There exists the potential for this community to be responsible for saving the lives of not just thousands or millions of lives, but billions maybe even trillions if we became an interstellar society in the future. So it would be an understatement to say that im interested in your work.
Yes, agreed. I come to this project primarily from the gold/silver community. As much as I love that, it has obvious problems when it comes to how to perform electronic transactions using that medium. Moreover, for the reasons you mentioned - I think we are morally required to help support projects like bitcoin since the potential payoff for humanity is so huge.
Also i understand what the theory behind the usefulness of proof of work systems, such as forcing a server to solve a problem before being willing to receive a message from it in order to prove that their is a cost involved for the sender limiting the potential profitability of spam, but i cant for the life of me figure out how it factors into the whole bitcoin equation. If im asked to solve a complex problem then rewarded for solving it, whos asking the question, what method is used to generate the problem.
Like you, I'm new too and not a cryptography expert. I will only add in addition to the excellent responses above (like mestar's nice summary) that basis for the proof-of-work is that the good guys will always outweigh the bad guys.
For instance, assume that utilizing the total computing power of all bitcoin nodes that a new block is generated every 10 mins, additionally assume that an individual computer may take say 12 months to generate a new block on its own....then you can see how the "good guys" will always be ahead of the "bad guys".
So if we, as a community, are on block 100K right now....and you being a rogue node want to generate a false transaction, so you spend some cash but immediately begin working on the next block that *does not* include the fact that you spent that money (ie. you are trying to erase your spending history)....well every 10 mins the community will be on the next node and it will quickly become impossible for you to ever catch up or surpass our effort.
Also isnt it possible that two different public keys could return the same hash value, i know its unlikely but if people are using this service 100 years from now on a global scale there could be a LOT of transactions by then.
While it is technically possible for that to happen, we must put that in context. Lets say for sake of argument that once every 100 years (in reality it would be an order of magnitude more, but for discussion sakes) a clash of keys would occur. So essentially we would have a single counterfeit transaction each 100 years....compare that to the real world.....has any other currency ever had a protection that great? The amount of fake $100 bills and fake gold dwarfs that by several million times.