Sunday, January 30, 2011

How the domain of math application restricts which part of math will be used/developed

Even World # 1 (my previous post, How to Easy Understand the Role of Mathematics in Physics, Economics, and Other Fields ,) has to have its own axiomatic systems and what you can do inside the world. Obviously, this set of axioms in World # 1 will dictate which axiomatics realizations we will have in the World # 2 (example, World # 1 are vectors and vector operations, and World # 2 is math, or World # 1 is physics, and World # 2 is mathematics). Confusingly, for instance, sometimes, the sub domain of mathematics of interest is called vector's mathematics, but there is no such thing. There is only a part of math constructs that are triggered or motivated by vectors. Vectors itself ARE NOT mathematics. They are spatial, arbitrary constructs, concerning length, direction, that happen to interest us. They also came out of the blue.

The confusion arises with rapid and continuous jumps between World # 1 and World # 2, so one can get a sense that math is so intrinsically connected with World # 1 that without it a specific formula would not exist. That's not true. Formula would exist in mathematics in any case, but what the numbers represent, i.e. what they are counts of, must be explained in World # 1.

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