Fearful Symmetry

At 45, Marcus du Sautoy is almost single-handedly responsible for making math accessible, and even fun, in England. To celebrate the release of his second book in Hebrew, he speaks about the math in soccer and Shakespeare, and why he lives in a Haredi area of London

Ten years ago, nearly to the day, the mathematician Marcus du Sautoy was at home in London with his family - his wife, Shani, and their son, Tomer. Shani was pregnant with their second son, whose expected delivery date was October 31, Halloween itself, but that evening she told her husband with some concern, "I haven't felt the baby move all day."

Tomer, 4, was already in bed, so Shani went to the hospital by herself. She called Marcus from there and told him: "There's no heartbeat."

Prof. Marcus du Sautory

"I kept thinking maybe they made some mistake, but they were adamant," du Sautoy recalls. "The doctors said there was no hope." Shani had to wait for contractions to begin so that she could give birth to a dead baby.

But that was only the beginning of the nightmare. In the middle of the night Shani lost consciousness, due to a blood clot. She regained consciousness but the situation was grave. The main artery to the uterus had been torn, she was losing blood rapidly and growing increasingly weaker. Marcus was by her side when she was rushed into the operating room. Her last words before being taken away were "I'm dying."

The entire night du Sautoy did not hear from the doctors, neither "Her condition will improve" nor "The operation was a success." It was only at dawn that he was told, "Your wife very nearly died. We still don't know whether she will survive the next hour. She is the sickest person in this hospital," du Sautoy wrote in The Daily Mail in January 2009.

Over the next few days Shani had four operations and 96 percent of her blood was replaced, using more than 100 units of blood and plasma. Eventually her leaking artery was repaired surgically. For the next two weeks, Shani was in a drug-induced coma, but even after the drugs were withdrawn she did not wake up. Du Sautoy began to prepare himself for the possibility that she had suffered brain damage.

Finally, the best news in what seemed like an eternity arrived: Shani woke up. But whereas Marcus was overjoyed at her return to life, she was mourning the dead baby and the loss of her ability to have another child. "We were in two very different places," du Sautoy says.

In the trying months that followed, the mathematician immersed himself in the world of numbers. He was in the midst of writing his first book. "Like many mathematicians, I use maths as a means of escape," he says. "It's a safe environment, almost like meditation, a great place to escape to. When a bomb like that explodes, without any explanation and lacking all logic, you find a haven in a secure world where things make sense. In mathematics, even with all the unsolved problems, you can still follow a logical course and find meaning. It's a lot more difficult to find a path like that in biology, which is a far messier discipline. Life is a lot more biology than mathematics and it's a challenge to understand why things happen. "We are still trying to understand what happened, and we don't know," du Sautoy continues. "That frustrates me terribly, because I am a person who always looks for answers, but of course life is filled with probabilities and sheer luck. Life deals you the cards and sometimes it's a cruddy hand with which you have to do your best. There's no logic of any kind," he says.

"Shani is Israeli," du Sautoy wrote of his wife in those painful times, "she is the strongest person I know." In an interview he explains, "It was like the feeling in Israel during the period of the suicide bombings - there's no way to prepare for it. A terror attack changes everything in an instant. Everything is all right and then everything is suddenly not all right, and that was our feeling. Everything was going well, we were within a week of a second son, Tomer was waiting to see his brother and suddenly everything changed dramatically. It was hard to explain to him why Mummy wasn't home and I had no answer to the question of whether she would ever return. You understand how fragile life is. When you're young you don't think about these things, it's a way to survive, but since then I have felt far more exposed."

Du Sautoy dedicated his first book, "The Music of the Primes," to Jonathan, the name they gave to the son who was never born.

Message to convey

Ten years have passed and Prof. du Sautoy, 45, is one of Britain's leading and most famous scientists, who is helping mathematicians and scientists in general to shed their nerdy image. A professor of mathematics at Oxford, he succeeded Richard Dawkins as Simonyi Professor for the Public Understanding of Science at the venerable institution. This year, he was appointed Officer of the Order of the British Empire, and he makes radio and television appearances in addition to writing. He spent the day before we met in the studio of the sculptor Anish Kapoor, in preparation for writing an article that will be included in a catalog of Kapoor's work. Du Sautoy is also working with a theater company on a play based on mathematics, is developing mental acuity games for the iPhone and has a special fondness for overly colorful pants.

