components. Code analysis is a significant component of the DevSecOps approach that enables enterprises to deliver code in small chunks. Thus, the threats and vulnerabilities can be identified more effectively and quickly. Change management is the next important component of DevSecOps which increases the efficiency and speed and allows other people to suggest changes and then decide whether to accept the changes or not. Another essential component, the compliance monitoring advances an audit at any time, such as GDPR compliance and PCI compliance. Threat investigation identifies upcoming threats with each code updated. Next one is the vulnerability assessment which deals with the assessment of new emerging threats with code analysis. Finally, the security training, as the name suggests, is about training the software engineers and IT engineers and provides them with some guidelines for set routines. DevSecOps will allow organizations to develop, plan, deploy, and operate the security function within the organization. Today, the users, especially the potential customers, expect the latest technological applications and updated features when they come in contact with the organization. Therefore, an effective security management system should be maintained by the enterprise. This creates opportunities for DevSecOps to perform with its new advancements, and organizations today have become keener to utilize them. Principles Underpinning DevOps Building an Enterprise API? DevOps is the Formula! DevOps Practices to Drive Scalability, the Success Catalyst The 'Know-About' of Devops in Business https://www.cioapplicationseurope.com/news/proven-opportunities-of-devsecops-in-security-management-nid-648.html	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	119
New Book from Charles Koch Coming this October Visionary CEO Charles G. Koch shares his unique and innovative management framework that built one of the world's largest and most successful companies. "Good Profit" to be published by Crown Business in October 2015. Crown Business, an imprint of the Crown Publishing Group, has agreed to publish Chairman of the Board and CEO Charles G. Koch's thought-provoking and prescriptive book detailing the proven success of the management principles and business philosophy at the center of Koch Industries, Inc. Good Profit: How Creating Value for Others Built One of the World's Most Successful Companies, will be published in North America in October 2015, in print, digital, and audio by Random House Audio. Read More: Charles Koch working on business book, scheduled for October The book's publication was announced today by Tina Constable, Senior Vice President and Publisher of Crown Business, who acquired world, audio, electronic, and first and second serial rights to the work. Leah Spiro of Riverside Creative Management, Inc. represented Koch Industries. Talia Krohn, Senior Editor at Crown Business, will edit the book. In the business community, Charles Koch is known as a visionary who grew Koch Industries into the second-largest private company in America with revenues of approximately $115 billion according to Forbes. Koch companies have a presence in about 60 countries and employ more than 100,000 people worldwide, with 60,000 of those in the U.S. Charles has been intimately involved in the day-to-day management of the company's business operations since 1961. He assumed the reins of the company in 1967 following his father's death. It is largely thanks to Charles' holistic approach to management – which he has dubbed and trademarked Market-Based Management – that the company's value has increased 4,600 times under his leadership. Good Profit details the management principles that have fueled Koch Industries' astounding rise—and shows readers how to apply them in any business or other organization, and in their personal life. "I believe good profit is the result of principled entrepreneurship," said Koch. "It occurs when businesses produce products and services that help people improve their lives, and do so while using fewer resources. This – rather than seeking corporate welfare – is the proper role of business. At Koch Industries, we use a framework called MBM®, which is based on a system of mutual benefit, respect for our customers' values and jobs that bring genuine fulfillment. I credit much of our remarkable success (and ability to overcome setbacks) to MBM. It is my hope that this book will enable many others to also succeed by benefitting society." "Charles Koch is undeniably one of the great business icons of our time. His MBM® technique is the definitive treatise on management that we look forward to bringing to a wide readership," said Constable. "We are thrilled to be Charles's publishing partner for his book." Koch IndustriesMedia Resources Press Releases 2015 New Book from Charles Koch Coming this October	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	9,665
It's nearly Stags season! What do you think of this year's line-up? The Southland Stags were named today in Invercargill. Who's going to Riverdale Arts' annual exhibition this year? The group is celebrating its 45th exhibition.	{ "redpajama_set_name": "RedPajamaC4" }	6,247
\section{Introduction} In a seminal paper published in 1962, Goldstone, Salam and Weinberg~\cite{GSW} proved that the physical particle spectrum of a theory in which a continuous, global symmetry is spontaneously broken must contain one massless, spin-zero particle for each broken symmetry. Massless particles of this type, today called Nambu-Goldstone bosons (NGB), were first theoretically discovered in particular models by Goldstone~\cite{Goldstone} and Nambu~\cite{Nambu}. In the following, they will collectively be denoted by the symbol $\mathcal{J}$. NGBs have the peculiar property that they couple to the divergence of the current $j^{\mu}(x)$ associated with the symmetry that is broken. This coupling has a strength which is inversely proportional to the scale of symmetry breaking $F$, \begin{eqnarray} \mathcal{L}_{\rm int} \ = \ \frac{1}{2\: F} \: \mathcal{J}(x) \cdot \partial_{\mu} j^{\mu}(x) \;. \label{eq1} \end{eqnarray} This form of interaction is invariant under the shift transformation, $\mathcal{J} \rightarrow \mathcal{J} + \omega$, where $\omega$ is an angle that parameterizes different vacuum field configurations. Since NGBs typically are amongst the lightest particles in a theory a large fraction of the other particles can decay into them through \eq{eq1}. For this decay to occur, these other particles, possibly scalars and/or quarks and leptons, must be charged under the same spontaneously broken global symmetry. It was first proposed by Suzuki and Schrock~\cite{SS} that if the Standard Model (SM) Higgs boson mixes with such a new scalar particle then it must have a decay channel into a pair of NGBs ($\mathcal{J}\mathcal{J}$) provided that the scale $F$ is of the order of the electroweak gauge boson masses, $F \approx 100~\mathrm{GeV}$. If such a Higgs boson decay exists then it should be searched for at colliders. The basic idea underlying this article is the existence of an additional global ``phantom'' symmetry, $G_{\rm P}=U(1)_{\rm P}$ (P stands for ``Phantom''), that is spontaneously broken at some scale $F$. Then following \eq{eq1}, $\mathcal{J}$ will couple to all fermions ($f$) that are charged under $G_{\rm P}$ since $\partial_{\mu} j^{\mu} = m_{f} \bar{f}\gamma_{5} f$. This coupling will be proportional to $m_{f}/F$. In the literature, there are three famous types of Nambu-Goldstone bosons: axions~\cite{Axion}, familons~\cite{Wilczek} and majorons~\cite{Moh} and their associated broken symmetries are the Peccei-Quinn symmetry~\cite{PQ}, and the family and lepton number symmetry, respectively. In the former two cases the global symmetry is carried by both quarks and leptons and in the latter case by leptons only. However, considerations of energy loss in stars, supernovae and/or in terrestrial collider experiments~\cite{PDG} conclude that $F \gtrsim 10^{9-10}$ GeV in these popular cases. This bound constrains the decays of Higgs particles into the NGBs of the aforementioned models to be completely unobservable at colliders. Recently, a Majoron model has been considered where lepton number is spontaneously broken at the electroweak scale but in accordance with astrophysical bounds \cite{pilaftsisMaj}, however we will not consider this class of models here. A different situation arises if we assume that such additional NGBs, if existent, must {\it exclusively} couple to phantom (SM gauge singlet sector) fields. It is important to note that the requirement of renormalizability poses some constraints on such a hypothetical phantom sector. In particular, it demands that the only places where a phantom sector can make connections to the SM are the Yukawa interactions of neutrinos and Higgs bosons and the $H^\dagger H$ ``mass'' term. Therefore, the only relevant phantom sector fields are a right-handed fermion (possibly coming in three copies) and (in general complex) scalar fields. This immediately triggers some thought on implications for neutrino masses. For them, there are two possibilities: Majorana or Dirac masses. The Majorana see-saw mechanism \cite{seesaw} in fact is nothing but a type of phantom sector. However, as already discussed, in the simplest models the possible spontaneously broken global symmetry is lepton number -- clearly not a purely phantom sector symmetry. So, what about the Dirac case? Sticking to the same principle that leads to suppressed neutrino masses in the Majorana see-saw scenario, an analogous non-renormalizable operator can be constructed. It reads \begin{eqnarray} \mathcal{L}_{\nu} \ = \ \frac{(\overline{L}\cdot \tilde{H}) \: (\Phi \cdot \nu_{R})}{\Lambda}\;. \label{eq2} \end{eqnarray} In the model proposed in this article, some (purely phantom sector) symmetry $G_{P}$, prevents the interaction $\overline{L}\cdot \tilde{H}\nu_{R}$ from providing neutrinos with electroweak-scale masses. Then, \eq{eq2} results in acceptably small Dirac neutrino masses after spontaneous symmetry breaking of $G_{\rm P}$ (and the extended SM gauge group $G_{\rm SM}$) at $\langle \Phi \rangle \approx \langle \tilde{H} \rangle\approx 100~\mathrm{GeV}$ provided that $\Lambda \sim 10^{16}$ GeV. Here, the field $H$ (where $\tilde{H}=i \sigma_2 H^$) is the standard model $SU(2)_L$ Higgs doublet and ``$\cdot$'' denotes the inner product within $G_{\rm SM}$ or $G_{\rm P}$. A renormalizable model resulting in the effective operator of \eq{eq2} was first built by Roncadelli and Wyler~\cite{roncadelliwyler}. It has been recently shown in \Ref{CDU} that this model would lead to successful baryogenesis via Dirac leptogenesis \cite{Lindner,DiracSS,CDU} if $0.1~\mathrm{GeV}\lesssim \langle \Phi \rangle \lesssim 2$ TeV. It is worth noting that this particular NGB evades many bounds applying to other species of NGB since the only fermions transforming under $G_{\rm P}$ are the $\nu_{R}$, and the coupling between the NGB and the neutrinos is proportional to $\frac{m_{\nu}}{\langle \Phi \rangle}\approx \frac{\langle \tilde{H}\rangle}{\Lambda}$. This is too small to affect neutrino flavour oscillations through $\nu \rightarrow \nu + \mathcal{J}$~\cite{MohPal}. It is not unreasonable to suppose that the effects of the phantom sector may already have been seen~\footnote{ One should also notice that, like $\mathcal{J}$s, the three right-handed neutrinos being SM-gauge singlets are the only light fermions that obey the shift invariance, $\nu_{R}\rightarrow \nu_{R} + \omega$ where $\omega$ is a Grasmann-type parameter. It may be tempting to interpret the $\nu_{R}$s as Goldstinos of an $N_{f}$ (with $n_{f}$ being the number of $\nu_{R}$ flavours) supersymmetric phantom sector where the $\mathcal{J}$s belong to the same supermultiplet. } in experiments revealing that neutrinos have small masses. The existence of such a phantom sector may also be responsible for electroweak symmetry breaking. This has recently been emphasized by Patt and Wilczek~\cite{wilczek} and also by the authors of \Ref{CDU}. Their argument is based on the fact that no symmetry principle can forbid the mixing of the Higgs sector with the phantom sector through the renormalizable link operator \begin{eqnarray} \mathcal{L}_{\rm link} \ = \ \eta \: H^{\dagger} H \Phi^{\dagger} \Phi \;. \label{eq3} \end{eqnarray} \Eq{eq3} suggests that the phantom sector field $\Phi$ triggers spontaneous electroweak symmetry breaking, i.e.\ $\langle H \rangle \equiv v \approx 246$ GeV once it develops a vacuum expectation value (vev), $\langle \Phi \rangle \equiv \sigma$. This holds true even in the absence of any tree-level Higgs mass term, $\mu^{2} H^{\dagger} H$~\cite{CW,quirosespinosa,scaleinv}. Furthermore, it is exactly the mixing term of \eq{eq3} that causes the Higgs boson to decay into a pair of NGBs, $H\rightarrow \mathcal{J}\mathcal{J}$. Since the $\mathcal{J}$s interact only very weakly with matter, this decay effectively constitutes an invisible decay of the Higgs boson. Of course, this discussion could be generalized to non-Abelian groups. However, for simplicity here and onwards the simplest group $G_{\rm P}=U(1)_{\rm P}$ is assumed. The Noether current associated with this symmetry is $j_{\mu}(x) = i\Phi^{}\overleftrightarrow{\partial_{\mu}}\Phi$. The phantom field $\Phi$ can be expanded about its vev $\sigma$ in the usual fashion, \begin{eqnarray} \Phi(x) \ = \ e^{i \mathcal{J}(x)/\sigma} \: [\sigma + \phi(x) ] /\sqrt{2} \;. \label{eq4} \end{eqnarray} Using \eq{eq1} the interaction between the massive Higgs boson $\phi(x)$ and the NGB is found to be $\mathcal{L}_{\rm int}=\frac{1}{\sigma} \phi(\partial_{\mu}\mathcal{J})^{2}$. The scalar potential is composed of the usual quadratic and quartic terms for $H$ and $\Phi$ as well as the link term of \eq{eq3}. It is independent of $\mathcal{J}$ i.e. $V(H,\Phi) = V(h,\phi)$, where $h$ is the neutral field component of the $SU(2)_{L}$-Higgs doublet. The fields $h=O_{i1} H_{i}$ and $\phi=O_{i2}H_{i}$ are rotated to their physical mass eigenstates, $H_{i}$, with an orthogonal rotation matrix $O$ (CP-conservation is assumed). After setting particles on their mass shell, ${\cal L}_{\rm int}$ becomes~\cite{SS}, \begin{eqnarray} \mathcal{L}_{\rm int} \ = \ - \frac{m_{H_{i}}^{2}}{2 \,\sigma} \: O_{i2}\: H_{i}(x) \: \mathcal{J}(x) \: \mathcal{J}(x) \;, \label{eq5} \end{eqnarray} where $i=1,2$ in this minimal $G_{\rm P}=U(1)_{\rm P}$ scenario\footnote{ The link term of \eq{eq3} also gives rise to quartic $H_{i}H_{j} \mathcal{J} \mathcal{J} (i,j=1,2)$ couplings which are given in Fig.\ \ref{quadverts} of~\ref{app:A}. These couplings contribute to the decay, $H_{2} \to H_{1} \mathcal{J} \mathcal{J}$. However, the decay rate for this channel is on the order of $10^{-9}$ GeV or less for benchmark scenarios considered in this paper. Hence, they will be completely neglected in the analysis presented here.}. In this case the rank-2 matrix $O$ contains one mixing angle $\theta$. Following the notation of \Ref{CDU}, it will be fixed by $O_{12} = -O_{21} = \sin\theta$ and $O_{11}=O_{22}=\cos\theta$. The limit $\eta =0$ implies $\theta = 0$, i.e.\ no mixing between the SM-Higgs and the phantom sector scalar fields. Obviously, in this limit the Standard Model is recovered. This article assumes a convention where $m_{H1} < m_{H2}$. Trading the vev of $\langle \Phi \rangle \equiv \sigma$ with the more familiar $\tan\beta \equiv v/\sigma$, the free parameters of the model read \begin{eqnarray} m_{H_{1}} \quad ,\quad m_{H_{2}} \quad ,\quad \tan\theta \quad ,\quad \tan\beta \;. \label{eq6} \end{eqnarray} \Eq{eq5} is the equation underlying all phenomenological analyses in this paper. It describes Higgs boson decays to the almost sterile NGB particles. There exists an extensive body of literature, which addresses various techniques for discovering an invisible Higgs boson at colliders. They can be assembled in three main strategies: \begin{itemize} \item Studying the recoil of the $Z$-gauge boson in the associated $Z+H_{i}$ production process. Experimental results from LEP are summarized in \cite{LEP} and simulations have been performed in \cite{LEPsim}. A study for this process at the Tevatron has been performed in \Refs{MW,Han} with the result that the collider needs substantially more integrated luminosity to improve the current LEP exclusion limit. Parton level simulation studies for the LHC exist in Refs.\cite{Kane,Godbole,Han}. Further hadron level/detector simulation studies for the LHC are currently under way~\cite{Freiburg,HZinv}. \item Vector boson fusion (VBF) processes. As suggested by Eboli and Zeppenfeld~\cite{EZ}, this has now been simulated at hadron/detector level for the LHC~\cite{Freiburg,VBFinv}. \item Central exclusive diffractive production has been studied for a particular model in \Ref{Khoze}. \end{itemize} It should be noted that in all the above analyses only models with {\em only one} Higgs boson decaying completely invisibly were considered. In this article the focus will be put on the first two search channels, namely $ZH$ production and VBF. In both cases, the coupling of the Higgs to the gauge bosons is crucial. In the model considered here, only the SM-like scalar field $h$, belonging to the $SU(2)_{L}$ Higgs-doublet, couples to vector bosons $V$. The corresponding SM coupling constant $[g_{HVV} ]_{\rm SM}$ is rescaled with the mixing angle such that \begin{eqnarray} g_{H_{i}VV} \ = \ O_{i1} \: [g_{HVV} ]_{\rm SM} \;. \label{eq7} \end{eqnarray} Since the matrix $O$ is real and orthogonal, its elements are smaller than unity. This immediately implies that all Higgs production cross sections and/or decay rates (to SM particles) in this model are suppressed relative to the SM by a factor $O_{i1}^{2}$. However, because of the orthogonality condition, $\sum_{i} [O_{i1}]^{2}=\sum_{i}[O_{i2}]^{2}=1$. Therefore, if for example $H_{1}$ is invisible then the other Higgs $H_{2}$ tends to be visible and vice-versa. Is this a no-lose theorem for a Higgs boson discovery in this type of model? This is one of the questions to be addressed in this paper. More specifically, in this article the following two questions will be discussed: \begin{itemize} \item[{\cal Q}1:] Is there any window in the parameter space (\ref{eq6}) where LEP failed to exclude {\em both} Higgs-bosons for $m_{H_{i}} \lesssim 114$ GeV ? \item[{\cal Q}2:] Is there any (natural) window in the parameter space (\ref{eq6}) where {\em both} Higgs bosons would hide undetected at LHC? \end{itemize} In this context ``natural'' means that the theory has a positive definite potential, with perturbative (non-trivial) couplings up to a high cut-off scale $\Lambda\approx 10^{16}$~GeV, where the mechanism for naturally light neutrino masses may be expected [recall \eq{eq2}]. Therefore, we begin our analysis with Section~\ref{theoryconstraints} where stability and triviality bounds are analyzed and plotted together with electroweak $\rho$-parameter constraints. In Section~\ref{Q1LEP}, we answer question Q1. We derive analytical formulae for the Higgs boson to ``visible'' ($\mathcal{R}^{2}$) and ``invisible'' ($\mathcal{T}^{2}$) decay rates and plot predictions of the model against experimental LEP exclusion data for Higgs masses less than, approximately, 114~GeV. A possible scenario explaining the LEP Higgs boson excess is also discussed in this section. In Section~\ref{Q2LHC}, we extend the region of validity of ($\mathcal{R}^{2}$) and ($\mathcal{T}^{2}$) to heavier Higgs boson masses, and justify five benchmark points. Next, in subsections~\ref{ZHproduction}-\ref{VBFprod}, we perform a detailed Monte-Carlo simulation for signals at these points and their backgrounds, and we discuss possible strategies useful for further theoretical and experimental consideration. Furthermore, in Section~\ref{sec:nona}, extensions of the Abelian to non-Abelian phantom sectors and some consequences relevant for Higgs boson phenomenology at the LHC are discussed. A discussion of our findings together with some remarks for alternative scenarios is presented in Section~\ref{sec:conclusions}. In \ref{app:A}, we display the relevant Feynman rules of the Abelian model. \setcounter{equation}{0} \section{Stability and Triviality Bounds} \label{theoryconstraints} In the minimal phantom model, the set of physical parameters in \eq{eq6} can be written\footnote{We adopt the notation of \Ref{CDU}.} in terms of the renormalization group running parameters $\lambda_{\rm H} \, H^{4}$, $\eta\, H^{2}\: \Phi^{2}$, and $\lambda_{\rm \Phi}\, \Phi^{4}$: \begin{eqnarray} \lambda_{\rm H} &=& \frac{1}{2}\, \frac{m_{H_{1}}^{2} \cos^{2}\theta + m_{H_{2}}^{2} \sin^{2}\theta}{v^{2}} \;, \label{eqlh} \\[3mm] \eta &=& \frac{1}{2} \: \frac{(m_{H_{2}}^{2} - m_{H_{1}}^{2}) \sin(2\theta) \tan\beta}{v^{2}} \;, \label{eqeta} \\[3mm] \lambda_{\rm \Phi} \ &=& \ \frac{1}{2}\, \frac{m_{H_{1}}^{2} \sin^{2}\theta + m_{H_{2}}^{2} \cos^{2}\theta}{v^{2}} \; \tan^{2}\beta \label{eqlphi} \end{eqnarray} with $v \approx 246$ GeV. Notice that in the limit where both $\tan\beta,\, \tan\theta \rightarrow 0$ the phantom sector completely decouples from the SM scalar sector. Also, note that $\lambda_{\Phi}$ depends quadratically on $\tan\beta$ and the Higgs boson masses. This implies that in the case of non-zero Higgs mixing there is always an upper bound on $\tan\beta$ if the theory is required to remain perturbative. For example, if $\tan\theta =1$ and $m_{H} \lesssim 200$~GeV then $\tan\beta \lesssim 2$. In all of our plots only the case $\tan\beta =1$ is considered although, as already explained, higher values of $\tan\beta$ would further reduce the number of visible Higgs events. There are two\footnote{The unitarity constraint here is avoided by assuming that all quartic couplings are in a perturbative region, $\lambda \lesssim 1$.} classic, ``theoretical'' constraints on models that have been worked out numerous times in great detail for the SM and in many of its extensions~\cite{bounds}. Firstly, the triviality constraint is essentially the requirement that the couplings in \eq{eqlh} - \eq{eqlphi} stay perturbative up to a certain scale $\Lambda_{T} \gg v$. Secondly, the vacuum stability constraint demands that the potential is bound from below up to a scale $\Lambda_{V} \gg v$. Applying both constraints yields $\Lambda_{T},\Lambda_{V}\lesssim 10^{16}$~GeV, where we recall the discussion following \eq{eq2}. The vacuum stability bound can be reduced to the requirement \begin{equation} 4\, \lambda_H(\mathcal{Q}) \lambda_{\Phi}(\mathcal{Q}) > \eta(\mathcal{Q})^2, \label{pos} \end{equation} at all scales $\mathcal{Q} \lesssim \Lambda_{V}$. The running parameters are defined at the scale $\mathcal{Q}_{0}=M_{Z}$ and then evolved up to higher scales with the following 1-loop renormalization group equations~\cite{MV,Wells2} \begin{eqnarray} 16 \pi^2\,\frac{d \lambda_H}{dt} & = & \eta^2 + 24\,\lambda_H^2 + 12\,\lambda \,Y_t^2 - 6\,Y_t^4 - 3\,\lambda (3\,g_2^2 + g'^2) + \frac{3}{8} \Big [ 2\,g_2^4 + (g_2^2 + g'^2)^2 \Big ]\,,\nonumber\\[3mm] 16 \pi^2\,\frac{d \eta}{dt} & = & \eta \Big[ 12\, \lambda_H + 8\, \lambda_{\Phi} - 4\,\eta + 6\,Y_t - \frac{3}{2} (3\,g_2^2 + g'^2) \Big]\,,\nonumber\\[3mm] 16 \pi^2\,\frac{d \lambda_{\Phi}}{dt} & = & 2\,\eta^2 + 20\,\lambda_{\Phi}^2\,. \label{RGE} \end{eqnarray} Here, $t \equiv \ln \mathcal{Q}/\mathcal{Q}_0$, $g'$ and $g_2$ are the $U(1)_Y$ and $SU(2)_L$ gauge couplings, respectively, and $Y_t$ is the top quark Yukawa coupling. We ignore all other Yukawa couplings because their effect in the running is negligible. The equations for $Y_t$, $g'$ and $g_2$ are well known \cite{RGs} and are left out for brevity. It is worth noticing that the parameter $\eta$ is multiplicatively renormalized at one loop. Although there is no particular reason for $\eta =0$, if this is the case at one energy scale then this will remain true at all energy scales. Fig.\ \ref{fig:lambda} shows the light Higgs boson mass $m_{H1}$ vs.\ $m_{H2}- m_{H1}$ plane for $\tan\beta = \tan \theta = 1$ where the background colours show the scale of new physics $\Lambda$ required either by positivity or triviality (whichever is lower). The curved contour shows the 95\% C.L.\ upper limit on the combined Higgs boson masses from precision electroweak data (see corresponding formula in \Ref{CDU}). Fig.\ \ref{fig:lambda} should be compared with Fig.\ \ref{fig2} of Section~\ref{Q2LHC}, to see the correspondence between easily accessible regions at the LHC and regions with a potentially high effective theory cut-off. The light (light green) shaded parameter region of Fig.\ \ref{fig:lambda} is what we will coin the {\em natural region} throughout this paper. \begin{figure}[t] \centering \includegraphics[width=4.7in]{triv} \parbox{0.9\textwidth}{ \caption{The light Higgs boson mass $m_{H_{1}}$ vs.\ $m_{H_{2}}-m_{H_{1}}$ plane for $\tan \beta = \tan \theta = 1$, showing the expected cut-off $\Lambda$ of the effective theory taking the triviality and positivity of the potential into account (the lower of either $\Lambda_{T}$ or $\Lambda_{V}$ is shown). The curved line shows the 95\% C.L.\ upper limit on the Higgs boson masses stemming from precision electroweak data.} \label{fig:lambda}} \end{figure} \setcounter{equation}{0} \section{LEP searches} \label{Q1LEP} The LEP experiments searched first for visible Higgs boson events in the Higgsstrahlung process $e^{+} e^{-}\rightarrow Z H$ with the Higgs boson decaying to $b$-quarks and leptons $\ell$ in final state stemming from the $Z$ boson decay. They presented~\cite{LEPres} 95\% C.L.\ upper limits for a parameter ${\cal R}^{2}$ (in their notation $\mbox{\rm S}_{95}$), defined as the ratio of the number of Higgs boson events expected in any given model to the number expected in the Standard Model for a Higgs boson with an identical mass, as a function of the Higgs boson mass. An important point to note in this context is that $\mathcal{R}^{2}$ {\em only} counts ``visible'' events. In particular, the data on decays to $b$-quarks will be used in the following. Then the ${\cal R}^{2}$ parameter translates into \begin{equation} {\cal R}^{2}_i \equiv \frac{\sigma(e^{+}e^{-}\to H_i\,X)\,{\rm Br}(H_i \to YY)}{\sigma(e^{+}e^{-}\to h \,X)\,{\rm Br}(h \to YY)}\,, \label{eqr} \end{equation} where $i=1,2$, $X$ are the remnants associated with the production of a $H_i$ or $h$ (the SM Higgs boson) and $YY$ could be in principle either $b\bar{b}$, or $\tau\tau$, but {\it not} $\mathcal{JJ}$. However, in the framework of the particular model studied here, another possibility is that $YY = H_{j} H_{j}$. Exclusion limits in this case have been presented in~\cite{LEPres}. The four LEP experiments~\cite{LEPin} also performed searches for acoplanar jets (as signal for $Z(\to q\bar{q}) \: H(\to\mathrm{invisible}$) or leptons (as signal for $Z(\to \ell\ell ) \: H(\to\mathrm{invisible}$), with $\ell = e,\mu$, apart from the DELPHI-collaboration which also used $\tau$'s in the final state. In all cases, the emergence of invisible decay products of the Higgs boson is identified with the production of missing energy ($\mbox{\slash \hspace{-0.25cm}$E$}\xspace$). Their study resulted in an upper limit on the branching ratio of $H\to \mathrm{invisible}$ as a function of the Higgs mass, multiplied by the production cross-section normalized to the rate expected from a SM Higgs decaying completely invisibly. In our case, this limit places constraints on the parameter \begin{eqnarray}\label{eqi} \mathcal{T}_{i}^{2} \ \equiv \ \frac{\sigma(e^{+}e^{-} \rightarrow H_{i} \, X)}{\sigma(e^{+}e^{-} \rightarrow h \, X)} \: \mathrm{Br}(H_{i}\rightarrow \mathcal{J}\mathcal{J}) \;, \end{eqnarray} where again $i=1,2$, $h$ is the SM Higgs boson and $X$ are the remnants associated with the production of $H_{i}$ or $h$ at LEP. A further important constraint comes from the OPAL collaboration who performed a model-\-independent analysis of the Higgs sector at LEP \cite{opalindep}. They searched for the generic process $e^{+} e^{-} \to Z S^0$ where $S^{0}$ is a completely neutral (and hence invisible) scalar boson. Since this analysis is independent of the eventual fate of the Higgs candidate it bounds the parameter \begin{equation} s_i^2 \equiv \frac{\sigma (e^+ e^- \to Z H_i)}{\sigma (e^+ e^- \to Z h)}\,, \end{equation} as a function of the Higgs boson mass. In this model $s_1 = \cos^2 \theta$ and $s_2 = \sin^2 \theta$. Particularly simple expressions may be derived for $\mathcal{R}^2_{i}$ and $\mathcal{T}^2_{i}$ in the minimal phantom scenario provided that the narrow width approximation may be assumed and that the Higgs boson to off-shell gauge boson decay modes may be neglected. Our analytical findings closely follow the model-\-independent analysis of \Ref{Wells1}. Consider the case where $YY = b\bar{b}$ in \eq{eqr}. For simplicity let us assume that the decay $H_{2}\to H_{1}H_{1}$ is kinematically forbidden, i.e.\ $m_{H_{1}} > m_{H_{2}}/2$. In this case $\mathrm{Br}(H_{i} \to b\bar{b}) +\mathrm{Br}(H_{i} \to \mathcal{JJ})\approx 1$. Applying this to \eq{eqr} in the LEP search region, $m_{H_{2}}/2 < m_{H1}\lesssim 115~\mathrm{GeV}$ and after some algebra we arrive at \begin{eqnarray} {\cal R}^{2}_1 & \simeq & \Bigg[(1 + \tan^2 \theta)\Big(1 + \frac{1}{12}\,\frac{m_{H_{1}}^2}{m_b^2}\,\tan^2 \theta\,\tan^2 \beta\Big)\Bigg]^{-1} \;, \label{eqr1} \nonumber \\[3mm] {\cal R}^{2}_2 & \simeq & \Bigg[(1 + \cot^2 \theta)\Big(1 + \frac{1}{12}\,\frac{m_{H_{2}}^2}{m_b^2}\,\cot^2 \theta\,\tan^2 \beta\Big)\Bigg]^{-1} \;. \nonumber \label{eqr2} \end{eqnarray} Firstly, notice that the number of Higgs boson events where the Higgs boson decays to $b\bar{b}$ (or indeed any other visible mode) are always suppressed relative to the SM prediction in which $\mathrm{Br}(h \to b\bar{b}) \approx 1$ for this particular Higgs boson mass region. Secondly, the number of visible Higgs boson events decreases in the limit $m_{H_{i}} \gg m_{b}$. Note also that if $\tan \beta > 1$, $\mathcal{R}^2_{i}$ receives an additional suppression. The importance of the Higgs boson to invisible decay and of model-\-independent Higgs boson analyses are highlighted when we consider the example $\tan\theta = 1$ and $\tan\beta=2$ where we obtain $\mathcal{R}^2_{i} = 0.012$ for $m_{H_{i}}=50$ GeV. In principle, this is within the region allowed by LEP ``visible'' Higgs search data \cite{LEPres} which excludes $0.015 \lesssim \mathcal{R}_{i}^{2}\lesssim 0.2$ for Higgs masses in the range $12~\mathrm{GeV} \lesssim m_{H_{i}} \lesssim 100~\mathrm{GeV}$. This could have been a ``nightmare'' scenario; LEP would have completely missed the Higgs sector! Fortunately, this nightmare is averted by both the LEP Higgs boson to invisible searches and the OPAL model-\-independent Higgs boson search, because the former, for instance, sets bounds on $\mathcal{T}_{i}^{2}$. In the relevant LEP mass region, $m_{H_{2}}/2 < m_{H1}\lesssim 115~\mathrm{GeV}$, \begin{eqnarray} \mathcal{T}_{1}^{2} \ &=& \ \cos^{2}\theta \ - \ R_{1}^{2} \;, \label{RTtheta1}\\ \mathcal{T}_{2}^{2} \ &=& \ \sin^{2}\theta \ - \ R_{2}^{2} \;. \label{RTtheta2} \end{eqnarray} Setting $R^{2}_{i} \rightarrow 0$ implies that $\mathcal{T}_{1}^{2} + \mathcal{T}_{2}^{2} \approx 1$. LEP searches for invisible Higgs bosons exclude $\mathcal{T}_{i}^{2} \gtrsim 0.5$ for masses below 110 GeV, $m_{H_{i}} \lesssim 110$~GeV. Therefore, {\em it is unlikely that there are two invisible Higgs bosons in the LEP search region with masses $m_{H_{i}} \lesssim 110$}~GeV. This answers question {\cal Q}1 posed in the introduction. In addition, using the model-\-independent analysis of OPAL \cite{opalindep}, $m_{H_i}\lesssim 85$~GeV is excluded for $s_i^2 > 0.5$. Since either $s^2_{1} = \cos^2 \theta \ge 0.5$ or $s^2_{2} = \sin^2 \theta \ge 0.5$ for any given $\theta$, {\em OPAL excludes the case where both} $m_{H_1}\lesssim 85$~GeV {\em and} $m_{H_2}\lesssim 85$~GeV, {\em independently of how the Higgs bosons actually decay}. It is interesting to note that one Higgs boson could still be hidden in the LEP search region even with these strong constraints, while the other Higgs boson then would wait for its discovery in the allowed region out of reach of LEP. \begin{center} \begin{figure}[t] \centering \begin{tabular}{cc} \includegraphics[width=0.48\textwidth]{newmh1} & \includegraphics[width=0.48\textwidth]{newmh2} \end{tabular} \parbox{0.9\textwidth}{\caption{LEP excluded regions (at 95 \% C.L.) (in dark blue) for $\tan\theta$ versus Higgs boson masses $m_{H_{1}}$ (left plot) and $m_{H_{2}}$ (right plot) for the minimal phantom scenario with $\tan\beta=1$. {\em Both} searches are clearly complementary to each other in this scenario.} \label{fig1}} \end{figure} \end{center} The results of a detailed analysis of this model, including visible, invisible and model-independent LEP bounds~\cite{LEPres,LEPin,opalindep} are summarised in Fig.\ \ref{fig1}. This numerical analysis confirms the analytical findings above. With $\tan\beta =1$, a light Higgs boson ($H_{1}$) with a mass as low as 65 GeV could have escaped unobserved at LEP if $\tan\theta \gtrsim 2$. For the same range of $\tan \theta$ the other Higgs ($H_{2}$) is constrained to be heavier than 114 GeV. From inspection of Fig.\ \ref{fig1} we can define a LEP-allowed benchmark scenario B1 for the phantom model presented here, namely: \begin{eqnarray} \mathrm{B1:} \quad m_{H_{1}} = 68~\mathrm{GeV} \quad &,& \quad m_{H_{2}} = 114~\mathrm{GeV} \quad , \quad \nonumber \\[2mm] \tan\theta = 2 \quad &,& \quad \tan\beta = 1 \;. \label{lepben} \end{eqnarray} In this case one Higgs boson is buried, undiscovered in the LEP search region due to the small values of $\mathcal{R}_{1}^{2}$ and $\mathcal{T}_{1}^{2}$ which have to satisfy $\mathcal{R}_{1}^{2} + \mathcal{T}_{1}^{2} = \cos^2 \theta = 0.2$ following eq.~(\ref{RTtheta1}). The other, heavier Higgs has $\mathcal{R}_{2}^{2} = 0.06$ and $\mathcal{T}_{2}^{2} = 0.74$. With this set of parameters, very few $H_2$ events are SM-like decays into ``visible'' final states and instead $H_2$ decays mainly into ``invisible'' NGBs. This scenario could well be classed as a (LEP) nightmare! As yet, no combined LEP limits exist on invisibly decaying Higgs bosons with masses below $m_H = 90$~GeV. Therefore, for $m_H < 90$~GeV the limits presented here are based on the individually published results from each experiment. However, some of the individual studies do not cover the whole Higgs mass range considered here and so the best available limit is used for any given Higgs mass. This is one of the causes of the sharp edges in Fig.\ \ref{fig1}. Clearly, a future combined LEP analysis may well exclude the benchmark B1 which lies close to being ruled out by ALEPH \cite{LEPin} which considered Higgs masses down to $m_H = 70$~GeV for which $\mathcal{T}^2 \simeq 0.1$ is excluded. \subsection{A digression: 2.3 $\sigma$ LEP Higgs search excess} The LEP experiments established a small, 2.3$\sigma$ effect in their Higgs boson searches corresponding to a Higgs boson mass of about 98~GeV \cite{lepexcess}. Explaining this excess would require a value of ${\cal R}_1^2 \simeq 0.2$, ruling out a Standard Model Higgs boson as plausible explanation. It is possible to provide a candidate Higgs boson in the phantom model discussed in this publication, which would have produced such an effect in the LEP data. Fig.\ \ref{fig:lepexcess} shows the allowed region in the $\tan \theta$ vs. $\tan \beta$ plane for $m_{H_1} = 98$~GeV. The allowed region is tightly constrained because of the searches for invisible Higgs bosons at LEP in this mass region. At the relatively small values of $\tan \beta$ still allowed, the main reason for such a small value of ${\cal R}_1^2$ is Higgs mixing rather than the extra invisible decay mode suppressing the Higgs branching ratio. \begin{figure}[t] \centering \includegraphics[scale=0.83]{LEPexcess} \parbox{0.9\textwidth}{\caption{The $\tan \theta$ vs. $\tan \beta$ plane for a lightest Higgs mass of $98~{\rm GeV}$. The lightest region indicates where the $2.3 \sigma$ effect in the LEP Higgs searches could be explained whilst still being consistent with other LEP Higgs search data (such as the search for invisible Higgs bosons).} \label{fig:lepexcess}} \end{figure} \begin{figure}[t] \centering \includegraphics[scale=0.98]{LEPexcesstriv} \parbox{0.9\textwidth}{\caption{The $\tan \theta$ vs. $\tan \beta$ plane for Higgs boson masses of $m_{H1} = 98~{\rm GeV}$ and $m_{H2} = 210~{\rm GeV}$. The region enclosed by the black line indicates where the $2.3 \sigma$ effect in the LEP Higgs searches could be explained whilst still being consistent with other LEP data for Higgs boson searches. The background colours indicate the scale of the expected cut-off $\Lambda$, of the effective theory taking the triviality and positivity of the potential into account. Darkly shaded regions are excluded by LEP Higgs search data. Contours for ${\cal R}^2_2$ are shown in white.} \label{fig:lepexcesstriv}} \end{figure} Fig.\ \ref{fig:lepexcesstriv} shows the constraints on this region of parameter space coming from considering the triviality and positivity of the potential. For a suitably heavy $m_{H2} \stackrel{>}{{}_\sim} 210$~GeV, most of the region suggested by the LEP excess is described by a theory which could be valid to scales as high as $10^{16}$~GeV. When $\tan \theta \sim 1$, as $\tan\beta \to 0$ ($\sigma \to \infty$) the values of $\eta$ and $\lambda_\Phi$ tend to 0. Looking at eqs.~(\ref{RGE}) it is apparent that small values of $\eta$ and $\lambda_\Phi$ will be relatively stable under renormalization group evolution since, for example, $\eta$ is multiplicatively renormalized. Higgs masses around the electroweak scale are maintained in this limit because $\mu_{H}^2 \to \infty$ whilst $\mu^{2}_{\Phi} \sim -v^2$. However, because $\eta \to 0$ the $\Phi$ and $H$ sectors are almost decoupled so that potentially destabilizing diagrams with a heavy $H$ will be proportional to $\eta$ and not greatly affect the mass of $\Phi$. Of course, the model is still quadratically sensitive to a high cut-off scale and thus still possesses the hierarchy problem of the SM. Note that the second Higgs boson mass is restricted by the upper limit on Higgs boson masses from precision electroweak data \cite{CDU}, however for $m_{H2} \stackrel{<}{{}_\sim} 210$~GeV the whole region suggested by the LEP excess is free from this constraint. Clearly further data would be required before this effect could be taken more seriously. In the next chapter we will address the question of whether the LHC has the sensitivity required to discover these scenarios, in particular the potential nightmare B1. The possible existence of other challenging scenarios with heavier Higgs bosons will also be examined. \section{LHC: expectations and strategic searches} \label{Q2LHC} In the LHC search region, the parameters $\mathcal{R}_{i}^{2}$ and $\mathcal{T}_{i}^{2}$ can be defined by expressions similar to those in \eqs{eqr}{eqi}, respectively, with the obvious replacement of the electron/positron initial state to a proton/proton initial state and $YY = \gamma \gamma , b\bar{b}, VV, gg,$ etc.. Two categories for the ratios ${\cal R}_{i}^{2}$ may be distinguished: ({\it a}) a region where $m_{H_{i}}< 2\, m_{V}$ and $H_{i}$ decays dominantly into $b\bar{b}$ and ({\it b}) a region where $m_{H_{i}}\stackrel{>}{\sim} 2\, m_{V}$ and the $H_{i}$ decays dominantly into a gauge boson pair, $VV$, with $V=Z,W$. In case ({\it a}), and under the assumption that gauge bosons are produced on-shell, analytical approximations for $\mathcal{R}^{2}_{i}$ are identical to those studied in the previous chapter. On the other hand, assuming a common gauge boson mass $m_{V}$, in region ({\it b}), we obtain \begin{eqnarray} {\cal R}^{2}_1 & \simeq & \Bigg[(1 + \tan^2 \theta)\Big(1 + \frac{1}{3\,g(x_1)}\,\tan^2 \theta\,\tan^2 \beta\Big)\Bigg]^{-1} \;, \nonumber \\[3mm] {\cal R}^{2}_2 & \simeq & \Bigg[(1 + \cot^2 \theta)\Big(1 + \frac{1}{3\,g(x_2)}\,\cot^2 \theta\,\tan^2 \beta + \frac{f(y)}{g(x_2)}\,\frac{\cot^2 \theta}{(1+\cot^2 \theta)^2}\,(\cot \theta - \tan \beta)^2\Big)\Bigg]^{-1} \;, \nonumber \\[3mm] \label{lhcr} \end{eqnarray} where $x_i = m^2_V/m^2_{Hi}$, and $g(x) = (1 - 4 x + 12 x^2)\,(1-4x)^{1/2}$. The last term in \eq{lhcr} is the contribution from the heavy Higgs boson decay $H_2 \to H_1 H_1$~\cite{Wells2,Grossman}. Furthermore, $y = m_{H1}^2/m_{H2}^2$ and $f(y) =(1 + 4 y + 4 y^2)\,(1-4y)^{1/2}\,\Theta(1-4y)$. Imposing some constraints to this analysis (see section \ref{theoryconstraints}), the mode $H_{2}\to H_{1} H_{1}$ will not be important in further discussions. It is apparent from \eq{lhcr} that a certain suppression of the observable rates ($\mathcal{R}^{2}_{i}$) is always present. Its origin is twofold. Firstly, the couplings between the $H_{i}$ and SM fields are always suppressed because of the mixing matrix $O$. Secondly, the decay widths of the Higgs bosons are enhanced by the extra decay mode $H_{i} \to {\cal JJ}$. The contribution of this additional decay mode is increased at large $\tan\beta$ and for $\tan\beta = 10$ and $\tan \theta = 1$ the suppression of visible events is always more than 90\% for $m_{H_{2}} \lesssim 200$~GeV. However, as we have already remarked in section \ref{theoryconstraints}, high values of $\tan\beta$ result in non-perturbative couplings and will therefore not be considered in this article. What then would be a nightmare scenario for the LHC? At present both the ATLAS and CMS collaborations have performed studies, at detector simulation level, to explore the discovery potential of their apparatus for both SM-like Higgs bosons which decay to visible final states, see e.g.~\cite{Mangano}, and Higgs bosons decaying to invisible final states, for example~\cite{VBFinv,HZinv}. These studies are sensitive to the ratios ${\cal R}_{i}^{2}$ and ${\cal T}_{i}^{2}$ as functions of the Higgs boson mass. For example, looking at the simulation results for the LHC with $\mathcal{L}=10(30)~\mathrm{fb}^{-1}$ integrated luminosity we estimate (with na\"ive scaling) that it would be difficult to discover a visibly-decaying Higgs if signal event rates were 30\%(20\%) of that expected in the SM (${\cal R}_{i}^{2} \lesssim 0.3(0.2)$). Furthermore, studies of the sensitivity of the ATLAS detector\footnote{Similar studies exist for the CMS detector~\cite{Clare}.} to invisibly decaying Higgs bosons suggest that after $\mathcal{L}=10(30)~\mathrm{fb}^{-1}$ integrated luminosity ATLAS could exclude Higgs bosons with ${\cal T}_{i}^{2} \gtrsim 0.30(0.25)$ at 95\% C.L.\ \cite{VBFinv,HZinv}. To further illustrate the necessity of the Higgs boson to invisible searches in this minimal phantom scenario, in Fig.\ \ref{fig2} areas on the $m_{H_{1}}$ vs.\ $m_{H_{2}} - m_{H_{1}}$ plane are plotted where $\mathcal{R}_{i}^{2}\ge 0.3 $ and/or $\mathcal{T}_{i}^{2} \ge 0.3$. These limits define na\"ive regions, where Higgs bosons will experimentally be accessible at the LHC, either in visible or invisible search channels. Clearly at this stage in this study these limits are assumptions, and in fact the true experimental reach of the LHC will not be known until after it has been running for some time and predictions for the levels of backgrounds have been confirmed (or not). These assumptions do, however, serve as a good first estimate on which to justify the further study undertaken here. In producing Fig.\ \ref{fig2} all Higgs boson decay modes including decays to off-shell vector bosons have been considered. Different colours indicate regions where either one, both or no Higgs bosons can be seen in different channels. It is clear that a truly challenging region for LHC region remains where $\mathcal{R}_{i}^{2}\le 0.3$ and $\mathcal{T}_{i}^{2} \le 0.3$. This motivates the further more detailed Monte Carlo analysis in the later sections of this article, which probe more carefully the possibility of discovering a Higgs boson in the invisible search channel when $\mathcal{T}_{i}^{2} \stackrel{<}{{}_\sim} 0.3$. \begin{figure}[t] \centering \includegraphics[width=.6\textwidth]{RT} \parbox{0.9\textwidth}{\caption{Regions in the $m_{H_{1}}$ vs. $m_{H_{2}}-m_{H_{1}}$ plane for $\tan \beta = 1$ and $\tan \theta = 1$, where different Higgs bosons are ``accessible'' at LHC. We define that a given $H_{i}$ is accessible if either $\mathcal{R}_{i}^{2} \ge 0.3$ or $\mathcal{T}_{i}^{2} \ge 0.3$. In the dark (blue) regions both Higgs bosons are accessible. In the white (beige) region no Higgs bosons are accessible.} \label{fig2}} \end{figure} Using equations~(\ref{RTtheta1}) and (\ref{RTtheta2}) it is easy to see that $\mathcal{R}_1^2 + \mathcal{R}_2^2 + \mathcal{T}_1^2 + \mathcal{T}_2^2 = 1$. The following no-lose theorem then exists: If experiments can discover a Higgs boson over the whole range of $\mathcal{R}_i^2$ down to $\mathcal{R}_i^2 = 0.25$ {\em or} over the whole range of $\mathcal{T}_i^2$ down to $\mathcal{T}_i^2 = 0.25$ then at least one Higgs boson should be found. Without real data, estimates of the capabilities of experiments like ATLAS and CMS may easily be too optimistic or too pessimistic. Therefore in this publication, a constructive approach is taken. The phantom model has been added to the Monte Carlo event generator \Sherpa \cite{sherpa}, ready to be used when real data arrive. For now Fig.\ \ref{fig2} may be used to define additional benchmark scenarios, some in potentially nightmarish regions, and these points can be studied in more detail. The particular scenarios are displayed in Table~\ref{tab:1}. \begin{table}[t] \vspace{0.5cm} \centering \begin{tabular}{\|c\|\|c\|c\|} \hline \multicolumn{3}{\|c\|}{$\tan\theta = 1 \quad \tan\beta =1$} \\ \hline {Benchmark} & $m_{H_{1}}$(GeV) & $m_{H_{2}}$(GeV) \\ \hline B2 & 112 & 130 \\ B3 & 140 & 165 \\ B4 & 160 & 190 \\ B5 & 185 & 190 \\ \hline \end{tabular} \parbox{0.9\textwidth}{\caption{Four LHC benchmark scenarios for the phantom model.} \label{tab:1}} \end{table} The LO branching ratios for both Higgs bosons are presented in Table~\ref{tab2}. These ratios are in agreement with the analytical LO expressions in \eq{lhcr} and Fig.\ \ref{fig2}, and the discussion following them. The most optimistic benchmark point is B1 and the most challenging one is B5. \begin{table}[t] \centering \begin{tabular}[h]{\|c\|c r\|r\|r\|r\|r\|} \hline Benchmark & Higgs & $\Gamma_{tot}$(GeV) & \parbox{15mm}{$b \bar{b}$} & \parbox{15mm}{$W^{+}W^{-}$} & \parbox{15mm}{$ZZ$} & \parbox{15mm}{$\mathcal{J} \mathcal{J}$} \\ \hline \hline B1 & $H_{1}$ & 0.041 & 0.694 & -- & -- & 99.222 \\ & $H_{2}$ & 0.051 & 3.567 & 0.289 & 0.020 & 95.533 \\ \hline \hline B2 & $H_{1}$ & 0.117 & 0.958 & 0.059 & 0.003 & 98.823 \\ & $H_{2}$ & 0.183 & 0.697 & 0.348 & 0.042 & 98.784 \\ \hline \hline B3 & $H_{1}$ & 0.229 & 0.593 & 0.779 & 0.103 & 98.408 \\ & $H_{2}$ & 0.490 & 0.319 & 23.769 & 0.498 & 75.339 \\ \hline \hline B4 & $H_{1}$ & 0.387 & 0.393 & 12.217 & 0.396 & 86.904 \\ & $H_{2}$ & 1.066 & 0.166 & 36.597 & 10.313 & 52.879\\ \hline \hline B5 & $H_{1}$ & 0.921 & 0.188 & 36.500 & 6.787 & 56.475 \\ & $H_{2}$ & 1.066 & 0.166 & 36.597 & 10.31 & 52.879 \\ \hline \end{tabular} \parbox{0.9\textwidth}{\caption{Branching ratios (in percent) and total widths (in units of GeV) for the Higgs bosons, $H_{i}(i=1,2)$, for the benchmark points of Table~\ref{tab:1}. Branching ratios that are not displayed, account for less than 0.4\%. } \label{tab2}} \end{table} Prospects for discovering the Higgs bosons in the various benchmark scenarios B1-B5 at the LHC will be studied in the following. Theoretical vacuum stability and triviality bounds as well as bounds from fitting electroweak (EW) observables have already been presented in Section~\ref{theoryconstraints}. All benchmark scenarios selected in Table~\ref{tab:1} satisfy the EW constraints and in some the effective theory may be valid even to scales as high as the Planck scale. \subsection{$ZH$-production} \label{ZHproduction} The first search channel for an invisibly decaying Higgs boson at the LHC considered here is the associated production of a $Z$ and a Higgs boson, where the $Z$ decays leptonically. This ensures that a corresponding event can be triggered. The backgrounds to this process include $ZZ$, $WW$, $WZ$ and $Z$ production with corresponding decays, and fully leptonic $t\bar t$ production\footnote{ Note that, in all processes, off-shell effects, $Z$-$\gamma$ interference etc.\ are fully included in the simulation.}. It should be noted here that in principle some information on the rates can be obtained directly from data: for $ZZ$ pairs, final states with four leptons may be reweighted with the corresponding $Z\to\nu\bar\nu$ branching ratio, in the $WW$ case, different sign, different lepton pairs may be invoked. For the $WZ$ background, it may be possible to extrapolate from events where three leptons are seen to those where one lepton is lost, i.e.\ either outside the detector acceptance or undetected. For top-pair production, semi-leptonic events may help. All processes have been simulated with \Sherpa~\cite{sherpa} in the following setup: In order to correctly model hard parton radiation \Sherpa employs the multijet matrix element-parton shower merging procedure of \cite{CKKW}. Therefore, for all processes discussed here and in the next section, matrix elements with at least one and in most cases two additional jets have been added to the simulation. This ensures that the simulation correctly describes the important high-$p_\perp$ tails of various distributions. However, all cross sections quoted are, in principle, obtained at leading-order accuracy, with no $K$-factors added to them. CTEQ6L parton distubution functions are used with $\alpha_{s}(M_Z)=0.118$ \cite{Pumplin:2002vw}. $\alpha_{s}$ is computed at two--loop accuracy. All scales are set according to the merging prescription of \cite{CKKW}. Jets have been defined in all cases through the $k_{T}$ algorithm \cite{KTjets}. The CKM matrix has been choosen to be diagonal. We have simulated and analysed events with electrons in the final state; mostly identical numbers would have been obtained if we had specialised for muon pairs instead. Obviously, this difference would be of great importance if detector effects had been included as well\footnote{ We refrained from including full detector simulations, or any Gaussian smearing or electron-jet conversion ``by hand'' and concentrated on an analysis at the hadron level, including all effects of fragmentation, hadron decays, final state QED bremsstrahlung etc..}. However it should suffice to state that we quote final results for leptons $\ell=e,\mu$. We also omitted all effects due to the underlying event because of the large uncertainties related to its modelling and the rather small impact it has on the observables we discuss. The selection cuts listed in Ref.~\cite{HZinv} have been applied. Thus we require: \begin{enumerate} \item one lepton pair of the same kind with opposite charges, where each lepton individually satisfies $p_{T,\ell}>15$ GeV and $\|\eta_\ell\|<2.5$; \item $\|M_{\ell\bar\ell}-M_Z\|\le 10$ GeV; \item $\mbox{\slash \hspace{-0.25cm}$E_{T}$}\xspace > 100$ GeV; \item a veto on jets with $p_T>20$ GeV, $\|\eta\|<4.9$; \item a veto on b-jets with $p_T>15$ GeV, $\|\eta\|<4.9$; \item $m_T>200$ GeV, where $m_T=\sqrt{2p_T^{\ell\bar\ell}\mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace (1-\cos\phi)}$. \end{enumerate} Additionally, we impose: \begin{enumerate} \item[6.] $\Delta R_{\ell\bar\ell}<1.75$; \item[7.] $p_{T}(\ell\bar\ell\mbox{\slash \hspace{-0.25cm}$E_{T}$}\xspace)<60$ GeV. \end{enumerate} For the various backgrounds listed above, cross sections before and after these additional selection cuts are listed in Table~\ref{Tab:ZHbackground}. Generation cross sections, selection cut efficiencies and the resulting selection cross sections for the signal in the different benchmark scenarios are given in Table~\ref{Tab:ZHsignal}. It should be stressed again that all cross sections quoted have been obtained at leading order accuracy. \begin{table} \begin{center} \begin{tabular}{\|l\|\|c\|c\|c\|c\|c\|} \hline & \parbox{15mm}{$ZZ$} & \parbox{15mm}{$W^\pm Z$} & \parbox{15mm}{$W^+W^-$} & \parbox{15mm}{$t\bar t$} & \parbox{15mm}{$Z$}\\\hline\hline $\sigma_{\rm tot}^{\rm gen}$ [fb] & 164 & 1.17$\cdot 10^{3}$ & 1.01$\cdot 10^{4}$ & 7.44$\cdot 10^{4}$ &1.81$\cdot10^{6}$ \\\hline\hline $\ell^+\ell^-$ only & 2.00$\cdot 10^{-1}$ & 1.10$\cdot 10^{-1}$ & 6.59$\cdot 10^{-2}$ & 8.40$\cdot 10^{-2}$ & 1.41$\cdot 10^{-1}$ \\ $\|m_{\ell \ell}-M_Z\|<10$ GeV & 1.87$\cdot 10^{-1}$ & 9.17$\cdot 10^{-2}$ & 8.92$\cdot 10^{-3}$ & 1.09$\cdot 10^{-2}$ & 1.25$\cdot 10^{-1}$ \\ $E\!\!\!/_T>100$ GeV & 3.69$\cdot 10^{-2}$ & 1.10$\cdot 10^{-2}$ & 5.91$\cdot 10^{-4}$ & 2.41$\cdot 10^{-3}$ & 1.94$\cdot 10^{-7}$ \\ jet veto & 1.64$\cdot 10^{-2}$ & 2.13$\cdot 10^{-3}$ & 3.53$\cdot 10^{-5}$ & 2.00$\cdot 10^{-6}$ & - \\ $m_T>200$ GeV & 1.54$\cdot 10^{-2}$ & 1.95$\cdot 10^{-3}$ & 2.74$\cdot 10^{-5}$ & 1.19$\cdot 10^{-9}$ & - \\ $\Delta R_{\ell\ell}<1.75$, $p_{T}(\ell\ell,\mbox{\slash \hspace{-0.25cm}$E_{T}$}\xspace)<60$ GeV & 1.23$\cdot 10^{-2}$ & 1.50$\cdot 10^{-3}$ & 2.23$\cdot 10^{-9}$ & 1.55$\cdot 10^{-10}$ & - \\ \hline\hline $\sigma_{\rm eff}$ [fb] & 2.02 & 1.75 & 2.25$\cdot 10^{-5}$ & 1.15$\cdot 10^{-5}$ & - \\\hline \end{tabular} \parbox{0.9\textwidth}{\caption{Generation characteristics for the background processes to the $ZH$-channel. In all cases we included all leptonic decay modes: In the $ZZ$ case, therefore the final state included a lepton and a neutrino pair, in the $WZ$ case, we included a lepton pair from the $Z$ and a lepton-neutrino pair from the $W$, the $WW$ channel was supposed to decay fully leptonically in all possible combinations, for the top pairs we assumed purely leptonic decays, and for the $Z$ a leptonic final state (no neutrinos) was demanded.} \label{Tab:ZHbackground}} \end{center} \end{table} \begin{table} \begin{center} \begin{tabular}{\|l\|\|c\|c\|c\|c\|c\|} \hline & $B_1$ & $B_2$ & $B_3$ & $B_4$ & $B_5$ \\\hline \hline $\sigma_{\rm tot}$ [fb] & 280 & 114.6 & 53.0 & 29.0 & 13.6 \\\hline \hline $\ell^{+} \ell^{-}$ only & 1.75$\cdot 10^{-1}$ & 1.98$\cdot 10^{-1}$ & 2.25$\cdot 10^{-1}$ & 2.40$\cdot 10^{-1}$ & 2.24$\cdot 10^{-1}$ \\ $\|m_{\ell \ell}-M_Z\|<10$ GeV & 1.62$\cdot 10^{-1}$ & 1.84$\cdot 10^{-1}$ & 2.10$\cdot 10^{-1}$ & 2.23$\cdot 10^{-1}$ & 2.08$\cdot 10^{-1}$ \\ $E\!\!\!/_T>100$ GeV & 3.12$\cdot 10^{-2}$ & 6.07$\cdot 10^{-2}$ & 8.91$\cdot 10^{-2}$ & 1.08$\cdot 10^{-1}$ & 1.12$\cdot 10^{-1}$ \\ jet veto & 3.00$\cdot 10^{-2}$ & 5.66$\cdot 10^{-2}$ & 7.85$\cdot 10^{-2}$ & 9.29$\cdot 10^{-2}$ & 1.08$\cdot 10^{-1}$ \\ $m_T>200$ GeV & 2.88$\cdot 10^{-2}$ & 5.49$\cdot 10^{-2}$ & 7.64$\cdot 10^{-2}$ & 9.08$\cdot 10^{-2}$ & 1.06$\cdot 10^{-1}$ \\ $\Delta R_{\ell\ell}<1.75$, $p_{T}(\ell\ell,\mbox{\slash \hspace{-0.25cm}$E_{T}$}\xspace)< 60$ GeV & 2.55$\cdot 10^{-2}$ & 4.93$\cdot 10^{-2}$ & 6.94$\cdot 10^{-2}$ & 8.35$\cdot 10^{-2}$ & 9.85$\cdot 10^{-2}$ \\ \hline\hline $\sigma_{\rm eff}$ [fb] & 7.15 & 5.65 & 3.68 & 2.42 & 1.34 \\\hline \end{tabular} \parbox{0.9\textwidth}{\caption{ Generation characteristics for the signal processes in the $ZH$-channel. In each case we assumed all leptonic decay channels for the $Z$ boson.} \label{Tab:ZHsignal}} \end{center} \end{table} The numbers from both Tables \ref{Tab:ZHbackground} and \ref{Tab:ZHsignal} suggest that the two most dangerous backgrounds to the $ZH$ signal are $ZZ$ and $WZ$ production, with corresponding decays. Following our discussion above, however, it seems that the total cross sections and distributions related to these backgrounds can be directly extracted from data in the $ZZ$ case or probably well extrapolated from measurements. After cuts we find that the backgrounds together account for roughly 8 fb, leaving us with signal-to-background ratios of the order of $S/B\approx 1/8$ up to 1. We therefore conclude that it should be possible to find the signal in all five benchmark scenarios. However, we would like to stress here that more conclusive numbers can be obtained after a simulation at detector level only. Such detector-level studies for an invisibly decaying Higgs boson have been for the ATLAS experiment \cite{HZinv} found signal--\-to--\-background ratios reaching up to $1/4$. Although this is of the same order of magnitude as our results, there are several differences: First of all, in our simulation the \Sherpa Monte Carlo event generator with multijet merging was used for both signal and background events, while the ATLAS study employed the \Pythia \cite{Pythia} event generator for the backgrounds and the program \htohv~\cite{h2hv} for the signal. While \Sherpa and \Pythia are formally of the same accuracy there are a number of differences, like \Sherpa multijet merging leading to an improved treatment of hard QCD radiation, and the full inclusion of spin correlations in \Sherpa, which are not present in \Pythia. This may have lead to a better separation of signal and background in \Sherpa. On the other hand, in ATLAS' simulation the $HVV$ couplings where assumed to have exactly the same strength as in the SM - which is not true for our analysis, where these couplings are reduced due to mixing effects. In addition, a 100\% branching ratio of Higgs boson to invisible was assumed for the ATLAS simulation, again in contrast with our simulation, where the relevant branching ratio ranged between roughly 50\% up to 100\%. These two facets of the study, of course, enhance the signal--\-to-\-background ratio in the ATLAS study. Of course, there are further differences, like the missing underlying event in \Sherpa, which has been included in the ATLAS study, like slightly different selection cuts, like a different choice of PDF (CTEQ5L in ATLAS, CTEQ6L in our study) and, most importantly, like the inclusion of detector effects through their fast detector simulation ATLFAST \cite{atlfast} in the ATLAS study that are totally absent in our case. To summarize: However different in detail the studies are, it is reassuring to see that in all cases this seems to be a feasible channel, at least at accumulated higher luminosities. In addition to the findings above, cf.\ Tables \ref{Tab:ZHbackground} and \ref{Tab:ZHsignal} we have identified two further distributions that may be worthwhile to study in the $ZH$ channel: \begin{itemize} \item The total transverse momentum of the leptons and $\mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace$, i.e.\ the total transverse momentum of the $H$ and $Z$ candidates (see Fig.\ \ref{fig:zh_plots1}). This observable shows a significantly different behaviour between the signals and the backgrounds, where the signal tends to be more strongly peaked towards small values. \item The azimuthal angle between $\mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace$ and the momentum of the lepton pair (see Fig.\ \ref{fig:zh_plots2}). Here the signal tends towards a more back-to-back configuration of the $Z$ and $H$ candidate. Seemingly, there is a significantly higher QCD activity in the backgrounds than in the signal, providing more jets for the $ZH$-candidate pair to recoil against in the backgrounds. \end{itemize} These findings may help to further improve the signal-to-background ratio. \begin{figure}[t] \centering \includegraphics[width=0.49\textwidth]{PT_e-e+ET_miss} \includegraphics[width=0.49\textwidth]{PT_e-e+ET_miss_2} \parbox{0.9\textwidth}{\caption{The $p_{T}(e^+e^-,\mbox{\slash \hspace{-0.25cm}$E_{T}$}\xspace)$ distribution for the signal in benchmark scenario B1 and the individual backgrounds. The left panel displays individual distributions while the right panel show the sum of backgrounds and signal, starting from the lowest significant background.} \label{fig:zh_plots1}} \end{figure} \begin{figure}[t] \centering \vspace{5mm} \includegraphics[width=0.49\textwidth]{C_e-e+ET_miss_5} \includegraphics[width=0.49\textwidth]{C_e-e+ET_miss_6}\\ \parbox{0.9\textwidth}{\caption{The $\Delta \phi(e^+e^-,\mbox{\slash \hspace{-0.25cm}$E_{T}$}\xspace)$ distribution for the signal in benchmark scenario B1 and backgrounds. The left panel displays individual distributions while the right panel show the sum of backgrounds and signal, starting from the lowest significant background.}\label{fig:zh_plots2}} \end{figure} \subsection{Vector Boson Fusion} \label{VBFprod} The other production channel we consider for invisibly decaying Higgs bosons at the LHC is vector boson fusion (VBF). As the name suggests, in this process the Higgs boson is produced through the fusion of two vector bosons emitted by quarks inside the protons, which typically carry comparably large momentum fractions of the protons. Therefore, at leading order (tree-level) there is no colour exchange between the two protons, and it can be expected that the central rapidity region remains to a large extent empty apart from the decay products of the produced system. The quarks on the other hand will be deflected, typically by transverse momenta of roughly half the mass of the produced system. This gives rise to two hard jets, which, due to the invisible nature of the Higgs boson, are essentially the triggers in this analysis. The main background processes to be taken into account are the production of $Z$ or $W$ bosons in association with two jets, which can originate either from QCD or through electroweak interactions, thus mimicking the topology of the VBF signal. In addition, top-pair production with subsequent semi-leptonic decays must be considered. Similar to the case of $W$ production, the lepton is then lost. Again, it is worth noting that it should be possible to extract information concerning the total rates of these backgrounds, even after selection cuts, directly from data. This is possible either by reweighting leptonic $Z$ decays to those into neutrino pairs, or, with a somewhat larger error, by extrapolating the modes where the individual lepton is seen (in $W$+jets or semileptonic top-pairs) into those regions where the lepton is lost. This is in analogy to the case discussed above. \begin{figure}[t] \centering \includegraphics[width=3.5in]{m_jet} \parbox{0.9\textwidth}{\caption{Tagjet invariant mass distribution for benchmark point B1 and the $Z$ and $W$ backgrounds.} \label{fig:mjj}} \end{figure} We employ the basic cuts listed in Ref.~\cite{VBFinv}, i.e.\ we require: \begin{enumerate} \item two tagging jets with \begin{enumerate} \item $p_{T,j} > 40$ GeV, $\|\eta_{j}\|<5$, \item $\|\eta_{j_1}-\eta_{j_2}\|>5$, $\eta_{j_1} \cdot \eta_{j_2} < 0$, \item $m_{j_1 j_2} > 1700$ GeV , \item $\Delta\phi_{j_1 j_2} = \|\phi_{j_1} - \phi_{j_2}\| < 1$, \end{enumerate} \item missing transverse momentum, $\mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace>100$ GeV; \item no identified lepton, i.e.\ no lepton with\\ $p_{T}^{e,\mu} > 5\;, 6$ GeV in $\|\eta_{l}\| < 2.5$, \item a central jet veto, i.e.\ no jets with\\ $p_T>20$ GeV, ${\rm min}\{\eta_{j_1},\eta_{j_2}\}<\eta<{\rm max}\{\eta_{j_1},\eta_{j_2}\}$. \end{enumerate} Additionally we impose: \begin{enumerate} \item[5.] $\|\eta_3^\| = \left\|\eta_{j_3} - \frac{1}{2}\left(\eta_{j_1}+\eta_{j_2}\right)\right\| > 1.5$, \item[6.] $\Delta\phi_{j_1,j_3},\;\Delta\phi_{j_2,j_3}\; < 1.25$. \end{enumerate} \begin{figure}[t] \centering \includegraphics[width=0.47\textwidth]{HT} \hspace{3mm} \includegraphics[width=0.46\textwidth]{Calc_jet_3}\\ \parbox{0.9\textwidth}{\caption{Left panel: $H_{T}$ distribution for benchmark point B1 and $Z$ background. Right panel: $\eta^{}_{3}$- distribution for benchmark point B1 and $Z$ background.} \label{fig:eta3}} \end{figure} The choice of the cut on the invariant tagging jet mass of $m_{jj}> 1700$ GeV is motivated by the corresponding invariant mass spectrum shown in Fig.\ \ref{fig:mjj}. We observe that the signal distribution crosses the background at $m_{jj}\approx 1700$ GeV. Of course this statement sensitively depends on the model parameters chosen; however, the common feature of all scenarios is that the higher the invariant mass cut, the better the signal--\-to--\-bachground ratio. This is due to the fact that in a large fraction of background events the two tagging jets originate from QCD or the decay of weak gauge bosons. After the above cuts the possibilities to check for the signal topology are limited in the VBF channel. Possible objects to be identified experimentally are the tagging jets, $\mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace$ and an eventually arising soft third jet. Therefore most observables show the same behaviour for signal and background, which is exemplified in the left panel of Fig.\ \ref{fig:eta3}, showing the $H_T$-distribution for the signal at benchmark point B1 and the $Z$ background. In the right panel of Fig.\ \ref{fig:eta3} we show for the same scenario the $\eta^{}_{3}$ distribution. It is clearly seen that for the background the third jet tends to be more central between the tagging jets, while for the signal it is rather forward or backward. This motivates the first of the additional cuts above. For the various backgrounds listed above, cross sections before and after additional selection cuts, and the number of generated events are listed in Table~\ref{Tab:VBFbackground}. Signal cross sections before and after additional selection cuts are listed in Table~\ref{Tab:VBFsignal}. \begin{table} \begin{center} \begin{tabular}{\|l\|\|c\|c\|c\|} \hline & \parbox{25mm}{\vspace{1mm}$Z$+jets (QCD+EW)\vspace{1mm}} & \parbox{25mm}{$W$+jets (QCD+EW)} & \parbox{25mm}{$t\bar t$}\\\hline\hline $\sigma_{\rm tot}^{\rm gen}$ [nb] & 9.41 & 51.8 & 0.145\\\hline\hline tagging jets & 1.80$\cdot 10^{-4}$ & 7.44$\cdot 10^{-5}$ & 1.62$\cdot 10^{-3}$ \\ $m_{jj}>$1700 GeV & 3.49$\cdot 10^{-5}$ & 1.64$\cdot 10^{-5}$ & 4.44$\cdot 10^{-4}$ \\ $\mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace>100$ GeV & 2.64$\cdot 10^{-5}$ & 9.73$\cdot 10^{-6}$ & 3.32$\cdot 10^{-4}$ \\ lepton veto & 2.63$\cdot 10^{-5}$ & 2.84$\cdot 10^{-6}$ & 1.28$\cdot 10^{-5}$ \\ $\Delta\phi_{j_1j_2}<$1 & 4.03$\cdot 10^{-6}$ & 9.87$\cdot 10^{-7}$ & 2.79$\cdot 10^{-5}$ \\ central jet veto & 1.54$\cdot 10^{-6}$ & 2.18$\cdot 10^{-7}$ & 1.44$\cdot 10^{-6}$ \\ $\|\eta^\|>1.5$ & 1.37$\cdot 10^{-6}$ & 1.95$\cdot 10^{-7}$ & 6.70$\cdot 10^{-7}$ \\ $\Delta\phi_{j_1j_3}$, $\Delta\phi_{j_2j_3}$ & 1.14$\cdot 10^{-6}$ & 1.44$\cdot 10^{-7}$ & 4.29$\cdot 10^{-7}$ \\ \hline\hline $\sigma_{\rm eff}$ [fb] & 10.7 & 7.45 & 0.0621 \\\hline \end{tabular} \parbox{0.9\textwidth}{\caption{Generation characteristics for the background processes to the VBF-channel. Here, the $Z$ boson decays to neutrinos, whereas the $W$ boson decays to any lepton--\-neutrino pair. For the top--\-pairs, semileptonic decays only have been considered.} \label{Tab:VBFbackground}} \end{center} \end{table} \begin{table} \begin{center} \begin{tabular}{\|l\|\|c\|c\|c\|c\|c\|} \hline & $B_1$ & $B_2$ & $B_3$ & $B_4$ & $B_5$ \\\hline\hline $\sigma_{\rm tot}^{\rm gen}$ [pb] & 5.46 & 4.46 & 2.99 & 2.06 & 1.32 \\\hline\hline tagging jets & 4.38$\cdot 10^{-2}$ & 5.59$\cdot 10^{-2}$ & 6.80$\cdot 10^{-1}$ & 7.54$\cdot 10^{-2}$ & 8.12$\cdot 10^{-1}$ \\ $m_{jj}>$1700 GeV & 1.69$\cdot 10^{-2}$ & 2.20$\cdot 10^{-2}$ & 2.74$\cdot 10^{-2}$ & 3.07$\cdot 10^{-2}$ & 3.36$\cdot 10^{-2}$ \\ $\mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace>100$ GeV & 1.46$\cdot 10^{-2}$ & 1.90$\cdot 10^{-2}$ & 2.37$\cdot 10^{-2}$ & 2.67$\cdot 10^{-2}$ & 2.92$\cdot 10^{-2}$ \\ lepton veto & 1.46$\cdot 10^{-2}$ & 1.90$\cdot 10^{-2}$ & 2.37$\cdot 10^{-2}$ & 2.66$\cdot 10^{-2}$ & 2.92$\cdot 10^{-2}$ \\ $\Delta\phi_{j_1j_2}<$1 & 5.76$\cdot 10^{-3}$ & 7.65$\cdot 10^{-3}$ & 9.46$\cdot 10^{-3}$ & 1.06$\cdot 10^{-2}$ & 1.18$\cdot 10^{-2}$ \\ central jet veto & 3.42$\cdot 10^{-3}$ & 4.33$\cdot 10^{-3}$ & 5.35$\cdot 10^{-3}$ & 6.06$\cdot 10^{-3}$ & 6.64$\cdot 10^{-3}$ \\ $\|\eta^\|>1.5$ & 3.40$\cdot 10^{-3}$ & 4.31$\cdot 10^{-3}$ & 5.32$\cdot 10^{-3}$ & 6.03$\cdot 10^{-3}$ & 6.60$\cdot 10^{-3}$ \\ $\Delta\phi_{j_1j_3}$, $\Delta\phi_{j_2j_3}$ & 3.11$\cdot 10^{-3}$ & 3.92$\cdot 10^{-3}$ & 4.81$\cdot 10^{-3}$ & 5.45$\cdot 10^{-3}$ & 5.97$\cdot 10^{-3}$ \\ \hline\hline $\sigma_{\rm eff}$ [fb] & 17.0 & 17.5 & 14.4 & 11.2 & 7.9 \\\hline \end{tabular} \parbox{0.9\textwidth}{\caption{Generation characteristics for the signal processes in the VBF-channel, for the different benchmark scenarios.} \label{Tab:VBFsignal}} \end{center} \end{table} Putting together numbers, we again find appreciable signal--\-to--\-background ratios between more than 1/3 up to nearly 1 for all the benchmark points in the model. However, this finding has to be taken with more than a pinch of salt: first of all, similar to the $ZH$ channel, we included all effects due to fragmentation, hadron decays, QED bremsstrahlung etc., and we typically added at least one further jet for a better modelling of additional hard QCD radiation. We did not, however, include the effects of the underlying event, which here could play a significant role in filling the rapidity gap between the two taging jets, and thus lead to a corresponding reduction in the effective cross section after selection cuts. In addition we did not include diagrams where the Higgs boson is produced through an effective $ggH$ coupling, mediated by heavy quarks. Although in principle the cross section for this mode is large, we note that previous work in the framework of the Standard Model suggests that the typical VBF cuts render this contribution insignificant \cite{DelDuca:2001fn,DelDuca:2001eu,Andersen:2007mp,Bredenstein:2008tm}. Also, again, we did not simulate events at the detector-level which could further modify our findings. However, again our results are in qualitative agreement with results of such a simulation at the detector level, which has been performed for the ATLAS experiment \cite{VBFinv}. The results of this study were obtained using a fast detector simulation, and they are quite encouraging, too. Although in qualititative agreement, there are several differences: Again, the first one lies in the choice of the evenet generator. ATLAS chose \Pythia to compute both signal and SM backgrounds at leading order, while we employed \Sherpa. In the ATLAS simulation SM coupling strength for the $HVV$ couplings has been assumed with a $100 \%$ branching fraction of the the Higgs decay to invisible, while in our study the $HVV$ coupling is shielded through the mixing of the scalars, and the relevant branching ratio ranges between 0.5 and 1. While in ATLAS' \Pythia simulation the effect of hard QCD radiation is typically accounted for by the parton shower, \Sherpa uses exact matrix element, leading to a significantly increased jet activity. Also, \Sherpa naturally includes spin correlations, and VBF-like background topologies are also taken care off, which have been missed in the ATLAS simulation. These effects, together, would typically reduce the signal--\-to--\-background ratio in our simulation with respect to the ATLAS study. On the other hand, the effect of the underlying event as well as the fast detector simulation, both included in the ATLAS analysis but ignored by us, may have the opposite implications on the visibility of the signal. Finally, it is worth stressing that we have also chosen different optimization cuts, in particular cuts 5 and 6, to enhance the signal over the background. Nevertheless, to summarize, we again find that the prospects of finding an invisibly decaying Higgs boson at the LHC are much better than naively anticipated, and the two channels considered here may very well play a significant role in the phenomenology of non-standard scalar sectors. \section{Non-Abelian Phantom Sector} \label{sec:nona} So far only a $G_P = U(1)$ group theoretic phantom sector has been considered. The obvious question to be asked is how the Higgs boson observability will be affected in the case of non-Abelian extensions of the phantom sector (like $G_P = SU(N)$). This will briefly be discussed in this section. As an overall result, in general, such extensions typically result in further suppression of the Higgs boson visible event rates, $\mathcal{R}_i^2$. Furthermore, in the case of more involved representations or multiple vector representations of $G_P$ the ``Higgs $\rightarrow$ invisible'' signal is decreased to a non-detectable rate. Some examples supporting this result will be presented in the following. Consider for instance a $G_P = SU(N)$ vector representation of scalar phantom fields, $\vec{\Phi}$. Then $SU(N)$ is spontaneously broken down to $SU(N-1)$ with $2N-1$ physical NGBs and one physical SM-singlet scalar field that eventually mixes with the $SU(2)_L$ Higgs field. It is a textbook exercise to prove that \eq{eq5} in such a framework becomes \begin{eqnarray} \mathcal{L}_{\rm int} \ = \ - \frac{m_{H_{i}}^{2}}{2 \,\sigma} \: O_{i2}\: H_{i}(x) \: \mathcal{J}^a(x) \: \mathcal{J}^a(x) \qquad \mathrm{with} \quad a=1...(2N-1) \;. \label{eq55} \end{eqnarray} This suggests that the Higgs boson decay width broadens compared to the $G_{P}=U(1)$ case. The visible Higgs boson event rates (there are still two physical states) read \begin{eqnarray} {\cal R}^{2}_1 & \simeq & \Bigg[(1 + \tan^2 \theta)\Big(1 + \frac{2N-1}{12}\,\frac{m_{H_{1}}^2}{m_b^2}\,\tan^2 \theta\,\tan^2 \beta\Big)\Bigg]^{-1} \;, \label{eqnonr1} \nonumber \\[3mm] {\cal R}^{2}_2 & \simeq & \Bigg[(1 + \cot^2 \theta)\Big(1 + \frac{2N-1}{12}\,\frac{m_{H_{2}}^2}{m_b^2}\,\cot^2 \theta\,\tan^2 \beta\Big)\Bigg]^{-1} \;. \nonumber \label{eqrnon2} \end{eqnarray} Hence increasing the rank of the phantom gauge group results in a ($1/N$ for large $N$) decrease in visible Higgs boson rates. Searching for ``Higgs $\rightarrow$ invisible'' is therefore vital. Note also that increasing the rank of the phantom symmetry group does not necessarily imply different ``Higgs $\rightarrow$ invisible'' rates. In fact, in the above example we still have two physical scalars in the spectrum for which the equation $\mathcal{T}_1 + \mathcal{T}_2 \approx 1$ is valid, similarly to the $G_P = U(1)$ case. It may also be the case that additional physical Higgs bosons fragment the ``Higgs $\rightarrow$ invisible'' rate into many small pieces such that any detection at the LHC seems completely impossible. This case can be illustrated with the following example: consider $G_P= SU(3)$ broken by 2 sets of vector representations down to the null group. We start with 12 degrees of freedom, out of which 8 become NGBs and the other 4 become massive scalar fields. These 4 fields will mix with the one $SU(2)_L$ Higgs field through the ($5\times 5$) matrix $O$ forming 5 physical Higgs-boson eigenstates. In this case, due to the unitarity of the matrix $O$ we have $\sum_{i=1}^5 \mathcal{T}_i^2 \approx 1$, which allows for $\mathcal{T}_i^2 \lesssim 0.25$. Such a ``Higgs $\rightarrow$ invisible'' rate is most probably beyond reach of discovery (or exclusion) at the LHC~\cite{VBFinv,HZinv} - a truly nightmarish scenario! \section{Additional Remarks} \label{sec-remarks} It should be emphasized that in the scenario considered in this article, invisible Higgs boson phenomenology, small neutrino masses and the correct baryon asymmetry (see also \Ref{CDU}) are all obtained without fine-tuning coupling constants. All scalars have masses at the EW scale ($\tan\beta \approx 1$) and so there are no ultra-heavy scalars to destabilize this hierarchy. However, the model does not include gravity nor does it contain a mechanism or theoretical explanation as to why $\sigma \ll M_{\rm Planck}$. Although the SM hierarchy problem is not solved in this model the question here is somewhat different: {\em Why is the phantom sector symmetry broken at the EW scale ?} We cannot provide a non-common ({\it i.e.}, non-supersymmetric) answer to this question, and refer to \cite{WilczekSUSY08,JungKo}. Instead of a theory with one global symmetry, one could imagine a theory where several symmetries were gauged (or left un-gauged), absorbing the NGBs into massive gauge bosons through the Higgs mechanism. This is an absolutely viable option, although the requirement of anomaly cancellation would result in model dependencies. Such models have been proposed before and studied in some detail in the recent literature \cite{gaugemodels}. Generally speaking, these models lead to phenomenology that includes the (observable) decays of the extra gauge bosons, with all constraints on their masses etc.. Recently there has been renewed interest in the possibilities offered by extending the Standard Model with a real scalar singlet \cite{langackeretal}. Depending on the symmetries of the model it is possible to provide a candidate for the cold dark matter in the universe (extra discrete symmetries needed) \cite{mcdonald} , and it is possible to provide a strong first-order electroweak phase transition suitable for electroweak baryogenesis \cite{quirosespinosa}. It should be noted in the latter case that an additional source of CP-violation would be necessary to provide a complete mechanism for baryogenesis. Models with broken discrete symmetries provide another possible way of avoiding invisible decays of Higgs boson(s). Clearly, spontaneous breaking of such symmetries does not lead to NGBs, making the Higgs boson signatures more visible. There are, however, so many possibilities of such groups that a particular choice renders this idea less appealing and convincing. Spontaneously broken discrete symmetries may also, in some cases, produce unwanted cosmological relics such as domain-walls, potentially placing severe constraints on this class of model. \section{Conclusions} \label{sec:conclusions} Physical NGBs arise when continuous global symmetries are spontaneously broken. Such broken symmetries may be related to the smallness of neutrino masses or the patterns of mixing angles (in the case of familons). In this article we show that the role of NGBs in Higgs boson phenomenology is very important; they lead to the dilution and potential invisibility of the expected SM signal. Working with approximate analytic formulae we first identified regions of parameter space [\eq{eq6}] where Higgs boson phenomenology is challenging both for past LEP data and for the future LHC experiments, and secondly implemented the model in \Sherpa, ready for further analysis by experimenters when real LHC data arrive. Our study shows that LEP excludes the minimal phantom sector case where both Higgs bosons have masses $m_H \stackrel{<}{{}_\sim} 85$~GeV irrespective of their decay modes. However, experimentally allowed scenarios exist where one Higgs boson mass is much lower than the SM Higgs boson exclusion limit, $m_{H_1} = 68$~GeV, and the other is just at this limit, $m_{H_2} = 114$~GeV. In light of the nightmarish potential of this scenario, Monte-Carlo simulation studies of invisible Higgs boson searches at the LHC are performed. Two search channels are looked at in detail; the associated production of a $Z$ and a Higgs boson, and the production of a Higgs boson in weak vector boson fusion. For $ZH$ associated production, it is found that in each of 5 benchmark scenarios, the invisible Higgs boson should be found at the LHC, with signal--\-to--\-background ratios of order $S/B \simeq 1/8$ to 1. Scope for improving this ratio is also found by looking either at the distribution of the total transverse momentum of the leptons and the \mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace, or at the distribution of the azimuthal angle between the \mbox{\slash \hspace{-0.2cm}$p_{T}$}\xspace~and the momentum of the lepton pair. Fairly good signal--\-to--\-background ratios are also found in the vector boson fusion search channel. However in this case the effects of the underlying event, which was not included in simulations, may reduce the amount of signal passing the selection cuts. Although our MC analysis focuses on the case with an Abelian phantom sector symmetry, we also examined cases with non-Abelian symmetries in the phantom sector using the analytic formulae provided in section~\ref{Q1LEP}. For the case $G_P = SU(N)$ we found that the visibility of the Higgs bosons is reduced when we increase the rank of the $SU(N)$ group making the LHC searches to invisible a necessity. In addition, by choosing appropriate representations of the group for breaking the symmetry we may further dilute the Higgs boson to invisible signature, leading to a very difficult scenario indeed for the LHC. Regarding the hierarchy problem, the model at hand is not better or worse than the Standard Model. Any difference could be interpreted as shifting the problem to the phantom sector which sets the scale of the symmetry breaking. \vspace{0.5cm} \noindent {\large \bf Acknowledgements} We would like to thank Karl Jacobs for letting us know about progress on ATLAS studies of Higgs to invisible. A.D.\ would like to thank the European Artemis network and especially Nikos Konstantinidis for discussions on ``Higgs to invisible'' at LEP. We are all fully (S.H.) or partially supported by the RTN European Programme, MRTN-CT-2006-035505 (HEPTOOLS, Tools and Precision Calculations for Physics Discoveries at Colliders) or by the RTN European Programme MRTN-CT-2006-035606 (MCnet). \renewcommand{\thesection}{Appendix~\Alph{section}} \renewcommand{\arabic{section}.\arabic{equation}}{\Alph{section}.\arabic{equation}} \setcounter{equation}{0} \setcounter{section}{0} \bigskip \section{$U(1)$ Phantom Model Feynman Rules}\label{app:A} In this appendix we present Feynman rules for the Higgs sector of $G_{SM} \times \{G_{P}=U(1)_{P}\}$ that are relevant for Higgs phenomenology at LEP and the LHC. Feynman rules for the trilinear couplings $H_{i} \mathcal{J} \mathcal{J}$, $H_{1}H_{2}H_{i}$, $H_{i}H_{i}H_{i}$, $W^{+}W^{-}H_{i}$, $ZZH_{i}$, and $f\bar{f}H_{i}$ for $i=1,2$ are shown in Fig.\ \ref{triverts}. For completeness in Fig.\ \ref{quadverts}, also Feynman rules for the quadrilinear couplings $H_{i}H_{j} \mathcal{J} \mathcal{J}$, $H_{i}H_{j}H_{k}H_{l}$, $H_{i}H_{j}ZZ$, and $H_{i}H_{j}W^{+}W^{-}$ are listed. $M_{W}$ and $M_{Z}$ are the masses of the $W$ boson and $Z$ boson, respectively and $m_{f}$ is the fermion mass which can be either a quark or a lepton. The $SU(2)_{L}$ coupling constant is $g_{2}$ and $\theta_{w}$ is the Weinberg mixing angle. $v$ is the vacuum expectation value for the standard model $SU(2)_{L}$ Higgs doublet $H$. $g_{\mu \nu}$ is the Minkowski spacetime metric $(1,-1,-1,-1)$. The orthogonal mixing matrix, $O$, is \begin{eqnarray} O=\left( \begin{array}{cc} O_{11} & O_{12} \\ O_{21} & O_{22} \end{array} \right) = \left( \begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array} \right) . \end{eqnarray} Here $ \tan \beta=v/\sigma$ with $\sigma \equiv \langle \Phi \rangle $. $m_{H_{1}}$ and $m_{H_{2}}$ denote the masses of the two Higgs bosons, $H_{1}$ and $H_{2}$, respectively. \begin{figure}[t] \begin{tabular}{cc} \parbox{2cm}{\includegraphics[scale=0.3]{ffhiggs}} & \parbox{7cm}{: ~$-i \frac{m_{f}}{v} ~O_{i1}$} \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{zzhiggs}} & \parbox{7cm}{: ~$i \frac{g_{2} M_{Z}}{\cos \theta_{w}} ~O_{i1} ~g_{\mu \nu}$} \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{wwhiggs}} & \parbox{7cm}{: ~$i g_{2} M_{W} ~O_{i1} ~g_{\mu \nu}$} \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{JJhiggs}} & \parbox{7cm}{: ~$-i \frac{m_{H_{i}}^{2}}{v} ~\tan \beta ~O_{i2}$} \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{h1h2hi}} & \parbox{7cm}{\begin{eqnarray} : ~& & \frac{i}{v} \left( m_{H_{1}}^{2} + m_{H_{2}}^{2}+ m_{H_{i}}^{2} \right) \\ &\cdot & O_{i1} O_{i2} \left( O_{1i}+ O_{2i} ~\tan \beta \right) \end{eqnarray}} \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{hihihi}} & \parbox{5cm}{: ~$-3i \frac{m_{H_{i}}^{2}}{v} ~\left(O_{i1}^{3}+O_{i2}^3 ~\tan \beta \right) $} \\ \\ \end{tabular} \caption{\em Trilinear couplings.} \label{triverts} \end{figure} \begin{figure}[t] \begin{tabular}{cc} \parbox{2cm}{\includegraphics[scale=0.3]{4higgs_i}} & \parbox{7cm}{\begin{eqnarray} :~&-&\frac{3i}{v^2} \left[ O_{1i}^{4} \left( m_{H_{1}}^{2} O_{11}^{2} + m_{H_{2}}^{2} O_{12}^{2} \right) \right. \\ &+& O_{i2}^{4} \left( m_{H_{2}}^{2} O_{11}^{2} + m_{H_{2}}^{2} O_{12}^{2} \right) \tan^{2} \beta \\ &-& \left. 2 O_{12}^{3} O_{11}^{3} \tan \beta \left( m_{H_{2}}^{2} - m_{H_{1}}^{2} \right) \right] \end{eqnarray} } \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{4higgs_ji} $(i \neq j) $} & \parbox{7cm}{\begin{eqnarray} : ~&+&\frac{3i}{v^2} O_{11} O_{ij} \left( O_{j2}+O_{j1} \tan \beta \right) \\ &\cdot & \left[ m_{H_{i}}^{2} \left( O_{i2}^{3} \tan \beta + O_{i1}^{3} \right) \right. \\ &+& \left. m_{H_{j}}^{2} \left(O_{i1} O_{j1}^{2} + O_{i2} O_{j2}^{2} \tan \beta \right) \right] \end{eqnarray} } \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{4higgs_12}} & \parbox{7cm}{\begin{eqnarray} :~&+&\frac{i}{v^2} O_{11} O_{12} \left[ \left( m_{H_{2}}^{2} - m_{H_{1}}^{2} \right) \tan \beta \right. \\ &\cdot& \left( O_{11}^{4} - 4 O_{12}^{2} O_{11}^{2}+O_{12}^{4} \right) \\ &+& 3 O_{11} O_{12} \left( m_{H_{1}}^{2} O_{11}^{2} + m_{H_{2}}^{2} O_{12}^{2} \right.\\ &+&\left. \left. \left( m_{H_{2}}^{2} O_{11}^{2} + m_{H_{1}}^{2} O_{12}^{2} \right) \tan^{2} \beta \right) \right] \end{eqnarray}} \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{ZZ2higgs}} & \parbox{7cm}{: ~$\frac{ig_{2}^{2}}{2} g_{\mu \nu} O_{i1} O_{j1}$} \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{WW2higgs}} & \parbox{7cm}{: ~$\frac{ig_{2}^{2}}{2 \cos^{2} \theta_{w}} g_{\mu \nu} O_{i1} O_{j1} $} \\ \\ \parbox{2cm}{\includegraphics[scale=0.3]{JJ2higgs}} & \parbox{7cm}{\begin{eqnarray} \nonumber :~ &+&\frac{i}{v^2} \left[- O_{i2} O_{j2} \left(m_{H_{1}}^{2} O_{12}^{2} + m_{H_{2}}^{2} O^{2}_{11} \right) ~\tan^2 \beta \right. \\ \nonumber &+& \left. \left(m_{H_{2}}^{2} - m_{H_{1}}^{2} \right) O_{12} O_{11} O_{i1} O_{j1} ~\tan \beta \right] \end{eqnarray} } \\ \\ \end{tabular} \caption{\em Quadrilinear couplings.} \label{quadverts} \end{figure} \clearpage	{ "redpajama_set_name": "RedPajamaArXiv" }	6,045
_A Star Shattered: The Rise & Fall & Rise of Wrestling Diva Tammy "Sunny" Sytch_© 2016 by Tamara Sytch All Rights Reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, without permission in writing from the publisher. For more information contact: Riverdale Avenue Books 5676 Riverdale Avenue Riverdale, NY 10471. www.riverdaleavebooks.com Design by www.formatting4U.com Cover by Scott Carpenter Digital ISBN 978-1-62601-256-1 Print ISBN 978-1-62601-257-8 First Edition February 2016 This Book Is Dedicated to: Chris, my one true love and soulmate; My father, who made me the woman I am today Stacey, my niece and soul sister, my fallen angel. # TABLE OF CONTENTS PROLOGUE 01 THE BABY STEPS 02 MY FIRST LOVE 03 A LONG, HOT SUMMER 04 FORCES OF NATURE 05 DID I EVER TELL YOU YOU'RE MY HERO? 06 A TWIST OF FATE 07 THE END OF AN ERA 08 GIMME A C! C! 09 THE SUN IS RISING 10 MOVE OVER PAMELA, THERE'S A NEW PIN-UP IN TOWN! 11 SLOP, DROP, AND ROLL 12 ALL HAIL, THE GLADIATOR! 13 A HEARTBREAKING ROMANCE 14 THE "LOVE TRIANGLE" AND THE MONTREAL SCREW JOB 15 OH, WHAT A RUSH! 16 ARIBA! MEXICO! 17 DIVA WARFARE 18 THE MOST ELECTRIFYING MAN IN THE WWF SCHOOL 19 MY EXTREME TRANSITION AND THE HYPNOTIST 20 HEAVEN NEEDED AN ANGEL 21 WCW-THE COMPANY FROM HELL 22 WELCOME TO MY NIGHTMARE! 23 AYE DIOS MIO! USTEDES ESTAN LAS CUCARACHAS! 24 ONLY THE GOOD DIE YOUNG 25 STARTING OVER 26 THE CREAM ALWAYS RISES 27 I'LL HAVE THE ALL-YOU-CAN -EAT RIBS, PLEASE? 28 OVER BARBED WIRE AND THROUGH THE WOODS, TO THE LIQUOR STORE WE GO! 29 THE DEVIL'S SON 30 MORE LOBSTER, PLEASE? 31 HOME SWEET HOME... OR SO I THOUGHT 32 HOME AWAY FROM HOME 33 MIRACLES HAPPEN 34 SLEEPING WITH THE ENEMY 35 SO MUCH FOR MY HAPPY ENDING 36 THE BIG 'C' 37 A NEW LEASE ON LIFE EPILOGUE ABOUT THE AUTHOR ACKNOWLEDGMENTS OTHER RIVERDALE AVENUE BOOKS # PROLOGUE Bruised. Battered. Broken ribs. Busted Lip. Broken. These are the physical feelings I have right now as I sit here, in an 8 x 8' cinderblock cell in the Mental Health Unit of the York Correctional Institution in Niantic, CT. All that surrounds me are four walls of concrete, painted a not-so-lovely shade of lavender, a sink, a toilet, a shower with no privacy, and a "Bunkie" who has enough of her own emotional instabilities to not be bothered with my shit. At the rate her brain is functioning, she probably couldn't understand my shit anyway. I'm lying under my hospital green sheet and blanket, excited that I received this writing tablet from the commissary today. Yes, that is a highlight of your week when you're an inmate at a women's state prison. Inmate # 393257, to be exact. You're probably wondering why I'm here, right? Well, to put it plainly, the man I loved most in the world, and whom I thought loved me, put me here. Yep, my fiancé... Damien. The man I was going to marry. Just 29 short days ago, he put a ring on my finger and asked me to be his wife. I said yes. Why the hell did I say yes? Was it because I truly did love him? Was it because it was the first time I've ever been officially proposed to? Was it just that the sex was so good that I didn't want to let it go? Maybe it was a combination of the three, because he really didn't have much else going for him. He was one of the sexiest men I've ever been with. The way his curly long hair would blow in the breeze; the way his smooth, caramel skin felt against mine. The way he would saunter up to me sensually when he wanted to make love, his big green eyes sparkling when he looked at me. It was enough to make me melt. On the other hand, he lived in a pigsty of a dumpy apartment, held a job (barely) at a home restoration company making $10.50 per hour, and his one, and only, credit card was still being managed by his Mommy. He was always behind on rent, and each time I moved back in, I had to clear up his bills. So, who was this man I loved so much? He is the man that has broken me down emotionally so much that I feel physically numb. I feel nothing whatsoever. I'm sitting here in a tiny jail cell, and I'm not even that distraught. I have my moments where I'll break down and lose it a little, especially when most meals consist of cream of wheat and white bread, or "slop" as they call it. I'm numb. But, deep down, there are still feelings swimming beneath the surface. Heartbroken. Cheated. Lied to. Betrayed. Used. Abused. Degraded. Demeaned. Brutalized. Hurt. Ashamed. Embarrassed. In a word, shattered. # CHAPTER 1 THE BABY STEPS _"Behold I send you out as sheep amidst the wolves; so be shrewd as serpents and innocent as doves"_ Matthew 10:16 This scripture from the New Testament is easily my favorite because it applies to every aspect of my life, especially now. I've never felt more like a sheep amidst wolves as I do now. I'm in prison. My life has fallen apart. My freedom is gone. Everything I own is in the possession of the man who put me here. A man. A man I had planned to marry. I never thought a man whom I've known for less than a year could have such control over my life. It's pathetic and I'm ashamed of myself, and this coming from a woman who has been headstrong, confident, and assertive all her life. I allowed this man to do this to me, to put me in this miserable place, to take my life from me. Things used to be different. I was born Tamara Lynn Sytch, 7 lbs., 6 oz., on December 7th, 1972, to Raymond and Noreen, a steelworker and a homemaker, respectively. My father owned a steel fabrication and construction company, while my Mom was perfectly content staying at home raising my two sisters, my brother, and me. We lived in a doublewide mobile home in a mid-sized town in New Jersey called Old Bridge. Yep, a trailer park. To this day, I still don't understand why we lived in a trailer, since Dad owned his own company. We always had everything we needed or wanted especially me because I was the baby so I can only chalk up our living arrangements to laziness. Dad always walked around with about $500 cash rolled up in the pocket of his navy blue work pants, and quite often I was sent to the store to buy a gallon of milk with a $50 bill and was told to keep the change. Needless to say, I was Daddy's little girl. Actually, I was from the very moment I was born. My father was retired Navy, so I was born in an Army hospital because of his benefits. I was to be named Jennifer Lynn, but that changed while my mother was in labor. See, my father was a bit of a drinker in his younger years. The fact that his wife, at 38 years old, was in labor for 36 hours with their fourth child on the way 16 years since their third child was born put him over the edge a little. He was drinking and driving all over the Army base, and I mean all over all over the curbs, the grass, bushes, everywhere. The military police finally caught up with this mad man to arrest him, but when he explained the circumstances, they rushed him into the delivery room, out of pity, I suppose. As my father rushed into delivery, drunk as a skunk, I was just coming out of the womb, and he proclaimed, "She's not Jennifer! She's Tamara!" as he waved the bottle of vodka he was drinking in the air with pride. Well, the vodka was aptly named "Tamara." There I was, daddy's little girl from the first second of my life. I was truly spoiled rotten, given anything and everything. I went fishing, crabbing, and hunting with Daddy. I went to amusement parks every weekend with my sisters and shopping daily with my Mom. There was nothing I ever needed because I had it all. I was around 7 or 8 years old when my neighbor Joseph came over on a Saturday morning and wanted to watch TV because he said his parents wouldn't let him watch at home. Joseph was just a year older than me, but we were play buddies since we were born. He turned on local channel 11 (no one had cable TV back then) and guess what came on the screen? WWF WRESTLING! Now, I had never watched it before, nor did I know who any of the wrestlers were, but within a few short weeks I knew every wrestler, every weight, every town they hailed from, the good guys, the bad guys, the announcers, the referees everything! It was like crack for a 7-year-old kid. I couldn't get enough. It didn't take long until my Mom and my sister began taking me to live shows at the Meadowlands in North Jersey, each and every month. I was hooked! I had every monthly wrestling magazine that was on the market; there must have been about 25 at the time, when you counted all of _Pro Wrestling Illustrated_ titles, _WWF Magazine_ , _Wrestling Eye_ , _Wrestling Fury_ , and so many more. I had every LJN rubber action figure as well, from Hulk Hogan to S.D. "Special Delivery" Jones. But the highlight of my month was seeing the WWF live, seeing all my favorites: Ricky "the Dragon" Steamboat, Ivan Putski, Barry Windham, "Mr. Wonderful" Paul Orndorff, and most of all, the Hulkster! Before a show one night, we hit the Howard Johnson's by Newark Airport for a pre-show dinner, and OH MY GOD! We got a lot more than dinner! A _whole_ lot more! It turned out that the HoJo's at the airport was the hotel where all the boys stayed. I couldn't believe my eyes when I saw each and every one of the WWF crew walk through the lobby, sit and eat dinner in the same restaurant that we were OH MY FREAKIN GOD! I was in sheer heaven. Luckily, my sister carried her camera everywhere, so I was getting photos and autographs galore. I was never turned down by anyone, probably because I was raised to be a sweet and polite kid. Month after month we hit the HoJo's for a good three or four autographs. I racked up a photo album and autograph collection that would have been the envy of the biggest superfan in the world! At one show, the main event was Hulk Hogan vs. Sgt. Slaughter for the title Now, I was the biggest Hulkamaniac ever, so I made sure my Mom got our seats directly on the entranceway railing, which she usually always did anyway. So it's time for the main event, and Hogan and Slaughter are battling like gladiators. Hulk got out of Sarge's finishing maneuver, the Cobra Clutch, a few times, but he got busted open in the course of the match. After Hulk got the win, as he was returning to the locker room, I patted him on the shoulder. When I looked at my hand, it was covered in his blood! Now, most 11-year-old girls would have screamed or cried, but I was so ecstatic that I made a hand print on the back of the program. That made my night. OMG! Hogan's blood! Yes! (OK, I was a demented child.). That same night, the WWF Women's Champion Wendi Richter (another fave) was defending her title against Leilani Kai, so I brought a bouquet of flowers for her that night. After her victory, and as the sound of Cyndi Lauper's "Girls Just Wanna Have Fun" hit the arena speakers, Wendi proceeded down the aisle and I reached over the railing with flowers in hand. Not only did she take them, but she gave me the biggest hug ever! Needless to say, I was the envy of every single fan in my ringside vicinity. Blood from Hulk and a hug from Wendi. This was as good as things got for a superfan like me. I have to credit Wendi Richter for inspiring me to get into the wrestling business at such a young age. Once I had a strong female role model to look up to, I started lifting weights, eating healthy, memorizing promos from TV, and practicing my "wrestling move repertoire." I had my Mom buy me elbow and knee pads, put on my old gymnastics leotard, tied neon-colored bandanas around my wrists and ankles, and even chose my entrance music: "Warrior" by Patti Smyth. My ring name was "The American Dream," Tammy Walker. OK, don't ask me how I came up with that one, I really had no clue. So, I would cue my music, get all dressed and ready and make my entrance down the hallway to my parents' bedroom, or what I would call "My Arena." Their bed was my ring, and the vast array of maneuvers and moves I would lay upon my invisible opponent was quite impressive. Dropkicks, elbow drops, camel clutches, figure four leg locks, you name it, at 11 years old, I knew my shit. I started to phase out of my wrestling obsession around age 13, and my last live show was actually an AWA show in Asbury Park, NJ. On this night I completely fell in love for the first time with a 21-year-old beautiful man with dirty blonde hair and a killer smile, the one and only Shawn Michaels. After that night, I started to watch a little more of the AWA on TV; those were the "Wrestle Rock Rumble" days. I followed him in magazines because the AWA didn't run shows very often in New Jersey, so it was love from afar. Of course, I figured I would probably never, ever meet him or see him again... or so I thought! # CHAPTER 2 MY FIRST LOVE _"Silhouette, of a perfect frame, shadows of your smile will always remain"_ Avant So now it's the late 1980's and I'm in my glorious high school years. Puberty hit and I wasn't really interested in wrestling anymore. I was more interested in my school activities and boys. My high school resume was quite impressive: captain of the cheerleading team, student council, National Honor Society, student of the month, ski club, peer leader, special-ed swim instructor, yearbook editor, Future Business Leaders of America, homecoming and prom queen nominee... the list goes on. I was also a straight-A student and ranked 19th out of 354 students academically in my class. Yeah, I was one of those goody two shoes nerds. But I was the HOT goody two shoes nerd; blond hair, big time flirt, with the shortest cheerleading skirt on the entire team. Yeah, I made sure of that. I got my fair share of attention from the boys, but didn't have many boyfriends because I intimidated just about all of them. I may have been the biggest flirt of the school, but I was also probably the only virgin left in the place. That was by choice though, not lack of offers. It was June of my senior year June 2, 1990 to be exact less than a month away from graduation. I was babysitting for my cousin Cara's newborn that night, when I got a phone call from my sister, Denise. She told me there was a small wrestling show in the high school gym, and a man she knew from back in our wrestling fan days, Professor Elliott Maron, was going to be there as the timekeeper. It sounded like fun, so I told her to go to the show, and when Cara came home, I'd head back down and see if I could join her there. By the time I got there, the show was almost over, but I sat down and looked up at the ring. Almost instantly, I fell in love. There was a muscled-up, bleached blonde wearing white trunks with a standout tan. Wow. This guy was my exact type! I was 17 at the time, and I knew he must have been much older, but I kept joking with my Mom and sister, saying, "See that guy in the white? I'm gonna take him home tonight." They laughed it off, but I wasn't kidding. I was thinking of some way to at least meet him, and since I've always been a creative girl, I had something in mind. I told my Mom and sis to go ahead home, since I had my own car there, and I was going to wait around a bit after the show. So I waited. And waited. And as the locker room emptied and he came walking by, I very smoothly asked, "Can I have your autograph?" Slick, huh? He writes on the little piece of paper I handed him, and he handed it back. It read: "Chris Candido" And his phone number SCORE! I knew I was irresistible that night in my sexy white outfit and flowing blonde hair. So he walked on and went out to the parking lot. I followed a few seconds later and got into my car. I noticed him sitting on the curb with his bag beside him. So, thinking quickly, I lowered the top of my 1989 Chevy Cavalier Z-24 white convertible, drove up to him in a slow and deliberate way, peered out over the door and in my sexiest 17 year old sex-kitten voice asked, "Do you need a ride?" Man, I had all the lines that night. He said his car was around the back of the gym, but he was waiting on his friends who must have left already. I told him to get in and that I would drive him around back to his car, which was a 1980 Monte Carlo, primer grey and, as Jim Ross would say, bowling shoe ugly. Not exactly the type of car my usual boys of choice would drive. See, in my school, the parking lot was full of sports cars, convertibles, BMWs, and Corvettes. Not broken down old Chevys. So we pulled up next to his car, I parked, and we start to talk. I tell him I'm 17, about to graduate high school, and I'm going to the University of Miami on an academic scholarship to be a doctor. He responds that he's 23, didn't get passed the 10th grade, and is an alcoholic, regularly going to AA meetings, and that he just got out of jail. WHOA! OK!! The thought now going through my mind just changed from "Wow, is he cute," to "Oh my God, how do I get this alcoholic criminal psycho out of my car before he steals it, rapes me, or worse?" He must have been able to tell by the look on my face that I was scared half to death, so he broke down, started laughing, and said, to my relief, "I'm 18 and about to graduate from Red Bank Catholic High School. I'm not an alcoholic and I've never been to jail." I had to have sighed out loud because at that moment, he grabbed the back of my head, pulled me in, and kissed me. He kissed me hard. It was easily the greatest kiss I had ever been given up to that point. When it ended, he apologized and said, "I'm sorry, I just had to." "Don't be sorry," I replied. "Just do it again." So he did. And he did. Again and again. Probably for about 30 minutes or so. Those 30 minutes felt like the world had stopped, time stood still, and we were the only people left on the earth. It was absolutely magical. Once again in my sex-kitten voice, I asked if he'd like to come over for a while. Of course, he said yes. Chris followed me home, which was only about two miles away, and he followed me up the walkway, up the front steps, and through the door of my parents' house. My father was already asleep, so I rounded the corner to the kitchen where I heard my Mom and sister's voices. "I'm home," I announced. "And I brought someone with me." The look on their faces was priceless! They could not believe that I did what I said I'd do, and brought home the wrestler I said I would. I introduced them to him, and then Chris and I went to my bedroom to hang out. Now, it's 1990, I'm 17 ½ years old, and I'm still a virgin. Yeah, I had my fair share of boyfriends, but I never gave it up. It was never right. So Chris and I talked for a while, watched TV, and made out excessively. Ok, yeah, I blew him. But no sex. What kind of a girl do you think I am? OK, don't answer that question. We stayed up until about 4:00 a.m. and I led him back to the Garden State Parkway so he could make his way home. I was head over heels in love, L-O-V-E, love! This was the first time I ever felt that way in my life. Christopher was my first love, even though I only knew him for a few hours. The next day, we spoke on the phone all day long, and I invited him over again that night. When he got there, it was like we had been dating for a year already; everything was so perfect and right. That night, June 3, 1990, was a monumental night for me well, for both of us. We made love. OK, we had beautiful sex, for the very first time, for the both of us. Turns out we were both virgins at 17 and 18 years old. I was, because of choice; he was because he was incredibly shy around girls, and girlfriends were always the last thing on his mind. Wrestling was first and foremost, followed by weightlifting. Those were his passions, his two true loves. And now I was his third true love. For two people who really had no idea what they were doing in the sex department, it was really good. Our bodies moved together at the right pace with the right rhythm. It was only the missionary position, but it was perfect. It lasted about five minutes and it was the very first time I had an orgasm because of someone else. I had been masturbating for about six years, so I had them on my own, but none of my boyfriends ever got me to the point of no return. Granted, there was plenty of finger action and oral play, but let's face it: teenage boys are pretty clueless as to what it takes to get a girl to that point. But Chris and I were just physically made for each other. There was never a time when I didn't have an orgasm from having sex with him. He was also the best kisser I had ever had—and I had kissed quite a few frogs looking for my prince. So that was it. June 2 became our anniversary, and June 3 became our "fucking anniversary," pun intended. The next day in school, I walked around like a proud peacock, bragging to all my girls that I wasn't the "last American virgin" anymore. They laughed at it, because most of them lost their virginity by the 10th grade. So maybe I was a prude in a way, but I could give a blowjob that could win awards! So there! That was the beginning a relationship that lasted almost 16 years. Everything moved so fast. Within two months, on August 10, I was supposed to leave for school in Miami. I had my U-Haul rented and a hitch put on my Z-24. I knew my roommate and we discussed who was bringing what to the dorm. Everything was in place and college was waiting... until... August 5, 1990. I broke down. I knelt in front of my dad on the living room floor as he sat in his recliner and I cried. "What's wrong, Squirt?" he asked. Squirt was my dad's nickname for me since I was a baby. "I can't go to Miami, Daddy," sobbed. "I love Chris and I want to stay here with him." My dad looked at me sternly and said, in his strong voice, "Then don't go. You're giving up a scholarship, but if you don't want to go, don't." There was a sense of disappointment in the tone of his voice, but I could see that gleam in his eyes, the gleam that gave him away. He was happy I wasn't going. He was as happy as a pig in shit that his baby girl wasn't driving 1,200 miles away and spending four years away from him. I was Daddy's little girl. All he wanted was for me to be happy. He gave me anything I wanted and did anything for me. It would have broken his heart for the little girl who made his lunch for work every day and played the piano for him to fall asleep to leave home for that long, that far away. I called Chris and told him I was staying home. I think he was crying on the other end of the phone! We spent the rest of the summer lounging on the beach, soaking up the sun and soaking in each other's company. In September I enrolled in Brookdale Community College, since I had turned down Rutgers University, the only local university I had applied. For the rest of the year, we carried on like two giddy lovebirds, hopelessly in love. I was going to college and he was wrestling his indie shows, and I was there for every single one of them. Within a few weeks of dating, he was a permanent fixture at my house four or five nights a week, staying over all of those nights, although Daddy had no idea. If Daddy had known we were sharing a bed five nights a week, his big, booming Russian voice would have cowered me into a corner, and his big, strong Russian palm would have slapped Chris so hard he would have flown across the room with one swat. He never knew. Until one night. At around 3:00 a.m., Chris got hungry so he wrapped himself in a towel and tiptoed into the kitchen. We had a huge pantry, and a light came on when the pantry doors were opened. Chris cracked open the pantry doors and scanned over the food and junk food packed inside, everything from potato chips to cookies to Entenmann's cakes. The plan was to grab something fast and retreat back to my bedroom. "Hungry?" My father's big, gravelly voice boomed out, nearly scaring Chris out of his towel. He was caught! In the kitchen at 3:00 a.m. Wearing nothing but a towel! The shit was about to hit the fan. Chris gaped at my father, a deer caught in the headlights. "Go start up the grill," my father commanded. Chris did as he was told and went outside, in a towel and bare feet, in 45 degree weather, at 3:00 in the morning, and lit the grill. My father pulled out a dozen filet mignons from the freezer, handed them to Chris, and told him to put them on the grill and don't come back in until they were fully cooked. So Chris goes outside and practically freezes his balls off for 20-30 minutes cooking up 12 2-inch thick steaks. When everything was cooked, he came back inside with the steaks, and my dad has a smorgasbord of food lined up on the kitchen table, enough to feed an army. Potato salad, macaroni salad, cole slaw, the works. He made Chris sit down. Dad took four steaks for himself and gave the other eight to Chris. "You said you were hungry, now eat," my father said, as he spooned heaps of salads onto Chris' plate, alongside about 40 ounces of juicy filet mignon. By this point, Chris was relieved he hadn't been shot, but he was still white as a ghost in fear. My dad could be a scary man. He stood 6'3", weighed 360 pounds, and had hands the size of bear claws. I once saw him make a grown man break down and cry. There was nothing else Chris could do except pick up his fork and knife and eat. He ate, and ate, and ate, for about an hour straight, until all the steaks were gone, and all the salads were gone, too. The entire time, while doing his best to not vomit, he tried to keep up conversation and give respectful answers to all of my Dad's small talk questions. "Yes, sir." "No, sir." "Yes, sir." I had been hiding in my room the whole time, terrified to even peek my head out of the door to see what's going on, so was clueless about Dad and Chris' late-night buffet. About two hours after he had snuck out of my room to grab a snack, he returned, just as the morning sun was coming up. "Oh my God! What happened?" I asked. "Is he pissed?" Chris looked at me, with a thoroughly confused expression on his face. "He fed me," he said. "A lot." I squealed with joy. "That means he LIKES you," I said. "Ohmigod, I am so happy he likes you!" And I hugged him like I hadn't seen him in years. See, this was my Dad's test. He was testing Chris' will and respect. And Chris passed, with flying colors. After that, we didn't have to hide his car around the corner anymore and sneak him in the back door. He was now part of the family. Thank God. # CHAPTER 3 A LONG, HOT SUMMER So Christopher and I began our journey into our relationship throughout the remainder of 1990 and into the spring of 1991. These months were dotted with many independent bookings for him up and down the eastern seaboard. Of course, his devoted girlfriend went with him everywhere. Already an avid photographer, I began shooting his matches while my video camera was set up somewhere filming. One way or another, my photographs landed in the hands of the very well-known magazine editor Bill Apter and he asked me to do some freelance work for him. Awesome! This was going to be easy money. I just had to shoot the matches I was at with Chris, then get paid for it! Not exactly. I did shoot the matches. Then I had to get the prints developed, and then send them to Bill. Then he picked which pictures he wanted to use in the dozen or so magazines he edited. Then he sent me a check for $10 for each photo used. By the time I spent money on buying film and getting six rolls or so developed, I usually broke even, and sometimes I lost money on the deal. But I did get photo credit and one of my shots did make it to a color centerfold! (That pic was of a tarred and feathered Ricky Morton. I can still see that picture in my head! It was a great shot!) That was my first paying job in the wrestling business. I thought it would be my only one, since I was elbow deep in biology books by then, but that wasn't to be. Chris got booked on a show run by Joel Goodhart in the Tri-State Wrestling Alliance. Chris wanted me to escort him to the ring as his valet, but Joel said there was no way he was paying someone who wasn't in the business to valet on his show. So I wasn't going to get paid. No big deal, this was for Chris anyway. I was 17 and all excited that I was actually going to "work" on my first pro wrestling show. Whoooo Hooooo!! I went to the mall and bought this fancy dress, white lace, off the shoulder, with ostrich feathers on the shoulders and shoes and jewelry to match. I must have spent $200 to work a show I was making nothing on, but I was so excited, I didn't care. We had one of Chris' friends do an impromptu photo shoot before the show so there would be actual photographic proof that it actually happened. Off to the Philadelphia Civic Center we go. On the card were Abdullah the Butcher, Woman, Kevin Sullivan, Baby Doll (who took a bump while six months pregnant), Magnum TA, and a host of Pennsylvania and New Jersey independent guys who no one had ever heard of, including the Sandman and the Rockin' Rebel. Chris was scheduled to be in a match with all the indie guys, a reverse steel cage battle royal. What is that, you ask? Well, all the guys start on the floor on the outside of the cage, and the winner is the first to climb and get into the cage. Stupid. Yes, I know. But I was all excited while I was getting ready. Nancy Sullivan, better known as Woman, started making small talk with me. "So, are you a heel or face?" she asked. I froze. I had no friggin' clue what she meant. By this time, I was smartened up to the business somewhat, but right then I realized I had a lot more to learn. Since I looked confused, she clarified. "Babyface or heel?" I finally caught on and nervously replied, "Oh, babyface. I'm sorry." I had just made a complete ass of myself with the very first real "name" I'd met in the business, and I found the first opportunity I could to sneak out of the room in embarrassment. Nancy was a very, very lovely woman, and I'm sure she didn't think any less of me for being so green. She probably likened it to her early days as the Fallen Angel, valet to the maniacal Kevin Sullivan in the early 1980's. We ran into each other on a few indies after that and always maintained a nice rapport. Unfortunately, the world lost beautiful Nancy just a few years ago at the hands of her husband, Chris Benoit. That tragedy will never be forgotten. Neither will Nancy. RIP. The next big show on Chris' agenda was an indie card for Dennis Corraluzzo's NWA in South Jersey. Headlining the card would be "Hot Stuff" Eddie Gilbert and God-knows who else, it was so long ago. Eddie took an instant liking to Chris, but it was obvious he took a liking to me as well. He was very nice, posed for a few pics for me, and we made some small talk. The next thing we know, Chris started getting phone calls from Dennis saying that Jerry "The King" Lawler wanted him down in Memphis in the USWA, on Eddie Gilbert's recommendation. OH MY GOD! This would be his first full-time wrestling job in an actual territory with television exposure! It was a dream come true for Chris. He was more excited than a kid in a candy store. Of course, being the ever-supportive girlfriend, I agreed to come along. Since it was over the summer, months before my first year in college, I wouldn't be missing any school, so I got my parents' blessing. We packed up his 1980 Chevy Monte Carlo with some clothes and a cooler of food, and hit the road for our 19-hour journey to good ol' Memphis, Tennessee! About 17 hours in, and only 130 miles or so from Graceland, his car died. It just died. It was 98 degrees of sweltering heat somewhere in Tennessee and we were stuck on the side of the road. Keep in mind it was a Friday night and Chris was supposed to start that very next day in the Memphis Coliseum. Shit! What the hell do we do? Luckily, we found a gas station close by, and they agreed to fix Chris' car at 6:00 a.m. the following morning. It turned out the water pump went kaput. They replaced it in a few hours, and we were back on the road. As we pulled up to the Coliseum that hot and sticky Saturday afternoon, we were greeted in the parking lot by a scrawny, dirty looking man who looked like he'd slept in a gutter the night before. It was Downtown Bruno, a Memphis heel manager who would later gain fame as Harvey Wippleman in the WWF. Bruno told us that the ring wasn't up yet, and that there was no air conditioning in the building, so he directed us to go to the resident Memphis motel and get our room. As we pulled up to the Admiral Benbow Inn, we noticed the vacancy sign read "$19/night." Holy cow! Memphis is cheap! As we entered the room, we immediately realized why it was so cheap. The bed was completely sunken in the middle; it was like the springs had been removed. The blue carpets were so stained they were more of a very dark gray. Since we were so sweaty from the breakdown and the 19-hour drive, I decided to take a shower. When I came out and began to dress, I realized that the filth from the carpet had made my feet even dirtier than they were before I went into the shower! Ewww! Being the spoiled, bratty 17-year-old that I was, I insisted we leave. We found the Howard Johnson's down the road for $40 bucks. By now, it was time to head to the show. As we pulled up to the arena, another car pulled up alongside us, a huge brown Cadillac packed with a very interesting cast of characters. At the wheel was a terribly ugly, scarred-up guy with long black hair, messed up teeth, and wearing a turban. In the passenger seat was an athletically built guy with a dark blonde ponytail who happened to resemble a certain action movie hero. And taking up most of the back seat was a guy with long curly brown hair, a pot belly, and a dimply smile that only a mother could love, wearing jean overalls. These three men turned out to be Sabu, Rob Van Dam, and Tex Salinger (who was later known as Phineas Godwin and Mideon in the WWF.) It was their first crack at the "big-time" too, and we all instantly became friends. Especially Sabu. He and Chris really hit it off, and since he is highly respectful towards women, so did we. This was the start of Chris' run with the USWA. When your boys on the indie scene talk about "paying their dues," most of them honestly don't know what that expression really means. Working the USWA was paying your dues. You got paid anywhere from $15 to $40 per night, six nights a week, and the $40 only happened once a week, on Monday nights in Memphis, the BIG show. Even in 1990, that pay was only enough to pay for gas to get you to the next town, which was between three and six hours away. How were you to pay for a hotel and food? I don't know how some other guys did it, but luckily for us, I had a very generous father who didn't want his little girl sleeping in a car and starving to death. I bought an electric burner and a pot and cooked some meals in our hotel room at times. Times were definitely tough, and I was not used to living this way, but it gave Chris the priceless experience of working with guys the likes of Eddie Gilbert, Jerry Lawler, Bill Dundee, Tony Anthony, Tracy Smothers, and Eric Embry. I also became friends with Stacy Carter, who soon after became Jerry Lawler's wife and found fame of her own in the WWF as The Kat. Once a week, the boys took a nine-hour bus ride to Dallas, Texas, for a TV taping. Girlfriends weren't allowed to go on the bus, so I stayed back in Memphis alone. Eddie Gilbert had heard that I was staying behind, as he always did, because he despised taking the bus ride, so he asked me to hang out with him, his brother Doug, Tony Anthony, and Eddie's childhood friend John Guillem (who was somewhat "off" if you know what I mean). I joined them for Chinese food, followed by Putt Putt Golf, and headed to my motel to check in. When I got there, they refused to rent me a room, even though I had stayed there many times before. Unbeknownst to me, Memphis had a law that stated that you had to be 18 to rent a hotel room. Shit! Chris was 18 and had always rented the room, but I was just 17. What the hell was I supposed to do? I drove back to Eddie's apartment and begged for help. We went back to the hotel and he asked for a room. The older woman working the desk must have thought I was a hooker or that Eddie was a pedophile, because she already knew I was 17 and Eddie's ID showed he was 31. The look on her face was worth a thousand words! Ha! But at least I had a safe, warm place to sleep that night. This became the weekly routine for our little Memphis crew—Chinese food, golf, Nintendo, and Eddie renting my room. Thank God for Eddie and his friendship, or else I never would have survived. In later years, when Jerry Lawler published his memoirs, I found out the REAL reason why Chris got the job in Memphis. Eddie had told Jerry of a sweet young blonde dating a kid with some decent in-ring talent. He didn't know exactly where this kid would fit in in Memphis, but he was damned sure he'd bring his blonde girlfriend with him. Eddie and Jerry agreed that they could each work on getting the girl in bed—or maybe even the both of them. That sweet, young blonde was me. And no, it didn't happen. If you don't believe me, buy Jerry's book and read for yourself (You're welcome, King!) Eddie and I remained great friends after our departure from Memphis, and Chris built a lifelong brotherhood with Sabu. It was now back to college for me, and off to the indies for Chris. # CHAPTER 4 FORCES OF NATURE There are some things in life we just can't control. Like the weather, or our own destinies. My destiny was all about to change without even giving me a hint to warning. I was just about finished with my second year of college at Monmouth University—pre-med, majoring in biology. Chris was set to work another show for Dennis, but this time the one and only Jim Cornette was on the show. Jim had a reputation for having an extremely hot temper and diarrhea of the mouth, but was also known for having one of the best minds in the business. He was a manager extraordinaire and worked with some of the best wrestlers ever to set foot in a ring. Dennis told Jim to take a look at a young kid he had on the show—Chris. Jim, always on the lookout for new young talent for his company, Smoky Mountain Wrestling, happily obliged. He liked what he saw. A lot. After the show, we all went out to a little rib place near the venue. Chris wasn't much of a conversationalist back then; he was usually too shy, especially when he was around other people in the business that he admired. But me, I was as perky and charming as ever. Within a couple of weeks after that meeting, Chris was invited down to begin working for JC and SMW. Based out of Knoxville, Tennessee, this would mean another road trip for us. Since this promised to be more of a long-term spot, I had to figure out what to do about school. I applied as a transfer student to the University of Tennessee in Knoxville, home of the Volunteers. I had no doubt that I would be accepted; after all, I had a 4.0 GPA at Monmouth and UT wasn't that tough of a school to get into. So once again, we packed up—both of our cars this time—and headed down to Knoxville. We found an apartment fairly quickly, a beautiful modern complex called Concept 21 for a whopping $395 per month. In New Jersey, that apartment would have easily been $800 or more. Living expenses were very low in Tennessee. We settled in; I went to UT to register for classes, and we hit the road for Chris' first SMW tour. In the USWA, we thought we had some long drives, driving for three hours each day. We weren't prepared for the Smoky Mountain hikes, which were regularly four to six hours per day, and usually those drives were into the winding roads of the Kentucky mountains. For the first month, every time Chris stepped into the ring, the fans looked baffled. He was in there doing all his fast-moving, rope-running spots and occasional high-flying maneuvers. The SMW fans looked like they'd seen an alien. They were so used to the "old school" style of the likes of Ricky Morton and Tracy Smothers, where a punch and a kick meant more than a moonsault. They didn't know how to respond to someone like Chris. Ricky and Tracy eventually pulled him aside and "showed him the ropes" of how to work a match in the South for those fans. Once he slowed down and adjusted his style, and perfected his whiny, crybaby heel promos, he fit in nicely. After that first month, we were invited to dinner by Jim Cornette and his wife at the time, Kelly. We were set to meet them at Calhoun's on the River, the best BBQ spot in Knoxville. We couldn't relax that whole day. If Jim was taking us out to dinner, he must have had something great to tell Chris about his career and his future in SMW. So we sat down to dinner, order our meals, and Jim looked at me. "I need a girl." "Hmmm?" I responded with a mouth full of BBQ sauce. "Just hear me out," Jim said. "I need a girl, a fresh face to be this Northern, bitchy college student. Someone nobody has ever seen before to be a heel manager. Someone to work ringside, cut promos. It'll only be for six months. You can go back to school after that." WHOA Nelly! Slow down just a minute. As I began to process it all, I thought this guy must REALLY be nuts! I was a pre-med student, I was going to be a plastic surgeon. Wrestling was Chris' dream, not mine. I had never been on camera before. I wouldn't have the faintest idea what I was doing. I had been a cheerleader, so I was used to being in front of crowds, but being on camera? No, not me, thanks. Besides, there was no way in hell I was taking off six months from school for any reason. Nevertheless, I agreed to give it a shot. I figured I could make a few bucks on the weekends and attempt to support myself, since I had been relying on money from my father up until then. So the day came when I needed to film a couple of promos for a months' worth of TV, introducing myself and eventually my first protégé, "Prime Time" Brian Lee. Brian was a huge guy, 6'6 and about 280 pounds, with long blond hair. Real nice guy, but dumb as a box of rocks and couldn't cut a promo if his life depended on it. Enter: Moi. Now I had never put a promo together before either, but I was gonna give it a whirl. Jim gave me four sheets of scripts, told me to be exact, take my time, do my best, and put everything into my own words. What Jim didn't realize was that part of the reason I was such a good student was because I had a photographic memory. I could read something once and give it right back to you, word for word. So after about three minutes of looking over the sheet, I said I was ready to go. He gave me a look of disbelief, but he told the cameras to roll. 3, 2, 1...Action! I gave him his promo word for word, with proper inflection and delivery, with good facials, without a hitch. That expression of disbelief slowly transformed into a look of excitement. Had he just stumbled across a diamond in the rough? His next big star? He had. But I wasn't just his next big star. I was about to become the biggest heel in the company. Tammy Fytch, student from Wellesley College, a prissy private women's college in Massachusetts. Her idol? Hillary Clinton. Her objective? To rule over SMW with her prima donna feminist act, and to dominate every man in the territory. It was perfect, a match made in heaven. Jim Cornette, Smoky Mountain Wrestling, and Tammy Fytch. Boy, was I hated! You see, down in the Tennessee/ Kentucky area, the fans still believed in everything. There were no "smart marks." Kayfabe was alive and well. The more I opened my mouth each and every week, the more they hated me. During a match between Chris and Brian and the Rock and Roll Express, I had to slap Ricky Morton. OH MY GOD! You would have thought I slapped the Pope by the fans' reaction! Every female, and most men, in that building wanted to rip my throat out and tear me from limb to limb. They would reach over the guardrail, which was just rope connected between two posts, and try their damnedest to grab a hold of me. One night, one of them succeeded. As my "heat" was building even more and surpassing even Jim Cornette status, I was attacked by a rather burly woman—ok, she was a 400-pound beast with three teeth and spit flying out of her mouth with every nasty word she screamed in my direction. We were in Barbourville, Kentucky, a rather "hick-filled" town, when Brian and I were leaving the ringside area. As we were halfway down the aisle to the locker room, out of the corner of my eye I saw a set of hands (ok, more like bear claws) reaching for my head. The next thing I knew, I was on the floor with this wildebeest next to me, her hands full of my hair. In a split second, I was being dragged across the floor by my hair. Brian had grabbed two fists full of her hair, while she still had my hair, and he was dragging both of us across the high school gym floor. He finally got her to loosen her grip and I wriggled out of her grasp. Now, having the little temper that I do, I wasn't going away with my tail between my legs, so I got up, stormed into the locker room, grabbed the quite heavy championship belt, and bee-lined for her back in the gym. I was going to permanently imprint that belt across her face. Corny, rightly afraid that I was going to bash her face in with the belt, screamed to Brian. "Dag gummit, Brian! Go get her before she kills someone!!" Brian followed me out, and in one quick swoop, he picked me up under his arm so I was parallel with the floor, and he carried me off to the locker room. I was furious! And bright red! And ready to kick some ass! Although I had never been in a fight in my entire life, I sure put on one hell of a believable act. We hit some pretty interesting towns with some pretty interesting folks, to put it nicely. Ok, who am I kidding? I'm not that nice and politically correct. In the hills of Kentucky, you'd be lucky if the entire front row would make up one complete set of teeth. And it was blatantly obvious that there was quite a bit of "brotherly lovin'" going on up in those hills. Incest was running rampant with the amount of deformities you'd see. One woman had no corneas or pupils in her eyes, her skin was purple, and she had three club-like stumps on each hand instead of five fingers. One man in Hazard, Kentucky, thought he was a dog and barked the entire night. There's some crazy shit you see up in those hills! My first experience working with another girl was when they put Brian in a program with the "Dirty White Boy" Tony Anthony, and JC brought in his wife Kimberly to work with him. Now, "Lil Kim," as Tony affectionately called her, hated me from Day One. She was so pissed that I was offered a job before she was, a spot she thought she was entitled to since she had been around the business longer than me. What she was too stupid to understand that there was no way she could play my role, because she had been known in that area for a couple of years as Tony's regular valet in the USWA and the independents. And Tony was too thick in the skull to be able to explain that to her. So we started our angle, and she took every opportunity she possibly could to get her hands on me and "stiff" me, one way or another. She'd pull my hair, scratch at my neck, kick my shins with her cowboy boots... she was horrible. I finally had to put my foot down and tell Cornette, "It's her or me. I've had enough. Either end this angle and get rid of her, or I quit" He promised me that there were only two more weeks left in the program and that I wouldn't have to deal with her again after that. He promised she wouldn't touch me again except for the match at the culmination of the angle, and even then it would be minimal. God knew he didn't want to lose his money maker, his number-one heel, Tammy Fytch. The final match was booked as a mixed tag team match, and the losers were the team whose girl got stripped first. Just great... not only do I have to wrestle her, but she's going to be tearing my clothes off. Again, I protested to JC. Yes, I was quite the spoiled bitch back then. He reassured me that there would be no wrestling and that I could get stripped any way I wanted. Hmm... Luckily for me, I have creativity coming out of every pore, so I cooked up a plan to get stripped "naked" in front of the fans without them seeing even one speck of skin. The night arrived for the match and I was ready with layers and layers of clothing on. The bell rang, she stormed in and tore my sweatshirt off revealing a T-shirt that read, "I'm too smart to wear just that!" Next, she tore off that T-shirt, only to reveal another shirt which read, "Ha ha, I'm still dressed!" We rolled around a little as she pulled off my shorts, this time to reveal a pair of bike shorts. As she chased me around the ring, I scurried out of her reach and crawled under the ring, where she followed. I quickly removed my T-shirt, (I was wearing a sports bra) and bike shorts and gave them to her, as well as the bra I had taped to my stomach. She then emerged from under the ring victorious, with my clothes and skivvies in hand—leaving me "butt naked" under the ring. Chris ran out to the ring with a huge quilt and threw it under the ring to me so I could cover up. I wrapped my "naked" self up in the quilt and Brian carried me over his shoulder, off into the sunset. There. Done. Match won by the Dirty White Girl. Fans happy I got "stripped" naked. Even though they never saw a thing, they thought they did, and that's all that mattered. Stupid hillbillies. They'd fall for anything. I'm sure you figured out that Lil Kim and I never got along back then, but that was 1993. We were kids. Recently I found her on Facebook and we "buried the hatchet" after all these years. Life is too short to have enemies. Now keep in mind, JC promised me I would have a six-month run and be out of the business, but I was too natural on promos, too good at ringside, and gained tremendous heat too easily to be finished up so soon. We were now two-and-a-half years into my run and I was a senior at UT with just over one semester to graduate. I was making $175 per weekend, and Chris was making $400, so together we were making a nice weekly salary, especially considering how affordable things were there. He and I managed to save up $12,000 in just over two years, which was quite good for a couple of 20 year-old kids. I was doing well in school, mostly A's, and going to classes on Mondays, Tuesdays, and Wednesdays, and studying in the car and locker room Thursday through Sunday. School was going great. And then, one evening, I got a phone call. # CHAPTER 5 DID I EVER TELL YOU YOU'RE MY HERO? "Daddy died." That's all I heard on the other end of the phone. "Daddy's dead, Tam." It was my brother, Raymond, with the most horrible two words a 20 year-old girl could ever hear. Daddy's little girl. I couldn't even respond. I just collapsed to the floor, sobbing. Sobbing became hysterics. Hysterics turned to shock. My father, the man I spent my tomboy years with hunting, fishing, and crabbing, building tree houses with was gone. The silent shock turned immediately to anger. Anger towards God. "How could you do this?" I screamed out loud. "How could you take my Daddy from me? Fuck you, God! If there really was a God, you would have kept him here with me! FOR me!!" Right then and there, I immediately lost all faith in God, Jesus, and religion as a whole. When something that devastating happens so suddenly to someone as young as me, you need someone to blame. I blamed God. Although God had nothing to do with it. For a few years, my Dad was battling with congestive heart failure. That means fluid collects around your heart, puts a strain on it, and makes it difficult to breathe. My Dad was 6'3", 360 pounds. His doctor told him to quit smoking, and he did, cold turkey. His doctor told him to lose weight. That was a bit more difficult. You see, my dad's favorite thing in life was food, and eating food. Eating a lot of it. He didn't just eat for nutrition; he thoroughly enjoyed the act of eating. He would never sit and have one serving. He enjoyed his way through two or three servings at a time. He enjoyed spending money on lavish cuts of meat—hence the dozen filet mignons that were in the freezer the night Chris was caught in a towel at 3:00 a.m. Chris probably got off lucky; knowing my dad, there were probably three dozen filets in the freezer at a time. And my Dad didn't care for "healthy" foods. Nevermind lean chicken and salads. He was Russian. He loved his beef, liver, gravies, sauces, potatoes, and especially butter and cheese! He used more butter than Paula Deen when he cooked! (This is most likely where I got my fixation with butter and cheese as well.) I would make him healthy turkey sandwiches to take to work every day for lunch, trying to get him to lose some weight. I took care of my Daddy. He still went out to the grease truck for lunch at work every day anyway. My Dad passed away of a massive heart attack at 6:00 p.m. on October 18, 1993. He had the heart attack during dinner. He was enjoying seafood takeout from his favorite fish place. He died while doing what he enjoyed the most. I was crushed. Devastated. I could not believe this was happening. I was only 20 years old. I wasn't ready to lose my father. I was in Tennessee, 750 miles away from my Dad in New Jersey. I was so far away that there was nothing I could do; there was nothing I could do to help him. I felt incredibly guilty. I still do. If only I could have been there. If only I wasn't doing this stupid wrestling thing in Tennessee... maybe I could have given him CPR and saved him. If only I was there. The next morning, Chris and I flew home. My sister picked us up at the airport. I cried the whole flight home. When I got to the house, I went into a state of shock again. I was in total denial and disbelief. I ran through my parents' home, determined I was going to find my Daddy there, alive and well. I was calling out his name, anxiously hoping to hear him yell back, "Hey squirt, I'm in the basement." He didn't yell back. He wasn't there. I ran into his closet and grabbed some of his clothes, stole my mother's car keys, and took off for the hospital. I was SURE I could find him there. I bolted into the ER, asking what room he was in. The nurse kept looking at the computer and looking up at me, not wanting to tell me what she had found. I told her that my brother told me he died the previous night. "I'm sorry, honey," she said. "He's probably in the morgue." I knew the morgue must have been in the basement, so I found a service elevator to take me there. Tears were streaming down my face as my heart pounded with fear. I wasn't going to believe he was gone until I saw him for myself. I was crying, thinking it was all some horrible mistake. "He's OK, he has to be OK." The elevator doors opened to a cold, dark, gray hallway. At the end of the hall were two big white doors, and at the top of the doors hung a sign. MORGUE. I found it. I found HIM! I had to break into the morgue, because for obvious reasons it isn't open to the public. But that wasn't stopping me. I approached the lady at the desk and said, "Where's my father? I need to see my father! I need to bring him home. She asked his name and I stuttered, "Raymond Sytch," choking on my tears. "I'm sorry honey, you can't see him," she said. "They haven't cleaned him up yet. There's all tubes and..." I broke down. Tubes? Tubes coming out of my father? It must have been true. My Daddy was gone. My mom eventually found me and took me to my doctor, actually my pediatrician. He gave me a prescription for 20 Valium to help me get through the next couple of days. Each Valium hit me like a ton of bricks and I slept most of the time leading up to the funeral. My Dad was one of a kind. A stubborn, strong-willed big bear of a Russian man. Navy retired. Blind in one eye from his service in the Navy. My dad would never curse. He didn't have to. Just the tone of his voice was enough to make you behave. The worst curse word that ever came out of his mouth was "shit." He was extremely generous and would do anything or give anything to his family or friends. There was never anything I wanted or needed since I got everything I asked for and more. My Dad never sounded happy when I would talk about SMW shows. He always called it "that stupid wrestling stuff you are doing." He would dismiss it as some hobby that I couldn't possibly take seriously. What I didn't know, and I found out after his death, is that he would go to the corner news stand by his business, sit on a milk crate, and flip page by page through the two dozen different wrestling magazines that they carried looking for my picture or even the slightest mention of my name. He bought every issue. He was proud of his little girl. He liked to brag to his employees and friends about me. I never knew all this while he was alive. I never got to smile at him looking at me proudly and to say "thank you." Unfortunately my Dad passed long before I could REALLY make him proud, long before I made my way to the WWF. He never got to see me perform on the big stage, on pay-per-views, in glossy color magazines instead of black and white. I take that back. He saw. He has the best seat in the house. And he watches over me always. I know he does. I love you Daddy. I miss you. # CHAPTER 6 A TWIST OF FATE Chris and I returned to Knoxville after the funeral and I tried to continue life as usual, but I couldn't. I was so grief-stricken and depressed that my grades started to fall in school. I was eventually failing organic chemistry, so I opted to drop the class and accept an incomplete instead of an "F." I attended the subsequent semesters on a part-time basis. I was just so devastated by my father's death that I couldn't concentrate. I couldn't focus. My work, however, was thriving. I continued to garner the most heat in the company and I was voted number-two in the Best Manager category in the _Wrestling Observer Newsletter_ year-end awards in 1993 (right behind my mentor, Jim Cornette). JC even placed a photocopy of it in my paycheck envelope with a note reading, "If you continue to get more heat than me, you're fired." He was joking, of course. This was an obvious compliment of a job well done, but it still didn't earn me a raise, damn it! 1994 was off to a good start. I was working on dealing with the death of my father, school was fine, and work was brilliant. Chris and I had made Knoxville our home and had no intentions of moving back to New Jersey in the foreseeable future. On December 4, the phone rang in our apartment. I answered. "Tammy? Hi, this is Bruce Prichard from the WWF calling. How are you today?" "Fine, thanks," I answered. "Can you hold on a second?" I covered the phone with my hand and yelled for Chris to come into the living room. "The WWF is calling for you," I whispered, pointing at the phone. Apparently I need to work on my whispering, because Bruce heard me on the other end of the line. "No, actually, I'm calling for you," he said. "We'd like to know if you would like to come up to Stamford for an audition." "An audition? Sure!" He told me that someone from the travel department would be calling me and we ended the conversation. An audition with the WWF, on Monday, December 7... my birthday! Could I have asked for a better birthday present? But wait, an audition for what? Now I was stumped. Maybe I should have asked him that question when I had him on the phone. Regardless, Chris and I started jumping for joy. I was headed to the WWF headquarters on my birthday for an audition. They must have seen a tape or two of my Smoky Mountain stuff and wanted to see me live. So I packed an overnight bag and prepared for my trip. I couldn't sleep the entire weekend. I was so anxious I couldn't sit still. Monday came. My 21st birthday. That wasn't important though, because as a young adult who was abstinent from alcohol, turning 21 was just another day. But I was on a 6:00 a.m. flight, headed to LaGuardia airport, where a big, black limo was sent to pick me up and take me to the Marriott in Stamford. This was my first real limo ride, with the exception of my junior and senior proms, which really don't count. I was overcome with excitement. How much better could this get? I was taken to the Titan TV studios. As I walked in, I was greeted by a few of the staff and then ushered up to the make-up room. I met the most wonderful lady there. Flaming red hair, big blue eyes, and tons of freckles. She introduced herself as Jill Getlan, make-up artist. Make-up artist extraordinaire would be more like it! In a mere 30 minutes, she turned this low maintenance college girl who never wore much make-up into a glamour-puss sex symbol, fit for any movie screen. Jill quickly became one of my best friends and confidants. They then brought me down to the studio, an empty, cold, dark studio with one camera set up and a backdrop. What in the world was going on? A producer came in and said, "Hi, nice to meet you. We're going to have you read from the teleprompter and we'll be all done." What? Read from the tele...who? All done? Wait, what exactly is going on? I excused myself and said, "I'm sorry, but I think there's been a mistake. I'm a heel manager. I work ringside. I don't even know what a teleprompter is." "Don't worry, you'll be fine," he said. "Just read the words as they scroll down the monitor under the camera lens." Ok, if you insist. They counted me down and the words started to scroll. They all kind of blurred together. I'm not sure if that was because I was so nervous, or if they were moving too fast for me. My palms were sweaty, my heart was racing, and my temperature rose even though the studio was so cold. I must have been nervous. But wait! I don't GET nervous! I never had, about anything. What the hell was happening to me now? I didn't even get nervous for my first SMW promo! WTF? I started to read. And stumbled. And stuttered. And mispronounced words. And stumbled some more. At one point I just stopped entirely. It had to be the single most embarrassing, terrible, horrific audition any that studio crew had ever seen. When I was done, just ten short minutes later, I was whisked away to my awaiting limo and taken back to the Marriott, where I would spend the night and fly home the next morning. I got to my room, dropped my bag, and shut the door. I walked straight over to the phone, stone-faced, picked it up, and dialed home. When Chris said, "Hello," all I could do was cry. I couldn't even speak. I cried. And cried. And cried. "Babe, what's wrong?" he asked. I went on a sobbing tirade about how it was the worst birthday ever, how I did so horribly, how they had me read stuff and that I had no idea what I was reading. I told him I totally bombed the audition and they would never look at me for anything ever again. I practically cried myself to sleep that night. I convinced myself that I was so bad that they'd never be interested in me. I got the WWF out of my head, so it wouldn't bother me so much. It was my one big shot. And I blew it, big time. On December 8, I flew back to Knoxville, miserable and hopeless. It took some time, but I eventually got myself out of the funk I was in, because I figured things couldn't get any worse. I was wrong. About a week, later we were working a shot in Morristown, Tennessee. Brian Lee and Chris were wrestling Tracy Smothers and Tony Anthony. Just as the match was about to start, I was getting out of the ring and standing on the apron, when Tracy suddenly decided to run the ropes, right in my direction. He hit the ropes where I was standing flat-backed, so I had nowhere to grab onto. As soon as he collided with me, I flew backwards towards the concrete floor at ringside. The first thing they teach you in wrestling is when falling, don't put your hands down to break your fall. What did I do? I threw my hands behind me to break my fall. But instead, the only thing that was broken was my hand; my entire hand! When I got up and looked at my mangled mess of a hand, I panicked and went into shock. I ran straight back to the locker room and sat down, hyperventilating. Jim came over to see what was wrong, and when he saw my hand he screamed. "Oh my God! Jiminy Crickets! What the hell happened?" New Jack, of The Gangstas, saw the look on my face and somehow knew I was going into shock, which wouldn't be good. A person can easily slip into a coma if they pass out from shock. Chris ran back from the ring completely distressed, and Jim and New Jack told him to get back out there and finish the match, that they had me under control. An ambulance arrived a short time later, because there was no way in hell I could have walked to a car to get to the hospital. As they carted me out on a stretcher, right through the fans, I heard them scream, "Tammy Fytch! We hope you die!!" Oh my God! These people wanted me to die! How could they be so cruel? Here I was, mangled hand, severely hurt and scared, and they wanted me dead. The thought made me tear up a little, but then a silent satisfaction came over me—they hate me! They really, really hate me! I'm doing my job! It feels very good inside when you try so hard to be a heel, and you generate enough heat with an audience that they want you dead. So off to the hospital we went, sirens and lights and everything. After a set of X-rays, the doctor determined that I had five fractures and four dislocations. I had fingers pointing in every direction. It was literally too gross to look at. They set my fingers and casted me up. Hence, I sustained my very first wrestling injury—and it was a doozie! Being the trooper that I was, I didn't miss a single show. I worked each night with my cast on. See, it COULD get worse! About a week later, just before Christmas, my phone rang again. "Tammy? It's Bruce Prichard from the WWF." Oh my God! What in bloody hell could HE want? "We looked over your audition tape and would like to know if you'd like to come up and start filming on Monday." Now it was Friday, I was on Christmas break from school, so I immediately shouted, "Yes! Yes! Of course I would!" Then reality hit. I had a fresh cast on my hand up to my elbow. I didn't exactly look as glamorous as I had on my last trip up to Stamford. "Don't worry, we'll work around it," Prichard said. "Go out and buy some business suits and bring the receipt. We'll do what we have to do to hide your arm." I hung up the phone and looked at Chris. "Oh my God! I'm starting on Monday!" But I still had no idea what I was actually starting, or what I was getting paid. I probably should have asked a few more questions. But we were overjoyed, and happiness was just pouring out of every pore. We spent the next two days shopping for the business suits I was told to buy. I packed up Sunday night and prepared to get to the airport Monday morning. When I arrived in Stamford, I was picked up and brought back to the studio. I was then given the details of my new position. I would be filming Monday, Tuesday, and Wednesday every week, and getting paid $500 per day, filming a segment for the televisions shows called the "Live Event News." I would be reading from the teleprompter (I hate that damn thing). My new name—Tamara Murphy. It turned out that Vince loved my given first name, but he wanted me to be Irish, like him, so he named me Murphy. (Coincidentally, one of his granddaughters is now named Murphy.) Vince took an instant liking to me, and actually sat in on some of my filming. He took it upon himself to coach me in my delivery and inflection, and losing my accent. By this time I had my native New Jersey accent with a touch of Tennessee southern added to it. He needed me to be accent free, straight broadcaster style. He especially hated the way I said the word "garden" when referring to Madison Square Garden. At first I thought he was picking on me a little, but I soon realized that if he was taking this much time out of his day, every day, he must have liked me and saw money in me. Vince McMahon doesn't personally coach just anyone. So, this was the game plan: fly to Connecticut every Monday morning, film "Live Event News" for three days, fly back to Knoxville on Thursday morning, work house shows and TV for SMW Thursday through Sunday, fly back to Connecticut Monday morning. But wait... where was there time for college? There wasn't any time for college. But for a 21-year-old kid from New Jersey making $1675 per week, every week, expenses paid, college really didn't seem to matter as much anymore. Beginning the spring semester of 1995, I was no longer a student at the University of Tennessee. Greed and gluttony had gotten ahold of me. Two of the seven deadly sins. Irresistible. I was now an employee of the World Wrestling Federation, and that was all that mattered. But in a way, I kind of felt bad, and a little guilty. Here I am, not wanting to be in the wrestling business and wanting to be a doctor instead, and here is Chris—busting his ass every night because this is all he's ever wanted to do—and I get hired and make it to the big time first. But Chris didn't seem to care. He was genuinely thrilled for me. Besides, our money all went to the same place, anyway. If it bothered him at all, he never showed it. So I went to work. I had my flight, rental car, and hotel and food paid for. All my clothes were paid for. I had a 24-hour passkey that gained me access to anywhere in Titan Towers or the studio. (I actually still have that passkey. I wonder if it still works?) Every day after filming at around 11:00 p.m. (yes, I had very, very long days...in make-up at 7:00 a.m., out of the studio at 10:30 p.m.) I would go to the office building and hit the gym. At the same time, fellow studio employee Stan Lane (made famous in his days as "Sweet" Stan Lane of The Midnight Express) would also hit the gym. I had a feeling that Stan would have liked our relationship to progress beyond being just work-out partners. Stan would hit on me daily, and even though he was a very attractive man, he was about 16 or 18 years older than me. Plus, when he would be on the leg press machine and I got a good look at the top of his head, it was all too obvious that Stan's beautiful head of blond hair was... um... enhanced with surgically implanted hair plugs. Kind of a turn off for a 21-year-old. Stan was very charming and very respectful though, and I did enjoy our time together in the gym. These were valuable days for me, my studio days. They gave me a chance to get to know some of the boys who would come into the studio now and then to film something and to get more comfortable speaking to a camera instead of a live audience. I'll never forget my first meeting with Owen Hart. It was early morning and I was headed upstairs to my dressing room, which was right around the corner from the make-up room. I opened the dressing room door (which was only ever used by me) and there was Owen getting changed—buck-naked with his pants around his knees about to pull them up! Ha! Thank God for him that his back was to me and not his front! When he emerged from the dressing room, red from embarrassment, I sweetly apologized and introduced myself. We eventually became pretty good friends and spent a good amount of time together on the road. # CHAPTER 7 THE END OF AN ERA While I was thoroughly enjoying my new line of work, the Smoky Mountain roster was expanding. This was a very valuable time for Chris and me—the SMW years—because of the vast array of talent we both got to work with and learn from. We had the experience and wisdom of the Rock and Roll Express, Tracy Smothers, the Armstrong family, and the Heavenly Bodies. We got to work with legends like Kevin Sullivan and Sherri Martel. New talent was all around us, such as The Gangstas (New Jack and Mustafa Saed), Lance Storm, Chris Jericho, and Dr. Isaac Yankem, who went on to über-fame as Kane in the WWE. Sherri Martel was very instrumental in my growth in SMW. She was brought in for a triple shot of shows to work ringside opposite me. When she arrived at the building for the first show, she wouldn't even look at me. I tried to introduce myself, but she wasn't having it. I thought, "Geez, what did I do to make her not like me already?" When it was time for our match, Jim explained what we were supposed to do. She was only supposed to stalk me around the ring a few times and reach through the ropes and grab me by the hair until Brian Lee could come over and save me. Well, stalk me she did. And when it came time for her to grab me by the hair, not only did she grab my hair, but she pulled me right up onto the ring apron by my hair. She then laid in four big, heavy forearms to my chest. She didn't work them, either; she laid them in! When she was through beating the ever-loving shit out of me, she released me, the match ended, and I sold the beating all the way back up the long, long dressing room aisle in the Knoxville Coliseum. I coughed, I stumbled, I heaved, I cried—I had to make it look good. Corny was waiting for me when I walked through the curtain. "Oh my God, what was she doing?" "I don't know," I said. "But I don't think she likes me very much. She almost killed me." My chest was beaten red and already swelling, and I was stunned. When Sherri emerged through the curtain, my first thought was to hide under a chair, afraid that she might want to dish out some more punishment on me. We made eye contact and she bee-lined right for me. She grabbed me... and hugged me. Totally NOT what I expected. "I knew you could handle it!" she said, squeezing me in a bear hug. "I had a feeling about you when we met." What the fuck? It turns out that her beating me was a test of my heart and will. She beat the crap out of me just to see if I could take it, handle it the right way, and not crumble. Well, her test was successful, and from that day forward, we were sisters in the business. I earned her respect that night, and she always had mine. And always will. Sherri Martel passed away in 2007. She was a legend in her time and one of the business' premier women wrestlers. She also was inducted into the WWE Hall of Fame in 2006, shortly before her death. Thank you, Sherri. You are greatly missed. RIP 6/15/2007. * * * Chris Jericho and Chris and I always had a good relationship from Day One. We all had the same favorite band, KISS, although Jericho's idol was Paul Stanley and ours was Gene Simmons. One night as we were leaving a show somewhere in Kentucky, Jericho asked us if he could follow us since I had a radar detector and he couldn't afford another speeding ticket. We said "sure" and I told him I would turn on the interior lights to signal to him if there was a cop around. So we were headed towards Knoxville, and the highway ran through a set of tunnels that had been bored right through the mountains. There were no other cars on the road except for us most of the way, so we were flying. As we made it through the last mountain, we noticed a silver bumper protruding ever-so-slightly from the dark shoulder, but the radar detector wasn't reading anything, so we plowed out of the tunnel at around 90 mph, with Jericho right on our tail. All of a sudden, lights and sirens pull out behind him, basically out of nowhere. That's when my radar detector started going berserk, but by then it was too late. Jericho got pulled over, and he asked the cop why he hadn't pulled me over since I was driving the leading car. "I would have," the cop replied. "But I couldn't catch them." I WAS driving my Z-24, and I WAS a speed demon! Chris got a ticket that night, and he still gives me grief about it to this day. Soon Jim decided to bring in a childhood friend of Chris' named John Rechner to be Chris' partner and to become my newest protégé. Jim named him Boo Bradley. His character was a simpleton—almost mentally retarded—that I would lead around on a chain like a dog, and treat even worse. Boo didn't like to shower much in those days, so I was happy to stay a safe distance from him, like the length of a five foot heavy link chain, upwound when possible. Our entrance music was "Magic Carpet Ride" by Steppenwolf, and his simpleton act soon proved effective, as he quickly became one of the fans' favorites. They loved him (because I guess they felt sympathy for him, or maybe they could relate to him) and hated me (for obvious reasons, but now even more so because of the harsh and inhumane ways I treated Boo). We eventually started to use my cat, Buffy, in the story line. Buffy's name was changed to "Boots the Cat" and she was my secret weapon to use with Boo, almost like his Kryptonite. When Boo would be losing a match, I would hold up Boots and threaten to do something terrible to her, and he would immediately gain the upper hand against his opponent. Jim brought in the one-and-only Cactus Jack (who would become better known as Mankind and Mick Foley, _New York Times_ bestselling author and three-time WWF Champion) to be Boo's mentor and persuade him to leave the "evil" Tammy Fytch and be a "good guy." Well, the combination of two simpletons as a team was more than the fans could as for; they were delighted! So over the course of a few weeks, Mick was Boo's coach and corner man at ringside for a series of matches against Chris with me in Chris' corner. This was all leading up to the big show Christmas night in the Knoxville Coliseum, "Christmas Chaos." The plan for the end of this match was for Chris and me to kill Boots the Cat. Ok, we weren't REALLY going to kill her. This is what went down: While Boo had the upper hand and was about to defeat Chris, I held Boots up in the air, stuffed her into a canvas bag, and threatened to toss her off a bridge into the river. Boo chased me down the aisle into the dressing room and then back out the other side. When I got back to ringside, I handed the canvas bag to Chris, who set it in the middle of the ring. He climbed to the top turnbuckle and came crashing down with a big leg drop, on top of Boots the Cat. There you go, we killed the cat. What fans didn't see is the switch in the dressing room. Cornette was waiting there with an identical canvas bag stuffed with a small pillow. No one was the wiser. So what Chris actually dropped the leg on was the pillow, while Boots was safely tucked away in her per carrier in my locker room. Voila! The old bait and switch! Works every time. After the match fans were furious! They were incensed. They had just witnessed us kill a cat, and on Christmas Night! Oh my God, we must be Satanists! Boo knelt in the ring, crying his eyes out, holding the bag in his arms like he just lost his best friend. This made him an even bigger babyface, which he remained right until the end of SMW. Boo Bradley would later become Balls Mahoney of ECW and WWE fame. By this time, Chris and I had run our course in SMW, and had already begun our journey for the WWF, as I'll get into in the next chapter. As for Smoky Mountain Wrestling, an era was coming to an end. The last great wrestling territory could no longer survive on its own, and in a few months, the tapes and archives were sold to Vince McMahon and the WWE. RIP, SMW. You were loved and admired by all. # CHAPTER 8 GIMME A C! C! It was somewhere in the late spring of 1995 and I was told I was being pulled from my Live Event News duties and put ringside as a manager. Perfect! Soon after, Chris was given the call and was brought up as well. Naturally, it made sense to put us together at ringside since we had so much experience at it already. We were brought into the office for a fitting for costumes and a meeting about our characters. We met with the Creative Department and went over designs. My outfit was a cheerleading skirt, a cape, a tank top, and gloves up to my elbows, and Chris' was a singlet and a cape. Our characters were supposed to be a cross between cheerleaders and superheroes— _ugh_. Babyfaces. Just what we both hated and despised being. We were natural heels. Couldn't they just stick with that? They had the costumes in mind but didn't have names for us yet. We were invited to attend WrestleMania 12 in Hartford, Connecticut right after we signed our contracts. Even though we weren't officially on the road yet, we were still in production. So we went to the show, and hung around at Axxess and the PPV. This was the first time I was actually around real Hollywood and sports celebrities, and I have to admit, it was really, really cool. And this show was _packed_ with celebrities! There were Pamela Anderson, Jonathan Taylor Thomas (from _Home Improvement_ ), Tommy Lee, Jenny McCarthy, Lawrence Taylor (who would wrestle Bam Bam Bigelow in the main event), and a host of NFL Giants including Carl Banks and Ken Norton Jr. Stars were everywhere. At Axxess that afternoon, we met a nice guy named Paul. He told us he was just hired as well and he worked a little for WCW. He didn't know a soul at Axxess or in the WWF, and really, neither did we, except for the few I met while filming LEN, so the three of us kind of buddied up the whole day. A few times Paul looked like a lost puppy dog and I felt bad for him. At least I had Chris there with me, while Paul had no one. Paul just kind of followed us around a little trying to not get in anyone's way. That didn't last long for Paul, as he soon became known as Hunter Hearst Helmsley and even better known as Triple-H. More about the name Triple-H later. We had a blast that day and that night at the after-party. We got our real first taste of what the big time was all about and what was in store for us. In the meantime, the powers that be had finally decided what we were to be called—Chris and Tammy, _Team Spirit_! Chris and Tammy, Team Spirit? That was the best thing they could come up with? I had been a cheerleader throughout my teen years and a very good one at that, but Chris was clueless. And now they wanted me to teach him how to be a cheerleader and how to do stunts. Now, Chris was a quick learner but I knew that he wouldn't be able to do partner stunts just by the mass of muscle he held on such a short frame. He just didn't have the range of motion or flexibility. Our first live event and TV taping was somewhere in Western North Carolina. Wouldn't you know it—the town was just 90 miles away from where we slaughtered Boots the Cat! Great. And we were supposed to be babyfaces. Half of the people in the arena were either there at the show on Christmas night and witnessed it live, or saw it on SMW TV that following week. Wonderful. We were just hoping they didn't recognize us... but recognize us, they did! As soon as we got in sight of the fans, they knew who we were, instantly. We got in the ring; I started my little cheer routine, and they started throwing things at us. There was _no way in hell_ we were going to get these SMW-bred fans to cheer us. It wasn't going to happen. As we returned to the locker room after a pitiful showing for our first night, we were met by Vince McMahon in the dressing room hallway. He stopped us dead in our tracks. "Maybe you two would be better off as heels." Ah. Thank God. Finally he saw it _our_ way....Whew! A couple weeks went by and we were in a meeting with VKM, Jim Ross, and Bruce Prichard. At that time, those were the big three in charge. As we made our way through some small talk with Jim and Bruce, Vince sat there with a grin from ear to ear just staring at me. Finally, he stood and spoke up. "I've got it," he announced. "You two are now heels. Your characters are a fitness-guru duo. Chris, I want you to be like Tony Little from the fitness infomercials, with his hype and energy. Your promos will sound just like his. We are going to call you the 'Body Donnas!' (This was a combination of body and prima donnas.) You are Skip and Tamara, you are now 'Sunny.'" Skip and Sunny, the Body Donnas. Chris' smile almost immediately turned to a scowl. Skip? What the hell kind of name is that? By the look on his face, I could tell he wasn't happy. But, Sunny! My eyes lit up and my smile got bigger. I LOVED IT!! What the name meant to me was sun... beach... beauty... a bright, shining star. I couldn't have been happier. But once again, I got the fruits of my labor and Chris was almost cursed with a terrible name. Remember the movie _Twins_ starring Arnold Schwarzenegger and Danny DeVito? Well, you can guess which one of us felt like Arnie at that moment. # CHAPTER 9 THE SUN IS RISING Sunny was born. This was my chance to take the ball and run with it. I knew exactly what I was capable of; now I just had to show everyone else. But I had a gut feeling that Vince already knew what I could do if I had the opportunity. We were back in the creative department working on designs for outfits. Naturally, I had better ideas for them than the people in that department, so with a few tweaks and some sly insistence, I eventually got things done my way. My first outfit was a sports bra-like tank top and bike shorts. A good idea, but not as tantalizing as I would have liked. What would a cute blond need to really catch the crowd's attention? I know. A short, flirty skirt. So I eventually started to design and make my own outfits, complete with a smaller, sexier version of the sports bra and tennis skirts I picked up in sporting goods stores. I was designing and sewing Chris' tights as well. I got pretty good at it, if I do say so myself. We were brought into the gym in the WWF offices to film the first four weeks of introductory promo vignettes that would air on TV before our first match. Vince was there again. He began to explain how he wanted us to act and talk in the promos. He wanted me to be bitchy and conceited and Skip to be overzealous and extremely punctuated. As he was instructing us on how to act, he thought it would be better if he showed us himself. So picture VKM, in a business suit, acting and talking like me—all feminine, cocky, and flirty. It was one of the most hysterical things I had ever seen! But here he was, again taking time out of his day to make sure I knew _exactly_ what he wanted from me. So we filmed four segments to air over the next four weeks, showing us working out and playing the part, each one more cocky, conceited, and annoying than the last. And wouldn't ya know it? It got us heat. When we were finally walking down the aisle to the ring for our first match, to our generic, nondescript theme music and Bertha Faye—like light show, we were heels. We were screamed and hollered at. And when I put the microphone to my mouth to cut a promo on our way to the ring, the fans yelled us at even more as they listened to my cocky rant of how they were all fat and out-of-shape disgusting excuses for human beings, while we were physical perfection. Yep, we had instant heat, thank God! We started out on the road with some easy wins over wrestlers such as Aldo Montoya, and eventually ended up in a program with Barry Horowitz. Barry had pretty much been a job guy his entire career, but a well-liked job guy. When he had his first match against Skip, the people actually got behind him and chanted his name, since they hated us so much. _We_ were getting _him_ over! So Vince let Barry take the ball and run with it, a sort of "pat on the back" for doing jobs for all those years with no complaints. All in all, it gave Barry a name. He got a T-shirt made for him because of it, and it proved that we were capable of taking someone the fans' hadn't cared much about and getting them over as big babyface. They found a spot for us. We became mid-carders who worked with new babyfaces to get them over with the crowd. This was something Chris was very good at and actually rather enjoyed. He especially liked the fact that he was compared to "Pretty Boy" Doug Somers, a well-known heel from the 1980's who was a more well-rounded wrestler than most and did an excellent job of playing the heel and making less-talented babyfaces look like superstars. Someone like that would always have a place in this business, and Chris knew it. There would always be a need for a good, solid heel that could take guys who struggled to get over on their own and help them get over with the fans. Next in line was Louie Spicoli, a big-hearted 280-pounder from Los Angeles with surfer-boy blonde hair and the baby face of a 3-year-old, dimples and all. I used to tell him he reminded me of a cross between John Goodman and Chris Farley, which surprisingly he didn't appreciate. Our feud with Louie was fun. He was an extremely talented guy with a vast knowledge of his craft, and the agility in the ring of a 170-pound luchador. We had a blast with him on the road. He was scheduled to play a "Body Donna-in-training" and prove himself to us in order for him to be accepted as one of us. Chris and I both became very good friends with Louie, and when we'd be working in Los Angeles, we'd stay a couple of extra days with him and do the town. One day, we were driving around Hollywood on a sunny afternoon in my rented candy apple red Mustang convertible. As we approached the front entrance of Planet Hollywood, we noticed a huge crowd of fans and a sign for a movie premiere. Basically, these fans were all gathered there in hopes of catching a glimpse of some movie stars arriving at the premiere. As we were crawling past them, we joked about how boring their lives must be, and just then Louie stood up in the backseat of the pony and yelled in their direction, "Go home and get a life, you bunch of marks!" Just like that, a small riot erupted headed our way. This particular bunch of moviegoers did not appreciate what Louie was spewing at them, and angrily started advancing towards our car. We were all laughing hysterically as we drove away from them, until... The traffic light turned red! We were now at a complete dead stop in the middle of Hollywood Boulevard, with an angry mob right on our tails. Shit! Now what? Just as the first fan reached our car and pounded on the trunk, the light turned green and we made our escape. We probably laughed for an hour after that. On another trip to LA, we were out driving again, this time on Oscar night. We decided to cruise around the after-party locations to see who we could catch a glimpse of (yes, we were doing the exact same thing that we had been making fun of those fans for doing). As we cruised by the famed Spago Restaurant owned by world-renowned chef Wolfgang Puck, we spotted actor Randy Quaid (Cousin Eddie from _National Lampoon's Christmas_ _Vacation_ , amongst other films) leaving the after-party wearing his tuxedo, riding away on a bicycle! Yep, a bicycle-riding, tuxedo-wearing Quaid made our night. You can definitely see some crazy things in Hollywood. That angle eventually wrapped up with Skip and I not accepting Louie into the Body Donnas, though the BDs were soon to become a tag team. During one match, Chris was getting his butt kicked really badly when the ref got knocked down. All of a sudden, a guy looking like Chris' twin popped out from under the ring and switched places with him to not only save Skip, but to gain the victory. Same height, same weight, same body type, same wrestling trunks, all the way down to the same bleached blonde buzz cut. After the three-count, I snatched the microphone away from the ring announcer. "This is what true teamwork is all about," I gloated. "Here is _Skip_ and _Zip_! The Body Donnas!"