How was the Bitcoin system initialized? Can one start the system with only a single node (computer)? Please explain it in plain English. Thanks, guys.
The first block is known as the "genesis block" or "block 0". It was mined using the same hashing algorithm as any other block, but at difficulty 1. It contains only one transaction, the coinbase, which gives 50 BTC to address 1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa.
Once the block had been successfully mined its hash was hardcoded into the Bitcoin client's source code so that it and it alone would be accepted as the official genesis block.
src/main.cpp contains this line:
Exactly like all of the other mined bitcoins.
There are some quirks about it, though. For example, the previous block hash is all zeros, because no block came before it. Also, those bitcoins can't be spent, because of a quirk in the code.
Of course, if there's only one node in the network, it's not really a decentralized payment processing system.