"Yes, life is wonderful," he tells me in his north London home. "I can't believe I get paid for what I do. There's definitely a feeling of geek chic here and now. Hollywood wants to make movies about science. There is a true appetite in Britain for engaging in things scientific. There would not be so many science programs on the BBC if there were no audience for them, and some of the subjects are somewhat arcane. Last week Radio 4 launched a new series on the history of ideas, including science: For 45 minutes three people talked about imaginary numbers and the square root of minus one. There was a tremendous response. It was written up in The Guardian and the critics wrote that it was marvelous that we have radio like this. And Radio 4 is not a niche station - influential people listen to it."

The Hebrew translation of du Sautoy's "Symmetry: A Journey into the Patterns of Nature," was released last week. The book follows a year in his life that he spent in the company of his son Tomer, now 14, in a journey through the physical world and the world of symmetry that included a visit to Alhambra, in Granada, his favorite building in the world, with its array of symmetrical designs. There, he also found his son playing with the site's symmetries on his Nintendo DS, a moment of great pride for the scientist father.

"It's a language that embodies much of science," he explains. "Symmetry deals with order and possesses logic, so we are programmed to be attracted to symmetry. It's a language that transmits a message and therefore has an important role in mathematics and science. For example, in the CERN particle accelerator we can look at the particles like butterflies, but that will not help us to understand other particles. Looking for multidimensional symmetry will help us make progress in research. Chemistry is like a three-dimensional Alhambra - the way in which crystals are ordered. By means of symmetry one can understand chemistry, the way viruses proliferate and the like."

Du Sautoy is part of a community of scientists who do not hesitate to defend science against ignorance, the clergy, charlatans and impostors. Dawkins came out against God, Simon Singh assailed the charlatans of alternative medicine, others denounce examples of bad and amateurish science or supposed experts who lack all training.

While not a militant, like Dawkins, du Sautoy is no less determined. "I feel that as holder of the chair for the public understanding of science I have a message to convey," du Sautoy says. "I am the ambassador of a foreign country for the majority of people, who do not speak its language. Science exercises such a profound influence over people's lives that it is essential for them to know more about it, so they will not be disconnected from what is going on. They need to understand what genetic engineering is in order to be able to make a decision about it."

What would you say about a chief scientist in the Ministry of Education who rejects the theory of evolution, as happened recently in Israel?

"I am worried. Scientists must therefore take a stand and demonstrate the unchallengeable facts. Alternative medicine infuriates me, and it's important to expose these irrational beliefs. There is a problem between these two states - religion and science. It's less obvious in Britain, because religion, thank God, is less dominant here, but we also have to remember that the two are not necessarily mutually exclusive. Religion is occupied with culture in a social aspect, and from my point of view that is not a big problem. To Dawkins, religion is an obstacle, but he worked for many years in America and his field is more threatened by religion."

The geometry of soccer

Still, mathematics is not everything. Du Sautoy is the defensive midfielder for a Sunday league soccer team and also for the English Writers Team, which visited Israel about a year ago to play in a three-way tournament against their Israeli and German colleagues.

"We had a wonderful tournament in Israel," du Sautoy says. "Everyone gets fired up when he represents his country. Against Germany I had to guard a huge German who once played in the Bundesliga and thinks he's still good. He broke a bone in my hand. I went on playing but I had the feeling that something was broken there. Three of the players - two Germans and an Englishman - went to a hospital in Kfar Sava and they couldn't figure out what had happened. The German sticker got his comeuppance in a game between Germany and Israel, when he was sent off for cursing the female referee."

There were other damages from soccer as well. "In a league game of my local team I managed to break my wrist," du Sautoy says. "The bone protruded and I have a large titanium plate there now. And in a game of the English writers against Sweden I went up for a header but instead of the ball I rammed into a Swedish writer, and I have a scar over my eye to show for it. I needed six stitches, he needed four. We won in the stitches but lost the game. Shani says there's a message in all this, but I refuse to retire."

About six months ago, the English team hosted its Israeli counterpart team in a rain-swept, stormy game. The Israelis were beaten and accused the organizers of harassment by the referee, choosing an unsuitable field, causing the inclement weather and being standoffish. Du Sautoy, who has lived in Israel, was not surprised. "I enjoyed my stay in Israel," he says. "People can get to the heart of the matter quickly. Everything is direct with you. And yes, I heard about it, and their allegations were unfair. They whined about the pitch. They didn't like to lose. We all played under the same conditions. What did they want, for the game to be canceled without them playing?"