—or something to that effect. Dr. Tom Prichard, formerly of USWA and one-half of the Heavenly Bodies in SMW (along with Jimmy Del Ray), was chosen to be that twin partner. What was funniest about his selection was that his brother, Bruce, who was in talent relations, begged to be the one to tell Tom about his new position. Tom was thrilled to be teaming with Chris, at first, because he and Chris always got along well since our Tennessee days, and they worked together even better. The funny part was when Bruce dropped the bomb on Tom that he had to cut his hair and bleach it blonde. "Whoa, wait a minute. Cut my hair and bleach it blonde?" Tom exclaimed. "Hang on, that could break the deal." You see, Tom was well known for his in-ring work, but even better known for his full head of brown hair with highlights, long and curly. Tom's flowing tresses would be the envy of any girl. It practically broke his heart when he thought of cutting off his luxurious locks, but hey—a job is a job, right? Making a paycheck is sometimes more important than your looks. We were in Hershey, Pennsylvania, the night Tom had to debut, so we all went to a beauty salon nearby the arena to get Tom's hair just right, his brother Bruce in tow with video camera in hand to record the shearing for posterity and Prichard family get-togethers for years to come. We walked into the salon and immediately the stylists starting fawning over his hair, saying, "Oh my God! Your hair is so gorgeous! What do you need done?" Dr. Tom looked at them with an expression of disgust on his face. They weren't making it any easier. He pointed at Chris' head. "I have to look like that!" The entire salon erupted in laughter, and the buzzers and bleach came out. This was a truly hilarious moment. So the tag team of the Body Donnas was formed, and by this point my popularity was starting to rise. Well, the female fans still hated me, but the men? Well, they were starting to like me more and more with every flirtatious flip of my skirt. At WrestleMania XXII, in 1996, the Body Donnas were scheduled for a match for the WWF tag team championship against the Godwins. The hog farmers were Henry O. Godwin (HOG) and Phineas I. Godwin (PIG). Phineas was none other than our old friend from the USWA, Tex Salinger. At the end of the match, I was to jump up onto the apron and flash Phineas my cute little butt under my skirt. When I did, he was so distracted that he was rolled up by Skip for the three-count. We were the champs! And of course I took all the credit for it. This was about the time when Vince started to notice my changing popularity. And what came next changed the course of who "Sunny" was to become, forever. # CHAPTER 10 MOVE OVER PAMELA, THERE'S A NEW PIN-UP IN TOWN! I was called into the office for a meeting and was told I was going to do my first bikini photo shoot. Fantastic! I had only done a couple of bikini photos in the privacy of my apartment and shot by Kelly Cornette in my SMW days. I had never done a complete photo shoot. I was super excited. We went to Miami Beach—me, the photographer Rich Freeda, and the crew; we hired a local girl for hair and makeup. We checked into our hotel, one of the classic art-deco hotels on South Beach. As we were checking in, we couldn't help but notice the fish bowl full of condoms on the front desk, and that the clientele lounging around the lobby chatting was all male. Turns out the hotel we selected was a gay hook-up hotel where most rooms were rented out by the hour! We got into the room, and it was as seedy and as sleazy as we expected. Umm, time for Sunny to check out. I ended up at the Eden Roc Hotel, another art-deco type place, but this one was very upscale and classy... and very expensive. Perfect. Expensive was just my style. So we organized my bikinis and cover-ups, chose the colors for my make up, and we were ready to shoot. My hair was done in a beach-blown sexy wave and my make up was dark, heavy, and sensual. I had dieted hard for two weeks leading up to this shoot so my body was lean and hard and toned. I was ready. We shot photo after photo on the sand, in the ocean, skating in Rollerblades, holding a blue macaw—we took every opportunity that South Beach had to offer. We shot for three days and came out unscathed. Well, the crew did, anyway. I sustained multiple jellyfish stings on both ankles that were tended to by two very handsome, tan lifeguards. I don't know who was the lucky one, me or them! We were finally finished and I anxiously awaited the development of the film. Yes, back in 1996 we used film. Digital cameras weren't around yet. I had such an amazing time shooting and filming that I thought to myself, "I could get used to this!" My music video that the WWF released shortly afterwards was the footage filmed during this shoot. I went to the office one day when the film had come back, and headed to the magazine department to check out the results. I was in awe. Complete and utter astonishment. My pictures were incredible! I felt as if I wasn't looking at myself, but instead looking at some model from the _Sports Illustrated_ swimsuit issue. I couldn't believe my eyes. I never knew I had it in me to shoot photos like that. I was given the chance to help choose what photos would be used in _WWF RAW_ _Magazine._ There were so many great shots to choose from that it was hard to narrow it down. When the magazine finally hit newsstands, it was a smash hit. I only made a small corner of the cover, while Vader was the main photo. That didn't matter, though, because the fans were buying it for _my_ layout! At the same time as the release of the magazine, my new music video to the track of "Sunny" by Bobby Hebb was playing as I made my entrance to the ringside area. I couldn't help but turn around and watch the enormous TitanTron as my image, larger than life and in living color, flashed across the screen. Almost overnight, my fan response grew from a third of the crowd cheering for me, to an overwhelming positive response from _all_ of them! It was incredible! Do you see what showing a little skin can do? Before long, I was 100% babyface, even though I was still managing heel tag teams. My magazine sales were through the roof, so Vince saw this as a golden opportunity and decided to make a T-shirt of me. He saw dollar signs, and he was right. My first T-shirt ever was a photo of me wearing a tight white button down top holding a pool cue seductively close to me, and the inscription on the shirt read, "I like it RAW." It was an instant hit and a huge seller. This gave Vince the idea of coming out with an entire line of merchandise with my face on it. More T-shirts, beach towels, pillows, CD-Roms, calendars, you name it. Then it was time for a one-hour home video to be made. I went into the studio to film it, and not only did I star in it and narrate it, I was allowed to help direct it and edit it, too. Filming the narration was particularly entertaining. These were the days when they trusted you by giving you a microphone and letting you run with it, total ad-libbing. I was never given a script, not for ringside or for the studio. Vince trusted in my talent enough to let me do my own thing. He knew I had it in me to captivate an audience, whether live or taped, just by being me and speaking. This is something that is completely unheard of today. Even superstars like John Cena are given a script nowadays. The video was a smash hit, and so were the sales of my merchandise. Within a short time, my royalty checks doubled my salary, but the WWF was making even more money on them. I was pulled into a meeting at a TV taping one day and Vince informed me that I had just become the first celebrity in history to hit 1 million downloads of a single photo on America Online! I had soared past the likes of Pamela Anderson, Cindy Margolis, and the most recent Queen of Cyberspace: Teri Hatcher wrapped only in that Superman cape! Oh my God! People were looking at my photo more than Pam Anderson's? I don't know about you, but I'd rather look at Pam than myself! I didn't believe it, but it was true. It was even confirmed by America Online when they flew me out to Phoenix, Arizona, to be a presenter at their annual awards ceremony and introduced me as "the Number One most downloaded celebrity on AOL." That was unreal. What was even more surreal was the amount of media my newly-found stardom had gotten me. I was the first wrestling personality, besides the illustrious Hulk Hogan, to ever hit mainstream media. I was interviewed and featured on Hollywood gossip and news shows such as _Extra, Access Hollywood, Entertainment Tonight, Inside Edition_ , and _MTV's Oddville_ and _Singled Out_. Soon after all this publicity, I got a phone call on one of my three days off from the road, that I needed to come into the office for an important meeting. I asked if we could discuss whatever we needed to over the phone, because I was only off for three days and then back on the road for a month. I was told that it was too important to be discussed over the phone. I needed to be done in person. Great. I'm getting fired. That was my first thought. What could be so important that we couldn't discuss it on the phone? So the next day, day two of my three days off, Chris and I drove up to Connecticut and walked into Vince's office. We sat down with Vince, JR, and Lisa Wolf, who was a higher-up in the office and sat in for meetings that touched on sensitive subjects. Vince looked at me. "We got a phone call," he said. Uh-oh. What did I do? Who did I piss off? " _Playboy_ called. Their readers have been writing in, wanting to see Sunny from the WWF in their magazine," Vince said. "The people at _Playboy_ didn't know who you were, so they called us. They loved the photos we sent them of you and want you to do a layout." What? _Playboy_ wants me? Were they serious? He went on to describe that the photo shoot could be done either partially nude or fully nude, whichever was I was more comfortable with, and the pay would adjust accordingly. Holy shit. _Playboy_ wants little ol' me? This was probably the highest compliment I had ever been given. I could be enshrined in the pages of _Playboy_ forever. I could be admired and drooled over (and I don't want to think about what else) by millions and millions of people across the globe, besides just wrestling fans. I could go down in history as the first female from the WWE to be featured on the cover and in the pages of the world's most highly acclaimed men's magazine. It took me all of five minutes to say no. I turned it down. It was presented to me as a golden opportunity, but I said no. I just couldn't do it. I was only 23 years old and still very conservative about my body at that time, and I thought my father would roll over in his grave if I posed nude. The look on Vince's face was of shock and a little disappointment, but he didn't try to push me or convince me to do it in any way. He understood where I was coming from and respected that. He always treated me like a daughter, and he probably wouldn't like his own daughter doing _Playboy_ , either. Vince treated me very well. I was his golden girl. In his eyes, I could do no wrong. And every time I flashed my million-dollar smile, the dollars just rolled in for him, and he knew that. # CHAPTER 11 SLOP, DROP, AND ROLL While all this media frenzy was going on about me, I was still on the road managing tag teams. I turned on my beloved Body Donnas, much to the fans' delight, and began managing the Godwins, who just so happened to be the team to beat the BD's for the tag team belts. So I was _still_ the manager of the tag team champs. The fans were very happy about my slight babyface turn to manage the Godwins, but Hillbilly Jim wasn't too thrilled (he had been their manager up until that point). I got Phineas to fall in love with me, thereby becoming my pig farming puppet, but Hillbilly Jim knew I had something up my sleeve. We went on for weeks, working shows where I acted like I was in love with Phineas, a totally dedicated girlfriend to this dumb hillbilly who wore his heart on his sleeve. Finally, in a match defending the belts against the Smokin' Gunns, Phineas' love for me blew up in his face. I hopped up on the ring apron, sauntered sexily down the length of the ring towards Billy Gunn—the tall, blonde, good-looking one—and when I flirtatiously got close enough, he grabbed me around the waist, pulled me in tight, and laid the biggest, wettest, longest kiss anyone had ever seen in a wrestling ring—especially Phineas Godwin. He stood in the center of the ring and watched in disbelief, as his "girlfriend" betrayed his love by kissing another man. Stunned, he was distracted long enough to get rolled up and pinned. 1-2-3, and the Smokin' Gunns were the tag team champs... with me as their new manager. I was now the manager of three consecutive sets of tag team champions, another first in the history of the WWF. Take that, Captain Lou Albano! Now I had to be a heel again, and although I tried my hardest, I still got the cheers, whistles, catcalls and "Sunny" chants due to the popularity of my bikini photos. Right after I screwed Phineas over, I had to go to the ring and give my "apology speech" to the world on live TV, and face-to-face to Phineas himself. This might have been a challenge for some people. When Jim Ross walks up to you and says, "You have 7-8 minutes total. You know what to do," it kind of puts a little pressure on you. Again, no script was handed to me. They trusted me to do the right thing and trusted that I could pull it off. I set off to the ring with JR. I started by telling the crowd how I knew how horrible I was towards Phin, how he didn't deserve to be treated like that, and how I wanted to apologize. Then I called him to the ring. When he hesitantly got in, I coaxed him to join me in the center. He had a look of confusion and trepidation on his face, while I had a look of guilt, sorrow, and sadness. I spent a few minutes explaining how sorry I was, how I was wrong to treat him like a mere possession, and that he deserved better. I told him that I cared about him deeply. Then I got him to say those three little words: "I love you." I showed my happiness that we were "reconciling" our relationship and told him to close his eyes because I was going to give him a big kiss. He did, and after I shot the most vindictive, menacing face into the camera...... ... _Wham!_ I slapped him good! Good and hard. When the look of shock registered on his face, I began to berate him and call him every name in the book; well, every name that was allowed on live television, of course. After about a minute of the trash talking, I called my trusted Gunns into the ring to deliver a beating to him. I'm such a heel! They did, even though they were late on their cue, and I hopped out of the ring. I was met at ringside by Hillbilly Jim. I turned and ran the other way only to bump into Henry Godwin. Apparently they weren't too pleased with me breaking Phinny's heart and slapping him across the mug. I turned and ran up the ring steps only to run into Phineas, who had made short work of Billy and Bart Gunn and now had his sights set on me. He was holding something in his hands... Yep. The dreaded bucket of _pig slop_! The Godwinns were well-known for dumping the pig slop over the heads of their opponents, but they couldn't possibly dump that on me, could they? Little ol' innocent me? A woman? Phineas must have remembered his Southern manners, because he hesitated for a moment. I took advantage of his hesitation and began taunting him. "He won't do anything," I purred into the camera, assuredly. I was wrong. When I looked back in his direction, I felt the entire bucket of cold pig slop pouring over my head and down my body. I couldn't believe it! The crowd couldn't believe it, either. They couldn't have been more ecstatic. Even though I was technically a "tweener" at this point, they were still happy to see me humiliated and embarrassed by the slopping. I made the most of it. I flailed around in the slop as I credited about it. This was my chance to exact a little revenge upon the fans that hated me for so long, so I took advantage of it. I grabbed handfuls of slop off the floor and flung it into the crowd. Haha! The perfect revenge. I made my way to the backstage area and got a standing ovation from the boys, not only for being slopped and taking it like a champ, but for the tremendous promo I cut before the deed was done. They knew I knew what I was doing. I was then told that I would be slopped every night on the road for the next month. So much fun was in store for me! What exactly was in the slop, you ask? Well, it was usually a combination of leftover salad from catering that afternoon, mixed in with some bread and water. I had heard stories in the past about the boys leaving the bucket in the guy's locker room all day for all the guys to ahem—urinate into, so I was careful. I told the road agents that I wouldn't get slopped unless I made the slop and I kept it in my locker room until it was time for our match. A lot of people, even to this day, ask me how I could have enjoyed doing something so gross and disgusting. I truly did; I enjoyed every minute of it. Just look at all the publicity I got out of it! I was seen on every TV show, over and over again, replaying the infamous slopping, and I got a RAW magazine cover out of the deal! Yay me! I'm really proud of the fact that the WWF had so much trust in me, letting me adlib my own promos (that's what they were; totally off the top of my head). I'm also proud of the fact that they knew I could handle anything they threw at me—from birthday cake to pig slop. Eventually the Gunns lost the tag team championship and I fired them. It was time for me to move onto bigger and better things... like my first singles champion. # CHAPTER 12 ALL HAIL, THE GLADIATOR! Ron Simmons is one of the most famous African-American wrestlers of our time. A natural athlete, he excelled in college football for the Florida State Seminoles and then played in the NFL for the Cleveland Browns. As many NFLers do, when his football career ended he looked towards pro-wrestling as his new cash flow. When he debuted, there weren't many black performers making it big, but Bill Watts, promoter of the Mid-South territory during the 1980's, liked what he saw in him, and he saw dollar signs. Watts had a great deal of success in promoting black wrestlers like Ernie Ladd and The Junkyard Dog, which is ironic because Watts had a reputation for being a bit racist. But he was impressed with Ron's athleticism and ability, and he made Ron a star, the first African-America World champion in NWA/WCW history in 1992. Ron worked in many territories before settling into the NWA and WCW. He eventually became one half of the team Doom (along with Butch Reed), managed first by Woman (Nancy Sullivan) and later by Teddy Long. Vince got hold of him in 1996. He couldn't wait to take this 285-pound monster and transform him into a top singles wrestler. But instead of using his name value and his popularity to their advantage, the WWF renamed him Farooq, and made him dress like a gladiator in shades of turquoise, black, and silver, silly helmet and all. Yeah, I know. It didn't make any sense to me, either. Ron was talented in the ring, but was lacking in the interview department. So what do you do when a wrestler can't talk? You give him a manager as a mouthpiece. Namely, me. When they came to me with the idea, I thought it was a great opportunity. It was more exposure for me and helped me branch out into the singles division. Then they explained to me that they wanted us to act like a "couple". Yes, _that_ kind of a couple. Damn! Now, I'm not racist in the least bit, but they wanted me to kiss him, tongue and all, on camera. I think that was the first time I think I ever said no to something they asked of me. Not only was I with Chris, but I just couldn't bring myself to kiss someone I wasn't attracted to, and I wasn't attracted to Ron in the least. They respected my wishes and Farooq and I made our debut. Now it was a little conflicting, because here I am, selling merchandise like hotcakes as a babyface, and they want me to be a heel with Farooq. Yet again, it didn't make sense. So we went out, and did our best. Of course, I was cheered, but the fans knew that Farooq was Ron Simmons (whom they liked) and were confused whether they should cheer him, which they wanted to do, or whether they should boo him, which is what the WWF was trying to make them do. Farooq plowed his way through opponent after opponent until we made it to the finals of the Intercontinental championship tournament against "Wildman" Marc Mero. This was one of the first times Marc introduced his wife, Rena, to the crowd as his valet. They called her Sable. Ugh. We'll get to her later. When it was all said and done, Farooq lost the match, and the title, to Marc with a little help from a brick that was stashed in _my_ purse—yes, my devious heelish plan had backfired. After this loss, I explained to the fans through an interview that Farooq and I were no longer business partners, and I was going to focus on what _really_ mattered: me! Sunny, herself! # CHAPTER 13 A HEARTBREAKING ROMANCE Late in 1996, things started to get pretty rocky between Chris and me and we decided to take a little break. Many nights he stayed at his mother's house, or his father's house, or got a hotel room. When you're on the road with someone 24/7, you tend to get on each other's nerves. We weren't totally broken up, but we weren't totally together, either. We kept up the charade of being a happy couple at work because it really wasn't anyone's business. As I mentioned in one of the early chapters, I was in love with Shawn Michaels when I was 13 years old. So now, being a co-worker and in the same locker room as him, I couldn't help but admire him, up close and personal. He was always very nice to me, much different from how he treated the boys—with the exception being the guys in "The Clique." He was extremely charming, and even more handsome and sexy than he was back when I was 13. One night we had a skit to do together. He was going to be in the ring when a bunch of heels hit to take him out. He was to fight each one of them off and then call me into the ring. I was supposed to get in the ring like a shy schoolgirl, and he would motion to me to pucker up, like he was going to kiss me. He would then turn away and "diss me," as the live TV show went off the air. After we faded to black, he was to turn around, grab me, and kiss me, much to the crowd's delight. Backstage, when everyone was talking over what they were going to do, Shawn pulled me aside and asked, "So, what kind of a kiss can I give you?" Any kind of kiss you want," I replied, in the sexiest voice I could conjure up, giving him a little wink and a smile. He was happy to hear that, smiled, and walked away. So it was time. I'm ringside and he calls me into the ring. I walk over to him, he turns away, turns back and grabs me and dips me. He laid the hottest, sexiest, wettest kiss I had ever experienced, right there in the center of the ring. As he was kissing me, which felt like five minutes and was probably darn close to that, he laid me down on the canvas and _continued_ to kiss me (and dry hump me a little as well.) I gotta tell you—it was _good_... and I _loved_ it! I didn't want it to end, and the crowd loved it more! They were howling like wolves, and I can bet you the women in the audience were wishing it was them. It was a hot, hot kiss. Call me crazy, but I felt sparks during that kiss. OK, I felt friggin' fireworks! I mean, come on! It was the "Heartbreak Kid," for cryin' out loud! The most beautiful man I ever saw! Ah, that kiss! The next week on TV, I was standing by the curtain watching the show, as we all usually do, and Shawn walked up behind me to look and watch over my head. As he inched closer and closer to me, I could feel his hot breath warming the hairs on the back of my neck. "Do you feel that?" he whispered. The "that" he was referring to was his hard dick pressed firmly up against my ass. Oh yes, I felt it all right. Good and hard. Instantly, I was turned on. I was moist. What red-blooded American girl wouldn't have been when the "Heartbreak Kid" pushes his erection up against you and gives you chills with his breath? I had a pretty good idea where this was going, and what his intentions were. And I was right. Later that evening he pulled me into an empty locker room and kissed me. And felt me. And groped me. And then, like a kid in high school, he fucked me. Yep, he banged me good, right there in the locker room. It was so dirty and sexy and so not allowed within the crew that it made it even hotter. Oh my God! It was mind-blowing sex! And that was the beginning of the love affair that would eventually lead to my first broken heart—ever. I was 23. He was 31. The age difference didn't matter. We got along like two peas in a pod. He was cocky, but so was I. We were both extremely attracted to each other and couldn't get enough of one another. He actually said once, "It makes perfect sense for the top guy and top girl to be together." I completely agreed. We were all over each other. We had sex everywhere; anywhere and everywhere. Every show. In empty locker rooms, vacant bathrooms, broom closets, electrical closets, production trucks, and even in Vince's private locker room. The only people who knew were the members of the Clique, and eventually Vince. Surprisingly, Vince actually approved! He had a strict rule back then about members of the crew not getting involved romantically, but he approved of us. That became apparent to me at one particular TV taping, when Vince was behind Shawn and me in line for catering. He leaned in and asked, "So, how are _we_ doing?" with a clear emphasis on the " _we_." Okay, Vinnie Mac, your caught us, red-handed. It wasn't uncommon for Shawn and me to go at it four times in one day at a TV taping, and a couple more times at night in our hotel. Members of the clique were designated to "watch the door" of whatever locker room we decided to occupy, usually Sean Waltman, the 1-2-3 Kid. I was still on the road with Chris, keeping up the charade, so no one knew about Shawn and me, especially Chris. Even though we were just cohabitating, I didn't see any reason to upset him. Once night after a TV taping in Syracuse, New York, I retired to my hotel room with Chris, and Shawn headed out to a bar with the rest of the boys. At about 2:30 am, there was a persistent knocking on the door to my room. It was Davey Boy Smith, the "British Bulldog." "Tammy, come next door," Davey said, in his thick but sexy British accent. "Shawn got beat up." Oh great. What happened? I rounded the corner—Shawn's room was right next to mine—and I walked in. Shawn was a bloody, swollen mess. He had cuts all over his face, with the worst gash right below his right eye. His entire face and head was so swollen with lumps that he looked like the Elephant Man. What worried me the most was that he was bleeding from the inside of his left ear, and he was barely conscious. Knowing that that could be potentially dangerous, I told Davey to call 911. I was worried about Shawn having suffered some inner ear damage or brain swelling. (I had been a pre-med student, ya know!) So the bus came for him and I went with him to the hospital. Upon arrival, I removed his diamond earring so it wouldn't disappear, because they needed to do an MRI on his head. The MRI came back clear, and Shawn came back sound asleep. He was either sleeping off all the alcohol he'd consumed that evening, or they'd doped him up enough at the hospital to not feel any pain. When he opened his eyes a few hours later, the first thing he saw was my face. He looked a little shocked at first that I had stayed by his side the whole night, and then it felt like he had a "Nurse Nightingale" moment, and his eyes began to sparkle. It must have touched him that I cared enough to take care of him, because up until that point our relationship had been purely sexual and physical. Then things began to change. He was given a month off from work to go home, rest and, recuperate. I called him daily, three times a day, to check on him. His mother, Ruth, went to stay with him in Ft. Worth to watch over him because he was getting bad dizzy spells daily. Our phone conversations only brought us closer. We would spend hours on the phone sometimes, just getting to know each other better. One day, during a nice talk about being on the road so much, I told him that I thought he needed a vacation. "Yeah, I really do," he replied. "Where do you want to go?" Me? Where do I want to go? He told me to pick a destination, and he would book it. "But what about my schedule? I'm on the road!" "Don't worry honey, I'll take care of that," he said. And take care of it, he did. So I did a little research and found a resort called Ciboney in Ocho Rios, Jamaica. He had his ex-mother-in-law, who was a travel agent, make the reservations, and then he made a phone call to Vince to get me off the road. Two weeks later, we were headed to Jamaica. I told everyone, including my mother and Chris, that I was taking a spa vacation by myself—that I needed some "me" time. I was scheduled to fly from Newark, he from Dallas, and we were meeting in Miami to connect to Montego Bay. I got to the airport, and I had a first class seat, naturally. When I met him in the Miami airport, we were so happy to see each other that we ran into each other's arms in the terminal, like something out of a romance novel. We boarded our plane, hand in hand, and the flight attendant brought him his Dewar's and soda, and me, my Diet Coke. The entire flight, we couldn't keep our hands off each other... kissing, touching—we were tempted to find a blanket and do some more underneath the covers. When we got to Jamaica, we boarded a small, old, rickety van to go to the resort. We were the only ones on board. We figured we'd take advantage of our first little bit of privacy—well, the driver was there, but hopefully not watching us—and I climbed onto his lap as he lowered my panties to my knees and I rode him as we rode the bus to the resort. Yeah, we couldn't keep our hands off each other. When we arrived at Ciboney, attendants in a golf cart greeted us and handed us mimosas. I still had never had a drink up until then, so he drank both. They drove us up the beautiful grassy hillside of the plantation, through all the fragrant banana and mango trees, to our room. Our suite, rather: a private honeymoon villa! Yep, he had gone all the way and booked the largest honeymoon villa they offered. The place was gorgeous! It had three huge sections: the kitchen and living room area, separated by the open-air pool and Jacuzzi room, which led into the master bedroom, equipped with a king sized bed and bathroom, with a bidet. There was a bottle of champagne and a fruit basket on the dining table, with a card, which read, "Congratulations on your marriage." Ha! They thought we were newlyweds! We thought we'd have a little fun with it and actually pretend we were married. I moved the gold thumb ring I always wore to my left ring finger and we were now known as Mr. and Mrs. Michael Hickenbottom. We were invited to all of the newlywed functions and parties, and had a blast faking it. We also had sex like honeymooners—lots and lots and lots of sex. Sex anywhere and everywhere. Privately and publically. (We were both mild exhibitionists.) In our private pool, our private Jacuzzi, in the public pool, in the ocean, on the beach under a blanket, against a tree on the plantation; sex was everywhere! By the third day, we were both so sore that we had to take a break. We were having sex about ten times a day, all day, every day. Up until then, and even since then, Shawn was the best partner I have ever had. He just knew what to do, and he was so sensual while he did it. We made love like champs. He did have this one small, strange fetish though. He liked to bend me over the bathroom counter and watch as he did me from behind, while I was applying ruby red lipstick, over and over again, just applying thick coats until I looked like the Joker from Batman. I never really understood what he got out of it, but it turned him on something fierce and got him rock hard. Whatever he wanted, I did for him. Anything. Dinner was even more special. Our personal chef cooked a private dinner in our suite every night, and we were serenaded by a guy with a guitar. This guy was great. He would play any request. Shawn loved Elvis Presley, so each night he would request all Elvis, and when he would play "Welcome to my World," Shawn would hold my hand, look into my eyes, and sing to me. He knew just when to be romantic. I would melt when he sang. Each night after dinner, we would make our way to the piano bar, which was very mellow and laidback, but extremely fun. The pianist could play anything, and the entire bar would join in singing. One night, when Shawn was ordering his regular Dewar's and soda, I told him I'd have one, too. He looked at me, confused. "But you don't drink. Are you sure?" I told him yes, and that one drink wouldn't kill me. After all, we were on the vacation of a lifetime. So I had my first drink. Ever. At 23 years old. A Dewar's and soda. Shawn's drink. The Clique's drink. Vince's drink. Just one drink. Then two. Then three. Then I don't know how many. I had a really good buzz, but I wasn't falling over myself drunk. The next morning, I felt fine. No hangover at all. I figured that since I didn't get crazy drunk, and I didn't get sick afterwards, that I might as well have more fun on the trip and keep drinking. What harm could it do, right? Wrong. These few casual drinks on vacation at 23 years old were the beginning of the end for me, as you'll read later. Our amazing vacation came to an end, and we grew closer over that week. We spent many late nights lying in bed talking, and we really started to bond. At the end of our trip, we went back home, Shawn to Texas and me to New Jersey. I had to get back on the road, but Shawn still had another two weeks off. During those two weeks, construction was under way on his new home in San Antonio. He had shown me the blueprints of the house... well, mansion is more appropriate than "house." He needed some help decorating and wanted a woman's touch in picking out the tiles and colors and cabinets and décor. His mom and I were more than happy to help. She and I had become close, through our many phone conversations while she was taking care of him. We helped him choose different shades of Mexican tile for different rooms, the dark cherry cabinets and dark granite for the kitchen, and paint colors with a Southwestern flair. A few weeks later, I was really going through a lot of stuff at home, and in my frustration I mentioned to Shawn that I wanted to get the hell out of there and move far away. "Well, move to Texas," he said. "Move in with me into the new house." Oh my God! Did Shawn just ask me to live with him? Was he serious? Was he joking? I was so startled by his statement; I didn't know quite how to respond to it, so I didn't. I just giggled it off. Finally, he came back on the road. I had really missed seeing him. He and I were booked on a tour of Canada together to do autograph signings at Wal-Marts, promoting the new line of merchandise the WWF released. It was just the two of us. This gave us some more much-needed alone time together. It was during this trip when I broke down and said it. Yep, I said it. We were lying in bed just after more beautiful sex, and I told him, "I love you." I really did. I meant it. I had fallen head over heels in love with him back in Jamaica, but was afraid to tell him. I didn't know what his reaction would be, or what he would say, if anything, so I held back. But this night, I couldn't hold back anymore. I loved him. Very much. He didn't speak a response, but he pulled me closer and kissed me. Did he love me back? Did he? I desperately needed to know, but was too terrified to ask. That tour ended and it was back to business as usual on the road. Chris and I were on better terms now, and getting along well, and he moved back home with me. Shawn and I were still together on the road, but he did _not_ like the fact that Chris and I were mending things. In fact, he hated Chris. He hated him because it seemed like no matter what, I couldn't break it off with him. This was a huge hit to Shawn's ego, as he was very used to getting whatever, or whomever, he wanted. He didn't like that I went home with Chris after every tour. He didn't like that one bit. He was extremely jealous. To tell you the truth, he was extremely jealous if I spoke to any of the guys on the crew too much... especially his arch-nemesis, Bret "The Hitman" Hart. We'll talk about that rivalry in a little bit. A few months passed, and Shawn's house was finished. He didn't ask me to move in again, but he was still waiting for an answer from the first time he had asked the question. He's not the kind of guy who begs. Shawn and I were in Las Vegas for the National Association of Television Producers and Executives convention. The WWF had a booth there every year. There were tons of celebrities everywhere, and we were the two top draws to the WWF booth. One of the nights, after Shawn and I shared a beautiful dinner of filet mignon at the MGM Grand Hotel, we headed upstairs. Then came "The Talk." He sat me down and said he didn't think I had any intention of leaving Chris for good, and he was offended that I hadn't taken his offer to move to San Antonio seriously. I began to cry. I knew where this was going. I cried harder. It didn't change his mind. I cried buckets. Right then and there, he broke my heart into a million pieces. I was shattered. I was truly and deeply in love with him, and he had just told me we were over. How could this be? How could he just end it like that? Well, a guy like Shawn did not take the backseat to anyone. No one. His ego was hit so hard, he wanted out. He wasn't going to be made to look like a fool in front of the boys if I chose Chris over him in the end. My heart was broken, for the first time in my life. About two months later, Shawn met a girl named Rebecca, who ironically was a Nitro Girl for the rival WCW. One month later, she was pregnant. Another month later, they were married and living together in the house that I helped design. They now have two beautiful children and have been together for 15 years. I often wonder what life would have become if I HAD moved in with him. Would I be his wife right now? Would I have been the one to give him children? I don't know. Did he ever love me? I don't know that either. I hope he did. I really hope he did. They don't call him "the Heartbreak Kid" for nothing. You're probably wondering if Chris ever knew about the affair I had with Shawn. I can honestly say I don't know. He never once brought it up to me, never once questioned it. He never once asked me where I was for hours at night in a hotel, while he waited up for me in our room. He never once questioned who I went to Jamaica with. He never once accused me of anything. Do I think he knew? Yes. I mean, how could he not? Then the questions remains, if he did know, why would he let it go on unnoticed and unaddressed? My only theory is that he loved me so much that he chose to overlook it. I think the thought of living without me was too much for him to bear, so he let me do what I wanted to do, as long as he could keep me in his life. I'm not saying this in an egotistical manner. I'm not saying I'm the best thing that ever came into his life. I'm saying that Chris and I were soul mates, true soul mates. And this was probably the reason I didn't leave him completely for Shawn. He was MY soul mate. We were best friends. No one ever treated me the way Chris did. And maybe no one ever will. He worshipped the ground I walked on. There was nothing he wouldn't do for me. So yeah, I think he knew, but the love he had for me was stronger than anything else in the world... stronger than any force of nature, stronger than life itself. # CHAPTER 14 THE "LOVE TRIANGLE" AND THE MONTREAL SCREW JOB I'm a very easy person to get along with. I get along better with men than I do with women, maybe because of how I was raised. Men find me easy to talk to and befriend; whether they'd like to get me in bed, or not. Throughout 1996 and 1997, I found myself to be very close to two people—Shawn Michaels and Bret "The Hitman" Hart. I was close with Shawn romantically. Bret and I were just good friends, believe it or not. There was always a lot of animosity between the two of them. They were always battling for the top position in the company, always fighting each other for popularity with the fans. I eventually made their hatred for each other even more intense, completely unintentionally. Let's analyze this: First we have Shawn Michaels—the arrogant, cocky, great-looking boy toy, known as much for his acrobatic ring style as he was for his handsome good looks and flowing dirty, blonde hair. Shawn and I dated for about nine months. I saw a side of him that no one else did, the generous, caring, loving side. Most people got the arrogant, cocky attitude that he displayed in public. Even though he could have anything, or anyone he wanted, he was also very insecure. His insecurity was sparked by his jealousy, and that is a recipe for disaster. Bret Hart is a well-rounded performer who claims that he is "the best there is, the best there was, and the best there ever will be." He comes from a legendary wrestling family, with the patriarch being the late Stu Hart. They are famous worldwide, and legends in their hometown of Calgary, Alberta, Canada. Among those who know him, Bret is often called "The Lone Wolf," and that name absolutely fits his personality. Bret likes to keep to himself. He doesn't like to be around the boys. He likes his privacy. He's not the flamboyant personality that Shawn maintains behind the scenes. For all of 1996, and some of 1997, I was the only girl on the road. I had my own locker room. In many of the venues we worked at that time, there would be a small backstage area, usually with only 2 locker rooms, one for me and one for all the boys. Bret hated that, and he started using my locker room every night. There was no way he was squeezing into a room with 20 other guys. Wasn't happening. So when I would change, he would leave. When he would change, I would leave. In between those times, if I wasn't off somewhere screwing Shawn, we had some really good conversations and became very good friends. After that, when he would bring his family on the road, I became the Hart Family babysitter. Bret would drop his four kids—Jade, Dallas, Beans, and Blade—off at my dressing room door. I quickly became well-liked by the entire Hart family—Stu, his wife Helen, and all 13 children and 42 grandchildren. I was even taught the "Hart Family handshake" by Owen and Bret. Shawn, whom I was dating, hated this. He didn't care about me babysitting the kids; he cared about how friendly his arch-nemesis Bret was towards me. He cared about Bret changing in the same locker room as me, wondering what was going on when we were both in the same room. He cared about the jokes and the rumors going around the locker room about Bret and me. Let's get one thing straight— _nothing_ happened with Bret. We were just good friends. OK... I take that back. Something happened with Bret. Something _no one_ knows about until now. I've never 'fessed up to in any interview. Ever. Bret did kiss me. Once. Only once. I didn't feel anything for him, only a very slight attraction, so the kiss went no further. Besides, I had too much respect for his family to disgrace them like that. I had intentions too, though. I did invite Bret to my hotel room once. He showed up, bright-eyed and bushy-tailed to my room. And he kissed me. Sorry, that's all. I didn't mean to disappoint you. Just a kiss. No sparks. Nothing more. And this kiss didn't happen while I was with Shawn. We had already split up. When Shawn and I broke up, his jealousy and suspicions actually got worse. He was convinced that if I wasn't sleeping with him, I must have been sleeping with someone else, and that someone else _had_ to be Bret. Oy! At one particular RAW taping, I had finished up early and got permission to leave and get back to my hotel. The next day at TV, the seamstresses and make-up girl ran up to me. "Did you hear what happened last night?" I was clueless. Apparently, Bret and Shawn had a face-to-face promo in the ring, and Shawn said, "So, I heard you've been having some Sunny days lately... " or something to that effect. The insinuation was clear. Of course, this infuriated Bret—which is exactly what Shawn intended to do. Bret's family always watched the show, and they liked me like me very well. Bret was livid. Shawn was certain I had moved on from him to Bret, and wasn't going to let it go unnoticed or unknown. I couldn't even understand why he would even care if something was happening or not. He was the one who broke up with me! It's not like I dumped him for someone else. It was all very childish. Ugh, men. Not long after, we had a PPV scheduled for Montreal, Quebec, Canada; Survivor Series, 1997. The main event scheduled was Bret Hart defending the WWF World Heavyweight Championship against Shawn Michaels. This is what those promos were essentially leading up to. Rumors had been swirling for weeks that Bret was going to leave the WWF for a while after this match, and maybe for good. Bret absolutely, 100 % refused to drop the belt that night for two reasons: 1) it would be to Shawn, whom he despised, and 2) it was in Canada, his homeland. Vince told him that he respected that, and that Bret could "retire" as the champion, something that is virtually unheard of in professional wrestling. Vince wasn't worried about the match. He knew Bret would put on a spectacular show with Shawn. Both of them always strove to be the best, and they would do everything in their power to put on an unforgettable match, even if they couldn't stand one another. What Vince _was_ worried about was Bret "retiring" with the belt, and then showing up on WCW television with the belt saying that no on in the WWF could beat him for it. Vince couldn't have that, no way, no how. That would be a huge victory for WCW in the Monday Night ratings war between the WWF and WCW. So the dreaded night came, and we all made our way to Montreal. Everything was business as usual. Bret's family was there, his wife Julie, and all four kids. There were cameras there filming a documentary about Bret (which would be eventually be titled _Wrestling with_ _Shadows_ ) and they were filming Bret throughout the day. They filmed me chatting with his wife. You could hear me say that I couldn't believe he was leaving. They caught me on camera playing a game of cat and mouse with his youngest son, Blade. When it was time for the main event, Shawn's music hit and the place went crazy. He made his usual entrance, hips wiggling, strutting, and stripping off his chaps like an exotic dancer. Then Bret's music hit and the place didn't go crazy: it came apart at the seams! This was their national hero and the fans simply roared. The sound was almost deafening. They really made it known who they wanted to win this one. The match began. Bret and Shawn both battled like gladiators, each executing all of their signature moves. It was tremendous. What happened at the end of the match has been the subject of intrigue, investigation, and speculation ever since. To this day, I don't think anyone really knows the truth—except Bret, Shawn, and Vince—and they're not telling. Bret's patented finishing maneuver was the "Sharpshooter," a variation of the Boston Crab where your opponent is on his elbows and chest and his back is arched up, and his legs are under your arms. No one in the WWF used this submission hold except for Bret. So when Shawn caught Bret in the Sharpshooter, every soul in that building knew it wasn't the end of the match. Nobody could _possibly_ beat Bret with his own finisher, _especially_ not Shawn. So, Bret was in the hold, clawing at the mat, grimacing in pain, and trying to reach the ropes or figure a way out of it. The two men were in the hold for a minute or two. Then, all of a sudden, Referee Earl Hebner waves his hand in the air and signals for the timekeeper, Mark Yeaton, to ring the bell. What? Ring the bell? The match was over? Bret submitted to his own finisher? It couldn't be. It wouldn't be true. Shawn let go of Bret's legs and turned around with a dazed and confused look on his face. Did Bret tap the mat and give up? Did Shawn just win the match and the belt? Bret got up with an entirely different look on his face. It was a look of rage and confusion. And betrayal. And utter disbelief. That wasn't the way the match was supposed to end. He wasn't supposed to lose the match and the belt that night. This wasn't what was agreed upon. He must have been double-crossed. But by who? Shawn? Vince? The referee? All of them? When Bret eventually left the ring, he stormed down the aisle like the Terminator, his eyes full of fury. He came into the backstage area, marched past me in the hallway where I was playing with Blade, headed right into Vince's locker room, and slammed the door behind him. I was standing about five feet from Vince's door, so naturally I was trying to eavesdrop, but I couldn't hear much, only a few muffled voices. About 30-seconds later, Bret stormed back out of the room, with his head down, grabbed his gear and his family and left the building. Maybe a minute later, Vince emerged from the room with a blackened left eye. Right on his tail was Vince's son, Shane. Oh my God! Bret just decked Vince and gave him a black eye for screwing him! Or, did he? Was it Vince who told the referee to make sure Bret lost the belt that night? Did he tell him to call the match when Bret was in his own submission hold? Or did the referee make a grave mistake by thinking he saw Bret's hand waving in submission, and not knowing if they changed the finish or not, went along with it and rang the bell? What really happened? No one knows, except those three people involved. But there are a lot of people who have their own ideas about what happened, including me. OK, here is my expert opinion as to what took place. Bret and Vince always had a good working relationship. They always did well by each other. Bret definitely didn't want to do a clean job to Shawn that night, and Vince didn't want to argue about it. Vince sure didn't want to disgrace Bret by having him lose a clean match in his homeland of Canada. But Bret was leaving, and Vince needed that title off of him before he left. I think all parties involved agreed that if Bret lost the belt due to some kind of "accident" or "screw finish" it wouldn't hurt his stature as a premiere champion because he wasn't losing cleanly. So I think they agreed that when Bret was in his own finisher, the time when not a single person in that building would ever believe he'd give up and lose, if they had the referee call the match it would look like Bret got double-crossed. And it did look like that. And Shawn played it off beautifully in the ring and backstage, acting like he had absolutely no idea what had happened. This would definitely save face for Bret, and give Vince what he needed—a change of champions. Why do I think this is what happened? Well, I'll tell you. When Bret left Vince's locker room, I was standing right there. Vince emerged only a mere minute later with a black eye. Now, I don't know if you've ever been punched in the eye before, but I have. It takes a little longer than a minute for an eye to blacken like that. It will swell right away, but the black coloring takes a little while for the blood to come to the surface. Then we have my "forensic evidence." Yeah, that's what I'll call it. I've done many autograph signings with Bret, and he is left-handed. Now if someone is a lefty and they were punching someone in the face, wouldn't it naturally be the right eye that gets hit? Left hand to right eye, right hand to left eye. It would be uncommon for a lefty to throw a starting punch with his right hand. Now onto our fifth person involved—Shane McMahon. Vince's son was in the locker room with Vince the entire length of the match, long enough for him to punch his own father in the eye and give it 30-minutes to blacken up. And when Vince and Shane came out into the hallway, they were both a little too calm for a scuffle to have just taken place a minute earlier. Vince walked by me not even breathing hard. Now, come on, if you just got hit in the face, wouldn't your adrenaline be pumping a little bit? Wouldn't your face be red from your blood pressure rising? Nope. Nada. Nothing. Not the slightest clue that anything had just taken place, except for that well-blackened eye. So, after reading my deductive reasoning, do you think I should become a detective? Maybe, maybe not. But it sure as hell makes some sense, doesn't it? I sure think so. It's been almost 20-years since that fateful night... maybe we'll never know. # CHAPTER 15 OH, WHAT A RUSH! After Farooq and I parted ways, the company didn't really know what to do with me. They needed me, but they didn't really have anyone for me to manage. We had a meeting, and they told me they wanted to put me on a production staff contract. I would now be working under Kevin Dunn, the head of the studio. My salary would be $100,000 per year. I would have an expense account (I wouldn't have to pay for _anything_ on the road any more), first class airfare, and I would only be working nine or ten days a month, whether it was in the studio or on the road. Fantastic! I'll take it! I really was excited about the expense account and the nine or ten days a month. See, when you're on the road 300 days a year, paying your own expenses, you can easily spend 30 % of your income to live on the road, between hotels, rental cars, gas, tolls, food, and—of course—liquor. Then, at the end of the year, you have to fork over 30 % to Uncle Sam. So a wrestler making $100,000 per year is really only taking home about $40,000. I remember writing checks to the IRS for $30,000 each year, and it sucked big time. So this deal was pretty peachy. They even let me expense my clothes! This was when I started hosting TV shows. Almost all of them: _Superstars, Mania, Live_ _Wire, Shotgun Saturday Night_. You name it, I hosted it. _Superstars_ and _Mania_ were your run of the mill weekly re-cap shows, but _Live Wire_ and _Shotgun_ were entirely different. _Live Wire_ was a Sunday morning show, live and completely off-the-cuff. It was an interactive show where fans could call in or email questions and speak to me, Todd Pettengill, Doc Hendrix, or any guest we might have at the time. It was a pretty cool concept, but since we didn't know what was going to be said by whom, we had to be on our toes and quick thinking. There probably weren't too many others who could have hosted this show and pulled it off. It was live, but we were on an eight-second delay, so if anyone said something they shouldn't or that was inappropriate, they could quickly edit it out. _Shotgun Saturday Night_ was a totally different animal. It was fun and scary and crazy and dangerous, all at the same time. The shows were live, every Saturday Night at 11:00 p.m. Eastern Time. We didn't film them in a studio or an arena, but rather some very unconventional and sometimes uncomfortable places. We filmed all across Manhattan, at the All-Star Café, Webster Hall, Penn Station, and a few nightclubs in town. Webster Hall was particularly crazy. It was a nightclub that catered to the eccentric type of crowd. You had your usual clubbers, mixed in with some punk, Goth, and some of the NYC gay community. It was very normal to have a couple dozen cross-dressers and transgendered partiers roaming the floor. They had go-go dancers (in tiny pieces of clothing, of course) dancing on pedestal-like platforms. Okay, correction, they were practically having sex with themselves on these pedestals. We were getting ready to go on live in about ten minutes, so Vince (my co-host for _SSN_ ) told me to go out and pump up the crowd. Okay, easy. That's what I do. Just hand me a microphone. Nope, no microphone. They didn't want to bring down the music. He wanted me to go out and dance. Dance? Me? Oh Lord, no. I couldn't dance! I had as much rhythm as a 90-year-old Chinese lady. There is no dancing queen here; hell, I didn't even know how to do the Macarena! But, being the consummate professional, I went out, picked an empty pedestal, and started wiggling my ghetto booty. Wouldn't you know it? They went crazy! I don't know why, because in no way was I dancing anywhere close to as appealing as the go-go girls, _and_ I had a lot more clothing on than they did. But they were eating it up! The one thing that stands out about the All-Star café was when I pulled Vince up onto our announce table and got him to dance with me. It always amazed people how Vince never intimidated me, when mostly everybody else found him intimidating. I'd sit on his lap, kiss him on the cheek, and get him to dance with me on a regular basis. Penn Station had to be the most fun of all the locations. The place was packed, wall-to-wall people. The show opened with a clip of the Undertaker acting as an engineer driving a train to the sound of Ozzy Osborne's "Crazy Train" playing in the background. The TV Hollywood gossip show, _Entertainment Tonight_ , was there that night to interview me, and to film me interviewing some of the fans. I grabbed my microphone and walked around ringside to find someone in the front row that I could get on camera. Luckily, I came across a longtime dedicated fan and soon-to-be friend, Front Row Charlie. I don't know Charlie's last name, but I called him Front Row Charlie because no matter what show he was at, no matter what venue, city, or state, Charlie was there in the front row every single time. To this day I still have no idea why. But Charlie was the perfect guy to interview—it made for a really good segment. The energy throughout Penn Station was electrifying. It really was one of the best shows I hosted. Unfortunately, _SSN_ didn't last very long. Even though the shows were very good, the ratings were lackluster because it was hard to get viewers to tune in at 11:00 p.m. on a Saturday night. When I was out on the road, I was primarily working the PPVs, TV, and doing autograph signings and PR appearances. My schedule was light and stress free. I was loving it. I was being flown around the world to make public appearances. One that particularly stands out in my memory is my first-ever trip to London. There is a yearly parade honoring the Lord Mayor of London, aptly called the "Lord Mayor of London Parade." Imagine that. Anyway, I had to stand on the featured float in the parade and wave to the Lord Mayor as we passed by his digs. I was also there to promote our upcoming PPV, "One Night Only," in Birmingham, England. The studio instructed me to bring my video camera and go sightseeing and film it all. I was going to get paid to be a total tourist. Awesome! I was roaming the city of London, alone, and soaking up all the culture I could through the lens of my camera. They made a nice little video montage of my trip for the TV shows when I got back called the "Sunny Cam." It was such a fun trip! My expense account was equally fun. Everything was taken care of—first class air, hotel, rental car, food, gas, tolls, and clothes. When I was still working with the Smokin' Gunns, I told the office that I needed a few pairs of cowboy boots in different colors to go with different outfits. As Chris and I were walking through this one boot outlet in Texas, he came across a beautiful pair of $500 Stingray skin boots. They were gorgeous, and he had to have them. So I just charged them along with the six pairs I was getting. When I got the receipt, I noticed that it only said "boots," not "men's boots." So I sent in my receipt to get reimbursed, and wouldn't ya know it? They didn't even question it, and I got reimbursed for his boots, too! Ha! Every time we were on a plane, there were only four people flying in first class—Bret Hart, Shawn Michaels, the Undertaker, and me. Not bad company, huh? The rest of the crew flew in coach. We flew US Air a lot, and back then they used to send upgrade certificates for companions instead of having to redeem miles, which is what you do today. Since I felt bad that Chris was in coach, I would upgrade him to first class. But then one flight I wanted to be generous, so I also upgraded Owen Hart, Bret's brother, and the Ringmaster (who later gained uber-fame as "Stone Cold" Steve Austin.) Yes, even Stone Cold had to fly coach! I continued to upgrade all three of them every flight I could, and everything was going smoothly until one flight attendant looked at me and the three of them around me in our cozy first class seats, with mimosas in hand, and said, "I'm sorry ma'am, but you are only allowed to upgrade one companion per flight." I looked at her, and put on my "poor me" face. "Oh, I didn't know," I said. "But they're all my boyfriends. You can't possibly make me choose between them!" She looked at me with a confused, embarrassed look, and walked away. I had left her speechless. After a time, Chris was no longer on the road, and was training the new kids in the training school along with Dr. Tom, and a few of the guys on the road caught on to my expense account deal. More and more of them started joining me at meals, knowing full well that I would pay the bill and send the receipt in to expense it. That worked for a few months until I got a phone call one day from Jim Ross, my immediate supervisor. "Tammy, may I ask you what you're eating for breakfast for $90 every day?" he asked. "J.R.," I responded, "You know how expensive it is to eat healthy off a menu when you're maintaining a strict diet." He just chuckled and continued cutting my checks anyway. I used to get away with murder! Steve Austin was just starting to gain his popularity as "Stone Cold," but he was still flying in coach. One day, during a flight, he learned that I had everything paid for, so he became my traveling partner for a few weeks. "Stone Cold" Steve Austin lived off of my expense account completely. He jumped in my car knowing that then he would get all his meals paid for, and wouldn't have to worry about gas or tolls, either. He wasn't a stupid man. After a couple of months, the powers that be found a new tag team for me to manage, and when they told me who it was, all I could think of was, "Oh....What a Rush!" That's right, I was now going to be the manager of the one and only Legion of Doom. The Road Warriors, Animal and Hawk, were one of the most well-known and popular, if not the most popular tag team in all of pro-wrestling. They dominated every company and territory they ever worked: the AWA in Minnesota, Mid-South, Florida, Portland, Japan, the NWA, WCW, and the WWF. Led by their brilliant manager "Precious" Paul Ellering, they were the only tag team to ever hold the tag team championship in every major federation where they competed. They faced the best of the best in the ring—the Steiner Brothers, Doom, the Rock and Roll Express, the Midnight Express, among others—and they beat every one of them. Hawk was the more technically skilled wrestler, who also had talent on the microphone. Animal was the powerhouse. He could press a 250-pound wrestler ten times over his head with ease. Together, they were one of the most powerful and formidable forces to be reckoned with in all of professional wrestling. Not only that, they were two of the nicest guys you could ever meet. I was thrilled to be their new manager. Who wouldn't be? So I went to the WWF's head seamstress, Julie Youngberg, to design the perfect outfit. Julie was the creative talent behind all of Shawn's fancy chaps with mirrors and chains and Bret's cool leather jackets. I knew she'd love to put her talents to work and come up with a female warrior's costume. Julie did not disappoint. She dreamt up the wildest outfit, fitted to the skin, made of only molded leather and chains. It looked like something right out of the TV show _Xena, Warrior_ _Princess_. It was to be red, black, and silver, and look like it was on fire. Her drawing was nothing compared to the actual outfit when she made it. When I went for the final fitting at midnight the night before I was to debut with the LOD, my eyes widened with surprise and delight. It was the coolest, sexiest, most skin-baring outfits I had ever worn. It didn't cover more than a bikini, and my bare butt would flash through the strappy leather on my derriere as I walked. It didn't cover much at all. So the night arrived when we were to make our first appearance, at WrestleMania XIV, March 29, 1998, in Boston, Massachusetts. We waited anxiously at the top of the stage behind the curtain as I helped them get fastened into their metal spiked shoulder pads and motorcycle helmets. All of a sudden, the house lights went dim, and the pyrotechnics on the stage began. The audio guys hit the magic button and the arena heard, "Oh, what a rush!" The building erupted in frenzy. The Legion of Doom had arrived. But what they didn't expect was for Sunny to be walking down the aisle with them. They went even crazier! I've got to tell you, the feeling that runs through your body when you hear that music _is_ a rush! I've never experienced such a feeling just from a ring entrance. It was truly incredible. The theory behind putting me with them was to make the fans look at them as a new tag team, not a couple of guys who have been around the block a few times. They thought I would bring youth and exuberance to the faction. Although it was an honor to work with them, it was honestly a little boring. There really isn't a whole lot for a babyface manager to do at ringside except be a cheerleader, so I had to humble myself and get the spotlight on my boys. Not easy to do with an ego like mine! I started to travel with them on the road as well. Joe (Animal) and Mike (Hawk) rode with Steve Blackman regularly, so when I came along, they split for a more comfortable ride. I rode with Joe and we made Steve Blackman drive Mike around. Steve wasn't too happy. It wasn't because he didn't like Mike; we all loved Mike. It's just that Steve would have to be Mike's babysitter in addition to being his traveling partner. Mike was one of the guys who liked to party. He loved his drink and he loved his drugs. I never personally saw him do any kind of recreational drug, but I sure saw him take his fair share of prescription pill. Then again, we all did. The hours-long drives with Joe were very valuable time for me. It gave us the chance to get to know each other in a way you normally wouldn't with a co-worker. We became great friends. We became family. To this day we remain that close. He has been my friend and brother for 16 years, and I love him for it. Sadly, a few years later, we lost Mike to a heart attack, caused by overuse of substances throughout the years. Mike was a really good person—caring, considerate, and funny. He was well liked by all. In 2011, alongside me, the WWE honored Mike and the Road Warriors by inducting them into the WWE Hall of Fame. They will go down in history as the greatest tag team that ever lived. RIP, Michael James Hegstrand, 10-19-03. You are missed by all. # CHAPTER 16 ARIBA! MEXICO! Since I mentioned the use of prescription drugs amongst some—rather most—of the crew, I figured I'd stick this chapter here. There really isn't a place in my timeline about this topic because it spans over a few years, from 1997 to 2001. Prescription pills were commonplace in the locker room, for all of the boys and myself as well. I can't remember exactly when I took my first pill, but it was shortly after I took my first drink with Shawn. And I honestly can't remember who gave me my first pill—either Shawn or Davey Boy Smith—but I do remember that that first pill was a Soma. Somas are muscle relaxers. When taken according to doctor's orders, they affect the central nervous system and block pain to the muscular-skeletal system. When taken against doctors' orders, in quantity, they give you a really foggy high; they slur your speech; they make you stutter; they make you lose control of muscular movements when you walk. It feels and looks like your feet won't touch the floor. Eventually, you fall asleep. The key to a good buzz is to take a few, depending on your tolerance, on an empty stomach and eat something 15 minutes later. Within a few bites, you will be in la la land. Somas were the pill of choice for us on the road. Of course we were using other pills as well—Vicodin, Percocet, Valium, Xanax, among others—but because somas are not a controlled substance or a narcotic, they were much easier to get. It wasn't uncommon for a wrestler to take 15 or 20 at one time. Your tolerance gets pretty high after prolonged use. If I had to guess, I'd say there was maybe one person on the crew that didn't take some kind of pill. Everyone else was taking something. On one of my trips to Los Angeles to go to some TV and movie auditions, I hooked up with my friend Louie Spicoli to take a drive down to Mexico. I had never been to Tijuana, so I wanted to go and do the touristy thing. Louie was a regular in Tijuana, and he told us how easy it was to buy pills there, and I'm not talking about a few pills here and there. I'm talking about pills in quantity. _Huge quantity._ Louie and I took our three-hour drive south to Mexico. We went from pharmacy to pharmacy asking for what we needed—a bottle here, a bottle there—and it was all very time consuming. It wasn't until I took my next trip alone that I found the secret to buying drugs in Tijuana. I was walking around town, after I was bombarded by children trying to sell me gum and Pez, and I thought I'd stop for a break and a bottle of water. I spotted an outdoor café, so I sat down at the one table that had an umbrella to get some shade from the hot Mexican sun. As soon as I sat down, a man walked over and sat down next to me with a pad and a pen in hand. "What are you looking for?" he asked. I assumed he meant what kind of drugs I needed, so I read him a list of pills and steroids and the quantities I wanted. He said "No problem," and disappeared up a staircase in an alleyway. About 15 minutes later, he returned with a brown paper grocery bag in hand. He told me how much I owed him, which was ridiculously cheap considering everything I was buying, and I graciously paid him. I was in awe. I couldn't believe how quick and easy that was. I got everything I needed in one stop! The bag contained: 1000 Vicodin 1000 Percocet 3000 Somas 2000 Xanax 2000 Valium 500 Rohypnol Testosterone pre-loaded syringes Vials of Winstol And Clenbuterol tabs. It was a pill-popper's dream! Why did I buy so much, you ask? Well, when the crew got wind of me taking a trip down to Tijuana, a few of them asked me to bring some things back for them. Why not, right? What harm could it do? With that quantity of pills, how did I possibly get them back across the border? Here was my trick—and I don't recommend this to anyone. Kids, do not try this at home. I would go to Tijuana each month wearing a pair of overalls with a lot of pockets. I'd wear a baseball cap and bring a camera—I looked like a complete tourist. I'd go to a few shops and buy eight or ten Mexican blankets, a piñata, and a bottle of tequila with the worm in it. The key is to park your car on the U.S. side, walk over a long bridge to cross the border, and walk back the same way. Why? Because if you drove across the border, there is a 99 % chance your car will be completely torn apart and searched when you cross back. When you walk, your bags go through a metal detector, but not your body. So I would layer the plastic pill bottles between the Mexican blankets, and anything with metal—like the syringes and vials—I would put in the pockets of my overalls. When you walk through security, they ask you what you need to declare. I acted like the happy tourist bringing blankets home for the family, and the tequila back for my Dad. And voila! I was now a pro at the drug-trafficking game! When you get away with that much, a feeling of exhilaration overtakes you, a complete rush of adrenaline. I was so proud of myself. When I look back at it, maybe it wasn't the smartest thing for me to do. I did this once a month, every month for about two years. If I ever got caught, I'd _still_ be in a Mexican prison to this day! I trafficked copious amounts of drugs that were worth a lot of money on the street in the States. Although I wasn't selling them for profit, I was still bringing them across the border illegally. I would go back on the road and distribute the boys' orders, primarily members of the Clique. At a show in Texas, I gave Sean Waltman a bottle of 90 Xanax, 2 milligrams each. By the end of the night, he had about 20 left in the bottle. How could he have taken that much and still be standing, albeit barely? After that show, Chris and I got into our car and Shawn and Sean got into another car and followed us to the hotel. When we arrived, Shawn got out of the driver's seat cursing like a madman, his jeans soaking wet. Sometime during the hour-long drive, Sean Waltman had to go to the bathroom. Being so out of it from ingesting so many pills, he whipped out his willy right there in the front seat, and started urinating all over the dashboard... and all over Shawn! Ha! Shawn was pissed off (pun fully intended) because he was supposed to wear those jeans the next day. Chris and Shawn carried Sean into the hotel with his arms around their shoulders and his toes dragging behind him. I was elected to drag in everyone's bags. When we entered the lobby, the front desk clerk looked startled and asked if he should call 911. We told him no, everything was fine, that he had just gotten off a long light from Australia, and was jetlagged. Believe it or not, the clerk bought it. I'm really happy I got over my pill-taking phase in 2003. A lot of my friends didn't get over it, and subsequently faced the consequences. I've lost countless friends and co-workers to pill overdoses, suicides, premature heart attacks, and car accidents due to intoxication. One very sad case led to a double homicide and a suicide. It's really a shame to lose so many people in this industry to drugs. If only the WWE would have implemented its Wellness Policy ten years earlier, maybe some of those people might still be on this Earth with us. # CHAPTER 17 DIVA WARFARE When I first went on the road with the WWF, the only other females in the locker room were Alundra Blaze, Bertha Faye, and Bull Nakano. Alundra (better known as Madusa Micelli) was the women's champion, and was only a wrestler; she didn't compete with me for any hosting, managing, or announcing spots. When she left and took the women's championship with her to WCW, I was the only woman employed by the company for more than a year. It was nice being the only girl for a while. I had my own locker room and I got all of the attention from the male fans. And quite frankly, I'm an attention whore. In 1996, Dustin Runnels, son of the legendary "American Dream" Dusty Rhodes, started in the company as "Goldust" and at his side was his lovely wife, Terri. Terri started in the business as a make-up artist for WCW and then garnered a TV role as "Alexandra York," the head of a group of wrestlers called the "York Foundation." Now she was Marlena, Goldust's manager and personal "director." I knew who she was, obviously, so I welcomed her with open arms. She was such a sweet person, with her Georgia southern hospitality, and we clicked right away. She would also bring their two year-old daughter, Dakota, on the road at times, and our locker room would become a giant playroom. Terri and I got along great we would share curling irons, hair spray, etc., and never had a problem with one another. We were at a RAW taping in Hershey, Pennsylvania, and we decided to go to catering together after we set our bags down in our locker room. In the room there were a couple chairs, and a folding table. We both opened up our gear bags on the table, and laid out our clothing for the night. When we returned from lunch, we walked into our dressing room to find our clothes and bags on the floor and someone else's bags spread all over the table. "Whose stuff is this?" I asked Terri. We were the only two girls on the crew! A few minutes later, a woman we had never seen before walked in and sat down at the table, not even making the effort to introduce herself to us, a cardinal sin in a wrestling locker room, and just plain rude anywhere. Already I didn't like her. "Um, who are you?" Terri asked the mystery woman. "I'm Marc Mero's wife," she replied. OK, but that still didn't explain why you are in our locker room and you're using our table. After some more interrogation by Terri, we found out she was going to be Marc Mero's new valet. "So, what's your name," Terri asked. "Rena," she said. "But I'll be known as Sable." "Sable? Like the car?" I spurted out, without thinking. The look on her face was priceless. "No," she said, in an arrogant and condescending voice. "Sable, as in dark or night." OK. Whatever you say, Biatch! So, right off the bat, she rubbed Terri and me the wrong way. But we figured that if we had to share a locker room with her, we might as well try and make nice. Now, I'm not going to go on about Rena, frankly because she's really not worth the energy, but I wanted to put this in the book to clear something up. I didn't like her. At all. No one did, really. Over the years, a lot of people have speculated that I didn't like her because I had professional jealousy towards her. That couldn't be further from the truth. She had her place on the roster, and I had mine. I was the girl you wanted to bring home to mom and marry, the all-American girl next door. She was the one you wanted to take to a hotel room that had an hourly rate. We didn't have the same character, just as Marlena was different from the both of us, so you couldn't compare us. This is why I didn't like her. She and Marc used to bring their eight year-old daughter, Mariah, on the road sometimes. She was a very quiet, but sweet girl. She had dark hair and a complexion like Marc, but I knew he wasn't her birth father. One day, while in the locker room with Rena and Terri, I asked Rena what happened to her daughter's real father. "Oh, he died in a car accident when she was just a baby," she said. "Oh my God! I'm so sorry to hear that," I said apologetically. "No, it's fine," Rena said, as cold and emotionless as a serpent. "Him dying was the best thing that ever happened to me. If he never would have died, I never would have met Marc." What? Oh my God! What? Terri and I looked at each other at the same time. Did she just say what we thought she said? Did she just say that she's happy her husband and her baby-daddy died so she could meet and marry Marc? Holy Shit! This woman had ice running through her veins! She was the most cold-hearted, selfish bitch I had ever met. Terri and I were stunned. That was all we needed to hear. That solidified the fact that Rena was _not_ to be liked. But, again, we had to share a locker room with her. We tried to be as cordial as possible, which was much easier for the sweet and southern Terri than the cocky northerner that I am. A little while later, Luna Vachon was brought in to work with Bam Bam Bigelow and the Oddities. Luna was extremely eccentric, to the point of being scary, and she wasn't the type of person you wanted to piss off. Luna was so tough she could beat up any woman, and most men for that matter. Thank God Luna liked me. I affectionately dubbed her "Mama Luna" and we became fast friends. One night at RAW, I had just finished at ringside, and I headed down the hallway to the locker room. As I opened the locker room door, Luna charged at me like a freight train, put two hands on my chest, and launched me across the hallway into an equipment crate. She then climbed on top of me, and started pounding away on my head until all ten of her knuckles were bleeding. She then went back into the locker room, grabbed my huge Tumi suitcase and Halliburton briefcase and threw them on top of me. I had absolutely no idea what was going on, other than that I was about to be murdered. Our road agents came running down the hallway, pulled her off of me, and pushed me into one of the agents' offices. Tony Garea and George Steele followed me in and asked what the hell had just happened. "Your guess is as good as mine!" What could have possibly made Luna flip out like that? What was going through her head? What was she thinking to attack me like that? What?? Actually, the question was "who?" _Sable_. About ten minutes later, the door to the office opened and in walked Luna. "Oh Christ, here she comes again. Time for Round Two," I thought. Instead, she walked in crying. Actually, sobbing. OK, she was hysterical as a baby who just lost her binky. She walked over to me, hugged me tight and wouldn't let go as she apologized to me over and over again. The words were pouring out of her so quickly, and between deep sobs, that I couldn't understand most of what she was saying, until I caught her mumble the word "Sable." Sable? Excuse me? What did she have to do with this? Well, it turned out that Sable was behind the whole abomination. Apparently, she was jealous of me and knew that Luna would rip a Koala bear's head off if it were talking shit about her, so she told her that I was doing just that. Luna reacted just as she had hoped. From that day on, none of the girls liked Rena. Rena is also a compulsive liar, besides just being a troublemaker. To this day, she tried to convince everyone that will listen that she was the first one to be offered to pose in _Playboy_. She tells people that I'm a liar and that I was never offered the chance. Well, the truth is, I was offered a _Playboy_ spread a full year before she even started with the company, so how would she even know? You see, that's what self-centered people do. They convince themselves of their own lies so others will believe them, too. She also had everyone else convinced that she was only three years older than me, and three years younger than Terri. That would have made us 23, 26, and 29 years old respectively. Well that was a lie as well. She is really six years older than me, the same age as Terri. So now she's 46 and not aging well. When she appeared on a UFC broadcast with husband, Brock Lesnar, everyone thought she was his Mom! And now, since her daughter Mariah had a baby, she's a grandma... Ha! And after I left the company, she made so many more enemies, that one of the boys (who will remain anonymous) took a poop in her gear bag. Yes, karma is _definitely_ a bitch. # CHAPTER 18 THE MOST ELECTRIFYING MAN IN THE WWF SCHOOL 1998 was an interesting year for me. Once again, I was doing double duty between two companies. Chris quit the WWF in 1997. He was miserable on the road. He felt like he wasn't working to his strengths and wasn't getting the push he deserved. In a fit of anger, he decided to walk up to Vince at a TV taping and tell him he wanted to leave the company. "Well, Skip, you need to do that in writing," Vince replied, and walked away from him. Chris, being the hothead that he could be, became even more furious. He walked up to Jim Cornette, who was now working for the company, ripped a sheet of paper out of Jim's notebook, and wrote: "TO VINCE. I QUIT. CHRIS CANDIDO." Yep, that's what he had the balls to write! So Chris was off the road. This was about the time I started working in the studio on Mondays, Wednesdays, and Fridays hosting the TV shows, and Chris helped out Dr. Tom Prichard in the training school/studio warehouse, teaching a group of new guys that were under developmental contracts. That group consisted of Olympic weightlifting champion Mark Henry, Sean Stasiak (the son of former WWF World champion Stan Stasiak), Sean Morley (who later became Val Venus), pro-bodybuilder Achim Albrecht (Brakkus), and a young, good-looking guy from a famous wrestling family named Dwayne Johnson. Dwayne's maternal grandfather was "High Chief" Peter Maivia, and his father was none other than Rocky Johnson, who gained fame in the 1980's as the partner of "Mr. USA" Tony Atlas in the WWF. Needless to say, it was natural for Dwayne to get into the business. He was a very sweet guy, and very humble. You could tell he was raised right and taught to respect those who came before him. Chris and Tom took a liking to him, and because of that, Dwayne received private training with both Tom and Chris. We could tell he had tremendous talent right off the bat, in the way he carried himself in the ring and the way he spoke. On filming days, I would finish up around 5:00 p.m., and then go out to the ring in the warehouse and watch the training sessions for another hour or so until they were finished. Afterwards, Chris and I would head down the street to this little pizza place that had a fabulous Italian menu in the back restaurant. One day, we asked Dwayne if he'd like to tag along for dinner and spend some time talking about our craft, because he was always eager to learn. "Aww thanks guys, I really appreciate the offer, but honestly I can't afford it," he said, sheepishly. "They only pay us $400 a week and I'm sharing an apartment with four other guys. But don't worry about me. I have some canned tuna fish at home." Come on. A young guy who weighs 260 pounds of muscle cannot possibly survive on canned tuna fish. I offered to treat him to dinner. He gratefully accepted. So there was the three of us—me, Chris and Dwayne—in the back of a pizza place ordering the best and the biggest dish they had on the menu the chicken montanara. It was this gigantic oval dish heaped with pasta, chicken, vegetables, and a creamy garlic sauce. And it was delish! I could only finish half of mine. Chris ate most of it, but left a lot of pasta. But Dwayne ate every last drop. He scraped his plate clean! He was so gracious and thankful when we fed him... it seemed like it had been quite some time since he had a filling meal like that. What do you expect? The poor kid was broke! He ended up coming to dinner with us three days a week for a few months, on our tab. We were happy to help. He was a good kid and we enjoyed his company. Besides, we couldn't let him starve. They finally started him on TV, and combined his father's and grandfather's names and called him Rocky Maivia. He was a babyface, but with the goofy outfit they put him in and his ridiculous Afro, the people farted on him. They couldn't stand him and they frequently made their way to the bathrooms or concessions stands when it was time for his matches. The office decided to give me the job of trying to get him over. They put me at the announce table at ringside to do color commentary for every one of his matches. I basically had to try and convince the fans that he was the greatest thing since sliced bread. I had to convince the ladies that he was the hottest thing since Brad Pitt. The problem was, when you try to force someone down the fans' throats like that, there's going to be a backlash, and Rocky felt the backlash full-force. The men hated that I was gushing over him so much and the women still weren't crazy about me so they despised any guy I liked. So he bombed. The office finally realized nothing was going to work and that Rocky was doomed as a babyface, so they made him a heel and put him with the Nation of Domination alongside my former protégé, Farooq. Farooq had ditched his gladiator togs and reinvented himself as the leader of a group of Islamic black militia types, and the fans hated them. Rocky took over the Nation from Farooq, and then eventually became a babyface again, this time a huge fan favorite, with a new look and a new name. He was now known as "The Rock," a name that will go down in WWE history.. He was a great guy and we were happy to have helped him. These days, he doesn't need _anyone_ to buy him dinner! He has become a multi-millionaire and action-movie star extremely well-known around the world. He remains extremely humble and gracious to this day, and deserves every ounce of his success. # CHAPTER 19 MY EXTREME TRANSITION AND THE HYPNOTIST By 1997, I was beginning to get frustrated with my position in the WWF. At that time, I was pretty much only being used as a model. They would hit my music, I'd walk down the stage and ramp wearing an Undertaker T-shirt and walk back. That's it. I was bored to death. I argued with Creative many times asking, "If you have nothing productive for me to do, can I as least pump up my _own_ T-shirt sales?" There was a definitive no. I was pretty aggravated about this, so I started accompanying Chris to ECW shows when I was off. Chris was now working for Extreme Championship Wrestling, which was owned and operated by Paul Heyman. Heyman had gained on-screen fame as Paul E. Dangerously a heel manager in WCW and the head of the "Dangerous Alliance." He was just as good on promos as Jim Cornette, but with a New York flair to him. He also had a genius mind for booking, comparable to Cornette and Bill Watts. He was a longtime friend and former roommate of my old friend "Hot Stuff" Eddie Gilbert, and he probably learned a lot of his booking ideas from him. Since I was hanging out at many ECW events, Paul figured he'd try and get the WWF's permission to use me on a few shows. They obliged as a favor to him, and to let me have a little fun. After all, I wasn't doing much in the WWF. I started making small appearances on some shows, going to the ring with Chris and the new faction he was now aligned with, consisting of "The Franchise" Shane Douglas, Bam Bam Bigelow, and the "Head Cheerleader" Francine. They were known as "The Triple Threat." I was having a blast. This was wrestling the way I liked it, and I was enjoying every second of it. April 13, 1997, was a huge night for ECW. It was the night of _Barely Legal_ , the company's first pay-per-view. ECW had built up a rabid fan base, but had nowhere near the financial resources of the WWF or WCW. Pay-per-view was the only way ECW could compete. But if that initial PPV flopped, it could have destroyed ECW. It was a huge gamble, and everything had to go off seamlessly. The night of the event, Paul asked me to be a part of the production team and to help direct the show. My job was to sit at a monitor, with a headset and a stopwatch, to time out the matches and segments, give the audio guys their cues, cue the wrestlers for their entrances, and to tell the referee when to tell the wrestlers to "go home" and end the match. This was a very important job because if the show wasn't timed out to a tee, we'd fade to black and go off the air with the main event still in the ring, which would have been an absolute disaster. Imagine all the buyers demanding refunds, or unsatisfied fans deciding to never again buy an ECW PPV. The main event for that night featured the legend himself—hailing from the notorious Double Cross Ranch in Amarillo, Texas—Terry Funk. At 52 years old, Funk was a sentimental favorite; the godfather of hardcore wrestling making one final run at championship glory before riding off into the sunset. He was The Desperado, his pain and his hunger were driving him home. Funk was facing The Sandman and Stevie Richards in a three-way match in the second-to-last match, with the winner of that match going on to face Raven for the ECW heavyweight title in the main event. Funk has always been a part of my "wrestling family," and I have been affectionately calling him Uncle Terry since I was 17 years old. There was no way I was going to screw up the timing of his match. So the PPV was underway, and everything was going smoothly. Nothing went overtime, everyone was right on cue. It was time for the three-way. Funk, Sandman, and Richards delivered a wild, 20-minute show-stealing brawl, and to the fans' delight, Uncle Terry came out on top, earning the right to face Raven in the main event. The match started right away, and all eyes were on the ring... except backstage, where all eyes were on the clock. The show had been timed-out to a tee, giving everyone enough time to shine on the PPV stage, but we were up against a hard deadline. Funk and Raven were going to war out in the ring. The crowd was rabid and cheering for Terry, wanting to see this historic night of extreme wrestling end on a feel-good note. We were down to three minutes left of live airtime. I gave the cue to the referee over the headset to take it home. The cue was ignored. I gave the cue a second time at 2:30 left, and it was ignored again. What was going on? Did the referee lose his earpiece? Are Terry and Tommy not hearing him? Two minutes left and they were nowhere near the planned finish. I started getting louder yelling into my headset. "Take it home! Tell them to go home! There's only 60 seconds left until black!" My pulse quickened, my heart was pounding, and my palms were sweaty. My blood was rushing through my veins. I just knew we were going to go overtime and fade to black before the match was over. And the fuck up would be all on my head. Unbelievable. The first time I'm given some real responsibility and control, I'm going to fuck it up. 45 seconds left; still going. 30 seconds left; still going. 15 seconds left and Terry finally beats Raven to win the match. Terry rolled out of the ring, leaned back into the fans at ringside. Five seconds left. He throws one arm up in the air in victory as he turns toward the hard camera... and we go off the air with a picture-perfect ending! The last 30 seconds couldn't have been timed better. It was a miracle! I did it! Paul was very happy with me that night, and shortly after that night, he asked Chris and me to join him for dinner at this great little Korean barbeque place in Manhattan. Uh oh. Another dinner invitation to another BBQ restaurant by another owner/booker? Was this déjà vu, or what? I didn't think this meeting had anything to do with me, but it did. Paul offered me a job. He would make me Chris' manager and part of the Triple Threat. He would pay me $20,000 more than I was being paid by the WWF. He promised to make a line of T-shirts for me, making me the first ECW girl with merchandise and to give me a higher percentage of the sales than the WWF gave me. He also promised that I would have more creative control and more of an on-camera role than I had had in the past few months with the WWF. He told me I would continue to help produce the PPV's, which I _loved_ to do. How could I say no? He promised me everything I wanted. He convinced me that this would be so much better for me. This why I call him the "Hypnotist." Paul Heyman has a way of convincing people of anything. He could put dog shit on a platter and convince you it's a $250 plate of steak tartare The problem with his offer was that I still had three years left on my new contract with the WWF. How would I get out of that without the noncompete clause taking effect? Well, get fired. That was Paul's solution to that question. So a couple weeks later, after I made a WWF-approved appearance on another PPV, I grabbed the microphone after the Triple Threat's match and yelled: "ECW is my new home!" The place went wild! I'm sure the people at home watching did as well. As for Vince McMahon watching at home, he wasn't too happy, obviously. The next morning, I had a fax from the office before I even woke up. It was my release. Normally, people would be crushed receiving their release. Not me. I was ecstatic. With all the promises Paul had made me, how could I go wrong? Well, I could. The first two months were fine. T-shirts were made. Checks were given on time, and cleared at the bank. Then Paul asked us to be the travel department as well. I would use the travel agency that the WWF used and book the entire crew's flights, charge them on my AMEX card, and get a reimbursement check once a month, for the entire monthly bill, approximately 30 grand each month. All was really good for a few months. For a FEW MONTHS... those are the key words. Out of nowhere, paychecks were late. Then our reimbursement checks were late. Really late, and the lag was growing each month. One day Chris and I got a phone call from Paul. We were suspended. "For what?" we asked. Paul went on this tirade that he wanted us to go to rehab for our "pill problem" and enroll in some college courses. Pill problem? College courses? What the fuck was he talking about? First of all, the entire ECW locker room was on pills, and half of them were on some pretty hard recreational drugs as well, which Chris and I weren't. And there was NO WAY we had more of a pill problem than anyone else. When we questioned him about it he said, "he loved us and cared about our futures." Bullshit, he did. Regardless, we were suspended without pay. Then the mail came, and so did my AMEX bill. There was another $30,000 charged on our bill for airline tickets! But how could that be when we weren't working or making the reservations? Well, it just so happens that Paul's assistant, Debbie, started making the flights in our absence, and telling the travel agency to continue charging them to the account on file, which had to be our personal account! Son of a bitch! Those bastards were not only not paying us, but now running up our AMEX card and not reimbursing that! After a few months, we owed American Express $175,000. Yep, you read that right. When we disputed the charges, we lost the claim because we had authorized charges for flights in the same names in the past, and had no proof we didn't authorize these new charges. Un-fucking-believable. So we were sitting home, in the new mini-mansion we had purchased a year earlier, paying the mortgage and bills out of our savings account. That depleted fast. We had to work, bottom line. We made a few phone calls and got word to the WCW office that we were interested in coming there to work. We got a call from Kevin Nash, who was one of the bookers at the time. He said they wanted us and would call us back with a start date. Great! We'd be working very soon. Fabulous. We went to our first TV taping and an hour before Monday Nitro was about to start, they got a fax from Paul saying we were still under contract with ECW and could not work for WCW. Fuck. He screwed us again. Four more weeks went by of us going to Nitro, and a fax came through each and every time. Bastard. Finally, after a month of Paul not answering our calls, he picked up the phone. We told him that if he cared about us at all, like he claimed to, he would either pay us what he owed us or give us our release so we could start working for WCW. He said he couldn't pay us because he was going bankrupt, but that he would give us our releases on one condition, and one condition only... that we sign off on the $175,000 AMEX bill and promise we wouldn't sue him for it. What the fuck? Are you kidding me? The only way we could work for WCW was to swallow $175,000? What were our options? There were no other options. It was either sign off on the debt, or not be able to work anywhere for another year. So Paul's attorney/father drew up the papers, and we signed them. Reluctantly. We would now be liable for the $175K, but at least now we could work and make money. American Express then proceeded to sue us! Our bank accounts were depleted. All we had left was our new house. This was my dream house, and we were forced to put it on the market. I hated to sell that house. I picked out every color, every countertop, every tile, every cabinet, every fixture, every carpet. My dream home. It was gorgeous. And soon it would be someone else's. Luckily, the house sold within three weeks of listing, so we would be able to get rid of the debt quickly. When we bought the house, I wrote a personal check for $125,000. The price was $425,000. We sold it for $525,000, but after the mortgage was paid off, AMEX got their money, and all the other credit cards that we owed money to were paid, we were left with just $35,000. I had spent $125,000 out of pocket, the house sold for $100,000 more than we paid for it, and after paying Heyman's bill, all we had left in the world was a lousy $35,000. But he cared about us and our futures. Right. Sure he did. This is why I hate Paul Heyman. If he was to die tomorrow, I'd dance on his grave. He definitely is on my list of the top two people I dislike a great deal. Who is the other person on that list? Read on, love. I do have to admit, ECW wasn't all bad, though. The crew was a very tight-knit family that stuck together through thick and thin, and we did have some pretty good times on the road together. Francine and I were always trying to see what kind of trouble we could get into. On one trip to Ft. Lauderdale, we became crazy girls. We would always stay at the Marriot on the beach, and this one particular trip we were kicked out of the pool area. Why? Because I was carrying her around on my shoulders. Wearing bikinis. Thong bikinis. Not only are they prohibited in Florida, but from the back we looked like two naked chicks with only some strings covering us! She and I would go shopping as much as possible to find new outfits to wear in the ring. This particular shopping spree had consequences, for me as well as Franny. Chris, Shane Douglas, Franny and I were cruising around in the convertible when we came up on this lingerie shop that specialized in rubber clothing; ya know, bondage-style. Well, the place was a little more hardcore than we expected, full of rubber masks, chains, whips, handcuffs... some pretty freaky stuff. I didn't find anything for me to wear, but Franny found this awesome red rubber dress that had a zipper all the way up the front and all the way up the back. It was pricey, $250, but she had to have it and it looked really good on her. As we were checking out, the strange-looking guy working behind the counter looked us over. "Hey, there's a bondage party tonight at Tens," he said. We didn't know what "Tens" was, but he told us it was a nightclub on the main drag. We decided to swing by the club that night to check it out, and we told the rest of the crew about it, too. Franny and I retired to our hotel rooms to shower and get ready to go out while Chris and Shane grabbed some dinner. We got all gussied up, dressed to the nines. I was wearing a two-piece turquoise holographic outfit with a zipper down the top and on the pants, and Franny was wearing a floral print cat suit with flared sleeves and bell bottoms. Ok, we looked like a couple of hookers! But how are you supposed to dress for a bondage party? So we went to the club, only to find that it wasn't a nightclub... it was a strip club! Oh well, we were already dressed and there, so we decided to go in. When we entered, we saw that their idea of a bondage party was having the strippers all dress in S&M wear, and there was a torture rack in the middle of the floor. There were men crawling around on the floor in rubber thongs and dog collars, being "walked" around by the strippers. Some bald guy, who obviously enjoyed being dominated, was strung up on the torture rack. His wrists, ankles and waist were strapped to a plane of wood shaped like an X and he was rotated so he was suspended in the air, parallel with the floor. He was being whipped and spanked by the strippers, and loving every minute of it. Freak! We all started pounding back the drinks and pills, and even Francine—who normally didn't take anything—took a couple somas to get happy. Well, she got happy alright. I wouldn't say Franny gets belligerent when she drinks, but she definitely gets bossy and assertive. She had to go to the bathroom, but the only women's bathroom was in the strippers' tiny dressing room. She didn't care. She stormed to the back, right through the door, swung open the one bathroom stall door and literally yanked the stripper that was in there out by her arm. She then turned to the rest of them and said, "Get the fuck out. I want to piss in piece," or something to that effect. They didn't mutter a word, and left. Franny wasn't someone you wanted to talk back to when she was drinking. She is the Queen of Extreme! The DJ found out that half the club was filled with professional wrestlers, and he announced our presence over the sound system. "We're loaded with some big, tough wrestlers tonight," he said. "If any of them had any balls, they'd get on the rack!" None of the boys stood up, except for the one crazy one... me! I've always been known to never turn down a dare, and if I could show up the guys in the process, even better. Besides, I love attention. So I strutted over to the torture rack, and let the girls strap me in. They tilted it forward until I was parallel with the floor. Then they proceeded to have their way with me. But they didn't beat me like the participant before me. Instead they tickled me with the cat o' nine tails and feathers and beads. I was laughing and turned on, all at the same time. But since my arms were stretched out so wide, the zipper on my top kept sliding down. At one point, my boobs actually fell completely out of my top. Thank God the girls were considerate and kept trying to zip me back up. All of a sudden, I saw a camera lens out of the corner of my eye. There was a photographer trying to photograph me on the rack! But before he could snap more than five pics, he got pie-faced and tossed across the room by Perry Saturn. Perry then threw him out of the front door, ripped the film out of the camera and smashed the camera to the ground. Turns out, he was from Playboy.com. Those pics would have been put on the website for all to see! There was NO WAY the boys were going to let anyone disrespect me. So next, they all circled around me and the rack and turned their backs to me. They wanted me to have my fun, while respecting me at the same time, and not letting other patrons watch. We always stuck together. Another time, we were at our monthly show in Philadelphia. The arena was in an old warehouse that doubled as a bingo hall. Above it was a bar for the Mummers of Philly. The mummers were an association of locals, kind of like the Elks—basically a bunch of drunks who get together and drink cheap liquor. Chris and I finished up with our match early, and because we had his little brother and two of his friends with us, we wanted to duck out early and grab some cheesesteaks from Tony Luke's. The parking situation always sucked there, so the boys would often double park each other's cars next to the side door. We walked out of the building to our black Sebring convertible, and started getting cursed at. There were two drunken women and one drunken guy yelling and cursing at us for blocking them in. They were Mummers from the bar upstairs The woman who was yelling then threw her drink at me, and tried to throw a punch. The guy then threw a shot at Chris. I yelled to Chris' brother to go back inside and get Bam Bam and Shane. They came out and got into the action. Meanwhile, the drunken woman ran upstairs to the Mummers club and came back down with about ten guys. So it was ten on three, our guys were obviously outnumbered, and the Mummers were certain they had this fight won. What happened next was a scene right out of an action movie, and couldn't have played out any better. Sabu was "resting" in a lawn chair on the roof of the Winnebago that he used to drive around the country to shows. When he "came to" and realized there was a fight going on right next to his RV, he got up, took a few steps back, ran and dove off the roof on the RV onto about five or six Mummers. Just as Sabu executed his RV plancha, the door to the building swung open and the entire ECW locker room emptied out onto the street! Well, the ten drunken Mummers turned ghostly white when they realized they were now the outnumbered ones. Now it was about 30 versus ten, no competition at all. EVERYONE got into the action: Taz, Tommy Dreamer, Rob Van Dam, 2 Cold Scorpio, the FBI, the Dudleys... everyone. It was a massive street fight which was eventually watched and cheered on by some fans that were alerted and rushed out the front door. The funniest moment of the entire fight, besides Sabu's death defying dive, was when "Wild Fire" Tommy Rich got involved. Tommy is a former NWA heavyweight champion, but after years of drug abuse and alcoholism, he isn't quite the same mentally as he once was. So instead of coming out like a ball of fire, swinging, he naturally grabbed a Mummer, put him in a headlock, and took him over onto the ground, like he was in a wrestling match! Then he just lay there, on the ground, with the guy's head still in his arms! He was probably shouting at the guy to sell! Francine's red rubber dress came into play on another show in Philly. This episode ended badly for Franny, but extremely well for the fans. We had just started an angle where Bam Bam would turn on the Triple Threat. After Bam Bam cleared the ring of Shane and Chris, he grabbed me and set me on his shoulder to deliver his "Greetings from Asbury Park" finisher, which was a variation of a power slam. After he hoisted me up, Francine made her way down the aisle to make the save. As she lifted her knee to the ring apron, the back zipper of the rubber dress completely popped open, revealing her bare back and bare butt cheeks with the slight glimpse of a thong between them. But hey, she's hardcore, so that didn't stop her. As she climbed through the ropes to get into the ring, low and behold, the FRONT zipper completely popped open! Now she was in the ring, with only a tiny thong and a wide-open rubber dress hanging off of her shoulders— Braless! But hey, she's a pro, so even that didn't stop her! She ran over to Bam Bam, who then hoisted HER up onto his other shoulder. Both of us in the air on his shoulders, we were supposed to be scared and screaming for our lives, about to meet our fate at the hands of the "Beast from the East." But instead of crying in fear, all I could do was laugh my ass off hysterically at the sight of a naked Francine, laughing at herself as well. Well, this was one moment in ECW history that was photographed a thousand times. Ah... the memories! I guess with the exception of my lost $175K, the good in ECW outweighed the bad. I, as well as most fans out there, wish it was still around. Those were some of the best live shows I had ever witnessed and I'd love to do it over again. Just not with Paul Heyman as a boss. # CHAPTER 20 HEAVEN NEEDED AN ANGEL In the spring of 1997, while I was still working my light schedule and Chris was already on the road for ECW, I was home for a few days and staying at my mother's house in New Jersey while Chris was in Poughkeepsie, New York. It was May. Still very cold at night, but a hint of spring would arrive when the sun rose each day. Spring skiing was coming to an end, and I had just taken my niece, Stacey, skiing a few weeks earlier. My sister, Lori, gave birth to Stacey Noreen on December 15, 1980; I was just eight years old. Because we were so close in age, we didn't have a typical aunt/niece relationship. We were more like sisters. Stacey was beautiful. She had an innocent face, fair skin, straight, silky blonde hair, and blue eyes. This kid could do anything. She was extremely talented and way too smart for her own good. She was intelligent, a straight A student. She could act, sing, and she was funny as hell. Whether she told a joke or contorted her face some crazy way, you couldn't help but laugh with her. She was also a natural athlete. When she was eight years old, I took her skiing for the first time. She was bored to death in the beginner's class and begged me to just let her hit the slopes. Reluctantly, I agreed. We got to the top of the mountain and, remarkably, she went soaring down the slope, dropping her poles in her wake. I couldn't believe it! Was there _anything_ she couldn't do? After that jaw-dropping day, we continued to go skiing together as much as possible, every weekend if we could. As she got into her teens, we became even closer. I was her big sister, her Aunt Tammy, her second mother. She would come to me with teenage issues that she didn't feel comfortable discussing with her mom. I was her ear, her therapist, when she was mad at her parents or friends. I had planned to buy her very first car, a Jeep, when she turned 16, and she wanted to come and live with Chris and me when she turned 18. My mom and I were sound asleep at 2:00 a.m. when I heard the phone ring in the kitchen. I jumped out of bed and picked up the receiver. It was my sister, Lori. She said that Stacey was in a bad car accident and was going into surgery, and it didn't look good. She said we should get up to Pennsylvania right away. It didn't look good? Surgery? What was going on? She didn't go into any details. I woke my Mom up and we got dressed. I called Chris next and told him to meet me at the hospital. I was about two hours away and he was three hours away. He said he was leaving Poughkeepsie immediately and would get there as soon as possible. My mom and I rushed to the hospital and arrived around 4:30 a.m. Stacey had already gone through surgery twice. She lay there in a hospital bed with her head shaved and wrapped in bandages, on life support. With the exception of the white bandages, she looked unharmed. Not a scratch or bruise on her face. No broken bones. The only blood was a slow trickle coming out of her right ear. She looked like an angel sleeping. What happened? And what was wrong with her? She was headed home from her boyfriend's house. Her curfew was 11:00 p.m., and she was never late. She had just gotten her driver's license less than six months earlier. At 11:20 p.m., her father started getting worried. Something was wrong. He headed out in the car down the road, headed towards her boyfriend's house. After about only a mile on the road, he saw a group of flashing lights up around the next bend. His heart sunk into his stomach. He just knew it had to be for her. As he approached, a lump formed in his throat when he saw a Nissan Altima up against a tree on someone's front lawn. It was Lori's car. The police and EMT's told him that she lost control of the car, skidded off the road, and hit the tree head-on. She hit her head on the windshield and was unconscious when they arrived. She wasn't wearing her seatbelt. The paramedics airlifted her to the hospital in Allentown, Pennsylvania, and they called a team of neurosurgeons in for her. She had no cuts. No bruises. No blood. But her brain was swelling at a rapid rate. They needed to go in and remove a part of her skull to hopefully relieve pressure and stop the brain from swelling even more. The first surgery didn't work. They had to do a second surgery. That didn't work either. The head surgeon came into the room and said that Stacey's had only about five percent of her brain function remaining. If she ever woke up, she would be mentally handicapped for life. Oh my God. Why Stacey? Why her? She had everything in the world going for her—everything. She was our angel... My only niece. My little sister. My daughter. My best friend. It was almost 9:00 a.m. when my sister and her husband decided to take their sweet baby girl off life support. Less than 15 minutes later, her heart came to a stop. I was holding her hand when it did. She was just 16 years old. It was my second major traumatic experience, and my second loss, after my father. I was crushed. I couldn't imagine life without her. This was when my drinking and pill taking increased to monumental levels. She was my little girl. I loved her as much as I loved Chris, and he loved her just as much as I did. Even though I don't have her in my life anymore, I will always have our memories. Chris, my mom, Stacey and I took a trip to Florida about a year before she died. We had so much fun. She was such a little prankster, too. One night, Chris and I were downstairs in the hotel Jacuzzi when Stacey came down with a devious look on her face. She emptied an entire bottle of shampoo into the tub, and the patio surrounding it soon looked like it had been hit by a blizzard. One night, at sunset, she wanted to take a walk on the beach, but we didn't want her to go alone. So Chris said he'd walk with her. She was cool with that because she really loved him. As they were walking past an elderly couple taking in the beautiful sky, she grabbed his hand, started pulling on his arm as if to try and get away, and started yelling, "Pedophile! Pedophile! Help me! Pedophile!" Chris immediately got red and sweaty from embarrassment, thinking the couple was going to call the authorities and report a pedophile on Clearwater Beach! Like I said, she was too smart and witty and funny for her own good. I love you and miss you, kiddo. The world is just not the same without you in it. RIP Stacey Noreen Cotton, 5-17-97. Our angel. # CHAPTER 21 WCW-THE COMPANY FROM HELL In late 1999, after our releases from ECW were finally granted, we began working for WCW. We were not only excited to be working and getting paid again, but we were anxious to share a locker room with some of the most well-known performers in the business, most notably the "Nature Boy" Ric Flair. Flair was the one person that Chris always dreamed of wrestling, and I had always dreamed of managing. Chris would get his wish. I, unfortunately, wouldn't. We entered WCW with high hopes of restoring our slightly tarnished careers to where they once were., but WCW proved very quickly that they did not know how to utilize the talent they had under contract. For example, I was the manager of champions. My strengths are my microphone skills and crowd appeal. Instead of using those skills, they had me wrestling in mixed tag team matches the entire time I was there. Chris and I either wrestled the teams of Crowbar and Daffney or Prince Iaukea and Paisley. One Nitro I even had a singles match against Mona (who later became Molly Holly). Now, I ask you: Would you put a girl who wasn't a wrestler, never had any experience as a wrestler, and who openly admitted that she wasn't any good at it, in wrestling matches? This is what I mean when I say that nothing WCW did made any sense. It was rather surprising too, because the booker was Vince Russo, and he knew my strengths from working with me in the WWF. But then again, with the WWF, Vince Russo was only the editor of _RAW Magazine._ WCW decided it would be a good idea to give him all the creative control over every wrestler, match, and angle in the company. Great idea, right? Wrong! Way wrong. Couldn't be more wrong. Vince Russo, under the guidance of Eric Bischoff, proceeded to run WCW into the ground. They put two people with absolutely no knowledge of how to book a wrestling company in charge of booking a wrestling company! Stupid. For a while, WCW looked promising. Throughout the famed "Monday Night Wars" between the WWF's RAW and WCW's Nitro, both companies pushed each other creatively, and weekly ratings (and quarterly ratings) were analyzed ad infinitum. WCW consistently beat the WWF in the Monday night ratings for about two years straight, before the WWF eventually surpassed them during the height of the popularity of "Stone Cold" Steve Austin and "The Attitude Era." But WCW's early dominance wasn't because it had better angles or matches or wrestlers, or an overall better product. It was because they gave it all away for free. You know that old saying, "why buy the cow when you can get the milk for free?" That's exactly what happened. What do I mean? Well, the key to having a financially successful wrestling company is to give just enough product for free on TV to tease and spark enough interest for fans to go out and pay $40, $50, $100 per ticket to see what happens live. Wrestling is a soap opera. All the angles, matches, interviews, sneak attacks and dastardly things wrestlers do are meant to make you want to watch your favorites beat your most hated to a pulp, once and for all. After watching all of this build up on TV, it should make you absolutely, no doubt about it, shell out that hard-earned money to see it the payoff matches, either live or on pay-per-view. WCW had a twisted vision. Bischoff and Russo were all about ratings. They wholeheartedly believed that if they beat the WWF in the Monday Night television ratings, they would be declared the superior wrestling organization. So what did they do? They put the culmination and climax of all their angles on _free_ live TV! They gave it all away! That's why their ratings were up. Why buy the cow when you can get the milk for free, right? Come time to sell tickets, no one was interested. They had already seen it all. While the WWF was consistently selling out arenas, WCW was drawing maybe a quarter of an arena's worth of fans. I was in shock when I worked my first WCW show. I couldn't believe they were only filling 5,000 seats in 20,000 seat arenas! I mean, couldn't someone just grab the two of them and shake some sense into them? Couldn't someone tell Ted Turner, the company's owner, that Russo and Bischoff were killing the company? The thing was, no one wanted to. No one cared. The entire locker room was disgruntled and complacent. Because of that disinterest, they were just happy to get their paychecks and go home. They had seen the company being run into the ground and their talents being wasted for so long, that they became selfish, and couldn't care less about the product. There was no teamwork, no family, no friends. That was the first time I had ever seen such a negative locker room dynamic in any company where I worked. There was no morale. There was no team spirit. Everyone was miserable. The saving grace for most involved was that, after the company had lost tens of millions of dollars, WCW was eventually sold for scrap to the WWF, and Vince McMahon picked up the contracts of more than half of its workers. Chris and I had left the company prior to its demise, though, with me being part of a little scandal. Yeah, imagine that. I've always been the queen of controversy, right? One TV taping, I can't remember where, I was pulled aside by the boss, Eric Bischoff. Eric informed me that one of the girls in the locker room found a certain drug in one of the stalls in the women's bathroom and said I left it there. The drug in question was the injectable painkiller Nubain. I'll give you the 411 on Nubain. It is a synthetic morphine/heroin type drug only found in injectable form used to kill pain or, for addictive drug users, to get high. It is frequently found in California, sold out of back storage rooms of bodybuilding shops, and widely and frequently used by bodybuilders and fitness competitors. Now, like I've said before, I've never been a recreational drug user. I was a heavy drinker and I took prescription pills. I have never smoked, snorted or shot _anything_! But I was the accused; it didn't cross Bischoff's mind at all that he had a locker room full of fitness models who escorted Scott Steiner to the ring each night, and that it made much more sense that one of them would be using the drug. Someone very persuasive must have told Bischoff it was mine. I told him that it wasn't mine, that I didn't use Nubain, and I wanted to see the vial. He refused, and said he got rid of it. I told him I'd pee in a cup right then and there to prove it wasn't mine. He then said he'd schedule me for a drug text in the morning and that I would be suspended until the results came back. Great. Suspended. For something I didn't do. Guilty until proven innocent. I wondered who could have disliked me enough to accuse me of this. Word of my suspension spread like wildfire in the locker room that night. Friends kept asking if I was OK and vented their frustration. The next morning, I went and gave a urine sample. I knew I didn't have Nubain in my system but was a little worried about the quantity of pills I normally ingested. Later that day, I walked into the locker room and almost immediately was pulled aside by Torrie Wilson and Stacey Keibler. They asked me if I was OK. "Yeah, but I'm suspended until my urine comes back negative," I said. They said they had heard what happened and they knew who set me up: Kimberly Page. Kimberly was married to "Diamond" Dallas Page at the time. She was initially brought into the company as the head of a dance troupe called "The Nitro Girls," who would perform dance routines in the ring at the beginning of every Nitro and between matches. She eventually started accompanying DDP to the ring as his valet after a short run with Johnny B. Badd. It was obvious that Kimberly didn't like me from day one. She was the top heel girl in the company, and when they brought me in as a heel, she felt threatened. She knew that I could get over as a heel more than anyone, and she was worried about me taking her spotlight. She rarely spoke two words to me, but in hindsight, she really didn't speak to anyone in the locker room. Not even Miss Elizabeth, who was one of the sweetest ladies you could ever meet. It was also very well known that Eric Bischoff and DDP were best friends and their wives were friends, as well. Too friendly, in fact, because it was also a well-known that Eric and Dallas would wife-swap. Yep! They were swingers. Kimberly was much better-looking than Eric's wife, so she had him wrapped around her little finger. Kimberly went to Eric and told him it was my Nubain hoping to get me fired. That rotten stinking bitch! I wanted to kill her. As soon as I found out it was Kim, I told some of the boys, including Scott Steiner. Scott doesn't like many people, but if he likes you, he'll stand by you forever. He and I had been friends since I was 19 and he was coming by our Smoky Mountain shows in Marietta, Georgia. Also, Scott is the last person you want to piss off. He had a very short fuse and an explosive temper. Needless to say, when I told him what Kimberly had done, he blew a fuse. His face got bright red and veins were popping out everywhere. He stormed past me yelling, "Where is she? Where is that fucking whore, Kimberly?" The boys that were in the hallway immediately glued themselves to the wall, anxious to get out of his line of fire. He rushed straight into the girl locker room, despite many of the women being half-naked, he stood over Kimberly like Zeus hovering over the gods. He screamed at the top of his lungs at her, so loudly that most of his words were muffled, and you couldn't make out what he was saying. The next thing we saw was Kimberly grabbing her suitcase and running down the hall and out the back door to the parking lot. He scared her so much he ran her out of the arena! But not only did she leave the arena, she left the company! That was the night she quit and never returned, all because of Scott Steiner defending my honor. Dallas didn't even think about confronting him about the way he'd yelled at his wife. Neither did Eric. No one got in Scott's face, ever. A week went by and I asked if my results were back. I was told no. Another week passed and I was told by Eric that they misplaced my results. Great, more time off. At the three-week mark, I was really pissed off. I stormed into Eric's office and demanded my results. "Oh yeah. They were negative," he said in a very condescending voice, like he didn't have the time to deal with someone like me. "They came in a week ago, but I forgot about it." That bastard! He just wanted me off TV and to not get paid for his own stubborn jollies and to pacify that two-faced bitch. He didn't want to admit he was wrong and he _definitely_ didn't want to apologize—which he never has done, to this day. Three weeks later, I was handed my release, anyway. Even though I had been falsely accused and tested negative, he couldn't face the fact that he had been wrong. That is what makes Eric Bischoff Number Two on my Top Two list of people I can't stand. Ironically, at WrestleMania 25, we were reluctantly forced to ride in the same limo together on our way to the arena from the hotel, along with a few other people. He was sitting right across from me, but did his best to avoid looking me in the eye. Bastard. Karma's a bitch. # CHAPTER 22 WELCOME TO MY NIGHTMARE! A couple months after I left WCW in 2000, Chris followed suit. We had never been more miserable working for any company in our entire lives than we had been there. Chris had begun going back to Japan, this time for New Japan Pro Wrestling. Japanese tours are typically one month in length, every other month. They can be especially profitable for a wrestler, although it makes for a very lonely time for his spouse and family. At the end of 2000, our house was finally sold, and we rented a small house on a little island right off of Atlantic City, New Jersey, called Brigantine. Brigantine was a cute little place, only two miles long and a half-mile wide, with a golf course in the center and the beach on the east coast. It was common to see more bicycles and boats than cars, even in the winter. My best friend from high school, Stefanie, had a condo there, so I was well-acquainted with Brigantine from all of our trips there in our senior year. It was beautiful, but there was one problem—we didn't know anyone and our families were more than an hour-and-a-half away. Chris got booked on a Japan tour that started the day after Christmas, 2000, and ended at the end of January, 2001. This would mark his first trip there since moving to Brigantine. We always hated being apart, but this trip was especially hard for me. I wasn't working. I wasn't even taking wrestling bookings. And I didn't know anyone. The only thing for me to do was eat, sleep... and drink, a lot. I started drinking more and more to pass the time, to make those five long weeks go by faster. Eventually, alcohol took the place of my loneliness. I became extremely depressed in a very short time, so I drank to self-medicate. I drank, and drank, and drank. I was going to the liquor store every day and bringing home a gallon jug of Dewar's scotch. I rode my bike there, even in the snow, because my driver's license was suspended. Nothing got in the way of me and my drink. I was easily downing a full gallon of scotch a day, every day. And because I was filling up on liquor, not only did I not have an appetite, but I was way too drunk to eat. All I cared about was drinking and sleeping and hoping he would come home sooner with each passing day. One day, I got a bad stomachache, with diarrhea and vomiting. (Sorry; the details aren't pleasant). This was strange because I never got hung over or sick from scotch. I thought nothing of it, drank some Pepto Bismol and went to sleep. The next day, I felt even worse. At this stage in my drinking, I wasn't even getting drunk anymore. I was just drinking to not feel sick. Maintaining. Over the next four days, the pain in my abdomen worsened to where I couldn't eat, couldn't stand up, couldn't sleep, could barely breathe, but I still had the power to guzzle that scotch. The pain was so severe; it felt like someone had jammed a chainsaw into my gut and was tearing it up. I had to crawl to the bathroom to poop. I kept a bucket near my bed to throw up into. I couldn't shower the whole time because I was so sick and in so much pain, so I smelled like shit and puke. The pain felt like something punched a hole in me and set my guts on fire. I would frequently pass out because the pain was so intense. I had never felt anything like it before in my life. Finally, after six days of utter agony, I dialed 911. I couldn't take the pain anymore. After I called, I crawled out on my hands and knees to the front porch to get some cold air while I waited for the ambulance. I was sweating profusely from the pain and the high fever I was running. My breathing was horribly labored. I seriously thought I was dying. And I was. They rushed me to the hospital and took blood and ran tests right away. As they were moving me from the stretcher to the bed, I started to hyperventilate from the pain and eventually passed out cold. Before I passed out, they asked me where my family and husband were. I was so out of it from the pain that I couldn't even remember my mom's phone number and all I could tell them about Chris was that he was somewhere in Japan. When I woke up, I wasn't in the emergency room; I was in the Critical Care Unit. I had all kinds of wires and tubes attached to me and I had no idea where they came from. How could all of this have happened? I just passed out. Well, it was actually three days later. I was unconscious for three days, and Chris was at my bedside. How the hell did he get there? All I knew to tell them at the hospital was he was in Japan. That's it. I knew the country he was in. And somehow they found him. When my family came down to the hospital, they went to my house to try and locate a phone number to track him down in Japan. They couldn't find anything. Then, the phone rang. It was Chris calling for me! Thank God. My sister Lori told him bluntly, "Chris, you need to take the next plane home, because she only has about 48 hours to live, and she might not even make it through the night." What? I had 48 hours to live? I might not even make it through the night? What in bloody hell was wrong with me? All of their blood work and testing showed that I had a severe case of pancreatitis. Pancreatitis is the inflammation of your pancreas, caused by excessive alcohol consumption. And I had consumed a ton during those six days. This is how your body metabolizes alcohol: After you drink it, it moves down the esophagus to the stomach, where it mixes with food and other fluids that you drink, diluting it. Then the diluted alcohol travels to your pancreas. Now, if there is no food or fluid in your stomach for it to dilute with (which there was none in mine for six days), it travels directly to your pancreas, becomes toxic, and your pancreas blows up. This also leads to liver and kidney failure, which I also had. Very quickly, my internal organs were dying; all of them. I found out that the doctors sedated me when I arrived at the hospital, not only to deal with the pain, but in case my organs began to shut down, I wouldn't know, and I would die in comfort. That's why it was three full days later before I came to. I was going to die. They had a priest come in and read me my last rites, twice. I was on my deathbed. Everyone came to the hospital—my family, Chris' family, friends. Everyone came to see me alive for the last time. I had all kinds of tubes hooked up to me. My arms looked terrible. They had collapsed all the veins in my arms over a few days, so they had to go into my femoral vein with a catheter for my IV fluids. (The femoral vein is in your groin. They have to make an incision in your skin and the vein and thread a thick tube all the way up to your heart. Then they sew the little plastic contraption that attaches to the tube to your skin so it doesn't pull out. And yes, you are awake for all of this.) I also had a Foley for the first time, a urinary catheter. That kind of freaked me out. I wasn't allowed to get up to use the bathroom, so I had to poop right there in the makeshift diaper I was wearing. Even if I wanted to get up to use the bathroom, I wouldn't be physically able to. There wasn't much poop though because I wasn't given any food. I was basically sustaining what little life I had left on the IV fluids. I was in some seriously bad shape. For a week and a half, I was touch and go. I had so much morphine and Demerol running through my veins that I had no idea what was happening around me. I was even hallucinating from the drugs, and I was seeing little flying dragons all over my room. Christopher stayed by my bedside 24-hours a day. He rarely slept. He didn't want to leave my side, just in case I died. One night I told him to go home and get some sleep. I felt so bad for him; he had been at my side for more than a week and a half, living on hospital food. His eyes were dark and swollen and his body ached all over from sleeping in a chair for so long. I told him to go home, get some rest, and come back in the morning. Reluctantly, he did. The next morning, around 8:00 a.m., I woke up. I just woke up and felt alert. I sat up in bed and pressed the call button for the nurse. The nurse came rushing in and asked me what was wrong. She was surprised to find me awake and coherent. "Nothing is wrong," I said. "Where did Chris go? Can you hook up my phone so I can call him, please? Oh, and can you hook up the TV? I'm bored." The nurse yelled, "Don't move!" She left the room, and returned 30 seconds later with six other nurses and all 13 of my doctors. They were all looking at me, and then my charts, then back at me, and then back at my charts. "This isn't the same person," one doctor said. "There is no way she could have recovered like this overnight." But somehow, I did. I woke up that day with no pain after I was in agony the night before. I was talking and moving fine, when the previous night I could only whisper and lay still. What could have happened overnight that brought me back from the brink of death? I don't know. My doctors didn't know. No one knew. It was like an angel came down from heaven and healed me. It was a miracle. No one could believe that the girl that was dying for a week-and-a-half was now on the phone, watching TV, and eating orange Jello. I called Chris, and he answered in shock. "Hey honey, where did you go last night? Are you coming back?" "Don't move!" he said and hung up the phone. About ten minutes later, he arrived at the hospital. He couldn't believe what he saw. No one could. Over the next week, I was eating more and more solid food, and began putting some weight back on. I was emaciated from only being on fluids the whole time, but my face and head were swollen from the bloat. I was finally allowed to get out of bed, once I got some strength back, to finally move my bowels in a toilet, instead of my diaper. I then decided that I didn't need the Foley catheter anymore, so I yanked it out. Just a word of advice: _never_ pull out your own catheter. It is held in place in your urethra by a hard balloon the size of a golf ball. It hurts _like hell_ coming out! Let the nurse do it the right way, OK? After two-and-a-half weeks in the hospital, my docs said that I could finally go home in a couple days, as long as everything was in order. My ridiculously inflamed pancreas was back to normal and my liver and kidneys were finally functioning on their own again. They then told me that if I had waited only two or three more hours before calling 911, I would have died at home. To this day, I am convinced that some supernatural entity saved my life. I feel that either my father or Stacey—or both of them—came to me and saved me. Something had to have. Because there is no logical or medical explanation as to why I bounced back from the dead. I am eternally grateful to the doctors and nurses of the Atlantic City Medical Center, and to my darling Christopher, who never left my side. Miracles do happen. Every day of our lives. # CHAPTER 23 AYE DIOS MIO! USTEDES ESTAN LAS CUCARACHAS! When I finally got out of the hospital, after three weeks of near-death misery, I had to take it easy. And not drink. Not drinking was doctors' order number one. I was told that if I drank again, I would surely die. My pancreas wouldn't have the strength to recover a second time. There was too much damage done. So Chris went back to work, but in this country. He didn't want to go back to Japan and risk something happening to me again while he was gone. Me? I couldn't work at all since I was so weakened by my condition. I even had to go to a beauty salon and get all my hair cut off, because the back of my head was so matted from lying in bed for three weeks. No comb or conditioner would get through the tangled mess. When you go from working in a million dollar company to working independent shows in this business, it's a shock to your financial stability. We had already lost so much money on our house, and now we were trying to make ends meet with only one income. The independent scene is like the stock market. Sometimes things can be profitable for a few months, and then it can crash... hard. It is very unpredictable. There were months that the amount of money Chris was bringing home wasn't even enough to cover all of our bills. We had to dip into our dwindling savings account some more. The winter of 2002 came fast, and we were almost broke. Our lease was almost up, and we weren't sure where we were going to go. That's when Chris got a phone call from Victor Quinones, in Puerto Rico. Victor was the owner of the International Wrestling Association there, and we had known him from our trip to Japan for Michinoku Pro Wrestling back in 1997. Victor was a really nice guy who always liked both of us, and he was very "out of the closet." He would make jokes with some of the boys about his homosexuality, and no one ever took offense to it. He liked to throw his money around and impress people with his generosity. Everyone genuinely liked him. Chris was offered a job with the IWA starting in April. Fabulous! This couldn't have had better timing. This meant we had to move to Puerto Rico, but where would we go on the meantime? We decided to put our things in storage and stay with Chris' family until we left for Puerto Rico. In the meantime, word got around that Chris was going to start for the IWA, and one day he got another phone call. This time is was his good friend, Sabu. Sabu is the nephew of the original hardcore legend, the Sheik. The Sheik made a name for himself in the 60's, 70's and 80's as one of the most violent, bloodthirsty wrestlers in the world. He carved a niche for himself in Japan and Puerto Rico, where extremely violent matches were predominant. In Puerto Rico, he worked primarily for Carlos Colon and the World Wrestling Council, the main competitor to the IWA. His was also the promotion in which the legendary Bruiser Brody was killed in a locker room shower. Carlos had heard about Chris going to Puerto Rico, so he called in a favor to the Sheik, who asked Sabu to call Chris. They wanted to know if Chris would go to work for Carlos instead of the IWA, because they were lacking the talent needed to surpass the IWA in ticket sales. Chris, being the loyal friend that he was, told Sabu and the Sheik that he would go to Puerto Rico for Carlos instead, and that I would come along with him as a package deal. We packed up and headed to Puerto Rico in April of 2003. I was SO looking forward to this. I had always been a beach lover, so the chance to live on a beautiful, tropical island was a dream come true. And the plan was to live there for two years. Perfect! When we got to Puerto Rico, we went to the hotel that the Americans working for both companies stayed. It was called the Empress Hotel in Isla Verde, and it wasn't quite the tropical paradise that we expected. It was a rundown slum of a motel on the beach, with beds that felt like they were 50 years old, and only half the rooms had TVs. The one redeeming quality it had was a restaurant that kicked ass! They had a good-sized menu, and everything on it was incredible. There was an old Italian man who ran the restaurant and managed the hotel named Mr. Carl Palermo, who instantly took a liking to us; especially since Chris had an Italian last name. We were promised $800 per week, and we started to look for an apartment while we stayed at the Empress. We were excited to get started working and enjoy our new island lifestyle. The problem was, our tropical dreams were just that—dreams. Dreams that would soon turn into a nightmare. For the first four weeks, we worked every show and got paid our guarantee. The shows were a little different than what we were used to. They were mostly outdoor shows, in open-air baseball parks. The locker rooms were hot, sticky, and filthy. The fans were barbaric. They believed in heels and babyfaces, and it was common to have 9-volt batteries and cups of urine propelled at your head. Yes, I said cups of urine. Puerto Rican pee pee. At these baseball parks, the dugouts were locker rooms and the fans were right above them. As you left the dugout you had to sprint past the fans, or you would get doused with piss. Barbaric. After our first month there, we found our apartment. It was beautiful. One bedroom, on the fourth floor in a five-floor apartment building on the beach in Isla Verde. It was furnished with beautiful furniture that had a Spanish flair, which I loved. A mango tree hung over the balcony, providing fresh fruit and fragrance daily. The bedroom had a view of the blue green waters of the Caribbean Sea. The slatted windows allowed cool ocean breezes into the bedroom and living room. The problem was you had to stay on the beach or in the apartment for the beauty of Puerto Rico, because the rest of it was not so nice. OK, it was pretty friggin' disgusting. My apologies to anyone reading who hails from there, or lives there currently. If you go there on vacation, you stay in a gorgeous resort, and you never get to see the "real" Puerto Rico. If you live there, you do. When we left the apartment we had to walk five blocks up to the main road to the bus stop. We took a bus into the city of Santurce in San Juan every Monday to go to the office to film promos and get paid. On the walk to the bus stop, the streets were filthy. There was raw sewage flowing down two blocks of street along the curb. The stench was vile and overwhelming. When we got on the bus, it was always overcrowded, with standing room only. We had to drive through a huge metal fence, into the projects, and out the other side on our way to Santurce. One particular ride through the projects was eventful. We drove up upon a large group of people standing in a circle facing outwards. In the middle, was the local drug lord, shot 12 times in the face. His guts and brains were splattered all over the pavement. The people circled him so the police couldn't get through to him. Street justice. They eventually had to call in a S.W.A.T. team and riot squad to recover the body. When we got to the bus stop in Santurce, we had to walk seven blocks along a tree-lined street in the middle of the business section of town. That seemed innocent enough, but there were dirty syringes stuck in every tree. Basically, the "real" Puerto Rico is disgusting. There is so much filth, crime, poverty, and drug use that it makes the island almost uncivilized. It was very common to walk down the street and pass someone sitting on the curb shooting up heroin. Like the saying goes: it's a nice place to visit, but you wouldn't want to live there! After we settled into our apartment, things started to change. Paychecks were late. Very late. And short. Our $800 per week became $600, then $400, then $200. We got paid weekly if we were lucky. Sometimes they wouldn't have the money one week, and would promise to make it up the following week, which never happened. Carlos had a "partner" named Victor Jovica. What we found out later was that Jovica was the real owner and Carlos was just the figurehead, on a small salary just like the rest of us. Then we started getting weekly pay in the amount of $50, we thought it couldn't get any worse. A bunch of us wanted to "strike" and not wrestle until we got paid, but when it came down to it, they didn't have the balls to stick to their guns. Jovica was as slimy as slimy comes. At the shows, he would give the boys empanadillas and beer in place of money. Some of the Puerto Rican guys were happy with that, usually the ones who weren't getting paid. We were draining our savings account more and more, until eventually we couldn't make the $1,000 per month rent and got evicted. Then, we were back at the Empress. Mr. Palermo gave us a room at no charge. And he would cook special meals for us in the kitchen. He was very generous, and he knew the type of scum we were dealing with in Colon and Jovica. We wondered how he could afford to give us a free room for two months and all the food we could eat for free. Well, we later discovered that Mr. Palermo was running the hotel and restaurant for the Mafia, so it was used as a way to launder money and would never go out of business. Thank God Chris had that Italian last name! (Even though there wasn't an ounce of Italian in him; he was Slovak!) After six months, I told Chris I just couldn't do it anymore. We were living on minimal food, and lost some of our belongings when we were evicted. I was leaving Puerto Rico, with or without him. I couldn't handle how horrific this place was. I wanted out. We gave Carlos our notice and a list of the paychecks we were short or missing. He said he'd buy our plane tickets and give us the money we were owed. A week and a half went by, and nothing. Finally we went to the office, hellbent and pissed off. He told us he couldn't afford the tickets, but if we worked another show, he'd pay us. OK, we would work another show, but this time I had a little something up my sleeve, in the form of a payback. It was a TV taping, so the ring truck and the production truck were both there... and so were the keys to the truck, left in the ignition. And we were a good four-hour drive from the studio. When all attention was on the show and not the trucks, I took the keys out of the ignition and threw them in my purse. At the end of the show, they had no way to get the trucks started. I had the only set of keys! When, I got back to Isla Verde, I took a moonlit stroll on the beach, made a wish, and threw the keys straight into the ocean. Ha! They don't fuck with me and get away with it! That week, we were given $200 (instead of the $3,000 we were owed) and our plane tickets. Carlos got away scot free on the plane tickets, though. He had to use his daughter's credit card to buy them. Pathetic. Just pathetic. We left Puerto Rico and never looked back. Years later, in 2011, I ran into Carlos Colon for the first time since we'd left. It was at the WrestleMania after-party, and I was behind him on line for a drink at the bar. As he turned around and was face-to-face with me, his black face turned ghostly white from embarrassment. He was speechless. He didn't know if he could, or should say anything to me. But this was the weekend I was inducted into the WWE Hall of Fame, so I was the bigger person and remained civil, knowing that I got him with the keys back in 2003. Karma. # CHAPTER 24 ONLY THE GOOD DIE YOUNG Leaving Puerto Rico was the best thing we could have done. It was truly Hell on Earth. That's where I started drinking again and, with somas being sold over the counter for a quarter each, it would have been too easy to fall back into the depths of addiction. The problem with coming home was that we were now broke. We had very little money left after trying to survive for six months on that island. We had to use our own money there, because if we didn't, we had only enough money from our pay to eat, once a day. So, we came home and went to live with my mother again. It was hard to do, but we really didn't have a choice. Chris started working indies again, but our experience in Puerto Rico soured me on the business to the point that I wanted nothing to do with it. I took some time off. I took a job at a friend's tanning salon as his manager. The shop was just around the corner from my mother's house, and I was getting decent money to run the place. Another reason I didn't work in the business at this time was because my weight had been drastically affected by the pancreatitis. See, your pancreas directly affects your insulin production, and your insulin levels have a direct impact on your weight. So over the three years since I was sick, my weight skyrocketed—hitting 187 pounds at one point. This was incredibly hard for me, especially since every wrestling website was so happy to report how much weight I had gained, speculating my over-eating and saying I "let myself go." Never once did they stop and think I might have had a medical issue that caused the weight gain, which I had no control over. The website's so-called "journalists" and fans around the world were so incredibly cruel, insensitive, and ruthless in their negative and demeaning comments about me. I was eventually forced to get rid of my computer and hole up at home. It was awful. A once confident, outgoing, beautiful woman, who was lusted after for years by men all over the world, and now a depressed recluse, too afraid to go anywhere, fearful that she might be recognized. Going to the grocery store was a scary thing. Walking the mall was terrifying. Going to the gym was brutal, because people expected to see the body I had in the '90s and my pre-pancreatitis curves. I grew deeply depressed and self-conscious. My self-esteem was gone. Do you have any idea what it's like for someone to recognize you, and then ask, "What happened to you?" Those same people don't even bother to try to hide the confusion and disgust in their face? It feels awful. I would cry when I tried on clothes, and mostly lived in sweatpants. I just wanted to hide in my bedroom, and I rarely went to indies with Chris. Then Chris got a phone call from a new company called TNA, Total Nonstop Action. They had been around for a year or so, and were on TV nationwide. The Jarretts and the Carters, Bob and Dixie owned them. Bob Carter is the owner of Panda Energy, who supplies energy and electricity to a large part of the country. He needed something to be a tax write-off, so he bought into TNA and gave it to his daughter, Dixie, to run. The booker at the time was "The American Dream" Dusty Rhodes and he had always liked Chris. Most of the older guys liked him, because he was very "old school" himself and had the utmost respect for his seniors. When Chris got the call from Dusty, he couldn't have been more excited. TNA had focused on smaller, technically sound wrestlers and their light-heavyweight (X Division) division was the feature of their program. It was the first time a wrestling promotion featured the smaller guys over heavyweight monsters, and it was working. The highest ratings the show got was for the X Division wrestlers and the girls, the TNA Knockouts. Chris was psyched. As a smaller guy, he had always been put on the back burner. This was his opportunity to shine. When he started, he was on Cloud 9. He hung out with Dusty a lot, and was asked for ideas for finishes almost nightly. He started dressing differently. The days of wearing gym attire to shows were gone. He now wore dress pants and nice buttoned down shirts to work. Dusty even likened him to his idol, Ric Flair, at one TV taping, saying, "Lookie here! Candido thinks he's the Nature Boy with them snazzy clothes." That made Chris' day. He was in his element. This was where he needed to work. He was finally happy, after so many years, and earning the respect he deserved. The pay wasn't fantastic, but it was enough to pay our bills and get out of the hole a little bit. A few months went by where he would fly to Orlando each week for TV tapings. Every time he came home, he had a bigger smile on his face than the week before, and more great stories to tell me. A PPV was coming up, and he was scheduled to be in a tag team match with Lance Hoyt taking on Gran Apollo and Sonny Siaki. I packed his bags, drove him to the airport, and sent him off to work. He kissed me goodbye as usual. We told each other we loved each other, and I said to him what I always said before a match: "Be careful." It was the night of the Lockdown PPV, April 24th, 2005, but I didn't order it. I never really watched wrestling while I was working, and I especially wasn't going to watch it now with the sour taste left in my mouth from Puerto Rico. I did what he and I would always do on a boring weekend night. I decided to take a drive into Manhattan and get a pizza and some pastries. Before the match, Chris called me, as usual. Everything was normal. He told me it was going to be an easy match. About 30 minutes later, as I was walking out of Ray's Pizza on Ninth Avenue, my phone rang. It was Chris. And he sounded frantic. He tells me he broke his ankle in the match and he's on his way to the hospital. I asked him how bad it was. "Pretty bad," he said. Well, pretty bad was the understatement of the year. It was so badly broken that his whole foot was pointed outward and he couldn't feel his toes. It was a freak injury. He took a bump off a dropkick from Siaki and his right leg crashed into Siaki and folded back underneath him as he landed. When they X-rayed it at the hospital, they found he broke both his tibia and fibula, and dislocated his ankle. They told him he needed surgery, and they would have to put in two titanium plates and numerous screws. Great. He had been lucky so far in his career. He'd had a lot of injuries, but hadn't needed any surgery thus far. He went into the operating room, and I nervously awaited a call from anyone telling me he was out of surgery and in recovery. I eventually got word that the surgery was a success, and that he was coming home a couple days later. The next day he managed the tag team Naturals (Andy Douglas and Chase Stevens) to the TNA tag team championships on TV, with his leg in a cast and on crutches. When I picked him up at the airport, he was waiting for me by baggage claim in a wheelchair. He was upset. He felt as if his dreams were just shattered, that he would never make it back to TNA. I took him home, he took the prescriptions the doctors gave him, and he went to sleep. The next day, he woke up in a lot of pain. We couldn't understand why the pain was worse except for the fact that the anesthesia had finally all worn off. So he did what any wrestler would do after an injury. More pain. More pain pills. On the second day home, the pain was unbearable. I asked him if he wanted to go to the hospital, and he said no. Chris never liked going to see a doctor, so there was no way I could persuade him to go. As the day went on, he took more pills to counter the horrific pain. It was too much for him to handle, and he cried most of the time. Around 4:00 p.m., he went to sleep. About an hour later, I tried to wake him up, but it seemed like he was out cold. His breathing had a funny sound to it—it was labored and congested. I didn't like what I saw or heard. I finally got him to wake up and come around, but he faded out again almost instantly. Something wasn't right. He couldn't breathe. On top of all that, his foot and upper leg were extremely swollen around the cast he was wearing. That was when I called 911. I had been pre-med in college, so I knew enough to know that there was definitely something wrong with his breathing. I rode in the ambulance to the hospital, and my mom followed us. His father met us there, and when we arrived, they brought Chris straight into a trauma room. He was still in and out of consciousness. I was telling him I loved him and I was trying to get him to say he loved me, too. After a few minutes of begging him, he finally got up enough strength to whisper, "I love you." Those would be his last words. The three of us went into a small waiting room around the corner so they could get to work on him. We sat there scared to death, wondering what was going on, wondering what was wrong with him. Ten minutes went by and the doctor walked in the room. "Mrs. Candido?" he said. "Yes." "I'm sorry. He's gone." What? What do you mean, "gone?" He had to be OK, I thought. I pushed past the doctor and rounded the corner and rushed to Chris' side. He was gone. I turned to the doctor and started pounding on his chest, demanding that he do something—something to bring him back. He held me and said, "I'm sorry, we did everything we could." No! He can't be gone! He is my husband, my best friend. We were just over a month away from our 16-year anniversary. What was I going to do without him? I was in total shock. I didn't believe he was dead. I _refused_ to believe it. I searched for his pulse—nothing. I listened for his breath—nothing. I lifted his eyelid—his pupils were dark, fixed and dilated. He was gone. That was April 28, 2005. Christopher Barrett Candido was only 33 years old. I couldn't believe my ears when the doctor told me what had happened. First, he had pneumonia. Pneumonia is a very common occurrence post-surgery because of the general anesthetic administered. That explained his difficulty in breathing. What they told me next, I couldn't believe. The cause of death was a blood clot. A blood clot formed in his ankle, dislodged, and traveled to his heart, causing a heart attack. But what could have caused a blood clot in an otherwise healthy 33 year-old male? It turns out blood clots are possible after surgery and can be treated, if the blood clot isn't in an accelerated dislodged state. High altitudes can cause the clot and accelerate it through the circulatory system. Christopher flew home at 36,000 feet two days following the surgery. The thing that bothered me was I didn't know if anyone at the hospital in Florida told him not to fly. I don't even know if they knew he had to fly home to New Jersey. If we had known, there were a ton of friends he could have stayed with for a week or two in Florida, if necessary. If we had known this, we may have been able to prevent his death, but no one knew. It was hands-down the single worst night of my life. Christopher was the most important thing in my life. We had spent half of our lives together. He was my best friend. I was a basket case. I couldn't imagine life without him. I had spent my entire adult life—17 years old to 32 years old—with him, and I was lost without him. Over the next week, things got worse. When it was time to make his final arrangements, I was supposed to meet his father, step-mother, mother, and step-father at the funeral home to decide what was going to be done. When I got there, the decision was already made by the four of them to have him cremated. Cremated? That was something Chris didn't believe in. He believed in a burial. But his parents were looking out for their own selfish needs and wanted to split the ashes between them. They didn't even ask my opinion. They acted like it didn't matter what I thought. When the wake and funeral came, I couldn't believe the turn-out. Over a thousand people came—friends, family, fans, and the entire TNA crew, including Bob and Dixie Carter. Most of the old ECW crew was there, some WWE and WCW guys, and legends like Terry Funk also showed up. It was really overwhelming. There was a line of people wrapped around the funeral home waiting to get in. At one point I walked up to Chris, leaned over him, and whispered to him. "Look baby. Look how many people love you. You sold the place out." I don't think Chris ever knew how many people loved and respected him and cared about him. If he could see all these people, he would have been in shock! But then again, he saw them. Each and every one. At the last viewing at the funeral home, someone said something to me that drove a dagger deep into my heart. Chris' mother. She walked up to me and said, "This is all your fault. You could have prevented this if you got him to the hospital sooner. This should have been you, not my son." This woman, who had been like a mother to me, was my family for 16 years, and now she has all this hatred towards me and wished I was dead? My heart sunk. I couldn't believe she could be so cruel. I understand she was grieving the loss of her son, but I was grieving, too... maybe more. After the funeral, Chris' final paycheck from TNA came in the mail. He was paid $1,500 for that last PPV match. I went to the bank to deposit it, but even with his ID, they wouldn't let me endorse the check. I called the TNA office to tell them my situation. I told them I needed them to cut me his final paycheck in my name so I could pay off some of his bills. We had a shared bank account and shared credit cards, so I was responsible for his bills. Terry Taylor called me back two days later and said they couldn't cut me a check in my name because he and I were never legally married. I was shit out of luck, and stuck with the bills. If you think about it, Chris lost his life for free. His final match where he broke his ankle—which was the root cause of his death—was literally for nothing. I hated the company after that point. A company that I had raved about and put over left and right as the greatest thing on TV had screwed me and, essentially, Chris as well. I couldn't believe the gall of these people. But they did send me something during the days of the funeral... A ham. They sent me a ham. A "condolences ham." From the home delivery store, Heavenly Hams. Yep, they couldn't send me his last paycheck, but hey, I got a ham! I should be more than pleased and grateful for their thoughtfulness. Maybe if I sliced the ham and sent pieces out in envelopes to credit card companies, they would have accepted that as payment. I could have included a post-it note saying, "I'm so sorry I can't send you a check, but please accept this slice of ham as payment for March." That would have worked, right? After all, the TNA office sure as hell thought that sending me a ham would make up for my grief and loss! "Oh, I just lost my husband and best friend, but _fuck_ , I got me a ham!" Needless to say, I threw the ham out. I couldn't fathom how insensitive they could be. Even after, at the funeral, Dixie Carter pulled me aside and said, "If there is anything you need, anything I could do for you, you just call me." Well, where the fuck is his last $1,500, bitch?? I guess you can say I'm a little bitter. Just a little bit. You can also