Maker of patterns, p.1

  Maker of Patterns, p.1

Maker of Patterns

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Maker of Patterns




  A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.




  1: Great Minds Around the Billiard Table

  2: War and Peace

  3: Truth and Reconciliation

  4: Cornell Student

  5: Go West, Young Man

  6: Demigods on Stilts

  7: Nolo Contendere

  8: Well, Doc, You’re In

  9: The Physicist in Love

  10: Cornell Professor

  11: Mycenean Tablets and Spin Waves

  12: Moscow and La Jolla

  13: The Forsaken Merman

  14: A Spaceship and a Wedding

  15: Homecoming

  16: Working for Peace

  17: Marching for Justice

  18: Sitting in Judgment

  19: Two Deaths and Two Departures

  20: Adventures of a Psychiatric Nurse

  21: Whale Worshippers and Moonchildren




  IN MARCH 2017, when this book was almost finished, my wife received a message from our twelve-year-old granddaughter: “We are all metaphors in this dark and lonely world.” Our daughter added her own comment, “The sentiment is tempered by the fact that she has a pink Afro.” The pink Afro displays a proud and joyful spirit, masking the melancholy thoughts of a teenager confronting an uncertain future. Our granddaughter is now emerging into a world strikingly similar to the world of 1936 into which I came as a twelve-year-old. Both our worlds were struggling with gross economic inequality, stubbornly persistent poverty, brutal dictators on the rise, and small wars presaging worse horrors to come. I too was a metaphor for a new generation of young people without illusions. Her declaration of independence is a pink Afro. Mine was a passionate pursuit of mathematics. I escaped from the barbaric world of Hitler and Stalin into the abstract world of Hardy. Hardy was the most famous mathematician in England when I came to him as a student in 1941. He taught me to be a maker of patterns. An even greater maker of patterns was the Indian genius Srinivasa Ramanujan, who had come to Hardy as a student in 1914 and died at age thirty-two in 1920. Through Hardy, I entered Ramanujan’s magical world. My first discoveries were concerned with the numbers 5 and 7 which play special roles in the weird arithmetical patterns of Ramanujan.

  Afterwards I found patterns of comparable beauty in the dance of electrons jumping around atoms. Patterns as elegant as those of Ramanujan had been discovered in the world of physics by Paul Dirac, whose lectures on quantum mechanics I also attended. Dirac was one of the pioneers who had entered the strange new world of quantum physics, where strict causality is abandoned and atomic events occur by chance. The idea that chance governs nature was then still open to question. In the world of human affairs, Lev Tolstoy asked the same question, whether free choice prevails. While Dirac proclaimed free choice in the world of physics, Tolstoy denied it in the world of history. The idea that Dirac called causality, Tolstoy called Providence. At the end of his War and Peace, he wrote a long philosophical discussion, explaining why human free will is an illusion and Providence is the driving force of history. When I was a student in Cambridge, the same Providence that had destroyed Napoleon’s army in Russia in 1812 was destroying Hitler’s army in Russia in 1943. I was reading Tolstoy and Dirac at the same time.

  The words maker of patterns had for Hardy a double meaning. Patterns could be made with words as well as with ideas, with books as well as with theorems. I once asked him why in his old age, when he was sixty-five and I was eighteen, he had stopped exploring new mathematics and was spending his time writing books. He answered without hesitation, “Young men should prove theorems: old men should write books.” He took pride in his style as a writer. He was a maker of patterns in English prose as well as in the theory of numbers. In my later life I followed his example. As a young man I wrote technical papers, exploring patterns of ideas in mathematics and physics. As an old man I write books, exploring patterns of words in literature and history.

  The letters collected in this book record a cycle in the history of the world from 1936 to 1978, from the civil war in Spain to the rise of Gorbachev in the Soviet Union. This was a cycle rolling from doom and gloom in the 1930s, to death and disaster in the 1940s, to fear and trembling in the 1950s, to smaller disasters in the 1960s, to recovery and promise in the 1970s. Contrasting with this cycle of death and rebirth in the political world, there was steady progress and a continued succession of major advances in the world of science. Two discoveries transformed our views of the biological and physical worlds. The discovery of the double helix structure of the DNA molecule by Francis Crick and Jim Watson in 1953 made the basic processes of life suddenly accessible to study with the tools of physics and chemistry. The mysteries of biological reproduction and heredity could be translated into testable molecular models. The discovery of the cosmic background radiation by Arno Penzias and Robert Wilson in 1964 opened the entire physical universe to our observation. Suddenly the whole universe back to its beginnings was visible to our instruments.

  In 1968 I read The Double Helix, the story written by Watson describing how he and Crick discovered the secret of life. The secret of life, as they proudly boasted after they made the discovery, was the structure of the DNA molecules that carry the genetic information in every cell of every living creature larger than a virus. The helical structure, with the genetic information written backward and forward in two complementary strands around the helix, gives the molecules the ability to replicate themselves precisely when the cell divides. The two daughter cells are born with exact copies of the mother’s genetic information. Watson’s book tells in vivid detail how the discovery happened, not by logical scientific reasoning but in a personal drama with real human characters. He brings the characters to life with verbatim accounts of their conversations, stumbling and squabbling as they grope their way toward the truth.