Du Sautoy and Tomer have season tickets for the Arsenal Football Club, which on a good day delivers an experience both aesthetic and mathematical. But du Sautoy still misses the great team of 2004. "It was like a game of chess," he says, showing a red team T-shirt. "Dennis Bergkamp knew exactly where Thierry Henry would be five seconds later, and how the game would develop. On the writers' team, Aidy Boothroyd, a former Watford manager, taught us to see the geometry of the pitch, the whole grid of triangles in which the game is played, and ever since, I see the game differently. It's pure geometry."

Indeed, a good game by Arsenal is also du Sautoy's example of a sublime mathematical model, the practical use of the elements of science, combining creativity, aesthetics and sheer pleasure. But a bad day for Arsenal - and there have been a few in recent years - is a nightmare for any math maven: a lot of work with little to show for it, all leading up to a dead end.

On a table in du Sautoy's home is a coffee mug with the Riemann zeta function and "What part didn't you understand?" He can trace his personal "revenge of the nerds" back to elementary school. "I wanted to study languages because I dreamed of becoming a spy, but languages frustrated me with all their exceptions to the rules," he relates. "When the teacher suggested that I read Frank Land's 'The Language of Mathematics,' which dealt with the language of symmetry, I was enchanted by the idea that it was possible to take something geometrical and transform it into the language of algebra. I liked the idea of being able to translate geometry into an abstract language. "Another book the teacher recommended was G.H. Hardy's 'A Mathematician's Apology,' which explains why mathematics lies on the border between science and art. The book opened up a new world for me, but it's also a book I hate, because the opening sentence is intended to deter anyone who wants to bring the field into the realm of general public knowledge. It says that it's a melancholy experience to write about mathematics. A mathematician's job is to prove theorems, not to write about them. I think we were in the shadow of this strict approach for too many years, but the whole book essentially disproves the argument, because it's written marvelously. And I actually helped to turn the book into a play."

One concept du Sautoy likes is "the Shakespeare of maths," by which he means the need to teach young people about the beauty, not the rules, of mathematics. "For example, the proof that there is an infinite number of prime numbers is quite beautiful," he says, citing a Shakespearean example. "You need a little mathematics, no more than what you learn in school, but regrettably the proof is not part of the curriculum. The language is taught, but not the great stories. I want youngsters to learn to read the artwork of the Alhambra palace, the interplay between the forms, to understand why two walls have the same symmetries even if they look different. The schools provide tools but don't let the students use them. The aims are too purposeful and utilitarian. You don't study Shakespeare because he's useful in daily life, and that's how it should be with mathematics, too. It's a field that we have to excite students to want to learn and try for themselves."

But with all due respect to the Bard, du Sautoy is also familiar with the dark side of mathematics, with feeling, as student and as teacher, that years of research have been wasted and led to a dead end.

"Psychology plays a large role in the study of mathematics. I find this time and again with my doctoral students. For years they worked on questions in examinations and papers, questions which have solutions and which they have the tools to solve. Then, suddenly they arrive at the doctoral dissertation, at huge problems which they are unable to solve. In fact, no one knows whether they have a solution at all, or if the human brain is capable of overcoming them. Half my time working with them is spent in boosting their self-confidence.

"I was in the same situation myself, and knowing that I did it in the past helps me to find a solution. Mathematicians usually live a long time: They want to be on hand to see if anyone has been able to solve the great problems."

Have you encountered academics who don't like the fact that you are popular?

"Some people think that serious scientists shouldn't engage in popular topics, but we live in a different world today. If we don't make mathematics accessible we won't get a budget, the youth won't come to us. Many of my colleagues thank me for what I am doing. I see it as part of teaching. This post lets me do something I'm good at. There are people who are envious or who look askance, but in general the mathematics community supports me impressively."

Marrying in

While du Sautoy and I were talking, on a rainy Simhat Torah morning, Shani returned from her morning run. She has completed a few marathons in the past few years and is in excellent shape. Shani was born on Kibbutz Yagur. Her father, Betzalel Ram, died in a diving accident while serving in a naval commando unit. She was a year old. She met du Sautoy while studying graphic design in Jerusalem, initially as a roommate. For their first date they attended a brit milah. He was not deterred.

