Math Theory

First: http://www.cosmicfingerprints.com/incompleteness/
Godel was probably just as important as Einstein. The implications of his work are still being felt. There will always be truths that are not provable. Math could tell us something is true, but we won’t be able to prove it, or we might know something is true, but math will never back it up. Math is logic at its best. Some logical things can never be proven then. In reality, most all of our knowledge is based on at least a few assumptions.
It’s almost disappointing what that means though..A complete theory of everything is impossible. We’ll get over it though.

I feel like 0 is the most interesting concept/number we know about. Math will break down around 0. It doesn’t work like anything else. We use it like a number, but it won’t work in every situation (as if its more of a concept) Try dividing 0 by 0. Now I know some people will disagree, but really if you actually work it out, that equation will equal any number you wish. That is why we call it undefined.
Take one step from 0 to 1 and you have infinity. Infinity is a strange strange concept. Some infinities are larger than other infinities. Ever imagine this?
okay draw a circle, and put a dot in the center. draw (if you can) an infinite amount of lines from the dot, to the outside of the circle. If you have an infinite amount of lines, then the circle is completely filled, and no space is left. This problem comes up when you draw a bigger circle around that circle. Now, extend all the lines. There are gaps now aren’t there? Why is infinity not enough?
(on a side note, the circle is THE most interesting shape. It has infinite shapes within itself. You can draw a triangle, and then draw a square inside it, and you’ll go for a while, and realize you can do that forever. Doesn’t really work with any shape.)

A problem we face is that we think we know what 0 and infinity is. 0 is a number yes, but its also a concept. A concept we haven’t really grasp. 2 apples minus 2 apples is 0 apples yes, but apples don’t stop existing elsewhere. Infinity is more of a concept, but still can be a number. There’s always bigger too (as explained with the circle example) Infinity is supposed to mean the biggest, but since you defined the ‘biggest’ as infinity, there can be a bigger number..it doesn’t end.

I’ll pause now, I want to know what you guys think.

Come on guys, gimme something. haha. this is like my favorite topic. :P

I’m beginning to feel like 0 and infinity are quite similar actually based on the above with circles. Negative numbers are interesting, because we never actually see absence of anything, we cannot observe it. Take that with imaginary numbers too, it gets weird. I can only think of it as all things fall on a grid. 0 is the origin, and we live in the positive number world. We can only experience ‘positive’ things. below the x axis must be the ‘imaginary’ numbers. Infinity can go any which way, but you can always derive any number based on the origin. It’s all very very interesting to me, especially since numbers have done so well at explaining the world around us.

Well, we USE negative numbers, and imaginary numbers to help understand and explain..but our physical world is just in the positive, save for our consciousness maybe. As in, all things around us are something, not nothing, and not negative something. I study physics and all that, personally. Not in college or formally or anything. I read probably about a book a week on different subjects like physics, math, religion, philosophy..etc.
I have heard of absolute zero, only in correlation to temperature. Isn’t it because heat is caused by the vibration of particles, and absolute zero is the lack of vibrations? I hear its impossible, but i’ve seen contradictory stuff about it saying that it is indeed possible.

Yeah, they use negative infinities to solve some problems. I wonder about imaginary infinities? 0.o that would be odd, but probably probable. The thing is, is we can’t be sure something is infinite. Something can only be infinite for the area it is described to. Take the circle example from above. Infinity was one thing for the first circle, but it was something different for the circle around it, even though they shared the same origin. Not all infinities are created equally I guess. :D
I wonder though, if absolute 0 is theoretically possible. In the very least we can imagine it, then what about absolute hot? what is the hottest something can get, and would it correlate to a potential absolute infinity?

Yes, exactly..which is why it baffles me. But, if there is an absolute zero, then maybe there is an absolute infinity, and its beyond our comprehension currently. If there are many forms of infinity, maybe there is an absolute form. Of course as soon as you say infinity, you can turn around and ask, “what is infinity + 1?” what is infinity – 1?
The problem is infinity is more of a concept, but it is STILL a number. 0 is more of a number, but ALSO a concept. The two are close enough related for me to feel that there is a hidden connection there.

Sure. :)
Bridges to Infinity by Michael Guillen.
Godel, Escher, Bach: An Eternal Golden Braid by Douglas R Hofstadter
Zero: Biography of a dangerous idea by Charles Seife

The 2nd book would be the one I’d suggest the most, it covers more than just ‘math’ theory, but that book is one of the greatest i’ve ever personally read.

http://www.helium.com/items/287084-the-importance-of-zero-in-mathematics