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.

A rational market price for something that is expected to increase in value will already reflect the present value of the expected future increases. In your head, you do a probability estimate balancing the odds that it keeps increasing.

I've been working on a new electronic cash system that's fully peer-to-peer, with no trusted third party.

It can already be used for pay-to-send e-mail. The send dialog is resizeable and you can enter as long of a message as you like. It's sent directly when it connects. The recipient doubleclicks on the transaction to see the full message. If someone famous is getting more e-mail than they can read, but would still like to have a way for fans to contact them, they could set up Bitcoin and give out the IP address on their website. "Send X bitcoins to my priority hotline at this IP and I'll read the message personally."

We're not "on the lookout" for double spends to sound the alarm and catch the cheater. We merely adjudicate which one of the spends is valid. Receivers of transactions must wait a few blocks to make sure that resolution has had time to complete. Would be cheaters can try and simultaneously double-spend all they want, and all they accomplish is that within a few blocks, one of the spends becomes valid and the others become invalid. Any later double-spends are immediately rejected once there's already a spend in the main chain.

In a few decades when the reward gets too small, the transaction fee will become the main compensation for nodes.

When there are multiple double-spent versions of the same transaction, one and only one will become valid.

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.

A transaction will quickly propagate throughout the network, so if two versions of the same transaction were reported at close to the same time, the one with the head start would have a big advantage in reaching many more nodes first. Nodes will only accept the first one they see, refusing the second one to arrive, so the earlier transaction would have many more nodes working on incorporating it into the next proof-of-work. In effect, each node votes for its viewpoint of which transaction it saw first by including it in its proof-of-work effort. If the transactions did come at exactly the same time and there was an even split, it's a toss up based on which gets into a proof-of-work first, and that decides which is valid.

The credential that establishes someone as real is the ability to supply CPU power.

How does everyone feel about the B symbol with the two lines through the outside? Can we live with that as our logo?

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.