On Tue, 17 May 2005 21:20:43 -0500, Doug Stewart <dastew@sympatico.ca> wrote:
jpkotta wrote:
On Mon, 16 May 2005 11:24:41 -0500, Vortex Swirling <vortexswirling@bigfoot.com> wrote:
But how could this be? Math is math isn't it? If it's not, then how could you use math to describe everything which would have to include these other universes.
Would anyone care to comment on this??? I'm no math guy here, but I've always been interested it. I know that math is a tool we've invented. But there are some things about math, such as the commutative property of addition that seem natural. Could we use math to include a set of universes where addition did not have this property? Or is it because we (well, at least I) can't even imagine it, that we can just leave something like that out?
I think math is something we've invented to model the universe. There are many instances of pure mathematics developed by mathematicians not to model anything, just to explore, and subsequently being reapplied to modeling real world phenomena. I believe that this is a reflection of how deep the underlying order of the universe is, and how good humans are at finding patterns. So I think that addition is commutative precisely because it seems natural.
There are plenty of natural systems that don't commute, though I can't think of one that is associated more with addition than some kind of multiplication. An abstract example would be transfinite numbers. It's interesting to think about non-commutative addition - that you could count things in two different ways and get different results.
jpkotta
I don't think that math is something that we have invented. Take prime numbers as an example. Is this an invention of man? No. If you are in any system that you can imagine and all the ones that you can't imagine :-) if you have 7 objects you can't divide then evenly in any number system, base 2, 3, 4, etc. It is not a result of anything that man has done. Doug
We have prime numbers in any number system (e.g. binary, hexadecimal, etc.) because the number systems are all exactly the same. The only difference is notation. The arithmetic that defines how they work is the same. I think the arithmetic is solely based on experience: 1 + 1 = 2 precisely because 2 liters of water is twice as much as 1. Out of this we get unintended consequences, such as the prime numbers. Just because something was designed for a specific purpose doesn't mean that it is limitted to that purpose or that its behavior is simple. Simple systems often display extreme complexity, such as fractals. jpkotta