Wednesday, 20 September 2017

What's The Answer To Reality's BIG Big Question?

The biggest philosophical question of all is Why is there something rather than nothing? That shouldn't just mean Why does our universe exist at all? - as it so often seems to have been adapted to mean, it should mean something even more profound: Why isn't it the case that absolutely nothing exists at all?

The most rigorous popular attempts to answer this have been put forward by the likes of Stephen Hawking and Lawrence Krauss, both of whom tried to solve the problem by positing highly spurious notions of what 'nothing' actually means and how 'something' can apparently come from this 'nothing' of theirs (I wrote a response to their dodgy hypothesis in this blog post).

The upshot is, even if we accept the highly dubious notion that universes can somehow arise from nothing, this doesn't give us any clue about why the things that supposedly came from nothing couldn't have been vastly different. Why couldn't there have been no laws of physics, or no things at all that are not 'nothing'?

I think what looks to me to be the most reasonable explanation is that every single thing that can be said to have existed - that is, every thing that is a something and not nothing - is at its most primary essence a mathematical object. Anything that is physical or has any kind of physical laws is made of mathematics (in that it has the fundamental property of mathematics). This means that the primary question - Why is there something rather than nothing? - is really a question about why mathematics seems to have a necessary existence - that, in fact, whatever 'nothing' means in terms of physical things that may or may not exist, mathematics seems to not be able to help existing - it cannot do anything but exist.

On a place like the Internet you will find people who insist that mathematics is a mere human invention that we use to explain theories about the physical world. It's a strange view to have, because it appears to be completely wrong. As an example, consider Fermat’s Last Theorem, which states that a, b, and c satisfy the equation an + bn = cn for any integer value of n that equals at least 3. In other words, if you write four positive numbers and n is greater than 2, the equation an + bn = cn  will never be true.

Fermat’s Last Theorem is not self-evidently true - it took nearly four centuries to prove, and is true based on propositions about the property of numbers, not based on anything physical or on anything anyone has invented. It was true long before we came along to think it, and it would be true in any in universe with any physical laws and properties. Consequently, then, it doesn't satisfy the proposition of being a human invention nor something we use to explain theories about the physical world.

Another reason to believe that numbers exist is that we directly perceive numbers, and we tend to believe that the things we perceive do exist in some meaningful sense. The brown table I'm sitting at seems to exist - I am directly perceiving it. But if I got up and stood at each corner, I would observe a slightly different table from different angles each time. The shading of the colour brown changes according to my relative positions in the room, and my perception changes in accordance with where the light is shining in. The smoothness exists, but its texture depends on my reference point of observation. From a distance I see the table as being smooth, but with a powerful microscope I see lots of pits and crevices.

Nobody who stands next to the table denies that it exists, nor my hands that are rested on it. The apparent reality of the physical world conceals much activity, of which our naked eye is largely unaware. My hand is made up of skin and flesh and bone, which are oscillating molecules, which are an arrangement of bonded atoms, which are an aggregation of particles about one-hundred-millionth of a centimetre. Once we zoom in on the atom its solidity becomes hazier and cloud-like until we encounter its empty space. If we look further we would find the atom's nucleus, around which we would find particles called protons and neutrons and electrons - hundreds of thousands of them within one atom.

If we could enlarge a single atom to measure fifty yards in diameter its nucleus would be about the size of a grain of sugar, and its electrons would be like a few specks of dust circling the nucleus at a distance of about twenty-five yards. That tiny grain of sugar-size nucleus amounts to most of the atom's solidity, yet it only occupies a comparatively small fraction of the atom’s total volume (only about one millionth). 

Given that the table is made of atoms, in what way can the table be said to exist? It exists though our sense data, what Kant called 'phenomena', and it gives its appearance relative to the person perceiving it. Do you still think the table exists - and if so, in what way can it be said to exist given that its existence relies so heavily on sensory perception?

Hold that thought. Let's now turn to Kurt Godel - one of the smartest mathematicians ever, and probably the smartest logician. Here's one of his most well known quotes:

"Despite their remoteness from sense experience, we do have something like a perception of the objects of set theory, as is seen from the fact that the axioms force themselves on us as being true. I don’t see any reason why we should have less confidence in this kind of perception, i.e. in mathematical intuition, than in sense perception."

Godel's position is the right one, I think. If you're going to trust that the reality you perceive is based on things that actually exist, it seems quite a bizarre strategy to believe that objects that change according to sensory perception are the things that really exist, and that numbers, which do not change according to sensory perception, don't really exist. If we're going to believe in the concrete existence of anything, mathematics seems to be the one thing we definitely can believe exists.

Whichever way you cut the cloth, the thing about which we can seemingly be most certain is that the answer to the question Why isn't it the case that absolutely nothing exists at all? is that numbers exist, they always have always will, and they cannot help but exist.