rest assured that I will never, ever, take a job with TNA. I lost all respect for that company, and I doubt if I'll ever respect it again. I miss you and love you, Christopher. You are always on my mind. RIP Christopher Barrett Candido, 3-21-72 to 4-28-05 # CHAPTER 25 STARTING OVER Losing Chris gutted me, absolutely gutted me. Never in my life had I been alone. I didn't know how to function. I didn't know how to live. I had spent the first 17 years of my life with my parents, and the last 16 years with Chris. I was lost. I felt like an orphan. I had now lost the three most important people in my life—my father, my niece, and now Chris. I felt like I had nothing and no one left. The trauma I was going through was tremendous. I didn't know how to deal with it all, so I turned to self-medicating, again. I picked up the bottle. I was in a deep depression for a few months. All I did was lay in bed, watch TV, and drink. I couldn't even cook for myself. I couldn't get to the gym. It was a struggle to even leave the house to go grocery shopping. I was a mess. Four months went by and I had to do something to get out of this funk I was in. I started going back to the gym a couple days a week, and one day I asked if they needed any help. They did. They needed someone in membership sales. I had worked in a gym while I was in college, so I figured it would be good to get me out of the house and get my mind on something else for a change. I started that September, and by November, I was the number one salesperson in the district, which included 24 gyms. When I do something, I really do it. I put 200% into it. Instead of working my 40 hour work week, I was doing 60-70 hours. Being at the gym so much kept my mind off of losing Chris, and allowed me to heal a little bit. In January, 2006, I met my new boyfriend, John, through mutual friends at the gym. I wasn't looking for a relationship so soon, but sometimes things just happen. When we met, he wasn't exactly my type, but after our first date, I was crazy about him. Two weeks later, I got his last name tattooed on my tailbone (which has since been covered up) and a month after that we got an apartment together. We moved really fast, and we were in love. I told you I do everything 200%! John is the one who gets the credit for getting me back in the gym, back on my diet, and back in "Sunny shape." This was evident less than two years later, when on December 10, 2007, I was asked by the WWE to make an appearance on the Monday Night RAW 15th anniversary show. I was excited, but I was also extremely nervous, because it would be the first time I was to step into that locker room since 1998... and it would also be the first time I saw Shawn since I left the company. In fact, that is what I was more nervous about—seeing Shawn. Walking down to the ring in front of 25,000 people was old hat. I could do that in my sleep. It felt incredibly awkward to see Shawn again. They called me three and a half weeks before the show. I got on the scale and I was 150 pounds. I looked good for a girl working at a gym, but not good enough for an appearance on TV. So John formulated a strict diet for me, upped my cardio, and in three and a half weeks I lost 17 pounds! A woman who weighed 187 pounds just a year and a half prior now weighed just 133! I couldn't believe I had done it. It took six years for my pancreas and insulin to finally regulate so I could drop all the weight I gained from my pancreatitis, but I did it! I was so proud of myself. It was the new me. I figured I'd try and start taking bookings again. I couldn't believe how fast they were coming in! I was getting booked every weekend again. I was working for everyone from Ring of Honor to the NWS back in New Jersey, and everyone in between. I was back! And I was finally happy again. It took a very long time to heal and get out of my depression, but with John's help, and time, I was able to break free. The WWE show date arrived, and we got in the car and headed up to Bridgeport, Connecticut. I was fine for the entire two-hour ride until we were about ten minutes from the building. That's when my anxiety rose, my stomach was nauseous, and my hands became sweaty. I couldn't believe I was this nervous all because of a man! But this wasn't just any man; this was the only man to have broken my heart. My heart was throbbing in my chest when we walked inside the arena, but as soon as I saw the first person—my old make-up girl, Jill Getlan—all my nerves subsided and I felt like I was home again. Jill greeted me with a huge hug and kiss, and then other members of the production staff began to flock to me to say hello. It was such a great feeling to be welcomed back by everyone. I saw a lot of the boys I already knew, and most of the younger guys came up to me and introduced themselves. John and I proceeded to catering where we got on line for lunch. When we chose our table, Ric Flair and CM Punk sat down with us. I've known Ric for years now, but I hadn't seen Punk for about nine years, and that was only once on an indie show. As it turns out, Chris was CM Punk's idol, and when he passed away, Punk got a tattoo for Chris that read "No Gimmicks Needed," which was Chris' moniker through ECW and WCW. I went back to the catering line for some more protein and while I was grabbing a piece of grilled chicken, I felt a tap on my shoulder. I turned around and, OH MY GOD! I was face to face with Shawn for the first time in nine years. OMG! What was I to do? I didn't have to think of what to do because he grabbed me and gave me the biggest hug of the day. Wow! Talk about awkward! There I am in the arms of the one man I loved and couldn't have, while my current boyfriend was sitting at a table with Ric Flair watching every bit of it. Shawn released me from his bear hug and looked me over. "Wow! You look amazing," he said. "You look exactly the same!" "Thanks! So do you! You haven't changed a bit," I said. OK, so I lied through my teeth. He didn't quite look the same. He looked aged and weathered, but still handsome. But hey, a little white lie never hurt anyone. Later that night, as the show began, I waited at the curtain for my big entrance. I was involved in the first segment of the night with Vince, his daughter (Stephanie), son (Shane), and Triple-H. Triple-H was on the microphone and when my music hit, the energy that flowed through my body was electrifying. Triple-H introduced me as "The Original Diva, Sunny," and I made my way to the ring. It was amazing! I was back! It felt like I never left. This opened the door for more return appearances. I was so very well received at RAW that they knew they could use me on more shows. It was late winter, 2009, when I got a phone call from John Laurinaitis. John is the younger brother of Animal, known from his days in the ring as Johnny Ace, and was then the head of talent relations for the WWE. He called about the upcoming WrestleMania PPV from Houston, Texas in April of 2009. They were having a 25 Diva battle royal, and he thought it would only be right to have me involved. I jumped at the chance, told him I'd love to do it, and then hung up the phone. Then I thought to myself, "Wait a minute. I'm not a wrestler, I've never been in a battle royal, and I've never gone over the tope rope." Well, I'd have to learn quickly because I had just agreed to do it. The day came and I was filled with anticipation. Kid Rock was the special musical guest and he was to sing on the ramp while all the girls made their entrances. As I walked past Kid Rock, I turned around in front of him, and opened my robe as if I flashed him. Then I threw it off to the side and got into the ring. This match was destined to be a clusterfuck from the very beginning. We had 25 girls in there, and there may have been five of us that actually knew how to wrestle; and I'm not a wrestler. The rest were clumsy, careless bikini models, and there was no way I was going to get injured by any of them. I was supposed to be the ninth eliminated, but I figured if I sped that up a little bit, I could get out sooner, avoid injury, and be in the locker room changing before the nine-minute match was over. And I did. I started off with someone I knew would be "safe"—Victoria. She and I got along very well, and I trusted her to do right by me. Next up, I had to beat on Maryse a little. She was to have no offense and just sell for me. Out of nowhere, I saw her foot coming right at my face. Thank God I have quick reflexes, as I just narrowly avoided a broken nose. Lastly, I was to go back and forth with Beth Phoenix, whom I also trusted, until she tossed me out of the ring. I ended up eliminating myself fourth instead of ninth, with my good friend Torrie Wilson right behind me. She and I helped each other up and limped down the aisle together in defeat. Whew! Thank God that was over and I came out unscathed! With these two appearances, I showed the world that Sunny was back in the saddle. The "Original Diva" had returned, better than ever. What was to come next _completely_ took me by surprise. I was about to make history, yet again. # CHAPTER 26 THE CREAM ALWAYS RISES There has always been speculation of when—not "if"—I would get inducted into the WWE Hall of Fame. To those of us in this crazy business, it is the pinnacle of our careers; the top of the top. Once you've gotten to the Hall of Fame, there is not much better you can do. In 1996 at 23 years old, I was the youngest performer ever to be inducted into the Cauliflower Alley Club Hall of Fame. The CAC is more or less our industry Hall of Fame, well known by us insiders, but not very publicly known (kind of like the SAG awards as opposed to the Oscars). In 1996, Vince asked me if I'd like to go to the CAC banquet and represent the company along with him, his wife Linda, Jim Cornette, Chris and a few others. Of course I said yes, but I thought I was just attending. I had no idea I was going there for other reasons. All night long at the banquet, people were getting inducted and receiving awards for their achievements in pro-wrestling. I wasn't paying very much attention as I was noshing on my dinner. I was halfway through my piece of cake when Freddie Blassie was on the stage talking about the next inductee, the Manager of the Year, when all of a sudden, Chris and Jim Cornette start saying, "Go! Tammy, go up there!" "For what?" "They just announced your name! You're being inducted!" Oh my God! Are you kidding me? I'm getting inducted into the CAC Hall of Fame? Holy Crap! I'm only 23! I thought only the old timers got inducted! OMG! Well, the CAC committee agreed I was ready for it. So I went on stage, took the microphone, and gave them the most improv on-the-fly acceptance speech they had ever heard. I glanced over to our dinner table and there were Vince and Linda beaming with pride, and chuckling inside because they had just gotten me with this surprise. It wasn't easy to give an eloquent speech on the spur of the moment, but I did my best, and I guess my best was good enough, because I got a standing ovation. Wow! I was in a Hall of Fame at 23 years old! This was a first in CAC history! I was extremely proud of that honor, and I still display my CAC award on my wall to this day. Fast forward 15 years later, just after New Year's, 2011. John and I were preparing to leave for our yearly trip to Riviera Maya, Mexico. It was a Monday night. John was at MMA class and I was home cleaning and packing for our flight to Mexico the following morning. It was about 9:15 p.m. on January 10, and the phone rang. My caller ID said "Johnny Ace." What was Ace doing calling me at 9:15 on a Monday night? Shouldn't he be at RAW? I picked up and said hello, and asked what was up. Ace made some small talk with me about the weather, what I was doing, and about my upcoming trip to Mexico. It was strange to me, because Ace never called just for the hell of it, especially when RAW was on live. He then asked if I was watching RAW. I said I had it on TV, but I wasn't really paying attention because I was elbow-deep in suitcases. "Well, sit down, and watch now," he said. I took a break, sat down, and turned my focus to the television. A segment began announcing the induction that April of Shawn Michaels into the WWE Hall of Fame. After the five-minute segment, I turned my attention back to the phone, and Ace. "Good for him!" I said. "If anyone deserves to be in the Hall of Fame, it's Shawn. I'm so happy for him." Then I thought, "What does this have to do with me?" "Well," Ace said, "let me tell you why I'm calling." Finally. Get to the point. Ace always has an agenda. "We'd like you to be the second inductee into the Hall of Fame this year." My jaw dropped. I was stunned into silence. I couldn't believe what I had just heard. He had to be just messing with me. After what felt like a year's worth of silence, I said the only thing I could think to say. "You're shitting me, right?" "No, I'm not shitting you," he replied with a chuckle. "We were discussing who we should induct this year and Vince thought it should be your year." Oh my God! Shut the front door! My silence and disbelief quickly turned to tears and happiness. Then I tried to give him every reason why he should _not_ induct me. "Don't you think I'm too young? Are you sure? Have you really thought this over? There has to be someone more deserving." He stopped me. "Nope, we are sure it's your year and you deserve it," he said. "Now, we want to keep it a secret so don't tell anyone until we announce it on TV. Well, you can tell your boyfriend, but that's it." "OK, Ace, no problem. My lips are sealed. Thank you so much!" With that, I hung up the phone. I started tearing up, screaming, laughing. Every emotion came rushing over my body, one blurring into the next. OMG! It's really happening! I have to tell somebody! Anybody! But I couldn't. John was at MMA class and never brought his phone in. I was literally shaking with excitement. I had such a strong need to tell someone, to let them share in my joy and accomplishment. But who? I picked up the phone and called my longtime friend and photographer, Bob Mulrenin. Bob is a great guy, who I affectionately call "Uncle Bob." This is the man who had consistently taken the most amazing pictures of me over the last seven years. He was so psyched for me when I told him. And I felt so much better that I let the cat out of the bag. But I needed to limit it to Bob and John and keep it quiet until the company announced it publicly. When John came home and I told him the news, he was ecstatic. He couldn't be happier for me. It was such a great was to start off our vacation. When we came back from Mexico, I made sure I watched RAW every Monday, waiting to see them announce me as the next inductee. Ace had told me they would give me a heads up so I would know when to tune in. Monday after Monday went by. No heads up. No announcement. Meanwhile, I decided that I had to get in the best shape of my life for the Hall of Fame ceremony, because for the pinnacle of my career, I should naturally look the best I ever had. It is all too common for inductees to show up at their induction looking like a shell of their former selves. After all, you are usually 50 years old—or dead—but the time you get inducted. I wanted to show up gorgeous and reinvented, in better shape than I had been in in my prime in my mid to late-20's. I was 38 years old. The youngest and only the fifth woman to ever be inducted into the Hall of Fame, and I had something to prove. This was my chance to tell the world to kiss my royal behind. Well, not ALL the world; just all the negative assholes that had ridiculed me over the years for my weight gain and periods of unemployment. This was my shot to shove it up all their asses and walk away with my head held high, and to walk away the better person. All of those fans, wrestlers and website writers that loved to badmouth me and kick me when I was down, could eat their words when I walk out on that stage, looking phenomenal! I really needed John to push me hard now. I had just 11-weeks to get in the best shape of my life, so out with the carbs and up with the cardio! Right then and there, I stopped eating carbs, _all_ carbs! I wouldn't see a potato, pasta, rice, or bread for 11 weeks. At the gym, I upped my cardio on the treadmill from 30-minutes to two hours running interval sprints, and shortened my weight lifting to 30-minutes with lighter weights. I also started training Muay Thai kickboxing. Let me tell you, 20 minutes of Thai burns more calories than two hours on the treadmill! It's grueling, but so worth it. Two months had passed by, and still no heads up. I was starting to wonder if they really were shitting me. I decided not to go dress shopping until the announcement was made, and not until I was close to my final weight and dress size. It was Monday, March 7, when I finally got "the call." My announcement was going to be on RAW that night. John and I asked a couple of friends if they wanted to join us at Buffalo Wild Wings to watch it all go down. I was sitting at the table eating mini corndogs when the segment came on. It was absolutely amazing! And tear jerking! I started to cry like a baby! I was so happy. I couldn't believe that I got to that point in my career at 38 years old. I couldn't believe the WWE was actually going to bestow that honor upon me. Now I was just over three weeks away from the big day. Waiting for the announcement to finally air was murder, but the real murder was going to be my final three weeks training in preparation for my moment. I started wearing a vinyl sauna suit while doing cardio. I added in more spin classes, up to three-a-day. My kickboxing was upped to 45 minutes and I was doing 50 push-ups at the end of every workout. My calorie intake was dropped dramatically and all carbs and fat were cut from my diet. I was sustaining on chicken and lettuce, and I really saw results. I was tanning every day and increasing my water intake to a gallon per day. I was very careful not to dehydrate, because that would be a huge setback that I couldn't risk. The hardest part now would be writing my acceptance speech. I had tried to write it when I first got the call, but I had no idea how to start it. Or finish it. Or write the middle. See, it is very easy for me to be Sunny, and ramble in character on the microphone for ten minutes. But I've never had to be myself—be Tamara—and speak from the heart. I found this to be incredibly scary and difficult to do. Then I thought to myself, when I cut a promo in character, I'm basically telling a story. So when I get on that stage, why don't I just tell my story—the story of becoming Sunny. When I realized that, writing my speech became second nature. The words seemed to flow onto paper so easily. My writer's block was gone, and I now had my speech written and ready to deliver to the world. On March 31, 2011, John and I made our way, in first class, down to Atlanta, Georgia, home to WrestleMania XXVII. A stretch limo picked us up at the airport and delivered us to the host hotel. We checked into the green room and I picked up my itinerary to see what appearances I was scheduled for at Axxess throughout the weekend. The weekend of my life had officially begun. I had never been so busy in my entire life. Between appearances at Axxess, a media day with the Rock, rehearsals, cocktail parties, the gym, tanning, and squeezing in small meals when I could, I may have had four hours of sleep each night. If not for the adrenaline and excitement of what was to come to me that Saturday night, I would have collapsed from exhaustion. Finally, the day had come. The Hall of Fame ceremony was that evening, the night before WrestleMania. The butterflies in my stomach had grown into Mothras and and my anxiety was through the roof. I sat in my hotel room that morning and I looked back over my entire life to that point. I had succeeded in every job I had ever been given. I made history over and over again in my industry. I lived through three incredibly trying times in my life when I lost Daddy, Stacey, and Christopher. I came back from the brink of death with my pancreatitis. I had persevered. And tonight was my reward. When I arrived at the arena, I got into hair and make-up, rehearsed my speech one more time, and put on my gorgeous red gown. Then it was showtime! Backstage, we had to be photographed and filmed with Vince McMahon presenting us with our rings. Always the ham, I thought of a way to make Vince laugh on camera, like I had always done in the past. As I walked up to him and put my hand out, he placed my Hall of Fame ring on my finger, and I said, "Yes, I'll marry you!" The entire room, including Vince, erupted in laughter. The clock was ticking and I waited my turn to walk on that stage and claim what was mine. I knew my speech from start to finish, every last word, but I jotted down notes on some cards, just in case. Then, it was finally time. Thirteen Divas walked passed me to join my presenters, Michelle McCool and Layla, on stage. My chest tightened and my hands shook. They showed a compilation video on the giant screen overhead, to educate the 12,000 in attendance and the millions who would be watching at home, of my accomplishments throughout the years. LayCool then began their introduction speech. I have to admit, I had wanted Trish Stratus to induct me, but I didn't have a choice in the matter as most inductees do. Then, it was time. It was finally time. I was standing at the curtain waiting to hear my introduction and theme music when, all of a sudden, I couldn't remember my speech! Not a single word of it! Not how it started, not how it finished, and definitely nothing in the middle! I started freaking out in my own head. I felt sweat beads forming on my forehead and nose. I felt the clamminess overcome my palms. Shit! I was going to totally fuck up my once-in-a-lifetime moment! Then I reminded myself—just tell your story. I never rehearsed or planned out any promos in the past, so why should I start now? I needed to calm down and have confidence in my abilities. My music hit. They said my name. I took a deep breath, and out I walked. I walked out on stage to a standing ovation, careful to not snag my six-inch stiletto platform heels on the carpet and fall ever-so-gracefully flat on my face. As I approached the podium, the applause got louder, and I basked in the crowd admiration for a few moments. "This is it," I thought. "Your turn to shine. Just breathe, relax, and do what you do best. Tell your story." Many people said that what followed over the next 15 minutes was the best speech of the night. I didn't ramble, I didn't stutter, I didn't slur, I didn't forget anything or anyone. I told my story. And what a story it was. That night, April 3, 2011, was truly amazing and life-changing for me. I achieved something that 98% of professional wrestlers only dream of achieving. I worked so diligently at my craft for more than 21 years and the WWE Universe, and the world finally recognized it. I was inducted along with Shawn Michaels, the Road Warriors, Hacksaw Jim Duggan, Bob Armstrong, Abdullah the Butcher, and comedian Drew Carey (who was inducted as a celebrity guest). It was ironic to be inducted with Shawn, wasn't it? When we took group photos, Shawn and I were in the middle, facing each other. They almost looked like wedding party photos, with us as the bride and groom and the other inductees as the groomsmen! Ha! The irony! The entire weekend was truly magical, a once in a lifetime experience. It was an experience I'll never forget. # CHAPTER 27 I'LL HAVE THE ALL-YOU-CAN -EAT RIBS, PLEASE? Ribs: Definition (1) n. The set of bones surrounding the chest cavity protecting the lungs and heart. (2) n. A tasty dish served at barbeque restaurants. (3) n. A prank pulled amongst bored, restless professional wrestlers for amusement and to break up the monotony of being on the road, often resulting in the embarrassment of the recipient. For this chapter, we are going with definition number three. The road can get crazy and monotonous and boring at the same time. When 30 or more wrestlers are together, day in and day out, for weeks on end, not only do they get tired of looking at each other, but they also need to do something to pass the time. This is when the rib comes into play. Most of the time, ribs are humorous and pulled between friends, mostly for the amusement and humiliation of the victim, but the ribs can be cruel, and often are. I wasn't sure where to put the stories that are in this chapter throughout the book, so I decided they deserved a chapter all their own. Whenever I do an interview or talk to fans, I always seem to get asked about the best ribs I've seen over the years. The following is a compilation of hilarious ribs, little known facts, and unbelievable stories I have experienced on the road. Enjoy! And read with caution... * * * The very first rib that was pulled on me in the WWF was by the master of ribs, Mr. Fuji. Fuji was well-known and feared for his ribs because his weren't always just fun and games. It wasn't uncommon for him to cause harm to someone. I had just begun on the road as Sunny, and I made sure I was cordial and respectful to everyone in the locker room, especially the old-timers. Mr. Fuji had the nightly job of braiding Yokozuna's hair. But this one night, as I was walking by them, he stopped me and asked me to braid Yoko's hair, because Fuji had a promo to shoot. Of course I wasn't going to say no to Mr. Fuji, so I walked behind Yoko and started combing and braiding. The seamstresses, who were right next to me, started laughing, but I didn't know why. Then Mr. Fuji walked by us, and laughed. Again, I had no idea why. Then I smelled something foul, but I didn't know what it was I realized what it was: YOKO'S HAIR! His hair reeked like shit and sewage! He was so obese that he couldn't raise his hands over his head to wash his hair, and it was pungent! When I was done, I ran to my locker room to wash my hands, but I couldn't get the stink off of them. It took three days for my hands to finally be Yoko-free. That's why everyone was laughing. Mr. Fuji 1—Sunny 0. * * * One afternoon, I was walking in the backstage hallway when I came upon Jeff Jarrett and Hunter Hearst Helmsley talking. I stopped, looked at them both, and said, "Double J... Triple H... Double J... Triple H!" That became my nickname for him from then on. Soon, Shawn was calling him Triple-H. Then the rest of the Clique caught on. Before you knew it, he was being introduced as Triple-H, and the name stuck. Now everyone knows him as Triple-H, and probably 70% of wrestling fans today wouldn't know who Hunter Hearst Helmsley was if their life depended on it. Yep, I gave Triple-H his name. Will I ever get credit for it? Probably not. * * * I "financially supported" "Stone Cold" Steve Austin and The Rock when they first started with the WWE by paying for their meals on a regular basis. * * * The USWA "borrowed" me from the WWE on a few occasions to work their Memphis TV tapings on Saturday morning. Instead of a hotel, I stayed at Casa de Lawler, at the urging of his then-wife Stacy. His house was very, very nice inside, especially the Coca-Cola room! It was a room off the kitchen completely decorated with Coca-Cola memorabilia. He had everything from a Coca-Cola jukebox to Coca-Cola straw and napkin dispensers! It was very cool. * * * The Kings of Ribs were undoubtedly Owen Hart and Davey Boy Smith. I was often either the victim of them or a willing participant. On a month long tour of Germany, we rode on a tour bus from city to city around the country. There was a tiny bathroom down a skinny set on stairs on the bus that I noticed none of the boys used. I figured it was because of the horrible stench the tiny latrine had, but I couldn't pee in a bottle like most of the boys. So on long ten hour rides, I had to go into it, because we didn't stop often enough at rest stops. On this one long trip, I snuck down into the bathroom while everyone was asleep. When I was through, I put my hand on the door handle and pushed the door. It didn't move. I pushed and pushed and pushed and pushed. It finally opened an inch. I peeked out and saw the whole stairway was blocked with every single suitcase that was on board! Somebody had barricaded me into the tiny, smelly, pee-covered bathroom. And I wasn't just in there for a few minutes; I was locked in there for two hours. I tried to bang on the door and push my way out, but to no avail. Then I heard a laugh. A very distinct, British laugh. The culprit was Davey Boy, the British Bulldog. If he and I weren't such good friends, I might have been pissed off, but I knew it was all in good fun. * * * Owen Hart had a reputation for being one of the cheapest guys on the road. He would spend the least amount of money possible and get as much for free as he could. On that same trip to Germany, we had a free full breakfast every day in our hotels. Owen took advantage of the free food and drink and filled his two duffel bags with pastries, bagels, and a quart of orange juice in each bag. That's all Owen would travel with, two small duffel bags, so he wouldn't have to check any luggage. He would just carry them on. Davey Boy knew this, and that was a huge mistake. When we arrived at the airport and went to the desk to check in, Owen was first in line. The desk attendant asked if he had any bags to check, and he said no. Then Davey, who was right behind him, chimed in. "I'm sorry ma'am, but those bags are too big to carry on," Davey chirped. "He'll have to check them." "Shut up, Davey," Owen muttered out of the corner of his mouth. "I always carry these on." The desk attendant took another look at Owen's carry-on bags. "Oh, I'm sorry sir, but they do look too big. I'll be happy to check them for you." She took his bags and put them on the conveyor belt. Owen was furious. He knew what was going to happen. When we arrived at our next city, we proceeded to the baggage claim belt. As the bags started coming out, we all saw Owen's two little duffel bags leaking orange juice out of every seam and running down the belt! All of his clothes were stained with orange, his regular clothes and his gear. That's what Owen got for sneaking O.J. in his bags. It was all too funny. Davey and Owen used to battle with one another over ribs. They were the champs. * * * Sometime in 2000, Chris, Sabu and I were booked on a two-week tour of Australia. It was my first trip there. so I was very excited. After a long 22-hour flight, we were in line at customs. Chris and I got through fine, but they decided to search Sabu. They confiscated all of Sabu's many pills. He was furious. When we got to our hotel, we were exhausted. Chris and I decided to order some food to our room. When I looked at the phone, I was confused. Besides the number buttons, there were three buttons to the side of them. They were labeled: Room Service Massage Doctor Room Service, Massage, and Doctor, oh my! What in the world were these for? So I pressed the Room Service button, and ordered some dinner. Then I pressed "massage," and after about 20 minutes, two masseuses came up with portable tables. Then we pressed "Doctor." Thirty minutes later, a doctor came to our room with a tackle box. He set it upon the bed, opened it up, and asked, in his thick Australian accent, "So, what were you looking for?" He had everything. Vicodin, Soma, Percocet, Demerol, Xanax, Valium, Clenbuterol, and various steroids. Of course, he also had antibiotics and antihistamines, but we weren't really interested in that. It cost $40 for a prescription, and he filled it right there. The best thing was, there was no limit! So we called Sabu the next day and told him to come to our room. I pressed the buttons. All three of them. Sabu was amazed when we got our food with a side of massages and prescription pills to wash it down! Ha! This obviously became our daily ritual. Room Service, Massage, and Doctor... Oh my! No wonder none of us could remember much of that two-week tour! * * * In 1997, Marc Mero needed knee surgery. When he was off the road, his wife, Sable, traveled with Ken Shamrock. We all soon found out that they were doing much more than "travelling" together... * * * Speaking of Sable, in the WWF, she used to talk about how she and Kimberly were such good friends. Come to find out, they knew each other long before their wrestling involvement from their days as strippers at the Gold Club in Atlanta. Who would'a thunk it? * * * Chris and I were traveling with Lex Luger and Davey Boy Smith in Vermont. Davey was driving and, in towns in Vermont, the roads are up and down hills with traffic lights at the bottom of each hill. The roads were pretty icy and Davey was driving pretty fast, so he blew through one, two, three, four red lights in a row! Of course, he got pulled over by a cop. The cop said, "Sir, you just ran four red lights in a row!" in an angry voice. Davey replied, in his heavy British accent, "Oh, I'm sorry sir, but I'm from England. And in England, red means go." The cop got flustered. "Well, alright sir, but just so you know, in the United States, red means stop and green means go. Now be careful and have a nice day." Ha! And we drove away, ticket free. Davey could convince anyone of anything. * * * In Germany, we had one afternoon off in West Berlin. Chris and I had a craving for McDonald's, so we hailed a cab and they took us to a McDonald's in a mall. It was kind of a long ride, so the cabbie gave us a business card with the phone number to call them to be picked back up. We ate, walked around the mall, and gave them a call. The cab dispatcher only spoke German, so we asked everyone we saw if they spoke English. One lady stopped to help. She got on the phone, spoke some German, and hung up. She said we were somewhere in East Germany, and the cab we called doesn't come out that far. Doesn't come out that far? But they brought us here, and we don't even know where we were! She told us to go up to the bus stop and catch a bus. So we walked up to the bus stop on the side of a busy street, but the bus route map was all in German. We didn't know where we were, but we knew we were far from the hotel... and we didn't even know the name of the hotel. It was 4:00 p.m. and our tour bus would be leaving for the show at 5:00 p.m. We were never going to make it back. I broke down and sat on the curb and cried. Fuck! We were lost in East Berlin, with no way of getting back to our hotel, wherever that was! We sat there hopeless and crying for about ten minutes, when suddenly, we heard something in the distance. Could it be? Could it be the WWF wrestling theme song album? Yep, we heard the faint sounds of Bret Hart's theme song. Then the song became louder and louder. One of the cars in the traffic jam in front of us must be playing it. Finally a car rode up, and started yelling at us. It was a small car, with four girls wearing Bret Hart T-shirts playing his music. Chris and I looked at each other and, without hesitation, ran up to the car, swung open the door, and dove in. We were saved! The girls knew a little English, but they were on their way to the show, and they knew the hotel where we were staying. After signing a few autographs and taking some pictures, the girls graciously dropped us off at the hotel just in time for us to get on the bus and head to the show. My eyes were a swollen mess from crying, but we were saved! Note to self: _Don't_ get in a strange cab in a strange country just because you're jones-ing for a Big Mac!! * * * I was the first wrestling personality besides Hulk Hogan to be featured on mainstream television programs such as _Entertainment Tonight, Extra, Access Hollywood, Inside Edition,_ _MTV's Singled Out_ , and _MTV's Oddville._ I was often referred to as "the female Hulk Hogan" due to my overwhelming popularity. * * * In 1996, at the WWF Slammy Awards, I was awarded the "Best Buns" and "Minds Behind the Mayhem" Awards. * * * I was the first, and only, manager in WWE history to be the manager of three consecutive sets of tag team champions. * * * The brand new Gund Arena in Cleveland, Ohio, had just opened, and the WWF was the first live event to be held there. This arena was beautiful. The locker rooms were spacious and carpeted wall-to-wall. Even the walls themselves were carpeted. I noticed Bret standing by a table looking down at it. I walked over to see that there was a sheet cake on the table with Bret's picture airbrushed on it, and it was a very good likeness. "Are you going to eat that?" I asked Bret. He said no, that it had come from a fan, and he walked away. A few minutes later, I saw Davey Boy standing by the cake. He called me over. "Tammy, smell the nose. It smells like strawberry," he said. Now, if it was anyone other than Davey, I may have smelled the nose. But there was no way in hell I was putting my face near that cake with him standing right there. So I thought I'd beat him at his own game. I stuck my hand deep in the center of the cake, lifted a good-sized chunk out, and smashed it right in Davey's face, on his glasses and all. He paused in shock, and as the cake fell from his face. "Oh, OK, Tammy," he said, as he regained his composure. "Shit's on now!" He picked up the entire sheet cake and chased after me down the long, carpeted locker room hallway. When I reached the end with nowhere to go, I felt a huge mound of cake splatter on the back of my head. When I turned around, Davey was standing next to Owen, who had just come out of the locker room to see what we were up to. Davey and I made eye contact. He gave me a wink, and the entire cake went up into Owen's face with such force that the back of his head hit the wall behind him. Owen slid the sheet cake down off of his frosting-covered face, into his arms. "OK, Davey," he said. He walked back into the locker room and dumped the entire cake into Davey's gear bag, making his trunks a sweaty-smelling dessert. At this point, the entire locker room was cracking up, including me, who was peering into the doorway, at Davey's misfortune. Davey saw me and yelled, "Tammy, you think that's funny, huh?" I ran for my life down the hallway with Davey hot on my trail. I ran into my locker room, another dead end, and passed Chris who was sitting in a chair, completely unaware of what was going on out in the hallway. Davey and I were at a stand-off, with our hands full of cake and icing, prepared for a duel. Only this time, Chris was sitting in the middle. Davey and I locked eyes again, winked, and we instantly knew we were on the same wavelength. At the same time, we turned and our handfuls of cake went flying at Chris' face, exploding all over the carpeted wall behind him. Just at that very moment, our road agent, Tony Garea, walked in. "What is this travesty?" he screamed. Davey and I scurried out of the room leaving Chris to take the brunt of Tony's scolding, even though he was just an innocent bystander. When it was all said and done, the brand spanking new carpeted walls and floors of the Cleveland Gund Arena were covered with buttercream icing. Davey and I were each fined $500 and we were made to stay after the show and clean the carpets with wet towels. It was absolutely hilarious as we were scrubbing the walls, still covered from head to toe in cake. It was the best $500 each of us had ever spent. * * * Percy Pringle (Paul Bearer) passed away as I was writing this memoir. The news of his death made me think of a rib the boys used to play, not on him, but on his son. His son was about seven or eight years old at the time; a roly-poly freckle-faced redhead who would come to shows often with his dad. One particular show, the boys really did a number on the kid. They hoisted him up to the ceiling and pressed his back against the metal air conditioning duct running across the ceiling. The Undertaker and Kane, the tallest guys on the bunch, taped him to the duct with duct tape. Around and around, over and over, until he was strapped to the ceiling by his waist, with his arms and legs flailing in the air! The kicker was that the boys left him there for the entire length of the show! Three hours! When Percy walked in, looked up, and saw his son strung up like a bug on a spider web, he just laughed a big belly laugh and left him there. You'd think the boy would never come back to a show because of this, but he was a glutton for punishment. And every time he came back, he was taped up to the ceiling again! * * * Every time we were booked in Canada, we dreaded the trip. It was boring, had bad food, and was full of ice-covered towns. This tour, we were going to be on the road for two weeks straight, all across Ontario and Quebec. We all decided to chip in on a 12-passenger van to save on rental, gas and toll money. There were nine of us: me, Chris, Davey Boy, Billy Gunn, Bart Gunn, Goldust, Marty Jannetty, Al Snow, and Owen Hart. In the first couple days of our tour, Owen rode with us, but then jumped in a van with a fan, which he did quite often. Owen was the cheapest man alive, so anywhere he could save a buck, he did. So the eight of us were riding in our brand new, white Ford 12-passenger van, with Al Snow at the wheel, and Owen driving the fan's van right behind us on the QEW. The QEW is a long highway spanning the width of Ontario past Toronto, through Quebec, up to Montreal. It's about eight lanes wide, so there is quite a bit of traffic on the expressway. There is nothing to see along this highway except the slew of gas stations, truck stops, and Tim Horton's coffee shops dotting the side of the road. As we quickly approached one truck stop, we noticed a sign that read, "Fireworks on sale here!" What? Fireworks? For sale legally at a truck stop? We just had to check this out. We stopped to grab a bite to eat and check out what explosives were available. We did our shopping and piled back in our van. We had rockets, Roman candles, stink bombs, smoke bombs, and sparklers. We were set. But we were on a four-hour drive into Quebec. What were we to do with them? Marty Jannetty was riding in the front passenger seat, so he acted as the DJ for our trip. He popped in a cassette tape of the soundtrack for the movie _Dangerous Minds_ , the Michelle Pfeiffer movie featuring Coolio's song, "Gangsta's Paradise." This tape got everybody a little pumped up, especially Goldust, Marty, and Davey, who started an impromptu wrestling match in one of the middle seats. They were rocking so feverishly back and forth on this middle bench seat that the bolts ripped right out of the floor. What were we to do with a dislodged middle bench seat? Well, what any bunch of responsible, grown men would do, naturally—open up the side door and toss it out onto the highway at 80 miles per hour! Oh my God! I couldn't believe they just threw out the seat! There were lots of other cars on the road, and they just opened the door and threw it out. We were driving in the middle of a blizzard, and there were already two feet or so of snow on the ground. Marty opened the front passenger side window to allow the blizzard to coat the inside of the van white. It was an old-fashioned manual crank window, so when it was all the way down, Marty broke the handle. Why did he break it? Because it was there. What were the repercussions? We couldn't close the window in the middle of a blizzard. Then came the fun part. We realized we had bought all those fireworks! Owen was still behind us, so Davey thought of a great way to rib him and the fan. We opened all the side windows of the van and armed ourselves with rockets and Roman candles. Upon Davey's orders, we lit them all, and shot balls of fire out of the van directly at Owen behind us. Owen caught on to what we were doing, so he strategically placed himself right behind us to catch the multi-colored fireballs in the grill of the van he was driving. We all died in laughter as the fan's van began filling up with smoke, almost to where you couldn't see their faces through the windows. Our adrenaline was so fired up, that we lit our multi-colored smoke bombs in our van, until the interior looked like a psychedelic kaleidoscope. Our fun came to an end when we arrived at the venue. The next few days we spent on the road in this completely trashed van with no middle seat, burns in the carpet, and a passenger front window that was permanently down. When it was time to return the van, Davey Boy confronted the rental agent, addressing him in his strong, convincing British accent. "I can't believe you rented me a van in this condition! The front window is broken, there is no middle seat, and it smells of smoke with burns all over the carpet! I had my wife and children in this van! This is a travesty! The rental agent was so embarrassed and convinced that the van was rented out in this condition that he refunded the two weeks rental onto Davey's credit card and gave him a free week's rental. Davey walked away laughing and smiling with pride at his accomplishment. Why? Because the funniest part was that he wasn't even the original rental! It wasn't rented on his credit card, but he got it refunded to him. He turned a profit on the deal! Ha! Oh, that crazy Davey Boy. * * * When I was a kid, meeting my favorite wrestlers at the Howard Johnson's, we became familiar faces since we were there every month. One night, as Paul Orndorff was leaving for the gym, he walked up to my sister and me and said, "Hey girls, I hate to bother you, but can you do me a favor? I forgot to wash my wrestling gear for tonight and I'm headed to the gym now. Can you wash and dry it for me so it'll be clean for tonight?" We quickly answered. "Of course!" So we had the honor of washing Mr. Wonderful's trunks and kneepads! We were tempted to walk off with them, but then that would probably have ruined our autograph and picture taking at the Newark Ho-Jo's! * * * In 1999 and 2000, I was doing some fitness modeling for bodybuilding magazines. All of my photo shoots were in Venice, California, so I would shoot out there when I went for TV and movie auditions. One of my photographers, Rick Schaff, was a really nice guy, and well known in the bodybuilding world. We were out on Main St. in Venice doing a shoot along a waterway that had some nautical pilings in tall green grass. I was wearing a one-piece bathing suit that barely covered more than a bikini. My skin was tanned and glistening with baby oil and sweat, and my poses were rather, shall we say, _provocative_ in nature. We were getting plenty of honks and catcalls from all the cars passing by and a few pedestrians stopped for a few minutes to watch the session. Down the sidewalk, we saw a rollerblader headed our way. His eyes were on me, and not on the sidewalk in front of him, where they should have been. As he passed by, he was looking over his shoulder at me, his neck twisted and contorted to what must have been a painful position. We turned our attention away from him and all of a sudden we heard a man screaming in pain! We looked back, and saw the rollerblader lying on the ground, holding his leg and yelling in agony. We called 911 from our cell phone, and Rick ran over to him to see if he was OK. It just so happened that as he was paying more attention to my near-naked body than the sidewalk, his skate caught on a large crack and he went tumbling down to the ground, and he broke his lower leg in the process! So I can now say that my sexy good looks not only broke men's hearts, but their limbs as well! # CHAPTER 28 OVER BARBED WIRE AND THROUGH THE WOODS, TO THE LIQUOR STORE WE GO! After my Hall of Fame induction, things began to deteriorate between John and me. I won't go into any details because what happened is personal, and we remain good friends to this day. After nearly six years together, we split in September of 2011. I had just come home from my first attempt at rehab, something I didn't want to do, but something I did upon his insistence. He thought I was drinking more than I was and gave me an ultimatum, so I called the WWE for treatment for the first time and went to Hazelden in Minnesota. This attempt at rehab was not successful, and I was drunk there almost the entire time. How was I drunk? Let's just say I became a master escape artist. Since I didn't want to be there, I wanted to drink. On my way into rehab in the limo provided by the WWE, I noticed a small liquor store in the little town outside of Hazelden's grounds. I knew I could find my way there if I was sneaky enough. There were security guards at the one entrance and exit to the grounds, so I couldn't go out that way. I had to find a shortcut or something. There was a long circular walking trail that went all around the facility, and I knew a part of it went out near the main road. So I walked on the trail to a point where I thought I was parallel with the road and jumped through the four-foot high sticker bushes into the woods. I walked about 200 yards through the woods, under broken tree branches and around tree stumps, until I came to a four-foot high barbed wire fence. With the caution of a ninja, I climbed the fence and leapt to the ground on the other side. I then walked through two residential backyards and up someone's long driveway to the main road. I made a left and about a quarter-mile down the road was the greatest discovery of all, the small mom and pop liquor store. I bought my bottle of Southern Comfort, stashed it in my Victoria's Secret tote bag, and headed back the same way. Down the road. Down the driveway. Through the backyards. Over the barbed wire fence. Through the 200 yards of woods. Through the sticker bushes. And back to the walking trail to the dorms. Ha! I was good. I took this journey every day for 15 days. I was drunk the entire time I was there. At the two-and-a-half week mark, I decided to leave treatment. As I was packing up my things, I pulled the bottle of SoCo out of the personal safe in my room and said, "See! Your stupid rehab doesn't work!" I've always said that when there's a will, there's a way, and rules were meant to be broken. Poor Hazelden Treatment Center. They never saw me coming. When I came home, I got my very own apartment for the first time in my life, on the beach in Long Branch, New Jersey. Being alone for the first time in my life was complicated, and I didn't handle it well. My drinking spiraled out of control. All I cared about was drinking, and how I was going to acquire my next drink. It was a very dark time in my life. I felt very alone. I was so sick from drinking that I spent Thanksgiving, my birthday, Christmas, and New Year's Eve alone at home, drunk on my couch. There were nights I wanted to die. I didn't want to kill myself; I wasn't suicidal. But I damned sure didn't want to wake up in the morning. I function a lot better when I have someone to take care of, but when I'm alone, I can't even take care of myself. I didn't have the tools or emotional stability to be a "single" person living alone. Things were really bad. My health was suffering. I had a viral infection for six weeks, and then I spent a week in the hospital with a very low, very dangerous, low platelet count. All of these illnesses were aggravated by my drinking. Something had to change. Something had to give. # CHAPTER 29 THE DEVIL'S SON Damien. Son of Lucifer. Spawn of Satan. From Day One, I should have known that name was a bad omen. I should have run my fingers through his long curly hair to search for the number of the beast etched into his scalp. My friends even joked about that name when they first heard of my new boyfriend. It was mid-May, 2012, and my friend Tracii, who spent more time at my beachfront apartment than her own home, was telling me about a guy who was dying to meet me. He was younger, 26, and a wrestler on the indie scene for four years. I had never heard of him or met him at any shows, even though he was from Staten Island and I was from Jersey. We just never crossed paths. So after some begging and pleading on his part, Tracii finally told me about him, and I looked him up on Facebook. She was going on and on about what a great guy he was, how much fun he was, blah, blah, blah, so I figured I'd check him out. At first look, I thought he was cute, but completely not my type. I wasn't into guys with long hair, I didn't want to get involved with another wrestler, and he, by her definition, was a "partier," which was not something that interested me. Yes, I was an alcoholic, but I've never been into the drug scene, so I was a little turned off by that. But I "friended" him on Facebook anyway, and we started chatting, then we exchanged numbers. We started texting, then talking. A lot. Every night. For five hours a night. For five nights straight. The first night we were finding so much we had in common. By the second night we were finishing each other's sentences. By the fifth night, I turned to Tracii and said, "I think I'm in love with this guy!" He was definitely quick-witted, and extremely charming, and he won me over fast. He was constantly complimenting me, and singing to me on the phone, since I found out he used to sing in a rock cover band. But he still wasn't my type. I'm into sports, especially MMA. He hated all sports. I wanted to be a doctor. He had to go to summer school in high school. He was really into music and fashion. I was stuck in the 80's and loved my sweatpants. On that fifth night of talking, a Thursday night, he asked if I wanted to go out the following night. I told him that I would have liked to, but I already had dinner plans with a guy named Adam whom I had already cancelled on once before. He was begging me to cancel on him again, but I said I couldn't do it, that it would be too mean. So our call ended at 2:00 a.m., and I went to sleep. By 9:00 a.m. the next morning, I cancelled my date with Adam, _again_ , and texted D and said that I was all his that night. I told him we'd use the dinner reservations I already had, but to bring his toothbrush, just in case. So D got out of work around 5:30 p.m. and headed down for our dinner reservations at 8:30. We had forgotten that it was Memorial Day weekend, so the highways were packed. He didn't get down to my place until 8:15 and he still had to shower before dinner. He called me as he was coming up my street, Melrose Terrace, so I told him I'd meet him downstairs in the parking garage because I had to get him a guest parking pass. As I was walking into the entrance of the garage, I just so happened to turn around, and at that moment I saw silver Nissan Maxima turn into the garage. Through the glare on the windshield I could make out a man with curly hair pulled back into a ponytail. Our eyes met, and I knew it was him. I turned around, walked up to his car; got in, reached across the dozen roses he had for me, grabbed him by the back of the head, and kissed him. No "hi." No "hello." No "how was your drive?" I just kissed him. Hard. It was instantaneous, love at first sight. I was dressed and all done up, he was sweaty and dirty from work, but that made him even sexier. His scent was undeniably sexy. There are such things as pheromones, and my sexual radar was definitely picking up on his. So we parked the car and headed up the elevator to apartment 414, my place. We went in, he pushed me up against the wall, and we made out, for about ten minutes. Finally I pushed him off and made him get in the shower, since now we were already late for our reservations. When he was done, he stepped out of the shower, fully naked. No shame. I had an exhibitionist on my hands. He had nothing to be ashamed of. A beautiful body—a little thin for my usual taste—and a very attractive penis. And probably the best butt I had seen in a long time. He definitely wasn't shy about being in his birthday suit, but then again, neither am I. He finally put on some clothes, looked fantastic, more fashionable than me, and we went to dinner. Throughout the meal, he was holding my hand, and kept getting out of his chair to come over and kiss me. A total romantic, I was falling in love fast. After dinner, we speed-walked back across the street to my apartment, flew up the stairs, and before we knew it, we were tearing each other's clothes off and were engaged in the most sensual, passionate sex session that I have had in a long time. Everything was perfect. Every movement, every thrust, every kiss, every drop of sweat from his chest that landed on my tongue—perfect. That night we stayed up until around 8:00 a.m. making love, over and over again. The next day, he was supposed to go to two Memorial Day barbeques, but he cancelled them both. What was to be a dinner date had now turned into a four-day weekend of sex, debauchery, and more sex. The only time we left the bedroom was to use the bathroom or go to the door for our food delivery. For four straight days. Unreal. By the third day, we were both so sore, but we kept going. On Monday, we both didn't want him to leave, but he got called in to work, so we kissed goodbye and made plans for the following weekend. I was in love. Undeniably and completely in love, and so was he. The next few weekends went exactly like the first. After work on a Thursday or Friday, he'd drive the two and a half hours down from Connecticut to spend the weekend with me. We went out, we cooked, we went to the beach, and we made love—a lot. Everything was falling into place beautifully. Until... ... During a mid-week phone call, he said he needed to tell me something. OK, here we go. What is it? He hesitantly tells me he has a roommate. Fine, no big deal. The roommate is his ex-girlfriend. OK. Really big deal! "Are you kidding me?" I said upset, angry and stunned. He explained to me that he'd been trying to get her to move out for months and that she wouldn't leave and had nowhere to go. Blah, blah, blah. I was stunned, confused, mortified. I was pissed the fuck off! This should have been the red flag of all red flags, but I brushed it off as him being too nice a guy to toss someone out on the street. I tried to deal with it the best I could, but my best turned out to be drinking more and more heavily, each and every day, morning until night. I would binge for four or five days straight with little food or water. The pattern turned out to be, when he was with me on weekends I hardly drank. I was happy. When he was home with her during the week, I drank like a fish. When I think about it, I guess it was my way of coping with the thoughts of him sharing an apartment with her, and me having to trust and believe that nothing sexual was going on. Needless to say, it was driving me absolutely insane to the point where I might as well have had an intravenous drip of vodka 24-hours a day. I just couldn't handle it. I wanted to believe that it was over between them, but I couldn't do it sober. So I drank. And drank. To the point where I ended up back in the hospital a few times. One time I woke up in the hospital and saw him sitting next to me. He had arrived at my place on his usual Thursday night and found me unresponsive. I had a blood alcohol level of .540. They told me a .40 was considered fatal. How the hell was I alive? That was when D and I sat down and decided it was time for me to go to rehab. I couldn't live like that anymore. I couldn't be the drunken lush that did nothing but lay on the couch 24 hours a day all week long with a bottle of vodka in my hand and a dozen empties lying around me on the floor. It got to the point where I wouldn't even get off the couch to throw anything out, not empty bottles, not food, nothing. I would live all week long on top of piles of trash and clean feverishly when D was on his weekly ride down to see me. The only time I saw my bed was with him. I was always too drunk or too sick from being drunk to get off the couch at all. I would go days without a shower. Days without brushing my teeth. THIS was my bottom. But I could still muster up enough energy to make the three-block trip to the liquor store when I ran out. Correction: I _never_ ran out. I would always make sure I had enough to get me through the morning until the liquor store opened at 10:00 a.m. If I didn't, I'd drag myself off the couch, even in a thunderstorm, and get to the store at 9:59 p.m., right before they closed, because God forbid I woke up at 5:00 a.m. dry, and shaking from withdrawal. The Pakistani owners of my friendly neighborhood booze shack knew me by name. They even let me take home bottles when I forgot my wallet, because I was too drunk to remember it on the way out. They always spotted me, because they knew I'd always be back for more. I even had a cabbie named Jessie—nice older Hindu guy—on speed dial on my phone. On those days when I didn't feel like going to the store myself, he'd pick up a bottle and deliver it to me at my building. Convenient, huh? This is what I had become. I was a drunken mess, no better than the homeless drunks sleeping in cardboard boxes under a bridge. The only difference is I had a place to sleep... barely. I was more concerned with having enough booze cash than paying my $1,500 monthly rent. Twice I was given eviction notices and had to go to court to pay the back rent by the thousands to be able to stay. This is what I had become, what I swore to myself I'd never become. But I did. # CHAPTER 30 MORE LOBSTER, PLEASE? I finally mustered up enough guts to pick up the phone and call Ann Russo, the head of the WWE Wellness Program Department. Let me tell you, this is NOT an easy phone call to make. Your whole body shakes as you dial. When she picks up, you have to fight the urge to not hang up, then comes the hard part. "Hi Ann, it's Tammy. I think I need help. Again." Whew! I did it. It's the hardest thing any alcoholic or addict will ever do, to ADMIT you need help. See, all alcoholics and addicts are in the same mindset—denial. We all think our problem isn't that bad, we can control it, and we can stop on our own if we want to. Bullshit! Our problem is that bad, we can't control it, and we _can't_ stop on our own! It's humanly impossible! (So all of you out there, quit fucking fooling yourselves, 'K?) So Ann told me she'd make a few calls and get right back to me. Within two hours, I got the call saying there was a bed waiting for me at 9:00 a.m. the next morning at Silver Hill Hospital in New Canaan, Connecticut. Here is where the fear sets in. Oh my fucking God. I'm going back in. What do I pack? I don't want to pack! I can't sleep. I can't go tomorrow! Oh my God. I'll try to stop on my own. The fear and panic is almost too much to bear. There is no semblance of relief by thinking, "Ah, I'm going to get sober and feel much, much better." Nope. None of that happens. None. All night long, I was freaking out, with D unsuccessfully trying to talk me down. Nothing worked. I was awake all night and decided to pack 20 minutes before we were supposed to leave for the place. Ugh. I was a mess, a complete and utter panicky mess. I forced myself into the shower, and then we were off to rehab. As we pulled up, I was delighted to see this beautiful country club setting, with beautiful horses, tennis courts, a pool and gym and happy people everywhere. We were greeted at admissions like we had just arrived at our resort for a lovely vacation. The dining room was staffed with four professional chefs who served us lobster two or three times a week. Seriously, lobster! Chef Henry, who became my close, personal friend, would grill me up some chicken breasts if the menu ever consisted of too many fried or saucy foods. The omelet station cook, Eddie, with his long dreadlocks and Bob Marley-like easy going attitude, wouldn't even need to ask how I wanted my omelet each morning—he knew. It was his job to know. I knew how to get the right people in my pocket, which I always did. The house I lived in was gorgeous; hard wood floors, some single bedrooms, granite kitchen, leather sofas; just gorgeous. OK, now that I'm done with the infomercial selling Silver Hill, I won't bore you with the details of what goes on at rehab, because you've probably read about it many times before. But this is what it sums up to: 1) Groups 2) One-on-one sessions 3) More groups 4) AA and NA meetings 5) More groups 6) And the occasional "rehab romance" (not for me, though) Another thing fantastic about SHH was that we had visiting hours every day. So D came four or five times a week to see me, and enjoyed Chef Henry's fine dining as well. Then he had me for dessert. Oh yeah, we shagged every time he came to visit. My room was in a private upstairs corner of the house, so it was very easy to sneak away for 20 minutes or so. My 33 days there came and went pretty quickly because of my posh accommodations, great cuisine, cool chicks as housemates, and seeing my Love almost every day. On August 23, the day of my discharge, my Prince Charming (ahem) picked me up in his chariot and delivered me to my new home, his apartment in Branford, Connecticut. When I walked through the door, I was in shock! Not a good shock, either. The place was a total pigsty. As it turns out, the piece of shit ex-girlfriend didn't move out until the day before! Talk about last minute! She took everything! She didn't even leave him a roll of toilet paper! What she did leave was a giant mess for me to clean up! I walked into the bathroom, and _oh my_ —. # CHAPTER 31 HOME SWEET HOME... OR SO I THOUGHT The bathroom looked like it hadn't been cleaned in months! The kitchen, too! Filthy. Just filthy. Even in my most drunken states, I still managed to clean the bathroom and the kitchen once a week. My belongings were already there in the storage unit beneath the apartment, but I couldn't possibly start unpacking until I had cleaned up this landfill first. So Cinderella, I became. Scrubbing, washing, cleaning, more scrubbing, disinfecting, deodorizing (the place reeked of cat piss), and de-staining. Wouldn't ya know it? The sink, toilet and tub really weren't all a lovely cream color! They were white! What a smashing discovery! But I swallowed my pride and cleaned, trying not to make him feel bad in the process. After three days of hard labor we moved my things up from storage. We were finally making this place livable. Everything was going fine, with the occasional coming across a picture of the witch that would totally set me off. We were trying to settle in and get used to living together, but this fucking bitch would not stop calling, texting, Facebooking or emailing him. Enough already! I put my foot down and told him he had to stop replying and cut ties, because of how uncomfortable it was making me. I was doing great with my sobriety, and I didn't need anything, especially her, putting that in jeopardy. He promised he would, and we went on with life; going to the gym together, meeting his friends, going out to dinner with them, and doing the "Number One" no-no straight out of rehab: going to bars with him and his friends a few nights a week. Big mistake. Huge. I don't recommend this to a newly sober person at all. Everything was going wonderfully for three and a half beautiful weeks. On Saturday night, September 11 (the date should have been another omen) we were all out at the local watering hole when D walked away from our table with a few of the guys. He left his cell phone with me... Big mistake on his part. He got a text message from HER asking, "Are you home?" I figured I'd answer back as him and see what she wanted. The conversation went like this: Me (as D): "Why?" Her: "Leave for a while." Me: "For what?" Her: "Let's fuck." Me: "Why would I want to do that?" Her: "Oh okay, don't act like we haven't been fucking." With that, I stormed out of the bar to find him. I was bright red with rage and I was shaking uncontrollably. I eventually found him in his car with the local drug dealer, snorting crushed Percocet 30's, which set me off even more. Like I said, I'm an alcoholic, not a drug addict. I pulled him out of the car and questioned him. He was already high, so in his worst lying voice he tried to tell me that she was bullshitting to cause trouble. I made him call her and put her on speakerphone. He accused her of making it up. She proceeded to describe their newly furniture-less friend Joe's apartment and how they had to fuck on a blanket on the floor. He just had a baffled look on his face as he was trying to convince me she was lying, but she knew too many details she shouldn't have known. And I'm not stupid. By this time I was so furious and shaking with fear, rage, and betrayal, I wanted to knock his drugged-up ass out. I stormed away and threatened to leave, and he pleaded with me to stay and to believe him that he didn't cheat on me. His furniture-less friend Joe even lied to my face for him. Scumbag. So stupid me gave him the benefit of the doubt and calmed down. The kicker of this entire sexual allegation was that it happened on August 31st, on his birthday , when I was home in the kitchen, making dinner for him, in lingerie , while he called and said he had to work an hour or two late that day. Really fucking nice, huh? So Monday, while he was at work, what did I do? Relapse. I couldn't bear to think about him possibly cheating on me just a week after I moved in with the bastard, so I drank. When he came home, we got into an argument about the allegations and me drinking, and he slapped me... So I hit him back! Harder. Then the MMA fighter in me came out and I put him in a guillotine chokehold. Yep, I choked his lying ass out. When he came to, he immediately grabbed the phone and called 911. Subsequently, arrest number one. # CHAPTER 32 HOME AWAY FROM HOME— THE BRANFORD POLICE DEPARTMENT AND NEW HAVEN COURTHOUSE I was arrested for "disorderly conduct." I had to spend the night on a cold metal cot in a dirty, dingy holding cell at the police station and go to court the next morning. In court, I was released on a "promise to appear" and a limited protective order was put in place. A limited PFA means I can return home, but can't argue, fight, harass, or stalk the "victim." I went home and drank. He came home. We argued. He called the cops. Here comes arrest number two; two arrests, two days in a row. Another cold, dirty, lonely night in the police station holding cell, and back to court the next morning. Another "promise to appear," and now the PFA was raised to a full order of protection, which means I can't go home. But where was I supposed to go? I lived there! I knew no one else in Connecticut besides his friends, and my family is in Jersey. So I went home. His parents were there and guess who else? The fucking bitch ex-girlfriend, sitting on my friggin' couch! Son of a bitch! D asked me to get in his car with him (he had stayed home from work) and we drove a couple blocks away and parked. He broke down and admitted to me that he did cheat on me with that pig. I lost it. I got out, went to the liquor store, and walked home. We argued again and WHAM! Wouldn't ya' know it, he called the cops! Arrest number three, three days in a row. Back to the hell, I mean, the holding cell and court. This time the SAME JUDGE looked at me and shook his head. This time my sister was in the courtroom, and pleaded for them to let me go home with her. They obliged, and she dropped me off at a diner so she could go to the apartment and get some of my things. She packed what she could, and we headed to Jersey. While she was there packing, there was a news van and camera crews all over the apartment complex, getting interviews with neighbors. By now, my three arrests had made national headlines, were airing all over the 6:00 o'clock and 11:00 o'clock news on every channel across the New England area, and it even made it on Hollywood tabloid shows _TMZ_ and _Dish Nation_. Great. Just what I fucking needed. They had already been in the courtroom with a camera for all three arraignments, and now they were stalking the neighborhood. I arrived at my mom's house, spent a few days there, and prepared myself for my upcoming court-ordered ten-day stint in rehab at the Carrier Clinic in New Jersey. By the time I went there, D and I were already speaking on the phone, and throughout my ten days there he pleaded and begged for forgiveness for what he had done—the cheating and the cop-calling. Because I'm a sucker and was in love with this asshole, I told him I would forgive him. My logic was; since I was caught cheating in a past relationship, and wasn't forgiven, I knew how much it hurt and how much he must have been hurting. I didn't want to make the man I loved go through that emotional pain like I did, so I forgave him, and we agreed that I would come home to him when I got out. He said he was so lonely, and couldn't stand spending one day without me, that he loved me more than anything... Blah, blah, blah. So I, the asshole, left that rehab, went back to my mother's, and waited for him to come pick me and my clothes up and head back "home" to Connecticut. On the ride, we had a long talk, and when we got home, we had an even longer talk—about how sorry we were, and how we were going to work it out, because we couldn't live without each other. Okay. Things were good for about a week, and we spent the weekend visiting his parents in Staten Island. On Sunday night, he told me that he got a text and phone call from work saying he had to go in for an emergency job at 10:30 p.m., that night. I was supposed to stay at his parents' house Sunday night and go into NYC on Monday for my outpatient treatment, but I told him I was going home with him that night and would commute to the city the next morning. I was suspicious, and he looked disgruntled. So we drove home, and I sent him off to work. He texted at around midnight and said he'd be home around 1:00 or 1:30 a. m., earlier than he thought. Great! I waited up, he came home, and we went to bed. The next morning, I wasn't feeling well, so I decided to skip my outpatient appointment and sleep in a little. I sent him off to work at 7:00 a.m., but couldn't fall back to sleep, so I figured I'd get online to see what was going on in the world. Big mistake. Huge! As I flipped open the laptop, his email popped on the screen, already logged in. About eight emails down, past the junk mail, was an email from you-know-who! Yep! Fucking whore! Son of a bitch! Naturally, I opened it. "It was great seeing you last night. I had fun. I can't believe I have a hickey—I feel like I'm 14! Ha-ha! I really missed you a lot, goodnight babe." That was all I fucking needed to read. I walked around the corner to you-know-where—the liquor store—with my cell phone in hand. I called him and in the most scared, angry, shaking voice screamed, "You did it to me again! Where did you go last night? Where were you last night?" "I had to work, like I told you," he said. "Why?" "Oh, yeah? Then what's this email from her? She has a hickey? She had fun last night? She missed you a lot? What the fuck?!" He tried to calm me down. "Listen to me, it's not what you think," he said, trying to sound earnest and genuine. "I did go to work, then she texted me to meet her at some bar she was at. I went, had a couple drinks. We talked, and I was only there for 15 minutes." "You're a fucking liar! I can't believe you did this to me again! I'm gonna fuck the next guy I meet so you can see how it feels!" I hung up on him, and guzzled from the liter-sized bottle of Svedka I had just purchased. My day went like this: drank, cried, ignored his calls and texts, drank, he came home, we argued, he called the cops. Arrest number four. Another violation of the full protective order. This is now my third violation. Great. Court the next morning was a little different. This time, they put a $25,000 surety bond on me, which meant I had to come up with ten percent and get a bondsman to get out. So I did. And the bondsman graciously drove me to the liquor store, then back home to our apartment, even though I wasn't supposed to be there. When I got there, I realized I didn't have my keys. Shit. Now what? My cell phone was in the apartment, and I needed to get in, grab some clothes, and leave. Go to a hotel room, somewhere. He was at work, so I wanted to get in and out fast. I didn't want to see his face again. So I did what all people naturally do when locked out of their homes. I scaled a wall and climbed up to the second floor balcony and went in through the sliding glass door. Yes, I'm a bit of a monkey. I went in, grabbed a bag, my phone, and started packing some clothes, so I could get the fuck out. Within five minutes, the cops were there! What the hell? He wasn't even home. We weren't even talking on the phone. Well, a neighbor saw me climb the balcony and knew I wasn't supposed to be there, so he took it upon himself to call the cops ! Fuck me! Arrest number five. This time, it was violation of the PFA and burglary (entering without a fucking key through the second floor balcony sliding glass door, even though it was my own apartment) and a $100,000 cash bond! That meant I needed $100,000 in cash to get out—no ten percent, no bondsman). I was fucked. Since $100,000 cash is near impossible for anyone to come up with, I was carted off to jail. State prison, to be exact. Stuck there until my next court date, which was in 20 days. I was fucking terrified. In Connecticut, a Violation of a Protective Order is a five-year felony, and I now had four counts of it and a crappy public defender to boot. Fuck my life. # CHAPTER 33 MIRACLES HAPPEN _"John the Baptist, who was in prison, heard about all the things the Messiah was doing. So he sent his disciples to ask Jesus, 'Are you the Messiah we've been expecting, or should we keep looking for someone else?'"_ —Matthew 11:23 I am now known as Inmate #393257. I'm sitting in jail with three "bunkies." Four miserable days go by—horrible food, a lumpy mat to sleep on, lots of Gin Rummy played—when they say I have a "professional visit." Having no idea what or who it is, I head down to the visitor's building. I walk into the room, and there's some guy I've never seen before sitting there in a sweater and jeans, with a legal pad in front of him. He introduces himself as Rob Serafinowicz—attorney at law. Hmmm. He goes on to explain that he's friends with the head legal counsel of the WWE, and saw my arrests on the news and in the newspapers. He wants to take on my case pro-bono. I accepted the offer, but I wanted to know why he was interested in representing me, for free no less. As it turns out, Rob is a huge wrestling fan and—wouldn't ya' know it—a Sunny fan from the 90's. Perfect, I thought. Now I have a Super Mark wanting to know all aspects of my life. But that wasn't the case. He was highly intelligent, respectful, well-spoken, and didn't even discuss wrestling. He was just a former fan who wanted to help me out, because I didn't deserve to be in jail. So on the eighth day in jail, a miracle happened. Rob got the judge to agree to send me to a long-term alcohol inpatient rehab instead of jail, and that when I was finished, I could withdraw my guilty plea to the PFA violations. Fabulous! Three more months in rehab, but that was way better than jail. After we left the courthouse together, and got through all the news cameras on the courthouse stairs just dying to get their story, we made our way to the nearest Burger King to get some sustenance in me. Yes, Burger King. Eight days in jail makes Burger King taste like filet mignon! We then arrived at his office, where a black limo, courtesy of the WWE was waiting to pick me up and drive me out to Reading, Pennsylvania, a four and a half hour journey to the Caron Treatment Center. On the car ride out, my phone buzzed with a text. It was D. "Call me, now. Please." I waited 20 minutes, and then called him. "What do you want?" He starts going on and on and crying, saying those were the worst eight days of his life, not hearing from me. He said he couldn't live without me. He said he downed a bottle of Xanax in one day trying to end his life from the thought of not having me. I had heard all of this before... But I fell for it again... hook, line, and mother-fucking sinker. I told him I still loved him after he professed his love for me, and I told him I'd call him later that night after I got settled in. Long story short, he sucked me back in, almost instantly. I was back in love, waiting impatiently and anxiously every day to call and hear his voice. I couldn't focus on treatment. I could only focus on repairing our relationship and our love. I swear, I must get more stupid and more gullible with age. We agreed that I would move back in with him once I completed treatment, which would be in three months. We were going to start over. During those three months, he swore he had changed. He promised that he had quit smoking (which I had always thought was a disgusting habit), drinking (for my sake), and doing drugs (thank God). He swore that he had been going to a therapist and to Al-Anon meetings. He swore that he was addressing his own issues as well. He promised me that he would NEVER call the police on me again, that we would talk and work anything out. He says that if we can get past this, we can get past anything, and there's nothing that could ever come between us. He told me he wanted to marry me and give me babies. He said he wanted to take care of me. Yep... hook, line, and sinker. Throughout my stay, we exchanged long, loving letters and cards, declaring our love for one another. He would include song lyrics from our favorite love songs, and I would just melt. He would write the most romantic things to me, and I would just fall deeper. Yes, he's a charmer. More like a wolf in sheep's clothing. So on January 4, 2013, after I spent Thanksgiving, my birthday, Christmas and New Year's Eve in rehab, I was discharged. WHOOOO HOOOO! FREE AT LAST!! I hopped on a train and headed straight to New Haven, Connecticut, where he would be waiting for me to pick me up. Now, Rob had advised me against moving back in with him so soon, before the PFA was lifted. But stubborn and in love, little ol' me didn't listen. After all, D had even managed to win the trust of my sister Lori, who had been my guardian angel through this entire stint in rehab. She was also convinced that he had changed, and everything was going to be fantastic. The two of them spoke on the phone every night and developed a close relationship. She was his shoulder to cry on, as well as mine. Lori is the best. She's very wise and compassionate, but will tell you like it is and not pull and punches. She's a tough one to get by. She doesn't take any shit. She assured me that he loved me; he had changed, and badly wanted me back home with him. I arrived at the train station after a grueling six hours on the train, to be welcomed into my love's arms, and I was home. Finally. # CHAPTER 34 SLEEPING WITH THE ENEMY _"He was oppressed and treated harshly, yet he never said a word. He was led like a lamb to the slaughter. And as a sheep is silent before the shearers, he did not open his mouth. Unjustly condemned, he was led away."_ —Isaiah 53:7—8 If anyone ever tells you to take the advice of your attorney, because he is probably right, then for God's sake, listen to them! January 4, I was home. Two days later, we had to attend D's grandmother's funeral. On the way home from Long Island, he pulled out a little black box. "I had planned the perfect way to do this, but I can't wait any longer," he said. "Will you marry me?" After a tear rolled down my cheek, I said, "Of course I will," and he placed the ring on my finger. I'd like to say it was the most beautiful and brilliant diamond ring I had ever seen, but sadly, it wasn't. I didn't care. I loved it, because I loved him. He didn't make a lot of money, so it didn't matter to me how big or expensive it was or wasn't. It was the symbol of his unconditional love for me. We were now engaged. Officially. It was the first time in my life someone officially proposed to me. Of course I was going to say yes. What else should I say? No? (Maybe that would have been a wiser choice). When we got home, we made love like two people planning to spend forever with each other. After all, that's what he would sign his letters with Love, Forever, D—— On January 9, we went to court and the PFA was modified from Full to Limited. D stood in front of the judge and begged her to lift it completely, stating that he wanted us to go on with our lives together and our future. The judge lifted it partially, promising to remove it completely at our next scheduled court date. We celebrated in his car after court. We were one step closer in the right direction, one step closer to being finished with all the court bullshit. The next couple of weeks were amazing. We painted the apartment, got all new furniture, and redecorated. We tried to erase all the bad memories that occurred there by making it fresh and new. We turned it into "our home," a place where we could start fresh and new. And I did see the changes in him. He wasn't smoking, drinking, or using drugs. He was home on time from work every day. He blocked the bitch's number from his cell phone and blocked her from his Facebook page. He was acting more like a husband than a boyfriend. We were trying tirelessly to get pregnant. I had no urge to drink. Not one teeny bit. None. Until... We were at the gym on a Wednesday night, January 23. We were almost done with our workout, when he left my side, walked halfway across the gym floor and greeted two women with hugs, kisses, and smiles. One looked to be in her 50's and the other one was a chubby girl in her late teens. I let him have a couple minutes of chat time, and then I walked over to be introduced. He waited. About a minute passed, as I still stood there like a dumbass with a half-assed smile on my face. Finally, he turned and gestured toward me. "Oh this is my girlfriend, Tammy." He was hesitant. What the fuck was going on? Who were these people? Why was he acting so strange around them? They finished their little pow-wow, and hugged and kissed again, and we parted ways. When we got back to our machine, I asked who they were. Naturally I was going to ask, right? After all, these two women were just all lovey-dovey with my fiancée for a few minutes. He was hesitant, again. Then with his head down and a sigh, said, "That was her mother and sister." What the flying mother fucking fuck! Are you kidding me right now? It was bad enough we saw her aunt and uncle at the gym on a nightly basis, but now he's all chummy with the whole friggin' family? Oh no, this was not happening. We left the gym immediately, with me in a fury. The whole way home I flipped out. I went off. Could we not get this home-wrecking bitch out of our lives? Every time I turned around, there was something else to remind us of her. I couldn't take it anymore. We went home, and continued to argue. How could he act the way he did with them? How could he completely disrespect me in front of them? How could he not have the balls to introduce me as his fucking fiancée to them? How could he? We went to bed, and Thursday I woke up just as angry. I sent him off to work and I did my best to put it out of my head. I did, for the most part, and got through my day. That evening we had an appointment at a new gym so we wouldn't bump into any more family members. Then I got the call. He had to "Work late." Remember what happened the last time he had to work late? Exactly. So I got a case of the "fuck its" and got a little vodka. Between last night and now this bullshit, I didn't care. I was pissed. I had a couple drinks, nothing crazy, and when he came home, we got into it again. This time he backhanded me and busted my top lip open. Then he threw me down on the bed, held me down by my throat, slapped me again, ripped my clothes off and forced himself on me. Was this rough make-up sex that he was accustomed to having? Or a sexual assault? There is such a fine line. When he was done, I was hurt. Battered. Bruised. Sore. I cried myself to sleep. I barely woke up the next day as he got ready for work. I didn't get out of bed to make his breakfast and lunch like I usually did. I lay there, sad. I slept until about noon and woke up in pain to a text from him saying, "Time to get up and start your day." Yeah, start my day with a swollen, blackened lip and a sore neck. Wonderful. So I did what every normal recovering alcoholic would do to relieve themselves from the pain. I drank. I self-medicated the emotional and physical pain that I was feeling. Again, I didn't over-do it. I self-medicated, although that's never a good excuse for a relapse. He came home from work around 6:00 p.m. He was late again, so what happened? We fought, again. This time, he tried to turn all the blame on me, saying that my drinking was the cause of our fight. But didn't he realize that it was his actions that caused my drinking? I never, ever had the urge to pick up a bottle for any other reason, except when she came back into our lives, somehow, or when he got violent. So we argued, argued and argued. We were now face to face in the kitchen when he hauled off and punched me in my left side, straight to my ribs. I dropped to the floor instantly with a pain so fierce, I couldn't breathe. I crawled over to the couch and sat down as he got in my face. "You're ugly," he said in a low, ugly tone, a tone dripping with sadism and hate. "I can do so much better than you." This was coming from the man who asked me to marry him just 20 short days ago. As I struggled to breathe and tears streamed down my face, he walked out of the apartment. A little while later, about 30 minutes or so, my phone rang. It was my neighbor. She told me there were cops outside. What the fuck did he do!? Well, what he did was go straight to the police station and say that I was in the apartment and I wasn't supposed to be there, per the protective order. Mother fucker. He did it again! I hid in the shower, but he had given the cops a key, so they let themselves in and found me. Arrest number six. I was in the apartment and wasn't supposed to be there? This came from the man who begged me to come back home and to forgive him. This from the man who rented a moving truck and drove to New Jersey to my mother's house to move all my things back to Connecticut. This from the man who put a ring on my finger and asked me to be his wife. This from the man who was trying his damnedest, six times a day, to start a family with me. This from the man who agreed that if we ever had a fight, we'd cool off separately and never involve the law again. This from the man whom I gave my total and complete trust to again when all signs told me I shouldn't. You know how that old saying goes: Fool me once, shame on you. Fool me twice, shame on me. Another three nights in a holding cell, $100,000 cash bond, and two broken ribs later, I was carted off to prison. Again. But not before I got X-rays to prove my injuries and gave a written statement of his abuse. Oh, by the way, did I mention that this all happened on January 25? Our eight-month anniversary? Oh yeah. Happy anniversary to me. So here I sit, Inmate #393257 of the Connecticut State Penal System. SHATTERED. # CHAPTER 35 SO MUCH FOR MY HAPPY ENDING So much for my happy ending. Six little words couldn't be truer right now. You know the expression "Be careful what you wish for?" Take heed in that, as I should have just eight short months earlier. I was wishing for the fairy tale, the happy ending, my Knight in Shining Armor. I wanted a husband, a family, a cute little house with a white picket fence and two dogs. Boy, did I choose the wrong guy for that, right? I didn't see it before, though. When I met him, I was blinded by an undying love. Or was it just lust and really good sex? At first I thought it was love, but now that fine line between love and lust was beginning to blur. If it was just lust, no wonder it went so far south that Satan had to designate a catcher. Lust is one of the seven deadly sins, after all. I must have taken one too many bites from the forbidden fruit for my own good. As I sat there in jail writing the previous chapters, I began to realize that there was never any stability to our relationship. My trust was blown out of the water by his cheating and it never came back (although I tried so hard to forgive and trust again). I overlooked so many of his faults because I was so desperate to be " in love." I had such a need to be loved by someone and live a "normal life" of marriage, babies, etc., that I jumped at the first thing that presented itself to me. Throughout the month of January, leading up to this last arrest, I did notice some things that were quite alarming. When I would talk about stepping away from the business completely to focus on going back to school, he would get really upset. When I said I would take some bookings for autograph signings but not to manage him on shows, he got highly offended. When I said we would not be attending the Hall of Fame or WrestleMania that spring, he was pissed off because he wanted the backstage access I could give him and his friends. When I made $3,000 cash fast to clear up his overdue and past due rent and bills, he loved me more. I learned, through a nightly ritual of sharing things about each other, that he was more promiscuous than I had ever imagined or feared; or even wanted to hear about. I can't even bring myself to share the details with you! I learned that he really had no intention of remaining smoke, alcohol, and drug-free for the sake of our relationship. I learned that he was completely content with living off his soon-to-be wife since he had zero ambition to better himself or support himself on his own. I learned that he was telling promoters that I would only work for them, if he got booked on the show as well. When I would slack in writing this book, he got furious that the "big payday" would be delayed even further, as he was counting on the profit from this book to pay for our wedding. When I sit back and take this all in, I say to myself, " What were you thinking, you crazy bitch?! Honestly, I do think that, even out loud sometimes! The forbidden fruit. Yep. It got a hold of me good. Was this God's way of teaching me something? Was it His way of teaching me about lust and greed? They say that everything happens for a reason, but I'm STILL trying to figure out what this reason is. Is it that God knew D wasn't the right one for me? Is it so I stop drinking once and for all? Is it a combination of all of it? I don't know. I just don't know. I'd like to now share a bit of the daily journal I kept while in jail at this time. FRIDAY, FEBRUARY 15, 2013, APPROX. 3:00 P.M. I'm still waiting for my lawyer, Rob, to show up to visit. He said he was coming last night, but I'm still waiting... waiting. 7:00 P.M. Oh well, Rob's a no-show. Something must have come up. He has become a good friend and confidante; he wouldn't just blow me off. WEDNESDAY, MARCH 13, 2013, 6:00 P.M. Well, I went to court yesterday. Nothing eventful, but I presented my new lawyer to the court. Rob was forced out of the case by the prosecution, so he found me someone to take over. I hope he's decent! All that's left in the case is the pre-sentence investigation and my sentencing. I want to be sentenced already to get it over with, but I'm also terrified to get sentenced. I almost feel better NOT knowing my fate. Not knowing how long I have to be here in jail. I have six weeks of lock-up already under my belt, so that will count towards whatever I get sentenced to. Because this charge is a five-year felony, I am realistically looking at a possible three to five years in jail. I'm also stressed out because D will not return calls to my mother and sister about them moving my things out of the apartment. I already have enough to worry about, and now I have that on my mind! Everything I own is there with him. I'm nervous about losing everything. After screwing up the last year of my life, he better do the right thing by me and get my stuff to my mother's house. THURSDAY, MARCH 14, 2013, 8:00 P.M. This jail thing is getting monotonous. I tried calling Rob to tell him the book is just about finished, but he's not picking up the phone... grrr. The food here is terrible, so you have to figure out meals to make with your commissary food and using the hot water pot as an oven. Tonight was chicken parm and pepperoni wraps—not too shabby for what I have to work with. You kind of turn into a modern day MacGyver in jail. You can make anything out of nothing. It kind of feels like you are in a college dorm the way rooms are set up. For the most part everyone gets along. The part that really sucks is having to poop right in front of your Bunkie (roommate). No privacy at all! I was in a group tonight, and the topic was "love." I'm the type of person that loves being in love, loves being loved, and loves to love someone. But after this last disaster at an attempt of being in love, I wonder if it's all worth the hassle. If being in love brings you heartache, headaches, and in my case, jail, is it really all worth it? I don't know anymore. I think I might just stay single for a while. SATURDAY, MARCH 16, 2013, 1:24 P.M. I was just taking a nap, when the corrections officer buzzed my room and told me I had a job here at the prison. The job is in the kitchen, not sure doing what yet, but I know I'll be making a whopping 75 cents per day! Whooo! I'm gonna be rich! Kitchen workers get 75 cents a day, laundry workers get $1.20, and seamstresses make 35 cents an hour. Yes, it's a sweatshop. Oh, did I forget to mention I have to wake up at 3:30 a.m.? Yep. A sweatshop. Rob should be coming to visit tomorrow. I have to give him the last two notebooks I wrote of this book so he can type them up for publishing. There are 460 pages so far to type up, so he definitely has some work cut out for him. I spoke to my mom last night. She's sending a moving company up to D's apartment on Saturday, the 23rd, to get all of my things. It's about time. He's been holding it all hostage for seven weeks now. He wasn't returning anyone's phone calls at all. He continues to prove to be a scumbag. All I know is it all better be there, not broken, either. If it is, I'll sue his ass in court... not that he has any money to sue for. As soon as all my things are at my mom's, I can finally wash my hands of him completely. It's about time. None of us will ever have to speak to him again. And mark my words—if he ever shows up at a wrestling event I'm working, I'll have his ass tossed out fast! SUNDAY, MARCH 17TH, 2013, 6:30 P.M. Well, today was my first day of work in the kitchen. I prepared trays for breakfast, then washed pans all day. It was the hardest $ .75 I've ever made. If jail is supposed to humble you, it's doing its job. SATURDAY, MARCH 23, 2013, 6:00 P.M. Well, we were bored today, so my Bunkie Sherri wanted to do something crazy, so we shaved half of her head! HA! TUESDAY, MARCH 26, 2013, 11:30 A.M. Well it's been an eventful couple of days. On Sunday, I got fired from my kitchen job. Yep, I lasted one whole week! They caught me taking cake out of the kitchen, which is a big no-no. I was bringing it back to make a birthday cake for a girl on my tier. So I got caught and fired. Oh well. I don't think I'll miss the hard labor for that whopping 75 cents a day. This morning I had a visit from probation. I had to tell her the whole story from start to finish about everything that has happened for the pre-sentence investigation. Basically she said she doesn't think I need jail time, and she is going to recommend just probation. Yay!! Things are finally starting to turn around. I have court next Tuesday, the 2nd, but it will just be continued. She said my sentencing will be in May, so I'll be here another month. C'est la vie. I'm also a bit agitated that I haven't been able to call Rob in over a week. Something screwy is going on with the phones, and I can't get through to him... grr. WEDNESDAY, MARCH 27, 2013 Ahhh! Jail can get worse!! I had to go in front of the disciplinary review board because I stole the cake from the kitchen. My punishment is Loss of Commissary for 30 days. Thirty days? That means no candy, no cookies, no brownies, no oatmeal cream pies, and no chips—nothing from commissary. How will I survive? I don't know, I guess it's a blessing. I wanted to drop a few pounds before I leave here anyway. I told my sister I had the meeting with the probation officer and that I'll probably get out in four or five weeks. Now it's time to plan my next step. I think I'll go to her house in Pennsylvania for a couple weeks and then move out to New Mexico with my brother. He has a big, beautiful home with a two-bedroom apartment above his garage. I'll go out there for about a year, get a job, and be normal for a change. After that, when this book comes out, I think I'll retire to San Diego, buy a nice condo on the beach and open a breakfast and lunch café. Sounds like heaven. # CHAPTER 36 THE BIG 'C' Today has not been a good day. I got some really bad news this morning, and I'm pretty upset about it. When I first got to prison, I had a gynecological exam and a Pap smear done, since I was almost due for my annual exam anyway. The Pap smear came back positive for abnormal cells—namely HPV. The Human Papillomavirus is a sexually transmitted disease carried and transmitted by men, but it afflicts women. There are no symptoms, but when left untreated, the abnormal HPV cells can turn into cervical cancer cells. After I tested positive for HPV, I had a biopsy done, something called a colposcopy, to further investigate how far advanced these abnormal cells were. There are three different strains of HPV: one that clears up on its own, a second that causes genital warts and a third that can progress to pre-cancerous cells. The pre-cancerous cells, if caught early enough, can be frozen and scraped off of the cervix, but if left untreated will eventually progress into cancer cells. Well, this morning, my colposcopy results came back positive for Cervical Squamous Cell Carcinoma. In layman's terms, I have cervical cancer. Yep, at 40 years old, I have cancer. I cried like a baby when I first found out, but now I'm just in shock and disbelief. How did I get cancer? Well, like I said, you get it from sexual contact with a man. My last Pap smear was one year ago, and it was negative for any abnormal cells. Since then, I have only had one sexual partner, so you can do the math. Fortunately, cervical cancer is treatable, but invasive and severe. I will be going to the University of Connecticut Medical Center to have surgery, a cone biopsy. They will be putting me under general anesthetic, and cutting a cone shaped chunk out of my cervix. Hopefully they get all the cancer cells out that way. If they don't get all the cells out—if the cells extend up into the uterus or if the cancer is too progressed—I will need a hysterectomy. Also, the cone biopsy is a very bloody procedure they say, so if I bleed too much or if the bleeding doesn't stop, they'll have to do a hysterectomy right then and there, without me even knowing. I never wanted to have a child until this past year, and now, after the cone biopsy, there will be only a one percent chance that I can ever get pregnant. And if they do a hysterectomy, well then, I'll never have a child of my own. So, needless to say, I'm pretty fucking upset. This is a life-changing event for me, no matter what. I hope the treatment is the lesser of the two, and that it will be all I need, but I'm scared shitless. I asked the doctor what would happen if I decided not to get it treated. "You'll endure a very slow, very painful death," she said. She said the pain from cervical cancer death is right up there with pancreatic cancer. It will kill you, and it will hurt tremendously. When will this madness end? Will I ever just be able to live a normal and happy life? What the hell have I done to deserve all this strife and heartache? I have been a good and generous person all my life. I've donated thousands of dollars to animal rescue groups. I've been polite and kind to everyone who crosses my path. I've always taken care of others needs before my own. And I get cursed with Cancer. Me. Cancer. Let this be a lesson to myself and all of you women reading this: always use a condom. No matter what, or who. It will save your cervix, and your life. WEDNESDAY, APRIL 3, 2013, 10:30 A.M. Court was yesterday. I met my new lawyer, Rose. Real nice lady. She met with the prosecutor. He's pushing for three years! Is he insane? Then Rose met with the judge. The judge was sympathetic towards me, thank God, and Rose said she is "on my side." Whew! I'm still hoping and praying that I only get probation, but there's still that one percent chance I may have to sit here in jail a little longer. MONDAY, APRIL 8, 2013, 4 P.M. I've been thinking about D a lot today. Probably because we were supposed to attend a wedding next weekend and WrestleMania was this past weekend. I wonder who he will be taking to the wedding? Not that I'm jealous in any way, I just wonder. I wonder what it would be like to go with him? Then I can't stop thinking three things: 1) He's a liar. 2) He's a cheater 3) He's a broke-ass loser OK. I'm over it. FRIDAY, APRIL 12, 8:00 P.M. Just got back from the hospital and my first real appointment about my cancer. It finally hit home when they wheeled me into the Cancer Unit at UCONN. The cancer unit! Oh my God. I never thought I'd ever be a patient there. It really is a scary thing, you know? Ok, maybe you don't know. In my appointment with my amazing doctor, we discussed my options. Basically, the cone biopsy isn't the best way to go. Too many risks and complications can arise. She wants to do the hysterectomy the first time in. Oh God, a hysterectomy. She said it's the best way to make sure all the cancer is out of me, and if we get it all now, I shouldn't need any radiation or chemotherapy. I can't believe this. Any hope I ever had of having a family is slowly slipping through my fingertips. I'm even more in shock now than ever. After my appointment, I went back into the waiting room and realized I have my period right now. This is going to be the last period I'm ever going to have. Then I looked up at the TV and an actor was on Ellen DeGeneres talking about his new baby girl... named Olivia. Well, wasn't that just a shot through the heart, because that's what I always wanted to name my daughter, if I ever had one. Man, all these thoughts and feelings running through me are out of control. I haven't really been that distraught over the surgery until now. It's really starting to hit home. Hard. MONDAY, APRIL 29, 2013, 7:00 P.M. I just came back from the hospital. They did all my pre-surgery stuff—physical, EKG, blood work. All my blood work was perfect! I'm in complete perfect health! My liver enzymes couldn't be better; my white and red cell counts are right on target. I'm as healthy as a horse internally. So how the hell did I develop cancer? Some things are just out of your control. It doesn't matter how healthy you eat or how much you exercise. Medical problems can hit anyone at any time. Cancer knows no boundaries. FAST FORWARD TO DECEMBER 2015........... I finally sat back down to write, because May through December of this year has been a crazy roller coaster. My hysterectomy is complete... after two surgeries. Yes, two! A DaVinci Robot did my first surgery and, wouldn't you know it... It screwed up! I had cervical cancer , and the robot and doctor left part of my cervix in! During this time, I was released from prison after the judge dropped the charges against me, and I went to a new oncologist. He performed a second surgery, removing the remainder of my cervix, an inch of my vagina, 26 pelvic lymph nodes, and all the ligaments that used to hold my uterus to my pelvic bones. I am home, recovering from this second, and much more painful, surgery and I still can't believe this has all happened to me in the course of one year. At least the worst is over...It's over. My tissues came back from Pathology, and I am officially cancer-free. I don't need any radiation or chemotherapy, which the doctors had originally assumed that I would need. I'm out of the water...At least for now. And I thank God every day for that. # CHAPTER 37 A NEW LEASE ON LIFE It is 2015. My cancer is gone. Prison is behind me. What now? What have I done since 2013? Well, being off the 'wrestling' scene through the duration of my cancer and surgeries did set me back a bit. I was living with my sister through recovery, not working, and depleting what savings I had throughout the year. I started taking phone calls from fans through a service called "Verified Calls" during my recovery, as a way to have some income while I was pretty much house-bound. Fans would purchase a block of time to talk to me on the phone, and at the end of the month, I would get a check from the company. This was doing well for a while, although I was taking in well under $1,000 per month, but at least it was giving me a little spending money so I wouldn't have to rely solely on my sister. One night, I had a brainstorm. If people were paying their hard-earned money to talk to me on the phone, what would they pay to talk to me and see me??? So I got the idea to start Skype video chats. I set up my Skype account, and advertised on social media that I was taking video calls... Strictly question and answer sessions. It started as X amount of dollars for X amount of minutes, and wasn't a lot... At first. I was getting Q&A calls for about six months, completely innocent chats. Until one night, when out of nowhere, a male fan decided to whip it out. Yes, he took his male reproductive organ out of his pants. "OMG,!!" I thought, "What in the world is going on??" Yep. He pretty much just wanted to look at me and masturbate. Right there on camera! He just whipped it out and started whacking off... "OMG." I couldn't believe what I was seeing. Then a light bulb lit up over my shocked and confused little head... If these guys want to look at me and relieve themselves, I can wear a little less and charge a little more. Hell, I can wear a lot less and charge a lot more!!! So what began as a simple, fully-clothed, Q&A session with a fan, turned into an all-out sexual, skin revealing, wank-fest for a lot more money... Ha-ha, some guys will do anything! I do joke about it, but honestly, I appreciate every single one of my customers. I see nothing wrong with what I, or they, do I've always been a very sexual person, a bit of an exhibitionist and voyeur, and this was just another way for me to explore my sexuality. After two and a half years of Skyping and building up my business, it has become as large as it is today, and I have about 50 returning customers from all over the world: the US, Canada, England, Ireland, Scotland, Germany, Portugal, India, Japan, Australia, and even Iraq. I won't discuss how much money I take in by Skyping, but I will say that I make more than double weekly what the WWE used to pay me to be out on the road full time. Plus , I had road expenses then! Now, I work out of my home... My bedroom is my office and my bed is my desk. What could be better! I am my own boss, make my own hours, enjoy what I do, and have the best and easiest job in the world! What could possibly top this!? Well, there is one thing that could top it... And many would say it's the natural progression of the business... Namely entertainment with a sexual overtone... In December 2014, I received a series of emails from a specific company wanting to do business with me. I simply chalked it up to a fan messing around with me through emails, so I ignored them. But after about eight unanswered emails, I decided to investigate further. These emails were from a woman named Jackie from Vivid Entertainment. Yes, Vivid. The porn company. No, wait, excuse me, the !!biggest porn company in the world! These emails repeatedly stated that Vivid was interested in doing a movie with me. Yeah, Okay. A movie. Vivid Video wants me to do a movie. Whatever. I mean, I even turned down _Playboy_ in 1996. There is no way I can film a porno, even if these were legitimate emails. So one day, I humored them and wrote them back. The reply I received was, "Yes, this is Vivid Video and we would like to feature you in a celebrity sex tape." What? Wait... What!!!!? Oh my God. Is this a joke? Me? In a celebrity sex tape? My first thought was "no." "Hell no!" There was no way I could do this. For a few reasons; 1) I had never had sex in front of anyone before... Ever. 2) I had never allowed anyone to film me having sex, for obvious reasons. As soon as I would have dumped the guy, the tape would surely be released all over the Internet. For about three weeks I was going back and forth... thinking, "Yeah, maybe I could do this," and "No, there's no Goddamn way..." Finally, I got on the phone with the big boss man, Steven Hirsch himself, the owner of Vivid Entertainment. He explained to me how they would film it, how it would be marketed, and that I could choose with whom I wanted to film. After all of these conversations with Steven, I was still on the fence about it, definitely leaning towards the "no" side of the fence. Then during one phone call, Steven said, "Well, let me send you a sample contract. Read it and see what we have to offer you, then get back to me." They forwarded me the contract. I was nervous just to open the email and read it!! But I did. I read it. Then I read it again. My next thought and question was, 'Okay, where do I sign?" This contract, and the offer that Vivid made me, was unbelievable. Almost too good to be true. Was this really happening to me? For me? Was I getting the chance of a lifetime, after 25 years of hard work and busting my ass in the wrestling business? After 25 years of ups and downs, making money and losing it, being wealthy and being broke, was I finally getting the chance to turn my financial well being around and live a secure and prosperous life? Once again, I'm not going into numbers here... But with the offer they made me, and the right investments, I can totally set myself up to be comfortable... And enjoy life for a change. So I signed the contract. I was now officially under a legally binding contract to make celebrity porn for Vivid Entertainment. Oh my God.... Shit was about to change!! Long story short, and I won't go into all the gory details, but I filmed the movie. My two co-stars were professionals, Derrick Pierce and Will Powers. And let me tell you. I give these guys, and all performers and crew in the adult film business, all the credit in the world. This shit's not easy!! It took 13 hours to get 120 minutes of usable footage on film!! Thirteen hours!! It was the longest day of my life! And if you think I had it rough, getting banged for 13 hours, just imagine the guys!! I filmed six hours with each one, and I have to hand it to them... they each kept it up for SIX straight hours! God only knows how... Well, God and the companies that make Cialis and Viagra, I assume... Ha! And the craziest part of working with all of these new people... I found that the actors and office personnel and crewmembers are some of the most professional and kind people I've ever worked with! The porn industry has this stigma that they are a seedy, shady business... And granted, maybe many of them are. But Vivid Entertainment blew me away with their professionalism and courtesy. They put the WWE and wrestling business to shame when it comes to how they treat their performers. There really is no comparison. Totally blew me away. So, it's in the books. It's official. Sunny made a porno. The Original Diva of the WWE and WWE Hall of Famer has made an adult film. "OH MY GOD." I have officially done the craziest thing I could possibly ever do. Craziest, and most brilliant. So now, the wait has begun for the release of the film...the long, much-anticipated wait. Cover art work done...Check. Trailer done... Check. PR statements done... Check. What's next for Tam? Well, the movie will come out in a few short weeks from now, and I have plans to start up a new Skype website, managing various male and female models underneath me. I have big ideas; I just need to work hard to bring them all to fruition. Of course I expect all the negative criticism in the world from media, fans, friends and family everywhere. I know it's coming. It's expected. It's welcomed. I have never shied away from the press and media, and I'm not about to start. After almost 26 years in the entertainment business, I have traded in my skin for a coating of Kevlar... Nothing can penetrate this outer shell and get to me. Through all my struggles and strife in life, I have managed to keep my head above water, and when all else fails, I resort back to what always works for me.... Being true to myself and working hard to be the best person I can be. I know that with my determination and perseverance, I will always survive. Survival of the fittest. That's how I live my life. And always will. So how and why did this all happen to me? Only God knows why... But I'll never stop trying to figure it all out. # EPILOGUE Six years. That is how long it took for me to write this book. I had the idea six years ago, but didn't know the message I wanted to convey until I ended up in prison. Everything I've gone through has made me appreciate life so much more—my successful career, my battle with alcoholism, my "glorious" stint in jail and my bout with cancer. What I wanted to express to everyone is that I am human. I am just like every one of you. I'm not any more special than the person next to me just because I have been famous. Everyone makes mistakes. Nobody is perfect. But when you've been blessed with success and good things all your life, and then you do one thing wrong, it is viewed as an earth-shattering tragedy—a fall from grace. I have been abused, ridiculed, harassed, imprisoned and blasted in the media for making the same mistakes that everyone in this world makes. Nobody's perfect. My hope is that you, in reading this book, can find solace and peace within yourselves, as I have done. Writing this book has allowed me to analyze my life, and has given me a great sense of closure. Sometimes a little closure is what is needed in your life to feel fulfilled. Through yoga, meditation and religion, I have found peace within myself and finally, at 43 years old, I am comfortable in my own skin. I know now that there is no challenge too great for me to conquer, no mountain too high. Struggling is a part of life. How you handle it is what makes the difference. My stint in jail taught me a lot. It is absolutely mind-blowing how many good women are in prison for multi-year sentences because of a man. My second roommate Sherri, for example, is serving a 25-year sentence for first degree murder. The thing is, she didn't kill anyone. Her boyfriend did, and because he scared the bejesus out of her, she got the same charge because she didn't give him up to the police. It's sad. Too many women in prison are victims. They are victims of abuse, rape and manipulation, and they are suffering consequences that they shouldn't have to. experiencing. What the world needs are more activists to get the justice system to see its faults and to not punish innocent women for the crimes their men commit. These women are terrified to stand up for themselves and threatened by their men if they do. If anything, these women need to be placed into programs to build their self-esteem and self-worth. They need help to build their inner strength to deal with the obstacles they face in their lives. I know this... I am one of those women. What the world has in store for me from this point forward is yet to be seen. I'm sure it all won't be a walk through the tulips or a bed of roses, but I can only hope for the best. That's all I can do. As long as I remain determined and persevere, nothing can stop me. My faith and passion will steer me in the right directions, and with a little help from my Kevlar skin, I'm shooting for the stars.... And besides, we've all known since 1996, that 'what Sunny wants, Sunny gets!!' # About the Author The legendary Sunny is known as "the original WWE Diva" and she is one of the most popular female wrestling personalities of all time. Her achievements include being a two time Slammy Award Winner, a member of the WWE Hall of Fame and New England Pro Wrestling Hall of Fame and a Pro Wrestling Illustrated Manager of the Year. Other Riverdale Avenue Books You Might Like # Acknowledgments This book would not be possible without the help, support and encouragement of the following people: All the wonderful men and women I met, learned from and befriended in my two decades in wrestling; My wonderful family who have stood by me through thick and thin; The incredible team at Vivid Entertainment, especially Jackie, Marci and Steven; My first editor, Dan Murphy, who really believed in this book, and my team of editors at Riverdale Avenue Books. # Other Books From Riverdale Avenue Books Unphiltered: Life On and Off the Rock'n'Roll Tour Bus By Phil Varone The Making of Going for the Gold By Taylor Lianne Chandler and Lissa Trevor Lindsay Lohan: Fully Loaded, From Disney to Disaster By Marc Shapiro Flashes: Adventures in Dating Through Menopause By Michelle Churchill Confessions of a Librarian – A Memoir of Loves By Barbara Foster	{ "redpajama_set_name": "RedPajamaBook" }	4,031
Sno Question Price; 11095: Gammy is considering building a facility to manufacture cupcakes to distribute nationally. Your assignment in: $25: 11094: Bruno Company. fears sharing the road with big rigs, and even more so after one plowed into her daughter's car last year in Nebraska. to.	{ "redpajama_set_name": "RedPajamaC4" }	9,030
\section{Introduction} Given a positive function $f$ on $\mathbb{R}^n$, we define the weighted perimeter and volume of a set $A \subset \mathbb{R}^n$ of locally finite perimeter as $${\rm Per}(A) = \int_{\partial A} f d \mathcal{H}^{n-1} \qquad {\rm{and}} \qquad {\rm Vol} (A) = \int_{A} f d \mathcal{H}^n.$$ Such a positive function $f$ is called a \emph{density} on $\mathbb{R}^n$. Here, $\mathcal{H}^m$ indicates the $m$-dimensional Hausdorff measure, and $\partial A$ refers to the essential boundary of $A$. A good reference for sets of locally finite perimeter and their properties is the book \cite{maggi_finite} by F. Maggi. We will use these conventions for the rest of this article, and we also note that all subsets of $\mathbb{R}^n$ involved in this article are of locally finite perimeter. One natural question immediately arises: for which volumes do isoperimetric regions exists, and can we describe the ones that do? Specifically, if we fix a positive weighted volume $M > 0$, does there exist a set $A \subset \mathbb{R}^n$ such that $ {\rm Vol} (A) = M$ and $${\rm Per}(A) = \inf_{\substack{ Q \subset \mathbb{R}^n \\ {\rm Vol} (Q) = M }} {\rm Per}(Q).$$ In \cite{morg_iso_1}, Rosales, Ca{\~{n}}ete, Bayle and Morgan consider this problem. One family of densities that they examine is radial log-convex densities, that is, densities of the form $$ f(x) = e^{g(\|x\|)} $$ where $g$ is a smooth, convex, and even function on $\mathbb{R}$. In particular, for such densities, they show that balls around the origin are stationary and stable (Corollary 3.11). By \emph{stable}, we mean that ${\rm Per}''(0) \geq 0$ under smooth, volume-conserving variations. In fact, they show that for any radial, smooth density $f = e^g$, balls around the origin are stable if and only if $g$ is convex (Theorem 3.10). This motivates Conjecture \ref{conj:main} ($3.12$ in their article), first stated by Kenneth Brakke: \begin{conj}[Log-Convex Density Conjecture] \label{conj:main} In $\mathbb{R}^n$ with a smooth, radial, log-convex density, balls around the origin provide isoperimetric regions of any given volume. \end{conj} This article seeks to completely solve Conjecture \ref{conj:main} by proving the following theorem. \begin{thm}[Centred Balls are Isoperimetric] \label{thm:main} Given a density $f(x) = e^{g(\|x\|)}$ on $\mathbb{R}^n$ with $g$ smooth, convex and even, balls around the origin are isoperimetric regions with respect to weighted perimeter and volume. \end{thm} We also prove an additional theorem which morally says that these are the only isoperimetric regions. If we have $f$ as in Theorem \ref{thm:main}, then let $$ \mathcal{R}(f) = \sup \{ \|x\| : f(x) = f(0) \}.$$ Since $f$ is convex and radially symmetric, $f = f(0)$ on all of $B_{\mathcal{R}(f)}$. The purpose of defining this centered ball is to handle the case of when $f$ is not strictly convex and is constant on some neighborhood of $0$. Given this notation, we have that the following uniqueness theorem is true. \begin{thm}[Uniqueness of Isoperimetric Regions] \label{thm:uniqueness} Up to sets of measure $0$, the only isoperimetric regions are balls centered at the origin, and balls that lie entirely in $$B_{\mathcal{R}(f)} = \{ x : \|x\| \leq \mathcal{R}(f) \}.$$ \end{thm} To prove these statements, we use the observation in \cite{morg_iso_2} that symmetrization of sets via spherical caps does not increase weighted perimeter and does not change weighted volume (see the definitions in the next section). This allows us to reduce our analysis to the case of such sets. Furthermore, due to the analysis in \cite{morg_reg_rie}, we may assume that the boundary of such a set $A$ has a high level of regularity. Since these sets are volumes of revolution, we can then use the first variation formula derived in \cite{morg_iso_1} to produce an ODE that is satisfied by each curve which, when revolved, produces a component of $\partial A$. The majority of the article is devoted to analyzing this ODE to prove Theorems \ref{thm:main} and \ref{thm:uniqueness}. We also note that the methods here work for all log-convex densities $f(x) = e^{g(\| x \|)}$ with $g$ in the class $C^3$. We also note that we do \emph{not} require $g$ to be strictly convex. A similar approach has also solved another isoperimetric problem involving $\mathbb{R}^n$ with density. Specifically, the author along with W. Boyer, W. Brown, A. Loving and S. Tammen proved that isoperimetric sets in $\mathbb{R}^n$ with density $f(x) = \|x\|^p$ are balls whose boundaries pass through the origin. Here, $p$ can be any positive real number. This result will appear in an upcoming article. This approach of looking at isoperimetric regions that are spherically symmetric and the associated ODE was used by Kolesnikov and Zhdanov in \cite{kolesnikov} to produce a partial solution to Conjecture \ref{conj:main}. By using these methods in combination with others, they proved that, if $g$ is strictly convex, then balls of large enough volume around the origin are isoperimetric regions. There have been a number of other partial results in the direction of this conjecture. For an overview of these, see \cite{fig}. \bigskip \noindent {\bf Acknowledgments.} This work was partially supported by an NSERC Canadian Graham Bell Graduate Scholarship, and by an Ontario Graduate Scholarship. The author would like to thank Almut Burchard, Yevgeny Liokumovich, Alexander Nabutovsky, Sarah Tammen, and Regina Rotman for insightful conversations related to this problem, and for helpful comments in regard to the manuscript. He would also like to thank Frank Morgan for communicating this problem to him, and for many useful comments concerning the initial version of this article. Lastly, he would like to thank Frank Morgan, Aldo Pratelli, and Francesco Maggi for observing that the original proof of the Second Tangent Lemma could be simplified by using the fact that the boundary of an isoperimetric minimizer is regular at a point if it locally lies in a half-space. \section{Structure of Proof} In this section, we shall describe the main ingredients of the proofs of Theorems \ref{thm:main} and \ref{thm:uniqueness}. To prove Theorems \ref{thm:main} and \ref{thm:uniqueness}, we first note that, without loss of generality, we may assume that the density function is not constant. This is because, for a constant density $f = e^c$ on $\mathbb{R}^n$, we have that a set $A \subset \mathbb{R}^n$ of weighted measure $M > 0$ is isoperimetric if and only if $A$ is isoperimetric in $\mathbb{R}^n$ with density $1$ among all sets of volume $\frac{M}{{e^c}}$. This is a classically solved problem - we know that, up to a set of measure $0$, a set is isoperimetric if and only if it is a ball. This proves Theorems \ref{thm:main} and \ref{thm:uniqueness} if $f$ is constant. For the rest of the article, let us assume that the density $f$ is not constant everywhere. We see that, since $f$ is log-convex and non-constant, $\lim_{x \rightarrow \infty} f(x) = \infty$. We can thus use Theorems 3.3 and 5.9 from \cite{morg_iso_2} to show that there exist isoperimetric regions for each weighted volume $M$, and that the boundary of each such region is bounded. We now summarize known properties of each isoperimetric set $A$. From \cite{morg_reg_rie}, we have that $\partial A$ is a smooth $n-1$ dimensional embedded manifold, except on a set of Hausdorff dimension at most $n-8$. We will call a point $x \in \partial A$ \emph{regular} if $\partial A \cap U$ is an embedded $n-1$ dimensional manifold, where $U$ is an open subset of $\mathbb{R}^n$ that contains $x$. By the above comments, the set of points that are not regular has Hausdorff dimension at most $n-8$. We also have, by Theorem 6.5 in \cite{morg_iso_2}, that $\partial A$ is mean curvature convex at all regular points, that is, the mean curvature is positive at each regular point on $\partial A$. Lastly, for every $x \in \partial A$, if there is a ball $B$ centered at $x$ such that $B \cap \partial A$ is located in a half-space with respect to an $n-1$ dimensional hyperplane through $x$, then $\partial A$ is regular at $x$. This is due to the fact that the oriented tangent cone at $x$ is in a half-space and $A$ is an isoperimetric minimizer, which in turn imply that the oriented tangent cone at $x$ is a hyperplane. As a result, since the density $f$ is positive everywhere, $\partial A$ is regular at $x$ (see Proposition 3.5 and Remark 3.10 in \cite{morg_reg_rie}). A corollary of this fact is that $\partial A$ is regular at each point $x$ with $$\|x\| = \sup_{y \in \partial A } \|y\|.$$ Next, we analyze the first variation formula at each regular point in the same way as in \cite{morg_iso_2}. We define a generalized mean curvature $H_f(x)$ at each regular point $x \in \partial A$ by $$ H_f(x) = H_0(x) + \frac{\partial h}{\partial \nu}(x)$$ where $H_0$ is the standard inward unaveraged mean curvature, and $\nu$ is the unit outward normal at $x$. Here, the function $h$ is defined by $f(x) = e^{h(x)}$. If $x \neq 0$, then this can be written as $$H_f(x) = H_0(x) + g'(\| x \|) \frac{x}{\| x \|} \cdot \nu(x),$$ where $g$ is as above, that is, $f(x) = e^{g(\|x\|)}$. Henceforth, we shall define $H_1(x) = \frac{\partial g}{\partial \nu}$, so that $H_f = H_0 + H_1$. Computing the first variation formula at each regular point $x$ and combining this with the fact that $A$ is an isoperimetric region, we have that there is some $c \in \mathbb{R}$ such that $H_f(x) = c$ at each regular point $x \in \partial A$. We summarize all of these results in the following theorem: \begin{thm}[Existence and Regularity of Minimizers] \label{thm:regularity} For each weighted volume $M$, there exists an isoperimetric region $A$ of weighted volume $M$. For each such minimizer $A$, we have the following properties: \begin{enumerate} \item $\partial A$ is bounded and is a smooth $n-1$ dimensional embedded manifold except on a set of Hausdorff dimension at most $n-8$. Additionally, $\partial A$ is regular at every point at which $\partial A$ locally lies in a half-space, which includes all points of maximal magnitude. \item $\partial A$ is mean curvature convex at all regular points. \item For some constant $c \in \mathbb{R}$, $H_f = c$ at all regular points of $\partial A$. \end{enumerate} \end{thm} We will first restrict our analysis to a certain type of isoperimetric region. Let $S_r$ be the $n-1$ dimensional centered sphere of radius $r \geq 0$. We say that a minimizer $A$ of weighted volume $M$ is \emph{spherically symmetric} if, for any $r \geq 0$, $S_r \cap A$ is equal to a closed spherical cap whose center lies on the non-negative $e_1$ axis. Additionally, if $S_r \cap A$ has $n-1$ dimensional Hausdorff measure equal to $0$, then $S_r \cap A$ is empty. Spherically symmetric isoperimetric regions have all of the properties described in Theorem \ref{thm:regularity}. In particular, all irregular points on $\partial A$ lie on the $e_1$ axis (see below), and cannot attain the maximum magnitude of $\partial A$. We now work on proving the following theorem, which will aid us in completing the proof. \begin{prop} \label{prop:centered_ball} If $f$ is not constant and $A$ is a spherically symmetric isoperimetric region about the $e_1$ axis with $$ {\rm Vol} (A) = M$$ and $$\mathcal{H}^n(A \cap B^c_{\mathcal{R}(f)}) > 0,$$ then $\partial A = \partial B_M$, where $B_M$ is the centered ball of weighted volume $M$. \end{prop} This characteristic will be called the \emph {distributed volume condition}. We will use the properties of isoperimetric regions described in Theorem \ref{thm:regularity} to prove this theorem. We deal first with the case of $n = 1$, which is very straightforward. This is because in this dimension $H_f(x) = \frac{\partial g} {\partial \nu}(x)$ at every regular point of $\partial A$. Since $A$ must clearly consist of one interval up to a set of measure $0$, $\partial A$ consists of the endpoints of this interval. The fact that $H_f = c$ at each of these endpoints immediately implies that the interval is centered at the origin, since at least one of the endpoints lies in a region where $g'$ is not 0. We are left with the case of $n \geq 2$. To prove Proposition \ref{prop:centered_ball}, we fix $n \geq 2$, and choose a spherically symmetric minimizer $A$ of weighted volume $M > 0$. Since it is spherically symmetric, there is a closed spherically symmetric set $C \subset \mathbb{R}^2$ such that, if $\partial C$ is rotated about the $e_1$ axis, we obtain $\partial A$. We observe that $\partial C$ is regular at all points that attain the maximum magnitude, and at all points that do not lie on the $e_1$ axis. Indeed, if there is a point $x \in \partial C$ which is not regular and which does not lie on the $e_1$ axis, then $\partial A$ contains a set of points of Hausdorff dimension $n - 2$ which are not regular. Since such a set must have Hausdorff dimension of at most $n - 7$, this is impossible. Furthermore, the perimeter of $C$ is finite. All of these properties are directly inherited from $A$. We would like to identify a certain continuous curve in $\partial C$. To identify this curve, we begin by defining $x^$ to be the unique point on the positive $e_1$ axis with $$\|x^\| = \sup_{y \in \partial C} \|y\|.$$ Since $A$ has positive measure and is spherically symmetric about the non-negative $e_1$ axis, such a point exists and is unique. Furthermore, $\partial C$ is locally a $1$-dimensional embedded smooth manifold around $x^$. We can use the spherically symmetric nature of $C$ show that the tangent space of this manifold at $x^$ is the collection of all multiples of $e_2$ attached to $x^$. As such, this manifold locally only intersects the $e_1$ axis at $x^$. Since $\partial C$ is a smooth embedded manifold at all points that do not lie on the $e_1$ axis, and since it has finite length, we can follow the curve leaving $x^$ in both directions until it intersects the $e_1$ axis at some other point. This produces a continuous curve $$ \gamma: [-\beta, \beta] \rightarrow \mathbb{R}^2 $$ with $\beta > 0$. $\gamma$ has the following properties, where $\gamma = (\gamma_1, \gamma_2)$: \begin{enumerate} \item $\gamma$ lies on $\partial C$. \item $\gamma(0) = x^$. \item $\gamma(x) \neq \gamma(y)$ unless $x = y$ or $x, y \in \{ \beta, -\beta \}$. In order words, $\gamma$ forms a simple closed curve. \item $\gamma_2 > 0$ on $(0, \beta)$, $\gamma_2 < 0$ on $(-\beta, 0)$, and $\gamma_2 = 0$ at $0$, $-\beta$ and $\beta$. \item $\gamma$ is smooth on $(-\beta, \beta)$. \item $\|\gamma'\| = 1$ on $(-\beta, \beta)$. \item $\gamma$ is a counterclockwise parametrization. In particular, since $C$ is spherically symmetric, $$ \| \gamma(x) \| \leq \| \gamma(y) \| $$ for $x \geq y \geq 0$, and $$\|\gamma(0)\| = \|x^\| > \mathcal{R}(f).$$ \item $\gamma(x) = \gamma(-x)$ for $x \in [0, \beta]$. \end{enumerate} This is shown in Figure \ref{fig:gamma}. \begin{figure}[ht] \caption{$C$, $\partial C$, $\gamma$, and $\mathcal{K}$.} \centering \includegraphics[width=1.00\textwidth]{gamma.pdf} \label{fig:gamma} \end{figure} Let $\mathcal{K} \subset \mathbb{R}^2$ be the closed, bounded region enclosed by $\gamma$. Since $\gamma$ is a simple closed curve, this is well defined. Due to the fact that $f$ is log-convex, $f$ is nondecreasing as a function of radius. Thus, the isoperimetric profile of $\mathbb{R}^n$ with density $f$ is nondecreasing; see Theorem 4.3 in \cite{morg_iso_2}. In other words, if $\mathcal{J}(V)$ is the minimal perimeter required to enclose volume $V$, then $\mathcal{J}$ is nondecreasing. This implies that $\mathcal{K} \subset C$, as if it does not, then consider the set $Q \subset \mathbb{R}^n$ defined as the union of $A$ and the result of $\mathcal{K}$ rotated about the $e_1$ axis. This set will have less perimeter than $A$, but will have larger volume. Thus, if $V$ is the volume of $A$ and $V'$ is the volume of $Q$, then $\mathcal{J}(V') < \mathcal{J}(V) = {\rm Per}(A)$. This, however, is a contradiction, since $V' > V$. The fact that $\mathcal{K} \subset C$ will be useful later in the argument. Due to the fact that $C$ is spherically symmetric, $\mathcal{K}$ is spherically symmetric as well. When we describe inward and outward normal vectors on $\gamma$, we will be doing so with respect to $\mathcal{K}$. We define some notation concerning $\gamma$ on $(-\beta, \beta)$. \begin{enumerate} \item $H_0(x)$ is the inward unaveraged mean curvature of $\partial A$ at any point that corresponds to $\gamma(x)$, and $H_f(x)$ is the generalized mean curvature of $\partial A$ at any point that corresponds to $\gamma(x)$. Note that all points corresponding to $x$ will have the same mean curvature and generalized mean curvature since $A$ is spherically symmetric. \item $\kappa(x)$ is the inward curvature of $\gamma$ at $\gamma(x)$. \item $n(x)$ is the unit outward normal vector to $\gamma$ at $\gamma(x)$. \item $g'(x)$ denotes $ g'( \| \gamma(x) \| )$. \item If $\gamma(x) \neq (0,0)$, then $N(x) = \frac{\gamma(x)}{\| \gamma(x) \|}$. This in the unit outward normal at $\gamma(x)$ to the centered circle which goes through $\gamma(x)$. \end{enumerate} Note that all of these quantities are defined on $(-\beta, \beta)$. We will require one more property of $\gamma$, which is control over its tangent vector close to $\beta$. \begin{lem} \label{lem:gamma_behavior_beta} If $\lim_{x \rightarrow \beta^-} \gamma'(x)$ exists and is equal to $\nu = (\nu_1, \nu_2)$, then $\nu_1 \leq 0$. \end{lem} \begin{proof} If $\nu_1 > 0$, then $\partial A$ is not regular at the point $x \in \partial A$ that corresponds to $\gamma(\beta)$. Furthermore, near $\gamma(\beta)$, the image of $\gamma$ lies to the left of the vertical line through $\gamma(\beta)$. Since $\mathcal{K} \subset C$ and $\gamma_1(\beta) < \gamma_1(0)$, this implies that, near $x$, $\partial A$ lies in a half-space. As such, due to Theorem \ref{thm:regularity}, $\partial A$ is regular at $x$. This is a contradiction, and so $\nu_1 \leq 0$. \end{proof} We will complete the proof of Proposition \ref{prop:centered_ball} by proving the following two theorems. Here, we assume the same hypotheses as in Proposition \ref{prop:centered_ball}, and that $n \geq 2$. \begin{lem}[First Tangent Lemma] \label{lem:first_tangent} Either $\gamma$ is a centered circle, or there is a point $x \in (0, \beta)$ with $\gamma'(x) = (0,-1)$, and $\kappa(x) > 0$. \end{lem} \begin{lem}[Second Tangent Lemma] \label{lem:second_tangent} If there exists a point $x \in (0, \beta)$ with $\gamma'(x) = (0,-1)$ and $\kappa(x) > 0$, then there is another point $y \in (0, \beta)$ with $\gamma'(y) = (0,1)$. \end{lem} These are shown in Figure \ref{fig:lemmas}. \begin{figure}[ht] \caption{Points $x$ and $y$ from Lemmas \ref{lem:first_tangent} and \ref{lem:second_tangent}, respectively.} \centering \includegraphics[width=1.00\textwidth]{lemmas.pdf} \label{fig:lemmas} \end{figure} We now observe that such a point $y$ described in Lemma \ref{lem:second_tangent} cannot exist. This is because of the following lemma, which is a simple result of the fact that $\mathcal{K}$ is spherically symmetric about $e_1$. In particular, this fact implies that $\|\gamma\|$ is a non-increasing function on $[0, \beta)$ (see property $6$), and so by differentiating $\|\gamma\|$, we obtain the following result. \begin{lem}[Tangent Restriction Theorem] \label{lem:tangent_restriction} For every $x \in (0, \beta)$, $N(x)$ is well-defined and $$\gamma'(x) \cdot N(x) \leq 0.$$ \end{lem} If a point $y$ exists that satisfied the conclusion of Lemma \ref{lem:second_tangent}, then by Lemma \ref{lem:tangent_restriction}, $$\gamma'(y) \cdot N(y) = \frac{\gamma_2(y)}{\| \gamma(y) \|} \leq 0.$$ Since $\gamma_2(y) > 0$ for each $y \in (0, \beta)$, we thus have a contradiction. This means that $\gamma$ must be a centered circle of radius $x^$. Thus, $C$ is contained in the closed disc of radius $x^$, which is equal to $\mathcal{K}$. Since we have already established that $\mathcal{K} \subset C$, this means that $C$ is equal to the closed disc of radius $x^$, and so $A = B_M$, as desired. This completes the proof of Proposition \ref{prop:centered_ball}. With this tool in hand, we can now prove Theorems \ref{thm:main} and \ref{thm:uniqueness}. \begin{proof}[Proof of Theorem \ref{thm:main} and Theorem \ref{thm:uniqueness}] By the logic at the start of this section, this theorem is true if $f$ is constant. Hence, assume that it is not constant everywhere. Let $M' = {\rm Vol} (B_{\mathcal{R}(f)})$, and fix $M > M' \geq 0$. By Theorem \ref{thm:regularity}, there exists at least one isoperimetric set of weighted volume $M$. Choose any such minimizer $A$ of weighted volume $M$, and apply the process of \emph{spherical symmetrization} to it. A good reference for this process and its properties is Section 9.2 of \cite{burago}. To produce $A^\star$, the result of this process, we consider $S_r$, the centered $n-1$-dimensional sphere of radius $r$. We then define $A^\star \cap S_r$ to be a closed spherical cap centered on the non-negative $e_1$ axis such that $$\mathcal{H}^{n-1}(A^\star \cap S_r) = \mathcal{H}^{n-1}(A \cap S_r).$$ If this measure is $0$, then $A^\star \cap S_r$ is empty. We then have that, by Theorem 6.2 from \cite{morg_iso_2}, $$ {\rm Vol} (A^\star) = {\rm Vol} (A)$$ and $${\rm Per}(A^\star) \leq {\rm Per}(A).$$ Since $A$ is an isoperimetric region, $A^\star$ is one as well, and so is a spherically symmetric isoperimetric region. As $A$ has the distributed volume condition, $A^\star$ does as well. Then, by Proposition \ref{prop:centered_ball}, $$ \partial A^\star = \partial B_M.$$ Looking again at the definition of $A^\star$, we see that this implies that $$ \partial A = \partial B_M,$$ which means that $A$ is a centered ball up to a set of measure $0$. In summary, if $M > M'$, at least one isoperimetric set $A$ with $ {\rm Vol} (A) = M$ exists, and for every such minimizer, it must be a centered ball up to a set of measure $0$. If $M' = 0$, this completes the proof. If $M' > 0$, then fix $0 < M \leq M'$. Again, by Theorem \ref{thm:regularity}, there is at least one isoperimetric set with weighted volume $M$. For any such minimizer $A$, if $A$ has the distributed volume condition then we may apply the above logic to conclude that $A$ is a centered ball, up to a set of measure $0$. However, since $A$ has the distributed volume condition, the radius of this ball must be more than $\mathcal{R}(f)$, and so $ {\rm Vol} (A) > M' \geq M$, which is a contradiction. Hence, $A$ lies inside $B_{\mathcal{R}(f)}$, up to a set of measure $0$. Let us now consider the problem of finding isoperimetric regions of weighted volume $M > 0$ in $\mathbb{R}^n$ with the constant density $h(x) = f(0)$. We know that the set of such minimizers is exactly the set of all balls of weighted volume $M$, up to sets of measure $0$. Thus, $A$ is an isoperimetric region if and only if it is a ball of weighted volume $M$ located entirely inside $B_\mathcal{R}(f)$, again up to a set of measure $0$. \end{proof} The remainder of this article is divided up into two sections. The first contains the proof to the First Tangent Lemma, and the second contains the proof to the Second Tangent Lemma. \section{Proof of First Tangent Lemma} This section is devoted to proving the First Tangent Lemma (Lemma \ref{lem:first_tangent}). We will prove this by contradiction: we will assume that $\gamma$ is not a centered circle, and then produce a point $p \in (0, \beta)$ with $\gamma'(p) = (0,-1)$ and $\kappa(p) > 0$. To go about doing this, we are going to consider two components of the curve $\gamma$, the upper curve, and the lower curve. Although the definitions of these two curves are slightly technical, the upper curve will turn out to be the entire first segment of $\gamma$ on $[0, \beta)$ such that $\gamma'$ lies in the second quadrant, and the lower curve will be the entire following segment of $\gamma$ such that $\gamma'$ lies in the third quadrant. Except for a special case, which is handled differently, we will prove additional properties of these two curves which allow us to make the following important conclusion. If we compare a point $x$ on the upper curve and a point $y$ on the lower curve such that $$ \gamma_2(x) = \gamma_2(y),$$ then $$\kappa(x) \leq \kappa(y).$$ Additionally, $\kappa(x) < \kappa(y)$ for a significant portion of pairs $(x,y)$. This will allow us to conclude that the lower curve curves faster than the upper curve, and so must terminate before it reaches the $e_1$-axis. We will show that the derivative at this point of termination is $(-1,0)$, as desired. This is shown in Figure \ref{fig:upper_lower_curve}. For the rest of this section, it will be useful to refer back to this figure. \begin{figure}[ht] \caption{The Upper and lower curves of $\gamma$. Note that $\kappa(x) \leq \kappa(y)$.} \centering \includegraphics[width=1.00\textwidth]{upper_lower_curve.pdf} \label{fig:upper_lower_curve} \end{figure} We will start with several computational results will will be useful to us later. We will then define the upper curve rigorously, and prove that it has the desired structure. Lastly, we will define the lower curve and complete the proof of Lemma \ref{lem:first_tangent}. \subsection{Preliminary Lemmas and Definitions} We first seek to produce a more manageable expression for the unaveraged mean curvature $H_0$. To do this, we define the \emph{canonical circle}: \begin{defn}[Canonical Circle] \label{defn:canonical_circle} Given a point $x \in (0,\beta)$, let $C_x$ be the unique oriented circle which goes through $\gamma(x)$, whose center lies on the $e_1$ axis, and whose unit tangent vector at $\gamma(x)$ is $\gamma'(x)$. We call this the canonical circle at the point $x$, and denote it by $C_x$. If $\gamma'(x) = (0,1)$ or $\gamma'(x) = (0,-1)$, then the canonical circle is an oriented vertical line. Note that this is well-defined since no points in $(0, \beta)$ lie on the $e_1$ axis. If $x = 0$, then we define $C_x$ as $\lim_{x \rightarrow 0^+} C_x$, which exists because $\gamma$ is regular at $0$. Lastly, let $\kappa(C_x)$ denote the signed curvature of $C_x$. If $C_x$ has radius $r$ (possibly $\infty$), then $\kappa(C_x) = \frac{1}{r}$ if $C_x$ is counterclockwise oriented, and $\kappa(C_x) = - \frac{1}{r}$ if it is clockwise oriented. From this definition, we see that $\kappa(C_0) = \kappa(0)$, the tangent of $C_0$ at $0$ is equal to $\gamma'(0)$, and both the center of $C_x$ and the curvature of $C_x$ are continuous functions of $x$ on $[0, \beta)$. If the canonical circle at a certain point is an oriented vertical line, then we call the point where it intersects the $e_1$ axis its center. \end{defn} We can now characterize the unaveraged mean curvature $H_0$ in terms of the inward curvature of $\gamma$ and the signed curvature of the canonical circle. Note that $\kappa(C_x)$ is a smooth function of $x$ on $(-\beta, \beta)$. \begin{prop} \label{prop:mean_curvature} Given a point $x \in [0, \beta)$, we have that $$H_0(x) = \kappa(x) + (n-2) \kappa(C_x).$$ \end{prop} \begin{proof} Let us first assume that $\gamma_2(x) > 0$, and that $\gamma'(x) \neq (0, \pm 1)$. We can then write $\gamma$ locally around $x$ as a smooth positive function of some portion of the $e_1$ axis. Let this smooth function be $p$, so that $(y_0,p(y_0)) = \gamma(x)$ and $(y, p(y))$ is equal to $\gamma$ on some local neighborhood of $\gamma(x)$. Now, we know that every $n$-tuple $(x_1, ..., x_n)$ on the boundary of our spherically symmetric minimizer $A$ in $\mathbb{R}^n$ that corresponds to a point $(y, p(y))$ satisfies the following equality: $$p(x_1) - \sqrt{\sum_{i=2}^n x_i^2} = 0.$$ Let $Q(x_1, ..., x_n) = p(x_1) - \sqrt{\sum_{i=2}^n x_i^2}$. We first compute $$div \frac{ \nabla Q}{\| \nabla Q \|}(x_1, \dots, x_n).$$ We have that $$ \frac{\nabla Q}{\| \nabla Q \|}(x_1, \dots, x_n) = \frac{1}{\sqrt{1 + (p'(x_1))^2}} (p'(x_1), -\frac{x_2}{\sqrt{\sum_{i=2}^n x_i^2}}, \dots, - \frac{x_n}{\sqrt{\sum_{i=2}^n x_i^2}}).$$ Taking the divergence of this, we obtain that \begin{align} div \frac{\nabla Q}{\| \nabla Q \|}(x_1, \dots, x_n) &= \frac{p''(x_1)}{\sqrt{1 + (p'(x_1))^2}} - \frac{(p'(x_1))^2 p''(x_1)}{(1 + (p'(x_1))^2)^\frac{3}{2}} \\ & -\frac{1}{\sqrt{1 + (p'(x_1))^2}} \sum_{i = 2}^n (\frac{1}{\sqrt{\sum_{j=2}^n x_j^2}} - \frac{x_i^2}{(\sum_{j=2}^n x_j^2)^{\frac{3}{2}}}) \\ &= \frac{p''(x_1)}{(1 + (p'(x_1))^2)^{\frac{3}{2}}} - \\ & (n-2) \frac{1}{\sqrt{(1 + (p'(x_1))^2) (\sum_{i=2}^n x_i^2)}} \end{align} Since $p(x_1) = \sqrt{\sum_{i=2}^n x_i^2}$, this becomes $$ \frac{p''(x_1)}{(1 + (p'(x_1))^2)^{\frac{3}{2}}} - (n-2) \frac{1}{p(x_1) \sqrt{1 + (p'(x_1))^2}}.$$ Recall that $\mathcal{K}$ is the bounded region enclosed by $\gamma$. We will break the proof into two cases, depending on whether the inward unit normal vector at $x$ with respect to $\mathcal{K}$ is upwards or downwards. If $n$ is this unit normal vector, then we say that it is upwards if $n \cdot (0,1) > 0$, and we say that it is downwards if $n \cdot (0,-1) > 0$. Since $\gamma' \neq (0, \pm 1)$, these are the only two possibilities. If $n$ is downwards, then from the list of formulae at the end of \cite{morg_rie_geom}, we have that the inward mean curvature of $\partial A$ at $(x_1, \dots, x_n)$ is equal to $$- div \frac{ \nabla Q}{\| \nabla Q \|}(x_1, \dots, x_n) = - \frac{p''(x_1)}{(1 + (p'(x_1))^2)^{\frac{3}{2}}} + (n-2) \frac{1}{p(x_1) \sqrt{1 + (p'(x_1))^2}}.$$ Since $n$ is downwards, the first term is $\kappa(x)$, and the second term is $(n-2) \kappa(C_x)$, as desired. In particular, we can show that the second term is $(n-2) \kappa(C_x)$ by using a method identical to that employed in Appendix 1, Lemma \ref{lem:inside_ball_details}. Similarly, if $n$ is upwards, then we have that the inward mean curvature of $\partial A$ at $(x_1, \dots, x_n)$ is equal to $$ div \frac{\nabla Q}{\| \nabla Q \|}(x_1, \dots, x_n) = \frac{p''(x_1)}{(1 + (p'(x_1))^2)^{\frac{3}{2}}} - (n-2) \frac{1}{p(x_1) \sqrt{1 + (p'(x_1))^2}}.$$ In this case, since $n$ is upwards, we have that the first term again corresponds to $\kappa(x)$, and the second term again corresponds to $(n-2) \kappa(C_x)$, as desired. Again, we can show that the second term is $(n-2) \kappa(C_x)$ by using a method identical to that employed in Appendix 1, Lemma \ref{lem:inside_ball_details}. If $\gamma'(x) = (0, \pm 1)$, then the fact that $x \in [0, \beta)$ implies that $\gamma$ is regular at $x$, and so $H_0$, $\kappa$, and $\kappa(C_x)$ are all smooth at $x$. Combined with the above result, this smoothness implies that $$H_0(x) = \kappa(x) + (n-2) \kappa(C_x)$$ for all $x$ in $[0, \beta)$. \end{proof} We will now prove that $\gamma$ has certain properties which will begin to narrow down its behavior. We first state a result that allows us to conclude that $\gamma$ is a circle from local data. \begin{lem} \label{lem:C_x_equality} For any point $x \in [0, \beta)$, if we have that the center of $C_x$ is the origin and $\kappa(x) = \kappa(C_x)$, then we have that $\gamma$ is a centered circle. \end{lem} \begin{proof} Since $H_f = c$ for a constant $c$ at all regular points, if $C_x$ is centered on the origin for some $x$ and $\kappa(x) = \kappa(C_x)$, we have that $c = g'(x) + (n-1) \kappa( C_x )$. The two curves $C_x$ and $\gamma$ satisfy the ordinary differential equation $H_f = c$, agree at the point $x$, and their tangent vectors agree at the point $x$. By standard theorems concerning the uniqueness of solutions from the theory of ODES, combined with the fact that $\gamma$ and $C_x$ are both arclength parametrizations, we have that these solutions must locally agree, so $\gamma = C_x$ around $x$. By successively applying this local result, we have that that $\gamma = C_x$ everywhere. \end{proof} We next characterize the possible centers of $C_x$, for every $x \in [0, \beta)$. \begin{lem} \label{lem:positive_e_1} For $x \in [0, \beta)$, if $\gamma'(x)$ is in the second quadrant, and if $a$ is the $e_1$-coordinate of the center of $C_x$, then $a \geq 0$. \end{lem} \begin{proof} First consider the case when $x \neq 0$. We then have that $\gamma_2(x) > 0$. As a result of Lemma \ref{lem:tangent_restriction}, $$N(x) \cdot \gamma'(x) \leq 0.$$ From the definition of $C_x$ along with the fact that $\gamma'(x)$ is in the second quadrant, we have that $$ \gamma'(x) = \frac{(-\gamma_2(x), \gamma_1(x) - a)}{\| (-\gamma_2(x), \gamma_1(x) - a) \|}.$$ Combining this with $N(x) = \frac{\gamma(x)}{\| \gamma(x) \|}$, we have that $$(\gamma_1(x), \gamma_2(x)) \cdot (-\gamma_2(x), \gamma_1(x) - a) \leq 0,$$ so we have that $-a \gamma_2(x) \leq 0$. Since $\gamma_2(x) > 0$, $a \geq 0$. If $x = 0$, then since $\kappa(C_0) = \kappa(0)$, the tangent of $C_0$ at $0$ agrees with $\gamma'(0)$, and $\kappa'(0) = 0$ (since $\gamma$ is symmetric about $0$), $C_0$ approximates $\gamma$ near $0$ up to the fourth order. Hence, if $a < 0$, then there are points in $[0, \beta)$ near $0$ on $\gamma$ that lie outside the centered circle of radius $\gamma(0)$. This is a contradiction, since all points on $\gamma$ must be less than or equal to $\|\gamma(0)\|$ in magnitude. Hence, $a \geq 0$ in this case as well. \end{proof} To improve readability, we shall define $\lambda(x) = \kappa(C_x)$ for all $x \in (-\beta, \beta)$. As already mentioned, $\lambda$ is a smooth function of $x$ on $(-\beta, \beta)$. We now prove several results, the proofs of which all work the same way. Given a point $x \in [0, \beta)$, we consider the unique oriented circle $A_x$ that is tangent to $\gamma$ at $x$, and whose signed curvature is equal to $\kappa(x)$. From the definition of curvature, $A_x$ approximates $\gamma$ locally up to the third order on $(0, \beta)$. Since $\gamma(x) = \gamma(-x)$ on $[0, \beta)$, we have that $\kappa'(0) = 0$, and so $A_0$ approximates $\gamma$ up to fourth order locally near $0$. Note that $A_x$ can be an oriented line. This will help us prove the following properties of $\gamma$ because we will show that the desired quantities of $\gamma$ at $x$ are unchanged if we replace $\gamma$ with $A_x$. In particular, let $\alpha$ be a unit-speed parametrization of $A_x$, with $\alpha(\widetilde{x}) = \gamma(x)$. We can define quantities for $\alpha$ in the same way that we do for $\gamma$. We shall denote the analogous quantity with a tilde, as follows: \begin{enumerate} \item $\widetilde{\kappa}(y)$ refers to the signed curvature of $\alpha$ at $y$. \item $\widetilde{H_1}(y)$ refers to $\frac{\partial g}{ \partial \nu}$ at $y$, where $\nu$ is the unit outward normal to $\alpha$ at $y$. \end{enumerate} Both of these quantities are smooth on the entirety of $\alpha$. We also define the canonical circle $\widetilde{C}_y$ for points $y$ on $A_x$. If $\alpha_2(y) \neq 0$, then $\widetilde{C}_y$ is defined as the canonical circle at $y$ on $A_x$ using the same definition as before. If $\alpha_2(y) = 0$ and $\alpha'(y) = (0, \pm 1)$, then $\widetilde{C}_y$ is defined to be $A_x$. If $\alpha_2(y) = 0$ and $\alpha'(y) \neq (0, \pm 1)$, then $\widetilde{C}_y$ is not defined. At each point $y$ where $\widetilde{C}_y$ is defined, the canonical circle is defined on a neighborhood of $y$. Additionally, we define $\widetilde{\lambda}(y)$ to be the signed curvature of $\widetilde{C}_y$ (defined at each point $y$ where $\widetilde{C}_y$ exists). Since $\widetilde{C}_y$ is defined on an open set, $\widetilde{\lambda}(y)$ is also defined on an open set. Furthermore, $\widetilde{\lambda}(y)$ is smooth on this domain of definition. We produce one more definition before we continue. \begin{defn} \label{defn:function_F} For each $x \in (-\beta, \beta)$, let $F(x)$ be the $e_1$-coordinate of the center of the canonical circle at $x$. Additionally, if $A_x$ is the circle as defined above, and $y$ is a point on $A_x$ where $\widetilde{C}_y$ is defined, then let $\widetilde{F}(y)$ be the $e_1$ coordinate of the circle $\widetilde{C}_y$. \end{defn} Clearly, $F$ is smooth at all points $x \in (-\beta, \beta)$ with $\gamma'(x) \neq (0, \pm 1)$. Additionally, $F$ is smooth at $0$. $\widetilde{F}$ is smooth on an open set containing every point $y$ with the properties that $\widetilde{C}_y$ is defined at $y$ and $\alpha'(y) \neq (0, \pm 1)$. For each of the proofs, we will summarize how this argument goes, using the above notation. \begin{lem} \label{lem:curvature_bound} Given a point $x \in [0, \beta)$, $\kappa'(x) \geq 0$ if the following properties hold: \begin{enumerate} \item $\gamma'(x)$ is in the second quadrant \item $\kappa(x) = \kappa(C_x) > 0$ \end{enumerate} If in addition, $\gamma(x) \not \in B_{\mathcal{R}(f)}$, $\gamma'(x) \neq (0,1)$, and $C_x$ is not centered at the origin, then $\kappa'(x) > 0$. \end{lem} \begin{proof} In this case, we have that $A_x = C_x$, and both have positive radii. As such, $A_x$ approximates $\gamma$ up to the third order at $x$. Because of this, we have that $$ \lambda'(x) = \widetilde{\lambda}'(\widetilde{x}) = 0. $$ We can now reduce the problem to determining the sign of $H_1'(x)$, since $H_f'(x) = 0$ and $\lambda'(x) = 0$. Again, because $\gamma$ is approximated up to the third order by $A_x$ near $x$, $$ H_1'(x) = \widetilde{H_1}'(\widetilde{x}).$$ Computing $\widetilde{H_1}'(\widetilde{x})$ is an easy exercise (see Appendix 1, Lemma \ref{lem:curvature_bound_details}) - it is always non-positive, and is negative if $\gamma(x) \not \in B_{\mathcal{R}(f)}$, $\gamma'(x) \neq (0,1)$, and $C_x$ is not centered at the origin. Note that we also use Lemma \ref{lem:positive_e_1} to show that the center of $C_x$ is greater than $0$. \end{proof} \begin{lem} \label{lem:second_derivative_kappa} If $\gamma$ is not a centered circle, then $\kappa''(0) > 0$. \end{lem} \begin{proof} In this case, we have that $C_0 = A_0$, and both approximate $\gamma$ up to the fourth order near $0$. As such, we again have that $\lambda''(0) = \widetilde{\lambda}''(\widetilde{0}) = 0$. Hence, since $H_f''(0) = 0$, we need only show that $H_1''(0) < 0$. We next observe that $C_0$ cannot be a centered circle, as $\kappa(0) = \kappa(C_0)$, and so by Lemma \ref{lem:C_x_equality}, $\gamma$ would be a centered circle. Since we assumed that this is not the case, $C_0$ is not centered. Combining this with the fact that $C_0$ approximates $\gamma$ up to the \emph{fourth} order, we have that $$H_1''(0) = \widetilde{H_1}''(\widetilde{0}),$$ which is negative by a straightforward computation (see Appendix 1, Lemma \ref{lem:second_derivative_kappa_details}). Note that this uses the fact that $\gamma(0) \not \in B_{\mathcal{R}(f)}$. \end{proof} \begin{lem} \label{lem:inside_ball} If $x \in [0, \beta)$, $\kappa(x) > \kappa(C_x) > 0$, $\gamma'(x)$ lies in the third quadrant and $x \in B_{\mathcal{R}(f)}$, then $\kappa'(x) \geq 0$, and $\lambda'(x) \leq 0$. \end{lem} \begin{proof} We again consider $A_x$, which approximates $\gamma$ at $x$ up to the third order. Let the center of $A_x$ be $(a,b)$. Since $\kappa(x) > \kappa(C_x) > 0$, $b > 0$. Due to the assumption that $x \in B_{\mathcal{R}(f)}$, $H_1'(x) = 0$, and so $H_0'(x) = 0$ as well. As such, if we can show that $\lambda'(x) \leq 0$, then we will be done. To do this, we observe that $$ \lambda'(x) = \widetilde{\lambda}'(\widetilde{x}) \leq 0.$$ This can be computed in a straightforward manner (see Appendix 1, Lemma \ref{lem:inside_ball_details}), using the fact that $\gamma'(x)$ lies in the third quadrant and $\kappa(C_x) > 0$. \end{proof} \begin{lem} \label{lem:outside_ball} If $x \in [0, \beta)$ with $\gamma'(x) = (-1,0)$, $\gamma_1(x) > 0$ and $\kappa(x) \geq \kappa(C_x) > 0$, and if $\gamma(x) \not \in B_{\mathcal{R}(f)}$, then $\kappa'(x) > 0$. \end{lem} \begin{proof} We have that $A_x$ approximates $\gamma$ at $x$ up to the third order. As such, $\lambda'(x) = \widetilde{\lambda}'(\widetilde{x})$. Since $\gamma'(x) = (-1,0)$, $\widetilde{\lambda}'(\widetilde{x}) = 0$, and so $\lambda'(x) = 0$ as well. Since $H_f'(x) = 0$, if we can show that $H_1'(x) < 0$, then this will imply that $\kappa'(x) > 0$. To facilitate this, we use the fact that $$H_1'(x) = \widetilde{H_1}'(\widetilde{x}) < 0.$$ The last fact can be computed directly using the premises of the lemma, especially the fact that $\gamma(x) \not \in B_{\mathcal{R}(f)}$ (see Appendix 1, Lemma \ref{lem:curvature_bound_details}). \end{proof} The last portion of this section is devoted to proving two theorems which will be useful tools later. The first allows us to translate statements about the curvature of the graphs of two functions into comparison statements regarding their values and derivatives, and the second will allow us to compare values of $H_1 = \frac{\partial g} {\partial \nu}$ for different unit vectors $\nu$. Let us consider a $C^2$ function $h$ with $h:(a,b) \rightarrow \mathbb{R}_{\geq 0}$, $b > a$. Let $t_{h} (x)$ denote the unit tangent vector $\frac{(1,h'(x))}{\|(1, h'(x))\|}$, $\theta: S^1 \rightarrow (- \pi, \pi]$ denote the counterclockwise angle from $0$ of a unit vector $v$, and lastly let $\kappa_{h} (x)$ denote the upward curvature of the graph of $h$ at $x$. \begin{prop}[Curvature Comparison Theorem] \label{prop:curvature_comparison} Consider two $C^2$ functions $f,g:(a,b) \rightarrow \mathbb{R}_{\geq 0}$ with $b > a$. Let us make the following assumptions on $f$ and $g$ (see Figure \ref{fig:curvature_comparison}): \begin{enumerate} \item $\lim_{x \rightarrow b^-} t_f (x)$ and $\lim_{x \rightarrow b^-} t_g (x)$ exist \item $\lim_{x \rightarrow b^-} f(x)$ and $\lim_{x \rightarrow b^-} g(x)$ exist \item $f'(x) \geq 0$ and $g'(x) \geq 0$ on $(a,b)$ \item $\lim_{x \rightarrow b^-} f(x) \leq \lim_{x \rightarrow b^-} g(x)$, $\lim_{x \rightarrow b^-} \theta(t_f(x)) \geq \lim_{x \rightarrow b^-} \theta(t_g (x))$, and $\kappa_f (x) \leq \kappa_g (x)$ for all $x \in (a,b)$ \end{enumerate} Then, for every $x \in (a,b)$, $$ f(x) \leq g(x) $$ and $$ \theta( t_f(x) ) \geq \theta( t_g(x) ). $$ Additionally, if there exists a point $y \in (a,b)$ such that $$\kappa_f(y) < \kappa_g(y),$$ then there is some $\phi > 0$ such that $$ \phi \leq \theta(t_f (x) ) - \theta(t_g (x) ) $$ for all $x \in (a, y)$. \end{prop} \begin{proof} At a given point $x \in (a,b)$, let $\theta_f(x) = \theta(t_f(x))$ and $\theta_g(x) = \theta(t_g(x))$. Since $t_f$ and $t_g$ both lie in the first quadrant, $\theta_f$ and $\theta_g$ both lie in the interval $[0, \frac{\pi}{2})$. Note that $f'(x) = \tan( \theta_f (x) )$ and $g'(x) = \tan( \theta_g (x) )$. Thus, if we can show that $\theta_f(x) \geq \theta_g(x)$ for all $x \in (a,b)$, then the fact that $\lim_{x \rightarrow b^-} f(x) \leq \lim_{x \rightarrow b^-} g(x)$ will also imply that $f(x) \leq g(x)$ for all $x \in (a,b)$. To this end, we know that $$\kappa_f(x) = \frac{f''(x)}{(1 + (f'(x))^2)^{\frac{3}{2}}}$$ and $$\kappa_g(x) = \frac{g''(x)}{(1 + (g'(x))^2)^{\frac{3}{2}}}.$$ Since $f''(x) = \frac{\theta'_f(x)}{\cos^2(\theta_f(x))}$ and $g''(x) = \frac{\theta'_g(x)}{\cos^2(\theta_g(x))}$, we have that these formulae become $$\kappa_f(x) = \cos(\theta_f(x)) \theta'_f(x) = (\sin(\theta_f(x)))'$$ and $$\kappa_g(x) = \cos(\theta_g(x)) \theta'_g(x) = (\sin(\theta_g(x)))'.$$ Hence, for every $x \in (a,b)$, $$ \sin(\theta_f(x)) - \sin(\theta_g(x)) \geq \int_x^b \kappa_g(t) - \kappa_f(t) dt, $$ since $\lim_{x \rightarrow b^-} \theta_f(x) - \theta_g (x) \geq 0$. If $\kappa_f \leq \kappa_g$, then $\sin(\theta_f) \geq \sin(\theta_g)$, and so $\theta_f \geq \theta_g$, as desired. If there exists a point $y \in (a,b)$ with $\kappa_f(y) < \kappa_g(y)$, then there is some neighborhood of $y$ on which this is true. As such, for any $x \in (a,y)$, $$\int_x^b \kappa_g(t) - \kappa_f(t) dt \geq c > 0,$$ implying that $\sin(\theta_f(x)) \geq \sin(\theta_g(x)) + c$ for all such $x$. This immediately yields the existence of a $\phi > 0$ such that $\theta_f - \theta_g > \phi$ on $(a, y)$. \end{proof} \begin{figure}[ht] \caption{The functions $f$ and $g$.} \centering \includegraphics[width=1.00\textwidth]{curvature_comparison.pdf} \label{fig:curvature_comparison} \end{figure} We will need a definition before continuing with our second theorem. \begin{defn} \label{defn:admissible} Consider a fixed pair of points $(x_1, y)$ and $(x_2, y)$ with $y > 0$ and $x_1 \geq x_2$, and a pair of unit vectors $v_1, v_2 \in \mathbb{R}^2$ such that $v_1$ is strictly in the second quadrant and $v_2$ is strictly in the third quadrant. Let $C_1$ be the canonical circle with respect to $v_1$ at $(x_1,y)$ with center $(a_1,0)$ and radius $r_1$, and $C_2$ be the canonical circle with respect to $v_2$ at $(x_2,y)$ with center $(a_2,0)$ and radius $r_2$. If $a_1 \geq 0$, $r_2 \geq r_1$, and $x_1 - a_1 \geq a_1 - x_2$, then we say that $(v_1, v_2)$ are admissible with respect to $(x_1, y)$ and $(x_2, y)$. Furthermore, let $N(x_1,y) = \frac{(x_1,y)}{\|(x_1,y)\|}$ and define $N(x_2,y)$ similarly. This is shown in Figure \ref{fig:admissible}. \end{defn} \begin{figure}[ht] \caption{A pair of vectors $v_1$ and $v_2$ which are admissible with respect to a pair of points $(x_1, y)$ and $(x_2,y)$.} \centering \includegraphics[width=1.00\textwidth]{admissible.pdf} \label{fig:admissible} \end{figure} \begin{prop}[$H_1$ Comparison Theorem] \label{prop:normal_computation} Consider a pair of points $(x_1,y)$ and $(x_2,y)$ with $y > 0$ and $x_1 \geq x_2$. Let $v_1$ and $v_2$ be two unit vectors. If $v_1$ and $v_2$ are admissible with respect to $(x_1,y)$ and $(x_2,y)$, then $$\|(x_1,y)\| \geq \|(x_2,y)\|.$$ Additionally, $$v_1^\perp \cdot N(x_1, y) \geq v_2^\perp \cdot N(x_2, y)$$ with equality if and only if $C_1$ is centered at the origin and $C_1 = C_2$. Note that here $\perp$ means the perpendicular unit vector formed by a clockwise rotation by $\frac{\pi}{2}$ radians. \end{prop} \begin{proof} To prove that $\|(x_1,y)\| \geq \|(x_2,y)\|$, we need only show that $\|x_1\| \geq \|x_2\|$. This fact follows immediately from the property that $x_1 \geq x_2$, that the center of $C_1$ has a non-negative $e_1$-coordinate $a_1$, and that $x_1 - a_1 \geq a_1 - x_2$, which are all part of the assumption that $v_1$ and $v_2$ are admissible with respect to $(x_1,y)$ and $(x_2,y)$. Let $\theta(w)$ denote the counterclockwise angle of the nonzero vector $w$, $\theta: S^1 \rightarrow [0, 2 \pi)$. We then have that $$v_1^\perp \cdot N(x_1,y) = \cos(\theta(v_1^\perp) - \theta(N(x_1,y)))$$ and $$v_2^\perp \cdot N(x_2,y) = \cos(\theta(v_2^\perp) - \theta(N(x_2,y))).$$ Let $\theta_1 = \theta(v_1^\perp) - \theta(N(x_1,y))$ and $\theta_2 = \theta(v_2^\perp) - \theta(N(x_2,y))$. We must show that $$\cos(\theta_1) \geq \cos(\theta_2)$$ with equality if and only if $C_1 = C_2$ and $C_1$ is a centered circle. We first observe that there is an $x_1^\star$ such that, if $C_1^\star$ is the canonical circle with respect to $v_1$ attached to $(x_1^\star, y)$, then $C_1^\star$ is centered. Furthermore, let $x_2^\star = - x_1^\star$, and let $v_2^\star$ be $v_1$ reflected through the $x$-axis. We then have that $v_1$ and $v_2^\star$ are an admissible pair with respect to $(x_1^\star,y)$ and $(x_2^\star,y)$. We now have that $C_1 = C_2$ and $C_1$ is centered if and only if $v_2 = v_2^\star$, $x_1 = x_1^\star$, and $x_2 = x_2^\star$. If these conditions are met, then clearly $\theta_1 = \theta_2 = 0$, and so we have equality. We will now show that, if at least one of these conditions is not met, then $\cos(\theta_1) > \cos(\theta_2)$, completing the proof. As a result of the hypotheses, we have that there is some $c,d \geq 0$ and $0 \leq \phi \leq \frac{\pi}{2}$ such that $\theta(v_2^\perp) = \theta({v_2^\star}^\perp) + \phi$, $x_1 = x_1^\star + c$, and $x_2 = x_2^\star + c + d$, as in Figure \ref{fig:normal_computation}. All of the requirements on $x_1, x_2$ and $v_2$ are met if and only if $c,d,\phi = 0$. Let us also note that, for a vector $(x,y)$ with $y > 0$, $\theta(N(x,y)) = \arccot(\frac{x}{y})$ and so $$\frac{\partial \theta(N(x,y))}{\partial x} = - \frac{y}{x^2 + y^2}.$$ Denote $\frac{\partial \theta(N(x,y))}{\partial x}$ as $\theta'(N(x,y))$. We now see that, since $\theta(N(x_1^\star,y)) = \theta(v_1^\perp)$ and $\theta(N(x_2^\star,y)) + \phi = \theta(v_2^\perp)$, \begin{align} \theta_1 &= \theta(N(x_1^\star,y)) - \theta(N(x_1,y)) \\ &= -\int_{x_1^\star}^{x_1^\star + c} \theta'(N(t,y)) dt \\ &= \int_{x_1^\star}^{x_1^\star + c} \frac{y}{t^2 + y^2} dt \end{align} and \begin{align} \theta_2 &= \phi + \theta(N(x_2^\star,y)) - \theta(N(x_2,y)) \\ &= \phi - \int_{x_2^\star}^{x_2^\star + c} \theta'(N(t,y)) dt - \int_{x_2^\star + c}^{x_2^\star + c + d} \theta'(N(t,y)) dt \\ &= \phi + \int_{x_2^\star}^{x_2^\star + c} \frac{y}{t^2 + y^2} dt + \int_{x_2^\star + c}^{x_2^\star + c + d} \frac{y}{t^2 + y^2} dt. \end{align} We first note that $0 \leq \theta_1, \theta_2 \leq \pi$, and so if we can show that $\theta_1 < \theta_2$ if at least one of $c,d$ or $\phi$ is positive, then we will have that $\cos(\theta_1) > \cos(\theta_2)$, the desired result. Due to the fact that $v_1$ lies strictly in the second quadrant, $x_1^\star > 0$ and $x_2^\star < 0$. As such, for each $q \in [0,c]$, $$\frac{y}{(x_1^\star + q)^2 + y^2} \leq \frac{y}{(x_2^\star + q)^2 + y^2}$$ with equality only at $q = 0$. Hence, if $c > 0$, then $$ \int_{x_1^\star}^{x_1^\star + c} \frac{y}{t^2 + y^2} dt < \int_{x_2^\star}^{x_2^\star + c} \frac{y}{t^2 + y^2} dt.$$ Since $\int_{x_2^\star + c}^{x_2^\star + c + d} \frac{y}{t^2 + y^2} dt \geq 0$ with equality if and only if $d = 0$ and $\phi \geq 0$ with equality if any only if $\phi = 0$, this completes the proof. \end{proof} \begin{figure}[ht] \caption{$v_1$, $v_2^\star$, $x_1^\star$ and $x_2^\star$ compared with $v_1$, $v_2$, $x_1$ and $x_2$.