DRMacIver's Notebook

Doing Mathematics to People

Doing Mathematics to People

It's very tempting to try to do mathematics to people - trying to model the world and the people in it as a simple mathematical systems. It's tempting in large part because it is in some sense very effective, but it has a tendency to go quite poorly in a number of ways.

James Scott's notion of Legibility is a classic critique of this.

I've been thinking about this and the nature of mathematics a bunch recently, and the other night I managed to express this in a way that I think captures an important feature of my thoughts on the subject.

The problem is this: One of the basic operations of mathematics is that you don't think about an entire mathematical object, you ask what its important properties are - it's a group, it's a topological space, it has a distinguished element with some properties, etc. This allows you to cleanly manipulate the object by ignoring most of the details about it, by pruning it down to only its most relevant features. The problem when you do this to people is that when dealing with real world objects, the question of what is relevant or irrelevant is an intrinsically political one, so when doing mathematics to people you're not solving "the" problem, but instead the variant of the problem which is convenient to those with power.