But hey, you're free to pay money because a system of an anonymous guy is performing math operations.
Yeah, I do like it that my money is based on math.
Well you can play semantics all you like, but you have no money. What you have is a number attached to your address, which resulted from math operations. The Satoshi's system is like calculator. It doesn't create money but numbers. But hey, you are free to play with a calculator and fantasize that you're creating money. Children do that all the time.