I am confused about miners being able to modify timestamp data within the header. I thought the only modifiable piece of data within the header was the nonce. I understand changing the Merkle root, through different transactions being included in a trial block, but how are timestamps modifiable? I thought the timestamps where reliant upon the sender, and when they pushed their transaction, is this incorrect?

I understand where the target value comes from now, much more so than last night. Now I'm wondering what happened if/when SHA-256 becomes compromised to some degree. Thanks for the input, goddog and achow101.

I'd still argue that it is doing work, in order to create a solution to a problem/question, but I do understand why that would be confusing terminology. Plus, it's clear that I understand very little about our protocol, so my arguments hold little weight.