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Mathematics and Madness


Joe Kaplinsky

Creativity in the sciences appears to be very different than in the arts. While an element of irrationality or madness is often thought to inspire great art, or even to be indispensable, it is seen in science only as a destructive force. This is, perhaps, why the sciences are some times not seen as 'truly' creative.

This is the split between 'two cultures' lamented by CP Snow in 1959. The split, however, is more than a century older than that. The beginning of the nineteenth century enjoyed a far more unified culture. The Romantic poets were closely engaged in with science, and less hostile to it than is often supposed. Most ambitiously, the philosophy of GWF Hegel encompassed all human knowledge under a single system.

By the turn of the nineteenth century the split between logic and spirit in mainstream thought had firmly set in. Partisans could be found on each side (Nietzsche, champion of spirit versus Russell, defender of logic), as could various attempts to overcome the divide, such as Cubism and psychoanalysis. But the split persisted, creating difficulties in understanding social life. Rational attempts to understand the irrational phenomena of war and economics have caused particular problems on both sides of the divide.

Roughly speaking the twentieth century began with an emphasis on the mathematical approach, which has gradually given way to the irrational one. As the twentieth century began the 'neoclassical revolution' in economics, with its rational economic men, was in full swing. As neoclassical economics came into full bloom its mathematical sophistication, and faith in abstract models, grew to extraordinary heights. But as time wore on the old methods proved limited. Economists may still hide behind thickets of equations, but their leading explanation of consumer behaviour today is addiction. Economic depressions are no longer to be explained by macroeconomics, but rather by the 'madness of crowds', as the stampedes of irrational investors cause wild market gyrations. International relations has faired no better, as theories of nations interacting like 'billiard balls' based on self interest have been replaced by the study of ethnic or religious fanaticism.

The split between art and science can be taken to pathological extremes. When divorced from the real world, each can become a closed system. In the case of science the product is pure mathematics. In the case of art it is madness.

Mathematics, of all the sciences, is least susceptible to inspiration by madness. Its careful and rigorous logical deductions are the very model of rationality. There seems to be no place for any of the spiritual elements that the arts use to such effect in their struggle to understand human life: the subjective experience of emotions, dreams and religion. Mathematics is coldly objective. Madness, on the other hand, is pathologically subjective. The twentieth century has seen a distressing number of flips from one extreme to the other.

Perhaps surprisingly, this theme can be traced in Hollywood films of recent years. A Beautiful Mind (Ron Howard, 2001), Good Will Hunting (Gus Van Sant, 1997), and Pi (Darren Aronfsky, 1998), can be understood as telling the story of the triumph of the spiritual over the logical. The mathematicians attempt to explain the world through the most extreme logic of objective processes. Coming up against the irrationalities of social experience, the conclusion is to turn to its polar opposite, madness. The films are faithful to historical experience, if in fictionalised form. (A Beautiful Mind is supposedly based on the life of John Nash, but has no more factual content than any other 'based on a true story' Hollywood blockbuster. Except where otherwise noted this review refers to the Hollywood Nash.)

The story starts with John Nash, as told in A Beautiful Mind. Nash (Russell Crowe) was a brilliant mathematician who embarked on graduate studies at Princeton in 1948. Science at the time had been profoundly shaped by the Second World War. Vannevar Bush had built on the war time experience to create modern university scientific research. Along with American science, Nash was sucked into the Cold War.

A hint of what was to come for Nash could be found in the presence of the brilliant Austrian logician Kurt Gödel at the Institute of Advanced Study near Princeton. Gödel had earlier proved the most remarkable mathematical theorems of all time showing that formal logic can never encompass every truth. In his everyday life in Vienna he did his best to ignore the catastrophe unfolding around him, until practical necessity forced a flight to the US.

But the coming of fascism and the Second World War had had a traumatic impact on him. Studying the US constitution to become a citizen in 1948, Gödel thought he detected a problem: the logical possibility of transformation from a democracy to a dictatorship. Gödel had every intention of informing the judge of his worries at his naturalisation interview, but was shepherded through by the worldlier Einstein. Gödel got his citizenship, but gradually descended into paranoia. His only productive work was a solution of Einstein's equations of general relativity that allowed travel backwards in time, perhaps symbolic of a desire to undo the tragedy of the twentieth century. Gödel met a sad end. He became a recluse and starved himself to death, believing his food to be poisoned.