They live in Stamford Hill, a largely ultra-Orthodox neighborhood in north London, on a street with mezuzahs on all the doorposts, and sukkot booths in the front yards at the time of my visit. In interviews, du Sautoy says he lives next door, in Stoke Newington, a trendy district with numerous excellent restaurants. It's also Arsenal territory, while Stamford Hill belongs to Tottenham.

"Yes, I tell the newspapers Stoke Newington and the cabbies Stamford Hill." Their house number is one, which as du Sautoy explains was once considered a prime number. His license plate is a prime number, 47, as is his soccer player number, 17.

He holds the Hebrew University of Jerusalem's Einstein Institute of Mathematics in very high regard ("phenomenal department, among the top five in the world, I would say" ), and he sometimes seems unsurprised at finding himself in Jewish surroundings despite having been raised in aristocratic Henley, in a family with prestigious roots.

"In 1745, Pierre Francois du Sautoy helped Bonnie Prince Charlie of Scotland in his war against the English. He was captured and became a prisoner of war. Since then we have been here against our will, and I'm waiting impatiently for the renewal of the French monarchy so we can get back our palaces," he says jokingly. "Mathematics has a significant Jewish component. People laugh and say I married Shani because, as a non-Jewish mathematician, that was my entree to the club."

Their children speak Hebrew and English, and Tomer attends a Jewish school even though his father is a committed atheist.

"Shani wanted the children to have an Israeli-Jewish identity. I'm not thrilled about mixing education and religion, but in a relationship there are compromises. The school wanted to see our ketubah [Jewish marriage contract] before accepting Tomer, but of course we couldn't get married in Israel because we're not the same religion - she's a Jew and I'm an Arsenal supporter. We married in Cyprus and we don't have a ketubah. We had to find Shani's mother's ketubah, but she was married on a kibbutz and doesn't have one, either.

"In the end, someone from the office of the Chief Rabbi of Britain called and tried to check whether Tomer was Jewish. He asked if I was the author of 'The Music of the Primes.' Shani said I was, and he said it was a wonderful book, and suddenly everything went more smoothly. If you're not Jewish, the next best thing is to be an intellectual."

Weren't you concerned that religion would come at the expense of education?

"I will not send my children to a school that questions the basics of science. I spent a lot of time at the school, which is exactly like the one I attended. Most of the teachers aren't Jewish, and the sciences are taught as in every school. The only difference is that in addition to the regular subjects they also teach Hebrew and Jewish subjects. My sense was that the educational aspect was not hurt by the religious one. I would have had a serious problem if they had cast doubt on science for religious reasons, and I am pleased that this is not the case. It is an excellent, normal school."

Is there an emphasis on Zionism, on the connection with Israel?

"I think they are aware that they cannot do that. They take pride in the ties with Israel but they realize they have pupils from every political background. As in Israel, they are not all settlers, and there are many, like Shani, who are very critical of the Israeli government. In my eyes, Judaism is a tribal-cultural thing. Shani gave up life in Israel for me, and that was a very significant step for her."

But the most significant step for du Sautoy was the family's adoption, from Guatemala, of Magaly and Ina, identical twins who are now seven.

"As a scholar of symmetry, I had a duty to adopt identical twins," du Sautoy says with a smile. We are in a very positive place today. The girls are a wonderful addition to the family, real balls of energy.

"They are identical genetically, but they are very different," he continues. "Magaly is very girly, she always wants to be the princess. Ina is more of a tomboy, she likes to be the superhero. Perhaps it shows the fragility of perfect symmetry. A small environmental disturbance and you get a completely different result. I am first and foremost their father, but I can't help looking at them as a scientist, too. It sometimes seems our family is almost an experiment in nature versus nurture, with one biological child and a pair of adopted twins."

The language of flowers


Why, though, is symmetry so pervasive in nature? It is not just a matter of aesthetics. Just as it is for me and mathematics, symmetry in nature is about language. It provides a way for animals and plants to convey a multitude of messages, from genetic superiority to nutritional information. Symmetry is often a sign of meaning, and can therefore be interpreted as a very basic, almost primeval form of communication. For an insect such as the bee, symmetry is fundamental to survival.
The eyesight of the bee is extremely limited. As it flies round negotiating the world, its brain receives images that are as distorted as if we were looking at the world through a thick sheet of glass. The bee can’t judge distances, so it continually crashes into things. The bee suffers a form of colour-blindness. The background green of the garden appears grey; red stands out more clearly as a blackness against the grey. But even through this thick-rimmed pair of glasses, there is one thing that burns strongly in the eyes of the bee: symmetry.

