I don't know what these other guys are talking about, of course you could create a fork where the mining is done completely differently.

Granted, the entire rest of the bitcoin network would consider your fork invalid, so it wouldn't do you any good unless you could convince a significant number of people to use it.  And there would be potential double-spend issues where anyone who had coins before the fork could spend them both on your network and on the main one.

That's assuming of course you wanted to keep the current ledger of who owns what. 

I don't see that this would serve any useful purpose, if you are starting with just one person using this currency, (you), you might as well start fresh, and not communicate with the bitcoin network at all.  That's what all the altcoins did.