Tuesday 2 November 2010

Trying to explain the weirdest idea in the universe.

This is going to sound utterly crackpot.

Sorry, but some of the big ideas can sound a bit weird.  To an atheist, the idea of a god seems a little out-there, and this is the flip side - an atheist suggesting something about the universe that not only might never be proved, but might not even be provable at all.

Or even wrong.

But hey, the whole ethos of science can be summarised by "I might be wrong, but what about...?", so I'm going to throw this idea out there and we'll see where we go with it.  So here we go, hold on tight, this is the big soundbite:

Mathematics might be real.

It's an idea that I've been throwing around in my head for a few years now.  It all started with physics, a subject which has been close to my heart since I first wondered just what the hell was going on.  For some reason physics seems to be very good at taking the stuff we see around us and distilling it down to a simple mathematical equation or, at the very least, one prefixed with "In a frictionless vacuum".  See, for example, gravity. 

Courtesy xkcd, prescient comedy god amongst men.

Drop any object, near any other object, anywhere in the known universe, and we pretty much know what's going to happen.  Newton got it right enough for everyday use, and Einstein's relativistic reinterpretation corrected Newton well enough to not only change our view of the structure of space and time, but also to run atomic clocks in orbit decades later.  This one little idea, using nothing mathematical beyond primary school maths (if the idea of a square root is still primary level) describes the vast majority of what happens in the range of any telescope we have.  One equation describes most things we can see.

Or let's take something else, like things bumping into each other.  Again, Newton laid the groundwork, and then James Clerk Maxwell refined the ideas with his theory of electromagnetism, and another huge lump of the universe was reduced to an equation.  Well, maybe three, but there's a lot of stuff in the universe.

By now things are starting to look a little suspicious.

It seems that everything we experience is a rough estimate (a fact that's easily demonstrated by a high speed cameras or electron microscopes), and that the closer we look the simpler things become in a way.  Take, for example, a book.  Prop one up on the far side of the room, as far away as you can.  Go on, I'll wait.., there's a book.  You can see that.  I'm sure you're well aware that it could be an optical illusion by a talented artist, but if you move around the room a little you'll prove to yourself that it's a real 3D object.  But it could be a clever film prop, so you can pick it up and flick through to convince yourself it's a real book.  Is it really the book it claims to be on the cover?  Well, read it and find out.

All of the time you're gathering new information, and yet the object you're observing becomes more simple.  As you look closer you see:

  1. An object that looks like a book, but could be a million other things.
  2. An object that looks like a book, or a very good effort at one.
  3. A book, one of countless billions.
  4. A book, by a specific author.
  5. A particular book by that author.
And so on and so forth.  As you look deeper and deeper you'll find a very small ASCII text file embedded on a paper based medium - a blank book plus an ebook.  Then you find yourself looking at molecules arranged in a particular way.  Then atoms.

When you get down to the subatomic level you're saying, in effect, "there's a quark here".  A quark can be described with just three numbers: the mass, the charge and the spin.  That's it.  You don't get big quarks or little quarks, you can't get a quark made from metal and a quark made from wood, you only get three numbers.  That's all a quark is, just three numbers.

Now we're not looking at a thing at all, just three numbers.  Add to that a few rules about what happens when these three numbers bump into another three and you're got something called quantum mechanics, and yes, it's really that simple.   Well...nearly.  The maths is a little tricky, but particle physics and quantum theory are both in effect just careful juggling of a few numbers, not objects.

It may be that we just don't know enough yet (see above, "science admits it might be wrong"), but it all seems to boil down to numbers.  Not objects, just numbers.

What we're looking at now is commonly called Platonism, after Plato's idea that maths is real, and that's absolutely what I'm supporting here, the idea that mathematical ideas are real in their own right.  We know Pythagoras' Theorem, and yet we're not able to build a mathematically perfect right-angled triangle.  We can get really close, but the best we can even theoretically manage at the moment is a triangle of Planck lengths - three by four by five of them.  And even then, it's still a bit hazy.  Maths is more perfect than reality can muster, but reality seems to be trying very hard indeed.

See, told you this was a bit of a wacky post.

For further reading, without much terminology and maths, see:

The Unreasonable Effectiveness Of Mathematics In The Physical Sciences
Eugene Wigner - a classic and readable academic paper on the subject, link courtesy of Buffalo State College, US

Neal Stephenson - a work of fiction covering the main themes and a beautiful work at that.  The inspiration behind this post in a way.

1 comment:

  1. Let's take your argument at face value. You wrote: " A quark can be described with just three numbers: the mass, the charge and the spin."
    So, the numbers are not abstractions at all, just ways people describe mass, charge and spin. Quarks will have these properties even without an observer to count them. I just wouldn't want people to think reality was built on pure abstraction, it isn't. It is.

    An analogy: Reality is a board game played by forces without an instruction book for rules of play. Mathematics is a human effort to create such a book based on observation of the game in play by those forces.