  Soon after I read Watson’s book, I met him in person. I asked him how he could possibly remember the details of the conversations and arguments that he put into his story. He answered, “Oh, that was easy. I wrote a letter every week to my mother in America describing my life in England, and she kept the letters.” I had been writing a letter every week to my parents in England, describing my life in America. That same day I wrote to my mother, urging her to keep the letters. She kept them, giving me the raw material for this book.

  I do not have any great discovery like the double helix to describe. The letters record the daily life of an ordinary scientist doing ordinary work. I find them interesting because I had the good fortune to live through extraordinary historical times with an extraordinary collection of friends. Letters are valuable witnesses to history because they are written without hindsight. They describe events as they appeared to the participants at the time. Later memories of the same events may be seriously distorted by hindsight. When I compare my memories with the letters, I see that I not only forget things, I also remember things that never happened.

  A striking example of a false memory was a lunch party in 1958 at the home of Robert Oppenheimer and his wife Kitty. Two other couples were there, the theologian Reinhold Niebuhr and his wife Ursula, who had come to the Institute for Advanced Study for a year, and the retired diplomat George Kennan and his wife Annelise, who had come permanently so that George could pursue his second career as a historian. After lunch we sat around a glowing wood fire in the living room. Oppenheimer pulled a beautiful leather-bound
volume from his bookcase and read a poem, “The Pulley” by George Herbert (1633), in a beautifully cadenced voice. George Kennan had not known Herbert’s poetry before. Oppenheimer said it was high time for the two Georges to get to know each other. Then he turned toward Ursula Niebuhr and said, “But you of course know him well.” It turned out that George Herbert was a distant ancestor of Ursula. Oppenheimer then continued to read other poems of Herbert, and so the afternoon continued with personal warmth and poetry around the fireside. I have a vivid memory of sitting with that group around the fireside. Recently I was reading some old letters and found one written long ago by Ursula Niebuhr, describing that lunch party and confirming my memory. Every detail of my memory is correct except for one. I was not there. My memory has somehow stolen that scene from Ursula and put me into it.

  All through a long life I had three main concerns, with a clear order of priority. Family came first, friends second, and work third. The same order of priority appears in the letters. The best passages describe the human story of two marriages and growing children. The next best describe the community of friends that I enjoyed as colleagues in science and in public affairs. The details of my work as a scientist are barely mentioned. The neglect of science is mainly due to the fact that my parents were not interested in technical details. I assume that readers of this book will also not be interested in technical details.

  I wrote the letters to my family as a dutiful son, whenever I was separated from them, beginning in 1941, when I went to Cambridge University as a student, and continuing intermittently until the death of my sister Alice in 2012. The family consisted of my father, Sir George, who died in 1964; my mother, Mildred, who died in 1975; and my sister, who lived independently in London for many years and moved to the parents’ home in Winchester to take care of our mother after our father died. All three wrote back to me frequently. I had originally intended to include in this book the letters of all four of us, giving the reader a picture of life as it was lived on both sides of the Atlantic Ocean. Reluctantly I decided to include only my own letters. To include the incoming letters would have doubled the size of the book and would have made the narrative less coherent. Readers who are interested in the life and work of my father should go to the excellent biography by Paul Spicer (2014).

  When the letters begin in 1941, World War II is raging in Russia. Hitler’s armies, after defeating France and occupying most of Europe, are marching deep into the Soviet Union. Britain is enjoying a peaceful interlude between the disasters in France in 1940 and in Singapore in 1942. My parents are bombed out of their house in London and have found refuge with a friendly family in Reading. My father is director of the Royal College of Music in London and is keeping the college open, having moved a bed into his office so that he can stay overnight during the bombing. The trustees of the college had wanted to close it, but he was determined to keep it open. He told them that he intended to stay there so long as there was a roof over his head. The trustees gave way and agreed to keep it open.

  Defying Hitler in 1940 was for my father, as it was for Winston Churchill, his finest hour. By keeping the college open, he set a good example for several other institutions that had made plans to evacuate but decided to stay open, notably the Sadlers Wells Opera and the Old Vic Theatre. All of them stayed active throughout the war and kept London alive as a cultural center. Paul Spicer in his biography quotes from a letter written by Hazel Bole, who was a student at the college in 1940: “I was fire-watching on the roof during the air raids. We students were there to throw sand on the incendiary bombs which the German bombers were raining down on us. One night I grabbed the large bucket, and someone else grabbed it too. I let go, and in a sudden flash of fireball I saw Sir George grinning at me.” Later in the war, my parents moved into an apartment close to the Royal College, and my sister moved to St. Thomas’s Hospital in London for training as a medical social worker. My father retired in 1952, and my parents then moved back to Winchester, where we had lived until 1938, when he became director.

