Tuesday, April 06, 2010

Apostolos Doxiadis, Christos H. Papadimitriou, Alecos Papadatos & Annie di Donna – ‘Logicomix: an Epic Search for Truth’

This popped up on Dad’s Amazon recommendations, as a result, he can only imagine, of buying comics for me, demographically shazam’d together with the kind of philosophy / maths things he tends to be interested in. It only goes to show – if you can imagine it, it probably exists. Left to my own devices, I think the awkwardness of the first part of the title together with the haughtiness of the second would have been enough to put me off. Not to mention the central conceit – to tell the story of Bertrand Russell’s attempt to establish a logical foundation for mathematics, through a comic. Is this really the best medium? Regarding the philosophy side of things, I am not remotely qualified to say, but in terms of creating drama out of academic crises, it succeeds, and spectacularly. A niggle remains that it must surely leave out most of the arguments upon which its own drama is based, but it’s not like I was ever going to read Principia Mathematica, Wittgenstein’s Tractatus Logico-Philosophicus, or indeed anything without characters and a story. This is the compromise Logicomix makes: just because the stuff in which it deals is very complicated indeed, doesn’t mean it isn’t important; and if it’s important, its story deserves to be told.

As a precocious young man, Russell comes up with his paradox, which attacks set theory:
‘Does the set of all sets which do not contain themselves contain itself?’ To which the answer is ‘If it does, then it doesn’t. And if it doesn’t, then it does!’ It sounds like a parlour witticism. But it subverts the notion of ‘set’ as a collection defined by a common property. (p. 168)
This is his moment of triumph, but it proves so problematical that it is easy to forget the Russell who arrived at it during the pages which follow. He grinds to a halt in his attempt, despite the paradox, to stick with logic: Principia Mathematica is written with the mathematician Alfred Whitehead over the following decade, and published between 1910-13. During the same period, Russell becomes estranged from his own wife and falls for Whitehead’s. The book sours at this point, losing the charm of a fierce young intelligence taking on stuffy old mathematics with a fond new wife in tow. Russell appears to consider Principia Mathematica a failure, and is reluctant to publish – which hardly anyone wants him to do anyway. It is redeemed much later in the story by Kurt Gödel, who uses its methods to prove the conclusion it is apparently desperate to avoid, that there are mathematical truths which not only haven’t been discovered, but which are also undiscoverable.

Then there is Wittgenstein. As presented here, through Russell’s tired perception, he comes across as a lunatic. Now, I remember from reading Ray Monk’s biography of him years ago that he was not a conventionally charming man – not even in the absent minded academic line. But still, one warmed to him for his integrity, and just sort of took for granted that his ideas were tremendously important*. Here, that importance – though not the integrity – is in doubt. He has two things to say: that logic is not divisible from language, and that ‘the things that cannot be talked about logically... are the only ones which are truly important!!!’ (p. 288). On the first point:
Russell: The ‘Picture’ theory is clear enough. But it gives us truth only because of the underlying higher language of logic.
Wittgenstein: There you go again! There’s no such thing as a ‘higher language’! Truth comes in only one variety! A ‘Picture Language’ is all you need to describe the world, i.e. all the facts!
Russell: …and logic?
Wittgenstein: Logic is the form of language, it’s embedded in it, like the iron structure that supports a building. But try living in that structure! (p. 258)
The italics and exclamation marks do look better in speech balloons, by the way. The end of that passage encapsulates the moral of the book. The whole thing is told from within two frames – firstly, the team who wrote and drew it appear as characters, allowing a built-in commentary on the flow of the narrative; and secondly, Russell gives a lecture to an American audience in 1939, which provides the narrative impetus and voice for his own reminiscences. His facial expressions during this talk, and the contrast between ‘now’ and his gradually ageing younger self are probably the best thing about the artwork, it is remarkable to watch him grow into himself. The lecture is picketed by protesters who don’t want the US to enter World War II – they want Russell’s support, reminding him of his pacifism during World War I. Nazism is an example of a rigid logical structure imposed on real life – the ultimate example, in fact, of why this is a bad idea. Frege, one of the men behind set theory, is shown late on as a crazed Nazi sympathiser.

So if the main achievement of Russell’s life was the fleeting moment in which he established that mathematical logic must be flawed, and if he tired himself out failing to disprove this over many years, what exactly is this book celebrating? The author-character Christos stands up for Principia Mathematica as the basis for Gödel’s breakthrough, and claims that with the holy grail of a perfectly logical mathematics gone, the way was clear for people such as John von Neumann (who was present at Gödel’s lecture, and reacted by saying ‘It’s all over’) to concentrate on what maths could actually be made to do, and – voilà! – you get the utopia of the internet. Without exactly knowing why, that seems suspect to me (the internet as a paragon of how not to waste time down esoteric blind alleys? And why did the practical have to wait until the impractical had been proved impossible?). All the same, a beautifully drawn, entertaining read, and an illuminating juxtaposition of politics and science during the first half of the twentieth century.

* You may notice a pattern forming here.

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