“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” – Wigner

How can it be that mathematics,being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality? – Einstein.

“While Fourier analysis is beyond reproach mathematically, even experts could not at times conceal an uneasy feeling when it came to physical interpretation of the results obtained by Fourier method.” – Dennis Gabor

It seems that like one can routinely deal with mathematical manipulations and ultimately what comes out will be in sync with reality provided that Mathematics had been done properly.

While orthogonality means something specific(in physical terms) to a person working in information theory, the same mathematical concept maps to some other physical reality to a person,say working on fluid dynamics.In other words maths is like “one size fits to all”, independently developed yet serving everyone.

As point out – nobody knows what integers are supposed to be, perhaps that’s the reason stephen hawking named his book – god created integers.

“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” – Wigner

How can it be that mathematics,being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality? – Einstein.

“While Fourier analysis is beyond reproach mathematically, even experts could not at times conceal an uneasy feeling when it came to physical interpretation of the results obtained by Fourier method.” – Dennis Gabor

It seems that like one can routinely deal with mathematical manipulations and ultimately what comes out will be in sync with reality provided that Mathematics had been done properly.

While orthogonality means something specific(in physical terms) to a person working in information theory, the same mathematical concept maps to some other physical reality to a person,say working on fluid dynamics.In other words maths is like “one size fits to all”, independently developed yet serving everyone.

As point out – nobody knows what integers are supposed to be, perhaps that’s the reason stephen hawking named his book – god created integers.

Nice series of articles. Btw, Vector spaces link refers to Linear Transformation pdf. You might want to update it.