I’ve been thinking a lot about the finitude of the world recently. What I mean by that is this: While we interact with the physical world as if it were infinitely variable – everything can be subdivided, including time and space – it seems scientifically quite likely that this is not in fact the case, that rather the world is finite, that there are finitely many particles in the universe, that each of them has finitely many positions, and thus that the universe has finitely many possible states – an absurdly large number, but still finitely many.
This possibility disturbs me, and I think I’ve figured out why. Mathematically speaking, if we have infinitely many points, we can find only one equation that fits it, for it is a smooth curve, a definite function – the universe would have only one explanation. But if we have finitely many points, there are infinitely many equations that would fit the given data – for example, if we just have the points (0,0) and (1,1), the equations y=x and y=x^2 both equally well describe the data. If we have (0,0), (1,1), and (2,0), both y=-(x-1)^2+1 and y=-(x-1)^4+1 work. Et cetera. And those were all just polynomials – there’s lots of other kinds of equations out there. So a finite universe means that the universe has many possible explanations, and even at the end of time, when all is said and done, there’s no way to know which one was correct.
So finitude somewhat scares me. Then again – if the universe is finite, there are many possible explanations, but one will, I hope, be much more elegant than the others, and that will be the “true” one… that, or, since by “the universe is finite” I really mean only the physical world, the atoms and quarks and leptons and dimensions of space and time, meaning will in the end be found not in the physical, but the metaphysical. That is, I suppose, what I believe – but I’d would like to be able to find meaning in both.
Does finitude scare anyone else, or is it just me?