Shakespeare was a gilded ape.

More later.

For now, join me in wondering something I’ve often wondered: What it would be like to experience an asteroid striking the earth. You might be dead before you knew it. You might be woken by the glare and be dead a few seconds later. Slain by the sound of the strike alone. Or the heat alone. There are asteroids that could wipe out every human on earth, or every vertebrate, or every complex form of life. Or you might survive and wish you hadn’t. After some asteroid-strikes, the living would envy the dead.

It’s a big way for the world to end. Bigger and more frightening than the ways in which a single world could suddenly end: my world or yours. We could be hit by a car, stabbed by a mugger, decapitated by a falling tile. But those mortal modalities don’t have the emotional weight, the head-hammering heft, of a world-wide wipe-out like an asteroid-strike. Or a mega-volcano. Or being skewered by gamma rays from a nearby nova. Nearby in the astronomical sense, that is. We’re talking light years: millions upon millions of kilometres. That’s why I find an gamma-ray nova, which could sterilize the entire earth, more frightening to contemplate than an asteroid-strike. The emotion aroused by a means of dying is directly proportional to the difficulty of escaping it.

And so, on a smaller scale, the thought of plague is more frightening than the thought of a house-fire. You don’t have to do much to get out of a burning house. You have to do a lot more to escape a plague. That’s why an asteroid-strike is more frightening than plague. You can sometimes run from a plague and live. You can’t run from an asteroid-strike. There would be nowhere on earth to hide. But you could, conceivably, leave the earth to avoid it. You’d have to do much more than leave the earth to escape a gamma-ray nova, but escape is still conceivable, given enough warning and advanced enough technology. But there is a way for the world to end that you couldn’t escape anywhere. Not here, not on the moon, not in orbit around Alpha Centauri, not anywhere at all in the universe. Because cosmologists have theorized that the whole universe might collide with a second universe. Get out of that! It would be like the earth being hit by a second earth, but on a cosmic scale. Everything, everywhere, would be hit by everything else.

It’s the ultimate Götterdämmerung (though Dämmerung is not the mot juste). I can’t imagine what it would be like to experience a universe-strike, because I’m not sure experience-of-it would be possible. The world – the whole universe – would presumably be over in less than an eyeblink. Apocalypse doesn’t come bigger than that: asteroid-strike is big, but asteroids are far less than dust-specks, on a cosmic scale. So universe-strike is as big as it gets. After all, cosmology deals in big ideas: the beginning of the universe, the end of the universe, the evolution of the universe. It deals in big understandings, too. That’s why it uses the most powerful tool man has ever invented: mathematics. “Give me a place to stand,” Archimedes once said, “and I will move the world.” He was talking about levers and fulcrums, but mathematics can move much more than the world. Nothing comes bigger than infinity (except other infinities – see Cantor), but human beings have been manipulating it for millennia. Here’s a very simple example: the proof of the infinitude of the primes (numbers divisible only by themselves and one). It is an astonishing thought that a human being can say of primes that they go on for ever. The Gods themselves could count for all eternity and they would never stop finding primes.

Tiny human beings know so, even though they can’t do so. The infinitude of the primes is extra-empirical: you could never confirm it by experience, you have to trust the logic in the proof. But it’s as certain as any human proof can be. So is the proof that the square root of 2 (the number that, multiplied by itself, equals 2) is irrational, i.e., impossible to match exactly with any ratio of whole numbers, like 3/2 or 17/12 or 1,023,286,908,188,737 / 723,573,111,879,672. And that proof is even more astonishing to contemplate. The Pythagorean sect first discovered it, or so the story goes. The story then says that one of the sect revealed it to the common people. And was killed by the gods, or by his fellow Pythagoreans, in punishment. True or false, the punishment is an appropriate tribute to the importance of the proof, which, for me, is the greatest intellectual discovery of all time.

The strangest, too. I only take two drugs, but they’re the strongest in the universe: H₂O and mathematics. Without water, I wouldn’t experience anything at all. Without mathematics, I wouldn’t have come across the infinitude of the primes, or the irrationality of √2, or probability theory, or statistics, or fractals, or many other strange and wonderful things. The strangest and most wonderful work of fiction I know is J.-K. Huysmans’ À Rebours (1884), which is about a Frenchman called des Esseintes who locks himself into a gilded cage – a lavishly decorated and equipped house – in the French countryside. But the gilded cage is entirely appropriate, because des Esseintes is, for me, a gilded ape. For all his aesthetic sensitivity, for all the richness and complexity of the art-works and experiences and memories he explores and dissects, he seems to know nothing about and care nothing about mathematics.

