The Science of Discworld IV

well-educated people than it is among the poorly educated. And it is the common experience of atheists and rationalists that people who embrace extreme versions of religion tend not to be good at critical thinking. Especially about their own beliefs.
    Psychologists study the whole human brain; neuroscientists look at the brain’s detailed workings, in particular how it controls the movements of the body. Many think that this is why the brain evolved to begin with, and sensory information-processing came later, along with all of the other subtler functions of the brain. Engineers, aiming to build better robots, are borrowing tricks from the brain. One of the fundamental features of the brain is how it deals with uncertainty.
    Our senses are imprecise, and their inputs to the brain are subject to ‘noise’ – random mistakes. The workings of the brain, being evolved wetware (the organic material of the nervous system) rather than carefully engineered hardware or software, are also subject to errors. The signals that the brain sends to the body suffer from unavoidablevariability. Try to sink a golf ball with a ten-metre putt, a hundred times. You won’t get it in the hole every time. Sometimes you may succeed, sometimes you’ll miss by a small amount, but occasionally you’ll miss by more. Professional golfers are paid a lot of money because they are marginally better at reducing this kind of variability than the rest of us.
    The same variability comes into play, usually in a more exaggerated form, when it comes to social and political judgements. Here the noise-to-signal ratio is even higher. Not only do we need to take into account all of the information that is being provided: we have to decide which of it is sensible and which is rubbish. How does the brain juggle all of these conflicting factors and come to some kind of decision? A theory that currently explains a great deal, and has a lot of experimental support, is that the brain can be well modelled as a Bayesian decision machine.
    It’s a mistake to say that any natural phenomenon is
the same as
some formal mathematical model, if only because mathematics is a system of human thought, and nature isn’t. Bayesian decision theory is a branch of mathematics, a way of formulating probabilities and statistics. The brain is an interconnected network of nerve cells, whose dynamics depend on chemistry and electrical currents. Bearing this in mind, it seems that over the megayears our brains have evolved networks that mimic the mathematical features of Bayesian decision theory. We can test whether such networks exist, but as yet we have little idea of how they actually work.
    In the 1700s, the Reverend Thomas Bayes unwittingly started a revolution in statistics when he suggested a new interpretation of probability. At the time this was a hazy concept anyway, but there was broad agreement that the probability of some event can be defined as the proportion of trials on which that event happens, in the long run. Pick a card at random from a pack, billions of times, and you will get the ace of spades about one time in 52. The same goes for any other specific card, and the reason is that there are 52 cards, and it’shard to see why any particular one should turn up more frequently than any other.
    Bayes had a different idea. There are many circumstances in which it is not possible to repeat a trial many times. What, for example, is the probability that God exists? Whatever our views, we can’t generate billions of universes and count how many of them have a deity. One way to handle such problems is to decide that such probabilities have no meaning. But Bayes argued that in many contexts, you could assign a probability to a one-off event: it was the degree of belief in the occurrence of that event. More strongly, if there was some genuine evidence, it was the degree of
confidence
in the evidence. We make this kind of snap judgement all the time, for example when thinking that Spain’s football team has roughly a 75% chance of winning the UEFA Europa League football championship, or that the chances of rain today are low.
    What Bayes did, sometime in the mid-1700s, was to find a mathematical formula, allowing these ‘prior probabilities’ to modify solid information obtained by other means. A friend of his published the formula in 1763, two years after his death. Suppose you know that Spain’s record of winning big football tournaments is only 60% (a figure we