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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.
If you're sad about paying the fee, you could always turn the tables and run a node yourself and maybe someday rake in a 0.44 fee yourself.
If you can keep a node running that accepts incoming connections, you'll really be helping the network a lot. Port 8333 on your firewall needs to be open to receive incoming connections.
Broadcasts will probably be almost completely reliable. TCP transmissions are rarely ever dropped these days, and the broadcast protocol has a retry mechanism to get the data from other nodes after a while. If broadcasts turn out to be slower in practice than expected, the target time between blocks may have to be increased to avoid wasting resources. We want blocks to usually propagate in much less time than it takes to generate them, otherwise nodes would spend too much time working on obsolete blocks.
When a node finds a proof-of-work, the new block is propagated throughout the network and everyone adds it to the chain and starts working on the next block after it. Any nodes that had the other transaction will stop trying to include it in a block, since it's now invalid according to the accepted chain.
The network is robust in its unstructured simplicity. Nodes work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can leave and rejoin the network at will, accepting the proof-of-work chain as proof of what happened while they were gone. They vote with their CPU power, expressing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism.
Nodes always consider the longest chain to be the correct one and will keep working on extending it. If two nodes broadcast different versions of the next block simultaneously, some nodes may receive one or the other first. In that case, they work on the first one they received, but save the other branch in case it becomes longer. The tie will be broken when the next proof-of-work is found and one branch becomes longer; the nodes that were working on the other branch will then switch to the longer one.
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.
Another option is to reduce the number of free transactions allowed per block before transaction fees are required. Nodes only take so many KB of free transactions per block before they start requiring at least 0.01 transaction fee. The threshold should probably be lower than it currently is. I don't think the threshold should ever be 0. We should always allow at least some free transactions.
In a few decades when the reward gets too small, the transaction fee will become the main compensation for nodes.
The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free.
If SHA-256 became completely broken, I think we could come to some agreement about what the honest block chain was before the trouble started, lock that in and continue from there with a new hash function.
The project needs to grow gradually so the software can be strengthened along the way. I make this appeal to WikiLeaks not to try to use Bitcoin. Bitcoin is a small beta community in its infancy.
Actually, it works well to just PM me. I'm the one who's going to be fixing it. If you find a security flaw, I would definitely like to hear from you privately to fix it before it goes public.
The design supports a tremendous variety of possible transaction types that I designed years ago. Escrow transactions, bonded contracts, third party arbitration, multi-party signature, etc. If Bitcoin catches on in a big way, these are things we'll want to explore in the future, but they all had to be designed at the beginning to make sure they would be possible later.
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.
When you generate a new bitcoin address, it only takes disk space on your own computer (like 500 bytes). It's like generating a new PGP private key, but less CPU intensive because it's ECC. The address space is effectively unlimited. It doesn't hurt anyone, so generate all you want.
But don't worry, there are another 6 decimal places that aren't shown, for a total of 8 decimal places internally. It shows 1.00 but internally it's 1.00000000. If there's massive deflation in the future, the software could show more decimal places.
The result is a distributed system with no single point of failure. Users hold the crypto keys to their own money and transact directly with each other, with the help of the P2P network to check for double-spending.