Madness was not mathematically productive for Gödel. Indeed, it was fatal. But his tangle with the immigration authorities demonstrates the problem for mathematicians at the time Nash was beginning his research. Hegel would have understood Gödel's worry about the logical possibility of transformation from democracy to dictatorship. But Gödel's logic was not Hegel's. Mathematical logic is a powerful tool in the natural sciences, but on its own it is inadequate to grasp the subjective. Seeing that his logic was not sufficient to make sense of fascism and war, Gödel took a leap into madness and fell into the abyss.

As a young man Nash was not yet touched by politics. He was obsessed by mathematics, and set his mind to finding a single original great idea. This, he believed was the way to make his name. The strategy was ambitious, not to say arrogant, but Nash was up to it. He came upon an idea in time to write up a thesis, a breakthrough in the field of game theory.

Mathematical game theory studies any situation where people compete against each other using different strategies. As an abstract theory it covers not just games like chess, poker or football but also economic bargaining, military conflict and political negotiation. Nash's contribution shed light on how to understand self interested co-operation in games, especially where there are more than two players, creating the possibility of complex alliances.

The illustration in A Beautiful Mind is the question of who should ask out which girl. This is about as mathematical as the film gets. But for cinematic purposes there is no need to delve into the mathematics. For the depiction of obsessive hard work the content of the ideas makes little difference. Focus is always required to develop new ideas. However, it is worth noting that Nash's work on game theory is more run of the mill than revolutionary. The real Nash rightly considered it trivial compared to his truly great imbedding theorem, which describes how mathematical spaces of different dimensions fit inside one another.

But Nash, along with his ideas, was to become caught up in politics and economics, and here intrinsic scientific interest took a back seat to more immediate practical needs. His mental instability is evident from the beginning of A Beautiful Mind, and is depicted there as an integral part of his capacity for work - the drive that makes him believe he can make a greater contribution than others is also a little antisocial. But the film also shows the impact of the wider world on Nash.

Cold War strategists took up Nash's game theory. Every development was pored over by Kremlinologists and taken as a carefully planned move in a plot for world domination. But an understanding of the forces behind either Soviet or western politics required more than pure mathematical logic. In the absence of any humanistic input it was impossible to make rational sense of Nash's equations. The 'Nash equilibrium' in the Cold War was mutually assured destruction. But the acronym MAD, like MANIAC, the acronym of the Mathematical Numerical Integrator and Computer built to design the hydrogen bomb, betrayed the collapse of rationality into insanity.

A Beautiful Mind shows Nash developing a private paranoia that closely mirrors America's more public Cold War. Nash becomes a code-breaking consultant to the Pentagon. It is through this work that his madness first becomes evident. His Pentagon work is highly classified, encouraging private delusions that had no reality check with other people. Nash convinces himself that he has been given a secret mission to detect elaborate codes in magazine advertising used by the Soviets to communicate with their undercover agents. Like the Kremlinologists, his task was a futile one, seeking a pattern that wasn't there.

Nash eventually collapses and is hospitalised. His wife, Alicia (Jennifer Connelly), slowly helps him to recovery. After years of difficult struggle he gradually recovers a mental equilibrium that allows him to find a place at the Princeton mathematics department. Eventually he is able to start speaking with students again, and begins teaching informally in the library. He lets them into a secret: mathematics 'is an art form, no matter what these people around here will tell you'.

This is a recovery of sorts. But Nash has given up a lot. He still has his visions, but chooses to ignore them. 'I chose not to indulge certain appetites, like my appetite for patterns, perhaps my appetite to imagine, to dream' he says, 'I think that's what it's like with all our dreams and our nightmares ... you've got to keep feeding them for them to stay alive.' Nash, then, cannot completely give up his madness without giving up his imagination, which would be an impossibility.

Turning his back on dreams and nightmares Nash achieves a happiness of sorts, or perhaps an ordinary unhappiness. He retreats into family life, where contradictions between logic and spirit are not a problem. But his visions persist, always reminding him of a wider world of possibility where mathematics and madness both have their limits.

The hero of Good Will Hunting, set in the 1990s, is a young autodidact and mathematical genius. But despite his talents Will Hunting (Matt Damon) seems happy with his blue-collar life as a construction worker. He divides his spare time between bars, brawling and, unlike his friends, reading his way through the public library.

