I think one of our math TAs proved that if you use one orange, you can peel it such that you can cover the entire surface of the earth with just one orange.
You’d have to peel it pretty thin.
You’d think so, but as far as I remember, the mathematical theorem basically states that surface area is not conserved. Apparently the example of the orange, while technically true, has no real meaning. My uncle tried explaining it to me, but my head imploded from the strain of trying to keep up with him.[/quote]
This is exactly what I meant.
It has no physical meaning.
Pookie, your example of using mathematical equations to model ballistic trajectories comes from a study of physics. That is, applied math, not math for math’s sake (which is usually what i mean when I speak solely of mathematics)
At the higher levels, math degenerates into what is essentially a wankfest of logic. Much of it does not have anything to do with reality. The orange was merely an example of this.
Sure, math is necessarily inspired by the real world, but the attempt to generalize makes it unrealistic. For example, basic linear algebra simply takes linear equations, puts them into matrices, and tells you how to solve them. When you approach lin al analytically however, you say that “hmm…these properties are useful, now let’s see if I can generalize it!” And then you abstract to transformations, which are then represented by matrices, and these transformations need not be linear equations.
And then once you’re done doing that, you (as a mathematician) say “Hey, that was cool, let’s see if I can generalize this for any arbitrary set of numbers and operations!” at which point you get abstract algebra…
And at which point it has diverged very far from reality