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How does Maths know these things before we do? Think of a sunflower and the pattern of its seeds, or the shape of ferns and leaves. John Barrow the Research Professor of Mathematical Sciences at Cambridge, and a mega heavyweight champion of the academic world (his C.V. fills 19 pages at last count) has said that these patterns or symmetries actually underlie the whole of Nature, 'from the clustering of galaxies to the crystalline structure of snowflakes.' That's not just utterly profound, it's also poetic.
Those people who think we invent maths are looking through the wrong end of the telescope. The 'whatsit' of gravity that makes some galaxies form spirals and others not - existed billions of years before evolution contrived the human brain - right! We just invented the squiggles that are a code to describe the 'whatsit'.
I want to avoid quantum physics because I'm feared you'll fall asleep. But you can't entirely if you want the whole picture. It's the world of the very very small. How can I describe it in just a few sentences? Let's take Steven Weinberg the granddaddy of modern physics, a Nobel winner and a double major dude. In the quantum world things are small, as someone once said, they are extravagantly small. Take the Planck Scale which is the smallest. Weinberg says it is '6.626 thousandth, millionth, millionth, millionth millionths,'of a centimeter. Try and cop that on your old school ruler! But stop. I mean seriously. No wonder he also said that, at this level, matter itself (real stuff), loses its central role in physics, and all that is left is principles of symmetry.
But even dummies like you and me and ordinary folk can suss a principle of symmetry. Its one of those things that are mathematical. In fact its
a purely mathematical object. Our friend John Barrow reinforces this by saying that if we, 'take matter to pieces, and probe to the root of what those pieces are then in the end we can say no more than that they are mathematics.' Hey, hey, hey - wait a minute! Is this for real ? Is everything - us and the whole universe - made of maths? It's enough to make you think you're hallucinating.
David Layzer, a Harvard professor, wonders how the abstract language of maths can capture the regularities that lie hidden deep beneath the surface of things - and equally, why it should be that they are even available to human reason.(my emphasis). He gets pretty dramatic, but what he says is true - 'these are the great mysteries at the heart of humankind's most sustained and successful rational enterprise'. He means the whole of science.
To avoid overstating things, Peter Atkins of Oxford University says that it is possibly not too extravagant to claim that the answer to the question of why maths works will be the final answer to all questions of being. I mean, this is pretty freaky stuff - right?
Gregory Chaitin, a winner of maths highest prize (there isn't a Nobel for maths), calls it 'quasi-empirical', meaning something semi-real. Roger Penrose, another mega heavyweight champion who is the Rouse Ball professor of Mathematics at Oxford, believes that maths is the actual ideal structure that underpins our real world.
Then there is the revolutionary, the Che Guevara of theoretical physics.David Deutsch, also of Oxford says, stop gazing at your navel guys. Maths is real - it's part of the fabric of reality. Although it's intangible and you can't see it, it exists objectively, and it's also independent of the laws of physics.
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