Since entropy in a region of finite extent and energy is bounded, it would appear that arbitrary precision real numbers are not physically realizable (otherwise, you would be able to store infinite information in a real-valued physical quantity, violating the bound). Unless one is a mathematical platonist (a religious position), that means real numbers don't exist. So why is it considered acceptable, other than for historic and/or wishful thinking reasons, to think about real numbers in a more serious manner than thinking about magical fairies, and it's still allowed to have much of mathematics relying on the assumption that uncountable infinities are a sensible concept? Mathematical thinking about real numbers directly maps to a finite physical process through said thought's neural correlates, and so is akin to a delusion. Where am I going wrong here?
There's nothing real or physical about maths. Maths is all about what you can imagine. I can try to imagine infinities. I can try to imagine a number that squares to give -1. I can try to imagine all sorts of things:)
The beauty of maths is that it is not linked ot the real world. It's the ultimate game and it is as crazy, subversive and downright strange as your imagination will allow.
It's its curse that it's also useful.
"A great many people think they are thinking when they are merely rearranging
their prejudices."
-- William James
Finitism (Score:2)
Re: (Score:2)
There's nothing real or physical about maths. Maths is all about what you can imagine. I can try to imagine infinities. I can try to imagine a number that squares to give -1. I can try to imagine all sorts of things :)
The beauty of maths is that it is not linked ot the real world. It's the ultimate game and it is as crazy, subversive and downright strange as your imagination will allow.
It's its curse that it's also useful.