This article is classified "Fictional"
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:
Infinity is:
* 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.