  The letters selected for this book cover only the period 1941–78, the first half of my adult life. The letters continue for thirty more years, but the second half of a life is usually less interesting than the first half. I believe it was Rudyard Kipling who said that a man should get half of his dying done before the age of forty. I decided to stop the selection at 1978, to keep the book short and readable while including the high points of my story. Throughout the book except in this preface, the texts of letters are printed in Roman font, and my later comments are printed in italics.

  I am grateful to Robert Weil, my editor at Norton, for his unfailing help and encouragement. I am grateful to my son George and to Kimberly Jacobsen for digitizing the letters and making them easy to read and search. Finally, I am grateful to my wife Imme for the tender loving care that keeps me alive.

  • 1 •


  THE LETTERS BEGAN when I arrived as a seventeen-year-old undergraduate at Trinity College, Cambridge, in September 1941. It was a great time to get an education, in the middle of World War II. The famous old professors were all there, but there were hardly any students. As a dutiful son, I wrote frequent letters to my parents. In this selection of the letters, nothing has been added, but a great deal has been silently subtracted. Here is a list of the main characters who appear in Chapter 1.

  Godfrey Harold Hardy, then aged sixty-four, the most famous pure mathematician in England, known to the public for his book, A Mathematician’s Apology (1940). The book is short and beautifully written. I quote in the epigraph two sentences from his book, from which I also borrowed the title for mine.

  John Edensor Littlewood, then aged fifty-six, had worked with Hardy in a famous collaboration for many years, exploring the theory of numbers. Some years earlier they decided that they had done enough with number theory and made a pact to work in the future on other subjects. Littlewood never married, but he had a daughter. When I knew him in Cambridge, the daughter was only a rumor. Many years later the daughter finally emerged as a real person.

  Abram Samoilovich Besicovitch, then aged fifty, was a Russian mathematician who stayed in Russia after the revolution and settled in Cambridge ten years later. He carried the ancient geometry of Euclid to a deeper level, discovering new and rich structures in the menagerie of sets of points in a Euclidean plane. He was separated from his wife, but she was also living in Cambridge, and they remained friends. Hardy, Littlewood, and Besicovitch were all living in rooms at Trinity College. Because of the war, there were no young mathematicians in Cambridge. The three who gathered around the billiard table all belonged to the nineteenth century. In Cambridge we learned nineteenth-century mathematics. We knew little of the twentieth-century mathematics that had grown up in the 1930s in France, with a far more abstract style and a new set of general concepts. Only later when the war was over, French mathematics swept over England and America, and our elderly heroes became quaint and old-fashioned.

  Yelizaveta Fyodorovna Hill, then aged forty, was head of the department of Slavic languages. She had grown up in St. Petersburg with a British father and a Russian mother. They emigrated to England in 1918.

  Prince Dimitri Obolensky, then aged twenty-three and a student at Trinity College, was later a distinguished scholar and professor of Russian history at Oxford. Born in Russia in 1918, he escaped to England as a baby with his parents.

  Paul Maurice Adrien Dirac, then aged thirty-nine, was the leading British physicist who stayed in Cambridge during the war.

  The billiard table was for two years the center of my life. It belonged to Besicovitch and stood in the big room where he entertained guests on the ground floor of his home in Neville’s Court. He was addicted to billiards, and Hardy, who had been a passionate cricketer in his youth, was a passionate billiard player in his old age. Whenever I needed to talk with either of them, I could usually find them at the billiard table. Fortunately my father had bought a
billiard table when I was a child and taught me how to play. Our table was more modest than Besicovitch’s, but I could play well enough to pass the time with the famous professors.

  My intense interest in Russia began when I was in high school and became even stronger when Hitler invaded in 1941 and the Russians became our heroic allies. I planned to go to the Soviet Union after the war to study the language and literature and work with Russian mathematicians and scientists. When the war ended, Stalin made it clear that foreign students were unwelcome, and I switched my travel plans to the United States.

  I wrote all the letters in this chapter to my parents from Trinity College, except for the two from the climbing hut in Wales.

  OCTOBER 19, 1941

  I have now consolidated my position and feel that I can begin doing things because I want to and not because I have to. I have joined two mathematical societies which hold meetings occasionally. The first meeting was a lecture to the “Archimedeans” on “The Place of Mathematics in a Planned Society” by Professor Bernal, the perpetrator of “The Social Function of Science.” The trouble with him, as I knew it would be, was that he knows nothing about mathematics, even in its most applied forms. The only good thing about it was that he did proclaim that there is something for mathematicians to do in the statistical side of things; but he did not say anything definite about it. Hardy was there and adopted a very tolerant attitude; he seems to have been more impressed than I was. I have also joined Trinity College Orchestra, which holds its first meeting today. I have so far only looked at my instrument once, when I practiced for an hour last night to see if I could still play. I found I could, and perhaps the orchestra will make me practice. If not, I will have to see about having lessons.

  My instrument was a violin, which I learned to play as a child. My father was wise enough to see that I had no real musical talent and never put pressure on me to play well. I played barely well enough to be acceptable in a student orchestra.

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