Thinking

I was in Los Angeles this spring on the day Richard Feynman died. The next morning I saw a banner lowered from the top of the tower block which stands in the middle of the Caltech campus. It read: ‘WE LOVE YOU DICK.’ The obituary of Feynman in the LA Times was awed and affectionate. It listed his achievements – his work in physics, the Nobel Prize it earned him and his work on the nuclear bomb. It also recalled his reputation as a womaniser, a drummer and a teacher, and the broadcast hearings of the inquiry into the Challenger disaster, and how Feynman demonstrated what might have gone wrong: he called for a glass of ice water, dunked in it for a few minutes a piece of the rubber used to seal the joints between the rocket stages, and showed how it had lost all its resilience. This example of practical science caught the imagination of the country in the same way that his lectures caught the imagination of students at Caltech. Here was the Sane Scientist – the heir of Benjamin Franklin. Feynman appears several times in Ed Regis’s wonderful book about the Institute for Advanced Study at Princeton (the members of which often appear in the Mad Scientist mode) as an advocate of worldly engagement. His words head an epilogue which asks difficult questions about the productivity of ivory towers:

When I was at Princeton in the 1940s I could see what happened to those great minds at the Institute for Advanced Study, who had been specially selected for their tremendous brains and were now given this opportunity to sit in this lovely house by the woods there, with no classes to teach, with no obligations whatsoever. These poor bastards could now sit and think clearly all by themselves. OK? So they don’t get an idea for a while. They have every opportunity to do something, and they’re not getting any ideas. I believe that in a situation like this a kind of guilt or depression worms inside of you, and you begin to worry about not getting any ideas. And nothing happens, still no ideas come.

    Nothing happens because there’s not enough real activity and challenge. You’re not in contact with the experimental guys. You don’t have to think how to answer questions from students. Nothing.

It was decided from the start that the Institute should be a place for thinking, and nothing else. It was set up in the early Thirties, with money provided by Louis Bamberger and his sister Caroline Bamberger Fuld, owners of a New Jersey department store. They sold out in 1929, just before the Crash, and wanting to give something to Newark, consulted Abraham Flexner. Flexner diverted their philanthropy from a new medical school in New Jersey to a new Platonic academy at Princeton, which would, incidentally, realise a special dream of his own. He wanted to set up a ‘free society of scholars’. ‘Free because mature persons, animated by intellectual purposes, must be left to pursue their own ends in their own way’, and free of distraction ‘either by worldly concerns or the parental responsibility for an immature student body’. The Institute’s reputation was much enhanced by the ill wind out of Europe which blew in Albert Einstein as its first professor.

The tales of eccentric genius in Regis’s book are hilarious and sad. Gödel, for example, almost did himself out of American citizenship because he would not let logical flaws go unremarked:

On April 2 1948. Gödel showed up at the government offices in Trenton, accompanied by Einstein and Morgenstern who were there as witnesses. On the drive down to Trenton, Einstein kept telling a bunch of stories and anecdotes to keep Gödel’s mind off the logical problems of the American Constitution. But then the proceedings began. ‘Up to now you have held German citizenship ... ’ the official began, but Gödel jumped in and corrected this immediately. He was an Austrian, not a German. ‘Anyhow,’ the official continued, ‘it was under an evil dictatorship, but fortunately that is not possible in America ... ’

‘On the contrary,’ Gödel cried out, ‘I know how that can happen.’

Gödel, whose proof of the necessary incompleteness of logical systems had undermined the best hopes of early 20th-century mathematics, starved himself to death, believing his doctors were poisoning him. Dirac, who said, ‘I think it’s a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don’t have any physical meaning at all,’ but correctly predicted the existence of anti-matter, was famous for his silences, saying nothing if there was nothing to be said. When two physicists who had come to him for some constructive criticism had elicited no word of comment after an hour of exposition he decided he must say something. So he asked where the post office was. Pauli, on the other hand, was famously rude and prodigiously arrogant. While still only a graduate student he stood up in a seminar given by Einstein and began: ‘You know, what Professor Einstein says is not so stupid.’

Most of the Institute’s illustrious members do their best work before they join it. They arrive with reputations which tend to isolate them from the post-docs on short-term fellowships. At this lower level the theory that creativity will flow if outside pressures are removed seems to work. Time is what the young need, and contact with their contemporaries as much as with great minds – which is just as well, because you have to have something pretty important to say to dare disturb one of the world’s great brains when it is thinking about the world’s deepest problems. There is none of the camaraderie of the laboratory, for there is no experimental work. Which is why the career of John von Neumann, who did do new work, and is the nearest thing the book has to a hero, is not typical. When he wanted to build a computer at the Institute he met resistance:

Harold Cherniss, a specialist in ancient Greek philosophy, became an Institute professor in 1948 when the machine was already under construction. ‘When you look back,’ Cherniss says today, ‘there are obviously strong arguments in favour of building the machine. But I would still have been against it. The computer had nothing to do with the purpose for which the Institute was founded. The computer was a practical venture, but the Institute is not supposed to be practical.’

