> What is left is keeping track what everyone has put in, and what they have taken out.

And that's exactly what Bitcoin is; a secure digital ledger. It's a way to securely and globally record "person A has 10 BTC, gave person B 5BTC, then person B gave persone C 3 BTC" in a way that doesn't allow person A to simultanously have given those same 5 BTC to person D (who, given the anonymity of the internet, may also be person A).

That's all Bitcoin does; it provides a secure way to record such transactions without having a trusted third party who must trust to increment and decrement the right accounts in the right way.

So is that not an impressive solution - if Alice wants to move 100 USD to France and Bob wants to move 100 USD out of France (let's say both want to buy a new textbook) then one could envisage a peer to peer money transfer system.

A site allows bob and Alice to find each other, agree a shared amount to transfer, agree to which end point they will onwards transfers (hmmm this might be the breakdown point) and then record that in the block chain

I think oddly there is still an enormous amount of trust involved - trust that Alice will complete the final important step of giving the money to Bobs silver haired grandmother or whatever

You can actually achieve the same thing with Coinjoin if all involved parties agree. Instead of a bunch of individual transactions, they collectively generate and sign one.