As a base let me explain what i think i understand of bit-coins so far. Each member of the network has a record of all transactions which have ever taken place in the community. Each record of a transaction is called a block. Each block records the amount transferred, the address of the sender and the address of the recipient. The address of the recipient is a hash value of their public key. The record as a whole is called the block chain which is nothing more than every known block organized chronologically. Member nodes broadcast the length of their block chain to all of the nodes they are connected to periodically, the receiving node then compares the length of their existing block chain to that of the sender, if the receiver finds that his block chain is shorter than the senders, he will send a request to the sender for the entire block-chain. When a node initiates a transaction it adds that transaction to its block chain stating that node now has x fewer coins and the receiving node now has x more coins, the nodes connected to the transacting node would then see that the transacting node has a longer block chain and send a request for the update, eventually the receiver of the transaction would receive an updated copy of the block chain proving that he now owns x coins. Now for what i dont understand which greatly outweighs what i do. The network uses pki, but what exactly is being encrypted. What is to stop someone else from sending a message to the network stating that he is you and he transacts x funds to y account, im sure this is where the encryption comes into the equation but how. 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. 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.

This message may seem confusing to some of you but it comes from my personal definition of understanding. I dont consider myself to understand something just because i can explain it or solve a problem relating to it. All through out my life i was so frustrated with public education because no one seemed to understand what it meant to understand, and no teachers ever required their students to be able to understand the material, only that they be able to answer questions correctly. To me understanding involves being able to draw a complex picture in my head accounting for all given variables and potentialities, explaining the relationships between how all parts of a system interact with all other parts, and right now im on a quest to understand bitcoin.