Theory: the purest mathematics, the most esoteric cosmology, the most abstruse particle physics, are the scientific fields the Institute has looked to for its professors. Regis’s scenes from the social comedy of the surface of Institute life are put into perspective by descriptions of the work in these fields which won the actors their places on the Institute stage. He is able to give the innumerate a sense of the beauty of equations, and of the force of the theories to which they give substance. His description of the effect of the theoretical bomb Gödel exploded under the foundations of mathematics is as dramatic as his account of Oppenheimer’s moment of truth in the New Mexico desert when the real nuclear bomb was detonated. The Institute mix of very distinguished faculty and very ambitious young people makes it an ideal place to observe scientific change and scientific fashions. One of the pieces of research Regis describes in some detail deals with fractals, a branch of mathematics which is concerned with the way extremely complex shapes are generated by rather simple equations. It seems likely to be relevant to explanations of morphogenesis of all sorts – from the growth of plants and animals to the evolution of the universe – and involves the production of beautiful, very complex images on computer screens. Regis reports a conversation with a senior professor of mathematics on the question of whether Benoit Mandelbrot, the inventor of fractal geometry, should be offered an appointment:

‘I don’t think we’d want him,’ the mathematics professor says. ‘I mean, he’s big in the popular mind, but is he really that big? I know what it says in the magazines. I’m sure he’s a good man.’

‘Don’t you think he’s put forward a fundamental new idea in mathematics?’

‘I’m not sure,’ the professor says.

‘Why not?’

‘You see these nice pictures that you get by simple patterns and so on. Very nice. I see there’s something to study.’

‘Isn’t it true that Euclidean geometry doesn’t capture the shapes of what we see in nature, the shapes of trees, clouds, and so on, whereas fractal geometry does that? And that therefore it’s a key to nature in a way that no previous geometry has been?’

‘I’m not sure about that, no.’

And so on. The professor didn’t want appointments made on the basis of ‘what it says on the front page of the Times magazine section’ – but he hadn’t read Mandelbrot either.

Such differences about what is significant have implications beyond the hiring policy of the Institute. They prove that you are dealing with New Science and its uncertainties, that the issues are not to do with truth but with changing paradigms. In the latter instance, the debate has been carried on within the Institute by Thomas Kuhn, who first described scientific revolutions in terms of ‘paradigm shifts’, and Dudley Shapere, who has tried to rescue the notion of objective truth, never complete but seen more and more correctly with the passing of time, from the limbo of relativism into which Kuhn’s analysis seemed to have cast it. Regis’s account of this debate is as close as he comes to dealing with the humanities at the Institute. The historians and sociologists there are even more remote from the scientists than the cliques of scientists are from each other: ‘It’s not an intellectual club where I talk to Gödel about the incompleteness theorem and he talks to me about the religions of Java,’ Clifford Geertz told Regis.

The Institute is also a place to study the nature of originality and what nurtures it. The old men of the Institute can look back thirty, forty and fifty years. To have got there they have to have done at least ‘two important things’. ‘The question is, of course,’ one professor says, ‘whether, having done two important things, you can do anything further.’ But the will to go on trying dies hard.

Von Neumann, who as a six-year-old had joked with his father in Greek and divided one eight-digit number by another in his head, didn’t slow down. He gave the best parties at Princeton; he loved women, jokes, fast cars, money and Mexican food. ‘The story used to be told about him that while he was indeed a demi-god he had made a detailed study of humans and could imitate them perfectly.’ He calculated the answer to the first test problem set for his computer faster than the computer itself. He was not one of those who patiently waited for the third inspirational flash. He went where the action was, whether that was Los Alamos or Wall Street. He invented games theory and made a lot of money explaining it to bankers and brokers. He was also the first to develop (and may have been the first to conceive – the history is obscure) a programmable computer. The first major task given the machine was what Julian Bigelow, an engineer who came to work with von Neumann on the project, called ‘a very historic computation’. The scientists at Los Alamos wanted to know if an H-bomb would explode. ‘The computation was the largest ever done up to that time, by man or machine, taking more than a billion elementary arithmetical and logical operations just to find out whether the reaction would propagate as desired.’ Running for 60 days and nights in 1950, the machine did the figuring and proved it would. When von Neumann died, the computer was dismantled. No one else quite knew what to do with it, and Freeman Dyson says: ‘The snobs at our institute could not tolerate having electrical engineers around them who sullied with their dirty hands the purity of our scholarly atmosphere.’

