That's a serious joke. See, I’ve studied mathematics as someone learning about mathematics. So I know how to follow and read equations, I can see what a given operation is doing in a particular step, I can look back at the whole thing and have a decent idea of how you got from the beginning to end.
It’s like being able to read a language, but not speak it.
I know enough mathematics to know that I’d be a terrible mathematician. When it comes to mathematics, I rely on colleagues I can trust. I run an idea by them – sometimes on a space like this blog. I ask them to comment, give a few thoughts. Tell me if I’m on the right track – definitely if I’m missing something.
I feel like university-trained researchers – I’m talking especially about the humanities and social sciences – get trapped in some paradoxes. Quite a lot of them. This one is mistaking a need to build expertise for your job, for expertise being the necessary condition of saying anything at all.
For instance, my case. If I were at a research conference, and there was a talk on some really interesting ideas in philosophy of mathematics in an otherwise lacklustre timeslot, I’d probably go. I’m pretty sure I have gone.
Sometimes – not all the time – folks would react with astonishment that I’d go see a talk in a field in which I wasn’t some level of expert. I do political theory, ethics, European thought, philosophy of ecology and biology.* Why would I go to a math theory talk?
* The people who know philosophy of ecology and biology would know that you have to understand mathematics at least as well as I do. But anyway.
|There is a solitude of space
A solitude of sea
A solitude of death, but these
Society shall be
Compared with that profounder site
That polar privacy
A soul admitted to itself—
Gilles Deleuze was a much better mathematician than I am. He studied mathematics well enough to teach it at the secondary level in France, which is more than I ever managed.
Study of Gottfried Leibniz’s work on differential calculus and Bernhard Riemann’s heterogeneous geometry helped Deleuze develop concepts of change and variety as fundamental principles of existence.
So when I read an article by someone who’s themselves become an expert in philosophy of mathematics and Gilles Deleuze’s philosophy, I’ll learn from what they say. Same way I learn from anyone who’s become an expert in what I want to learn about.
I read about how Deleuze interpreted Riemann’s work as tracing the mathematical structures of heterogeneous spaces – spaces that have entirely different properties, but are contiguous, that flow into each other. Objects can travel casually among all these spaces – ordinary as a walk between neighbourhoods – and be unaltered.
They just tumble differently. Into a valley, up a hill, around a bend, around several bends that seem like straight paths when you walk through them. Whatever. Doo bee doo.
Reality seen topologically. Perfectly legitimate – simply not quite what most of us are accustomed to. Let’s explore what makes us uncomfortable. And rely on people we trust – in their expertise and their character – to be our guides so we don’t lose ourselves.