Once upon a time in math, I studied metric spaces, spaces for which there exists a way to measure distances between points. At first glance the non-mathematician might say: yuck, this is the genesis and justification of corporate bean counting and turning people into numbers, stay the heck away from me.
But this is not the mathematical point of view of metric spaces at all. There are things that are metrizable, and there are things that can be proven to be unmetrizable. That’s why I love mathematics so much. It’s about the ideas. It doesn’t say: hey to be successful you have to figure out some good metrics and collect data and optimize. Mathematics says: what is a metric, anyway? When does it make sense, and when does it not? What does the unmetrizable look like? Can I tell if something is metrizable at first glance? Sometimes I can — which is exciting — and sometimes I can’t — a reality to be accepted.
What the mathematics gives us is a way to talk precisely about these kinds of questions, in specific circumstances. If we understand a few specifics with some depth, we are in much better shape to extend to generalities and the fuzziness and incompleteness and incomprehensibility of the real world, than if we don’t have any depth at all. Provided of course we develop along the way a feeling for the limits of those specifics.
Having a way to talk precisely about specifics can be surprising, not limiting, because with precision you can effectively ask outrageous questions, and see if you get outrageous answers. If you look up examples of unmetrizable spaces, you might see what I mean. The subject definitely gets weird.
I don’t understand why as a society we don’t treasure these tools, tools of thinking and exploring, more broadly and more affectionately. I just don’t.