Will is more comfortable with his working class friends than the stuck up students at Harvard. He scorns academia. At first this appears an unambiguously healthy attitude. Drinking in a Harvard University bar, one of the students tries to impress a girl by showing up Will's friend, Chuckie (Ben Affleck), as uneducated. Will intervenes, taking the student down a peg and leaving him in the dust with his erudition. Will tells his antagonist that not only does he not have an original thought in his head, but he wasted his money on a Harvard education he could have had for a dollar fifty in late charges at the public library. He gets back the retort: 'Yeah, but I will have a degree and you'll be serving my kids fries at a drive-thru on our way to a skiing trip.'

It looks like Will is the one who cares about ideas. But there's a stumbling block. Will has natural talent, but no enthusiasm for learning.

The turning point in Will's life comes when the probation service assigns him a job as a janitor at the Massachusetts Institute of Technology. He is caught by Gerald Lambeau (Stellan Skarsgård) completing a prize mathematics problem that Lambeau has posted for his students. Lambeau intervenes with the courts, and rather than prison Will is sentenced to mathematics lessons with Lambeau and compulsory counselling.

Initially Will finds the mathematics tolerable but the counselling unacceptable. He faces down each of the therapists, leading them on by playing the victim role only to shock them by revealing that the stereotype is an act. Each therapist gives up in disgust. In desperation Lambeau turns to his old college roommate, Sean (Robin Williams).

Sean is a good psychologist, but unlike Lambeau he put his personal life above professional success. Sean agrees to take on Will as a patient, and here Will meets his match. Sean gets Will to see that for all his smarts, his knowledge is only derived from books. Will thinks he's being radical by recommending that Sean throw out his academic history texts in favour of Howard Zinn's People's History of the United States. But unlike Will, Sean has fought in war as a soldier and lived in a loving marriage, experiences that are absolutely unavailable from books.

Sean's counselling uncovers Will's weakness, his fear of human relationships. Here the film descends into unfortunate cliché, as it turns out that Will cannot love because he was abused by his father and then abandoned. His past prevents him committing to either mathematics or to a relationship with his girl friend Skylar (Minnie Driver).

As Will makes friends with Sean he comes to resent Lambeau's ambition to educate him. Will is no ordinary genius, he is amongst the greatest who ever lived, and Lambeau is determined that Will should not waste his talent. Lambeau's ambition generates tremendous tension with Sean, who argues that happiness is more important than hard work and points out the dangers of pushing Will too hard. The norms of the 1990s favour Sean, and there is simply no way that Lambeau can say to Will's face that it's not OK to be a failure.

As they are arguing over Will's future, Sean throws out an angry example: 'Hey, Gerry. In the 1960s there was a young man graduated from the University of Michigan. Did some brilliant work in mathematics. Specifically bounded harmonic functions. Then he went on to Berkeley, was assistant professor, showed amazing potential, then he moved to Montana and he blew the competition away.' So who was he? asks Lambeau. Ted Kaczynski, comes the answer: the Unabomber.

The true story of Theodore Kaczynski is set in the period between A Beautiful Mind and Good Will Hunting, and explains why Sean and Lambeau have such difficulty providing direction for Will. What makes the bourgeoisie so dangerous, remarked Karl Marx, is that it recruits the best of the proletariat into its ranks. But in more recent times that has proved not to be true. The second world war was the last time that a solid American elite was formed. The experience of Nash, Kaczynski and Will all testify to the difficulty of forging an elite in the post-war period.

After a promising career in mathematics Kacyznski fled civilisation to a Montana log cabin from where he despatched bombs in an attempt to bring down technological society. The FBI named him the Unabomber for his initial targets of universities and airlines. In 1995 Kaczynski blackmailed the New York Times and Washington Post into publishing his 35,000-word essay, Industrial Society and Its Future. His brother recognised Kaczynski's writing style and turned him into the police.

'The Industrial Revolution and its consequences have been a disaster for the human race' runs the opening of Industrial Society and Its Future. As Alston Chase, the most astute writer on the Unabomber, notes the essay as a whole is 'an academic - and popular - cliché.' As striking as its rejection of the present is its rejection of alternatives: 'We have no illusions about the feasibility of creating a new, ideal form of society. Our goal is only to destroy the existing form of society.' (Kaczynski is for nature but, as he points out, that is not a form of society.)

