What We Cannot Know. Marcus du Sautoy

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СКАЧАТЬ a stable banking system seemed very parochial, but May has recently been applying his models of the spread of infectious diseases and the dynamics of ecological food webs to understanding the banking crisis of 2008. Working with Andrew Haldane at the Bank of England, he has been considering the financial network as if it were an ecosystem. Their research has revealed how financial instruments intended to optimize returns to individual institutions with seemingly minimal risk can nonetheless cause instability in the system as a whole.

      May believes that the problem isn’t necessarily the mechanics of the market itself. It’s the way small things in the market are amplified and perverted by the way humans interact with them. For him the most worrying thing about the banking mess is getting a better handle on this contagious spreading of worry.

      ‘The challenge is: how do you put human behaviour into the model? I don’t think human psychology is mathematizable. Here we are throwing dice with our future. But if you’re trying to predict the throw of the dice then you want to know the circumstance of who owns the dice.’

      That was something I hadn’t taken into account in my attempts to predict the outcome of my casino dice. Perhaps I need to factor in who sold me my dice in the first place.

      ‘I think many of the major problems facing society are outside the realm of science and mathematics. It’s the behavioural sciences that are the ones we are going to have to depend on to save us.’

      Looking round the canteen at the House of Lords, you could see the sheer range and complexity of human behaviour at work. It makes the challenge of mathematizing even the interactions in this tiny microcosm of the human population nigh impossible. As the French historian Fernand Braudel explained in a lecture on history he gave to his fellow inmates in a German prison camp near Lübeck during the Second World War: ‘An incredible number of dice, always rolling, dominate and determine each individual existence.’ Although each individual die is unpredictable, there are still patterns that emerge in the long-range behaviour of many throws of the dice. In Braudel’s view this is what makes the study of history possible. ‘History is indeed “a poor little conjectural science” when it selects individuals as its objects … but much more rational in its procedure and results when it examines groups and repetitions.’

      But May believes that understanding the history and origins of the collection of dice that make up the whole human race is not as straightforward as Braudel makes out. For example, it’s not at all clear that we can unpick how we got to this point in our evolutionary journey.

      ‘I’ll tell you one of the questions that I think is a particularly interesting one: trying to understand our evolutionary trajectory as humans on our planet. Is the trajectory we seem to be on what happens on all or most planets, or is it the result of earlier fluctuations in the chaos which took us on this trajectory rather than another. Will we ever know enough to be able to ask whether the disaster we seem to be heading for is inevitable or whether there are lots of other planets where people are more like Mr Spock, less emotional, less colourful, but much more detached and analytical.’

      Until we discover other inhabited planets and can study their trajectories, it’s difficult to assess whether evolution inevitably leads to mismanaged ecosystems based on just one dataset called Earth.

      ‘The question of whether where we’re heading is something that happens to all inhabited planets or whether there are other planets where it doesn’t happen is something I think we’ll never know.’

      And with that May polished off the last few crumbs of his chocolate cake and plunged back into the chaos of the select committees and petty politics of Westminster.

      May’s last point relates to the challenge that chaos theory poses for knowing something about the past as much as the future. At least with the future we can wait and see what the outcome of chaotic equations produces. But trying to work backwards and understand what state our planet was in to produce the present is equally if not more challenging. The past even more than the future is probably something we can never truly know.

       LIFE: A CHANCE THROW OF THE DICE?

      May’s pioneering research explored the dynamics of a population as it went from season to season. But what determines which animals survive and which die before reproducing? According to Darwin, this is simply down to a lucky roll of the evolutionary dice.

      The model of the evolution of life on Earth is based on the idea that once you have organisms with DNA, then the offspring of these organisms share the DNA of their parent organisms. But parts of the genetic code in the DNA can undergo random mutations. These are essentially down to the chance throw of the evolutionary dice. But there is a second important strand to Darwin’s proposal, which is the idea of natural selection.

      Some of those random changes will give the offspring an increased chance of survival, while other changes will result in a disadvantage. The point of evolution by natural selection is that it is more likely that the advantageous change will survive long enough to reproduce.

      Suppose, for example, that I start with a population of giraffes that have short necks. The environment of the giraffes changes such that there is more food in the trees, so that any giraffe born with a longer neck is going to have a better chance of survival. Let’s suppose that I throw my Vegas dice to determine the chance of a mutation for each giraffe born in the next generation following this environmental change. A roll of a 1, 2, 3, 4 or 5 condemns the giraffe to a neck of the same size or shorter, while a throw of a 6 corresponds to a chance mutation which causes a longer neck. The lucky longer-necked giraffes get the food and the shorter-necked giraffes don’t survive to reproduce. So it is just the longer-necked giraffes that get the chance to pass on their DNA.

      In the next generation the same thing happens. Roll a 1, 2, 3, 4 or 5 on the dice and the giraffe doesn’t grow any taller than its parents. But another 6 grows the giraffe a bit more. The taller giraffes survive again. The environment favours the giraffes that have thrown a 6. Each generation ends up a bit taller than the last generation until there comes a point where it is no longer an advantage to grow any further.

      It’s the combination of chance and natural selection that results in us seeing more giraffes with ancestors that all threw 6s. In retrospect it looks like amazing chance that you see so many 6s in a row. But the point is that you don’t see any of the other rolls of the dice because they don’t survive. What looks like a rigged game is just the result of the combination of chance and natural selection. There is no design or fixing at work. The run of consecutive 6s isn’t a lucky streak but is actually the only thing we would expect to see from such a model.

      It’s a beautifully simple model, but, given the complexity of the changes in the environment and the range of mutations that can occur, this simple model can produce extraordinary complexity, which is borne out by the sheer variety of species that exist on Earth. One of the reasons I never really fell in love with biology is that there seemed to be no way to explain why we got cats and zebras out of this evolutionary model and not some other strange selection of animals. It all seemed so arbitrary. So random. But is that really fair?

      There is an interesting debate going on in evolutionary biology about how much chance there is in the outcomes we are seeing. If we rewound the story of life on Earth to some point in the past and threw the dice again, would we see very similar animals appearing or could we get something completely different? It is the question that May raised at the end of our lunch.

      It does appear that some parts of evolution seem inevitable. It is striking that throughout evolutionary history the eye evolved independently 50 to 100 times. This is strong evidence for the fact that the different rolls of the dice that have occurred across different СКАЧАТЬ