Ok, so forgive my ignorance here, but am I right in thinking that as a result of Bitcoin and the literally hundreds of alternate currencies springing up daily, we, the human race are using BILLIONS UPON BILLIONS of processing cycles to calculate worthless sums? I say worthless because the hashing is mostly wasted effort, am I right in understanding that?
The processing power is not wasted because the process that is called "mining" is the way by which creates the credibility of the whole Bitcoin payment system. Without that processing taking place, there would be no Bitcoin system. What is called mining is actually the process of creating a confirmed chain of blocks of transaction. By "confirmed" I mean that most part of the Bitcoin network agree to the validity of the blocks. The Bitcoins that are given to the miners are rather an incentive for the miners to keep going with this process.