What is more interesting than these clichés is Chase's description of the experience as an undergraduate at Harvard that shaped the young Kaczynski, and later gave birth to the Unabomber. It is here, at an elite US university, that we see the birth of an ideology of nihilistic terrorism. Those seeking the roots of today's terror will find far more useful material in Chase's Harvard and the Making of the Unabomber than the collected works of an Al Qaeda ideologist like Sayyid Qutb.

Chase draws attention to two important influences on Kaczynski. The first was Harvard's General Education programme, developed after the Second World War in order to ensure that all undergraduates received a clear grounding in the values of the Judeo-Christian tradition. (This was the sort of Great Books course taught at Yale by Nash's imaginary friend Charles in A Beautiful Mind.) The conclusion Kacyznski took away from his studies was apparently that Western civilisation was worthy of destruction. But this was not simply a pathological response on Kaczynski's part. What Chase, a near contemporary of Kaczynski's at Harvard, points out is that the professors were themselves unable to mount the defence of Western Civilisation that was demanded by the curriculum.

The faculty was divided, writes Chase, between the humanists 'who, chastened by their experience in World War II and especially by the bombings of Hiroshima and Nagasaki, saw science and technology as a threat to Western values and even human survival', and the scientists. But the scientists were equally one sided:

'Superficially, the positivist message appeared to be an optimistic one, concerning the perfectibility of science and the inevitability of progress. It taught that reason was a liberating force and faith mere superstition; the advance of science would eventually produce a complete understanding of nature. But positivism also taught that all the accumulated non-scientific knowledge of the past, including the great religions and philosophies, had been at best merely an expression of 'cultural mores' and at worst nonsense; life had no purpose and morality no justification.'

Kaczynski absorbed the positivist message. But fleeing in horror from its failure to provide any values, he found nothing in the arts, either. All that the opposite pole had to offer was madness. Kaczynski's journey took him to the conclusion that the labels of mental illness were nothing but tools of social control. He no doubt felt he had found justification when the court system forced him to plead guilty rather than face a trial in which an insanity plea would be entered against his will.

The second influence on Kaczynski identified by Chase is an even more graphic illustration of the way in which the Cold War elite imploded. Kaczynski, like Will, was shaped by a psychological intervention. But while Will experiences a 1990s counsellor, Kaczynski was the subject of a 1950s experiment. The experiences were rather different, but both were concerned with the problem of finding something to believe in.

While Sean is a 1990s counsellor, Kaczynski's the real life psychologist, Henry A Murray, was very much of the 1950s. According to Chase, 'no figure at Harvard at this time better embodied the ongoing war between science and humanism than Henry A 'Harry' Murray ... A wealthy and blue-blooded New Yorker, Murray was both a scientist and a humanist'. During the second world war Murray had worked for the Office of Strategic Services, the forerunner of the CIA, developing psychological tests for selecting agents.

During the Korean War there was much concern about 'brain washing', arising from fears about the disloyalty amongst captured American troops. The peculiar fear of 'brain washing', which saw the challenge in psychological rather than political terms, said more about the weakness of America's self image than any mystical power of run-of-the-mill Korean propaganda. It is unclear to what extent Murray's post war work was directly connected with the military, but it seems clear that he was motivated to explore the problem of 'brain washing'.

The experiment that Kaczynski was recruited into was entitled 'Multiform Assessments of Personality Development Among Gifted College Men.' Murray designed his experiment to see how his subjects responded when their self described 'philosophy of life' was hostilely and systematically questioned under conditions of intensive interrogation. The experiment seems to have pushed several subjects to breaking point.

In the past, elite universities like Harvard had allowed the older generation to pass on to their students the self confidence to take on the task of ruling the country. With Kaczynski at Harvard the process unconsciously went into reverse. Not only did the curriculum express a barely disguised pessimism, but Murray actively sought out the best of the generation in order to break up any emerging philosophy of life.

