One is obliged to admit that perception and what depends upon it is inexplicable on mechanical principles, that is, by figures and motions. In imagining that there is a machine whose construction would enable it to think, to sense, and to have perception, one could conceive it enlarged while retaining the same proportions, so that one could enter into it, just like into a windmill. Supposing this, one should, when visiting within it, find only parts pushing one another, and never anything by which to explain a perception. Thus it is in the simple substance, and not in the composite or in the machine, that one must look for perception.

It would be easy to make experience easier to endure by making the feelings of unpleasantness less intense. But the point about aesthetics is that it is selective. Only some experiences trigger it.

It’s a bit of a generalisation, but to some extent our aesthetic sense is based around the idea of spotting patterns in something that initially seems complicated and incomprehensible that enable us to understand it in terms of far simpler rules and relationships. It amounts to the data compression ratio – the ratio of the complexity of the raw input, to that of the simple rules and relationships, with a bonus when the relationships are less obvious and more challenging to extract.

A square is simple, but it is not particularly beautiful because its simplicity is so obvious. You can’t compress it much further. However, a square tessellation, or even better a complex tessellation with a square symmetry group is far more pleasing to the eye, because the image can be compressed much more. Fractals are even more beautiful for the same reason.

This same principle applies also to the explanations we generate about the world, and the feeling of pleasure when we experience that Aha! moment, spotting a simplifying connection or relationship that makes sense of the world, has a clear evolutionary benefit. It motivates us to construct parsimonious explanations of more (and more complicated) phenomena that help us better predict the behaviour of our world.

The reason it works is that the appearance of complexity of our world at every level is based on the elaboration and recursive application of simple rules. It evolved to take advantage of this property at one level of observation (where hunter-gatherers operate), but the principle applies universally, and so it has proved equally useful in domains that our hunter-gatherer ancestors could never have considered.

Humans 100,000 years ago were every bit as intelligent as humans today. Have you never wondered what they used those big brains for?

He can simply put it everywhere.

You need to ask the question the other way round.

Why should we have evolved an aesthetic sense that turns out to be useful in interpreting the behaviour of the universe we live in?

Arguably, all the real numbers are “in the middle” of the Reals, including zero. It depends which dictionary you read, I guess.

Quite so. How could there be infinitely many numbers on the number line, with a zero in the middle of them?