Are you a platonist when it comes to mathematics - do you believe that purely abstract objects exist for mathematical ideas that are both independent?

[Unity+]

Can you explain that a bit further?

 

I remember asking Sir Michael Atiyah a similar question; "what is geometry?"

 

His reply was more or less that geometry is algebra when you can think in terms of pictures. This I liked as modern geometry like algebra in which you can think geometrically, often with some abuse of language.

What I meant was the numbers from one part of mathematics can represented in geometric form(picture form), whether or not it was intended for geometry. However, somethings(such as complex numbers) can only be represented with geometries that are outside the norm.

[Sato]

What I meant was the numbers from one part of mathematics can represented in geometric form(picture form), whether or not it was intended for geometry. However, somethings(such as complex numbers) can only be represented with geometries that are outside the norm.

 

Eh, I think that while it's true that you can represent algebras and algebraic relations geometrically, and geometric examples and proofs look a lot more pretty and intuitive than otherwise, those are only specific representations while things like groups (and other algebraic/mathematical structures) themselves are general and cannot be wholly considered geometrically.

[ajb]

However, somethings(such as complex numbers) can only be represented with geometries that are outside the norm.

Complex numbers you can represent by two real numbers, so they have a geometric representation as vectors in R^2.

 

Anyway, you are right that one can do a lot of algebra using pictorial representations. For example we have Penrose notation, which I have in fact never used myself.

 

I am not sure if everything is geometry as I am not sure what we really mean by geometry. For sure not everything is a set-theoretical, but modern geometry takes care of that.

[hoola]

unity, I am not being serious or not serious, I simply ask the question, why anything? and see a flow chart based on how could something arise from a "void" ? It seems our reality stems from a long series of evolutions starting from the "concept of oneness" to the chaos, to logic, to maths, to us...If there were a concept of oneness, that developed prior to logic, then concept's theoretical output would be "chaotic" and random, as logic hadn't intervened to organize and structure anything from the unstable values of proto-information. Out of this chaos of unstable information, developed a region of random occasional stability. This I see as the beginnings of logic, which eventually developed the maths that allows the theoretical point void to begin to output the current pattern of PI...in other words to get the void to "do work", by reducing entropy..that created the IBH, which determines reality...I don't think so much that this idea is true, but seems a placeholder till someone can explain a less ridiculous way of getting here...if another more plausible scenario is presented to me, I'd appreciate it greatly...

Edited May 12, 2014 by hoola

[Unity+]

I don't think so much that this idea is true, but seems a placeholder till someone can explain a less ridiculous way of getting here...if another more plausible scenario is presented to me, I'd appreciate it greatly...

Just because there may be no other theory doesn't mean yours will be accepted...