The honeybee likes the pentagonal symmetry of honeysuckle, the hexagonal shape of the clematis, and the highly radial symmetry of the daisy or sunflower. The bumblebee prefers mirror symmetry, such as the symmetry of the orchid, pea or foxglove. The eyesight of bees has evolved sufficiently for them to pick out these significant shapes. For in symmetry there is sustenance. The bees that are drawn to shapes with pattern are the insects that will not go hungry. For the bee, survival of the fittest means becoming an expert at symmetry. The bee that could not read the signs and signals of sustenance was left buzzing randomly round the garden, unable to keep up with its superior competitors who could spot the patterns.

Because the plant is equally dependent on attracting the bee to its flower for pollination and prolonging its genetic heritage, it too has played its part in this natural dialogue. The flower that can achieve perfect symmetry attracts more bees and survives longer in the evolutionary battle. Symmetry is the language used by the flower and bee to communicate with each other. For the flower, the hexagon or the pentagon is like a billboard shouting out ‘Visit me!’ For the bee, encoded in the symmetrical shape is the message that ‘Here is food!’ Symmetry denotes something special, something with meaning. Against the static white noise that makes up most of the bee’s visual world, the six perfect petals of the clematis stand out like a musical phrase full of harmony.
As nature’s garden evolved, so too did the variety of shapes and colours exploited by the plant world. After millions of years of spring following winter to produce another year of geometric evolution, the garden is now a plethora of patterns trumpeting their greetings and promises of sweet sustenance.

But symmetry is not an easy thing to achieve. A plant has to work hard and be able to divert important natural resources to achieve the balance and beauty of the orchid or the sunflower. Beauty of form is an extravagance. That is why only the fittest and healthiest individual plants have enough energy to spare to create a shape with balance. The superiority of the symmetrical flower is reflected in a greater production of nectar, and that nectar has a higher sugar content. Symmetry tastes sweet.

The flower or animal with symmetry is sending out a very clear signal of its genetic superiority over its neighbours. That is why the animal world is populated by shapes that strive for perfect balance. Humans and animals are genetically programmed to look upon these shapes as beautiful− we are attracted to those animals whose genetic make-up is so superior that they can use energy to make symmetry.

Humans and animals alike will choose a face that has perfect left-right mirror symmetry over an unsymmetrical face. Most of the animals in the natural world favour such bilateral mirror symmetry. A line down the middle separates the shape into two different halves. But although they are different, there is a perfect correspondence which matches one half to the other. At least externally. The asymmetry of our internal organs is still something of a mystery and only goes to reinforce the wonder at how symmetrical the exterior is.

Studies indicate that the more symmetrical among us are more likely to start having sex at an earlier age. Even the smell men emit seems to be more appealing to women when the male has more symmetry. In one study, sweaty tee-shirts that had been worn by men were offered to a selection of women, and those who were ovulating were drawn to the tee-shirts worn by the men with the most symmetrical bodies. It seems, though, that men are not programmed to pick up the scent of a symmetrical woman.

Animal rights activists have used symmetry as evidence of cruelty to animals. Battery farm eggs are likely to be far less symmetrical than free-range eggs: battery hens are suffering trauma and wasting energy that could have been used to realize perfection. Unlike the tortured artist thriving in adversity to create great art, the hen needs comfort and luxury to produce perfect symmetry.

But symmetry isn’t just a genetic language for declaring to potential mates how good one’s DNA is. Back in the hive, away from the search for symmetrical flowers and nectar, symmetry also pervades the bee’s home life. As the young bees gorge themselves on the honey that has been collected, they secrete small slivers of wax. The temperature of the hive is maintained at 35C by the concentration of bees, which makes the wax malleable enough to be shaped by the worker bees, who collect the wax secretions and mould the cells in which the honey will be stored. The hexagonal lattice that the bees use to store their honey exploits another facet of symmetry. Not only is it a harbinger of meaning and language, but also symmetry is nature’s way of being efficient and economical. For the bee, the lattice of hexagons allows the colony to pack the most honey into the greatest space without wasting too much wax on building its walls.

Excerpts from Marcus du Sautoy’s ‘Symmetry: A Journey Into the Patterns of Nature.’