The Science of Discworld Revised Edition

start from the right thing. We don’t know. So for this very simple mathematical system, with one simple rule, and a very simple question, where we
know
the Theory of Everything … it doesn’t tell us the answer.
    Langton’s Ant will be our icon for a very important idea:
emergence
. Simple rules may lead to large, complex patterns. The issue here is not what the universe ‘really does’. It is how we understand things and how we structure them in our minds. The simple Ant and its tiled universe are technically a ‘complex system’ (it consists of a large number of entities that interact with each other, even though most of those entities are simply squares that change colour when an Ant walks on them).
    We can create a system, and give it simple rules which ‘common sense’ suggests should lead to a rather dull future, and we will often find that quite complex features will result. And they will be ‘emergent’ – that is, we have no practical way of working out what they are going to be apart from … well, watching. The Ant must dance. There are no short cuts.
    Emergent phenomena, which you can’t predict ahead of time, are just as causal as the non-emergent ones: they
are
logical consequences of the rules. And you have no idea what they are going to be. A computer will not help – all it will do is run the Ant very fast.
    A ‘geographical’ image is useful here. The ‘phase space’ of a system is the space of all possible states or behaviours – all of the things that the system could do, not just what it
does
do. The phase space of Langton’s Ant consists of all possible ways to put black and white squares on a grid – not just the ones that the Ant puts there when it follows its rules. The phase space for evolution is all conceivable organisms, not just the ones that have existed so far. Discworld is one ‘point’ in the phase space of consistent universes. Phase spaces deal with everything that might be, not what is.
    In this imagery, the features of a system are structures in phase space that give it a well-defined ‘geography’. The phase space of an emergent system is indescribably complicated: a generic term for such phase spaces is ‘Ant Country’, which you can think of as a computational form of infinite suburbia. To
understand
an emergent feature you would have to find it
without
traversing Ant Country step by step. The same problem arises when you try to start from a Theory of Everything and work out
what it implies
. You may have pinned down the micro-rules, but that doesn’t mean that you understand their macro-consequences. A Theory of Everything would tell you what the
problem
is, in precise language, but that might not help you solve it.
    Suppose, for instance, that we had very accurate rules for fundamental particles, rules that really do govern everything about them. Despite that, it’s pretty clear that those rules would not greatly help our understanding of something like economics. We want to understand someone who goes into a supermarket, buys some bananas, and pays over some money. How do we approach that from the particle rules? We have to write down an equation for every particle in the customer’s body, in the bananas, in the note that passes from customer to cashier. Our description of the transaction – money for bananas –
and
our explanation of it is in terms of an incredibly complicated equation about fundamental particles.
    Solving that equation is even harder.
And it might not even be the only fruit they buy
.
    We’re not saying that the universe hasn’t
done
it that way. We’re saying that even if it has, that won’t help us
understand
anything. So there’s a big, emergent gap between the Theory of Everything and its consequences.
    A lot of philosophers seem to have got the idea that in an emergent phenomenon the chain of causality is
broken
. If our thoughts are emergent properties of our brain, then to many philosophers they are not physically caused by the nerve cells, the electrical currents, and the chemicals in the brain. We don’t mean that. We think it’s confused nonsense. We’re perfectly happy that our thoughts are
caused
by those physical entities, but you can’t describe someone’s perceptions or memory in terms of electrical currents and chemicals.
    Human beings never understand things that way. They understand things by keeping them simple – in Archchancellor Ridcully’s case, the simpler the better. A little