maths and men

September 7, 2007

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When I see how science is sometimes championed against religion, I am a little taken aback

Because, you see, the science that is thought to be able to explain and make use of the Universe… is based on mathematics; and that cannot be right. For one thing, the idea that mathematics and physics are somehow intertwined belongs to the realm of philosophy. Of course, this could be only me splitting hairs; but there are many more reasons to discredit mathematics as our next saviour. We boggle in amazement at the marvels that the marriage of maths and physics has produced in our lifetime; but you see, that’s just the effect that colour, movement and excitement from some useful or entertaining gadgets has on our naked-ape brains, which are barely out of the caves, groping about for meaning in everything.

Mathematics is a sort of game. We add or multiply real-world objects and get apparently consistent results. We can explain quite a lot of things by using maths, such as why apples fall on our heads while we take a nap under an apple tree. With maths, we can also develop ideas into concrete objects. But as we use mathematics to move further and further towards explaining the very small and the very big, our concepts begin to behave very oddly. Can that be because very small and very big things are themselves odd to our middle-of-the-way brains? I don’t think so. I think the oddness is itself a result of the inadequacy of numbers to describe the real world with total precision (or, in other words, to calculate and produce truth).

Let me give you a simple example. You’re doing some experiment with a particle accelerator, and for some reason you need to know the exact length between opposite corners of a 1-inch square. Piece of cake, you say: it’s the square root of 2 (let me call this “V2” here). However, V2 is what’s called an “irrational” number, meaning that after the point, we get an infinite number of digits. V2’s infinity starts at 1.4142135623730950488016887… and then this completely random series of digits extends infinitely to the uttermost reaches of the Universe and beyond, towards multiple universes and then back again infinite times and it never EVER ends. You could fill the entire Universe infinite times with the digits of V2 and you’d still be infinitely away from reaching a number that would give you 2 if multiplied by itself. All you’d get is something like 1.999999999… extending infinitely and back infin… oh, it does get boring.

If you always look on the bright side of life, this means that mathematics can describe orders of magnitude that are infinite times smaller than what can actually exist in or between the littlest particles. But to me, all it means is that mathematics can never be precise, it can only be approximate. And there’s the snag: the real world cannot be an approximation: everything must be precisely whatever it is.

Now look around you. We live in a maths-driven, maths-organised society. If you look (for want of a better word) “between” the wonders that mathematics has produced, you’ll see a lot of things that are left behind – the molecules that continuously fall off the not-completely smooth surface on a hard-disk, the diminutive speck of smoke that goes up from a chip when you turn on your iPhone –, which are sometimes treated as garbage, sometimes as dust, sometimes as minor bothers, but most often just get ignored. They are, so to speak, the difference between 2 and what you get when you multiply 1.414213… by itself – the residue of imprecision.

The trouble is we ignore them at our own peril. Forgotten things tend to collect, just as an infinite sum of V2’s leftovers could collect a residue exactly equal to 2. When enough of the real world residue generated by the use of mathematics collects somewhere, we give it a name: pollution, squalor, rap music (joking!).

On the other end from practical concerns, there’s theoretical inquiry, philosophy and mysticism: ideas, theories and beliefs that help give shape to our concept of ourselves and our place in time and space. What mathematics does to those pursuits mirrors exactly what it does to society: because no precision can obtain from mathematics, a lot of detritus is collected near the outer boundaries of the marriage between maths and physics, maths and mysticism, &c. But because we’re used to thinking of mathematics as infallible, the detritus that eventually gets collected is thought to constitute physical entities in their own right. Some of the resulting ideas may lead to interesting insights; but many of the mystic theories put forward by physicists and other scientists make use of residual garbage that goes unrecognized as such. The result is a plethora of different sorts of increasingly wacky explanations for the very small and the very big, the places where human-created digits and concepts cease to make any sense because that’s where infinity takes over. The film/book What the Bleep do we Know is a case in point.

William Golding, author of Darkness Visible, once said in a interview, “a Universe that goes on forever is the ultimate damnation”. I would say that the ultimate damnation is a maths-driven Universe. Since neither science nor religion will ever be able to answer any of our deepest questions, couldn’t we just leave it be and concentrate on what’s here?

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