Kaczynski reacted in an extreme way against the disintegration of any notion of progress. For Will, a generation later, the failure of progress is an accomplished fact. It doesn't drive him mad, it is simply part of his being. The impossibility of incorporating Will into the ruling elite under these conditions becomes evident with his response to a job interview at the National Security Agency:

'Why shouldn't I work for the NSA? That's a tough one. But I'll take a shot. Say I'm working at the NSA, and somebody puts a code on my desk, somethin' no one else can break. Maybe I take a shot at it and maybe I break it. And I'm real happy with myself, cus' I did my job well. But maybe that code was the location of some rebel army in North Africa or the Middle East and once they have that location, they bomb the village where the rebels are hiding... Fifteen hundred people that I never met, never had no problem with get killed. Now the politicians are sayin', 'Oh, Send in the marines to secure the area' cus' they don't give a shit. It won't be their kid over there, gettin' shot. Just like it wasn't them when their number got called, cus' they were off pullin' a tour in the National Guard. It'll be some kid from Southie over there takin' shrapnel in the ass. He comes back to find that the plant he used to work at got exported to the country he just got back from. And the guy who put the shrapnel in his ass got his old job, cus' he'll work for fifteen cents a day and no bathroom breaks. Meanwhile he realizes the only reason he was over there in the first place was so that we could install a government that would sell us oil at a good price. And of course the oil companies used the little skirmish over there to scare up domestic oil prices. A cute little ancillary benefit for them but it ain't helping my buddy at two-fifty a gallon. They're takin' their sweet time bringin' the oil back, of course, maybe even took the liberty of hiring an alcoholic skipper who likes to drink martinis and fuckin' play slalom with the icebergs, it ain't too long till he hits one, spills the oil and kills all the sea life in the North Atlantic. So now my buddy's out of work. He can't afford to drive, so he's walking to the fuckin' job interviews, which sucks because the shrapnel in his ass is givin' him chronic haemorrhoids. And meanwhile he's starvin' cus' every time he tries to get a bite to eat the only blue plate special they're servin' is North Atlantic scrod with Quaker State. So what did I think? I'm holdin' out for somethin' better. I figure fuck it, while I'm at it why not just shoot my buddy, take his job, give it to his sworn enemy, hike up gas prices, bomb a village, club a baby seal, hit the hash pipe and join the National Guard? I could be elected president.'

It seems safe to assume that Will is not planning to vote for George W Bush. (For a film released in 1997 it also demonstrates the remarkable indifference of anti-American complaints to the specifics of new developments. That Will made this speech long before the invasion of Iraq suggests that such generic criticisms have little to do with the reality of the Middle East.)

It is unclear what drives Will. His own claim, that he has become a genius with no effort or enthusiasm at all is totally implausible. As Sean points out, there must be some motivation underneath the cynical mask. However, there is little hint in the film that such motives arise in a wider public world. The exceptional factor in Will's life is abuse.

At the conclusion of the film Will has to make a choice. Neither Sean nor Lambeau can tell him that it's not OK to be a failure, but Chuckie can: 'Look, you're my best friend, so don't take this the wrong way. In twenty years, if you're still livin' here, comin' over to my house to watch the Patriots games, still workin' construction, I'll fuckin' kill you. That's not a threat. Now, that's a fact. I'll fuckin' kill you.' This seems to motivate Will better than any counselling. But he does rely on Sean to confront the experience of childhood abuse. With the assurance that 'it's not your fault' he is able to move on. Having exorcised his demons Will no longer feels inadequate or any need to prove himself. He chooses Sean's path to emotional fulfilment over Lambeau's commitment to hard work.

In Darren Aronofsky's film madness takes an extreme form. By the end of Pi we can no longer rely on a boundary between madness and reality. Pi is filmed in binary black and white. In A Beautiful Mind and Good Will Hunting, black and white is a sign of the spooks, the men in black set against a bright background blocking out any vision of the surroundings. In Pi black and white is everywhere, a sign of Manichean paranoia. The confrontation between mathematics and society becomes acute in the stream of numbers flowing out of the stock market.

Pi is the story of Max Cohen (Sean Gullette), a young mathematician working obsessively and in isolation from his apartment where he is building a supercomputer named Euclid to unravel the mysteries of the universe. His project recalls that of the real life Chudnovsky brothers, whose homemade Manhattan supercomputer broke the then world record by calculating pi to over 4 billion digits, only Max is rather more possessed by mathematics. He relies on drugs rather than social interaction to keep going.

