Quote:
Originally Posted by arkain101
smoking?  (I'll take that as a joke) 
I was asking ...For example; isn't the math and visualization different depending on the geometry and dimensions used to represent or analyze reality?... |
Yes, it was a joke.
But only a little one.
Your question is a valid one. And any number of philosophers, teenagers and other folks have tried to argue that very point. Generally speaking, none of them are familiar with the way that geometry and dimensions are used to represent reality.
So, it always boils down to this: find a problem that can be represented by two different geometries, and do the physics (correctly!) in each. You will get the same answer. One may be easy and the other frightfully difficult. But if you do the math with integrity, you get the same or similar answers. (Some choices of geometry will incur larger error factors.)
Given a problem with an object traveling at a speed of 100 MPH, Newton and Einstein will give you the same answers. But Newton will give it in 5 minutes; Einstein will take 5 days.
And basically, this is what underlies the philosophy of physics. The math is showing us reality, not just some specific viewpoint of reality. Because the math, however modeled, whatever base arithmetic we use, however many "degrees" we define to be in a "circle", -- the math gives us consistent and useful answers, as long as we don't get sloppy.
Different maths can indeed open up new insights for us. But insights into the same reality. Differential equations can allow us to describe some problems that cannot be tackled with any amount of algebraic equations. Polar coordinates make some geometrical problems vastly easy -- others, almost head-breakingly hard. But they don't represent a different "reality". 11+7 is still 18 whether you use decimal, octal or ancient greek hexadecimal notation.
