Thanks guys, but I still don't get it. Can you walk me through it step by step? I thought solving a block was just a guess-and-check, so my thinking is that the "check" step is what takes all the computational resources. So by "checking" two different chains, you're doubling the cost.
Obviously I'm wrong, can someone clear up my misunderstanding? Thanks!
"Guess" is what takes up all the resource, "check" is easy and doesn't require much at all.
"Difficulty" is in reference to how low a number must be before it is valid, the smaller the number the larger the difficulty. Since the Namecoin difficulty is lower than Bitcoin difficulty, that means that any Bitcoin block solutions are automatically also valid for Namecoin because they are equal to or better than the required difficulty.