} \centering \includegraphics[width=1.00\textwidth]{normal_computation.pdf} \label{fig:normal_computation} \end{figure} \subsection{Upper Curve} Here we rigorously define the upper curve, and then use results from the previous section to describe its behavior. One should refer to Figure \ref{fig:upper_lower_curve}. \begin{defn} \label{defn:upper_curve} Let the set $K \subset [0, \beta)$ be defined as follows. A point $x$ is in $K$ if and only if, for all $y \in [0, x]$, the following properties are satisfied: \begin{enumerate} \item $\gamma'(y)$ lies in the second quadrant. \item $\kappa(y) \geq \kappa(C_y) > 0$. \item $F$ is smooth at $y$ and $F'(y) \geq 0$ (where $F$ is defined as in Definition \ref{defn:function_F}). \end{enumerate} Let $\delta = \sup K$. \end{defn} We prove a short lemma which will provide sufficient criteria to conclude that $F$ is smooth on a neighborhood of a point, and $F'(x) \geq 0$. \begin{lem} \label{lem:F_and_R} If $x \in (0, \beta)$ and $\kappa(x) \geq \kappa(C_x) > 0$, then $F$ is smooth at $x$, and $F'(x) \geq 0$. \end{lem} \begin{proof} As mentioned previously, $F$ exists and is smooth at $x$ since $\gamma_2(x) > 0$, and $\gamma'(x) \neq (0, \pm 1)$ (since $\kappa(C_x) > 0$). Using notation from the previous section, $A_x$ locally approximates $\gamma$ at $x$ up to the third order. Our first observation is that $\widetilde{F}'(\widetilde{x}) = F'(x)$. This is because $\widetilde{F}$ approximates $F$ near $x$ up to the second order, which is a direct consequence of the fact that $A_x$ approximates $\gamma$ at $x$ up to the third order. Now we must just show that $\widetilde{F}'(\widetilde{x}) \leq 0$. This is the result of a straightforward computation along with the assumptions in the statement of the lemma (see Appendix 1, Lemma \ref{lem:inside_ball_details}). \end{proof} We can now prove the key properties of the upper curve. We start by demonstrating that $\delta > 0$. \begin{lem} \label{lem:delta_not_0} We have that $\delta > 0$. \end{lem} \begin{proof} To prove that there exists a $\rho > 0$ so that $[0, \rho] \subset K$, we must produce $\rho_1, \rho_2, \rho_3 > 0$ so that $\gamma'(y)$ lies in the second quadrant for $y \in [0, \rho_1]$, $\kappa(y) \geq \kappa(C_y) > 0$ for $y \in [0, \rho_2]$, and $F'(y) \geq 0$ for $y \in [0, \rho_3]$. We will then choose $\rho = \min(\rho_1, \rho_2, \rho_3) > 0$. Since $\gamma$ lies inside the centered ball of radius $\|\gamma(0)\| < \infty$, $\kappa(0) > 0$. Because $\gamma$ is smooth on $[0, \beta)$, $\kappa$ is continuous on this interval, and so there is some $\epsilon > 0$ so that $\kappa(y) > 0$ on $[0, \epsilon]$. Furthermore, since $\gamma$ is symmetric about the $e_1$ axis, $\gamma'(0) = (0,1)$. Combining these results yields the fact that there is some $\rho_1 > 0$ so that $\gamma'(y)$ is in the second quadrant on $[0, \rho_1]$. As a result of the fact that $\gamma$ is symmetric about the $e_1$ axis and the definition of the canonical circle, we have that $\kappa(0) = \kappa(C_0) > 0$. Hence, referring to the discussion pertaining to approximating circles in the previous section, $A_0 = C_0$ and so $A_0$ approximates $\gamma$ up to the fourth order near $0$ (since $\kappa'(0) = 0$). Using the notation $\lambda(x)$ as before, we see that $\lambda(x)$ is constant up to the third order near $0$. However, by Lemma \ref{lem:second_derivative_kappa}, $\kappa''(0) > 0$, and so there is some $\rho_2 > 0$ so that, on $[0,\rho_2]$, $\kappa(x) \geq \kappa(C_x)$. We may also assume that $\kappa(C_x) > 0$ on this interval because $\kappa(C_0) > 0$ and $\kappa$ is continuous on $[0, \beta)$. Lastly, we clearly have that $F'(0) = 0$, since $F$ exists and is smooth at $0$, and since $\gamma$ is symmetric about the $e_1$ axis. From the previous paragraph, we can find a $\rho_3 > 0$ such that, for $y \in (0, \rho_3]$, $\gamma'(y)$ lies strictly in the second quadrant, and $\kappa(y) \geq \kappa(C_y) > 0$. By Lemma \ref{lem:F_and_R}, we thus have that $F'(y) \geq 0$ on $(0, \rho_3]$, and so this choice of $\rho_3$ is satisfactory. \end{proof} We now prove the critical properties of the upper curve. \begin{prop}[Structure of Upper Curve] \label{prop:structure} $K$ is not empty, and so $\delta$ exists. Furthermore, if $\gamma$ is not a centered circle, then $\delta$ has the following properties: \begin{enumerate} \item $\delta < \beta$ \item $\delta \in K$ \item $\gamma_1(\delta) \geq F(x)$ for any $x \in [0, \delta]$. \item $\gamma_1(\delta) > 0$ \item $\gamma'(\delta) = (-1,0)$ \end{enumerate} \end{prop} \begin{proof} From Lemma \ref{lem:delta_not_0}, we have that $\delta$ exists, and $\delta > 0$. We will begin by proving the first four properties of $\delta$ described in the statement of the theorem. Since $\gamma'(x)$ lies in the second quadrant for $x \in [0, \delta)$, and $\gamma'(x) \neq (-1,0)$ on a neighborhood of $0$, $\gamma_2(x)$ is a non-decreasing function on $[0, \delta)$ and increases on some interval. We thus have that $\lim_{x \rightarrow \delta^-} \gamma_2(x)$ exists and is positive, and so $\delta \neq \beta$. Since $\gamma'(0) = (0,1)$, the above paragraph implies that $\gamma$ is smooth on $[0, \delta]$. Hence, all relevant quantities are continuous on this interval, and so the fact that $\delta \in K$ follows directly from this continuity, along with the fact that $\gamma'(\delta) \neq (0,1)$, and $\kappa > 0$ on $K$. The property that $F(\delta) \geq F(x)$ for all $x \in [0, \delta]$ is a direct result of the fact that $F'(x) \geq 0$ on $[0, \delta]$, and the fact that $F(\delta) \leq \gamma_1(\delta)$ (which is because $\gamma'(\delta)$ lies in the second quadrant). We next show that $\gamma_1(\delta) > 0$. Since $\gamma$ is smooth at $\delta$, $\gamma'(\delta)$ is in the second quadrant. Hence, $\gamma_1(\delta) \geq F(\delta)$. As a result of the fact that $\kappa(0) = \kappa(C_0)$, Lemma \ref{lem:positive_e_1} and the assumption that $\gamma$ is not a centered circle imply that $F(0) > 0$. Since $F' \geq 0$ on $[0, \delta]$, $F(\delta) > 0$, completing the proof. The last item that we must prove is that $\gamma'(\delta) = (-1,0)$. We will prove this by contradiction: if $\gamma'(\delta) \neq (-1,0)$, then there is some $\epsilon > 0$ so that $[\delta, \delta + \epsilon] \in K$. We will break this proof down into two cases. The first case is if $\kappa(\delta) > \kappa(C_\delta) > 0$, and the second case is if $\kappa(\delta) = \kappa(C_x) > 0$. Since $\delta \in K$, we know that these two cases encompass all possibilities. In both cases, since $\delta > 0$ and $\gamma'(\delta) \neq (-1,0)$, $\gamma'(\delta)$ is strictly in the second quadrant. Let us first assume that $\kappa(\delta) > \kappa(C_\delta) > 0$. Due to the smoothness of $\gamma$, there exists an $\epsilon > 0$ such that $\gamma'$ is in the second quadrant on $[\delta, \delta + \epsilon]$. Furthermore, since $\lambda(x) = \kappa(C_x)$ and $\kappa$ are both smooth, we may also assume that $\kappa(x) > \kappa(C_x) > 0$ on this interval as well. Lastly, $F'(x) \geq 0$ on this interval as a direct result of Lemma \ref{lem:F_and_R}. Hence, $[\delta, \delta + \epsilon] \subset K$. Let us now assume that $\kappa(\delta) = \kappa(C_\delta) > 0$, and let us consider two sub-cases. The first sub-case is if $\gamma(\delta) \not \in B_{\mathcal{R}(f)}$. In this sub-case, Lemma \ref{lem:curvature_bound} tells us that $\kappa'(\delta) > 0$. We now have that $A_\delta = C_\delta$, and so $C_\delta$ approximates $\gamma$ near $\delta$ up to the third order. As such, we see that $\lambda'(\delta) = 0$, and so there exists an $\epsilon > 0$ such that $\kappa(x) \geq \kappa(C_x) > 0$ on $[\delta, \delta + \epsilon]$. Since $\gamma'(\delta)$ is strictly in the second quadrant and $\kappa(x) > 0$ on this interval, we can choose $\epsilon$ so that $\gamma'$ is strictly in the second quadrant on $[\delta, \delta + \epsilon]$ as well. The only other fact to check is that we can choose $\epsilon$ so that $F'(x) \geq 0$ on this interval, which is a consequence of Lemma \ref{lem:F_and_R}. The remaining sub-case is if $\gamma(\delta) \in B_{\mathcal{R}(f)}$ and $\kappa(\delta) = \kappa(C_\delta) > 0$. In this case we see that $\gamma$ and $C_\delta$ agree at the point $\gamma(\delta)$, and their tangents also agree at this point. As a result, for some $\epsilon > 0$, $\gamma = C_\delta$ on $[\delta, \delta + \epsilon]$. This is because $g'(\|x\|) = 0$ on $B_{\mathcal{R}(f)}$, and so $C_\delta$ and $\gamma$ both satisfy the ODE $\kappa(x) + (n - 2) \kappa(C_x) = \kappa(\delta) + (n - 2) \kappa(C_\delta)$. We can apply standard theorems concerning the uniqueness of solutions from the theory of ODEs to obtain that, since $C_\delta$ and $\gamma$ are both arclength parametrizations, they must be equal on some neighborhood of $\delta$. As such, we see that $F'(x) = 0$, $\kappa(x) = \kappa(\delta) = \kappa(C_\delta) = \kappa(C_x) > 0$, and $\gamma'$ lies in the second quadrant on $[\delta, \delta + \epsilon]$, as desired. \end{proof} \subsection{Lower Curve} We first will require a definition of the \emph {lower curve}. We will then compare the lower curve to the upper curve to prove Lemma \ref{lem:first_tangent}, as described in the introduction. Again, it is useful to refer to Figure \ref{fig:upper_lower_curve} throughout this section. \begin{defn} \label{defn:lower_curve} Let $L \subset [\delta, \beta)$ defined as follows. A point $x \in [\delta, \beta)$ is in $L$ if and only if, for every $y \in [\delta, x]$, we have that: \begin{enumerate} \item $\gamma'(y)$ is in the third quadrant \item If $\overline{y}$ is the unique point on the upper curve with $\gamma_2(\overline{y}) = \gamma_2(y)$, then $\kappa(\overline{y}) \leq \kappa(y)$. \end{enumerate} Now define $$\eta = \sup L.$$ Since $\delta \in L$, $\eta$ exists. \end{defn} As with the upper curve, we first prove some properties about the lower curve. To begin, note that $\gamma_1(x) \leq \gamma_1(\delta)$, and $\gamma_2(x) \leq \gamma_2(\delta)$ for all $x \in L$, since $\gamma'$ is in the third quadrant on $L$. Additionally, observe that, for every $z \in L$, there is a unique $\bar{z}$ in the upper curve such that $\gamma_2(\bar{z}) = \gamma_2(z)$. This is a result of the fact that $\kappa > 0$ on the upper curve, $\gamma'$ is in the second quadrant on the upper curve, and $0 \leq \gamma_2(z) \leq \gamma_2(\delta)$. We make some preliminary conclusions: since $\kappa(x) > 0$ and $\gamma'(x)$ in the third quadrant for every $x \in L$, if we choose any $z_1, z_2 \in L$, then $\gamma_2(z_1) \neq \gamma_2(z_2)$. These comments imply that, for a fixed $x \in L$, we may produce functions $k$ and $h$ defined on $(\gamma_2(x), \gamma_2(\delta))$ such that $k(t)$ is the unique point $p_1$ in $L$ with $\gamma_2(p_1) = t$, and $h(t)$ is the unique point $p_2$ in $[0, \delta]$ such that $\gamma_2(p_2) = t$. Consider now the functions $$ Q = 2\gamma_1(\delta) - \gamma_1(h) $$ and $$ W = \gamma_1(k) $$ defined on $(\gamma_2(x), \gamma_2(\delta))$. This is shown in Figure \ref{fig:Q_and_W}. \begin{figure}[ht] \caption{The functions $Q$ and $W$.} \centering \includegraphics[width=1.00\textwidth]{Q_and_W.pdf} \label{fig:Q_and_W} \end{figure} We now prove the key properties of the lower curve. Here again $\theta$ denotes the counterclockwise angle of a nonzero vector, where $\theta$ takes values in $(-\pi, \pi]$. \begin{lem} \label{lem:lower_curve_properties} The following properties of the lower curve are true. For each $z \in L$, \begin{enumerate} \item $\gamma_1(\bar{z}) - \gamma_1(\delta) \geq \gamma_1(\delta) - \gamma_1(z)$ \item $\theta( \gamma'(\bar{z})) \geq - \theta(\gamma'(z))$ \end{enumerate} \end{lem} \begin{proof} This is a direct consequence of Proposition \ref{prop:curvature_comparison} applied to $Q$ and $W$. \end{proof} We now begin to prove important properties of $\eta$. \begin{lem} \label{lem:lower_curve_eta} If $\gamma$ is not a centered circle, then we have that $\eta < \beta$, and $\eta \in L$. \end{lem} \begin{proof} Consider again the functions $Q$ and $W$. If $\eta = \beta$, then they are both defined on $(0, \gamma_2(\delta))$. We will show that, for some $\mu \in (0, \gamma_2(\delta))$, $\kappa_W(\mu) > \kappa_Q(\mu)$ (here, we use the upward curvature). By the second part of Proposition \ref{prop:curvature_comparison}, we then have that there is some $\phi > 0$ and $\epsilon > 0$ such that $\theta_W + \phi \leq \theta_Q$ at all points in $(0, \epsilon)$. This translates into the fact that, if $z \in L$ with $\gamma_2(z) \in (0, \epsilon)$, then $$\theta(\gamma'(\bar{z}) ) \geq \phi - \theta(\gamma'(z)).$$ Since $\lim_{x \rightarrow 0^+} \theta(\gamma'(x)) = \theta(\gamma'(0)) = \frac{\pi}{2}$, this implies that there is some $z \in L$ with $\gamma_2(z) \in (0, \epsilon)$, $\gamma'(z) \neq (-1,0)$, and $-\theta(\gamma'(z)) < \frac{\pi}{2}$. One of the properties of $z \in L$, however, is that $\gamma'(z)$ must lie in the third quadrant, so this yields a contradiction. Since $\eta < \beta$, $\gamma$ is smooth at $\eta$. Hence, $\gamma'(\eta)$ is in the third quadrant, and $\kappa(\eta) \geq \kappa(\overline{\eta})$, and so $\eta \in L$. We have thus reduced the problem to showing that such a $\mu > 0$ exists. Since $\gamma(0) \not \in B_{\mathcal{R}(f)}$, there is some $0 < \epsilon < \delta$ such that $\gamma(\bar{z}) \not \in B_{\mathcal{R}(f)}$ for all $z \in [\delta, \beta)$ with $\bar{z} \in [0, \epsilon]$. If we choose any pair $(z, \bar{z})$ with $\bar{z} \in [0, \epsilon]$, $\gamma'(z)$ and $\gamma'(\bar{z})$ are admissible vectors with respect to $\gamma(z)$ and $\gamma(\bar{z})$, in terms of Definition \ref{defn:admissible}. This is a result of Lemma \ref{lem:lower_curve_properties} and the fact that $F(\bar{z}) \leq F(\delta)$ (Proposition \ref{prop:structure}). Letting $C_1$ and $C_2$ be the two circles as per this definition, we cannot have that $C_1 = C_2$ and $C_1$ centered since $\| \gamma_1(z) \| < \| \gamma_1(\bar{z}) \|$ as a result of the fact that $\gamma_1(\delta) > 0$ (Proposition \ref{prop:structure}) and $\gamma_1(\delta) - \gamma_1(z) \leq \gamma_1(\bar{z}) - \gamma_1(\delta)$ (Lemma \ref{lem:lower_curve_properties}). As such, Proposition \ref{prop:normal_computation} yields the conclusion that $$\| \gamma(z) \| \leq \| \gamma(\bar{z}) \|$$ and $$N(\gamma(z)) \cdot \gamma'(z)^\perp < N(\gamma(\bar{z})) \cdot \gamma'(\bar{z})^\perp.$$ Combining these results with the facts that $g'(\|\gamma(\bar{z})\|) > 0,$ and $g'(\|\gamma(z)\|) \leq g'(\|\gamma(\bar{z})\|)$, we can conclude that $$ g'(\|\gamma(z)\|) (N(\gamma(z)) \cdot \gamma'(z)^\perp = \frac{\partial g}{\partial \nu}(z) < \frac{\partial g}{\partial \nu}(\bar{z}) = g'(\|\gamma(\bar{z})\|) N(\gamma(\bar{z})) \cdot \gamma'(\bar{z})^\perp.$$ Furthermore, from Lemma \ref{lem:lower_curve_properties}, we have that $$\theta(\gamma'(\bar{z})) \geq - \theta(\gamma'(z)),$$ and so $\kappa(C_z) \leq \kappa(C_{\bar{z}})$. Using the fact that $H_f(z) = H_f(\bar{z})$, we get that $\kappa(z) < \kappa(\bar{z})$ for all $z$ with $\bar{z} \in (0, \epsilon)$. This concludes the proof. \end{proof} \subsection{Proof of First Tangent Lemma} Before completing the proof of Lemma \ref{lem:first_tangent}, we will need an additional lemma. \begin{lem} \label{lem:boundary_points} If there exists a point $p \in (0, \delta]$ in the upper curve such that $$ p \in \partial B_{\mathcal{R}(f)}$$ and $$ \kappa(C_p) = \kappa(p), $$ then there exists an $\omega > 0$ such that $p > \omega$, and $$ \sup_{y \in [p - \omega, p]} \kappa(y) = \kappa(p).$$ \end{lem} \begin{proof} If such an $\omega$ does not exist, then we can find an increasing sequence $a_i \in (0, p)$ with the properties that \begin{enumerate} \item $\sup_{y \in [a_i,p]} \kappa(y) = \kappa(a_i) > \kappa(p)$ \item $\lim_{i \rightarrow \infty} a_i = p.$ \end{enumerate} For each $a_i$, choose $b_i \in [a_i,p]$ so that $$\kappa(b_i) = \inf_{y \in [a_i,p]} \kappa(y).$$ Of course, $\kappa(b_i) \leq \kappa(p)$ for each $i$. We next make several observations. First, we can find an $\epsilon > 0$ such that $p > \epsilon$ and, on $[p - \epsilon, p]$, $$H_1' \leq 0.$$ This result can be proved by using the fact that $A_x$ approximates $\gamma$ up to the third order for every regular $x$, combined with Lemma \ref{lem:curvature_bound_details} in Appendix 1. Indeed, since $\kappa(C_p) = \kappa(p)$ and $p \neq 0$, if we choose $\epsilon$ to be small enough, then for every $x \in [p - \epsilon, p]$, all criteria of Lemma \ref{lem:curvature_bound_details} are satisfied, yielding the desired result. This observation means that, for each $a_i$ and $b_i$ with $i$ sufficiently large, $$H_1(a_i) \geq H_1(b_i).$$ The second observation is that there exists a $\xi > 0$ such that, for $a_i$ large enough and for any $r, s \in [a_i, p]$, $$\|\kappa(C_r) - \kappa(C_s)\| \leq \xi (p - a_i) \cdot (\kappa(a_i) - \kappa(b_i)).$$ Let $D = \kappa(a_i) - \kappa(b_i)$. The proof of this statement involves comparing $\gamma$ near $p$ to the arc of $C_p$ from $\gamma(p)$ clockwise to the $e_1$-axis. By analyzing these two curves in a manner similar to that used to prove Proposition \ref{prop:curvature_comparison}, we have that the derivatives differ by a constant times $(p - a_i) \cdot D$. As such, the difference between the curves themselves is bounded by a constant times $(p - a_i)^2 \cdot D$. Using the definition of $\kappa(C_x)$, we have that $\kappa(C_r)$ and $\kappa(C_s)$ thus both differ from $\kappa(C_p)$ by a quantity bounded by a constant times $(p - a_i) \cdot D$, completing the proof. Note that these estimates make use of the fact that $p - a_i$ and $D$ are sufficiently small, which we have since $D \rightarrow 0$ as $a_i \rightarrow p^-$. We now use these two observations to produce a contradiction. Choose an $a_i$ so large such that $0 < p - a_i < \frac{1}{2 n \xi}$, $H(b_i) \leq H(a_i)$, and the second observation above holds for $a_i$. Using the fact that the generalized mean curvature is constant, we have that \begin{align} 0 &= H_f(a_i) - H_f(b_i) \\ &= (n-2)(\kappa(C_{a_i}) - \kappa(C_{b_i})) + (\kappa(a_i) - \kappa(b_i)) + ( H_1(a_i) - H_1(b_i)) \\ &\geq (n-2)(-\xi (p - a_i) \cdot (\kappa(a_i) - \kappa(b_i))) + \kappa(a_i) - \kappa(b_i) \\ &\geq (1 - (n-2)\xi (p - a_i)) ( \kappa(a_i) - \kappa(b_i) ) \\ &\geq \frac{\kappa(a_i) - \kappa(b_i)}{2} \\ &> 0 \end{align} which is a contradiction, completing the proof. \end{proof} We can now prove Lemma \ref{lem:first_tangent}. To begin, assume that $\gamma$ is not a centered circle - if it is, then we are done. In particular, Proposition \ref{prop:structure} and Lemma \ref{lem:lower_curve_properties} are true. Also, we will use the fact that $\eta \in L$ from Lemma \ref{lem:lower_curve_eta}. In particular, $\eta \in (0, \beta)$, $\kappa(\eta) > 0$, and $\gamma$ is smooth at $\eta$. Thus, if $\gamma'(\eta) = (0,-1)$, then we will be done. This is exactly what we will prove. We will break the rest of the proof into two cases based on whether $\gamma(\delta) \in B_{\mathcal{R}(f)}$. We first consider the case when $\gamma(\delta) \not \in B_{\mathcal{R}(f)}$: \begin{proof}[Proof of First Tangent Lemma - First Case] In this case, by Lemma \ref{lem:outside_ball}, we have that $\kappa'(\delta) > 0$. This combined with the fact that $\kappa(\delta) > 0$ means that $\eta > \delta$. Now let us assume that $\gamma'(\eta) \neq (0,-1)$. By Lemma \ref{lem:lower_curve_properties} along with the fact that $F(\bar{\eta}) \leq F(\delta)$ from Proposition \ref{prop:structure}, we have that the vectors $\gamma'(\eta)$ and $\gamma'(\bar{\eta})$ are admissible with respect to the points $\gamma(\eta)$ and $\gamma(\bar{\eta})$, as per Definition \ref{defn:admissible}. We can now use Proposition \ref{prop:normal_computation} to conclude that $\kappa(\eta) > \kappa(\bar{\eta})$, since $\gamma( \bar{\eta}) \not \in B_{\mathcal{R}(f)}$, $\gamma_1(\delta) > 0$, and $\gamma_1(\delta) - \gamma_1(\eta) \leq \gamma_1(\bar{\eta}) - \gamma_1(\delta)$. Combined with the fact that $\kappa(\eta) > 0$, this means that there is some $\epsilon > 0$ such that $[\eta, \eta + \epsilon] \subset L$, contradicting the definition of $\eta$. Hence, $\gamma'(\eta) = (0,-1)$. \end{proof} We now turn to the case when $\gamma(\delta) \in B_{\mathcal{R}(f)}$: \begin{proof}[Proof of First Tangent Lemma - Second Case] We first reduce the problem to the case where $\kappa(\delta) = \kappa(C_\delta)$. If this is not the case, then $\kappa(\delta) > \kappa(C_\delta)$. Since $\gamma(\delta) \in B_{\mathcal{R}(f)}$, $\gamma(x) \in B_{\mathcal{R}(f)}$ for $x \in [\delta, \beta)$. Let $\mathcal{S}$ be the set of all points $x$ such that, for $y \in [\delta,x]$, $\gamma'(y)$ is in the third quadrant, and $$ \kappa(y) > \kappa(C_y) > 0.$$ Consider $\alpha = \sup \mathcal{S}$. We claim that, for all $x \in [\delta, \alpha)$, $$ \kappa(x) > \kappa(\delta) \geq \kappa(C_x) \geq 0.$$ To accomplish this, we use Lemma \ref{lem:inside_ball}. This lemma says that $\kappa' \geq 0$ and $\lambda' \leq 0$ on $[\delta, \alpha)$. In particular, $\kappa(x) > \kappa(C_\delta)$ for all $x \in [\delta, \alpha)$. We then have that $\alpha < \beta$ by comparing $\gamma$ on $[\delta, \alpha)$ to the portion of $C_\delta$ from $\delta$ to $\beta$ using Proposition \ref{prop:curvature_comparison}. In other words, $\gamma$ curves faster that $C_\delta$ on $[\delta, \alpha)$, and so $\alpha < \beta$. Furthermore, we have that $\gamma'(\alpha) = (0,-1)$. If this were not the case, then $\gamma'(\alpha)$ would be in the third quadrant, and because $\kappa' \geq 0$ and $\lambda' \leq 0$ on $[\delta, \alpha)$, $$ \kappa(\alpha) \geq \kappa(\delta) > \kappa(C_\delta) \geq \kappa(C_\alpha) > 0.$$ Hence, $\kappa'(\alpha) \geq 0$ and $\lambda'(\alpha) \leq 0$, and so $\alpha \neq \sup \mathcal{S}$, a contradiction. Thus, $\alpha$ satisfies the conclusions of Lemma \ref{lem:first_tangent}. The last case that we must deal with is when $\gamma(\delta) \in B_{\mathcal{R}(f)}$, and $\kappa(\delta) = \kappa(C_\delta)$. In this case, the two curves and their tangents agree at $\delta$. By applying standard theorems concerning the uniqueness of solutions from the theory of ODEs to the ODE $H_f = c$, we see that $\gamma$ must be equal to $C_\delta$ on $\gamma \cap B_{\mathcal{R}(f)}$, since both are arclength parametrizations. Since we assumed that a portion of $\gamma$ lies outside $B_{\mathcal{R}(f)}$, there must exist a point $y$ on the upper curve such that $y \in \partial B_{\mathcal{R}(f)}$. Additionally, $\gamma'(y)$ is not in the tangent space of $\partial B_{\mathcal{R}(f)}$, since by Lemma \ref{lem:C_x_equality}, we would have that $\gamma = B_{\mathcal{R}(f)}$, and so $\gamma$ would be a centered circle, which is assumed to not be the case. Hence, $\gamma = C_\delta$ on $[y, \beta]$, and $\gamma$ lies outside $B_{\mathcal{R}(f)}$ on $[0, y)$. Since $\kappa(C_y) = \kappa(y)$, Lemma \ref{lem:boundary_points} implies that there is some $\omega > 0$ such that $y > \omega$ and $\kappa \leq \kappa(C_\delta)$ on $[y - \omega, y]$. Consider the lower curve, which ends at $\eta < \beta$. We first observe that $\bar{\eta} \leq y - \omega$, since $\kappa(x) = \kappa(C_\delta)$ for all $x \in [\delta, \eta]$, and so the definition of $\omega$ implies that, if $\bar{\eta} \geq y - \omega$, then $\eta$ cannot be the endpoint of the Lower Curve (since, in this case, the lower curve can be extended past $\eta$). We now play the same game as in the first part of this proof. If $\gamma'(\eta) \neq (0,-1)$, then we can use Proposition \ref{prop:normal_computation} along with Lemma \ref{lem:lower_curve_properties} and Proposition \ref{prop:structure} to show that $\kappa(\eta) > \kappa(\bar{\eta})$, which allows us to conclude that $\eta$ is not actually the endpoint of the lower curve, yielding a contradiction. \end{proof} \section{Proof of Second Tangent Lemma} In this section, we will prove Lemma \ref{lem:second_tangent}. If there exists a point $x \in [0, \beta)$ with $\gamma'(x) = (0,-1)$ and $\kappa(x) > 0$, then there exists a point $y \in (0, \beta)$ with $\gamma'(y) = (0,1)$. Our main tool will be Lemma \ref{lem:gamma_behavior_beta}; we will show that, if such a point $y$ does not exist, then we obtain a contradiction to this lemma. The following proposition will constitute the bulk of the work in this section; it investigates the possible behavior of $\gamma$ as $x \rightarrow \beta^-$. Again, $\theta$ denotes the counterclockwise angle of a unit vector, yielding values in the interval $[0, 2 \pi)$. \begin{prop} \label{prop:continuity_tangent} Let $P$ be a point in $(0, \beta)$ with $\gamma'(P) = (0,-1)$, and $\kappa(P) > 0$. Then either there exists $\nu \in (P,\beta)$ such that $\gamma'(\nu) = (0,1)$, or the following facts are true: \begin{enumerate} \item For each $x \in [P, \beta)$, $\kappa(x) > 0$. \item For each $x \in (P, \beta)$, $\gamma'(x)$ strictly lies in the fourth quadrant. \item $\lim_{x \rightarrow \beta^-} \gamma'(x)$ exists, lies in the fourth quadrant, and is not $(0,-1)$. \end{enumerate} \end{prop} \begin{proof} Consider $\mathcal{S}$, defined as the set of all points $x \in [P, \beta)$ such that, for all $y \in [P, x]$, $\gamma'(y)$ lies in the first or fourth quadrant. Let $\Omega = \sup \mathcal{S}$, and let us consider whether $\Omega = \beta$. If $\Omega \neq \beta$, then we shall show that we may chose $\nu = \Omega$, that is, $\gamma'(\Omega) = (0, 1)$ and $\Omega \in (P, \beta)$. We first observe that, since $P \in (0,\beta)$ and $\kappa(P) > 0$, $\Omega > P$. Since $\Omega \neq \beta$, we have that $\Omega \in (P, \beta)$. Assume that $\gamma'(\Omega) \neq (0,1)$. We then see that the curvature of $C_\Omega$ is less than or equal to 0, and since $C$ is mean-convex at all regular points (Theorem \ref{thm:regularity}), the fact that $\Omega$ is a regular point implies that $\kappa(\Omega) > 0$. There is then some $\epsilon > 0$ such that, for $x \in [\Omega, \Omega + \epsilon]$, $x \in \mathcal{S}$. This contradicts the definition of $\Omega$, and so $\gamma'(\Omega) = (0,1)$, as desired. Thus, if $\Omega \neq \beta$, then we are in the first situation. If $\Omega = \beta$, we shall show that all of the properties listed above hold true: \begin{enumerate} \item This is a result of the fact that $\gamma$ is mean-curvature convex at every regular point, and the curvature of $C_x$ is not positive for all $x \in [P, \beta)$. \item This is a result of the fact that $\kappa > 0$ on $(P, \beta)$. If there was a point $x \in (P,\beta)$ with $\gamma'(x)$ not strictly in the fourth quadrant, then this positive curvature property means that the derivatives at all points $y \in [x,\beta)$ are in the first quadrant, by the definition of $\mathcal{S}$ and the assumption that $\Omega = \beta$. Hence, $\lim_{r \rightarrow \beta^-} \gamma_2(r) \geq \gamma_2(x) > 0$, which is impossible. \item As a consequence of the fact that $\gamma'(x)$ lies strictly in the fourth quadrant for all $x \in (P,\beta)$, and $\kappa(x) > 0$ for all such values, $\theta(\gamma'(x))$ is a bounded, increasing function on $[P, \beta)$, and so it has a limit in $[\frac{3 \pi}{2}, 2 \pi]$. Since the angle is strictly increasing, the limit cannot be $\frac{3 \pi}{2}$, and so $\lim_{x \rightarrow \beta^-} \gamma'(x)$ lies in the fourth quadrant and is not $(0,-1)$. \end{enumerate} \end{proof} We now prove the Second Tangent Lemma: \begin{proof}[Proof of Second Tangent Lemma] Let $P \in (0,\beta)$ be the given point with $\gamma'(P) = (0,-1)$ and $\kappa(x) > 0$. Assume that there does not exist a point $y \in (0, \beta)$ such that $\gamma'(y) = (0,1)$. By Proposition \ref{prop:continuity_tangent}, this implies that $\lim_{x \rightarrow \beta^-} \gamma'(x)$ exists, lies in the fourth quadrant, and is not $(0,-1)$. If we let $\nu = (\nu_1, \nu_2) = \lim_{x \rightarrow \beta^-} \gamma'(x)$, then this implies that $\nu_1 > 0$. This contradicts Lemma \ref{lem:gamma_behavior_beta}, completing the proof. \end{proof} \section{Appendix: Computations} In this section, we fill in some computational gaps in the proofs of some of the lemmas in Section 2. We begin by proving the computational details used in the proof of Lemmas \ref{lem:curvature_bound} and \ref{lem:boundary_points}: \begin{lem} \label{lem:curvature_bound_details} Consider a circle of radius $r > 0$ centered at point $(a,b)$ with $a \geq 0$ and $b \geq 0$. Give this curve a counterclockwise orientation, and parametrize it by arclength using $$ \alpha(x) = (a + r \cos(\frac{x}{r}), b + r \sin(\frac{x}{r})), $$ where $x \in [0, 2 \pi r)$. For any $x \in [0, \frac{\pi r}{2}]$, if $a \sin(\frac{x}{r}) \geq b \cos(\frac{x}{r})$, then $$ H_1'(x) \leq 0.$$ Furthermore, if $\alpha(x) \not \in B_{\mathcal{R}(f)}$ and $a \sin(\frac{x}{r}) > b \cos(\frac{x}{r})$, then $$ H_1'(x) < 0.$$ In particular, if $b = 0$, then the above statements simplify to the following: for any $x \in [0, \frac{\pi r}{2}]$, $$H_1'(x) \leq 0,$$ and if $x \in (0, \frac{\pi r}{2}]$, $\alpha(x) \not \in B_{\mathcal{R}(f)}$, and $a > 0$, then $$H_1'(x) < 0.$$ \end{lem} \begin{proof} For any $x \in [0, \frac{\pi r}{2}]$, we have that $\gamma(x) \neq (0,0)$. As such, $$ H_1(x) = g'( \| \alpha(x) \| ) ( N(x) \cdot n(x) ).$$ Computing, we have that \begin{align} (g'( \| \alpha \| ) N \cdot n )'(x) &= g''( \| \alpha(x) \| ) (\alpha'(x) \cdot \frac{\alpha(x)}{\| \alpha(x) \|}) ( N(x) \cdot n(x) ) + \\ & g'( \| \alpha(x) \|) ( N'(x) \cdot n(x) ) + g'( \| \alpha(x) \|) ( N(x) \cdot n'(x) ). \end{align} We next compute $\alpha'(x) \cdot \alpha(x)$: \begin{align} \alpha'(x) \cdot \alpha(x) &= (- \sin(\frac{x}{r}), \cos(\frac{x}{r})) \cdot (a + r \cos(\frac{x}{r}),b + r \sin(\frac{x}{r})) \\ &= - a \sin(\frac{x}{r}) + b \cos(\frac{x}{r}) \end{align} Since we assumed that $a \sin(\frac{x}{r}) \geq b \cos(\frac{x}{r})$, $\alpha'(x) \cdot \alpha(x) \leq 0$. We also know that, due to the convexity of $g$, $g''(\| \alpha(x) \|) \geq 0$. Furthermore, since $\alpha'(x)$ is in the second quadrant and $b \geq 0$, we have that $n(x)$ and $N(x)$ are both in the first quadrant. As such, $N(x) \cdot n(x) \geq 0$, and so the first term in this expression is less than or equal to $0$. We also know that $g'(\| \alpha(x)\|)$ is non-negative, and is positive if $\alpha(x) \not \in B_{\mathcal{R}(f)}$. Thus, what remains is to show that $$N'(x) \cdot n(x) + N(x) \cdot n'(x) \leq 0$$ with strict inequality if the conditions in the statement of the lemma are met. To this end, we have that \begin{align} N(x) &= \frac{(a + r \cos(\frac{x}{r}), b + r \sin(\frac{x}{r}))}{\sqrt{(a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2}} \\ N'(x) &= \frac{(- \sin(\frac{x}{r}), \cos(\frac{x}{r}))}{\sqrt{(a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2}} + \\ & (a + r \cos(\frac{x}{r}), b + r \sin(\frac{x}{r}))\frac{ a \sin(\frac{x}{r}) - b \cos(\frac{x}{r}) } { ((a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2)^\frac{3}{2}} \\ n(x) &= (\cos(\frac{x}{r}), \sin(\frac{x}{r})) \\ n'(x) &= \frac{( - \sin(\frac{x}{r}), \cos(\frac{x}{r}))}{r} \\ \end{align} As such, we have that \begin{align} N(x) \cdot n'(x) + N'(x) \cdot n(x) &= \frac{- a \sin( \frac{x}{r}) + b \cos( \frac{x}{r})} {r \sqrt{(a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2}} + \\ & (r + a \cos(\frac{x}{r}) + b \sin(\frac{x}{r})) \cdot \\ & \frac{ a \sin(\frac{x}{r}) - b \cos(\frac{x}{r}) } { (\sqrt{(a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2})^{\frac{3}{2}}} \end{align} This simplifies to \begin{align} N(x) \cdot n'(x) + N'(x) \cdot n(x) &= (((a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2) \cdot \\ &(- a \sin( \frac{x}{r}) + b \cos( \frac{x}{r})) + r (r + a \cos(\frac{x}{r}) + \\ & b \sin(\frac{x}{r})) (a \sin(\frac{x}{r}) - b \cos(\frac{x}{r}))) \cdot \\ & \frac{1}{r ((a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2)^\frac{3}{2}} \\ &= (-r (r + a \cos(\frac{x}{r}) \\ & - b \sin(\frac{x}{r})) + ((a + r \cos(\frac{x}{r}))^2 + (b + \\ & r \sin(\frac{x}{r}))^2)) \cdot \\ & \frac{-a \sin(\frac{x}{r}) + b \cos(\frac{x}{r})}{r ((a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2)^\frac{3}{2}} \\ \end{align} Rearranging this, we have that \begin{align} N(x) \cdot n'(x) + N'(x) \cdot n(x) &= (ar \cos(\frac{x}{r}) + \\ & 3 b r \sin(\frac{x}{r}) + a^2 + b^2) \cdot \\ & \frac{-a \sin(\frac{x}{r}) + b \cos(\frac{x}{r})}{r ((a + r \cos(\frac{x}{r}))^2 + (b + r \sin(\frac{x}{r}))^2)^\frac{3}{2}} \\ \end{align} Since $x \in [0, \frac{\pi r}{2}]$, $\sin(\frac{x}{r})$ and $\cos(\frac{x}{r})$ are both non-negative. Since $a, b \geq 0$, we thus have that all factors in the above expression are non-negative, except for possibly $$ -a \sin(\frac{x}{r}) + b \cos(\frac{x}{r}).$$ Since $a \sin(\frac{x}{r}) \geq b \cos(\frac{x}{r})$, then this term is non-positive, and since $g'(\| \alpha(x) \|)$ is also non-negative, $$H_1'(x) \leq 0.$$ If $\alpha(x) \not \in B_{\mathcal{R}(f)}$, then $g'( \| \alpha(x) \|) > 0$. If, in addition, $a \sin(\frac{x}{r}) > b \cos(\frac{x}{r})$, then $-a \sin(\frac{x}{r}) + b \cos(\frac{x}{r}) < 0$. Additionally, $a > 0$, and so $$a r \cos(\frac{x}{r}) + 3 b r \sin(\frac{x}{r}) + a^2 + b^2 > 0.$$ Hence, $$ H_1'(x) < 0.$$ This completes the proof. \end{proof} A remark is in order with regard to the conditions $a \sin(\frac{x}{r}) \geq b \cos(\frac{x}{r})$ and $a \sin(\frac{x}{r}) > b \cos(\frac{x}{r})$. Let $y \in [0, \beta)$, and suppose that $\kappa(y) > 0$. Consider $A_y$, the unique circle which approximates $\gamma$ up to the third order at $\gamma(y)$. $A_y$ can be parametrized by $\alpha(x) = ( a + r \cos(\frac{x}{r}), b + r \sin(\frac{x}{r}))$, where $(a,b)$ is the center of $A_y$ and $r > 0$ is its radius. If $\alpha(x) = \gamma(y)$, then due to Lemma \ref{lem:tangent_restriction}, $$ (a + r \cos(\frac{x}{r}), b + r \sin(\frac{x}{r})) \cdot (-\sin(\frac{x}{r}), \cos(\frac{x}{r})) \leq 0, $$ and so $$ b \cos(\frac{x}{r}) \leq a \sin(\frac{x}{r}). $$ Hence, for each circle formed in this way, we automatically have one of the conditions of the theorem. We use additional information about $C_y$ and $\kappa(y)$ to obtain the other conditions. In the applications of the form of this lemma where we require that $b \cos(\frac{x}{r}) < a \sin(\frac{x}{r})$, we also use information about $C_y$ and $\kappa(y)$ to conclude that the above inner product has a strict inequality. Next, we compute the details used in the proof of Lemma \ref{lem:second_derivative_kappa}: \begin{lem} \label{lem:second_derivative_kappa_details} Consider a circle $\mathcal{C}$ with radius $r > 0$ and center $(a,0)$ with $a > 0$. Give this curve a counterclockwise orientation, and parametrize it by arclength using $$\alpha(x) = (a + r \cos(\frac{x}{r}), r \sin(\frac{x}{r})),$$ where $x \in [- \pi r, \pi r)$. If the point $(a + r , 0)$ is not in $B_{\mathcal{R}(f)}$, we then have that $H_1''(0) < 0$. \end{lem} \begin{proof} Since $r > 0$, we have that $\alpha(x) \neq (0,0)$ for every $x \in (-\pi r, \pi r)$, and so $$H_1(x) = (g'( \| \alpha \| ) (N \cdot n)) (x).$$ Hence, $$H_1''(0) = (g'( \| \alpha \| ) ( N \cdot n ))''(0).$$ Computing, we have that \begin{align} (g'( \| \alpha \| ) ( N \cdot n ) )''(0) &= (g''( \| \alpha \| ) (\alpha' \cdot \frac{\alpha}{\| \alpha \|}) ( N \cdot n))'(0) + \\ & (g'( \| \alpha \|) (N' \cdot n))'(0) + (g'( \| \alpha \|) ( N \cdot n' ))'(0). \end{align} Computing the first term, we have that \begin{align} (g''( \| \alpha \| ) (\alpha' \cdot \frac{\alpha}{\|\alpha\|})( N \cdot n))'(0) &= g'''( \| \alpha(0) \| ) (\alpha'(0) \cdot \frac{\alpha(0)}{\| \alpha(0) \|})^2 (N(0) \cdot n(0)) \\ & + g''( \| \alpha(0) \| ) ((\alpha' \cdot (\frac{\alpha}{\| \alpha \|}))'(0)) (N(0) \cdot n(0)) \\ & + g''( \| \alpha(0) \| ) (\alpha'(0) \cdot \frac{\alpha(0)}{\| \alpha(0) \|}) ((N \cdot n)'(0)) \end{align} Since $\alpha'(0) \cdot \alpha(0) = 0$, we have that the first and third term are $0$. Using the fact that $\alpha'(0) \cdot \alpha(0) = 0$, the second term becomes \begin{align} g''( \| \alpha(0) \| ) (N(0) \cdot n(0)) ( \alpha''(0) \cdot \frac{\alpha(0)}{\| \alpha(0) \|} & \\ + \alpha'(0) \cdot (\frac{\alpha'(0)}{\| \alpha(0) \|} - \frac{\alpha(0)}{\| \alpha(0) \|^3} (\alpha'(0) \cdot \alpha(0)))) &= \frac{g''( \| \alpha(0) \| ) (N(0) \cdot n(0))}{\| \alpha(0) \|} \cdot \\ & ( \alpha''(0) \cdot \alpha(0) + \alpha'(0) \cdot \alpha'(0)) \end{align} We see that $$ \alpha'(x) = (-\sin(\frac{x}{r}), \cos(\frac{x}{r})),$$ and so $$ \alpha''(x) = (-\frac{\cos(\frac{x}{r})}{r}, -\frac{\sin(\frac{x}{r})}{r}).$$ As such, we then have that the above expression becomes $$\frac{g''( \| \alpha(0) \| ) (N(0) \cdot n(0))}{\| \alpha(0) \|} (-\frac{a}{r} -1 + 1) \leq 0.$$ Let us now consider the other terms. They are \begin{align} (g'( \| \alpha \|) (N' \cdot n))'(0) + (g'( \| \alpha \|) (N \cdot n'))'(0) &= g''( \| \alpha(0) \| ) (\alpha'(0) \cdot \frac{\alpha(0)}{\| \alpha(0) \|}) \\ & (N'(0) \cdot n(0)) + g''( \| \alpha(0) \| ) \cdot \\ & (\alpha'(0) \cdot \frac{\alpha(0)}{\| \alpha(0) \|}) (N(0) \cdot n'(0)) + \\ & (g'( \| \alpha(0) \|) (N' \cdot n + N \cdot n')'(0) \end{align} The first two terms are zero because $\alpha'(0) \cdot \alpha(0) = 0$. Since $\alpha(0) = (a + r, 0) \not \in B_{\mathcal{R}(f)}$, we have that $g'( \| \alpha(0) \| ) > 0$. Hence, we must show that $(N' \cdot n + N \cdot n')'(0) < 0$. Since the center of $\mathcal{C}$ is $(a,0)$ with $a > 0$, we can use the method of computation used in the proof of Lemma \ref{lem:curvature_bound_details} to tell us that $$N'(x) \cdot n(x) + N(x) \cdot n'(x) = \frac{(-a \sin(\frac{x}{r}))(ar \cos(\frac{x}{r}) + a^2)}{r (a^2 + 2ar \cos(\frac{x}{r}) + r^2)^\frac{3}{2}} $$ We can now compute $(N' \cdot n + N \cdot n' )'(x)$: \begin{align} (N' \cdot n + N \cdot n' )'(x) &= \frac{a^2 \sin^2(\frac{x}{r}) - a^2 \cos^2(\frac{x}{r}) - \frac{a^3}{r}\cos(\frac{x}{r})}{r (a^2 + 2ar \cos(\frac{x}{r}) + r^2)^\frac{3}{2}} \\ & + (-a \sin(\frac{x}{r}))(ar \cos(\frac{x}{r}) + a^2) \cdot \\ & \frac{3a \sin(\frac{x}{r})}{r (a^2 + 2ar \cos(\frac{x}{r}) + r^2)^\frac{5}{2}} \end{align} At $x = 0$, this just becomes $$ - \frac{a^2 + \frac{a^3}{r}}{r (a + r)^3}$$ which is strictly less than $0$ because $r, a > 0$. This completes the proof. \end{proof} Lastly, we give the computational details used in the proof of Lemmas \ref{lem:inside_ball} and \ref*{lem:F_and_R}: \begin{lem} \label{lem:inside_ball_details} Let $\mathcal{C}$ be a circle with center $(a,b)$, $b \geq 0$, and radius $r > 0$. Give $\mathcal{C}$ a counterclockwise orientation, and parametrize it by arclength using $$ \alpha(x) = (a + r \cos(\frac{x}{r}), b + r \sin(\frac{x}{r})),$$ where $x \in [0, 2 \pi r)$. Furthermore, let $\lambda(x)$ be defined in the same way as before: $\lambda(x) = \kappa(C_x)$, where $C_x$ is the canonical circle at $x$. Here, $C_x$ is defined in the usual way if $\alpha_2(x) \neq 0$. If $\alpha_2(x) = 0$ and $\alpha'(x) = (0, \pm 1)$, then we define $C_x$ as $\mathcal{C}$. If $\alpha_2(x) = 0$ and $\alpha'(x) \neq (0, \pm 1),$ then $C_x$ is not defined. Additionally, let us define $F(x)$ as the $e_1$ coordinate of the center of $C_x$, also as before. We then have that $\lambda$ and $\kappa$ both exist and are smooth on $(0, \pi r)$. Furthermore, on $[\frac{\pi r}{2}, r \pi)$, $\lambda'(x) \leq 0$, and on $(0, \frac{\pi r}{2}]$, $F'(x) \geq 0$. \end{lem} \begin{proof} Fix $x \in (0, \pi r)$; we will produce expressions for $\lambda(x)$ and for $F(x)$. Since $b \geq 0$, $\alpha_2(x) > 0$, and so we know that the line from $\alpha(x)$ through the center of $C_x$ is not parallel to the $e_1$ axis. Hence, we can determine $F(x)$ by computing the point of intersection between these two lines, and we can determine $\lambda(x)$ by computing the length of the line segment connecting $\alpha(x)$ to the center of $C_x$. At $\alpha(x)$, the tangent vector to $C_x$ is $(- \sin(\frac{x}{r}), \cos(\frac{x}{r}))$, and so the unit inward normal is $(-\cos(\frac{x}{r}), -\sin(\frac{x}{r}))$. Let $r'$ be the radius of $C_x$. As a result of the above discussion, we have that $$ b + r \sin(\frac{x}{r}) - r' \sin(\frac{x}{r}) = 0,$$ and so $$ r' = \frac{r \sin(\frac{x}{r}) + b}{\sin(\frac{x}{r})}.$$ As such, $$ \lambda(x) = \frac{\sin(\frac{x}{r})}{r \sin(\frac{x}{r}) + b}. $$ In addition, we clearly have that $$ F(x) = a + r \cos(\frac{x}{r}) - r' \cos(\frac{x}{r}),$$ which becomes $$ F(x) = a - b \frac{\cos(\frac{x}{r})}{\sin(\frac{x}{r})}.$$ Using these expressions, we see that $F$ and $\lambda$ are both smooth on $(0, \pi r)$. Differentiating $\lambda$, we obtain $$ \lambda'(x) = \frac{b \cos(\frac{x}{r})}{r(r \sin(\frac{x}{r}) + b)^2},$$ which is less than or equal to $0$ on $[\frac{\pi r}{2}, \pi r)$. Differentiating $F(x)$, we obtain that $$ F'(x) = \frac{b}{r} \frac{1}{\sin^2(\frac{x}{r})},$$ which is greater than or equal to $0$ on $(0, \frac{\pi r}{2}]$. \end{proof} \bibliographystyle{amsplain}	{ "redpajama_set_name": "RedPajamaArXiv" }	311
Alaska Airlines adds two new routes from Southern California Alaska Airlines announced two new routes from Southern California that will begin flying this spring. The airline will launch daily, nonstop service between LAX and AUS on March 18, with an increase to three daily departures on May 20. Daily, nonstop service between SAN and JFK starts on April 4. SEATTLE, Jan. 7, 2021 /PRNewswire/ — Alaska Airlines announced today two new routes from its key hubs in Southern California that will begin flying this spring. The airline will launch daily, nonstop service between Los Angeles (LAX) and Austin on March 18, with an increase to three daily departures on May 20. Daily, nonstop service between San Diego and New York JFK starts on April 4. "Southern California is an integral part of Alaska's network and continues to offer valuable opportunities for selective expansion," said Brett Catlin, Alaska Airlines vice president of network and alliances. "These two new routes enhance our guest proposition in Southern California while providing valuable connectivity to our global partners as we join oneworld on March 31." City Pair Los Angeles – Austin 3x Daily San Diego – New York JFK In 2020, Alaska added 12 new routes from LAX. With the new flight to Austin, the airline will fly to more than 40 nonstop destinations from LAX this spring. Alaska already has nonstop flights to the Texas capital city from five other West Coast cities: Seattle; Portland, Oregon; San Francisco; San Jose, California; and San Diego. The new nonstop service between San Diego and New York JFK is part of Alaska's growth to the Northeast from its West Coast hubs. This spring, the airline will also have nonstop service between San Diego and both Newark and Boston. Alaska has implemented more than 100 measures to enhance the safety of its employees and guests, part of the airline's Next-Level Care, with enhanced cleanings, mandatory masks for everyone, touch-free technology, and sophisticated air filtration systems. Onboard HEPA filters remove 99.9% of particulate contaminants and viruses from the air, which means there's a full exchange of air every two to three minutes. Tickets for all flights are now available for purchase at alaskaair.com. About Alaska Airlines Alaska Airlines and its regional partners serve more than 115 destinations across the United States and North America. The airline provides essential air service for our guests along with moving crucial cargo shipments, while emphasizing Next-Level Care. Alaska is known for low fares, award-winning customer service and sustainability efforts. Guests can earn and redeem miles on flights to more than 800 destinations worldwide with Alaska and its Global Partners. On March 31, 2021, Alaska will officially become a member of the oneworld global alliance. Learn more about Alaska at newsroom.alaskaair.com and blog.alaskaair.com. Alaska Airlines and Horizon Air are subsidiaries of Alaska Air Group (NYSE: ALK).	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	4,453
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Through intense and rigorous re-imagining and recreations of texts via close collaboration between its members, The Group is reinventing theatre. Beginning Again - Rolex Mentor Protégé Masanori Handa, a young visual artist from Japan, explores human experience via his own sensations, imagination and memory – a process that he calls "surfing the world" – creating a series of original works that defy categorization and dazzle, rather than scandalize, the viewer. In the Rolex Arts Initiative, he found an ideal mentor in revered German artist Rebecca Horn, a pioneer in the art of turning experience inside out. Shared uncertainty - Rolex Mentor Protégé One of the world's most accomplished directors across an extraordinary range of theatre, encompassing serious drama, musicals, opera and Shakespeare on film, Julie Taymor had no inhibitions about sharing with young British director Selina Cartmell the mechanics and the headaches behind creating a new opera, Grendel. Cartmell's own rich theatrical vision, crossing disciplines and taking inspiration from today's most daring directors, Taymor included, meant that these two theatre-makers had a wealth of ideas and experience to share with each other. New Horizons - Rolex Mentor Protégé Embarking on the second cycle of the Rolex Mentor Protégé Arts Initiative, Sir Peter Hall had a logical, coherent plan. His agenda for the year included several of his specialties: among them Shakespeare (<i>As You Like It</i>, for the first time in his career), Harold Pinter (a revival of <i>Betrayal</i>, of which he directed the premiere in 1978), and opera (<i>La Cenerentola</i>, the Rossini version of <i>Cinderella</i>). Artists in wonderland - Rolex Mentor Protégé Year after year, Anish Kapoor, one of the world's most famous living artists, astonishes the international arts community with his gigantic, enigmatic creations that fill the biggest exhibition spaces in the world's best-known galleries. Nicholas Hlobo, a young artist from Johannesburg whose output is closely watched by collectors longing to buy, weaves together rubber, leather and fabric to produce intimate objets and performances that evoke an enticing but provocative beauty. The master and the iconoclast - Rolex Mentor Protégé The late Patrice Chéreau was interested in watching Michał Borczuch forge his own path, letting their numerous encounters of the mentoring year develop naturally into a conversation that thrived on their differences. Robert Lepage & Matías Umpierrez - Rolex Mentor and Protégé Artistic soulmates who refuse to be typecast, Robert Lepage and his protégé Matías Umpierrez borrow from various disciplines to furnish their eclectic, maverick productions. The selection - Rolex Mentor Protégé One of today's most respected violinists, Pinchas Zukerman, has a special love for the viola. In choosing as his protégé the highly gifted string player David Carpenter, Zukerman has found someone who can benefit, as he has, from the rich interchange between the two instruments. Landscapes of light - Rolex Mentor Protégé Throughout the mentoring year young Mexican lighting designer Sebastián Solórzano Rodríguez sat alongside Jennifer Tipton, one of the world's greatest exponents of the art of lighting, as she lit up rehearsals and performances in London, Barcelona, Paris, New York, Houston and Madrid. Rodríguez also invited his mentor to Mexico City, his home town. They had a concrete plan of action at the beginning of the mentoring year, the results of which, Rodríguez later said, were that his life "has changed forever." Meetings - Rolex Mentor Protégé "I thought that Federico was in some ways the least likely of them (possible protégés). First I said to myself: 'No.' Then I thought that with him I'd be taking the biggest risk. It's exciting when you really don't know yet what will develop." The Nurturer and the Hunter - Rolex Mentor Protégé Brian Eno, who became famous in the 1970s as part of the glam-rock band, Roxy Music, has never stopped finding new ways to be creative, using all the media that today's fast-developing technology can provide. Partnership - Rolex Mentor Protégé For both Jessye Norman and her Rolex protégée Susan Platts, singing is an exploration of the words: what they meant to the composer setting them to music, what the fusion of literature and music has manifested and whether the opera stage is the ideal place to sing them. A stranger at home - Rolex Mentor Protégé The discovery of a world of music totally new to him intrigued the well-known Senegalese musician, Youssou N'Dour, when he chose his protégé Aurelio Martínez, a Garifuna from Honduras. Beyond his desire to succeed, it was Caballé-Domenech's passion for music that caught Sir Colin's eye. "He's pretty wild. One should be wild when one is young." "At one stage, I thought of putting my manuscript on hold and beginning something entirely different. Toni shook her head: 'No, no.'" Protégée Julia Leigh, speaking about the encouragement she received from Toni Morrison. Encounters on the digital frontier - Rolex Mentor Protégé A shared interest in history, technology and religion created an immediate rapport between mentor Margaret Atwood and her protégée Naomi Alderman. Literary relationship - Rolex Mentor Protégé Antonio García Ángel thought Mario Vargas Llosa was going to help him write a new novel. In fact, Llosa showed him a whole new way of working. Travellers - Rolex Mentor Protégé A young mother, beginning her career as a novelist in Australia, and a renowned Nigerian author, often in demand internationally for his opinions and insights, are worlds apart in terms of geography, culture and experience. A harmony of musical souls In encounters in cities from Los Angeles to Helsinki, the mentorship of Finland's Kaija Saariaho and Portugal's Vasco Mendonça unfolded smoothly, establishing a joyful professional friendship that was both dynamic and highly productive. Maps for a writer's journey - Rolex Mentor Protégé With much in common – they have both changed countries and cultures, and have careers as both teachers and writers – Canadian Michael Ondaatje and United States-based Bulgarian Miroslav Penkov quickly developed a strong literary friendship, exchanging messages and travelling to Bulgaria together. A meeting of minds - Rolex Mentor Protégé What could a polymath patrician of German intellectual life have in common with a young, African-American poet? A lot more than you would think, but the singular truth is that it is their differences that seem to make the mentorship flourish. Mia Couto & Julián Fuks - Rolex Mentor and Protégé A shared sense of inherited exile is one affinity between Mia Couto and his protégé Julián Fuks, who wants help to venture from family history into invented worlds. Breaking ground - Rolex Mentor Protégé A year of mentoring - Rolex Mentor Protégé During the year of mentoring, Méndez shot his feature film <I>Dioses</I> with the guidance of Stephen Frears. While they initially met in Lima, the real discussions between mentor and protégé began on a trip to the long-lost, mountain-top, Inca city of Machu Picchu – an hour by plane plus four hours by bus from the capital. Shared lenses - Rolex Mentor Protégé On a mellow summer afternoon, Celina Murga sits under a vast, old tree on the grounds of a derelict 19th-century insane asylum outside Medfield, Massachusetts. Alchemy in the editing room - Rolex Mentor Protégé The mentoring year allowed Sara Fgaier, who teaches film editing, to observe and work with Walter Murch as he made the final edits of a new documentary, Particle Fever. The art and heart of making films - Rolex Mentor Protégé The spectacular, exquisitely coloured scenes and riveting storylines created by Zhang Yimou in some of contemporary cinema's most iconic works, including Raise the Red Lantern, To Live and Hero, have won the Chinese director an unparalleled global audience, going far beyond the normal fan base for "foreign films". On location - Rolex Mentor Protégé Signing on for the Rolex Mentor and Protégé Arts Initiative, Mira Nair let it be known just what sort of young partner she wanted: "Find me a girl from Karballah!" Yet Nair chose a boy, or rather, a young man, from Thailand: Aditya Assarat, 33. Like a Hollywood script - Rolex Mentor Protégé In a highly eventful mentoring year, protégé Tom Shoval was invited to watch post-production work on Alejandro G. Iñárritu's masterpiece, <i>Birdman</i>, and was present when his mentor received three Academy Awards for his film at the 2015 Oscars. Alone among the senior partners of the Rolex Mentor and Protégé Arts Initiative, Forsythe proposed a steady collaboration throughout the mentoring year. Pilgrimage for body and soul - Rolex Mentor Protégé Eduardo Fukushima moved to Taiwan for the mentoring year in order to observe how Lin Hwai-min's company, the Cloud Gate Dance Theatre, works at home and on tour. Merging differences - Rolex Mentor Protégé When it came to choosing who was to be her protégé for a year, Belgian choreographer Anne Teresa De Keersmaeker took a risk. A clear plan - Rolex Mentor Protégé It began with Junaid watching Saburo Teshigawara managing lights and arranging the stage. It ended with him dancing a major role in the Tokyo premiere of <i>Kazahana</i> A pas de deux of ideas - Rolex Mentor Protégé Classical ballet is not frozen in the past but is a living, evolving art – this conviction provided a shared faith for mentor Alexei Ratmansky and protégé Myles Thatcher. After holding key roles at a world-famous dance company for over three decades, celebrated Czech-born choreographer and Rolex dance mentor Jiří Kylián was seeking a new direction in his work, focusing on cross-disciplinary projects and the great potential of contemporary technology. Dance and the art of subversion - Rolex Mentor Protégé For more than three decades, Trisha Brown has dominated the dance firmament like a blazing sun. Not only has she created a series of the most memorable contemporary choreographies, she has also turned dance on its head, breaking rules and crossing boundaries. Those who have had the privilege of working with her have seen their lives transformed. Now Lee Serle, a young dancer from Australia, is thrust – to his delight – into the complex, demanding dance arena that is the Trisha Brown Dance Company. One of the world's greatest architects, Alvaro Siza from Portugal, and a young Jordanian architect, Sahel Al-Hiyari, found common ground in their views on the theory and practice of architecture, which enhanced their many intense discussions and outings, especially to visit Siza's groundbreaking works. Zen and the art of mentoring - Rolex Mentor Protégé During the mentoring year, young Chinese architect Yang Zhao designed a Home-for-All, a communal gathering place that was part of a project created by his mentor Kazuyo Sejima and other leading Japanese architects in response to the devastation caused by the 2011 tsunami in Japan. A feeling for atmosphere - Rolex Mentor Protégé Switzerland, Paraguay and South Korea were the principal settings for Peter Zumthor and Gloria Cabral's busy, collaborative partnership which grew rapidly from the start. David Adjaye & Mariam Kamara - Rolex Mentor et Protégé A visit to Mariam Kamara's native Niger was the turning point in the relationship between her and world-famous Ghanaian-British architect David Adjaye. Sir David Chipperfield & Simon Kretz - Rolex Mentor and Protégé Instead of collaborating on a building during the mentoring year, Sir David Chipperfield and his Swiss protégé Simon Kretz decided to investigate how planning shapes a city and gives voice to the aspirations of its citizens. Recent mentorships - The Rolex Mentor & Protégé Arts Initiative Recent Mentorships - Rolex Mentor and Protégé - Video Emerging young artists had the unique opportunity to collaborate with world-renowned mentors in their disciplines during the 2020–2022 cycle of the Rolex Mentor and Protégé Arts Initiative. Joan Jonas and Thao Nguyen Phan - Video "Art is a spiritual practice," says Joan Jonas, pioneer of performance and video art. For her Vietnamese protégée Thao Nguyen Phan, the experience of working with Jonas and observing her constant experimentation has taught her to be more open to what she can use to tell the stories that underlie her work. Kazuyo Sejima and Yang Zhao - Video Japanese mentor Kazuyo Sejima and protégé Yang Zhao believe architecture is about more than constructing buildings – it's about changing lives. They put their conviction into practice with a humanitarian project as Zhao designs a community gathering place in a tsunami-devastated area. Carrie Mae Weems & Camila Rodríguez Triana - Rolex Mentor and Protégé - Video Carrie Mae Weems was drawn to choose Camila Rodríguez Triana as a protégée in the 2020−2022 cycle of the Rolex Mentor and Protégé Arts Initiative, as, although the young Colombian visual artist came from a different country and different world, there was a deep connection. Phyllida Lloyd & Whitney White - Rolex Mentor and Protégé - Video Drawn together by a mutual love of Shakespeare and of music, as well as an interest in telling women's stories, Phyllida Lloyd, London-based director of such worldwide hits as the musical and film 'Mamma Mia', and American director, actor and musician Whitney White, found that their relationship in the 2020−2022 cycle of the Rolex Mentor and Protégé Arts Initiative quickly grew. Rolex.org - Our apologies Lin-Manuel Miranda & Agustina San Martín - Rolex Mentor and Protégé - Video As part of the 2020−2022 cycle of the Rolex Mentor and Protégé Arts Initiative, Lin-Manuel Miranda and his protégée Argentinian filmmaker Agustina San Martín met while he was making his film directorial debut after a string of Tony award-winning musicals including 'Hamilton' and 'In the Heights'. Spike Lee & Kyle Bell - Rolex Mentor and Protégé - Video Spike Lee, one of today's most socially conscious filmmakers, chose to mentor Kyle Bell, a young filmmaker from the Thlopthlocco Creek Tribal Town of Oklahoma, to help expand the boundaries of his evocative filmmaking. Perpetual spirit, the story of Rolex Perpetual Spirit To a future filmmaker Filmmakers Martin Scorsese, James Cameron, Alejandro G. Iñárritu and Kathryn Bigelow have each made an enduring impact on cinema. They inspire the next generation of filmmakers to pursue their own ideas with the uncompromising passion that characterizes their own work. James Cameron, the art of storytelling James Cameron represents the pinnacle of filmmaking, with a boldness of vision and focus on technical innovation evident throughout his many movies. <i>Titanic</i>, which won 11 Oscars®, is tied for the most awards ever, while Avatar holds the record as the highest-grossing film in history. Four iconic filmmakers pay tribute to their mentors - Video Martin Scorsese, Kathryn Bigelow, Alejandro G. Iñárritu and James Cameron are legendary directors who remember the challenges that confront young filmmakers. Celebrating masters of cinema The history of cinema has been defined by the work of those who combine exquisite artistry with technical mastery. Rolex is proud to support Oscar-winning directors Martin Scorsese, James Cameron, Kathryn Bigelow and Alejandro G. Iñárritu, as they continue to push the boundaries of the art of filmmaking. The Rolex Mentor and Protégé Arts Initiative - Video In 2002, Rolex established the Rolex Mentor and Protégé Arts Initiative to encourage the transmission of artistic knowledge. A passion for architecture - Arts When Rolex constructs or expands its headquarters and production facilities, it brings the same attention to aesthetics and detail as it gives to designing one of its prized chronometers. Learning from a Master - Arts The fiercely tender art of Alejandro G. Iñárritu, Oscar-winning director of Birdman, first touched young cineaste Tom Shoval at a movie theatre in Tel Aviv. A decade and a half later, Shoval found himself under Iñárritu's wing as a protégé in the Rolex Mentor and Protégé Arts Initiative. He learned first-hand from his mentor how to be a complete film-maker, absorbing more life lessons along the way. Here, Shoval gives us memorable snapshots of his experience during his mentoring year in 2014–2015. A dynamic tower for Dallas - Arts Rolex's ethos of design and innovation of the highest quality extends to the buildings the company commissions all over the world. In Dallas, Japanese architect Kengo Kuma has designed an office tower that twists out of the ground. I'm not a young conductor anymore - Arts Rolex Testimonee Gustavo Dudamel has the world at his feet. The charismatic Venezuelan conductor has shaken the foundations of classical music with his open mind and bold, new interpretations of old classics. Series of concerts breathes life back into musical world - Video David Adjaye & Mariam Kamara - Video Convinced that the goal of architecture is to transform, British-Ghanaian architecture mentor Sir David Adjaye and his protégée Mariam Kamara from Niger set about producing a concrete result for social good, with Kamara designing a major cultural complex for her country's capital, Niamey. Alexei Ratmansky & Myles Thatcher - Video Russian-born choreographer Alexei Ratmansky and his protégé Myles Thatcher share a deep respect for the "language" that is classical dance. Both are intensely involved in reinvigorating their art form for the 21st century. A perfect partnership. Alfonso Cuarón and Chaitanya Tamhane - Video For Indian protégé Chaitanya Tamhane, his mentoring year with Academy-award winning film director Alfonso Cuarón was a stroke of fortune. He describes his mentor's image-based film-making as "like watching magic". Tamhane says his approach to cinema will never be the same again. Kaija Saariaho and Vasco Mendonça - Video Composing music is a solitary occupation. For Finland's Kaija Saariaho and her protégé, Portugal's Vasco Mendonça the mentorship delivered a rare opportunity to "enrich" each other discussing music in concert halls around Europe and in the United States. About the Rolex arts initiative - Rolex Mentor and Protégé Rolex Mentors & Protégés Community The Rolex Arts Initiative has evolved into a global creative community that has enabled an enriching dialogue between artists of different generations, cultures and disciplines. Since 2002 more than 1,100 people in 105 countries have been nominated for the programme. Advisors include 123 major artists and creative leaders, while 253 influential figures in the arts have nominated young artists and selected finalists. More than 50 of the world's greatest artists have served as mentors. Wole Soyinka and Tara June Winch - Video Declaring their mentorship to be "a process of development", Wole Soyinka, first African Laureate of the Nobel Prize for Literature, encourages his protégée, Tara June Winch, as she agonizes over her writing. When anyone writes, he says, himself included, "it's all over the place." It's the rewriting that follows that marks out a true writer. Julie Taymor and Selina Cartmell - Video Julie Taymor, famous for creating spectacular theatre, film and opera, wanted to mentor "someone I can have a dialogue with". She found her in British director Selina Cartmell, for whom the mentorship is an ideal opportunity for the rare privilege of watching another director at work as Taymor creates a new opera, Grendel. Michael Ondaatje and Miroslav Penkov - Video Bulgarian protégé Miroslav Penkov could not believe that his mentor was Michael Ondaatje, "someone who stands so tall in a field of giants". For Ondaatje, author of The English Patient, "our lives are utterly disordered", so watching Penkov bring order into life by writing fiction was a source of pleasure. Zakir Hussain & Marcus Gilmore - Video Indian tabla virtuoso Zakir Hussain and young American drummer Marcus Gilmore believe that creating music must be based on keeping the past but also exploring new possibilities. Rebecca Horn and Masanori Handa - Video Two enigmatic visual artists, Rebecca Horn and Masanori Handa, from very different countries, Germany and Japan, quickly develop a strong friendship and a mutual admiration for each other's category-defying work. Communication during their mentorship is not confined to language – drawing together enables them to boost their joint creativity. John Baldessari and Alejandro Cesarco - Video Renowned American conceptual artist John Baldessari believes that "art is more than just painting". His mentorship of Alejandro Cesarco (from Uruguay) is an intense collaboration that combines visuals, text, irony and humour in the creation of a new work of art. Peter Sellars and Maya Zbib - Video With a live performance and both Chicago and Beirut as the backdrop, Peter Sellars and Maya Zbib give surprising – and very different – explanations of the nature of art, as well as describing each other, their mentorship and how to change the world. Anish Kapoor and Nicholas Hlobo - Video In a mentorship that is a process, rather than a collaboration on a joint work, Nicholas Hlobo's art, which springs from many hours of precise handicraft, is contrasted with the monumental pieces created by his mentor Anish Kapoor, that seem "to be made by the gods". Stephen Frears and Josué Mendez - Video "For a Peruvian to work with [Stephen] Frears, it's just not possible", says young Lima film-maker Josué Mendez of the respected British director. But that's exactly what happens when Frears chooses Mendez as his protégé and they share the "very precise art" of film-making, with Mendez directing his second full-length feature. Walter Murch and Sara Fgaier - Video What does a film editor do? Walter Murch, editor of many iconic films, and his protégée, Italian film editor Sara Fgaier, provide succinct descriptions of the complex skill of constructing a feature film, the focus of their year-long mentorship. Anne Teresa De Keersmaeker and Anani Dodji Sanouvi - Video Anne Teresa De Keersmaeker, one of the world's most distinguished choreographers, says of her protégé, Togolese dancer Anani Dodji Sanouvi, "he is like the sun … he has an energy that is inspiring." Sanouvi in turn declares that a year being mentored by De Keersmaeker is the chance of a lifetime. Colm Tóibín & Colin Barrett - Video Irish writer Colin Barrett recognizes that writing is a solitary pursuit, but also acknowledges the need to escape solitude and meet other people and fellow authors. Trisha Brown and Lee Serle - Video For young Australian dancer Lee Serle, a year in New York being mentored by one of the world's greatest choreographers, Trisha Brown, is an opportunity to "go back to the source", as both mentor and protégé search for originality, humanity and beauty of movement. Lin Hwai-min and Eduardo Fukushima - Video Young Brazilian dancer Eduardo Fukushima moves from São Paulo to Taiwan, where his mentor, Asia's premier choreographer Lin Hwai-min, elaborates his unique philosophy of movement and being. A year with this "very generous person" has "transformed my life", Fukushima declares. Zhang Yimou and Annemarie Jacir - Video For Zhang Yimou, China's creator of dazzling films, success is not about inspiration but the fruit "of hardships and efforts" as he meticulously masters every single scene. For his protégée Annemarie Jacir, working alongside him on set and in the editing room as he makes The Flowers of War, his supreme "visual sense" is the key to his rich and moving stories. Rolex.org - Mario Vargas Llosa and Antonio García Ángel - Video "One cannot teach how to write, but one can teach a young writer what not to do when writing a novel," declares Peru's Nobel literature laureate, Mario Vargas Llosa. This and many other lessons are the basis of a highly productive mentorship with his protégé, novelist Antonio García Ángel, from Colombia, who emails his writing to his mentor every week and then engages in a literary critique by telephone. Mira Nair and Aditya Assara - Video When Thai film-maker Aditya Assarat shadows his mentor, Mira Nair, on set as she directs The Namesake in Kolkata, India, he discovers some of the secrets of her lavish cinematography. "She's like the host of a party. That goes a lot towards holding the film crew together." Nair describes it differently: "It's about orchestrating chaos," she says. Olafur Eliasson and Sammy Baloji - Video For Sammy Baloji, who had mainly worked in photography, immersion in the life and work of mentor and multimedia artist Olafur Eliasson brought a transformation, enriching his work and bringing a greater complexity of language as he discovered new materials and modes of expression. William Kentridge and Mateo López - Video Visual arts protégé Mateo López is, thanks to his architecture background, "incredibly precise", says mentor William Kentridge. In his Johannesburg studio, Kentridge pushes his protégé out of his "comfort zone", helping him to develop a more spontaneous approach to creativity. Sir Peter Hall and Lara Foot - Video Under the subtle and experienced eye of British director Sir Peter Hall, his protégée, South Africa's Lara Foot, directs a play – that she also wrote – exposing a taboo subject in her country. "South Africa is a country of contradictions," she says, and these contradictions lend themselves to brilliant theatre, as Lara Foot demonstrates. Álvaro Siza & Sahel Al-Hiyari - Video For Álvaro Siza, Portugal's master architect, his profession is not about copying designs of the past. His protégé, Sahel Al-Hiyari, says "with Siza … it's much deeper than that." Al-Hiyari explains that "architecture is synonymous with human existence. It's one's second skin." Robert Wilson and Federico León - Video Mentoring is not learning in the conventional sense. It's really the idea of interacting. Two artists meet and interact," says gifted Argentinean director Federico León of his year of collaborating with his mentor, the legendary director and artist Robert Wilson. Robert Lepage and Matías Umpierrez - Video Canada's Robert Lepage is world famous for his mastery of multidimensional productions. With his global outlook and mastery of technology, his protégé, Matías Umpierrez of Argentina, is also pushing the boundaries of theatre. Their pairing produced a fascinating exchange that Lepage described as "the best relationship possible". Patrice Chéreau and Michał Borczuch - Video The late French director Patrice Chéreau described himself as "a slave to the text". His protégé Michał Borczuch takes the opposite approach, with an "anarchistic" style of direction. "I wasn't interested in somebody who was doing something similar to me," Chéreau said. David Hockney and Matthias Weischer - Video "I've never done any teaching," says David Hockney, Britain's most famous living artist. He agreed to be a mentor in the hope he would not only teach, but also learn. Traveling and painting with his protégé, Germany's Matthias Weischer, Hockney says, "I've got a new friend, a young painter. A good teacher learns from pupils." Philip Glass and Pauchi Sasaki - Video For composer Philip Glass, "music is a place". He chose Pauchi Sasaki, from Peru, as his protégée because he was convinced she would gain most from the mentoring year. He helped her navigate not only the subtleties of composing but also the practicalities of living as a professional musician. Youssou N'Dour and Aurelio Martínez - Video A year's mentorship with Youssou N'Dour gives Aurelio Martínez, from Honduras, not only an opportunity to boost his musical skills and self-confidence in the company of "the icon of African music", but also to learn more about the historic and musical background of his African ancestors as he visits N'Dour's continent for the first time. Jennifer Tipton and Sebastián Solórzano Rodríguez - Video Jennifer Tipton, one of the world's greatest lighting designers, declares that "light is the substance of our existence". Her protégé, Mexico's Sebastián Solórzano Rodríguez, agrees completely as he witnessed Tipton creating lighting for performances at theatres and opera houses all over the world. Kate Valk and Nahuel Perez Biscayart - Video Argentinian actor Nahuel Perez Biscayart shifts to New York to spend a year with his mentor, Kate Valk, a founding member of the Wooster Group. There he finds that inspiration comes as a result of producing, trying, failing and finding the beauty in accidents. Sir Colin Davis and Josep Caballé-Domenech - Video One of the world's greatest conductors, (the late) Sir Colin Davis believed that "you don't control an orchestra, you are allowing things to happen." Preparation and a deep cultural sense are what a conductor needs – lessons that Sir Colin instilled into his brilliant protégé, Josep Caballé-Domenech, from Spain. Pinchas Zukerman and David Aaron Carpenter - Video World-renowned violinist and conductor Pinchas Zukerman says "the fiddle is synonymous with my existence". He finds the same commitment in his protégé, young American violist David Aaron Carpenter, from the United States. Jessye Norman and Susan Platts - Video Rolex Mentor and Protégée in Music, 2004 - 2005 Brian Eno and Ben Frost - Video As they create a track of electronic music during their mentoring year, multimedia artists Brian Eno and Ben Frost reveal the two sides of composition, finding inspiration and analyzing the music they create and how it will be heard. Margaret Atwood and Naomi Alderman - Video Canada's grand mistress of fiction Margaret Atwood likens mentoring to door-opening. "We speak the same language," Atwood says of her protégée, young British author Naomi Alderman. Their relationship even extends to writing a zombie novella together. Hans Magnus Enzensberger and Tracy K. Smith - Video In a mentorship that they describe as an intense and joyful conversation, poets Hans Magnus Enzensberger (from Germany) and Tracy K. Smith (American) explore the nature of poetry – "Everyone has poetry in their head," Enzensberger proclaims. But their quest goes further, examining history and identity as Smith realizes a longstanding desire to write her family memoir. Mia Couto and Julián Fuks - Video Mia Couto's mentoring relationship with Julián Fuks was a fusion of interests wrought by their mutual experiences as writers living in former colonies of Portugal. Liberated from his "autofiction" style of writing by his mentor, Fuks found he was able to explore his imagination in a different way. Toni Morrison and Julia Leigh - Video Nobel literature laureate Toni Morrison is not only a novelist and teacher, she is also an experienced editor – the perfect mentor for young, Australian writer Julia Leigh as she starts on her second novel. Tahar Ben Jelloun and Edem Awumey - Video Moroccan-born and now one of France's most fêted writers, Tahar Ben Jelloun declares that "literature is not reassuring, it's disturbing". Edem, from Togo, writing a novel of "dark nights and ghosts", was the ideal protégé to accompany in the challenging process of creating fiction. Alejandro G. Iñárritu and Tom Shoval - Video Young Israeli director Tom Shoval's year of mentoring evolved with the excitement worthy of a Hollywood film script. Shoval spent weeks on the set of Alejandro G. Iñárritu's film 'The Revenant' with the Oscar winner revealing all the "infinite possibilities" of film-making. Martin Scorsese and Celina Murga - Video For American master of cinema Martin Scorsese, to be a good film director, you need to become part of the world you are filming. His protégée, Argentinean director Celina Murga, does so with passion, he declares, describing her as a natural film-maker. The admiration is mutual. "Marty's the perfect mentor," says Murga. Jiří Kylián and Jason Akira Somma - Video Jason Akira Somma describes himself as "a dance visual artist", transcending artistic boundaries. In Jiří Kylián he finds not only a mentor, but also a generous "life coach" happy to share a lifetime's experience. The mentorship, says Somma, "has absolutely changed my life". William Forsythe and Sang Jijia - Video William Forsythe, one of the greatest innovators of modern dance, believes that ballet "shouldn't be left in the 19th century". His radical approach finds the perfect protégé in Sang Jijia, a gifted Chinese dancer of Tibetan origin. "Sang-ba is like unpolluted water," says Forsythe. "He runs clear." Crystal Pite & Khoudia Touré - Video Dance is a wordless art form with few guidebooks, so for two choreographers − hip-hop dancer Khoudia Touré, from Senegal, and Canadian superstar choreographer Crystal Pite — to work face-to-face was a priceless experience. Saburo Teshigawara and Junaid Jemal Sendi - Video "Rolex has introduced me to the world," says Ethiopia's Junaid Jemal Sendi, whose life has been transformed by dance. His mentorship, under leading Japanese choreographer Saburo Teshigawara, takes Sendi to Europe and Japan. "Now he has just opened his own future door," says Teshigawara in admiration. "And he wants to go further." Ohad Naharin and Londiwe Khoza - Video South African Londiwe Khoza started dancing at age five, but when she joined Ohad Naharin's Batsheva Dance Company in Tel Aviv for the mentoring year, she had to learn to dance in a way that required a new kind of body awareness. After three months, she "stopped thinking and started feeling it". Sir David Chipperfield and Simon Kretz - Video For Sir David Chipperfield and his Swiss protégé Simon Kretz, the mentoring year provided the perfect opportunity for a detailed examination of the impact of architecture on society – how buildings can create strong communities if they relate to people and the environment. Peter Zumthor and Gloria Cabral - Video Gloria Cabral, from Asunción in Paraguay, spent weeks at the Swiss studio of her mentor Peter Zumthor, who involved her in the whole process of building a tea chapel in South Korea, opening up her mind "in a radical way". An interview with Martin Scorsese - Rolex and Cinema To future filmmakers Martin Scorsese says: "Don't be afraid to try anything, no matter how crazy it might seem to others." These are encouraging words from this director, producer and screenwriter who is responsible for many of the biggest classics in film history. He is always pushing boundaries and helping to promote the creative spark in others. An interview with James Cameron - Rolex and Cinema James Cameron is acknowledged for using trail-blazing technology in his films, but when it comes to advice for emerging filmmakers he says to "stay in touch with the human heart". The director of <i>Titanic</i> and <i>Avatar</i> believes nothing is more important than "speaking with an authentic voice and portraying the human condition at its most elemental level".	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	1,746
Located within Chowk Wazir Khan, an ancient square in the Walled City of Lahore which is connected to the most popular of the thirteen gates of old Lahore, Delhi Gate, is the Wazir Khan Masjid. It was built in the rule of Mughal Emperor Shah Jahan and is the only mosque which was build inside a bazaar in its time. Intricately decorated walls with Arabic calligraphy, faience tile work, muqarnas and delicate carvings, chevron patterns of the dome roof, colorful artwork and a majestic courtyard are the soul of this grand structure.	{ "redpajama_set_name": "RedPajamaC4" }	9,809
import * as React from 'react' import { ModuleImage } from './ModuleImage' import { ModuleInfo } from './ModuleInfo' import { ModuleUpdate } from './ModuleUpdate' import { ModuleControls } from '../ModuleControls' import styles from './styles.css' import type { AttachedModule } from '../../modules/types' import { TEMPERATURE_MODULE_TYPE, THERMOCYCLER_MODULE_TYPE, } from '../../modules' type Props = {\| module: AttachedModule, controlDisabledReason: string \| null, availableUpdate?: ?string, \|} export function ModuleItem(props: Props): React.Node { const { module, controlDisabledReason } = props return ( <div className={styles.module_item}> <div className={styles.module_content}> <ModuleImage model={module.model} /> <ModuleInfo module={module} /> <ModuleUpdate hasAvailableUpdate={!!module.hasAvailableUpdate} controlDisabledReason={controlDisabledReason} moduleId={module.serial} /> </div> {(module.type === THERMOCYCLER_MODULE_TYPE \|\| module.type === TEMPERATURE_MODULE_TYPE) && ( <ModuleControls module={module} controlDisabledReason={controlDisabledReason} /> )} </div> ) } export { NoModulesMessage } from './NoModulesMessage'	{ "redpajama_set_name": "RedPajamaGithub" }	8,760
Doctor Who: Macra Terror (Part of the Target Books Doctor Who Numerical Order (#123) Series, Doctor Who Novelisations (#34) Series, and Doctor Who: BBC Radio Collection Series) by Ian Stuart Black Hardcover -- Paperback -- Audio CD -- Like New Unavailable Very Good Unavailable Good Unavailable Acceptable Unavailable New Unavailable See All 3 Editions 12 people are interested in this title. Mass Market Paperback. First Edition. No. 127 This description may be from another edition of this product. Publisher:Universal Publishing & Distributing Corporation Dimensions:7.3" x 0.5" x 4.5" Fiction Literature & Fiction Science Fiction Science Fiction & Fantasy Good story crawls out of BBC's vaults The BBC, in the days before home video, decided that some of its programs were no longer required in its archives. In a somewhat unsystematic purging, many classics were consigned to the flames, including several Doctor Who stories. Fortunately, some fans of the series had made their own audio recordings, and these (following a thorough re-mastering by the BBC) are being released."The Macra Terror" is one of these releases. The story features a human colony under siege from a race of monsters - not an unusual description of a Patrick Troughton story. What makes this story unique is the nature of the colony - set up like an archetypical British holiday camp, the enforced bon hommie and cheerful tunes cast it in a different light... The comparatively recent addition of Jamie to the TARDIS crew mean that all three companions (the other two being Ben and Polly) have smaller roles than might be desirable. The Doctor is very much on centre stage in this story, and Pat Troughton is well in his stride in the part.Linking narration is by Colin Baker, who played the Doctor's sixth incarnation, and is surprisingly subdued given Baker's portrayal of the Doctor. The visual aspects of the show would probably added quite a bit to the enjoyment of the show (particularly in setting the holiday camp tone), but based on stills the appearance of the Macra is probably not truly missed.The story is quite strong and not unduly tied in to the shows ongoing history, so is suitable for both fans and casual listeners...	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	1,886
{"url":"https:\/\/oneapi-src.github.io\/oneDAL\/daal\/algorithms\/stump\/regression.html","text":"# Regression Stump\u00b6\n\nA Regression Decision Stump is a model that consists of a one-level decision tree where the root is connected to terminal nodes (leaves) [Friedman2017]. The library only supports stumps with two leaves based on regression decision trees. The one method of split criteria is available: mse. See Regression Decision Tree for details.\n\n## Batch Processing\u00b6\n\nA regression stump follows the general workflow described in Regression Usage Model.\n\n### Training\u00b6\n\nFor a description of the input and output, refer to Regression Usage Model.\n\nAt the training stage, a regression decision stump has the following parameters:\n\nParameter\n\nDefault Value\n\nDescription\n\nalgorithmFPType\n\nfloat\n\nThe floating-point type that the algorithm uses for intermediate computations. Can be float or double.\n\nmethod\n\ndefaultDense\n\nPerformance-oriented computation method, the only method supported by the algorithm.\n\nvarImportance\n\nnone\n\nNote\n\nVariable importance computation is not supported for current version of the library.\n\n### Prediction\u00b6\n\nFor a description of the input and output, refer to Regression Usage Model.\n\nAt the prediction stage, a regression stump has the following parameters:\n\nParameter\n\nDefault Value\n\nDescription\n\nalgorithmFPType\n\nfloat\n\nThe floating-point type that the algorithm uses for intermediate computations. Can be float or double.\n\nmethod\n\ndefaultDense\n\nPerformance-oriented computation method, the only method supported by the algorithm.\n\n## Examples\u00b6\n\nBatch Processing:\n\nstump_reg_mse_dense_batch.cpp\n\nNote\n\nThere is no support for Java on GPU.\n\nBatch Processing:\n\nStumpRegMseDenseBatch.java\n\nBatch Processing:","date":"2021-04-14 08:42:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.32780662178993225, \"perplexity\": 4195.8502850093655}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-17\/segments\/1618038077336.28\/warc\/CC-MAIN-20210414064832-20210414094832-00327.warc.gz\"}"}	null	null
Please note that RGB and HTML color codes represent illuminated colors for display on computer monitors and other electronic devices. MyPerfectColor does its best to convert the digital color values to a physical color but keep in mind that a physical paint color which is viewed via reflected light cannot be as bright as a color that is projected as an illuminated light. Similarly, CMYK (refers to the four inks used in some color printing: cyan, magenta, yellow and key) colors do not translate well to paint, because it is a device dependent color space, meaning the values themselves do not communicate enough information for us to reproduce a color with accuracy. We can make a color, but we would not be able to ensure it is the color you would be expecting. The best method is to match a physical sample, because we know exactly what to target.	{ "redpajama_set_name": "RedPajamaC4" }	6,516
The Last Asylums Exhibit Peer Support & Activism Survivor Culture Ponoka Queen Street Verdun / Douglas Hospice Saint-Jean-de-Dieu Hôpital Saint-Michel-Archangel Nova Scotia Hospital The Provincial Hospital After the Asylum » Policy and Practice » The Last Asylums Exhibit » By L. Baker, L. Beckman, M. Davies, C. Dooley, and E. Dyck With the development of community-based mental health in the 1960s, Canada's large long-stay mental hospitals were repurposed as smaller, mainly short-stay facilities. This path-breaking, bilingual exhibit charts the pace, scale, and shape of this institutional adaptation and the evolving patient and staff experience. Tasked with the work of creating a national overview of deinstitutionalization, researchers from across Canada mined public records and institutional histories to create these communiqués to stimulate further work on this important subject. Surveying this research, we observe varying, and sometimes dramatic rates of institutional depopulation in different parts of the country. But it is clear that the umbrella term deinstitutionalization encompasses more than just changes to patient demographics and staffing configurations. Profound, life-altering changes for institutionalized patients, practitioners, administrators, and support staff lie behind the statistics, legislative initiatives, and policy documents that we have gathered. Inside the old mental hospitals, evolving therapeutics fostered new professional configurations, and work therapy was replaced by job and life skills training intended to prepare clients for community living. A reinterpretation of the patient as "person" was reflected in shifting institutional policies and new recreational options for residents. Aging institutions took on new roles and developed programs undreamed of in the era of the long-stay mental hospital. Some facilities closed their doors entirely, becoming playgrounds for movie makers and urban explorers, or were torn down and erased from the physical landscape. The central premise—and promise—of the shift away from the use of large mental health institutions was the integration of former patients into the life of the broader society. But in spite of the benign motives of the professional pioneers in community mental health, the marginalization of people with psychiatric labels continued, and it took new forms. Trans-institutionalization, where patients were redistributed across a series of smaller institutionalized settings—including boarding houses, group and foster homes, and nursing homes, and even jails—emerged as a new pattern, and may in fact be the most useful way of understanding these sweeping changes to mental health provision. Even those whose circumstances allowed them to live independently often found their lives closely managed by social workers and community care teams. Others fell between the cracks as, by the late 1970s, cost-containment increasingly took precedent over the social integration of former patients as the driver of deinstitutionalization. In the post-asylum era, continuity of care has been replaced by a patchwork system of treatment by private practice physicians and local mental health teams, back-stopped by crisis intervention in general hospital psychiatric wards. Social isolation, a deeply stigmatized identity, exclusion from the work force, persistent poverty, and even homelessness, often frame the lived experience of former patients. It is easy for the imaginative eye to see the ghost-like walls of the old asylum standing among the programs that make up today's community mental health system.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	8,789
Q: AttributeError: 'str' object has no attribute 'annotate_video' Using the following code on JupyterLab in order to run Google Video Intelligence Package: from google.cloud import videointelligence import os client = videointelligence.VideoIntelligenceServiceClient('VidIntelligence.JSON') job = client.annotate_video( input_uri='gs://vidintelligencebucket/The Simpsons - Monopoly Night.mp4', features=['LABEL_DETECTION', 'SHOT_CHANGE_DETECTION'], ) result = job.result() When I run it, the following error appears: AttributeError: 'str' object has no attribute 'annotate_video' Any suggestions? A: This happens because as ex4 pointed out variable client is of type str and just contains an error message. The error occurs because you are trying to authenticate in a non correct way. The argument passed to the credentials parameter of the client cannot be of type str but should be a Credentials object as stated in the client description. You can check this overview for all the valid ways to authenticate the client. Since you have a json file with the credentials you just need to point to it using an environment variable named GOOGLE_APPLICATION_CREDENTIALS: $ export GOOGLE_APPLICATION_CREDENTIALS="/path/to/VidIntelligence.json" Then you will be able to initialize your client without passing any arguments: client = videointelligence.VideoIntelligenceServiceClient() Hope that this helps!	{ "redpajama_set_name": "RedPajamaStackExchange" }	513
art, books, culture, literature, pop culture 'Cheryl Heard A Wet Thud': Tread Softly by Richard Kelly There's a moment in Peter Bagge's immortal Generation X soap opera comicbook Hate¹ where a character says "That need to reclaim a dusty corner of your youth can be overwhelming at times" and even when I first read that in my late 20s, the truth of the statement seemed obvious; and of course the need only gets stronger as time goes by and your youth recedes into the distance.² And those corners can be pretty dusty. Today, for the third time, I bought a copy of Richard Laymon's Dark Mountain (1987). My introduction to this book now seems archaic, although it was fairly typical of its time. When I first read Dark Mountain, in 1988, horror novels made up the bulk of my reading. If I had had to name my favourite writers at the time I would probably have listed four main ones, in any order; James Herbert, Stephen King, Clive Barker and Shaun Hutson, although I had an open mind about anything that looked gory. The first UK edition of Tread Softly, with Danny Flynn's classic cover art Like Dark Mountain itself, this is a very 80s story. When I first heard of the book, it was called Tread Softly and nominally by "Richard Kelly", a pseudonym Laymon mysteriously (to me at least) used to write several novels of exactly the same type and in exactly the same style as the bestsellers he was known for, such as The Cellar and The Beast House. I have never read either of those, but they are worth mentioning because both titles are invariably appended to the phrase "Richard Laymon, author of…" in my memory³; I read the blurbs on at a lot of books back then. I first came across Tread Softly via a negative review (oddly, not the only time I've been intrigued enough by a bad review to check something out) in Fear Magazine, an invaluable resource (that is, "a good magazine") for horror fans such as myself in those pre-internet days. The review (not sure by whom unfortunately) obviously made an impression on me – I remember with apparent clarity (possibly not accurately, I don't have my Fears anymore to check, alas) that the writer referred to 'lashings of teeny sex' (the selling point to me I would imagine) and concluded with '…a downbeat ending. Does nothing for the genre.' (that last phrase makes me think it may have been written by Fear editor John Gilbert, whose concerns with literacy, imagination and quality pushed me towards writers like Clive Barker, Ramsey Campbell and Nicholas Royle, where my instincts might have led me more towards Guy N Smith and – of course – Tread Softly). But it was one thing to read a review and see a cover picture (another selling point) in a magazine – how to get the book itself? In a way, this was possibly even easier then than it would be now for a young teenager with no money; I asked for it in my local library. Within a few days, I had my clammy adolescent paws on the WH Allen UK hardback copy of the book, its dust jacket pristine beneath the clear plastic protective cover. I remember distinctly mine being the first stamp on the card, which was obscurely pleasing. Fear issue 1 with cover art by Oliver Frey As that detail suggests, this whole story is one of those memories that is more vivid than it has any reason or right to be.⁴ There was no real frisson, I had no sensation of forbidden fruit; I had read far more extreme things, such as Shaun Hutson's Spawn (borrowed from the same library, incidentally), one of only two novels to ever make me feel physically queasy (I got over it though. With the other one, Bret Easton Ellis' American Psycho, I haven't yet and hope not to). But still, it was exciting. The cover by Danny Flynn was eye-catching, if extremely typical of its era (partly, it turns out, because Danny Flynn painted lots of the covers that define that era for me, including the several key Shaun Hutsons) and a million times better than the style-less and boring edition I bought today), but part of the excitement was because of the resemblance it bears to the artwork of the thousands of alluring, generic slasher movies that then lined the shelves of video shops. It might be worth mentioning for younger readers, that video (rental) shops then existed in any town bigger than a small village, but even in small villages, the local 'convenience store' would usually have at least a couple of shelves of videos. These movies were all the more alluring because at that point, they were still beyond my grasp. It was odd to me then and is still odd to me now, that at 13 or 14 I could buy, borrow and read, without any adult objection beyond the odd funny look, books about any kind of violent or depraved act imaginable (which was good), but couldn't rent even the lame, often almost bloodless Friday the 13th clones that were a staple of 80s horror cinema and which – surely – had little appeal to the over-18s they were in theory restricted to. In fact, the ideas in both the movies and most of the books I was reading were deeply conservative and (especially in the films) relied on the equally conventional reaction to them for what little shock value they had. And in fact, Tread Softly was – and Dark Mountain remains – more like an 80s teen horror movie than any other book I've ever read. The story (two families, both with sulky teenage children, go on a camping trip in the wilds of California, where they are terrorised by a "swamp witch" and her depraved idiot son) and the structure of the book are, it feels, deeply indebted to the standard slasher movie. There's a brief, establishing but fairly restrained prologue (couple attacked in tent), then the introduction of the families and the tensions within them, before the vacation – and the horror – begins. It's extremely formulaic; the women examine their naked bodies critically in mirrors for the reader's benefit, the men are 'rugged' and clear eyed, teenage boys are 'athletic', teenage girls have 'smooth curves' and pout sulkily – and extremely predictable. As with films though, you can get away with any number of well worn formulae as long as the execution isn't boring. Tread Softly was rarely boring but, more surprisingly – by Shaun Hutson standards at least, and something else it had in common with the standard slasher film – it wasn't all that bloody, really. The story is fairly perfunctory, as one would expect; the group goes camping, the idiot son attacks them, is killed, the witch tries to avenge him, all against a backdrop of hot, insect infested summery swamps and simmering teenage hormones. The ending – spoiler alert I suppose – is kind of downbeat, but only in the bathetic sense that it's actually upbeat; it's unexpectedly happy and harmonious and lacks the final, punchy, expected-unexpected twist that a film would have had. But teenage me found it wholly satisfactory. In fact, I found the whole sentimental, nasty adventure extremely enjoyable. It may not have done much for the genre, but it did something for the part of me that enjoyed and still enjoys Friday the 13th Part 3 and Police Academy 5: Assignment Miami Beach more than many obviously better movies. Clearly, when I read the bad review that lured me towards Tread Softly, I didn't want it to be "good", I wanted it to be exactly what it is; trashy and titillating and simplistic, and – with no insult intended – it didn't disappoint me. I didn't buy the book at the time, but oddly, although better books (back then this would have meant things like IT, Weaveworld, Domain and Victims) and theoretically similar books (Rex Miller's Slob springs to mind) came along, I never forgot Tread Softly. Why the appeal? No doubt it had something to do with the teenage protagonists and my own adolescence. That conservatism – the (mildly) dysfunctional families pull together and defeat the threat, the teenagers pair off as the reader is supposed to want them to, the arrogant characters become humble, the insecure ones find their courage and all is well with the world – has a deep appeal to teenagers. The formula of the teen horror movie – even the cynical twist ending that Tread Softly strangely lacks – wasn't only there to sell more, similar movies. The comfort of the familiar, the safe scare is a huge part of the appeal of the genre to a young audience. As one gets older, that appeal fades (I find at least), but, from browsing in bookshops (I still usually have a quick look at the horror section) it would appear that the 'young adult' wing of horror fiction (now very much a specific subgenre) seems to be in healthier shape than horror as a whole. the inferior 90s "Dark Mountain" I have read a few other Richard Laymon books since, but although they were essentially very similar to Tread Softly, they were enjoyed (albeit to a lesser degree) and then almost immediately forgotten. But then, I didn't read those when I was 14. But. At some point in the late 90s, I nostalgically bought Tread Softly itself in a charity shop, and though I found it sillier than it seemed before, it remained just as enjoyable and – far more unexpectedly – the emotional attachment to the hackneyed story and the sketchily drawn characters (or to my 14 year-old self?) remained intact. But – annoyingly (it was an original Richard Kelly edition) – I didn't bother to keep it. Then, in the early 2000s, I ended up buying a copy of Dark Mountain. The title was wrong, the cover was wrong, but the book was still very much right. And then I let it go again; like it though I do, it never feels like a priority when having a clear-out. Now, inevitably, I have bought it once more; seeing it, even in its inferior form, brought back the memories; of the book, of the library, of that bad review. And, having started re-reading it, the magic, more mysteriously than ever, is still there. This time it has the dubious bonus of being paired with an earlier Laymon novel, Beware! With fairly low expectations (I didn't read that when I was 14 either), I'll give it a go. the incredibly perfunctory 2009 edition of Beware!/Dark Mountain – nice barcode placement! ** 2021 Postscript** Now, in the midst of a pandemic that the 14 year old me would have thought was like something out of a horror novel, although a surprisingly boring one, I finally possess the classic 1988 Richard Kelly edition again. Finally, because this time I feel like I'll probably keep hold of it; but who knows? back on the shelf – the 1988 Star edition ¹ That moment, fact fans, is in the bottom left hand panel on page 24 of Buddy Go Home! Vol IV of the complete Buddy Bradley Stories from Hate (Fantagraphics Books, 1997) ² There are several good articles about this and related subjects on the blog Into The Gyre, most recently this one ³ See also Burt Hirschfeld, "author of Fire Island" (not read) and Guy N. Smith, "author of Night of the Crabs" (read and liked) ⁴ Another pointlessly intense memory from the same period – essentially a memory of sitting in a room not doing much – was awoken in a Proustian kind of way recently by hearing the intro to Alice Cooper's classic late 80s comeback single 'Poison' in a cafe Further Reading; Paperbacks From Hell by Grady Hendrix is an excellent & highly entertaining book that's well worth a look for any fan of 80s horror fiction, or anyone nostalgic about it 1980s 80s horror Alice Cooper Beware! Burt Hirschfield Clive Barker Danny Flynn Dark Mountain Fear magazine Fire Island Friday the 13th gore Guy N Smith Hate horror horror fiction horror movies James Herbert John Gilbert Night of the Crabs novel Oliver Frey Peter Bagge poison Police Academy Proust Rex Miller Richard Kelly Richard Laymon Shaun Hutson slasher movies Slob stephen king swamp witch Tread Softly video nasties	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	8,946
\section{Introduction} Let $U$ be a smooth quasiprojective surface, and let $S$ be a smooth compactification such that $D=S\setminus U$ is a normal crossing divisor. The open surface $U$ is said to be of general type if $K_S+D$ is big. This condition and the spaces of pluri log canonical sections $H^0(n(K_S+D))$ for all $n\ge0$ depend only on $U$ and not on the choice of a particular normal crossing compactification $(S,D)$. Since $K_S+D$ is big, the number of its sections grows quadratically: $h^0(n(K_S+D)) \sim c n^2/2$. After passing to the log canonical model $(S\can, D\can)$ where $K_{S\can}+D\can$ is ample, one sees that $c= (K_{S\can}+D\can)^2$ and it is called the \emph{volume} of the pair $(S,D)$, equivalently the volume of $U$, and is denoted by $\vol(K_S+D)= \vol(U)$. Vice versa, if $(X,B)$ is a log canonical pair with reduced boundary $B$ and ample $K_X+B$, and if $f\colon S\to X$ is its log resolution with exceptional divisors $\{E_i\}$ then \[ \vol\big(S \setminus (f\inv(B)\cup E_i)\big) = \vol(K_S+f_\inv B + \sum E_i)=\vol(K_X + B)=(K_X+B)^2. \] \begin{question} How small could a volume of an open surface $U$ of general type be? Equivalently, how small could $(K_X+B)^2$ be for a log canonical pair with reduced boundary $B$ and ample $K_X+B$? \end{question} The basic result in this direction is the following quite general \begin{theorem}[Alexeev, \cite{alexeev1994boundedness-and-ksp-2}] Let $(X, B=\sum b_iB_i)$ be a log canonical pair with coefficients $b_i$ belonging to a DCC set $\cS\subset[0,1]$ (that is, a set satisfying descending chain condition). Then the set of squares $(K_X+B)^2$ is also a DCC set. In particular, it has a minimum, a positive number real number, rational if $\cS\subset\bQ$. \end{theorem} We will denote this minimum by $K^2(\cS)$. Some interesting DCC sets are $\cS_0=\emptyset$, $\cS_1=\{1\}$, $\cS_2'=\{1-\frac1{n},\ n\in\bN\}$, $\cS_2=\cS'_2 \cup \{1\}$. The paper \cite{alexeev2004bounding-singular} gives an effective, computable lower bound for $K^2(\cS)$ in terms of the set $\cS$, which is however too small to be realistic, cf. Section~\ref{sec:k2-lower-bound} where we spell it out for the sets $\cS_0$ and $\cS_1$. A version of the above definition is to look at the pairs $(X,B)$ with nonempty reduced part of the boundary $\bry\ne0$. We will denote the minimum in this case by $K^2_1(\cS)$. Clearly, one has \begin{displaymath} K^2(\cS_2) \le K^2(\cS_1) \le K^2(\cS_0) \quad\text{and}\quad K^2(\cS_1) \le K^2_1(\cS_1). \end{displaymath} Some published bounds for $K^2(\cS)$ and $K_1^2(\cS)$ for the above sets include: \begin{enumerate} \item $K^2(\cS_0)\le \frac3{55}$. \item $K^2_1(\cS_1) \le \frac1{60}$. \item $K^2_1(\cS_2) = \frac1{42^2}=\frac1{1764}$, and thus $K^2_1(\cS_1) \ge\frac1{\num{1764}}$. \item $K^2(\cS_2)\le \frac1{(42\cdot 43)^2}$ and the bound is conjectured to be sharp. \end{enumerate} The first of these bounds follows from an example of Blache \cite{blache1995example-concerning}. The others are due to Koll\'ar \cite{kollar1994log-surfaces, kollar2013moduli-varieties}. There are also many other examples of log terminal surfaces with ample $K_X$ appearing in the literature. For example, hypersurfaces $S(a_1,a_2,a_3,a_4)$ of the form $x_1^{a_1}x_2 + x_2^{a_2}x_3 + x_3^{a_3}x_4 + x_4^{a_4}x_1=0$ in weighted projective spaces $\bP(w_1,w_2,w_3,w_4)$ provide such examples under some mild conditions on the $a_i$'s. These surfaces were studied in \cite{orlik1977structure-weighted, Kouchnirenko1976polyedres-Newton, kollar2008is-there, hwang2012construction-singular, urzua2016characterization-Kollar}. The last three papers also study surfaces $S^(a_1,a_2,a_3,a_4)$ obtained by contracting two curves on such surfaces, as in the last section of \cite{kollar2008is-there}. These papers are not specifically concerned with the minimal possible value of $K_X^2$, but certainly better bounds than $\frac3{55}$ can be achieved. Jos\'e Ignacio Y\'a\~nez informed us that the following example appears to achieve the minimum among the surfaces $S(a_1,a_2,a_3,a_4)$ with $\gcd(w_1,w_3)=\gcd(w_2,w_4)=1$. \begin{example}[Urz\'ua-Y\'a\~nez] \label{ex:urzua} The hypersurface $S(2,2,4,10)$ of degree $159$ in the weighted projective space $\bP(49,61,37,11)$ has an ample canonical class $K_X$, cyclic quotient singularities, and \begin{displaymath} K_X^2 = \frac{159 \cdot (159 - 49 - 61 - 37 - 11)^2}{49\cdot 61\cdot 37\cdot 11} = \frac{159}{\num{1216523}} \approx \frac1{\num{7651}}. \end{displaymath} \end{example} \medskip Knowing the exact bounds is important for many applications. As explained in \cite{kollar1994log-surfaces}, a stable limit of surfaces of general type of volume $d$ has at most $d/K^2_1(\cS_1)$ irreducible components. Thus, as a corollary of Koll\'ar's bound $K^2_1(\cS_1) \ge\frac1{\num{1764}}$ the number of irreducible components is at most $\num{1764}\, d$. Other applications include bounds for the automorphism groups of surfaces and surface pairs of general type, see e.g. \cite{kollar1994log-surfaces, alexeev1994boundedness-and-ksp-2} for more discussion. The constant $K^2(\cS_1)$ is certainly a very fundamental global invariant in its own right: the smallest volume of a smooth open surface. \medskip The main result of this paper is the following: \begin{theorem} One has $K^2_1(\cS_1)\le\frac1{462}$, and $K^2(\cS_1) = K^2(\cS_0) \le \frac1{\num{48 983}}$. \end{theorem} Section~\ref{sec:method} explains the method which we used to find the new examples. We restate it in Section~\ref{sec:game} as a purely combinatorial game with weights $(w_0,w_1,w_2,w_3)$. Section~\ref{sec:weights1} contains some easy instances of this game for the simplest weights $(0,1,1,1)$, $(1,1,1,1)$ giving in particular Koll\'ar's example with $(K_X+B)^2=\frac1{60}$. Sections~\ref{sec:with-boundary} and \ref{sec:empty-boundary} contain our champion examples for the winning weights $(1,2,3,5)$: surfaces with a nonempty boundary and $(K_X+B)^2=\frac1{462}=\frac1{11\cdot 42}$, and surfaces without boundary and $K_X^2=\frac1{\num{48 983}}=\frac1{11\cdot 61\cdot 73}$. In characteristic 0 the champion surfaces have Picard number $\rho(X)=2$ and they have 4 (resp. 3) singularities. But in characteristic 2 the rank of the Picard group drops by 1 and there is an additional $A_1$-singularity. The surfaces with ample $K_X$ and such configurations of singularities would provide counterexamples to the algebraic Montgomery-Yang problem, were they to exist in characteristic 0. We discuss this connection in Section~\ref{sec:montgomery-yang}. Related to this, in Section~\ref{sec:pic1} we list some surfaces of small volume that have Picard rank $\rho(X)=1$. In particular, we prove that for the surfaces $S^(a_1,a_2,a_3,a_4)$ with $\gcd(w_1,w_3)=\gcd(w_2,w_4)$ the minimum is $K_X^2=\frac1{6351}$. Section~\ref{sec:four-lines} explains why we restricted to the case of only four lines in our search. Finally, Section~\ref{sec:k2-lower-bound} spells out the effective (but very small) bound for $K_X^2$ which follows from \cite{alexeev2004bounding-singular, kollar1994log-surfaces}. \medskip Further, we note that Koll\'ar's lower bound for $K^2_1(\cS_2)$ is a combination of two inequalities. One defines two invariants of a DCC set $\cS$: \begin{definition}\label{def:epsilon-delta} ${}$ \begin{enumerate} \item Let $(X,B)$ be a log canonical surface with ample $K_X+B$ and $\bry\ne0$. Then \[ \epsilon_1(X,B):=\min_{B_0\subset\bry}\{(K_X+B)B_0\} \] and $\epsilon_1(\cS)$ is the minimum of these numbers as $(X,B)$ go over all pairs with coefficients in $\cS$. \item $\delta_1(\cS)$ is the minimum of $t>0$ such that there exists a log canonical pair $(X, (1-t)B_0 + \Delta)$ with $K_X+(1-t)B_0+\Delta\equiv 0$ such that the coefficients of $\Delta$ are in $\cS$. \item We also define a closely related invariant of an individual big log canonical divisor: $\delta_1(X,B)$ is the minimum of $t$ such that $K_X+B-tB_0$ is not big for some $0\ne B_0\subset\bry$, or 1 if this minimum is $>1$. \end{enumerate} \end{definition} Then according to \cite{kollar1994log-surfaces} one has $(K_X+B)^2\ge \epsilon_1(\cS)\delta_1(\cS)$ and $\epsilon_1(\cS_2)= \delta_1(\cS_2)=\frac1{42}$. In Section~\ref{sec:with-boundary} we give an example that shows that the equality $\epsilon_1(\cS_1)=\frac1{42}$ also holds. As for $\delta_1(\cS_1)$, we were not able to find better than $\frac1{13}$ with the present method, which is the same as in Koll\'ar's example with $(K_X+B_0)^2=\frac1{60}$. \medskip All constructions and examples in this paper work over an algebraically closed field of arbitrary characteristic. \begin{acknowledgements} The work of the first author was partially supported by NSF under DMS-1603604. He would like to thank Giancarlo Urz\'ua and Jos\'e Ignacio Y\'a\~nez for helpful discussions. The second author was supported by NSFC (No.~11501012) and by the Recruitment Program for Young Professionals. He would like to thank S\"onke Rollenske and Stephen Coughlan for helpful discussions about log canonical surfaces with small volumes. Especially S\"onke Rollenske helped to transform Koll\'ar's example to $\bP^2$ with four lines, as illustrated in Section~\ref{sec:weights1}. \end{acknowledgements} \section{The method of construction} \label{sec:method} We begin with four lines $L_0, L_1, L_2, L_3$ in $\bP^2$ in general position. Let $f\colon \wX\to \bP^2$ be a sequence of blowups, each at a point of intersection of two divisors that appeared so far: exceptional divisors, lines, and their strict preimages. We will call thus obtained divisors on $\wX$ the \emph{visible curves}. We will assume that enough blowups were performed so that the strict preimages of lines satisfy $L_k^2\le -1$. Thus, all visible curves will have negative self-intersection. Let $E_i$ be the visible curves with $E_i^2\le -2$ and $C_j$ be the visible curves with $C_j^2=-1$. Now assume that the curves $\{E_i\}$ form a \emph{log terminal configuration}, i.e., a configuration of exceptional curves on the minimal resolution of a surface with log terminal singularities. Each connected component of the dual graph is of type $A_n$ (i.e. a chain) with no further restrictions on self-intersections $E_i^2$, and one of the graphs of types $D_n$ and $E_n$, with restrictions on self-intersections, see e.g.~\cite{alexeev1992log-canonical-surface}. Log terminal configurations are rational and, by Artin \cite{artin1962some-numerical}, the curves $E_i$ on $\tilde X$ can be contracted to obtain a projective surface $X$. Let $\pi\colon \wX\to X$ be the contraction morphism. (More generally, one may assume that $\{E_i\}$ form a log canonical configuration. In our examples, only log terminal singularities occur.) The surface $\wX$ is then the minimal resolution of singularities of~$X$ and one has \begin{displaymath} K_\wX = \pi^ K_X + \sum a_i E_i, \quad \pi^* K_X = K_\wX+\Delta := K_\wX + \sum b_i E_i. \end{displaymath} Here, $a_i$ are the \emph{discrepancies} and $b_i=-a_i$. The numbers $b_i$ satisfy the following linear system of $n$ equations in $n$ variables: \begin{equation}\label{eq:discrepancies} (K_\wX + \sum b_iE_i)E_j = 0 \iff \sum_i b_i E_iE_j= E_j^2+2 \quad \text{for any } j \end{equation} By Mumford, the matrix $(E_iE_j)$ is negative-definite, so this system has a unique solution. By Artin \cite{artin1962some-numerical}, all entries of the matrix $(E_iE_j)\inv$ are $\le 0$. Since the right-hand sides are $E_j^2+2 \le0$, it follows that $b_i\ge0$. \cite{alexeev1992log-canonical-surface} contains some convenient closed-form formulas for $b_i$'s, see also \cite{miyanishi2001open-algebraic}. \begin{theorem}\label{thm:no-bdry} Let $C_j$ be the visible $(-1)$-curves on $\wX$. Assume that: \begin{enumerate} \item For all $C_j$ one has $K_X\pi_(C_j) \ge 0$ (resp. $K_X\pi_(C_j) > 0$). \item $K_X^2 > 0$. \item There exist four rational numbers $d_0,d_1,d_2,d_3$ with $\sum d_k=3$ such that the coefficients of $C_j$ in the formula below are all $d_j\le 0$ (resp. all $d_j<0$): \begin{displaymath} K_\wX + \wD := f^(K_{\bP^2} + \sum d_k L_k) = K_\wX + \sum d_i E_i + \sum d_j C_j. \end{displaymath} \end{enumerate} Then the divisor $K_X$ is big and nef (resp. ample). \end{theorem} \begin{proof} Of course, (1) and (2) are necessary for $K_X$ to be big and nef (resp. ample). Condition (3) implies that $K_X$ is an effective linear combination of the curves $\pi(C_j)$. Indeed, $K_\wX+\wD = f^(0)=0$, so $K_X = \pi_(-\wD) = \sum (-d_j) \pi_(C_j)$. So, $K_X$ intersects any irreducible curve on $X$ non-negatively. Thus, $K_X$ is nef. For ampleness, note that union of visible curves supports an effective ample divisor. Thus, any curve on $X$ intersects its image, $\cup \pi(C_j)$. Therefore, any irreducible curve on $X$ intersects $\sum (-d_j)\pi_(C_j)$ positively, and so $K_X$ is ample by Nakai-Moishezon criterion. \end{proof} \begin{remark} Even if $K_X$ is only big and nef, it is semiample by Abundance Theorem in dimension 2, so its canonical model has ample $K_{X\can}$ and the same square $K_{X\can}^2=K_X^2$. \end{remark} \begin{remark} We usually assume that $0\le d_k \le 1$ (so that $\sum d_kL_k$ is a ``boundary'' in the standard MMP terminology), or at least that $d_k\le 1$ (so that it is a ``sub boundary''). But this is not necessary for the above proof. \end{remark} The coefficients $d_i$, $d_j$ in the divisor $\wD$ for the visible curves $E_i,C_j$ are readily computable. The formula is especially simple in terms of the quantities $(1-d_i)$, which are just the \emph{log discrepancies} of $(\bP^2, \sum d_kL_k)$: after blowing up the point of intersection of two curves with log discrepancies $1-d_1$, $1-d_2$, the new log discrepancy is $1-d_3 = (1-d_1)+(1-d_2)$. In other words, the log discrepancies add up. The above will be our essential method for finding new examples in the case of the empty boundary. For the examples with a nonempty boundary, we do not contract the strict preimage of the line $L_0$, which we denote by $\wB_0$. We no longer include $\wB_0$ in either collections $\{E_i\}$, $\{C_j\}$. We modify the assumption made at the beginning of this Section to allow $\wB_0^2$ to be non-negative, since it is a ``special'' curve. Let $B_0$ be the image of $\wB_0$ on $X$. Then we define the discrepancies for the pair $(X,B_0)$ via \begin{displaymath} \pi^ (K_X+B_0) = K_\wX+\Delta := K_\wX + \wB_0 + \sum b_i E_i. \end{displaymath} With this modification, Theorem~\ref{thm:no-bdry} readily extends: \begin{theorem}\label{thm:bdry} Let $C_j$ be the visible $(-1)$-curves on $\wX$. Assume that: \begin{enumerate} \item For all $C$ in $\{\pi(C_j),B_0\}$ one has $(K_X+B_0)C \ge 0$ (resp. $(K_X+B_0)C > 0$). \item $(K_X+B_0)^2 > 0$. \item There exist four rational numbers $d_0,d_1,d_2,d_3$ with $\sum d_k=3$ such that the coefficients of $C_j$ in the formula below are all $d_j\le 0$ (resp. all $d_j<0$): \begin{displaymath} K_\wX + \wD := f^(K_{\bP^2} + \sum d_k L_k) = K_\wX + d_0\wB_0 + \sum d_i E_i + \sum d_j C_j \end{displaymath} In addition, assume that $d_0\le 1$ (resp. $d_0<1$). \end{enumerate} Then the divisor $K_X+B_0$ is big and nef (resp. ample). \end{theorem} \begin{proof} The same proof as in Theorem~\ref{thm:no-bdry} gives that $K_X+ d_0B_0$ is an effective (resp. strictly positive) combination of the curves $\pi(C_j)$. But then so is $K_X+B_0 = K_X+d_0B_0 + (1-d_0)B_0$. If $d_0<1$ then $B_0$ appears in this sum with a positive coefficient. The rest of the proof is the same. \end{proof} We now state without proof some easy formulas. \begin{lemma}\label{lem:EK-K2} The following hold. (For the surface without a boundary, omit $B_0$.) \begin{enumerate} \item $(K_X+B_0) \pi_(C_j)=(K_\wX+\Delta)C_j = -1 + \wB_0 C_j + \sum_i b_i E_iC_j$. \item $(K_X+B_0)^2= (K_\wX+\Delta)^2 = K_\wX^2 + K_\wX\Delta + (\Delta-\wB_0)\wB_0 - 2.$ For the surface without a boundary, $K_X^2= (K_\wX+\Delta)^2 = K_\wX^2 + K_\wX\Delta.$ \item $K_{\wX}^2 = 9 - (\text{the number of blowups in } \wX\to\bP^2)$. \item $K_\wX E_i= -E_i^2-2$ and $K_\wX \wB_0 = -\wB_0^2-2$. \end{enumerate} \end{lemma} \section{Combinatorial game} \label{sec:game} As usual, we associate with a configuration of curves on a surface its dual graph. The vertices are labeled with marks $-E_i^2$ (we call them \emph{marks} because we use \emph{weights} for a different purpose). Thus, the initial configuration of lines on $\bP^2$ corresponds to a complete graph on four vertices with marks $-1, -1, -1, -1$, and we have a graph describing the visible curves on $\wX$. To simplify the typography, the $(-1)$-curves $C_j$ are shown in white with no marks. The exceptional curves $E_i$ are shown in black, and the marks $2$ are omitted. The reduced boundary $\wB_0$, if present, is shown as a crossed vertex. We call the dual graph of the visible curves on $\wX$ the \emph{visible graph}. It can be obtained by performing a series of insertions in the initial graph on four vertices with given marks $-1,-1,-1,-1$. Each instance is an insertion of a new vertex $v_3$ with mark 1 between two vertices $v_1, v_2$, at the same time increasing the marks of $v_1$ and $v_2$ by 1. Now we attach a weight to each vertex of the visible graph. First we choose rational numbers $w_0, w_1, w_2, w_3$ for the four vertices of the initial graph, called the \emph{initial weights}. We define the weights for the other vertices inductively in the process of inserting vertices as follows. As a new vertex $v_3$ is inserted between two vertices $v_1, v_2$ with already assigned weights $w(v_1)$ and $w(v_2)$, we define the weight of $v_3$ to be $w(v_3)=w(v_1)+w(v_2)$. Indeed, our weights are just the suitably normalized log discrepancies for the pair $(\bP^2, \sum_{k=0}^3 d_k L_k)$: $w_s = n(1- d_s)$ for some positive rational number $n$, for all the visible curves. We can always rescale $n$ to make $w_s$ integers, if we like. \begin{lemma}\label{lem:weight-conds} In terms of the weights, the conditions on the coefficients $d_k,d_0,d_j$ in Theorems~\ref{thm:no-bdry} and \ref{thm:bdry} translate to the following: \begin{enumerate} \item $d_0+d_1+d_2+d_3=3$ $\iff$ $n=w_0+w_1+w_2+w_3$. \item $d_j\le 0$ (resp. $d_j<0$) for a visible $(-1)$-curve $C_j$ $\iff$ the weight $w_j\ge n$ (resp. $w_j>n$) for the corresponding white vertex. \item In the case with a nonempty boundary, $d_0\le 1$ (resp. $d_0<1$) for the curve $\wB_0$ $\iff$ $w_0\ge0$ (resp. $w_0>0$) for the corresponding crossed vertex. \end{enumerate} \end{lemma} For as long as the weights satisfy these conditions, all we have to do is this: \begin{enumerate} \item Make sure that the configuration of the black vertices $\{E_i\}$ is log terminal. \item Compute the negatives of the discrepancies $b_i$ from the linear system~\ref{eq:discrepancies}, or using the formulas from \cite{alexeev1992log-canonical-surface}, or by any other method. \item Make sure that $K_X\,\pi_(C_j)\ge0$, $K_X\wB_0>0$ (if $\wB_0$ is present), and $K_X^2>0$ (resp. $(K_X+B_0)^2>0$) using the formulas in Lemma~\ref{lem:EK-K2}. \end{enumerate} If all of these are satisfied then we get ourselves an example of a log canonical surface (which is either $X$ or $X\can$) with ample (log) canonical divisor. \medskip The visible graph is homeomorphic to a complete graph on four vertices, but the edges between the corners may contain many intermediate vertices. \begin{definition} We call an edge a \emph{Calabi-Yau (or CY) edge} if all the white vertices on this edge have weights $n$, that is, they have discrepancies $d_i=0$. \end{definition} The picture below shows two examples of edges that we use. \begin{center} \begin{tikzpicture} \begin{scope}[every node/.style={draw,color=black,inner sep=2pt,fill,circle}] \node[fill=white] (a0) at (0,0) {}; \node (a1) at (1,0) {}; \node (a2) at (2,0) {}; \node (a3) at (3,0) {}; \node (a4) at (4,0) {}; \end{scope} \draw[very thin] (a0)--(a1); \draw[ultra thick] (a1)--(a2) (a3)--(a4); \draw[dashed] (a2)--(a3); \end{tikzpicture} \end{center} \begin{center} \begin{tikzpicture} \begin{scope}[every node/.style={draw,color=black,inner sep=2pt,fill,circle}] \node[fill=white] (a0) at (0,0) {}; \node (a1) at (1,0) {}; \node (a2) at (2,0) {}; \node (a3) at (3,0) {}; \node (a4) at (4,0) {}; \node (a5) at (5,0) {}; \node (a6) at (6,0) {}; \node (a7) at (7,0) {}; \node[fill=white] (a8) at (8,0) {}; \end{scope} \node[above of=a4, node distance=1em] {3}; \draw[very thin] (a0)--(a1) (a7)--(a8); \draw[ultra thick] (a1)--(a2) (a3)--(a4)--(a5) (a6)--(a7); \draw[dashed] (a2)--(a3) (a5)--(a6); \end{tikzpicture} \end{center} In general, if the end vertices have weights $w_1$, $w_2$ then vertices in the interior of this chain have weights of the form $m_1w_1+m_2w_2$ for some coprime positive integers $m_1,m_2$, and the way in which these integers are produced in the sequence of blowups is equivalent to the well known in number theory Stern-Brocot tree. Thus, every edge is encoded by a sequence of positive rational numbers $\{m_{1,i}/m_{2,i}\}$ for the white vertices. For the two examples above, the sequences are $\{m/1\}$ and $\{m/1, 1/m'\}$. For a CY edge, these numbers must satisfy the condition $m_{1,i}w_1+m_{2,i}w_2 = n$. \medskip The following two lemmas are very easy and are given without proof. \begin{lemma}\label{lem:near-CY} ${}$ \begin{enumerate} \item Suppose that all edges in the visible graph are CY edges. If $B_0\ne0$ then in addition suppose that the weight $w_0=0$. Then one has $K_X\equiv 0$ (resp. $K_X+B_0\equiv 0$). \item Suppose that all edges are CY, except for one where there is a unique white vertex of weight $n+1$. If $B_0\ne0$ then in addition suppose that the weight $w_0=0$. Then $K_X \equiv \frac1{n}C$, where $C$ is an image of a $(-1)$-curve corresponding to that special white vertex (resp. $K_X+B_0\equiv\frac1{n}C$). \item In the case with the nonempty boundary, suppose that all edges are CY and that the weight of $L_0$ is 1. Then $K_X+B_0\equiv \frac1{n}B_0$ and $K_X \equiv -\frac{n-1}{n} B_0$. \end{enumerate} \end{lemma} \begin{lemma}\label{lem:delta-eps-computed} In the last case (3) of Lemma~\ref{lem:near-CY}, the invariant $\delta_1$ defined in \eqref{def:epsilon-delta} equals $\delta_1(X,B_0)=\frac1{n}$. In all cases with nonempty boundary, one has $\epsilon_1(X,B_0) = -2 + \sum b_i E_i\wB_0$. \end{lemma} Our main strategy for finding interesting examples is this: start with a CY situation, i.e., case (1) of Lemma~\ref{lem:near-CY}, and then go just one step up, to get in the situation of cases (2) or (3). The (log) canonical divisor is then guaranteed to be quite small. \begin{remark} The surfaces $X$ appearing in case (1) of Lemma~\ref{lem:near-CY} with empty boundary satisfy $K_X\equiv 0$ and $H^1(\cO_X)=0$, and are sometimes called log Enriques surfaces. Our construction with weights provides a huge supply of such surfaces. \end{remark} \begin{remark} Another convenient way to compute $(K_X+B)^2$, resp. $K_X^2$, is the following. If $K_X+B = \frac1{n}C$ then certainly $(K_X+B)^2 = \frac1{n} (K_X+B) C$. So one has to maximize the sum of the weights $n$ and to minimize $(K_X+B)C$. \end{remark} \section{Simplest weights $(0,1,1,1)$ and $(1,1,1,1)$} \label{sec:weights1} Figure~\ref{fig:60-462} gives the smallest volumes that can be achieved playing the combinatorial game with $B\ne0$ and weights $(0,1,1,1)$, and with $B=0$ and weights $(1,1,1,1)$. \begin{figure}[!h] \includegraphics{fig60-462} \caption{Surfaces with $(K_X+B)^2=\frac1{60}$ and $K_X^2=\frac1{462}$} \label{fig:60-462} \end{figure} \begin{notation} The large numbers are marks, when not equal to 1 or 2. The blue small numbers underneath are the weights, and the red fractional numbers on top are $b_i$, the negatives of discrepancies. \end{notation} For the first pair $(X,B)$ one has $\epsilon_1=1-\frac13-\frac14-\frac15 = \frac{13}{60}$. There is an alternative choice of weights $(1,3,4,5)$ in this case, for which this pair fits into the case (3) of Lemma~\ref{lem:near-CY}, i.e. all edges are CY. Then $\delta_1=\frac1{13}$ by Lemma~\ref{lem:delta-eps-computed}, and $(K+B)^2 = \frac{13}{60}\cdot\frac1{13} = \frac1{60}$. In fact, another description for this pair is $(X,B) = (\bP(3,4,5), D_{13})$ where $D_{13}$ is a degree 13 weighted hypersurface, and this is exactly Koll\'ar's example from \cite{kollar2013moduli-varieties}. One has $\rho(X)=\rank\Pic X=1$, and $K_X+B$, $B$, and $-K_X$ are ample. For the second pair we can also choose the weights $(1-2\epsilon, 1, 1+\epsilon, 1+\epsilon)$, $0<\epsilon<\frac12$, for which \eqref{thm:no-bdry}, \eqref{lem:weight-conds} give that $K_X$ is ample and not just big and nef. \section{Example with nonempty boundary: $1/{462}$} \label{sec:with-boundary} Figure~\ref{fig:462s} shows two non-isomorphic visible graphs producing pairs $(X,B)$ of the smallest volume with nonempty boundary that we were able to find by our method. \begin{figure}[!h] \includegraphics{fig462s} \caption{Surfaces with $(K_X+B)^2=\frac1{462}=\frac1{11\cdot 42}$ and $B\ne0$} \label{fig:462s} \end{figure} The winning weights are $(1,2,3,5)$. Both pairs achieve the minimal possible value of $\epsilon_1 = 1 - \frac12 - \frac13 - \frac17 = \frac1{42}$. On the other hand, one has $K_X+B \equiv \frac{1}{11}B$ and $\delta_1=\frac1{11}$ by Lemma~\ref{lem:delta-eps-computed}. Thus, one has $(K_X+B)^2 = \epsilon_1 \delta_1$. The divisor $K_X+B$ is big and nef but there are no weights for which \eqref{thm:no-bdry}, \eqref{lem:weight-conds} or a variation of them show that $K_X+B$ is ample. The canonical model has ample $K_{X\can}+B\can$ and $(K_{X\can}+B\can)^2 = (K_X+B)^2 = \frac1{462}$. \begin{notation} We use Figure~\ref{fig:462s} for an alternative labeling of the curves, as follows. We denote the strict preimages of the four lines by $\wL^w$, where the superscript $w=1,2,3,5$ is the (blue) weight of the corresponding vertex. Similarly, we denote one of the remaining curves by $\wF_w^{i,j}$ if its vertex lies on the edge between $\wL^i,\wL^j$ and has weight $w$. In the same vein, we call the initial lines in the plane $L^w$ and the intersection points $P^{i,j} = L^i\cap L^j$. Finally, we use this labeling for the standard orthogonal basis of $\Pic\wX$ consisting of the pullback $H$ of a line from $\bP^2$ and the full preimages of the $(-1)$-curves from the intermediate blowups $\wX\to\bP^2$. Thus, in $\Pic\wX$ we have $\wL^1 = H - F^{1,3}_4 - F^{1,5}_6$, $\wF^{1,3}_4 = F^{1,3}_4 - F^{1,3}_7 - F^{1,3}_{11}$, $\wF^{1,3}_7 = F^{1,3}_7 - F^{1,3}_{11}$, $\wF^{1,3}_{11} = F^{1,3}_{11}$, etc. \end{notation} \begin{theorem}\label{thm:is_K+B_ample} The two visible graphs of Figure~\ref{fig:462s} describe the same surface $X$. If $\chr k\ne2$ then $K_X+B$ is ample, $\rho(X)=2$, and $X=X\can$ has 4 singularities. If $\chr k=2$ then $K_X+B$ is big, nef, but not ample, and it contracts a $(-2)$-curve. One has $\rho(X\can)=~1$, and $X\can$ has 5 singularities, the last one a simple $A_1$. \end{theorem} \begin{proof} The second graph has an extra $(-1)$-curve $F^{1,5}_{11}$ not present in the first graph. It is easy to see that with respect to the first graph it is simply the strict preimage of the line in $\bP^2$ connecting the points $P^{1,5}$ and $P^{2,3}$. Thus, the surfaces are the same but different curves are illuminated as being visible. Let us work with the first representation. Suppose that there exists another, not visible curve $\wD$ such that $\wD\cdot\pi^K_X=0$, which is then contracted by a linear system $\|N\pi^* K_X\|$ for $N\gg0$. Since $\rho(X)=2$, there could only be one such irreducible curve. We write \begin{math} \wD = d H - \sum m^{ij}_w F^{ij}_w. \end{math} The divisor $\wD$ intersects by zero the curves $\wL^1$, $\wF^{1,3}_4$, $\wF^{1,5}_6$, $\wL^2$, $\wF^{2,3}_5$, $\wF^{2,3}_8$ since the full pullback $\pi^* K_X=\frac1{11}\pi^* B_0$ is a strictly positive combination of these curves. Also, $\wD$ intersects non-negatively all the other visible curves. This gives an explicit set of identities and inequalities. One checks that the only solution~is \begin{displaymath} \wD = c \big[ 3H - (2F^{1,3}_4 + F^{1,3}_7 + F^{1,3}_{11} ) - (F^{1,5}_6 + F^{1,5}_{11}) - (F^{2,5}_7 + F^{2,5}_9 + F^{2,5}_{11}) \big]. \end{displaymath} Then $\wD K_\wX=0$ and $\wD^2=-2c^2$. It follows from the genus formula that $c=1$, and $\wD$ is a smooth rational $(-2)$-curve. It must be a strict preimage of a cubic curve $D$ in $\bP^2$ which has: \begin{enumerate} \item a cusp at $P^{1,3}$ with the tangent direction $L^3$, \item a flex at $P^{2,5}$ with the tangent direction $L^2$, \item a tangent at $P^{1,5}$ to the line $L^5$. \end{enumerate} Thus, $D$ is a cuspidal cubic, and the set of points of $D\setminus P^{1,3}$ has the structure of the additive group $\bG_a$. We see that the cubic $D$ with the above properties exists if and only if the system of equations $3P^{2,5}=P^{2,5} + 2P^{1,5}=0$ has a solution in the base field $k$ with $P^{2,5}\ne P^{1,5}$. This is possible iff $\chr k=2$; then $P^{2,5}=0$ and $P^{1,5}$ is any other smooth point. This completes the proof. A second proof using the alternative presentation of surface $X$ works in characteristics 2 and 0, and by extension in all but finitely many other positive characteristics. The second visible graph of Figure~\ref{fig:462s} leads to a smooth rational $(-2)$-curve \begin{displaymath} \wD = 4H - (2F^{1,3}_4 + F^{1,3}_7 + F^{1,3}_{11} ) - (2F^{1,5}_6 + 2F^{1,5}_{11}) - (F^{2,3}_5 + F^{2,3}_7 + F^{2,3}_9 + F^{2,3}_{11}). \end{displaymath} It must be then a strict preimage of a quartic curve $D$ on $\bP^2$ that has: \begin{enumerate} \item an $A_2$-singularity (a cusp) at $P^{1,3}$ with the tangent line $L^3$, \item an $A_3$ (a tachnode) or $A_4$-singularity at $P^{1,5}$ with the tangent line $L^5$, \item a hyperflex at $P^{2,3}$ with the tangent direction $L^2$, i.e. $L^2\cap D$ is a smooth point of $D$ and the intersection is of multiplicity $4$. \end{enumerate} If $\chr k=0$ then such quartic curves do not exist. Indeed, \cite[Table 2]{wall1995geometry-quartic} shows that irreducible quartic curves in characteristic 0 with $A_2A_3$ or $A_2A_4$ singularities do not have any hyperflexes. Since the property of $K_X+B$ being ample is open, the same is true in all but finitely many prime characteristics. On the other hand, if $\chr k=2$ then there exists a unique such curve (with $A_2A_3$), which can be concluded from the normal forms of quartics given in \cite{wall1995quartic-curves}. Explicitly, the equation of $D$ can be taken to be $f=x^4 + x^2yz + x^2y^2 + y^2z^2$ and the lines are $L^1=(x)$, $L^2=(y+z)$, $L^3=(x+z)$, $L^5=(y)$. \end{proof} \begin{remark} Combining the two presentations of surface $X$ in the proof, we see that a quartic with the above configuration of singularities and tangent lines does not exist in prime characteristics $p\ne2$. \end{remark} \begin{remark}\label{lem:ints_w_visible} The intersections of $\wD$ with the visible curves are zero except for the following: \begin{enumerate} \item For the first graph, $\wD\wF^{1,3}_{11}=\wD\wF^{1,5}_{11}=\wD\wF^{2,3}_{11}=1$. \item For the second graph, $\wD\wF^{1,5}_{11}=2$ and $\wD\wF^{1,3}_{11}=\wD\wF^{2,3}_{11}=1$. \end{enumerate} \end{remark} \section{Example with empty boundary: $1/{\num{48 983}}$} \label{sec:empty-boundary} There exist at least four visible graphs that produce surfaces $X$ without a boundary and $K_X^2 = \frac1{\num{48983}} = \frac1{11\cdot 61\cdot 73}$. Three of them share the same list of singularities; the list is different for the fourth graph. The first two graphs can be obtained directly by inserting 10 vertices into the edge from $\wL^1$ to $\wL^2$, i.e. by blowing up the surfaces $\wX$ of Figure~\ref{fig:462s} above the point $P^{1,2}$ 10 times. We show one of these surfaces in Figure~\ref{fig:48983}. It leads to a surface with $\rho(X)=2$ and three singularities. The fourth graph describes a surface $X'$ with $\rho(X')=3$ which has four singularities: the singularity with the minimal resolution $[2,4,2,2,2]$ of Figure~\ref{fig:48983} is replaced by two singularities $[2,6]$ and $[2,3,2,2]$. \begin{figure}[!h] \includegraphics{fig48983} \caption{Surface with $K_X^2=\frac1{\num{48983}}=\frac1{11\cdot 61\cdot 73}$} \label{fig:48983} \end{figure} The set of winning weights in these cases is again $(1,2,3,5)$. Since $\num{48983} > 42^2$, these examples show that $K^2(\cS_1)$ is achieved when the boundary is empty, that is, $K^2_1(\cS_1) > K^2(\cS_1) = K^2(\cS_0)$. Similarly to the previous case, the divisor $K_X$ is big and nef but there are no weights for which \eqref{thm:no-bdry}, \eqref{lem:weight-conds} or a variation of them show that $K_X$ is ample. But the canonical model $X\can$ has ample canonical class and $K_{X\can}^2=K_X^2 = \frac1{\num{48983}}$. \begin{theorem}\label{thm:is_K_ample} The three distinct visible graphs describe the same surface $X$. The fourth graph describes a different surface $X'$ which however has the same canonical model since there is a crepant blow down $X'\to X$ contracting the image of a $(-1)$-curve from $\wX'$. % If $\chr k\ne2$ then $K_X$ is ample, $\rho(X)=2$, and $X=X\can$ has 3 singularities. If $\chr k=2$ then $K_X$ is big, nef, but not ample, and it contracts a $(-2)$-curve; $\rho(X\can)=~1$, and $X\can$ has 4 singularities, the last one a simple $A_1$. \end{theorem} \begin{proof} The proof of the equivalence for the first three graphs is the same as in Theorem~\ref{thm:is_K+B_ample}. Since the surface in the end is unique we do not draw the other two graphs but indicate the two invisible curves that have to be added to Figure~\ref{fig:48983} to obtain them. These are the strict preimages of a line in $\bP^2$ joining $P^{1,5}$ and $P^{2,3}$, and of a conic passing through $P^{1,2}$ generically, through $P^{1,5}$ with the tangent $L^5$, and through $P^{2,3}$ with the tangent $L^3$. Similarly, the surface $X'$ described by a fourth graph, which we do not draw, has an invisible curve $C$, a strict preimage of a line through $P^{1,2}$ and $P^{3,5}$ such that $C\cdot \pi^K_{X'}=0$. Contracting this curve gives the same surface as in Figure~\ref{fig:48983}. From now on, we work with the surface $X$ described by Figure~\ref{fig:48983}. Again, if there exists an invisible curve $\wD$ with $\wD\cdot \pi^K_X=0$ then it must have zero intersection with the curves effectively supporting $\pi^K_X$, which include the 10 newly inserted curves $\wF^{12}_w$. Thus, the inequalities in this case are reduced to those in Theorem~\ref{thm:is_K+B_ample}, and the rest of the proof is the same. \end{proof} As in Remark~\ref{lem:ints_w_visible}, the intersections of $D$ with the visible curves are zero except for those listed there. \section{Connection with the algebraic Montgomery-Yang problem} \label{sec:montgomery-yang} The algebraic Montgomery-Yang problem \cite[Conj. 30]{kollar2008is-there} asks whether there exists a surface with $\rho(S)=1$ and $\pi_1(S\setminus\Sing S)=1$ that has \emph{four} quotient singularities. Conjecturally, the answer is no. All the possibilities for such surfaces were ruled out except when $K_S$ is ample, see \cite{hwang2012construction-singular}. It is amusing to note that if the characteristic 2 surface $S=X\can$ with 4 singularities which we constructed in Theorem~\ref{thm:is_K_ample} existed in characteristic 0 then it would provide a counterexample to the above conjecture. Let $U_s\ni s$ be a small neighborhood of a singular point $s$ and $L_s=U_s\setminus s$. Then the three singularities whose determinants $m=11,61,73$ are coprime to $2$ are quotient singularities and one has $\pi_1^{\rm alg}(L_s) = \bZ_m$. For the fourth singularity obtained by contracting a $(-2)$-curve one has $\pi_1^{\rm alg}(L_s) = 1$ in characteristic 2. One can prove that $\pi_1^{\rm alg}(S\setminus\Sing S)=1$ by the usual methods, by considering the images of the $(-1)$-curves $C_j$ connecting the singularities and using van Kampen theorem, which still holds for the \'etale fundamental group in positive characteristic by \cite[IX, Th.5.1]{grothendieck1971sga1-2}, cf. \cite{mathoverflow110511}. In any case, this surface also violates the orbifold Bogomolov-Miyaoka-Yau inequality $c_1^2(S) \le 3e_{\rm orb}(S)$, for which one may see the discussion in \cite[\S1]{kollar2008is-there}. Namely, it violates its corollary, the inequality \begin{displaymath} \sum_{s\in\Sing S} \left(1 - \frac1{\|\pi_1(U_s\setminus s)\|}\right) \le 3, \end{displaymath} if one literally replaces $\pi_1$ with $\pi_1^{\rm alg}$, or if one replaces $\|\pi_1(U_s\setminus s)\|$ with $m_i$. Thus, this configuration of singularities can not appear in characteristic 0 if $\rho(X)=1$. \section{The case of Picard rank 1} \label{sec:pic1} In part because of the connection with the algebraic Montgomery-Yang problem, it is of interest to know the minimal volume for surfaces with the additional condition $\rho(X)=1$, in characteristic 0. For surfaces without the boundary, the best we were able to find is $K_X^2 = \frac1{6351} = \frac1{3\cdot 29\cdot 73}$. There are three possible graphs for the visible curves in this case, and one of them describes a surface that can be obtained by contracting two curves on the hypersurface in a weighted projective space from Example~\ref{ex:urzua}. Thus, it is one of the surfaces $S^(2,2,4,10)$ studied in \cite[Sec.43]{kollar2008is-there}. The other two graphs are not of this type, and we give one of them in Figure~\ref{fig:6351}. However, all three graphs share the same list of singularities. Indeed, the argument we gave in the proof of Theorems~\ref{thm:is_K+B_ample}, \ref{thm:is_K_ample} shows that the three visible graphs describe the same surface. \begin{figure}[!h] \includegraphics{fig6351} \caption{Surface with $K_X^2=\frac1{6351}=\frac1{3\cdot 29\cdot 73}$ and $\rho(X)=1$} \label{fig:6351} \end{figure} \begin{remark} Comparing Figures~\ref{fig:48983} and \ref{fig:6351}, one can see that our surface with the minimal volume can be obtained from the surface $S^(2,2,4,10)$ by a weighted blowup at one point. \end{remark} In \cite{hwang2012construction-singular} Hwang and Keum construct, for any $a_1,a_2,a_3,a_4\ge2$, a surface $T=T(a_1,a_2,a_3,a_4)$ with $\rho(T)=1$ obtained by blowing up the 4-line configuration; it has two cyclic singularities corresponding to the chains $[2(a_4-1), a_3, a_1, 2(a_2-1)]$ and $[2(a_3-1), a_2, a_4, 2(a_1-1)]$. In particular, these surfaces include all the surfaces $S^(a_1,a_2,a_3,a_4)$ with $\gcd(w_1,w_3)=\gcd(w_2,w_4)=1$ by \cite{urzua2016characterization-Kollar}. \begin{theorem}\label{thm:special-surfaces} Let \begin{eqnarray} A &=& a_1a_2a_3a_4 -a_2a_3a_4 -a_1a_3a_4 -a_1a_2a_4 -a_1a_2a_3 + \\ && a_1a_2 +a_2a_3 +a_3a_4 +a_1a_4 -a_1 -a_2 -a_3 -a_4 +3 \\ B_1 &=& a_1a_2a_3a_4 -a_1a_3a_4 -a_1a_2a_3 +a_2a_3 +a_1a_4 -a_1 -a_3 +1\\ B_2 &=& a_1a_2a_3a_4 -a_2a_3a_4 -a_1a_2a_4 +a_1a_2 +a_3a_4 -a_2 -a_4 +1 \end{eqnarray} Then the following is true: \begin{enumerate} \item The surface $T(a_1,a_2,a_3,a_4)$ has ample canonical class $K_T$ iff $A>0$. \item The determinants of the two singularities are $B_1$ and $B_2$. \item $K_T^2 = A^2 / B_1B_2.$ \item The minimum $K_T^2 = \frac1{6351}$ is achieved for $(a_i)=(2,2,4,10)$, up to a cyclic rotation. \end{enumerate} \end{theorem} \begin{proof (1) We compute $\pi^*K_X\cdot C$ for a $(-1)$-curve $C$ by Lemma~\ref{lem:EK-K2}(1) and find that it is a product of $A$ and some positive terms. (2) is \cite[Lemma 2.4]{hwang2012construction-singular}. (3) follows by a direct computation, applying Lemma~\ref{lem:EK-K2}(2). (4) It is somewhat more convenient to use the variables $x_i=a_i-1$. Then \begin{displaymath} \frac{A}{x_1x_2x_3x_4} = 1- \frac1{x_1}\frac1{x_3}\left( 1+\frac1{x_2}+\frac1{x_4} \right) - \frac1{x_2}\frac1{x_4}\left( 1+\frac1{x_1}+\frac1{x_3} \right). \end{displaymath} One easily checks that for $j=1,2$ the partial derivatives $\partial (A/B_j) / \partial x_i\ge0$ when $A>0$ and $x_i\ge1$. Thus, it is sufficient to check the minimal collections $(a_i)$ for which $A>0$, meaning: for any other collection $(a_i')$ with $A>0$ one has $a_i'\ge a_i$ $\forall i$. We first find the ``critical'' collections, for which $A=0$. These are $(3,3,3,3)$, $(2,8,3,3)$, $(2,3,\frac{11}{2},3)$, $(2,3,3,8)$, $(2,2,4,9)$, $(2,2,5,6)$, $(2,2,6,5)$, $(2,2,9,4)$. Then, modulo rotational symmetry, the smallest collections $(a_i)$ for which $A>0$ are $(4, 3, 3, 3)$, $(2, 9, 3, 3)$, $(2, 8, 4, 3)$, $(2, 8, 3, 4)$, $(2, 3, 6, 3)$, $(2, 4, 3, 8)$, $(2, 3, 4, 8)$, $(2, 3, 3, 9)$, $(3, 2, 4, 9)$, $(2, 3, 4, 9)$, $(2, 2, 5, 9)$, $(2, 2, 4, 10)$, $(3, 2, 5, 6)$, $(2, 3, 5, 6)$, \linebreak $(2, 2, 6, 6)$, $(2, 2, 5, 7)$, $(3, 2, 6, 5)$, $(2, 3, 6, 5)$, $(2, 2, 7, 5)$, $(2, 2, 6, 6)$, $(2, 3, 9, 4)$, \linebreak $(2, 2, 10, 4)$, $(2, 2, 9, 5)$. Among these, the minimal value $A^2/B_1B_2 = \frac1{6351}$ is achieved for $(a_1,a_2,a_3,a_4)=(2,2,4,10)$. \end{proof} \bigskip For the surfaces with boundary, we found a pair with $(K_X+B_0)^2 = \frac1{78}$. The marks of the corners are 1, 3, $2'$, $2''$ ($B_0$ goes first, we use the notation $2',2''$ to distinguish the two vertices with the same marks), and the curves along the edges have marks 1--3, 1--2--2--1--$2'$, 1--2--1--$2''$, 3--$2'$, 3--1--2--2--2--$2''$, $2'$--$2''$. The weights that work for Lemma~\ref{lem:near-CY}(3) are $(1,1,2,3)$, $n=7$, $\delta_1=\frac17$, and $\epsilon_1=1-\frac12-\frac13-\frac1{13}=\frac7{78}$. \section{Why only four lines?} \label{sec:four-lines} It may seem naive and insufficient in search of examples to reduce oneself only to the simplest of line arrangements: four lines in the plane. Why not consider some more interesting configurations, e.g. a Fano or anti-Fano configuration of 7 lines or Segre (resp. dual Segre) configuration of 12 (resp. 9) lines? And why lines and not conics or curves of higher degree? In fact, there are good ad hoc reasons for this: (1) For all examples of log surfaces arising from 4 lines, one \emph{apriori} has $K_X^2 \le (K_{\bP^2} + \sum_{i=0}^3L_i)^2 = 1$. Similarly, for $d$ lines in general position an upper bound is $(d-3)^2$. For special line arrangements the upper bound is smaller but it starts with 2 for a special configuration of 5 lines. Although this is an \emph{upper} and not a lower bound, it shows how hard one has to work to achieve a minimum. Indeed, for $d\ge7$ lines in general position it is easy to show that \begin{displaymath} K_X^2 \ge 9-\frac{d(d-1)}{2} + \frac{d-4}{d-2}(d-4)d = \frac{d^2}{2} -\frac{11d}{2} +13 +\frac{8}{d-2} \ge \frac35, \end{displaymath} with the minimum achieved by blowing up all of the $\frac{d(d-1)}{2}$ intersection points of the $d$ lines. (2) The combinatorial game, similar to the one we described in Section~\ref{sec:game}, becomes very hard to play for more than 4 lines. E.g., for 5 lines the condition on the weights becomes $w_0+\dotsb +w_4=2n$, and there are very few interesting examples. A similar thing happens if one works with conics instead of lines. (3) We also note that constructions of many interesting log surfaces with ample $K_X$ can be reduced to blowups of the same 4-line configuration in $\bP^2$, even when the initial definition is different, see e.g. \cite{kollar2008is-there, hwang2011maximum-number, hwang2012construction-singular, urzua2016characterization-Kollar}. The surfaces of \cite{hwang2012construction-singular} that use conics and cubics all have bigger volumes. \section{Lower bound for $K^2(\cS_1) = K^2(\cS_0)$.} \label{sec:k2-lower-bound} In this section, we spell out the explicit effective lower bound for $K^2(\cS_0)$ provided by Theorem 4.8 of \cite{alexeev2004bounding-singular}. In our present notations, it says the following: \begin{displaymath} K_X^2 \ge \frac1{\ell \cdot (2\ell)^N}, \quad\text{where } N=128\ell^5+4\ell \text{ and } \ell = \ulc 1 / {\delta_1(\cS_1)} \urc. \end{displaymath} Together with Koll\'ar's bound $\delta_1(\cS_1)\ge \frac1{42}$, this gives \begin{displaymath} K_X^2 \ge \frac 1 {42 \cdot 84^{128\cdot 42^5 + 4\cdot 42}} \approx 10^{ - 3.22 \cdot 10^{10}}. \end{displaymath} Certainly this is not a realistic bound. Many improvements can be made to the estimates in \cite{alexeev2004bounding-singular} but they would not cardinally change the estimate without introducing some cardinally new methods. The true lower bound for $K^2(\cS_0)$ may be closer to Koll\'ar's conjectural bound for $K^2(\cS_2) = \frac1{(42\cdot 43)^2}$. Indeed, we dare to think that it could be close, or equal to $\frac1{\num{48983}} \approx \frac{67} {(42\cdot 43)^2}$ that we give here. \def$'${$'$} \providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace} \providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR } \providecommand{\MRhref}[2]{% \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2} } \providecommand{\href}[2]{#2}	{ "redpajama_set_name": "RedPajamaArXiv" }	4,657
\section{Introduction} Nuclear magnetic resonance (NMR) has developed many techniques to control physical systems and maintain their coherence \cite{Freeman99, Claridge99}. A composite pulse is one of such techniques, in which a sequence of pulses is employed to cancel out a systematic error inherent in the pulses \cite{Jones09}. A systematic error is an unwanted imperfection in control parameters, such as poor calibration, and should not be confused with a random noise. The composite $\pi$-pulse by Levitt and Freeman \cite{Levitt79}, developed with intuitive but convincing account of its robustness, opened up a new field of research. Now we have hundreds of composite pulses \cite {Levitt86, Levitt96} and dozens of methods to design them, such as iterative expansion \cite{Tycko85}, gradient ascent pulse engineering (GRAPE) \cite{Khaneja05,Machnes11} and concatenation \cite{Ichikawa11}. Recently, quantum information processing (QIP) \cite{Nielsen00, Bengtsson06, Gaitan08, Nakahara08} has an influence over the composite pulse design. Very accurate control of a quantum system is required for a successful quantum error correction, as shown in \cite{Gaitan08} for example. Any quantum algorithm can be simulated by quantum circuits composed of one-qubit unitary operations and the controlled-NOT (CNOT) operations. As a result, robustness is required for {\it arbitrary} one-qubit operations and CNOT operation. In contrast, operations with limited angles and phases have been required in conventional NMR manipulations. Numerous composite pulses have been proposed to date in the context of QIP \cite{Ichikawa11, Jones11, Jones03, Hill07, Testolin07, Tomita10, Cummins03, Brown04, Alway07}. Geometric quantum computation \cite{Zanardi99, Zhu00} has been proposed to attain reliable quantum control. In addition to the dynamical phase, cyclic evolution of a quantum system allows for various geometric phases \cite{Shapere89, Berry84, Wilczek84, Aharonov87, Mead92}, which are controllable and thereby can be utilised for unitary operations. We call a gate implemented with a geometric phase a geometric quantum gate (GQG) hereafter. Mathematically, a geometric phase is regarded as a holonomy associated with a closed path in a suitable base manifold associated with a cyclic evolution \cite{Simon83, Nakahara03, Page87}. Random fluctuations along the integration path are expected to cancel out, leading to a quantum gate robust against random noise. Although there is numerical support for the robustness of GQGs \cite{Zhu05}, this issue is still under debate \cite{Blais03}. In this article, we unite these two apparently different constructions of robust unitary operations. More precisely, we reveal that composite pulses robust against certain kinds of systematic errors are nothing but GQGs. This has been observed previously in one-qubit operations \cite{Kondo11}. Now we elaborate and generalise this observation to two-qubit operations, which are indispensable for a universal set of quantum gates in QIP. Our work reveals that many composite pulses are geometric in nature and their robustness is attributed to the robustness of GQGs against certain errors. This article is organised as follows. Geometric phase, in particular Aharonov-Anandan phase and its application to implementation of a quantum gate are introduced in Sec.~2. We employ the perturbation theory as a guiding principle to design composite pulses and derive the robustness condition in Sec.~3. In Sec.~4, we present the main statement of this article, that is, existing composite pulses to suppress the pulse length error and the $J$-coupling error are GQGs. We will employ a group theoretical argument to present our statement in a unified manner. The assertion in Sec.~4 is exemplified in Sec.~5 and 6 by analysing various composite pulses from our viewpoint. Section~7 is devoted to conclusion and discussions. \section{Geometric Quantum Gates} \label{GQG} Geometric phase, anticipated in many branches of physics and chemistry \cite{Shapere89}, was formulated first by Berry in an adiabatic evolution of a quantum system. In \cite{Berry84}, Berry considered a cyclic evolution of a quantum system whose Hamiltonian has time-dependent parameters, and pointed out that after the cyclic and adiabatic evolution, the system may acquire not only the dynamical phase factor, but also a geometric phase factor, which is given by a circuit integral in the parameter manifold. This integral is geometric, in the sense that it is independent of how fast the circuit is traversed. The Berry phase has been generalised in many ways. One of such generalizations is Wilczek-Zee holonomy: In the presence of $n$-fold degeneracy, the geometric phase factor can be replaced to an element of a unitary group U($n$), which is also independent of how fast the circuit is traversed \cite{Wilczek84}. Aharonov and Anandan showed in \cite{Aharonov87} that the geometric phase appears even in a non-adiabatic evolution. Consider an $n$-level system, whose normalised state vector at time $t\in [0,T]$ is given by $\ket{\psi(t)}\in\mathbb{ C}^n$. Dynamics of the system is characterised by the Schr\"odinger equation \begin{eqnarray} \ri\frac{\rd}{\rd t}\|\psi(t)\rangle=H(\lambda(t))\ket{\psi(t)}, \end{eqnarray} where the Hamiltonian $H(\lambda(t))$ is Hermite and time-dependent through parameters $\lambda(t)=(\lambda_1(t), \ldots, \lambda_N(t))$. Here we set $\hbar=1$. When the evolution is cyclic with a period $T$, i.e., \begin{eqnarray} \ket{\psi(T)}=\re^{\ri\gamma}\ket{\psi(0)}, \qquad \gamma\in\mathbb{ R}, \end{eqnarray} then the phase $\gamma$ the system acquires after the cyclic evolution includes geometric contribution $\gamma_{\rm g}$, which is defined in terms of the dynamical phase $\gamma_{\rm d}$ as \begin{eqnarray} \gamma_{\rm g}=\gamma-\gamma_{\rm d}, \qquad \gamma_{\rm d}=-\int_0^T\mathrm{d} t\bra{\psi(t)}H(\lambda(t))\ket{\psi(t)}. \end{eqnarray} This phase $\gamma_{\rm g}$ is called the Aharonov-Anandan phase. It is possible to interpret the Aharonov-Anandan phase in terms of geometric structure of the Hilbert space $\mathbb{ C}^n$. See \ref{appHol} for details. Also, for another expression of the Aharonov-Anandan phase, see, {\it e.g.}, \cite{Aharonov87, Mead92, Page87}. Applications of geometric phases are found in QIP. For example, Zanardi and Rasetti proposed to use the Wilczek-Zee holonomy to implement unitary gates \cite{Zanardi99}. It is also possible to implement unitary gates by using the Aharonov-Anandan phase \cite{Ichikawa11, Zhu00, Kondo11, Ota09a, Ota09b}. To see this, let $\{\ket{\psi_a}\}_{1 \leq a \leq n}$ be the eigenvectors of a Hamiltonian $H(\lambda(0))$ and suppose their dynamical evolution is cyclic, that is, \begin{eqnarray} \ket{\psi_a(T)}=U(T)\ket{\psi_a}, \qquad U(T)={\cal T}\re^{-\ri\int_0^T\mathrm{d} s H(\lambda(s))} \label{adb} \end{eqnarray} and \begin{eqnarray} \ket{\psi_a(T)}=\re^{\ri\gamma^a}\ket{\psi_a}, \qquad \gamma^a\in\mathbb{ R}, \label{cyc} \end{eqnarray} where the time-ordered product is denoted by ${\cal T}$. Equating Eqs.~(\ref{cyc}) and (\ref{adb}), we observe that $\ket{\psi_a}$ is an eigenvector of $U(T)$ with the eigenvalue $\re^{\ri\gamma^a}$, that is, \begin{eqnarray} U(T)\ket{\psi_a}=\re^{\ri\gamma^a}\ket{\psi_a}. \label{eigen} \end{eqnarray} When there is no degeneracy, the spectral decomposition of $U(T)$ is written as \begin{eqnarray} U(T)=\re^{\ri\gamma^1}\ket{\psi_1}\bra{\psi_1}+\dots+\re^{\ri\gamma^n}\ket{\psi_n}\bra{\psi_n}. \end{eqnarray} The phase $\gamma^a$ is decomposed as $\gamma^a=\gamma_{\rm g}^a+ \gamma_{\rm d}^a$ in terms of the dynamical phase defined as \begin{eqnarray} \gamma_{\rm d}^a=-\int_0^T\mathrm{d} t\bra{\psi_a(t)}H(\lambda(t))\ket{\psi_a(t)}, \qquad \ket{\psi_a(t)}=U(t)\ket{\psi_a}. \end{eqnarray} A unitary operator $U(T)$ is called a geometric quantum gate (GQG) if $\gamma_{\rm d}^a$ vanishes for all $a$. \section{Perturbative Construction of Composite Pulses} In actual situations in NMR, the dynamics is controlled by a sequential application of rf-pulses with constant field strength. Accordingly, the time interval $[0, T]$ is divided into $k$ intervals, in each of which the Hamiltonian is constant. More precisely, we define the $i$-th temporal interval $[t_ {i-1}, t_i]$, where $t_i$ satisfies $0=t_0<t_1<\ldots<t_k=T$, and define a piecewise constant Hamiltonian, which takes the form $H(\lambda^i)$ in the $i$-th interval $[t_{i-1}, t_i]$. Here $\lambda^i=(\lambda_1^i, \dots, \lambda_N^i)$ is a constant parameter vector while $N$ is the number of control parameters. Then, the $i$-th rf-pulse gives rise to a unitary operator \begin{eqnarray} \re^{-\ri W^i}, \qquad W^i=H(\lambda^i)\cdot(t_i-t_{i-1}), \end{eqnarray} and $U(T)$ can be written as \begin{eqnarray} U(T)=\re^{-\ri W^k}\cdots \re^{-\ri W^1}. \end{eqnarray} Now we wish to implement a \lq target\rq~unitary operator $U$ as $U=U(T)$. The target $ U$ should be implemented in a way robust against the error under consideration as much as possible. Hereafter we seek a condition for such robust implementation. We consider errors which cause displacement \begin{eqnarray} W^i\rightarrow W^i+\delta W^i, \label{dis} \end{eqnarray} where $\delta W^i$ is a self-adjoint operator corresponding to the error. When $\delta W^i$ is sufficiently small in the sense of the operator norm, we can use the perturbation theory and find \begin{eqnarray} \re^{-\ri (W^i+\delta W^i)}\approx\re^{-\ri W^i}$\mathbbm{1}_n-\ri\delta W_{\rm I}^i$; \qquad \delta W^i_{\rm I}:=\int_0^1\mathrm{d} x\,\mathrm{e}^{\mathrm{i} x W^i}\delta W^i\mathrm{e}^{-\mathrm{i} x W^i}, \label{discHint} \end{eqnarray} to the first order in $\delta W^i$. Here the identity operator on $\mathbb{ C}^n$ is denoted by $\mathbbm{1}_n$. The operator $\delta W^i_{\rm I}$ is the error operator $\delta W^i$ in the interaction picture. Then, the unitary operator $U^\prime$ implemented with the error $\delta W^i$ is given by \begin{eqnarray} U^\prime=\re^{-\ri (W^k+\delta W^k)}\cdots \re^{-\ri (W^1+\delta W^1)}\approx U$\mathbbm{1} _n-\ri\Delta W$, \end{eqnarray} where \begin{eqnarray} \Delta W=\sum_{i=1}^k{V^{i-1}}^\dag\delta W^i_{\rm I}V^{i-1}, \qquad V^i=\re^{-\ri W^i}\cdots\re^{-\ri W^1} \quad {\rm for} \quad i=1,2,\dots k-1, \end{eqnarray} with $V^0=\mathbbm{1}$. Many, albeit not all, composite pulses satisfy the following robustness condition \begin{eqnarray} \Delta W=0, \label{lt} \end{eqnarray} which we can evaluate once we specify $\delta W^i$. This condition guarantees the effect of the error vanishes to the first order in $\delta W^i$. Now we wish to address the relation between the robustness condition (\ref{lt}) and a classification of composite pulses common in the NMR community. There are two types, Type A and Type B, of composite pulses \cite{Levitt86, Jones11}. The error tolerance is independent of the initial state vector for Type~A composite pulses, whereas it is not the case for Type~B composite pulses. In view of this, the composite pulses satisfying (\ref{lt}) are clearly of Type~A. \section{Composite Pulses as Geometric Quantum Gates} \label{CPGQG} To see the geometric nature of Type A composite pulses, we follow the argument introduced in \cite{Kondo11}, which has been generalised to multi-qubit system in \cite{Ichikawa11}. Suppose that the systematic error is proportional to $W^i$: \begin{eqnarray} \delta W^i=\epsilon W^i. \label{eW} \end{eqnarray} As shown later, two kinds of systematic errors are of this form. The robustness condition (\ref{lt}) reads \begin{eqnarray} \Delta W=\epsilon\sum_{i=1}^k{V^{i-1}}^\dag W^iV^{i-1}=0, \label{DHcom} \end{eqnarray} where use has been made of the identity $\delta W^i_{\rm I}=\delta W^i$ derived from Eq.~(\ref{discHint}) and Eq.~(\ref{eW}). Taking the expectation value of $\Delta W$ with respect to $\ket{\psi_a}$, we obtain \begin{eqnarray} \gamma_{\rm d}^a=\sum_{i=1}^k\gamma_{\rm d}^a(i)=0, \qquad \gamma_{\rm d}^a(i):=-\bra{\psi_a(i-1)} W^i\ket{\psi_a(i-1)}, \label{nulldyn} \end{eqnarray} where $\ket{\psi_a(i)}:=V^{i}\ket{\psi_a}$. Hence, any composite pulse which is designed by the perturbation theory and compensates the error (\ref{eW}) is GQG. In what follows, we will show that composite pulses associated with two kinds of relevant systematic errors are GQGs. \subsection{Error on One-Qubit System} We turn to a one-qubit system, whose Hilbert space is $\mathbb{ C}^2$. An SU(2) operations we can implement with a single rf-pulse in NMR is limited to the form \begin{eqnarray} W^i=\theta_i\,\bm{n}_i\cdot\bm{\sigma}/2, \label{decW1} \end{eqnarray} where $ \bm{n}_i=$\cos\phi_i, \sin\phi_i, 0$ $ and $\bm{\sigma}=(\sigma_x,\sigma_y,\sigma_z)$ due to the apparatus limitation. Nevertheless, we can implement any SU(2) operation by combining at most three such pulses using the Euler angle decomposition \cite{Nielsen00, Nakahara08}. The displacement (\ref{dis}) under the error (\ref{eW}) is seen as \begin{eqnarray} \theta_i\rightarrow(1+\epsilon)\theta_i. \label{ple} \end{eqnarray} This is a well-known systematic error called the pulse length error in the NMR community \cite{Levitt86}. Hence, from the previous argument, we observe that any composite pulse compensating for the pulse length error is a GQG. \subsection{Error in Two-Qubit System} \label{2qubit} For a two-qubit system, the relevant Hilbert space and the set of unitary operations are $\mathbb{ C}^{2\ot2}$ and ${\rm SU(4)}$, respectively. In view of quantum information processing, the controlled-NOT (CNOT) operation \begin{eqnarray} U_{\rm CNOT}=\ket{0}\bra{0}\otimes\mathbbm{1}_2+\ket{1}\bra{1}\otimes\sigma_x \end{eqnarray} is important.\footnote{Precisely speaking, $\det U_{\rm CNOT}= -1$ and it is not an element of SU(4). Nevertheless, we can multiply this matrix by an unphysical phase $\re^{i \pi/4}$ to make it an element of SU(4). Two quantum gates that differ by an overall phase will be identified hereafter.} Here, $\ket{a}\in\mathbb{ C}^2$ with $a=0,1$ is the eigenvector of $\sigma_z$ with the eigenvalue $(-1)^a$. The relevance of CNOT operation originates from the fact that any QIP can be implemented as a quantum circuit composed of one-qubit unitary operations and CNOT operations \cite{Barenco, Nielsen00, Nakahara08}. By using the Cartan decomposition \cite{Nakahara08}, CNOT operation can be rewritten as $ U_{\rm CNOT}=K_1H K_2, $ with \begin{eqnarray} H=\re^{\ri \alpha_x \sigma_x \otimes \sigma_x} \re^{\ri \alpha_y \sigma_y \otimes \sigma_y} \re^{\ri \alpha_z \sigma_z \otimes \sigma_z} \qquad K_1, K_2\in {\rm SU(2)}\otimes{\rm SU(2)}. \end{eqnarray} Since $\sigma_x \otimes \sigma_x$ is generated from $\sigma_z \otimes \sigma_z$ through the following identity \begin{eqnarray} \re^{\ri \alpha_x \sigma_x\otimes\sigma_x} = \re^{\ri\pi(\sigma_y\otimes \mathbbm{1}_2+\mathbbm{1}_2 \otimes \sigma_y)/4} \re^{\ri\alpha_x \sigma_z\otimes \sigma_z} \re^{-\ri\pi(\sigma_y\otimes \mathbbm{1}_2+\mathbbm{1}_2 \otimes \sigma_y)/4}, \end{eqnarray} the Ising-type Hamiltonian \begin{eqnarray} H=J\sigma_z\otimes\sigma_z/4 \end{eqnarray} is essential to implement CNOT operations which is commonly realised in a weak coupling limit. Hereafter we shall be concerned with the $J$-coupling error defined by \begin{eqnarray} J\rightarrow(1+\epsilon)J. \label{eO} \end{eqnarray} Several composite pulses robust against the $J$-coupling error have been proposed assuming that one-qubit operations are free from errors. These existing composite pulses \cite{Jones03, Hill07, Testolin07, Tomita10} are designed by making use of the following three generators only: \begin{eqnarray} X:=\sigma_z\otimes\sigma_z, \qquad Y:=\sigma_z\otimes\sigma_x, \qquad Z:=\mathbbm{1}_2\otimes\sigma_y, \label{xyz} \end{eqnarray} among the fifteen generators of SU(4). Evidently these operators satisfy $\mathfrak{su}(2)$ algebra: \begin{eqnarray} [X/2,Y/2]=\ri Z/2, \qquad [Y/2, Z/2]=\ri X/2, \qquad [Z/2, X/2]=\ri Y/2. \end{eqnarray} Thus, we can construct an SU(2) subgroup by exponentiating the generators (\ref{xyz}). Let us denote this subgroup by $G$. Now, let us put \begin{eqnarray} &&\Omega_i=J(t_i-t_{i-1})/2,\nonumber\\ &&W^i=\Omega_i$\cos\phi_i X+\sin\phi_i Y$/2=\re^{-\ri\phi_iZ/2}$\Omega_i X/2$\re^{\ri \phi_iZ/2}. \end{eqnarray} Then, we observe that \begin{eqnarray} \re^{-\mathrm{i} W^i}=\re^{-\ri\phi_iZ/2}\re^{-\mathrm{i} \Omega_iX/2}\re^{\ri\phi_iZ/2} \in G. \label{decW2} \end{eqnarray} Thus, for this $W^i$, we observe the identification between $\Omega_i, X, Y$, and $Z$ and $\theta_i, \sigma_x, \sigma_y$, and $\sigma_z$ in Eq.~(\ref{decW1}), respectively. Since the $J$-coupling error (\ref{eO}) is equivalent to the pulse length error (\ref{ple}) under this identification, we can construct a ``composite pulse'', which is robust against the $J$-coupling error, if we merely replace $\theta_i, \sigma_x, \sigma_y$, and $\sigma_z$ by $\Omega_i, X, Y$, and $Z$, respectively. In fact, as stated before, such composite pulses based on the identification have been proposed in \cite{Jones03, Hill07, Testolin07, Tomita10}. One of these composite pulses shall be examined later. Composite pulses designed under this identification are GQGs, since this identification keeps the mathematical structure of the theory unchanged. Two remarks are in order. First, the definition of $Z$ tells us that we can freely tune the parameter $\phi_i$ by changing the rf-field along the $y$-axis of the second qubit. Second, we can define the Bloch sphere for an orbit generated by $G$ and $\ket{\psi}\in\mathbb{ C}^{2\ot2}$ if $\ket{\psi}$ is an eigenvector of some element $U\in G$. In other words, if there exists $U \in G$ such that \begin{eqnarray} U\ket{\psi}=\re^{\ri\gamma}\ket{\psi}, \end{eqnarray} then the $G$-orbit $G\|\psi \rangle$ of $\|\psi \rangle$ is identified as the Bloch sphere $S^2$. This observation ensures that we can visualise the time evolution of a cyclic state associated with $U\in G$ as a trajectory in the Bloch sphere, as long as we use the composite pulses proposed so far. \section{Examples of Geometric Composite Pulse} In this section, we give several examples demonstrating our claim that two types of composite pulses introduced in the previous section are GQGs. To this end, we shall evaluate the dynamical phase of several composite pulses and verify that the dynamical phase indeed vanishes in all cases. \subsection{One-Qubit System} We parametrise our target $U$ as \begin{eqnarray} U=\exp$-\ri\theta\bm{n}\cdot\bm{\sigma}/2$, \qquad \bm{n}=(\cos\phi, \sin\phi,0). \label{target} \end{eqnarray} Then, from Sec.~\ref{GQG}, a cyclic state $\ket{\psi_a}$ associated with $U$ is given as an eigenvector of $U$, that is, \begin{eqnarray} \ket{\psi_a}=\ket{(-1)^{a}\bm{n}}, \qquad a=0, 1, \label{bloch_vector} \end{eqnarray} where $\ket{(-1)^{a}\bm{n}}$ is the eigenstate of $\bm{n}\cdot\bm{\sigma}$ such that \begin{eqnarray} \bm{n}\cdot\bm{\sigma}\ket{(-1)^{a}\bm{n}} = (-1)^{a}\ket{(-1)^{a}\bm{n}}. \end{eqnarray} We shall often use the following useful formula: \begin{eqnarray} \bra{\ve{n}}\ve{m}\cdot\ve{\sigma}\ket{\ve{n}}=\ve{n}\cdot\ve{m}. \label{formula} \end{eqnarray} Note that the vector $\bm{n}$ is the Bloch vector for the state $\ket{\bm{n}}$ and we have \begin{eqnarray} U\ket{(-1)^a\bm{n}}=\omega_a\ket{(-1)^a\bm{n}}, \qquad \omega_a=\exp[(-1)^{a+1}\ri\theta/2]. \label{eigenU} \end{eqnarray} All composite pulses, for which we evaluate the dynamical phases, are composed from $k=2l-1$ pulses, which satisfy the \lq time-symmetric\rq~condition \begin{eqnarray} W^i=W^{k+1-i}. \end{eqnarray} Many implications of this condition are found in \cite{Levitt86}. Now we address that this condition leads to \begin{eqnarray} \gamma_{\rm d}^a(i) = \gamma_{\rm d}^a(k+1-i). \label{gg} \end{eqnarray} See \ref{appA} for the proof. Hence, the dynamical phase is rewritten as \begin{eqnarray} \gamma_{\rm d}^a=2\[\gamma_{\rm d}^a(1)+\dots+\gamma_{\rm d}^a(l-1)\]+\gamma_{\rm d}^a(l) \end{eqnarray} for a composite pulse, which is made of $k=2l-1$ pulses. \subsubsection{$90^\circ$-$180^\circ$-$90^\circ$ pulse} The first composite pulse was proposed by Levitt and Freeman in 1979 based on a trajectory on the Bloch sphere \cite{Levitt79}. This is a $k=3$ symmetric composite pulse defined by \begin{eqnarray} \theta_1=\theta_2/2=\theta_3=\pi/2, \qquad \phi_1=\phi_3=0, \quad \phi_2=\pi/2. \end{eqnarray} We immediately find \begin{eqnarray} W_1=W_3=(\pi/4)\hat{\bm x}\cdot\bm{\sigma}, \qquad W_2=(\pi/2)\hat{\bm y}\cdot\bm{\sigma}, \end{eqnarray} which leads to \begin{eqnarray} U=\re^{-\ri W_1}\re^{-\ri W_2}\re^{-\ri W_1}=-\ri\sigma_y. \label{Uy} \end{eqnarray} Hence, we observe that the target is fixed to $\theta=\pi$ and $\phi=\pi/2$ and there are no free parameters we may adjust. It follows from Eq.~(\ref{Uy}) that $\ket{\psi_a}=\ket{(-1)^a\hat{\bm{y}}}$. Let us proceed to the calculation of the dynamical phase. First, we have \begin{eqnarray} \gamma_{\rm d}^a(1)=-(\pi/4)\bra{(-1)^a\hat{\bm{y}}}\hat{\bm x}\cdot\bm{\sigma}\ket{(-1)^a\hat{\bm{y}}}=(-1)^{a+1}(\pi/4)\hat{\bm x}\cdot\hat{\bm{y}}=0 \end{eqnarray} from the formula (\ref{formula}). Next, we observe \begin{eqnarray} \ket{\psi_a(1)}=\re^{-\ri W^1}\ket{\psi_a}=\re^{-\ri\pi\sigma_x/4}\ket{(-1)^a\hat{\bm y}}=\ket{(-1)^a\hat{\bm z}} \end{eqnarray} to obtain \begin{eqnarray} \gamma_{\rm d}^a(2)=-(\pi/2)\bra{(-1)^a\hat{\bm{z}}}\hat{\bm y}\cdot\bm{\sigma}\ket{(-1)^a\hat{\bm{z}}}=(-1)^{a+1}(\pi/2)\hat{\bm y}\cdot\hat{\bm{z}}=0. \end{eqnarray} Summing up these, we reach \begin{eqnarray} \gamma_{\rm d}^a=2\gamma_{\rm d}^a(1)+\gamma_{\rm d}^a(2)=0. \end{eqnarray} We can confirm Eq.~(\ref{gg}) by further calculation. We find \begin{eqnarray} \ket{\psi_a(2)}=\re^{-\ri W^2}\re^{-\ri W^1}\ket{\psi_a}=\re^{-\ri W^2}\ket{(-1)^a\hat{\bm z}}=\ket{(-1)^{a+1}\hat{\bm z}}, \end{eqnarray} from which it follows that \begin{eqnarray} \gamma_{\rm d}^a(3)=-(\pi/4)\bra{(-1)^{a+1}\hat{\bm{z}}}\hat{\bm x}\cdot\bm{\sigma}\ket{(-1)^{a+1}\hat{\bm{z}}}=(-1)^{a}(\pi/4)\hat{\bm x}\cdot\hat{\bm{z}}=0=\gamma_{\rm d}^a(1).\nonumber\\ \end{eqnarray} The time-evolution of the cyclic states ends up with \begin{eqnarray} \ket{\psi_a(3)}=\re^{-\ri W^3}\ket{\psi_a(2)}=\ket{(-1)^a\hat{\bm y}}=\ket{\psi_a}, \end{eqnarray} as expected. These results are summarised as \begin{eqnarray} \ket{\pm\hat{\bm y}}\xrightarrow{\re^{-\ri W^1}} \ket{\pm\hat{\bm z}}\xrightarrow{\re^{-\ri W^2}} \ket{\mp\hat{\bm z}}\xrightarrow{\re^{-\ri W^3}} \ket{\pm\hat{\bm y}}, \qquad \gamma_{\rm d}^a(i)=0. \end{eqnarray} See Fig.~\ref{levitt} for the graphical representation of this excursion. \begin{figure}[t] \begin{center} \includegraphics[width=2.5in]{levitt.eps} \caption{(Colour online) Excursion of the cyclic state $\ket{\hat{\bm{y}}}$ under the 90$^\circ$-180$^\circ$-90$^\circ$ pulse on the Bloch sphere. The green arrow is the Bloch vector of the cyclic state. The solid angle of the blue area enclosed by the trajectory of the Bloch vector is equal to $\pi=\theta$, which also shows that this composite pulse is a GQG (See Appendix A).} \label{levitt} \end{center} \end{figure} The lesson we learn from this composite pulse is that the converse of our statement is not always true: Not all GQGs for a spin-1/2 system are Type A composite pulses robust against the pulse length error. Indeed, this pulse is of Type B since $\Delta W\neq0$. This has been overlooked in \cite{Kondo11}. \subsubsection{SCROFULOUS} SCROFULOUS is a $k=3$ time-symmetric composite pulse constructed by Cummins, Llewellyn and Jones \cite{Cummins03}. This composite pulse was designed by using perturbation theory and quaternion algebra. Given a target (\ref{target}), SCROFULOUS takes the form \begin{eqnarray} && \theta_1 = \theta_3 = {\rm arcsinc}[2\cos(\theta/2)/\pi],\qquad \theta_2 = \pi\nonumber\\ && \phi_1 = \phi_3 = \phi + \arccos[-\pi\cos\theta_1/(2\theta_1\sin(\theta/2))],\nonumber\\ && \phi_2 = \phi_1 - \arccos[-\pi/(2\theta_1)], \end{eqnarray} where ${\rm sinc}\, x=\sin x/x$. Note that SCROFULOUS implements any one-qubit unitary operator of the form (\ref{target}). \begin{figure}[t] \begin{center} \includegraphics[width=2.5in]{SCRF.eps} \caption{(Colour online) Excursion of the cyclic state $\ket{\hat{\bm{x}}}$ of the SCROFULOUS for a target $\theta=\pi, \phi=0$ on the Bloch sphere. The green arrow is the Bloch vector of the cyclic state. The state $\re^{-\ri W^1}\ket{\hat{\bm{x}}}$ pauses during the application of the pulse $W^2$, since it is an eigenstate of the pulse $W^2$. The solid angle of the blue area is equal to $\theta$; this composite pulse is a GQG.} \label{SCRF} \end{center} \end{figure} Let us evaluate the dynamical phase. We set $\phi=0$ for simplicity, while extension to an arbitrary $\phi$ is straightforward. First, we have \begin{equation} \gamma_{\rm d}^a(1) = -\theta_1\bra{(-1)^a\bm{n}}\bm{n}_1\cdot\bm{\sigma}/2\ket{(-1)^a\bm{n}} = (-1)^{a+1}\theta_1\bm{n}\cdot\bm{n}_1/2= (-1)^{a+1}(\theta_1/2)\cos{\phi_1}. \end{equation} Next, observe that \begin{equation} {V^1}^\dag W^2V^1 =\frac{\theta_2}{2} \[ \cos^2(\theta_1/2)\bm{n}_2 +\sin^2(\theta_1/2)\bm{m} -\sin\theta_1(\bm{n}_1\times\bm{n}_2) \] \cdot\bm{\sigma}, \label{lemma1} \end{equation} where \begin{eqnarray} \bm{m}=2(\bm{n}_2\cdot\bm{n}_1)\bm{n}_1-\bm{n}_2. \end{eqnarray} Since we have \begin{eqnarray} &&\bm{n}_2\cdot\bm{n}=\cos\phi_2=-\pi\cos\phi_1/(2\theta_1)+\sin\phi_1\sin[\arccos(-\pi/(2\theta_1))],\nonumber\\ &&\bm{m}\cdot\bm{n}=\cos(2\phi_1-\phi_2)=-\pi\cos\phi_1/(2\theta_1)-\sin\phi_1\sin[\arccos(-\pi/(2\theta_1))],\nonumber\\ &&(\bm{n}_1\times\bm{n}_2)\cdot\bm{n}=0, \end{eqnarray} we observe \begin{eqnarray} &&\gamma_{\rm d}^a(2)=-\bra{\psi_a}V^{1\dag}W^2V^1\ket{\psi_a}\nonumber\\ &&\hspace{26pt}=(-1)^a(\pi/2)\{(\pi/(2\theta_1))\cos\phi_1 + \cos\theta_1\sin[\arccos(-\pi/ (2\theta_1))]\sin\phi_1\}.\nonumber\\ \end{eqnarray} Using $\sin(\arccos x) = \sqrt{1-x^2}$ and \begin{eqnarray} \sin\phi_1 = \sqrt{1-(\pi/(4\theta_1))^2}/\sin(\theta/2), \end{eqnarray} we immediately derive \begin{eqnarray} &&\gamma_{\rm d}^a = 2\gamma_{\rm d}^a(1)+\gamma_{\rm d}^a(2)\nonumber\\ &&\quad\ = (-1)^a\{\theta_1[1-(\pi/(2\theta_1))^2]\cos\phi_1 + (\pi/2)\cos\theta_1\sin[\arccos(-\pi/(2\theta_1))]\sin\phi_1\}\nonumber\\ &&\quad\ = (-1)^a[1-(\pi/(2\theta_1))^2] [\theta_1\cos\phi_1 + \pi\cos\theta_1/(2\sin(\theta/2))]\nonumber\\ &&\quad\ = 0. \end{eqnarray} Hence SCROFULOUS is a GQG. The trajectory of the cyclic state is given in Fig.~\ref{SCRF}. \subsubsection{Broad Band 1 (BB1)} Now we turn to the BB1, which was proposed by Wimperis \cite{Wimperis94}. For brevity\rq s sake, we treat a $k=5$ time-symmetric variant of the BB1 sequence. We call this variant time-symmetric BB1. The BB1 pulse sequence is useful for the implementation of QIP, since it compensates for the pulse length error up to the second order in perturbative expansion \cite{Jones11}. There are two techniques to generalise the BB1 pulse sequence \cite{Brown04}. Using these techniques, we can design a composite pulse sequence, which compensates for the pulse length error up to an arbitrary higher order in perturbative expansion. For a target (\ref{target}) with angles $\theta$ and $\phi$, the time-symmetric BB1 consists of \begin{eqnarray} &&\theta_1=\theta_5=\theta/2, \quad\ \, \theta_2=\theta_3/2=\theta_4=\pi, \nonumber\\ && \phi_1=\phi_5=\phi, \qquad \phi_2=\phi_4=\phi+\kappa, \qquad \phi_3=3\phi+\kappa, \label{BB1} \end{eqnarray} with \begin{eqnarray} \kappa=\arccos[-\theta/(4\pi)]. \end{eqnarray} Let us evaluate the dynamical phase associated with the time-symmetric BB1. First, we note from $U=\re^{-2\ri W^1}$ that \begin{eqnarray} V^1\ket{\psi_a}=\re^{-\ri W^1}\ket{\psi_a}=\pm\sqrt{\omega_a}\ket{\psi_a}. \end{eqnarray} Then, we have \begin{eqnarray} \gamma_{\rm d}^a(1)=-\bra{\psi_a}W^1\ket{\psi_a}=(-1)^{a+1}\theta_1\bm{n}_1\cdot\bm{n}/2=(-1)^{a+1}\theta/4. \end{eqnarray} Next we find from $\theta_2=\pi$ and $\phi_2=\phi+\kappa$ that \begin{equation} \gamma_{\rm d}^a(2)=-\bra{\psi_a}{V^1}^\dag W^2V^1\ket{\psi_a}=-\bra{\psi_a}W^2\ket{\psi_a}= (-1)^{a+1}\pi\bm{n}_2\cdot\bm{n}/2 =(-1)^{a}\theta/8 \end{equation} and \begin{eqnarray} \re^{-\ri W^2}\ket{\psi_a}=\ket{(-1)^a\bm{n}^\prime}; \qquad \bm{n}^\prime=(\cos(\phi+2\kappa), \sin(\phi+2\kappa), 0). \end{eqnarray} This leads to \begin{eqnarray} \gamma_{\rm d}^a(3)=-\bra{\psi_a}{V^2}^\dag W^3V^2\ket{\psi_a}=(-1)^{a+1}\pi\ \bm{n}_3\cdot\bm {n}^\prime=(-1)^{a}\theta/4. \end{eqnarray} By adding individual dynamical phases, we finally obtain \begin{eqnarray} \gamma_{\rm d}^a = 2\gamma_{\rm d}^a(1) +2 \gamma_{\rm d}^a(2)+\gamma_{\rm d}^a(3)=(-1)^{a+1} (\theta/2-\theta/4-\theta/4)=0. \end{eqnarray} This result confirms that the time-symmetric BB1 is also a GQG. \subsubsection{Knill\rq s sequence} Knill\rq s sequence \cite{Ryan10,Souza11} is a $k=5$ time-symmetric composite pulse. This sequence implements the target $U$ given by \begin{eqnarray} \theta=\pi, \qquad \bm{n}=(\cos(\alpha-\pi/6), \sin(\alpha-\pi/6),0) \end{eqnarray} where $\alpha$ is a free parameter. The sequence is defined by \begin{equation} \theta_i=\pi\ (1 \leq i \leq 5), \qquad \phi_1=\phi_5=\alpha+\pi/6, \qquad \phi_2=\phi_4=\alpha, \qquad \phi_3=\alpha+\pi/2. \end{equation} This sequence is used in experiments to maintain the coherence of nitrogen-vacancy centres in diamond \cite{Ryan10} and to decouple a system from the environment \cite{Souza11}. Note that this sequence is robust against not only the pulse length error, but also the off-resonance error \cite{Souza11}. Let us calculate the dynamical phase. First, we have \begin{equation} \gamma_{\rm d}^a(1) =-\bra{\psi_a}W^1\ket{\psi_a} =(-1)^{a+1}\pi\bm{n}_1\cdot\bm{n}/2 =(-1)^{a+1}(\pi/2)\cos(\pi/3) =(-1)^{a+1}\pi/4. \end{equation} We find $V^1\ket{\psi_a}=\ket{(-1)^a\bm{n}^\prime}$ with \begin{eqnarray} \bm{n}^\prime=(\cos(\alpha+\pi/2), \sin(\alpha+\pi/2),0). \end{eqnarray} Then, by the similar argument as that used for the first step, we have \begin{equation} \gamma_{\rm d}^a(2) =0. \end{equation} Further, we observe $V^2\ket{\psi_a}=\ket{(-1)^a\bm{n}^{\prime\prime}}$ with \begin{eqnarray} \bm{n}^{\prime\prime}=(\cos(\alpha-\pi/2), \sin(\alpha-\pi/2),0). \end{eqnarray} Then, we have \begin{equation} \gamma_{\rm d}^a(3) =(-1)^a\pi/2. \end{equation} We find, by adding individual dynamical phases, \begin{eqnarray} \gamma_{\rm d}^a = 2\gamma_{\rm d}^a(1) +2 \gamma_{\rm d}^a(2)+\gamma_{\rm d}^a(3)=(-1)^{a+1} (\pi/2+0-\pi/2)=0. \end{eqnarray} This example shows that the composite pulses robust against several systematic errors are also GQGs, if they compensates for at least the pulse length error. Thus, by construction, the composite pulses proposed in \cite{Ichikawa11, Alway07}, which are simultaneously robust against the above two errors, are also GQGs. \subsection{Two-Qubit System} Since our interest lies in the CNOT operation, we choose the target \begin{eqnarray} U=\re^{-\mathrm{i} \Omega X/2}, \end{eqnarray} which is the entangling part in the CNOT gate. The cyclic state $\ket{\psi_a}$ is an eigenstate of $X$ in Eq.~(\ref{xyz}). In the binary notation $a=2p+q$ where $p, q\in\{0,1\}$, we find \begin{eqnarray} \ket{\psi_a}=\ket{p}\otimes\ket{q}. \end{eqnarray} Jones designed a composite pulse sequence for a two-qubit system from a one-qubit composite pulse sequence~\cite{Jones03}, by employing the isomorphism among the generators given in Sec.~\ref{CPGQG}~(\ref{2qubit}). Let us introduce a notation $(\Omega)_\phi = \exp[-\ri\Omega(\cos\phi X + \sin\phi Y)/2]$ and set the target to $(\pi/2)_0$ in this notation. Jones' sequence is given by \begin{eqnarray} (\pi/4)_0 (\pi)_\kappa (2\pi)_{3\kappa} (\pi)_\kappa (\pi/4)_0, \qquad \kappa=\arccos(-1/8). \label{jones_seq} \end{eqnarray} Since the isomorphism maps $X$, $Y$, and $Z$ to the Pauli matrices $\sigma_x$, $\sigma_y$, and $\sigma_z$, respectively, Jones' sequence is a two-qubit analogue of the BB1 sequence: the combination of the first and last pulses is the target pulse ($\theta=\pi/2$, $ \phi=0$) and the others are the same as the BB1 sequence (\ref{BB1}). Similarly, the composite pulses in \cite {Hill07, Testolin07, Tomita10} are the two-qubit counterparts of those in \cite{Brown04}. Evaluation of the dynamical phase is easy if we make use of the isomorphism already mentioned. Since $X$ is mapped to $\sigma_x$, the cyclic vector $\ket{p}\otimes\ket{q}$ should be sent to $\ket{(-1)^{p+q} \hat{\bm{x}}}$, which is also an eigenvector of the target $U=\exp(-\ri\pi\sigma_x/4)$. Thus the dynamical phase of Jones' sequence is transferred to that of the BB1 sequence, which leads to \begin{eqnarray} \gamma_{\rm d}^{a}=0, \end{eqnarray} showing the sequence has vanishing dynamical phase. One can also achieve the same result by direct calculation without employing the isomorphism. \section{Two Composite ${\bm{z}}$-Rotations} In NMR, rotations around the $z$-axis must be implemented by a sequence of pulses, since the rf-pulses (\ref{decW1}) have the restriction $\bm{n}_i\perp\hat{\bm{z}}$. Thus, it is of interest to investigate whether the sequences are geometric. First, we consider the following $k=3$ sequence to realise a target $U=\re^{-\ri\theta\sigma_z/2}$: \begin{eqnarray} \theta_1=\theta_3=\pi/2, \qquad \theta_2=\theta, \qquad \phi_1=-\phi_3=\pi/2, \qquad \phi_2=0. \label{cpz1} \end{eqnarray} The cyclic states are $\ket{\psi_a}=\ket{(-1)^a\hat{\bm{z}}}=\ket{a}$. Let us calculate the dynamical phase. The first one is \begin{eqnarray} \gamma_{\rm d}^a(1)=-(\pi/4)\bra{\psi_a}\hat{\bm{y}}\cdot\bm{\sigma}\ket{\psi_a}=(-1)^{a+1}(\pi/4)\hat{\bm{y}}\cdot\hat{\bm z}=0. \end{eqnarray} We find $V^1\ket{\psi_a}=\ket{(-1)^a\hat{\bm x}}$, which leads to \begin{eqnarray} \gamma_{\rm d}^a(2)=-(\theta/2)\bra{(-1)^a\hat{\bm x}}\hat{\bm{x}}\cdot\bm{\sigma}\ket{(-1)^a\hat{\bm x}}=(-1)^{a+1}\theta/2. \end{eqnarray} Furthermore, we obtain $V^2\ket{\psi_a}=\exp[{(-1)^{a+1}\ri\theta/2]}\ket{(-1)^a\hat{\bm x}}$. Thus, we observe \begin{eqnarray} \gamma_{\rm d}^a(3)=(\pi/4)\bra{(-1)^a\hat{\bm x}}\hat{\bm{y}}\cdot\bm{\sigma}\ket{(-1)^a\hat{\bm x}}=(-1)^{a}(\pi/4)\hat{\bm{y}}\cdot\hat{\bm x}=0. \end{eqnarray} We conclude \begin{eqnarray} \gamma_{\rm d}^a=(-1)^{a+1}\theta/2\neq0. \end{eqnarray} Hence the pulse sequence (\ref{cpz1}) is not a GQG. Note that this sequence is not robust against the pulse length error, that is, $\Delta W\neq0$, which is exactly the contraposition of our claim. \begin{figure}[t] \begin{center} (a)\includegraphics[width=2.2in]{z1.eps} (b) \includegraphics[width=2.2in]{z2.eps} \caption{(Colour online) Excursions of the cyclic states on the Bloch sphere. (a) The trajectory of the cyclic state $\ket{\hat{\bm z}}$ under the pulse sequence (\ref{cpz1}). Note that the trajectory fails to close, which shows that this sequence is dynamical. (b) The trajectory of the cyclic state $\ket{-\hat{\bm z}}$ under the pulse sequence (\ref{cpz2}) for $\theta=\pi$. The solid angle subtended by the trajectory of the Bloch vector is $\pi = \theta$, which shows the geometric nature of the sequence.} \label{CZs} \end{center} \end{figure} Second, we investigate a $k=2$ pulse for $U=\re^{\ri\theta\sigma_z/2}$: \begin{eqnarray} \theta_1=\theta_2=\pi, \qquad \phi_1=0, \qquad \phi_2=\theta/2. \label{cpz2} \end{eqnarray} The cyclic states are the same as those of the previous sequence. We have \begin{eqnarray} \gamma_{\rm d}^a(1)=-(\pi/2)\bra{\psi_a}\hat{\bm{x}}\cdot\bm{\sigma}\ket{\psi_a}=(-1)^{a+1}(\pi/2)\hat{\bm{x}}\cdot\hat{\bm z}=0. \end{eqnarray} By the same way, we compute \begin{eqnarray} \gamma_{\rm d}^a(2)=0, \end{eqnarray} which clearly shows \begin{eqnarray} \gamma_{\rm d}^a=0. \end{eqnarray} Hence the pulse sequence (\ref{cpz2}) is a GQG. This pulse is not robust against the pulse length error. Indeed, we may check \begin{eqnarray} \Delta W=\epsilon\frac{\pi}{2}\[$1+\cos\frac{\theta}{2}$\sigma_x-\sin\frac{\theta}{2}\sigma_y\]\neq0 \end{eqnarray} by direct calculation. This also tells us that not all GQGs are robust against the pulse length error. The difference of these two composite $z$-rotations are visualised in Fig.~\ref{CZs}. \section{Conclusion and Discussions} In this article, we uncovered the relation between GQGs and the composite pulses robust against certain kinds of systematic errors. For the error (\ref{eW}), proportional to the Hamiltonian times the operation time, the compensation of the error automatically leads to vanishing dynamical phase. Thus, a non-trivial operation by a composite pulse robust against such an error is a GQG. We pointed out that there are two kinds of errors assuming the form (\ref{eW}). One is the pulse length error and the other is the $J$-coupling error. This implies that the composite pulses robust against these errors are GQGs. This observation was illustrated and confirmed by directly showing that the dynamical phase vanishes for several typical composite pulses: $90^\circ $-$180^\circ$-$90^\circ$, SCROFULOUS, BB1, Knill\rq s sequence for the pulse length error and Jones' pulse sequence for the $J$-coupling error. The two most common composite $z$-rotations were also examined. Our work has shown that we can construct a universal gate set composed of GQGs simply by using the composite pulses. This suggests that NMR is quite a useful test bench of geometric quantum computation. In view of this, further study of composite pulses, {\it e.g.} \cite{Ota09a}, is desirable for deeper understanding of the geometric quantum computation. \begin{acknowledgements} We would like to thank Jonathan~A.~Jones and Yukihiro~Ota for valuable discussions and Dieter~Suter for drawing our attention to Knill\rq s sequence. This work is supported by `Open Research Center' Project for Private Universities: matching fund subsidy from MEXT (Ministry of Education, Culture, Sports, Science and Technology), Japan. YK and MN would like to thank partial supports of Grants-in-Aid for Scientific Research from the JSPS (Grant No.~23540470). \end{acknowledgements}	{ "redpajama_set_name": "RedPajamaArXiv" }	4,265
