The Science of Discworld IV

calculations show that an infinite pile of stationary turtles can support itself in a universe in which gravity is a constant force in a fixed direction (call this ‘down’). This rather improbable structure works because the force of gravity acting on each turtle is exactly balanced by the reaction force where it stands on the turtle below, so Newton’s third law of motion – action equals reaction – is obeyed. Similarly, there is no problem with causality in the infinite temporal pile of universes: each is caused by the previous one, so every universe has a cause. But psychologically, human beings are entirely happy with infinite piles of causality, yet find an infinite pile of turtles ridiculous.
    We seem to accept or reject infinite piles of causality in a rather haphazard way, however. The philosopher David Hume rejected one example of what he called ‘infinite progression’ in his 1779
Dialogues Concerning Natural Religion
. The context was a discussionof a creator God as an explanation of the material world. The obvious question ‘what created God?’ leads all too naturally to ‘creators all the way back’, a line of thinking that Hume wanted to close off. He says:
    Have we not the same reason to trace that ideal world into another ideal world, or new intelligent principle? But if we stop, and go no further; why go so far? Why not stop at the material world? … after all, what satisfaction is there in that infinite progression? … If the material world rests upon a similar ideal world, this ideal world must rest upon some other; and so on, without end. It were better, therefore, never to look beyond the present material world. By supposing it to contain the principle of its order within itself, we really assert it to be God; and the sooner we arrive at that Divine Being, so much the better. When you go one step beyond the mundane system, you only excite an inquisitive humour which it is impossible ever to satisfy.
    In short, if we identify God with the material universe, we need go no further, and that’s great because it stops us asking awkward questions. However, this does seem to imply that the universe created itself. And that seems to leave open exactly the line of thinking that Hume was trying to close (but Spinoza, two hundred years earlier, had already espoused that idea…).
    Other scientific issues can be similarly swayed by human psychology. It is difficult to imagine Einstein’s curved space (though not impossible for a trained mathematician or physicist), because we foolishly ask ‘curved round what?’ The answer is that it’s not curved
round
anything – it’s just curved. Its natural metric – its mathematical measure of distance – is not flat. Space seems to bunch up or spread out compared to a naive model based on Euclid’s geometry. On the other hand, we are very happy with an infinite flat Euclidean plane or its three-dimensional analogue, space. It never occurs to usto ask ‘flat along what?’ But it’s an equally sensible (or equally senseless) question.
    These cognitive biases probably stem from the model of space that our brains have evolved to contain, which seems to be Euclidean. This may perhaps be the simplest model that fits our experiences of the nearby world, extrapolated in the simplest way to avoid space having a boundary. Which would be appealing because we don’t
see
any boundary. Our minds are very parochial. Our model of causality presumably evolved to match sequences of events that are common in our immediate vicinity, the human-scale world.
    When it comes to the crunch, looking at both the theory that time had a specific origin, a finite period into the past, and the theory that it did not, but has always been in existence, then
both
have inherent flaws. This suggests that we are not thinking about the right question. Our view of the universe may be just as parochial and unreasonable as the world-bearing animals of ancient cultures were. Future scientists may view both the Big Bang, and four elephants riding on a turtle, as conceptual errors of a very similar kind.
    fn1 Like all really nice stories this tale, told by a ‘country parson’, may be false. Other versions say that Newton kept losing time from his research by letting the cat out. Selig Brodetsky’s
Sir Isaac Newton
and Louis Trenchard More’s
Isaac Newton: a Biography
both state that the great mathematician did not allow either a cat or a dog to enter his chamber. But in 1827