Tuesday, September 14, 2010

To infinity, and...wait for it...wait...

Something that occasionally raises my blood pressure is the abuse of the words "infinite", "infinity", and the related idea of "eternity."

"The possibilities are nearly infinite," people say. No, they're not! The biggest number you can imagine is still pathetically finite. There is no such thing as nearly infinite.

The problem, aside from my tendency towards pathological pedantry, is that people who use words in this way have no idea what mind-bending concepts they are belittling.

So, let me try to open up a tiny window onto the infinite. Or rather, onto eternity, which is nothing more than an infinite amount of time. No, this is not to give believers in an eternal afterlife pause for thought (though that would be fun), but simply because I find it easier to talk about in a way that might go beyond the intellectual definition and reach into your imagination.

Even so, it isn't too easy. I'm going to approach it kinda sideways in the hope that I can startle this simple but elusive idea into revealing itself. So here goes ...

Imagine a diamond. Shiny, flawless.

Imagine you've coated the diamond in something that attracts flies.

The diamond is crawling with flies, landing, walking around, taking off.

Would they make a mark on it? Probably not in your lifetime. But what if it was there for thousands of years? Is it conceivable that eventually all this insect-trampling will start to take the gloss off that perfect surface?

Well, it might take a heck of a long time, but sooner or later, atom by atom, those flies must eventually make some kind of impression. And if they can make even the slightest impression, then sooner or later they will be able to make a visible scratch on the surface.

Given enough time.

But we're talking about eternity here, so we've got as much time as we want.

And then there are real world examples of "soft" things making a real impression on "hard" things. Think of the stone staircases of an Oxford college, distinct treads worn out of their centres through centuries of trudging feet. Think of the infamous "licking stones" at Carlisle castle, with deep indentations worn out by parched prisoners' tongues. When you put it in those terms it doesn't sound so far-fetched. And we can give it as much time as it takes.

So, fix it in your mind that, never mind how long, eventually all those tiny feet can make a visible scuff even on hard diamond.

So far, so good? Now let's step it up a bit.

Imagine a whole planet made of solid diamond. Stop drooling. You can't have it. It's somewhere out in space far away from us. Far away from anything, in fact. No starlight, cosmic dust, or anything to disturb its impossible perfection.

Except that, once every million years, an immortal fly zooms in, lands, and takes off again. Nothing happens for another million years, then the fly returns, lands in the same spot, and takes off again. And so on.

OK, don't get nit-picky about the physical absurdity of this, or ask whether the planet has an atmosphere, or how a fly manages to escape into space again. Or even how the fly knows which spot on a flawless surface it landed on last time. You didn't bat an eyelid at the idea of an immortal fly, did you?

Now think back to the first scenario. Nothing has really changed, except for a matter of scale. The diamond is bigger, and we've stretched it out in time. Rather a lot. And there's only one fly.

But even in this stretched out scenario, that persistent fly must eventually start to make a microscopic mark on the surface of the planet.

Not in the life of this Universe. Or many times that life. But it will happen.

That microscopic mark will turn into a visible scratch. The scratch into a hole. Maybe a millimetre across.

And you're out there watching it.

Having fun yet?

So, we start all over with another hole next to the first one. Then another. Keep going ... We've now pitted a tiny piece of the surface the size of a newspaper. Start over next door. And again. And again. Eventually that patient (and immortal!) fly has pitted an area the size of your backyard. Your neighbourhood. Your municipality. Your parish or county. You can imagine this carrying on, endlessly, one visit at a time, a million years apart.

But we have all the time we want, so that doesn't matter.

Keep going! You're on a roll! You've covered an area the size of a country. Now cross the border and start all over again on the neighbouring country. Fill in the map. Picture the borders of all the countries of Earth (long since vanished) projected onto this diamond planet and fill them in, one by one. And the seas and oceans.

You now have a whole planet pitted all over like a cosmic golf ball.

Now start at the beginning again, and wear down the ridge around the first little hole. And the next. Oh yes...you're not done yet!

Let's make the diamond smooth again, until we're back to a flawless planet-sized diamond that looks just like it did all those aeons ago.

But one millimetre smaller across.

Now guess what? We're going to start out all over. A complete repeat of all that mind-numbing waiting we just finished. Then we're going to do it all over again. And again. Wearing the planet down, layer by layer, until there is nothing left.

Having trouble grasping that? Not surprising. Your mind probably never got past the "million year" bit, because that is already more time than most people can imagine. And the human mind tends to scale thing up logarithmically, so that each new order of magnitude feels like just another step like the last one, instead of resetting back to the beginning and starting all over again and again and again.

So if your mind started boggling somewhere along the way, don't worry. Just grasp it as best you can. Get past the absurdity of the scenario and really think about each stage in the process until you simply can't get your head around it any more.

It doesn't matter where you fall off the rails, because the real point is that, after all this time, all these many ages of our Universe, time beyond imagining, you haven't even begun to scratch the surface of eternity.

You could reset the clock back to the start and do the whole thing over again. You could do it over a million times, and you would still be firmly stuck in the realms of the finite.

No closer to eternity than you were at the end of reading this post.

Infinity is gob-smackingly big. Please treat it with respect.

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