Writing a description for this thing for general audiences is bloody hard. There's nothing to relate it to.
Quotable Satoshi
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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.
The main properties:
Double-spending is prevented with a peer-to-peer network.
No mint or other trusted parties.
Participants can be anonymous.
New coins are made from Hashcash style proof-of-work.
The proof-of-work for new coin generation also powers the network to prevent double-spending.
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.
I've developed a new open source P2P e-cash system called Bitcoin. It's completely decentralized, with no central server or trusted parties, because everything is based on crypto proof instead of trust. Give it a try, or take a look at the screenshots and design paper:
Download Bitcoin v0.1 at 
Bitcoin - Open source P2P money
Bitcoin is an innovative payment network and a new kind of money. Find all you need to know and get started with Bitcoin on bitcoin.org.
When a node receives a block, it checks the signatures of every transaction in it against previous transactions in blocks. Blocks can only contain transactions that depend on valid transactions in previous blocks or the same block. Transaction C could depend on transaction B in the same block and B depends on transaction A in an earlier block.
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.
The problem of course is the payee can't verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.
The recipient just needs to verify it back to a depth that is sufficiently far back in the block chain, which will often only require a depth of 2 transactions. All transactions before that can be discarded.
Writing a description for this thing for general audiences is bloody hard. There's nothing to relate it to.
It's not a problem if transactions have to wait one or a few extra cycles to get into a block.
It might make sense just to get some in case it catches on. If enough people think the same way, that becomes a self fulfilling prophecy. Once it gets bootstrapped, there are so many applications if you could effortlessly pay a few cents to a website as easily as dropping coins in a vending machine.
It is strictly necessary that the longest chain is always considered the valid one. Nodes that were present may remember that one branch was there first and got replaced by another, but there would be no way for them to convince those who were not present of this. We can't have subfactions of nodes that cling to one branch that they think was first, others that saw another branch first, and others that joined later and never saw what happened. The CPU power proof-of-work vote must have the final say. The only way for everyone to stay on the same page is to believe that the longest chain is always the valid one, no matter what.
When there are multiple double-spent versions of the same transaction, one and only one will become valid.
To Sepp's question, indeed there is nobody to act as central bank or federal reserve to adjust the money supply as the population of users grows. That would have required a trusted party to determine the value, because I don't know a way for software to know the real world value of things.
It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it's timestamped in. He can't check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it.
As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification.
Any owner could try to re-spend an already spent coin by signing it again to another owner. The usual solution is for a trusted company with a central database to check for double-spending, but that just gets back to the trust model. In its central position, the company can override the users, and the fees needed to support the company make micropayments impractical.
Bitcoin's solution is to use a peer-to-peer network to check for double-spending. In a nutshell, the network works like a distributed timestamp server, stamping the first transaction to spend a coin. It takes advantage of the nature of information being easy to spread but hard to stifle.
Writing a description for this thing for general audiences is bloody hard. There's nothing to relate it to.
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.
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.