Paint mixing is a good way to think about the one-way nature of hash functions, but it doesn’t capture their unpredictability. If you substitute light pink paint for regular pink paint in the example above, the result is still going to be pretty much the same purple, just a little lighter. But with hashes, a slight variation in the input results in a completely different output:
Computing power is often bundled together or "pooled" to reduce variance in miner income. Individual mining rigs often have to wait for long periods to confirm a block of transactions and receive payment. In a pool, all participating miners get paid every time a participating server solves a block. This payment depends on the amount of work an individual miner contributed to help find that block.
Another advancement in mining technology was the creation of the mining pool, which is a way for individual miners to work together to solve blocks even faster. As a result of mining in a pool with others, the group solves many more blocks than each miner would on his own. Bitcoin mining pools exist because the computational power required to mine Bitcoins on a regular basis is so vast that it is beyond the financial and technical means of most people. Rather than investing a huge amount of money in mining equipment that will (hopefully) give you a return over a period of decades, a mining pool allows the individual to accumulate smaller amounts of Bitcoin more frequently.
In January 2009, the bitcoin network was created when Nakamoto mined the first block of the chain, known as the genesis block. Embedded in the coinbase of this block was the following text: "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks." This note has been interpreted as both a timestamp and a comment on the instability caused by fractional-reserve banking.:18