{"url":"https:\/\/tug.org\/pipermail\/texhax\/2007-August\/008954.html","text":"[texhax] Something's wrong--perhaps a missing \\item\n\nburlen burlen at apollo.sr.unh.edu\nThu Aug 30 18:31:00 CEST 2007\n\nI am compiling a document and I get this error message:\n\n.\/astronum2007.bbl:8:Something's wrong--perhaps a missing \\item.\n\\bibitem[Balsara(2001)]{Balsara2001}\n\nI have looked at the .bbl file referenced but can't seem to figure what\nis wrong. I have included it below. I was working on this report a\nmonth or so ago and remember figuring out that if I deleted some of the\nlines in .bbl and rearranged I could get it to work, but now I can't\nfigure out exactly what I had done to make it work can anyone help??\n\n\\begin{thebibliography}{7}\n\\providecommand{\\natexlab}[1]{#1}\n\\providecommand{\\url}[1]{\\texttt{#1}}\n\\expandafter\\ifx\\csname urlstyle\\endcsname\\relax\n\\providecommand{\\doi}[1]{doi: #1}\\else\n\\providecommand{\\doi}{doi: \\begingroup \\urlstyle{rm}\\Url}\\fi\n\n\\bibitem[Balsara(2001)]{Balsara2001}\nD.~Balsara.\n\\newblock Divergence free adaptive mesh refinement for magnetohydrodynamics.\n\\newblock \\emph{Journal of Computational Physics}, 174:\\penalty0 614--648,\n2001.\n\n\\bibitem[Berger and Collela(1989)]{Berger1989}\nM.~J. Berger and P.~Collela.\n\\newblock Local adaptive mesh refinement for shock hydrodynamics.\n\\newblock \\emph{Journal of Computational Physics}, 82:\\penalty0 64--84,\n1989.\n\n\\bibitem[Evans and Hawley(1988)]{Evans1988}\nC.~Evans and J.~Hawley.\n\\newblock Simulation of magnetohydrodynamic flows: A constrained transport\nmethod.\n\\newblock \\emph{The Astrophysical Journal}, 332:\\penalty0 659--667, 1988.","date":"2019-09-20 18:04:04","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9192458391189575, \"perplexity\": 7909.505777717246}, \"config\": {\"markdown_headings\": false, \"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-2019-39\/segments\/1568514574058.75\/warc\/CC-MAIN-20190920175834-20190920201834-00293.warc.gz\"}"}	null	null
If you fancy a few days away from work, away from the city stress, or if you just want to escape for a long weekend with your friends, than one of these mini breaks in the mountains might be of interest to you. These have been selected for you as a great way to escape and recharge your batteries and most importantly, to have fun! Katarina Kralova, who is a French qualified Mountain Bike instructor and International Mountain Leader, together with her professional team, will take you on one of the following selected trips. Customized and à la carte escapes are possible too, as well as tailor made activities for seminars, incentives and team building exercises. "We let you travel further and faster with high end full suspension Electric Mountain Bikes" Edelweiss E-Bike Escapes offers half day and full day tours allowing you to soak up the stunning views while pedaling through and up the mountains on a high-end full suspension Electric mountain bike. You can choose between gastronomic routes and sportive routes.	{ "redpajama_set_name": "RedPajamaC4" }	9,733
Q: Excluding 3dots additional to other characters with regex in a string I have such an http-url detector regex: (?:http\|https)(?::\/{2}[\w]+)(?:[\/\|\.]?)(?:[^\s<"]) It works pretty well for the following url representation: http://www.acer.com/clearfi/download/ What kind of modification I can do to extract http://schemas.microsoft.com/office/word/2003/wordml2450 from Huanghhttp://schemas.microsoft.com/office/word/2003/wordml2450...)()()()()() ? A: I've changed your expression here and there: (.)(https?:\/{2}[\w]+[\/\|\.]?[^\s<"])(\.{3}.) and get only second capturing group from it. See example here: https://regex101.com/r/0viPC5/2 This expression probably can be simplified further but I don't know your exact input and search criteria so let's stick with what you already wrote. A: You can modify it to capture: * group of http stuff followed by (group of) subdomain stuff followed by as many as possible groups of: one point or slash followed by a group of characters (non-point, non-space, non-", non-<) (?:http\|https)(?:\/{2}[\w]+)([\/\|\.][^\s<"\.]+)* I made capturing groups to visualize the results	{ "redpajama_set_name": "RedPajamaStackExchange" }	5,371
<?php declare(strict_types=1); /* * This file is part of the RollerworksDatagrid package. * * (c) Sebastiaan Stok <s.stok@rollerscapes.net> * * This source file is subject to the MIT license that is bundled * with this source code in the file LICENSE. / namespace Rollerworks\Component\Datagrid\Util; use Rollerworks\Component\Datagrid\Column\ColumnTypeExtensionInterface; use Rollerworks\Component\Datagrid\Column\ColumnTypeInterface; use Rollerworks\Component\Datagrid\Column\ColumnTypeRegistry; use Rollerworks\Component\Datagrid\Column\ResolvedColumnTypeFactory; use Rollerworks\Component\Datagrid\Column\ResolvedColumnTypeFactoryInterface; use Rollerworks\Component\Datagrid\DatagridExtensionInterface; use Rollerworks\Component\Datagrid\DatagridFactory; use Rollerworks\Component\Datagrid\DatagridRegistry; use Rollerworks\Component\Datagrid\DatagridRegistryInterface; use Rollerworks\Component\Datagrid\PreloadedExtension; /* * @author Sebastiaan Stok <s.stok@rollerscapes.net> / final class DatagridFactoryBuilder { private $resolvedTypeFactory; private $datagridRegistry; private $extensions = []; private $types = []; private $typeExtensions = []; /* * @param ResolvedColumnTypeFactoryInterface $resolvedTypeFactory * * @return DatagridFactoryBuilder / public function setResolvedTypeFactory(ResolvedColumnTypeFactoryInterface $resolvedTypeFactory): self { $this->resolvedTypeFactory = $resolvedTypeFactory; return $this; } /* * @param DatagridRegistryInterface $datagridRegistry * * @return DatagridFactoryBuilder / public function setDatagridRegistry(DatagridRegistryInterface $datagridRegistry): self { $this->datagridRegistry = $datagridRegistry; return $this; } /* * @param DatagridExtensionInterface $extension * * @return DatagridFactoryBuilder / public function addExtension(DatagridExtensionInterface $extension): self { $this->extensions[] = $extension; return $this; } /* * @param DatagridExtensionInterface[] $extensions * * @return DatagridFactoryBuilder / public function addExtensions($extensions): self { $this->extensions = array_merge($this->extensions, $extensions); return $this; } /* * @param ColumnTypeInterface $type * * @return DatagridFactoryBuilder / public function addType(ColumnTypeInterface $type): self { $this->types[get_class($type)] = $type; return $this; } /* * @param ColumnTypeInterface[] $types * * @return DatagridFactoryBuilder / public function addTypes(array $types): self { foreach ($types as $type) { $this->types[get_class($type)] = $type; } return $this; } /* * @param ColumnTypeExtensionInterface $typeExtension * * @return DatagridFactoryBuilder / public function addTypeExtension(ColumnTypeExtensionInterface $typeExtension): self { $this->typeExtensions[$typeExtension->getExtendedType()][] = $typeExtension; return $this; } /* * @param ColumnTypeExtensionInterface[] $typeExtensions * * @return DatagridFactoryBuilder / public function addTypeExtensions(array $typeExtensions): self { foreach ($typeExtensions as $typeExtension) { $this->typeExtensions[$typeExtension->getExtendedType()][] = $typeExtension; } return $this; } /* * @return DatagridFactory */ public function getDatagridFactory(): DatagridFactory { $extensions = $this->extensions; if (count($this->types) > 0 \|\| count($this->typeExtensions) > 0) { $extensions[] = new PreloadedExtension($this->types, $this->typeExtensions); } $typesRegistry = new ColumnTypeRegistry( $extensions, $this->resolvedTypeFactory ?: new ResolvedColumnTypeFactory() ); return new DatagridFactory($typesRegistry, $this->datagridRegistry ?: new DatagridRegistry()); } }	{ "redpajama_set_name": "RedPajamaGithub" }	5,505
{"url":"http:\/\/mathoverflow.net\/questions\/89575\/whats-the-difference-between-pde-and-geometric-analysis","text":"MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06\/24\/2013) at approximately 9:00 PM Eastern time (UTC-4).\n\n## What\u2019s the difference between PDE and geometric analysis [closed]\n\nWhat's the difference between PDE and geometric analysis? Are there any survey or introduction on PDE, especially PDE of mixted type.I'm a freshman. Many thanks\n\n-\nWhy are you, only a freshman, already interested in PDE's of mixed type? \u2013\u00a0Deane Yang Feb 26 2012 at 12:20\nFor starters, geometric analysis $\\setminus$ PDE $\\cap$ geometry $\\neq \\emptyset$? \u2013\u00a0Willie Wong Feb 26 2012 at 15:46\nBTW, I don't think that the question as stated is a good fit for MathOverflow. PDE and geometric analysis are both huge subjects, with certain degree of overlap (as well as nonempty symmetric difference), if you are asking \"what's the difference between PDE and geometric analysis\", you are actually basically asking \"What is PDE\" and \"What is geometric analysis\", both of which are extremely broad questions! \u2013\u00a0Willie Wong Feb 26 2012 at 15:53\nWillie, you're right. Lancy should start by talking to his classmates and teachers and come back to MathOverflow with more specific questions that his classmates and teachers aren't able to answer. \u2013\u00a0Deane Yang Feb 26 2012 at 18:13\nWillie, I beg to differ with your first comment, which expresses a widely held view that geometric analysis always means geometric applications and properties of PDE\"s. In fact, I was told that it also means only geometric applications and properties of elliptic and parabolic PDE's. Admittedly, that's what 99% of all geometric analysts seem to do. But, besides the rather important topic of hyperbolic PDE's that arise in geometry, geometric analysis does encompass other areas that do not involve PDE's. Integral and convex geometry is one particular example of this. \u2013\u00a0Deane Yang Feb 26 2012 at 20:44","date":"2013-06-19 23:36:54","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5856729745864868, \"perplexity\": 1361.2977292583794}, \"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\/1368709805610\/warc\/CC-MAIN-20130516131005-00025-ip-10-60-113-184.ec2.internal.warc.gz\"}"}	null	null
\section{Introduction} Single-emitter spectroscopy is essential to build a comprehensive microscopic picture of the physical processes involved in fluorescent emitters. In experiments on ensembles of (slightly) inhomogeneous emitters, many processes are hidden by averaging. For example, only single-emitter experiments have been able to reveal that the emission from many types of fluorescent species exhibits spectral diffusion \cite{Ambrose1991}, blinking \cite{Nirmal1996,Vandenbout1997}, and anti-bunching \cite{Fleury2000,Lounis2000}. \\ The photophysical properties of single molecule emitters such as organic dye molecules \cite{Ambrose1991,Vandenbout1997,Lounis2000}, and colloidal quantum dots \cite{Nirmal1996,Mason1998,English2002,Shimizu2002,Martin2008,Chizhik2009,Spinicelli2009,Wang2009,Kusova2010,Galland2012,Schmidt2012,Rabouw2013} have been examined extensively for the past two decades. Samples for single molecule photoluminescence spectroscopy are usually prepared by spin-coating a dilute solution of the emitters from a liquid or polymer solution onto a glass or quartz cover slip \cite{Nirmal1996,Mason1998,English2002,Martin2008,Chizhik2009,Wang2009,Spinicelli2009,Schmidt2012,Rabouw2013}. The surface density of emitters must be sufficiently low ($<$1 $\mu$m$^{-2}$), so that the diffraction-limited excitation spot of a continuous-wave (cw) or pulsed laser can address an individual molecule. Most studies have focused on relatively bright emitters, with large absorption cross-sections, high quantum efficiencies and/or short photoluminescence lifetimes. Experiments on dimmer emitters (such as Si \cite{Mason1998,English2002,Martin2008,Chizhik2009,Kusova2010,Schmidt2012}, InP \cite{Dennis2012}, InAs \cite{Bischof2014}, or CuInS$_2$ (see below)) are more challenging, because the signal is easily obscured by background counts from fluorescence of the substrate, laser reflections, and detector dark counts. For a proper interpretation of experimental data on relatively dim emitters, it is important to understand the origin of background signals. \\ Here we show that microscope cover slips of silica (glass or quartz), commonly used for single-emitter studies, contain intrinsic single-photon emitting centres. Photoluminescence (PL) from such centres is observed under excitation at 532 nm, both from cover slips of borosilicate glass and fused quartz. The centres have a characteristic emission spectrum with two or three Gaussian peaks, and PL lifetimes of a few nanoseconds. Single-photon emitters with very similar characteristics have been observed before in several studies \cite{Mason1998,English2002,Martin2008,Chizhik2009,Wang2009,Kusova2010} where silica cover slips were used as a substrate to spin-coat the sample. While in these studies the PL was ascribed to nanocrystals (of various types), our results imply that it may in fact have originated from luminescent centres intrinsic to the silica substrate. \section{Results} We investigate the fluorescence from bare silica microscope cover slips (borosilicate glass or fused quartz) cleaned with hydrochloric acid, followed by isopropanol. The cover slips were excited with a pulsed (10 MHz) Nd:YVO$_4$ laser (532 nm). See Methods for details. \\ \begin{figure}[ht] \centering \includegraphics[width=\linewidth]{Donega_Fig1.pdf} \caption{ \textbf{Single-emitter luminescent centres on a microscope glass cover slip.} \textbf{(a)} A fluorescence image of a bare borosilicate glass cover slip epi-illuminated with the laser (532 nm; 200 $\mu$W) defocussed to a $\sim$50 $\mu$m diameter spot reveals luminescent spots at a surface density of 0.01--0.1 $\mu$m$^{-2}$. \textbf{(b)} A typical intensity time trace of a single spot. The emission is non-blinking, but the spot bleaches after 21 s. \textbf{(c)} The emission spectrum of the spot shows a main peak in the orange with side bands at longer wavelengths. The solid line is a fit to a series of three Gaussians regularly spaced at a separation of 179 meV. \textbf{(d)} The PL decay trace of the spot is single exponential, with a fitted PL lifetime of 3.4 ns (solid line). \textbf{(e)} The two-photon correlation function demonstrates anti-bunching, indicating that we are observing a single-photon emitter. \label{fig:borosilicate} } \end{figure} Fig.~\ref{fig:borosilicate} gives an overview of the properties of the luminescent defects we found in microscope cover slips of borosilicate glass. Fig.~\ref{fig:borosilicate}a is an epi-fluorescence wide-field microscopy image of a bare glass cover slip. Isolated luminescent spots are clearly visible with a density of 0.01--0.1 $\mu$m$^{-2}$. The image closely resembles a typical fluorescence image of single molecules or single quantum dots deposited on a substrate. The substrate observed in Fig.~\ref{fig:borosilicate} is however bare. We conclude that the PL must originate from luminescent centres in or on the substrate itself. Focusing the laser excitation to a diffraction limited spot, we can investigate individual centres. Fig.~\ref{fig:borosilicate}b presents a typical intensity trace of a centre, showing that the emission is non-blinking. We find that most centres photobleach within a minute (as the one in Fig.~\ref{fig:borosilicate}b), while only a few remain emissive for several minutes. \\ The emission spectrum of the centre is presented in Fig.~\ref{fig:borosilicate}c. The PL peaks at 583 nm, but is clearly asymmetric with strong sidebands to the red of the main peak. The PL spectrum can be fitted to a progression of three Gaussians at regular energy separation (solid line), yielding a peak separation of 179 meV. The time-resolved PL decay curve of the centre (Fig.~\ref{fig:borosilicate}d) is single-exponential over three orders of magnitude in dynamic range, with a PL lifetime of 3.4 ns (solid line). In Fig.~\ref{fig:borosilicate}e we plot the two-photon correlation function $g^{(2)}$, i.e. the probability distribution of delay times between consecutive photon detection events \cite{Nair2011,Cui2014}. The absence of coincidence counts at zero delay proves that the emission is anti-bunched, i.e. the luminescent centre emits no more than a single photon per excitation pulse. \\ By examining over 20 individual centres in a glass cover slip, we investigated how the PL properties are distributed. The results are presented in Fig.~\ref{fig:statistics}. Fig.~\ref{fig:statistics}a shows the emission spectra of three individual centres (red, green, and blue), as well as the `ensemble emission spectrum' (black) obtained by averaging over measurements on 27 different individual centres. The ensemble spectrum is approximately twice as broad as the individual spectra, indicating a considerable inhomogeneous distribution in the PL spectral properties of the centres. We see that while each individual spectrum seems to consist of several peaks (as in Fig.~\ref{fig:borosilicate}c), this structure is hidden after ensemble averaging. In Fig.~\ref{fig:statistics}b we plot the fitted separation between peaks in the emission spectrum of an individual centre, versus the energy of the main peak. The separations are mostly between 160 and 180 meV, without a correlation with peak energy over this small energy range. The time-resolved PL decay curves of the centres are all nearly single-exponential, as in Fig.~\ref{fig:borosilicate}d. The lifetimes are however distributed between 2 and 6 ns (Fig.~\ref{fig:statistics}c), with an average of 3.8 ns. \\ \begin{figure}[ht] \centering \includegraphics[width=\linewidth]{Donega_Fig2.pdf} \caption{ \textbf{The properties of single-photon emitting centres in a borosilicate cover slip.} \textbf{(a)} Emission spectra of three different individual centres (red, green, blue), as well as the `ensemble' emission spectrum obtained by averaging over 27 centres (black). A long-pass filter at 540 nm cuts the blue side of the spectra. Each individual spectrum has a double-peak shape, but this shape is hidden after ensemble averaging. \textbf{(b)} There is not a strong correlation between the energy of the main peak, and the separation between the peaks, as obtained from a triple-Gaussian fit (with regular spacing) to spectra of individual centres. The separations are between 150 and 200 meV, while the peak energy varies between 2.07 eV and 2.20 eV. \textbf{(c)} The fitted PL lifetimes of centres vary between 2 ns and 6 ns, with an average of 3.8 ns. \label{fig:statistics} } \end{figure} We confirmed that the luminescent centres observed (Figs.~\ref{fig:borosilicate},\ref{fig:statistics}) are intrinsic to silica, by also investigating a 'fused quartz' cover slip. The top surface of the quartz slips was difficult to image with the oil immersion setup that we used for borosilicate glass, possibly because the refractive index of borosilicate glass is higher than that of fused quartz. Instead, we used a water immersion objective and a slightly higher laser power (see Methods for details). \\ \begin{figure}[ht] \centering \includegraphics[width=\linewidth]{Donega_Fig3.pdf} \caption{ \textbf{Individual defects in quartz cover slips.} \textbf{(a)} A fluorescence image of a fused quartz cover slip, epi-illuminated with the laser (532 nm; 600 $\mu$W) defocussed to a spot with $\sim$50 $\mu$m diameter. \textbf{(b)} The intensity trace of an individual spot, that bleaches within 5 s. The PL decay trace during these first 5 s is single-exponential, with a fitted PL lifetime of 3.4 ns. \textbf{(c)} The emission spectra of the spots in fused quartz have the characteristic multi-peaked appearance. They can be fitted to a series of three Gaussians, with separations of on average 170 meV. \label{fig:quartz} } \end{figure} The observations on the fused quartz cover slips are summarized in Fig.~\ref{fig:quartz}. There are individual emitting spots with a surface density of 0.01--0.1 $\mu$m$^2$ (Fig.~\ref{fig:quartz}a), although their brightness is considerably lower than that from the defects in borosilicate glass. We conclude that not only borosilicate glass, but also fused quartz contains luminescent defect centres. The centres in quartz bleached typically within a few seconds (Fig.~\ref{fig:quartz}b), probably because we used a high excitation power to get sufficient signal from the weak emitters in the quartz. We were nevertheless able to study the PL characteristics of several individual centres. The PL decay is single exponential, with PL lifetimes of a few nanoseconds (inset of Fig.~\ref{fig:quartz}b). Most importantly, the emission spectrum has the characteristic multiple-peak appearance (Fig.~\ref{fig:quartz}c), although the signal-to-noise is poorer for the quartz defects. The splitting between the emission peaks is very similar to that observed in borosilicate glass, with an average of 170 meV over 17 centres in quartz. The similarities between the PL spectra and lifetime for the two substrates suggests that the centres examined here are intrinsic to silica, appearing both in borosilicate glass and in fused quartz. \\ We further emphasize that the appearance of luminescent defects did not depend on the cleaning procedure of the cover slips. Cover slips taken directly from the box showed characteristics very similar to cover slips that were first cleaned in hydrochloric acid and isopropanol (see Methods). Baking the substrate at 150$^\circ$C for 1 min to remove any organic contaminations adsorbed did not have an effect either. Even surface functionalization with hexamethyldisilazane had no consequences for the density nor the properties of the luminescent defect centres. \section{Discussion} Single-photon emitters with characteristics similar to those we have observed on bare silica substrates (i.e. multi-peaked spectra, ns PL lifetime, non-blinking emission), have been reported before. For example, Wang \emph{et~al.} \cite{Wang2009} reported non-blinking single-photon emission with a PL lifetime of 4--5 nanoseconds and an emission spectrum characterised by multiple peaks separated by $\sim$164 meV. They ascribed it to CdZnSe/ZnSe QDs with a composition gradient at the core--shell interface. These surprising characteristics, inconsistent with the ensemble PL, were explained by a model in which the QDs are permanently positively charged. Our findings here imply that, instead, the PL observed could have originated from luminescent centres in the cover slips used for the experiments in Ref.~\cite{Wang2009}. \\ PL with identical characteristics to those of the centres in silica, has previously also been reported for individual Si QDs \cite{Mason1998,English2002,Martin2008,Kusova2010,Schmidt2012} or SiO$_2$ nanoparticles \cite{Chizhik2009}. While the PL properties of an ensemble of Si QDs depend strongly on the preparation method and on the surface chemistry, individual Si QDs always show PL with the same characteristics (and very similar to those shown in Fig.~\ref{fig:borosilicate},\ref{fig:statistics},\ref{fig:quartz}). In Refs.~\cite{Chizhik2009,Schmidt2012} it was proposed that this PL originates from defects in the amorphous SiO$_2$ surface layer of the QDs, while the much weaker excitonic emission from Si QDs is hard to observe \cite{Schmidt2012}. The peak splitting of (consistently) approximately 160 meV is ascribed to coupling to phonons in SiO$_2$. The same type of defect responsible for emission in Si QDs, may be present at a low density in silica cover slips. Alternatively, the multi-peaked emission spectra ascribed to Si QDs or SiO$_2$ nanoparticles in Refs.~\cite{Mason1998,English2002,Martin2008,Chizhik2009,Kusova2010,Schmidt2012} may in fact have originated from centres in the silica substrates used for the experiments. \\ \begin{figure}[ht] \centering \includegraphics[width=\linewidth]{Donega_Fig4.pdf} \caption{ \textbf{Photon emission rates from single-photon emitters.} We compared the estimated photon emission rates of QDs with an absorption cross-section of $\sigma=10^{-15}$ cm$^2$ and a default PL lifetime of $\tau =$ 30 ns (similar to the dot-in-rods of Ref.~\cite{Rabouw2013}) to centres in silica with $\sigma=10^{-16}$ cm$^2$ and $\tau =$ 5 ns. The default excitation intensity is 200 nW focussed to a spot with a diameter of $532~\textrm{nm}/2$. The default laser repetition period is 100 ns. We consider QDs with quantum efficiencies of 1 (purple), 0.5 (blue), and 0.1 (green). In each panel, the red dot marks the experimental parameters for the dot-in-rods in Ref.~\cite{Rabouw2013}. The dashed line is the emission rate from a luminescent centre in silica. Note that for these calculations we assume a zero quantum efficiency of multi-exciton emission (see Methods). Emitters exhibiting biexciton emission would be brighter under strong excitation than calculated here. One should furthermore realize that in practice under strong excitation, the intensity of emitters may decrease because of charging or bleaching, but these effects are not considered here. \textbf{(a)} The photon emission rate as a function of the PL lifetime of the QDs. \textbf{(b)} The photon emission rate as a function of the excitation power. \textbf{(c)} The photon emission rate as a function of the laser repetition period, at a constant average excitation power of 200 nW. This means that for longer repetition periods, the energy per pulse is higher. \label{fig:emrates} } \end{figure} In Fig.~\ref{fig:emrates} we compare the estimated brightness of QDs to that of the centres in silica in a single-emitter experiment using a pulsed excitation source of 532 nm, as a function of (a) the PL lifetime of the QDs, (b) the excitation power of the laser, and (c) the repetition period of the laser. See Methods for details of the calculation. We see that with the experimental parameters used in this work (which are the same as in Ref.~\cite{Rabouw2013}, i.e. excitation power = 200 nW, laser repetition period $T=$ 100 ns), a typical QD (red circle) is approximately 10$\times$ as bright as a centre. The emission rate of a centre is estimated at $8\times 10^5$ s$^{-1}$. When considering that the collection and detection efficiency of our setup is approximately 1\%, this value corresponds well to the observation of $6\times 10^3$ counts per second (Fig.~\ref{fig:borosilicate}b). \\ The defect PL from silica is approximately a factor 10 less bright than exciton PL from CdSe/CdS dot-in-rods investigated on the same setup and under the same conditions \cite{Rabouw2013}. In a wide-field image, PL of the centres \emph{in} the silica substrate (Fig.~\ref{fig:borosilicate}a) cannot be distinguished from PL of individual weak emitters intentionally spun-coat \emph{on} the substrate. In our previous work \cite{Rabouw2013}, we were able to properly analyse the CdSe/CdS dot-in-rods (as evidenced by single-emitter characteristics consistent with the ensemble properties), because the dot-in-rods were by far the brightest emitters in the sample. PL from the centres in the substrate became observable (and are even the brightest source of PL) when we attempted to examine CuInS$_2$ QDs. CuInS$_2$ QDs are weaker emitters than CdSe/CdS dot-in-rods, because they have longer PL lifetimes (\textit{viz.} tens to hundreds of nanoseconds) and lower PL quantum efficiencies. In addition, they may have a lower absorption cross-section at 532 nm, and may be more vulnerable to photobleaching. \\ For the experimental parameters used in this work a typical QD is significantly brighter (red circle) than the defects. However, if any of the relevant parameters changes (emitter PL lifetime, quantum efficiency, excitation power, laser repetition rate; see Fig.~\ref{fig:emrates}), the brightness ratio can shift in favour of the luminescent centres. Indeed, since the excited state lifetime of QDs is relatively long-lived and the absorption-cross section is large, the fluorescence signal from QDs saturates more easily than that from the centres in silica. This analysis explains why in experiments on `dim QDs' with a low quantum efficiency, long PL lifetime (such as CuInS$_2$ or Si), and/or poor photostability, the signal from emitting centres in the silica substrate can be the brightest source of PL in the field of observation. \section{Conclusion} Silica cover slips contain intrinsic single-photon emitting centres, at a low surface density of 0.01--0.1 $\mu$m$^{-2}$. The emission spectrum of the centres shows a progression of peaks separated by $\sim$170 meV, with the main peak around 600 nm. The photoluminescence lifetime is a few nanoseconds. The realisation that silica contains such defects is important for the interpretation of spectroscopic experiments on individual emitters when using a silica substrate (glass or quartz). Emission from these defects has probably been observed previously, but was then misinterpreted as originating from the emitters under investigation. \section{Methods} \subsection{Experimental procedure} Before measurement, Menzel Gl\"{a}ser 24$\times$24 \# 1 borosilicate cover slips were cleaned by sequential dipping for $\sim$30 s in an HCl bath (36\%), a water bath, and a bath of isopropanol, and then blown dry with N$_2$. Quartz cover slips (Esco Optics, Inc.) were cleaned by bath sonicating in acetone for 15 minutes, soaking in a 1 \% Hellmanex solution at 35$^\circ$C for 30 minutes, soaking in 6 M HCl for 60 minutes, and bath sonicating in methanol for 15 minutes; 5 minutes of bath sonication in Nanopure water occurred between each step. After the final methanol wash, the coverslips were allowed to air dry. \\ Measurements were done with a 10 MHz pulsed laser operating at 532 nm, exciting individual defects with 200 nW focused to a diffraction-limited spot. Excitation and collection of luminescence was done with the same NA = 1.4 100$\times$ oil-immersion objective using Fluka immersion oil `UV transparent fluorescence free' (for borosilicate glass), or with an NA = 1.2 60$\times$ water-immersion objective using deionized water (for fused quartz). Reflected laser light was filtered out with a 540 nm long-pass filter. The fluorescence images were recorded on a Nikon CCD-camera (DS-Qi 1 MC) with an integration time of 300 ms. Time-correlated single photon counting was done with two ID Quantique id100-20 avalanche photo-diodes in a Hanbury-Brown-Twiss setup. Emission spectra are integrated for 5 s (borosilicate glass) or 20 s (fused quartz) on an Acton Research SpectraPro 2300i spectrometer equipped with a PIXIS:100 CCD array by Princeton Instruments. \subsection*{Estimating the photon emission rate of a single-photon emitter} We consider a single-photon emitter with absorption cross-section $\sigma$ that is excited with a pulsed laser of average intensity $I$ and repetition period $T$ (where continuous-wave excitation corresponds to the limit $T\rightarrow 0$). The statistics of photon absorption is Poissonian (at least for non-resonant absorption, where the effects of absorption-induced bleach or Stark effects on the energies or strengths of transitions can be neglected). The probability that $n$ photons are absorbed is \begin{equation} p(n) = (IT\sigma/\hbar\omega)^n \mathrm{e}^{-IT\sigma/\hbar\omega}/n!, \end{equation} where $IT\sigma/\hbar\omega$ is the expectation value for the number of absorption events per pulse. For our model, we consider emitters with a zero quantum efficiency of multi-exciton emission, as is common for conventional quantum dots. The luminescent centres in silica have zero multi-exciton emission too, as evidenced by the absence of a zero-delay peak in the photon correlation function. One should however keep in mind that high-quality (heterostructured) nanocrystal structures with finite biexciton quantum efficiencies will be somewhat brighter under strong excitation conditions than calculated here. Neglecting the contribution of QD multi-exciton emission has however no effect on the overall conclusion that the defect emission in silica will only be comparable with single-QD PL when the PL lifetime is long or the quantum efficiency of the QD is low. A zero quantum efficiency of multi-exciton implies that following absorption, the emitter immediately and non-radiatively relaxes to the emissive single-exciton state, irrespective of how many photons are absorbed. The probability that a laser pulse excites the emitter is then \begin{equation} \label{eq:exc} X = 1 - p(0) = 1 - \mathrm{e}^{-IT\sigma/\hbar\omega}. \end{equation} After excitation, the probability that the emitter is excited decays exponentially with a characteristic time equal to the excited state lifetime $\tau$. Note that this characteristic time is independent of the number of photons initially absorbed, under the assumption that multi-exciton states have a zero quantum efficiency and therefore immediately relax to the single-exciton state. At time $T$ the next excitation pulse hits, and has again a probability to excite the emitter to its excited state. The excited-state population following the second laser pulse can be higher than after the first laser pulse unless $T$ is much longer than $\tau$. The excited state population evolves by sequential excitation and decay, until a `steady state' situation exists where the decay following laser pulse $i$ is exactly compensated by excitation by laser pulse $i+1$: \begin{equation} P \left(1-\mathrm{e}^{-T/\tau}\right) = X \left(1 - P \mathrm{e}^{-T/\tau}\right), \end{equation} where $P$ is the excited state population (i.e. the probability that the emitter is excited) directly following a laser pulse. We can solve that the `steady state' excited-state population directly after a laser pulse is \begin{equation} \label{eq:pop} P = \frac{X}{1+(X-1)\mathrm{e}^{-T/\tau}}, \end{equation} where $X$ is given by Eq.~\ref{eq:exc}. \\ The photon emission rate averaged over a repetition period $T$ is given by \begin{equation} \label{eq:emrate} \langle\Phi\rangle = \frac{\eta}{\tau} \, \frac{1}{T} \int_0^T P \mathrm{e}^{-t/\tau} \, \mathrm{d}t = \frac{\eta P}{T} \left(1-\mathrm{e}^{-T/\tau}\right), \end{equation} where $\eta$ is the quantum efficiency of the emitter, and $P$ is given by Eq.~\ref{eq:pop}. From the general equation for the photon emission rate $\langle\Phi\rangle$ (Eq.~\ref{eq:emrate}) we can obtain approximate expressions in the low-intensity limit ($IT\sigma/\hbar\omega\ll 1$), for continuous wave excitation or for pulsed excitation with a repetition period much longer than the excited state lifetime. Continuous wave excitation corresponds to the limit that $T\rightarrow 0$, i.e. pulses follow each other directly. Then the photon emission rate is \begin{equation} \langle\Phi\rangle_\textrm{cw} = \frac{\eta}{\tau} \, \frac{I\sigma/\hbar\omega}{1/\tau+I\sigma/\hbar\omega}. \end{equation} The same expression would be obtained from a rate equation model with excitation rate $I\sigma/\hbar\omega$ and decay rate $1/\tau$. Pulsed excitation with a long excitation period corresponds to the limit that $T/\tau \gg 1$: \begin{equation} \label{eq:pulsed} \langle\Phi\rangle_{T\rightarrow\infty} = \eta I\sigma/\hbar\omega, \end{equation} i.e. the emission rate no longer depends on the excited state lifetime $\tau$. \\ To estimate the expected brightness of the defects in silica under various experimental conditions, we compare them to the dot-in-rods examined in Ref.~\cite{Rabouw2013}. The brightness of an individual emitter is proportional to the product of PL quantum efficiency $\eta$ and absorption cross-section $\sigma$ (see Eq.~\ref{eq:pulsed}), assuming that the absorption-cross section is sufficiently small ($< 10^{-14}$ cm$^{2}$) that the excitation is not saturated ($\ll 1$ absorption per pulse). For the dot-in-rods investigated in Ref.~\cite{Rabouw2013} the quantum efficiency of the bright state is close to 1 \cite{Lunnemann2013}, and the absorption cross-section at 532 nm is approximately $\sigma = 10^{-15}$ cm$^{2}$ \cite{Leatherdale2002}. The defects in silica are approximately 10 times less bright, so we estimate that for the defects $\eta\sigma\approx 10^{-16}$ cm$^{2}$. For the calculations in Fig.~\ref{fig:emrates} we assume that $\eta=1$ and $\sigma= 10^{-16}$ cm$^{2}$, but the results would change only slightly if the individual values were a little different. We use the full expression for the photon emission rate (Eq.~\ref{eq:emrate}).	{ "redpajama_set_name": "RedPajamaArXiv" }	4,771
\section{Preliminaries} \noindent We recall the following concepts and results, which are needed to define the problem and to prove the main result: \begin{definition}{\rm\cite{lumer}}\label{s1d1} Let $X$ be a vector space over the field $\mathbb{K} = \mathbb{R}$ (or $\mathbb{C}$) of real (or complex) numbers. A functional $[\cdot,\cdot] : X\times X \to \mathbb{K}$ is called a semi-inner product if it satisfies the following conditions: \begin{enumerate} \item[{\rm(1)}] $[x+y,z]=[x,z]+[y,z], \forall x,y,z\in X;$ \item[{\rm(2)}] $[\lambda x,y]=\lambda[x,y], \forall \lambda \in \mathbb{K} ~ and~ \forall x,y\in X;$ \item[{\rm(3)}] $[x,x] > 0, ~for~ x \neq 0;$ \item[{\rm(4)}] $\|[x,y]\|^2 \leq [x,x][y,y], \forall x,y\in X.$ \end{enumerate} \end{definition} The pair $(X,[\cdot,\cdot])$ is called a semi-inner product space. As it is observed in {\rm\cite{lumer}} that $\\|x\\|=[x,x]^{1/2}, \forall x\in X$, is a norm on $X$. Hence every semi-inner product space is a normed linear space. On the other hand, in a normed linear space, one can generate semi-inner product in infinitely many different ways. Further, it is noted that a Hilbert space $H$ can be made into a semi-inner product space, while a semi-inner product is an inner product if and only if the norm it induces verifies the parallelogram law.\\ Let $Y$ be a semi-inner product space and let $T:X\to Y$ be an arbitrary operator. \begin{definition}{\rm\cite{pap}}\label{s1d2} The generalized adjoint operator $T^+$ of an operator $T$ is defined as follows: The domain $D(T^+)$ of $T^+$ consists of those $y\in Y$ for which there exists $z \in X$ such that \begin{equation} [Tx,y]_{Y}=[x,z]_{X}\nonumber \end{equation} for each $x\in X$ and $z=T^+y$. \end{definition} \begin{remark} $T^+$ is an operator from $D(T^+)$ into $X$ with the nonempty domain $D(T^+)$, since $0\in D(T^+)$. Hence $T^+(0)=0$. As it is observed in [3] that if $X$ and $Y$ are Hilbert spaces then the generalized adjoint operator is the usual adjoint operator. In general, $T^+$ is not linear even for $T$ is a bounded linear operator. \end{remark} Let $C$ be a nonempty closed and convex subset of a Banach space $E$. Let $E^$ be the dual space of $E$ and $\langle\cdot,\cdot\rangle$ denote the pairing between $E$ and $E^$. The normalized duality mapping $J:E\to 2^{E^}$ is defined by \begin{equation} J(x)=\{f\in E^:\langle x,f\rangle=\\|x\\|^2, \\|f\\|=\\|x\\|\}\nonumber \end{equation} for all $x\in E$. We denote by $j$ the single normalized duality mapping, i.e., $j(x)\in J(x),~x\in E$. \begin{definition}{\rm\cite{xu}}\label{s1d3} Let $U= \{x\in E:\\|x\\|=1\}$. A Banach space $E$ is said to be: \begin{enumerate} \item[{\rm(1)}] uniformly convex if, for any $\epsilon \in (0,2]$, there exists $\delta>0$ such that for any $x,y\in U$, \begin{equation} \\|x-y\\|\geq\epsilon ~ implies~ \left\\|\frac{x+y}{2}\right\\|\leq1-\delta ;\nonumber \end{equation} \item[{\rm(2)}] smooth if the limit $\lim_{t\to 0}\frac{\\|x+ty\\|-\\|x\\|}{t}$ exists for all $x,y\in U$; \item[{\rm(3)}] uniformly smooth if the limit is attained uniformly for $x,y\in U$. \end{enumerate} \end{definition} \begin{definition}\label{s1d4} The modulus of smoothness of a Banach space $E$ is defined by \begin{equation} \rho(\tau)={\rm sup}\left\{\frac{1}{2}(\\|x+y\\|+\\|x-y\\|)-1:x,y\in X, \\|x\\|=1, \\|y\\|=\tau\right\},\nonumber \end{equation} where $\rho:[0,\infty)\to [0,\infty)$ is a function. \end{definition} \begin{remark} $E$ is uniformly smooth if and only if $\lim_{t\to 0}\frac{\rho(\tau)}{\tau}=0$. If $E$ is smooth then normalized duality mapping $J$ is single-valued and if $E$ is uniformly smooth then $J$ is uniformly norm to norm continuous on bounded subsets of $E$. If $E$ is a Hilbert space then $J=I$, where $I$ is the identity mapping. \end{remark} In 1967, Giles {\rm\cite{giles}} proved that if the underlying semi-inner product space $X$ is a uniformly convex smooth Banach space then it is possible to define a semi-inner product uniquely which has the following properties: \begin{enumerate} \item[{\rm(i)}] $[x,y]=0$ for some $x, y\in X$ if and only if $y$ is orthogonal to $x$, i.e., if and only if $\\|y\\| \leq \\|y+\lambda x\\|$, for all scalars $\lambda$. \item[{\rm(ii)}] The semi-inner product is continuous, i.e., for each $x,y\in X$, we have ${\rm Re}[y,x+\lambda y]\to {\rm Re}[y,x]$ as $\lambda \to 0$. \item[{\rm(iii)}] The semi-inner product is with the homogeneity property, i.e., \begin{equation} [x,\lambda y]=\|\lambda\|[x,y], \forall \lambda\in \mathbb{K} ~ {\rm and}~ \forall x,y\in X.\nonumber \end{equation} \item[{\rm(iv)}] Generalized Riesz representation theorem: If $f$ is continuous linear functional on $X$ then there is a unique vector $y\in X$ such that $f(x)=[x,y], \forall x\in X$. \end{enumerate} The sequence space $l^p, p > 1$ and the function space $L^p, p > 1$ are uniformly convex smooth Banach spaces. More precisely, $L^p$ is min$\{p,2\}$-uniformly smooth for every $p>1$. So one can define semi-inner product on these spaces uniquely. \begin{example}{\rm\cite{giles}} The real sequence space $l^p$ for $1<p<\infty$ is a semi-inner product space with the semi-inner product defined by \begin{equation} [x,y]=\frac{1}{\\|y\\|^{p-2}_p}\sum_{i}x_iy_i\|y_i\|^{p-2}, \forall x,y\in l^p.\nonumber \end{equation} \end{example} \begin{example}{\rm\cite{giles}} The real Banach space $L^p(X,\mu)$ for $1<p<\infty$ is a semi-inner product space with the semi-inner product defined by \begin{equation} [f,g]=\frac{1}{\\|g\\|^{p-2}_p}\int_{X}fx\|gx\|^{p-1}sgn(gx)d\mu, \forall f,g\in L^p.\nonumber \end{equation} \end{example} Now, we summarize the following properties of the generalized adjoint operator from the results given in {\rm\cite{pap}}. \begin{proposition}\label{s1p1} Let $X$ and $Y$ be $2$-uniformly convex smooth Banach spaces and let $T:X\to Y$ be a bounded linear operator. Then \begin{enumerate} \item[{\rm(i)}] $D(T^+)=Y$; \item[{\rm(ii)}] $T^+$ is bounded, and it holds that \begin{equation} \\|T^+y\\| \leq \\|T\\|\\|y\\|, \forall y\in Y.\nonumber \end{equation} \end{enumerate} \end{proposition} \begin{definition}{\rm\cite{reich}}\label{s1d5} Let $D$ be a subset of $C$ and $Q_C$ be a mapping of $C$ into $D$. Then $Q_C$ is said to be sunny if \begin{equation} Q_C(Q_Cx+t(x-Q_Cx))=Q_Cx,\nonumber \end{equation} whenever $Q_Cx+t(x-Q_Cx)\in C$ for $x\in C$ and $t\geq 0$. \end{definition} \begin{definition}{\rm\cite{reich}}\label{s1d6} A subset $D$ of $C$ is called a sunny nonexpansive retract of $C$ if there exists a sunny nonexpansive retraction from $C$ into $D$. \end{definition} The following result describes a characterization of sunny nonexpansive retractions on a smooth Banach space. \begin{proposition}{\rm\cite{reich}}\label{s1p2} Let $E$ be a smooth Banach space and let $C$ be a nonempty subset of $E$. Let $Q_C:E\to C$ be a retraction. Then the following are equivalent: \begin{enumerate} \item[{\rm(i)}] $Q_C$ is sunny and nonexpansive; \item[{\rm(ii)}] $\\|Q_Cx-Q_Cy\\|^2 \leq \langle x-y, J(Q_Cx-Q_Cy)\rangle, \forall x,y\in E$; \item[{\rm(iii)}] $\langle x-Q_Cx, J(y-Q_Cx)\rangle \leq 0, \forall x\in E, y\in C$. \end{enumerate} \end{proposition} \begin{lemma}{\rm\cite{xu}}\label{s1l1} Let $p>1$ be a real number and $E$ be a smooth Banach space. Then the following statements are equivalent: \begin{enumerate} \item[{\rm(i)}] $E$ is $2$-uniformly smooth; \item[{\rm(ii)}] There is a constant $c>0$ such that for every $x,y\in E$, the following inequality holds \begin{equation} \\|x+y\\|^2\leq \\|x\\|^2+2\langle y,J(x) \rangle + c\\|y\\|^2.\nonumber \end{equation} \end{enumerate} \end{lemma} \begin{remark}\label{s1r1} \begin{enumerate} \item {\rm\cite{giles,lumer,sahu}}: Every normed linear space is a semi-inner product space. In fact by Hahn Banach theorem, for each $x\in E$ there exists at least one functional $f_x\in E^$ such that $\langle x, f_x\rangle=\\|x\\|^2$. Given any such mapping $f$ from $E$ into $E^$, we can verify that $[y,x]=\langle y, f_x\rangle$ defines a semi-inner product. Hence, we can write the inequality given in Lemma {\ref{s1l1}} as \begin{equation} \\|x+y\\|^2\leq \\|x\\|^2+2[y,x] + c\\|y\\|^2, \forall x,y\in E.\nonumber \end{equation} The constant $c$ is chosen with best possible minimum value. We call $c$ as the constant of smoothness of $E$. \item The inequalities given in Proposition {\ref{s1p2}} (ii) \& (iii) can be written as \begin{enumerate} \item[{\rm(ii)}] $\\|Q_Cx-Q_Cy\\|^2 \leq [ x-y, Q_Cx-Q_Cy], \forall x,y\in E$; \item[{\rm(iii)}] $[ x-Q_Cx, y-Q_Cx] \leq 0, \forall x\in E, y\in C$. \end{enumerate} \end{enumerate} \end{remark} \begin{example}{\rm\cite{sahu}} The function space $L^p$ is $2$-uniformly smooth for $p\geq 2$ and it is $p$-uniformly smooth for $1<p<2$. If $2\leq p <\infty$, then we have for all $x,y\in L^p$, \begin{equation} \\|x+y\\|^2\leq \\|x\\|^2+2[y,x] + (p-1)\\|y\\|^2,\nonumber \end{equation} where $(p-1)$ is the constant of smoothness. \end{example} Let $E_1$ and $E_2$ be $2$-uniformly convex, smooth Banach spaces and for each $i\in \{1,2\}$; let $C_i\subset E_i$ be a nonempty, closed and convex set and let $J_1:E_1\to 2^{E_1^}$ and $J_2:E_2\to 2^{E_2^}$ be the normalized duality mappings. Let $F,G:C_1\to E_1$ and $f,g:C_2\to E_2$ be nonlinear mappings, and let $A:E_1\to E_2$ be a bounded linear operator. We introduce the following system of split variational inequality problems (in short, SSpVIP): Find $(x_1,y_1)\in C_1\times C_1$ such that $$\langle \lambda F y_1+x_1-y_1, J_1(z_1-x_1)\rangle\geq 0,~~\forall z_1\in C_1, $$ and such that $(x_2,y_2)$ with $x_2=Ax_1\in C_2, y_2=Ay_1\in C_2$ solves $$\langle \gamma f y_2+x_2-y_2, J_2(z_2-x_2)\rangle\geq 0,~~\forall z_2\in C_2; $$ $$\langle \lambda G x_1+y_1-x_1, J_1(z_1-y_1)\rangle\geq 0,~~\forall z_1\in C_1, $$ and such that $(x_2,y_2)$ solves $$\langle \gamma g x_2+y_2-x_2, J_2(z_2-y_2)\rangle\geq 0,~~\forall z_2\in C_2, $$ for any $\lambda, \gamma > 0$.\\ Above SSpVIP is equivalent to find $(x_1,y_1)\in C_1\times C_1$ such that $$[ \lambda F y_1+x_1-y_1, z_1-x_1]\geq 0,~~\forall z_1\in C_1, \eqno(1.1)$$ and such that $(x_2,y_2)$ with $x_2=Ax_1\in C_2, y_2=Ay_1\in C_2$ solves $$[\gamma f y_2+x_2-y_2, z_2-x_2]\geq 0,~~\forall z_2\in C_2; \eqno(1.2)$$ $$[ \lambda G x_1+y_1-x_1, z_1-y_1]\geq 0,~~\forall z_1\in C_1, \eqno(1.3)$$ and such that $(x_2,y_2)$ solves $$[ \gamma g x_2+y_2-x_2, z_2-y_2]\geq 0,~~\forall z_2\in C_2, \eqno(1.4)$$ for any $\lambda, \gamma > 0$.\\ \noindent {\bf Some special cases:}\\ {\bf 1.} If we set $E_1=H_1,~E_2=H_2$, where $H_1,~H_2$ are Hilbert spaces, then SSpVIP (1.1)-(1.4) reduces to the following system of split variational inequality problems (SSpVIP) in Hilbert spaces: Find $(x_1,y_1)\in C_1\times C_1$ such that $$\langle \lambda F y_1+x_1-y_1, z_1-x_1\rangle\geq 0,~~\forall z_1\in C_1, \eqno(1.5)$$ and such that $(x_2,y_2)$ with $x_2=Ax_1\in C_2, y_2=Ay_1\in C_2$ solves $$\langle \gamma f y_2+x_2-y_2, z_2-x_2\rangle\geq 0,~~\forall z_2\in C_2; \eqno(1.6)$$ $$\langle \lambda G x_1+y_1-x_1, z_1-y_1\rangle\geq 0,~~\forall z_1\in C_1, \eqno(1.7)$$ and such that $(x_2,y_2)$ solves $$\langle \gamma g x_2+y_2-x_2, z_2-y_2\rangle\geq 0,~~\forall z_2\in C_2, \eqno(1.8)$$ for any $\lambda, \gamma > 0$.\\ {\bf 2.} If we set $F=G, ~f=g,~ \lambda = \gamma,~ y_1=x_1$, then $y_2=x_2$ and hence SSpVIP (1.1)-(1.4) reduces to the following split variational inequality problem (in short, SpVIP): Find $x_1\in C_1$ such that $$[ Fx_1, z_1-x_1] \geq 0, ~~\forall z_1\in C_1, \eqno(1.9)$$ and such that $x_2=Ax_1\in C_2$ solves $$[ fx_2, z_2-x_2] \geq 0, ~~\forall z_2\in C_2, \eqno(1.10)$$ {\bf 3.} In Case 2, if $E_1=H_1,~ E_2=H_2$, then SpVIP (1.9)-(1.10) reduces to the split variational inequality problem considered and studied by Censor et al. {\rm\cite{cen3}}. It is worth mentioning that the SpVIP is quite general and permit split minimization between two spaces so that the image of a minimizer of a given function, under a bounded linear operator, is a minimizer of another function. It includes as a special case, the variational inequality problem, the split zero problem and the split-feasibility problem which have already been studied and used in practice as a model in the intensity-modulated radiation therapy planning, see {\rm\cite{cen2,cen1}}. For a further related work, see {\rm\cite{byr,kaz1,kaz5,kazm1,kazm2,mou}}.\\ Further, it is worth mentioning that so far the iterative approximations of split variational inequality problem and its generalizations have been studied in the setting of Hilbert spaces. Therefore, a natural question appears as to whether or not one can study these problems in setting of Banach spaces.\\ In this paper, we use the retraction technique to propose and analyze an iterative algorithm for computing the approximate solution of SSpVIP (1.1)-(1.4) in $2$-uniformly convex smooth Banach spaces. Further, convergence analysis of the iterative algorithm is discussed. Several special cases which can be obtained from the main result are also discussed. The problems and the results discussed in this paper are new and different from the existing problems and results in the literature.\\ \section{Iterative Algorithms} By making use of Proposition {\ref{s1p2}} , we easily observe that SSpVIP (1.1)-(1.4) can be formulated as follows: Find $(x_1,y_1)\in C_1\times C_1$ with $(x_2,y_2)=(Ax_1,Ay_1)\in C_2\times C_2$ such that $$x_1=Q_{C_1}(y_1-\lambda Fy_1), \eqno (2.1)$$ $$x_2=Q_{C_2}(y_2-\gamma fy_2), \eqno (2.2)$$ $$y_1=Q_{C_1}(x_1-\lambda Gx_1), \eqno (2.3)$$ $$y_2=Q_{C_2}(x_2-\gamma gx_2), \eqno (2.4)$$ for $\lambda, \gamma > 0$.\\ Based on above arguments, we propose the following iterative algorithm for approximating a solution to SSpVIP (1.1)-(1.4).\\ Let $\{\alpha_n\}\subseteq (0,1)$ be a sequence such that $\sum\limits^{\infty}_{n=1}=\infty$.\\ \noindent {\bf Iterative Algorithm 2.1.} Given $(x^0_1,y^0_1)\in C_1\times C_1$, compute the iterative sequence $\{(x^n_1,y^n_1)\}$ defined by the iterative schemes: $$a^n_1=Q_{C_1}(y^n_1-\lambda Fy^n_1), \eqno (2.5)$$ $$a^n_2=Q_{C_2}(y^n_2-\gamma fy^n_2), \eqno (2.6)$$ $$b^n_1=Q_{C_1}(x^n_1-\lambda Gx^n_1), \eqno (2.7)$$ $$b^n_2=Q_{C_2}(x^n_2-\gamma gx^n_2), \eqno (2.8)$$ $$x^{n+1}_1=(1-\alpha^n)x^n_1+\alpha^n\left(a^n_1+\rho A^+(a^n_2-Aa^n_1)\right), \eqno (2.9)$$ $$y^{n+1}_1=(1-\alpha^n)y^n_1+\alpha^n\left(b^n_1+\rho A^+(b^n_2-Ab^n_1)\right), \eqno (2.10)$$ for all $n=0,1,2,....$ and $\lambda, ~\gamma, ~\rho > 0$, where $A^+$ is the generalized adjoint operator of $A$, and $x^n_2=Ax^n_1$ and $y^n_2=Ay^n_1$ for all $n$.\\ If we set $E_1=H_1, ~E_2=H_2$, where $H_1,~H_2$ are Hilbert spaces, then Iterative Algorithm 2.1 reduces to the following iterative algorithm for computing the approximate solution of SSpVIP (1.5)-(1.8):\\ \noindent {\bf Iterative Algorithm 2.2.} Given $(x^0_1,y^0_1)\in C_1\times C_1$, compute the iterative sequence $\{(x^n_1,y^n_1)\}$ defined by the iterative schemes: $$a^n_1=P_{C_1}(y^n_1-\lambda Fy^n_1), \eqno (2.11)$$ $$a^n_2=P_{C_2}(y^n_2-\gamma fy^n_2), \eqno (2.12)$$ $$b^n_1=P_{C_1}(x^n_1-\lambda Gx^n_1), \eqno (2.13)$$ $$b^n_2=P_{C_2}(x^n_2-\gamma gx^n_2), \eqno (2.14)$$ $$x^{n+1}_1=(1-\alpha^n)x^n_1+\alpha^n\left(a^n_1+\rho A^(a^n_2-Aa^n_1)\right), \eqno (2.15)$$ $$y^{n+1}_1=(1-\alpha^n)y^n_1+\alpha^n\left(b^n_1+\rho A^(b^n_2-Ab^n_1)\right), \eqno (2.16)$$ for all $n=0,1,2,....$ and $\lambda, ~ \gamma,~ \rho > 0$, where $A^$ is the adjoint operator of $A$ with $\\|A^\\|=\\|A\\|$, and $P_{C_i}$ is the metric projection of $H_i$ onto $C_i$ for each $i \in \{1,2\}$.\\ If we set $F=G, ~f=g, ~\lambda = \gamma,~ y_1=x_1$, then $y_2=x_2$ and hence Iterative Algorithm 2.1 reduces to the following iterative algorithm for computing the approximate solution of SpVIP (1.9)-(1.10):\\ \noindent {\bf Iterative Algorithm 2.3.} Given $x^0_1\in C_1$, compute the iterative sequence $\{x^n_1\}$ defined by the iterative schemes: $$a^n_1=Q_{C_1}(x^n_1-\lambda Fx^n_1), $$ $$a^n_2=Q_{C_2}(x^n_2-\lambda fx^n_2),$$ $$x^{n+1}_1=(1-\alpha^n)x^n_1+\alpha^n\left(a^n_1+\rho A^+(a^n_2-Aa^n_1)\right), $$ for all $n=0,1,2,....$ and $\lambda,~ \gamma, ~\rho > 0$. \section{Main Result} First, we define the following concepts. \vspace{.3cm} \begin{definition}\label{s3d1} A mapping $F:E_1 \rightarrow E_1$ is said to be \begin{enumerate} \item[{\rm(1)}] $\alpha$-{\it strongly monotone} if there exists a constant $\alpha>0$ such that $$[Fx_1-Fy_1,x_1-y] \geq \alpha\Vert x_1-y_1\Vert^2,~~~ \forall x_1,y_1\in E_1;$$ \item[{\rm(2)}] $\beta$-{\it Lipschitz continuous}, if there exists a constant $\beta > 0$ such that $$\\|Fx_1-Fy_1\\|\leq \beta \\|x_1-y_1\\|,~~~ \forall x_1,y_1\in E_1.$$ \end{enumerate} \end{definition} Now, we prove that the sequence of approximate solutions of SSpVIP (1.1)-(1.4) generated by Iterative Algorithm 2.1 converges strongly to the solution of SSpVIP (1.1)-(1.4). \begin{theorem}\label{s3t1} For each $i\in\{1,2\},$ let $C_{i}$ be a nonempty, closed and convex subset of $2$-uniformly convex smooth Banach space $E_{i}$ with constant of smoothness $c_i$. Let $F: C_1\to E_1$ be $\alpha_{1}$-strongly monotone and $\beta_{1}$-Lipschitz continuous; let $G: C_1\to E_1$ be $\alpha_{2}$-strongly monotone and $\beta_{2}$-Lipschitz continuous; let $f: C_2\to E_2$ be $\sigma_{1}$-strongly monotone and $\eta_{1}$-Lipschitz continuous, and let $g: C_2\to E_2$ be $\sigma_{2}$-strongly monotone and $\eta_{2}$-Lipschitz continuous. Let $A:E_1 \to E_2$ be bounded linear operator. Suppose $(x_1,y_1) \in C_1 \times C_2$ is a solution to SSpVIP(1.1)-(1.4) then the sequence $\{(x_1^n, y_1^n)\}$ generated by Iterative Algorithm 2.1 converges strongly to $(x_1,y_1)$ provided that the constant $ \lambda>0$ satisfies the condition: $$\max_{1\leq i\leq 2}\left\{\frac{\alpha_i-\sqrt{\alpha_i^2-c_1\beta_i^2(1-p_i^2)}}{c_1\beta_i^2}\right\}<\lambda < \min_{1\leq i\leq 2}\left\{\frac{\alpha_i+\sqrt{\alpha_i^2-c_1\beta_i^2(1-p_i^2)}}{c_1\beta_i^2}\right\} \eqno (3.1)$$ $$\alpha_i>\beta_i\sqrt{c_1(1 -p_i^2)};~~p_i=\frac{1-m\theta_{i+2}}{1+m};~~~m=\rho\\|A^+\\|\\|A\\|;$$ $$\theta_{i+2}=\sqrt{1-2\gamma\sigma_i+c_2\gamma^2\eta_i^2};~~~ \gamma>0.$$ \end {theorem} \noindent {\bf Proof.} Given that $(x_1,y_1)$ is a solution of SSpVIP (1.1)-(1.4), that is, $x_1, y_1$ satisfy the relations (2.1)-(2.4). Since $F:C_1\to E_1$ is $\alpha_1$-strongly monotone and $\beta_1$-Lipschitz continuous, from Iterative Algorithm 2.1 (2.5) and (2.1), we estimate\\ $$\\|a^n_1-x_1\\| = \\|Q_{C_1}(y^n_1-\lambda Fy^n_1)-Q_{C_1}(y_1-\lambda Fy_1)\\| \hspace{.95in}$$ $$\leq \\|y^n_1-y_1-\lambda (Fy^n_1-Fy_1)\\| \hspace{1in}$$ $$\hspace{1in} \leq \left(\\|y^n_1-y_1\\|^2-2\lambda \left[Fy^n_1-Fy_1,y^n_1-y_1\right]+c\lambda^2\\|Fy^n_1-Fy_1\\|^2\right)^{\frac{1}{2}}$$ $$\leq \theta_1 \\|y^n_1-y_1\\|, \hspace{1.75in} ~~~\eqno(3.2)$$ where $\theta_1=(1-2\lambda\alpha_1+c_1\lambda^2\beta^2_1)^{\frac{1}{2}}.$\\ Next, since $G:C_1\to E_1$ is $\alpha_2$-strongly monotone and $\beta_2$-Lipschitz continuous, from Iterative Algorithm 2.1 (2.7) and (2.3), we have $$\\|b^n_1-y_1\\|=\\|Q_{C_1}(x^n_1-\mu Gx^n_1)-Q_{C_1}(x_1-\mu Gx_1)\\| \hspace{1in}$$ $$\leq \theta_2\\|x^n_1-x_1\\|, \hspace{1.75in} ~~~\eqno(3.3)$$ where $\theta_2=(1-2\lambda\alpha_2+c_1\lambda^2\beta^2_2)^{\frac{1}{2}}.$\\ Again, since $f:C_2\to E_2$ is $\sigma_1$-strongly monotone and $\eta_1$-Lipschitz continuous, from Iterative Algorithm 2.1 (2.6) and (2.2), we have $$\\|a^n_2-x_2\\| \leq \theta_3\\|y^n_2-y_2\\|, ~~~\eqno(3.4)$$ where $\theta_3=(1-2\gamma\sigma_1+c_2\gamma^2\eta^2_1)^{\frac{1}{2}}.$\\ Since $g:C_2\to E_2$ is $\sigma_2$-strongly monotone and $\eta_2$-Lipschitz continuous, from Iterative Algorithm 2.1 (2.8) and (2.4), we have $$\\|b^n_2-y_2\\| \leq \theta_4\\|x^n_2-x_2\\|, ~~~\eqno(3.5)$$ where $\theta_4=(1-2\gamma\sigma_2+c_2\gamma^2\eta^2_2)^{\frac{1}{2}}.$\\ Now, using the fact that $A^+$ is bounded, we have \begin{eqnarray} \\|x^{n+1}_1-x_1\\| &\leq & (1-\alpha^n)\\|x^n_1-x_1\\|+\alpha^n\\|a^n_1-x_1+\rho A^+(a^n_2-Aa^n_1)\\|\nonumber\\ &\leq & (1-\alpha^n)\\|x^n_1-x_1\\|+\alpha^n\\|a^n_1-x_1\\|+\alpha^n\rho\\|A^+\\|\\|a^n_2-Aa^n_1\\|\nonumber\\ &\leq & (1-\alpha^n)\\|x^n_1-x_1\\|+\alpha^n\\|a^n_1-x_1\\|+\alpha^n\rho\\|A^+\\|\left(\\|a^n_2-x_2-Aa^n_1+x_2\\|\right)\nonumber\\ &\leq & (1-\alpha^n)\\|x^n_1-x_1\\|+\alpha^n\\|a^n_1-x_1\\|+\alpha^n\rho\\|A^+\\|\left(\\|a^n_2-x_2\\|+\\|A\\|\\|a^n_1-x_1\\|\right)\nonumber\\ &=& (1-\alpha^n)\\|x^n_1-x_1\\|+\alpha^n\theta_1\\|y^n_1-y_1\\|+\alpha^n\rho\\|A^+\\|\left(\theta_3\\|y^n_2-y_2\\|+\\|A\\|\theta_1\\|y^n_1-y_1\\|\right)\nonumber\\ &\leq & (1-\alpha^n)\\|x^n_1-x_1\\|+\alpha^n\theta_1\\|y^n_1-y_1\\|+\alpha^n\rho\\|A^+\\|\\|A\\|\left(\theta_3\\|y^n_1-y_1\\|+\theta_1\\|y^n_1-y_1\\|\right)\nonumber\\ &=& (1-\alpha^n)\\|x^n_1-x_1\\|+\alpha^n\left(\theta_1+\rho\\|A^+\\|\\|A\\|(\theta_1+\theta_3)\right)\\|y^n_1-y_1\\|. \hspace{1.2in} (3.6) \nonumber \end{eqnarray} Similarly, we obtain $$\\|y^{n+1}_1-y_1\\| \leq (1-\alpha^n)\\|y^n_1-y_1\\|+\alpha^n\left(\theta_2+\rho\\|A^+\\|\\|A\\|(\theta_2+\theta_4)\right)\\|x^n_1-x_1\\|. \hspace{.5in} \eqno(3.7)$$ Now, define the norm $\|\|\cdot\|\|_{\star}$ on $E_1\times E_2$ by $$\|\|(x,y)\|\|_{\star} =\|\|x\|\|+\|\|y\|\|,~~~(x,y)\in E_1\times E_2.$$ We can easily show that $(E_1\times E_2, \|\|\cdot\|\|_{\star})$ is a Banach space. \vspace{.3cm} By making using of (3.6) and (3.7), we have the following estimate: $$\\|(x_1^{n+1},y_1^{n+1})-(x_1,y_1)\\|_* =\\|x_1^{n+1}-x_1\\|+\\|y_1^{n+1}-y_1\\|\hspace{2.4in}$$ $$\leq (1-\alpha_n)\left(\\|x_1^{n}-x_1\\|+\\|y_1^{n}-y_1\\|\right)\hspace{.4in}$$ $$\hspace{.6in} +\alpha_n\left(\theta_1+\rho\\|A^+\\|\\|A\\|(\theta_1+\theta_3)\right)\\|y^n_1-y_1\\|\\|y_1^{n}-y_1\\|$$ $$\hspace{.08in}+ \alpha_n\left(\theta_2+\rho\\|A^+\\|\\|A\\|(\theta_2+\theta_4)\right)\\|x^n_1-x_1\\|$$ $$\leq (1-\alpha_n)\left(\\|x_1^{n}-x_1\\|+\\|y_1^{n}-y_1\\|\right)\hspace{.4in}$$ $$\hspace{.15in} +\alpha_n \max\{k_1, k_2\}\left(\\|x^n_1-x_1\\|+\\|y_1^{n}-y_1\\|\right)$$ $$= \left(1-\alpha_n(1-\theta)\right)\\|(x_{n},y_{n})-(x,y)\\|_,\hspace{.27in}\eqno(3.8)$$ where $\theta= \max \{k_1,k_2\};~~k_1=\theta_1+m(\theta_1+\theta_3);~~k_2=\theta_2+m(\theta_2+\theta_4);~~m=\rho\\|A^+\\|\\|A\\|.$ \vspace{0.3cm} Thus, we obtain $$\\|(x_{n+1},y_{n+1})-(x,y)\\|_ < \prod\limits^{n}_{r=1}\left(1-\alpha_r(1-\theta)\right) \\|(x_1^{0},y_1^{0})-(x_1,y_1)\\|_*. \eqno(3.9)$$ It follows from given condition (3.1) on $\lambda$ that $\theta \in (0,1)$. Since $\sum \limits^{\infty}_{n=1} \alpha_n=\infty$ and $\theta \in (0,1)$, it implies that $$\lim\limits_{n\to \infty}\prod\limits^{n}_{r=1}\left(1-\alpha_r(1-\theta)\right)=0.$$ Thus, it follows from (3.9) that $\{(x_1^{n+1},y_1^{n+1})\}$ converges strongly to $(x_1,y_1)$ as $n \to \infty$, that is, $x_1^n \to x_1$ and $y_1^n \to y_1$ as $n \to \infty$. Further, it follows from (3.2) and (3.3), respectively, that $a_1^n \to x_1$ and $b_1^n \to y_1$ as $n \to \infty$. Hence, it follows from (3.4) and (3.5), respectively, that $a_2^n\to x_2=Ax_1$ and $b_2^n \to y_2=Ay_1$ as $n \to \infty$. This completes the proof. \vspace{.3cm} Now, we give the following corollaries which are consequences of Theorem {\ref{s3t1}}. \vspace{.3cm} If we set $E_1=H_1,~E_2=H_2$, then Theorem {\ref{s3t1}} reduces to the following result for the convergence analysis of Iterative Algorithm 2.2 for SSpVIP (1.5)-(1.8). \begin{corollary}\label{s3t2} For each $i\in\{1,2\},$ let $C_{i}$ be a nonempty, closed and convex subset of real Hilbert space $H_{i}$. Let $F: C_1\to H_1$ be $\alpha_{1}$-strongly monotone and $\beta_{1}$-Lipschitz continuous; let $G: C_1\to H_1$ be $\alpha_{2}$-strongly monotone and $\beta_{2}$-Lipschitz continuous; let $f: C_2\to H_2$ be $\sigma_{1}$-strongly monotone and $\eta_{1}$-Lipschitz continuous, and let $g: C_2\to H_2$ be $\sigma_{2}$-strongly monotone and $\eta_{2}$-Lipschitz continuous. Let $A:H_1 \to H_2$ be bounded linear operator. Suppose $(x_1,y_1) \in C_1 \times C_2$ is a solution to SSpVIP(1.5)-(1.8) then the sequence $\{(x_1^n, y_1^n)\}$ generated by Iterative Algorithm 2.2 converges strongly to $(x_1,y_1)$ provided that the constant $ \lambda>0$ satisfies the condition: $$\max_{1\leq i\leq 2}\left\{\frac{\alpha_i-\sqrt{\alpha_i^2-\beta_i^2(1-p_i^2)}}{\beta_i^2}\right\}<\lambda < \min_{1\leq i\leq 2}\left\{\frac{\alpha_i+\sqrt{\alpha_i^2-\beta_i^2(1-p_i^2)}}{\beta_i^2}\right\}$$ $$\alpha_i>\beta_i\sqrt{(1 -p_i^2)};~~p_i=\frac{1-m\theta_{i+2}}{1+m};~~~m=\rho\\|A\\|^2;$$ $$\theta_{i+2}=\sqrt{1-2\gamma\sigma_i+\gamma^2\eta_i^2};~~~ \gamma>0.$$ \end {corollary} \vspace{.2in} If we set $F=G, ~f=g,~ \lambda = \gamma, ~y_1=x_1$, then $y_2=x_2$ and hence Theorem {\ref{s3t1}} reduces to the following result for the convergence analysis of Iterative Algorithm 2.3 for SpVIP (1.9)-(1.10): \begin{corollary}\label{s3t3} For each $i\in\{1,2\},$ let $C_{i}$ be a nonempty, closed and convex subset of $2$-uniformly convex smooth Banach space $E_{i}$ with constant of smoothness $c_i$. Let $F: C_1\to E_1$ be $\alpha_{1}$-strongly monotone and $\beta_{1}$-Lipschitz continuous, and let $f: C_2\to E_2$ be $\sigma_{1}$-strongly monotone and $\eta_{1}$-Lipschitz continuous. Let $A:E_1 \to E_2$ be bounded linear operator. Suppose $x_1 \in C_1 $ is a solution to SpVIP(1.9)-(1.10) then the sequence $\{x_1^n\}$ generated by Iterative Algorithm 2.3 converges strongly to $x_1$ provided that the constant $ \lambda>0$ satisfies the condition: $$\left\| \lambda-\frac{\alpha_1}{c_1\beta_1^2}\right\| < \frac{\sqrt{\alpha_1^2-c_1\beta_1^2(1-p_1^2)}}{c_1\beta_1^2}$$ $$\alpha_1>\beta_1\sqrt{c_1(1 -p_1^2)};~~p_1=\frac{1-m\theta_{2}}{1+m};~~~m=\rho\\|A^+\\|\\|A\\|;$$ $$\theta_{2}=\sqrt{1-2\gamma\sigma_1+c_2\gamma^2\eta_1^2};~~~ \gamma > 0.$$ \end {corollary} \begin{remark} The extension of the method presented in this paper to split equilibrium problem {\rm\cite{kaz5}} and split variational inclusion {\rm\cite{mou}} needs further research efforts. \end{remark}	{ "redpajama_set_name": "RedPajamaArXiv" }	6,742
Q: Best Practice Microservice Authorization Hi I was hoping some clarification on the proper way to handle Micro Service Authorization. I have been trying to research the structure but haven't found a lot of great resources. From my understanding there is 2 possible flows. Flow 1- Authorization server provides a token to the user on log in. All other API services requested then check for a token. Once seeing a token it would request the authorization server to check it is valid and ask if it is valid what user it is. Flow 2- Authorization server provides a token. All API request for other services go to the Authorization server which then hits the other API service and returns the needed data. My questions on this are: * Which flow is best standard practice? What is the best way to structure user data in the other API services? Should they just have the standard user_id on a table and once the token is proven good ask for a user_id from the Authorization Server *(Flow 1) - Is there any way to skip going back and fourth between APIs and Authorization server every request. Such as storing an id or a marker for that user in a session or is this bad practice and unsafe? I know this is a lot of questions but want to make sure I have a firm handle on the structure and flow. Thanks for any help	{ "redpajama_set_name": "RedPajamaStackExchange" }	1,441
Q: Обработка коллекций React Есть компонент <Definitions data={definitions} /> Который принимает в props объект const definitions = [ { dt: 'one', dd: 'two' }, { dt: 'another term', dd: 'another description' }, ]; Должно отрендерится <dl> <dt>one</dt> <dd>two</dd> <dt>another term</dt> <dd>another description</dd> </dl> Как получить коллекцию и отрендерить я понял, но как сделать вложенность не могу сообразить. Выбрасывает ошибку Warning: validateDOMNesting(...): <dd> cannot appear as a descendant of <dt>. Вот что получилось написать: export default class Definitions extends Component { render() { const { data } = this.props; return <dl> {data.map((item, index) => <dt key={index}>{item.dt} </dt>)} </dl> } } A: В данном случае нужно воспользоваться React.Fragment, как контейнером в котором выводятся два соседних элемента function Definitions({data}){ return (<dl> { data.map((item, index) => <React.Fragment key={index}> <dt>{item.dt}</dt> <dd>{item.dd}</dd> </React.Fragment>) } </dl>) } function App(){ const definitions = [ { dt: 'one', dd: 'two' }, { dt: 'another term', dd: 'another description' } ]; return <Definitions data={definitions} />; } ReactDOM.render(<App />, document.getElementById('container')) <script src="https://cdnjs.cloudflare.com/ajax/libs/react/18.1.0/umd/react.production.min.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/react-dom/18.1.0/umd/react-dom.production.min.js"></script> <div id="container"></div>	{ "redpajama_set_name": "RedPajamaStackExchange" }	7,492
Angelina Jolie "Crazy" Brad Pitt Is Ready To Date? Angelina Jolie "Crazy" Brad Pitt Is "Ready To Date," Wants To "Find Love" First? Angelina Jolie is "crazy" Brad Pitt is "ready to date," and she's "determined to find love first." At least that's what a notorious webloid wants readers to believe. But Gossip Cop can reveal the truth. Yet just six months ago, the outlet claimed Jolie was not only dating but "prepping for [a] wedding." The online publication insisted Jolie was in a "secret romance" with a "mystery man," but a month later tried to weasel out of its fake narrative about Jolie dating by asserting she didn't have time for a boyfriend and only had a "lover." Conveniently, the blog has forgotten about all those lies so it can now peddle new lies about Jolie wanting to "find love" before Pitt. The webloid insists she's "about to lose her mind" and "wants to win the race," but there's no real competition between the estranged spouses. In fact, it's HollywoodLies that's really in a race. The site knows fans are still interested in Brangelina stories, so it serves up such content whenever possible, all in the hopes of getting ranked on search engines and scoring traffic. Just transparent as its motivations is the fact that no one close to Jolie speaks to the outlet about her love life. If the publication truly had such insight and access, it wouldn't have published the prior tales and wouldn't be blatantly flip-flopping now. But Gossip Cop is again told that those close to the star aren't dishing to HollywoodLies on the subject. Furthermore, an insider who spoke on the condition of anonymity maintained that Jolie is not the least bit "crazy" over Pitt eventually dating.	{ "redpajama_set_name": "RedPajamaC4" }	3,128
[![Version](https://img.shields.io/cocoapods/v/XMSegmentedControl.svg?style=flat)](http://cocoapods.org/pods/XMSegmentedControl) [![License](https://img.shields.io/cocoapods/l/XMSegmentedControl.svg?style=flat)](http://cocoapods.org/pods/XMSegmentedControl) [![Platform](https://img.shields.io/cocoapods/p/XMSegmentedControl.svg?style=flat)](http://cocoapods.org/pods/XMSegmentedControl) ## Overview XMSegmentedControl is a customizable segmented control. It allows using Text, Icons, or a combination of Icons and Text as the segments. ![Screenshot](https://thumbs.gfycat.com/BelovedWellinformedAustralianshelduck-size_restricted.gif) ## Requirements * iOS 8+ ## Installation You can install XMSegmentedControl manually by simply copying `XMSegmentedControl.swift` into your project's workspace. XMSegmentedControl is available through [CocoaPods](http://cocoapods.org). To install it, simply add the following line to your Podfile: ```ruby pod "XMSegmentedControl" ``` ## Usage * Import XMSegmentedControl into your project. ```Swift import XMSegmentedControl ``` * Use the Storyboard and drag a UIView. * Select the view and under the Identity Inspector select `XMSegmentedControl` under class. * Conform to the `XMSegmentedControlDelegate` protocol by implementing `func xmSegmentedControl(xmSegmentedControl: XMSegmentedControl, selectedSegment: Int)` to receive notifications on which segment was selected. ```Swift func xmSegmentedControl(xmSegmentedControl: XMSegmentedControl, selectedSegment: Int) { print("SegmentedControl Selected Segment: \(selectedSegment)") } ``` Alternatively, create a XMSegmentedControl from code. ### Text Only Segmented Control The example below creates a text-only segmented control. ```Swift let segmentedControl3 = XMSegmentedControl(frame: CGRect(x: 0, y: 224, width: self.view.frame.width, height: 44), segmentTitle: ["Hello", "World", "Three"], selectedItemHighlightStyle: XMSelectedItemHighlightStyle.topEdge) segmentedControl3.backgroundColor = UIColor(red: 22/255, green: 150/255, blue: 122/255, alpha: 1) segmentedControl3.highlightColor = UIColor(red: 25/255, green: 180/255, blue: 145/255, alpha: 1) segmentedControl3.tint = UIColor.white segmentedControl3.highlightTint = UIColor.black self.view.addSubview(segmentedControl3) ``` ![TextOnly](https://dl.dropboxusercontent.com/u/72507896/XMSegmentedControlScreenshots/textonly.png) ### Icon Only Segmented Control The example below creates an icon-only segmented control. ``` Swift let icons1:[UIImage] = [UIImage(named: "icon1")!, UIImage(named: "icon2")!, UIImage(named: "icon3")!, UIImage(named: "icon4")!, UIImage(named: "icon5")!, UIImage(named: "icon6")!] let segmentedControl4 = XMSegmentedControl(frame: CGRect(x: 0, y: 274, width: self.view.frame.width, height: 44), segmentIcon: icons1, selectedItemHighlightStyle: XMSelectedItemHighlightStyle.background) segmentedControl4.backgroundColor = UIColor(red: 128/255, green: 59/255, blue: 159/255, alpha: 1) segmentedControl4.highlightColor = UIColor(red: 144/255, green: 79/255, blue: 173/255, alpha: 1) segmentedControl4.tint = UIColor.white self.view.addSubview(segmentedControl4) ``` ![IconOnly](https://dl.dropboxusercontent.com/u/72507896/XMSegmentedControlScreenshots/icononly.png) ### Horizontal Icon + Text Segmented Control The example below creates a horizontal Icon + Text segmented control. ``` Swift let backgroundColor = UIColor(red: 205/255, green: 74/255, blue: 1/255, alpha: 1) let highlightColor = UIColor(red: 226/255, green: 114/255, blue: 31/255, alpha: 1) let titles = ["Hello", "World", "Two"] let icons = [UIImage(named: "icon1")!, UIImage(named: "icon2")!, UIImage(named: "icon3")!] let frame = CGRect(x: 0, y: 114, width: self.view.frame.width, height: 44) let segmentedControl2 = XMSegmentedControl(frame: frame, segmentContent: (titles, icons), selectedItemHighlightStyle: XMSelectedItemHighlightStyle.bottomEdge) segmentedControl2.backgroundColor = backgroundColor segmentedControl2.highlightColor = highlightColor segmentedControl2.tint = UIColor.white segmentedControl2.highlightTint = UIColor.black self.view.addSubview(segmentedControl2) ``` ![IconText](https://dl.dropboxusercontent.com/u/72507896/XMSegmentedControlScreenshots/texticon.tiff) ### Vertical Icon + Text Segmented Control The example below creates a vertical Icon + Text segmented control. ``` Swift let backgroundColor8 = UIColor(red: 160/255, green: 74/255, blue: 1/255, alpha: 1) let highlightColor8 = UIColor(red: 181/255, green: 114/255, blue: 31/255, alpha: 1) let titles8 = ["Hello", "World", "Eight"] let icons = [UIImage(named: "icon1")!, UIImage(named: "icon2")!, UIImage(named: "icon3")!] let segmentedControl8 = XMSegmentedControl(frame: CGRect(x: 0, y: 164, width: self.view.frame.width, height: 54), verticalSegmentContent: (titles8, icons), selectedItemHighlightStyle: XMSelectedItemHighlightStyle.bottomEdge) segmentedControl8.backgroundColor = backgroundColor8 segmentedControl8.highlightColor = highlightColor8 segmentedControl8.tint = UIColor.white segmentedControl8.highlightTint = UIColor.black self.view.addSubview(segmentedControl8) ``` ![IconText](https://dl.dropboxusercontent.com/u/72507896/XMSegmentedControlScreenshots/hybridverticaltexticon.tiff?raw=1) For more examples see the Example Project provided. ## Example Project To run the example project, clone the repo, and run `pod install` from the Example directory first. Icons in the example project are provided by http://icons8.com ## Author Xavier Merino, xaviermerino@gmail.com ## License XMSegmentedControl is available under the MIT license. See the LICENSE file for more info.	{ "redpajama_set_name": "RedPajamaGithub" }	2,945
{"url":"http:\/\/www.danielrothenberg.com\/blog\/2017\/Jul\/declarative-visualization-in-python-update\/","text":"# Declarative Visualization in Python - Update\n\nLast Fall, I wrote a short piece on the state of toolkits for declarative visualization within Python. As a brief re-cap, most Python users lean on matplotlib to plot their data (although the Python visualization landscape is rapidly evolving!). When it comes to building complex scientific visualizations which try to summarize lots of data in a succinct way, matplotlib works, but is difficult to use; you often have to write very long scripts and use weird tricks to get your data to look the way you want - and then you probably have to go into Illustrator and clean it up afterwards.\n\nIn the following few steps, I'll create one such plot. These plot will compare 6 different climate model simulations - specifically, global-average surface temperature anomalies (versus each simulation's long-term average for a baseline). The 6 simulations comprise a 2x3 ensemble where I've simulated two different emissions cases with three different model configurations. The data a series of monthly means for each simulation. Prepping and processing this data is trivial, and was just a handful of lines of code using experiment and pandas. From this code I've saved a DataFrame in tidy format:\n\nIn\u00a0[2]:\nanomalies_df.head()\n\nOut[2]:\nact aer time month RN TS\n0 arg_comp PD 2001-02-01 2 1.065971 0.669912\n1 arg_comp PD 2001-03-01 3 -0.300655 0.391183\n2 arg_comp PD 2001-04-01 4 -0.538509 0.501736\n3 arg_comp PD 2001-05-01 5 0.249762 0.611735\n4 arg_comp PD 2001-06-01 6 -0.593146 0.528018\n\nMy actual plot is going to have 3 sub-panels: one for each model configuration. Each panel will contain the monthly timeseries for each emissions case using that configuration; I want them to appear as different colors. I also want to add a smoothing function to each timeseries so I can quickly eyeball what's going on. As I previously showed, this is easy to do with matplotlib, but it requires a lot of boilerplate.\n\n## Enter plotnine\u00b6\n\nSince I wrote my post last Fall, there's a newcomer to the Python declarative visualization community. plotnine aims to be a fully-featured implementation of ggplot2 for Python. Really, ggplot2 is the 'gold standard' for grammar of graphics toolkits; I sometimes drop into R just to quickly whip up a plot using it.\n\nBut with plotnine, I can essentially emulate my ggplot2 code directly within Python. Let's build our plot using these core concepts.\n\nWe begin by mapping our data to some aeshtetics, and adding some geometries to our plot to represent these relationships.\n\nIn\u00a0[3]:\nfrom plotnine import \n\nfield = 'TS'\n\np = (\nggplot(anomalies_df, aes('time', field))\n+ geom_line()\n)\nprint(p)\n\n<ggplot: (-9223372036564749901)>\n\n\nLike magic, we have an aggregation plot! However, we're going to want to break down our different panels and colors - to do so, we'll facet like we would with seaborn, and use a factored \"color\" mapping to one of our simulation ID fields. Adding the colors is easy: we just call our variable a \"factor\", and map it at our top ggplot invocation and when we apply the smoothing function.\n\nIn\u00a0[4]:\nfrom plotnine import \n\nfield = 'TS'\n\np = (\nggplot(anomalies_df, aes('time', 'TS', color='factor(aer)'))\n+ geom_line()\n+ facet_wrap('~ act', dir='v')\n)\nprint(p)\n\n<ggplot: (-9223372036564663594)>\n\n\nIt's that easy. Note that there are some minor differences in how we supply arguments to the functions versus in standard ggplot2 (specifically how we indicate a factor by including it in the string representing our field).\n\nAnalytically, we just have one more thing to add to the plot: our lowess smoother. In ggplot2 world, we simply add a stat_smooth function into our pipeline. Here, we do the same. plotnine allows you to supply your own smoother functions, but here we'll use a built-in one (provided via statsmodels).\n\nIn\u00a0[5]:\nfrom plotnine import \n\nfield = 'TS'\n\np = (\nggplot(anomalies_df, aes('time', 'TS', color='factor(aer)'))\n+ geom_line()\n+ stat_smooth(aes(color='factor(aer)'), method='lowess')\n+ facet_wrap('~ act', dir='v')\n)\nprint(p)\n\n<ggplot: (290751366)>\n\n\nThat's essentially it - we have our core plot now! We can also tweak all of the aesthetics of the plot. I'll start with the most complicated part - 'nice' tick labels on our x-axis. This is the biggest weakness with plotnine right now; it doesn't yet have smart date labeling functionality. But we can easily construct our own labels by specifying where the ticks should occur (\"breaks\") and what their corresponding \"labels\" should be.\n\nIn\u00a0[6]:\nfrom pandas import date_range\nfrom plotnine import \n\nfield = 'TS'\n\nlimits = ('2000-01', '2075-01')\nbreaks = date_range(limits, freq='10AS')\nlabels = breaks.year\n\np = (\nggplot(anomalies_df, aes('time', field, color='factor(aer)'))\n+ geom_line()\n+ stat_smooth(aes(color='factor(aer)'), method='lowess')\n+ scale_x_date(\nlimits=limits,\nbreaks=breaks.astype('str').tolist(),\nlabels=labels.astype('str').tolist()\n)\n+ facet_wrap(('act', ), dir='v')\n)\nprint(p)\n\n<ggplot: (-9223372036563750631)>\n\n\nNext, let's fix our plot color theme. We can use a nice colorbrewer palette, and seaborn-like aesthetics.\n\nIn\u00a0[7]:\nfrom pandas import date_range\nfrom plotnine import \n\nfield = 'TS'\n\nlimits = ('2000-01', '2075-01')\nbreaks = date_range(limits, freq='10AS')\nlabels = breaks.year\n\np = (\nggplot(anomalies_df, aes('time', field, color='factor(aer)'))\n+ geom_line()\n+ stat_smooth(aes(color='factor(aer)'), method='lowess')\n+ scale_color_brewer('qual', 'Dark2')\n+ scale_x_date(\nlimits=limits,\nbreaks=breaks.astype('str').tolist(),\nlabels=labels.astype('str').tolist()\n)\n+ facet_wrap(('act', ), dir='v')\n+ theme_seaborn(style='ticks', context='talk', font_scale=0.75)\n)\nprint(p)\n\n<ggplot: (291198342)>\n\n\nI prefer cleaner plots with fewer lines and chart elements save for what is really necessary. We'll modify the theme to kill the top\/right spines, and add a y=0 line to guide our eye inside the plot.\n\nIn\u00a0[8]:\nfrom pandas import date_range\nfrom plotnine import \n\nfield = 'TS'\n\nlimits = ('2000-01', '2075-01')\nbreaks = date_range(limits, freq='10AS')\nlabels = breaks.year\n\np = (\nggplot(anomalies_df, aes('time', field, color='factor(aer)'))\n+ geom_line()\n+ stat_smooth(aes(color='factor(aer)'), method='lowess')\n+ scale_color_brewer('qual', 'Dark2')\n+ scale_x_date(\nlimits=limits,\nbreaks=breaks.astype('str').tolist(),\nlabels=labels.astype('str').tolist()\n)\n+ facet_wrap(('act', ), dir='v')\n+ geom_hline(aes(yintercept=0.), linetype='dashed')\n+ theme_seaborn(style='ticks', context='talk', font_scale=0.75)\n+ theme(\naxis_line_x=element_line(color='black'),\naxis_line_y=element_line(color='black')\n)\n)\nprint(p)\n\n<ggplot: (292675069)>\n\n\nFinally, let's tweak the y-axis and legend labels, and clean up the facet titles to get rid of the backgroud grey box. In ggplot2\/plotnine, the facet titles are an element called a \"strip\".\n\nIn\u00a0[9]:\nfrom pandas import date_range\nfrom plotnine import \n\nfield = 'TS'\n\nlimits = ('2000-01', '2075-01')\nbreaks = date_range(limits, freq='10AS')\nlabels = breaks.year\n\np = (\nggplot(anomalies_df, aes('time', field, color='factor(aer)'))\n+ geom_line()\n+ stat_smooth(aes(color='factor(aer)'), method='lowess')\n+ scale_color_brewer('qual', 'Dark2')\n+ scale_x_date(\nlimits=limits,\nbreaks=breaks.astype('str').tolist(),\nlabels=labels.astype('str').tolist()\n)\n+ guides(\ncolor=guide_legend(title='Emissions Case')\n)\n+ ylab('{} Anomalies'.format(field))\n+ facet_wrap(('act', ), dir='v')\n+ geom_hline(aes(yintercept=0.), linetype='dashed')\n+ theme_seaborn(style='ticks', context='talk', font_scale=0.75)\n+ theme(strip_background=element_rect(fill='white'),\naxis_line_x=element_line(color='black'),\naxis_line_y=element_line(color='black'),\n)\n)\nprint(p)\n\n<ggplot: (290997203)>\n\n\n## Putting it all together\u00b6\n\nFinally, we can combine all of the previous code snippets (including imports) to produce our final figure. We actually haven't really solved our \"lines of code\" problem... however, the code we've written is fundamentally different than the imperative matplotlib code which could reproduce this figure. In fact, most of the code is just tweaking plot aesthetics, which we could easily save as a theme and never have to worry about again - and if you're in an exploratory data analysis mode, you probably wouldn't even other with aesthetics in the first place!\n\nIf you can get over the length and verbosity of the code, you're left with a \"recipe\" for what you want your plot to contain. That lets you focus on interpreting the results, instead of building plotting scripts.\n\nIn\u00a0[5]:\nfrom pandas import date_range\nfrom plotnine import \n\nfield = 'TS'\n\nlimits = ('2000-01', '2075-01')\nbreaks = date_range(*limits, freq='10AS')\nlabels = breaks.year\n\np = (\nggplot(anomalies_df, aes('time', field, color='factor(aer)'))\n+ geom_line()\n+ stat_smooth(aes(color='factor(aer)'), method='lowess', se=False)\n+ scale_color_brewer('qual', 'Dark2')\n+ scale_x_date(\nlimits=limits,\nbreaks=breaks.astype('str').tolist(),\nlabels=labels.astype('str').tolist()\n)\n+ guides(\ncolor=guide_legend(title='Emissions Case')\n)\n+ ylab('{} Anomalies'.format(field))\n+ facet_wrap(('act', ), dir='v')\n+ geom_hline(aes(yintercept=0.), linetype='dashed')\n+ theme_seaborn(style='ticks', context='talk', font_scale=0.75)\n+ theme(figure_size=(8, 8),\nstrip_background=element_rect(fill='white'),\naxis_line_x=element_line(color='black'),\naxis_line_y=element_line(color='black'),\nlegend_key=element_rect(fill='white', color='white')\n)\n)\nprint(p)\n\n<ggplot: (291527856)>\n\n\nNote that here we've also tweaked the plot size and attempted to get rid of the grey background in the legend \"keys\". For some reason, this isn't working at the moment, but this should be the correct calling sequence.\n\n## Differences with Existing Toolkits\u00b6\n\nplotnine is a worthy heir to ggplot2. It's more fully-featured than yhat's ggplot project and the altair project, although the latter aims for a slightly different use-case (translating to d3-esque plotting frameworks). It's not quite as low-level as seaborn, but could probably reproduce most seaborn figures with ease.\n\nMy biggest issue with plotnine is the lack of examples, but that'll probably change as more users try it out and contribute them to the community. A smaller issue is that using plotnine requires you to abandon your years worth of knowledge about matplotlib. It would be awesome if I could go in after I construct a plot and then tweak the aesthetics using my working knowledge of matplotlib. Sometimes there are weird edge cases that cause plotnine plots to break (although as an important note, resetting your kernel tends to fix them. I have no idea why this happens and I can't faithfully reproduce it), and they arise from complicated layering of plot elements. If I could do my core plotting via plotnine, then have a FacetGrid-like object to manually tweak (fixing spines, ticks, labels, annotations, etc), that would be an ideal situation.\n\nIf this is useful to you, please check out plotnine on github and encourage its author to keep developing it!","date":"2018-12-10 11:49:05","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.31672969460487366, \"perplexity\": 7172.599794888248}, \"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-2018-51\/segments\/1544376823322.49\/warc\/CC-MAIN-20181210101954-20181210123454-00354.warc.gz\"}"}	null	null
Q: pgfplots: filled markers without border I am trying to draw a PGF plot with markers only. I want the markers to be filled squares, but pgfplots keeps adding a differently colored border to these marks. How can I stop that from happening? I want plain filled squares consisting of one color each. MWE: \documentclass{standalone} \usepackage{pgfplots} \begin{document} \begin{tikzpicture} \begin{axis}[tiny] \addplot[ mark=square, only marks, mark options={draw=none}, % this line does not do anything scatter] {sin(deg(x))}; \end{axis} \end{tikzpicture} \end{document} A: You have to play with scatter/use mapped color option; in this case, to "remove" the border, you can set both draw and fill with the same color or you can set the draw opacity=0. The latter method makes markers' size narrow as the border is removed while the former method keeps the markers' size. The complete example: \documentclass{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.9} \begin{document} \begin{tikzpicture} \begin{axis}[tiny] \addplot[ mark=square, only marks, scatter, scatter/use mapped color= {draw opacity=0,fill=mapped color}% to remove the border %{draw=mapped color,fill=mapped color}% for same size ] {sin(deg(x))}; \end{axis} \end{tikzpicture} \end{document} The result:	{ "redpajama_set_name": "RedPajamaStackExchange" }	4,326
\section{Introduction} \label{sec:introduction} In financial markets, the price movement is not only related to the good or bad news for the related company but also to people's understanding of the information and their preferences for trading\cite{stauffer1,lin1}. For a homogeneous population, the same beliefs and strategies may lead to the same buying-selling actions, which may further lead to the occurrence of herding effect and crowding effect\cite{zhang1,zhang2}. For a heterogeneous population, the different beliefs and strategies may lead to the different buying-selling actions, which may further lead to the slow changes of the prices\cite{medo1,chau1,zhong1,wiesinger1,sasidevan1,martino1,wong1}. Understanding the effects of homogeneous and heterogeneous population on the evolution of stock market is quite important for the risk management and the construction of an efficient market\cite{manrique1,cao1, burkholz1,zhang3,wawrzyniak1,biswas1,xie1}. In the study of the effects of individual preferences on the evolutionary dynamics, a variety of agent-based models have been borrowed to model people's social and economic behaviors\cite{schweitzer1,hadzibeganovic1,hadzibeganovic2,gao1,hart2,lo1,lo2,hod1}, among which the minority game and the majority game are mainly used to simulate people's trading behaviors and explore the possible strategic effects and psychological effects\cite{zhang4,challet2,challet3,challet4,challet5,challet6}. Depending upon the minority game, the effects of response time on the evolution of stock prices have been investigated\cite{mosetti1}. The delayed response to the historic information leads to the lag effect of price fluctuations. Depending upon the majority game, the effects of imitation on the evolution of stock prices have been investigated\cite{alfi1,martino2}. Buying and selling the stocks according to most people's choices lead to the occurrence of herding effects in the stock market. Depending upon the mixed minority game, the majority game and the dollar-game\cite{challet1}, the effects of sophisticated individuals on the evolution of stock prices have been investigates. Different kinds of trader-trader interactions lead to typical stylized facts in the stock markets\cite{gabaix1,jiang1,bianconi1,galla2,barato1,marsili1}. In the study of the effects of investment strategies on the evolution of stock prices, the pair pattern strategy and the reference point strategy are two typical strategies proposed by zhang et al\cite{zhang5,zhang6,ren1}. Depending upon the pair pattern strategies, people buy and sell the stocks frequently, which leads to the occurrence of a power-law return distribution similar to that in real stock markets\cite{mantegna1,mantegna2,cizeau1,gopikrishnan1,plerou1}. Different from the pair pattern strategies which depend on the history of price movement, the reference point strategy is a myopic strategy, which depends on people's subjective cognition and provides us an anchor to simplify our complex decision-making processes\cite{baker1,shi1}. In real markets, the reference point strategies help us finish the transactions in a simplified way. In this paper, we incorporate the investors with pair pattern strategies and reference point strategies into a trading model. The role of heterogeneities in investment strategies and risk tolerance in the evolution of stock prices is investigated. The following are our main findings. (1)The heterogeneities in investment strategies and risk tolerance effectively suppress the price fluctuations. As nearly all the investors have similar investment strategies or risk tolerance, the price has a large fluctuation. For the market with heterogeneous investment strategies and heterogeneous risk tolerance, the price fluctuation becomes moderate. (2)The competition between different investment strategies is related to the coexistence of different strategies. As compared with the strategy which leads to a large price fluctuation, the strategy which leads to a stable price is more competitive. (3)The coexistence of the investors with pair pattern strategies and reference point strategies makes some of the investors earn more and the others lose more, over-frequent trading is disadvantageous for the investors to earn more. The paper is organized as follows. In section 2, the agent-based model with pair pattern strategies and reference point strategies is introduced. In section 3, the numerical results are presented. In section 4, a theoretical analysis is given. In section 5, the conclusions are drawn. \section{The model} \label{sec:model} In the present model, there are two kinds of investors: the investors with pair pattern strategies and the investors with reference point strategies. In the following, we introduce the characteristics of different strategies, the updating of strategies and the evolution of stock prices respectively. \subsection{\label{subsec:levelA}Pair pattern strategies and reference point strategies} In the present model, there are two kinds of strategies, pair pattern strategies and reference point strategies, which are used to make one's buying and selling decisions. The pair pattern strategy space consists of a series of buying-and-selling strategy pairs. A buying strategy or a selling strategy consists of a m-bit long binary array. For example, if an individual i's buying strategy is $S_i^{buy}=(110)$ and his selling strategy is $S_i^{sell}=(101)$, facing the latest history of $M=3$ price changes, (rise-rise-drop), individual i buys a stock on condition that the number of stocks in his hand is below the maximum value of $K_{max}$. Facing the latest history of $M=3$ price changes, (rise-drop-rise), individual i sells a stock on condition that the number of stocks in his hand is above the minimum value of $K_{min}$. Or else, individual i does nothing. The reference point strategy space consists of a series of expected prices, called reference points $P^{ref}$ in the present model. If the latest price $P$ is lower than an individual j's reference point, $P<P_j^{ref}$, individual j buys a stock with probability $\frac{P_j^{ref}-P}{P}$ on condition that the number of stocks in his hand is below the maximum value of $K_{max}$. If the latest price is higher than individual j's reference point, $P>P_j^{ref}$, individual j sells a stock with probability $\frac{P-P_j^{ref}}{P}$ on condition that the number of stocks in his hand is above the minimum value of $K_{min}$. Or else, individual j does nothing. \subsection{\label{subsec:levelB}Evolution of investment strategies} An individual i's pair pattern strategy evolves as follows. Initially, individual i randomly chooses $n_S$ strategies from the pair pattern strategy space. At each time step, he gives each strategy a virtual score, which is obtained as if the strategy were being used and the virtual score changes continuously. He makes his buying or selling decision according the strategy with the highest score. An individual j's reference point strategy evolves as follows. Initially, an individual j randomly chooses a gene $g_j$ from the range of $g_j\in[0,g^{max}]$, which is kept with no change in the evolutionary process.He randomly chooses a strategy $P^{exp}$ from the range of $P^{exp}\in [\bar Pe^{\frac{-\alpha g_j}{N}},\bar Pe^{\frac{\alpha g_j}{N}}]$, in which $\bar P$ is the averaged price in the latest $\Delta t$ steps and $\alpha$ is a pre-given constant. At each time step, he makes his buying or selling decision according to this strategy. If his strategy deviates from the range of $P^{exp}\in [\bar Pe^{\frac{-\alpha g_j}{N}},\bar Pe^{\frac{\alpha g_j}{N}}]$, he randomly chooses a new strategy $P^{exp}$ from the range of $P^{exp}\in [\bar Pe^{\frac{-\alpha g_j}{N}},\bar Pe^{\frac{\alpha g_j}{N}}]$. Or else, he keeps his strategy. From the above evolutionary mechanism we know that, in the present model, a large gene means that an individual has strong risk tolerance and is quite possible to change his strategy less frequently. A small gene means that an individual has weak risk tolerance and is quite possible to change his strategy more frequently. \subsection{\label{subsec:levelC}Evolution of stock prices} After all the individuals have made their buying, selling or doing nothing decision, i.e. $a_i$=+1, -1 or 0, the price is updated according to the equation \begin{equation} P(t)=P(t-1)e^{\frac{\alpha A}{N}}, \end{equation} in which $A=\Sigma^N_{i=1} a_i$ and $\alpha$ is a pre-given constant. \section{Simulation results and discussions} \label{sec:results} In numerical simulations, we firstly examine whether the proposed model can reproduce the stylized facts in real financial markets. Secondly, the coupled effects of pair pattern strategies and reference point strategies on price fluctuations are investigated extensively. \subsection{\label{subsec:level}Reproduction of the stylized facts} In the study of real financial markets, the distribution of price returns and the autocorrelation of price returns are usually investigated, which reflect the characteristics of price movement. For a random price movement, the distribution of price returns is close to a Poisson distribution. For an autocorrelated price movement, the distribution of price returns is close to a power-law distribution\cite{gu1,gu2}. Some studies have shown that a power-law distribution and long-range autocorrelation exist in real financial markets. We firstly examine whether the present model can reproduce the characteristics of price movement in real financial markets or not. \begin{figure} \includegraphics[width=12cm]{fig1 \caption{\label{fig:epsart}(a)The distribution of price returns $R$ for the ratio of investors with reference point strategies $\rho_{ref}$=0 and the memory size $M$=3 (circles), 5(squares); (b) the distribution of absolute price returns $\vert R \vert$ for $\rho_{ref}$=0 and $M$=3 (circles), 5(squares); (c)The distribution of price returns $R$ for $M$=3 and $\rho_{ref}$=0 (circles), 0.5 (squares); (d) the distribution of absolute price returns $\vert R \vert$ for $M$=3 and $\rho_{ref}$=0 (circles), 0.5 (squares). Other parameters are: the total population $N=5000$, the number of strategies for each investor with pair pattern strategies $n_s=2$, the averaged time $\Delta$ =10, the maximum gene for the investors with reference point strategies $g^{max}$=5000, maximum and minimum stocks for each investor $K_{max}$=1 and $K_{min}$=-1, constant $\alpha$=10.} \end{figure} Figure 1 (a) and (b) show that, as all the investors adopt pair pattern strategies, the distribution of price returns is like a power-law distribution, the tail of which is satisfied with the equation $P(\vert R\vert)\sim \vert R \vert^{-\gamma}$. An increase in memory size $M$ leads to a decrease in the exponent $\gamma$. For $M=3$, $\gamma\sim 4.8$. For $M=5$, $\gamma\sim 4$. Figure 1 (c) and (d) show that, for a given memory size $M$=3, the distribution of price returns is closely related to the ratio of the investors with reference point strategies $\rho_{ref}$. An increase in $\rho_{ref}$ leads to an increase in the exponent $\gamma$. For $\rho_{ref}$=0, $\gamma\sim 4.8$. For $\rho_{ref}$=0.5, $\gamma\sim 8$. Such results indicate that the distribution of price returns in the present model is closely related to the memory size $M$ and the ratio of the investors with reference point strategies $\rho_{ref}$. Compared with the situation where there is a small $M$ and a small $\rho_{ref}$, a large $M$ and an intermediate $\rho_{ref}$ lead to a broader distribution of price returns. \begin{figure} \includegraphics[width=12cm]{fig2 \caption{\label{fig:epsart}(a)DFA of returns for the ratio of investors with reference point strategies $\rho_{ref}$=0 and the memory size $M$=3 (circles), 5(squares); (b) DFA of absolute returns for $\rho_{ref}$=0 and $M$=3 (circles), 5(squares); (c)DFA of returns for $M$=3 and $\rho_{ref}$=0 (circles), 0.5 (squares); (d) DFA of absolute returns for $M$=3 and $\rho_{ref}$=0 (circles), 0.5 (squares). Other parameters are: total population $N=5000$, number of strategies for each investor with pair pattern strategy $n_s=2$, the averaged time $\Delta$ =10, maximum gene value for the investors with reference point strategy $g^{max}$=5000, maximum and minimum number of stocks for each investor $K_{max}$=1 and $K_{min}$=-1, constant $\alpha$=10.} \end{figure} The long-range correlations are usually examined depending upon the detrended fluctuation analysis (DFA). The root mean square of the detrended series $F$ is satisfied with an equation $F(S)\sim S^h$, in which $S$ is the length of local data and $h$ is called hurst exponent. The value of $h$ reflects the moving patterns of price returns. For $h<0.5$, the price returns are satisfied with a short-term correlation. For $h=0.5$, the price returns are satisfied with a random walk. For $h>0.5$, the price returns are satisfied with a long-range correlation. Figure 2 (a) and (b) show that, for a given ratio of the investors with reference point strategies $\rho_{ref}$=0, the root mean square of the detrended series $F$ is closely related to the memory size $M$. An increase in $M$ leads to an overall decrease in $F$ within the whole range of $S\ge 2$. Figure 2 (c) and (d) show that,for a given memory size $M$=3, the root mean square of the detrended series $F$ is closely related to the ratio of the investors with reference point strategies $\rho_{ref}$. An increase in $\rho_{ref}$ leads to an overall decrease in $F$ within the whole range of $S\ge 2$. Comparing the results in figure 1(a)-(d), we find that the values of hurst exponent $h$ are nearly the same for different $M$ and $\rho_{ref}$, which is $h\sim 1$. Such results indicate that the DFA of returns and the DFA of absolute returns are closely related to the memory size $M$ and the ratio of the investors with reference point strategies $\rho_{ref}$. Compared with the situation where there is a small $M$ and a small $\rho_{ref}$, a large $M$ and an intermediate $\rho_{ref}$ lead to an overall decrease in $F$. There exist long-range autocorrelations of price returns for different $M$ and $\rho_{ref}$. \subsection{\label{subsec:level}Competition between pair pattern strategies and reference point strategies} In the present model, we are especially concerned about how the heterogeneities in investment strategies affect the price fluctuations. In the following, we firstly examine how the coupling of the memory size of the investors with pair pattern strategies $M$, the maximum gene of the investors with reference point strategies $g^{max}$ and the ratio of the investors with reference point strategies $\rho_{ref}$ affects the time-dependent behaviors of the stock prices. \begin{figure} \includegraphics[width=13cm]{fig3 \caption{\label{fig:epsart}The time-dependent price $P$ (a)for the ratio of the investors with reference point strategies $\rho_{ref}$=0 and the memory size $M=2$ (slashes), 5 (slash dotted lines); (b)for $\rho_{ref}$=1 and the maximum gene of the investors with reference point strategies $g^{max}$=100 (circles),1000 (squares); (c) for $M=3$, $g^{max}=1000$ and $\rho_{ref}$=0.1(slashes), 0.5(slash dotted lines). Other parameters are: total population $N=1000$, the number of strategies for each investor with pair pattern strategies $n_s$=2, the averaged time $\Delta$ =10, maximum and minimum stocks for each investor $K_{max}$=1 and $K_{min}$=-1, constant $\alpha$=10.} \end{figure} Figure 3 (a) shows that, as all the investors adopt pair pattern strategies, the price movement is closely related to the memory size $M$. For $M$=2, the price has a large fluctuation. For $M=5$, the price fluctuation becomes ease. In the present model, a large $M$ implies that the investors with pair pattern strategies have more opportunities to choose his personal investment strategies. Given a large $M$ and $S=2$, it is quite possible that all the investors have different investment strategies. The results in figure 3 (a) imply that the heterogeneities in pair pattern strategies suppress the price fluctuations. Figure 3 (b) shows that, as all the investors adopt reference point strategies, the price movement is closely related to the maximum gene $g^{max}$. For $g^{max}=100$, the price has a zigzag fluctuation. For $g^{max}=1000$, the price becomes stable. In the present model, a large $g^{max}$ implies that the genes of the investors with reference point strategies scatter about a large range of $0<g<g^{max}$. Given a large $g^{max}\sim N$, it is quite possible that all the investors have different genes. The results in figure 3 (b) imply that the heterogeneities in genes suppress the price fluctuations. Figure 3 (c) shows that, as the investors with pair pattern strategies coexist with the investors with reference point strategies, the price movement is closely related to the ratio of the investors with pair pattern strategies and reference point strategies. An increase in the ratio of the investors with reference point strategies leads to a decrease in the price fluctuations. As compared with the situations in figure 3 (a) and (b), we find that a large $M$ coupled with a large $g^{max}$ can not only inhibit the occurrence of large price fluctuations but also the occurrence of no-trading states. Such results indicate that the heterogeneities in investment strategies and individual genes has a great impact on the evolution of prices. A homogeneous population promotes price fluctuations while a heterogeneous population suppresses price fluctuations. In the heterogeneous environment where the investors with pair pattern strategies coexist with the investors with reference point strategies, the pair pattern strategies drive the system away from the equilibrium while the reference point strategies draw the system back to the equilibrium. Heterogeneities in the present model are beneficial for stabilizing the stock prices. \begin{figure} \includegraphics[width=10cm]{fig4 \caption{\label{fig:epsart}The standard deviation of stock prices $\sigma_P$ (a) as a function of the memory size $M$ for the maximum gene of the investors with reference point strategies $g^{max}=1000$ and the ratio of the investors with reference point strategies $\rho_{ref}$=0 (circles), 0.8 (squares); (b) as a function of $g^{max}$ for $M=3$ and $\rho_{ref}$=1 (circles), 0.8 (squares). Other parameters are: total population $N=1000$, number of strategies for each investor with pair pattern strategy $n_s$=2, the averaged time $\Delta$ =10, maximum and minimum stocks for each investor $K_{max}$=1 and $K_{min}$=-1, constant $\alpha$=10. Final data are obtained by averaging over 100 runs and $10^4$ times after $10^5$ relaxation times in each run.} \end{figure} In order to get a clear view of the relationship between the price fluctuations and the heterogeneities in pair pattern strategies and individual genes, in figure 4 (a) and (b) we plot the standard deviation of stock prices $\sigma_P$ as a function of the memory size $M$ and the maximum gene $g^{max}$ respectively. Figure 4 (a) shows that, as all the investors adopt pair pattern strategies, the price fluctuations are determined by the memory size $M$. As $M$ increases from $M=2$ to $M=10$, the standard deviation of stock prices $\sigma_P$ decreases from $\sigma_P\sim 22$ to $\sigma_P\sim 0.1$. An increase in the ratio of the investors with reference point strategies $\rho_{ref}$ leads to an overall decrease of $\sigma_P$ within the whole range of $2\le M\le 10$. An increase in $\rho_{ref}$ does not affect the changing tendency of $\sigma_P$ vs $M$. Figure 4 (b) shows that, as all the investors adopt reference point strategies, the price fluctuations are determined by the maximum gene $g^{max}$. There exist two critical points $g^{max}_{c1}\sim 500$ and $g^{max}_{c2}\sim 1100$. As $g^{max}$ increases from $g^{max}=1$ to $g^{max}=500$, $\sigma_P$ keeps a fix value of $2\times 10^5$. As $g^{max}$ increases from $g^{max}=500$ to $g^{max}=1100$, $\sigma_P$ drops quickly from $\sigma_P\sim 2\times 10^5$ to $\sigma_P\sim 0.01$. As $g^{max}$ increases from $g^{max}=1100$ to $g^{max}=1800$, $\sigma_P$ keeps the value of $\sigma_P\sim 0.01$. A decrease in the ratio of the investors with reference point strategies $\rho_{ref}$ leads to a decrease in the critical points $g^{max}_{c1}$ and $g^{max}_{c2}$. Within the range of $1\le g^{max}\le g^{max}_{c2}$, a decrease in $\rho_{ref}$ leads to an overall decrease of $\sigma_P$. Within the range of $g^{max}>g^{max}_{c2}$, a decrease in $\rho_{ref}$ leads to an overall increase of $\sigma_P$. A decrease in $\rho_{ref}$ does not affect the changing tendency of $\sigma_P$ vs $g^{max}$. Such results indicate that both heterogeneous investment strategies and heterogeneous individual genes have a great impact on the price movement. For the system with either pair pattern strategies or reference point strategies, the heterogeneity suppresses the price fluctuations. For the system with the coexistence of pair pattern strategies and reference point strategies, the price fluctuations may be promoted within some range and may be suppressed within other range. \begin{figure} \includegraphics[width=10cm]{fig5 \caption{\label{fig:epsart}The predictability $H$ of stock prices (a)as a function of the memory size $M$ for the maximum gene of the investors with reference point strategies $g^{max}=1000$ and the ratio of the investors with reference point strategies $\rho_{ref}$=0 (circles), 0.8 (squares); (b)as a function of $g^{max}$ for $M$=3 and $\rho_{ref}$=1 (circles), 0.8 (squares). Other parameters are: total population $N=1000$, number of strategies for each investor with pair pattern strategies $n_s$=2, the averaged time $\Delta$ =10, maximum and minimum stocks for each investor $K_{max}$=1 and $K_{min}$=-1, constant $\alpha$=10. Final data are obtained by averaging over 100 runs and $10^4$ times after $10^5$ relaxation times in each run.} \end{figure} In a predictable market, people usually make a deal according to the historic information, which may lead to people's common behaviors. In the present model, even if people have the same historic information, because they have heterogeneous strategies, it is quite possible that their common behaviors may be inhibited. In order to examine whether the reduction of price fluctuations in the present model results from the reduction of the predictability of price movement, in figure 5 (a) and (b) we plot the predictability of stock prices $H$ as a function of the memory size $M$ and the maximum gene $g^{max}$ respectively. Figure 5 (a) shows that, as all the investors adopt pair pattern strategies, the predictability of stock prices $H$ is closely related to the memory size $M$. As $M$ increases from $M=2$ to $M=10$, $H$ decreases from $H\sim 6.8$ to $H\sim 0.05$. An increase in the ratio of the investors with reference point strategies $\rho_{ref}$ leads to an overall decrease in $H$ within the whole range of $2\le M\le10$. An increase in $\rho_{ref}$ does not affect the changing tendency of $H$ vs $M$. Comparing the results in figure 4 (a) with the results in figure 5 (a), we find that a more predictable market has a larger price fluctuation. Figure 5 (b) shows that, as all the investors adopt pair pattern strategies, the predictability of stock prices $H$ is closely related to the maximum gene $g^{max}$. There exist two critical points $g^{max}_{c1}\sim 500$ and $g^{max}_{c2}\sim 1100$. As $g^{max}$ increases from $g^{max}=1$ to $g^{max}=500$, $H$ keeps a fix value of $1\times 10^5$. As $g^{max}$ increases from $g^{max}=500$ to $g^{max}=1100$, $H$ drops quickly from $H\sim 1\times 10^5$ to $H\sim 0.002$. As $g^{max}$ increases from $g^{max}=1100$ to $g^{max}=1800$, $H$ keeps the value of $H\sim 0.002$. A decrease in the ratio of the investors with reference point strategies $\rho_{ref}$ leads to a decrease in the critical points $g^{max}_{c1}$ and $g^{max}_{c2}$. Within the range of $1\le g^{max}\le g^{max}_{c2}$, a decrease in $\rho_{ref}$ leads to an overall decrease of $H$. Within the range of $g^{max}>g^{max}_{c2}$, a decrease in $\rho_{ref}$ leads to an overall increase of $H$. A decrease in $\rho_{ref}$ does not affect the changing tendency of $H$ vs $g^{max}$. Comparing the results in figure 4 (b) with the results in figure 5 (b), we find that a more predictable market has a larger price fluctuation. Such results indicate that the predictability of price movement is closely related to the heterogeneities in investment strategies and individual genes. For the system with either pair pattern strategies or reference point strategies, the heterogeneities are quite possible to make the market become unpredictable, which is similar to the situation in an efficient market. For the system with the coexistence of pair pattern strategies and reference point strategies, the price movement may become more predictable within some range and may become more unpredictable within other range. \begin{figure} \includegraphics[width=10cm]{fig6 \caption{\label{fig:epsart}(a)The averaged wealth of the investors with pair pattern strategies $\bar W_{pair}$ as a function of the memory size $M$ for the maximum gene of the investors with reference point strategies $g^{max}=1000$ and the ratio of the investors with reference point strategies $\rho_{ref}$=0 (circles), 0.8 (squares); (b) $\bar W_{pair}$ as a function of $g^{max}$ for $M=3$ and $\rho_{ref}$= 0.8 (squares); (c)the averaged wealth of the investors with reference point strategies $\bar W_{ref}$ as a function of $M$ for $g^{max}=1000$ and $\rho_{ref}$= 0.8 (squares); (d) $\bar W_{ref}$ as a function of $g^{max}$ for $M=3$ and $\rho_{ref}$=1 (circles), 0.8 (squares). Other parameters are: total population $N=1000$,the number of strategies for each investor with pair pattern strategies $n_s$=2, the averaged time $\Delta$ =10, maximum and minimum stocks for each investor $K_{max}$=1 and $K_{min}$=-1, constant $\alpha$=10. Final data are obtained by averaging over 100 runs and $10^4$ times after $10^5$ relaxation times in each run.} \end{figure} In order to find a competitive strategy in the present model, in figure 6 (a) - (d) we plot the averaged wealth $\bar W$ of the investors with pair pattern strategies and reference point strategies respectively. Figure 6 (a) and (c) show that, as all the investors adopt pair pattern strategies, the wealth of the investors with pair pattern strategies $\bar W_{pair}$ is closely related to the memory size $M$. There exists a critical point $M_c=4$. As $M$ increases from $M=2$ to $M=4$, $\bar W_{pair}$ increases quickly from $\bar W_{pair}\sim -2.4\times 10^4$ to $\bar W_{pair}\sim -479$. As $M$ increases from $M=4$ to $M=10$, $\bar W_{pair}$ increases slowly from $\bar W_{pair}\sim -479$ to $\bar W_{pair}\sim -6.3$. An increase in the ratio of the investors with reference point strategies does not affect the critical point $M_c=4$. As $M$ increases from $M=2$ to $M=4$, $\bar W_{pair}$ increases from $\bar W_{pair}\sim -3.2\times 10^4$ to $\bar W_{pair}\sim -224$ while the wealth of the investors with reference point strategies $\bar W_{ref}$ firstly increases from $\bar W_{ref}\sim -367$ to $\bar W_{ref}\sim 191$ and then drops from $\bar W_{ref}\sim 191$ to $\bar W_{ref}\sim -1$. As $M$ increases from $M=4$ to $M=10$, $\bar W_{pair}$ increases from $\bar W_{pair}\sim -224$ to $\bar W_{pair}\sim -20$ while $\bar W_{ref}$ decreases from $\bar W_{ref}\sim -1$ to $\bar W_{ref}\sim -16$. Within the range of $M\le M_c$, the coexistence of pair pattern strategies and reference point strategies is beneficial for the investors with reference point strategies. Figure 6 (b) and (d) show that, as all the investors adopt reference point strategies, the wealth of the investors with reference point strategies $\bar W_{ref}$ is closely related to the maximum gene $g^{max}$. There exist two critical points $g^{max}_{c1}\sim 500$ and $g^{max}_{c2}\sim 700$. Within the range of $g^{max}<500$, $\bar W_{ref}$ fluctuates within the range of $\bar W_{ref}\sim -7\times 10^9$. As $g^{max}$ increases from $g^{max}=500$ to $g^{max}=700$, $\bar W_{ref}$ increases from $\bar W_{ref}\sim -7\times 10^9$ to $\bar W_{ref}\sim -3\times 10^7$. As $g^{max}$ increases from $g^{max}=700$ to $g^{max}=1800$, $\bar W_{ref}$ increases from $\bar W_{ref}\sim -3\times 10^7$ to $\bar W_{ref}\sim -3.8$. A decrease in the ratio of the investors with reference point strategies $\rho_{ref}$ leads to a decrease in the critical points $g^{max}_{c1}$ and $g^{max}_{c2}$. For $\rho_{ref}$=0.8, as $g^{max}$ increases from $g^{max}=1$ to $g^{max}=300$, the wealth of the investors with pair pattern strategies $\bar W_{pair}$ fluctuates around $\bar W_{pair}\sim 8\times 10^7$ while the wealth of the investors with reference point strategies $\bar W_{ref}$ fluctuate within the range of $\bar W_{ref}\sim -8\times 10^8$. As $g^{max}$ increases from $g^{max}=300$ to $g^{max}=500$, $\bar W_{pair}$ decreases from $\bar W_{pair}\sim 8\times 10^7$ to $\bar W_{pair}\sim -5\times 10^4$ while $\bar W_{ref}$ increases from $\bar W_{ref}\sim -8\times 10^8$ to $\bar W_{ref}\sim -2\times 10^5$. As $g^{max}$ increases from $g^{max}=500$ to $g^{max}=1800$, $\bar W_{pair}$ increases from $\bar W_{pair}\sim -5\times 10^4$ to $\bar W_{pair}\sim -3\times 10^3$ while $\bar W_{ref}$ increases from $\bar W_{pair}\sim -2\times 10^5$ to $\bar W_{pair}\sim -2\times 10^3$. Within the range of $g^{max}\le g^{max}_{c2}$, the coexistence of pair pattern strategies and reference point strategies is beneficial for the investors with pair pattern strategies. Comparing the results in Figure 6 (a) and (c) with the results in Figure 6 (b) and (d), we find that the coexistence of the investors with pair pattern strategies and reference point strategies is not always good for both sides. In some cases the investors with reference point strategies may defeat the investors with pair pattern strategies and in other cases the investors with pair pattern strategies may defeat the investors with reference point strategies. \section{Theoretical analysis} \label{sec:analysis} \subsection{\label{subsec:levelA} Relationship between price fluctuations and heterogeneities in pair pattern strategies and risk tolerance} \begin{figure} \includegraphics[width=13cm]{fig7 \caption{\label{fig:epsart}The time-dependent price $P$ for (a) $\rho_{ref}$=0 and $M$=1(circles), 3(squares); (b) $\rho_{ref}$=0.5, $g^{max}=100$ and $M$=1(circles), 3(squares); (c) $\rho_{ref}$=0.5, $g^{max}=1000$ and $M$=1(circles), 3(squares); (d) $\rho_{ref}$=1 and $g^{max}$=100(circles), 1000(squares). Other parameters are: total population $N=1000$, number of strategies for each investors with pair pattern strategy $n_s$=2, the averaged time $\Delta$ =10, maximum and minimum number of stocks for each investor $K_{max}$=1 and $K_{min}$=-1, constant $\alpha$=10.} \end{figure} The price fluctuation is determined by the difference in the number of investors buying and selling the stocks, which is satisfied with the equation \begin{equation} ln\frac{P(t)}{P(t-1)}={\frac{\alpha \Delta N}{N}}. \end{equation} On condition that all the investors adopt pair pattern strategies, for a given population $N$, the heterogeneity in pair pattern strategies is determined by the memory size $M$. For $M=1$, the total number of pair pattern strategies is $n_{pair}=2^M=2$, i.e. $s_1$=(0,1) and $s_2$=(1,0), which means that, facing an increase in the latest price, $s_1$ tells the investors to sell and $s_2$ tells the investors to buy. Facing a decrease in the latest price, $s_1$ tells the investors to buy and $s_2$ tells the investors to sell. Therefore, facing a typical change in the latest price, the difference in the number of investors buying and selling the stocks should be \begin{equation} \mid\Delta N\mid=\mid N_{s_1}-N_{s_2} \mid, \end{equation} in which $N_{s_1}$ and $N_{s_2}$ are the number of investors buying and selling the stocks respectively. For quite a large $M$, i.e. $M=10$, the number of the combination of $M$ latest price changes is $2^M$=1024. The total number of pair pattern strategies is $n_{pair}=C_{1024}^1C_{1023}^1=1024\times 1023$. For a given $N=1000$, facing a typical combination of the latest $M$ price changes, the difference in the number of investors buying and selling the stocks should be \begin{equation} \mid\Delta N\mid\sim 1. \end{equation} On condition that all the investors adopt reference point strategies, for a given population $N$, the heterogeneity in reference point strategies is determined by the maximum value of risk tolerance $g^{max}$. Facing the latest price $P(t-1)$, the difference in the number of investors buying and selling the stocks should be \begin{equation} \mid\Delta N\mid=\mid N_{P^{ref}>P}-N_{P^{ref}<P} \mid, \end{equation} in which $N_{P^{ref}>P}$ and $N_{P^{ref}<P}$ are the number of investors buying and selling the stocks respectively. For quite a small $g^{max}$, i.e. $g^{max}=1$, all the reference points are within a small range \begin{equation} \frac {\bar P}{e}\le P^{ref}\le e\bar P, \end{equation} in which $\bar P$ is the averaged value of stock prices in the latest $\Delta t$ steps. For quite a large $g^{max}$, i.e. $g^{max}=N$, all the reference points are within a wide range \begin{equation} \frac {\bar P}{e^N}\le P^{ref}\le e^N\bar P. \end{equation} Given a typical $\Delta N=N_{P^{ref}>P}-N_{P^{ref}<P}$=2, for $g^{max}=1$, $\Delta N$ is quite possible to become $\Delta N=N_{P^{ref}>P}-N_{P^{ref}<P}$=-2 in the next step because nearly all the investors are within a small range around $P(t-1)$. For $g^{max}=N$, $\Delta N$ is quite possible to become $\Delta N=N_{P^{ref}>P}-N_{P^{ref}<P}$=1 or $\Delta N=N_{P^{ref}>P}-N_{P^{ref}<P}$=0 in the next step because the investors scatter within a wide range around $P(t-1)$. On condition that the investors with pair pattern strategies coexist with the investors with reference point strategies, the price fluctuation is determined by the coupling of the heterogeneities in investment strategies and risk tolerance. In a heterogeneous population, the existence of the investors with pair pattern strategies helps the investors with reference point strategies away from a no-trading state while the existence of the investors with reference point strategies helps the investors with pair pattern strategies away from a large fluctuation. The price has the characteristics of a random walk which slowly fluctuates around an equilibrium state. The above analyses indicate that, for a small $M$ and a small $g^{max}$, a zigzag price fluctuation is more possible to occur. For a large $M$ and a large $g^{max}$, a slow price fluctuation like a random walk is more possible to occur. The theoretical analysis is in accordance with the simulation data in figure 7. \subsection{\label{subsec:levelB} Competition between pair pattern strategies and reference point strategies} The wealth of the investors with pair pattern strategies and reference point strategies is determined by the difference between the buying price and the selling price. \begin{equation} \bar W=\Sigma (P_{sell}-P_{buy}). \end{equation} The price change $\Delta P=P(t)-P(t-1)=\Sigma a_{pair}+ \Sigma a_{ref}$. If $\vert\Sigma a_{pair}\vert>>\vert\Sigma a_{ref}\vert$, the price change is determined by the investors with pair pattern strategies. If $\vert\Sigma a_{pair}\vert<<\vert\Sigma a_{ref}\vert$, the price change is determined by the investors with reference point strategies. \begin{figure} \includegraphics[width=13cm]{fig8 \caption{\label{fig:epsart}The averaged wealth of the investors with pair pattern strategies (circles) and reference point strategies (squares) for (a)$M=1$, $g^{max}=100$;(b)$M=1$, $g^{max}=1000$;(c)$M=3$, $g^{max}=100$;(d)$M=3$, $g^{max}=1000$. Other parameters are: total population $N=1000$, the ratio of the investors with reference point strategies $\rho_{ref}$=0.5, number of strategies for each investor with pair pattern strategy $n_s$=2, the averaged time $\Delta$ =10, maximum and minimum number of stocks for each investor $K_{max}$=1 and $K_{min}$=-1, constant $\alpha$=10. Final data are obtained by averaging over 100 runs and $10^4$ times after $10^5$ relaxation times in each run.} \end{figure} On condition that only the investors with pair pattern strategies exist, facing a typical combination of $M$ latest price changes, if there are more buyers than sellers, the price increases. The investors buying the stock with a higher price is more than the investors selling the stock with a higher price. Facing another typical combination of $M$ latest price changes, if there are more sellers than buyers, the price decreases. The investors selling the stock with a lower price is more than the investors buying the stock with a lower price. Therefore, buying high and selling low lead to the negative wealth of the investors with pair pattern strategies. On condition that only the investors with reference point strategies exist, facing the latest price $P(t-1)$, if there are more buyers than sellers, the price increases. The number of investors buying the stock with a higher price is more than the number of investors selling the stock with a higher price. Facing the latest price $P(t-1)$, if there are more sellers than buyers, the price decreases. The investors selling the stocks with a lower price is more than the investors buying the stocks with a lower price. Therefore, buying high and selling low lead to the negative wealth of the investors with reference point strategies. On condition that the investors with pair pattern strategies coexist with the investors with reference point strategies, the price movement is determined by the strategy governing the moving trend of the price, no matter whether the strategy is pair pattern strategy or reference point strategy. The investors in the minority side gain more than the investors in the majority side. For a small memory size $M$ and a small maximum gene $g^{max}$, the moving patterns is closely related to the ratio of the investors with pair pattern strategies and reference point strategies. For a small and an intermediate $\rho_{ref}$, because a small $g^{max}$ has a greater impact on the price movement than a small $M$, a large $\rho_{pair}$ has a greater impact on the price movement than a small $\rho_{ref}$. The moving trend of the stock prices is governed by both the investors with pair pattern strategies and reference point strategies. The wealth of the investors with pair pattern strategies is similar to the wealth of the investors with reference point strategies. For a large $\rho_{ref}$, the price movement is governed by the investors with reference point strategies, which means that, if the investors with reference point strategies buy more, the price increases. If the investors with reference point strategies sell more, the price decreases. The majority choice of the investors with reference point strategies determines the moving trend of the price. Therefore, buying high and selling low lead to the negative wealth of the investors with reference point strategies. For the investors with pair pattern strategies, if they have the buying and selling behaviors similar to the investors with reference point strategies, buying high and selling low lead to their negative wealth. If they have the buying and selling behaviors different from the investors with reference point strategies, buying low and selling high lead to their positive wealth. Therefore, compared with the wealth of the investors with reference point strategies, the wealth of the investors with pair pattern strategies is quite possible to be larger than 0. For a small memory size $M$ and a large maximum gene $g^{max}$, because a large $g^{max}$ has little impact on the price movement, the moving trend of the price is determined by the investors with pair pattern strategies. If the investors with pair pattern strategies buy more, the price increases. If the investors with pair pattern strategies sell more, the price decreases. Therefore, buying high and selling low lead to the negative wealth of the investors with pair pattern strategies. For the investors with reference point strategies, if they have the buying and selling behaviors similar to the investors with pair pattern strategies, buying high and selling low lead to their negative wealth. If they have the buying and selling behaviors different from the investors with pair pattern strategies, buying low and selling high lead to their positive wealth. Therefore, compared with the wealth of the investors with pair pattern strategies, the wealth of the investors with reference point strategies is quite possible to be larger than 0. For an intermediate memory size $M$ and a small maximum gene $g^{max}$, similar to the situation where there is a small memory size $M$ and a small maximum gene $g^{max}$, the moving patterns is closely related to the ratio of the investors with pair pattern strategies and reference point strategies $\rho_{ref}$. For a small and an intermediate $\rho_{ref}$, because a small $g^{max}$ has a greater impact on the price movement than an intermediate $M$ and a large $\rho_{pair}$ has a greater impact on the price movement than a small $\rho_{ref}$, the moving trend of the price is governed by both the investors with pair pattern strategies and reference point strategies. The wealth of the investors with pair pattern strategies is similar to the wealth of the investors with reference point strategies. For a large $\rho_{ref}$, the price movement is governed by the investors with reference point strategies, which means that, if the investors with reference point strategies buy more, the price increases. If the investors with reference point strategies sell more, the price decreases. The majority choice of the investors with reference point strategies determines the moving trend of the price. Therefore, buying high and selling low lead to the negative wealth of the investors with reference point strategies. For the investors with pair pattern strategies, if they have the buying and selling behaviors similar to the investors with reference point strategies, buying high and selling low lead to their negative wealth. If they have the buying and selling behaviors different from the investors with reference point strategies, buying low and selling high lead to their positive wealth. Therefore, compared with the wealth of the investors with reference point strategies, the wealth of the investors with pair pattern strategies is quite possible to be larger than 0. For an intermediate memory size $M$ and a large maximum gene $g^{max}$, similar to the situation where there is a small memory size $M$ and a large maximum gene $g^{max}$, because a large $g^{max}$ has little impact on the price movement, the moving trend of the price is determined by the investors with pair pattern strategies. If the investors with pair pattern strategies buy more, the price increases. If the investors with pair pattern strategies sell more, the price decreases. Therefore, buying high and selling low lead to the negative wealth of the investors with pair pattern strategies. For the investors with reference point strategies, if they have the buying and selling behaviors similar to the investors with pair pattern strategies, buying high and selling low lead to their negative wealth. If they have the buying and selling behaviors different from the investors with pair pattern strategies, buying low and selling high lead to their positive wealth. Therefore, compared with the wealth of the investors with pair pattern strategies, the wealth of the investors with reference point strategies is quite possible to be larger than 0. The above analyses indicate that the strategy that drives the system far away from the equilibrium loses more while the strategy that draws the system back to the equilibrium gains more. The theoretical analysis is in accordance with the simulation data in figure 8. \section{Summary} \label{sec:summary} In an efficient market, the price movement fully reflects good or bad news for the related companies. However, in real societies, in the face of common information, the price movement often depends upon the characteristics of the investors. Homogeneous population and heterogeneous population have an entirely different effect on the price movement. By incorporating pair pattern strategies and reference point strategies into a trading model, we have investigated the coupled effects of heterogeneous investment strategies and heterogeneous risk tolerance on price movement. In the stock market flooded with the investors with pair pattern strategies, homogeneous investment strategies lead to the occurrence of large price fluctuations. An increase in the heterogeneity in investment strategies leads to a decrease in price fluctuations. In the stock market flooded with the investors with reference point strategies, the dispersion of individual genes determines the characteristics of price fluctuations. As the investors have similar genes, a large price fluctuation is easy to occur. As the individual genes are well diversified, the price fluctuations can be effectively suppressed and the market is quite possible to be stuck in a no-trading state. The coexistence of pair pattern strategies and reference point strategies not only helps the stock market refrain from large fluctuations but also be stuck in a no-trading state. In the stock market flooded with the investors with heterogeneous investment strategies and heterogeneous individual genes, the investors with pair pattern strategies push the stock market away from the equilibrium while the investors with reference point strategies pull the stock market back to the equilibrium. The role of heterogeneities in price movement is a quite important issue for us to understand the evolutionary dynamics in financial markets. In the future, people's heterogeneous cognitive behaviors will be further considered in the investigation of the evolutionary dynamics of socioeconomic systems. What the differences between a homogeneous environment and a heterogeneous environment are and how these differences affect the evolution of socioeconomic systems are the favorites of ours. \section*{Acknowledgments} This work is the research fruits of Social Science Foundation of Zhejiang Province, National Social Science Foundation of China (Grant No. 20BJL147), Humanities and Social Sciences Fund sponsored by Ministry of Education of China (Grant Nos. 19YJAZH120, 17YJAZH067), National Natural Science Foundation of China (Grant Nos. 71371165, 11865009, 71871094, 71631005, 71773105). Thank professor Yi-Cheng Zhang for his suggestions and discussions about the reference point mechanisms. \bibliographystyle{model1-num-names}	{ "redpajama_set_name": "RedPajamaArXiv" }	5,206
Watch Online Jal (2013) From Player 1 Below. Watch Online Jal (2013) From Player 2 Below. Watch Online Jal (2013) From Player 3 Below. Direct Download Link of Jal (2013). Jal (2013) Full Movie Watch Online In HD Free Download DvD, Full Movie Jal (2013) Watch Online In 1080p Print Download Free.	{ "redpajama_set_name": "RedPajamaC4" }	1,578
Q: Doubt in a figure which explains rainbow formation This figure is given in wikipedia to explain rainbow formation, l know that if light travels from denser medium to rarer medium and if angle of incidence is greater than crictal angle light will reflect back frmo inner surface of drop, but here in this figure a parallel ray(paraxial rays) to diameter is shown as reflecting back from surface. It is clear from figure that they do not make angle more than critical angle, I want to know whether it is partial reflection or total internal reflection of paraxial rays. https://en.wikipedia.org/wiki/Rainbow This sentence is also given in wikipedia: The overall effect is that part of the incoming light is reflected back over the range of 0° to 42°, with the most intense light at 42°. A: It's a partial reflection. For an ideal sphere, it's not possible for an external ray to achieve total reflection. Any ray that enters must necessarily be at less than the critical angle. This ray will intersect the sphere at two points, and the angle it creates with the surface of the sphere will be identical. Therefore it will be below the critical angle at both surfaces. Not shown is that a percentage of the light will leave and not reflect at each intersection. The important thing in that image is that regardless of where incoming ray strikes, there is a maximum deviation possible when there are two reflections. This maximum angle depends on the refractive index.	{ "redpajama_set_name": "RedPajamaStackExchange" }	4,707
only in Typography lAll (543)r lAntiquarian (479)r lNew (64)r Subject/Author/Title Author Title Highest Price Lowest Price Most Recent Publisher Newest Published Oldest Published Results 1 - 25 (of 543) A SIGNED COPY BY THE AUTHOR OF THIS LOVELY BOOK Young, Matthew McLennan. THE RISE AND FALL OF THE PRINTERS' INTERNATIONAL SPECIMEN EXCHANGE. New Castle, Delaware: Oak Knoll Press, 2012. 8.5 x 11 inches. hardcover, dust jacket. 160 pages. A SIGNED COPY BY THE AUTHOR OF THIS LOVELY BOOK "Matthew Young's book showcases over 80 specimens (full size and in color), and gives a detailed account of the behind-the-scenes machinations that affected the course of the Specimen Exchange.... If you are interested in the history of graphic design, Young's book is a wonderful account of a lesser-known part..... READ MORE about THE RISE AND FALL OF THE PRINTERS' INTERNATIONAL SPECIMEN EXCHANGE Order nr. 133467 (Acorn Press). ONE LINE SPECIMEN BOOK. Forest Park, IL: Acorn Press, (1962). 8vo. stiff paper wrappers, front wrapper gilt-stamped. (vi), 29, (3) pages. Limited to 350 copies. Type faces available at the Acorn Press. Foreword and explanation. Indexed. Wrappers faded. READ MORE about ONE LINE SPECIMEN BOOK Adolph, Rudolf. KLEINES KALEIDOSKOP. Frankfurt: Linotype GmbH, (1962). square 8vo. paper-covered boards. 79, (7) pages. A collection of literary excerpts related to books and typography published by Linotype as a New Year's gift. Some wear to the head of spine. Else very good. READ MORE about KLEINES KALEIDOSKOP (Aldus Manutius). Staikos, Konstantinos Sp. THE GREEK EDITIONS OF ALDUS MANUTIUS AND HIS GREEK COLLABORATORS. New Castle, Delaware: Oak Knoll Press, 2016. 6.7 x 9.5 inches. hardcover, dust jacket. 312 pages. The Greek Editions of Aldus Manutius and his Greek Collaborators was first published in Greek in 2015, in order to commemorate the 500th anniversary of the death of the Venetian printer. A succinct introduction on the pioneers of Renaissance humanism in Crete is followed by a thorough presentation of the graphic aspect of Aldus's Greek editions, that is, initials..... READ MORE about THE GREEK EDITIONS OF ALDUS MANUTIUS AND HIS GREEK COLLABORATORS Almquist, Johan Axel. SVERIGES BIBLIOGRAFISKA LITTERATUR FORTECKNAD AF J...TREDJE DELEN, HAFT 1, TYPOGRAFI OCH BOKHANDTVERK SAMT SUPPLEMENT TILL FOREGAENDE DELAR [SWEDEN'S BIBLIOGRAPHIC LITERATURE LISTED BY (THE AUTHOR), THE THIRD PART, FASICLE 1, TYPOGRAPHY AND BOOK ARTS, WITH SUPPLEMENT TO PRECEDING PARTS]. Stockholm: n.p. (Royal Library)), 1912. 8vo. sewn, stiff paper wrappers. (ii), 152 pages. Part III, fasc. 1 of the work listed in Besterman 5949. Entries no. 4951-5810 (i.e. 860) of this work. The making and selling of books, and the history thereof. The supplement lists bibliographies, biobibliographies, books on library science and archives, and library catalogues. Concludes with list of corrections and errata. Unopened. Covers detached and missing pieces; backing missing. READ MORE about SVERIGES BIBLIOGRAFISKA LITTERATUR FORTECKNAD AF J...TREDJE DELEN, HAFT 1, TYPOGRAFI OCH... Alvarez, Pablo. ALONSO VÍCTOR DE PAREDES' INSTITUTION, AND ORIGIN OF THE ART OF PRINTING, AND GENERAL RULES FOR COMPOSITORS [MADRID: CA. 1680]. Ann Arbor, MI: The Legacy Press, 2018. 8vo. cloth, dust jacket. 466 pages. Pablo Alvarez offers the first complete English translation of Alonso Víctor de Paredes Institucion, y origen del arte de la imprenta, y reglas generales para los componedores [Institution, and Origin of the Art of Printing, and General Rules for Compositors]. This 96-page printing manual set and printed by Paredes himself was issued in Madrid around 1680. It opens with an introductory digression..... READ MORE about ALONSO VÍCTOR DE PAREDES' INSTITUTION, AND ORIGIN OF THE ART OF PRINTING, AND GENERAL RULES... Anthoensen, Fred. JOHN BELL TYPE ITS LOSS AND REDISCOVERY. With a Type-facsimile of John Bell's first Type Specimen, 1788. Portland, ME: Southworth-Anthoensen Press (But Printed by The Meriden Gravure Co. in 1965 for the Heritage of the Graphic Arts). 1939. 8vo. paper wrappers. 20, (8) pages. With a Type-facsimile of John Bell's first Type Specimen, 1788. Limited to 250 copies. A fine copy. READ MORE about JOHN BELL TYPE ITS LOSS AND REDISCOVERY Order nr. 97 Arnold, Edmund C. ARNOLD'S ANCIENT AXIOMS: TYPOGRAPHY FOR PUBLICATIONS EDITORS. Chicago, IL: Ragan Report Press, 1978. 12mo. stiff paper wrappers, spiral bound. (iv), 135+(1) pages. Third printing. Table of contents, glossary. Instructions for the publishing of newspapers and magazines. Previous owner's name on title. Spiral binding cracked. READ MORE about ARNOLD'S ANCIENT AXIOMS: TYPOGRAPHY FOR PUBLICATIONS EDITORS Barker, Nicolas. THE FUTURE OF TYPOGRAPHICAL STUDIES. Chapel Hill, NC: Hanes Foundation, 1996. 8vo. stiff paper wrappers. (iv), 28, (2) pages. First edition. Printing of a lecture given by Nicolas Barker in Wilson Library at the University of North Carolina/Chapel Hill. The lecture was tenth in the Hanes Lecture Series. Presented by the Hanes Foundation for the study and the origin and development of the book. READ MORE about THE FUTURE OF TYPOGRAPHICAL STUDIES Bartlett, Edward Everett. TYPOGRAPHIC TREASURES IN EUROPE AND A STUDY OF CONTEMPORANEOUS BOOK PRODUCTION IN GREAT BRITAIN, FRANCE, ITALY, GERMANY, HOLLAND AND BELGIUM. With an Addendum by J.W. Muller giving the Principal Dates and Personages in Printing History. New York: G.P. Putnam's Sons, 1925. folio. cloth-backed boards, top edge gilt, slipcase. 185, (3) pages. With an Addendum by J.W. Muller giving the Principal Dates and Personages in Printing History. First edition, limited to 585 copies. Contains five plates and much information. Spine spotted in places. Slipcase bottom creased. READ MORE about TYPOGRAPHIC TREASURES IN EUROPE AND A STUDY OF CONTEMPORANEOUS BOOK PRODUCTION IN GREAT BRITAIN,... Bartram, Alan. TYPEFORMS: A HISTORY. New Castle, Delaware and London: Oak Knoll Press and The British Library, 2007. 9.5 x 10 inches. cloth, dust jacket. 128 pages. First edition. This book is the long-awaited successor to the classic An Atlas of Typeforms, the great visually-led history of type that Alan Bartram and James Sutton produced in 1968. Much has changed in the last 40 years, not least the teaching of typography and the means by which it is created. Because..... READ MORE about TYPEFORMS: A HISTORY (Bayberry Hill Press). Johnson, Foster Macy. A BACKWARD GLANCE. Meriden, CT: Bayberry Hill Press, 1975. 4to. quarter cloth, marbled paper-covered boards, paper spine and front cover labels. (iv), 27+(1) pages. Limited to 100 numbered copies, signed by author on colophon. Poem by J. Johnson on title. A reflection on the demise of the typographer and the compositor with the onslaught of "Cold Type" and the computer. Illustrated. Complimentary gift card laid in. READ MORE about A BACKWARD GLANCE (Bell, John). Morison, Stanley. JOHN BELL, 1745-1831, BOOKSELLER, PRINTER, PUBLISHER, TYPEFOUNDER, JOURNALIST, & C. Cambridge: Cambridge University Press, 1930. tall 8vo. cloth, leather spine label, dust jacket. xi, 165, (5) pages. First edition, limited to 300 copies. (Appleton 94). Spine faded, else near fine. Sections on Bell as bookseller and partner in The Morning Post, The British Letter Foundry (1788-89), and his other publishing ventures. Contains three appendices commenting on Bell's book typography, newspaper typography, his types in the United States and his type specimens. A Century for the..... READ MORE about JOHN BELL, 1745-1831, BOOKSELLER, PRINTER, PUBLISHER, TYPEFOUNDER, JOURNALIST, & C Bennett, Paul A. BOOKS AND PRINTING, A TREASURY FOR TYPOPHILES. Cleveland and New York: World Publishing Co., (1951). 8vo. cloth, dust jacket. (ii), xviii, 418, (2) pages. First edition. Illustrated. Essays by Wroth, Warde, Dwiggins, Rogers, Ransom, Pollard, Grabhorn, Morison, Gill, Goudy and others. Near fine. READ MORE about BOOKS AND PRINTING, A TREASURY FOR TYPOPHILES Berliner, Harold. A GARDEN OF PRINTERS' FLOWERS. Nevada City, CA: Harold Berliner's Typefoundry, (1982). large 8vo. paper wrappers. 31+(1) pages. Catalogue of typographical ornament. READ MORE about A GARDEN OF PRINTERS' FLOWERS (Bibliography). BIBLIOGRAPHIES AND REFERENCE BOOKS. New York: Lathrop C. Harper, Inc., n.d. 8vo. stiff paper wrappers. 112 pages. "European, English and American Literature - The Fine Arts, including Painting, Engraving and Architecture - Genealogy & Heraldry - Incunabula - Manuscripts - Dictionaries and Vocabularies - The Arts of teh Book, including formation of libraries, the Book Trade, Typography, Illustration and Binding - mainly from the library of Sir William Stirling-Maxwell, the noted 19th century historian and collector, co-founder of the..... READ MORE about BIBLIOGRAPHIES AND REFERENCE BOOKS Bigelow, Charles, Paul Hayden, and Linnea Gentry (editors)16151. FINE PRINT ON TYPE. San Francisco: Fine Print, 1989. 4to. stiff paper wrappers. (viii), 148 pages. First edition. The Best of Fine Print Magazine on Type and Typography. An anthology of the most interesting and informative articles published in Fine Print under the title "On Type." Covers a wide range of topics from the sixteenth century to the present day. Fine condition. READ MORE about FINE PRINT ON TYPE Biggs, John R. AN APPROACH TO TYPE. London: Blandford Press, (1961). small 4to. cloth. 136 pages. Second edition. Well illustrated introduction to typography. Minor jacket chipping. Bookplate. READ MORE about AN APPROACH TO TYPE (Bird & Bull Press). PROSPECTUS FOR SO LONG, HOT-METAL MEN. Newtown, PA: Bird & Bull Press, 2007. Broadside (11 3/4 by 8 inches). Prospectus for Henricus de Nova Villa, So Long, Hot-metal Men: The Comprehensive Bird & Bull Type Specimen Book. READ MORE about PROSPECTUS FOR SO LONG, HOT-METAL MEN Black, Alison. TYPEFACES FOR DESKTOP PUBLISHING, A USERS GUIDE. London: Architecture Design and Technology Press, 1990. 4to. stiff paper wrappers. ix, 106 pages. First edition. Well-illustrated. READ MORE about TYPEFACES FOR DESKTOP PUBLISHING, A USERS GUIDE Blumenthal, Joseph. ART OF THE PRINTED BOOK 1455-1955; MASTERPIECES OF TYPOGRAPHY THROUGH FIVE CENTURIES FROM THE COLLECTIONS OF THE PIERPONT MORGAN LIBRARY. New York: Pierpont Morgan Library, (1984). 4to. stiff paper wrappers. 192 pages. First edition, fourth printing. Profusely illustrated. Name in ink. READ MORE about ART OF THE PRINTED BOOK 1455-1955; MASTERPIECES OF TYPOGRAPHY THROUGH FIVE CENTURIES FROM THE... THE PRINTED BOOK IN AMERICA. Hanover, NH: Dartmouth College Library, (1989). 4to. cloth, dust jacket. xvi, 250, (2) pages. Reprint of first edition. A study of the more interesting of American typographers from colonial times to the present. Well illustrated. READ MORE about THE PRINTED BOOK IN AMERICA Hanover, NH: Dartmouth College Library, (1989). 4to. stiff paper wrappers. xvi, 250, (2) pages. Reprint of first edition. A study of the more interesting of American typographers from colonial times to the present. Well-illustrated. Loosely inserted in a commorative bookplate of William Sihler. READ MORE about THE PRINTED BOOK IN AMERICA Boston: David R. Godine, (1977). 4to. cloth, dust jacket. xvi, 250, (2) pages. First edition. A study of the more interesting of American typographers from colonial times to the present. Well-illustrated. Jacket spine faded; chipped around edges. READ MORE about THE PRINTED BOOK IN AMERICA Boston: David R. Godine, (1977). 4to. cloth, dust jacket. xvi, 250, (2) pages. First edition. A study of the more interesting of American typographers from colonial times to the present. Well-illustrated. With a small paper label on the free endpaper calling attention to the fact that this book was printed on Mohawk Superfine Text. READ MORE about THE PRINTED BOOK IN AMERICA	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	483
{"url":"https:\/\/byjus.com\/questions\/what-is-the-relationship-between-total-utility-and-marginal-utility\/","text":"# What Is the Relationship Between Total Utility and Marginal Utility?\n\nTotal utility is the aggregate of all the utility that is derived from the consumption of all units of the commodity, while the marginal utility is the additional utility that is obtained from the consumption of an additional unit of that commodity.\n\nTherefore, we can say that the relationship between total utility and marginal utility is that total utility is the summation of the marginal utility.\n\nLearn about more questions and answers on business studies and various other commerce topics from our website.","date":"2021-09-24 02:32:31","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\": 0.8725153207778931, \"perplexity\": 525.4078346076162}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-39\/segments\/1631780057496.18\/warc\/CC-MAIN-20210924020020-20210924050020-00528.warc.gz\"}"}	null	null
Maddie Brown Brush says being a mom was her calling in life Maddie and Caleb Brush from social network post The star of 'Sister Wives' is very happy and loves being a mom to a new baby. by Mandy Robinson (article) and Jane Flowers (video) January 21, 2018 at 8:31 PM Sun 21 Jan 2018 11:11:11 PM EST 'Sister Wives': Maddie Brown Brush loves being a mum - Video Last week on "Sister Wives," maddie Brown Brush shared the news that she is expecting a baby. She already had this little boy, but now she is speaking out about how she feels like being a mom is what she was made to do. This week on the show they announced the big pregnancy news to the family. It was fun and everyone seemed really excited about the news. What did Maddie have to say about being a mom? Maddie Brown Brush went to her Instagram page and shared that she loves being a mom. She started out saying, "Being a mother is learning about strengths you didn't know you had, and dealing with fears you didn't know existed." Maddie shared that she thinks that she surprised a lot of people when she got married. Maddie and Caleb were just the perfect match for each other. She admitted that she was never a maternal person, but now she feels like it was her calling. Maddie Brown Brush feels like she was meant to be a mom. She loves it and seems to be doing a great job with taking care of her little boy. You can easily assume they will have more in the future. She feels like this gives her "meaning" and she hopes someday her son finds his calling that will be the same for him. Kody Brown wasn't even 50 yet when the baby was born and Robyn became a grandma at the young age of 38. This is pretty young to be grandparents, but they are loving the news. Kody and Janelle already knew about the baby before it was revealed to the family on the show. With Mykelti married now and Logan and Aspyn both engaged, it sounds like it might not be too long before more grandchildren are born. What else did they reveal on the show? The other big news that Maddie and Caleb Brush shared is that they are moving home. They are going to be near the family in Las Vegas so that the baby can have their family there and close. This is going to make it where they have family nearby and they can finish out school. It sounds like the best decision for them. They waited until Mykelti's wedding to move back home. This means that the couple has been back for around a year in Vegas, but somehow the fans didn't even realize this was going on at all. Do you think that Maddie and Caleb Brush will have more children soon? Sound off in the comments below on your thoughts, and don't miss new episodes of "Sister Wives" on Sunday nights on TLC. You are going to love getting to see how things have changed with Maddie moving back to Las Vegas and it should make for an interesting rest of the season. Scott Stapp leaps into night of glorious rock, lessons in grace at Dallas House of Blues Tresa Patterson 'Days Of Our Lives' rumors: Kristen turns into Susan with another mask 'GH' alludes to Nikolas still being alive Mandy Robinson Mandy Robinson has been a freelance writer for eight years. She will never shy away from a good story and loves to write on the best reality TV spoilers, celeb news and more. Follow Mandy on Facebook Follow Mandy on Twitter Read more on the same topic from Mandy Robinson: Jill and Derick Dillard spent their fifth anniversary with an out-of-town trip Anna Duggar celebrates her 31st birthday with family 'Counting On': Jessa Duggar Seewald shows off baby bump, baby could arrive any day Blasting News recommends 'RHOBH': Lisa Vanderpump never saw the final of the show, but blasted the cast Video 'RHOBH': Andy Cohen will add a new member to his 'powerhouse cast' Video 'General Hospital' spoilers: Peter shot by Dante, upsetting Maxie Video 'General Hospital' spoilers: Nikolas might still be alive Video 'RHOBH': Andy Cohen thinks a change of direction's on the cards for the Bravo show 'GH' rumors: Obrecht tells Nina that Shiloh may not be Wiley's baby daddy	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	7,748
Q: Opening current directory from a terminal onto a file browser? My current directory is buried deep in multiple subfolder layers from my home directory. If I want to open this directory in a gui-based file browser, I have to double click folder after folder to reach it. This is very time consuming. On the other hand, with very few key strokes and several times hitting the tab button, it is very easily reachable via a terminal. I want to know if there is a way to open the current directory in a terminal onto a a file browser. What is the command to do this? For reference, I have an ubuntu system, but I'd like to know what the commands are across the various distributions of linux. A: xdg-open . xdg-open is part of the xdg-utils package, which is commonly installed by default in many distributions (including Ubuntu). It is designed to work for multiple desktop environments, calling the default handler for the file type in your desktop environment. You can pass a directory, file, or URL, and it will open the proper program for that parameter. For example, on my KDE system: * xdg-open . opens the current directory in the Dolphin file manager xdg-open foo.txt opens foo.txt in emacsclient, which I've configured to be the default handler for .txt files xdg-open http://www.google.com/ opens google.com in my default web browser The application opens as a separate window, and you'll get a prompt back in your terminal and can issue other commands or close your terminal without affecting your new GUI window. I usually get a bunch of error message printed to stderr, but I just ignore them. Edit: Adding the arguments xdg-open . >/dev/null 2>&1 redirects the errors and the output. This call won't block your terminal. Binding this to an alias like filemanager='xdg-open . >/dev/null 2>&1' can come in handy. A: Simply use gio open Use - gio open . gio open example/ A: Ubuntu uses as default file browser nautilus as far as I remember. Therefore to open a certain folder from terminal you can type something like the following: nautilus /path/to/your/dir or cd /path/to/your/dir && nautilus . nautilus automatically deataches itself from the terminal it was called, but suppose you are using another file browser, and you want to close the terminal from which you called your file browser, you can use nohup to do so. If you are using, let's say, thunar (another file browser), you can type the following: nohup thunar /path/to/your/dir & exit A: Almost any GUI application (on X window systems) can be opened from a terminal window within that GUI. To open any GUI app, type the name of the executable at the shell prompt. Most file browsers take a directory as a command line argument, so you should usually pass . as the parameter. Here are some examples for some popular systems, most X based systems work similarly. On Gnome, you can run nautilus (the default file browser) directly, or on Gnome 2, you can use gnome-open to open any file (including directories) with the configured Gnome file handler application: $ nautilus . or $ gnome-open . On KDE, there are two popular file browsers, I'm not aware of a command similar to gnome-open, though gnome-open can be executed within KDE, but by default it opens Gnome apps. $ dolphin . or $ konquerer . On OS X, as mentioned in comments, a similar command line program, open can be used. $ open . What if you don't know the executable name of your system's file browser? If on Gnome 2, use gnome-open . If on OS X, call open .. Each of these will execute the configured file browser for your GUI environment. If you don't know of such a command in your window system, here's one way to find out on systems with a ps command that understands the options -u USER and -o FORMAT: In your terminal window, type ps -u$USER -o comm > /tmp/$$A In your GUI, start the file browser. Back in your terminal window, type ps -u $USER -o comm > /tmp/$$B (Notice the B suffix, this is a different file than step 1). Also in the terminal, type diff /tmp/$$[AB]. Should display the name of your file browser. It's possible you could see more than one name, if another program happened to start under your user id during the time between the calls to ps. For example: $ ps -u $USER -o comm > /tmp/$$A $ # open file browser in gui $ ps -u $USER -o comm > /tmp/$$B $ diff /tmp/$$[AB] 95a96 > nautilus	{ "redpajama_set_name": "RedPajamaStackExchange" }	7,068
