the difference between mathematics and physics

created by ariels
(idea) by ariels (18.9 hr) (print)   (I like it!) 2 C!s Fri Sep 29 2000 at 6:18:30
According to my brother, "the difference between mathematics and physics is that mathematics deals with reality."

Think about it.

What mathematics tells you is objective truth. Not all mathematical theorems may be applicable in all situations (for instance, if you're trying to navigate on the surface of the Earth, clearly spherical trigonometry and spherical geometry are relevant, while hyperbolic geometry is not). But all theorems are true whenever applicable. Mathematics deals with reality.

What physics tells you is (usually) empirical truth. When you get down to the bottom of matters, physics only generalises measurements performed on the real world. And these measurements could always be wrong, or worse, be measurements of the wrong thing. For instance, verification of Newtonian mechanics didn't deal with high velocities or very small scales, because of an incorrect homogeneity assumption. And relativistic verification always seems to assume anisotropy (of space), for very good reasons. Physics deals with perceived reality.

Of course, a side-effect of all this is that physics can say a lot more about the world than mathematics. It goes out on a limb, and this is the payoff.

NOTE

Physics isn't really all that "bad". Some great ideas in physics have a distinctly mathematical character. Schrödinger is said to have written down the wave equation out of the blue (say, inventing it by intuition alone). In other words, the wave equation is the only way for the state of a (quantum mechanical) particle to evolve, so it is "unavoidable". But we still prefer the wave equation to other equations because of empirical verification, not just because of its mathematical elegance. And we could be wrong, even if no errors have been made in the derivation of quantum mechanics, simply because the world doesn't work in the way we thought it did!
(idea) by mblase (1.8 wk) (print)   (I like it!) 1 C! Fri Sep 29 2000 at 6:53:41

Actually, the difference between math and physics is the same as the difference between the English language and a shelf of books. The difference is that you can actually pick up physics and touch it.

Physics is the science of the physical universe, a collection of theories, laws, theorems and axioms that explain how things move, how energy actually works, why the universe is expanding, what everything is made of, and so forth. Today, it's as much theoretical as empirical. But physics, like every other science to a certain degree, is described using the language of mathematics.

Math, you see, isn't about objective truth. Most people think math is somehow intristic to the world around us, when it's actually an invention, something man created in order to quantify the world around us. Mathematics does not deal with reality; it deals entirely with unreal quantities and ideas, with abstract numbers and shapes and forces and formulas.

Mathematics is not tied to any actual things, but it's the language of logic on which all the sciences are built -- and physics most of all.

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