by Dick Bentley
My mother, bless her dear old heart, lives in Wimborne, Dorset, a town which is popular with tourists seeking temporary relief from the fleshpots of Bournemouth. One of Wimborne’s many fine tourist attractions is the Model Town, which is – you’ve guessed it – a model of the town of Wimborne to a one-tenth scale. Not many of the happy grockles who visit the Model Town will realise that it is not a perfect model town, for it does not itself contain a model of the Model Town. Even if it did it still could not be perfect because the model of the Model Town would have to hold another, smaller, model of the Model Town, and that smaller model of the Model Town would have to hold yet another, yet smaller, model of the Model Town, and so on to infinity, which is not actually possible in the real world. A Russian doll cannot be infinitely nested.
You may think that this is mere logic-diddling for the sake of geekish amusement, but it is a pleasant example of the ubiquity of Godel’s theorem. Kurt Godel was a pretty fair example of the mad professor. Albert Einstein and Jonnie von Neuman once had to spend an hour with him before his assumption of American citizenship, talking him out of pointing out to the judge doing his naturalisation that the American Constitution contained a number of serious logical flaws. Born in 1906 in Brno, he died in 1978 in New Jersey after starving himself to death because of paranoia about poisoned food. He was on another planet to the rest of us, but Albert and Jonnie loved him dearly for, in 1931, the four-eyed scallywag had proved that arithmetic is incomplete, and that there are numbers that can never be calculated, not even if you have a computer of infinite power and can run it until infinity comes and goes twice over. Arithmetic is ‘incomplete’ in the same way that the Wimborne Model Town is also incomplete; it cannot contain itself because that would lead logically to an infinite recursion. Kurt Godel had used logic to establish the limits of logic. Why an Austrian discovered this and not an Irishman is one of the imponderable mysteries of our time.
Godel’s theorem has all sorts of uses. For example, physicists will never be able to create a Theory Of Everything, for such a theory must necessarily contain an explanation of itself, or else it doesn't cover everything. A seemingly trivial point, but it is the thread from which all over-confident theories unravel. Even Steven Hawking tripped himself up with that one, and predicted in his book A Brief History of Time that soon there would be a TOE, and had to recant later and admit that he was a dork. Those academics are cruel, but Godel’s theorem is one of God’s best jokes, so why should Hawking escape the cosmological banana-skin? Nice one, your Almightiness!
It applies nicely to politics, too. The lesson of the Twentieth Century is that all ideologies are delusions, and dangerous delusions at that. Communism, fascism, capitalism, every single "ism" has crashed and burned, all the way back to feudalism and beyond. Godel's theorem explains it all beautifully. Just as in arithmetic and physics, a logical system of analysis cannot analyse itself, and this means that there cannot be a single answer to all questions, politics included. An ideology will often work very well as the solution to a particular well-defined set of problems, limited in time and space, but if it is successful then it becomes seen as the paradigm for solving ALL problems, and that it cannot do. The Marxist-Leninist ideology was pretty efficient at getting rid of Czar Nicolas, but the next thing the Bolsheviks are talking about 'Marxist art', 'Leninist writing' and even Lysenko’s ‘Marxist-Leninist biology’, and you just know that the whole thing is going to end badly, even if it did take seventy years to reach a final collapse.
Is there a pattern emerging here? America has functioned as a political entity for over two centuries because it is not governed by a single ideology, but rather by an ad-hoc collection of theories each used on a defined problem then discarded or modified, the Constitution being merely a statement of intent and not a list of unbreakable rules. The end of the Cold War convinced many Americans that 'The American Way' was an ideology with universal application, and after that it all went wrong for them very quickly. That is why Barak Obama is such a cheering development, for he is a roots-up pragmatist not a top-down ideologue, and the American people were really smart to elect him. Meanwhile in Britain we have a similar non-ideology, one without even a written constitution, but here things are increasingly headed the other way, with more rules, more discussion of the 'meaning of British nationality', more centralisation of power, and our premier wasn't even elected by anybody, so he's bound to have a unified world-picture, his own personal ideology. Need I say more?
The ‘credit crunch’ was caused by a failure to understand Godel’s theorem, too. The Scholes-Black equation and trading-rooms full of computers had convinced all those suits in the City and Wall Street that they had a Complete Theory Of Money which would make them rich for ever. Whoops-a-daisy! The insistence on a single theory that explains everything is at the heart of every crank cult, too. “If you just listen to our Leader and accept his Big Idea into your hearts and minds you’ll be happy and everything will be just fine!” said the followers of Jim Jones, David Koresh and Marshall Applewhite. All tyrannies spring from a Big Idea. Kim Jong-il has his Juche, which can even be translated as ‘the Big Idea’, Osama bin Laden’s boys are selling his Big Idea to some hapless yak-meat-kebab-seller in Helmand right this very minute.
Hang on, though, if you think about it, Godel’s theorem itself is the answer to everything! I am the prophet of a new golden age, a new Godelian Age! Listen to me! Godel’s Big Idea explains everything! That’s right, everything! Send me your money and my sacred Crusade for Recursive Anti-Politics will solve all the problems of the world! Come and join us! Our Ashram of Recursive Serenity and Enlightenment is in the very, very, smallest of the nested model towns of Wimborne Model Town, behind the razor-wire fence with the guard-towers, where the cricket pitch used to be.