The Texas Department of Criminal Justice (TDCJ) is a department of the government of the U.S. state of Texas. The TDCJ is responsible for statewide criminal justice for adult offenders, including managing offenders in state prisons, state jails, and private correctional facilities, funding and certain oversight of community supervision, and supervision of offenders released from prison on parole or mandatory supervision. The TDCJ operates the largest prison system in the United States. The department has its headquarters in the Brad Livingston Administrative Headquarters in Huntsville and offices at the Price Daniel Sr. Building in downtown Austin. History 1800s In 1848, the Texas Legislature passed "An Act to Establish a State Penitentiary", which created an oversight board to manage the treatment of convicts and administration of the penitentiaries. Land was acquired in Huntsville and Rusk for later facilities. The prison system began as a single institution, located in Huntsville. A second prison facility, Rusk Penitentiary, began receiving convicts in January 1883. Before the Ruiz v. Estelle court case, the Texas Department of Corrections had 18 units, including 16 for males and two for females. Various administrative changes where the organization of the managing board of the department occurred over the next 100 years. 1900s In 1921, George W. Dixon of The Prison Journal published a report on the Texas Prison System facilities. His article stated that the prisons were among the most "brutal" in the world. Dixon said that the prisons featured corporal punishment such as whipping, beatings, and isolation. In July and August 1974, a major riot at the Huntsville Walls prison resulted in the murder of two hostages. This was not a riot, but an escape attempt in which the whole Huntsville Unit was shut down. Inmates were Fred Gomez Carrasco, Rudolpho Domingez and Ignacio Cueves. In 1979, Ruiz v. Estelle found that the conditions of imprisonment within the TDC prison system constituted cruel and unusual punishment in violation of the United States Constitution. The decision led to federal oversight of the system, with a prison construction boom and "sweeping reforms ... that fundamentally changed how Texas prisons operated." In 1989, the TDCJ and the Board of Criminal Justice were created. The board is composed of nine members appointed by the governor with the advice and consent of the senate to six-year, overlapping terms. This new agency absorbed functions of three state agencies - the Texas Department of Corrections, the Texas Board of Pardons and Paroles, and the Texas Adult Probation Commission. In the 1980s, the government of Texas began building more prisons. During that decade, impoverished rural communities viewed the prisons as a boon, as they provided jobs. In 1987, the Texas State Board of Corrections voted to build two new 2,250-inmate maximum-security prisons in Gatesville and Amarillo and several 1,000-inmate medium-security prisons in Liberty County, Marlin, Snyder, and Woodville. The TDC units in Amarillo and Snyder were the first ones located outside of Central Texas and East Texas. James Anthum "Andy" Collins, the executive director of the TDCJ from April 10, 1994, to around December 1995, became a consultant for VitaPro, a company selling a meat substitute that was used in Texas prisons. Shirley Southerland, a prisoner at the Hobby Unit, stated that her fellow prisoners discovered that the VitaPro product was intended for consumption by canines. Collins arranged for VitaPro to be used while he was still the head of the TDCJ. Collins had awarded a $33.7 million contract to the company. Robert Draper of the Texas Monthly accused various TDCJ board members and state officials in the early to mid-1990s of capitalizing on the rapid expansion of Texas prisons – from 1994 to 1996 the number of prisoners almost doubled and the number of the prison units increased from 65 to 108 – and trying to establish favorable business contracts and/or get prisons named after them. Draper reasoned, "If [Allan B. Polunsky] and other board members didn't care about ethics, why should Andy Collins?" 2000s and 2010s According to a December 2007 survey of prisoners from the U.S. Bureau of Justice Statistics, five TDCJ units, Allred Unit, Clemens Unit, Coffield Unit, Estelle Unit, and Mountain View Unit, were among those in the United States with the highest numbers of reported prison rape cases in 2006. In 2007, the TDCJ reported a total of 234 reported sexual assaults in its prisons. Michelle Lyons, the TDCJ spokesperson, said, "The actual reports we have are not consistent with the results in the survey, but because it's anonymous, there's no way for us to verify that additional number." In 2008, the TDCJ planned to install cell phone-jamming devices at its units, but encountered resistance from cell phone companies. In 2014, the Human Rights Clinic of the University of Texas School of Law released a report stating that the temperatures in many TDCJ units are too high over the summer and that at least 14 inmates had been killed by the heat since 2007. In 2013, the TDCJ had signed a deal for a climate-controlled housing system for pig breeding; this was worth $750,000. In response, John Whitmire of the Texas State Senate stated, "the people of Texas don't want air-conditioned prisons, and there's a lot of other things on my list above the heat. It's hot in Texas, and a lot of Texans who are not in prison don't have air conditioning." That year, a federal judge declared that the TDCJ is making it impossible for Muslim inmates to practice their religion. In 2017, the use of solitary confinement as punishment was ended. Governance The Texas Board of Criminal Justice oversees the TDCJ. The board selects the executive director, who manages the TDCJ. The members of the board are appointed by the Governor of Texas. Current board members Bryan Collier (executive director) Oscar Mendoza (deputy executive director) Patrick O'Daniel (chairman) Derrelynn Perryman (vice chairman) Pastor Larry Miles (secretary) E.F. "Mano" DeAyala (member) Molly Francis (member) Faith Johnson (member) Sichan Siv (member) Eric Nichols (member) Rodney Burrow, M.D. (member) Major divisions The department encompasses these major divisions: Correctional Institutions Division Parole Division Community Justice Assistance Division Correctional Institutions Division The Correctional Institutions Division, which operates secure correctional facilities for adults, has its headquarters in the Brad Livingston Administrative Headquarters in Huntsville. TDCJ-CID, formed in 2003, was a merger of the Institutions Division, the Operations Division, the Private Facilities Division, and the State Jail Division. The division operates prisons, which are facilities for people convicted of capital offenses and people convicted of first-, second-, and third-degree felony offenses, and state jails, facilities for people convicted of state jail felony offenses. Before the 2003 formation of the Correctional Institutions Division, the Institutional Division operated prisons and the State Jail Division (TDCJ-SJD) operated state jails. As of 2010, of the counties in Texas, the five with the highest numbers of state prisons and jails were Walker, Brazoria and Coryell (tie), and Anderson and Liberty (tie). As of 2001, prisons may be named after people who are dead or who are still alive, and namesakes have included Governors of Texas, TDCJ employees, members of the Texas House of Representatives, mayors, police officers, and judges. In previous eras, prisons were only named after deceased TDCJ employees and state governors. By the 2000s, so many new prisons were being built that the TDCJ had to change its naming policy. Regional offices of the CID are: Region I, headquartered in Huntsville; Region II, headquartered on TDCJ prison property in Anderson County, near Palestine; Region III, headquartered on the property of the Darrington Unit in Brazoria County, near Rosharon; Region IV, headquartered in the former Chase Field Industrial Complex (a TDCJ property) in Beeville; Region V, headquartered in Plainview; and Region VI, headquartered on TDCJ property in Gatesville. Correctional institutions Most of the TDCJ prisons are located in the historic cotton slavery belt around the former location of Stephen F. Austin's colony. Counties that have housed adult correctional facilities, such as Brazoria, Fort Bend, Polk, and Walker, once had slave majority populations. Many of the largest prison farms and prison properties in the state, including Goree Unit, the Jester units, Polunsky Unit, the Ramsey units, and Wynne Unit, are located in those counties. The state of Texas began building adult prisons outside of the historic cotton belt in the 1980s. Some units have employee housing; most employee housing was constructed prior to the TDCJ's early to mid-1990s prison expansion. As of 2008, of the 22 units that are staffed below 80% of their employee capacities, eight (36%) of the units have officers' quarters. As of that year, the TDCJ requested funding from the Texas Legislature for three 80-bed officers' quarters to be built next to three prisons that the agency considers to be "critically staffed." An employee who obtains a residence in a state-owned house on or after September 1, 1997, pays $50 per month during the fiscal year of 1998, and for each subsequent year, 20% of the fair market rental valuation of the property. A resident of state-owned bachelor officers' quarters or a renter of a state-owned mobile home lot pays $50 per month. The Texas Prison System purchased its first prison farm in 1885. The oldest TDCJ units still in operation, originally established between 1849 and 1933, include Huntsville Unit (1849), Wynne Unit (1883), Jester I Unit (1885, brick building in 1932), Vance (Harlem/Jester II) Unit (1885, brick building in 1933), Clemens Unit (1893), Ramsey (I) Unit (1908), Stringfellow (Ramsey II) Unit (1908), Goree Unit (1907), Memorial (Darrington) Unit (1917), and J. Dale Wainwright (Eastham) Unit (1917); prior to their closures Central Unit (1909, rebuilt in 1932) and Retrieve (later Wayne Scott) Unit (1919) were among the oldest prisons. In addition, the Hilltop Unit uses buildings from the former Gatesville State School, a juvenile correctional facility, making the Hilltop Unit's prison facility the third-oldest correctional facility still-used in Texas after the Huntsville and Jester I. The largest TDCJ prison is the Coffield Unit, with a capacity of 4,021 inmates. The largest female prison is the Christina Crain Unit, with a capacity of 2,013 inmates. Originally, many Texas prison farms had no cells; the prisoners were housed in racially segregated dormitory units referred to as "tanks". In the 1960s, the Texas Prison System began referring to the prisons as "units". Chad R. Trulson and James W. Marquart, authors of First Available Cell: Desegregation of the Texas Prison System, said that the word unit was a euphemism that probably was intended to refer to progressive penal practices, professionalism, and a distancing from a legacy of racism. State jails State jails house inmates convicted of state jail felony offenses, which include lower-level assault and drug, family, and property offenses. In addition the Texas Board of Criminal Justice designated state jails as transfer units for individuals who are bound for prisons. Individuals in a state jail who are convicted of a state jail offense must be held for at least 75 days and may not be held longer than 2 years. Individuals may not parole or have mandatory supervision release from state jails. The state jail felony classification was created in 1993 as part of a reformation of sentencing laws. In July 1998, Texas had 18 state jails (including six privately operated facilities) with 9,023 state jail felons and 14,940 people awaiting transfer to prisons. During that year, 53.3% of state jail felons were convicted of possession or delivery of a controlled substance. As of 1998, 85% of the state jail felons had prior arrest records, and 58% of the state jail felons had previously never been incarcerated. The highest level of educational programming available in state jails are general equivalency diploma classes. Psychiatric units The TDCJ operates three psychiatric units, including Jester IV Unit, Skyview Unit, and the John Montford Psychiatric Unit. As of March 2013, the units are at capacity. Brandi Grissom of the Texas Monthly said, "So acute is the need for psychiatric prisoners that if Texas built a fourth facility, it would be full as soon as it opened." Intake and unit assignment The State Classification Committee and designated Classification and Records Office staff members assign each institutional prisoner to his or her first unit after the prisoner completes his or her tests and interviews; offenders are not allowed to choose their units of assignment. The state assigns each state jail offender to the unit closest to his or her county of residence. Death-row offenders and offenders with life imprisonment without parole enter the TDCJ system through two points; men enter through the Byrd Unit in Huntsville, and women enter through the Reception Center in Christina Crain Unit, Gatesville. From there, inmates with life without parole sentences go on to their assigned facilities. Male death-row offenders go to the Allan B. Polunsky Unit, and female death-row offenders go to the Mountain View Unit. Transportation The prisoner transportation network of the TDCJ is headquartered in Huntsville. As of 2005, the network has 326 employees, including 319 uniformed employees. The TDCJ's regional prisoner transportation hubs are located in Abilene, Amarillo, Beeville, Huntsville, Palestine, and Rosharon. Of the transportation hubs, the Central Region hub in Huntsville transports the largest number of prisoners to the greatest number of units. The Abilene hub controls the largest land area. Prisoners in the general population are seated together, with prisoners handcuffed in pairs. Prisoners in administrative segregation and prisoners under death sentences are seated individually; various restraints, including belly chains and leg irons, are placed on those prisoners. Each prisoner transport vehicle has two urinals and two water dispensers. As of 2005, all of the transportation vans and half of the chain buses have air conditioning. Offender rules The Texas Department of Criminal Justice has the Offender Orientation Handbook, a guidebook explaining the rules prisoners are required to follow, posted on its website in English and Spanish. Individual prisoners receive formal orientations and copies of the manual after undergoing initial processing. The manual has 111 pages of rules of behavior. It is intended to establish governance over all aspects of prison life. The prison rule system is modeled on the free-world penal system, but it does not have judicial review and rights. The number of regulations has increased due to court orders, incidents, and managerial initiative. Robert Perkinson, author of Texas Tough: The Rise of America's Prison Empire (2010), wrote that the Offender Orientation Handbook "encapsulates the weary institutional dream of imposing perfect discipline on potential chaos" and that the "sweeping and tedious rules" "cover a bewildering range of restrictions and obligations." As examples Perkinson referred to the "no fighting," "offenders will brush their teeth daily," and "horseplay is prohibited," which he refers to, respectively, as "sensible," "well meaning," and a "catchall." Perkinson said that in practice, "totalitarian order" is not established in the prison because the "churlish" inmates do not have the inclination and "often," the reading ability to follow the "finer dictates" of the handbook, and the correctional officers, "moderately trained, high-turnover stiffs earning Waffle House wages," do not have the energy and time to enforce the rules strictly. According to Perkinson, the handbook is never consistently or fully enforced, but it is invoked by officials whenever a daily conflict occurs. In case of an escalated dispute, officers submit a "case" and an inmate or multiple inmates appear in front of a court described by Perkinson as "makeshift." Perkinson explains that several federal court orders have shaped the prison courts, which "have all of the trappings of adversarial justice," including a defense counsel (a correctional officer appointed by a presiding major), physical evidence, and witnesses. According to Perkinson, though, "the house [(the prosecution)] rarely loses." Jorge Renaud, a man who served as a prisoner in Texas's state prisons, said usually when an inmate is charged with a prison offense, the sole question to be determined is the severity of the punishment to be given to the inmate. Smoking is prohibited at all TDCJ facilities. On November 18, 1994, the Texas Board of Criminal Justice voted to ban smoking at all TDCJ facilities, beginning on March 1, 1995. The Holliday Unit in Huntsville already had a smoking ban in place prior to the TDCJ system-wide ban. Offender dress code Offenders in all TDCJ units wear uniforms consisting of cotton white pullover shirts and white elastic-waist trousers. The TDCJ requires prisoners to wear uniforms so they can easily be identified and to prevent correctional officers from forming associations and giving preferential treatment to any prisoners. The TDCJ retired clothing with belts and buttons and introduced trousers with expandable waists. Shoes worn by prisoners may be issued by the state or purchased from the commissary. Male prisoners must be clean-shaven, unless they have been approved to grow a 1/2 inch religious beard, a provision that went into effect August 1, 2015. Usually their hair is required to be trimmed to the backs of their heads and necks. TDCJ-CID says that "Female offenders will not have extreme haircuts." In 2016, the 5th U.S. Circuit Court of Appeals ruled that religious inmates such as Muslims are allowed to grow 4-inch beards as well as wear religious clothing, so long as prisoners do not hide contraband. Inmate with longer hair are inspected by shaking their hair with their fingers. Prisoners must have hair cut around their ears. Native American prisoners, since 2019, received the right to wear long hair after court action. Robert Perkinson, author of Texas Tough, says that the uniforms make prisoners "look like shapeless hospital orderlies." Jorge Renaud, a former prisoner, states that the uniforms are part of the prison system's depersonalization process. Book review The TDCJ reviews books to determine whether they are appropriate for prisoners. In 2010, the agency disclosed that it reviewed 89,795 books, with 40,285 authors represented. The agency did not disclose how many of those books were banned. The system's banned list includes some novels that were written by National Book Award winners, Nobel laureates, and Pulitzer Prize-winners, and some books of paintings made by notable artists. The Austin American-Statesman and the Houston Press compiled lists of some books that have been banned by the TDCJ, noting some are considered classics of the literary canon. Prisoner release The TDCJ uses regional release centers for male prisoners. Most male prisoners are released to be closer to their counties of conviction, approved release counties, and/or residences. Male prisoners who have detainers, are classified as sex offenders, have electronic monitoring imposed by the Texas Board of Pardons and Paroles, and/or have certain special conditions of the Super Intensive Supervision Program are released from Huntsville Unit, regardless of their counties of conviction, residences, and/or approved release counties. Regional release facilities for men include the Huntsville Unit, the William P. Clements Jr. Unit near Amarillo; the Hutchins State Jail in Hutchins, near Dallas; the French M. Robertson Unit in Abilene; and the William G. McConnell Unit near Beeville. All female prisoners who are not state jail prisoners or Substance Abuse Felony Punishment Facility prisoners are released from the Christina Crain Unit (formerly the Gatesville Unit) in Gatesville. Rick Thaler, the director of the Correctional Institutions Division, predicted in 2010 that the Huntsville Unit, which serves as the regional release center for greater Houston, would remain the TDCJ's largest release center despite the decrease of traffic of released prisoners. State jail offenders are released from their units of assignment. All people released receive a set of nonprison clothing and a bus voucher. State jail offenders receive a voucher to their counties of conviction. Prison offenders receive $50 upon their release and another $50 after reporting to their parole officers. Released state jail offenders do not receive money. Inmates in Substance Abuse Felony Punishment Facilities are also directly released. History of prisoner release Prior to September 2010, most male prison offenders were released from the Huntsville Unit. However, since the beginning of the COVID-19 pandemic in 2020, most inmates are now released from the last unit they're assigned to in their incarceration. Male inmates with health and mental health difficulties and sex offenders are still mostly released from Huntsville. Death row The TDCJ houses male death-row inmates in the Polunsky Unit and female death-row inmates in the Mountain View Unit. The Huntsville Unit is the location of the state of Texas execution chamber. The Polunsky death row has about 290 prisoners. As of March 2013, eight male death-row prisoners are housed in Jester IV Unit, a psychiatric unit, instead of Polunsky. The state of Texas began housing death-row inmates in the Huntsville Unit in 1928. In 1965, the male death-row inmates moved to the Ellis Unit. In 1999, the male death row moved to Polunsky. In the 1923-1973 period, Texas state authorities had three female death-row inmates; the first, Emma "Straight Eight" Oliver, was held at Huntsville Unit after her 1949 sentencing, but had her sentence commuted to life imprisonment in 1951. Mary Anderson, sentenced to death in 1978, was held at Goree Unit. Her death sentence was reversed in 1982, and the sentence was changed to life. Health care The University of Texas Medical Branch provides health care to offenders in the eastern, northern, and southern sections of Texas. The Texas Tech University Health Sciences Center provides health care to offenders in the western part of Texas. In addition, private corporations provide healthcare services. Hospitalized offenders may go to the Hospital Galveston Unit, the Montford Unit in unincorporated Lubbock County, or area hospitals. In 1993, Texas State Comptroller John Sharp proposed that the TDCJ end its healthcare department and transfer responsibilities to the universities to reduce costs. During that time, most TDCJ prison units were in south and east Texas, and UTMB was to provide for the care of 80% of the managed care for TDCJ, while Texas Tech was to provide the remaining 20%. In September 1994, UTMB and Texas Tech took responsibility for 3,000 healthcare workers and a $270 million budget. In 2011, the board considered ending its contract with UTMB and having regional hospitals provide care for prisoners. In 2018, the department said it needed an additional $281 million in its 2020 budget to provide the required minimum amount of health care. To save money, the department rarely provides prisoners dentures, finding it cheaper to simply produce a blended diet in such cases. As of 2017, 2.3 million incarcerated Americans depend on prisons for their healthcare. These incarcerated individuals face limited access to medical exams and prescriptions medications compared to the general population as they are not eligible for Medicaid while incarcerated. On top of that, inmates face fees for seeking medical treatment. In 35 states, inmates have medical co-payments which come out of their commissary accounts (made up of prison job payments and contributions from their family). The copays are enforced to prevent inmates from abusing the healthcare system, however, it becomes a burden on inmates whose job makes little to no money and can become a financial strain on the family. Private Healthcare in Public Facilities In some prisons, the healthcare is private which can drastically change how inmates are treated. As of 2012, more than 20 states switched over to private health care providers in order to cut back on costs. These states don't have to provide benefits and pension costs to state workers, since they are hiring private companies, which significantly reduces the price they pay. However, this calls into question the quality of care inmates receive and many human rights groups in addition to federal judges are investigating these private companies. The TDCJ has a 120-bed medical facility at University of Texas Medical Branch in Galveston. In 1987 the Texas Legislature voted in a ban on most cosmetic surgery for prisoners, and UTMB began denying such in 1989. Private Healthcare in Private Facilities The two largest private prison companies, CoreCivic (formerly known as Corrections Corporation of America) and the CEO Group, run over 170 correctional facilities. In Texas, they have five facilities. These companies keep their operating costs low by using less dollars than allocated per inmate, especially in the area of Healthcare. Additionally, these companies and similar ones, avoid taking inmates over 65 or with chronic illnesses. When they can't avoid it, they improvise ways to make it hard for the inmate to receive medical care. Specifically, CoreCivic has a history of denying hospital requests and punishing inmates when they make repeated requests. Additionally, the records of private prisons are not subject to public access laws. For these reasons, access to health care in private prisons is something that must require more scrutiny. Requesting Care Requesting care in prison systems involves a simple procedural checklist that must be met in order to see any type of medical professional. Firstly, an incarnated person must fill out Sick Call Request form that should be answered within a 48-hour time period. After 48 hours, If there is no response, the person is to advance to fill out an I-60 form which states general issues faced. If the process continues to yield no approval, a Step 1 Grievance is to filled out. This level of documentation is very strictly reviewed. Continuing to hear no response for an extended period of time indicates the time to advance to a Step 2 Grievance. After these options, the prisoner may now file a lawsuit for 'exhausting administrative remedies.' A Sick Call Request form is a specified form that is specific towards what was wrong with the inmate medically. The progression to an I-60 form leads to a more generalized form that addresses seeing a doctor, contact visit, address changes and the like. A Step 1 Grievance are very strict and viewed very critically with certain guide-lines such as: only one problem can be addressed per grievance, only one grievance per week, must be reported within 15 days, and must be written with proper language. This form alone may take up to 40 days to be processed. A Step 2 Grievance is directly reviewed by TDCJ health committee and will have a response by 35 days. If these options are still not satisfactory, the inmate is then allowed to file a lawsuit because he/she has "exhausted administrative remedies." Care through these methods is possible but is still a timely cost. Depending on how the prisoner is, the time between signing a form and receiving medication can mean life or death. Even though there is a defined process for requesting medical care in prison systems, the prisoner is still trying to fill out theses forms while considered 'sick.' Along with this, the prisoners are expected to cover the costs associated with filing out these expensive papers. For the first healthcare visit in a year, an inmate will be charged one-hundred dollars to their trust fund. However, there are still instances where the inmate would not have to attend to cost of care such as chronic illnesses, follow-up visits, emergency treatments, etc. Most visits to a medical professional costs inmates $2–8, in which they use they copay to relief these costs. At first, this rate sounds not too harsh but an important factor to put in is how much inmates earn. For most inmates, a wage is consistent of maybe a few cents per hour. This small set could mean that it would take an inmate a very long time before a "checkup" can be "bought". Fortunately though, care is not restricted if one does not have the necessary funds. Additionally, University of Texas Medical Branch (UTMB) decided that the easiest and most cost-effective way to dole out prescription medications to inmates was to distribute it from their own pharmacy. This pharmacy is based in an unmarked building in Huntsville, TX and serves 130 facilities throughout the state, including juvenile facilities, by filling over 20,000 prescriptions per day. Orders are sent out through an electronic medical record system and are processed with custom made conveyor belts and automated machines. The pharmacy has a 24-hour next-business-day turnaround ensuring medications can get to inmates as soon as possible. History of Healthcare Healthcare in Texas was mostly straight forward. Not much of it was changed over time due to its simplicity. One aspect that did change was how the cost of healthcare for incarcerated persons fluctuated. An issue that was prominent in prison systems was the associated costs with treatment. For this reason, the Correctional Managed Health Care Committee (CMHCC) was established in 1993. This committee focused their attention to the rising costs of healthcare today and how that effects inmates inside custody. The CMHCC hopes to open a statewide managed health care plan giving offenders the ability to afford care with timely access. Mental Health The decline of mental health treatment within detainees has become a major concern in the prison system, especially in the Texas prison departments. While the Texas Department of Criminal Justice claims that most of its facilities are capable of treating mental health issues, this does not seem to be the case. Texas provides at least 20% of inmates mental health treatment and this small percentage could be explained by the shortage of volunteers and staff to provide these mental treatments. There is also failure to recognize mental symptoms and make a correct diagnosis for these detainees. Lack of mental aid has increased serious assaults and violent behaviors in which most of these cases have been declined by the Bureau of Prisons for "privacy reasons." Policies have been changed by the Bureau of Prisons to increase check-ins by once a month or weekly. However, the TDCJ has attempted to minimize these issues as best as it can. Detainees are offered guidelines on how to manage their stress and sanity before being released to the public. In terms of support and care, there is the Offender Grievance Program that allows offenders to communicate with faculty staff about questions, regards, or concerns associating with their sentence. In addition, the TDCJ Ombudsman Program makes referrals to an agency staff to help resolve problems and answer questions regarding a specific offender. The Peer Recovery Support Services hold classes to allow prisoners to help one another recover from their issues. Those that obtain a certificate from the program are eligible to work or volunteer as a Peer Recovery Support Specialist. This further build a community-based environment where prisoners can understand each other's mistakes and problems and cooperate as a team to provide solutions to better themselves. Specific programs are held for detainees that are of a particular background and history. The Chaplaincy Program is a nondiscriminatory program that permits prisoners to pursue their religious faiths, reconcile relationships, and strengthen families. The program offers mentoring, space for spiritual growth, pastoral care, life skill classes, accountability/support groups, etc. Similarly, the "InnerChange" Faith-Based- Pre-Release Program functions in the same way as the Chaplaincy Program to further help detainees recover well. For younger offenders, the Youthful Offender Program aids young offenders with special needs to the Mentally Retarded Offenders Program (MROP) or Physically Hanicapped Offenders Program (PHOP). Regular youth offenders are placed in interdisciplinary programming established on a weekly schedule, including: education social skills training anger management values development goal setting cognitive restructuring substance abuse education conflict resolution aggression replacement and life skills. Recreation and Fitness Leisure activities are meant for enhancing potential life skills post-release and allowing inmates an opportunity to complete one or two activities of their choice. In terms of recreation and fitness, inmates have the chance to participate in structured fitness sessions that offer regular and moderate levels of exercises monitored by staff. Staff members are to take into account the kind of activity the detainee wants to do, the amount of time spent on that activity, and given permission. These fitness sessions occur in the "Big Yard," where gym equipment is stored and common past time favorites are held, such as volleyball, baseball, softball, wrestling, basketball, tennis, handball, boxing, and soccer/futbol. The yard is surrounded by a barbed-wire fence for extra supervision. During a detainee's time in prison, they are given a physical assessment that focuses on cardiovascular endurance, flexibility, body fat percentage, and dynamic strength. To further sharpen community-building skills, inmates are eligible to run special fitness and health events, including: Run/Walk Marathons Health fairs; health book fairs Nationally recognized health events In addition to these health events, inmates have the opportunity to educate themselves in other health and sanity organizations. Staff will provide discussions concentrating on: Weight management Stress management Human anatomy Aerobic exercises Smoking cessation Back pain relief Nutrition Ultimately, prisoners are able to utilize these resources to make them better returning members of society. Incarceration of women The Correctional Institutions Division has eight main facilities, including five prisons and three state jails, that house women; Five of the women's units, including four prisons and one state jail, are in the City of Gatesville. Jorge Renaud, author of Behind the Walls: A Guide for Family and Friends of Texas Inmates, said that female prisoners in the TDCJ generally "undergo the same tribulations, are affected by the same policies, must adhere to the same regulations, and are treated the same by TDCJ staff." Originally, women were housed in the Huntsville Unit. Beginning in 1883, women were housed in the Johnson Farm, a privately owned cotton plantation near Huntsville. After Governor Thomas Mitchell Campbell took office in January 1907, he moved the women from Johnson to the Eastham Farm (now Eastham Unit) to try to protect women from predatory prison guards. For a period in the early 20th century, Eastham housed women before a sexual abuse scandal caused the Texas prison system to move women closer to Huntsville. Before the prisons in Gatesville opened in the 1980s, women in the Texas prison system were housed in the Goree Unit in Huntsville. In 2010, a study from the National Women's Law Center and the Rebecca Project for Human Rights ranked the Texas prison system as giving "B+" care to women. A 2018 report by the Texas Criminal Justice Coalition stated that women in the TDCJ have fewer career-training and employment programs available than men; women had only two certification programs, while men had 21. In 2019, the Texas Senate passed a bill, allowing inmates to have access to a greater variety of feminine hygiene products. They have access to various sized tampons and pads and can receive up to 10 free products per day. Texas Prison Nurseries There is currently no standard policy for what happens when a woman gives birth while incarcerated, because only recently have states begun to ban the shackling of pregnant women during active labor and childbirth. The Texas Department of Criminal Justice has created an initiative in collaboration with the University of Texas Medical Branch, called BAMBI (Baby and Mother Bonding Initiative). Within this program, eligible offenders will be provided with an opportunity to bond and form attachments, "...which is important to healthy growth and development, socialization, and psychological development during the infant's formative years, while in a safe and secure environment." However, all mothers within this program are only allowed to remain in it for 12 months. After this period they must have completed their sentence, and be prepared to transition back into society. The University of Texas Medical Branch found through their research with the BAMBI program that, "As the number of women giving birth in prisons continues to trend upward, the need for more programs to promote [the] best outcomes for both mother and infants is crucial." On average, about 250 babies are born to the Texas Department of Criminal Justice. The Santa Maria Hostel provides a residential setting for these mothers and their infants. However, compared to other states, Texas' prison nursery system is limited in accessibility to mothers and infants. Texas has one of the highest populations within its prisons, but resources to women and their infants is still limited. On September 1, 2009, two laws were passed in the 81st Texas legislature. One prohibited the use of restraints on female prisoners during childbirth. The other asked that the counties write and implement procedures in regards to the health of their pregnant inmate population. Another law was passed in 2019 that stipulated that pregnant inmates cannot be shackled at all during their pregnancy or when they are recovering after childbirth. As there is no set policy for how long a mother can remain with her infant after birth, the other proposal that has yet to be passed would allow 72 hours of bonding time if the inmate does not qualify for the BAMBI program. Also, it mandates more formal training for officers to protect the physical and mental safety of pregnant inmates. Prison nurseries are imperative for both the wellbeing of the child and the mother. The CDC reported that infant mortality rates for "...babies separated from their incarcerated mothers is 7.9 infant deaths per 1,000 live births for Hispanic inmates and 14.3 for Black inmates. By comparison, the national infant mortality rate is 5.96 deaths per 1,000 live births." Thus, there is also a racial component to the treatment of pregnant women within the Texas prison. This may have to do with the fact that Texas prison healthcare does not offer screenings and treatments for high-risk pregnancies. They also lack resources to implement policy to give expectant mothers advice on nutrition, activity level, and safety. In addition, records of pregnancies and deliveries do not have to be written, and thus this could be another factor to explain the higher infant mortality. Unfortunately, in the general population within Texas, black non-Hispanics families were disproportionately affected by infant mortality. The prison trend follows the societal trend of infant mortality, which shows that there are disparities both within the prison system and the general population in terms of healthcare and preventative care. Correctional officer training The TDCJ maintains training academies in Beeville, Gatesville, Huntsville, Palestine, Plainview, and Rosharon. Trainees who do not live within a commuting distance to the training academies take state-owned housing, only if room is available. Demographics In 1974, the TDC had about 17,000 prisoners; 44% were black, 39% were non-Hispanic white, 16% were Hispanic and Latino, and 1% were of other races. About 96% were male and 4% were female. At the time, all 14 prison units of the TDC were in Southeast Texas. Parole Division The TDCJ Parole Division supervises released offenders who are on parole, inmates in the preparole transfer program, and inmates in the work program. The division also investigates proposed parole plans from inmates, tracks parole eligible cases, and submits cases to the Texas Board of Pardons and Paroles. The division does not make decisions on whether inmates should be released or whether paroles should be revoked. The TDCJ Parole Division has its central office in Austin. Halfway houses The parole division contracts with several agencies which operate halfway houses. Organizations that contract with the TDCJ include GEO Group (previously Cornell Corrections), Southern Corrections, Wayback House, E.P. Horizon Management, L.L.C., and Avalon. As of 2004,e nine halfway houses are in Texas. According to state law, former prisoners must be paroled to their counties of conviction, usually their home counties, if those counties have acceptable halfway-housing facilities available. Most counties do not have such facilities available. As of 2004, three facilities accept sex offenders and parolees from other counties; they are the halfway houses in Beaumont, El Paso County, and Houston. The Ben A. Reid Community Corrections Center, a halfway house operated by GEO and previously operated by Cornell, is located in the former Southern Bible College facility in Houston. As of 2004, the facility housed almost 400 parolees; 224 of them were subject to sex offender registration. Because of aspects of state law and because of a shortage of halfway houses, almost two-thirds of the sex offenders were from outside of Harris County. Reid is the largest of the three halfway houses that take sex offenders and out of county parolees, so Reid gets a significant number of paroled sex offenders. Cornell operates a halfway house in Beaumont, which as of 2004 houses 170 people. Horizon Management, L.L.C. operates the El Paso facility in unincorporated El Paso County, which houses 165 people. In addition, Wayback House operates the Wayback House in Dallas, E.P. Southern Corrections operates the Austin Transition Center in Austin, and Avalon operates the Fort Worth Transitional Center in Fort Worth. Community Justice Assistance Division The Community Justice Assistance Division supervises adults who are on probation. In 1989, the 71st Texas Legislature began using the term "community supervision" in place of the term "adult probation." CJAD has its central office in the Price Daniel, Sr. Building in Austin. Enrichment programs In the 1990s, Governor Ann Richards created enrichment programs for prisons. Michael Hoinski of the Texas Monthly stated that they "had helped spawn a golden age of paño-making in Texas." The programs were ended during the terms of Governors George W. Bush and Rick Perry, and paños are now prohibited in the TDCJ. Other divisions The Human Resources Division also serves the agency. As of August 23, 2010, the Human Resources Headquarters moved to Suite 600 of 2 Financial Plaza in Huntsville. The division was located at 3009 Texas State Highway 30 West. The Rehabilitation Divisions Program operates programs to rehabilitate prisoners. The division is headquartered in Huntsville. Texas Correctional Industries, a division of the TDCJ, was established in 1963 when the Prison Made Goods Act, Texas Senate Bill 338, passed. The division manages the production of prisoner-made products. Prison reform Texas state senator John Whitmire served as chair of the Senate Criminal Justice Committee from 1993 to present. With Texas representative Jerry Madden, chairman of corrections since 2005, Whitmire helped institute prison reform in the state. The creation of drug rehabilitation programs, the reduction of sentencing for drug crimes, an increase in the number of parole officers and the creation of special courts for specific crimes helped to reduce the state prison population and even led to the first prison closures in state history. The agency has also implemented a "Safe Prisons" program with the goal of implementing PREA policy throughout the state prisons and jails and reducing the incidents of prison rape. Media Historically, The Echo was published in the Huntsville Unit. Prisoners served as the staff and the reader base. It began publication in 1928. As of 2009, it was mostly published continuously, although some periods occurred when the newspaper was not published. In 2001, after the escape of the Texas 7, TDCJ officials stated that the room where the newspaper was published was a security risk and suspended the publication. The TDCJ fired the four prisoners who previously were responsible for composing the issues, and the control over the publication was passed to the Windham School District. Windham School District The Windham School District provides offenders of the TDCJ with educational services. The district was created in 1969 to provide adult education in Texas prisons. The district was the first school system of its size to be established within a statewide prison system. Windham is one of the largest correctional education systems in the United States, providing educational programs and services in most TDCJ facilities. The school district is a separate and distinct organization from the TDCJ. Fallen officers Since the inception of the Texas Department of Criminal Justice, 65 officers and one canine have died in the line of duty. Equipment Current Uniforms Uniformed staff wear the Class A grey uniform and pant or Class B blue polo shirt and grey BDU pant. Honor Guard officers wear a ceremonial dress uniform similar to other law enforcement agencies with the TDCJ badge on the left chest area. Badges are not issued to officers outside of the Honor Guard except to assistant wardens and above; however, correctional officers are not prohibited from purchasing and displaying the badge on belts, jackets, or nonuniform clothing. Correctional training officers (academy training) wear red polo shirts as an optional uniform, which has correctional training-specific patches. Canine (K9) officers have been authorized to wear TDCJ K9 T-shirts as an optional uniform with the BDU pants. Outside field officers are permitted to wear dark grey jeans and a white TDCJ issued cowboy hat. Officers are required to wear black-colored belts with their uniforms. Officers are allowed to bring their own holsters and belt for carrying equipment that is issued by TDCJ. All equipment including OC spray, handcuffs, radios, and weapons is issued by TDCJ. Service weapons Smith & Wesson Model 65 Smith & Wesson M&P (K9 and Transportation) Remington 870 Colt AR-15 Ruger M77 Former Uniforms The uniformed staff wore brown uniforms with black ties from 1955 to 1969. Female officers wore blue uniforms with a red ascot and were also available in a dress from 1969 to 1980. Black ties continued to be a part of the grey uniform until being removed from the uniform during the 1980s. Officers were issued metal badges for their shirts and hats until 1990, when fabric patches replaced them. Camouflage jackets and hats were briefly issued in the early 1980s, but were discontinued due to their illegible appearance. Service weapons Smith & Wesson Model 10 Colt Official Police Savage double-barrel shotgun Ingram and Thompson submachine guns (retired 1970s) Winchester 1894 (retired in 2000) Headquarters The TDCJ has its headquarters in Huntsville. The administrative facility, known as the Brad Livingston Administrative Headquarters, and previously BOT Complex (for its former owner, see below), is located at Spur 59 off Texas Highway 75 North. The complex also faces Interstate 45. The complex includes the Central Region Warehouse and the Huntsville Prison Store. The Texas prison system had been headquartered in Huntsville since Texas's founding as a republic, and the TDCJ is the only major state agency not headquartered in Austin, the state capital. The complex was originally owned by Brown Oil Tools, a subsidiary of Baker Hughes. Completed in 1981, the plant had a price tag of $9 million. The plant was built to replace the company's Houston plant. The plant employed 200 people. In 1987, Baker Hughes announced that it would close the plant and consolidate its operations to facilities in Houston; the company said that the Huntsville facility's large capacity caused it to be less efficient at lower operating levels. Judith Crown of the Houston Chronicle described the plant as "relatively modern" in 1987. TDCJ purchased the BOT Complex in 1989.<ref>"ihw_dump_bus_desc.txt." Texas Commission on Environmental Quality. Retrieved on July 19, 2010. "322240Texas Department of Criminal Justice purchased the Brown Oil Tool Complex at Spur 59, Huntsville, TX, from Hughes Tool Co in June, 1989."</ref> Historically, the Huntsville Unit served as the administrative headquarters of the Texas Prison System; the superintendent and the other executive officers worked in the prison, and all of the central offices of the system's departments and all of the permanent records were located in the prison. In the two decades leading to 2011, many proposals were placed in the Texas Legislature to move the TDCJ headquarters to Austin. One reason why the proposals failed was because Huntsville-area prison officials opposed the move. In the 1990s, John Whitmire, a member of the Texas Senate, made an effort to have the TDCJ headquarters moved. During the last state legislative session before September 1, 2011, Texas House of Representatives member Jerry Madden decided not to ask for the TDCJ headquarters to be moved to Austin. In August 2011 Whitmire told the Austin American Statesman that he would bring up the idea of moving the TDCJ headquarters to Austin during the next legislative session. Whitmire argued that while a Huntsville headquarters made sense when all of the prison units were in east and south Texas, since the TDCJ now has facilities around the entire state, the TDCJ headquarters should be consolidated in Austin. Steve Ogden, another state senator, said that a headquarters move is "not going to happen while I'm in office." Prison cemetery The Captain Joe Byrd Cemetery, the state's main prison cemetery, is where prisoners not claimed by their families are buried. It is located on of land on a hill, from the Huntsville Unit and in proximity to Sam Houston State University. It is the largest prison cemetery in Texas. Byrd's first prisoners were interred there in the mid-1800s, and the prison agencies of Texas have maintained the cemetery since then. See also 1974 Huntsville Prison siege Texas Juvenile Justice Department Texas Youth Commission Capital punishment in Texas George Beto Tom Mechler Texas Prison Rodeo General: List of law enforcement agencies in Texas National: List of United States state correction agencies References Further reading Harnsberger, R. Scott. A Guide to Sources of Texas Criminal Justice Statistics [North Texas Crime and Criminal Justice Series, no.6]. Denton: University of North Texas Press, 2011. Campbell, Ryan. Correctional Cowboy. ''Amazon 2013. https://www.amazon.com/Ryan-Campbell/e/B00EHKIWVI "Texas Department of Criminal Justice" (Archive). The Human Rights Clinic, University of Texas Law School. April 2014. "This report does not represent the official position of the School of Law or of The University of Texas, and the views presented here reflect only the opinions of the individual authors and of the Human Rights Clinic." External links Texas Department of Criminal Justice Texas Board of Pardons and Paroles Windham School District Texas Prison Museum TDCJ Internal Affairs Division (Archive) State corrections departments of the United States Department of Criminal Justice Department of Criminal Justice Department of Criminal Justice Department of Criminal Justice	{ "redpajama_set_name": "RedPajamaWikipedia" }	4,977
{"url":"https:\/\/cs.stackexchange.com\/questions\/128490\/is-it-possible-to-form-a-pda-for-this-language","text":"# Is it possible to form a PDA for this language?\n\n$$L=\\left \\{ a^nb^m\|n\\leq m\\leq 2n \\right \\}$$ Is this even context free?\nI am asking because by looking at the condition, for an expression that holds:$$n< m<2n$$ can be written as : $$a^nb^nb^c (c.\nFollowing this term(taken from geeks for geeks https:\/\/www.geeksforgeeks.org\/check-if-the-language-is-context-free-or-not\/) :\"An expression that involves counting and comparison of three or more variables independently is not context free language, as stack allows comparison of only two variables at a time.\"\nSo here I need to make sure that number of first b's is the same as a's and the second b's are less than n$$(c, which makes me think that L might not be context free(although it specified clearly to build PDA for this).\n\nHint: The language has the form $$L = \\{a^j a^k b^k b^{2j}\\}$$. Build a PDA that non-deterministically guesses $$j$$. (I assume you know how to build a PDA for $$\\{a^n b^n\\}$$ and $$\\{a^n b^{2n}\\}$$.)","date":"2021-09-17 07:48:01","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 8, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7705850601196289, \"perplexity\": 375.3305124481838}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-39\/segments\/1631780055601.25\/warc\/CC-MAIN-20210917055515-20210917085515-00029.warc.gz\"}"}	null	null
\section{Introduction} \label{Intro} The theory of non-gravitational interactions between dark matter and dark energy is the main concern of this work. The origin of such interacting theory did not appear suddenly in the cosmological scheme. It has a well motivated history that we shall discuss here. However, before that, we need a basic introduction about the dark matter and dark energy. According to latest observational suggestions \cite{Ade:2015xua} dark matter (DM) and dark energy (DE) are the main influential sources of the total energy budget of the universe where the dark matter contributes around 26\% of its total energy density, is pressureless and unseen while the dark energy, a hypothetical fluid occupying 68\% of the total energy density of the universe is accelerating the expansion history of the universe. The best description for such observational information is the $\Lambda$CDM cosmology where $\Lambda$ acts as the dark energy fluid and the CDM is the cold dark matter that is pressureless. This is a non-interacting scenario in the sense that both $\Lambda$ and CDM are conserved separately. Despite of great success of $\Lambda$CDM cosmology, the cosmological constant problem \cite{Weinberg} still lacks a satisfactory explanation. The cosmological constant problem is basically confined with the mismatched value of the cosmological constant predicted from the high and low energy scales of the universe. In the following we shall discuss how the interacting dynamics is closely related to the cosmological constant problem. In fact this coupling mechanics was originated because of the cosmological constant problem and finally it became very useful to explain some other issues. Let us move to the next section for an elaborative discussion on the origin of interacting dark matter and dark energy. In the late eighties, there was no concept of dark energy but the discrepancy in $\Lambda$ was remaining to be a serious issue for modern cosmology. To account of such issue, one of the attempts was to consider a toy model where scalar field is coupled to gravity \cite{Wetterich:1994bg}. The energy-momentum tensor of such coupled scalar field introduces a time dependent cosmological constant and consequently, it became a possible solution to the cosmological constant problem since the objection on the time-independent cosmological constant is naturally solved due to having a variable nature of the cosmological constant. After the official introduction of dynamical dark energy models in several forms (see \cite{Copeland:2006wr, AT, Bamba:2012cp} for a detailed survey on them), it was found that they automatically induce coincidence problem \cite{Zlatev:1998tr}. We note that the cosmological constant being time-independent cannot escape from the same problem. Quite interestingly, it was reported in \cite{Amendola:1999er} that if dark energy and dark matter are allowed to interact non-gravitationally with each other, the coincidence problem can be solved. Following this, a series of works with coupled dark matter and dark energy had the same conclusions \cite{Chimento:2003iea,Cai:2004dk, Hu:2006ar, delCampo:2008sr,delCampo:2008jx}. However, some recent results fueled the investigations of coupled dark matter and dark energy with the claim that the observational data favor an interaction in the dark sector \cite{Salvatelli:2014zta,Nunes:2016dlj,Kumar:2016zpg,Yang:2016evp,vandeBruck:2016hpz,Yang:2017yme,Kumar:2017dnp,Yang:2017zjs,Kumar:2017bpv,Yang:2017ccc}. Additionally, again some very recent investigations in this direction strongly claim that the tension on the local Hubble constant can be released if the interaction in the dark sector is allowed. However, the most important question in the coupling dynamics is, what should be the energy transfer rate between the dark sectors? Before we look for an appropriate transfer rate we recall that the nature of both dark matter and dark energy is unknown. On this ground the sensible approach is to consider some well motivated phenomenological transfer rates, or interaction functions and test the expansion history with the available astronomical data. A number of different interaction rates between dark matter and dark energy have been studied in the last several years \cite{Billyard:2000bh,Gumjudpai:2005ry,Barrow:2006hia,% Zimdahl:2006yq,Amendola:2006dg,CalderaCabral:2008bx,% Chimento:2009hj,Quartin:2008px,Valiviita:2009nu,% Clemson:2011an,Thorsrud:2012mu,Pan:2013rha,% Yang:2014hea,Faraoni:2014vra,Yang:2014gza,Nunes:2014qoa,% Pan:2014afa,Chen:2011cy,G:2014mea,Pan:2012ki,Li:2013bya,Duniya:2015nva,% Valiviita:2015dfa,Sola:2016ecz,Mukherjee:2016shl,% Pan:2016ngu,Dutta:2017kch,Cai:2017yww,Odintsov:2017icc,Pan:2017ent,% Yang:2018pej, Yang:2018ubt, Yang:2018euj}. For a comprehensive review on different interaction rates, we refer to \cite{Bolotin:2013jpa, Wang:2016lxa}. We also note that the interaction between the dark sectors has also been examined in a more general framework where the geometry of the universe is inhomogeneous \cite{Izquierdo:2017igb,Izquierdo:2017pnp}. In this work we concentrate on the spatially flat Friedmann-Lema\^itre-Robertson-Walker universe where we introduce an interaction between dark energy and pressureless dark matter that exactly solves the background evolution. That means the evolution equations for dark matter and dark energy are analytically solved. The appearance of analytic structure of the background evolution makes the cosmological model quite interesting because the cosmological parameters associated with this model take analytic forms too. However, this is not new because the analytic structure for such interaction model has already been reported by some of the authors in a previous work \cite{Sharov:2017iue}. But the motivation of the present work is completely different. Here we aim to test the large-scale stability of the model which is very important because without stable perturbations there will be no such structure formation of the universe. The analysis of structure formation in models of DE and DM, from the point of view of the cosmological perturbations theory, plays an essential role when the different models are confronted with the observations-data \cite{Hwang:2009zj}. As it is well known, these dark scenarios imprint a signature on the cosmic microwave background (CMB) power spectrum \cite{Bean:2003fb,Weller:2003hw}. Thus, the study of the cosmological perturbations is important and also need to be well-analyzed. In particular, for models with interaction between DE and DM, with adiabatic initial conditions and the perturbation theory were studied in Ref. \cite{Bean:2007ny}, see also \cite{Herrera:2016uci, delCampo:2013hka, Wang:2016lxa}. Also an analysis in models with an interacting DE-DM with a constant equation of state, was analyzed in \cite{Valiviita:2008iv}. Here, the authors demonstrated that perturbations were unstable together with a rapid growth of DE fluctuations. In this sense the test the large-scale stability is fundamental, since without stable perturbations there will be no such structure formation. We organize the work in the following way. In section \ref{sec-eqns} we describe the basic equations for the interacting model both at background and perturbative levels. The analytical solutions are discussed in section \ref{sec-solutions}. The section \ref{sec-results} details the results of the analysis following the observational data used in this work. Finally, we close our work with a brief summary in section \ref{sec-conclu}. \section{Interacting Dynamics in flat FLRW} \label{sec-eqns} We consider a spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe where pressureless dark matter, also known as cold-dark-matter (CDM), interacts with a dark energy fluid. The interaction is non-gravitational, that means gravity does not play any role in their interaction. Additionally, we consider the existence of baryons and radiation in the universe sector. To avoid any kinds of inflexible constraints like ``fifth force'', we assume that neither baryons nor radiation takes part in the interaction. In other words, they are conserved separately. Since the interaction exists between CDM and DE, the total conservation of this (CDM$+$DE) sector is, \begin{eqnarray}\label{total-cons} \dot{\rho}_c+ 3 H (1+w_c) \rho_c= -\dot{\rho}_x - 3 H (1+w_x )\rho_x \, , \end{eqnarray} where ($\rho_c$, $\rho_x$) are respectively the energy density of CDM and DE. The parameter $H \equiv \dot{a}/a$, corresponds to the Hubble rate, $a$ being the FLRW scale factor. The quantity $w_x = p_x/\rho_x$, corresponds to the equation of state for DE and $p_x$ is the pressure of the DE fluid. Also, we note that $w_c = p_c/\rho_c$ since $p_c$, the pressure of CDM is zero, hence $w_c= 0$. The total conservation equation (\ref{total-cons}) can be decoupled into the following equations \begin{eqnarray} &&\dot{\rho}_{c} + 3 H \rho_{c} = - Q \, ,\label{conservation1}\\ &&\dot{\rho}_{x} + 3 H (1+w_x )\rho_x = Q\, ,\label{conservation2} \end{eqnarray} where an overhead dot represents the cosmic time differentiation. The parameter $Q$ denotes the energy transfer between the dark sectors. In this sense, the sign of $Q$ determines the direction of energy transfer. For instance, $Q < 0$ indicates the energy transfer from dark energy to CDM while $Q > 0$ means the energy flow occurs from CDM to DE. In terms of the Hubble parameter, $H$, we have the following constrain or Friedmann equation \begin{eqnarray} H^2 &=& \frac{8 \pi G}{3} (\rho_r+\rho_b+\rho_{c}+ \rho_{x}).\label{friedmann1} \end{eqnarray} Thus, the dynamical evolution of the universe can be determined from eqns. (\ref{conservation1}), (\ref{conservation2}) and (\ref{friedmann1}) once the interaction rate $Q$ is specified. Introducing, $\rho_t= \rho_{c}+ \rho_{x}$, as the total energy density of the dark sector, one can express the energy densities for dark energy and dark matter respectively as \begin{eqnarray} \rho_{x} =-\left(\frac{\rho^\prime _{t}+ 3 \rho_{t}}{3 w_{x}}\right), \label{DE-density}\\ \rho_{c}=\left(\frac{\rho^\prime _{t}+ 3 (1+ w_{x})\rho_{t}}{3 w_{x}}\right), \label{DM-density} \end{eqnarray} where the prime stands for the differentiation with respect to the lapse function $N = \ln (a/a_0) = \ln a$ (Here, we set $a_0$, the present day value of the scale factor to be unity). Now, inserting (\ref{DE-density}) into (\ref{conservation2}) or (\ref{DM-density}) into (\ref{conservation1}), we find that the differential equation by the total energy density of the dark sector is given by \begin{eqnarray} \rho^{\prime\prime}_{t}+ 3 \Bigg[2+ w_{x}- \frac{w^\prime_{x}}{3w_{x}}\Bigg]\rho^\prime_{t}+ 9 \Bigg[(1+w_{x})-\frac{w^\prime_{x}}{3w_{x}} \Bigg]\rho_{t} \nonumber\\ = -\, 3 \bar{Q} w_{x},\label{ode12} \end{eqnarray} where $\bar{Q} = Q/H$. Giving the interaction $Q$ and the equation of state $w_x$, the differential equation (\ref{ode12}), if solved, can determine the evolution of each dark sector separately which can be obtained from equations (\ref{DE-density}) and (\ref{DM-density}). In this context because both dark components are assumed to interact with each other, we must define the interaction rate $Q$ in order to obtain analytical solutions. As we mentioned before different expressions have been considered in the literature for the interaction rate $Q$. The most commonly studied energy transfer between the dark sectors depends on the energy densities ($\rho_x$, $\rho_c$, $\rho_t$) or some combinations of these, multiplied by a quantity with units of the inverse of time, that could be a rate or a differentiation with respect to the time. Commonly, this rate corresponds to the Hubble rate. In particular, in the scenario of the reheating, this rate was considered as a constant \cite{Turner:1983he} and an analogous situation for the curvaton field case \cite{Malik:2002jb}. In the following we will consider that the transfer rate $Q$ is proportional to the Hubble rate, as discussed above. Thus, we have \begin{eqnarray} Q &=& - \xi (\dot{\rho}_{c}+\dot{\rho}_{x}) = - \xi \dot{\rho}_{t},\label{interaction} \end{eqnarray} where $\xi$ being the coupling parameter of the interaction characterizing the strength and direction of energy transfer between the dark sectors. We note that the negative sign before the coupling parameter in (\ref{interaction}) does not relate anything with the physics of dark matter and dark energy interactions. The typical choice of the interaction (\ref{interaction}) is actually motivared from the phenomenological ground together with the fact that the background energy conservation equations are easily solved. In this sense, other interaction rates in the literature have been studied such as, $Q \propto \rho_c$ \cite{Valiviita:2009nu}, $Q \propto \rho_x$ \cite{Clemson:2011an}, $Q \propto (\rho_c +\rho_x)$ \cite{Quartin:2008px}, $Q \propto (\rho_c \rho_x)$ \cite{Chimento:2009hj}, $Q \propto (\rho_x\rho_c)(\rho_c +\rho_x)^{-1}$ \cite{Li:2013bya}, $Q \propto \rho_x^2/\rho_c $ \cite{Yang:2017zjs}, $Q \propto \dot{\rho}_x$ \cite{Yang:2017ccc}, as some particular cases (also see \cite{Bolotin:2013jpa} for some other interaction models). We also mention that the evolution of an inhomogeneous mixture of nonrelativistic pressureless CDM, coupled to DE in which the interaction term proportional to the DE density was studied in Ref. \cite{Izquierdo:2017pnp}. Here, from the spherically symmetric Lema\^{i}tre-Tolman-Bondi metric, the authors found that the interaction $Q$ can be written as $Q\propto \dot{\rho_x}$ as used in \cite{Yang:2017ccc}. In this sense, from Eqn. (\ref{interaction}) the presence of $\dot{\rho}_t$ offers some consequences that differs it from the usual and well known interaction models. Looking at (\ref{interaction}), one can understand that for positive coupling parameter ($\xi >0$), the sign of the interaction rate could be positive, i.e., $Q > 0$ (energy flows from CDM to DE) if $\dot {\rho}_t <0$, that means the total energy density of the dark fluids should decrease with the evolution of the universe while the interaction rate could be negative, i.e., $Q <0$ (energy flows from DE to CDM) if $\dot{\rho}_t >0$ which means that the total energy density of the dark fluids increases with the evolution of the universe. Similarly, for $\xi <0$, one also encounters with the following two possibilities. The interaction rate in this case is positive (i.e., $Q> 0$) for $\dot{\rho}_t >0$ and it is negative (i.e., $Q <0$) if $\dot {\rho}_t <0$. Thus, one can see that the flow of energy between the dark sectors is not only governed by the sign of the coupling parameter, rather it also depends on the evolution of the total dark fluid. This might be considered to be an interesting property of the present interaction since in most of the usual interaction models, the direction of energy flow is actually determined from the coupling parameter only. The interaction (\ref{interaction}) was explicitly studied in \cite{G:2014mea} where a particular case, namely, the interaction between the cosmological constant with matter was considered. However, a careful survey of literature will prove the existence of this interaction in \cite{Chimento:2009hj} much earlier of \cite{G:2014mea}. Subsequently, using the same interaction, the background evolution of the universe was investigated in a generalized way where the dark energy equation of state was considered to be either constant or variable \cite{Sharov:2017iue}. However, no such perturbation analysis was performed for this interaction and this analysis is an essential issue related to the structure formation of the universe. We also observe another interesting feature in this interaction and we believe this is worth for further investigations. In order to understand this feature, we can rewrite eq.(\ref{interaction}) in a different way which can be found using the conservation equations (\ref{conservation1}) and (\ref{conservation2}) where precisely the rate corresponds to the Hubble parameter such that: \begin{eqnarray}\label{eq-int} Q &=& 3\, \xi H\, \Bigl[\rho_{c}+ (1+w_x )\rho_x \Bigr]. \end{eqnarray} One can now notice that the interaction (\ref{eq-int}) includes the dark energy equation of state $w_x$ aside from the coupling parameter. This differs from the well known interactions where only the energy densities are considered. The incorporation of the energy transfer $Q\propto\dot{\rho}_t$ and hence the inclusion of the equation of state could result in a non-interacting scenario (equivalently, $Q =0$) even if the coupling parameter is nonzero. In other words, for $w_{x} = - 1- \rho_c/\rho_x = -1 - r < -1$, where $r= \rho_c/\rho_x >0$, is the coincidence parameter, the non-interacting physics is still realized even for $\xi \neq 0$. We call it the ``\textit{zero coupling condition}''. This kind of interaction is rare in the literature which retrieves the non-interaction cosmology although there exists some non-zero coupling strength. We further notice that the dark energy equation of state in this case belongs to the phantom regime. We admit that the physics of such zero coupling condition is very strange at least at the present stage, and it surely deserves further investigations. We note that a more general interaction scenario recovering the above interaction (\ref{interaction}) (or (\ref{eq-int})) was introduced first in Ref. \cite{ Chimento:2009hj} and recently in Ref. \cite{Pan:2017ent} where the authors discussed the analytical solutions for dark matter and dark energy. Certainly, a general interaction recovering different interaction rates as special cases, includes a large number of coupling parameters. The stability of such general interaction model is surely interesting, however, in this work we focus only on the stability of the simplest interaction model that offers an analytic structure. \section{Exact Solutions} \label{sec-solutions} The differential equation (\ref{ode1}) is the main source to understand the evolution of the dark sector, provided this is exactly solved. For constant equation of state in dark energy, the differential equation (\ref{ode1}) is simplified into \begin{align} \rho^{\prime\prime}_t+ 3 \Bigl[2+ w_{x}\Bigr]\rho^\prime_t+ 9 \Bigl[1+w_{x} \Bigr]\rho_t = -\,3 \bar{Q} w_{x} = 3 \xi w_x \rho_t^{\prime},\label{ode1} \end{align} and with the use of the interaction (\ref{interaction}), the auxiliary equation becomes $m^2 + 3 \left( 2+w_{x}- \xi w_{x} \right) m + 9 (1+w_x) = 0$. Now, under the condition of $\Delta > 0$ where $\Delta$ is the discriminant of the above auxiliary equation, the exact solution of the above differential equation is, \begin{eqnarray} \rho_t&=& \rho_1 a^{m_1}+ \rho_2 a^{m_2},\label{solution-constant-EoS} \end{eqnarray} where $\rho_1$, $\rho_2$ are the constants of integration. The integration constants must be positive, otherwise, if one of them is negative then at some finite scale factor, $\rho_t \equiv 0 \Rightarrow 3 H^2 \approx \rho_b +\rho_r$, which means that the evolution of the universe is governed by the baryons and radition, this is purely unphysical from the observational data we have. Thus, we shall strictly assume that $\rho_1 >0$ and $\rho_2 >0$. The roots of the auxiliary equation, $\big(m_1, m_2\big)$ are given by \begin{eqnarray} m_1= \frac{3}{2}\left[-\left(2+w_{x}- \xi w_{x} \right)+ \sqrt{\Delta}\right],\label{m1}\\ m_2= \frac{3}{2}\left[-\left(2+w_{x}- \xi w_{x} \right)- \sqrt{\Delta}\right],\label{m2} \end{eqnarray} where $\Delta = (1 - \xi )^2 w_{x}^2- 4 \xi w_{x}$. In particular for the case in which $\mid\xi\mid\ll 1$ and as $\mid w_x\mid\sim\,\mathcal{O}(1) $, we have $\Delta \sim w_x^2>0$. In this sense, for $\Delta >0$, the exact evolution equations for dark energy and cold dark matter become \begin{eqnarray} \rho_{x} = -\left(\frac{1}{3 w_{x}}\right)\Bigg[\rho_1(m_1+ 3) (1+z)^{-m_1} \nonumber\\+ \rho_2(m_2+ 3) (1+z)^{-m_2}\Bigg],\label{DE-constantA} \end{eqnarray} \begin{eqnarray} \rho_{c}=\left(\frac{1}{3 w_{x}}\right)\Bigg[\rho_1(m_1+ 3+ 3w_{x}) (1+z)^{-m_1} \nonumber\\+ \rho_2(m_2+ 3+ 3w_{x}) (1+z)^{-m_2}\Bigg],\label{DM-constantB} \end{eqnarray} where $1+z = a_0a^{-1}= a^{-1}$ (since we have set $a_0 = 1$). Using the present day values of the cosmological parameters, the evolution equations for dark energy and dark matter can respectively be recast as \begin{widetext} \begin{eqnarray} \rho_{x} = -\left(\frac{1}{3 w_{x}}\right)\Bigg[ \left(\frac{(m_2+3+3 w_{x})\rho_{x,0}+(m_2+3)\rho_{c,0}}{m_2-m_1} \right)(m_1+ 3) (1+z)^{-m_1} \nonumber\\+ \left( \frac{(m_1+3+3 w_{x})\rho_{x,0}+(m_1+3)\rho_{c,0}}{m_1-m_2}\right) (m_2+ 3) (1+z)^{-m_2}\Bigg] \end{eqnarray} \begin{eqnarray} \rho_{c}=\left(\frac{1}{3 w_{x}}\right)\Bigg[\left(\frac{(m_2+3+3 w_{x})\rho_{x,0}+(m_2+3)\rho_{c,0}}{m_2-m_1} \right)(m_1+ 3+ 3w_{x}) (1+z)^{-m_1} \nonumber\\+ \left( \frac{(m_1+3+3 w_{x})\rho_{x,0}+(m_1+3)\rho_{c,0}}{m_1-m_2}\right) (m_2+ 3+ 3w_{x}) (1+z)^{-m_2}\Bigg]. \end{eqnarray} \end{widetext} Furthermore, in terms of the new quantities ($\rho_1$, $\rho_2$, $m_1$, $m_2$), the usual density parameters for dark energy and dark matter at current time are calculated as \begin{eqnarray} \Omega_{x,0} = -\left(\frac{1}{3 w_{x}}\right)\Bigl[\Omega_1(m_1+ 3)+ \Omega_2(m_2+ 3)\Bigr],\label{DEDP} \end{eqnarray} \begin{align} \Omega_{c,0} = \left(\frac{1}{3 w_{x}}\right)\Bigg[\Omega_1(m_1+ 3+ 3 w_{x}) + \Omega_2(m_2+ 3+ 3 w_{x})\Bigg],\label{DMDP} \end{align} with $\Omega_{x,0}+\Omega_{c,0}= \Omega_1+ \Omega_2$, where $(\Omega_1, \Omega_2) = (\rho_1/\rho_0, \rho_2/\rho_0)$ and $\rho_0 = 3H_0^2/8\pi G$. We note that solving the above equations (\ref{DEDP}) and (\ref{DMDP}) one can easily find $\Omega_1 = \Omega_1 (m_1, m_2, w_{x})$ and $\Omega_2 = \Omega_2 (m_1, m_2, w_{x})$. The explicit forms for $\Omega_1$ and $\Omega_2$ are, $\Omega_1= \frac{(m_2+3+3 w_{x})\Omega_{x,0}+(m_2+3)\Omega_{c,0}}{m_2-m_1},\, \Omega_2= \frac{(m_1+3+3 w_{x})\Omega_{x,0}+(m_1+3)\Omega_{c,0}}{m_1-m_2}$. In particular, we consider the case when dark energy is the cosmological constant, i.e., the case when $w_x = -1$. For convenience, we label IDE as the interacting dark energy scenario where DE is not the cosmological constant (i.e., $w_x \neq -1$) while by IVS we mean the interacting vacuum scenario, that means when the DE is represented by the cosmological constant itself. \section{Dynamics at Large scales: Cosmological Perturbations} \label{sec-perturbations} The study of cosmological perturbations unveils the hidden nature of the model. The large scale stability thus has been a very important issue to check the viability of any cosmological model. Indeed, for coupled dark energy one needs to check the same. Precisely, we are interested on the structure formation when the background has a coupling between the dark matter and dark energy governed by the interaction rate specified in equation (\ref{interaction}). Thus, we consider the perturbed FLRW metric with scalar mode $k$ as \cite{Mukhanov, Ma:1995ey, Malik:2008im} \begin{eqnarray}\label{perturbed-metric} ds^{2}=a^{2}(\tau )\Bigg[-(1+2\phi )d\tau ^{2}+2\partial _{i}Bd\tau dx^{i}\nonumber\\+ \Bigl((1-2\psi )\delta _{ij} +2\partial _{i}\partial _{j}E\Bigr)dx^{i}dx^{j} \Bigg], \end{eqnarray} where $\phi $, $B$, $\psi $, $E$, are the gauge-dependent scalar perturbation quantities and $\tau $ is the conformal time. Thus, using the metric (\ref{perturbed-metric}), one can find the perturbed equations \cite{Majerotto:2009np, Valiviita:2008iv, Clemson:2011an}, \begin{equation} \nabla _{\nu }T_{A}^{\mu \nu }=Q_{A}^{\mu },~~~~\sum\limits_{\mathrm{A}}{% Q_{A}^{\mu }}=0, \end{equation}% where the symbol $A$ represents the fluid (dark matter or dark energy) and $Q_{A}^{\mu }=(Q_{A}+\delta Q_{A})u^{\mu }+F_A^{\mu}$, where the quantities $Q_A$ is the energy transfer rate and $F_A^{\mu} = a^{-1} (0, \partial^{i} f_A)$ is the momentum density transfer relative to the four-velocity $u^{\mu }$, for more discussions in this direction, we refer to some earlier works \cite{Majerotto:2009np, Valiviita:2008iv, Clemson:2011an}. We consider that in the rest frame of dark matter, the momentum transfer potential is zero \cite{Valiviita:2008iv,Clemson:2011an, Koyama:2009gd}. Thus, the momentum transfer potential becomes $k^{2}f_{A}=Q_{A}(\theta -\theta _{c})$. The pressure perturbation is defined by \cite{Kodama:1985bj,Hu:1998kj,Valiviita:2008iv} \begin{equation} \delta p_{A}=c_{sA}^{2}\delta \rho_{A}+(c_{sA}^{2}-c_{aA}^{2})\rho _{A}^{\prime }(v_{A}+B), \end{equation} where $c_{aA}^2$ is the square of the physical sound speed of the fluid `$A$' in the rest frame and it is defined as $c_{aA}^{2}=p_{A}^{% \prime }/\rho _{A}^{\prime }=w_{x}+w_{x}^{\prime }/(\rho _{A}^{\prime }/\rho _{A})$. Now, introducing the density perturbation by $\delta _{A}=\delta \rho _{A}/\rho _{A}$ and considering no contribution from the anisotropic stress, i.e., $\pi _{A}=0$, the density perturbation and the velocity perturbation equations for the dark matter and dark energy fluids \cite{Majerotto:2009np, Valiviita:2008iv, Clemson:2011an} \begin{widetext} \begin{eqnarray} \delta_A^{\prime} + 3 \mathcal{H} \left(c_{sA}^2 - w_A \right) \delta_A + 9 \mathcal{H}^2 \left(1+w_A \right) \left(c_{sA}^2- c_{aA}^2 \right)\frac{\theta_A}{k^2} + \left(1+w_A \right) \theta_A -3 \left(1+w_A \right) \psi^{\prime} + \left(1+w_A \right) k^2 \left(B- E^{\prime} \right)\nonumber\\ = \frac{a}{\rho_A} \left(\delta Q_A - Q_A \delta _A \right) + \frac{a Q_A}{\rho_A} \left[\phi + 3 \mathcal{H} \left(c_{sA}^2- c_{aA}^2 \right)\frac{\theta_A}{k^2}\right],\\ \theta_A^{\prime} + \mathcal{H} \left(1-3 c_{sA}^2 \right)\theta_A - \frac{c_{sA}^2}{1+w_A} k^2 \delta_A -k^2 \phi = \frac{a}{(1+w_A)\rho_A} \Bigl[ \left(Q_A \theta -k^2 f_A \right) - \left(1+ c_{sA}^2 \right) Q_A \theta_A \Bigr], \end{eqnarray} \end{widetext} where the new quantities $c_{sA}^2$, $c_{aA}^2$, are the adiabatic and physical sound velocity for the fluid $A$, respectively, and $\theta = \theta_{\mu}^{\mu}$ is the volume expansion scalar. Let us note that to avoid from any kind of instabilities, $c_{sA}^2 \geq 0$ has been imposed. We also note that here $c_{sc}^2 =0$ since we assume cold dark matter (i.e., $w_c$ = 0). In the synchronous gauge, (i.e., $\phi =B=0$, $\psi =\eta $, and $k^{2}E=-h/2-3\eta $), the density and the velocity perturbations for the dark fluids follow \begin{widetext} \begin{eqnarray} \delta _{x}^{\prime } &=&-(1+w_{x})\left( \theta _{x}+\frac{h^{\prime }}{2}% \right) -3\mathcal{H}(c_{s,x}^{2}-w_{x})\left[ \delta _{x}+3\mathcal{H}% (1+w_{x})\frac{\theta _{x}}{k^{2}}\right] -3\mathcal{H}w_{x}^{\prime }\frac{% \theta _{x}}{k^{2}} \notag \\ &+&\frac{aQ}{\rho _{x}}\left[ -\delta _{x}+\frac{\delta Q}{Q}+3\mathcal{H}% (c_{s,x}^{2}-w_{x})\frac{\theta _{x}}{k^{2}}\right] , \\ \theta _{x}^{\prime } &=&-\mathcal{H}(1-3c_{s,x}^{2})\theta _{x}+\frac{% c_{s,x}^{2}}{(1+w_{x})}k^{2}\delta _{x}+\frac{aQ}{\rho _{x}}\left[ \frac{% \theta _{c}-(1+c_{s,x}^{2})\theta _{x}}{1+w_{x}}\right] , \label{theta-x}\\ \delta _{c}^{\prime } &=&-\left( \theta _{c}+\frac{h^{\prime }}{2}\right) +% \frac{aQ}{\rho _{c}}\left( \delta _{c}-\frac{\delta Q}{Q}\right) , \label{eqn:delta-c}\\ \theta _{c}^{\prime } &=&-\mathcal{H}\theta _{c}, \end{eqnarray}% \end{widetext} where the term $\delta Q/Q$ includes the perturbation term for the Hubble expansion rate $\delta H$. Now inserting the interaction rate (\ref{interaction}) into the above equations, one can write down the explicit perturbation equations as \begin{widetext} \begin{eqnarray} \delta'_x &=&-(1+w_x)\left(\theta_x+\frac{h'}{2}\right) -3\mathcal{H}(c^2_{sx}-w_x)\left[\delta_x+3\mathcal{H}(1+w_x)\frac{\theta_x}{k^2}\right] \nonumber \\ &+&3\mathcal{H}\xi\left[\frac{\rho_c}{\rho_x}+(1+w_x)\right]\left[\frac{\rho_c(\delta_c-\delta_x)}{\rho_c+(1+w_x)\rho_x}+\frac{\theta+h'/2}{3\mathcal{H}}+3\mathcal{H}(c^2_{sx}-w_x)\frac{\theta_x}{k^2}\right], \\ \theta'_x &=&-\mathcal{H}(1-3c^2_{sx})\theta_x+\frac{c^2_{sx}}{(1+w_x)}k^2\delta_x +3\mathcal{H}\xi\left[\frac{\rho_c}{\rho_x(1+w_x)}+1\right]\left[\theta_c-(1+c^2_{sx})\theta_x\right], \\ \delta'_c &=&-\left(\theta_c+\frac{h'}{2}\right) +3\mathcal{H}\xi\left[1+(1+w_x)\frac{\rho_x}{\rho_c}\right]\left[\frac{(1+w_x)\rho_x(\delta_c-\delta_x)}{\rho_c+(1+w_x)\rho_x}-\frac{\theta+h'/2}{3\mathcal{H}}\right], \label{delta_c}\\ \theta'_c &=&-\mathcal{H}\theta_c~. \label{eq:perturbation} \end{eqnarray} \end{widetext} Let us now focus on the growth-rate of matter perturbations for the prescribed interaction in this work. Here, we neglect the clustering of dark energy with the assumption of $c_{sx}^2 = 1$. However, depending on the strength of the interaction, the dark energy perturbations could be an important issue, but on the sub-Hubble scale, such perturbation is not important provided that the sound speed of dark energy perturbations is assumed to be positive \cite{Koyama:2009gd}. The evolution equation for $\delta_c$ can be written as \begin{widetext} \begin{eqnarray} &&\delta ''_c+\left\{1-3\xi\left[1+(1+w_x)\frac{\rho_x}{\rho_c}\right]\right\}\mathcal{H}\delta '_c =4\pi Ga^2\rho_b\delta_b + \nonumber \\ &&4\pi Ga^2\rho_c\delta_c \left\{1+2\xi\frac{\rho_{t}}{\rho_c}\left[1+(1+w_x)\frac{\rho_x}{\rho_c}\right] \left[ \frac{\mathcal{H}'}{\mathcal{H}^2}+1-3w_x+3\xi\left(1+\frac{\rho_x}{\rho_c}\right) +3\xi(1+w_x)\frac{\rho_x}{\rho_c}\left(1+\frac{\rho_x}{\rho_c}\right) \right] \right\}, \label{eq:deltacprime2} \end{eqnarray} \end{widetext} where $\mathcal{H} = a H$, is the conformal Hubble parameter and $H$ can be found from (\ref{friedmann1}). It is evident that putting $\xi =0$ into (\ref{eq:deltacprime2}), one gets back the evolution equation for $\delta_c$ for the non-interacting cosmologies, i.e. $ \delta_m ''+\mathcal{H} \delta_m ' = 4 \pi G \rho_m \delta_m$ (Note that, $\rho_m = \rho_c +\rho_b$). Furthermore, one can also measure the deviations in the expansion history through \begin{eqnarray} \frac{\mathcal{H}_{eff}}{\mathcal{H}}=1-3\xi\left[1+(1+w_x)\frac{\rho_x}{\rho_c}\right], \label{eq:Heff} \end{eqnarray} and also in the gravitational constant $G$ as \begin{align} \frac{G_{eff}}{G}=1+2\xi \left( \frac{\rho_{t}}{\rho_c} \right) \left[1+(1+w_x)\frac{\rho_x}{\rho_c}\right] \Bigg[ \frac{\mathcal{H}'}{\mathcal{H}^2}+1-3w_x \nonumber\\+3\xi\left(1+\frac{\rho_x}{\rho_c}\right) +3\xi(1+w_x)\frac{\rho_x}{\rho_c}\left(1+\frac{\rho_x}{\rho_c}\right) \Bigg]. \label{eq:Geff} \end{align} \begin{figure} \includegraphics[width=0.35\textwidth]{CMBpower.pdf} \includegraphics[width=0.35\textwidth]{CMBpower_vs.pdf} \caption{Color Online $-$ The behaviour of the IDE scenario in the large scales has been presented for different measures of the coupling parameter $\xi$. \texttt{Left Panel:} Here we display the evolutions of the CMB TT spectra for different values of the coupling parameter representing its strength. We see that with the increase in the magnitude of the coupling parameter, the interaction scenario effectively deviates from the usual non-interacting $\Lambda$CDM cosmology. We note that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM are almost indistinguishable from one another. \texttt{Right Panel:} Here, the relative deviation in the CMB TT spectra in compared to the non-interacting $\Lambda$CDM model has been shown. This confirms the observation as found in the left panel of this figure. In this figure, we observe that a very small difference between the curves presenting $\xi =-0.0001$ and $\Lambda$CDM exists but that is very hard to detect. } \label{fig:CMB-ide} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{Mpower.pdf} \includegraphics[width=0.35\textwidth]{Mpower_vs.pdf} \caption{Color Online $-$ The behaviour of the IDE scenario in the large scales has been presented for different measures of the coupling parameter. \texttt{Left Panel:} We show the evolutions of the matter power spectra for different coupling strengths of the interaction model. We find that with the increase of the coupling strength, the interaction scenario has a deviation from the usual non-interacting scenario (i.e., $\xi =0$) $\Lambda$CDM. Let us note that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM are almost indistinguishable from one another. \texttt{Right Panel:} The relative deviation in the matter power spectra in compared to the non-interacting $\Lambda$CDM model has been shown and we find similar observation as realized from its left panel. In this figure, we observe that a very small difference between the curves presenting $\xi =-0.0001$ and $\Lambda$CDM exists, and it is clearly visible. } \label{fig:Mpower-ide} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{Heff_v5.pdf} \includegraphics[width=0.35\textwidth]{Geff_v5.pdf} \caption{Color Online $-$ \texttt{Left Panel:} The dynamical evolution of the quantity $\mathcal{H}_{\text{eff}}/\mathcal{H}$ has been depicted in presence of different coupling parameters of the interaction rate (\ref{interaction}). The curves from upper to lower respectively stand for $\Lambda$CDM ($\xi =0$) model, $\xi = -0.0001, -0.01, -0.03, -0.05$. We notice that the curves presenting non-interacting $\Lambda$CDM and $\xi= -0.0001$ are practically indistinguishable from one another. \texttt{Right Panel:} The evolution of the quantity $G_{\text{eff}}/G$ has been shown for different coupling parameters of the interaction rate (\ref{interaction}). The curves from lower to upper levels respectively stand for $\Lambda$CDM ($\xi =0$) model, $\xi = -0.0001, -0.01, -0.03, -0.05$. Similar to the left panel, here we also notice that the curves presenting $\Lambda$CDM and $\xi= -0.0001$ are practically indistinguishable from each other. From both the panels, we arrive at a common conclusion which states that, as $\xi$ increases (considering its magnitude), the model starts deviating from the non-interacting $\Lambda$CDM cosmology and the coupling parameter $\xi =-0.05$ can be safely excluded from the consideration. } \label{fig-Heff-Geff} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{fc_v5.pdf} \caption{Color Online $-$ The evolution of growth rate for the cold dark matter in presence of the interaction rate (\ref{interaction}) has been shown for different values of the coupling strength. The curves from upper to lower respectively stand for the non-interacting $\Lambda$CDM model (where $\xi=0$) and with other coupling parameters $\xi= -0.0001, -0.01, -0.03, -0.05$. Here too, the curves for $\Lambda$CDM and $\xi= -0.0001$ are indistinguishable from one another. From the figure we observe that as long as the strength or magnitude of the coupling parameter increases, the growth rate for the cold dark matter sector significantly deviates from $\xi = 0$ (no-interaction, $\Lambda$CDM). The physical scenario indicates that with the increase of the coupling strength, the growth-rate for the cold dark matter decreases with the evolution of the universe. } \label{fig-fc} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{CMBpower_ILCDM.pdf} \includegraphics[width=0.35\textwidth]{CMBpower_ILCDM_vs.pdf} \caption{Color Online $-$ The behaviour of the interacting vacuum scenario (IVS) in the large scales has been presented for different measures of the coupling parameter $\xi$. \texttt{Left Panel:} In this plot, we show the evolutions of the CMB TT spectra for different coupling strengths of the interaction model. One can clearly see that as the magnitude or strength of the coupling parameter increases, te deviation of the interaction model becomes prominent from the non-interacting $\Lambda$CDM cosmology. We note that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM cannot be differentiated from one another. \texttt{Right Panel:} The relative deviation in the CMB TT spectra in compared to the non-interacting $\Lambda$CDM model has been shown here. From this plot, one can easily conclude that the increament in $\xi$ results in significant deviation from the corresponding non-interacting scenario. Here, we observe that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM overlap with each other.} \label{fig:CMB-ivs} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{Mpower_ILCDM.pdf} \includegraphics[width=0.35\textwidth]{Mpower_ILCDM_vs.pdf} \caption{Color Online $-$ The behaviour of the interacting vacuum scenario (IVS) in the large scales has been displayed for different measures of the coupling parameter $\xi$. \texttt{Left Panel:} We show the evolutions of the matter power spectra for different coupling strengths of the interaction model which shows that with the increase of the coupling parameter, the interaction model results in significant deviation from the non-interacting $\Lambda$CDM cosmology. We notice that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM cannot be differentiated from one another. \texttt{Right Panel:} The relative deviation in the matter power spectra in compared to the non-interacting $\Lambda$CDM model has been shown with similar conclusions as observed from the left panel of this figure. From this plot we see that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM cannot be distinguished from one another although a very minimal difference between them is present. } \label{fig:Mpower-ivs} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{Heff_iLCDM.pdf} \includegraphics[width=0.35\textwidth]{Geff_iLCDM.pdf} \caption{Color Online $-$ \texttt{Left Panel:} The dynamical evolution of the modified expansion history $\mathcal{H}_{\text{eff}}$ has been depicted in presence of different couplings of the interaction rate (\ref{interaction}) for the interacting vacuum scenario. The curves from upper to lower respectively stand for the non-interacting $\Lambda$CDM model ($\xi=0$) and for other coupling parameters, $\xi= -0.0001, -0.01, -0.03, -0.05$. \texttt{Right Panel:} The evolution of the quantity $G_{\text{eff}}/G$ has been shown for different coupling parameters for the interacting vacuum scenario. The curves from lower to upper levels respectively stand for the non-interacting $\Lambda$CDM model ($\xi=0$) and for other coupling parameters, $\xi= -0.0001, -0.01, -0.03, -0.05$. From both the panels, we arrive at a common conclusion which states that, as $\xi$ increases, the model starts deviating from the non-interacting $\Lambda$CDM cosmology. In both left and right panels, one can see that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM cannot be differentiated from one another} \label{fig-Heff-Geff-ivs} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{fc_iLCDM.pdf} \caption{Color Online $-$ For the interacting vacuum scenario we display the evolution of growth rate for the cold dark matter for different coupling strengths. The curves from upper to lower respectively stand for non-interacting $\Lambda$CDM model ($\xi=0$) and for other coupling parameters, $\xi= -0.0001, -0.01, -0.03, -0.05$. However, we observe that if the coupling strength increases, then the growth-rate for the cold dark matter decreases with the evolution of the universe. Similar to previous observations, here too we see that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM cannot be distinguished from one another. } \label{fig-fc-ivs} \end{figure} One can see that $\xi =0$ in both (\ref{eq:Heff}) and (\ref{eq:Geff}) recovers the standard evolutions of the corresponding quantities where no interaction is present. Further, we consider the growth rate of cold dark matter defined by $f_c \equiv \frac{d}{d\ln a}(\ln \delta_c) $. One may notice that the presence of interaction into the dark sector automatically modifies the Euler equation, that means, the dark matter may not follow the geodesics \cite{Koyama:2009gd}. Thus, in presence of interaction, the above quantities give a qualitative nature of the interaction rate and its behaviour in compared to the non-interacting cosmologies quantified by $\xi =0$. Let us first focus on the dynamics of the IDE model in the large scale of the universe. The behaviour of this model has been displayed through the evolution of the CMB TT spectra and the matter power spectra. In the left panel of Fig. \ref{fig:CMB-ide}, we show the behaviour of IDE model through the CMB TT spectra which shows that as long as the coupling strength of the interaction increases, the model is significantly deviates from the non-interacting $\Lambda$CDM model. The deviation is also clear from the relative deviation $\Delta C_{l}^{TT}/C_{l}^{TT}$ (here $\Delta C_{l}^{TT}$ measures the deviation of the model from $\Lambda$CDM), one can see that the nonzero deviation from $\Lambda$CDM is prominent for all the coupling parameters considered in the analysis which is evident in the low multipoles $l$. On the other hand, for large coupling strength, the model significantly deviates from $\Lambda$CDM which is clear from both the left and right panels of Fig. \ref{fig:CMB-ide}. Similarly, for different coupling strengths of the interaction rate, we have shown the evolution of the matter power spectra in the left panel of Fig. \ref{fig:Mpower-ide}. Again we see that for a large coupling strength, the model significantly deviates from the $\Lambda$CDM cosmology and this deviation is prominent for large $k$, while for very small coupling, the interaction model is very close to $\Lambda$CDM. However, the deviation from the $\Lambda$CDM, even for a very small but nonzero coupling strength, still exists which is clear from the relative deviation shown in the right panel of Fig. \ref{fig:Mpower-ide}. The analyses from both CMB and matter power spectra as well as from the corresponding relative deviations, one may argue that the coupling strength $\xi =-0.05$ is very high and can be excluded from the picture. Furthermore, we depict the modified expansion history $\mathcal{H}_{\text{eff}}$ (eqn. (\ref{eq:Heff})) and the effective gravitational constant (eqn. (\ref{eq:Geff})) respectively in the left and right panels of Fig. \ref{fig-Heff-Geff}. Both the plots in Fig. \ref{fig-Heff-Geff} show that indeed for large coupling strength, the modified expansion history and the effective gravitational constant offer significant changes from that of the non-interacting $\Lambda$CDM cosmology. Finally, from the growth rate of cold dark matter, $f_c$, displayed in Fig. \ref{fig-fc} we observe similar trend, that means, here too, large coupling strength implies the deviation of the model from non-interacting $\Lambda$CDM cosmology. We conclude that for large coupling strength, the growth rate of cold dark matter significantly decreases. The dynamics of this interaction scenario in the large scale of the universe has also been investigated. In the left panel of Fig. \ref{fig:CMB-ivs} we have shown the variation in the CMB TT spectra for different strengths of the coupling parameter, $\xi$ and compared them with the non-interacting $\Lambda$CDM scenario. We see that as $\xi$ increases its strength, a significant changes in the CMB TT spectra is observed with respect to the non-interacting scenario while for lower coupling strengths, the deviation from the non-interacting $\Lambda$CDM model becomes low. However, since the observational data predict a very small coupling parameter allowing its zero value in the 68.3\% confidence level, thus, it is expected that a small deviation from the $\Lambda$CDM model should be present. In order to measure such small deviation, we measure the relative deviation of the interacting model with different coupling strengths with respect to the $\Lambda$CDM model, and this is shown in the right panel of Fig. \ref{fig:CMB-ivs}. This plot (right panel of Fig. \ref{fig:CMB-ivs}) practically tells that $\xi \neq 0$, however small it is, the deviation from $\Lambda$CDM should exist, although it is also true that such deviation is very very small which is not much significant. A similar pattern is found when the large scale dynamics is described in terms of the matter power spectra shown in Fig. \ref{fig:Mpower-ivs}. The left panel of the Fig. \ref{fig:Mpower-ivs} shows a qualitative changes in the matter power spectra for different coupling strengths while the right panel tells us how much the model with different coupling strengths are far from $\Lambda$CDM. Overall, from the analyses for IVS one can realize that the coupling strength $\xi =-0.05$ presents a significant deviation from the $\Lambda$CDM cosmology and which according to the present observational data is not reliable, and hence this strong mangitude of the coupling parameter should be avoived. \begin{table} \begin{center} \begin{tabular}{c\|c\|c} Parameter & Prior (IDE) & Prior (IVS) \\ \hline $\Omega_{b} h^2$ & $[0.005,0.1]$ & $[0.005,0.1]$\\ $\tau$ & $[0.01,0.8]$ & $[0.01,0.8]$\\ $n_s$ & $[0.5, 1.5]$ & $[0.5, 1.5]$\\ $\log[10^{10}A_{s}]$ & $[2.4,4]$ & $[2.4,4]$\\ $100\theta_{MC}$ & $[0.5,10]$ & $[0.5,10]$ \\ $w_x$ & $(-3, -1)$ & $-$ \\ $\xi$ & $[-1, 0]$ & $[-1, 0]$ \end{tabular} \end{center} \caption{The table summarizes the flat priors on the cosmological parameters for the interacting scenario with $w_x < -1$ (IDE) and interacting vacuum scenario (IVS). } \label{priors-I} \end{table} \section{Data and Results} \label{sec-results} In this section we first describe the astronomical data with the statistical technique to constrain the present interacting scenarios and the results of the analyses. We include the following sets of astronomical data. \begin{itemize} \item {\it Cosmic microwave background (CMB) observations:} We use CMB data from the Planck's 2015 observations \cite{Adam:2015rua, Aghanim:2015xee}. Precisely, we use the likelihoods $C^{TT}_l$, $C^{EE}_l$, $C^{TE}_l$ in addition to low$-l$ polarization data (i.e. Planck TT, TE, EE+ low TEB). \item {\it Baryon acoustic oscillations (BAO) data:} For BAO data, the estimated ratio $r_s/D_V$ as a `standard ruler' has been used in which $r_s$ is the co-moving sound horizon at the baryon drag epoch and $D_V$ is the effective distance given by $D_V(z)=\left[(1+z)^2D_A(a)^2\frac{z}{H(z)}\right]^{1/3}$. Here $D_A$ is the angular diameter distance. In this analysis we use four data points from different astronomical surveys, namely, from the 6dF Galaxy Survey (6dFGS) redshift measurement at $z_{\emph{\emph{eff}}}=0.106$ \cite{Beutler:2011hx}, the Main Galaxy Sample of Data Release 7 of Sloan Digital Sky Survey (SDSS-MGS)measurement at $z_{\emph{\emph{eff}}}=0.15$ \cite{Ross:2014qpa}, and the CMASS and LOWZ samples from the latest Data Release 12 (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) measurements at $z_{\mathrm{eff}}=0.57$ \cite{Gil-Marin:2015nqa} and $z_{\mathrm{eff}% }=0.32$ \cite{Gil-Marin:2015nqa}. \item {\it Redshift space distortion (RSD) data:} We use the RSD data from two observational surveys namely CMASS sample \cite{Gil-Marin:2016wya} and the LOWZ sample \cite{Gil-Marin:2016wya}. The effective redshifts for the CMASS and LOWZ samples are respectvely at $z_{\mathrm{eff}}=0.57$ and and $z_{\mathrm{eff}}=0.32$. We note that when these two RSD data points are considered in the analysis, then DR12 of BOSS from BAO will not be considered. \item {\it $H_0$ from Hubble Space Telescope (HST):} The local Hubble constant measured from the HST by Riess et al. \cite{Riess:2016jrr} that yields $H_0= 73.02 \pm 1.79$ km/s/Mpc with 2.4\% precision. \item {\it Joint light curve analysis (JLA):} This is the Supernovae Type Ia sample that contains 740 data points spread in the redshift interval $z \in [0.01, 1.30]$ \cite{Betoule:2014frx}. This low redshifts sample is the first indication for an accelerating universe. \item {\it Hubble parameter measurements from cosmic chronometers (CC):} We choose the cosmic chronometers to measure the Hubble parameter values at different redshifts. The cosmic chronometers are basically the galaxies that are most old and huge massive and the technique that we apply to measure the Hubble parameter values, is the differential age evolution of the galaxies. For a detailed description we refer to \cite{Moresco:2016mzx} and the references cited therein for more information about their implementation. In this work we consider thirty Hubble parameter values spread in $z \in (0, 2)$ and they are found in \cite{Moresco:2016mzx}. \item {\it Weak lensing (WL):} The weak gravitational lensing data from the Canada$-$France$-$Hawaii Telescope Lensing Survey (CFHTLenS) \cite{Heymans:2013fya,Asgari:2016xuw}. \end{itemize} In order to extract the observational constraints of the interacting scenarios, we use the publicly available Monte Carlo Markov Chain (MCMC) package \texttt{cosmomc} \cite{Lewis:2002ah, Lewis:1999bs} equipped with a convergence diagnostic followed by the Gelman and Rubin statistics \cite{Gelman-Rubin}. The parameters space for interacting dark energy and interacting vacuum scenarios respectively are \begin{align} \mathcal{P}_1 \equiv\Bigl\{\Omega_bh^2, \Omega_{c}h^2, 100 \theta_{MC}, \tau, w_x, \xi, n_s, log[10^{10}A_S]\Bigr\}, \label{eq:parameter_space1} \end{align} and \begin{align} \mathcal{P}_2 \equiv\Bigl\{\Omega_bh^2, \Omega_{c}h^2, 100 \theta_{MC}, \tau, \xi, n_s, log[10^{10}A_S]\Bigr\}, \label{eq:parameter_space2} \end{align} where in both (\ref{eq:parameter_space1}) and (\ref{eq:parameter_space2}), $\Omega_bh^2$, $\Omega_{c}h^2$, are respectively the baryons density and the cold dark matter density; $100 \theta_{MC}$, $\tau$, $n_s$, $A_S$, are respectively the ratio of sound horizon to the angular diameter distance, optical depth, scalar spectral index, and the amplitude of the initial power spectrum. The parameter $\xi$ is the coupling strength while $\mathcal{P}_1$ has one extra parameter $w_x$. Thus, we see that the interacting dark energy has eight free parameters and the interacting vacuum scenario has seven free parameters. During the MCMC analysis, we generally fix some priors on the model parameters. In Table \ref{priors-I} we show the priors fixed on various cosmological parameters while constraining both the interacting models, namely, IDE and IVS. The priors mainly on $w_x$ and $\xi$ play an essential role in the analysis because the early time instabilities associated with the model, if any, significantly depend on the parameters space of $(w_x, \xi)$. Now, if we closely look at the model (\ref{eq-int}), one can see that the interaction model (\ref{eq-int}) actually incorporates two separate interaction rates, namely, $Q \propto \rho_c$ and $Q \propto \rho_x$, hence, the stability of the entire model (\ref{eq-int}) depends on the region where both of them do not lead any early time instabilities. However, one can note that for some specific regions of the parameters space of $w_x$ and $\xi$, early time instabilities can be avoided \cite{Gavela:2009cy} while the entire region for $\xi$ allowing both positive and negative values may not be always suitable to avoid such instability. This actually depends on the interaction model. Thus, motivated by this fact, we divided several regions of the model parameters $w_x$ and $\xi$ to test the stability of the IDE scenario, for instance, ``$w_x$ free and $\xi$ free''; ``$w_x>-1$ and $\xi$ free''; ``$w_x>-1$ and $\xi \geq 0$''; ``$w_x>-1$, $\xi \leq 0$''; ``$w_x<-1$ and $\xi$ free''; finally with ``$w_x<-1$ and $\xi \leq 0$''. We found that only for the region ``$w_x<-1$, $\xi \leq 0$'', the model does not lead to any early time instabilities while for the other regions the model meets with early time instabilities. Quite interestingly, this allowed region (i.e., $w_x < -1$) has an additional feature. It has been found that in presence of a non-gravitational interaction in the dark sectors, when the dark energy equation of state is allowed to cross the cosmological constant boundary, that means for $w_x< -1$, the tension on $H_0$ can be alleviated \cite{Kumar:2017dnp, DiValentino:2017iww}. In this context we would like to add that some previous studies have found that for the non-interacting cosmologies with constant dark energy equation-of-state ($w_x$), the region $w_x> -1$ is also allowed and even preferred by some observational data \cite{Aubourg:2014yra,Hee:2016nho,Zhao:2017cud}. Now, following the similar trend, for the interacting vacuum scenario, we performed similar analyses with different priors on $\xi$, namely, $\xi \geq 0$, $\xi \leq 0$ and $\xi$ to be free. We found that for $\xi \leq 0$, early time instabilities do not appear. \begingroup \squeezetable \begin{center} \begin{table} \begin{tabular}{cccccccccccc} \hline\hline Parameters & CMB & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{HST} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{RSD} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{RSD+HST} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+ \mbox{RSD+HST}\\+\text{JLA+CC} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+ \mbox{RSD+HST}\\+\text{JLA+CC}\\+\text{WL} \end{array}$\\ \hline $\Omega_c h^2$ & $ 0.1260_{- 0.0059}^{+ 0.0035}$ &$ 0.1204_{- 0.0015}^{+ 0.0017}$ & $ 0.1205_{- 0.0013}^{+ 0.0014}$ & $ 0.1201_{- 0.0014}^{+ 0.0013}$ & $ 0.1197_{- 0.0013}^{+ 0.0012}$ & $ 0.1191_{- 0.0011}^{+ 0.0011}$\\ $\Omega_b h^2$ & $ 0.0223_{- 0.0002}^{+ 0.0002}$ &$ 0.02231_{- 0.0002}^{+ 0.0002}$ & $ 0.0223_{- 0.0002}^{+ 0.0002}$ & $ 0.0223_{- 0.0002}^{+ 0.0002}$ & $ 0.0223_{- 0.0002}^{+ 0.0002}$ & $ 0.0223_{- 0.0001}^{+ 0.0001}$\\ $100\theta_{MC}$ & $ 1.0310_{- 0.0005}^{+ 0.0007}$ &$ 1.0405_{- 0.0005}^{+ 0.0006}$ & $ 1.0405_{- 0.0003}^{+ 0.0003}$ & $ 1.0405_{- 0.0003}^{+ 0.0003}$ & $ 1.0406_{- 0.0004}^{+ 0.0003}$ & $ 1.0406_{- 0.0003}^{+ 0.0003}$ \\ $\tau$ & $ 0.0711_{- 0.0187}^{+ 0.0184}$ & $ 0.0811_{- 0.0204}^{+ 0.0214}$ & $ 0.0687_{- 0.0163}^{+ 0.0167}$ & $ 0.0621_{- 0.0160}^{+ 0.0171}$ & $ 0.0820_{- 0.0160}^{+ 0.0164}$ & $ 0.0636_{- 0.0159}^{+ 0.0163}$\\ $n_s$ & $ 0.9678_{- 0.0056}^{+ 0.0057}$ & $0.9739_{- 0.0051}^{+ 0.0051}$ & $ 0.9728_{- 0.0038}^{+ 0.0039}$ & $ 0.9730_{- 0.0041}^{+ 0.0041}$ & $ 0.9746_{- 0.0035}^{+ 0.0037}$ & $ 0.9751_{- 0.0036}^{+ 0.0037}$\\ ${\rm{ln}}(10^{10} A_s)$ & $ 3.0824_{- 0.0362}^{+ 0.0356}$ & $3.1032_{- 0.0386}^{+ 0.0418}$ & $ 3.0770_{- 0.0316}^{+ 0.0349}$ & $ 3.0642_{- 0.0309}^{+ 0.0338}$ & $ 3.1043_{- 0.0314}^{+ 0.0332}$ & $ 3.0658_{- 0.0308}^{+ 0.0318}$\\ $\Omega_{m0}$ & $ 0.3523_{- 0.0693}^{+ 0.0394}$ &$ 0.2865_{- 0.0092}^{+ 0.0092}$ & $ 0.3105_{- 0.0098}^{+ 0.0100}$ & $ 0.2990_{- 0.0091}^{+ 0.0083}$ & $ 0.2942_{- 0.0074}^{+ 0.0075}$ & $ 0.2994_{- 0.0073}^{+ 0.0073}$\\ $\sigma_8$ & $ 0.8221_{- 0.0350}^{+ 0.0392}$ &$ 0.8635_{- 0.0192}^{+ 0.0192}$ & $ 0.8279_{- 0.0136}^{+ 0.0137}$ & $ 0.8311_{- 0.0143}^{+ 0.0146}$ & $ 0.8516_{- 0.0160}^{+ 0.0162}$ & $ 0.8250_{- 0.0147}^{+ 0.0132}$\\ $H_0$ & $ 65.5213_{- 3.9333}^{+ 4.5145}$ & $70.7651_{- 1.1482}^{+ 1.1132}$ & $ 67.9685_{- 1.0243}^{+ 0.8324}$ & $ 69.1889_{- 0.8904}^{+ 0.8698}$ & $ 69.6402_{- 0.8523}^{+ 0.8265}$ & $ 68.8940_{- 0.8176}^{+ 0.6849}$\\ $w_x$ & $ -1.1093_{- 0.0509}^{+ 0.0828}$ &$ -1.1511_{- 0.0586}^{+ 0.0529}$ & $ -1.0603_{- 0.0201}^{+ 0.0427}$ & $ -1.0940_{- 0.0394}^{+ 0.0407}$ & $ -1.0960_{- 0.0365}^{+ 0.0375}$ & $ -1.0608_{- 0.0238}^{+ 0.0289}$\\ $\xi$ & $> -0.004884$ & $>-0.001285$ & $> -0.001384$ & $> -0.001278$ & $> -0.000959$ & $> -0.000935$\\ \hline\hline \end{tabular} \caption{The table summarizes the observational constraints on the cosmological parameters of IDE at 68.3\% confidence-level for different combinations of the observational data. For the coupling parameter, we only report their values at 95.4\% lower confidence-level.}\label{tab:results-I} \end{table} \end{center} \endgroup \begin{figure} \includegraphics[width=0.7\textwidth]{contour_vs.pdf} \caption{Color Online $-$ Contour plots for different combinations of the cosmological parameters in the 68.3\% and 95.4\% confidence levels have been displayed for distinct observational combinations. Additionally, we also show the one-dimensional posterior distributions for those parameters at the extreme right corners of each row. From the two-dimensional contour plots one can notice that the addition of any external data to CMB decreases the error bars of the cosmological parameters in a significant way. } \label{fig-contour1} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{2d_xiH0.pdf} \includegraphics[width=0.35\textwidth]{2d_xiwx.pdf} \includegraphics[width=0.35\textwidth]{2d_xiom.pdf} \caption{Color Online $-$ The dependence of the coupling strength on some important cosmological parameters has been shown in the ($\xi, H_0$), $(\xi, w_x)$ and ($\xi, \Omega_{m0}$) planes at 68.3\% and 95.4\% confidence levels using different combinations of the observational data displayed above. We observe that the correlations between the parameters shown in the plots exist. \textit{Upper left panel:} We see that the CMB data allow a nonzero interaction in the dark sector for lower values of the Hubble parameter, however, from the combined analysis no conclusive statement can be made on the dependence of $H_0$ and the coupling strength $\xi$. \textit{Upper right panel:} The plot shows that the allowance of $w_x < -1$ is an indication of an interaction in the dark sector. \textit{Lower panel:} One can notice that only CMB data indicate that coupling strength has a direct dependence on the density parameter $\Omega_{m0}$ while the combined analysis cannot make any deciding relation between the parameters involved. Thus, in order to clarify such issues we have shown three-dimensional scattered plots in Fig. \ref{fig-scattered-ide} with detailed discussions. } \label{fig-xi-H0-Om} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{2d_wxH0.pdf} \includegraphics[width=0.354\textwidth]{2d_wxom.pdf} \caption{Color Online $-$ 68.3\% and 95.4\% confidence-level contour plots in the two dimensional planes ($w_x, H_0$), ($\Omega_{m0}, w_x$) have been displayed for different combined analyses. \textit{Left panel:} One may notice that for lower values of the Hubble parameter, the dark energy equation of state increases, that means $\|w_x\|$ decreases. \textit{Right panel:} Here we notice that as $\Omega_{m0}$ decreases, the dark energy equation of state moves toward more phantom region. } \label{fig-wx-H0-Om} \end{figure} \begin{figure} \includegraphics[width=0.35\textwidth]{2d_s8xi.pdf} \includegraphics[width=0.33\textwidth]{2d_s8wx.pdf} \includegraphics[width=0.34\textwidth]{2d_s8H0.pdf} \caption{Color Online $-$ 68.3\% and 95.4\% confidence-level contour plots in the two dimensional ($\sigma_8, w_x$), $(\sigma_8, H_0)$ and $(\sigma_8, \xi)$ planes have been shown. \textit{Upper Left Panel:} One may notice that if the strength of the interaction increases, then $\sigma_8$ takes lower values. \textit{Upper Right Panel:} It is clearly seen that as long as the dark energy equation of state moves toward a more phantom region, the parameter $\sigma_8$ takes bigger values. \textit{Lower Panel:} The larger values of the Hubble parameter allows larger values of $\sigma_8$. } \label{fig-sigma8} \end{figure} \begin{figure} \includegraphics[width=0.325\textwidth]{3d_wxomH0_CMB+BAO+HST.pdf} \includegraphics[width=0.325\textwidth]{3d_xiomH0_CMB+BAO+HST.pdf} \includegraphics[width=0.325\textwidth]{3d_xiwxH0_CMB+BAO+HST.pdf} \includegraphics[width=0.325\textwidth]{3d_wxomH0_CMB+BAO+RSD.pdf} \includegraphics[width=0.325\textwidth]{3d_xiomH0_CMB+BAO+RSD.pdf} \includegraphics[width=0.325\textwidth]{3d_xiwxH0_CMB+BAO+RSD.pdf} \includegraphics[width=0.325\textwidth]{3d_wxomH0_CMB+BAO+RSD+HST.pdf} \includegraphics[width=0.325\textwidth]{3d_xiomH0_CMB+BAO+RSD+HST.pdf} \includegraphics[width=0.325\textwidth]{3d_xiwxH0_CMB+BAO+RSD+HST.pdf} \includegraphics[width=0.325\textwidth]{3d_wxomH0_CMB+BAO+RSD+HST+JLA+CC.pdf} \includegraphics[width=0.325\textwidth]{3d_xiomH0_CMB+BAO+RSD+HST+JLA+CC.pdf} \includegraphics[width=0.325\textwidth]{3d_xiwxH0_CMB+BAO+RSD+HST+JLA+CC.pdf} \includegraphics[width=0.325\textwidth]{3d_wxomH0_CMB+BAO+RSD+HST+JLA+CC+WL.pdf} \includegraphics[width=0.325\textwidth]{3d_xiomH0_CMB+BAO+RSD+HST+JLA+CC+WL.pdf} \includegraphics[width=0.325\textwidth]{3d_xiwxH0_CMB+BAO+RSD+HST+JLA+CC+WL.pdf} \caption{Color Online $-$ In each panel we show the three dimensional scattered plots colored by the $H_0$ values of the markov chain monte carlo (mcmc) chains of the corresponding combined analysis. The combined analysis from the top to the bottom panels are respectively (i) CMB+BAO+HST, (ii) CMB+BAO+RSD, (iii) CMB+BAO+RSD+HST, (iv) CMB+BAO+RSD+HST+JLA+CC, and (v) CMB+BAO+RSD+HST+JLA+CC+WL. \texttt{First column:} From the mcmc chains of all combined analyses, one may notice that as the values of $H_0$ decrease (represented by the points in blue) the dark energy equation of state moves toward the cosmological constant boundary. \texttt{Second column:} The mcmc chains of all combined analyses infer that the lower values of $H_0$ prefer a nonzero coupling in the dark sector which is statistically consistent with zero. \texttt{Last column:} With the lower values of $H_0$, the dark energy equation of state moves toward the cosmological constant boundary and a nonzero coupling in the dark sector is favored which is indeed very close to zero. } \label{fig-scattered-ide} \end{figure} \subsection{IDE: Results} \label{sec-int-general} In Table \ref{tab:results-I} we summarize the 68\% confidence-levels constraints on the cosmological parameters for $\xi \leq 0$ and $w_x <-1$ using a variety of astronomical data displayed in the table. In Fig. \ref{fig-contour1}, 68.3\% and 95.4\% confidence-level contour plots for different combinations of the model parameters have been shown including one dimensional posterior distribution for some selected parameters of the interacting scenario as well. We notice that the combined data set CMB+ext, where ``ext'' is the combination of any two data sets from BAO, RSD, HST, JLA, CC, WL, significantly reduces the allowed region in the parameters space. From the analyses presented in Table \ref{tab:results-I}, one can easily state that the coupling parameter is very low. The coupling parameter, $\xi$ (at 95.4\% lower CL), are constrained to be (see Table \ref{tab:results-I}): \begin{itemize} \item $\xi>-0.004884$ (CMB only), \item $\xi>-0.001285$ (CMB+BAO+HST), \item \text{$\xi>-0.001384$} (CMB+BAO+RSD), \item $\xi>-0.001278$ (CMB+BAO+RSD+HST), \item $\xi >-0.000959$ (CMB+BAO+RSD+HST+JLA+CC), \item $\xi>-0.000935$, for the last combined analysis (CMB+BAO+RSD+HST+JLA+CC+WL), \end{itemize} while we must note that within 68.3\% CL, $\xi= 0$ is allowed, that means, effectively, IDE may recover the non-interacting $w_x$CDM cosmology. In Fig. \ref{fig-xi-H0-Om}, we show the dependece of $\xi$ over other cosmological parameters for this model. Now, from the constraints on the dark energy equation of state summarized in Table \ref{tab:results-I}, it is quite clear-cut that, $w_x$ assumes values that are close to ``$-1$''. In Fig. \ref{fig-wx-H0-Om}, we show the dependence of $w_x$ with other important cosmological parameters for a better understanding. From the left panel of Fig. \ref{fig-wx-H0-Om} we see that as $H_0$ decreases, $w_x$ approaches toward the cosmological constant limit, while from the right panel of Fig. \ref{fig-wx-H0-Om} we observe that $\Omega_{m0}$ takes large values as $w_x \rightarrow -1$. Further, in Fig. \ref{fig-sigma8}, we explicitly show the two dimensional contour plots in the planes ($\sigma_8$, $w_x$), $(\sigma_8, H_0)$ and $(\sigma_8, \xi)$ in order to measure the variations in $\sigma_8$ in presence of the coupling. Our analysis shows that, an increased coupling strength effectively lowers the values of $\sigma_8$, that means the model significantly deviate from the $\Lambda$CDM model. One can also observe that for more phantom state in the dark energy equation of state the values of $\sigma_8$ increase. In addition, we also observe that, in presence of the coupling, higher values of the Hubble parameter also indicate higher values of $\sigma_8$. Furthermore, we analyzed the mcmc chains for all combined analyses focusing on the behaviour of the coupling strength, dark energy equation of state and the density parameter for the matter sector monitored by the Hubble parameter values. The analysis has been displayed in Fig. \ref{fig-scattered-ide}. Precisely, such analysis provides with the qualitative behaviour of the interacting model in terms of the coupling strength and the dark energy equation of state. The analysis shows that the lower values of the Hubble parameter signal for a non-zero interaction in the dark sector but the dark energy equation of state still lies within a close neighborhood of the cosmological constant boundary ``$-1$''. Also, the density parameter for matter takes bigger values for lower values of the Hubble parameter as well. Lastly, we compare the $\chi^2_{min}$ values bewtween IDE and $\Lambda$CDM model obtained for different combined analyses (see Table \ref{tab:chi2}). We observe that for some combined analyses, the $\chi^2_{min}$ achieved for IDE is bigger than the $\Lambda$CDM model. One may notice that almost all combined analyses return a greater $\chi_{min}^2$ for IDE in compared to the standard $\Lambda$CDM. \begingroup \squeezetable \begin{center} \begin{table} \begin{tabular}{cccccccccccc} \hline\hline Model & CMB & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{HST} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{RSD} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{RSD+HST} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+ \mbox{RSD+HST}\\+\text{JLA+CC} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+ \mbox{RSD+HST}\\+\text{JLA+CC}\\+\text{WL} \end{array}$\\ \hline IDE: $\chi^2_{min~\mbox{(best-fit)}}$ & 12960.778 & 12981.276 & 12975.450 & 12982.168 & 13689.092 & 13723.708\\ IVS: $\chi^2_{min~\mbox{(best-fit)}}$ & 12961.606 & 12980.844 & 12971.080 & 12982.742 & 13693.894 & 13724.124\\ $\Lambda$CDM: $\chi^2_{min~\mbox{(best-fit)}}$ & 12964.062 & 12978.886 & 12974.124 & 12981.336 & 13693.560 & 13722.170\\ \hline\hline \end{tabular} \caption{Table displaying the $\chi^2_{min}$ obtained for the best-fit values of the parameters of the two interacting dark energy scenarios and the non-interacting $\Lambda$CDM cosmolofy. }\label{tab:chi2} \end{table} \end{center} \endgroup \begingroup \squeezetable \begin{center} \begin{table} \begin{tabular}{cccccccccccc} \hline\hline Parameters & CMB & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{HST} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{RSD} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{RSD+HST} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+ \mbox{RSD+HST}\\+\text{JLA+CC} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+ \mbox{RSD+HST}\\+\text{JLA+CC}\\+\text{WL} \end{array}$\\ \hline $\Omega_c h^2$ & $ 0.1225_{- 0.0031}^{+ 0.0021}$ & $ 0.1178_{- 0.0010}^{+ 0.0010}$ & $ 0.1193_{- 0.0011}^{+ 0.0011}$ & $ 0.1183_{- 0.0012}^{+ 0.0011}$ & $ 0.1182_{- 0.0011}^{+ 0.0011}$ & $ 0.1178_{- 0.0010}^{+ 0.0010}$\\ $\Omega_b h^2$ & $ 0.0223_{- 0.0002}^{+ 0.0002}$ & $ 0.0224_{- 0.0001}^{+ 0.0001}$ & $ 0.0223_{- 0.0001}^{+ 0.0001}$ & $ 0.0224_{- 0.0001}^{+ 0.0002}$ & $ 0.0224_{- 0.0001}^{+ 0.0001}$ & $ 0.0224_{- 0.0001}^{+ 0.0001}$\\ $100\theta_{MC}$ & $ 1.0402_{- 0.0004}^{+ 0.0004}$ & $ 1.0408_{- 0.0003}^{+ 0.0003}$ & $ 1.0405_{- 0.0003}^{+ 0.0003}$ & $ 1.0407_{- 0.0003}^{+ 0.0003}$ & $ 1.0407_{- 0.0004}^{+ 0.0003}$ & $ 1.0407_{- 0.0003}^{+ 0.0003}$ \\ $\tau$ & $0.0765_{- 0.0178}^{+ 0.0192}$ & $ 0.0915_{- 0.0155}^{+ 0.0185}$ & $ 0.0781_{- 0.0157}^{+ 0.0138}$ & $ 0.0796_{- 0.0163}^{+ 0.0165}$ & $ 0.0793_{- 0.0162}^{+ 0.0156}$ & $ 0.0750_{- 0.0160}^{+ 0.0169}$\\ $n_s$ & $0.9695_{- 0.0049}^{+ 0.0048}$ & $ 0.9788_{- 0.0038}^{+ 0.0037}$ & $ 0.9750_{- 0.0036}^{+ 0.0035}$ & $ 0.9771_{- 0.0038}^{+ 0.0039}$ & $ 0.9773_{- 0.0041}^{+ 0.0039}$ & $ 0.9783_{- 0.0038}^{+ 0.0035}$\\ ${\rm{ln}}(10^{10} A_s)$ & $ 3.0966_{- 0.0339}^{+ 0.0373}$ & $ 3.1214_{- 0.0311}^{+ 0.0373}$ & $ 3.0960_{- 0.0283}^{+ 0.0275}$ & $ 3.0979_{- 0.0319}^{+ 0.0311}$ & $ 3.0965_{- 0.0350}^{+ 0.0316}$ & $ 3.0863_{- 0.0316}^{+ 0.0327}$\\ $\Omega_{m0}$ & $0.3425_{- 0.0271}^{+ 0.0159}$ & $ 0.3064_{- 0.0064}^{+ 0.0063}$ & $ 0.3167_{- 0.0071}^{+ 0.0074}$ & $ 0.3096_{- 0.0077}^{+ 0.0068}$ & $ 0.30911013_{- 0.0077}^{+ 0.0065}$ & $ 0.3064_{- 0.0065}^{+ 0.0061}$\\ $\sigma_8$ & $ 0.8118_{- 0.0170}^{+ 0.0212}$ & $ 0.8262_{- 0.0127}^{+ 0.0156}$ & $ 0.8169_{- 0.0120}^{+ 0.0120}$ & $ 0.8167_{- 0.0125}^{+ 0.0124}$ & $ 0.8161_{- 0.0143}^{+ 0.0134}$ & $ 0.8108_{- 0.0127}^{+ 0.0128}$\\ $H_0$ & $ 65.2375_{- 1.1629}^{+ 1.8234}$ & $ 67.8090_{- 0.4817}^{+ 0.5004}$ & $ 67.0308_{- 0.5437}^{+ 0.5368}$ & $ 67.5675_{- 0.5259}^{+ 0.5413}$ & $ 67.6067_{- 0.5032}^{+ 0.5796}$ & $ 67.7953_{- 0.4735}^{+ 0.4983}$\\ $\xi$ & $\xi > -0.001953$ & $\xi > -0.000490$ & $\xi > -0.000726$ & $\xi > -0.000549$ & $\xi > -0.000563$ & $\xi > -0.000557$\\ \hline\hline \end{tabular} \caption{The table summarizes the observational constraints of the cosmological parameters for the interacting vacuum scenario (IVS) at 68.3\% confidence-level for different combinations of the observational data. For the coupling parameter $\xi$, we report only their values at 95.4\% lower confidence-level. }\label{tab:results-II} \end{table} \end{center} \endgroup \subsection{IVS: Results} \label{sec-vaccum-scenario} As a particular case we consider the simplest possibility when dark energy is the cosmological constant. Now, we have also constrained this interacting scenario using the same combined analyses as employed in section \ref{sec-int-general}. The results have been summarized in Table \ref{tab:results-II} and Fig. \ref{fig-contour-vacuum1} shows the two dimensional contour plots at 68.3\% and 95.4\% confidence-levels for different combinations of the free model parameters using the six different combined analyses. Additionally, in the extreme right corner of each row of the Fig. \ref{fig-contour-vacuum1} we further show the one-dimensional posterior distributions for some selected model parameters of this interacting scenario. From Fig. \ref{fig-contour-vacuum1} one can see that the addition of any other external data to CMB significantly decreases the allowed region in the parameters space and hence the parameters are well constrained when any external data set is added to CMB. From the analysis we notice that the coupling strength of the interaction is very very small and it is very close to zero. In particular, in 95.4\% lower confidence-level, we find that, \begin{itemize} \item $\xi > -0.001953$ (for CMB alone), \item $\xi > -0.000490$ (CMB+BAO+HST), \item $\xi > -0.000726$ (CMB+BAO+RSD), \item $\xi > -0.000549$ (CMB+BAO+RSD+HST), \item $\xi > -0.000563$ (CMB+BAO+RSD+HST+JLA+CC), and finally, \item $\xi > -0.000557$, for the last combined analysis (CMB+BAO+RSD+HST+JLA+CC+WL). \end{itemize} Additionally, we must mention that within 68.3\% confidence level, the non-interacting scenario (i.e., $\xi =0$) is recovered (excluding the CMB analysis). Thus, one can see that this interaction scenario is effectively very close to the non-interacting $\Lambda$CDM scenario. Similar to the IDE model described in section \ref{sec-int-general}, here too we have investigated the three dimensional scattered plots in the $(\xi, \Omega_{m0})$ plane for all the combined analyses colored by the Hubble parameter values. The analysis has been presented in Fig. \ref{fig-scattered-ivs} from which one can notice that, for lower values of the Hubble parameter, the coupling parameter seems to have a tendency to take values away from $\xi =0$ while for the higher values of $H_0$, the coupling parameter takes values very close to zero. Following the similar trend as done for IDE model, we compare the $\chi^2_{min}$ values for this scenario with respect to the base cosmological model $\Lambda$CDM. We have similar conclusion for this interaction scenario, that means, the $\chi^2_{min}$ values for this model are bigger for almost all combined analyses in respect to the $\Lambda$CDM cosmological model. \begingroup \squeezetable \begin{center} \begin{table} \begin{tabular}{cccccccccccc} \hline\hline Parameter & CMB & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{HST} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{RSD} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+\text{RSD+HST} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+ \mbox{RSD+HST}\\+\text{JLA+CC} \end{array}$ & $\begin{array}[c]{c} \text{CMB+BAO}\\+ \mbox{RSD+HST}\\+\text{JLA+CC}\\+\text{WL} \end{array}$\\ \hline $H_0$ (IDE) & $ 65.52_{- 3.93- 8.02- 10.22}^{+ 4.51+ 7.53+ 9.45}$ & $ 70.77_{- 1.15- 2.32- 2.47}^{+ 1.11+ 2.31+ 2.78}$ & $ 67.97_{- 1.02- 1.77- 2.05}^{+ 0.83+ 1.86+ 2.56}$ & $ 69.19_{- 0.89- 1.72- 2.22}^{+ 0.87+ 1.79+ 2.46}$ & $ 69.64_{- 0.85- 1.75- 2.20}^{+ 0.83+ 1.69+ 2.79}$ & $ 68.89_{- 0.82- 1.36- 1.88}^{+ 0.68+ 1.52+ 1.93}$\\ $H_0$ (IVS) & $65.24_{- 1.16- 3.06- 4.14}^{+ 1.82+ 2.67+ 3.21}$ & $ 67.81_{- 0.48- 0.98- 1.24}^{+ 0.50+ 0.97+ 1.17}$ & $ 67.03_{- 0.54- 1.09- 1.41}^{+ 0.54+ 1.08+ 1.46}$ & $ 67.57_{- 0.53- 1.01- 1.35}^{+ 0.54+ 0.96+ 1.31}$ & $ 67.61_{- 0.50- 1.03- 1.34}^{+ 0.58+ 0.98+ 1.39}$& $ 67.80_{- 0.47- 1.04- 1.54}^{+ 0.50+ 1.06+ 1.23}$\\ \hline\hline \end{tabular} \caption{Table displaying the 68\%, 95\% and 99\% confidence level constraints on $H_0$ and $\sigma_8$ for different combined analyses for the interacting scenario with $w_x < -1$ (IDE) and $w_x= -1$ (IVS). We note that the estimation of $H_0$ by latest Planck missions for the base $\Lambda$CDM model yields $H_0= 67.27 \pm 0.66$ km/s/Mpc (Planck TT, TE, EE+lowP) \cite{Ade:2015xua}. }\label{tab:H0} \end{table} \end{center} \endgroup \begin{figure} \includegraphics[width=0.7\textwidth]{contour_ilcdm_vs6.pdf} \caption{Color Online $-$ Contour plots for different combinations of the cosmological parameters in the 68.3\% and 95.4\% confidence levels for the interacting vacuum scenario (IVS) have been displayed for distinct observational combinations. Additionally, we also show the one-dimensional posterior distributions for those parameters at the extreme right corners of each row. From the two-dimensional contour plots one can see that the addition of any external data to CMB decreases the error bars of the cosmological parameters.} \label{fig-contour-vacuum1} \end{figure} \begin{figure} \includegraphics[width=0.34\textwidth]{3d_ilcdm_xiomH0_CMB+BAO+HST.pdf} \includegraphics[width=0.34\textwidth]{3d_ilcdm_xiomH0_CMB+BAO+RSD.pdf} \begin{center} \includegraphics[width=0.355\textwidth]{3d_ilcdm_xiomH0_CMB+BAO+RSD+HST.pdf} \end{center} \includegraphics[width=0.34\textwidth]{3d_ilcdm_xiomH0_CMB+BAO+RSD+HST+JLA+CC.pdf} \includegraphics[width=0.34\textwidth]{3d_ilcdm_xiomH0_CMB+BAO+RSD+HST+JLA+CC+WL.pdf} \caption{Color Online $-$ For the interacting vacuum scenario, we have analyzed the mcmc chains of the combined analysis in the two dimensional $(\xi, \Omega_{m0})$ planes colored by the Hubble parameter values. The upper left and upper right panels respectively represent the analyses CMB+BAO+HST, CMB+BAO+RSD. The center plot stands for the combined analysis CMB+BAO+RSD+HST. Finally, the lower left and right panels respectively represent the analyses CMB+BAO+RSD+HST+JLA+CC and CMB+BAO+RSD+HST+JLA+CC+WL. From all the plots, one thing is clear that the lower values of the Hubble parameter signal for a non-zero interaction in the dark sector while statistically this is consistent with zero and in addition, the density parameter for the matter sector is also allowed to take higher values. } \label{fig-scattered-ivs} \end{figure} \subsection{On the Tension of $H_0$: The role of interaction} \label{sec-tension} One of the most talkative issues in current cosmological research is the tension on the parameter $H_0$. Some recent investigations in the context of interacting dark energy models fueled its further investigations aiming to reach a definite and satisfactory explanation towards this direction, and consequently, people are more focused on how interacting dark energy models may alleviate the tension on $H_0$. The first question that immediately arises is, what exactly such tension is. To illustrate this notion, we need to take into account its distinct measurements from different observational missions. The estimation of $H_0$ by Planck 2015 missions from the $\Lambda$CDM based cosmological model yields $H_0= 67.27 \pm 0.66$ km/s/Mpc (Planck TT, TE, EE+lowP) \cite{Ade:2015xua} while the local measurement of $H_0$ using the Hubble Space Telescope gives $H_0 = 73.24 \pm 1.74$ km/s/Mpc \cite{Riess:2016jrr}, and puts a huge difference between these estimations. This effect is generally known as the tension on the Hubble constant. Some recent investigations already shown that interacting dark energy might be able to release such tension on $H_0$ \cite{Kumar:2017dnp, DiValentino:2017iww}. Since the interacting dark energy is purely model dependent, so naturally, it is quite justified to see how other phenomenological interaction models react with the tension on $H_0$. For a better viewing, in Table \ref{tab:H0}, we summarize the constraints on $H_0$ for both IDE and IVS up to $3\sigma$ confidence level. We see that the addition of one extra degrees of freedom in terms of the coupling parameter significantly increases the error bars on $H_0$ in compared to Planck 2015 \cite{Ade:2015xua}. And the increase of error bars on $H_0$ is prominent for IDE in compared to IVS because the estimated values of $H_0$ for IVS using different combined analyses look similar to Planck 2015 \cite{Ade:2015xua}. Naturally, for the IDE scenario, one may infer that, due to the large error bars present on $H_0$, the estimated values of $H_0$ are in agreement with the local measurement ($H_0 = 73.24 \pm 1.74$ km/s/Mpc \cite{Riess:2016jrr}). Thus, one can see that the interaction in the dark sector may provide an explanation towards the reduction of the tension on $H_0$. \begingroup \begin{center} \begin{table}[htb] \begin{tabular}{ccc} \hline\hline $\ln B_{ij}$ & Strength of evidence for model ${M}_i$ \\ \hline $0 \leq \ln B_{ij} < 1$ & Weak \\ $1 \leq \ln B_{ij} < 3$ & Definite/Positive \\ $3 \leq \ln B_{ij} < 5$ & Strong \\ $\ln B_{ij} \geq 5$ & Very strong \\ \hline\hline \end{tabular} \caption{Revised Jeffreys scale used to test the observational support of any model $M_i$ with respect to another model $M_j$. }\label{tab:jeffreys} \end{table} \end{center} \endgroup \begingroup \begin{center} \begin{table}[htb] \begin{tabular}{cccccc} \hline Data set & Model &~~~~$\ln B_{ij}$ &~ Strength of evidence for model $\Lambda$CDM \\ \hline CMB & IDE & $-2.0$ & Positive \\ CMB & IVS & $-1.9$ & Positive\\ CMB+BAO+HST & IDE & $-4.8$ & Strong \\ CMB+BAO+HST & IVS & $-3.5$ & Strong \\ CMB+BAO+RSD & IDE & $-2.9$ & Positive \\ CMB+BAO+RSD & IVS & $-1.7$ & Positive \\ CMB+BAO+RSD+HST & IDE & $-3.6$ & Strong\\ CMB+BAO+RSD+HST & IVS & $-3.3$ & Strong \\ CMB+BAO+RSD+HST+JLA+CC & IDE & $-1.7$ & Positive \\ CMB+BAO+RSD+HST+JLA+CC & IVS & $-2.2$ & Positive\\ CMB+BAO+RSD+HST+JLA+CC+WL & IDE & $-4.0$ & Strong \\ CMB+BAO+RSD+HST+JLA+CC+WL & IVS & $-3.7$ & Strong \\ \hline \end{tabular} \caption{Summary of $\ln B_{ij}$, for the two interacting scenarios with respect to the reference model $\Lambda$CDM, for different observational data sets. From the Bayesian evidence point of view, the negative values of $\ln B_{ij}$ mean that the reference model $\Lambda$CDM is preferred over the two interacting scenarios. }\label{tab:bayesian} \end{table} \end{center} \endgroup \subsection{The Bayesian Evidence} \label{sec-information} Model selection \cite{Liddle:2007fy} plays an important role in distinguishing various cosmological models. Keeping the same motivation, in this work we compare both the interacting dark energy scenarios with the $\Lambda$CDM cosmological model using the Bayesian analysis. The Bayesian evidence is a powerful statistical technique that quantifies the cosmological models based on their performance with the observational data. In the following we shortly describe how the Baysian evidence is calculated for a cosmological model. In the Bayesian analysis one needs the posterior probability of the model parameters (denoted by $\theta$), given a particular data set $x$ to test the model, any prior information and a model $M$. Now, recalling the Bayes theorem, one may write \begin{eqnarray}\label{BE} p(\theta\|x, M) = \frac{p(x\|\theta, M)\,\pi(\theta\|M)}{p(x\|M)} \end{eqnarray} where $p(x\|\theta, M)$ is the likelihood function dependent on the model parameters $\theta$ with the data set fixed; $\pi(\theta\|M)$ is the prior used in the analysis. The denominator $p(x\|M)$ in the right hand side of eqn. (\ref{BE}) is the Bayesian evidence for the model comparison and it is the integral over the unnormalised posterior $\tilde{p} (\theta\|x, M) \equiv p(x\|\theta,M)\,\pi(\theta\|M)$ as \begin{eqnarray}\label{sp-be01} E \equiv p(x\|M) = \int d\theta\, p(x\|\theta,M)\,\pi(\theta\|M). \end{eqnarray} We note that the above equation (\ref{sp-be01}) is also referred to as the marginal likelihood. Now, for any particular model $M_i$ and the reference model $M_j$ (which is the base model and it is $\Lambda$CDM here), the posterior probability is given by \begin{eqnarray} \frac{p(M_i\|x)}{p(M_j\|x)} = \frac{\pi(M_i)}{\pi(M_j)}\,\frac{p(x\| M_i)}{p(x\|M_j)} = \frac{\pi(M_i)}{\pi(M_j)}\, B_{ij}. \end{eqnarray} where $B_{ij} = \frac{p(x\| M_i)}{p(x\|M_j)}$, is the Bayes factor of the model $M_i$ relative to the base or reference model $M_j$. For $B_{ij} > 1 $, we refer that the data support the model $M_i$ more strongly than the model $M_j$. The behavior of the models is usually quantified using different values of $B_{ij}$ (or alternatively, $\ln B_{ij}$). Here, we shall use the widely accepted Jeffreys scales \cite{Kass:1995loi} (see Table \ref{tab:jeffreys}) that summarizes the model comparison. Now, one can calculate the Bayesian evidence using the MCMC chains which directly extract the parameters of the underlying cosmological model. For a detailed explanation on the implementation of the Bayesian evidence for any cosmological model we refer to \cite{Heavens:2017hkr,Heavens:2017afc} where we use the code \texttt{MCEvidence}\footnote{This code is available for free at \href{https://github.com/yabebalFantaye/MCEvidence}{github.com/yabebalFantaye/MCEvidence}.}. Thus, using the code \texttt{MCEvidence}, we have calculated the logarithm of the Bayes factor, i.e., $\ln B_{ij}$ where $i$ stands for IDE or IVS and $j$ is the reference model $\Lambda$CDM. In Table \ref{tab:bayesian} we have shown the calculated values of $\ln B_{ij}$ for the two interacting scenarios with respect to the reference model $\Lambda$CDM. From the table, we see that for all the observational data employed in this work, the values of $\ln B_{ij}$ are negative which from the point of view of the Bayesian evidence, one can identify that the reference model $\Lambda$CDM is preferred over the two interacting scenarios. For some combined analysis, the preference of $\Lambda$CDM is strong while for some combined analysis, it is positive. Overall, we see that the present observational data always favor $\Lambda$CDM is favored in respect to the interacting scenarios discussed in this work. \section{Concluding remarks} \label{sec-conclu} An interacting scenario between a pressureless dark matter and a dark energy fluid availing constant barotropic equation of state has been considered. The underlying geometry of the universe is characterized by the spatially flat FLRW line element and the interaction rate $Q = Q (\rho_t^\prime) = Q (\rho_c, \rho_x)$ has been given explicitly in eqn. (\ref{interaction}) or eqn. (\ref{eq-int}). This interaction rate is very appealing in the sense that the evolution equations for the dark sectors (cold dark matter and dark energy) can be exactly solved, and thus, one can directly measure their deviation from the standard evolution laws of the dark fluids with no-interaction. We note that initially this kind of interaction was introduced by Chimento \cite{Chimento:2009hj} where the author proposed a very general interaction rate that recovers the interaction in eqn. (\ref{eq-int}) and discussed its theoretical implications. Later on its observational viability was tested when dark energy is the cosmological constant but at the background level \cite{G:2014mea}, consequently, in a recent article \cite{Sharov:2017iue}, the authors generalized this study for both $w_x = -1$ and $w_x \neq -1$ at the background level with the recent observational data. However, it is quite certain that the dynamics of such interaction models at the large scale of the universe, is promising for a better understanding of the entire scenario. That means, the most important question related with the interaction model is, how the structure formation of the universe depends when such interaction is included in the cosmological scenario. Thus, in the present work we discuss the perturbations and the structure formation of the universe when such interaction is present between the dark fluids. Now, in order to test the resulting cosmological scenarios with the available observational data, we use \texttt{cosmomc}, a markov chain monte carlo package that extracts the model parameters with a sufficient convergence following the Gelman-Rubin statistics \cite{Gelman-Rubin}. The observational data include cosmic microwave background radiation, baryon acoustic oscillations, redshift space distortions, local Hubble constant, supernovae type Ia from joint light curve analysis, Hubble parameter values at different redshifts from cosmic chronometers and finally the weak gravitational lensing data. For a better analysis, we have considered two distinct interacting scenarios, namely when the dark energy is other than the cosmological constant (i.e., $w_x \neq -1$) and the other one is the cosmological constant itself. For IDE scenario, the constraints on the model parameters have been summarized in Table \ref{tab:results-I} where we present the 95.4\% limits (lower) on the coupling parameter $\xi$. And in Fig. \ref{fig-contour1}, we show the contour plots for different combinations of the model parameters at 68.3\% and 95.4\% confidence levels. The right corners of Fig. \ref{fig-contour1} also shows the one-dimensional posterior distributions for some selected model parameters as well. From the observational constraints on the coupling parameter, $\xi$, summarized in the last row of the Table \ref{tab:results-I}, we find that $\xi =0$ is consistent with the observational data. Moreover, from the constraints on the dark energy equation of state, $w_x$, one can see that it is actually very very close to the cosmological constant boundary. Thus, we see that the interaction model is actually equivalent to the non-interacting $\Lambda$CDM background. However, in the large scale distribution, the interaction model may exhibit some differences even for a very small coupling strength. From the imprints on the CMB TT spectra (see the right panel of the Fig. \ref{fig:CMB-ide}) and also from the matter power spectra (see the right panel of the Fig. \ref{fig:Mpower-ide}), it is evident that for a very small coupling strength ($\xi =-0.0001$), the model presents a very minimal deviation from the non-interacting $\Lambda$CDM cosmology. Now, for the interacting cosmological constant (labeled as IVS), the results have been summarized in Table \ref{tab:results-II}. The corresponding contour plots at 68.3\% and 95.4\% confidence-levels are also shown in Fig. \ref{fig-contour-vacuum1} with the one-dimensional posterior distributions for some selected parameters of this model. From the estimation of the coupling strength shown in Table \ref{tab:results-II}, one can see that $\xi$ is concistent with the non-interaction limit (i.e., $\xi =0$), at least according to the current observational data. In fact, for this model we have realized a similar trend as in IDE. For instance, from Fig. \ref{fig-scattered-ivs}, similar to IDE model, we find that lower values of the Hubble parameter allow non-zero interaction in the dark sector. The deviation of this interaction scenario from the non-interacting $\Lambda$CDM cosmology is also found to be insensitive (see the right panels of Fig. \ref{fig:CMB-ivs} and Fig. \ref{fig:Mpower-ivs}) unlike the IDE scenario where although the deviation is small but they are detectable. We also raise one interesting point that has become a hot issue at current cosmological research $-$ the observed tension on the $H_0$ parameter from its global \cite{Ade:2015xua} and local measurements \cite{Riess:2016jrr}. We found that the allowance of the interaction increases the error bars on the Hubble parameter measurements, and consequently, the parameters space for $H_0$ is increased. This becomes effective to release the tension partially and is reflected from some combinatons for IDE only. While the interacting vacuum model is not suitable to release the tension. One may argue that the allowance of extra degrees of freedom in the parameters space of the interacting dark energy models (for IDE, the number of parameters is 8 while for IVS this number is 7) might be suitable to alleviate such tension. Similar results have been reported in some recent works \cite{Kumar:2017dnp, DiValentino:2017iww}, but however, since the theory of interaction is phenomenological and hence its conclusions too, therefore, the analysis with a different interaction model might be perhaps important to see whether the model can avail the same property or not. The relation of the extra degrees of freedom to the tension on $H_0$, in the interacting dark energy models surely needs further attention. Finally, we computed the Bayesian evidence for each interacting scenario with respect to the non-interacting $\Lambda$CDM model (see Table \ref{tab:bayesian}). Our analysis shows that the non-interacting $\Lambda$CDM is preferred over the two interacting dark energy scenarios, at least according to the current observational data sets. \section*{ACKNOWLEDGMENTS} The authors thank the referee for his/her constructive and illuminating comments that improved the work considerably. W. Yang's work is supported by the National Natural Science Foundation of China under Grants No. 11705079 and No. 11647153. RH was supported by Proyecto VRIEA-PUCV N$_{0}$ 039.309/2018. SC acknowledges the financial support from the Mathematical Research Impact Centric Support (MATRICS), project reference no. MTR/2017/000407, by the Science and Engineering Research Board, Government of India. SP thanks Rafael C. Nunes, Burin Gumjudpai and J. A. S. Lima for useful discussions and comments while working on the draft.	{ "redpajama_set_name": "RedPajamaArXiv" }	4,265
P-sprog er en sprogleg, den bruges af nogle børn (og voksne) som et slags kodesprog. En person som ikke snakker p-sprog vil kun dårligt kunne forstå hvad der bliver sagt, især hvis det snakkes hurtigt. Sådan gør man P-sprog kan læres simpelt på følgende måde, man skriver en sætning, hvorefter man under hver vokal sætter et p og samme vokal neden under således: Hej med dig, hvad hedder du? Kan du også snakke p-sprog? p p p p p p p p p p p p p p p e e i a e e u a u o å a e e o Man læser så ordet der fremkommer. så det bliver til "Hepej meped dipig..." Konstantinopolitanerinderne er et godt ord at øve sig på Konstantinopolitanerinderne p p p p p p p p p p p o a i o o i a e i e e Ordet bliver gjort en del sværere af at "po" indgår i ordet, det bliver således til koponstapantipinopopopolipitapaneperipindepernepe. Dialekter En variation af p-sprog udøves efter følgende regler: Enhver stavelse i et ord gentages således, at gentagelsen af stavelsen starter med p I stavelser, der starter med en konsonant, erstatter p'et denne i gentagelsen af stavelsen (flo-den bliver til floplo-denpen) I stavelser, der starter med en vokal, sættes p'et blot foran i gentagelsen af stavelsen (å-en bliver til åpå-enpen) Den kendte frase, rødgrød med fløde, bliver således til rødpødgrødprød medped fløplødepe. Se også Røversprog Sproglege	{ "redpajama_set_name": "RedPajamaWikipedia" }	2,149
import {module, test} from 'qunit'; import {setupTest} from 'ember-qunit'; import Service from '@ember/service'; import type FastBootAdapter from 'ember-best-language/services/best-language/fastboot'; module('Unit \| Service \| best-language/fastboot', hooks => { setupTest(hooks); module('when accept-language header is sent', hooks => { hooks.beforeEach(function () { class FastbootStub extends Service { isFastBoot = true; request = { headers: new Headers({ 'Accept-Language': 'en-US,en;q=0.8,fr;q=0.6', }), }; } this.owner.register('service:fastboot', FastbootStub); }); module('fetchHeaderLanguages', () => { test('should fetch the languages from the `Accept-Language` header', function (assert) { const service = this.owner.lookup('service:best-language/fastboot') as FastBootAdapter; const expectedLanguages = [ {language: 'en-US', score: 1}, {language: 'en', score: 0.8}, {language: 'fr', score: 0.6}, ]; assert.deepEqual(service.fetchLanguages(), expectedLanguages); }); }); }); module('when accept-language header is missing', hooks => { class FastbootStub extends Service { isFastBoot = true; request = { headers: new Headers(), }; } hooks.beforeEach(function () { this.owner.register('service:fastboot', FastbootStub); }); module('fetchHeaderLanguages', () => { test('should fetch an empty string from the `Accept-Language` header', function (assert) { const service = this.owner.lookup('service:best-language/fastboot') as FastBootAdapter; const expectedLanguages = [{language: '', score: 1}]; assert.deepEqual(service.fetchLanguages(), expectedLanguages); }); }); }); });	{ "redpajama_set_name": "RedPajamaGithub" }	7,719
Synopsis: True and the Rainbow Kingdom follows 8-year-old True and her best friend Bartleby the cat, as they help the whimsical citizens of the Rainbow Kingdom, a wondrous, colorful universe filled with delightful and fantastical citizens. True is the only one with the ability to activate the magical powers of The Wishes of the wishing tree, solve problems in the Rainbow Kingdom and empower viewers with her imagination, mindfulness and empathy. The series is produced by Guru Studio, in collaboration with Pharrell Williams' i am OTHER, world-renowned artist collective, FriendsWithYou and Home Plate Entertainment. Stars: Michela Luci, Jamie Watson, Dante Zee.	{ "redpajama_set_name": "RedPajamaC4" }	265
Die Monarque-Klasse war eine Klasse von drei 74-Kanonen-Linienschiffen 2. Ranges der französischen Marine, die von 1747 bis 1781 in Dienst stand. Allgemeines Die Klasse wurde ursprünglich von dem Marinearchitekten Blaise-Joseph Ollivier entworfen und unter seiner Bauaufsicht begonnen. Da dieser aber 1746 verstarb wurde seine Arbeit durch Jacques-Luc Coulomb fortgesetzt bzw. beendet. Einheiten Technische Beschreibung Die Klasse war als Batterieschiff mit zwei durchgehenden Geschützdecks konzipiert und hatte eine Länge von 53,92 Metern (Geschützdeck) bzw. 51,00 Metern (Kiel), eine Breite von 14,13 Metern und einen Tiefgang von 6,66 Metern bei einer Verdrängung von 1500/2718 Tonnen. Sie waren Rahsegler mit drei Masten (Fockmast, Großmast und Kreuzmast). Der Rumpf schloss im Heckbereich mit einem Heckspiegel, in den Galerien integriert waren, die in die seitlich angebrachten Seitengalerien mündeten. Die Besatzung hatte im Frieden eine Stärke von 660 Mann und im Kriegsfall 744 Mann (6 bzw. 10 Offiziere und 650 bzw. 734 Unteroffiziere bzw. Mannschaften). Die Bewaffnung der Klasse bestand aus 74 Kanonen. Bemerkungen Literatur Weblinks Monarque-Klasse (Sceptre-Klasse) auf threedecks.org (englisch) Monarque (franz. Marine) auf threedecks.org (englisch) Monarch (brit. Marine) auf threedecks.org (englisch) Intrépide auf threedecks.org (englisch) Sceptre auf threedecks.org (englisch) Einzelnachweise Militärschiffsklasse (Frankreich) Linienschiffklasse	{ "redpajama_set_name": "RedPajamaWikipedia" }	376
\section{Introduction} In the chiral limit of massless quarks isovector components of both vector and axial quark currents are conserved. Though the hadrons acquire masses via the mechanism of spontaneous symmetry breaking, hadronic currents are still conserved. While it is rather straightforward for the vector current, conservation of the axial current looks nontrivial, and is possible only due to the presence of a pseudo-scalar term in the current, which has to be singular at $Q^2=0$ \cite{nambu}. This singularity is associated with massless Goldstone particles \cite{goldstone} or pions, which appear due to spontaneous chiral symmetry breaking. Beyond the chiral limit, the pions acquire a small mass and the axial current conservation is not exact, so one can consider a partial conservation of the axial current (PCAC), \beq \partial_\mu J^A_\mu=m_\pi^2\,f_\pi\,\phi_\pi, \label{20} \eeq where $m_\pi$ and $f_\pi\approx 0.93 m_\pi$ are the pion mass and decay coupling, and $\phi_\pi$ is the pion field. A beautiful manifestation of PCAC is the Goldberger-Treiman relation \cite{treiman}, which bridges weak and strong interaction. It miraculously connects the pion decay constant with the pion-nucleon coupling, which seem to have very little in common. Indeed, the former depends on the pion wave function, while the latter is controlled by the wave function of the nucleon. Nevertheless, data on $\beta$-decay and muon capture confirm this relation between very different physical quantities. This astonishing relation between the pion pole (suppressed in beta-decay due to conservation of the lepton current) and heavier states having no natural explanation, except PCAC, was called Goldberger-Treiman conspiracy \cite{bell-book} (see more below). Another intensive source of axial current is high energy neutrino interactions. In this case PCAC leads to the Adler relation (AR) between the cross sections of processes initiated by neutrinos and pions \cite{adler}, \beq \left.\frac{d^2\sigma(\nu p\to l\,X)}{dQ^2\,d\nu}\right\|_{Q^2=0} = \xi^2(E,\nu)\,\sigma(\pi p\to X). \label{40} \eeq Here the kinematic factor is \beq \xi^2(E,\nu)=\frac{G^2}{2\pi^2}\,f_\pi^2\,\frac{E-\nu}{E\nu}; \label{50} \eeq $E$ is the neutrino energy; $G=1.166\times 10^{-5}\,GeV^{-2}$ is the electro-weak Fermi coupling; $Q^2=-q_\mu^2$, where $q_\mu=k_\mu-k^\prime_\mu$ and $\nu=E-E^\prime$ are the 4-momentum and energy transfer in the $\nu\to l$ transition (the same notation as for neutrinos should not cause confusion). For the sake of concreteness the target is the proton, but it may be any hadron or a nucleus. A high-energy neutrino exposes hadronic properties interacting via its hadronic fluctuations \cite{goldman}. Similar to the Goldberger-Treiman relation the AR (\ref{40}) should not be interpreted as pion pole dominance. Neutrino cannot fluctuate to a pion, $\nu\to\!\!\!\!\!\!/\ \ \pi l$, because the pion pole in the dispersion relation in $Q^2$ for the axial current does not contribute to the interaction of the neutrino at high energies \cite{bell,bell-book,p-s,km}. Indeed, the axial current $J^A_\mu(Q^2)$ can be presented as, \beqn J^A_\mu(Q^2)&=&\frac{q_\mu\,f_\pi}{Q^2+m_\pi^2}\,T(\pi p\to X) \nn\\ &+& \frac{f_{a_1}}{Q^2+m_{a_1}^2}\,T_\mu(a_1 p\to X)\,+\,... \label{100} \eeqn Here the second and following terms represent the contributions of the $a_1$ meson and (implicitly) other heavier axial-vector states. The first term in (\ref{100}), corresponding to the pion pole, contains the factor $q_\mu$, which then terminates its contribution to the cross section, Eq.~(\ref{40}). Indeed, the amplitude of the reaction is \beq A(\nu\,p\to l\,X) \propto L_\mu\,J^A_\mu, \label{120} \eeq where $L_\mu=\bar l(k^\prime)\gamma_\mu(1+\gamma_5)\nu(k)$ is the lepton current, which is transverse, i.e. $q_\mu\,L_\mu=0$ (for simplicity hereafter we entirely neglect the lepton mass). Therefore, the pion term in (\ref{100}) does not contribute to the amplitude Eq.~(\ref{120}), and this is true at any $Q^2$. Thus, although it is tempting to interpret the AR Eq.~(\ref{40}) as a manifestation of the pion pole dominance, this is not correct. PCAC connects the contribution of heavy axial states (the second line in Eq.~(\ref{100})) with the nonexistent pion contribution at $Q^2=0$ \cite{bell,bell-book,p-s,km}. Such a fine tuning, which is very similar to the Goldberger-Treiman conspiracy, looks miraculous, and the PCAC hypothesis for neutrino interactions should be tested thoroughly. A simple way to see in data whether light or heavy states dominate the dispersion relation for the axial current, is to measure the $Q^2$-dependence of the neutrino cross section at small $Q^2$. Extrapolating the cross section Eq.~(\ref{40}) with the parametrization $(Q^2+M_{eff}^2)^{-2}$, one can find the position $Q^2=-M_{eff}^2$ of the essential singularity in the dispersion relation (\ref{100}). It is easy to disentangle between the effective masses which are as small as the pion mass and heavy singularities, like the $\rho$-$\pi$ cut, $a_1$ meson, etc. Data clearly prefer the latter, $M_{eff}\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$} 1\,\mbox{GeV}$ \cite{km}. \section{Diffractive neutrino-production of pions}\label{sect2} This reaction offers probably the most stringent test of PCAC in neutrino interactions. Indeed, the analysis performed by Piketty and Stodolsky \cite{p-s} revealed a potential problem related to the above dispersion representation for the AR. They made use of the relation between the pion pole and heavy states contribution in Eq.~(\ref{100}) imposed by PCAC, complemented with few assumptions. The assumed dominance of the axial vector $a_1$ meson, i.e. neglected the higher terms implicitly contributing in (\ref{100}). Also assumed a smooth $Q^2$-dependence of the hadronic amplitudes in (\ref{100}), and related the lepton coupling $f_{a_1}$ to that for $\rho$ meson relying on the Weinberg sum rules \cite{weinberg}. Eventually, they arrived at a relation between the elastic and diffractive pion-nucleon cross section, $\sigma(\pi p\to a_1 p)\approx\sigma(\pi p\to\pi p)$. This relation strongly contradicts data: diffractive production of $a_1$ meson is more than an order of magnitude suppressed compared with the elastic cross section. This puzzle was relaxed in \cite{belkov,km} by pointing out its shaky point, namely, the $a_1$ pole cannot dominate in the axial current, since it is quite a weak singularity compared to the $\rho$ pole in the vector current. In fact, the main contribution to the expansion Eq.~(\ref{100}) comes from the $\rho$-$\pi$ cut, related to diffractive pion excitations. The invariant mass distribution for diffractive $\pi\to3\pi$ excitations peaks at $M_{3\pi}\approx 1.3\,\mbox{GeV}$ and is well explained by the so called Deck mechanism \cite{deck} of diffractive excitation $\pi\to\rho\pi$. The interpretation of the observed peak has been a long standing controversy, until a phase-shift amplitude analysis (see references in \cite{pdg}) eventually revealed the presence of the very weak $a_1$ resonance having a similar mass. Moreover, it was found in \cite{belkov} that even the contribution of the $\rho$-$\pi$ cut in the dispersion relation for the diffractive amplitude has a $Q^2$-dependence similar to the $a_1$ pole. Summing up all diffractive excitations (excluding large invariant masses corresponding to the triple-Pomeron term), one concludes that the magnitudes of single-diffractive and elastic pion-proton cross section are indeed similar. This helps to resolve the Piketty-Stodolsky puzzle. Basing on these observations, in what follows we employ the simple two-channel model, replacing all heavy singularities contributing to the AR, by one effective pole $a$ representing $a_1$, $\rho-\pi$, etc. We assume that \beq \sigma_{sd}^{\pi p}(\pi p\to ap)=\sigma^{\pi p}_{el}, \label{130} \eeq and this allows the AR to hold. Notice that applying the AR to neutrino-production of the effective state $a$, $\nu+p\to l+a+p$, we should also conclude that \beq \sigma_{tot}^{ap}=\sigma_{tot}^{\pi p}. \label{135} \eeq We also assume that the same impact parameter dependences of the elastic $\pi\to\pi$, $a\to a$ and diffractive $\pi\to a$ amplitudes. At this point we do not pursue a high accuracy of the dispersion approach, which needs much more model dependent information about many singularities contributing to the AR. Our objective here is to highlight the importance of absorptive corrections which affect differently the diagonal and off-diagonal terms in the hadronic current (\ref{100}), which results in an unavoidable breakdown of the AR. The proposed simple model, which may be not accurate numerically, provides an excellent playground for study of the effects of absorptive corrections keeping physics transparent, and also allows to estimate the magnitude of the absorptive corrections. \section{Diagonal vs off-diagonal diffraction}\label{sect3} The relation (\ref{130}) between off-diagonal and diagonal diffractive cross sections cannot be universal and independent of energy and target. This can be understood within the general quantum-mechanical interpretation of diffraction \cite{fp,gw,kl78,mp,kst2,brazil}. A hadron has a composite structure, and its light-cone wave function consists of different hadronic components, the Fock states, which interact with the target differently, what leads to a modification of their weights. Such a modified wave packet is not orthogonal any more to other hadrons, what makes possible production of new hadrons. It turns out that the off-diagonal diffractive amplitude can be expressed in terms of diagonal ones. Let us consider two different sets of states, one consisting of the mass matrix eigenstates, $\|h\ra$, and another one of the states $\|\alpha\ra$, which are eigenstates of the interaction Hamiltonian, i.e. satisfy the condition, $\hat f_{el}\|\alpha\ra = f_\alpha\,\|\alpha\ra$, where $\hat f_{el}$ is the elastic amplitude operator. Both sets of states are assumed to be complete, so one of them can be expanded over the full basis of states in the alternative representation, \beq \|h\ra = \sum\limits_{\alpha=1}C^h_{\alpha}\,\|\alpha\ra. \label{700} \eeq Due to completeness and orthogonality of each set of these states, the coefficients $C^h_{\alpha}$ in (\ref{700}) satisfy the relations, \beqn \la h'\|h\ra &=& \sum\limits_{\alpha=1}(C^{h'}_{\alpha})^C^h_{\alpha} = \delta_{hh'} \nonumber\\ \la \beta\|\alpha\ra &=& \sum\limits_{h'}(C^{h'}_{\beta})^C^{h'}_{\alpha} = \delta_{\alpha\beta} \label{800} \eeqn The elastic and single diffraction amplitudes can therefore be expressed via the eigenamplitudes as, \beqn f_{el}^{h\to h} &=& \sum\limits_{\alpha=1}\|C^h_{\alpha}\|^2\,f_\alpha \nonumber\\ f_{sd}^{h\to h'} &=& \sum\limits_{\alpha=1}(C^{h'}_{\alpha})^C^h_{\alpha}\,f_\alpha \label{900} \eeqn These relations show that diagonal and off-diagonal diffractive amplitudes are affected by the unitarity (or absorption) corrections quite differently. For instance, in the black disk limit, which is expected to be reached in the Froissart regime at very high energies (or in central collisions with a heavy nucleus), all the partial eigenamplitudes reach the unitarity bound, ${\rm Im}\,f_\alpha=1$. Then, according to the completeness and orthogonality conditions Eqs.~(\ref{900}), the diffractive amplitudes in the black disk limit read, \beqn f_{el}^{h\to h} &\Rightarrow& \sum\limits_{\alpha=1}\|C^h_{\alpha}\|^2=1 \nonumber\\ f_{sd}^{h\to h'} &\Rightarrow& \sum\limits_{\alpha=1}(C^{h'}_{\alpha})^C^h_{\alpha} =0 \label{920} \eeqn Off-diagonal diffraction is impossible within a black disc, and may only happen on its periphery, $b\sim R$. Since in the Froissart regime the interaction radius rises with energy as $R\propto \ln(s)$, the elastic and diffractive cross sections, which are the amplitudes squared integrated over impact parameter, acquire different energy dependence, \beqn \sigma_{el}&\propto& \ln^2(s) \nonumber\\ \sigma_{sd}&\propto& \ln(s)\ , \label{940} \eeqn i.e. $\sigma_{sd}/\sigma_{el}\propto 1/\ln(s)$, apparently breaking relation (\ref{130}). Similarly, off-diagonal diffraction on a heavy nucleus is also suppressed, \beq \frac{\sigma_{sd}^A}{\sigma_{el}^A} \propto A^{-1/3}. \label{960} \eeq Thus, we conclude that the relation (\ref{130}), which follows from AR, can be strongly broken either at high energies, or on nuclear targets. \section{Absorptive corrections to the Adler relation on the proton}\label{sect4} As was argued above, the absorptive corrections break down validity of Eq.~(\ref{130}). In order to estimate the magnitude of deviation from the AR on a proton target, we rely on the simple Regge model proposed in Sect.~\ref{sect2}, with two channels in the axial current, the pion pole and the effective axial-vector pole $a$ representing the $a_1$ pole and other singularities producing the bump at $M\approx 1.3\,\mbox{GeV}$ in the invariant mass distribution of the $3\pi$ diffractive excitation of a pion. As a starting point, we assume that in the single-Pomeron approximation the AR holds, i.e. the diffractive and elastic amplitudes are equal, i.e. Eq.~(\ref{130}) holds. Now we introduce absorptive corrections related to the multiple Pomeron exchanges the in initial and final states, and see how much the relation (\ref{130}) is broken for the output amplitudes. This can be considered as an estimate for the magnitude of deviation from the AR on a proton. We rely on the same two-channel model for multi-Pomeron corrections. The unitarized elastic cross section reads, \beq \sigma^{\pi p}_{el}=\int d^2b\, \left[1-e^{-{\rm Im} f^{\pi p}_{el}(b)}\right]^2. \label{1020} \eeq Although this expression looks like the conventional single-channel Glauber model, it remains unchanged within the two-channel model under consideration. For the sake of simplicity we neglect the real part of the amplitude. Similarly the cross section of the diffractive excitation $\pi p\to a p$, corrected for absorption, reads, \beqn \sigma_{sd}^{\pi p} &=& \int d^2b\, \left\|f_{sd}^{\pi p}(b)\right\|^2\, \left[\frac{e^{-{\rm Im} f^{\pi p}_{el}(b)}-e^{-{\rm Im} f^{a p}_{el}(b)}} {{\rm Im} f^{a p}_{el}(b)-{\rm Im} f^{\pi p}_{el}(b)}\right]^2 \nonumber\\ &\approx& \int d^2b\, \left[{\rm Im} f^{\pi p}_{el}(b)\right]^2\,e^{-2{\rm Im} f^{\pi p}_{el}(b)}. \label{1040} \eeqn At the last step here we used the relation (\ref{135}). We see that the unitarity corrections to the elastic cross section, Eq.~(\ref{1020}), and the absorptive corrections to diffraction, Eq.~(\ref{1040}), act in opposite directions: they enhance the diagonal, but suppress the off-diagonal diffractive processes. To estimate the magnitude of the difference between the cross sections (\ref{1020}) and (\ref{1040}) we employ the conventional Gaussian form of the impact parameter dependence for the input single-Pomeron elastic partial amplitude, \beq \,\mbox{Im}\, f_{el}^{\pi p}(b)=\frac{\sigma_{tot}^{\pi p}}{4\pi\,B_{el}^{\pi p}}\, \exp\left(-\frac{b^2}{2B^{\pi p}_{el}}\right). \label{980} \eeq Then we can evaluate the correction factor $K_{AR}=\sigma_{sd}^{\pi p}/\sigma_{el}^{\pi p}$, which should be applied to the right-hand side of Eq.~(\ref{40}). We used (\ref{1020}), (\ref{1040}) and (\ref{980}) with $\sigma_{tot}^{\pi p}=13.6\,\mbox{mb}\times s^{0.08}+19.24\,\mbox{mb}\times s^{-0.458}$, $B^{\pi p}_{el}=B_0+2\alpha_{{ I\!\!P}}^\prime\ln s$, where $s$ is in $\,\mbox{GeV}^2$, $B_0=6\,\mbox{GeV}^{-2}$, $\alpha_{{ I\!\!P}}^\prime=0.25\,\mbox{GeV}^{-2}$. The results are depicted in Fig.~\ref{proton-corr} as function of $\nu$. \begin{figure}[htb] \begin{center} \includegraphics[height=6cm]{kv.eps}\hspace{10mm} \end{center} \caption{\label{proton-corr} (Color online) The absorptive correction factor for the Adler relation for diffractive neutrino-production of pions on protons.} \end{figure} We see that the absorptive corrections cause a deviation from the AR of about $30\%$, which is not a dramatic effect. This is because the $\pi$-$p$ elastic amplitude is still far from the unitarity bound. However, at much higher energies (still unreachable in neutrino experiments) the correction factor is expected to drop significantly. \section{Coherent neutrino-production of pions on nuclei} According to the conventional terminology, coherent production on nuclei is a process which leaves the nucleus intact. Correspondingly, in an incoherent process the nucleus is supposed to break up to fragments. In what follows we assume the validity of the AR for a nucleon target (unless specified), in order to identify the net nuclear effects for the AR. This section is devoted to coherent diffractive pion production. The production amplitudes on different nucleons interfere, and the interference is enhanced by the condition that the nucleus remains in the ground state. Such effects of coherence can lead to substantial deviations from the AR and from simplified expectations, as is demonstrated below. \subsection{Important time scales} There are several length scales characterizing the coherence effects in diffractive neutrino scattering on nuclei. The first length scale is controlled by the longitudinal momentum transfer $q_L^\pi$ in diffractive production of a pion by an axial current of energy $\nu$ and virtuality $Q^2$, \beq l_c^\pi=\frac{1}{q_L^\pi}= \frac{2\,\nu}{Q^2+m_\pi^2}. \label{1060} \eeq Within this distance the pion production amplitudes $\nu N\to l\pi N$ on different nucleons interfere and shadow each other. If the axial current virtuality is small $Q^2\sim m_\pi^2$, the coherence length $l_c^\pi$ is rather long even at low energies. It reaches the size of a heavy nucleus at energies as low as several hundreds MeV. Such an early onset of coherence is a peculiar feature of the axial current. It would be impossible for the vector current,even for real photoproduction of $\rho$-mesons the onset of shadowing is delayed up to the energies of several GeVs. Notice that besides diffractive neutrino-production of pions, the early onset of shadowing also occurs for the total neutrino-nucleus cross section \cite{k-shad,gransasso,shad-jetp} at low $Q^2$. Another, much shorter length scale corresponds to diffractive transitions between the axial current and heavy states, which are represented by the effective axial-vector meson $a$ in our model, \beq l_c^a=\frac{1}{q_L^a}= \frac{2\,\nu}{Q^2+m_a^2}. \label{1070} \eeq This coherence length controls neutrino diffractive dissociation to heavy hadronic states, and also the energy dependence of absorptive corrections to the cross section of neutrino-production of pions on nuclei (see below). At small $Q^2\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$} m_\pi^2$ it is two orders of magnitude shorter than $l_c^\pi$. \subsection{The amplitude} The process of coherent neutrino-production of pions on nuclei, $\nu A\to l\pi A$, is possible only if $l_c^\pi\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$} R_A$, otherwise the nuclear form factor suppresses the cross section \cite{belkov}. Even if $l_c^\pi$ is long, the second length scale $l_c^a$ might be still short. Correspondingly there are few energy regimes where the coherent length scales vary from very short up to much longer values than the nuclear radius. Correspondingly, the imaginary part of the partial amplitude of coherent production of a pion contains two terms, \beq M_{\nu A\to l\pi A}(\nu,Q^2,b)=M_1(\nu,Q^2,b)-M_2(\nu,Q^2,b), \label{140} \eeq where \begin{widetext} \beqn M_1(\nu,Q^2,b)&=&M_{\nu N\to l\pi N} (\nu,Q^2) \int\limits_{-\infty}^\infty dz\, e^{iq_L^\pi z}\, \rho_A(z,b)\,e^{-{1\over2}\sigma_{tot}^{\pi N}T_A(b,z)}; \label{160}\\ M_2(\nu,Q^2,b) &=& M_{\nu N\to laN}(\nu,Q^2)\, M_{aN\to \pi N}(\nu) \int\limits_{-\infty}^\infty dz\, e^{i(q_L^\pi-q_L^a) z}\, \rho_A(z,b)\,e^{-{1\over2}\sigma_{tot}^{\pi N}T_A(b,z)} \nonumber \\&\times& \int\limits_{-\infty}^z dz_1 e^{iq_L^a z_1}\,\rho_A(z_1,b)\, e^{-{1\over2}\sigma_{tot}^{a N}[T_A(b,z_1)-T_A(b,z)]}. \label{200} \eeqn \end{widetext} Here the first term $M_1$ is the amplitude of pion production at the point with longitudinal coordinate $z$ and impact parameter $b$, integrated over $z$ weighed by the nuclear density $\rho_A$ \cite{belkov}. The $z$-dependent nuclear thickness function is defined as \beq T_A(b,z)=\int\limits_z^\infty dz'\,\rho_A(b,z'), \label{180} \eeq and we denote $T_A(b)\equiv T_A(b,z\to -\infty)$. The second term $M_2$ corresponds to diffractive production of the heavy state $a$ preceding the pion production. This is the first order Gribov inelastic shadowing correction \cite{gribov} to the coherent pion production amplitude. As far as the amplitude Eq.~(\ref{140}) is known, we can calculate the cross section of coherent pion production, \beq \frac{d\sigma(\nu A\to l\pi A)}{dQ^2\,d\nu\,d^2p_T}= \left\|\int \frac{d^2b}{2\pi}\,e^{i\vec p_T\cdot\vec b}M_{\nu A\to l\pi A}(\nu,Q^2,b)\right\|^2, \label{210} \eeq where $\vec p_T$ is the transverse momentum transfer to the target, and we neglect the real part of the ampltude. The cross section on a nucleon target according to (\ref{980}) has the form, \beq \frac{d\sigma(\nu N\to l\pi N)}{dQ^2\,d\nu\,d^2p_T}= \frac{e^{-B_{el}^{\pi p}p_T^2}}{(2\pi)^2}\, \left\|M_{\nu N\to l\pi N}(\nu,Q^2)\right\|^2 \label{215} \eeq \subsection{Characteristic regimes in the energy dependence} In the general expression Eq.~(\ref{140})-(\ref{200}) one can identify several characteristic regimes, which are controlled by the interplaying coherence scales $l_c^\pi$ and $l_c^a$. \subsubsection{\boldmath$l_c^\pi\lesssim R_A$}\label{sub1} In this regime the AR on a nucleus trivially breaks down, as one can see from Eq.~(\ref{160}). The cross section is falling with decreasing $l_c^\pi$ and vanishes at $l_c^\pi\ll R_A$, as it was calculated in \cite{belkov}. The reason is obvious: the AR relation is supposed to hold at the pion pole at $Q^2=-m_\pi^2$, and the extrapolation to $Q^2=0$ leads to a strong variation of the amplitude, if the longitudinal momentum transfer $l_c^\pi$ is comparable with $R_A$, or shorter. Notice that one should be cautious applying Eq.~(\ref{160}) at low energies where the neglected contribution of s-channel resonances and/or reggeons is important \cite{khlopov1,khlopov2}. Also the neglected real part of the amplitude becomes large. Therefore, our calculations for this energy regime of $l_c^\pi\lesssim R_A$ only present an estimate of the effects related to the nuclear formfactor \cite{belkov}. \subsubsection{\boldmath$l_c^\pi\gg R_A$, $l_c^a\ll R_A$}\label{sub2} Eqs.~(\ref{160})-(\ref{200}) are significantly simplified in this regime of very long $l_c^\pi$ and very short lifetime $l_c^a$ of the $\pi\to a$ fluctuations compared to the nuclear radius $R_A$. In this case the amplitude $M_2(\nu,Q^2,b)$, Eq.~(\ref{200}) is strongly suppressed by the oscillating exponential and can be neglected. At the same time, $l_c^\pi\gg R_A$, therefore the non-vanishing term in (\ref{140}), the amplitude $M_1(\nu,Q^2,b)$, can be also simplified by integrating over $z$ in Eq.~(\ref{160}) analytically, \beq M_1(\nu,Q^2,b)= \frac{2M_{\nu N\to l\pi N}(\nu,Q^2)}{\sigma_{tot}^{\pi N}}\, \left[1-e^{-{1\over2}\sigma_{tot}^{\pi N}T_A(b)}\right] \label{220} \eeq At this point we concentrate on nuclear effects leading to breakdown of the AR, therefore hereafter we assume that the amplitude of pion neutrino-production on a nucleon satisfies the AR Eq.~(\ref{40}), \beq M_{\nu N\to l\pi N}(\nu,Q^2=0)= \xi(E,\nu)\,{1\over2}\sigma^{\pi N}_{tot}(\nu), \label{240} \eeq where we employ the optical theorem neglecting the real part of the diffractive amplitude. The amplitudes are normalized as $d\sigma/dQ^2d\nu=\left\|M_{\nu N\to l\pi N}(\nu,Q^2)\right\|^2$. Applying (\ref{180}) to (\ref{160}) we get the relation, \beq M_1(\nu,Q^2=0,b)= \xi(E,\nu)\,\left[1-e^{-{1\over2}\sigma_{tot}^{\pi N}T_A(b)}\right], \label{260} \eeq which is exactly the AR for the partial amplitude of neutrino-production of pions. We conclude that if the AR is correct for a pion production on a nucleon, it should be also correct for a nuclear target, provided that $l_c^\pi\gg R_A$, but $l_c^a\ll R_A$. \subsubsection{\boldmath$l_c^a\gg R_A$}\label{sub3} In this regime all the phase shifts in Eq.~(\ref{140}) can be neglected and the integration over $z$ and $z_1$ can be performed analytically, \begin{widetext} \beqn M_2(\nu,Q^2,b)\Bigr\|_{l_c^a\gg1} &=& M_{\nu N\to aN}(\nu,Q^2)\, M_{aN\to \pi N}(\nu)\, \frac{4}{\sigma_{tot}^{a N}} \Biggl\{\frac{1}{\sigma_{tot}^{\pi N}}\, \left[1-e^{-{1\over2}\sigma_{tot}^{\pi N}T_A(b)}\right] \, -\, \frac{e^{-{1\over2}\sigma_{tot}^{a N}T_A(b)} - e^{-{1\over2}\sigma_{tot}^{\pi N}T_A(b)}} {\sigma_{tot}^{\pi N}-\sigma_{tot}^{a N}} \Biggr\} \nonumber\\ &=& M_{\nu N\to aN}(\nu,Q^2)\, M_{aN\to \pi N}(\nu)\, \frac{4}{\left(\sigma_{tot}^{a N}\right)^2} \Biggl\{1-\left[1+{1\over2}\sigma_{tot}^{\pi N}T_A(b)\right] e^{-{1\over2}\sigma_{tot}^{\pi N}T_A(b)} \Biggr\} \label{280} \eeqn \end{widetext} The first term in (\ref{140}), the amplitude $M_1$, was already calculated in this limit ($l_c^a\gg R_A$) above in (\ref{220}). In both expressions the neutrino-production amplitudes $M_{\nu N\to hN}(\nu,Q^2)$ are related to the hadronic ones, $a+N\to h+N$, by the AR . Besides, based on the assumed dominance in the axial current of the effective pole $a$, we can extrapolate these relations to nonzero $Q^2$ with the pole propagator $(Q^2+m_a^2)^{-1}$. Thus, we get new relations,\\ \beq M_{\nu N\to laN}(\nu,Q^2)=\frac{\xi(\nu)\,m_a^2}{Q^2+m_a^2}\,M_{aN\to a N}; \label{290} \eeq \beq M_{\nu N\to l\pi N}(\nu,Q^2)=\frac{\xi(\nu)\,m_a^2}{Q^2+m_a^2}\,M_{aN\to \pi N}, \label{300} \eeq We rely on these relations in what follows. Eventually, summing the amplitudes Eqs.~(\ref{220}) and (\ref{280}) we arrive at \beq \frac{M_{\nu A\to l\pi A}(\nu,Q^2,b)} {M_{\nu N\to l\pi N}(\nu,Q^2)}\Biggr\|_{l_c^a\gg1} = T_A(b)\,e^{-{1\over2}\sigma_{tot}^{\pi N}T_A(b)}. \label{320} \eeq One can observe the striking difference in the $A$ dependence of the cross sections corresponding to the regimes of short and long coherence length $l_c^a$, equations (\ref{220}) and (\ref{320}) respectively. The AR holds in the former case and nuclear cross section behaves as $A^{2/3}$ (for very heavy nuclei). However, at latter case the cross section is $\propto A^{1/3}$, so the AR breaks down. Notice that in this regime of $l_c^a\gg R_A$ the calculations \cite{belkov} based on AR are not correct. Also the results of \cite{rs} are not correct at any energy, since rely on a wrong model for the pion-nucleus cross section (see discussion in \cite{belkov}). \subsection{Numerical results}\label{sect:numerical} Such a nontrivial behavior of nuclear effects as function of energy is confirmed by the results of numerical calculations of the $p_T$-integrated cross sections with Eqs.~(\ref{140})-(\ref{200}). The ratio \beqn && R^{coh}_{A/N}(\nu,Q^2) = \frac{d\sigma(\nu A\to l\pi A)/dQ^2\,d\nu} {A\,d\sigma(\nu N\to l\pi N)/dQ^2\,d\nu} \nonumber\\ &=& \frac{4\pi B^{\pi N}_{el}}{A}\, \int d^2b \left\|M_{\nu A\to l\pi A}(\nu,Q^2,b)\right\|^2 \label{340} \eeqn is plotted in Fig.~\ref{fig:coh-Adep} for lead, aluminium and carbon targets as function of $\nu$ at $Q^2=0$. \begin{figure}[htb] \begin{center} \includegraphics[height=7cm]{coh-Adep.eps}\hspace{10mm} \end{center} \caption{\label{fig:coh-Adep} (Color online) {\it Solid curves:} nuclear ratio $R^{coh}_{A/N}(\nu,Q^2)$ of $p_T$-integrated cross sections of coherent neutrino-production of pions, $\nu+A\to l+\pi+A$, calculated with Eq.~(\ref{340}) at $Q^2=0$. {\it Dashed lines:} the results of the Adler relation applied to nuclear targets, lead, aluminium and carbon, from top to bottom.} \end{figure} For the sake of simplicity the calculations were performed with a constant cross section $\sigma_{tot}^{\pi N}=25\,\mbox{mb}$. We see that at low energies $\nu\lesssim 1\,\mbox{GeV}$ the nuclear ratio $R^{coh}_{A/N}$, plotted by solid curves, rises with $\nu$ and saturates at the level corresponding to the AR applied to nuclei, depicted by dashed horizontal lines. Because the survival probability of a pion propagating a long path length in the nuclear medium is low, the pion production points are pushed to the back surface of the nucleus (compare with Eq.~(\ref{220})). Therefore, the cross section depends on nuclear atomic number as $\sim A^{2/3}$ and coincides with the prediction of AR in the saturated regime of $q_c^\pi\ll1/R_A$. The observed strong deviation from the AR prediction at very low energies is a simple consequence of the suppression of the coherent cross section caused by the nuclear formfactor due to finiteness of the momentum transfer, $q_c^\pi\sim 1/R_A$. The energy dependence of nuclear ratio forms a plateau from several hundreds MeV up to several GeV in the regime described in Sect.~\ref{sub2}. It also well agrees with the prediction of the AR shown by dashed lines in Fig.~\ref{fig:coh-Adep}. At energies $\nu\gsim10\,\mbox{GeV}$ the nuclear cross section considerably drops and saturates at a new level exposing a significant deviation from the expectations based on the AR, depicted by dashed curves. This happens due to the transition to the new regime of full coherence explained in Sect.~\ref{sub3}. It worth commenting that the height of the plateaus for different nuclei shows that the $A$-dependence of the cross section in this regime is slightly steeper than linear. This is different from the simple expectation of $R^{coh}_{A/N}\propto A^{-1/3}$ corresponding to the black disc limit. This happens because the cross section $\sigma^{\pi N}_{tot}$ is rather small and the pion-nucleus partial amplitude is still far from the unitarity bound. So the pion-nucleus elastic cross section is quite smaller than the $\pi R_A^2$. This is why it rises as $A^\alpha$ with $\alpha>1$. Thus, the cross section of diffractive coherent neutrino-production of pions on nuclei exposes a peculiar energy dependence. It starts from zero at very small energies, then rises and saturates at a large magnitude, and eventually drops down to a value $\propto A^{1/3}$ at higher energies. The AR relation is severely broken at the regimes of short $l_c^\pi\ll R_A$ and long $l_c^a\gg R_A$, but is rather accurate within the intermediate regime. The specific energy dependence of nuclear effects presented in Fig.~\ref{fig:coh-Adep} at $Q^2=0$ drastically changes with rising $Q^2$. Indeed, the plateau in the energy dependence, which spans across the wide energy range, is related to the significant difference between the length scales Eqs.~(\ref{1060})-(\ref{1070}), $l_c^\pi\gg l_c^a$. This holds, however, only for tiny values of $Q^2\lesssim m_\pi^2$. With rising $Q^2$ both scales contract down to the same order of magnitude, and the plateau in the energy dependence of $R_{A/N}^{coh}$ shrinks and becomes a peak. This is illustrated in Fig.~\ref{fig:coh-Qdep} for neutrino-production of pions on lead for few values of $Q^2=0,\ 0.2,\ 0.5$ and $1\,\mbox{GeV}^2$. \begin{figure}[htb] \begin{center} \includegraphics[height=7cm]{coh-Qdep.eps}\hspace{10mm} \end{center} \caption{\label{fig:coh-Qdep} (Color online) The same as in Fig.~\ref{fig:coh-Adep} for lead at $Q^2=0,\ 0.2,\ 0.5$ and $1\,\mbox{GeV}^2$.} \end{figure} We do not extend our predictions to larger values of $Q^2$ for several reasons. First of all, at large $Q^2$ the effects of color transparency make the nuclear medium more transparent than we evaluated. These effects cannot be reproduced within the employed two-channel model. In hadronic representation color transparency results from superposition of many singularities in the dispersion relation with masses up to $M^2\sim Q^2$ \cite{zkl,jk}. Besides, one should take care of the correct (negative) signs of the off-diagonal diffractive amplitudes, and provide a fine tuning between different amplitudes, which must essentially cancel each other at high $Q^2$, in order to end up with color transparency. This is a difficult task, which can be solved much more effectively within the dipole representation \cite{zkl}. Another reason for not extending our calculation to larger values of $Q^2$ is the missed contributions of the transverse component of the axial current and of the vector current. Both vanish at $Q^2\to 0$, but should be added and have growing importance with rising $Q^2$. We presented numerical results for nuclear effects only for $p_T$-integrated cross sections, since their $p_T$-dependence is rather simple and well known. The $p_T$-distribution of coherent pion production forms a narrow peak at small $p_T$, with a slope of the order of ${1\over3}R_A^2$, caused by the nuclear form factor. More accurately, the $p_T$-dependence of the cross section is given by Eq.~(\ref{210}). The large $p_T$-slope of the cross section is the signature of the coherent process, which is usually used to disentangle it from the incoherent background having a much smaller slope, similar to production on a free nucleon. \section{Incoherent pion production}\label{sect:incoh} As a result of momentum transfer in diffractive neutrino-production on a bound nucleon, the nucleus can be excited or break-up to fragments, $\nu+A\to l+\pi+A^$. Although pions diffractively produced at different impact parameters do not interfere in this process, characterized by rather large transverse momentum transfer, the amplitudes on bound nucleons with the same impact parameter do interfere. Evaluation of the cross section is more involved that in the case of coherent production, but can be simplified by summing up all nuclear final states and employing completeness. We perform calculations within the two-channel model for the axial current introduced earlier. The results are presented in the form of nuclear ratio defined similar to the case of coherent production, Eq.~(\ref{340}), \beq R^{inc}_{A/N}(\nu,Q^2) = \frac{d\sigma(\nu A\to l\pi A^)/dQ^2\,d\nu} {A\,d\sigma(\nu N\to l\pi N)/dQ^2\,d\nu}. \label{360} \eeq \subsection{Effects of coherence for incoherent production} Like in the case of coherent production, one can identify several contributions in the nuclear factor $R^{inc}_{A/N}$, characterized with different mechanisms \cite{hkn-glaub}. \beq R^{inc}_{A/N}=R^{inc}_1+R^{inc}_2-R^{inc}_3. \label{370} \eeq The three terms in the right-hand side of this equation correspond to the following mechanisms of incoherent pion production. I) The incoming neutrino does not interact in the nucleus up to the point with coordinates $(b,z)$, where it diffractively produces the pion, $\nu+N\to l+\pi+N$, which survives propagating through the nucleus. The corresponding amplitude squared, summed over the final state of the nucleus, and integrated over coordinates of the bound nucleon has the form, \beqn R^{inc}_1&=& {1\over A}\ \int d^2b \int\limits_{-\infty}^{\infty} dz\ \rho_A(b,z)\,e^{-\sigma^{\pi N}_{in} T_A(b,z)} \nonumber\\ &=& \frac{1}{A\sigma^{\pi N}_{in}} \int d^2b\,\left[1-e^{-\sigma^{\pi N}_{in} T_A(b)}\right] \label{380} \eeqn II) Prior the pion production the neutrino interacts with another bound nucleon at the point ($b,z_1$), and produces diffractively an $a$-meson, $\nu+N\to l+a+N$, which is the effective state representing different products of diffractive excitation of a pion, as it was introduced in Sect.~\ref{sect2}. Then the $a$-meson propagates further and produces diffractively a pion, $a+N\to\pi+N$ ($z>z_1$). The corresponding term in the nuclear factor derived in \cite{hkn-glaub} has the form, \begin{widetext} \beqn R^{inc}_2 &=& \frac{\sigma^{\pi N}_{tot}} {2A\,\sigma^{\pi N}_{el}}\ (\sigma^{\pi N}_{in} - \sigma^{\pi N}_{el})\,\int d^2b \int\limits_{-\infty}^{\infty} dz_1\ \rho_A(b,z_1)\ \int\limits_{z_1}^{\infty} dz_2\ \rho_A(b,z_2)\, \cos\left[q_c^\pi(z_2-z_1)\right]\ \nonumber\\ & \times& \exp\left[- {1\over 2}(\sigma^{\pi N}_{in} - \sigma^{\pi N}_{el})\ T_A(b,z_2) - {1\over 2}\sigma^{\pi N}_{tot} T_A(b,z_1) \right] \label{400} \eeqn \end{widetext} Here we fixed $\sigma^{a N}_{tot}=\sigma^{\pi N}_{tot}$, as follows from the AR in the employed two-channel model; $z_1$ and $z_2$ are (\ref{400}) the longitudinal coordinates of diffractive neutrino-production of the intermediate $a$-meson in the two interfering amplitudes. The final pion is produced diffractively, $a+N\to\pi+N$, but incoherently, i.e. on the same nucleon, with coordinates $(b,z)$ in both amplitudes. III. In the first two terms of (\ref{370}) we summed up all final state of the nucleus including the ground state. The latter corresponds to coherent pion production evaluated in the previous section, and should be subtracted. Thus, \beq R^{inc}_3 = \frac{\left(\sigma^{\pi N}_{tot}\right)^2}{4A\,\sigma^{\pi N}_{el}} \int d^2b \left\| \int\limits_{-\infty}^{\infty} dz\,\rho_A(b,z)\ e^{iq_c^\pi z} e^{-{1\over 2}\sigma^{\pi N}_{tot}\ T_A(b,z)} \right\|^2 \label{420} \eeq Like in the case of coherent production, one can identify three regimes of energy dependence of the incoherent cross section. \subsubsection{\boldmath$l_c^\pi\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$} R_A,\ \ l_c^a\ll R_A$} In the low energy limit of $q^\pi_c\gg R_A$ only the first term in (\ref{370}) survives and $R^{inc}_{A/N}\Bigr\|_{q^\pi_c\gg R_A}=R^{inc}_1$ given by Eq.~(\ref{380}). At higher energies, when $q^\pi_c\to 0$ all integrations on longitudinal coordinates in (\ref{380})-(\ref{420}) can be performed analytically, \beq R^{inc}_{A/N}\Bigr\|_{q_c^\pi \to0}=\int d^2b\,T_A(b) e^{-\sigma^{\pi N}_{in} T_A(b)}. \label{440} \eeq This shows a considerable drop of the nuclear ratio from the low energy limit given by Eq.~(\ref{380}) toward the high energy limit. The interpolation between the two regimes is performed by the full expression Eqs.~(\ref{340}). The numerical results at $Q^2=0$ for several nuclei depicted in Fig.~\ref{fig:inc-Adep} indeed demonstrate a considerable drop with energy of the nuclear ratio. \begin{figure}[htb] \begin{center} \includegraphics[height=7cm]{inc-Adep.eps}\hspace{10mm} \end{center} \caption{\label{fig:inc-Adep} (Color online) The same as in Fig.~\ref{fig:coh-Adep} for incoherent pion production $\nu+A\to l+\pi+A^$.} \end{figure} Notice that a similar behavior predicted in \cite{hkn-glaub} for electroproduction of vector mesons, was nicely confirmed later the by HERMES experiment \cite{hermes} (see also \cite{knst}). At large values of $Q^2$ the regime of short $l_c^\pi$ propagates to higher energies, as is demonstrated in Fig.~\ref{fig:inc-Qdep}. \begin{figure}[b] \begin{center} \includegraphics[height=7cm]{inc-Qdep.eps}\hspace{10mm} \end{center} \caption{\label{fig:inc-Qdep} (Color online) The same as in Fig.~\ref{fig:inc-Qdep} for lead at $Q^2=0,\ 0.2,\ 0.5$ and $1\,\mbox{GeV}^2$.} \end{figure} So far we assumed that $l_c^\pi$ may be short or long, but the second length scale $l_c^a$ is always short. In this case, similar to the coherent process in this regime, the AR is valid. Indeed, Eq.~(\ref{440}) is equivalent to the Glauber formula for nuclear ratio in quasi-elastic pion scattering on a nucleus, i.e. is exactly what follows from the AR. \subsubsection{\boldmath$l_c^a\gg R_A$} At higher energies $l_c^a$ also becomes long, what has led to breakdown of the AR in the coherent process (see the previous section and Fig.~\ref{fig:coh-Adep}). What happens in this case with an incoherent pion production ? In the asymptotic regime of $l_c^a\gg R_A$ the answer is easy, \beq R^{inc}_{A/N}\Bigr\|_{q_c^a\gg R_A}= \int d^2b\,\frac{e^{-\sigma^{a N}_{in} T_A(b)}-e^{-\sigma^{\pi N}_{in} T_A(b)}} {\sigma_{in}^{\pi N}-\sigma_{in}^{aN}}. \label{460} \eeq We have shown above, Eq.~(\ref{135}), that in the two-channel model under consideration the AR leads to the equality $\sigma^{a N}_{in}=\sigma^{\pi N}_{in}$. In this case Eq.~(\ref{460}) is equivalent to (\ref{440}). Thus, we arrived at a remarkable conclusion that in the case of incoherent neutrino-production of pions on nuclear targets the AR is always correct. \section{Summary} At high energies neutrinos expose hadronic properties similar to photons, since they also interact with a target via hadronic fluctuations. Although it is tempting to interpret the AR as pion dominance, the pion pole is excluded due to conservation of the leptonic current (for neutral current, otherwise is suppressed by the lepton mass). In fact, the AR imposes a mysterious relation between the pion interaction with the target and the contribution of heavy axial states to the neutrino interaction. The former corresponds to elastic pion scattering in the process of diffractive neutrino-production of pions, while the latter is related to off-diagonal diffraction of a pion, excluding elastic scattering. It is known that these two processes are subject to absorptive corrections which affect them quite differently, namely, they enhance diagonal diffraction (elastic scattering), but suppress inelastic diffraction. Therefore, the AR cannot be universal, target independent. We checked the role of absorptive corrections for diffractive neutrino-production of pions on protons and nuclei. Assuming that the AR holds on a proton target without absorptive corrections, we estimated the magnitude of deviation from AR at about 30\% (see Fig.~\ref{proton-corr}). Much stronger effects were found on heavy nuclei. In coherent production of pions, $\nu+A\to l+\pi+A$, the AR holds with a good accuracy at energies $\nu\approx 1-10\,\mbox{GeV}$. However, it is severely broken at lower and higher energies (see Fig.~\ref{fig:coh-Adep}). Our numerical results at low energies in the regime of $l_c^\pi\lesssim R_A$ are rather schematic, since do not include the contribution of resonances and large real part of the diffractive amplitudes. For incoherent pion production, $\nu+A\to l+\pi+A^$, when the nucleus decays into fragments, we found a considerable variation of nuclear effects with energy (see Fig.~\ref{fig:inc-Adep}), similar to photoproduction of vector mesons. Remarkably, however, no deviations from the AR were detected, and it holds at all energies. While the employed two-channel model may be numerically not very accurate, it allows to simplify the calculation of the absorptive corrections and estimate the magnitude of deviations from the AR. Besides, explicit involvement of heavier singularities in the dispersion relation would lead to appearance of many unknown parameters. An alternative description, which allows to include all of them would be the light-cone color dipole representation \cite{zkl}. The corresponding results will be published elsewhere \cite{dipole1}. \begin{acknowledgments} We are thankful to Daniel Ega$\tilde{\rm n}$a, Genya Levin and Arkady Vainshtein for useful discussions. This work was supported in part by Fondecyt (Chile) grants 1090236, 1090291, 1100287 and 1090073, and by Conicyt-DFG grant No. 084-2009. \end{acknowledgments}	{ "redpajama_set_name": "RedPajamaArXiv" }	7,888