Max is convinced that mathematics holds answers to deeper mysteries. He sees patterns everywhere. Refusing to believe those who say that the world is too complex or chaotic to comprehend he seeks to apply the mathematics of nature to human history ... and ultimately the New York Stock Exchange. The fantasy is an old one. In the age of Mercantilist capitalism it was the dream of the philosopher's stone. The Industrial Revolution brought with it innumerable schemes for perpetual motion machines. And in today's financialised economy the quest is for a mathematical formula to predict the movements of the markets.

The ants that crawl through Euclid, gumming up its circuits, are a nice touch. They are, of course, computer bugs. But they are also drug-induced hallucinations, of a world that comes alive out of your control. Finally they are not just the cause of crashes, but the very operating principle of the computer. The methods of complexity theory often make reference to the behaviour of ant colonies as a model. Euclid is simulating market traders as ants crawling backward and forth, smelling out profit, and when it breaks down the ants overflow from the machine....

The bugs have crashed Euclid. But as the programme collapses it spits out a series of numbers. At first they appear to be nonsense, but when the market, too, crashes Max realises that there is meaning to be uncovered in what looked like a breakdown. Max has stumbled on something profound but doesn't yet know what he possesses.

Over games of go (also played by mathematicians at Princeton) Max's mentor, Sol (Mark Margolis), advises him to slow down. The obsessive, drug-fuelled style has its place in mathematics. Paul Erdös, the most productive mathematician of the twentieth century, inspired the comment that a mathematician is a machine for turning coffee into theorems. His later dependence on amphetamines provoked his friends to bet him that he couldn't quit. Four weeks later Erdös won the bet but was dismayed, claiming that the advance of mathematics had been set back by a month. But the drug-fuelled style is certainly not for everyone (Erdös' only hesitation in speaking publicly about his amphetamine use was a fear that children might believe this was the only route to mathematical success).

In Max's case the advice to cut back looks good. Mathematics needs work but the insight can often comes with the relaxation, when months of struggle come together in a moment of insight. Archimedes' eureka moment as he sank into his warm bath speaks across the centuries.

But Sol is also a conservative influence. He represents the wisdom of experience (Solomon). In the old days he came close to the truth Max is seeking, but its searing power convinced him to retreat. Some things are better left unknown. Max the young revolutionary is undeterred. Sol's caution only spurs him on, as he recognises that new advances are only made at the edge.

Others are also after the Truth. Unlike Max, they know the power of the numbers he has discovered, and are determined to take it from him. His first pursuers are corporate interests, who have sinister military connections and offer him classified technology in return for his results, which they plan to use to make a killing on Wall Street. His second pursuers are Jewish Kabbalists. They believe that the Torah encodes numerological messages, and that Max's numbers encode the true name of God whose incantation will hasten the coming of the Messiah.

Max is pulled from one to the other, then makes good an escape. But he has seen the wisdom in renouncing knowledge. The film ends with the use of a power drill in an act that echoes the shamanistic ritual releasing evil spirits. The drill relieves Max of his burden. He has lost his gift of calculation, he is no longer plagued by the messianic delusions - of himself or others - and he can return to an ordinary life. But he is also no longer driven to work.

The final pacification has something of a lobotomy about it. The attempt to grapple with economics and religion stretch reason past breaking point, and the loss of drive brings calm.

Pi refers to numerous fashionable and not so fashionable ideas. It is thick with Greek references, starting with the title. Max claims to have gained his gift when he looked into the sun as a child. The story recalls Plato's simile comparing the Form of the Good to the sun: it cannot be looked upon directly but nevertheless illuminates the truth.

Plato certainly informs Max's philosophy in which 'the world is made of numbers'. But the story of looking upon the blinding light also occurs in the Kabbalah of Jewish mystics. Kabbalah is far more fashionable in popular culture than rationalistic Platonism. Kabbalistic codes features in best sellers like Dan Brown's potboiler The Da Vinca Code, or the equally dire 'non-fiction' genre represented by Michael Drosnin's The Bible Code.

The hope invested in the Kabbalah is that religious works contain hidden messages that we have not yet decoded. The association of numbers with letters provides a means to this end. In Pi it also provides a connection between religion and mathematics. But its popularity is down to a feeling that while contemporary religion is unsatisfactory it addresses a subject matter that natural science seems not to. Sol is right to warn Max that mysticism is a dead end. But Max is right to insist back that social life contains comprehensible patterns and laws. The challenge is to find a rational extension of science, one that can understand human experience without resorting to untruths.

