The Bitcoin whitepaper written by Satoshi Nakamoto in 2008 defines Bitcoin, its purpose, and how it works.
Satoshi Nakamoto created Bitcoin and had a lot to say about it. Here are some of his quotes.
The existing Visa credit card network processes about 15 million Internet purchases per day worldwide. Bitcoin can already scale much larger than that with existing hardware for a fraction of the cost. It never really hits a scale ceiling. If you're interested, I can go over the ways it would cope with extreme size.
By Moore's Law, we can expect hardware speed to be 10 times faster in 5 years and 100 times faster in 10. Even if Bitcoin grows at crazy adoption rates, I think computer speeds will stay ahead of the number of transactions.
The design outlines a lightweight client that does not need the full block chain. In the design PDF it's called Simplified Payment Verification. The lightweight client can send and receive transactions, it just can't generate blocks. It does not need to trust a node to verify payments, it can still verify them itself.
The lightweight client is not implemented yet, but the plan is to implement it when it's needed. For now, everyone just runs a full network node.
I anticipate there will never be more than 100K nodes, probably less. It will reach an equilibrium where it's not worth it for more nodes to join in. The rest will be lightweight clients, which could be millions.
At equilibrium size, many nodes will be server farms with one or two network nodes that feed the rest of the farm over a LAN.
Long before the network gets anywhere near as large as that, it would be safe for users to use Simplified Payment Verification (section 8) to check for double spending, which only requires having the chain of block headers, or about 12KB per day. Only people trying to create new coins would need to run network nodes. At first, most users would run network nodes, but as the network grows beyond a certain point, it would be left more and more to specialists with server farms of specialized hardware. A server farm would only need to have one node on the network and the rest of the LAN connects with that one node.
The bandwidth might not be as prohibitive as you think. A typical transaction would be about 400 bytes (ECC is nicely compact). Each transaction has to be broadcast twice, so lets say 1KB per transaction. Visa processed 37 billion transactions in FY2008, or an average of 100 million transactions per day. That many transactions would take 100GB of bandwidth, or the size of 12 DVD or 2 HD quality movies, or about $18 worth of bandwidth at current prices.
If the network were to get that big, it would take several years, and by then, sending 2 HD movies over the Internet would probably not seem like a big deal.
Source: Cryptography mailing list
Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions, and there is a broader cost in the loss of ability to make non-reversible payments for non-reversible services. With the possibility of reversal, the need for trust spreads.
Source: Bitcoin Whitepaper
What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party. Transactions that are computationally impractical to reverse would protect sellers from fraud, and routine escrow mechanisms could easily be implemented to protect buyers.
Source: Bitcoin Whitepaper
The nature of Bitcoin is such that once version 0.1 was released, the core design was set in stone for the rest of its lifetime. Because of that, I wanted to design it to support every possible transaction type I could think of. The problem was, each thing required special support code and data fields whether it was used or not, and only covered one special case at a time. It would have been an explosion of special cases. The solution was script, which generalizes the problem so transacting parties can describe their transaction as a predicate that the node network evaluates. The nodes only need to understand the transaction to the extent of evaluating whether the sender's conditions are met.
Banks must be trusted to hold our money and transfer it electronically, but they lend it out in waves of credit bubbles with barely a fraction in reserve. We have to trust them with our privacy, trust them not to let identity thieves drain our accounts. Their massive overhead costs make micropayments impossible.
Forgot to add the good part about micropayments. While I don't think Bitcoin is practical for smaller micropayments right now, it will eventually be as storage and bandwidth costs continue to fall. If Bitcoin catches on on a big scale, it may already be the case by that time. Another way they can become more practical is if I implement client-only mode and the number of network nodes consolidates into a smaller number of professional server farms. Whatever size micropayments you need will eventually be practical. I think in 5 or 10 years, the bandwidth and storage will seem trivial.
The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.
Source: Bitcoin Whitepaper
In a few decades when the reward gets too small, the transaction fee will become the main compensation for nodes. I'm sure that in 20 years there will either be very large transaction volume or no volume.
Source: bitcointalk.org topic 48 msg 329