<?php namespace Rcm\Exception; use Rcm\Exception\ExceptionInterface as RcmExceptionInterface; class PluginInstanceNotFoundException extends \RuntimeException implements RcmExceptionInterface { }	{ "redpajama_set_name": "RedPajamaGithub" }	8,113
\section{Introduction} The electronic band structure of graphene, characterized by a linear dispersion relation, makes it an ideal material for the study of the fundamentals of light-matter interactions \cite{Geim2007, CastroNeto2009}. In fact, because of the small value of its Fermi velocity and the absence of a bandgap in monolayer graphene, multiphoton transitions in the strong-field regime correspond to accessible laser frequencies, i.e. in the visible range or smaller. As a direct result of these properties, graphene is sensitive to the temporal shape of strong-field, few-cycle pulses \cite{Lefebvre2017}. This sensitivity has led to many applications of laser-driven graphene such as controlling directional photo-currents \cite{higuchi2017light}, graphene polarizers \cite{bao2011broadband,Farmani2018b} and giant lateral shifts \cite{Farmani2018a,Farmani2017}. The research field of ``high-field physics'' in graphene has gained momentum with the advent of intense terahertz (THz) radiation sources \cite{Razavipour2015, McGouran2016}: short pulses with peak electric fields in the kV/cm range are now commonplace \cite{Ropagnol2013, Hafez2016}, with some leading-edge sources even reaching the MV/cm threshold \cite{Ishikawa2013}. As an illustration, THz radiation can lead to high-harmonic radiation when used to pump a graphene mono-layer \cite{Al-Naib2014}. In addition, the ultra-fast carrier dynamics in graphene induced by short THz pulses can be probed using techniques such as angle-resolved photoemission spectroscopy (ARPES) \cite{Ishikawa2013, Sentef2015, Kelardeh2016, Aeschlimann2017}. The result of momentum-resolved experiments with graphene has been the subject of several articles in recent years, most of which consider the effect of a short optical or THz pulse on the conduction band population in reciprocal space \cite{Ishikawa2013, Kelardeh2015, Kelardeh2016, Fillion-Gourdeau2015, Fillion-Gourdeau2016, Lefebvre2017}. Theoretical investigations have revealed that the details of the temporal pulse shape, for instance the carrier-envelope phase, can have a manifest impact on the momentum space patterns \cite{Ishikawa2013, Lefebvre2017}. In this article, we consider the \emph{inverse} problem, namely finding the temporal pulse shape which minimizes the photo-induced carrier density in graphene over a pre-defined momentum window. The numerical solution of this problem is performed using differential evolution (DE), a high-level optimization algorithm. Pulse shaping problems are also encountered in several other areas of physics, for instance atomic and molecular physics, quantum electrodynamics (QED) and quantum information, and are tackled using various high-level techniques \cite{Chu2001, Christov2001, Balogh2014, Hebenstreit2016, Fillion-Gourdeau2017}. The results of this article may thus find application in other subfields of physics besides laser-irradiated graphene and related Dirac materials. Control over THz pulse shapes through spectral amplitudes or phases has been performed recently using several techniques such as photoexcited semiconductors \cite{doi:10.1063/1.4907635}, dynamic waveguides \cite{Gingras:18} and plasmonic metasurfaces \cite{Rahimi:16}. In this work, optimization constraints on the THz spectrum are chosen to obtain short pulses that can be generated experimentally. To achieve this theoretically, the pulse spectrum is parametrized using a $B$-spline polynomial basis, and the corresponding expansion coefficients are used as inputs of the DE solver following a procedure described in Ref. \cite{Fillion-Gourdeau2017} for the optimization of Schwinger's mechanism in QED. This parametrization ensures a certain level of smoothness in the spectrum of the resulting THz pulses, and results in a low-dimensional search space, thus speeding up optimization runs. Other than this choice of a $B$-spline basis, few assumptions are made as to the details of the final pulse. The main finding of the article is that the photo-induced carrier density in graphene can be varied by a factor of 4 for a fixed THz fluence, leading to the possibility of using spectral optimization as a control knob over scattering mechanisms in Dirac materials. In addition, we are able to selectively suppress or enhance multiphoton absorption features by using the pulse fluence as an additional control parameter in optimization calculations. This article is organized as follows. The pulse shaping problem central to this work is presented in section \ref{sec:problem}. Specifically, we discuss the $B$-spline parametrization used for optimization calculations (Sec. \ref{sec:param}), as well as the optimization solver itself (Sec. \ref{sec:de}). Two different problems are then discussed (Sec. \ref{sec:results}) and a summary is given (Sec. \ref{sec:summary}). \section{Problem definition}\label{sec:problem} Consider Dirac fermions in a graphene mono-layer in the presence of a linearly polarized electric field, which is uniform in space and parallel to the graphene plane. Assuming that electron-electron interactions and carrier relaxation can be neglected (the validity of these assumptions is discussed in Sec. \ref{sec:cfluence}), the fermion dynamics are governed by the time-dependent Dirac equation (TDDE) in reciprocal space, or $\mathbf{p}$-space (we use units such that $\hbar = 1$): \begin{equation}\label{eq:Dirac} i\partial_t \psi_{s,\textbf{K}_{\pm}}(t,\textbf{p}) = H_{\textbf{K}_{\pm}} \psi_{s,\textbf{K}_{\pm}}(t,\textbf{p}), \end{equation} where $\psi_{s,\textbf{K}_{\pm}}(t_f,\textbf{p})$ is the wavefunction, $s$ is the physical spin of the electron and $\textbf{K}_{\pm}$ are non-equivalent Dirac points, corresponding to the valley pseudospin. The graphene Hamiltonian is characterized by the usual linear dispersion relation and the absence of a mass term: \begin{equation}\label{eq:Hamiltonian} H_{\textbf{K}_{\pm}} (t,\textbf{p}) = \pm v_{F} \bm{\alpha} \cdot \big(\textbf{p}+e\textbf{A}(t) \big) \end{equation} where $\textbf{A}(t)$ is the time-dependent vector potential, $v_F$ is the graphene Fermi velocity and $\bm{\alpha}$ is the dyad of Pauli matrices in the space of the two sublattices of graphene \cite{Rodionov2016}. In this work, we consider the problem wherein a short THz pulse described by the vector potential $\textbf{A}(t)$ drives non-adiabatic transitions from the valence to the conduction band of graphene. A non-adiabatic transition from the valence to the conduction band corresponds to a ``flip'' of the sublattice pseudospin \cite{Song2015, Aeschlimann2017}. This dynamical interband process may result in a finite conduction band population after the passage of the pulse \cite{Kelardeh2015, Lefebvre2017}, a population which can then be probed using time-resolved ARPES \cite{Ishikawa2013, Sentef2015, Kelardeh2016, Aeschlimann2017}. An alternative way of describing this physical process is that, for a given quasiparticle momentum $\textbf{p}$, the valence and conduction band of graphene behave like a driven two-level atom. When the driving amplitude is large, as is the case for a strong THz pulse, multiphoton processes become relevant \cite{Shevchenko20101}. In this article, the physical observable used in optimization calculations is the electron momentum density (EMD), similar to other theoretical studies of laser-irradiated graphene \cite{Ishikawa2013, Kelardeh2015, Fillion-Gourdeau2016, Lefebvre2017}. This observable is calculated as follows: for a given value of $\textbf{p}$, a free negative energy state is ``prepared'' and propagated numerically up to the final time $t_f$ (i.e. when the vector potential does not vary anymore) using a split-operator decomposition described in Refs. \cite{Fillion-Gourdeau2016, Fillion-Gourdeau2017a}. The EMD is then obtained by projecting the numerically computed wavefunction onto a free positive energy state of the TDDE $u_{s,\textbf{K}_{\pm}}^{\mathrm{out}\dagger}$ : \begin{equation}\label{eq:pairDensity} f(t_f, \mathbf{p}) = \frac{1}{2 \epsilon_{\textbf{p}}^{\mathrm{out}}2 \epsilon_{\textbf{p}}^{\mathrm{in}}}\arrowvert u_{s,\textbf{K}_{\pm}}^{\mathrm{out}\dagger}(\textbf{p}) \psi_{s,\textbf{K}_{\pm}}^{\mathrm{out}}(t_f,\textbf{p})\arrowvert ^2, \end{equation} where $\epsilon_{\textbf{p}}^{\mathrm{in,out}}$ are the asymptotic eigen-energies. This observable is equal to the photo-induced pseudospin flip probability, in other words the induced carrier density \cite{Fillion-Gourdeau2016}. To obtain the total carrier density, this number may be multiplied by 4 to take into account the physical spin and valley pseudospin degeneracies. We assume undoped graphene in this article in other words a Fermi energy equal to zero. This implies that all transitions between the hole-like states with momentum $-\textbf{p}$ and electron like-states with momentum $\textbf{p}$ are allowed. Control of the Fermi energy in graphene at THz frequencies can be achieved through gating of the sample \cite{Razavipour2015}. We also assume that the sample is at absolute zero during the interaction time with the pulse. Thus, our calculations do not include the effect of electron-electron interactions \cite{DasSarma2011} as well as thermal intraband transitions that can occur at non-zero temperatures \cite{Farmani2018b}. The validity of these assumptions is discussed in section \ref{sec:cfluence}. The basic procedure used in this work is as follows: an objective function which depends on the physical observable $f(t_f, \mathbf{p}) $ -- \eqref{eq:pairDensity} -- is defined. Then, decision variables related to an appropriate parametrization of the vector potential $\textbf{A}(t)$ entering in \eqref{eq:Hamiltonian} are chosen. These decision variables are used as inputs of the DE solver, and the vector potential $\textbf{A}(t)$ which minimizes the objective function is found numerically. The parametrization of the vector potential is detailed in subsection \ref{sec:param}, while the specifics of the DE solver are presented in subsection \ref{sec:de}. \subsection{Terahertz field parametrization}\label{sec:param} \begin{figure} \centering \includegraphics[width=0.4\textwidth]{lightmatter} \caption{Graphene sheet irradiated by an linearly polarized excitation. The driving field $E(t)$ is polarized in the $x$-direction, corresponding to normal incidence.} \label{fig:lightmatter} \end{figure} In this article, linearly polarized oscillating fields in the THz frequency range are considered [see Fig. \ref{fig:lightmatter} for a schematic]. The fields vary only in the time-domain, and are assumed homogeneous in space. Starting from the definition of the velocity gauge, one can write \begin{equation}\label{eq:gauge} \mathbf{E}(t) = - \dfrac{d \mathbf{A}(t)}{dt} = E(t) \hat{\mathbf{e}}_x. \end{equation} The time-dependent field is fully characterized by its spectral density $\tilde{E}(\omega)$. Following the approach described in Ref. \cite{Fillion-Gourdeau2017}, the density is expanded over a polynomial basis as \begin{equation}\label{eq:density} \tilde{E}(\omega) = \sum_{i=1}^{N_{s}} a_i B_{i}(\omega) \end{equation} where $N_s$ is the number of basis elements, $a_i$ are expansion coefficients and $B_i$ are the basis elements. As will be described in subsection \ref{sec:de}, the expansion coefficients $a_i$ are chosen as inputs of the optimization solver. This choice is motivated by the fact that it allows one to search a low-dimensional parameter space, and then ``oversample'' the optimized spectral density described by \eqref{eq:density}, thus yielding a smooth, physically realistic THz pulse. The choice of basis elements is not unique. In this work, $B$-spline polynomials of order $k$ are used by design: \begin{equation} B_i(\omega) = b_i^{(k)}(\omega). \end{equation} A detailed description of $B$-splines can be found in Ref. \cite{Bachau2001}, while their application to pulse shaping problems is described in Ref. \cite{Fillion-Gourdeau2017}. In a nutshell, they are favored over other orthogonal polynomials because of their compact support, positive definiteness, the fact that they are easy to generate numerically and the ease of managing boundary conditions with $B$-splines. $B$-splines are fully determined by their polynomial order, $k$, and a knot vector $(\omega_{i})_{i=1,\ldots,N_{s}+k}$ according to the recurrence relation \cite{Bachau2001, DeBoor1978} \begin{align} b_{i}^{(k)}(\omega)&= \frac{\omega-\omega_{i}}{\omega_{i+k-1} - \omega_{i}}b^{(k-1)}_{i}(\omega) + \frac{\omega_{i+k} -\omega}{\omega_{i+k}-\omega_{i+1}} b^{(k-1)}_{i+1}(\omega). \end{align} The following initial condition is used to generate $B$-spline coefficients \begin{equation} b_{i}^{(1)}(\omega)=\begin{cases} 1 & \mbox{for} \quad \omega_{i} \leq \omega < \omega_{i+1}\\ 0 & \mbox{otherwise}\end{cases}. \end{equation} The number of knots at a given frequency determines the continuity condition at that point. In this article, we use the standard choice with knots of multiplicity $k$ at the endpoints $\omega_{\rm{min}}$ and $\omega_{\rm{max}}$, and knots of multiplicity 1 (simple knots) at the interior points \cite{Bachau2001} \begin{align}\label{eq:knot} \omega_{\rm{min}} = \omega_{1} = \ldots & = \omega_{k} < \cdots \nonumber \\ < \omega_{k+n-1} & = \ldots =\omega_{2k+n-2} = \omega_{\rm{max}} \, , \end{align} where $n$ is the number of breakpoints and $2k+n-2$ is the number of knot points. These two quantities are related to the total number of $B$-splines as $N_{s} = n+k-2$. The bandwidth of the parametrized spectrum is fixed by the endpoints $\omega_{\mathrm{min}}$ and $\omega_{\mathrm{max}}$. Outside of this interval, the spectral density is zero by definition. Boundary conditions can be enforced at the edges of the spectrum by simply removing functions from the basis set, \eqref{eq:density}, although this is not necessary in principle \cite{Fillion-Gourdeau2017}. This approach is equivalent to changing the multiciplicity of knots at the endpoints of the knot vector, \eqref{eq:knot}. At $\omega = \omega_{\mathrm{min}}$, we impose that the spectral density is zero, but do not enforce continuity. The corresponding condition is \begin{equation}\label{eq:smooth0} a_1 = 0. \end{equation} since $B_1$ it is the only non-zero spline at $\omega = \omega_{\mathrm{min}}$ \cite{Bachau2001}. At $\omega = \omega_{\mathrm{max}}$, we require that the spectrum is zero, but that it decreases to zero in a smooth manner. Since $B_{N_s - 2}$ is the last spline in the basis set which tends to zero smoothly, the condition used to enforce this behavior is \begin{equation}\label{eq:smooth1} a_{N_s} = a_{N_s - 1} = 0. \end{equation} We have found this choice to yield the most physically realistic THz pulse spectrum possible, that is a spectral density that is continuous everywhere except at $\omega = \omega_{\mathrm{min}}$ where it may reach zero in a nearly discontinuous way \cite{Lee2002, Hafez2016}. Given a $B$-spline parametrization, one can determine the temporal field shape by resampling the spectrum at equidistant angular frequencies $\Omega_j = (N_\mathrm{min} + j) \Delta \omega$ where $j \in [0,j_\mathrm{max}] \subset \mathbb{N}$. A given spectral resolution $\Delta \omega$ results in a periodicity $T = 2 \pi / \Delta \omega$ of the temporal field profile. The bounds on the sampled spectrum are thus $\Omega_j \in [\omega_\mathrm{min}, \omega_\mathrm{max}]$ where $\omega_\mathrm{min} = N_\mathrm{min} \Delta \omega$ and $\omega_\mathrm{max} = (N_\mathrm{min} + j_\mathrm{max})\Delta \omega$. Using this sampling, the temporal shape of the applied electric field is given by a superposition of $N+1$ harmonic modes: \begin{equation}\label{eq:temporal} E(t) = \sum_{j=0}^N \tilde{E}(\Omega_j) \cos (\Omega_j t). \end{equation} Since the spectral phase is set to zero in this work, \eqref{eq:temporal} describes a field which reaches zero at the endpoints of the temporal interval, i.e at $t=\pm T/2$. The corresponding vector potential can be calculated directly by combining \eqref{eq:gauge} and \eqref{eq:temporal}, yielding \begin{equation} A(t) = - \sum_{j=0}^N \tilde{E}(\Omega_j) \frac{\sin (\Omega_j t)}{\Omega_j}, \end{equation} with $\textbf{A}(t) = A(t) \hat{\mathbf{e}}_x$. In actuality, before computing the vector potential $A(t)$ from the value of the applied electric field $E(t)$, the field expression \eqref{eq:temporal} is renormalized to obtain a given value of the pulse fluence, or energy density: \begin{equation} U=\frac{c \epsilon_0}{2} \int_{-\infty}^{\infty}{\mkern-10mu dt\, E^2(t)}. \end{equation} As described further in Sec. \ref{sec:results}, the fluence of the pulse $U$ may remain fixed in calculations or be used as a decision variable. Fluences around $10^{-4}$ J/cm$^2$ are used in this article. The $B$-spline parametrization presented in this work, \eqref{eq:density}, can be extended to treat circular polarizations \cite{Fillion-Gourdeau2017} or other simple electric field configurations. However, we assume an homogeneous time-dependent electric field in the form of \eqref{eq:temporal} to solve the optimization problem in a reasonable time, and because this simple model captures the main physical processes of laser-graphene interactions in the case of normal incidence [see Fig. 1]. \subsection{Optimization solver}\label{sec:de} The problem considered in this article consists in finding a THz pulse shape that results in a given carrier density over a pre-defined quasiparticle momentum range. As stated earlier, the decision variables are related to the pulse fluence as well as the spectral parametrization via $B$-splines, \eqref{eq:density}. In mathematical terms, this can be written as a minimization problem \begin{equation}\label{eq:problem} \tilde{J} = \min_{\vec{X} \in \mathbb{R}^N} J(\vec{X}) \end{equation} where $\tilde{J}$ is a minimum of the objective function $J$ in parameter space, $\vec{X} = \big\lbrace X_1, X_2 , \cdots , X_N \big\rbrace$ is a decision vector composed of $N$ decision variables (the choice of these variables will be detailed in section \ref{sec:results}). The objective function $J(\vec{X})$ is defined in terms of the integrated carrier density in graphene: \begin{equation} \label{eq:opt_prob} J(\vec{X}) =\pm \int_{\mathcal{D}_{\mathbf{p}}}{\mkern-10mu d^2 p\,f(t_f,\mathbf{p})} \end{equation} where $\mathcal{D}_{\mathbf{p}}$ is a pre-defined integration range in momentum space and $f$ is defined in \eqref{eq:pairDensity}. The sign in front of the integral in \eqref{eq:opt_prob} can be chosen positive if one wishes to minimize the carrier density, and negative if one wishes to maximize it. The search space of the optimization problem \eqref{eq:problem} is a $N$-dimensional hypercube, where $N$ is the number of decision variables. We start from the hypothesis that the effect of individual decision variables on \eqref{eq:opt_prob} can not be readily isolated, in other words that the search landscape is non-linear. Accordingly, we use DE, an algorithm that has been successfully applied to the suppression of multiphoton resonances in driven two-level systems \cite{Gagnon2017b} and to the maximization of pair production in QED \cite{Fillion-Gourdeau2017}. The algorithm begins with a randomly chosen set of initial guesses called ``individuals', then mutation and recombination operators direct the search towards good solutions using vector differences \cite{Talbi2009}. It is similar to other population-based algorithms that are often used to tackle pulse shaping problems, for example the genetic algorithm (GA) \cite{Chu2001, Christov2001, Balogh2014, Hebenstreit2016}. To be concise, DE is a population based, evolutionary optimization algorithm targeted at continuous parameter spaces [see Fig. \ref{fig:de} for visualization]. Several variants of DE exist, most of which differ only in the specifics of how individuals are updated (mutations and recombinations). The variant used in this article (DE/rand/1/bin in DE notation \cite{Talbi2009}) is the same as in Ref. \cite{Fillion-Gourdeau2017}, thus we refer the interested reader to this article for details. In this work we make use of the \textsc{Pagmo} optimization library \cite{izzo2012pygmo} which contains the aforementioned variant of the DE solver \cite{Storn1997,das2011differential}. \begin{figure} \centering \includegraphics[width=\columnwidth]{de} \caption{High-level template of DE. Different initial conditions or ``individuals'' (black squares) are generated randomly in the parameter space (enclosing circle). This population of individuals is iteratively improved using successive applications of mutation, crossover and selection operators. Every generation features individuals successively closer to local minima (small circles) of the problem. Inspired by \cite{Talbi2009}.} \label{fig:de} \end{figure} To conclude this description of pulse shaping calculations, let us summarize the basic procedure used to generate numerical results in this article. \begin{enumerate} \item A momentum range $\mathcal{D}_{\mathbf{p}}$ and the objective function $J(\vec{X})$, \eqref{eq:opt_prob}, are defined, either with respect to maximization or minimization of the induced carrier density. \item Optimization variables are chosen. In this work we use the coefficients of the $B$-spline parametrization of the spectrum, \eqref{eq:density}, and/or the pulse fluence. \item The chosen decision variables, which are stored in a vector $\vec{X}$ are used as inputs of the DE solver: an initial population of solutions is chosen randomly, and is evolved via DE for a fixed number of iterations (often called ``generations''). For every individual and generation, the objective function $J(\vec{X})$ is evaluated by evolving the TDDE and computing the subsequent density, \eqref{eq:pairDensity}. This step returns a possible ``optimum'' of the problem, that is the value of the decision vector $\vec{X}$ which best optimizes the objective function. \end{enumerate} Step 3 may be repeated using different random initial populations until a satisfactory solution is found. \section{Results and discussion} \label{sec:results} As stated earlier, the goal of the calculations presented in this work is to optimize the spectral content of a THz pulse for the suppression or enhancement of the induced carrier density over a pre-defined momentum range. For comparison purposes, the THz bandwidth and the $B$-splines parametrization of the spectrum [see \eqref{eq:density}] are the same throughout the article [see Table \ref{tab:pulse} for details]. The bandwidth of the pulse is set to 30 THz, and the number of $B$-splines is fixed to 10. Keeping in mind that some $B$-spline coefficients are fixed to zero [see \eqref{eq:smooth0} and \eqref{eq:smooth1}], the number of decision variables accessible to the DE solver is 7 or 8, depending on if the pulse fluence is kept constant or is varied. Two different situations are considered in this article: the case of fixed pulse fluence (sec. \ref{sec:cfluence}) and the case of a variable pulse fluence (sec. \ref{sec:fluence}). We detail the choice and bounds of decision variables in each of these sections, then show optimized pulse shapes and the resulting carrier density in reciprocal space. \begin{table}[t!] \begin{tabular}{lc} \hline \hline Simulation parameter & Value \\ \hline Minimum frequency ($\nu_{\mathrm{min}} = \omega_{\mathrm{min}}/2\pi$)& 1 THz \\ Maximum frequency ($\nu_{\mathrm{max}} = \omega_{\mathrm{max}}/2\pi$)& 30 THz \\ Total length ($T=2 \pi/\Delta\omega$) & 2 ps \\ Number of $B$-splines ($N_s$) & 10 \\ $B$-spline order ($k$) & 3 \\ \hline \hline \end{tabular} \caption{Simulation parameters used in pulse shaping calculations throughout this work. The pulse fluence is not fixed in advance as it can be used as a decision variable.} \label{tab:pulse} \end{table} \subsection{Carrier density optimization}\label{sec:cfluence} In this section, we consider minimization and maximization of the carrier density over a wide momentum range for a fixed pulse fluence, The variables composing the decision vector $\vec{X}$ are selected as the non-zero coefficients in \eqref{eq:density}, that is \begin{equation} X_n = a_{n+1}, \end{equation} with the number of decision variables set to $N = N_s -3$, i.e. $N=7$. Bounds on $\vec{X}$ are fixed as \begin{equation} \begin{aligned} \min(X_n) & = 0, \\ \max(X_n) & = 1, \end{aligned} \end{equation} and the harmonic superposition, \eqref{eq:temporal} is re-normalized at every objective function evaluation such that the applied THz field has a constant fluence from iteration to iteration. The reciprocal space window over which optimization takes place is chosen as $\mathcal{D}_{\mathbf{p}}$ = $\lbrace 0 \leq k_x \leq 2.6 \times 10^{-1} \mbox{ \AA}^{-1}, 0 \leq k_y \leq 7.2 \times 10^{-2} \mbox{ \AA}^{-1} \rbrace$. This 2D window covers all the quasi-particle states that can become excited via a THz pulse for the parameters found in Table \ref{tab:pulse} and a fluence below $2\times 10^{-4}$ J/cm$^2$. For a given fluence value, minimization via DE is carried out for 300 generations using a randomly initialized population of 8 individuals. This calculation is repeated for maximization using the same optimization parameters. Minimization and maximization calculations are performed for a range of fluence values ranging from 0.02 to $1.64 \times 10^{-4}$ J/cm$^2$. The results of this parameter sweep are shown in Fig. \ref{fig:fluence_plot}. \begin{figure} \includegraphics[width=0.5\textwidth]{fig0} \caption{Values of the optimized carrier density for a range of THz pulse fluences. Every point on the plot corresponds to an optimized configuration found via DE, with 300 generations and a population size of 8. The problem parameters are specified in Table \ref{tab:pulse} and the optimization window is $\mathcal{D}_{\mathbf{p}}$ = $\lbrace 0 \leq k_x \leq 2.6 \times 10^{-1} \mbox{ \AA}^{-1}, 0 \leq k_y \leq 7.2 \times 10^{-2} \mbox{ \AA}^{-1} \rbrace$. The valley and physical spin degeneracies are taken into account in the carrier density values. The dashed line indicates the fluence value for the results shown in Figs. \ref{fig:maximization}--\ref{fig:minimization}.} \label{fig:fluence_plot} \end{figure} The spectral content of the optimized pulse can be used to control the photo-induced carrier density, as shown by the optimization results in Fig. \ref{fig:fluence_plot}. As a matter of fact, for pulse fluences around $1.5 \times 10^{-4}$ J/cm$^2$, the maximum achievable carrier density can be as high as 4 times the minimum achievable carrier density. We stress the fact that only the spectral content varies for pulses of equal fluence: the total energy deposited in the graphene sample remains the same. Let us examine in more detail the pulse shapes resulting in maximization/minimization of the carrier density for a fluence of $4.11 \times 10^{-5}$ J/cm$^2$, indicated by a dashed line in Fig. \ref{fig:fluence_plot}. The optimized spectral pulse shapes, as well as the associated temporal shapes and momentum-resolved carrier density, are shown in Fig. \ref{fig:maximization} (maximization) and in Fig. \ref{fig:minimization} (minimization). For this fluence value, carriers are created only within the optimization window $\mathcal{D}_{\mathbf{p}}$, with a zero probability of photo-excitation outside of the window (see Figs. \ref{fig:maximization}a and \ref{fig:minimization}a). As can be seen by comparing Fig. \ref{fig:maximization}b and Fig. \ref{fig:minimization}b, the DE solver tends to converge towards few-cycle THz pulses when asked to maximize the carrier density, and to multi-cycle pulses when asked to minimize. Further information can be obtained by comparing the optimized spectra in Fig. \ref{fig:maximization}c and Fig. \ref{fig:minimization}c: a broadband spectrum results in more momentum states being excited by the pulse, whereas a narrower spectrum results in less states being excited. Interestingly, although it results in a complicated momentum-space pattern (Fig. \ref{fig:minimization}a), the spectrum optimized for suppression exhibits a simple shaped peak around 22 THz, which corresponds to the carrier frequency of the temporal signal. At this point of the discussion, we recall that the way the optimized spectra tend to zero at 1 THz and 30 THz is partly constrained by the $B$-spline parametrization detailed in Sec. \ref{sec:param}. We also recall that the calculated values of the EMD fall between 0 and 4, because they account for the two-fold physical spin and two-fold valley pseudospin degeneracies in graphene. The appearance of a large number of oscillations in the momentum-space pattern for a narrow spectrum [see an example in Fig. \ref{fig:minimization}a] can be explained by considering periodic driving of a quantum system through an avoided energy crossing. This effect, also called Landau-Zener-St\"uckelberg (LZS) interferometry, manifests itself in the form of interference fringes in reciprocal space. This time-domain quantum interference was detailed in previous publications, both in the generic \cite{Shevchenko20101} and graphene-specific case \cite{Fillion-Gourdeau2016}. In short, extremal values of the transition probability from the valence to the conduction band correspond to constructive or destructive interference between different quantum pathways. If the number of optical cycles in the driving pulse increases, so does the number of possible pathways leading to constructive/destructive interference: thus, more oscillations in momentum space are observed \cite{Fillion-Gourdeau2016}. \begin{figure} \includegraphics[width=0.5\textwidth]{fig1} \caption{Best found solution for the maximization of the induced carrier density at a THz fluence of $U=4.11 \times 10^{-5}$ J/cm$^2$. (a) Optimized density in momentum space. (b) Associated temporal pulse shape. The peak field is determined by the pulse fluence. (c) Optimized spectral density from which the temporal shape is obtained (arbitrary units). The markers in (c) are re-sampling points used to calculate the temporal pulse shape, different from the number of $B$-splines which is $N_s = 10$.}\label{fig:maximization} \end{figure} \begin{figure} \includegraphics[width=0.5\textwidth]{fig2} \caption{Best found solution for the minimization of the induced carrier density at a THz fluence of $U=4.11 \times 10^{-5}$ J/cm$^2$. (a) Optimized density in momentum space. (b) Associated temporal pulse shape. The peak field is determined by the pulse fluence. (c) Optimized spectral density from which the temporal shape is obtained (arbitrary units). The markers in (c) are the sampling points used to calculate the temporal pulse shape, different from the number of $B$-splines which is $N_s = 10$.} \label{fig:minimization} \end{figure} The fact that pulse shaping can be used to change the photo-induced carrier density for fluences around $1.5 \times 10^{-4}$ J/cm$^2$ [see Fig. \ref{fig:fluence_plot}] provides a control knob over scattering channels in graphene, in addition to gating. As described in Ref. \cite{DasSarma2011}, different scattering processes have different functional dependences on the excess carrier density $\bar{n}$ in Dirac materials such as graphene \cite{DasSarma2011}. At low temperatures, the scattering rate from short-range disorder in graphene is proportional to $\sqrt{\bar{n}}$ . In contrast, as the carrier density $\bar{n}$ increases, Coulomb interactions become screened, leading to a $1/\sqrt{\bar{n}}$ proportionality for this scattering channel. The effect of both mechanisms has been experimentally quantified for chemical-vapor-deposited (CVD) graphene in Ref. \cite{Yu2016}. In short, the results of this section show the potential of THz pulse shaping for increasing or decreasing scattering times in graphene by a factor of $\sim 2$. Let us conclude this section by a discussion of the validity of the assumptions made in this article from the point of view of scattering channels. Theoretical studies have shown that carrier relaxation in graphene usually takes place in two steps. The first step is thermalization due to carrier-carrier and carrier-phonon scattering. Thermalization takes place on a time-scale of the order of $~50$ fs \cite{Malic2017}. The second step is carrier cooling, wherein excited carriers transfer their excess energy to the lattice on a time-scale of $\sim$ 1 ps \cite{Malic2017}. Therefore, to be experimentally useful, the duration of optimized pulses should be sub-picosecond, and care should be taken to subject the graphene layer to environmental conditions such that the thermalization time is increased. This may include, for instance, performing experiments below 10 K temperature \cite{Al-Naib2014} and embedding the graphene mono-layer in a medium with a sufficiently high dielectric constant \cite{Basov2014}. The latter precaution aims to ensure that electron-electron interactions are suppressed \cite{Couto2011}. This suppression could in principle increase the thermalization time of the dynamical system to values over 100 fs, thus enabling the measurement of an anisotropic momentum space distribution with a THz pump beam. Another possibility for increasing the carrier lifetime beyond 100 fs would be to use $n$-doped graphene \cite{Aeschlimann2017}, although in this case some transitions close to the Dirac point will be forbidden. \subsection{Control of multiphoton absorption}\label{sec:fluence} In the previous section, it was shown that the total photo-induced carrier density in graphene could be controlled by the shape of a few-cycle THz pulse. We now turn our attention to the suppression of specific multiphoton absorption features in the momentum-integrated spectrum of irradiated graphene, i.e. optimization over a narrow momentum window. As described in Ref. \cite{Gagnon2017b}, selective suppression of multiphoton features is useful not only for the control of scattering mechanisms in Dirac materials, but also from a quantum computing perspective. In the given reference, the suppression of multiphoton peaks was studied from the point of view of Floquet theory, which applies \emph{stricto sensu} for periodic excitations that exist for all time. Since the present article is concerned with calculations using the TDDE and pulses of finite duration, it can be viewed as a follow-up on Ref. \cite{Gagnon2017b}. As explained in the previous subsection, interference fringes in reciprocal space [see an example in Fig. \ref{fig:maximization}a] can be interpreted in terms of LZS interferometry \cite{Fillion-Gourdeau2016}. By approaching the LZS problem from the point of view of Floquet theory, it can be shown that the peak amplitude of the applied field has an influence on the suppression of resonances via the phenomenon known as coherent destruction of tunnelling (CDT) \cite{Grifoni1998, Shevchenko20101}. This can be explained by the fact that a linearly polarized excitation opens a dynamical gap between the valence and conduction band, with the width of the gap a function of the spectral content of the periodic driving pulse. In optimization calculations presented in this section, we allow the fluence to vary in addition to the spectral content, since this provides an additional control knob for suppressing or enhancing individual peaks in the absorption spectra. For the remainder of this section, the first $N-1$ variables composing the decision vector $\vec{X}$ are selected as the non-zero coefficients in \eqref{eq:density}, that is $X_n = a_{n+1}$, with the number of decision variables set to $N - 1 = N_s -3$, i.e. $N=8$. The last variable of the decision vector is a real number which allows the pulse fluence to vary between two predetermined values. We set \begin{equation}\label{eq:xn} X_N = \frac{U}{U_0}, \end{equation} where $U_0$ is the maximum attainable pulse fluence. Bounds on $\vec{X}$ are fixed as \begin{equation} \begin{aligned} \min(X_n) & = \begin{cases} 0, &n < N \\ \frac{1}{3}, &n = N \end{cases} \\ \max(X_n) & = 1. \end{aligned} \end{equation} The harmonic superposition, \eqref{eq:temporal}, is re-normalized at every objective function evaluation such that the applied THz field has a fluence $U$ which is dictated by the value of $\vec{X}$, i.e. \eqref{eq:xn}. The lower bound on the fluence is a necessary constraint in the case of minimization over a momentum window since the DE solver must be prevented from converging to fluence values for which the induced carrier density is trivially equal to zero. We however allow the lower bound to be relaxed in order to provide paths to optimal solutions in the search space, although final pulses are all characterized by $U/U_0 \geq 1/3$. \begin{figure} \includegraphics[width=0.5\textwidth]{fig3} \caption{Best found solution for selective maximization of the carrier density. (a) Optimized density in momentum space, with the maximization window indicated by a rectangle. (b) Momentum-integrated density, in arbitrary units, showing enhancement in the shaded region. (c) Associated temporal pulse shape. The peak field is determined by the pulse fluence, $U = 2.01 \times 10^{-5}$ J/cm$^2$ . (d) Optimized spectral density from which the temporal shape is obtained (arbitrary units).} \label{fig:maximization_fluence} \end{figure} \begin{figure} \includegraphics[width=0.5\textwidth]{fig4} \caption{Best found solution for selective minimization of the carrier density. (a) Optimized density in momentum space, with the maximization window indicated by a rectangle. (b) Momentum-integrated density, in arbitrary units, showing suppression in the shaded region. (c) Associated temporal pulse shape. The peak field is determined by the pulse fluence, $U = 6.94 \times 10^{-6}$ J/cm$^2$. (d) Optimized spectral density from which the temporal shape is obtained (arbitrary units).} \label{fig:minimization_fluence} \end{figure} The narrow reciprocal space window over which optimization takes place is chosen as $\mathcal{D}_{\mathbf{p}} = \lbrace 5.07 \times 10^{-2} \mbox{ \AA}^{-1} \leq k_x \leq 5.58 \times 10^{-2} \mbox{ \AA}^{-1}, 0 \leq k_y \leq 7.60 \times 10^{-2} \mbox{ \AA}^{-1} \rbrace$. The maximum pulse fluence is fixed to $U_0 = 2.057 \times 10^{-5}$ J/cm$^2$, meaning that optimized configurations are characterized by a fluence varying between $U_0/3 = 6.86 \times 10^{-6}$ J/cm$^2$ and $U_0$. Similar to the case of fixed fluence, maximization is carried out via DE for 200 generations using a randomly initialized population of 10 individuals [see Fig. \ref{fig:maximization_fluence}]. This calculation is performed with 4 different random population seeds in order to sample a wider search space. A minimization calculation is repeated with the exact same parameters [see Fig. \ref{fig:minimization_fluence}]. Let us examine in more detail the pulse shapes resulting in maximization/minimization of the carrier density over narrow bands in reciprocal space. The strength of the selective suppression/enhancement is manifest from the momentum integrated spectrum shown in Figs. \ref{fig:maximization_fluence}b and \ref{fig:minimization_fluence}b, which show a peak-to-valley ratio of 2 between suppressed/enhanced peaks and immediately adjacent peaks or valleys. As can be seen by comparing Figs. \ref{fig:maximization_fluence}c and \ref{fig:minimization_fluence}c, the pulse shapes that result in either minimization or maximization are characterized by a peak field of the same order of magnitude ($\sim 5-7 \times 10^7$ V/m), although the fluence of the pulses which maximizes the carrier density over the selected range is $\sim 3$ times higher than the pulse which minimizes ($2.01 \times 10^{-5}$ J/cm$^2$ and $6.94 \times 10^{-6}$ J/cm$^2$). This result suggests that it is actually the interplay between spectral components of the pulse, and not merely the peak value of the field, which provides a control knob over the closing or opening of a dynamical gap between the valence and the conduction band of graphene, with a closing leading to CDT, as described in Refs. \cite{Gagnon2017, Gagnon2017b}. The impact of the spectral content of the pulse can be seen by inspecting Figs. \ref{fig:maximization_fluence}d and \ref{fig:minimization_fluence}d. In the case of maximization, a relatively broad two-peak structure can be discerned around 20 THz [see Fig. \ref{fig:maximization_fluence}d], whereas in the case of minimization, a narrower peak is apparent around 25 THz in the spectrum [see Fig. \ref{fig:maximization_fluence}d]. This result seems to suggest that in the case of enhancement, a broad spectrum (short pulses) is favored, whereas in the case of suppression, a narrower spectrum (longer pulses) is favored. This finding is in line with the results obtained in Sec. \ref{sec:cfluence} in the case of maximization over the whole reciprocal space for fixed fluence. This result should however be taken with care since, as described in Sec. \ref{sec:cfluence}, pulse duration should be as short as possible to prevent carrier cooling from taking place. \section{Summary}\label{sec:summary} In this article, we have used differential evolution (DE) to find THz pulse shapes which result in suppression or enhancement of the laser-induced carrier density in graphene. Besides providing empirical pulse shapes suited for a specific reciprocal space target, the use of the DE solver enables one to find general trends which should be considered in pulse shaping experiments with Dirac materials. For example, we found that shorter pulses are generally best suited for maximization of the carrier density, whereas minimization is associated with longer pulse durations. We also showed that it is possible to vary the photo-induced carrier density by a factor of 4 for a fixed pulse fluence around $1.5 \times 10^{-4}$ J/cm$^2$, using only spectral shape parameters as decision variables of the optimization solver. This result hints at the fact that THz pulse shaping provides an additional control knob over carrier scattering in graphene \cite{Deffner2015}. This work may also stimulate the comparison of evolutionary algorithms for pulse shaping problems with established approaches which include numerical ensemble control \cite{Li2006, Li2009, Li2011, Leghtas2011, Chittaro2017}, and emergent tools such as machine learning \cite{Wigley2016, Krefl2017}. The authors acknowledge C. Lefebvre for useful discussions and P. Blain for code development. D. Gagnon is supported by a postdoctoral research scholarship from Fonds de recherche du Qu\'ebec -- Nature et technologies (FRQNT). Computations were made in part on the supercomputer \emph{Mammouth} from Universit\'e de Sherbrooke, managed by Calcul Qu\'ebec and Compute Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation (CFI), minist\`ere de l'\'{E}conomie, de la Science et de l'Innovation du Qu\'{e}bec (MESI) and FRQNT.	{ "redpajama_set_name": "RedPajamaArXiv" }	1,318
\section{Conclusions} \label{sec:conclusions} In this paper, we observe that state-of-the-art similarity estimation methods MinHash and OPH are indeed sampling methods for graph streams consisting of only item insertions, and exhibit a sampling bias for fully dynamic graph streams. To solve this problem, we develop a sampling method VOS. VOS uniformly samples at most $k$ connected items for each user. It fast processes each edge in the graph stream with small time complexity $O(1)$. Based on two users' sampled items, we propose a fast method to estimate not only the Jaccard coefficient between their connected items but also the number of their common connected items. We perform experiments on a variety of publicly available graphs, and experimental results demonstrate that our method VOS significantly outperforms the state-of-the-art methods. \section{Acknowledgment} The research presented in this paper is supported in part by National Key R\&D Program of China (2018YFC0830500), National Natural Science Foundation of China (U1736205, 61603290), Shenzhen Basic Research Grant (JCYJ20170816100819428), Natural Science Basic Research Plan in Shaanxi Province of China (2016JQ6034). \balance \bibliographystyle{IEEEtran} \section{Introduction} \label{sec:introduction} Many real-world network systems such as online social networks (OSNs) and mobile phone networks are given as graph streams represented as sequences of edges over time, where entities are modeled as nodes and entity relations are modeled as edges. Estimating the similarities of users in large graph streams has been successfully used for applications such as duplicate detection~\cite{Xia2011silo} and collaborative filtering~\cite{Guo2015trustsvd}. However, the graph streams studied in all these works only consist of edge insertions. In practice, real-world networks contain not only edge insertions but also deletions. For example, users on OSNs such as Twitter and Pinterest can follow other users, and can also unfollow users that they followed previously; users on YouTube can subscribe to interested channels, and can also unsubscribe from channels that they subscribed previously. For similarity estimation, MinHash~\cite{BroderSTOC2000} is a popular sketch method for approximately computing the Jaccard coefficient similarity, which builds a sketch of $k$ registers with $k$ distinct hash functions for each user and updates the minimum hash values of its subscribed items for each register. To reduce the memory usage of MinHash, \cite{PingWWW2010,MitzenmacherWWW14} develop methods \emph{b-bit minwise hashing} and \emph{odd sketch}, and the basic idea behind them is to use probabilistic methods such as sampling and sketching to build a compact digest for each user's MinHash sketch. b-bit minwise hashing, odd sketch, and MinHash update each item with a high time complexity $O(k)$. To solve this problem, Li et al.~\cite{Linips2012} further develop a method OPH and use only one hash functions to reduce the time complexity of updating each item from $O(k)$ to $O(1)$. Also there are many other works based on OPH such as~\cite{ShrivastavaUAI2014,ShrivastavaICML2014,ShrivastavaICML2017} to improve its estimation accuracy. In detail, they fill empty registers generated from OPH by ``rotation" with the value of the closest non-empty registers towards right~\cite{ShrivastavaICML2014}, left or right with probability $\frac{1}{2}$~\cite{ShrivastavaUAI2014}, or based on tailored 2-universal hashing~\cite{ShrivastavaICML2017}. \cite{Ioffe2010improved,ShrivastavaNIPS2016,WuICDM2016,WuWWW2017} develop a fast method to estimate the Jaccard coefficient between weighted vectors, where the general Jaccard coefficient between two positive real value vectors $\vec x\!=\!(x_1, x_2, \ldots, x_p)$ and $\vec y\!=\!(y_1, y_2, \ldots, y_p)$ is defined as $J(\vec x, \vec y)\!=\! \frac{\sum_{1\le j\le p}\min (x_j, y_j)}{\sum_{1\le j\le p}\max (x_j, y_j)}$. Unfortunately, all these methods indeed are sampling methods customized for statistic datasets, but fail to uniformly sample edges from fully dynamic graph streams including item-subscriptions and item-unsubscriptions, which results in large estimation errors. To solve the above challenges, we develop a fast and accurate sketch method VOS (virtual odd sketch) for estimating the similarities of users occurred in fully dynamic graph streams. VOS processes each edge with small time complexity $O(1)$ and uses small memory space to build a compact sketch of the graph stream over time. For each user, we build an odd sketch of its subscribed items on the fly, which is a binary sketch of $k$ bits and embeds each subscribed item with xor (i.e., exclusive-or) operations. In graph streams, it is wasteful to assign a large $k$ for each user to achieve reasonable estimation accuracy, especially for users with few subscribed items. Thus instead of directly keeping the odd sketch in memory, we store the sketch in $k$ bits randomly selected from a shared bit array to reduce the memory usage. Based on the built virtual sketch, we develop a novel method to accurately estimate user similarities, and provide a theoretical proof for the estimation accuracy. We conduct extensive experiments on a variety of real-world graphs, and experimental results show that our method VOS is more accurate than state-of-the-art methods. \section{Our Sketch Method} \label{sec:methods} Our sketch method VOS consists of a one-dimension bit array $A$ of length $m$, a hash function $\psi$ that maps items into integers in $\{1, \ldots, k\}$ at random, and $k$ independent hash functions $f_1, \ldots f_k$ that map users into integers in $\{1,\ldots, m\}$ at random. As shown in Figure~\ref{fig:vos} for each user $u$, we virtually build an odd sketch $O_u^{(t)}$ of set $S_u^{(t)}$ on the fly and embed $O_u^{(t)}$ into $A$. Formally, $O_u^{(t)}$ is a bit array of length $k$, where each bit $O_u^{(t)}[j]$ is the parity of the number of items in $S_u^{(t)}$ of which hash value equals $j$ with respect to function $\psi$, i.e., $O_u^{(t)}[j] = \oplus_{i\in S_u^{(t)}} \textbf{1}(\psi(i)=j), 1\le j\le k,$ where $\oplus$ is the xor operation. The above equation tells us that any two elements $(u, i, ``+")$ and $(u, i, ``-")$ occurred before and including time $t$ offset to each other and they together are irrelevant to the value of $O_u^{(t)}$. Our method VOS differs from the original odd sketch method~\cite{MitzenmacherWWW14} in two aspects: 1) We directly build an odd sketch $O_u^{(t)}$ of $S_u^{(t)}$ for each user $u$ rather than generate a MinHash sketch first; 2) We do not directly store the odd sketch $O_u^{(t)}$ in memory, but use hash functions $f_1, \ldots f_k$ to randomly select $k$ bits from a shared bit array $A$ to \emph{approximately} store $O_u^{(t)}$. In addition, for each occurred user $u$, we use a counter $n_u$ to keep tracking of the number of its subscribed items over time. We also update bit array $A$ and a counter $\beta$ as $A[f_{\psi(i)}(u)] \gets A[f_{\psi(i)}(u)] \oplus 1,$ $\beta \gets \beta + \frac{2[(A[f_{\psi(i)}(u)] \oplus 1) - \frac {1}{2}]}{m},$ where $\beta$ is initialized to 0 and used to keep tracking of the fraction of 1-bits in $A$ over time, Thus, the time complexity of updating each element is $O(1)$. \begin{figure}[htb] \centering \includegraphics[width=0.45\textwidth]{vos} \caption{Overview of our method VOS. The red and bold bits are contaminated.}\label{fig:vos} \end{figure} At time $t$, for each bit $O_u^{(t)}[j]$, $1\le j\le k$, we randomly select a bit from $A$ using hashing function $f_j$ and xor the bit with $O_u^{(t)}[j]$, i.e. $A[f_j(u)]\gets A[f_j(u)]\oplus O_u^{(t)}[j]$. We easily find that the value of $A$ at time $t$ is irrelevant with the order of occurred users and the order of the bits in their odd sketches iterated in the above procedure. Therefore, we assume that $O_u^{(t)}[j]$ is the last bit hashed into $A$. Let $\beta_{u,j}^{(t)}$ is the fraction of 1-bits in $A$ before the event of hashing $O_u^{(t)}[j]$ into $A$. We easily obtain that $O_u^{(t)}[j]$ is hashed into a 1-bit in $A$ with probability $\beta_{u,j}^{(t)}$. Hashing $O_u^{(t)}[j]$ into $A$ changes at most one bit in $A$, therefore we have $\|\beta_{u,j}^{(t)}-\beta^{(t)}\|\le \frac{1}{m}$. In this paper, we approximate $\beta_{u,j}^{(t)}$ as $\beta^{(t)}$ because $m\gg 1000$. Based on the above observations, we model our method VOS as: we rebuild each bit $O_u^{(t)}[j]$ at time $t$ as $\hat O_u^{(t)}[j] = A[f_j(u)],$ which does not equal $O_u^{(t)}[j]$ with probability $P(\hat O_u^{(t)}[j] \ne O_u^{(t)}[j]) = \beta^{(t)}.$ To estimate the similarity $s_{u,v}^{(t)}$ of two users $u$ and $v$, we first compute a sketch $\hat O_{u,v}^{(t)}$ by combining $\hat O_u^{(t)}$ and $\hat O_v^{(t)}$ using the xor operation, i.e., $\hat O_{u,v}^{(t)}[j]\!=\!\hat O_u^{(t)}[j]\oplus \hat O_v^{(t)}[j].$ Define $\alpha_{u,v}^{(t)}$ as the fraction of 1-bits in $\hat O_{u,v}^{(t)}$, $\alpha_{u,v}^{(t)}\!=\!\frac{\sum_{j=1}^k \hat O_{u,v}^{(t)}[j]}{k},$ and $n_{u\Delta v}^{(t)}$ as the cardinality of the symmetric difference of sets $S_u^{(t)}$ and $S_v^{(t)}$, i.e., $n_{u\Delta v}^{(t)}\!=\!\|S_u^{(t)}\Delta S_v^{(t)}\|\!=\!\|(S_u^{(t)}-S_v^{(t)})\cup (S_v^{(t)}-S_u^{(t)})\|.$ From~\cite{MitzenmacherWWW14}, we obtain $P(O_{u,v}^{(t)}[j]\!=\!1)\!=\!\frac{1-(1-2/k)^{n_{u\Delta v}^{(t)}}}{2}.$ Since $P(\hat O_u^{(t)}[j]\!\ne\!O_u^{(t)}[j])\!=\!P(\hat O_v^{(t)}[j]\!\ne\!O_v^{(t)}[j])\!=\!\beta^{(t)}$ we easily obtain $P(\hat O_{u,v}^{(t)}[j]\!=\!1)\!=\!((\beta^{(t)})^2 + (1-\beta^{(t)})^2)P(O_{u,v}^{(t)}[j]\!=\!1)+2\beta^{(t)}(1-\beta^{(t)}) P(O_{u,v}^{(t)}[j]\!=\!0)\!=\!\frac{1-(1-2\beta^{(t)})^2 (1-2/k)^{n_{u\Delta v}^{(t)}}}{2}.$ Then we have \begin{equation}\label{eq:Eaphla} \begin{split} \text{E}(\alpha_{u,v}^{(t)}) &= \frac{\text{E}\left(\sum_{j=1}^k \textbf{1}(\hat O_{u,v}^{(t)}[j] = 1)\right)}{k}\\ &\approx \frac{1-(1-2\beta^{(t)})^2 e^{-2n_{u\Delta v}^{(t)}/k}}{2}. \end{split} \end{equation} According to the above equation, we estimate $n_{u\Delta v}^{(t)}$ as \[ \hat n_{u\Delta v}^{(t)} = -\frac{k(\ln (1-2\alpha_{u,v}^{(t)})- 2\ln (1-2\beta^{(t)}))}{2}. \] Since $s_{u,v}^{(t)} = \frac{n_u^{(t)} + n_v^{(t)} - n_{u\Delta v}^{(t)}}{2}$, then we estimate $s_{u,v}^{(t)}$ as \[ \hat s_{u,v}^{(t)} = \frac{n_u^{(t)} + n_v^{(t)}}{2} + \frac{k(\ln (\|1-2\alpha_{u,v}^{(t)}\|)- 2\ln (\|1-2\beta^{(t)}\|))}{4}. \] We easily find that the time complexity of computing $\hat s_{u,v}^{(t)}$ is $O(k)$. Moreover, the Jaccard coefficient $\hat J(S_u^{(t)}, S_v^{(t)})$ can be estimated as $\hat J(S_u^{(t)}, S_v^{(t)})=\frac{\hat s_{u,v}^{(t)}}{n_u + n_v - \hat s_{u,v}^{(t)}}.$ Furthermore, the expectation and variance of its estimate $\hat s_{u,v}^{(t)}$ are computed as \[ \text{E}(\hat s_{u,v}^{(t)}) \approx s_{u,v}^{(t)}+\frac{1}{8}-\frac{k \beta^{(t)} e^{2n_{u\Delta v}^{(t)}/k}}{(1-2\beta^{(t)})^{2}}-\frac{e^{4n_{u\Delta v}^{(t)}/k}}{8(1-2\beta^{(t)})^4}, \] \[ \text{Var}(\hat s_{u,v}^{(t)}) \approx -\frac{k}{16}+\frac{k^2 \beta^{(t)} e^{2n_{u\Delta v}^{(t)}/k}}{2(1-2\beta^{(t)})^{2}}+\frac{k e^{4n_{u\Delta v}^{(t)}/k}}{16(1-2\beta^{(t)})^4}. \] \section{Shortcomings of Existing Methods}\label{sec:preliminaries} For any two sets $S_1$ and $S_2$, MinHash~\cite{BroderSTOC2000} applies $k$ independent hash functions $h_1, \ldots, h_k$ to obtain an accurate estimation of $J(S_1, S_2)$, where any hash function $h_j, 1 \leq j \leq k$ can be described as a random permutation from $I$ to $I$ itself. For a set $S \subset I$, let $h_j^(S)$ denote the minimum hash value of items in $S$ with respect to hash function $h_j$, i.e., $h_j^(S)\!=\!\min_{i\in S} h_j(i).$ Therefore, MinHash computes $h_1^(S_1)$, $\ldots$, $h_k^(S_1)$ and $h_1^(S_2)$, $\ldots$, $h_k^(S_2)$, and then estimates $J(S_1, S_2)$ as $J(S_1, S_2)\!=\!\frac{\sum_{j=1}^k \mathbf{1}(h_j^(S_1) = h_j^(S_2))}{k},$ where $\mathbf{1}(\mathbb{P})$ is an indicator function that equals 1 when predicate $\mathbb{P}$ is true and 0 otherwise. Actually, the MinHash sketch of a set $S$ can be viewed as a vector of $k$ items sampled with replacement from $S$ using $k$ hash functions respectively. Denote by $\phi_j(S)$ the item in $S$ with the minimum hash value with respect to hash function $h_j$, i.e., $\phi_j(S)\!=\!\arg \min_{i\in S} h_j(i).$ Because hash function $h_j$ maps items in $I$ into distinct integers, i.e., $h_j(i_1)\!\ne\!h_j(i_2)$ when $i_1\!\ne\!i_2$, the MinHash sketch of $S$ can be simply represented as a vector $(\phi_1(S), \ldots, \phi_k(S))$, where each element $\phi_j(S)$ is randomly sampled with replacement from $S$ by function $h_j$. For any two sets $S_1$ and $S_2$, we easily find that $h_j^(S_1\cup S_2)\!=\!\min (h_j^(S_1), h_j^(S_2)), 1\le j\le k.$ Therefore, the underlying MinHash sketch of the union $\phi_j(S_1\cup S_2)\!=\!\phi_j(S_1)$ when $h_j(\phi_j(S_1))\le h_j(\phi_j(S_2))$ and $\phi_j(S_2)$ otherwise. $\phi_j(S_1\cup S_2)$ is an item in $S_1 \cap S_2$ if and only if $\phi_j(S_1)\!=\!\phi_j(S_2)$, and we can have $P(\phi_j(S_1)\!=\!\phi_j(S_2))\!=\!P(\phi_j(S_1\cup S_2)\in (S_1\cap S_2))\!=\!\frac{\|S_1\cap S_2\|}{\|S_1\cup S_2\|}\!=\!J(S_1, S_2).$ Moreover, one can extend MinHash to handle each element $(u, i, a)$ arriving on fully dynamic stream $\Pi$ as follows: \textbf{case 1}) when $a\!=\!``+"$, update $\phi_j$ like a regular MinHash, i.e., set $\phi_j(S_u)\!=\!i$ if $\phi_j(S_u)\!=\!\emptyset$ or $h_j(i)< h_j(\phi_j(S_u))$ and keep $\phi_j(S_u)$ unchanged otherwise; \textbf{case 2}) when $a\!=\!``-"$ and $\phi_j(S_u)\!=\!i$, set $\phi_j(S_u)\!=\!\emptyset$; \textbf{case 3}) when $a\!=\!``-"$ and $\phi_j(S_u)\!=\!\emptyset$, keep $\phi_j(S_u)\!=\!\emptyset$. However, this extension of MinHash samples an item not according to uniform distribution when item-unsubscriptions occur. The sampling bias is not only related with the number of user's subscribed items but also the order of item subscriptions and unsubscriptions occurred in stream $\Pi$. It is challenging to model and remove the sampling bias when a user has more than one unsubscriptions in stream $\Pi$. To reduce the time cost, OPH~\cite{Linips2012} only uses one hash function $h$ to process each item, which is a random permutation from $I\!=\!\{0,1,\ldots, p-1\}$ to $I$ itself and $p$ is the maximum number of items. OPH equally divides $I$ into $k$ bins: $[\frac{p(j-1)}{k}, \frac{pj}{k})$, $1\le j\le k$. For a set $S \subset I$, define $S(h,j)\!=\!\{i: i\in S\wedge h(i)\in [\frac{p(j-1)}{k}, \frac{pj}{k})\}$, and then OPH computes a variable $oph_j(S)\!=\!h^*(S(h,j))$ when $S(h,j)\ne \emptyset$ and $\emptyset$ otherwise. At last, it estimates $J(S_1, S_2)$ as $J(S_1, S_2)\!=\!\frac{\sum_{j=1}^k \mathbf{1}(oph_j(S_1)=oph_j(S_2)\ne \emptyset)}{\sum_{j=1}^k \mathbf{1}(oph_j(S_1)\ne \emptyset \vee oph_j(S_2)\ne \emptyset)},$ and the time complexity of updating each item is $O(1)$. Similarly, OPH can also be treated as a sampling method and exhibits a sampling bias when there exist item-unsubscriptions in $\Pi$. Furthermore, there exist methods such as random pairing (RP)~\cite{GemullaVLDBJ2008} for uniformly sampling from dynamic graph streams. One can extend RP to sample $k$ items $(\phi_j(S_u))_{1\le j\le k}$ (resp. $(\phi_j(S_v))_{1\le j\le k}$) from $S_u^{(t)}$ (resp. $S_v^{(t)}$). In this case, $(\phi_j(S_u))_{1\le j\le k}$ and $(\phi_j(S_v))_{1\le j\le k}$ generated are independent, i.e., $\phi_j(S_u)\!=\!\phi_j(S_v)$ happens with probability $\frac{1}{\|S_u\|\|S_v\|}$, which significantly differs from the probabilistic model of MinHash. Therefore, the number of common items can be estimated as $s_{u,v}\!=\!\|S_u\|\|S_v\|\sum_{j=1}^{k} \mathbf{1}(\phi_j(S_u)\!=\!\phi_j(S_v))$. \section{Problem Formulation} \label{sec:problem} In this paper, we focus on bipartite graphs, while our method can be easily extended to regular graphs. Let $U$ and $I$ denote the set of users and items respectively. Let $\Pi\!=\!e^{(1)} e^{(2)} \cdots e^{(t)} \cdots$ denote the graph stream of interest, where $e^{(t)}\!=\!(u^{(t)}, i^{(t)}, a^{(t)})$ is the element (or, edge) of $\Pi$ occurred at discrete time $t> 0$, $u^{(t)}\in U$, $i^{(t)}\in I$, and $a^{(t)}\in \{``+", ``-"\}$ are the $t^\text{th}$ element's user, item, and action (i.e., subscription and unsubscription). Let $S_u^{(t)}$ be the set of items subscribed by user $u$ at the end of time $t$, $S_u^{(0)}=\emptyset$. Similar to~\cite{GemullaVLDBJ2008,StefaniKDD16}, we restrict attention to ``\emph{\textbf{feasible}}" fully dynamic graph steams. In detail, if item $i$ is in (resp. not in) the item set $S_u^{(t-1)}$ of user $u$, then element $(u, i, ``+")$ (resp. element $(u, i, ``-")$) cannot occur in stream $\Pi$ at time $t$. Let $s_{u,v}^{(t)}$ denote the number of common items that users $u$ and $v$ subscribe to at time $t$ and is computed as $s_{u,v}^{(t)}\!=\!\|S_u^{(t)}\cap S_v^{(t)}\|\!=\!\frac{J(S_u^{(t)}, S_v^{(t)}) (\|S_u^{(t)}\| + \|S_v^{(t)}\|)}{J(S_u^{(t)}, S_v^{(t)})+1},$ where $\|S\|$ refers to the cardinality of a set $S$. One can use a counter to easily keep tracking of the number of items (i.e., $\|S_u^{(t)}\|$) subscribed by each user $u$ over time $t$. Besides, another popular similarity measure the Jaccard coefficient $J(S_u^{(t)}, S_v^{(t)})\!=\!\frac{\|S_u^{(t)}\cap S_v^{(t)}\|}{\|S_u^{(t)}\cup S_v^{(t)}\|}\!=\!\frac{s_{u,v}^{(t)}}{\|S_u^{(t)}\| + \|S_v^{(t)}\| - s_{u,v}^{(t)}}$ can be easily computed from $s_{u,v}^{(t)}$, and vice versa. In this paper, we aim to develop a fast and accurate method to estimate $s_{u,v}^{(t)}$ and $J(S_u^{(t)}, S_v^{(t)})$ for any two users $u$ and $v$ over time. \section{Evaluation} \label{sec:results} We perform our experiments on several publicly available real-world datasets YouTube, Flickr, Orkut and LiveJournal~\cite{MisloveIMC2007}. To generate fully dynamic graph streams including item-subscriptions and item-unsubscriptions, we follow the experiment settings in~\cite{StefaniKDD16} and set the parameters as $q=2,000,000^{-1}$ and $d=0.5$, which means there is a massive deletion of expected $50 \%$ edges every $2,000,000$ edges in each graph dataset. Specially, we mainly focus on similarity estimation for users with a large number of subscribed items, which requires extremely large memory and computational resources for similarity estimation. Therefore, in our experiments, we first select $5,000$ users with largest cardinalities to generate user pairs of any two users in each graph dataset, and then retain the set of user pairs that have at least one common item to keep tracking of over time. We employ three baselines MinHash, OPH and RP as described in Section~\ref{sec:problem} and~\ref{sec:preliminaries} to compare with our method VOS for estimating similarities over time. Here we use the metrics \emph{average absolute percentage error} (AAPE) to measure the accuracy of estimating the number of common items $\hat s_{u,v}^{(t)}$, and \emph{average root mean square error} (ARMSE) to evaluate the performance of estimating the Jaccard coefficient similarity $\hat J(S_u^{(t)},S_v^{(t)})$ over time. Formally, the metrics are defined respectively as $\text{AAPE}^{(t)}\!=\!\frac{1}{\|P\|} \sum_{(u,v) \in P} \|\frac{s_{u,v}^{(t)} - \hat s_{u,v}^{(t)}}{s_{u,v}^{(t)}}\|$ and $\text{ARMSE}^{(t)}\!=\!\sqrt{\frac{\sum_{(u,v) \in P}(\hat J(S_u^{(t)},S_v^{(t)}) - J(S_u^{(t)},S_v^{(t)}))^2}{\|P\|}}.$ In our experiments, we compare the performance of all these methods under the same memory size $m=32k\|U\|$ bits, where the memory size of each value of the $k$ registers in its generated sketch for each user $u \in U$ is set as $32$ bits. As for the parameter $k$ for the size of virtual odd sketch of our method VOS, we can enumerate all possible values from $1$ to max-cardinality to find an optimal value for each graph dataset, which minimizes either $\text{AAPE}^{(t)}$ or $\text{ARMSE}^{(t)}$ of selected user pairs at any time $t$. Also we can directly set it as $\lambda$ times (i.e., $\lambda=2,3,\ldots$) larger than the memory space used by each sketch of MinHash, OPH and RP. In the later experiments, we set $\lambda=2$. Figure~\ref{fig:runtime} (a) shows the runtime of our method VOS in comparison with other three baselines in the dataset YouTube when the sketch size $k$ varies from $1$ to $10^5$, and Figure~\ref{fig:runtime} (b) shows the runtime of all methods when $k=10^5$. In our experiments, we measure the runtime during which we implement all four methods respectively to update the sketch for each user. We can see that our method VOS and OPH are faster than MinHash and RP, and only require the time complexity $O(1)$. Meanwhile, we fix the sketch size $k=100$ and then compare the estimation accuracy of all four methods. The experimental results are shown in Figure~\ref{fig:accuracy}. Figures~\ref{fig:accuracy} (a) and (c) show the accuracy of estimating $\hat s_{u,v}^{(t)}$ and $\hat J(S_u^{(t)},S_v^{(t)})$ in dataset YouTube over time respectively, and Figures~\ref{fig:accuracy} (b) and (d) show the accuracy in all datasets at time $t$ when all elements in graph streams arrive. We observe that our method VOS are more accurate than other three methods and significantly reduce the estimation bias for fully dynamic graph streams. \begin{figure}[t!] \centering \subfigure[YouTube]{\includegraphics[width=0.23\textwidth]{runtime_youtube}} \subfigure[All Datasets]{\includegraphics[width=0.23\textwidth]{runtime_alldata}} \caption{Runtime of our method VOS in comparison with MinHash, OPH, and RP for different memory space $m$ (bits).} \label{fig:runtime} \end{figure} \begin{figure}[t!] \centering \subfigure[YouTube]{\includegraphics[width=0.23\textwidth]{common_youtube}} \subfigure[All Datasets]{\includegraphics[width=0.23\textwidth]{common_alldata}} \subfigure[YouTube]{\includegraphics[width=0.23\textwidth]{jaccard_youtube}} \subfigure[All Datasets]{\includegraphics[width=0.23\textwidth]{jaccard_alldata}} \caption{Accuracy of our method VOS in comparison with MinHash, OPH, and RP for different memory space $m$ (bits) when $k=100$.} \label{fig:accuracy} \end{figure}	{ "redpajama_set_name": "RedPajamaArXiv" }	9,351
Q: "Wrong number of args (-1) passed to: core/blahblah" in Clojure Can someone explain me how arguments count can be less then 0? This is my code, JIC. But I don't really care why it is not working - I just want to know how it is even theoretically possible to get less then 0 arguments. (defmacro infix [[x op & r]] (if-not (empty? r) (if (or (= op "*") (= op "/")) (infix (conj (rest r) (list op x (first r)))) (list op x (infix r))) x)) (infix (1 + 2))	{ "redpajama_set_name": "RedPajamaStackExchange" }	3,021
Audio Projects – 25 W Stereo Amplifier This page includes supporting information for the 25 W stereo amplifier project described Chapters 10 and 12 in The TAB Guide to Vacuum Tube Audio, along with commentary from the author. This page picks up where the book left off. Shown on the right is the second-generation 20 W stereo amplifier described below. The basic 12.5 W amplifier circuit of the final design implementation includes solid-state rectifiers for the B+ power supply. Mounting for these devices is accommodated on the PWB, as described in Chapter 10 and Chapter 12 of the book. At the reader's option, it is possible to use a vacuum tube rectifier in place of the diodes. A 6CA4 tube functions well and matches the 9-pin style of the other tubes used in the amplifier. The 6CA4 is still being manufactured and is readily available. No changes to the PWB are required, other than routing leads that would go to the diodes to the tube socket. The original RCA design described in Chapter 10 of the book calls for a 5BC3 rectifier tube. This device will certainly work fine in this application, but it appears to be available only from NOS and can therefore be somewhat difficult to find. If a rectifier tube is used, be certain to route the B+ transformer secondary leads to the PWB and then, using jumper wires, to the rectifier socket. This is necessary in order to provide an input for the bias power supply. Operation of the circuit without proper bias will result in component failure. In the description of the 12.5 W amplifier in Chapter 10, the option of using a 6U8A tube in place of the 7199 as specified was discussed. The 7199 pentode/triode performs very well in this amplifier. The problem, however, is that the tube is no longer in production and finding NOS devices can be difficult (and expensive). As described in Chapter 10, it is possible to substitute a 6U8A so long as certain socket pin connection changes are made. The necessity to reroute three pins makes such a change difficult after the amplifier has been built, particularly if a PWB is used. An interesting option involves a plug-in adapter available from at least one vendor that makes the necessary pin changes between the chassis socket and the tube. The adapter is sold by Antique Electronic Supply (part # T-7199-ADT). The adapter is designed specifically for 6GH8A to 7199 applications. The 6GH8A is a medium-mu sharp-cutoff triode/pentode, as is the 6U8A. Fortunately, the pin changes needed to use a 6GH8A as a substitute for a 7199 are the same as for a 6U8A. The author has tried the adapter on a 6U8A as a substitution for a 7199, with good results. Listening tests revealed no obvious differences between the tubes. Bench measurements followed. Measurements were taken on one channel of the amplifier with the 6U8A installed using the plug-in adapter. No significant differences were observed in frequency response, THD, IMD, or noise. The photo on the left shows the amplifier on the bench under test. The photo on the right shows the plug-in adapter. You will note that aesthetically the device may leave something to be desired in applications where the tube is visible. Still, it is an easy and inexpensive modification, and it avoids the difficulty of finding the 7199 type. The cost difference between a 6U8A and a 7199 is quite significant (in one case nearly a 10x difference). The larger question, however, is how long the 7199 will continue to be available—at any price. Therefore, having a backup-device type is important. Following the successful tests of the 6U8A substitution for the 7199, tests were made on the 6GH8A as a substitute for the 7199, again using the 9-pin socket adapter. Listening tests were conducted that compared one channel with the 7199 and the other with the 6GH8A. No significant differences were detected. Bench tests showed performance comparable to the 7199 and the 6U8A. It should be noted that some users have a preference for the sound of the 7199 over the lower-cost substitutes. The listening tests by the author as described here were not exhaustive. All other things being equal, the author recommends using the 7199. The problem, however is the difficulty of finding the 7199. At some point device availability must take precedence over preferences. The Bill of Materials for the 20 W stereo amplifier described in Chapter 10 of the book specifies a rating for circuit breaker CB1 of 5 A. This is actually higher than needed. Something in the 2 to 3 A range would be quite adequate. Builders may wish to try a 2 A device, such as the TE Connectivity W58-XB1A4A-2 (Allied Stock #70199386). If nuisance trips are encountered, a 3 A device may be used instead, such as the TE Connectivity W58-XB1A4A-3 (Allied Stock #70199433). Apart from the fixed load of the tube filaments, the bias setting on the final tubes is the major determinant of average power draw of the amplifier. At a bias setting of –30 V, the amplifier draws about 900 mA with no audio input applied. As described on the Regulated Power Supply page, builders may want to change the value of VR1 to something higher than the 2.5 ohms (cold) specified in Chapter 12. VR1 is a power varistor intended to limit current inrush when the power supply is first switched on. Once the supply has reached operating temperature, VR1 is taken out of the circuit (shorted) by RYL-1. A slightly higher value for VR1 will provide greater benefit. A value of 5 ohms (cold) works well with this circuit (GE Infrastructure Sensing #CL-40, Allied stock #70181325), limiting the measured inrush current to just over 3 A. With a 10 ohm (cold) device (GE Infrastructure Sensing #CL-60, Allied stock #70181341), the inrush current is reduced to about 2A. For builders who use a 2 A circuit breaker for CB-1 (which is recommended), the 10 ohm device is a good choice. Users may hear shortly after the amplifier is powered on a slight buzzing noise from the chassis (not from the speakers) for a few seconds. This is normal. As the amplifier warms up, the surge-limiting power thermistor bypass circuit of VR2 and C11 ramps up the voltage to relay RYL1. During a brief portion of this ramp, the relay may vibrate slightly; however, within a few seconds the relay will close. The speed of this action is a function of the ambient temperature. Also, it may be observed that when the amplifier is first turned on, a faint hum can be heard from the speakers. This hum will go away within about 30 seconds of power on. Because the amplifier power supply uses silicon rectifier diodes, the B+ voltage is available immediately upon power up. This can allow any residual supply hum to be heard in the speakers. As the output tubes warm up and begin to conduct, the residual hum is canceled out by the push-pull output tubes (the residual noise is 180° out of phase). After the amplifier has warmed-up, the typical noise floor of –80 dB to –90 dB is achieved. An interesting condition can be observed with this amplifier when measuring square wave performance. Certain settings of the volume control provide for better square wave traces. To illustrate: Apply a 1 kHz signal to the input with the volume control fully clockwise. Adjust the generator to produce 8 V rms output at the speaker terminals into an 8 ohm load. Observe the trace displayed on the oscilloscope. Some ringing can be seen on the leading edge of the trace. Now adjust the volume control so that the ringing is minimized. This is usually around the 3 o'clock position. Readjust the signal generator to produce 8 V rms output at the speaker terminals. Note that the oscilloscope trace is clean. The measurements documented in Chapter 12 of the book were based on this technique. Fortunately, very little listening is done at full-open volume control settings. This situation is a function of the characteristics of the input pentode stage, and was observed with both a 7199 and 6U8A tubes. In addition, a similar condition was observed with the 50 W stereo amplifier, which uses the same input pentode arrangement. Another version of this amplifier was produced that incorporated a few small changes that were useful additions to the basic design. This amplifier is described as a 20 W stereo unit. Although each channel is capable of 12.5 W power output at low distortion, performance over time is unpredictable at maximum output. For this reason, the amplifier's stated rating is conservatively specified. Version 2 of the amplifier, shown on the left, added headphone jacks to the front panel and a speaker on/off switch. The speaker switch is used to mute the output at the speaker terminals when the headphones are used. To avoid running the output transformer secondary wires from the rear panel to the front panel, and back to the rear terminals, a pair of relays was included. The speaker on/off switch on the front panel switches a 5 V dc source (taken from the VR1 relay bypass circuit) to control the relays. When the relays (one for each channel) are energized, the 8 ohm secondary of each output transformer is applied to 8 ohm 10 W resistors. The added headphone output was a feature suggested by a friend who wanted to use the amplifier for headphone listening, as well as for speakers. The other major change, cosmetic in nature, was the addition of a Plexiglas cover over the amplifier, as shown. This gives the amplifier an interesting look and tends to protect the tubes from casual contact. A modified circuit board was used that incorporates quick-disconnect terminals for connections to the transformers and other chassis-mounted components. The goal was to reduce the number of off-board connections in order to simplify construction. The new PWBs feature a ground plane over the component side with a solder mask and silk screened legends. Two boards are used for the implementation; the power supply components are installed on only one board. In addition, a pair of speaker terminal PWBs is used to terminate the output transformer secondary windings. The input stage uses a 6U8A pentode/triode, replacing the 7199 tube used in the original RCA circuit. The automatic protection board developed for the Dorm Amp (see the New Projects Page, Dorm Amp) was incorporated in the Version 2 20 W stereo amplifier. As described on the New Projects page, this circuit board includes several system-protection features including: automatic shutoff, over-temperature shutdown, and B+ under-voltage shutdown. Because the physical layout of the 20 W stereo amplifier and the Dorm Amp are essentially identical, it was possible to assemble another auto-protect PWB and install it in the 20 W amplifier with no modifications. This project underlines the value of having a documented, set layout for components. Among the benefits are device interchangeability and upgrade options. The cost of building any project is an important consideration for the audio enthusiast and hobbyist. The focus of the first-generation 25 W stereo amplifier was to optimize the various elements that went into the project. Cost was a secondary consideration. For the second-generation unit, an effort was made to accurately determine the bill of material (BOM) costs and the time needed to build the amplifier. The total BOM (including shipping expenses) for the second-generation stereo amplifier was $1,936. The major cost centers included: • Transformers = $500 • Decals = $75 Builders could eliminate the PWB cost by using hand-wired terminal strip construction. Note that two PWB designs are used in this amplifier—one for each channel and one for each speaker output circuit, for a total of four boards. Other potential areas of cost reductions include the back and top-side decals, and the Plexiglas cover. The total time required to build the second-generation stereo amplifier—from ordering parts to completing performance measurements—was approximately 21 hours. The BOM cost for the optional auto-protect board (described elsewhere) was $686. The cost breakdown was roughly 50% for parts and 50% for the PWB. Construction time was about 2 hours. As with any electronic product, costs fall rapidly as the volume (number of units produced) increases. For a one-off project, however, there are are not many ways to reduce the cost without reducing the feature set. Note 8 (January 2017) Continued work to improve the 20 W stereo amplifier has resulted in an updated second generation amplifier. Detailed step-by-step documentation is provided in a 194 page User and Assembly Manual that is available for download. If you are familiar with the Heathkit assembly manuals of the past, the approach taken with this new manual should seem comfortable. For those who want a printed version, it is available for purchase on Lulu—a web site for specialized, print-on-demand documents. (There is charge of $14.95 for the printed manual; see "20 W Stereo Amplifier: User and Assembly Manual" on the Lulu web site,) In addition, a ZIP file is available for download that will assist in building this amplifier. The ZIP file contains the following individual files: • Schematic diagrams of the amplifier and auto-protect circuits as Acrobat (".pdf") files • Bill of materials for the amplifier and auto-protect circuits as an Excel file • Printed wiring board layout files for the amplifier, speaker terminal, and auto-protect boards as ".pcb" ( ExpressPCB) files • Chassis layout, bottom view, as an Acrobat" file Note that the files above are provided as-is. Every effort has been made to make sure they are complete and accurate, but no warranties are expressed or implied. Builders are encouraged to double-check the information contained in the above files prior to proceeding. For the front panel layout, users can customize the text as desired; e.g., "Built by John for Mary, January 2017." All files are provided for personal use only. No further distribution is allowed. The current version of the 20 W amplifier builds upon the previous versions, adding some new features and simplifying construction. A description of the latest design can be found in the User and Assembly Manual, and for the sake of simplicity will not be repeated here. The estimated cost to build the amplifier is $3,900 for parts, and about 25 hours assembly time. As noted previously, cost reductions are possible, depending on the preferences of the builder. For example, the BOM cost can be cut almost in half by eliminating the add-on circuits (preamp power supply, auto-protect board, and auto-off board), which then places the BOM cost in the same range as detailed in Note 7 above.. Considering the price tag, this project may be outside the range of some builders. However, you may find that elements of the available downloads will be useful in other projects, or wish to adapt some of the circuits for your own projects. The available documents are, thus, offered as a starting point for future efforts.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }	7,203
package com.google.ads.googleads.v12.errors; public interface FeedAttributeReferenceErrorEnumOrBuilder extends // @@protoc_insertion_point(interface_extends:google.ads.googleads.v12.errors.FeedAttributeReferenceErrorEnum) com.google.protobuf.MessageOrBuilder { }	{ "redpajama_set_name": "RedPajamaGithub" }	4,004
#include "ttransitem.h" #include <QGraphicsSceneMouseEvent> #include "objs/timedtransition.h" TTransItem::TTransItem(std::string id, QMenu contextMenu, QGraphicsItem parent) :AbstractPetriItem(id, contextMenu, parent) { myPetriType = IPetriItem::TTrans; drawItem(); } TTransItem::~TTransItem() { } void TTransItem::updateLabel(spnp::IData data) { spnp::TimedTransition it = static_cast<spnp::TimedTransition>(data); this->setLabel(it->getName()); } void TTransItem::drawItem() { const int vert = 30; const int hor = 12; QPainterPath path; path.addRect(-hor/2, -vert/2, hor, vert); myPolygon = path.toFillPolygon(); AbstractPetriItem::drawItem(); } void TTransItem::mouseMoveEvent(QGraphicsSceneMouseEvent event) { //TODO conferir QGraphicsItem::mouseMoveEvent(event);/* spnp::TimedTransition _data = static_cast<spnp::TimedTransition>(this->getData()); _data->x = event->pos().x(); _data->y = event->pos().y();/ } void TTransItem::onContextMenu(QAction act) { if(act->data().toBool()) { } }	{ "redpajama_set_name": "RedPajamaGithub" }	5,970
\section{Introduction} Many problems of practical importance can be formulated in terms of packings. Intuitively, a packing is any arrangement of non-overlapping copies from a (usually finite) collection of objects ${\mathcal P}$ within a prescribed part of a large(r) set ${\mathcal E}$. It often happens that both the large set and the objects being packed can be naturally endowed with the same type of discrete structure. In such cases, general packings can be successfully modeled by packings of graphs. If, for example, ${\mathcal E}$ can be represented by a graph $G$ and elements of ${\mathcal P}$ by graphs $H_1, \ldots , H_k$, then a ${\mathcal P}$-packing of $G$ is a collection of vertex-disjoint subgraphs of $G$ such that each of them is isomorphic to some $H_i$, $i = 1, \ldots , k$. When ${\mathcal P}$ consists of a single element $H$, one simply speaks of $H$-packings of $G$. Clearly, one would expect that the difficulty of packing problems increases with the increase of the complexity of $H$. Indeed, the simplest non-trivial case, $H = K_2$, is well researched, while the results on larger $H$ are much less abundant. This does not prevent graph packings from being a very versatile tool; even the simplest case of packing dimers ($H = K_2$) into a larger graph is one of most commonly used models in several areas of physics and chemistry. It suffices to mention the Ising model of magnetic materials and the concept of the topological resonant energy, crucial for stability of conjugated molecules. Both models employ perfect matchings, i.e.\ packings of dimers covering all vertices of the underlying graph. For a very brief introduction to both topics we refer the reader to \cite[\S 8.7]{LP86} and references therein. For some recent results on packing larger $H$ see, for example, \cite{doslicASR,doslicPSF}. In this paper we look at a problem which can be modeled by packing even simpler graphs, the copies of $K_1$, into finite portions of regular rectangular lattice. Without further restrictions this problem would be trivial, but our problem imposes restrictions that arise quite naturally in the context of settlement growth and planning. It turns out that with those restrictions even packing the simplest possible graphs, $K_1$, into finite pieces of the square lattice gives rise to very interesting behavior and exhibits often surprising relations with several other classes of combinatorial objects. (Another non-trivial problem which can be reduced to restricted packings of trivial graph $K_1$ is the problem of finding a large independent set in a given graph.) All the aforementioned packing problems can be studied in a static or a dynamic variant. In the present work we focus only on the static models with the aim to enumerate all configurations that arise in such models and that satisfy certain additional requirements. The study of the dynamic variant of the same models aims to find the distribution of configurations constructed by a random process in which the pieces from $\mathcal{P}$ arrive sequentially and are placed randomly onto available locations in ${\mathcal E}$ until saturation. These kinds of models that evolve over time are extensively studied, see \cite[\S 7]{Krapivsky_et_al} for introduction, and \cite{Krapiv20, Krapiv22, Krapiv19, KraRedBird} for some recent results in this direction. The efforts to extend our results in this direction are currently underway. \medskip In \cite{PSZ-21} three of the present authors introduced the following settlement model. A rectangular $m\times n$ tract of land, with sides oriented north-south and east-west, is divided into $mn$ unit squares, see Figure \ref{fig:tract_of_land}. Each square lot can be either occupied (by a house) or left vacant. An arrangement of houses on such a tract of land is called a \emph{configuration} and can be encoded as an $m\times n$ matrix $C$, where $c_{i,j}=1$ if the lot $(i,j)$ is occupied, and $c_{i,j}=0$ otherwise. \begin{figure}[h] \centering \begin{tikzpicture}[scale = 0.5] \draw[step=1cm,black,very thin] (0, 0) grid (7,5); \draw [-Stealth] (9,1) -- (9,4); \node[anchor=west] at (9,4) {North}; \end{tikzpicture} \caption{An example of a tract of land ($m = 5$, $n = 7$).} \label{fig:tract_of_land} \end{figure} A configuration $C$ is \emph{permissible} if no occupied lot $(i,j)$ borders simultaneously with three other occupied lots to its east, south and west --- in other words --- the house on the position $(i,j)$ receives the sunlight during at least one part of the day (be it in the morning from the east, or during the midday from the south, or in the evening from the west). As is the case with other packings, one is, naturally, interested in \emph{large} permissible configurations, since the small ones tend to be trivial and easy to construct. One way of being large is to have the largest possible number of occupied lots, hence the largest possible size. We call such configurations \emph{maximum} configurations (in \cite{PSZ-21,PSZ-21-2} these were called \emph{efficient}). Another, more interesting, way of being large is in the sense of set inclusion. A permissible configuration $C$ is \emph{maximal} if no additional houses can be added to the configuration without rendering it impermissible, see Figure \ref{fig:examples}. Unlike the maximum configurations, the maximal ones usually come in a range of different sizes, and it is of interest to know the exact distribution of sizes. Moreover, here also the smallest such configurations are interesting (in \cite{PSZ-21,PSZ-21-2} these were called \emph{inefficient}), as they describe either the worst possible outcome if we are interested in packing as many elements as possible, or the best possible outcome if we are trying to satisfy certain needs by the smallest possible number of packed objects. \begin{figure} \begin{subfigure}{0.3\textwidth}\centering \begin{tikzpicture}[scale = 0.5] \draw[step=1cm,black,very thin] (0, 0) grid (4,5); \fill[blue!40!white] (0,1) rectangle (1,2); \fill[blue!40!white] (0,3) rectangle (1,4); \fill[blue!40!white] (0,4) rectangle (1,5); \fill[blue!40!white] (1,1) rectangle (2,2); \fill[blue!40!white] (1,2) rectangle (2,3); \fill[blue!40!white] (1,3) rectangle (2,4); \node[] at (1.5,3.5) {x}; \fill[blue!40!white] (2,0) rectangle (3,1); \fill[blue!40!white] (2,1) rectangle (3,2); \fill[blue!40!white] (2,2) rectangle (3,3); \node[] at (2.5,2.5) {x}; \fill[blue!40!white] (2,3) rectangle (3,4); \fill[blue!40!white] (3,0) rectangle (4,1); \fill[blue!40!white] (3,2) rectangle (4,3); \draw[step=1cm,black,very thin] (0, 0) grid (4,5); \end{tikzpicture} \caption{Impermissible} \end{subfigure} \begin{subfigure}{0.3\textwidth}\centering \begin{tikzpicture}[scale = 0.5] \draw[step=1cm,black,very thin] (0, 0) grid (4,5); \fill[blue!40!white] (0,1) rectangle (1,2); \fill[blue!40!white] (0,3) rectangle (1,4); \fill[blue!40!white] (0,4) rectangle (1,5); \fill[blue!40!white] (1,1) rectangle (2,2); \fill[blue!40!white] (1,3) rectangle (2,4); \fill[blue!40!white] (2,0) rectangle (3,1); \fill[blue!40!white] (2,1) rectangle (3,2); \fill[blue!40!white] (2,2) rectangle (3,3); \fill[blue!40!white] (2,3) rectangle (3,4); \fill[blue!40!white] (3,0) rectangle (4,1); \fill[blue!40!white] (3,2) rectangle (4,3); \draw[step=1cm,black,very thin] (0, 0) grid (4,5); \end{tikzpicture} \caption{Permissible} \end{subfigure} \begin{subfigure}{0.3\textwidth}\centering \begin{tikzpicture}[scale = 0.5] \draw[step=1cm,black,very thin] (0, 0) grid (4,5); \fill[blue!40!white] (0,0) rectangle (1,1); \fill[blue!40!white] (0,1) rectangle (1,2); \fill[blue!40!white] (0,2) rectangle (1,3); \fill[blue!40!white] (0,3) rectangle (1,4); \fill[blue!40!white] (0,4) rectangle (1,5); \fill[blue!40!white] (1,1) rectangle (2,2); \fill[blue!40!white] (1,3) rectangle (2,4); \fill[blue!40!white] (2,0) rectangle (3,1); \fill[blue!40!white] (2,1) rectangle (3,2); \fill[blue!40!white] (2,2) rectangle (3,3); \fill[blue!40!white] (2,3) rectangle (3,4); \fill[blue!40!white] (2,4) rectangle (3,5); \fill[blue!40!white] (3,0) rectangle (4,1); \fill[blue!40!white] (3,2) rectangle (4,3); \fill[blue!40!white] (3,4) rectangle (4,5); \draw[step=1cm,black,very thin] (0, 0) grid (4,5); \end{tikzpicture} \caption{Maximal} \end{subfigure} \caption{Examples of impermissible, permissible and maximal configuration on a $5 \times 4$ tract of land. `x' marks a house blocked from the sunlight.}\label{fig:examples} \end{figure} The authors in \cite{PSZ-21} found maximal configurations with the lowest \emph{occupancy} (the number of houses in a configuration) among all the maximal configurations on an $m \times n$ grid. They also obtained bounds on the highest occupancy possible. A natural next step would be to find the total number of all maximal configurations for a given grid and to refine the enumeration by the number of occupied lots. The problem seems to be too hard in the general $m \times n$ case. Hence, in this paper we consider its restriction to the one-dimensional case $1 \times n$ to which we can apply the transfer matrix method. This method allows us to obtain a complete solution of the one-dimensional case by computing and analyzing the bivariate generating functions for the corresponding enumerating sequences. Our results could be, in principle, generalized to larger grids; indeed, for grids of size $2\times n$ and $3\times n$ we derive (bivariate) generating functions counting the number of maximal configurations by the same transfer matrix method used in the $1 \times n$ case. However, the calculations get increasingly infeasible for larger strips and we decided not to pursue it beyond $m = 3$. The transfer matrix method, see \cite[\S 4.7]{Stanley} or \cite[\S V]{FlajoletSedgewick}, and also \cite[\S 2--4]{SymbDynCoding}, is a well known method for counting words of a regular language. Applicability of this method to our setting relies on the fact that permissibility as well as maximality of a configuration can be verified by inspecting only finite size patches of a given configuration. The limitation, however, is that the method deals with, essentially, one dimensional objects, so we first consider a modification of the settlement model on the $1\times n$ grid. This modification, defined later in text, we call the Riviera model. It turns out that the Riviera model can be seen as a variant of Flory polymer model \cite{Flory} which is in turn related to Page-R\'enyi parking process \cite{GerinPRparkingHAL,Page}. Surprisingly, the maximal configurations of the Riviera model turn out to be related to a certain kind of restricted permutations introduced in \cite{Baltic}. We were able to construct an explicit bijection translating between the two. Also, we construct another bijection connecting the Riviera model with the closed walks on $P_3$ graph with an added loop. The paper is organized as follows. In Section \ref{sec:Riviera} we introduce the Riviera model. We find the bivariate generating function counting the number of maximal configurations of length $n$ with precisely $k$ houses ($n, k \in \mathbb{N}$). Furthermore, we relate the Riviera model with some other combinatorial objects that were already studied in the literature. In Section \ref{sec:multi-story} we generalize the Riviera model introduced in Section \ref{sec:Riviera} in the sense that we allow houses to have multiple stories. Additionally, we comment on the close relation between the Riviera model and the famous Flory model. In Section \ref{sec:mxnForSmallm} we deal with configurations on $m \times n$ grids with $m = 2$ and $m = 3$. Finally, in Section \ref{sec:concluding} we recapitulate our findings and indicate several possible directions of future research. Some lengthy formulas are relegated to Appendix in order to improve legibility. \medskip A note on notation: Whenever a non-integer decimal is encountered in the text, its value should be interpreted as an approximation of the true value rounded to six decimal places. By $a_n\sim b_n$ (as $n\to\infty$) we mean $\lim_{n\to\infty} \frac{a_n}{b_n} =1$. In several places in the text we use the same name for different functions. Most prominently, the generating function for almost every model is denoted as $F(x)$, $F(x,y)$, or $F(x,y,z)$. This should not lead to any confusion, as it is always clear from the context to which function the text refers. \section{Riviera model}\label{sec:Riviera} We introduce a $1D$-modification of the above settlement planning model which ignores the possibility of obtaining sunlight from the south, but instead retains only the constraints pertaining to the east and west directions. As this is a model on a strip of land, it resembles a Mediterranean settlement along the coast (riviera), hence the name. The configuration of built houses is represented with a row vector\footnote{We write configurations as strings of $0$'s and $1$'s, and we refer to any consecutive sequence of letters in a configuration as a substring or a (sub)word in that configuration.} $C = (c_k)$, where $c_k=1$ if the lot $k$ is occupied and $c_k=0$ otherwise. Similarly as before, a configuration is said to be permissible if every occupied lot has at least one neighboring lot unoccupied (except maybe for the first and the last lot which receive sunlight from the boundary) so that it is not blocked from the sunlight. Among permissible configurations, we are interested in the maximal ones, namely configurations such that any addition of a house on an unoccupied lot would result in an impermissible configuration. The properties of maximality and permissibility are locally verifiable in a sense that, if one wants to check whether a state of a certain lot (occupied or unoccupied) has caused the configuration to be impermissible or not maximal, one only needs to check the situation on the lots in a certain finite radius of the observed lot, where that radius is uniform for each lot on the tract of land. More precisely, to verify that a configuration is permissible, one needs to check that no occupied lot has both of its neighboring lots occupied as well. This can be done by inspecting all the length $3$ substrings of a configuration. And to verify that a configuration is maximal, one needs to check, additionally, that no unoccupied lots can be built on. This can be done by observing the eastern two and western two lots around the unoccupied lot, i.e.\ by inspecting all the length $5$ substrings of a padded (see Remark \ref{rem:padding}) configuration. This property of local verifiability of a constraint which describes the model is a recurring motif throughout our analysis of related models in this paper. \begin{lemma} \label{lemma_forbidden_words} Let $n\in \mathbb{N}$. A configuration $C \in \{0,1\}^n$ in the Riviera model is maximal if and only if, when padded with zeros, it does not contain any of the following (decorated) substrings: \begin{equation} 1\underline{1}1, \quad 0\underline{0}0, \quad 01\underline{0}0, \quad 0\underline{0}10. \end{equation} \end{lemma} \begin{remark}\label{rem:padding} Throughout the paper, unless stated otherwise, we assume that the lots on the boundary can get sunlight from the boundary side, i.e.\ we assume that our configurations are padded with zeros. When inspecting whether a configuration $c_1\dots c_n$ contains a decorated word $d_1\dots \underline{d_k}\dots d_l$, we check against a padded word $\dots000c_1\dots c_n000\dots$ but with the underlined letter of the decorated word aligned with $c_i$ for $i=1,\dots, n$. This is necessary as e.g.\ the configuration $10011$ would otherwise be considered allowed (not containing any of the forbidden substrings), although it is not maximal. \end{remark} \begin{proof}[Proof of Lemma \ref{lemma_forbidden_words}] A configuration $C$ is maximal if and only if it is permissible and for each $k=1,\dots,n$ one has \begin{equation} c_k =0 \Longrightarrow \begin{array}{cc} (c_{k-1}=1 \mbox{ and } c_{k+1}=1) \mbox{ or } (c_{k-1}=1 \mbox{ and } c_{k-2}=1) \\ \mbox{ or } (c_{k+1}=1 \mbox{ and } c_{k+2}=1). \end{array} \end{equation} The contrapositive of the above implication reads \begin{equation}\label{eq:condition1} \begin{array}{cc} & (c_{k-1}=0 \mbox{ or } c_{k+1}=0) \mbox{ and } (c_{k-1}=0 \mbox{ or } c_{k-2}=0) \\ & \mbox{ and } (c_{k+1}=0 \mbox{ or } c_{k+2}=0) \end{array}\Longrightarrow c_k =1. \end{equation} This illustrates the fact that, if there is no danger of losing permissibility by setting $c_k =1$, then one should put $c_k = 1$ (with the agenda of obtaining maximality). By using the distributive property and after removing redundant terms the left hand side of \eqref{eq:condition1} can be rewritten as \begin{equation}\label{eq:condition} \begin{array}{cc} (c_{k-1}=0 \text{ and } c_{k+1}=0) \text{ or } (c_{k-1}=0 \text{ and } c_{k+2}=0) \\ \text{ or } (c_{k+1}=0 \text{ and } c_{k-2}=0) \end{array}\Longrightarrow c_k =1. \end{equation} From here we can compile the list of forbidden words. We include $1\underline{1}1$ to ensure permissibility, and \eqref{eq:condition} gives us five more words $0\underline{0}0$, $0\underline{0}{}0$, $0{}\underline{0}0$ where $$ stands for any symbol. As the words $0\underline{0}00$ and $00\underline{0}0$ are already excluded by $0\underline{0}0$, the set of forbidden (decorated) words is $$\{1\underline{1}1, 0\underline{0}0, 0\underline{0}10, 01\underline{0}0\}.$$ \end{proof} \begin{remark} An alternative approach for constructing the set of forbidden words, once we know that it suffices checking substrings of length $5$, is to consider all $2^5$ binary words of length $5$ and, out of those, take words that do not appear in any finite maximal configuration to be the forbidden set of words. This approach is more amenable for use in a computer algorithm and we will make use of it later on. Using this approach one would come up with the set of forbidden length $5$ words $$\{{}1\underline{1}1{},\quad {}0\underline{0}0{},\quad 01\underline{0}00,01\underline{0}01,\quad 00\underline{0}10,10\underline{0}10\},$$ which again can be reduced to $\{1\underline{1}1, 0\underline{0}0, 0\underline{0}10, 01\underline{0}0\}$. As before, $$ stands for any symbol, and e.g.\ the string ${}1\underline{1}1{}$ actually accounts for $4$ different (decorated) words. \end{remark} \subsection{Counting maximal configurations} Upon examining the Lemma \ref{lemma_forbidden_words}, one sees that it is possible to encode each maximal configuration as a walk on the directed graph in Figure \ref{fig:transfer_graph_Riviera} whose vertices represent all allowed substrings of length $3$ and the directed edges represent allowed transitions (namely, transitions which comply with the condition stated in Lemma \ref{lemma_forbidden_words}), see \cite[\S 2.3]{SymbDynCoding} for more details on this construction. There is an edge from the word $u_1u_2u_3$ to $v_1v_2v_3$ if they \emph{overlap progressively}, meaning that $u_2u_3=v_1v_2$, and if the word $u_1u_2u_3v_3=u_1v_1v_2v_3$ is not forbidden. (Our graph is therefore a subgraph of the $3$-dimensional de Bruijn graph over symbols $\{0,1\}$. Not all edges are present, since the transitions that correspond to forbidden $4$ letter words must be deleted.) Thus, a transition simply represents the addition of a new lot to the right of the configuration, state of which is described with the last letter of the string of the target node. \begin{figure}[h] \begin{tikzpicture}[node distance=5em, nodeStyle/.style={draw, circle, minimum size=2.5em}] \node (A) [nodeStyle] {100}; \node (B) [right of = A, nodeStyle] {001}; \node (C) [right of = B, nodeStyle, fill=blue!20] {011}; \node (D) [right of = C, nodeStyle, fill=blue!20] {110}; \node (E) [right of = D, nodeStyle, fill=blue!20] {101}; \node (F) [right of = E, nodeStyle] {010}; \draw[-Stealth,above] (A) edge[bend left] (B); \draw[-Stealth,above] (B) edge[bend left] (C); \draw[-Stealth,above] (F) edge[bend left] (E); \draw[-Stealth,above] (D) edge[bend left] (E); \draw[-Stealth,above] (D) edge[bend left] (A); \draw[-Stealth,above] (C) edge[bend left] (D); \draw[-Stealth,above] (E) edge[bend left] (F); \draw[-Stealth,above] (E) edge[bend left] (C); \end{tikzpicture} \caption{Transfer digraph $\mathcal{G_R}$ for the Riviera model. For example, a maximal configuration 110011010110 is represented with a walk: \\ $ 110\to 100 \to 001 \to 011 \to 110 \to 101 \to 010 \to 101 \to 011 \to 110 $. Each walk must start and end at shaded nodes.}\label{fig:transfer_graph_Riviera} \end{figure} Depending on the choice of boundary conditions, we are left with a constrained subset of vertices which may serve as a starting point or an ending point of the walk which encodes the configuration. The default boundary condition states that the first and the last lot in a configuration obtain sunlight from the boundary. One can easily check that in this situation, the only allowed starting and ending vertices are $110$, $101$, $011$ (Otherwise, one would not obtain a maximal configuration from the walk). An alternative to this boundary condition is the setting where the first and the last lot do not obtain sunlight from the boundary. In this situation, the allowed starting vertices are $100$, $011$, $101$, $010$, while the allowed ending vertices are $001$, $110$, $101$, $010$. A third option which one may consider is the periodic boundary condition in which case, one simply searches for closed walks. One can count the number of walks of fixed length $n$ on the graph in Figure \ref{fig:transfer_graph_Riviera} by examining the powers of the transfer matrix $A$ associated with that graph: \begin{equation} \kbordermatrix{ & \text{100} & \text{001} & \text{011} & \text{110} & \text{101} & \text{010}\\ \text{100} & 0 & 1 & 0 & 0 & 0 & 0\\ \text{001} & 0 & 0 & 1 & 0 & 0 & 0\\ \text{011} & 0 & 0 & 0 & 1 & 0 & 0\\ \text{110} & 1 & 0 & 0 & 0 & 1 & 0\\ \text{101} & 0 & 0 & 1 & 0 & 0 & 1\\ \text{010} & 0 & 0 & 0 & 0 & 1 & 0\\ } =: A. \end{equation} Namely, we have: \begin{equation} \begin{array}{c} \# \mbox{ of walks of length $n$} \\ \mbox{starting with the node $i$ and ending in the node $j$ } \end{array} = [A^n]_{i,j}. \end{equation} This gives us a neat way of counting the maximal configurations since \begin{equation} \begin{array}{c} \# \mbox{ of walks of length $n$} \\ \mbox{starting with $110$ or $101$ or $011$} \\ \mbox{and ending with $110$ or $101$ or $011$} \end{array} = \begin{array}{c} \# \mbox{ of maximal configurations} \\ \mbox{of length $n+3$}. \end{array} \end{equation} This is due to the fact that each transition adds another lot to the configuration, which at the beginning of the walk had $3$ lots. By introducing the vector $a = (0,0,1,1,1,0)^T$, we have the following: \begin{equation} \label{sequence_an} \# \mbox{ of maximal configurations of length $n$} =: a_n = a^T \cdot A^{n-3}\cdot a, \quad n\ge 3. \end{equation} \begin{remark}\label{rem:PF-Riviera} A straightforward asymptotic formula for $a_n$ can be obtained by calculating the Perron-Frobenius eigenvalue $\lambda$ of the matrix $A$, namely the largest real eigenvalue of $A$. There exist a constant $C$ such that \begin{equation} a_n \sim C \, \lambda^n, \text{ as } n \to \infty. \end{equation} This is due to the fact that vector $a$ possesses a nontrivial component in the direction of the Perron-Frobenius eigenvector. The Perron-Frobenius eigenvalue of our matrix $A$ is equal to $\lambda = \frac{1}{w} = 1.401268$. The numerical value of the constant $C= \frac{\lambda^6+\lambda^5+\lambda^3-\lambda}{2\lambda^4+3\lambda^3+4\lambda^2-6} = 0.803796$ can be obtained from the generating function \eqref{eq:GF4offA080013} using Theorem \ref{tm:asymp} below. \end{remark} \begin{remark}\label{rem:differentBoundary} If one would study the alternative boundary conditions of no sun from the boundary, instead of \eqref{sequence_an}, one would obtain: \begin{equation} \label{sequence_bn} \begin{array}{cc} \# \mbox{ of maximal configurations of length $n$} \\ \mbox{ with no-sun boundary condition } \end{array} =: b_n = b^T \cdot A^{n-3}\cdot d, \quad n\ge 3, \end{equation} where $b = (1,0,1,0,1,1)$, $d = (0,1,0,1,1,1)$. This sequence appears on the OEIS \cite{oeis} under the number \href{https://oeis.org/A253412}{A253412}. In the case of periodic boundary conditions, there is a clear $1$ to $1$ correspondence between the maximal configurations of length $n$ and closed walks on the graph in Figure \ref{fig:transfer_graph_Riviera}. Thus, we have: \begin{equation} \label{sequence_dn} \begin{array}{cc} \# \mbox{ of maximal configurations of length $n$} \\ \mbox{ with periodic boundary conditions } \end{array} =: d_n = \mathop\text{tr}(A^n) , \quad n\ge 1. \end{equation} This sequence appears on the OEIS under the number \href{https://oeis.org/A253413}{A253413}. \end{remark} \subsubsection{Generating functions for the Riviera model}\label{subsec:gen_fun_for_Riviera} From the structure of the sequence $(a_n)$, one can easily calculate its generating function $f=f(y)$ by calculating the resolvent $(I-yA)^{-1}$, where $y$ is a formal variable. This is a somewhat standard calculation for which we explicitly need to determine the first $3$ values of $(a_n)$. We have: \begin{align}\label{eq:GF4offA080013}\nonumber f(y) & = 1+y+y^2+ \sum_{n = 3}^{\infty} a^T \cdot A^{n-3}\cdot a \cdot y^n \\\nonumber & = 1+y+y^2+ a^T\cdot \OBL{\sum_{n = 0}^{\infty} (yA)^n} \cdot a \cdot y^3 \\\nonumber & = 1+y+y^2+ a^T \cdot (I - yA)^{-1} \cdot a \cdot y^3\\ & = \dfrac{1+y+y^3-y^5}{1-y^2-y^3-y^4+y^6}. \end{align} For inverting matrix functions, we have used the software for symbolic calculation, Maxima \cite{maxima}. \begin{remark} The generating function $f$ encodes the infinite sequence $(a_n)$ into a simple rational function. Immediately we deduce that the sequence $(a_n)$ satisfies the following $6$\textsuperscript{th} order linear recurrence relation: \begin{equation} \begin{array}{cc} a_n = a_{n-2} + a_{n-3} + a_{n-4} - a_{n-6}, \quad n \geq 7, \\ a_1 = 1, \quad a_2 = 1, \quad a_3 = 3, \quad a_4 = 3, \quad a_5 = 4, \quad a_6 = 6. \end{array} \end{equation} The sequence $(a_n)$ cannot easily be represented with an explicit formula as it would involve the roots of the polynomial $p(y) = y^6-y^4-y^3-y^2+1$. \end{remark} The information on the number of maximal configurations of fixed length is already useful, but our aim is to determine the precise number of maximal configurations of length $n \in \mathbb{N}$ with a fixed number of houses $k \in \mathbb{N}$, which we denote by $J_{k,n}$. This information gives us insight into the distribution of the \emph{occupancy} $\|C\|:= \sum_{i=1}^n c_i$ among maximal configurations of length $n$, for all values of $n \in \mathbb{N}$. Knowing this quantity would lead to determining the so-called \emph{complexity} (see Remark \ref{rem:complexity}) of our model, namely a distribution of occupancy (or associated \emph{building density} which is defined as $\frac{\|C\|}{n}$) when the length of configurations $n$ grows large. To this end, we calculate the bivariate generating function $g(x,y)$, where $x$ is a formal variable associated with the occupancy of a configuration, while $y$ remains a formal variable associated with the length of the configuration. We define the following matrix function: \begin{equation} \kbordermatrix{ & \text{100} & \text{001} & \text{011} & \text{110} & \text{101} & \text{010}\\ \text{100} & 0 & x & 0 & 0 & 0 & 0\\ \text{001} & 0 & 0 & x & 0 & 0 & 0\\ \text{011} & 0 & 0 & 0 & 1 & 0 & 0\\ \text{110} & 1 & 0 & 0 & 0 & x & 0\\ \text{101} & 0 & 0 & x & 0 & 0 & 1\\ \text{010} & 0 & 0 & 0 & 0 & x & 0\\ } =: A(x). \end{equation} The purpose of this matrix function is to encode when a transition on the graph in Figure \ref{fig:transfer_graph_Riviera} results in the increase of number of occupied lots. Namely: \begin{equation} i \to j \mbox{ is a transition which adds an occupied lot} \iff [A(x)]_{i,j} = x, \end{equation} while the rest of the transitions which do not contribute an occupied lot are denoted with $1 = x^0$. The powers of $A(x)$, namely $(A(x))^n$, encode the distribution of occupancies for the configurations of length $n$. We have: \begin{equation} [(A(x))^n]_{i,j} = p_0^{i,j} + p_1^{i,j} x + p_2^{i,j} x^2 + \dots + p_n^{i,j} x^n, \end{equation} where \begin{equation} p_k^{i,j} = \begin{array}{cc} \# \mbox{ of walks of length $n$ on the graph in Figure \ref{fig:transfer_graph_Riviera} } \\ \mbox{starting with node $i$ and ending with $j$} \\ \mbox{where the number of occupied lots was increased by $1$, $k$ times. } \end{array} \end{equation} In order to take into account the number of occupied lots with which we start the walk, we define vectors: \begin{equation} a(x) = (0,0,x^2,x^2,x^2,0)^T,\quad b = (0,0,1,1,1,0)^T. \end{equation} By plugging this into the familiar formula and determining the first few terms, we obtain: \begin{align} g(x, y) & = 1+xy+x^2y^2+ \sum_{n = 3}^{\infty} a(x)^T \cdot (A(x))^{n-3}\cdot b \cdot y^n \\ & = \frac{1+xy-(x-x^2)y^2+x^2y^3-x^3y^5}{1-xy^2-x^2y^3-x^2y^4+x^3y^6} \\ & = \sum_{n=0}^\infty\sum_{k=0}^\infty J_{k,n}x^ky^n, \end{align} where $J_{k,n}$ is precisely a number of maximal configurations of length $n$ with $k$ occupied lots. The bivariate generating function $g(x,y)$ encodes, among other things, the information on the asymptotic behavior of our sequence $(a_n)$ (the same we have recovered from the Perron-Frobenius eigenvalue of the transfer matrix $A$), and also enables us to determine the expected values of two quantities of interest -- the expected number of buildings in a maximal configuration of a given length, and the expected length of a maximal configuration with a given number of buildings. The starting point is the following classical result, a version of Darboux's theorem as formulated in \cite{bgw}. For more information on obtaining the asymptotics of a sequence from its generating function we refer the reader to \cite{bgw,wilf}. \begin{theorem}\label{tm:asymp} If the generating function $f(x) = \sum _{n \geq 0} a_n x^n$ of a sequence $(a_n)$ can be written in the form $f(x) = \left ( 1 - \frac {x}{w} \right ) ^\alpha h(x)$, where $w$ is the smallest modulus singularity of $f$ and $h$ is analytic in $w$, then $a_n \sim \frac {h(w) n ^{- \alpha -1}}{\Gamma (- \alpha) w^n}$, where $\Gamma $ denotes the gamma function. \end{theorem} Now the expected number of built sites in a maximal configuration of length $n$ can be computed (see \cite{wilf}) as $$\frac{[y^n] \frac{\partial g (x,y)}{\partial x} \left\|_{x = 1}\right.}{[y^n] g (x,y) \left\|_{x=1}\right.},$$ where $[y^n] F(y)$ denotes the coefficient of $y^n$ in the expansion of $F(y)$. Since $g(1,y) = \frac{p(1,y)}{q(1,y)}$ is rational, its smallest modulus singularity is the smallest (by absolute value) root of its denominator $q(1,y)$. While it does not have a closed-form expression, its approximate numerical value is readily computed as $w = 0.713639$, the reciprocal value of the Perron-Frobenius eigenvalue $1.401268$. Now we can write $$g(x,y)\left \|_{x = 1}\right . = \left ( 1-\frac{y}{w} \right )^{-1} g_1(y)$$ and $$\frac{\partial g (x,y)}{\partial x} \left \|_{x = 1} \right . = \left ( 1-\frac{y}{w} \right )^{-2}g_2(y),$$ where $$g_1(y) = \frac{p(1,y) (w-y)}{w q(1,y)} \,\,{\rm and}\,\, g_2(y) = \frac{q(1,y) \frac{\partial p}{\partial x} (x,y) \left \|_{x = 1} \right . - p(1,y) \frac{\partial q}{\partial x} (x,y) \left \|_{x = 1} \right .}{\left (w \frac{q(1,y)}{w-y}\right ) ^2}.$$ By evaluating the ratio $r(y) = \frac{g_2(y)}{g_1(y)}$ at $w$ we finally obtain $$r(w) = \frac{1}{w} \frac{\frac{\partial q}{\partial x} (x,w) \left \|_{x = 1}\right .}{\frac{\partial q}{\partial y} (1,y) \left \|_{y = w} \right .} = 0.577203$$ and the expected number $\langle k(n) \rangle$ of buildings in a maximal configuration of length $n$ is given as $$\langle k(n) \rangle = 0.577203 \,\,n.$$ If one defines the \emph{efficiency} of a maximal configuration as the ratio of the actual number of occupied lots and the largest possible number of occupied lots, which is $\left \lceil \frac{2n}{3} \right \rceil $, one gets the \emph{expected efficiency} of a maximal configuration as $$\varepsilon = \frac{0.577203 \,\,n}{\left \lceil \frac{2n}{3} \right \rceil } = 0.865804.$$ This efficiency is higher than the efficiency of unrestricted $P_m$-packings of $P_n$ for small $m$ (cf. \cite{doslicASR}). \begin{remark}\label{rem:GFhFixHouses} Clearly, by choosing $x=1$ we obtain $f(y)$. However, by choosing $y=1$, we obtain $h(x)=g(x,1)$ which is a generating function for the sequence $(h_k)$ which counts the number of maximal configurations with a fixed number of occupied lots (with variable length). One easily computes this function as \begin{equation} h (x) = \dfrac{1+2x^2-x^3}{1-x-2x^2+x^3}. \end{equation} Straight away we read the recurrence relation for the sequence $(h_k)$: \begin{equation} \begin{array}{cc} h_k = h_{k-1} + 2h_{k-2} - h_{k-3}, \quad k \geq 4, \\ h_1 = 1, \quad h_2 = 5, \quad h_3 = 5. \end{array} \end{equation} By a completely analogous procedure, with switched roles of $x$ and $y$, one can now compute the expected length $\langle n(k) \rangle$ of a maximal configuration with $k$ buildings as $$ \langle n(k) \rangle = 1.758283 \,\,k.$$ We omit the details. It is, perhaps, interesting to note that $\frac{1}{1.758283} = 0.568737$ which is, as one might hope, close to previously computed $0.577203$. Although this is what one might expect, there is no reason, in general, why should $\frac{\langle n(k)\rangle}{k}$ be equal (or even close) to $\frac{n}{\langle k(n)\rangle}$. \end{remark} \begin{remark}\label{rem:complexity} For a building density $\rho\in[0,1]$ one can introduce the number $J_n(\rho) = J_{\floor{\rho n},n}$ which counts the number of configurations of length $n$ with exactly $\FLOOR{\rho n}$ occupied lots. The function \begin{equation} f(\rho) = \lim_{n\to \infty}\frac{\ln J_n(\rho)}{n} \end{equation} is called the complexity and it represents the exponential growth rate of the number of configurations with building density $\rho$ as their length $n$ increases. With this function in hand, one can express the asymptotic behavior of the sequence $(J_n(\rho))$ for large $n$ as: \begin{equation}\label{eq:complexity} J_n(\rho)\sim h(n)\, e^{nf(\rho)} = h(n)\, \left(e^{f(\rho)}\right)^n, \qquad n\to \infty, \quad\rho \in [0,1] \end{equation} where $h(n)$ is some subexponential growing function. One can easily verify that $\operatorname{supp} f= \left[\frac12,\frac23\right]$. Also, comparing \eqref{eq:complexity} with Remark \ref{rem:PF-Riviera} we infer: \begin{equation} \max_\rho f(\rho) =\ln \lambda=\ln 1.401268 = 0.337377. \end{equation} However, determining the precise formula for $f$ remains an open problem. In Figure \ref{fig:complexity} the precise values of $J_{k,100}$ are plotted on the log-scale. For large $n$, one expects the shape of this bar plot to approximate the true shape of the complexity function $f(\rho)$. \end{remark} \begin{figure}[h!] \begin{tikzpicture} \begin{axis} [ybar, bar width=7pt, ymode=log, xlabel = {$k$}, ylabel = {$J_{k, n}$}] \addplot coordinates { (50, 1) (51, 40950) (52, 47298420) (53, 7491483870) (54, 308534750280) (55, 4489680958620) (56, 27525656572050) (57, 79341335532896) (58, 115332553142708) (59, 88281950244176) (60, 36391488209400) (61, 8109317836050) (62, 961479094515) (63, 58247672238) (64, 1668933267) (65, 19597456) (66, 70345) (67, 34) }; \end{axis} \end{tikzpicture} \caption{Precise values of $J_{k, n}$ (log-scale) for $n = 100$.}\label{fig:complexity} \end{figure} \subsection{Surprising relationship between the Riviera model and other combinatorial objects} The integer sequence $(a_n)$ associated with the generating function $f=f(y)$ can be evaluated for any $n \in \mathbb{N}$ simply by expanding $f$ into the formal power series in powers of $y$. Even more, by expanding the bivariate generating function $g=g(x,y)$, we obtain the precise distribution of the occupancies of maximal configurations relative to their length. The first few coefficients in the expansion of $g(x,y)$ are given in Table \ref{tab:gf}. By inspecting the non-zero coefficients in the table, we see that the ratio $\frac{k}{n}$ is in-between $\frac{1}{2}$ and $\frac{2}{3}$, for large $n$. \begin{table}[!h] \caption{The first few coefficients in the expansion of the bivariate generating function $g(x,y)$.}\label{tab:gf} \small \begin{tabular}{c\|cccccccccccccccccc} $k\backslash n$ & $1$ & $y$ & $y^2$ & $y^3$ & $y^4$ & $y^5$ & $y^6$ & $y^7$ & $y^8$ & $y^9$ & $y^{10}$ & $y^{11}$ & $y^{12}$ & $y^{13}$ & $y^{14}$ & $y^{15}$ & $y^{16}$ & $y^{17}$ \\\hline $1$ & $1$ & & & & & & & & & & & & & & & & & \\ $x$ & & $1$ & & & & & & & & & & & & & & & & \\ $x^2$ & & & $1$ & $3$ & $1$ & & & & & & & & & & & & & \\ $x^3$ & & & & & $2$ & $3$ & & & & & & & & & & & & \\ $x^4$ & & & & & & $1$ & $6$ & $6$ & $1$ & & & & & & & & & \\ $x^5$ & & & & & & & & $3$ & $10$ & $6$ & & & & & & & & \\ $x^6$ & & & & & & & & & $1$ & $10$ & $20$ & $10$ & $1$ & & & & & \\ $x^7$ & & & & & & & & & & & $4$ & $22$ & $30$ & $10$ & & & & \\ $x^8$ & & & & & & & & & & & & $1$ & $15$ & $49$ & $50$ & $15$ & $1$ & \\ $x^9$ & & & & & & & & & & & & & & $5$ & $40$ & $91$ & $70$ & $15$ \\ $x^{10}$ & & & & & & & & & & & & & & & $1$ & $21$ & $100$ & $168$ \\ \end{tabular} \end{table} The first several values of $(a_n)$ can be read as column sums: $1$, $1$, $3$, $3$, $4$, $6$, $9$, $12$, $16$, $24$, $33$, $46$, $64$, $\dots$ On the other hand, one might do the same for the generating function $h = h(x)$ and the associated sequence $(h_k)$. The first several values of $(h_k)$ can be read as row sums: $1$, $5$, $5$, $14$, $19$, $42$, $66$, $131$, $\dots$ Also, the expansion of $g$ gives insight into the distribution of lengths of maximal configurations relative to the number of occupied lots. Upon consulting The On-Line Encyclopedia of Integer Sequences \cite{oeis}, we have come across the fact that these sequences were studied in quite different settings (cf.~\href{https://oeis.org/A080013}{A080013} \& \href{https://oeis.org/A096976}{A096976}). We illustrate these connections in the following subsections. \subsubsection{Bijection with strongly restricted permutations} The notion of strongly restricted permutations was introduced by Lehmer in \cite{Lehmer}. If $W$ is some fixed subset of integers, one would like to count the number of all the permutations $\pi\in S_n$\footnote{$S_n$ denotes the set of all permutations of the set $[n]=\{1,\dots,n\}$.} such that $\pi(i)-i \in W$, for all $i\in[n]$. In \cite[Examples 4.7.9, 4.7.17--18]{Stanley} two techniques are presented for obtaining the generating function for the number of strongly restricted permutations for some particular sets $W$, namely the transfer-matrix method and the technique using factorization in free monoids. In \cite{Baltic} the author devised a new technique for counting restricted permutations in case $\min W =-k$ and $\max W =r$ for some positive integers $k\le r$. When $W=\{-2,-1,2\}$, the sequence counting the corresponding restricted permutations of length $n$ appears in the OEIS under the number \href{https://oeis.org/A080013}{A080013}. The generating function of that sequence is $\dfrac{1-y^2}{1-y^2-y^3-y^4+y^6}$. Note that $$ \frac{1-y^2}{1-y^2-y^3-y^4+y^6} = 1+y^3+y^4\cdot \frac{1+y+y^3-y^5}{1-y^2-y^3-y^4+y^6} = 1+y^3+y^4 \cdot f(y),$$ where $f(y)$ is the generating function for the number of Riviera configurations \eqref{eq:GF4offA080013} of fixed length $n$. From here, the following result is immediate. \begin{theorem} The number of maximal configurations of length $n$ in the Riviera model is equal to the number of permutations $\pi$ of length $n+4$, which satisfy the constraint \begin{equation} \label{permutationsconstraint} \pi(i)-i\in\{-2,-1,2\}. \end{equation} \end{theorem} It turns out that one can construct a natural bijection between these two types of objects. The idea is to encode restricted permutations as walks on some digraph, similar to the one in Figure \ref{fig:transfer_graph_Riviera}. If those two graphs are isomorphic, this isomorphism would automatically produce a bijection between the underlying combinatorial objects. To construct this digraph we, once again, use the transfer-matrix method. One can argue as in \cite[Example 4.7.9]{Stanley} to show that the method is applicable in this case. Let $\pi\in S_n$ be a permutation for which $\pi(i)-i\in W=\{-2,-1,2\}$, for all $i\in[n]$. One can rewrite such a permutation as a sequence of symbols in $W$. In order to check that such a sequence $u_1\dots u_n$ corresponds to a valid permutation, it suffices to check all the substrings of length $5$. This is because the function $\FJADEF{\sigma}{[n]}{[n]}$ defined as $\sigma(i)=i+u_i$ will be a permutation as soon as it is onto; and for this, one only needs to check whether $i\in \{\sigma(i-2), \sigma(i-1), \sigma(i), \sigma(i+1), \sigma(i+2)\}$, for all $3\le i \le n-2$. Additionally, one needs to check that $1$ and $2$ are in the set $\{\sigma(1), \sigma(2), \sigma(3), \sigma(4)\}$, and that $n-1$ and $n-2$ are in the set $\{\sigma(n-3), \sigma(n-2), \sigma(n-1), \sigma(n)\}$. The effect of this being that the walks must start and end at a certain subset of vertices of the constructed digraph. From here, one can write Algorithm \ref{alg:digrafPerm} that produces this digraph which is an induced subgraph of the de Bruijn graph over the set of all $5$ letter words in the alphabet $\{-2,-1,2\}$. \begin{algorithm} \caption{The creation of the digraph $\mathcal{G}$ for strongly restricted permutations}\label{alg:digrafPerm} \begin{algorithmic} \State AllowedNodes $=\emptyset$ \State StartNodes $=\emptyset$ \State EndNodes $=\emptyset$ \For{$u_1u_2u_3u_4u_5 \in {\{-2,-1,2\}^5}$} \If{$3\in \{ 1+u_1,2+u_2,3+u_3,4+u_4,5+u_5 \}$} \State add node $u_1u_2u_3u_4u_5$ to AllowedNodes \If{$1,2\in \{ 1+u_1,2+u_2,3+u_3,4+u_4,5+u_5 \}$} \State add node $u_1u_2u_3u_4u_5$ to StartNodes \EndIf \If{$4,5\in \{ 1+u_1,2+u_2,3+u_3,4+u_4,5+u_5 \}$} \State add node $u_1u_2u_3u_4u_5$ to EndNodes \EndIf \EndIf \EndFor \\ \State $\mathcal{E} = \emptyset$ \For{$u_1u_2u_3u_4u_5, v_1v_2v_3v_4v_5\in$ AllowedNodes} \If{$u_2u_3u_4u_5 = v_1v_2v_3v_4$} \State add edge $u_1u_2u_3u_4u_5 \to v_1v_2v_3v_4v_5$ to $\mathcal{E}$ \EndIf \EndFor \\ \State $\mathcal{V} = \emptyset$ \For{$u_1u_2u_3u_4u_5\in$ AllowedNodes} \If{there is a path starting in StartNodes, passing through $u_1u_2u_3u_4u_5$ and ending in EndNodes} \State add node $u_1u_2u_3u_4u_5$ to $\mathcal{V}$ \EndIf \EndFor \\ \State remove from $\mathcal{E}$ all the edges not involving nodes in $\mathcal{V}$ \State\Return $\mathcal{G}=(\mathcal{V},\mathcal{E})$ \end{algorithmic} \end{algorithm} The digraph $\mathcal{G}$ constructed in Algorithm \ref{alg:digrafPerm} has the vertex set $\mathcal{V}$ consisting of $30$ allowed words of length $5$. It turns out that this graph can be further condensed to give a smaller representation of our strongly restricted permutations. If one considers all the $4$-letter words $\{-2,-1,2\}^4$ that do not appear as substrings of the $30$ allowed words, one gets $59$ forbidden words of length $4$. By inspection, one can check that each of the $213=3^5-30$ forbidden $5$-letter words contains one of the $4$-letter forbidden words which means that the same information contained in $\mathcal{G}$ can be encoded in a digraph with a vertex set consisting of only $22=3^4-59$ $4$-letter words. Finally, if we use edges to encode allowed words, rather than just taking the whole induced subgraph of the corresponding de Bruijn graph, we can condense this digraph even further, and obtain the digraph in Figure \ref{fig:amforapermutacije} with 15 nodes representing allowed 3-letter words and an edge from $u_1u_2u_3$ to $v_1v_2v_3$ if and only if $u_1u_2u_3v_3=u_1v_1v_2v_3$ is allowed $4$-letter word. The highlighted nodes are either starting or ending nodes, or, in one case, both. \begin{figure} \begin{subfigure}{.495\linewidth}\centering \begin{tikzpicture}[scale=1.8, nodeStyle/.style={draw, circle, minimum size=4em}, edgeStyle/.style={-Stealth}]\tiny \node[nodeStyle] at (0,0) (-222) {-222}; \node[nodeStyle, fill=blue!20] at (-1,1) (22-2) {22-2}; \node[nodeStyle, draw=blue, line width=2pt] at (0,1) (2-2-2) {2-2-2}; \node[nodeStyle] at (1,1) (-2-22) {-2-22}; \node[nodeStyle] at (-1.5,2) (-122) {-122}; \node[nodeStyle] at (-.5,2) (-1-12) {-1-12}; \node[nodeStyle, fill=blue!20, draw=blue, line width=2pt] at (.5,2) (2-1-1) {2-1-1}; \node[nodeStyle] at (1.5,2) (-22-1) {-22-1}; \node[nodeStyle] at (-1,3) (-2-12) {-2-12}; \node[nodeStyle] at (0,3) (-12-1) {-12-1}; \node[nodeStyle, fill=blue!20] at (1,3) (2-12) {2-12}; \node[nodeStyle, draw=blue, line width=2pt] at (-.5,4) (2-2-1) {2-2-1}; \node[nodeStyle] at (.5,4) (-12-2) {-12-2}; \node[nodeStyle] at (-.5,5) (-22-2) {-22-2}; \node[nodeStyle] at (.5,5) (2-22) {2-22}; \draw[edgeStyle] (-2-12) to (-122); \draw[edgeStyle] (-2-12) to (-12-1); \draw[edgeStyle] (-122) to (22-2); \draw[edgeStyle] (-12-1) to (2-12); \draw[edgeStyle] (-12-1) to (2-1-1); \draw[edgeStyle] (-2-22) to (-222); \draw[edgeStyle] (-2-22) to (-22-1); \draw[edgeStyle] (-222) to (22-2); \draw[edgeStyle] (-22-1) to (2-12); \draw[edgeStyle] (-22-1) to (2-1-1); \draw[edgeStyle] (-1-12) to (-122); \draw[edgeStyle] (-1-12) to (-12-1); \draw[edgeStyle] (-22-2) to (2-2-1); \draw[edgeStyle] (-22-2) to [bend right] (2-22); \draw[edgeStyle] (2-2-1) to (-2-12); \draw[edgeStyle] (2-22) to [bend right] (-22-2); \draw[edgeStyle] (2-2-2) to (-2-22); \draw[edgeStyle] (22-2) to (2-2-2); \draw[edgeStyle] (2-12) to (-12-2); \draw[edgeStyle] (-12-2) to (2-2-1); \draw[edgeStyle] (-12-2) to (2-22); \draw[edgeStyle] (2-1-1) to (-1-12); \end{tikzpicture} \caption{} \label{fig:amforapermutacije} \end{subfigure} \begin{subfigure}{.495\linewidth}\centering \begin{tikzpicture}[scale=1.8, nodeStyle/.style={draw, circle,minimum size=4em}, edgeStyle/.style={-Stealth}]\tiny \node[nodeStyle] at (0,0) (001100) {001100}; \node[nodeStyle, fill=blue!20] at (-1,1) (011001) {011001}; \node[nodeStyle, draw=blue, line width=2pt] at (0,1) (110011) {110011}; \node[nodeStyle] at (1,1) (100110) {100110}; \node[nodeStyle] at (-1.5,2) (101100) {101100}; \node[nodeStyle] at (-.5,2) (110110) {110110}; \node[nodeStyle, fill=blue!20, draw=blue, line width=2pt] at (.5,2) (011011) {011011}; \node[nodeStyle] at (1.5,2) (001101) {001101}; \node[nodeStyle] at (-1,3) (010110) {010110}; \node[nodeStyle] at (0,3) (101101) {101101}; \node[nodeStyle, fill=blue!20] at (1,3) (011010) {011010}; \node[nodeStyle, draw=blue, line width=2pt] at (-.5,4) (101011) {101011}; \node[nodeStyle] at (.5,4) (110101) {110101}; \node[nodeStyle] at (-.5,5) (010101) {010101}; \node[nodeStyle] at (.5,5) (101010) {101010}; \draw[edgeStyle] (010110) to (101100); \draw[edgeStyle] (010110) to (101101); \draw[edgeStyle] (101100) to (011001); \draw[edgeStyle] (101101) to (011010); \draw[edgeStyle] (101101) to (011011); \draw[edgeStyle] (100110) to (001100); \draw[edgeStyle] (100110) to (001101); \draw[edgeStyle] (001100) to (011001); \draw[edgeStyle] (001101) to (011010); \draw[edgeStyle] (001101) to (011011); \draw[edgeStyle] (110110) to (101100); \draw[edgeStyle] (110110) to (101101); \draw[edgeStyle] (010101) to (101011); \draw[edgeStyle] (010101) to [bend right] (101010); \draw[edgeStyle] (101011) to (010110); \draw[edgeStyle] (101010) to [bend right] (010101); \draw[edgeStyle] (110011) to (100110); \draw[edgeStyle] (011001) to (110011); \draw[edgeStyle] (011010) to (110101); \draw[edgeStyle] (110101) to (101011); \draw[edgeStyle] (110101) to (101010); \draw[edgeStyle] (011011) to (110110); \end{tikzpicture} \caption{} \label{fig:amforakucice} \end{subfigure} \caption{ The digraph $\mathcal{G_P}$ in \ref{fig:amforapermutacije} encodes strongly restricted permutations satisfying the constraint \eqref{permutationsconstraint}. The starting nodes are \textcolor{blue!70}{shaded} and \textcolor{blue}{thicker outlines} indicate the ending nodes. The digraph $\mathcal{G_R'}$ in \ref{fig:amforakucice} encodes configurations of the Riviera model using substrings of length $6$. The nodes corresponding to the highlighted nodes in \ref{fig:amforapermutacije} via the unique digraph isomorphism are shaded and outlined in this graph too.}\label{fig:amfora} \end{figure} We would now like to match the digraph in Figure \ref{fig:amforapermutacije}, call it $\mathcal{G_P}$, with the digraph in Figure \ref{fig:transfer_graph_Riviera}, call it $\mathcal{G_R}$. Unfortunately, they are not isomorphic, but we can try to create higher edge graphs from the digraph $\mathcal{G_R}$, details below, which encode the same information as $\mathcal{G_R}$ --- in hope of obtaining a graph isomorphic to $\mathcal{G_P}$. This process is opposite of `condensation' we have performed to the digraph produced by the Algorithm \ref{alg:digrafPerm} in order to obtain the digraph $\mathcal{G_P}$. We have already noted that the graph $\mathcal{G_R}$ shown in Figure \ref{fig:transfer_graph_Riviera} is a subgraph of the $3$-dimensional de Bruijn graph over the alphabet $\{0,1\}$. We can construct a subgraph of the $n$-dimensional de Bruijn digraph, where $n>3$, over the same alphabet, which will encode the same information as $\mathcal{G_R}$. It turns out that $n=6$ will do. The vertex set of this, so called, higher edge graph $\mathcal{G_R'}$ consists of all the allowed words of length $6$, which one can think of as all the possible walks of length $3$ on the graph $\mathcal{G_R}$. A directed edge from $c_1\dots c_6$ to $d_1\dots d_6$ is added to the edge set of $\mathcal{G_R'}$ if and only if the corresponding words overlap progressively ($c_2\dots c_6 = d_1\dots d_5$). The digraph $\mathcal{G_R'}$ is, therefore, the vertex-induced subgraph of the corresponding $6$-dimensional de Bruijn graph. For more details on construction of higher edge graphs, see \cite[Definition 2.3.4]{SymbDynCoding}. The graph $\mathcal{G_R'}$ obtained by the above procedure, is shown in Figure \ref{fig:amforakucice}. Note that it is isomorphic to $\mathcal{G_P}$, and that this isomorphism is unique. Also note that the set of nodes at which the walks on $\mathcal{G_R'}$ would be allowed to start and end is much larger than the set highlighted in Figure \ref{fig:amforakucice}. More precisely, any node $c_1\dots c_6$ for which $c_1c_2c_3 \in \{110,101,011\}$ would be a starting node, and if $c_4c_5c_6 \in \{110,101,011\}$, it would be an ending node. But the walks of length $n+1$ on $\mathcal{G_R'}$ would then account for all the maximal configurations in the Riviera model of length $n+7$ --- and that is not what we want, since the walks of length $n+1$ on $\mathcal{G_P}$ encode the strictly restricted permutations of $[n+4]$. If we consider the walks on $\mathcal{G_R'}$ which start and end at the nodes that correspond to starting and ending nodes in $\mathcal{G_P}$, we immediately note that all the configurations obtained in such a way always start with $0110$ and end with $011$. Using the graph $\mathcal{G_R}$ in Figure \ref{fig:transfer_graph_Riviera} it is clear that adding the prefix $0110$ and suffix $011$ to a maximal configuration, again produces a 7-blocks longer (permissible) maximal configuration. This is because from each starting node, there is a backward path (going along edges in the direction opposite to the arrow direction) of length $4$ which produces the prefix $0110$; also from each ending node, there is a $3$-step continuation of path which produces the suffix $011$. Conversely, removing that same prefix and suffix from a maximal configuration of length $n+7$, produces a maximal configuration of length $n$. We can again argue using the graph $\mathcal{G_R}$. Any walk starting with $011 \to 110$ after three steps must again reach one of the starting nodes; and walk ending in $011$ when traced backwards must, after three steps going backwards, reach one of the ending nodes. This shows that there is a bijective correspondence between all the maximal Riviera configurations of length $n$ and the maximal Riviera configurations of length $n+7$ starting with $0110$ and ending with $011$ which in turn are in a bijective correspondence with the strongly restricted permutations of length $n+4$. The bijection is obtained by translating walks on $\mathcal{G_P}$ to walks on $\mathcal{G_R'}$ and the other way around. It is, in fact, possible to specify this bijection even more concisely, circumventing the graphs in Figure \ref{fig:amfora} altogether. Compare each edge in $\mathcal{G_R}$ with all its associated edges in $\mathcal{G_R'}$ and note that the corresponding edges in graph $\mathcal{G_P}$ all represent adding the same symbol at the end. E.g.\ the transition $011 \to 110$ in $\mathcal{G_R}$ corresponds to transitions $101011 \to 010110$, $011011 \to 110110$ and $110011 \to 100110$ in $\mathcal{G_R'}$ and all of them in $\mathcal{G_P}$ correspond to adding the letter $2$ at the end. Collecting all this information together, we can label the edges of the graph $\mathcal{G_R}$ in Figure \ref{fig:transfer_graph_Riviera} with the appropriate letter which is being added in the permutation graph $\mathcal{G_P}$ corresponding to that transition. This edge-labeled graph is given in Figure \ref{fig:graf_za_bijekciju}. We now summarize how to bijectively map any maximal Riviera configuration of length $n$ to a strongly restricted permutation of length $n+4$ using Figure \ref{fig:graf_za_bijekciju}. Take any such maximal configuration and prefix it with $0110$ and suffix it with $011$. Then take a walk over the graph in Figure \ref{fig:graf_za_bijekciju} (which will be of length $n+7-3=n+4$) and collect the labels $u_1\dots u_{n+4}$ of all the edges traversed. Finally, construct the bijection $\FJADEF{\sigma}{[n+4]}{[n+4]}$ as $\sigma(i)=i+u_i$ for $i\in [n+4]$. As an example, the maximal configuration $10110$ is first enlarged to the maximal configuration $\textcolor{blue}{0110}\|10110\|\textcolor{blue}{011}$. Next, we examine the unique walk determined by this configuration: $\text{011} \stackrel{2}{\longrightarrow} \text{110} \stackrel{-1}{\longrightarrow} \text{101} \stackrel{2}{\longrightarrow} \text{010} \stackrel{-2}{\longrightarrow} \text{101} \stackrel{-1}{\longrightarrow} \text{011} \stackrel{2}{\longrightarrow} \text{110} \stackrel{2}{\longrightarrow} \text{100} \stackrel{-2}{\longrightarrow} \text{001} \stackrel{-2}{\longrightarrow} \text{011}$. This walk generates the permutation $\sigma$ encoded with the string 2-12-2-122-2-2, which is the permutation $\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 3 & 1 & 5 & 2 & 4 & 8 & 9 & 6 & 7 \end{pmatrix}$. \begin{figure} \begin{tikzpicture}[node distance=5em,nodeStyle/.style={draw, circle, minimum size=2.5em}] \node (A) [nodeStyle] {100}; \node (B) [right of = A, nodeStyle] {001}; \node (C) [right of = B, nodeStyle, fill=blue!20] {011}; \node (D) [right of = C, nodeStyle, fill=blue!20] {110}; \node (E) [right of = D, nodeStyle, fill=blue!20] {101}; \node (F) [right of = E, nodeStyle] {010}; \draw[-Stealth,above] (A) edge[bend left] node {-2} (B); \draw[-Stealth,above] (B) edge[bend left] node {-2} (C); \draw[-Stealth,above] (F) edge[bend left] node[below] {-2} (E); \draw[-Stealth,above] (D) edge[bend left] node {-1} (E); \draw[-Stealth,above] (D) edge[bend left] node[below] {2} (A); \draw[-Stealth,above] (C) edge[bend left] node {2} (D); \draw[-Stealth,above] (E) edge[bend left] node {2} (F); \draw[-Stealth,above] (E) edge[bend left] node[below] {-1} (C); \end{tikzpicture} \caption{The digraph $\mathcal{G_R}$ with labeled edges which encodes the bijection between maximal configurations of length $n$ in the Riviera model and strongly restricted permutations of length $n+4$ where $W=\{-2,-1,2\}$.} \label{fig:graf_za_bijekciju} \end{figure} We end this section with a remark which will prove useful in the next subsection. \begin{remark}\label{rem:1001} Above, we have argued that taking any maximal configuration $c_1 \dots c_n$ and prefixing it with $0110$ and suffixing it with $011$ yields a bijection between all the maximal Riviera configurations of length $n$ and the maximal Riviera configurations of length $n+7$ starting with $0110$ and ending with $011$. If we further add prefix $10$ and suffix $001$ to these already extended configurations, we obtain a bijective correspondence between the maximal Riviera configurations $c_1 \dots c_n$ of length $n$ and the configurations of length $n+12$ starting with $100110$ and ending with $011001$ which, although not maximal (because of the boundary condition), do not contain\footnote{Here, and throughout this section, by contained we mean contained as a substring in unpadded configurations.} any substrings forbidden by Lemma \ref{lemma_forbidden_words}. Each of those extended configurations can, therefore, be represented as a walk on $\mathcal{G_R}$ (Figure \ref{fig:transfer_graph_Riviera}) starting at the node $100$ and ending at the node $001$. Conversely, if a configuration $100110 c_1\dots c_n 011001$ (of length $n+12$) does not contain any substrings forbidden by Lemma \ref{lemma_forbidden_words}, or equivalently, can be represented as a walk on $\mathcal{G_R}$ (of length $n+9$) starting at $100$ and ending at $001$, then after removing prefix $ 100110$ and suffix $011001$ one is left with a proper maximal configuration $c_1\dots c_n$ of length $n$. This is because removing prefix and suffix corresponds to cutting off the first part of the walk $100$-$001$-$011$-$110$-$10c_1$-$0c_1c_2$ and the last part of the walk $c_{n-1}c_n0$-$c_n01$-$011$-$110$-$100$-$001$. Note that regardless of what $c_1$, $c_2$, $c_{n-1}$, and $c_n$ are --- the next node after $0c_1c_2$ as well as the node just before $c_{n-1}c_n0$ will always have to be one of the starting/ending nodes, which means that the remaining part of the walk encodes a proper maximal configuration $c_1c_2\dots c_{n-1}c_n$. \end{remark} \subsubsection{Bijection with the closed walks on the $P_3$ with a loop} \begin{figure} \begin{subfigure}{.49\linewidth}\centering \begin{tikzpicture}[node distance=5em,every loop/.style={}] \node (A) {\bf\color{red}\Large$\bullet$}; \node (B) [right of = A] {$\bullet$}; \node (C) [right of = B] {$\bullet$}; \draw[above] (A) edge (B); \draw[above] (B) edge (C); \draw (C) edge[loop,out=45,in=-45,looseness=8] (C)[below]; \end{tikzpicture} \caption{$P_3$ with a loop, $\mathcal{P}$ for short}\label{fig:p3withloop} \end{subfigure} \begin{subfigure}{.49\linewidth}\centering \begin{tikzpicture}[node distance=5em,every loop/.style={}] \node (A) {\bf\color{red}1001}; \node (B) [right of = A] {11}; \node (C) [right of = B] {101}; \draw[above] (A) edge (B); \draw[above] (B) edge (C); \draw (C) edge[loop,out=45,in=-45,looseness=8] (C)[below]; \end{tikzpicture} \caption{$\mathcal{P}$ with labeled nodes}\label{fig:LabeledP_3} \end{subfigure} \caption{} \end{figure} In Remark \ref{rem:GFhFixHouses} we have derived the generating function $h(x)$ for the number of Riviera configurations (of variable length) containing a fixed number $k$ of occupied lots. This sequence appears on OEIS \cite{oeis} in two instances as \href{https://oeis.org/A052547}{A052547} with offset 3 and as \href{https://oeis.org/A096976}{A096976} with offset 5. There are three more related sequences: \href{https://oeis.org/A006053}{A006053}, \href{https://oeis.org/A028495}{A028495}, and \href{https://oeis.org/A096975}{A096975}, satisfying the same recurrence relation with different initial conditions. Each of these sequences is connected to the number of walks on the graph $P_3$ (the path graph over three nodes) with a loop added at one of the end nodes. This graph is represented in Figure \ref{fig:p3withloop} and we denote it by $\mathcal{P}$. The precise connection relating this graph with our sequence is given in the following theorem. \begin{theorem} The number of maximal Riviera configurations containing exactly $k$ occupied lots is equal to the number of closed walks of length $k+4$ on the graph $\mathcal{P}$ which start and end at the node of degree $1$. There is a natural bijection relating these quantities. \end{theorem} \begin{proof} From Lemma \ref{lemma_forbidden_words} we know that no three consecutive $0$'s are allowed in a maximal configuration. That means that each two neighboring $1$'s must be separated by zero, one or two $0$'s. This further means that, after ignoring leading and trailing $0$'s each maximal configuration can be identified by a sequence of strings in the set $\{11, 101, 1001\}$. We assume here that the last $1$ in one string overlaps with the first $1$ in the next. E.g.\ we would split the configuration $11011001101$ as $11$-$101$-$11$-$1001$-$11$-$101$. From Lemma \ref{lemma_forbidden_words} we also see that $11$ cannot be followed or preceded by $11$ (as this would produce $111$); $101$ and $1001$ cannot be followed or preceded by $1001$ (as this would produce $0100$ or $0010$). It is easy to see that the remaining transitions: $1001$-$11$ and $11$-$101$ going in either direction, and the loop at $101$ --- can all appear in a maximal configuration and are, thus, all allowed. These transitions are shown in the node-labeled graph $\mathcal{P}$ in Figure \ref{fig:LabeledP_3}. We use undirected edges as in each case the transitions going either way are allowed. Consider now the mapping which to each maximal Riviera configuration $c_1\dots c_n$ assigns the configuration $100110c_1\dots c_n011001$. By Remark \ref{rem:1001} we know that this map is a bijection from the set of all maximal Riviera configurations with exactly $k$ occupied lots to the set of configurations of the form $100110c_1\dots c_n011001$ which have exactly $k+6$ occupied lots. Those obtained configurations are not maximal but do not contain substrings forbidden by Lemma \ref{lemma_forbidden_words}. Now each of those configurations of the form $100110c_1\dots c_n011001$, where $c_1\dots c_n$ is a proper maximal configuration with $k$ occupied lots, can be represented as a walk of length $k+4$ on the graph $\mathcal{P}$ in Figure \ref{fig:LabeledP_3} which starts and ends at $1001$. Conversely, one easily checks (by inspecting all length $2$ walks) that a walk on this graph can never produce a configuration containing a substring which is forbidden by Lemma \ref{lemma_forbidden_words}. Therefore, each walk of length $k+4$ starting and ending at $1001$ will necessarily produce a configuration of the form $100110c_1\dots c_n011001$ which does not contain a substring forbidden by Lemma \ref{lemma_forbidden_words} and has $k+6$ $1$'s. By Remark \ref{rem:1001}, the word $c_1\dots c_n$ will be a proper maximal configuration with exactly $k$ $1$'s. Putting everything together gives us the required bijection. A maximal Riviera configuration $c_1 \dots c_n$ containing exactly $k$ occupied lots is written as the string $100110c_1\dots c_n 011001$, which is then represented as a walk of length $k+4$ over the graph $\mathcal{P}$. As an example, the maximal configuration 10110 is mapped to $10110 \to \textcolor{blue}{100110}\|10110\|\textcolor{blue}{011001}$ which corresponds to the walk: $1001 \rightarrow 11 \rightarrow 101 \rightarrow \text{101} \rightarrow \text{11} \rightarrow \text{1001} \rightarrow \text{11} \rightarrow \text{1001}$ which begins and ends with the node $1001$. \end{proof} \section{Multi-story models}\label{sec:multi-story} A natural generalization of the Riviera model is an analogous model where the lots are occupied with houses consisting of multiple stories. The configurations of houses in this case are represented with a row vector $C=(c_1,\dots,c_n) \in \mathbb{N}_0^n$, where $c_i$ is the number of stories that the house on the lot $i$ has, and $c_i = 0$ represents an empty lot, as before. For the sake of simplicity, the assumption is that the sunlight falls at the angle of $45$ degrees and that each floor of every house is a perfect cube, see Figure \ref{fig:sjene}. This assumption requires the building configurations to spread out more so that the lower stories can obtain sunlight and not be blocked by other houses. Thus, the following definition arises: A building of $k$ stories positioned on the lot $i$ blocks sunlight, from one side, to each lot $ i-k \leq j \leq i+k$ up to the height of $k - \aps{i - j} + 1$ stories. \begin{figure} \includegraphics{slikaSjene} \caption{Both stories of the middle house are blocked from the sunlight from the east, while only the first story is blocked from the west.}\label{fig:sjene} \end{figure} The permissibility constraint in such models can be concisely stated in the following way: Every story of each house must obtain sunlight from at least one side (east or west) during the day, namely, not to be blocked from sunlight from both sides by other buildings. Naturally, we are again interested in maximal configurations. The maximality of the configuration $C \in \mathbb{N}_0^n$ would mean that for each lot $i$, $1\leq i \leq n$, no additional stories can be built on it. In other words, if an addition of a single story to any lot in $C$ would still result in a permissible configuration, then it is not maximal. In this section we also comment a logical counterpart of a multi-story Riviera model, namely a multi-story Flory model. As already stated, in the Riviera model we require that each story obtains sunlight from the east \textbf{or} the west. However, one could alternatively require that each story obtains sunlight from the east \textbf{and} from the west. In this case, we would obtain models of Flory type, which in the single-story case comes down to the classical Flory model introduced in \cite{Flory}. We comment on both of these variants, which we can refer to as the \textbf{AND} and the \textbf{OR} variant. \subsection{OR variant} Our intention here is again to count the number of maximal configurations. To this end, we apply the transfer matrix method, for which we are required to construct a digraph which allows us to encode our configurations in terms of walks on that graph. It is somewhat obvious that, on this level of generality, this is impossible, due to the fact that the minimal set of impermissible substrings of maximal configurations cannot be reduced to a finite set. However, by fixing a maximal number of stories allowed, we denote it with $k$, we are still in the domain of transfer matrix method. Once we fix $k$, in order to construct a digraph, we must know the minimal length of the nodal strings which would guarantee the permissibility and maximality of the configurations associated with walks. Next, we must find all of the possible substrings of that length which occur in maximal configurations. One way of doing this is by an exhaustive search among all the maximal configurations until one is sure that all the substrings have been found. This, however, is quite involved, which can be deduced from the following two lemmas. \begin{lemma}\label{lm:4k+1} Let $k \in \mathbb{N}$ be the maximal number of stories allowed. It is enough to take substrings of length $4k + 1$ to form nodes of the graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ (which can be constructed analogously as in Algorithm \ref{alg:digrafPerm}) to be certain that this graph $\mathcal{G}$ can be used in the transfer matrix method for counting the corresponding maximal configurations. \end{lemma} \begin{proof} As already mentioned, applicability of the transfer matrix method relies on the fact that permissibility, as well as maximality of a configuration, can be verified by inspecting only finite size patches of a given configuration. More precisely, if one wants to check whether a state of a certain lot (occupied or unoccupied) has caused the configuration to be impermissible or not maximal, one only needs to check the situation on the lots in a certain finite radius of the observed lot, where that radius is uniform for each lot on the tract of land. What we are claiming in this lemma is that, when the maximal number of stories allowed is $k$, than this radius is $2k$, i.e.