Another fashionable attempt to bridge the gap featured in Pi is the mathematics of chaos, complexity and pattern formation. Often it is mathematics of biology that gets most attention, as in Pi's references to the growth of the logarithmic spiral and swarm behaviour. But the popularity of complexity theory has been driven less by its successes than by the collapse of the social sciences in the wake of the cold war. Beneath the computer simulations and mathematical equations runs a deep streak of irrationalist philosophy.

The ideas of complexity theory themselves have a complex history. One strand is rooted in mathematics and biological science. But another strand can be traced back to ideas on the other side of the logic / spirit divide that were popularised in the wake of the first world war: the holism of Jan Smuts, Gestalt psychology, the 'creative evolution' of Henri Bergson and the crowd psychology of Gustave Le Bon.

Despite its interesting contributions to the natural sciences, the resonance of complexity theory in today's popular culture (and the social sciences) relies on little more than the idea that everything is connected and directed by a universal, vaguely biological, pattern. This looks like a cross between the mystical unorganised religion of Kabbalah, conspiracy mongering, and an environmental consciousness of unity with the Earth.

The relentless beat of Pi's soundtrack works as a pounding heart, giving the sense that our biological being, gut instinct, is the source of knowledge. It is this meaning of biology, not biological science, which drives Max's work. In Pi mathematical insight comes from Bergsonian intuition, not rational calculation.

The consequence is that an irrational world cannot be understood in a mediated way through culture, art or theory. It can only be felt immediately. But the necessary internalisation of irrationality is tantamount to madness, and once again our mathematician succumbs to insanity.

All three films show a retreat into the personal. Nash retreats to family life, Will puts the pursuit of love above a career, and Max renounces the attempt to understand the public world.

A privatised life can allow for a peaceful co-existence between different outlooks by relieving the pressure to resolve contradictions. But by the same measure it blocks the creative development of ideas. The problem is illustrated by Nash's Nobel acceptance speech at the end of A Beautiful Mind:

'I've always believed in numbers; in the equations and logics that lead to reason. But after a lifetime of such pursuit I ask, what truly is logic? Who decides reason? My quest has taken me through the physical, the metaphysical, the delusional and back. But I have made the most important discovery of my career. The most important discovery of my life. It is only in the mysterious equations of love that any logic or reason can be found.'

No sane Nobel acceptance speech has ever sounded like that. Not because love is unimportant, but because Nobels are not awarded for personal experience. On our own we may stumble across knowledge that, like love, is true or beautiful. But this will never be science or art. Science and art are part of the same enterprise of understanding the world. They are unified by, amongst other things, their collaborative nature, which takes the insights of individuals and transforms them through interaction with the world.

Science is the more developed form of knowledge. It is more reliable than art. It often corrects misunderstandings, in surprising and counter-intuitive ways. But investigation begins with art. Art is the leading edge of knowledge. If science refuses to follow where art leads then art left is stranded. It is under these conditions that art will always have a tendency toward madness.

Science and art each contribute to our understanding of social problems. Together they create an understanding of society as a whole. But they are split apart, and crippled, by today's suspicion that any form of public knowledge that claims to know totalities.

Both classical liberalism and post-modernism are paralysed by a fear that creating public knowledge raises the possibility of totalitarianism, equated with imposing your own view on others. In art this manifests itself in non-judgemental anti-elitism. In science new approaches are constantly accompanied by an abjuration of using new knowledge to actively intervene in the world.

The equation of knowledge with violence is summed in the title of Wole Soyinka's lecture, 'I am right; you are dead'. While Soyinka's title accurately describes the outlook of Al Qaeda, Soyinka casts his net wider. He applies it equally to George W Bush, a man who believes in nothing much, except maybe a confused mixture of electoral pragmatism and paranoid fear. If even Bush can be cast as a fanatic then this is, in effect, a blanket condemnation of any one who claims to know what is right.

So long as we fear to carry through the public consequences of our ideas, social science and art will retain their tendency toward becoming insane, circular, private games.

REFERENCES:

A Beautiful Mind

Good Will Hunting

Pi

Alston Chase, Harvard and the Making of the Unabomber, The Atlantic Monthly June 2000

The Unabomber, Industrial Society and its Future

Dan Brown, The Da Vinci Code

Michael Drosnin, The Bible Code

Wole Soyinka, I am Right; You are Dead

 
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