Scivillage.com Casual Discussion Science Forum - The inherent beauty of mathematics

Trigonometry studies right triangles and measures angles in either degrees or radians.

We envision the real numbers as laid out on a line. And locate them from left to right on this line. a<b means that a lies to the left of b.

Geometry and algebra are useful tools for describing relationships among static quantities. But for describing change we need a new operation. One that is provided by Calculus, the mathematics of change.

In the spirit of Philosophy, we develop mathematics from observation of the real world. The map IS the territory in this case.

(Nov 9, 2025 04:54 PM)Ostronomos Wrote: [ -> ]Trigonometry studies right triangles and measures angles in either degrees or radians.

We envision the real numbers as laid out on a line. And locate them from left to right on this line. a<b means that a lies to the left of b.

Geometry and algebra are useful tools for describing relationships among static quantities. But for describing change we need a new operation. One that is provided by Calculus, the mathematics of change.

In the spirit of Philosophy, we develop mathematics from observation of the real world. The map IS the territory in this case.

Quote:Heyo said:
Have you read 5 Planes of Existence?
I agree that ideals are "abstract, perfect forms that exist beyond our physical reality" - and therefore they are not real, because they are abstract and exist beyond our physical reality.

You are relegating the abstract to secondary status. This is once again wrong.

To suppose that the abstract world of mathematics - the Platonic ideals - are unreal is to ignore the deeper planes in favor of the superficiality of matter, a complete dismissal of Quantum theory. Thereby dismissing the entire metaphysical reality that is accessible through logical deduction, less so empiricism. Nevertheless, theories like string theory posit the existence of higher dimensions which would contradict the atheist opinion if taken to the extreme.