\ it is enough to check the $2k$ immediate neighbors to the west of a lot and the $2k$ immediate neighbors to the east of a lot to be certain whether this central lot violates permissibility or maximality. Let us first discuss what needs to be checked to be sure that building an additional story on that central lot will not violate permissibility and then we will discuss what needs to be checked to ensure that not building an additional story on this lot will not violate maximality. There are two ways in which permissibility can be violated. On one hand, it can happen that the built story itself will not be exposed to sunlight and on the other hand, the built story can block a story of another house from the sunlight. The radius that needs to be checked is the biggest in the case when we want to build as many stories as allowed, so we assume from now that we want to build a $k$-story house and that its first neighbors to the east and to the west are also $k$-story houses. To check whether the central lot is already blocked from the sunlight, we only need to check $k$ lots to the east and $k$ lots to the west. Notice now that if the first neighbor to the east of the central lot is more than $k$ empty lots away, then this neighbor is definitely getting sunlight from the west and building a house on a central lot will not block the sunlight to that neighboring house. If that neighbor is less than $k$ empty lots away, then building a $k$-story house on the central lot would block the sunlight from the west at least to the first story of the mentioned neighbor. In that case, the question is whether this first neighbor to the east is exposed to sunlight from the east. To verify that, we again need to check what happens on $k$ immediate neighboring lots to the east of it. Hence, the worst-case scenario is that we need to check $2k$ lots to the east of the central lot. Due to the symmetry, the same holds while checking lots to the west of the central one. It is now easy to see that applying the same logic and checking $2k$ lots immediately to the east and immediately to the west of a central lot is enough to verify whether we can build additional stories on that central lot and in this way we check maximality. \end{proof} \begin{lemma}\label{lm:8k+1} Let $k \in \mathbb{N}$ be the maximal number of stories allowed. Then the maximal configurations of length $8k + 1$ contain as substrings all the strings of length $4k + 1$ that can appear in any maximal configuration of arbitrary length. Moreover, if such a string is at the beginning/end of a maximal configuration then it is possible to choose a maximal configuration of length $8k+1$ in which it also appears at the beginning/end. \end{lemma} \begin{remark} Notice that Lemma \ref{lm:8k+1} tells us that if we find all the maximal configurations of length $8k + 1$ (which can be done by exhaustive search using a computer), and then go through those maximal configurations with the window of size $4k + 1$, we will find all the vertices that we need for the graph $\mathcal{G}$. Moreover, using these maximal configurations of length $8k + 1$ we can easily extract the vertices with which the maximal configuration can start and end (see Algorithm \ref{alg:cap}). \end{remark} \begin{proof}[Proof of Lemma \ref{lm:8k+1}] It is clear from Lemma \ref{lm:4k+1} that the state of a certain lot in a maximal configuration, padded with zeros, is a function of the states of $2k$ lots immediately to the east and $2k$ lots immediately to the west of it. More precisely, the state $s$ of that lot is the largest number $0\le s \le k$ which keeps the configuration permissible. This means that it is impossible to have two nodes in the graph $\mathcal{G}$ such that they only differ in the state of the central lot. The above mentioned function $f({u_1\dots u_{2k}},{v_1\dots v_{2k}})$, which to each pair of permissible words of length $2k$ assigns the largest number of stories that could be built on the central lot of a configuration obtained by concatenating the word $u_1\dots u_{2k}$ to the left and the word $v_1\dots v_{2k}$ to the right of that central lot whilst not violating permissibility, is monotonic in the sense that if $u_i\le u_i'$ and $v_i\le v_i'$ for all $1\le i\le 2k$ then $f({u_1\dots u_{2k}},{v_1\dots v_{2k}}) \ge f({u_1'\dots u_{2k}'},{v_1'\dots v_{2k}'})$. What we need to show here is that every substring of length $4k + 1$ that can appear in some maximal configuration of arbitrary length, also appears in some maximal configuration of length $8k + 1$. We prove this by showing that any substring of length $4k + 1$ that can appear in a maximal configuration can be expanded to a maximal configuration by adding additional $2k$ lots to the east and to the west of it and building additional houses only on those $4k$ added lots. As announced, we start from a substring $u_1 u_2 \dots u_{4k+1}$ of length $4k + 1$ which appears in some maximal configuration. We then extract this substring along with $2k$ lots to the east of that substring within this maximal configuration in which it appears and also $2k$ lots to the west of it, padding with zeros when necessary. This gives us a string $u_{-2k+1} \dots u_0 u_1 \dots u_{4k+1} \dots u_{6k+1}$ of length $8k + 1$ which we further pad with zeros to the left and right to obtain an infinite word $(u_i)_{i\in\mathbb{Z}}$. Note that the maximality of the initial configuration in which the substring $u_1 u_2 \dots u_{4k+1}$ appeared implies that the relation $u_i=f(u_{i-2k}\dots u_{i-1},u_{i+1}\dots u_{i+2k})$ holds for any $1\le i\le 4k+1$. We now start changing the entries $u_0, u_{-1}, \dots , u_{-2k+1}$, and $u_{4k+2}, u_{4k+3}, \dots , u_{6k+1}$ one-by-one, in this order, according to the output of $f$ on the current state of the $2k$ lots to the left and right of the observed block. We first change $u_0$ to $u_0'=f({u_{-2k}\dots u_{-1}}, {u_1 u_2 \dots u_{2k}})$, then $u_{-1}$ to $u_{-1}'=f({u_{-2k-1}\dots u_{-2}}, {u_0' u_1 \dots u_{2k-1}})$ and so on. Continuing in this way, we will construct the configuration $$u_{-2k+1}'\dots u_{0}' u_1 u_2 \dots u_{4k+1} u_{4k+2}' \dots u_{6k+1}'$$ of length $8k+1$ which, we claim, is maximal. Observe that since we have started with a permissible configuration, the updates provided by $f$ can only ever increase the number of the stories already present at the inspected lot. Also note that the configuration we obtain after performing these updates is also permissible as the updates provided by the function $f$ never violate permissibility. Now, to verify maximality note that, by the definition of function $f$, the number $u_{i}'$, where $-2k+1\le i\le 0$ or $4k+2\le i\le 6k+1$, was as large as permitted at the time the update $u_i \mapsto u_i'$ was performed. Taking into account the monotonicity of $f$, it is clear that $u_i'$ is as large as possible in the final configuration obtained. Finally note that, again, because of the monotonicity of $f$, $u_i$ for $1\le i\le 4k+1$ is still as large as possible. To see that the `moreover' part of the statement is true, note that an analogous procedure can be followed if the initial substring appears at the beginning/end. In this case we extract the substring from its maximal configuration along with $4k$ additional lots to its right/left and then pad with zeros. The updates via $f$ are again performed only on these extra lots and similar arguments show that the obtained configuration of length $8k+1$ which starts/end with the chosen substring is maximal. \end{proof} Now we propose an algorithm (see Algorithm \ref{alg:cap}) for calculating the $(k+1)$-variate generating function related to a Riviera model where it is possible to have houses with different number of stories, but the maximal number of stories allowed is a fixed number $k \in \mathbb{N}$. Variables $x_r$, $r \in \{1, 2, \ldots, k\}$, are formal variables associated with the number of $r$-story houses in the maximal configuration and $y$ is a formal variable associated with the length of a maximal configuration. The proposed algorithm is written in a very general way and it works even in situations where all the $r$-story houses appear ($r \in \{1, 2, \ldots, k\}$), but in the case when we allow only $k$-story houses for one fixed $k \in \mathbb{N}$, we use slightly simpler notation than the one in Algorithm \ref{alg:cap}. \begin{algorithm} \caption{The calculation of the $(k +1)$-variate generating function}\label{alg:cap} \begin{algorithmic} \State MaximalConfigurations $=$ all the maximal configurations of length $8k + 1$ \State \Comment{this is found by an exhaustive search} \State AllowedNodes $=\emptyset$, StartNodes $=\emptyset$, EndNodes $=\emptyset$ \For{mc $\in$ MaximalConfigurations} \State add substring(mc, start $ = 1$, end $ = 4k + 1$) to StartNodes \State add substring(mc, start $ = 4k + 1$, end $ = 8k + 1$) to EndNodes \For{$1 \le i \le 4k + 1$} \State add substring(mc, start $ = i$, end $ = 4k + i$) to AllowedNodes \EndFor \EndFor \\ \State $n = $ length(AllowedNodes) \State $A = $ null matrix(nrow $ = n$, ncol $ = n$) \For {$1 \le i \le n$} \For {$1 \le j \le n$} \If {substring(AllowedNodes$[i]$, start $ = 2$, end $ = 4k + 1$) $ = $ $\quad\backslash\backslash$\\ substring(AllowedNodes$[j]$, start $ = 1$, end $ = 4k$)} \State $r = $ substring(AllowedNodes[j], start $ = 4k + 1$, end $ = 4k + 1$) \If{$r = 0$} \State $A[i, j] = 1$ \Else \State $A[i, j] = x_r$ \EndIf \EndIf \EndFor \EndFor \\ \State $a = $ null vector(length $ = n$), $b = $ null vector(length $ = n$) \For{$1 \le i \le n$} \If{AllowedNodes$[i] \in $ StartNodes} \State $a[i] = 1$ \For{$1 \le r \le k$} \State $c = $ count($r$ in AllowedNodes$[i]$) \State $a[i] = a[i] \cdot x_r^c$ \EndFor \EndIf \If{AllowedNodes$[i] \in $ EndNodes} \State $b[i] = 1$ \EndIf \EndFor \\ \State $a_{c_1, c_2, \ldots, c_k, j} = $ the number of maximal configurations of length $j$ with precisely $c_r$ $r$-story houses \Comment{this is found by an exhaustive search for $0 \le j \le 4k$} \State $F_1(x_1, x_2, \ldots, x_k, y) = \sum_{j = 0}^{4k} \sum_{c_1, c_2, \ldots, c_k = 0}^{j} a_{c_1, c_2, \ldots, c_k, j} \prod_{r = 1}^{k} x_r^{c_r}y^j$ \State $F_2(x_1, x_2, \ldots, x_k, y) = \sum_{j = 4k + 1}^{\infty} a^T \cdot A^{j - 4k} \cdot b \cdot y^j = a^T\cdot(I-Ay)^{-1}\cdot A\cdot b\cdot y^{4k+1}$ \\ \State\Return $F(x_1, x_2, \ldots, x_k, y) = F_1(x_1, x_2, \ldots, x_k, y) + F_2(x_1, x_2, \ldots, x_k, y)$ \end{algorithmic} \end{algorithm} \subsubsection{Two-story Riviera model} In the two-story Riviera model, all the houses on our $1 \times n$ tract of land have precisely two stories. This means that, to ensure permissibility of the configuration, each house needs to have at least two empty lots immediately to the east or at least two empty lots immediately to the west of itself (we again assume that there is no obstruction to sunlight on the east and west boundary of the tract of land). Maximal configurations are, as before, those that are permissible, but become impermissible as soon as we add one more house on any of the empty lots. Representing configurations of length $n$ with row vectors $C=(c_1,\dots, c_n) \in \mathbb{N}_0^n$ where $c_i = 2$ denotes that on the lot $i$ ($i \in \{1, 2, \ldots, n\}$) there is a house with $2$ stories (and $c_i = 0$ denotes that the lot $i$ is not occupied by a house), one example of maximal configuration in the two-story Riviera model is $0202000022$. It is easy to check that each of the two stories of every house in this configuration is exposed to sunlight from at least one side (east or west), and that adding another two-story house on any of the empty lots would turn this configuration into an impermissible one. The goal now is to repeat the same procedure as for the original Riviera model and to obtain bivariate generating function which will give us information not only about the number of maximal configurations with a fixed length, but also about the number of maximal configurations with a fixed number of houses. Using Algorithm \ref{alg:cap}, we can construct the digraph that enables us to encode maximal configurations with walks on that digraph. Analogously as in Subsection \ref{subsec:gen_fun_for_Riviera} we define the matrix function $A(x)$, which is not only the adjacency matrix of the mentioned digraph, but additionally encodes whether a transition from one node of the graph to another one results in the increase of the total number of occupied lots. Due to the dimension of the matrix $A(x)$ and the technicalities in developing bivariate generating function, we omit the details. The precise shape of the generating function $F(x, y)$ (given in Appendix --- see \eqref{it:two-story_Riviera}) was obtained following Algorithm \ref{alg:cap} and using R programming language \cite{Rcite} for creating the necessary objects (matrix $A$, vectors $a$ and $b$) and Maxima software to perform the calculation of the generating function using objects created in R. The first few coefficients in the expansion of $F(x,y)$ are given in Table \ref{tab:gf2}. By inspecting the non-zero coefficients in the table, we see that the ratio $\frac{k}{n}$ is in-between $\frac{2}{7}$ and $\frac{1}{2}$, for large $n$. \begin{table}[!h] \caption{The first few coefficients in the expansion of the bivariate generating function $F(x,y)$.}\label{tab:gf2} \small \begin{tabular}{c\|cccccccccccccccc} $k\backslash n$ & $1$ & $y$ & $y^2$ & $y^3$ & $y^4$ & $y^5$ & $y^6$ & $y^7$ & $y^8$ & $y^9$ & $y^{10}$ & $y^{11}$ & $y^{12}$ & $y^{13}$ & $y^{14}$ & $y^{15}$\\\hline $1$ & $1$ & & & & & & & & & & & & & & & \\ $x$ & & $1$ & & & & & & & & & & & & & & \\ $x^2$ & & & $1$ & $3$ & $6$ & $5$ & $3$ & $1$ & & & & & & & & \\ $x^3$ & & & & & & $2$ & $4$ & $5$ & $2$ & & & & & & & \\ $x^4$ & & & & & & & $1$ & $5$ & $16$ & $27$ & $31$ & $24$ & $13$ & $5$ & $1$ & \\ $x^5$ & & & & & & & & & & $3$ & $12$ & $28$ & $36$ & $29$ & $14$& $3$ \\ $x^6$ & & & & & & & & & & & $1$ & $7$ & $31$ & $80$ & $142$& $177$\\ $x^7$ & & & & & & & & & & & & & & $4$ & $24$ & $82$ \\ \end{tabular} \end{table} From Table \ref{tab:gf2} we read that there are $44$ maximal configurations of length $10$, out of which $31$ configurations have precisely $4$ two-story houses built on them. This means that, apart from the maximal configuration that we gave as an example ($0202000022$), there are $43$ more maximal configurations with the same length and $30$ more maximal configurations with the same length and the same number of houses. The first several values of the integer sequence that counts the number of maximal configurations in the two-story Riviera model of length $n$ can be read as column sums: $1, 1, 3, 6, 7, 8, 11, 18, 30, 44, \dots$ and this sequence is still not a part of the On-Line Encyclopedia of Integer Sequences. On the other hand, by expanding $F(x, y)$ into the formal power series in powers of $x$, (i.e.\ taking row sums) we can see that, beside the mentioned maximal configuration with precisely $4$ two-story houses, there are $122$ more maximal configurations with the same number of houses. The first several values of the integer sequence that counts the number of maximal configurations in the two-story Riviera model with precisely $k$ houses can be read as row sums: $1, 19, 13, 123, 125, 811, 1069, 5435, 8605, 36939, \dots$. This sequence is also not yet included in the OEIS. By performing the same analysis as in the case of one-story houses, one can obtain the expected number of occupied lots in a maximal configuration of length $n$ as $\langle k_2(n) \rangle = 0.388957 \,\,n $, and the expected length of a maximal configuration with $k$ two-story houses as $\langle n_2(k)\rangle = 2.706054 \,\,k$. Since the largest possible number of buildings in a maximal configuration is, roughly, $n/2$, one can see that the expected efficiency $\varepsilon _2$ is lower than in the case of one-story buildings: $\varepsilon _2 = 0.777914$. However, by counting each house as two basic units (two flats), it follows that on a maximal configuration of the same length $n$ one can build, on average, $2 \cdot 0.388957 / 0.577203 = 1.34773$ times more basic units by opting for two-story houses. It is reassuring that our model, although very simple, captures the common wisdom of planners and builders. It would be interesting to investigate how this gain in efficiency is affected by further increase in the number of stories. \subsubsection{Mixed Riviera model} By the mixed Riviera model, we refer to the model where one-story houses and two-story houses can be built on the same $1 \times n$ tract of land. Notice that, even though we cannot add additional two-story house on any of the empty lots in the configuration $0202000022$, we could add one-story house without making the configuration impermissible. One possible position to add one-story house to this configuration is $i = 6$. If we set $c_6 = 1$ we get the configuration $0202010022$. This one-story house is not blocking the sun to any of the stories of already built houses, and the one-story house itself is exposed to sunlight. It is easy to check that this new configuration with one-story house is maximal since we cannot add additional stories to any of the empty lots nor to the lot where there is a one-story house. In this model, words that represent configurations have three letters ($0$, $1$ and $2$). However, the transfer matrix method and Algorithm \ref{alg:cap} can again be used to obtain the digraph through which we encode all the maximal configurations in this mixed Riviera model. Once we have the digraph, we have the adjacency matrix, but as before, we use this adjacency matrix for more than just counting the number of maximal configurations of fixed length. Depending on whether a transition from node $i$ to node $j$ results in addition of an empty lot, a lot on which one-story house is built or a lot on which two-story house is built, matrix function $A$ has $1$, $x$ or $y$ on the position $(i, j)$, respectively. Hence, $A$ is a function of two variables ($x$ and $y$) where $x$, rather than $x_1$, is a formal variable associated with the number of one-story houses in the configuration and $y$, rather than $x_2$, is a formal variable associated with the number of two-story houses in the configuration. Denoting the formal variable associated with the length of the configuration by $z$, rather than $y$, and using similar calculations as in Subsection \ref{subsec:gen_fun_for_Riviera} we obtain trivariate generating function. The precise shape of this generating function is again obtained by R and Maxima and it is given in Appendix (see \eqref{it:mixed_Riviera}). By expanding $F(x, y, z)$ into the formal power series in powers of $z$, we get {\small \begin{align} F & (x, y, z) = 1 \\ & + yz \\ & + y^2z^2 \\ & + 3y^2z^3 \\ & + (2x + 4)y^2z^4 \\ & + (2y^3 + (x^2 + 6x + 1)y^2)z^5 \\ & + (y^4 + 4y^3 + (7x^2 + 6x)y^2)z^6 \\ & + (5y^4 + (2x^2 + 2x + 3)y^3 + (2x^3 + 11x^2 + 2x)y^2)z^7 \\ & + ((4x + 13)y^4 + (10x^2 + 4x)y^3 + (x^4 + 8x^3 + 5x^2)y^2)z^8 \\ & + (3y^5 + (3x^2 + 18x + 15)y^4 + (4x^3 + 18x^2 + 2x)y^3 + (7x^4 + 8x^3 + x^2)y^2)z^9 \\ & + (y^6 + 12y^5 + (30x^2 + 34x + 8)y^4 + (4x^4 + 16x^3 + 10x^2)y^3 + (2x^5 + 11x^4 + 2x^3)y^2)z^{10} \\ & + \dots \end{align}}% Our example of a maximal configuration in the mixed Riviera model has length $10$, $1$ one-story house and $4$ two-story houses. From this expansion it is easy to read that there are $33$ more maximal configurations of length $10$ with $1$ one-story house and $4$ two-story houses. Notice that plugging $y = x$ in the trivariate generating function $F(x, y, z)$ gives bivariate generating function in variables $x$ and $z$ where formal variable $x$ is associated with the number of houses (regardless of the number of stories) and formal variable $z$ is still associated with the length of the maximal configuration. Similarly, setting $y = x^2$ we get bivariate generating function where formal variable $x$ is associated with the number of stories on maximal configurations. The most natural sequence related to this model is the one that counts the number of maximal configurations of length $n$. The first several values of this sequence are $1, 1, 3, 6, 10, 18, 27, 45, 79, 130, \dots$. This sequence is not found on the OEIS. \subsection{AND variant} As explained at the beginning of this section, the AND variant, unlike the OR variant, requires that each story of each house gets sunlight from the east and from the west, and in the one-story case this comes down to the classical Flory polymer model introduced by Flory \cite{Flory} already in 1939. The sequence $(a_n)$ that counts the number of maximal configurations of length $n$ in the one-story Flory model is the famous Padovan sequence (see \href{https://oeis.org/A000931}{A000931}) with offset $6$ or, equivalently, the number of compositions (ordered partitions) of number $n+3$ into parts $2$ and $3$ (i.e.\ \href{https://oeis.org/A182097}{A182097} with offset $3$). Moreover, if we are interested in the asymptotic formula for $a_n$, we can obtain it as explained in Remark \ref{rem:PF-Riviera}. It holds that $a_n \sim C\,\lambda^n$ as $n$ tends to infinity where $\lambda$ is the well-known plastic number $\lambda = \frac{1}{w} = 1.324718$. The numerical value of $C=\frac{\lambda^3+\lambda^2+\lambda}{2\lambda+3}=0.956611$ can, as before, determined using Theorem \ref{tm:asymp}. In the next two subsections we discuss variants of Flory model where we can have houses that have more than one story. \begin{remark} Note that there are more maximal configurations in the Riviera model than in the Flory model since the Perron-Frobenius eigenvalue in the Riviera model is bigger than the plastic number (which is the Perron-Frobenius eigenvalue in the Flory model). It is also interesting to compare these constants with $2$ since there are $2^n$ binary sequences of length $n$ when we do not impose any restrictions on those sequences. \end{remark} \subsubsection{Multi-story Flory models} Using the same technique as in the last two subsections, we could easily obtain generating functions related to the multi-story Flory models, but sequences that count the number of maximal configurations (in multi-story Flory models) with fixed length or with fixed number of houses are some well-known sequences. Therefore, we will just relate our sequences to those already known by establishing the appropriate bijections. The simplest way to explain the connection of the sequences that arise from the multi-story Flory models and some already known sequences is by using an example. Let us consider the two-story Flory model. In this model, all the houses have precisely two stories and each story of each house needs to get sunlight from both east and west (we assume that there is no obstruction to sunlight on the east and west boundary of the tract of land). This implies that each house needs to have at least two empty lots immediately to the east and immediately to the west of it (except those houses that are near the boundary). Let us have a look at all the maximal configurations of length $6$. Those are $200200, 200020, 020020, 200002, 020002$ and $002002$. Clearly, between each two houses we can have $2, 3$ or $4$ empty lots. Less than $2$ empty lots would mean that those houses are not getting the sunlight from both east and west (hence, the permissibility would be violated) and more than $4$ empty lots would mean that we can add additional house between those two houses without violating permissibility (hence, the maximality would be violated). This implies that if we take a block of lots that includes all the empty lots to the west of the house and the house itself, this block can have length $3, 4$ or $5$. This is true for all the houses except maybe the first one since this one can get the sunlight from outside of the tract of land. For the first house this block including all the empty lots to the west of it and the first house itself can be of size $1$, $2$ or $3$. For that reason, we artificially add $2$ empty lots in front of our maximal configurations. Also, if the configuration doesn't end with a house, empty lots at the end of the configuration will not be a part of any block. To solve this problem, we artificially add $002$ at the end of each maximal configuration since in this way we will create a block at the end that has length $3$, $4$ or $5$. After adding these $5$ additional lots, we ended up with strings of length $11$. Each of these strings is different and they can be divided into blocks that contain one house and all the empty lots preceding that house. As explained, these blocks will be of length $3$, $4$ and $5$ and hence will give as a representation of number $11$ as a sum of numbers $3$, $4$ and $5$. In our example we have \begin{align} 200200 & \to \textcolor{red}{00}\|200200\|\textcolor{red}{002} \to \underbrace{002}_3\underbrace{002}_3\underbrace{00002}_5 \\ 200020 & \to \textcolor{red}{00}\|200020\|\textcolor{red}{002} \to \underbrace{002}_3\underbrace{0002}_4\underbrace{0002}_4 \\ 020020 & \to \textcolor{red}{00}\|020020\|\textcolor{red}{002} \to \underbrace{0002}_4\underbrace{002}_3\underbrace{0002}_4 \\ 200002 & \to \textcolor{red}{00}\|200002\|\textcolor{red}{002} \to \underbrace{002}_3\underbrace{00002}_5\underbrace{002}_3 \\ 020002 & \to \textcolor{red}{00}\|020002\|\textcolor{red}{002} \to \underbrace{0002}_4\underbrace{0002}_4\underbrace{002}_3 \\ 002002 & \to \textcolor{red}{00}\|002002\|\textcolor{red}{002} \to \underbrace{00002}_5\underbrace{002}_3\underbrace{002}_3 \end{align} It is also trivial to go in the other direction. If we are given one possible ordered partition of number $11$ into parts $3$, $4$ and $5$, we can just concatenate the blocks whose lengths will correspond to those parts and in the end we just remove the first two and the last three lots. For example \begin{equation} 11 = 3 + 5 + 3 \to \underbrace{002}_{3}\underbrace{00002}_{5}\underbrace{002}_{3} \to \textcolor{red}{00}\|200002\|\textcolor{red}{002} \to 200002. \end{equation} It is clear from here that there is a bijection between maximal configurations of the two-story Flory model of length $n$ and compositions (ordered partitions) of number $n + 5$ into parts $3$, $4$ and $5$. The sequence that counts the number of ordered partitions of $n$ into parts $3$, $4$ and $5$ can be found on the OEIS under name \href{https://oeis.org/A017818}{A017818}. Of course, there is nothing special about the two-story Flory model and the same reasoning can be applied to any multi-story Flory model. If we consider $k$-story Flory model, then we get maximal configurations with at least $k$ empty lots and at most $2k$ empty lots between each two occupied lots. Adding $k$ empty lots in front of each maximal configuration and $k$ empty lots and one occupied lot at the end of each configuration we get a string of length $n + 2k + 1$. Splitting this string into blocks containing an occupied lot and all the empty lots to the west of it, we get decomposition of the number $n + 2k + 1$ into parts $k + 1, k + 2, \ldots, 2k + 1$. On the other hand, if we start from a composition of the number $n + 2k + 1$ into parts $k + 1, k + 2, \ldots, 2k + 1$, we can trivially reconstruct the corresponding maximal configuration. Hence, we have the following proposition. \begin{proposition} The number of maximal configurations with fixed length $n \in \mathbb{N}$ in the $k$-story Flory model ($k \in \mathbb{N}$) is equal to the number of compositions (ordered partitions) of number $n + 2k + 1$ into parts $k + 1, k + 2, \ldots, 2k + 1$. \end{proposition} For $k \in \{3, \ldots, 9\}$ those sequences can be found on the OEIS under the following names \begin{itemize} \item $k = 3$ -- compositions of $n$ into parts $p$ where $4 \le p \le 7$ -- \href{https://oeis.org/A017829}{A017829}, \item $k = 4$ -- compositions of $n$ into parts $p$ where $5 \le p \le 9$ -- \href{https://oeis.org/A017840}{A017840}, \item $k = 5$ -- compositions of $n$ into parts $p$ where $6 \le p \le 11$ -- \href{https://oeis.org/A017851}{A017851}, \item $k = 6$ -- compositions of $n$ into parts $p$ where $7 \le p \le 13$ -- \href{https://oeis.org/A017862}{A017862}, \item $k = 7$ -- compositions of $n$ into parts $p$ where $8 \le p \le 15$ -- \href{https://oeis.org/A017873}{A017873}, \item $k = 8$ -- compositions of $n$ into parts $p$ where $9 \le p \le 17$ -- \href{https://oeis.org/A017884}{A017884}, \item $k = 9$ -- compositions of $n$ into parts $p$ where $10 \le p \le 19$ -- \href{https://oeis.org/A017895}{A017895}. \end{itemize} Since maximal configurations of length $n = 1$ are in bijection with the ordered partitions of the number $2k + 2$, we have to look at all the above sequences with the offset of $2k + 1$. Note that it is straightforward to obtain the recurrence relation for these sequences (and from that recurrence relation also the generating function) regardless of the value of $k$. Hence, even though the sequences for $k \ge 10$ do not appear on the OEIS, we can easily calculate their elements. Let us explain how to get the recurrence relation and the generating function in the case $k = 3$ and then formulate the general result. Denote by $a_n$ the number of compositions of $n$ into parts $4, 5, 6$ and $7$. Clearly, $a_0=1$ since there is one way to get $0$ from parts $4, 5, 6$ and $7$, we do not take any of the parts. For integers smaller than the smallest available part there are zero compositions, hence $a_1 = a_2 = a_3 = 0$. Since available parts are integers between $k + 1$ and $2k + 1$, they can be composed in only one way, therefore $a_4 = a_5 = a_6 = a_7 = 1$. For any $n \ge 8$ the logic is that we can first compose $n - 4$ from available parts and then just add $4$ and similar for other available parts. Hence, we have the following recurrence relation \begin{equation} a_n = a_{n - 4} + a_{n - 5} + a_{n - 6} + a_{n - 7}. \end{equation} From this recurrence relation, we clearly have that the generating function of the sequence $a_n$ is given with \begin{equation} F(x) = \frac{1}{1 - x^4 - x^5 - x^6 - x^7}. \end{equation} It is clear now that we can follow the same logic in the general case with $k$-story houses. \begin{proposition} Fix $k \in \mathbb{N}$. Let $(a_n)_{n \ge 0}$ be the integer sequence where \begin{equation} a_n = \textnormal{the number of compositions of $n$ into parts $k + 1, k + 2, \ldots, 2k + 1$}. \end{equation} Then for every $n \ge 2k + 2$ the sequence $(a_n)_{n \ge 0}$ satisfies the recurrence relation \begin{equation} a_n = \sum_{i = k + 1}^{2k + 1} a_{n - i}, \end{equation} with initial conditions \begin{align} a_0 & = 1, \\ a_i & = 0, \quad 1 \le i \le k \\ a_i & = 1, \quad k + 1 \le i \le 2k+1. \end{align} Furthermore, the generating function $F(x)$ of the sequence $(a_n)_{n \ge 0}$ is given with \begin{equation} F(x) = \frac{1}{1 - \sum_{i = k + 1}^{2k + 1} x^i}. \end{equation} \end{proposition} The situation with maximal configurations with fixed number of houses in the $k$-story Flory model is even simpler. Let us again describe what happens in the case $k = 2$ and then formulate the general result. To find all the maximal configurations with exactly $3$ houses, we start with the maximal configuration $2002002$ which has $3$ houses. Now we can obtain all the maximal configurations with exactly $3$ houses from this one in the following way: for each house, we choose whether we want to put $0$, $1$ or $2$ additional empty lots to the west of it and for the last house, we also choose whether we want to put $0$, $1$ or $2$ additional empty lots to the east of it. Since we have $3$ houses, we need to make $4$ decisions and we have $3$ options in each of those $4$ decisions. Hence, to each ordered quadruple of elements $0$, $1$ and $2$, we can assign a unique maximal configuration with precisely $3$ houses. For example \begin{align} (1, 2, 2, 1) & \to \textcolor{red}{0}\|200\|\textcolor{red}{00}\|200\|\textcolor{red}{00}\|2\|\textcolor{red}{0}, \\ (0, 1, 2, 1) & \to 200\|\textcolor{red}{0}\|200\|\textcolor{red}{00}\|2\|\textcolor{red}{0}, \\ (1, 1, 2, 0) & \to \textcolor{red}{0}\|200\|\textcolor{red}{0}\|200\|\textcolor{red}{00}\|2, \\ (0, 0, 0, 0) & \to 2002002. \end{align} Since we start with $2$ empty lots between each two houses, by adding $0$, $1$ or $2$ more empty lots, we end up with $2$, $3$ or $4$ empty lots between each two houses which still guarantees maximality and we obviously cannot violate permissibility with adding empty lots. Also, since we started from a configuration that has houses on the easternmost and on the westernmost lots, adding $0$, $1$ or $2$ additional empty lots before the first house or after the last house, will not violate maximality. On the other hand, if we are given a maximal configuration in the two-story Flory model with precisely $3$ houses, we can easily obtain the corresponding ordered quadruple of elements $0$, $1$ and $2$. Each maximal configuration has to have $0$, $1$ or $2$ empty lots before the first house and after the last one and it has to have at least $2$ and at most $4$ empty lots between each two houses. First element of the ordered quadruple corresponds to the number of empty lots in front of the first house. Counting the number of empty lots between each two houses and subtracting $2$ gives as all the other elements of our ordered quadruple, except for the last one. The last one corresponds to the number of empty lots after the last house. For example \begin{equation} 02000200200 \to \underbrace{0}_{1}2\underbrace{000}_{3}2\underbrace{00}_{2}2\underbrace{00}_{2} \to (1, 3-2, 2-2, 2) = (1, 1, 0, 2). \end{equation} Hence, the total number of maximal configurations with precisely $3$ houses in the two-story Flory model is $3^4$. Again, there is nothing special about the two-story Flory model and the same logic can be applied to any $k$-story Flory model. If we want to count the number of maximal configurations with precisely $n$ houses in the $k$-story Flory model, we start with the configuration \begin{equation} \overbrace{k\underbrace{00\ldots00}_{k\textnormal{ zeros}}k\underbrace{00\ldots00}_{k\textnormal{ zeros}}k0\ldots0k}^{n \textnormal{ houses}} \end{equation} and then we choose ordered $(n+1)$-tuple of elements $0, 1, \ldots, k$. Denote this $(n+1)$-tuple with $(k_0, k_1, \ldots, k_n)$. To this $(n+1)$-tuple we assign the maximal configuration \begin{equation} \overbrace{\underbrace{00\ldots00}_{k_0 \textnormal{ zeros}}k\underbrace{00\ldots00}_{k\textnormal{ zeros}}\underbrace{00\ldots00}_{k_1 \textnormal{ zeros}}k\underbrace{00\ldots00}_{k\textnormal{ zeros}}\underbrace{00\ldots00}_{k_2 \textnormal{ zeros}}k0\ldots0\underbrace{00\ldots00}_{k_{n - 1} \textnormal{ zeros}}k\underbrace{00\ldots00}_{k_n \textnormal{ zeros}}}^{n \textnormal{ houses}} \end{equation} In this way we obtain a configuration where in front of the first house and after the last house we have at most $k$ empty lots, and between each two houses we have between $k$ and $2k$ empty lots. Such configurations are obviously maximal. On the other hand, if we start from a maximal configuration with precisely $n$ houses, we can trivially reconstruct the corresponding $(n+1)$-tuple of elements $0, 1, \ldots, k$. \begin{proposition} The number of maximal configurations with fixed number of houses $n \in \mathbb{N}$ in the $k$-story Flory model ($k \in \mathbb{N}$) is equal to the the number of ordered $(n+1)$-tuples of elements $0, 1, \ldots, k$ which is equal to $(k + 1)^{n + 1}$. \end{proposition} \subsubsection{Mixed Flory model} Just as in the case of the mixed Riviera model, mixed Flory model refers to the model where one-story and two-story houses can be built on the same $1 \times n$ tract of land. For this model we again obtain trivariate generating function $F(x, y, z)$, where $x$ is a formal variable associated with the number of one-story houses in the configuration, $y$ is a formal variable associated with the number of two-story houses in the configuration and $z$ is a formal variable associated with the length of the configuration. The explicit form of this trivariate generating function was obtained using R and Maxima and it is given in Appendix (see \eqref{it:mixed_flory}). By expanding $F(x ,y ,z)$ into formal power series in powers of $z$, we get \begin{align} F(x, y, z) & = 1 \\ & + yz \\ & + 2yz^2 \\ & + (3y + x^2)z^3 \\ & + (y^2 + 2y + 2x^2)z^4 \\ & + (3y^2 + y + x^3 + x^2)z^5 \\ & + (6y^2 + 2x^2y + 2x^3)z^6 \\ & + (y^3 + 7y^2 + 6x^2y + x^4 + x^3)z^7 \\ & + (4y^3 + 6y^2 + (2x^3 + 8x^2)y + 3x^4)z^8 \\ & + (10y^3 + (3x^2 + 3)y^2 + (6x^3 + 6x^2)y + x^5 + 3x^4)z^9 \\ & + (y^4 + 16y^3 + (12x^2 + 1)y^2 + (2x^4 + 8x^3 + 2x^2)y + 4x^5 + x^4)z^{10} + \dots \end{align} The first several elements of the sequence that counts the number of different maximal configurations of length $n$ are $1, 2, 4, 5, 6, 10, 16, 23, 32, 47, \dots$ This sequence does not appear on the OEIS. \section{One-story model on an \texorpdfstring{$m\times n$}{mxn} grid for \texorpdfstring{$m=2,3$}{m=2,3} and \texorpdfstring{$n\in\mathbb{N}$}{n∈N}}\label{sec:mxnForSmallm} In this section we come back to the original settlement model introduced in \cite{PSZ-21} in which we have a rectangular $m \times n$ tract of land where $m > 1$ and the sun can come from the east, south and west. The question that we were interested in is what is the total number of all maximal configurations for all grid sizes $m \times n$. This is exactly the question posed in \cite[Question 2.2]{PSZ-21-2}. We give a partial answer to this question when the considered tract of land is narrow. As already announced in the introduction, we were unable to obtain a closed-form formula for all grid sizes, but for grids of size $2\times n$ and $3\times n$ we derive the (bivariate) generating functions counting the number of maximal configurations. The method we use is again the transfer matrix method which could be similarly adopted for bigger $m$'s, but the calculations soon get increasingly infeasible. In this section we only consider one-story houses and we do not look at the Flory's version of the problem where each house would need to get sunlight from east, south and west. Of course, those models could be studied with the same method. Recall that every configuration on an $m \times n$ tract of land can be encoded as a $m \times n$ matrix $C$, where $c_{i,j} = 1$ if the lot $(i, j)$ is occupied and $c_{i,j} = 0$ otherwise. We now treat all the possible different columns of such matrices as letters in our alphabet. Notice that those are just binary numbers of length $m$ written as column vectors. Once we interpret each column of such a matrix as a letter, every configuration can be viewed as a word of length $n$. As already explained in the introduction, the transfer matrix method can be applied if the properties of permissibility and maximality of a configuration can be verified by inspecting only finite size patches of a given configuration. Luckily, in our model, the properties of maximality and permissibility are locally verifiable, i.e.\ if one wants to check whether a state of a certain lot (occupied or unoccupied) has caused the configuration to be impermissible or not maximal, one only needs to check the situation on the lots in a finite radius of the observed lot. These verifications whether some configuration is permissible and maximal are done directly on the matrix $C$, but as soon as we find a forbidden pattern, we forbid the corresponding word. More precisely, to verify that a configuration is permissible, one needs to check that no occupied lot $(i, j)$ borders simultaneously with tree other occupied lots to its east, south and west. This can be done by inspecting whether the forbidden pattern shown in Figure \ref{fig:forbidden_pattern} appears anywhere in the matrix $C$. \begin{figure} \begin{tikzpicture}[scale = 0.8] \filldraw [fill=white, draw=black] (0,0) rectangle (1,1); \filldraw [fill=white, draw=black] (1,0) rectangle (2,1); \filldraw [fill=white, draw=black] (2,0) rectangle (3,1); \filldraw [fill=white, draw=black] (1,-1) rectangle (2,0); \node[] at (0.5,0.5) {$1$}; \node[] at (1.5,0.5) {$1$}; \node[] at (2.5,0.5) {$1$}; \node[] at (1.5,-0.5) {$1$}; \end{tikzpicture} \caption{The forbidden pattern.}\label{fig:forbidden_pattern} \end{figure} To verify that a configuration is maximal, one needs to additionally check that no unoccupied lots can be built on. Since it holds that \begin{equation} c_{i, j} =0 \Longrightarrow \begin{array}{cc} (c_{i, j - 2} = 1 \mbox{ and } c_{i, j - 1} = 1 \mbox{ and } c_{i + 1, j - 1} = 1) \mbox{ or } \\ (c_{i, j + 1} = 1 \mbox{ and } c_{i, j + 2} = 1 \mbox{ and } c_{i + 1, j + 1} = 1) \mbox{ or } \\ (c_{i - 1, j - 1} = 1 \mbox{ and } c_{i - 1, j} = 1 \mbox{ and } c_{i - 1, j + 1} = 1) \mbox{ or } \\ (c_{i, j - 1} = 1 \mbox{ and } c_{i, j + 1} = 1 \mbox{ and } c_{i + 1, j} = 1), \end{array} \end{equation} this can be done by inspecting all the lots surrounding the lot $(i, j)$ that appear in the above expression. Those are precisely the shaded lots in Figure \ref{fig:maximality_check}. \begin{figure} \begin{tikzpicture}[scale = 0.8] \filldraw [fill=blue!40!white, draw=black] (0,0) rectangle (1,1); \filldraw [fill=blue!40!white, draw=black] (1,0) rectangle (2,1); \filldraw [fill=white, draw=black] (2,0) rectangle (3,1); \filldraw [fill=blue!40!white, draw=black] (3,0) rectangle (4,1); \filldraw [fill=blue!40!white, draw=black] (4,0) rectangle (5,1); \filldraw [fill=blue!40!white, draw=black] (1,-1) rectangle (2,0); \filldraw [fill=blue!40!white, draw=black] (2,-1) rectangle (3,0); \filldraw [fill=blue!40!white, draw=black] (3,-1) rectangle (4,0); \filldraw [fill=blue!40!white, draw=black] (1,1) rectangle (2,2); \filldraw [fill=blue!40!white, draw=black] (2,1) rectangle (3,2); \filldraw [fill=blue!40!white, draw=black] (3,1) rectangle (4,2); \node[] at (2.5,0.5) {\small $i, j$}; \end{tikzpicture} \caption{Lots that need to be checked to verify maximality of a configuration.}\label{fig:maximality_check} \end{figure} Therefore, the transfer matrix method can be applied in a completely analogous way as before, but as the number of rows grows, the alphabet becomes bigger so we only consider the cases $m = 2$ and $m = 3$. \subsection{\texorpdfstring{$2 \times n$}{2xn}} In this subsection, we derive the bivariate generating function from which we can extract the sequence that counts the total number of different maximal configurations of fixed length $n$ (and width $2$) and the sequence that counts the total number of different maximal configurations with precisely $k$ houses on all the $2 \times n$ grids ($n \in \mathbb{N}$). One example of a maximal configuration on a $2 \times 6$ tract of land is \begin{equation} \begin{bmatrix} 1 & 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 0 & 1 \end{bmatrix}. \end{equation} Since we can apply the transfer matrix method, we can again use Algorithm \ref{alg:cap} to construct the digraph with which we can encode all the maximal configurations. Once we have the digraph, we can define the matrix function $A(x)$. This matrix is obtained from the adjacency matrix of the corresponding digraph, but instead of putting $1$ on the position $(i, j)$ when the transition from node $i$ to node $j$ is possible, we put $x$ if the transition from node $i$ to node $j$ adds one house to the configuration and we put $x^2$ if the transition from node $i$ to node $j$ adds two houses to the configuration (notice that it is impossible that the transition from node $i$ to node $j$ adds zero houses to the configuration because the word $(0, 0)^T$ never appears since it would cause that the resulting configuration is not maximal). As before, the bivariate generating function is obtained using R and Maxima and the precise shape can be found in the Appendix (see \eqref{it:2xn}). The first few coefficients in the expansion of $F(x, y)$ are given in Table \ref{tab:gf3}. By inspecting the non-zero coefficients in the table, we see that the ratio $\frac{k}{n}$ is in-between $1$ and $\frac{5}{3}$, for large $n$. \begin{table}[!h] \caption{The first few coefficients in the expansion of the bivariate generating function $F(x,y)$.}\label{tab:gf3} \small \begin{tabular}{c\|cccccccccccccccccc} $n\backslash k$ & $1$ & $x$ & $x^2$ & $x^3$ & $x^4$ & $x^5$ & $x^6$ & $x^7$ & $x^8$ & $x^9$ & $x^{10}$ & $x^{11}$ & $x^{12}$ & $x^{13}$ & $x^{14}$ & $x^{15}$ & $x^{16}$ & $x^{17}$\\\hline $1$ & $1$ & & & & & & & & & & & & & & & & & \\ $y$ & & & $1$ & & & & & & & & & & & & & & & \\ $y^2$ & & & & & $1$ & & & & & & & & & & & & & \\ $y^3$ & & & & & & $4$ & & & & & & & & & & & & \\ $y^4$ & & & & & & & $4$ & $2$ & & & & & & & & & & \\ $y^5$ & & & & & & & & $4$ & $5$ & $1$ & & & & & & & & \\ $y^6$ & & & & & & & & & $4$ & $4$ & $8$ & & & & & & & \\ $y^7$ & & & & & & & & & & $4$ & $4$ & $18$ & $3$ & & & & & \\ $y^8$ & & & & & & & & & & & $4$ & $4$ & $25$ & $16$ & $1$ & & & \\ $y^9$ & & & & & & & & & & & & $4$ & $4$ & $33$ & $31$ & $13$ & & \\ $y^{10}$ & & & & & & & & & & & & & $4$ & $4$ & $41$ & $42$ & $50$ & $4$ \\ \end{tabular} \end{table} Notice that there are $16$ maximal configurations on $2 \times 6$ tract of land and $8$ of those have $10$ houses. This means that in addition to our example, there are $15$ more maximal configurations on $2 \times 6$ tract of land and $7$ more on that tract of land that have precisely $10$ houses. The first several elements of the integer sequence that counts the number of maximal configurations of fixed length $n$ (and width $2$) can be read as row sums: $1, 1, 4, 6, 10, 16, 29, 50, 85, 145, \dots$ and this sequence is still not included in the OEIS. On the other hand, by expanding $F(x, y)$ into the formal power series in powers of $x$ (i.e.\ taking column sums), we can see that, beside the mentioned maximal configuration with precisely $10$ houses, there are $15$ more maximal configurations with the same number of houses. The first several elements of the integer sequence that counts the number of maximal configurations with precisely $k$ houses on all the $2 \times n$ grids ($n \in \mathbb{N}$) can be read as column sums: $0, 1, 0, 1, 4, 4, 6, 9, 9, 16, \dots$ This sequence is not found on the OEIS. Here again we compute the expected number of occupied lots in a maximal $2 \times n$ configuration and the expected length $n$ of a maximal $2 \times n$ configuration with $k$ houses. The obtained values are $$\langle k_{2,n}(n) \rangle = 1.437496 \,\,n \quad {\rm and} \quad \langle n_{2,n}(k) \rangle = 0.724696 \,\,k.$$ \subsection{\texorpdfstring{$3 \times n$}{3xn}} In this subsection, we derive the bivariate generating function from which we can extract the sequence that counts the total number of different maximal configurations of fixed length $n$ (and width $3$) and the sequence that counts the total number of different maximal configurations with precisely $k$ houses on all the $3 \times n$ grids ($n \in \mathbb{N}$). One example of a maximal configuration on a $3 \times 5$ tract of land is \begin{equation} \begin{bmatrix} 0 & 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 & 1 \end{bmatrix}. \end{equation} Similarly as in the case $2\times n$ we obtain the bivariate generating function (see \eqref{it:3xn}). The first few coefficients in the expansion of $F(x, y)$ are given in Table \ref{tab:gf4}. By inspecting the non-zero coefficients in the table, we see that the ratio $\frac{k}{n}$ is in-between $\frac{3}{2}$ and $\frac{7}{3}$, for large $n$. \begin{table}[!h] \caption{The first few coefficients in the expansion of the bivariate generating function $F(x,y)$.}\label{tab:gf4} \small \begin{tabular}{c\|cccccccccccccccccc} $n\backslash k$ & $1$ & $x$ & $x^2$ & $x^3$ & $x^4$ & $x^5$ & $x^6$ & $x^7$ & $x^8$ & $x^9$ & $x^{10}$ & $x^{11}$ & $x^{12}$ & $x^{13}$ & $x^{14}$ & $x^{15}$ & $x^{16}$ & $x^{17}$\\\hline $1$ & $1$ & & & & & & & & & & & & & & & & & \\ $y$ & & & & $1$ & & & & & & & & & & & & & & \\ $y^2$ & & & & & & & $1$ & & & & & & & & & & & \\ $y^3$ & & & & & & & & $9$ & $1$ & & & & & & & & & \\ $y^4$ & & & & & & & & & $4$ & $8$ & $7$ & & & & & & & \\ $y^5$ & & & & & & & & & & & $12$ & $8$ & $20$ & $1$ & & & & \\ $y^6$ & & & & & & & & & & & & & $24$ & $12$ & $65$ & $4$ & & \\ $y^7$ & & & & & & & & & & & & & & $24$ & $12$ & $84$ & $122$& $27$ \\ $y^8$ & & & & & & & & & & & & & & & $4$ & $40$ & $40$ &$228$ \\ $y^9$ & & & & & & & & & & & & & & & & & $24$ & $44$ \\ \end{tabular} \end{table} Notice that there are $41$ maximal configurations on $3 \times 5$ tract of land and $12$ of those have $10$ houses. This means that in addition to our example, there are $40$ more maximal configurations on $3 \times 5$ tract of land and $11$ more on that tract of land that have precisely $10$ houses. The first several elements of the integer sequence that counts the number of maximal configurations of fixed length $n$ (and width $3$) can be read as row sums: $1, 1, 10, 19, 41, 105, 269, 651, 1560, 3861, \dots$ and this sequence is still not included in the OEIS. On the other hand, by expanding $F(x, y)$ into the formal power series in powers of $x$ (i.e.\ taking column sums), we can see that beside the mentioned maximal configuration with precisely $10$ houses, there are $18$ more maximal configurations with the same number of houses. The first several elements of the integer sequence that counts the number of maximal configurations with precisely $k$ houses on all the $3 \times n$ grids ($n \in \mathbb{N}$) can be read as column sums: $0, 0, 1, 0, 0, 1, 9, 5, 8, 19$. This sequence cannot be found on the OEIS. In this case, the expected number of occupied lots in a maximal $3 \times n$ configuration and the expected length $n$ of a maximal $3 \times n$ configuration with $k$ houses are given as $$\langle k_{3,n}(n) \rangle = 2.071886 \,\,n \quad {\rm and} \quad \langle n_{3,n}(k) \rangle = 0.503345 \,\,k.$$ Since the largest possible number of occupied lots is, roughly, of the order $5n/3$ in the $2 \times n$ strip and $7n/3$ in the $3 \times n$ strip for large $n$, the respective efficiencies are given by $$ \varepsilon _{2 \times n} = 0.862498 \quad {\rm and } \quad \varepsilon _{3 \times n} = 0.887951.$$ One can see that the efficiency of $2 \times n$ strip is lower than for the Riviera model. This low value is easily explained by the effects of the fully built lower row. As expected, its effects decrease with the increasing strip width. \section{Concluding remarks}\label{sec:concluding} In this paper we have considered a one-dimensional toy-model of a settlement planning problem introduced recently by three of the present authors. In particular, we studied maximal configurations of buildings in a narrow strip of land oriented east--west subject to the condition that each building must receive sunlight from either east or west or from both sides. We have formulated the problem of enumerating such maximal configurations as a problem of counting binary words of a given length satisfying certain additional conditions on the allowed patterns. By reducing the new problem to counting certain types of walks on a small directed graph with only six vertices we were able to employ the transfer matrix method which yielded generating functions for the enumerating sequences, and hence also their asymptotics. Along the way we discovered that our maximal configurations are equinumerous with certain type of restricted permutations and provided a combinatorial proof of this fact by explicitly constructing a bijection between two sets. We have also considered some generalizations of the original problem, such as allowing the buildings to have more than one floor and varying the type of restrictions on the sunlight direction. The methods developed on the toy model were successfully adapted to the more complex settings and allowed us to obtain multivariate generating functions for the corresponding enumerating sequences. We have also obtained generating functions for the sequences enumerating maximal configurations on strips of width 2 and 3, in most cases obtaining sequences not (yet) in the OEIS. There are other ways, not explored here, to formulate the original problem and hence to extend our results. For example, one could consider our problem ``in negative'' and consider unoccupied places instead of occupied ones. In that case, the unoccupied places in a maximal configuration must form a dominating set. For our Riviera model, the maximality condition implies that such a dominating set would induce a graph of maximum degree one, hence a dissociation. (Dissociations interpolate between matchings and independent sets; see \cite{Bock1,Bock2} for definition and some basic properties.) We are not aware of any results on such dominating sets. However, closely related (and less general) independent dominating sets are being intensely studied, along with other types of domination in graphs. Our problem could be also formulated and studied on other types of lattices. Some of them, say the hexagonal one, could be better suited to modeling real planning applications. On the other hand, the triangular lattice might prove more tractable and might lead to closed-form results for the considered quantities. Another problem, closely related to the present one, is to study temporal evolution of built configurations subject to given rules. It is known that the jamming density of the static and dynamic variant of the Flory model is not the same; in the static cases, all configurations are considered to be equally likely, while in the dynamic case some of them are less likely to evolve than some others. It would be interesting to explore how additional restrictions (with respect to the Flory model) affect the difference. Finally, it would be interesting to model the evolution of configurations in terms of antagonistic games. It seems plausible that the interest of a developer is not aligned with the interests of inhabitants -- one would prefer more buildings, hence more profit, while the others might prefer more sunshine, hence less profit for the former. Some toy-model simulations of several variants on dynamics are currently under way. \section*{Acknowledgments} \noindent We want to express our deep gratitude to Pavel Krapivsky from Boston University for contacting us and starting an extremely interesting and fruitful communication that is still ongoing and through which we learned so much from him as an expert in the field. He was the one who inspired us to write this particular paper and to consider many more interesting questions that we are still working on. Partial support of the Slovenian ARRS (Grant no. J1-3002) is gratefully acknowledged by T. Do\v{s}li\'c. \bibliographystyle{bababbrv-fl}	{ "redpajama_set_name": "RedPajamaArXiv" }	5,963
\section{Introduction} \label{section:Introduction} Radio pulsars are unique objects in astronomy: they are neutron stars (NSs) that emit a regular train of radio pulses whose times of arrival at the telescope (TOAs) can be measured with great precision \citep{Lorimer&Kramer2005}. This allows the determination of extremely precise spin periods (sometimes better than a few femtoseconds), the rate of variation of this spin period, and astrometric parameters such as positions and proper motions that are precise to microarcseconds, similar to the precision obtained from very large baseline interferometry (VLBI). In the case of pulsars in binary systems, pulsar timing allows exquisitely precise measurements of their orbital motion, which can be used for precise measurements of the components of the binary \citep{2016ARA&A..54..401O} and tests of gravity theories \citep{Wex2014,2021PhRvX..11d1050K}. The MeerKAT 64-dish array \citep{2009IEEEP..97.1522J} now provides excellent sensitivity (and thus timing precision) for Southern radio pulsars. Precision pulsar timing is carried out under the MeerTime large science project (LSP; \citealt{BailesEtAl2020}); the first results are extremely promising and show a performance that is significantly better than expected. Within the MeerTime LSP, there is a program targeting relativistic binary pulsars, henceforth ``RelBin". The objective of this program is to use the excellent timing precision provided by the MeerKAT to improve the measurement or detection of new relativistic effects in the orbital motion of known binary pulsars, with the aim of a) increasing the number of neutron stars (NS) with precise mass measurements and b) increasing the number, nature and precision of pulsar tests of gravity theories (for details, see \citealt{ksv+21}). One of the early additions to the RelBin program was PSR~J0955$-$6150, a binary millisecond pulsar with a low-mass companion and a 24.6-d orbit with an unusual eccentricity ($e = 0.11$) that was discovered with the CSIRO Parkes 64-m radio-telescope (recently given the indigenous Wiradjuri name ``Murriyang'') in a survey of unassociated {\em Fermi} sources \citep{CamiloEtAl2015}. In that paper, no phase-coherent timing solution was presented for this pulsar, owing to its extreme faintness, only an orbital solution derived from the observed variation of the spin period (the ``Doppler'' method). We were able to derive a phase-connected timing solution for this pulsar based on its Parkes long term timing data. Still, even at that stage, with orbital parameters thousands of times more precise than those derived from the Doppler method, we could only detect one relativistic effect in the orbit (the advance of periastron, which proceeds at a rate known as $\dot{\omega}$), and that with low significance. Because of the limited timing precision, no other relativistic effects on the timing of the pulses could be detected. This unpublished timing solution was the basis for the timing solution presented in this work. \begin{table}[h] \caption[]{ \label{table:eccentric_MSPs} Parameters for the eccentric MSPs known in the Galactic disk. Note the similarity of the parameters for the first {\bf five} pulsars, and how they differ significantly from PSR~J1903+0327. The first five systems and PSR~J1146$-$6610 all have mass functions, spin periods and period derivatives typical of MSPs with He~WD companions. The 8th column states the He~WD mass interval expected from the $P_{\rm b}-M_{\rm WD}$ correlation of \cite{1999A&A...350..928T}. For PSR~J1903+0327, the mass uncertainties refer to a 99.7\,\% confidence limit; the companion of that pulsar is a main-sequence star. For the other systems, the companions are presumably He~WDs; this has been confirmed in the case of PSR~J2234+0611 by \cite{2016ApJ...830...36A}.} \centering \begin{tabular}{c r l l l l l l c} \hline \hline PSR & $P$ (ms) & $P_{\rm b}$ (d) & $e$ & $M_{\rm T}$ ($M_{\odot}$) & $M_{\rm p}$ ($M_{\odot}$) & $M_{\rm c}$ ($M_{\odot}$) & $M_{\rm theo}$ ($M_{\odot}$) & References \\ \hline J0955$-$6150 & 1.9993 & 24.5784 & 0.1175 & 1.96(3) & 1.71(2) & 0.254(2) & 0.271--0.300& 1, 2 \\ J1618$-$3921 & 11.9873 & 22.7456 & 0.0274 & - & - & - & 0.269--0.297& 3, 4 \\ J1946+3417 & 3.1701 & 27.0199 & 0.1345 & 2.094(22) & 1.827(13) & 0.2654(13) & 0.275--0.303& 5, 6 \\ J1950+2414 & 4.3048 & 22.1914 & 0.0798 & 1.779(25) & 1.496(23) & $0.2795^{+0.0046}_{-0.0038}$ & 0.268--0.296& 7, 8 \\ J2234+0611 & 3.5766 & 32.0014 & 0.1293 & $1.6518^{+0.0033}_{-0.0035}$ & $1.353^{+0.014}_{-0.017}$ & $0.298^{+0.015}_{-0.012}$ & 0.281--0.310& 9, 10 \\ \hline J1146$-$6610 & 3.7223 & 62.7712 & 0.0074 & - & - & - & 0.307--0.339 & 11 \\ \hline J1903+0327 & 2.1499 & 95.1741 & 0.4367 & 2.697(29) & 1.667(21) & 1.029(8) & --- & 12, 13 \\ \hline \end{tabular} \tablebib{(1)~\cite{CamiloEtAl2015}; (2)~this work; (3)~\cite{2018AA...612A..78O}; (4)~\cite{2001ApJ...553..801E}; (5)~\cite{2013MNRAS.435.2234B}; (6)~\cite{2017MNRAS.465.1711B}; (7)~\cite{2015ApJ...806..140K}; (8)~\cite{2019ApJ...881..165Z}; (9)~\cite{2013ApJ...775...51D}; (10)~\cite{2019ApJ...870...74S}; (11)~\cite{2021MNRAS.507.5303L}; (12)~\cite{2008Sci...320.1309C}; (13)~\cite{2011MNRAS.412.2763F} } \end{table} This pulsar was added to the RelBin program because of the prospect of a high-precision mass measurement. Indeed, for three systems similar to PSR~J0955$-$6150 \, (see Table~\ref{table:eccentric_MSPs}), the large orbital eccentricities and the high precision of Arecibo timing allowed precise measurements of $\dot{\omega}$ and a measurement of a relativistic, orbital-phase dependent delay in the arrival times of the pulses, known as the Shapiro delay \citep{1964PhRvL..13..789S}, which is a direct consequence of the fact that the radio waves from the pulsar propagate in a curvature of space-time. The combination of these effects is enough for a precise determination of the component masses, even at low inclinations \citep{2019ApJ...870...74S}. It was expected that the precise MeerKAT timing of PSR~J0955$-$6150\, would allow similarly precise measurements of these relativistic effects in this system and therefore yield a precise measurement of its component masses. As described in detail below, the quality of the MeerKAT L-band detections of this pulsar exceeded all expectations, and precise masses, and much else, can be derived from these detections. The remainder of this paper is organised as follows: in section~\ref{sec:eMSPs}, we will set the stage by elaborating on the nature of eccentric MSPs binaries like PSR~J0955$-$6150, and discuss what was previously known about their evolution. In section~\ref{section:Observations}, we describe the radio observations of this pulsar and how the resultant data were processed. In section~\ref{section:profile_analysis}, we present the results from our analysis of the pulsar's radio emission, with a focus on its pulse profile: its flux, polarisation, spectral index and scattering measurements. In section~\ref{sec:timing} we present our timing results, these include a discussion of the relativistic effects detected in this system and mass estimates and orbital inclination based on these. In section~\ref{sec:rvm}, we discuss some of the constraints the orientation of the spin axis of the pulsar that result from our polarimetric measurements and compare this orientation with the constraints on the orbital geometry, finding a misalignment between the spin axis of the pulsar and the orbital angular momentum. Finally, in section~\ref{section:Discussion}, we use our mass measurements and the aforementioned orbital misalignment to evaluate the different hypotheses proposed for the evolution of the eccentric MSP+He~WD systems. We summarise our results in section~\ref{sec:summary}. \section{Eccentric millisecond pulsars} \label{sec:eMSPs} \subsection{PSR~J0955$-$6150, a peculiar system} As mentioned above, PSR~J0955$-$6150 was discovered in a Parkes survey of unidentified Fermi-LAT sources \citep{CamiloEtAl2015}, it coincides with LAT source 3FGL J0955.6$-$6148 \citep{2015ApJS..218...23A}. Such surveys are part of a successful global effort to find pulsar counterparts to unidentified Fermi-LAT sources, many of these are gamma-ray MSPs \citep{2012arXiv1205.3089R}. The pulsar has a spin period of 1.99 ms, hence is a recycled ``millisecond pulsar'', henceforth "MSP" (this is confirmed by the small value for the spin-down, to be discussed later). Like most MSPs, it is in a binary system, in this case with an orbital period $P_{\rm b} \sim 24.58\,\rm d$; the companion has a relatively low mass and is presumably a helium white dwarf star (He~WD). The unusual feature of this system is its orbital eccentricity, $e \simeq 0.12$, which is much larger than the eccentricities of most MSP+He~WD systems. However, these properties are very similar to those of a few systems discovered over the last decade (listed in Table~\ref{table:eccentric_MSPs}). Those systems have orbital periods between 22 and 32 d and orbital eccentricities of the order of 0.1; we will refer to these as eMSP systems. A recent possible addition to this category, PSR~J1146$-$6610, has an orbital period that is twice as large and an orbital eccentricity that is one order of magnitude smaller than those of the other eMSPs, so it is still unclear to what extent this is related to them \citep{2021MNRAS.507.5303L}. However, its eccentricity is still 2 orders of magnitude larger than that of other MSP - He WD systems with the same orbital period; for this reason we also list it in Table~\ref{table:eccentric_MSPs}. The evolution of MSP+He~WD systems generally involves a long period ($\sim {\rm Gyr}$) of accretion of matter onto the NS from a low-mass star \citep[][and references therein]{tv22}. During this stage, the system is detectable as a low-mass X-ray binary (LMXB). In these systems, the orbits are invariably circularised by the tidal interaction with the red-giant companion \citep{1992RSPTA.341...39P}. After Roche-lobe overflow (RLO), the pulsar becomes a radio MSP, and the companion becomes a WD. In high-mass X-ray binary systems, where the companion star is massive enough to terminate its life in a supernova (SN), the orbit is disturbed by the instantaneous mass loss and the momentum kick imparted onto the newborn NS. In this case, a double NS system is formed if the binary remains bound. Such massive companions evolve much faster, therefore the RLO episode is much shorter. The consequence is that pulsars in these systems do not spin as fast as ``fully'' recycled MSPs like PSR~J0955$-$6150\, (the fastest pulsar in a Galactic disk double NS system, PSR~J1946+2052, has a spin period of $\sim$17 ms \citep{2018ApJ...854L..22S}; see also \citet{tkf+17} for further discussions). In globular clusters, some of the MSP+He~WD systems acquire eccentric orbits, but these result either from close encounters with other stars in these clusters \citep{1992RSPTA.341...39P} or, in some extreme cases they result from the replacement of the former mass donors with much more massive degenerate companions, possibly NSs (like NGC~1851A, \citealt{2019MNRAS.490.3860R}, NGC~6544B, \citealt{2012ApJ...745..109L}, NGC 6624G, \citealt{2021MNRAS.504.1407R} and NGC~6652A, \citealt{2015ApJ...807L..23D}). Outside globular clusters, the vast majority of all binary millisecond pulsars have very small residual eccentricities consistent with the expectation for the gravitational interaction of the neutron star with the convection cells in the envelope of the WD progenitor star during the last stages of its evolution \citep{1992RSPTA.341...39P}. The exceptions are the systems in Table~\ref{table:eccentric_MSPs}: their orbital eccentricities are 2 - 3 orders of magnitude larger than the prediction. \subsection{Formation of the eccentric MSPs in the Galaxy} The presence of eMSPs with their eccentric orbits in the Galactic disk represents a deviation from the predictions of standard evolutionary theory. In the case of PSR~J1903+0327, a 2.15-ms pulsar in an eccentric ($e \, = \, 0.43$) 95-d orbit \citep{2008Sci...320.1309C}, the companion star turned out to be a $1.03 \, M_{\odot}$ main-sequence star \citep{2011MNRAS.412.2763F,2012ApJ...744..183K}. A detailed analysis of the characteristics of this system leads to the conclusion that it very likely originated as a triple system, which later became unstable, a conclusion that was reached by empirical exclusion of all likely alternatives \citep{2011MNRAS.412.2763F} and independently by numerical simulations \citep{2011ApJ...734...55P,2012MNRAS.424.2914P}. This mechanism is therefore a candidate for the formation of the remaining eMSPs. However, as first pointed out by \cite{2014MNRAS.438L..86F} and \cite{2015ApJ...806..140K}, their characteristics are too similar for such an origin as the disruption of a triple system, which is generally a chaotic process: their observed orbital periods exist within a narrow range between 22 and 32~d, and the orbital eccentricities are also seen in a narrow range between 0.027 and 0.14. It is this similarity of characteristics that defines, for the moment, the class of eMSPs. Furthermore, the chaotic destruction of a triple system would, generally, lead to the formation of a binary system consisting of the MSP with the more massive of the remaining two stars as the companion. While this is the case for PSR~J1903+0327, which has an unusually massive (and un-evolved) main sequence companion --- a unique case among the known MSPs in the Galactic disk --- this is not the case for the remaining binaries, where the companion masses measured to date (presented in Table~\ref{table:eccentric_MSPs}) are as expected for He~WD companions for these orbital periods \citep{1999A&A...350..928T}, or slightly smaller (e.g., \citealt{2017MNRAS.465.1711B}). In one case, the relatively nearby PSR~J2234+0611 \citep{2013ApJ...775...51D,2019ApJ...870...74S}, the He~WD nature of the companion has been confirmed by optical observations \citep{2016ApJ...830...36A}. If not formed in the disruption of a triple system, then how did eMSPs form? The similarity of their orbital periods and eccentricities suggests a process with a relatively fixed outcome. There are at least 5 hypotheses presented in the literature so far. The first two involve a phase transition of the object that becomes the present-day MSP \citep{2014MNRAS.438L..86F,2015ApJ...807...41J}. The next two involve thermonuclear runaway burning \citep{2014ApJ...797L..24A,2021ApJ...909..161H}. Finally, a more recent hypothesis involves resonant convection \citep{Ginzburg21}. In the first hypothesis by \cite{2014MNRAS.438L..86F}, the phase transition was from a rotationally-delayed accretion-induced collapse (RD-AIC) of a massive WD with a mass above that of the Chandrasekhar limit. The delay of the AIC is possible if the WD is sustained by a fast rotation, where the resulting centrifugal forces prevent the collapse of the WD during RLO. As this rotation slows down after mass accretion has ceased, the centrifugal forces decrease and the collapse of the massive WD becomes inevitable, although whether this can form a MSP directly is still debatable. The second hypothesis involves a phase transition within the neutron star \citep{2015ApJ...807...41J}, for instance, between normal neutron matter and quark matter, also caused by its spin-down and associated decrease in centrifugal forces. Both hypotheses predict interesting optical transient counterparts and produce MSPs within a relatively narrow range of masses: the first hypothesis produces MSPs with masses below $1.32\;M_{\odot}$ (unless differential rotation was at work in the collapsing WD, allowing for significantly more massive NSs to be produced), the second hypothesis would produce MSPs with larger masses, corresponding to the central density at which nuclear matter undergoes a phase transition to a more compact type of matter; but the exact values of the transition mass would depend on the detailed microscopic model for super-dense nuclear matter. Both hypotheses are therefore unable to describe the large range of NS masses already observed for eMSP systems. The third and fourth hypothesis, put forward by \cite{2014ApJ...797L..24A} and \cite{2021ApJ...909..161H}, respectively, rely on the expectation that for WDs within the range of the masses predicted for this interval of orbital periods, there should be significant H-shell flashes \citep[i.e. thermonuclear runaway burning episodes,][]{2013A&A...557A..19A,2016A&A...595A..35I} near the surface of the (proto) He~WD. In the hypothesis of \cite{2014ApJ...797L..24A}, this ejects enough material to produce a circumbinary disk that perturbs the orbit and fosters significant eccentricity. In the hypothesis of \cite{2021ApJ...909..161H}, the eccentricity is produced by the ejection of material from the region(s) where runaway nuclear burning is happening --- in effect a ``thermonuclear rocket''. According to this hypothesis, these burning episodes and their associated net ``kicks'' (of order $1-8\;{\rm km\,s}^{-1}$) can then create not only a measurable change in eccentricity, but also a change in the orbital period. As an example, following the recipe of \citet{2021ApJ...909..161H}, applying a NS+WD system with total mass similar to that of PSR~J0955$-$6150\, ($M=M_{\rm p}+(M_{\rm c}+\Delta M)=1.71\;M_\odot + 0.255\;M_\odot = 1.965\;M_\odot$), a relatively large instantaneous kick of $w=8\;{\rm km\,s}^{-1}$, an amount of ejected mass of $\Delta M=10^{-3}\;M_\odot$ and a pre-flash orbital period of $P_{\rm b}=20\;{}\rm d$, results in a post-flash orbital period between $P_{\rm b}\simeq 16.1-26.5\;{\rm d}$, depending on kick direction. While all hypotheses acknowledge the need for a $P_{\rm b}-M_{\rm WD}$ correlation \citep[such as the one given by][]{1999A&A...350..928T}, none of the helium-flash hypotheses make any specific predictions for the MSP masses; merely that they should reflect the range of masses observed for other MSPs, which seems to be the case \citep{2016ARA&A..54..401O,2016arXiv160501665A}. In the fourth hypothesis, with multiple rocket episodes, we might also have significant changes in the orbital plane, producing a misalignment with the spin axis of the pulsar. This is an important prediction that will be especially important for this work. Finally, a more recent hypothesis for the formation of the eMSPs has been proposed by \cite{Ginzburg21} who expanded on the work of \citet{1992RSPTA.341...39P} and argue that formation of eMSPs might be due to resonant convection. In the earlier work, it had already been noticed that the timescale of convective eddies within the red giant WD progenitors is about 25~d, which is, again, similar to that of the orbital periods of eMSP systems. To explain their high eccentricities, \cite{Ginzburg21} postulate a coherent resonance between the orbital period and the convective eddies in the red giant progenitors, which drives the anomalously large eccentricities in eMSPs by convective flows. \section{Observations} \label{section:Observations} \begin{figure} \centering \includegraphics[scale=0.45]{average_mkt_uwl_profiles_v5.pdf} \caption{Flux calibrated total intensity profiles made from observations made with MeerKAT (left plot) and Parkes (right plot) radio telescopes. The MeerKAT profile was made from a total of $\sim32.6$ h of observations with L-band receiver centred at 1284 MHz with a bandwidth of 856 MHz. The Parkes profile was made from a total of $\sim14.9$ h of observations with the two lower sub-bands of the UWL receiver with a centre frequency of 1536 MHz and a bandwidth of 1664 MHz. The profiles have been bin-scrunched down to 512 bins across the pulse phase in order to increase the S/N ratio per phase bin. Bottom panels show the dynamic spectra, made from 8 and 16 contiguous frequency bands for MeerKAT and Parkes respectively. The number of bands was chosen to result in the same frequency width per band for both telescopes and correspond to flux measurements shown in Fig.~\ref{figure:spectral_index}. The frequency range of the dynamic spectrum from the MeerKAT has been aligned to that of Parkes for the ease of comparison. The frequency evolution of the pulse profile and the steep spectral index is clearly visible.} \label{figure:uwl_mkt_profiles} \end{figure} \subsection{Parkes observations} Following its discovery in late 2012 \citep{CamiloEtAl2015}, search mode observations of the pulsar were undertaken with the Parkes 20-cm multibeam receiver \citep{Staveley-SmithEtAl1996} using at first the $2 \, \times \, 512 \, \times \, 0.5$ MHz Analogue Filterbank backend (AFB). This back-end was used until June 2015. In 2013 August, we started using the Digital FilterBank (DFB) versions 3 and 4 to obtain a preliminary timing solution. These observations were described by \cite{CamiloEtAl2015}. From mid-2015 until late 2016, folded mode observations were obtained with the same receiver, but with the CASPER Parkes Swinburne Recorder (CASPSR) backend. CASPSR operates at a centre frequency of 1382 MHz with a usable bandwidth of 340 MHz and is capable of performing real-time coherent dedispersion at the dispersion measure of the pulsar before folding at its topocentric period. \cite{ManchesterEtAl2013} and \citet{VenkatramanKrishnanPhDThesis} provide more information on the DFB and CASPSR backends respectively. The same receiver-backend set up was used for observations between December 2019 and January 2020 to obtain overlap between Parkes and MeerKAT data sets for better measurement of the timing jump between the two data sets. This was performed as a part of the project P1032 (PI: Venkatraman Krishnan), a project focused on obtaining complementary data to MeerKAT's relativistic binary programme (see \citealt{ksv+21} for more details). As part of P1032, we also performed a total of $\sim 14$ hours of observations with the new UWL receiver at Parkes \citep{HobbsEtAl2020}. The data recording was performed using the \textsc{medusa} backend that records coherently dedispersed fold-mode data centred at 2368 MHz with a bandwidth of 3328 MHz. Due to the pulsar's steep spectrum (see Section \ref{section:profile_analysis}), we were able to get useful data only from the lower 1664 MHz of the band. For the same reason, we find that the ToAs at the bottom 512 MHz of the Parkes UWL receiver provides times of arrivals that are $\sim 8 \times$ better than the previous multibeam data. An integrated profile from the UWL receiver can be seen in Fig.~\ref{figure:uwl_mkt_profiles}. \subsection{MeerKAT observations} The pulsar observing set up at MeerKAT is explained in detail by \cite{BailesEtAl2020}, while the details on polarisation and flux calibration are outlined in \cite{sjk+21} and \cite{SpiewakEtAl2021} respectively. All timing observations were performed with the L-band receiver under two sub-themes of MeerTime: The aforementioned RelBin \citep{ksv+21}, and the MeerKAT census of southern millisecond pulsars \citep{SpiewakEtAl2021}. MSP census observations were short ($\sim5$ min) while the RelBin observations ranged from 2048 seconds to 4 hours depending upon the orbital phase, for the necessary orbital coverage. The data presented here are from March 2019 to September 2021, and amounts to a total of $\sim32.6$ hours. The quality of the MeerKAT L-band profiles are remarkable. The timing precision, per unit time, is $> 12\times$ better than the earlier Parkes timing. This improvement is larger than expected given the MeerKAT's $\sim6$-fold improvement in sensitivity and $\sim2$-fold increase in bandwidth compared to the Parkes multi-beam system. The steep spectral index of the pulsar measured with the combined MeerKAT + UWL dataset (see Section \ref{subsec:integrated_profile}) is a likely explanation for this this disparity as the MeerKAT usable L-band frequency goes as low as 900 MHz; even its central frequency of 1284 MHz is 100 MHz lower than that of the Parkes multibeam data sets. The pulsar's pulse profile with the MeerKAT L-band receiver is presented in Fig.~ \ref{figure:uwl_mkt_profiles}. \section{Profile analysis} \label{section:profile_analysis} In this section, we report our analysis of the pulsar's flux density, spectral index, polarisation and pulse broadening due to interstellar scattering using the Parkes UWL and MeerKAT L-band datasets. Unless otherwise specified, all the analyses were performed on the integrated profile that is obtained by summing up all the observations of the pulsar per backend. This includes a total of 32.6 hours and 14.9 hours for MeerKAT L-band and Parkes UWL data respectively. \subsection{Flux density spectrum} \begin{figure} \centering \includegraphics[width=\columnwidth]{spectral_index_v4.pdf} \caption{Mean flux density measurements for the observations performed with MeerKAT L-band (red squares) and Parkes UWL receivers (blue diamonds) with error bars indicating nominal $1 \sigma$ uncertainties, fit with power law model (black dashed line) to determine $\rm S_{\rm 1400}$ and the spectral index, $\rm \alpha$. The number of measurement points for each telescope has been chosen to result in equal bandwidth.} \label{figure:spectral_index} \end{figure} The flux density calibration of the Parkes UWL receiver was performed using observations of the Hydra A radio galaxy as well as standard pulsar reference pointings utilising pulsed source of noise (i.e. noise diode) in the ULW receiver. In the next step, a standard flux calibration technique utilising a combination of \textsc{psrchive} programs, i.e. \textsc{fluxcal} and \textsc{pac} was performed as is described in detail in \cite{2012ART....9..237V}. We have decided to divide observing bands of both telescopes such that fractional per-band frequency would be the same, thus simplifying the fitting procedure. In order to estimate the flux densities for each frequency band we have created an analytical pulse profile using the \textsc{paas} program. Subsequently \textsc{psrflux} program from the same package was used to cross-correlate it with each band's profile. The uncertainties of flux densities in each of the frequency bands were estimated by an algorithm that robustly estimates off-pulse baseline and is part of the \textsc{psrchive} package. The flux density measurements of MeerKAT data was obtained using a scaling relation from the radiometer equation as explained in \citep{SpiewakEtAl2021}. Fig.~\ref{figure:spectral_index} presents flux density measurements made with both telescopes, as well as best fit of a power-law model, $S = S_{1400}\,(\nu/1400\,\textrm{MHz})^\alpha$. The flux density spectrum of the MeerKAT L-band data (Fig.~\ref{figure:spectral_index}) is found to be well fit by a steep spectral index, $\alpha$ of $-3.13 \pm 0.02$, providing a mean flux density of $0.53 \pm 0.01$\,mJy at 1400 MHz. We note that in the region where data points from MeerKAT and Parkes UWL overlap, a slight offset between the points can be seen, with MeerKAT data points being slightly above those of Parkes UWL. We deduce this is due to MeerKAT antenna system temperature that was assumed in the flux density measurement method mentioned above and varying number of antennas used per observation that were integrated into the average profile used in this analysis. Additionally, we note a slight deviation from the best fit line seen for the Parkes UWL data points extending outside frequency overlap. We conclude that this effect could be due to the \textsc{psrflux} underestimating flux in the frequency bands where the pulsar signal-to-noise (S/N) ratio is low. This is especially seen in the frequency resolved plot of Fig.~\ref{figure:prof} for the Parkes UWL data at frequencies above 1.6 GHz. \subsection{Polarisation properties} \label{subsec:integrated_profile} \begin{figure} \centering \includegraphics[width=\columnwidth, angle=0]{pol0955_v2.2.pdf} \caption{ Polarisation profile as observed with MeerKAT at a central frequency of 1284 MHz, integrating a total of 32.6 hours. The top panel shows the total intensity (black), the linear (red) and circular polarisation (blue) intensity. The bottom panel shows values of the position angle (PA) swing. A Rotating Vector Model has been fitted to the PA values as shown as a red solid line and repeated offset by $180\, \deg$, while the dashed line indicates the RVM solution separated by $90\, \deg$ and intended to fit the interpulse. The grey band indicates the derived uncertainties in the determined RVM description. See Section~\ref{sec:rvm} for details.} \label{figure:prof} \end{figure} Fig.~\ref{figure:prof} presents a flux- and polarisation-calibrated average profile for PSR~J0955$-$6150\, at L-band using MeerKAT. The profile is created from integrating a total of 32.6 hours and the full MeerKAT observing band (for these observations $\sim 775$\,MHz) after radio frequency interference removal. The pulsar shows a wide profile shape with broad multiple component features and a duty cycle in excess of 80\% at L-band. The small-amplitude component trailing the main pulse by $\sim100$ deg of longitude (called ``post-cursor''; or preceding it by about $\sim80$ deg, then called ``pre-cursor'') is not unusual for recycled pulsars but is a typical feature that distinguishes the emission from millisecond pulsars from that of ``normal'' pulsars \citep{kxl+98}. It may originate from the magnetic pole opposite to the one responsible for the main pulse (as it appears to be emitted in an polarisation mode orthogonal to the main pulse, cf.~\ref{sec:rvm}) but it may also come from a different location more generally. The wide main pulse shows only a very small degree of polarisation, both for the linearly polarised (red) and circularly polarised (blue) component. The fact that the degree of circularly polarisation exceeds that of the linear component is uncommon for normal pulsar but is not atypical for millisecond pulsars \citep{xkj+98}. In contrast, the pre/post-cursor feature is nearly completely linearly polarised with non-detectable circular polarisation. We have calculated the phase-averaged linear polarisation fraction to be $\mathrm{L / I} = 6.2 \pm 1.6 \%$. In the main pulse, the circular polarisation shows a sense reversal, which in normal pulsars is usually identified with the longitude of the magnetic axis \citep{Lorimer&Kramer2005}. The phase-averaged absolute circular polarisation fraction is $\mathrm{\|V\| / I} = 10.2 \pm 0.1 \%$. We will discuss the geometric interpretation of the polarisation properties, especially that of the position angle swing shown in the lower panel of Fig.~\ref{figure:prof} in Section~\ref{sec:rvm}. \subsection{No evidence for scattering} We investigate evidence for scattering (i.e.~multi-path propagation) in the interstellar medium (ISM) by fitting a pulse broadening model to the profile shapes obtained from integrating the high S/N ratio profile to four frequency channels. From these we follow two approaches. At first, the complete pulse shapes are modelled using a five-component Gaussian model (representative of the intrinsic profile), convolved with an interstellar transfer function $\propto e^{-t/\tau_s}$, where $\tau_s$ is the characteristic ISM scattering time scale \citep{Williamson1972}. The Gaussian components and $\tau_s$ values are simultaneously fit. While the channelised data are well fit by this model, as shown in Fig.~\ref{figure:scat} we observe only marginal evolution of $\tau_s$ with frequency; with best-fit $\tau_s$ values all lying between 0.02\,ms and 0.03\,ms using four channels across the band. The power law scaling, $\tau \propto \nu^{-\alpha}$, provides a flat $\alpha = -0.5 \pm 0.5$. As such $\alpha$ is poorly constrained and much less than 4 or 4.4 typically associated with simple scattering models of radio frequencies by the ionised component of the ISM (e.g. \citealt{Rickett1970} and \citealt{Rickett1977}). We note that for all our scattering fits large covariances between $\tau_s$ and many of the Gaussian component widths, used to model the underlying profile, exist. For the lowest frequency channel in Fig.~\ref{figure:scat} the anti-correlation of $\tau_s$ with the three principal Gaussian component width is > 0.8. We conclude that the obtained $\tau_s$ estimates are more likely a result of the profile's asymmetric shape and its intrinsic profile evolution, rather than due to scattering by the ISM. As a second test, we investigated the isolated component (at phase 0.95) for evidence of scattering. The $\tau_s$ values associated with the isolated component are found to be consistent with zero as seen in the bottom panels of Fig.~\ref{figure:scat}, and are fully correlated (>0.9) with the width of this isolated component. We conclude that we do not find evidence for pulse broadening via the ISM. We also fail to find convincing evidence for scattering in the L-band MeerKAT data of PSR~J1006$-$6311, which has similar Galactic coordinates to PSR~J0955$-$6150\, (separated by 1.9$^\circ$ in Galactic longitude and 0.3$^\circ$ in latitude) and a DM of 195.99\,cm$^{-3}$\,pc \citep{DAmico98}. The NE2001 \cite{Cordes&Lazio2002} and YMW16 \cite{YaoEtAl2017ApJ} electron density models of the Galaxy predict significantly different scattering timescales of $\tau_s^{\rm YMW16} = 0.15~\rm{ms}$ and $\tau_s^{\rm NE2001} = 0.011~\rm{ms}$\footnote{obtained using pygedm: \url{https://github.com/FRBs/pygedm}}. Correspondingly they place the pulsar at a distance of 2.17 kpc and 4.04 kpc respectively. Comparing these estimates to the results above, we note that the NE2001 model's results are more akin to our measurements. The lack of evidence for scatter broadening of PSR~J0955$-$6150's profile\, allows us to put limits on the intrinsic radio duty-cycle, which when considering the isolated component to be the inter-pulse to this pulsar, provides us with a duty-cycle > 95\%. We can also ultimately make comparisons between its intrinsic radio and the gamma ray emission, the latter of which is expected to have a wider pulse profile (more in Paper~II, in prep.). Furthermore, the apparent lack of scattering makes timing of this pulsar with the MeerKAT UHF receiver even more promising. \begin{figure} \centering \includegraphics[width=\columnwidth, angle=0]{scattering.pdf} \caption{Top four panels: the profile shapes of PSR J0955$-$6150 across four MeerKAT L-band frequencies fitted with a scatter broadening model (blue, dashed lines). The obtained $\tau_s$ values do not show significant evolution with frequency, as is typical of ISM scattering. Bottom panels: Isolating the lone component at phase $\sim$ 0.95 we find a symmetric shape consistent with $\tau_s = 0$, further substantiating a lack of scattering broadening.} \label{figure:scat} \end{figure} \section{Timing analysis} \label{sec:timing} \begin{table}[h] \caption[]{ \label{table:observing_details} Details on the observing system and the timing dataset on PSR~J0955$-$6150 \, used in this paper. } \centering \begin{threeparttable} \begin{tabular}{p{0.5in} l l l l l l l l l r} \hline \hline Telescope & Receiver & Backend & Centre & BW$^\star$ & nchans & CD$^$ & Time span & \#TOAs & EFAC$^{\dagger}$ & EQUAD$^{\dagger}$ \\ & & &Freq(MHz) & (MHz) & & & (MJD) & & & \\ \hline \multirow{5}{}{Parkes} & & AFB & 1390 & 256 & 512 & No & 56277-57077 & 40 & 0.9& -6\\ &20-cm&PDFB3 & 1369 & 256 & 256 & No & 56505-56943 & 23 & 0.8 & -9.0\\ &multibeam&PDFB4 & 1369 & 256 & 512 & No & 56943-57620 & 50 & 0.75 & -5.15\\ &&CASPSR & 1382 & 340 & 512 & Yes & 57181-58855 & 50 &0.95 & -6.59\\ \cline{2-11} & Ultra-Wide- & MEDUSA& 1536 & 1664 & 1664 & Yes & 58760-58996 & 192 & 1.5& -5.11\\ & band Low &&&&&&&&& \\ \hline MeerKAT & L-band & PTUSE & 1283.582 & 775.75 & 928 & Yes & 58568-59358 & 832 & 1.05& -6.16\\ \hline \hline \end{tabular} \begin{tablenotes} $^\star$ Effective usable bandwidth. \\ $^$ Intra-channel coherent dedispersion.\\ $^{\dagger}$ EFAC and EQUAD follows \textsc{temponest} definitions \citep{LentatiEtAl2014}. \end{tablenotes} \end{threeparttable} \end{table} \subsection{Data reduction} The data reduction for pulsar timing used standard pulsar timing analysis techniques using the \textsc{psrchive} \citep{HotanEtAl2004,2012ART....9..237V} software package and all the commands/programs specified in this section are part of this package unless explicitly mentioned/cited otherwise. We used the initial analogue filterbank (AFB) data as-is from the discovery paper of PSR J0955$-$6150 \citep{CamiloEtAl2015}. All other Parkes multibeam data were first manually mitigated of radio frequency interference (RFI) using \textsc{pazi} and \textsc{psrzap} and were scrunched to 5-minute integrations. These were polarisation calibrated using observations of a noise diode that was performed before every pulsar observation. The noise diode injects a square wave signal cycled at 11.123 Hz at $45$ degrees to each of the orthogonal signal probes. This is used to measure and compensate for the differential gain and phase that is induced across the two polarisations. The polarisation calibrated data were further scrunched such that there is one integration per observation, and two channels across the band. The data reduction for Parkes UWL was similar except that the final products had 0.7-hr integrations and 13 channels across the band. The reduction of MeerKAT data used the \textsc{meerpipe} pipeline that performs RFI excision using a modified version of \textsc{coastguard} \citep{LazarusEtAl2016}, performs polarisation and flux calibration, and produces decimated data products that can be readily used for timing. Depending on the observing time (which in turn depended on which Meertime ``theme'' it belonged to, and what the orbital phase was), the final data product contained time integrations from 300 to 2048 seconds, and 8 channels across the observing bandwidth. High S/N ratio observations were summed on a per backend basis to obtain a good frequency resolved pulse profile. For every backend, 2D-analytical templates were obtained by iteratively running the \textsc{paas} command for every channel from these high S/N profiles. The resultant analytical templates were then used to obtain frequency resolved time of arrivals (TOAs) using the \textsc{pat} command. More information on the observing system and the data set is given in Table \ref{table:observing_details}. \begin{table} \caption{Timing parameters for PSR~J0955$-$6150, obtained from the {\sc tempo2} timing package using the DDH binary model. In this and the following table, all uncertainties in the measured values are 68.3\,\% confidence limits. } \centering \begin{tabular} {l c} \hline \hline \multicolumn{2}{c}{Observation and data reduction parameters}\\ \hline Solar System ephemeris\dotfill & DE436 \\ Timescale \dotfill & TCB \\ Reference epoch for period, position and DM (MJD)\dotfill & 56983.0167959\\ First observation (MJD)\dotfill & 56277 \\ Last observation (MJD)\dotfill & 59358 \\ Solar wind electron number density, $n_{0}$ (cm$^{-3}$)\dotfill & 10.0 \\ \hline \multicolumn{2}{c}{Spin and astrometric parameters}\\ \hline Right ascension, $\alpha$ (J2000, h:m:s)\dotfill & 09:55:20.84737(9) \\ Declination, $\delta$ (J2000, d:m:s)\dotfill & $-$61:50:16.8945(6) \\ Proper motion in $\alpha$, $\mu_{\alpha}$ (mas\,yr$^{-1}$)\dotfill & 0.2(1) \\ Proper motion in $\delta$, $\mu_{\delta}$ (mas\,yr$^{-1}$)\dotfill & $-$0.1(1) \\ Spin frequency, $\nu$ (Hz)\dotfill & 500.15992019837(8) \\ Spin-down rate, $\dot{\nu}$ ($10^{-15}$\,Hz\,s$^{-1}$)\dotfill & $-$3.5663(4) \\ Dispersion measure, DM (cm$^{-3}$\,pc)\dotfill & 160.918(8) \\ First Derivative of DM, DM1 ($10^{-3}$\,cm$^{-3}$\,pc\,yr$^{-1}$)\dotfill & $-$6(2) \\ Second Derivative of DM, DM2 ($10^{-4}$\,cm$^{-3}$\,pc\,yr$^{-2}$)\dotfill &11(5) \\ Rotation measure, RM (rad\,m$^{-2}$)\dotfill & $-48(5)^{\textit{a}}$ \\ \hline \multicolumn{2}{c}{Derived parameters}\\ \hline Galactic longitude, $l$ ($^{\circ}$)\dotfill & 283.684986 \\ Galactic latitude, $b$ ($^{\circ}$)\dotfill & $-$5.737093 \\ Total proper motion, $\mu_{\text{T}}$ (mas\,yr$^{-1}$)\dotfill & 0.2(1) \\ Position angle of proper motion, J2000, $\Theta_{\mu}$ ($^{\circ}$) \dotfill & 171(5) \\ Position angle of proper motion, Galactic, $\Theta_{\mu}$ ($^{\circ}$) \dotfill & 133(5) \\ DM-derived distance (NE2001), $d$ (kpc)\dotfill & 4.04$^{\textit{b}}$ \\ DM-derived distance (YMW16), $d$ (kpc)\dotfill & 2.17$^{\textit{b}}$ \\ Parallax, $\bar{\omega}$ (mas)\dotfill & 0.24$^{\textit{c}}$ \\ Galactic height, $z$ (kpc)\dotfill & $-0.40(6)^{\textit{c}}$ \\ Heliocentric transverse velocity, $v_{\text{T}}$ (km\,s$^{-1}$)\dotfill & $13(2)^{\textit{c}}$ \\ Spin period, $P_{0}$ (ms)\dotfill & 1.9993605237367(2) \\ Spin period derivative, $\dot{P}$ ($10^{-20}$\,s\,s$^{-1}$)\dotfill & 1.42601(17) \\ Total kinematic contribution to period derivative, $\dot{P}_{\text{k}}$ ($10^{-20}$\,s\,s$^{-1}$)\dotfill & $-0.075$ \\ Intrinsic spin period derivative, $\dot{P}$ ($10^{-19}$\,s\,s$^{-1}$)\dotfill & 1.501(9) \\ Surface magnetic field strength, $B_{\text{surf}}$ ($10^{9}$\,G)\dotfill & 0.17 \\ Characteristic age, $\tau_{\text{c}}$ (Gyr)\dotfill & 2.1 \\ Spin-down power, $\dot{E}$ ($10^{34}$\,erg\,s$^{-1}$)\dotfill & 7.4 \\ \hline \hline \multicolumn{2}{l}{$^{\textit{a}}$ Obtained using \textsc{rmfit} program in the \textsc{psrchive} software package.}\\ \multicolumn{2}{l}{$^{\textit{b}}$ Assuming a $20\%$ uncertainty in the distance}\\ \multicolumn{2}{l}{$^{\textit{c}}$ Assuming DM-derived distance (NE2001)}\\ \label{tab:timing} \end{tabular} \end{table} \begin{table} \caption{Binary parameters measured for PSR\,J0955$-$6160 obtained using \textsc{tempo2}. Square brackets indicate derived quantities. For the DDGR solution, the $\dot{P}_{\rm b}$ is fitted as a term in addition to the (very small) orbital decay caused by the emission of gravitational waves. For the grid solution, the values for the $\chi^2$ correspond to those of the best point in the grid, they are slightly lower than the DDGR solution because for each point in the grid there are two parameters ($M$ and $M_{\text{c}}$) that are assumed, not fitted. } \centering \begin{tabular} {l c c c } \hline \hline Binary model\dotfill & DDGR & DDH & DDGR $\chi^{2}$ grid \\[0.5ex] Number of ToAs \dotfill & 1186 & 1186 & 1186 \\ weighted rms of ToA residuals ($\mu s$) \dotfill & 2.02 & 2.02 & 2.02 \\ $\chi^2$ of fit \dotfill & 1197.82 & 1199.91 & 1196.11 \\ $\chi^2$ / number of degrees of freedom\dotfill & 1.009 & 1.011 & 1.009 \\ \hline \multicolumn{4}{c}{Keplerian orbital parameters}\\[0.5ex] \hline Orbital period, $P_{\text{b}}$ (days)\dotfill & 24.57839502(6) & 24.57839502(6) & - \\[0.5ex] Projected semi-major axis of the pulsar orbit, $x$ (lt-s)\dotfill & 13.282477(2) & 13.2824767(6) & - \\[0.5ex] Epoch of periastron, $T_{0}$ (MJD)\dotfill & 56287.604348(6) & 56287.604349(6) & - \\[0.5ex] Orbital eccentricity, $e$\dotfill & 0.11750575(1) & 0.11750575(1) & - \\[0.5ex] Longitude of periastron at $T_{0}$, $\omega$ ($^{\circ}$)\dotfill & 202.92940(9) & 202.92941(9) & - \\[0.5ex] \hline \multicolumn{4}{c}{Post-Keplerian orbital parameters}\\[0.5ex] \hline Rate of advance of periastron, $\dot{\omega}$ ($^{\circ}$\,yr$^{-1}$)\dotfill & [0.0014809] & 0.00152(1) & - \\[0.5ex] Einstein delay, $\gamma$ (ms) \dotfill & [0.5362] & [0.5417] & - \\ (Excess) Orbital period derivative, $\dot{P_{\text{b}}}$ ($10^{-12}$\,s\,s$^{-1}$)\dotfill & 11(7) & 11(7) & - \\[0.5ex] Orthometric amplitude of Shapiro delay, $h_{3}$ ($\mu$s)\dotfill & - & 0.89(7) & - \\[0.5ex] Orthometric ratio of Shapiro delay, $\varsigma$\dotfill & - & 0.88(2) & - \\[0.5ex] \hline \multicolumn{4}{c}{Mass and inclination measurements}\\ \hline Mass function, $f$ (M$_{\odot}$)\dotfill & 0.004164980(1) & 0.0041649796(5) & - \\[0.5ex] Total mass, $M$ (M$_{\odot}$)\dotfill & 1.96(2) & [1.9602] & 1.96(3) \\[0.5ex] Pulsar mass, $M_{\text{p}}$ (M$_{\odot}$)\dotfill & 1.71(3) & - & 1.71(2) \\[0.5ex] Companion mass, $M_{\text{c}}$ (M$_{\odot}$)\dotfill & 0.254(2) & - & 0.254(2) \\[0.5ex] Orbital inclination, $i$ ($\deg$)\dotfill & - & - & $83.2(4)$ \\[0.5ex] \hline \hline \label{tab:binary} \end{tabular} \end{table} \begin{figure} \centering \includegraphics[width=0.8 \textwidth]{J0955-6150_residuals_R1.pdf} \caption{Top to bottom: Post-fit residuals for the timing of PSR~J0955$-$6150, obtained with the {\sc tempo2} DDH solution as a function of (1) time, (2) orbital phase without subtracting the full Shapiro delay signal and (3) orbital phase after subtracting the Shapiro delay signal. The orbital phase is measured from periastron; the superior conjunction happens at a mean anomaly of 259.9 degrees. The colours denote the different telescopes and back-ends used in the timing. {\em Blue}: Parkes Analogue Filterbank (AFB) data, {\em Brown and Yellow}: Parkes Digital Filterbank (DFB) data, {\em Red}: CASPER Parkes Swinburne Recorder (CASPSR) data, which was taken both before 2017 and after 2019, thus establishing timing continuity for the whole data set, {\em Gray}: Parkes UWL data and {\em Teal}: MeerKAT L-band data. The middle plot also shows the theoretical Shapiro delay signal for the best value of the orbital inclination. In the bottom two plots, TOAs with precision worse than 10$\mu$s are made semi-transparent for clarity.} \label{figure:residuals} \end{figure} \subsection{Timing} For the TOA analysis we used the {\sc tempo2} pulsar timing package \citep{HobbsEtAl2006} and {\sc temponest}, a bayesian parameter estimation plugin to {\sc tempo2} that also facilitates fits for, among other things, power law models for red and DM noise in the data \citep{LentatiEtAl2014}. To describe the telescope's motion relative to the Solar System Barycentre, we used JPL's DE436 Solar System ephemeris. All ToAs were transferred to Universal Coordinated Time (UTC) and then to the terrestrial time standard, ``TT(TAI)" that is derived from the ``International Atomic Time" timescale. To describe the pulsar's orbital motion, we use two models related to the theory-independent model of \cite{DD2} (henceforth designated as "DD"). The DD model describes the orbital motion as being essential a Keplerian orbit with small relativistic perturbations. With pulsar timing, we can only measure five of its elements: the orbital period ($P_{\rm b}$), orbital eccentricity ($e$), the semi-major axis of the pulsar's orbit projected along the ling of sight ($x$), the longitude of periastron ($\omega$) and the time of passage of periastron ($T_0$). The relativistic perturbations are quantified, in a general and theory independent way \citep{DamourTaylor1992}, by the so-called ``Post-Keplerian'' (PK) parameters, which are: rate of advance of periastron ($\dot{\omega}$), the variation of the orbital period ($\dot{P}_{\rm b}$, which includes the orbital decay caused by the emission of gravitational waves) and the Einstein delay ($\gamma$, which is caused by the orbital variation of the special relativistic time dilation and general relativistic gravitational redshift). In addition, the model includes the aforementioned Shapiro delay. The first model we used is the DDGR orbital model, which assumes the validity of GR to describe all relativistic effects and fits directly for the masses of the two objects in the system. In parallel, we used the theory-independent orbital model (DDH) in order to understand which relativistic effects are effectively being measured; this is important for verifying whether they are all consistent with each other within the framework of GR. This model is nearly identical to the DD model; the only difference is the PK parameters used to describe the Shapiro delay: in the DD model these are the ``range'' ($r$) and ``shape'' ($s$) parameters, in the DDH model these are the orthometric amplitude ($h_3$) and the orthometric ratio ($\varsigma$, \citealt{2010MNRAS.409..199F}). The advantage of using $h_3$ and $\varsigma$ is that they have, particularly for lower inclinations, a much lower correlation between themselves than $r$ and $s$; hence, they provide a better description of mass and inclination constraints introduced by the Shapiro delay. For orbital inclinations close to $90^\circ$, the two models are equivalent. For both DDH and DDGR timing models, we performed Bayesian non-linear fits of the timing model to our data using \textsc{temponest}. Apart from the timing parameters, we fit for white noise parameters; EFAC and EQUAD, per backend that modify the formal TOA uncertainties, and a power law DM noise model as described in \cite{LentatiEtAl2014}. We also performed fits for a red timing noise model, but the posteriors indicated that the red noise in the data set is negligible. Hence we ignored red timing noise for the rest of our analysis. The estimates of the pulsar parameters can be found in Table \ref{tab:timing} and \ref{tab:binary}, the uncertainties on the parameters represent 68.3\% confidence levels that are scaled to a reduced $\chi^2$ of 1. The first table has the spin and astrometric parameters for the pulsar; the second has the binary parameters derived according to the DDGR, DDH models, and the results of our Bayesian analysis of the masses of the components using a $\chi^2$-grid, which is described in section~\ref{section:chi2map}. The TOA residuals (i.e., the TOA minus the prediction of the ephemeris for that rotation) are depicted in Figure~\ref{figure:residuals}. Figure \ref{fig:corner} shows the marginalised 1D-posterior distributions and the 2D-correlation contours for the orbital and post-Keplerian parameters that are relevant for this paper. In the remainder of this section we call the reader's attention to some of the timing parameters we have measured, and discuss their significance, with a special focus on the post-Keplerian parameters and the masses of the pulsar and its companion. \subsection{Position and Proper motion} The timing yields a very precise position of the pulsar in the sky. This allows a search for counterparts at optical wavelengths. Inspecting the GAIA data release 3 \citep{2021A&A...649A...1G}, we find no counterparts within 3\arcsec of the position of the pulsar. However, this goes only to a magnitude of about 20. A deeper optical map of the Southern Galactic plane has been obtained by Cerro Tololo's DECam Plane Survey \citep{2018ApJS..234...39S}, where the faintest objects have magnitudes of 23.7, 22.8, 22.3, 21.9, and 21.0 mag (AB) in the grizY bands, respectively, and average seeing of about 1\arcsec. Again, no clear counterparts can be detected within 3\arcsec of the position of the pulsar. In the direction of this pulsar, the extinction is 1.15, 0.773, 0.567, 0.432 and 0.376 magnitudes for the g, r, i, z and Y bands, respectively \citep{2011ApJ...737..103S}. This implies that the companion WD must be fainter (in the g band) than magnitude $\sim$21.1. This is not surprising: the WD companion of the eccentric MSP PSR~J2234+0611 has a g magnitude of 22.17 \citep{2016ApJ...830...36A}. Furthermore, PSR~J2234+0611 is at a distance $0.95 \pm 0.04$ kpc \citep{2019ApJ...870...74S}; the estimated distance to PSR~J0955$-$6150\, is at least twice as large, which would increase its magnitude by 1.5. This means that even without extinction, the companion of PSR~J2234+0611 would not be detectable at the distance of PSR~J0955$-$6150. We have also looked for counterparts in the near-infrared VISTA Hemisphere Survey, which has a target depth is 20.6,19.8 and 18.5 magnitudes for the J, H and K bands respectively \citep{2019A&A...630A.146S}. Again, no clear counterparts are seen at the position of the pulsar. Thus, we cannot confirm that the companion is a He WD - if so, it is too faint to be detectable in current surveys. Our measurement of the proper motion of PSR~J0955$-$6150\, shows it is unusually small, and consistent with no detectable motion both in Right Ascension ($\alpha$) and Declination ($\delta$); the total proper motion $\mu$ is only 0.2(1) mas/yr. This yields a very small Heliocentric velocity: if we use the NE2001 model of the electron distribution of the Galaxy \citep{Cordes&Lazio2002}, then the distance is around 4.0(8) kpc (after assuming a distance uncertainty of about 20 \%) and the resulting heliocentric velocity is $3.8\, \pm \, 2.5 \, \rm km \, s^{-1}$; using the YMW16 model \citep{YaoEtAl2017ApJ} we obtain a distance of 2.2(4) kpc and a heliocentric velocity of $2.0\, \pm \, 1.3 \, \rm km \, s^{-1}$ (these estimates assume only the uncertainty in the proper motion, which is, in relative terms, much larger than the uncertainty in the distance). This is very small compared to the average velocities of MSPs (e.g., \citealt{2011ApJ...743..102G,2016MNRAS.458.3341D,2018ApJS..235...37A}), and even smaller compared to the velocities of normal pulsars \citep{2005MNRAS.360..974H}. However, the velocity of the pulsar relative to its local standard of rest is much larger. Following the simple method described by \cite{2019ApJ...881..165Z}, we obtain peculiar velocities of $\sim 133 \, \rm km \, s^{-1}$ and $\sim 78 \, \rm km \, s^{-1}$ for the two distances listed above. These are nearly parallel to the Galactic plane: for instance, for the NE2001 distance, the perpendicular velocity is only $\sim 8 \, \rm km \, s^{-1}$. These peculiar velocity estimates are much more typical of what one finds among the general MSP population. \subsection{Spin period derivative} \label{sec:pdot} The proper motion measured is important for estimating the intrinsic spin-down of the pulsar, $\dot{P}_{\rm int}$, from the observed spin-down, $\dot{P}_{\rm obs}$: \begin{equation} \frac{\dot{P}_{\rm int}}{P} = \frac{\dot{P}_{\rm obs}}{P} - \frac{\mu^2 d}{c} - \frac{a}{c}, \end{equation} where $d$ is the distance from the Earth to the system, $a$ is the difference of the accelerations of the Solar system and of the pulsar's system in the gravitational field of the Galaxy, projected along the direction from Earth to pulsar, and $c$ is the speed of light. The contribution to $\dot{P}$ that depends on $\mu$ is the Shklovskii effect \citep{1970SvA....13..562S}, for the NE2001 distance estimate this is very small, only $P \mu^2 d/c = 7.7 \, \times \, 10^{-25}$, a consequence of the small Heliocentric proper motion of the system. The Galactic acceleration can be calculated using the analytical expressions in, e.g., \cite{2009MNRAS.400..805L}; these are sufficiently accurate given the small Galactic latitude of the pulsar. In these expressions, we used an estimate of the distance of the Solar System to the Galactic centre and rotational velocity of the Galaxy ($D = 8.275(34)\,$kpc, $v_{\rm Gal} \, = \, 240.5(41)\, \rm km \, s^{-1}$) from \cite{2021arXiv210701096A}. For the pulsar distance, we used the NE2001 estimate. From this, we get $P a/c \, = \, -0.75 \, \times \, 10^{-21}$. Adding these two contributions, we obtain a total $\dot{P}$ correction $\dot{P}_{k} = -0.75 \, \times \, 10^{-21}$, which is completely dominated by the Galactic acceleration term. From this, we obtain an intrinsic spin-down of $1.501(9) \, \times \, 10^{-20}$, which is similar, but slightly larger, than $\dot{P}_{\rm obs}$. From this, we estimate the characteristic age, magnetic field and spin-down power values presented in Table~\ref{tab:timing}. \begin{figure} \centering \includegraphics[width=\textwidth]{J0955-6150_corner_R1.pdf} \caption{ A corner plot showing the posterior distributions of the orbital and Post-Keplerian parameters and the correlations between them for PSR J0955-6150 obtained from the non-linear timing of the pulsar with the DDH binary model using \textsc{temponest}. The off-diagonal elements show the correlation between the parameters and are marked contours that define 39\%, 86\% and 98\% C. L. while the diagonal elements show the marginalised 1D posterior distributions of the parameters with the shaded region marking nominal 1$\sigma$ or 68.27\% of the probability.\label{fig:corner}} \end{figure} \subsection{Post-Keplerian parameters} \begin{figure} \centering \includegraphics[width=0.8\textwidth]{mass_mass.pdf} \caption{Mass and orbital inclination constraints for the PSR~J0955$-$6150\, binary system. In both panels, the lines represent the nominal and $\pm \, 1 \, \sigma$ mass and inclination constraints derived from the PK parameters of the {\sc tempo2} DDH solution in Table~\ref{tab:binary} (orthometric amplitude of the Shapiro delay, $h_3$, in dashed blue, the orthometric ratio, $\varsigma$, in solid blue and the rate of advance of periastron, $\dot{\omega}$, in solid orange), these constraints are calculated assuming that they are purely relativistic and that GR is the correct theory of gravity. The grey dotted lines show the \cite{1999A&A...350..928T} for the $M_{\rm c}$ of this system given its orbital period. The green circles indicate the best-fit masses and orbital inclination determined with the DDGR model. {\em Left}: $\cos i$ - $M_{\rm c}$ plane. {\em Right}: $M_{\rm p}$ - $M_{\rm c}$ plane. The grey area is excluded because $\sin i \, \leq \, 1$.} \label{figure:mass_mass} \end{figure} As shown in Table~\ref{tab:binary}, using the DDH solution, we can measure three PK parameters, $\dot{\omega}$, $h_3$ and $\varsigma$, with high significance. The mass and inclination constraints that result from these parameters according to GR are depicted graphically in Figure~\ref{figure:mass_mass}, where each triplet of lines depicts the mass and inclination constraints derived from their nominal values and $68.3\%$ confidence level uncertainties. \subsubsection{The rate of advance of periastron} \label{sec:omdot} If the rate of advance of periastron ($\dot{\omega}$) is purely relativistic, then in GR this effect yields the total mass of the system, in solar masses: \begin{equation} M \, = \, \frac{1}{T_\odot} \left[ \frac{\dot{\omega}}{3} (1 - e^2) \right]^{\frac{3}{2}} \left( \frac{P_{\rm b}}{2 \pi} \right)^{5/2}, \end{equation} where $T_\odot \equiv {\cal G M_{\odot}^{\rm N}} / c^3$, with ${\cal G M_{\odot}^{\rm N}}$ being the solar mass parameter \citep{2016AJ....152...41P}. Since this and the speed of light $c$ are defined exactly, the same applies to $T_{\odot}$, which has a numerical value of $4.9254909476412675...\, \rm \mu s$. The constraint on the total mass of the binary that results from $\dot{\omega}$ ($M = 1.96(2) M_{\odot}$) is depicted graphically by the orange lines in Fig.~\ref{figure:mass_mass}. From this, we obtain from Kepler's third law an inclination-independent estimate of the orbital separation, \begin{equation} a = c \left[ M T_{\odot} \left( \frac{P_{\rm b}}{2 \pi} \right)^2 \right]^{1/3} = 30.96 \, \rm Gm, \end{equation} a value that we will need below. However, for binary systems with wide orbits, the observed $\dot{\omega}$ might not be purely relativistic. Generally, the second most important contribution is a geometric contribution from the proper motion, $\dot{\omega_{\mu}}$. Re-arranging the expressions in \cite{1996ApJ...467L..93K}, we obtain: \begin{equation} \dot{\omega}_{\mu} \, = \, \frac{\mu}{\sin i} \cos \left( \Theta_{\mu} - \Omega \right),\label{eqn:omega_mu} \end{equation} where $\Theta_{\mu}$ is the position angle of the proper motion and $\Omega$ is the position angle of the line of nodes. This expression is valid if we use the ``observer's reference frame'', where the position angles start from the North and increase anti-clockwise through the East. In this system, an orbital inclination smaller than $90\, \deg$ implies that the line of sight component of the orbital angular momentum points towards the Earth. In the DDGR solution we get a nominal estimate of $i = 83.2 \deg $ or its equally likely counterpart, $180-i = 96.8 \deg$. Luckily, the sign of $\sin i$ for both the cases (which is what is needed in \ref{eqn:omega_mu}) is positive. Based on this value and our current estimate of $\mu$, the maximum value of $\dot{\omega}_{\mu}$ is $\sim \, 5 \, \times \, 10^{-8}\, \deg\, \rm yr^{-1}$; which is uniquely small among eMSPs. This is $\sim 250$ times smaller than the current measurement uncertainty for $\dot{\omega}$. Generally, other contributions to $\dot{\omega}$ are very small compared to $\dot{\omega}_{\mu}$, however, this is not the case in this pulsar. Using eq. (5.17) of \cite{Damour&Schafer1988}, we find that the contribution due to the Lense-Thirring effect caused by the spin of the pulsar has a maximum value of the order of: \begin{equation} \| \dot{\omega}_{\rm LT} \| = 5.8 \times 10^{-8} \, \deg\, \rm yr^{-1}, \end{equation} assuming the moment of inertia of the pulsar is $10^{38} \, \rm kg \, m^2$. This is very similar to our current estimate of $\dot{\omega}_{\mu}$. All of this means that the observed $\dot{\omega}$ is purely relativistic. It also implies that a two order of magnitude improvement of the precision of $\dot{\omega}$ will result in a similar improvement in the precision of $M$, i.e., an eventually achievable uncertainty of about $10^{-4} \, M_{\odot}$, an extraordinarily precise measurement of the mass of a MSP binary. \subsubsection{The Shapiro delay} \label{sec:shapiro} One of the main results in this paper is the precise measurement of the Shapiro delay. This is only possible given the high timing precision achievable with MeerKAT and, of course, the high orbital inclination of about $83^\circ$ (or $180- 83^\circ$). In Figure~\ref{figure:mass_mass}, we can see the mass constraints introduced, according to GR, by the two Shapiro delay parameters represented by blue lines, solid for $\varsigma$ and dashed for $h_3$ (see eqs. 22 and 23 in \citealt{2010MNRAS.409..199F}). By itself, the Shapiro delay already yields useful mass estimates: they already characterise the WD companion as a likely He~WD and the pulsar as likely massive, however, these constraints are not particularly precise. It is when this effect is combined with the the measurement of $\dot{\omega}$, we obtain an order of magnitude improvement on the precision of the mass measurements. This and other results will be discussed more quantitatively in section~\ref{section:chi2map}. The fact that all PK parameters cross at the same locations in the two panels of Fig.~\ref{figure:mass_mass} constitutes a successful test of GR. However, this is not of great interest given the low precision of the masses obtained via the Shapiro delay. Instead, we can think of this multiple coincidence of PK parameters as a confirmation of the basic validity of the mass-measuring method being used, and in particular as a verification of our assertion that $\dot{\omega}$ is a purely relativistic effect, i.e., it has no quantifiable classical contributions caused by e.g., the rotation of the companion. \subsubsection{Variation of the orbital period} For the masses determined by the DDGR model, the orbital decay caused by the emission of gravitational waves is negligible, $-3.8 \, \times \, 10^{-17}$. Much larger is the kinematic contribution to $\dot{P}_b$ ($\dot{P}_{b, \rm K}$) caused by the acceleration of the system in the gravitational field of the Galaxy (this also includes an almost negligible contribution from the Shklovskii effect). Using the same methods as those used in section~\ref{sec:pdot}, we estimate $\dot{P}_{b, \rm K}\, = \, -0.80\, \times\, 10^{-12}$ for the NE2001 distance ($d \, \sim \, 4.0\,$kpc) and $-0.44\, \times\, 10^{-12}$ for the YMW16 distance $d \, \sim \, 2.2\,$kpc. Fitting for $\dot{P}_{b}$ in the DDH model (something not done in the solution presented in Table~\ref{tab:binary}), we obtain $\dot{P}_{b} \, = \, 9\, \pm 6 \, \, \times \, 10^{-12}$ (68.3 \% confidence limit). This is 2-$\sigma$ consistent with the much smaller expectation for the kinematic contribution to $\dot{P}_b$. This means that we will have to improve the precision of $\dot{P}_{b}$ by more than one order of magnitude in order to start detecting the kinematic contribution. This is desirable since a precise measurement of the kinematic $\dot{P}_b$ can yield a precise distance to the system \citep{1996ApJ...456L..33B,StairsEtAl1998}; it is also achievable because the precision of the measurement of $\dot{P}_b$ will improve dramatically over the next few years with continued MeerKAT timing of the pulsar, particularly with the UHF receiver. However, without the TOAs from that receiver, we cannot yet simulate how long it will take until a the measurement of $\dot{P}_{b, \rm K}$ can yield a precise distance to the pulsar. Detailed simulations including the UHF data will be published elsewhere. \subsubsection{Variation of the projected semi-major axis and the Einstein delay} The proper motion also produces a secular variation of the semi-major axis. Again, re-arranging the expressions in \cite{1996ApJ...467L..93K} and using the convention described in section~\ref{sec:omdot}, one obtains: \begin{equation} \dot{x}_{\mu}\, = \, x\, \mu \cot i \sin(\Theta_{\mu} - \Omega), \end{equation} which for PSR~J0955$-$6150\, yields an estimate\footnote{This is assuming the nominal value of the proper motion, which is only 1.5-$\sigma$ significant} of at most $\pm \, 5 \, \times \, 10^{-17} \, \rm lt-s\, s^{-1}$. Fitting for $\dot{x}$ in the DDH model (something that was also not done in the solution presented in Table~\ref{tab:binary}), we obtain $\dot{x} \, = \, 4 \, \pm \, 6\, \times\, 10^{-15} \rm lt-s\, s^{-1}$. The uncertainty in this measurement is still $\sim 130$ times larger than the maximum value of $\dot{x}_{\mu}$. The $\dot{x}_{\mu}$ is unusually small among eMSPs, partly because of the small proper motion, but also because of the high inclination. For this reason, we will now estimate the future ability to measure the Einstein delay, $\gamma$. For timing baselines that are much shorter than the precession timescale of binary (which is certainly the case for PSR~J0955$-$6150, where the precession timescale is $360\, \deg / \dot{\omega} \sim 0.24\,$ Myr), both $\dot{x}_{\mu}$ and $\gamma$ are hopelessly correlated. The reason for this is that, under this condition, the effect of $\gamma$ on the timing is merely to produce an additional secular, linear contribution to the observed variation of the projected semi-major axis $\dot{x}_{\rm obs}$, this is given by eq. 25 of \cite{2019MNRAS.490.3860R}: \begin{equation} \dot{x}_{\rm obs} \, = \, \dot{x}_{\mu} - \frac{\gamma \dot{\omega}}{\sqrt{1 - e^2}} \sin \omega. \end{equation} For the masses in the DDGR solution in Table~\ref{tab:binary}, GR predicts $\gamma \, = \, 0.536 \, \rm ms$. From this, we estimate that the second term on the right is $- \, 1.7 \, \times \, 10^{-17} \, \rm lt-s\, s^{-1}$, still twice as small as the maximum value for $\dot{x}_{\mu}$. Thus, although $\dot{x}_{\mu}$ is exceptionally small in this system, the effect of $\gamma$ in the timing is still smaller than that, and therefore $\gamma$ is not independently measurable - unless the proper motion proves to be much smaller than our current estimate. This superposition with the $\dot{x}$ from proper motion prevents the measurement of $\gamma$ in most eccentric, wide binary pulsars, the exception being, to date, the system studied by \cite{2019MNRAS.490.3860R}, PSR~J0514$-$4002A. \subsection{Bayesian mass estimates assuming GR} \label{section:chi2map} We now proceed to estimate the component masses and their uncertainties using a self-consistent Bayesian approach commonly used for this purpose (see e.g., \citealt{2002ApJ...581..509S}); this is based on the quality of the {\sc tempo2} timing fit (measured by the resulting $\chi^2$) for the relevant physical parameters we want to measure, in this case the orbital inclination and the masses. Because the kinematic effects on $\dot{\omega}$ and $\dot{x}$ are not measurable, we have no information whatsoever on the line of nodes, $\Omega$ (see sections~\ref{sec:omdot} and \ref{sec:shapiro}). This means that, instead of mapping the $\chi^2$ for a 3-D space, with axes given by $\Omega$, $\cos i$ and $M$, as in \cite{2011MNRAS.412.2763F} and \cite{2019ApJ...870...74S}, we can just map the $\cos i$ - $M$ space, as done by \cite{2017MNRAS.465.1711B} and \cite{2019ApJ...881..165Z}. The previous discussion also implies that, within this restricted parameter space, we can safely assume that GR correctly accounts for all relativistic effects; for this reason we used the DDGR orbital model to do the mapping. We refer the reader to \cite{2017MNRAS.465.1711B} for a detailed description of how the 2-D probability density functions (pdfs) are derived. For the PSR~J0955$-$6150\, system, the 2-D pdfs are depicted in the main panels of Fig.~\ref{figure:mass_mass} by the closed black contours; these include 68.3 and 95.4 \% of the total 2-D probability, which is equivalent to the 1 and 2-$\sigma$ percentiles. The 1-D marginalisation of these 2-D pdfs along the relevant axes are presented in the side panels of that figure. Projecting this 2-D pdf along different axes results in the mass and inclination estimates reported in the last column of Table~\ref{tab:binary}, which we also list in the abstract. These are fully consistent with the DDGR estimates, although slightly less precise. \section{Geometry of PSR~J0955$-$6150\ from pulse structure data} \label{sec:rvm} The variation of the position angle, $\psi$, of the linearly polarised component as shown in the lower panel of Fig.~\ref{figure:prof} is often described by the Rotating Vector Model (RVM; \citealt{Radhakrishnan&Cooke}). The RVM describes $\psi$ as a function of the pulse phase $\phi$, depending on the magnetic inclination angle, $\alpha$ and the viewing angle, $\zeta$, which is the angle between the line of sight vector and the pulsar's spin. We show its modified form as presented in \citet{jk19}: \begin{equation} \label{eqn:rvm} {\rm \psi} = {\rm \psi}_{0} + {\rm arctan} \left( \frac{{\rm sin}\alpha \, {\rm sin}(\phi - \phi_0 - \Delta)}{{\rm sin}\zeta \, {\rm cos}\alpha - {\rm cos}\zeta \, {\rm sin}\alpha \, {\rm cos}(\phi - \phi_0 - \Delta)} \right) \end{equation} where the position angle $\psi$ increases \emph{clockwise} on the sky. This definition of $\psi$ is opposite to the astronomical convention (also known as the ``observers'' convention or the PSR/IEEE convention defined in \citealt{psrchive_ieee}) that $\Psi$ increases counterclockwise on the sky, from North to East (cf.~\citealt{DamourTaylor1992, EverettAndWeisberg2001}). Therefore, when fitting Eqn.~\ref{eqn:rvm} to position angles measured using the astronomical convention, as in Fig,~\ref{figure:prof}, we invert the sign of the numerator in Eqn.~\ref{eqn:rvm}. See \cite{ksv+21} for details. In the above, $\phi_0$ is the pulse longitude at which $\psi=\psi_{0}$ and $\zeta=\alpha+\beta$, where $\beta$ is the minimum impact angle of the line of sight with respect to the magnetic axis. The additional term $\Delta$ is is defined as \[ \Delta(\phi)= \begin{cases} \Gamma, & a \leq \phi \geq b\\ 0, & \text{otherwise} \end{cases} \] where $a$ and $b$ are the start and end of the range of phases identified as the pre/post-cursor and $\Gamma$ is the free parameter that allows a shift in longitude (owing to a variation of either the emission height or the refractive properties of the magnetospheric plasma) Performing a fit of Eqn.~\ref{eqn:rvm} using the method of \cite{jk19} to the position angle of PSR~J0955$-$6150{} as shown in Fig.~\ref{figure:prof}, we obtain for $\Delta \equiv 0$, $\alpha = 73.7 \pm0.6$ deg and $\zeta = 77.4\pm 0.7$ deg. Interestingly, the determined $\phi_0=86.5\pm0.1$ places the fiducial plane (given by the magnetic and rotation axes and the line-of-sight to the observer) at a longitude where the circular polarisation shows its sense reversal, giving the geometrical interpretation of the position angle already some credibility. In the resulting solution, the pre/post-cursor's position angle is separated from the main pulse by an orthogonal shift of 90 deg, which is not uncommon for emission from the opposite pole (e.g.~\citealt{jk19}). For binaries where the spin of the pulsar is aligned with the orbital angular momentum, in the above definition of angles, $\zeta \equiv i$ (i.e.~$i$ is defined as implemented in {\sc Tempo} or {\sc Tempo2}, see \citealt{ksv+21} for details). Our measurement of the inclination angle from timing (see Table~\ref{tab:binary}) of $i=83.2\pm 0.4$ deg is significantly different from the value of $\zeta$ obtained from RVM fits. Allowing $\Gamma$ to obtain a non-zero value in the fit, i.e.~separating the emission heights of main pulse and the pre/post-cursor, does not improve the fit (as indicated by computing the Bayesian Information Criterion) and yields a very similar geometry, $\alpha = 72.4 \pm0.9$ deg and $\zeta = 76.2\pm 0.9$. The resulting $\Gamma = -6 \pm 4$ deg is still consistent with no shift, so that we will assume $\Delta\equiv0$ in the following. It is of course possible that the position angle swing of recycled pulsars is not well described by a RVM. The clear deviation of the measured position angles in the longitude range at about 100 deg may be an indication of this. Indeed, there are clearly a number of average pulse profiles of recycled pulsars that are apparently difficult, or impossible, to describe with a RVM. We refer to the recent discussion in \cite{ksv+21} for more details. In such cases, it may be possible that the underlying magnetic field geometry may be non-dipolar (e.g.~caused by sweep-back of the magnetic field lines in the compact magnetosphere of millisecond pulsars that lead naturally to large emission emission heights relative to the light cylinder). Alternatively, an average profile may mask underlying orthogonal jumps in the position angle that distort the measured average, as known from non-recycled pulsars (e.g.~\citealt{gl95}). Interestingly, the deviation from the RVM fit around longitude 100 deg is indeed where the model places a transition between two orthogonal branches of the RVM. We note that the emission over a large longitude range, especially the position angles of the nearly completely polarised pre/post-cursor provide a significant ``leverage arm'' that is able to constrain possible geometries very significantly, as it is well known from interpulse pulsars (e.g.~\citealt{jk19}). Moreover, recently, despite the overall difficulty in describing the position angles of recycled pulsars with RVMs, a number of cases has been presented where the orbital inclination angle determined from RVM-fits was indeed in very good agreement with the value inferred from pulsar timing (see e.g.~\citealt{gfg+21} and \citealt{ksv+21}). Motivated by these previous findings, and with the described caveats in mind, we investigate if the difference between $\zeta$ and $i$ could also be due to our assumption of spin-orbit alignment. Given the unknown nature of the binary evolution of eMSPs, it is prudent to consider the possibility that the spins are indeed not aligned. In such a case, we can relate $\zeta$ and $i$ more generally following \cite{DamourTaylor1992}: \begin{equation} \label{eqn:sg1} \cos\zeta = \sin \delta \sin(180- i) \cos \Phi_p - \cos (180-i) \cos \delta , \end{equation} where $\delta$ is the misalignment angle between the pulsar spin axis and the orbital momentum vector.\footnote{Note that in \cite{DamourTaylor1992}, the inclination angle is defined as $i_{\rm DT92}=180-i$, which we accounted for.} In the case of $\delta>0$, the pulsar spin will precess about the orbital angular momentum vector with a phase angle $\Phi_p$, as it has been observed for a number of relativistic double neutron star systems (see e.g.~\citealt{kra14}). Hence, \begin{equation} \label{eqn:sg3} \Phi_p = \Phi_0 + \Omega_{\rm geod} ( t-t_0), \end{equation} In our case of PSR~J0955$-$6150, the expected precession rate, $\Omega_{\rm geod}$, will be negligible, and over the timing baseline of $\sim 10$ years we can safely assume $\Phi_p= \Phi_0 = const$. With this in place we perform Markov-Chain Monte-Carlo (MCMC) fits to the position angle curve applying Eqns. \ref{eqn:rvm} and \ref{eqn:sg1} simultaneously. We assume $i$ to be identical to the value determined by pulsar timing (or $180-i$ deg, respectively). The posterior distributions of the model parameters are shown in Fig.~\ref{fig:rvmposteriors}. It is interesting to note that the posterior distribution of $\delta$, while broad, has two clear peaks just below 10 deg and around 160 deg. In both (prograde and retrograde) cases, $\delta$ differs significantly from $\delta=0$ or 180 deg, respectively. The first peak has a much larger amplitude. Using its location as our most likely value, we obtain $\delta = 6.1$ deg while if we constrain for the prograde case ($0\le\delta\le 90$ deg), we obtain $\delta > 4.8$ deg with 99\% CI. This result suggests that there could indeed be (prograde) spin-orbit misalignment in this system. We note that when inspecting the retrograde solution ($90\le\delta\le180$ deg), we find the peak of the PDF as $\delta = 159.3$ deg and $\delta < 160.8$ deg with 99\% CI. The ratio between the peak probability of $\delta$ for the prograde and retrograde case is 1.59. \begin{figure} \centering \includegraphics[width=\textwidth]{0955_rvm.pdf} \caption{Posterior distributions resulting from applying the Rotating Vector Model (RVM) to the observed position angle variation, allowing for a non-zero misalignment between the spin axis and the orbital momentum vector, ie, $0< \delta < 180$ deg.} \label{fig:rvmposteriors} \end{figure} \begin{table}[h] \label{table:rvm} \caption[]{Measured parameter values and their 68.3\% C. L. for the different kinds of Rotating Vector Model (RVM) fits to the position angle of the linear polarisation of PSR~J0955$-$6150, as shown in Fig. \ref{figure:prof}.} \def1.2{1.2} \centering \begin{tabular}{l c c c c c c r} \hline \hline Description & Magnetic & Co-latitude & Impact angle& Emission & Spin misalignment &\\ & inclination,& of spin axis, & of line of sight, & height offset,& angle, & Technique\\ & $\alpha$ (deg) &$\zeta$ (deg) &$\beta$ (deg) & $\Gamma$ (deg) &$\delta$ (deg) & Reference \\ \hline Classic RVM &$73.7 \pm 0.6$&$77.4 \pm 0.7$&$3.7 \pm 0.9$&$\equiv 0$&$\equiv 0$& 1 \\ RVM with varying&$72.4 \pm 0.9$&$76.2 \pm 0.9$&$3.8 \pm 1.3$&$-6 \pm 4$&$\equiv 0$& 2\\ emission height &&&&&& \\ RVM with spin- & $73.7 \pm 0.3$ & $77.4\pm 0.3$ & $3.7\pm 0.5$ &$\equiv 0$& $6.1^{+16}_{-1.3}$$\dagger$ & 3\\ orbit misalignment &&&&&&\\ \hline \end{tabular} \tablebib{(1)~\cite{Radhakrishnan&Cooke}, (2)~\cite{jk19}, (3)~This work; See Section \ref{sec:rvm}} \tablefoot{$\dagger$ This value assumes a likely prograde misalignment. The slope of the distribution to the left of the maximumum likelihood point is so steep that after integrating about 6\% of the probabilities (until 4.8 degrees), the distribution ends. Since in all our measurements, we quote 68\% confidence interval by integrating 34\% of the probabilities on each side of the maximum likelihood point, we can consider 4.8 degrees as both the 68\% and 99\% lower limit. } \end{table} In order to verify our method, we repeated the exact same procedure for PSR J1811$-$2405 whose original RVM fits were presented in \cite{ksv+21}. Following a similar approach, we obtain a distribution of $\delta$ that is well in agreement of spin-orbit alignment, i.e.~the corresponding distribution peaks at $\delta=0$ as expected from circular He-WD binaries. \section{Discussion} \label{section:Discussion} Looking at Table~\ref{table:eccentric_MSPs}, we see that the mass of PSR~J0955$-$6150\, is intermediate between that of PSR~J1950+2414 ($\sim 1.50\,M_{\odot}$) and that of PSR~J1946+3417 ($\sim 1.83\,M_{\odot}$). The NS mass distribution observed in these systems seems to be similar to that observed among MSPs in systems with He~WDs in general. This is what should be expected according to both \cite{2014ApJ...797L..24A} and \cite{2021ApJ...909..161H}. This reinforces the idea that eMSPs have a broad range of masses, which disfavours the hypotheses associated with sudden phase transitions in the interior of the MSP or its super-Chandrasekhar WD progenitor as the origin of the enhanced eccentricity. As mentioned previously, e.g. the RD-AIC hypothesis predicts that all MSPs formed that way should have a mass smaller than $\sim 1.3 \, M_{\odot}$, which is not observed. The internal phase transition theory does predict larger NS masses, but with a relatively narrow range, which is not observed either. However, as we will see below, our new measurement ($0.254(2)\,M_\odot$) of the mass of the WD companion to PSR~J0955$-$6150\, independently disfavours {\em all} hypotheses suggested to date for the formation of eMSPs. The reason is that its mass is significantly smaller than the predictions of \cite{1999A&A...350..928T} for its orbital period, and this $P_{\rm b}-M_{\rm WD}$ correlation is the backbone in all hypotheses for the formation of eMSPs. More specifically, using eqs.~(20+21) in \cite{1999A&A...350..928T}, for an orbital period of 24.58~d, the predictions for $M_{\rm c}$ vary between $\sim 0.271\, M_{\odot}$ for Population~I progenitors (corresponding to a metallicity of $Z=0.02$ and independent of the initial mass of the low-mass progenitor star) and $\sim 0.300\, M_{\odot}$ for a Population~II progenitor ($Z=0.001$). At first sight, a WD mass deviation of order $0.02\;M_\odot$ may not seem like a lot. However, the difference of $0.017\;M_{\odot}$ relative to the lower limit of the $P_{\rm b}-M_{\rm WD}$ predictions, is 7.4 times larger than the measurement uncertainty. And more importantly, for the observed $M_{\rm c}$, the corresponding orbital periods are only about 14~d for Population~I progenitors of the He~WD and 6~d for Population~II progenitors. That is a very significant deviation from the observed value of 24.58~d. Previous comparison with wide-orbit binary MSPs, although for binaries without precise mass measurements, has indicated that the $P_{\rm b}-M_{\rm WD}$ correlation may overestimate the WD masses \citep{StairsEtAl2005}. The small WD mass of PSR~J0955$-$6150\, may possibly be explained by an unusual high metallicity content of its progenitor star or due to incorrect input physics in current modelling of the correlation. However, it is important to mention that independent theoretical support for the applied $P_{\rm b}-M_{\rm WD}$ correlation has been provided by several more recent studies \citep[e.g.][]{2011ApJ...732...70L,2016A&A...595A..35I,sk21}; see Fig.~14.14 in \citet{tv22} for an updated compilation of data. The new result for PSR~J0955$-$6150\, is unique among eMSPs, for which previously measured He~WD masses conform to the relation found by \cite{1999A&A...350..928T} --- although the companion to PSR~J1946+3417 is also slightly less massive than the prediction. The small value of $M_{\rm c}$ for, in particular, PSR~J0955$-$6150\, is a highly significant result, and yet puzzling as all the suggested hypotheses naturally produce the observed range of orbital periods of eMSPs. We will now look at possible explanations for this, and its implications. \subsection{On the measurement precision and reliability of $\dot{\omega}$} A possibility is that our measurement of $\dot{\omega}$ is hampered by the low quality of earlier Parkes measurements. If this were true, then future MeerKAT measurements are bound to correct this situation very quickly. Furthermore, when we exclude the earliest filterbank data (including only the more reliable coherently dedispersed data taken since June 2015), we obtain very similar masses to those reported above: $M_{\rm c} \, = \, 0.253(3)$ and $M_{\rm p} \, = \, 1.70(3)\, M_{\odot}$. Including only the high-quality MeerKAT and Parkes data taken since 2019, we obtain $M_{\rm c} \, = \, 0.252(3)$ and $M_{\rm p} \, = \, 1.69(3)\, M_{\odot}$. All these values are consistent well within their uncertainties; this means that those early data do not have a significant weight on our mass estimates, and certainly they do not bias them appreciably. \subsection{Mass loss from the WD?} Since our mass measurement appears to be reliable, the deviation from the predictions of \cite{1999A&A...350..928T} is real. A possible explanation is that the mass deficiency of the companions is caused by ablation by the pulsar winds. Indeed, the two systems with larger mass deficiencies, PSR~J0955$-$6150\, and J1946+3417, are associated with $\gamma$-ray emission (see \citealt{CamiloEtAl2015,2019ApJ...871...78S}). Again, this is difficult to reconcile with the fact that no significant outgassing and ablation is seen in any of the eccentric MSP+He~WD systems. Such outgassing would be readily detected by the existence of eclipses and DM variations, such as those observed in many eclipsing binary pulsars. Such phenomena are not detectable in our observations of PSR~J0955$-$6150\, at any orbital phase, even at superior conjunction. \subsection{Something unique to eccentric MSPs?} If mass loss from the WD cannot explain the measured low mass, we must entertain the possibility that this low mass is somehow linked to the fact that this system is an eccentric MSP. First, given the ability to measure $\dot{\omega}$ in these systems, we can obtain unusually precise measurements of the masses of their pulsars and He~WDs. Thus, it is in principle possible that the existence of under-massive He~WDs is a common occurrence among the circular MSP+He~WD systems; a fact that could have been undetected until now because of the low precision for the measurements of the masses in the vast majority of those systems. However, this is unlikely, since there is strong independent evidence that the T\&S99 relation really is universal (see e.g., \citealt{2014ApJ...781L..13T}): even the highly precise measurements for the two WDs in the triple system \citep{2020A&A...638A..24V} conform exactly to the prediction of \cite{1999A&A...350..928T}. Thus we conclude the low mass of the companion to PSR~J0955$-$6150\, could be an important, but thus far hard to interpret, clue on the poorly understood formation of eMSPs. However, as discussed below, this measurement rules out current hypotheses for the formation of these systems, if one assumes that the unique orbital period--mass correlation for He~WDs \citep{1987Natur.325..416S,1995MNRAS.273..731R,1999A&A...350..928T,2011ApJ...732...70L,2016A&A...595A..35I}, which is based on the well-known correlation between stellar radius and degenerate core mass for low-mass giant stars \citep{1971A&A....13..367R}, holds during the formation of MSP+He~WD systems. \begin{figure} \centering \includegraphics[width=0.60\textwidth, angle=-90]{J0955-AIC.pdf} \caption{Distribution in the $(P_{\rm b},\,e)$--plane of eMSPs simulated via the RD-AIC scenario. The red circle represents PSR~J0955$-$6150. The black solid star is the result of a symmetric ($w=0$) AIC from a $1.96\;M_{\odot}$ super-Chandrasekhar WD with a pre-AIC orbital period, $P_{b,0}=14.2\;{\rm d}$ (open star) and a He~WD companion star of mass, $M_{\rm c}=0.254\;M_{\odot}$. The V-shaped coloured distributions are for the same system but applying a kick of $w=5$, 20, and $50\;{\rm km}\,{\rm s}^{-1}$, respectively, in a random (isotropic) direction. The grey and light-grey distributions superimposed are the outcome of simulations with more relaxed assumptions on the input physics parameters --- see text. The RD-AIC scenario fails to explain PSR~J0955$-$6150.} \label{figure:RD+AIC} \end{figure*} \subsection{PSR~J0955$-$6150\, independently rules out phase-transition models} According to the $P_{\rm b}-M_{\rm WD}$ correlation from \citep{1999A&A...350..928T}, the companion star mass of {$M_{\rm c}\simeq 0.254\;M_\odot$ for PSR~J0955$-$6150\, reveals that this He~WD companion must have had an orbital period between $P_{b,0}=6.19\;{\rm d}$ (Pop.~II) and $P_{b,0}=14.2\;{\rm d}$ (Pop.~I)} at the time of its formation, depending on the chemical composition of its progenitor star \citep[see eqs.~20+21 in][]{1999A&A...350..928T}. Following as an example the RD-AIC scenario, from the current pulsar mass of $M_{\rm p}\simeq 1.71\;M_\odot$, we can estimate the mass of its super-Chandrasekhar mass WD progenitor, taking into account the loss of gravitational binding energy in the AIC process. The NS binding energy depends on the still somewhat uncertain equation-of-state. Here, we adopt the binding energy calculation from \citet{1989ApJ...340..426L}, which as a result reveals a pre-AIC WD mass, $M_{\rm AIC}=1.96\;M_\odot$, i.e. corresponding an instantaneous mass loss in the AIC process of about $\Delta M \simeq 0.246\;M_\odot$. Given now the pre-AIC orbital period (depending on metallicity) and mass of the collapsing WD, we can calculate the post-AIC orbital parameters and compare to those of PSR~J0955$-$6150. The post-AIC eccentricity (assuming no kick at birth) is simply given by: $e=\Delta M/M_{\rm T}$ (where $M_{\rm T}=M_{\rm p}+M_{\rm c}$), which for the derived masses yields $e\simeq 0.125$. This value is only marginally larger than the observed eccentricity of $e=0.1175$; and adopting a slightly smaller value for the binding energy ($\Delta M=0.231\;M_\odot$) would easily reproduce the exact value of the observed eccentricity. However, the problem is to reproduce the post-AIC (present) orbital period. Assuming first a high metallicity environment ($Z=0.02$, i.e. Pop.~I), means that the pre-AIC orbital separation was $P_{b,0}=14.2\;{\rm d}$ from the orbital period--mass correlation. For a symmetric collapse (i.e. with no kick), the change in orbital period is given by\footnote{See e.g. \cite{tv22}.}: \begin{equation} \frac{P_{\rm b}}{P_{b,0}} = M_{\rm T}\,\sqrt{\displaystyle\frac{M_{\rm T}+\Delta M}{(M_{\rm T}-\Delta M)^3}} \label{eq:P_SN-symm} \end{equation} such that the present (post-AIC) orbital period should be $P_{\rm b}=18.4\;{\rm d}$, which is significantly smaller than the observed value of 24.58~d. This discrepancy is only exacerbated if we assume a low-metallicity (Pop.~II) chemical abundance of the progenitor star of the current He~WD, which would then produce a post-AIC orbital period of only 8.05~d. Note that no orbital evolution of PSR~J0955$-$6150\, has taken place since its formation. The tidal torques and rate of circularization due to GR are minuscule. To explore whether an applied momentum kick to the newborn NS could resolve the problem of reproducing the observed values of ($P_{\rm b},\,e$), we ran a number of numerical Monte Carlo simulations. We assumed the pre-AIC system was circular with an orbital period of $P_{b,0}=14.2\;{\rm d}$ (Pop.~I star progenitor). Figure~\ref{figure:RD+AIC} shows the results of our simulations. The open star marks the pre-AIC system. The solid star marks the post-AIC system for a symmetric ($w=0$) AIC event. The yellow, purple and light blue points are the outcome of AIC events with a kick velocity of $w=5$, 20 and $50\;{\rm km\,s}^{-1}$, respectively, and assuming a random (isotropic) direction of the kick. The equations governing the outcome are found in e.g. \citet{hil83}. We see that none of the simulated systems come close to the parameter space in vicinity of PSR~J0955$-$6150, and thus these simulations based on the RD-AIC model are not successful in explaining the formation of this eMSP. To take into account the uncertainties in the gravitational binding energy for the NS, and also for the orbital period--mass correlation, we ran two extra sets of simulations, where, in both cases: the pre-AIC mass ($M_{\rm AIC}$) was randomly drawn from a flat probability distribution between $1.86-2.06\;M_\odot$; the pre-orbital period ($P_{b,0}$) was randomly drawn from a flat probability distribution between $12.2-16.2\;{\rm d}$; and the mass of the present He~WD ($M_{\rm c}$) was randomly drawn from a flat probability distribution between $0.251-0.257\;M_\odot$. The grey and light grey points show the resultant post-AIC systems assuming randomly-directed kicks of $w=20\;{\rm km\,s}^{-1}$ and $w=50\;{\rm km\,s}^{-1}$, respectively, during the AIC events. Even choosing such large AIC kicks is probably unrealistic \citep[see e.g.][]{2006ApJ...644.1063D,2018ApJ...865...61G}. Nevertheless, even relaxing generously on the assumed physical parameters prevents us from reproducing a system similar to PSR~J0955$-$6150. Therefore, we conclude that the RD-AIC hypothesis of \citet{2014MNRAS.438L..86F} can no longer be considered a potential model for explaining the existence of eMSPs. Whereas the RD-AIC model could explain very well the formation of the eMSPs known at that time, PSR~J2234+0611 and PSR~J1946+3417, it fails to explain PSR~J0955$-$6150\, due to its relatively low-mass He~WD companion, which dictates a short orbital period that cannot be reproduced. The same arguments can be used to rule out the internal phase transition model proposed by \cite{2015ApJ...807...41J}, since it predicts similar constant losses in binding energy during the phase transition, \subsection{PSR~J0955$-$6150\, rules out H-shell flash models}\label{subsec:rule-out-flashes} According to \cite{2014ApJ...797L..24A}, the eMSPs were produced like regular MSP+He~WD systems, which likewise follow the predictions of \cite{1999A&A...350..928T}. Under this hypothesis, the orbital eccentricity was caused by eccentricity pumping via a circumbinary disk of material ejected by H-shell flashes in the outer layers of the proto-He~WD. These H-shell flashes are likely to happen in a wide range of He~WD masses between $\sim \, 0.16-0.32\;M_{\odot}$ \citep[depending on metallicity,][]{2013A&A...557A..19A,2016A&A...595A..35I}, which should then occur in the corresponding range of orbital periods observed for the eMSPs. The expected mass loss via RLO from such vigorous thermonuclear runaway episodes is only of the order of $10^{-5}$ to $10^{-3} \, M_{\odot}$, a difference that cannot, by itself, explain the small mass of the companion to PSR~J0955$-$6150. Furthermore, the ejection of such a small amount of matter is unlikely to significantly change the semi-major axis of the binary. Depending on the specific orbital angular momentum carried away by the ejected material, if anything, this ejection of should actually {\em decrease} the orbit, thus bringing the new orbital period closer to the \cite{1999A&A...350..928T} prediction for the slightly decreased He~WD mass. Thus, even after acquiring the new eccentricity, the system should retain values of $M_{\rm c}$ and $P_{\rm b}$ close to the relation predicted by \cite{1999A&A...350..928T}. Regarding the remaining two recent hypotheses by \citet{2021ApJ...909..161H}, related to H-shell flashes (thermonuclear rocket effect), and \citet{Ginzburg21} on resonant convection, it is not obvious that they are successful in the end. The former model has the advantage of begin able to explain a broad range of eMSPs (roughly $18-45\;{\rm d}$ according to the authors), but the assumption of an instantaneous kick may not apply in reality. Furthermore, the predicted range of WD masses for which H-shell flashes are expected \citep{2016A&A...595A..35I} goes much beyond the narrow range of WD masses for eMSPs. The latter model has perhaps the weakness of not explaining well why some MSP binaries with similar orbital periods as the eMSP did not experience resonant interactions and remained in circular orbits with $e\simeq 10^{-5}$ \citep[see fig.~1 in][]{2019ApJ...870...74S}. Nor is it clear if the model can explain the offset of PSR~J0955$-$6150\, from the $P_{\rm b}-M_{\rm WD}$ correlation. \subsection{Is the misalignment angle a clue to the origin of PSR~J0955$-$6150?}\label{subsec:clue} It is expected from binary star evolution that the spin axis of the MSP aligns with the orbital angular momentum vector as a result of mass transfer. Here we follow the arguments by \citet{tv22}. During RLO, accretion torques align the spin axis of the first-born compact object (here the NS) with the orbital angular momentum vector during the recycling process \citep[e.g.][]{hil83,bv91,ba21}. Observational evidence for such an alignment to actually occur in nature was demonstrated for LMXBs by \citet{gt14}, who found agreement between the viewing angles of binary MSPs (as inferred from $\gamma$-ray light-curve modelling) and their orbital inclination angles. Therefore, it is reasonable to assume $\delta\simeq 0$ for recycled MSPs (i.e. that the MSP spin axis is, at least close to, parallel to the orbital angular momentum vector of the binary system. In this work, we have demonstrated that for PSR~J0955$-$6150\, if assuming an ideal dipolar magnetic field, then, surprisingly, $\delta > 4.8 \deg$. The combined unexpected result of a significant misalignment angle and this MSP being an eMSP, makes it tempting to suggest that there might be a relation between between these two circumstances. To test this idea, it is therefore important to measure (or significantly constrain) the value of $\delta$ for all other eMSP systems. In addition, we may ask: which progenitor scenarios may account for such misalignment? At first sight, the ``thermonuclear rocket'' hypothesis of \cite{2021ApJ...909..161H} may be a natural way to explain such a misalignment, if indeed the orbit is tilted as a result of thermonuclear runaway burning events (e.g. H-shell flashes). To investigate this question, we simulated a large population of NS+ELM~He~WD systems similar to PSR~J0955$-$6150\, undergoing a large H-shell flash with a relatively large kick of $w=8\;{\rm km\,s}^{-1}$ (in a random direction), a large amount of ejected material of $\Delta M=10^{-3}\;M_\odot$ and a pre-shell orbital period of $P_{\rm b}=20.0\;{\rm d}$. All systems had $M_{\rm p}=1.71\;M_\odot$ and $M_{\rm c}+\Delta M=0.255\;M_\odot$ (to leave a final $0.254\;M_\odot$ WD). The resulting misalignment angles are always $\delta < 4.7^\circ$. Even though we adopted rather large values of $w$ and $\Delta M$ in our simulation, the ``thermonuclear rocket'' scenario of \citet{2021ApJ...909..161H} seems to produce too small misalignment angles to explain the observed value of $\delta$ in PSR~J0955$-$6150. Potentially more serious is that the assumption in this hypothesis of an instantaneous kick (compared to the timescale of $P_{\rm b}$) is likely not justified. Assuming instead mass loss in the form of a fast wind (i.e. the Jeans' mode over a timescale of several times $P_{\rm b}$) would cause an orbital widening to only $\Delta P_{\rm b}\simeq 0.016\;{\rm d}$, i.e. the orbit remains more or less constant with a negligible eccentricity increase. Finally, as discussed in Section~\ref{subsec:rule-out-flashes} and similarly to the other models discussed in this paper, there are issues with reproducing the observed orbital period for the observed WD mass in PSR~J0955$-$6150\,. We conclude therefore, that none of the formation hypotheses suggested in the literature to date is able to explain well the low mass of the He~WD companion to PSR~J0955$-$6150\, and its orbital misalignment. This means that the formation of eMSPs remains a major puzzle of close binary stellar evolution. \section{Summary and conclusions} \label{sec:summary} In this paper, we described our observations of PSR~J0955$-$6150\, with the MeerKAT and Parkes telescopes. Previously, this pulsar did not have a phase-coherent timing solution, we report it here for the first time. The high S/N ratio and the resultant high-precision timing obtained with MeerKAT was instrumental for the detection and precise measurement of three PK parameters; the measurement of the rate of advance of periastron was also made possible by the large timing baseline and the fact that the system is unusually eccentric ($e \, = \, 0.11$) for an MSP, which makes it a member of a growing class of MSPs with He~WD companions with eccentric orbits. The measurements of these three PK parameters yielded precise mass measurements, which we discuss in light of the different hypotheses that have been advanced to explain the formation of these unusual and intriguing systems. One intriguing finding is that the He~WD mass is significantly lower than predicted by current stellar evolution models. The significance of this finding is very important and could be a clue to new progress on the poorly understood formation mechanism for these eMSP systems. It is clear, however, that it independently rules out all of the proposed formation hypotheses presented until now, since in all these models the systems should obey the $P_{\rm b}-M_{\rm WD}$ correlation \citep{1999A&A...350..928T}. Additionally, if we assume the pulsar's radio emission is purely dipolar where the position angle of the linear polarisation ideally follows the RVM, we find a $\delta > 4.8 \deg$ misalignment between the spin axis of the pulsar and the orbital angular momentum. While this result must be take with a pinch of salt due to the yet not fully understood nature of millisecond pulsar polarisation, it is nevertheless an interesting hint that could be solidified by analysing other eMSPs. None of the formation hypotheses predict such a large misalignment, except for the ``thermonuclear rocket'' of \cite{2021ApJ...909..161H}. Assuming the assumptions behind this hypothesis to hold true, our simple toy simulation of this model indicates that the resulting misalignment angles are likely to be too small to explain the observed value of $\delta$, although more work is needed to fully exploit this scenario. We believe that our measurement of a misalignment angle is an important datum for understanding the origin of eMSPs. Continued observations with MeerKAT, in particular a second orbital campaign done with the UHF band, will greatly improve the precision and accuracy of the measurement of $\dot{\omega}$ and of the Shapiro delay as well, and allow a much improved determination of the masses of the components in this system and an improved $\dot{\omega}$ - $h_3$ - $\varsigma$ test of GR. Continued timing will also allow a much improved measurement of $\dot{P}_b$, this will eventually result in a much more precise distance to the system. The polarimetry of the system at UHF bands, where the pulsar is much brighter, and especially a detailed study of the $\gamma$-ray emission of the system (Paper~II, in prep.) have the potential to further refine our knowledge of the spin geometry of the pulsar, and confirm (or refute) our finding of the misalignment of the pulsar spin with the orbital angular momentum, which relies on the validity of the RVM model for PSR~J0955$-$6150. Confirming this finding, preferentially in a way that is independent of the RVM, would provide a very important and unexpected datum for understanding the origin of eMSPs. \begin{acknowledgements} The authors would like to thank Rosie Chen for help with analysis relating to search of the counterpart in optical and near-infrared survey data and John Antoniadis for the discussions on the evolution of the He~WD companion to PSR~J0955$-$6150. The MeerKAT telescope is operated by the South African Radio Astronomy Observatory, which is a facility of the National Research Foundation, an agency of the Department of Science and Innovation. SARAO acknowledges the ongoing advice and calibration of GPS systems by the National Metrology Institute of South Africa (NMISA) and the time space reference systems department department of the Paris Observatory. MeerTime data is housed on the OzSTAR supercomputer at Swinburne University of Technology. The Parkes radio telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. We acknowledge the Wiradjuri people as the traditional owners of the Observatory site. This research has made extensive use of NASAs Astrophysics Data System (https://ui.adsabs.harvard.edu/) and includes archived data obtained through the CSIRO Data Access Portal (http://data.csiro.au). Parts of this research were conducted by the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), through project number CE170100004 and the Laureate fellowship number FL150100148. VVK, PCCF, MK, AP and MCiB acknowledge continuing valuable support from the Max-Planck Society. APo and MBu acknowledge the support from the Ministero degli Affari Esteri e della Cooperazione Internazionale - Direzione Generale per la Promozione del Sistema Paese - Progetto di Grande Rilevanza ZA18GR02. MBu and APo acknowledge support through the research grant "iPeska" (PI: Andrea Possenti) funded under the INAF national call Prin-SKA/CTA approved with the Presidential Decree 70/2016. RMS acknowledges support through Australian Research Council Future Fellowship FT190100155. Pulsar research at UBC is supported by an NSERC Discovery Grant and by the Canadian Institute for Advanced Resarch. This publication made use of open source python libraries including Numpy \citep{numpy}, Matplotlib \citep{matplotlib}, Astropy \citep{astropy} and Chain Consumer \citep{Hinton2016_ChainConsumer}, along with pulsar analysis packages: \textsc{psrchive} \citep{HotanEtAl2004}, \textsc{tempo2} \citep{HobbsEtAl2006}, \textsc{temponest} \citep{LentatiEtAl2014}. \end{acknowledgements} \bibliographystyle{aa}	{ "redpajama_set_name": "RedPajamaArXiv" }	7,263
Theodor Zwinger III, fils de Johann Zwinger, est un médecin suisse, né à Bâle le et mort à Fribourg-en-Brisgau le . Biographie Ayant achevé ses humanités, il fit son cours de philosophie et, en 1675, reçut le grade de maître ès arts. Se destinant à l'exercice de la médecine, il joignit à l'étude de l'art de guérir celle de toutes les sciences accessoires et fit succéder à la lecture des ouvrages des Anciens celle des meilleurs écrits modernes. Il se rendit, en 1678, à Schaffhouse, pour y suivre des leçons et à Zurich, où il se perfectionna dans la connaissance de la botanique et de l'histoire naturelle, par sa lecture de Gesner, de Scheuchzer, etc. De retour à Bâle en 1680, il y fut reçu docteur en médecine. Quelques années plus tard, il est nommé professeur de rhétorique à l'académie en 1684, il permuta, trois ans après, cette chaire contre celle de physique. Il sera plus tard admis à l'Académie des sciences de Berlin et, inscrit sous le nom d'Aristote, à l'Académie des Curieux de la nature. On lui offrit, en 1700, la première chaire de médecine de l'académie de Leyde. Le landgrave de Hesse-Cassel et le roi de Prusse cherchèrent à se l'attacher par des offres ; mais rien ne put le décider à quitter sa ville natale. Nommé médecin et conseiller aulique du duc de Wurtemberg et du marquis de Bade-Dourlach, il reçut les mêmes titres de plusieurs princes et de diverses villes d'Allemagne. Au mois de décembre 1703, il passa de la chaire de physique à celle d'anatomie et de botanique. L'hiver il présidait aux dissections dans l'amphithéâtre, et l'été, suivi de ses élèves, il parcourait les montagnes de la Suisse, pour y recueillir de nouvelles plantes, dont il enrichissait le jardin de l'académie. La ville de Fribourg-en-Brisgau, affligée d'une épidémie en 1710, réclama les soins de Zwinger. Il passait le jour à visiter les malades et une partie de la nuit à rédiger ses observations. L'année suivante, il fut chargé du cours de médecine théorique et pratique. Ce fut dans l'exercice de cette place qu'il termina sa vie, en . Bibliographie Outre un grand nombre de thèses et d'observations, dans les Actes des Curieux de la nature et de la Société de physique de Breslau, on lui doit de nouvelles éditions, augmentées, d'un Lexique latin et allemand (Bâle, 1700, in 8) sous le nom de Spieser, et des Secrets de médecine de Wecker. Ses principaux ouvrages sont : le Théâtre botanique (en allemand), Bâle, 1696, in-folio, fig ; Zwinger y a rassemblé toutes les plantes décrites par Gesner, Camerarius et Bauhin, en y joignant leurs propriétés médicales (l'édition publiée par son fils Friedrich Zwinger, en 1744, est beaucoup plus ample) ; Epitome totius medicinœ, Londres, 1701, in-8 ; Bâle, 1706, et 1738, in-8 (c'est un abrégé des œuvres de Michael Ettmüller) ; Spécimen physicœ cclectico-experimentalis, Bâle, 1707, in-12, sous le nom de Jacques Zwinger ; Fasciculus dissertationum medicorum selectiorum, ibid., 1710, in-8 ; Theatrumpraxeos medicœ, ibid., 1710, 1740, in-4 ; Pœdoiatreiapractica, seu Curatio morborum puerilium, ibid., 1722, 2 vol., in-8. Sources Médecin suisse du XVIIIe siècle Membre de l'Académie royale des sciences de Prusse Membre de l'Académie allemande des sciences Leopoldina Personnalité bâloise Naissance en août 1658 Naissance à Bâle Décès en avril 1724 Décès à Fribourg-en-Brisgau Décès à 65 ans	{ "redpajama_set_name": "RedPajamaWikipedia" }	1,897
function gs_install { if [[ $CONDA == "false" ]]; then # install virtualenv check=`virtualenv --version` [ $? != 0 ] && sudo pip3 install virtualenv # create env virtualenv -p python3 env; # activate virtualenv source env/bin/activate else # check for env conda create -n piipod python=3.4 # activate env source activate piipod; fi # install pip install --upgrade pip pip install -r requirements.txt pip install git+https://github.com/python-constraint/python-constraint.git # add configuration file if does not exist if [ ! -f "configvars.py" ]; then cp sampleconfigvars.py configvars.py fi echo "--- [OK] Installation complete. Use 'make db' to create the database. Use 'make refresh' to DELETE the old database and recreate one using the new schema. " } function gs_check { echo '3 checks:' exit=`python3 --version` if [ $? != 0 ]; then echo '[Error] Python3 not found'; else echo '[OK] Python3 found' fi exit=`mysql --version` if [ $? != 0 ]; then echo '[Error] MySQL not found'; else echo '[OK] MySQL found' fi exit=`conda --version` if [ $? != 0 ]; then echo '[Error] (Optional) Anaconda not found'; else echo '[OK] Anaconda found' fi } function gs_activate { if [[ $CONDA == "true" ]]; then # check for virtualenv if [ -d "env" ]; then python3 -m venv env fi # activate virtualenv source env/bin/activate else # activate env source activate piipod; fi echo "--- [OK] Virtualenv activated. " } ### # Commands # source manage.sh [command] ### if [[ $1 == "activate" ]]; then gs_activate fi if [[ $1 == "check" ]]; then gs_check fi if [[ $1 == "install" ]]; then gs_install fi	{ "redpajama_set_name": "RedPajamaGithub" }	252
{"url":"http:\/\/illuminations.nctm.org\/Lesson.aspx?id=2765","text":"\u2022 Lesson\n9-12\n1\n\nStudents often ask, \u201cWhen are we ever going to use this?\u201d Compound interest is a topic that provides an inherent answer to this question. In this activity, students use their knowledge of exponents to compute an investment\u2019s worth using a formula and a compound interest simulator. Students also use the simulator to analyze credit card payments and debt.\n\nThe Savings Account activity sheet begins with a statement of how much certain products have increased in price over time and how hard it is to predict these increases. To get this discussion going, the day before this lesson, have students interview their parents about how much products such as a gallon of gas, a gallon of milk, a loaf of bread, etc cost when they were growing up. Alternatively, have students research the prices of these items 30 years ago. When they return to class, record their answers on the board and compute the percent increase of each item.\n\n To calculate percent increase use the formula\n\nStudents should notice that each item has a different percent increase. Ask students, Why were all the percent increases different? What could be the reason for this?\n\n[There are several factors that may contribute to price increases. One possible response could be that different items are affected by inflation to different degrees.]\n\nAfter this discussion, lead students to understand the need to predict the future. Inform them that in terms of invested money, accurate predictions are possible. The purpose of this lesson is to engage and excite students about financial investments, and to educate them about credit card debt.\n\nDistribute the Savings Account activity sheet and have students read the introductory text and work through the first table.\n\n Savings Account Activity Sheet\n\nHere are the correct results for the first table:\n\n Years Investment Has Been in the Bank Balance at the Start of the Current Year Interest Earned for the Year (3%) Balance at the End of the Current Year 1 $100.00$3.00 $103.00 2$103.00 $3.09$106.09 3 $106.09$3.18 $109.27 4$109.27 $3.28$112.55 5 $112.55$3.38 $115.93 After students complete the first table ask, \"Would you want to do this calculation for each investment year from 1 to 80?\" [Hopefully, students will say no.] While students may not want to do the hand calculations, tell them you just want the amount in the bank after 80 years. Pose the question, \u201cHow can we find this out?\u201d [Possible student responses might be to use spreadsheets, computers, calculator programs, etc.] If students do not suggest it, propose looking for a pattern and developing a formula. Then, have students complete the algebraic table and work together to generate the formula. The completed table appears below. If students need help with the Simplified Amount column, show them that the entries in this column are based on the factor by grouping method. For example: In the expression 5x(x + 1) + 7(x + 1), the term (x + 1) is a common factor of both terms, so it can be factored out. This leaves the simplified expression (x + 1)(5x + 7). You could also complete the second row, as an example: P(1.03) + 0.03P(1.03) = (1.03)(P + 0.03P) * Factored (1.03) from both terms = P(1.03)(1.03) * Factored P from the binomial = P(1.03)2 *** Rewrote the expression using expone Years Investment Has Been in the Bank Balance at the Start of the Current Year Interest Earned for the Year (3%) Balance at the End of the Current Year Previous Balance + Interest Simplified Amount 1 P 0.03P P + 0.03P P(1.03) 2 P(1.03) 0.03P(1.03) P(1.03) + 0.03P(1.03) P(1.03)2 3 P(1.03)2 0.03P(1.03)2 P(1.03)2 + 0.03P(1.03)2 P(1.03)3 4 P(1.03)3 0.03P(1.03)3 P(1.03)3 + 0.03P(1.03)3 P(1.03)4 5 P(1.03)4 0.03P(1.03)4 P(1.03)4 + 0.03P(1.03)4 P(1.03)5 Savings Account Activity Sheet Answers 1.a) This formula calculates the value of the investment, the previous balance plus the interest. If r was used alone, the formula would only calculate the amount of interest earned. 1.b)$6,524.08\n\n2.a)r\/n is the interest rate used for each compounding period.\n\n2.b) Earlier we noticed that the exponent in the formula was the number of times interest was assessed over the lifetime of the investment. Since interest is now assessed n times a year and t is measured in years, nt is the number of times interest will be assessed over the life of the investment.\n\n3.a) $6,610.57 3.b) It is greater because interest is being compounded more than once a year. While this formula is helpful, it cannot handle investments that also have a monthly contribution. To perform those calculations another formula is needed. To gain an appreciation of the convenience provided by the Compound Interest Simulator, have any students who are interested in using spreadsheets compute the amounts in the savings account after each monthly contribution of$50. Allow these students to observe the number of calculations required to find the amount in the savings account at the end of one year.\n\nIntroduce students to the Compound Interest Simulator and how quickly it works to generate these values. Have students use the simulator for Question 4 on the activity sheet.\n\nSavings Account Activity Sheet Answers continued\n\n4.a) 13 years, 11 months\n\n4.b) 1 year, 6 months\n\nWhen comparing the two individuals who start their investments at different ages, have the students input the given information into the simulator to confirm the given predicted difference and to again demonstrate how quickly the simulator works.\n\nAs students are finding their own way to reach $1 million dollars by age 65 in Question 5, record the various strategies on the board as they are discovered. See how many different ways students can come up with. Also comment on each student\u2019s graph on the simulator. Ask questions to help students see that each curve grows exponentially. Some of these questions could be: \u2022 Does the graph increase at a constant rate? [No, the graph increases at a greater rate as time increases.] \u2022 Is the a straight line or is it curving upward? [The graph is curving upward.] Savings Account Activity Sheet Answers continued 6. 46 years, 3 months 7. This will vary depending on the student\u2019s age. Age 15 = 23.3%, Age 16 = 24.5%, Age 17 = 25.9%, Age 18 = 27.4% 8. Answers will vary. 9. Annual rate is the percentage of growth an investment had over a year; the annual yield is the amount of money an investment made over a year. 10. You should start investing as early as possible. Students will now consider credit card debt and how quickly it can get out of control. Distribute the next activity sheet: Credit Card Activity Sheet To begin this section of the lesson, you may want to ask if any of your students have a credit card or know someone who has one. Ask those individuals, \"What the Annual Percentage Rate is for the card?\" The APR is the interest rate you pay for any purchases made with a credit card if you do not pay the full amount owing by the end of the monthly billing cycle. Be sure to make the observation that this APR is much higher than the interest rates banks offer on savings accounts, which students learned about in Question 8 of the Savings Account activity sheet. Credit Card Activity Sheet Answers 1. In this situation, the balance on the credit card will reach$8,500 in 7 years, 8 months.\n\n3. 10 years, 10 months.\n\n4. $1,791.97 5.$2,915\n\nAssessments\n\n1. Consider two investments, Plan A and Plan B:\nPlan A: $20,000 investment for 5 years at 10% interest rate Plan B:$14,000 investment for 15 years at 15% interest rate with monthly contributions of $50 Which is the better investment? In what situations would each of these plans be the best option to choose? 2. Have students compare scenarios with varying compounding periods, including annually, monthly, weekly, daily, hourly, etc. Extensions 1. Doubling Time A well known formula for calculating the doubling time of an investment is 72\/interest rate. This tells us the number of years it will take for an investment to double its value if interest is compounded yearly. If interest is compounded quarterly, then divide the result by 4, and so on. Have students use the simulator and calculate the doubling time for an investment of$1,000 with no monthly contributions. Once that is done, have them change the investment amount to a different amount. The doubling time will remain the same. Tell them that the number 72 is related to this and challenge the class to explain why this doubling formula works regardless of the investment amount.\n\n2. Fill out the following table, plot it, and then run a regression. This is a fun activity to do as a curve-fitting exercise.\n Interest Rate Years for Principal to Double when Compounded Yearly 1% 70 2% 35 3% ... 4% ...\nAfter some trial and error, students will observe that the correct regression to choose is the power regression. The exact equation for the fitted curve is f(x)\u00a0=\u00a070.76x\u20130.99, but an approximate equation is y\u00a0=\u00a072\/x, hence the name \u201cThe Rule of 72.\u201d To get better results, more data points are needed. The equation above was arrived at using 4 data points. If a unit on statistics is going to be covered next, this would be a great time to introduce the concept of sample size. The larger the sample, the closer the results mimic the expected value. This is also known as the law of large numbers.\n\nQuestions for Students\n\n1. For invested money, is the growth linear or exponential?\n\n[The growth is exponential because the interest earned with each compounding is added to the original amount. This results in receiving interest on the interest on the interest... etc. Linear growth would have a constant rate of increase. Another way to state this is that invested money increases by the same percent each year, so the growth is exponential. If it were increased by the same dollar amount each year, it would be linear.]\n\n2. Which is more important, the amount invested or the interest rate?\n\n[When comparing investments with different percentages of growth, the interest rate is \u00a0\u00a0\u00a0\u00a0the most important. When comparing actual dollar amounts that investments will be worth \u00a0\u00a0\u00a0\u00a0in the future, it is a combination of both and depends on the length of the investment. \u00a0\u00a0\u00a0\u00a0Given enough time, the higher interest rate will always be the best choice. To see a \u00a0\u00a0\u00a0\u00a0situation where the lower interest rate yields a higher future investment value see the first Assessment question below.]\n\nTeacher Reflection\n\n\u2022 What learning styles does this lesson address?\n\u2022 Did using technology enhance or hinder the mathematical idea being presented?\n\u2022 What advantages are there in presenting mathematical topics in this setting?\n\u2022 What were some of the ways your students illustrated that they were actively engaged in the learning process?\n\u2022 What did you learn, as a teacher, by orchestrating this activity?\n\n### Learning Objectives\n\nStudents will:\n\n\u2022 Determine the future value of an investment using the formula A\u00a0=\u00a0P(1\u00a0+\u00a0r\/n)nt\n\u2022 Decide how much to invest to guarantee a future amount\n\u2022 Realize how damaging carrying credit card debt can become, even when making the monthly minimum payment","date":"2014-10-25 16:42:59","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\": 0.30839014053344727, \"perplexity\": 1026.0370135577482}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-42\/segments\/1414119648706.40\/warc\/CC-MAIN-20141024030048-00078-ip-10-16-133-185.ec2.internal.warc.gz\"}"}	null	null

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