Or nothing about explicit mathematics. Implicit mathematics is in everything he does and everything he experiences, because, as the Pythagoreans used to say, Hoi Arithmoi Arkhousin To Sympan: Numbers Rule the Whole. You couldn’t run from a universe-strike, and you can’t run from maths. It’s not just everywhere, governing the behaviour of everything from gluons to galaxies: some physicists argue that it is everything, that the ultimate substrate of reality is mathematics. There are lots of strange and wonderful ideas like that in physics, but I can’t appreciate them as I’d like to, because I’m not mathematically literate enough. Physics is intrinsically difficult. There’s a simple reason for this: it’s because physics is intrinsically simple.

Paradox? No. I’m using “physics” in two senses. The human activity of physics – observing, theorizing, experimenting – requires advanced understanding of very complex and difficult mathematics. But that’s because the phenomena of physics – matter, energy, and their interactions – are simple enough to be captured by human mathematics. The way of a snake on a stone, of an eagle in the sky, of a man with a maid – phenomena like those are presently beyond mathematics. It’s easier to investigate the nature and behaviour of stones or the sky than to investigate the nature and behaviour of snakes or eagles, let alone of men and maids. That is part of why you can’t get away with talking nonsense in physics as you can in sociology or psychology. The simpler the subject, the more scope there is for mathematics and the less there is for charlatanry.

And the more scope there is for understanding and prediction. That’s why I started this essay by calling Shakespeare a gilded ape. For all his genius, without mathematics he did not truly step beyond his animal ancestry and did not glimpse the true nature and grandeur of reality. No artistic genius does, unless he knows maths or, even better, mixes maths into his art, the way H.P. Lovecraft did. Lovecraft offers strangeness and wonders that Shakespeare doesn’t, although Shakespeare was a god of language and Lovecraft a garden-gnome. Lovecraft’s use of science is very important too, but science is mathematical. That’s why it’s been the second-most powerful tool humans have ever invented. And why it may end up destroying the human race, literally or figuratively, in ways that art or ideology never could. Mathematics, by itself, couldn’t destroy us either: you can’t flatten a city with an equation, though an equation (E=mc²) can teach you how to flatten a city. But mathematics is still the most powerful tool humans have ever invented. There are echoes of almost everything humans do in the animal kingdom, from language to art. And what Shakespeare, Beethoven and Michelangelo did had been done before, in smaller ways, on smaller scales, by our hominid and primate ancestors.

But mathematics – the purposeful, systematic, explicit manipulation of number and shape – was something new, something that had to wait for Homo sapiens and civilization. No animal does maths explicitly, though all life does it implicitly. The simpler the life, the more explicit the implicitness gets: some micro-organisms are blatantly geometric. Human beings are complex, so our implicit maths is harder to see. All geniuses are great mathematicians, because maths is what brains run on, but unless he’s aware of mathematics, even the greatest genius remains a gilded ape, tethered to his animal ancestry, blind to glories and grandeurs brighter than the sun and wider than the sky. Darwin summed it up by saying this: “Mathematics seems to endow one with something like an extra sense.” That is what it’s like. Magazines used to run adverts for X-ray spectacles that, according to the ads, allowed you to see through clothing and walls. Maths puts the ultimate X-ray specs on your nose. You can see through the walls of the universe and contemplate √2, or use maths to investigate the beginning and end of everything there is or ever could be. The end of everything is where I began. My ultimate Götterdämmerung would be universe-strike, which is a concept taken from the highly mathematical discipline of physics. My ultimate genius would be a cross between Shakespeare, Beethoven, Michelangelo, and Gauss. If you don’t know who Gauss was, I have only one thing to say to you:

Have a banana.

Elsewhere other-posted:

• More articles on maths

“The world – the whole universe – would presumably be over in less than an eyeblink.”

Nope:

As an alien cosmos came crashing into ours, its outer boundary would look like a wall racing forward at nearly the speed of light; behind that wall would lie a set of physical laws totally different from ours that would wreck everything they touched in our universe.

Will Our Universe Collide With a Neighboring One?