Infinity, The Trouble With
Infinity is a wholly remarkable concept, being so mind-bogglingly huge that it is virtually impervious to the effects of standard mathematics. Infinity also has the singular distinction of causing more trouble than any other number in the whole of existence. (The number `i' comes in a close second, and will be discussed in a later article, which will be appropriately classified as `unreal'.) How infinity causes so much trouble will be illustrated shortly. First let's sort out the math.
While researchers in the oxygen-deficient realms of higher mathematics assert that infinity can be coaxed to have an interesting effect on other numbers, it stoicly refuses to let other numbers have any effect upon itself. Dar Beton, the famous Theoretical Theorist and haberdasher of Oonoogle III, theorized that other numbers simply choose not to interact with infinity because they think it a bit of a snob. This is not one of the theories for which he is well known, although it does seem to account for the strange way in which infinity almost, but not quite completely refuses to interact with others.
For example... add any other number to infinity and you get infinity. Subtract any other number from infinity and you also get infinity. Multiplying or dividing infinity by any other number proves equally pointless. Infinity is, on the whole, rather hard to pin down, and doesn't give a tinker's cuss about your mathematical expectations. It is hard to measure, mostly useless, and defies easy definition. Attempts to define infinity usually go something like this:
- the mid-point of the reproductive cycle of the zero.
- what you get when you add one to the absolutely biggest number possible.
- what you get when you add one to that.
- what you get when an eight loses its footing.
And so on.
The only being actually claiming to really know what infinity is, also uses it as his home address, and so no one believes a word of it. Truth is, the notion of a magnitude just slightly beyond the highest conceivable magnitude is by definition just slightly beyond the conceptual abilities of most species in the Universe. And this is where infinity causes trouble.
For illustration, let us use the historical example of a small, blue-green planet inhabited by some rather curious ape-descended life-forms. The inhabitants of our subject world had evolved intellectually to the point where they had a word for the concept of infinity, but they still had no idea what it actually was. Because of this they tended to confuse any really big number with infinity.
They looked at the water, the soil, the air of their beautiful planet and said, "Here are unfillable resources into which we may throw our endless supply of waste without ever sullying them." (Infinity plus any other number equals infinity.)
They looked at the vast and wonderful profusion of life in the sea and the huge forests filled with trees and said, "Here is a limitless bounty from which we may harvest forever without restraint." (Infinity minus any other number equals infinity.)
They looked at their own population and said, "We will be fruitful and multiply without ceasing, for there will always be enough resources for everyone." (Infinity multiplied by any other number equals infinity.)
They looked at the wondrous diversity of animal and plant life with which they shared their planet and said, "We can destroy any fraction of these with impunity, for the whole is so great that it cannot be diminished." (Infinity divided by any other number equals infinity.)
After many thousands of years of evolution one or two of the ape-descended life-forms began to say that maybe they had it wrong. Maybe infinity is not equal to any really big number, and maybe any really big number that is not equal to infinity can be effected by any other number if that other number is allowed to get big enough.
Of course this was only said by a very small number of the ape-descended life-forms, and since there were an awful lot of them in general, the opinion of such a small group was of no consequence. (Any other number divided by infinity equals zero.) So, nobody paid any attention to them.
Anyone interested in studying this phenomenon more closely may want to hitch a ride to Earth as soon as possible. Contrary to popular opinion there, this can't go on forever.