I’m not sure if this is for SO or not. I am reading some of my old math textbooks and trying to understand math in general. Not how to figure something. I can do that but rather what is it that math is doing.
I’m sure this is painfully obvious but I never thought about it until I thought more about game programming. Is it right to think about math as the “language” that is used to explain, precisely explain, why things work?
I’m having a hard time asking it and again, I’m sure it’s obvious to most, but after years of math I’m finally thinking when someone asks to “find the equation of a line” that people recognized certain characteristics of a line (y=mx+b) in space and found relationship. They needed something beside a huge paragraph (like this one) and something very precise. We call this math and at its base it’s nothing more than a symbolic way to represent things.
Really, I was thinking, “I know why they said ‘find the equation of a line’.”
So now I am thinking, not just googling for a formula that tells me how to turn a curve with a walking man or follow a path, but why and how do I represent this mathematically and then programatically.
Just hoping for comments on math in programming.
To my way of thinking, I create a “model” of some aspect of the world. Examples:
I then represent the model in a computer program. So some kind of abstaction underpins the program, sometimes the math is so “obvious” we hardly notice it, sometimes (eg. simulation games) it’s both very clearly there and pretty darn tricky.
Key idea: math can be used to model reality, most business systems can be viewed as represented as a model of reality.
Having said that, in 30 years of programming the amount of true (algebra, calculus) maths I have done is negligable.