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12-03-2008 @ 7:10PM
Ok, ok. This is totally off topic now, but here's what I mean. Think about mathematical infinity (I'm thinking specifically of Dedekind's definition, but it doesn't really matter which one you pick), which is defined as follows:A set B just infinite if and only if there is a proper subset of B, call it C, such that B is equinumerous to C.A proper subset of a collection is a subset that is not simply identical with the collection (so, e.g., the collection of male WoW players is a proper subset of the collection of WoW players. This means that all male WoW players are WoW players (subset) and that there is at least one WoW player that isn't male (this makes it "proper").)A set A is equinumerous to a set B just in case there is a bijection from A to B. This means that there is a function that takes each member of A and maps it to a unique member of B such that each member of B has exactly one member of A mapped to it. Such a function is sometimes called "1 to 1" which is perhaps easier to think about.We can see from this that even extremely large numbers (say, 2,000,000) are still finite. To see this, imagine trying to map each number up to 2,000,000 bijectively onto each number up to 1,999,999. It can't be done. You'd have to either map one number to two different numbers (in which case you wouldn't have a function) or leave one out (in which case you wouldn't have a bijection). The same reasoning works for any large finite number including, say, the number of particles in the known universe.So why is this at all relevant? Suppose there was a way for a mod to display an infinite amount of information. I presume that, to display something, you need at least 1 pixel. So we need an infinite number of pixels. But this is, as we see, a very, very large number. It (1) exceeds the number of particles in the known universe, and (2) even if we had an infinite amount of particles to put together, the assembly would take an infinite amount of time. I think this makes it pretty plausible that we don't have a way to display an infinite amount of information.**provided, of course, that each bit of information has to be in a discreet chunk, which in this case it has to be.
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