Saturday, 5 May 2012

The Grothendieck Syndrome

Alexandre Grothendieck, a brilliant French mathematician of the Bourbaki fame, is said to have invented a new kind of language for geometry and algebra that allowed mathematicians to articulate ideas which were previously inexpressible. (Marcus du Sautoy, The Music of the Primes, p. 300) But brilliance in dense, abtruse abstractions is not without its hazards.

Grothendieck bought into the idea that his revolutionary mathematics was messianic in nature. After an unfortunate series of challenges to his world-view (that the Institut was getting funding from military sources, the deteriorating geopolitical situation of the cold-war era, his inability to complete his vision of mathematics, etc.) he lost his mind. He also couldn't accept the fact that his disciples eventually became new leaders in his revolution, making their own contributions to the subject, right before his jealous eyes.

He became obsessed with the Devil whom he held responsible for "destroying the divine harmony.'

He held the Devil responsible for, among other things, changing the speed of light from a nice round value of 300,000km/s to the 'ugly' 299,887km/s. All mathematicians [claims du Sautoy] need to have a little bit of madness if they are to feel at home in the mathematical world. The sheer number of hours Grothendieck had spent exploring at the edges of the world of mathematics left him unable to chart his way home. (ibid, p. 304)

This, to me, sounds a bit like what right-wing extremists (from Harper's government to the Tea partyers, to Islamic fundamentalists) go through in that their preconceived notions of what the world should be takes over any semblance of a balanced world-view.

Listening to Harper's big 'C' Conservatives as they make pronouncements from on high is like listening to the almost autistic Jehovah's Witnesses - it is not so much to communicate with potential converts as their drivel is to reaffirm their fragile faith in their own sanity. Besides this quality, there is an unchecked willingness to usurp conventional notions of political, scientific and economics' discourse to suit their own needs which is not unlike infomercial-speak.

Radicals, money-laundering, foreign political influence, nazi-sympathizers, left-leaning media... Harper's government goes so far as to attach minders (thought police, really) to government scientists in scientific conferences and media scrums to ensure that "science" does not go contrary to Harper's agenda!

I'm saddened and disappointed by the lack of public reaction and outcry to the now obligatory baby-sitters for Canadian scientists. This is muzzling of free-speech and destruction of credibility not just for Canadian scientists but all of Canada in the world stage. Nazis, Soviets, Macarthyism and revolutionary France all branded (poisoned) public and academic discourse by insisting on "x-way of doing things". The Harper imperative is no different.

In scientific and other public knowledge-based forums, the discourse is not supposed to be determined by preconceptions but guided by non-partisan findings which adjust the theoretical frameworks and paradigms when the findings contradict them, where the marketplace of ideas rigorously determine the veracity or falsity of the ideas and ideals of the day. The circle can be squared, but impossible by using a compass and straight edge alone (ie, by conventional measure of rigour and "good form"); the world is much too complex to describe by rational numbers alone.

du Sautoy, again:

The old guard, those mathematicians active before the Second World War, began to complain that they no longer recognised the subject that they had worked in for many years. Siegel had this to say about an account of his own work that was casted in the new language:

I was disgusted with the way in which my own contributions to the subject had been disfigured and made unintelligible. The whole style...contradicts the sense of simplicity and honesty which we admire in the works of the masters in number theory - Lagrange, Gauss, or on a smaller scale, Hardy, Landau. I see a pig broken into a beautiful garden and rooting up all flowers and trees... I am afraid that mathematics will perish before the end of this century if the present trend for senseless abstraction - as I call it: the theory of empty set - cannot be blocked up. (ibid, p. 301)

The problem is not the speed of light itself as suggested by Grothendieck; the roundness of its measure depends on what standard is used. With meter-gram-second (ie, ISU) measuring standards it is that 'ugly' 299,887km/s but only because ISU has increments not 'amenable' to its roundness. The choice of unit of measure has less reality than the actual speed of light; to suggest, to insist, otherwise is sheer insanity and unreasonableness.

Democracy (and its regulatory safe-guards), in like fashion, often appears messy and unweldy as compared to totalitarian systems but history often proves it was the best, long-lasting, meaningful way of doing things while totalitarian systems last only as long as their cult figure-heads. Macarthyism, Stalinism, Reagan economics, Harperism, are artificial ideologies not founded on any semblence of reality; insisting that they last beyond their due date is at best anachronistic, at worse mindless, pathetic cults of personality.

Jay

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