So, for one thing, this -> http://youtu.be/THt99IzFFRE. There are simply so many addresses available, it's impossible to guess the addresses that are being used.
It's a bit mind-boggling -- like -> http://youtu.be/SLIvwtIuC3Y
Anyways ... all transactions on this network are stored in a public ledger called the Blockchain. Blocks of transactions are bundled-up and added to this Blockchain every 10 minutes orso (it's now over 50GB) and every miner has a copy. This guy does a pretty good job summing up mining -> http://youtu.be/UrrBcaXuaq8
This distributed, blockchain way of doing things (not necessarily the Bitcoin blockchain in particular) .. it's a new paradigm. And it's being applied in a variety of interesting ways (solving some of the toughest problems inherent in our existing approaches). Problems of scale, trust, reliability -- they are not problems in the context of this new architecture. And all because of big hairy numbers.
Now -- this all depends on having a *really good* random number generator. And once the desktop quantum computer is invented -- and some snot-nosed gamer in his Mom's basement cracks the math -- well, then all bets are probably off ;-)
If you want to go down the rabbit-hole, I recommend this lecture to a bunch of E.E. students at Stanford. It's about a next-gen protocol framework for the web (based on this more distributed / decentralized way of thinking) -- a little over an hour long, but worth it IMHO -- (a bit like a peek into the future)
Inter-Planetary File System (IPFS)
Stanford Seminar - Juan Benet of Protocol Labs
http://youtu.be/HUVmypx9HGI
Stanford Seminar - Juan Benet of Protocol Labs
http://youtu.be/HUVmypx9HGI