King of Infinite Space

We could be bounded in a nutshell, but evidence would suggest otherwise. I rolled over the other night and looked at the spot where by rights some exhausted ingenue should be sleeping sweetly, and instead saw through my bedroom window the less immediately enchanting but nonetheless attractive site of Table Mountain's floodlit face. The Tavern of the Seas never had so presentable an ambassador, travelling across the world as it does in so many postcards, photographs and paintings. It even has a constellation in the Southern Sky: Mons Mensa.

That got me thinking. If Table Mountain was not obstructing my view, I would see through the night sky and into the star-filled depths of space beyond. I am told that there would be as many molecules in my line of sight between me and the limits of the Earth's atmosphere as there would be from there to the edge of the Universe. Which got me thinking further: Where is the "edge"? Luckily, and in keeping with my belief that all the wisdom of the world can be found in pop lyrics, the answer was getting airtime every morning on my way to work. In her song "9 Million Bicycles in Beijing", Katie Melua informs us that we are "12 billion light-years from the Edge." Sage stuff. More starlets should take an interest in Cosmology. Whilst the subtleties of Tensor Calculus and Gravitational Lensing might be lost on Paris or Britney, it would surely make them more interesting at dinner parties. I imagine the latter receiving an award:

"I would like to, like, thank my dog for sticking by me when I lost my mobile the other day, and um, oh yeah! I'd really like to thank the Fine Structure Constant for making this all possible, 'cause as we all know, if it was only a little bit different we'd either have failed to coalesce after the Big Bang from free nucleons into the atoms we know today, or we would have been ripped apart long ago by runaway cosmic acceleration."

Thunderous applause.

Anyway, it's not quite that simple - the Universe isn't just a big sphere that's been expanding for the last 12 billion (closer to 13 and-a-half in fact) years, with a nice, definable "edge", beyond which lies an infinite void of nothingness. Ignoring for a moment the complications that Relativity, curved space-time, Inflation, etc. add to this picture, cosmologists cannot currently assert that the Universe is finite in size at all, or even that it is not only one of many - possibly infinitely many - "universes". Sticking with one for now, when they say things like, "x many fractions of a second after the Big Bang, the universe was packed into an area the size of a golf ball," they're not saying that the whole Universe was that size, but that the part we can currently observe was that size. Subtle difference, because the Universe could be infinitely big, which means that back then it was also infinitely big, just a whole more squashed.

The point of all this is the inescapable conclusion of living in an infinite space: anything physically possible is not only possible, but guaranteed. Some simple combinatorial maths will show you that there are only so many ways of arranging a finite set of things, e.g. all the particles in our Solar System. There would be an almost uncountable number of permutations, but the number would be finite. So if you were to lay out all the possible arrangements across space, sooner or later you'd have to repeat, and voila! another Solar System, exactly like this one, with me typing exactly the same sentence. I could be a google kilometres away, but if the Universe is indeed infinite - and there's no good reason why it isn't - I'll be there alright. In fact there would be an infinite number of copies of me, and you could work out the average distance between us. It follows that there would be any number of minor variations too. Uniqueness becomes a hazy concept. Let's not even start to consider the possibility of varying laws of physics in different parts of space.

So if the Universe is truly boundless, we are not alone. We can take solace in the fraternity of our distant doubles, as they are likewise doing as you read this. And if I/we am/are not bounded in a nutshell(s), could I/we yet hope to oneday count one/some of myselves/ourselves King(s) of Infinite Space(s)? Tough one, but at least I can be sure that there are indeed more things in Heaven and Earth, infinitely more things, than are dreamt of in our philosophy.