In Regis’s account von Neumann stands as the link with the future, for while the old men sit thinking, the young are leading a slightly different life:

    The younger generation tends to show up a little later for lunch ... they, much like their elders, bunch together at the tables ... talking about their respective subjects. Back in their offices they spend the rest of the afternoon in front of the computer, debugging a program, or working on an article. If they do any reading at all it’s likely to be a matter of checking a reference in a scientific journal before citing it in a footnote. Perhaps they return a few phone calls or reply to computer mail.

Von Neumann’s legacy is at the centre of a number of the pieces of New Science which Regis describes. Take, for example, the work of Stephen Wolfram. An Etonian who published his first paper on particle physics at the age of 15 and got his PhD from Caltech at 20, Wolfram wanted (in Regis’s words) to explain, ‘not the complexity of any given phenomenon, but complexity itself, wherever it might be found, whether in the structure of galaxies, or in turbulent fluids, or in the nucleotide sequences of a DNA molecule’. Regis describes the kind of incident which makes workers think they are hacking into the great computer which controls life, the universe and everything. Wolfram was working with a ‘cellular automaton’, a program only a few lines long which covered the screen with an irregular pattern of triangular shapes. It reminded him of a shell he had seen in a marine biology catalogue. Put side by side, the pattern his computer produced and the pigmentation of the shell exactly matched. Wolfram has now left the Institute and has made the ultimate upward move: he has an institute of his own, the Centre for Complex Systems Research, at the University of Illinois.

In his descriptions of the work of Wolfram and Mandelbrot, Regis achieves clarity without suggesting that one can know for certain that the work is leading anywhere important. He quotes Freeman Dyson as saying: ‘Wolfram has a dream that he’s somehow or other going to understand complexity, and that the complexity of the real world is mirrored in cellular automata. It’s a big gamble.’ It is a gamble, but is it crazy enough? It is Dyson who says of the Institute: ‘I wish we had more crazy people here.’

Another great enterprise which Regis describes, the theory of superstrings, is more difficult for outsiders to understand. Its protagonists may be on the track of a unified theory of matter and of all the forces – gravitational, nuclear and electromagnetic. It was just such a unified theory that Einstein was looking for during his years at the Institute. It uses concepts like extra dimensions, a concept which only makes shadowy sense in ordinary language, and is, one is told, very difficult even for physicists to understand. It is also right where the Institute’s founders would want its work to be done – on the far theoretical edge of human thought. Regis can even explain the quality of an excitement like this.

James Gleick’s Chaos tells an exhilarating tale. It starts a quarter of a century ago with work on weather forecasting by Edward Lorenz and finishes with an account of the penetration of ‘chaos’ research into sciences as different as epidemiology and astronomy. Science has traditionally turned a blind eye when a graph fluttered unmanageably and thus the future could not be plotted on a straight line or a smooth curve. It is such nonlinear phenomena which chaos research investigates.

‘Chaos’, as it is used in this context, is confusing. It is not, for instance, a synonym for ‘random’. Weather is chaotic: you never know exactly when the next cyclone will come across the Atlantic – but it is not random. The behaviour of warm damp air, on any scale from a cupful to a cyclone, follows the general laws of expansion, contraction and movement which apply in more predictable systems. In terms of averages and general patterns, it is stable and describable. Science up to now has looked to deal with phenomena which settle to regular patterns. It has assumed that in chaotic systems like the weather the problem was a scarcity of data, a confusion of superimposed patterns and rhythms, all interacting with each other. If only you could get all the detail right, the rest would look after itself. How can a process be both part of a world which obeys physical laws and also impossible to predict in principle?

Lorenz’s discovery of the meaning which can be given to this proposition occurred when he was trying to model world weather. He had set up a highly unrealistic, very simple computer program in which variables (temperature, air pressure and so on) produced a circulation pattern. The picture the program gave of swirling air masses bore a decent resemblance to real maps of world weather. But the interaction of the equations was complex. Lorenz could not predict what was coming up next. At one point he wanted to examine one part of a computer run at greater length. As a shortcut he keyed in the values as they stood at the starting-point of the section he was interested in, rather than re-run the whole thing from the beginning. At first, the output chugged out of the printer in the same pattern as it had on the first run, but it quickly began to diverge, and soon bore no resemblance to the original run. Eventually Lorenz worked out what he had done: the computer worked to six decimal places, the print-out only showed three and in keying in the values he had assumed that the difference – one part in a thousand – was inconsequential. It was not. The evidence that equations which gave a good approximation of weather were so sensitive to small changes in initial conditions was bad news for the future of long-range weather forecasting. Even if your sampling grid was six feet (and not sixty miles, which is the scale used at present), the effect of small sampling errors would spread through the system very fast; and no matter how fine you made your grid, the amount of information needed for perfect predictions would be a set further away. As you moved towards the infinitely small, the impossibility of knowing the effect of an even finer dimension would pursue you. Small errors, Lorenz showed, can have large effects. It is not surprising that the huge computing power put into weather forecasting has had only fair results.

