Okay yeah, that makes sense. There needs to be a chain in the current system for it to work.

But say the UK and US governments decide that bitcoins are a threat to the national currency and ban them. Couldn't the existing infrastructure be modified and used as a kind of computational mechanical turk? Miners use their computers to solve problems, they are checked several times and then once verified miners are paid by the people who posed the problem based on the complexity of the problem?

Hi,
  I've just heard of Bitcoin, I'm trying to get started but I doubt I'll get set up before things kick off. It seems that in a month you guys are all going to be rich, or the BTC will drop massively, or various governments will kick in and make it illegal. Good luck. But when researching the system I noticed something.

To get bitcoins you randomly generate hashes to try and find a hash with lots of 0s at the start right? And the computing power it takes to do this is what limits the input of bitcoins?

That seems like a humongous waste of processing power. There are people buying specialised rigs to get bitcoins, massive co-operatives forming to pool resources, all to generate pointless strings of literally random data.

Solving a block is a type of problem called an NP problem. It is hard to work out the solution (basically impossible, hence the masses of trial and error) but easily verifiable. This is the basis of the entire bitcoin currency generation. But the NP problems being solved are worthless. Who cares that the random hash generated has lots of 0s? Nobody. But there are many other NP problems out there for which solutions would be useful, for example the travelling salesman problem (google it if you don't know it). Solving one of these would still be difficult so could used in place of the existing hash function problem, but also useful so someone could do something with the solution.

From a newscientist article: "The current longest solution [to the travelling salesman problem] visits 85900 points. It took 136 CPU-years, or 14 months in real time, and improved a chip-making process".

The system could be modified to a different NP problem, or maybe even any NP problem if you change the bitcoin production rate to be proportional to the effort required to solve the problem. The network of miners would then be churning out answers to problems that are useful. From there IMO the future gets a lot brighter.

I'd imagine that because there would be a service underlying the currency it could no longer be counted as fraud by any stretch of a governments imagination. The only possible setback for the future would be a yes to P=NP, but then cryptography in general gets made redundant and life gets interesting.

Don't ask me how to implement this, I'm not a programmer, just a casual scientist.

Hope this makes sense
-DannySpud