How do Scientists Translate Physical Systems into Mathematical Models?

[EngWiPy]

Hello,

In engineering, for instance, we set up the problem mathematically, and solve it mathematically. The question is: How did scientists interpret the physical systems into mathematical systems? and based on what? Did all come from experiments?

Regards

 

[elect_eng]

Hello,

In engineering, for instance, we set up the problem mathematically, and solve it mathematically. The question is: How did scientists interpret the physical systems into mathematical systems? and based on what? Did all come from experiments?

Regards

I don't think it all came from experiments, but that is the ultimate verification of the validity of mathematical modeling. Mathematics is often developed from the desire to understand the real world.

I'll just throw out some random things that come to my mind, but I'm not much of a science historian.

Newton pretty much invented basic calculus in order to mathematically describe his understanding of mechanical experiments which seemed to fit simple rules. He also invented the first form of rudimentary variational calculus to solve a real world problem.

Before this, Kepler showed that the orbit of the planets around the sun were elliptical. I think that Kepler had a mystical notion that God designed the universe according to a mathematical order that was intrinsically simple and beautiful.

Of course, mathematics was used long before this to describe the world. Euclid's geometry can directly model real world objects, and even if Euclid's school of thought is based on abstract logic, it can't be denied that the intuition of this basic geometry came from observation of the physical world.