This may be an odd question, but what is your computer doing while "mining"? I keep seeing things about it solving parts of algorithms and such, but to what end? Are we building a video game? Mapping the genome? Hacking some government database? It seems that people may be happy to have a chance at these bitcoins without wondering where the "work" is going. Or maybe I just didn't read enough.
(Probably the latter.)
I probably shouldn't try to explain something I don't understand, but I googled a couple things after reading these threads, so I'll try for a few half-assed comparisons -- just bear in mind I might be completely misinforming you.
if you look at any dollar bill, you'll see it's id'd by a serial number.
some guy is cranking a printing press somewhere to create those things, but it's a little more complicated than the printing at kinko's because we don't want kinko's creating money.
I don't know if you're familiar with peer to peer file sharing, torrents, etc, but if I upload a file (tv show, or whatever) it gets id'd with a unique hash like A00C1D0E82B86E93B849478D8B37E6FCD11876EB
so, obviously, there isn't a unique file in physical form, like the bill, but that code uniquely id's the copies of that particular file.
if you take parts from both these examples and complicate it about a million times you get a peer to peer currency .
I think 'mining' might not be as good a term for this as 'farming' because I think what your processor is doing is actually spending time and work to actually create and maintain currency.
you can't have people just making their own bitcoins as they feel like it, so each bitcoin has a supercomplicated hash id code that basically gets resolved by processing power from all these farmers., and increases in complexity as they get figured out more frequently --- this acts as a governor on money creation, and lets the supply grow naturally at it's predetermined rate.
rather than one guy cranking a printing press somewhere, this guy set it up so that the currency exists independently of any one source, and is continually being created, as it's entire existence is just a very complicated hash code, rather than a short number on a piece of paper.
I think what your computer is actually doing is figuring out these hash codes, and when one is finally calculated, a bitcoin is born.
to throw out one more random simile -- let's say I told you the unique serial number of a particular bitcoin was pi to 10k decimal places.
you could have your computer figure that out, and whoever manages to do that has just created that bitcoin.