Inherent in this discovery was rather shocking news. The assumption that a good approximation will always produce results in due proportion had been proved wrong. The figures had only to be a little bit out for some predictions to be way out, and this limit applied even in systems like damped pendulums which seemed, on the face of it, unlikely to behave chaotically. Chaotic effects can be found in very simple systems. A waterwheel fed by a regular stream will behave chaotically at some rates of flow, and not at others. Regions of instability may be surrounded by stable regions. At some rates of increase animal populations fluctuate randomly from year to year, at others they stabilise, or follow regular cycles of increase and decrease.

Computers were the tool which made the mapping of chaos possible. When millions of computations are made, patterns begin to appear. A few hundred dots may make no pattern, but as they build up (apparently randomly), shapes begin to appear. For many researchers, the experience of watching patterns arise on a screen as unpredictable results arrive seems to have been crucial. The topological transformations which drew the patterns out of the data opened new windows. When these phenomena were investigated, Mandelbrot’s fractal geometry began to come into the picture. His discoveries dealt with patterns which repeated at smaller and larger scales. A coastline has gulfs which have bays which have smaller bays which have ragged rocks which have jagged edges, and so on. The mathematics of patterns which repeat themselves in this way at different scales was relevant to chaotic systems. One example is provided by the theoretical orbits of stars in galaxies which, when examined at higher and higher energies, turn out to behave with patterned unpredictability. The ability to reveal an infinity of detail, to be complex but patterned, suggests a better analogy for brain function and biological morphogenesis than models based on linear descriptions.

To the layman the ideas of chaos are wonderfully attractive. They are difficult but not opaque, they seem to correspond to experience. To some (Kuhn amongst them) they constitute a paradigm shift, a new view which the mis-match between the evidence of experience and an existing theoretical structure forces on a sceptical scientific community.

Gleick’s book is enthralling. It is hard for the innumerate, like me, to hold back the thought that the world is chaotic in this precise way. The illustrations he gives of images generated on computer screens are just such combinations of the mechanical and the unpredictable as instinct would suggest underlie the natural world. The astonishing thing is that it is possible to simulate them. The exploration of the universe of numbers has become possible. It turns out to be more diverse than anyone guessed and that this diversity seems to have a strong connection with diversity in the physical universe. Perhaps that is why God gets seven mentions in the index. Chaos theory seems to resolve at least the more mechanistic anxieties about determinism, and among the answers to Einstein’s remark about God not playing dice is one from Joseph Ford: ‘He does, but they are loaded.’

Gleick and Regis both tell their stories using the common science writer’s mix of biographical sketch, exposition and quotation. They are lucky to have such stories, and readers are lucky that they tell them so well. Anthony Storr’s title might lead you to suppose that he would have some insights into the mix of craziness and creativity which gives Regis his subtitle. He does not. He feels obliged to italicise the remark, ‘But this does not mean that solitary pursuits are themselves pathological,’ and sets out to cure his readers of the belief, ‘widely held, especially since the time of Freud’, that ‘men and women of genius are necessarily unstable.’ He wrestles this opinion to a quick fall by assembling anecdotal accounts of creative activity which show that it requires concentration, may be assisted by voluntary or involuntary isolation, and that some degree of solitariness is regarded as desirable by most people. His conclusion that ‘the happiest lives are probably those in which neither interpersonal relationships nor impersonal interests are idealised as the only way to salvation’ is not going to get him into any trouble, or anyone else out of it. His theories are of the soft baggy sort which can contain any evidence. Saki, Kipling and P.G. Wodehouse were all separated from their parents when children. ‘As a result all three suffered subsequently from difficulties in making close relationships and tended to show more affection towards animals or children than they were able to show towards adults.’ Aha, a theory. Let’s look at the childhoods of animal writers and pet lovers, and the adult behaviour of gifted children whose parents put them out to care. But no, for the next paragraph begins: ‘However, not every isolated person, even if gifted, turns either to fiction or to the animal kingdom. Nor can difficulties in making relationships necessarily be attributed to adverse circumstances in childhood.’

This is a game of platitudes anyone can play. How about: ‘people who spend a lot of time by themselves, particularly as children, sometimes make up stories’? Or: ‘people who are very interested in thinking very hard about difficult subjects are not usually as interested in spending a lot of time with other people as people who like chatting’? I could go on for a long time: Storr does, coming to conclusions no more remarkable than these. If it is true, as the blurb claims, that Storr ‘successfully demolishes a great deal of what is currently accepted as “true” psychology’, the structure of the subject must be shakier than even its critics suppose.