Abstraction in mathematics

I wish I could just dump stuff from my brain into a blog entry right now.

I had lunch with my friend Olof, who’s into applied math, and I had asked him if there are any parallels in mathematics to abstraction in code (software). There are, but it’s hard to draw straight lines between the two. You do do things in mathematics that resemble abstraction.

For example, Olof said that you use approximation to simplify the scenario (forgive me if these terms aren’t at all applicable) and that it’s often a question of finding the best approximation, in order to produce as exact results as possible, when things are so complex that exactness is impossible. As I understood it, it is about finding a piece of the puzzle that you can work with, when the entire puzzle is infinitely complex.

Olof used a hypothetical example with a car manufacturer (Volvo, if that matters to you) that employs mathematicians to explain why the car engine makes too much noise. Doing computation on the entire engine might be impossible, but perhaps they find that it is likely to be caused by some pipe in the engine, so they analyze that and do calculations.

Or something like that. I’m writing this as hooks to remember what we talked about.