Identity and Approximation

My friend Brandon recently wrote a post responding to a post by Manu about identity. While I mostly agree with what they both wrote, I want to take this opportunity to share some thoughts that I’ve had about personal identity for a long while. In his post, Manu wrote:

I find broad group definitions so annoying. Lumping together potentially billions of people using arbitrary traits as the dividing line is such a lazy way to look at the richness of human diversity and experience.

The theme of both posts is that defining people via labels is stupid. People are much too complex to be described in simple terms and it feels like any short description of someone (or group) will inevitably miss their essence. Broadly, I agree with this idea. I’m absolutely not about to say: “Sure. Go ahead. Lump people in to stupid groups.”

What I want to point out is that approximations are helpful. This is a big theme in mathematics and there are lots of elegant examples of approximation yielding deep ideas. The best known example is probably decimal representations of numbers. We all know the famous approximation of $\pi$, the ratio of a circle’s perimeter to its diameter: \[ \pi \approx 3.1415. \]

And that approximation represents a whole lot of insight about the number $\pi$. I can imagine some Ancient Greeks scratching their heads:

Somebody: “How is a circle’s perimeter related to its diameter?”

Archimedes: “I dunno. It looks like about three or four of them.”

And now you’ve got some idea of what $\pi$ does. It’s not the best estimate, it doesn’t tell you the whole truth about $\pi$, but it’s something. Saying that $\pi$ is about three is the start of a conversation. We can refine this estimate and say: “Yeah, maybe it’s close to three. Four is way too much. The perimeter is just a bit bigger than three diameters.” Thousands of years later, people are still adding to this conversation about approximation.

And, I think that this applies to people as well. We can approximate people by labels. Of course, you’ll never know the full and inexhaustible truth of a person. That’s just impossible; you can live with someone your whole life and never know everything about them. However, I think that it is possible, in principle, to learn a lot about someone via their labels.

Sometimes you approximate someone pretty well very quickly. For example, there are (to the best of my knowledge) three adult Esperanto-speaking Quakers in Canada. It’s a very small pool of people. That approximation, just four terms, distinguishes me and two other people from everyone else on Earth. Brandon writes:

I like to hear the personal details. Tell me what your hobbies are or what you are interested in. Tell me how many pets you own and what car you drive.

I think that what Brandon really likes here is accurate approximations. He wants you to give a specific, vivid, picture of yourself. If you say “He’s just some random Canadian” then you’re talking about ~20,638,255¹ people in a world of 8,000,000,000 people. If, on the other hand, you say “He’s an Esperanto speaking adult Canadian” then you’re talking about one of three people. This is way more accurate.

One thing that’s worth pointing out here is that accuracy is not always useful. It doesn’t particularly help anyone to know these weird bits of trivia about me. At the best, you’ll get the impression that I’m a bit eccentric. I find that it helps, when presenting myself, to think about the labels that I choose. There are certain conventions to be observed. My homepage currently says:

Hi! I’m Parker Glynn-Adey. I teach math at the University of Toronto Scarborough Campus, and at various outreach events in the Greater Toronto Area.

That is a bit out of date, but it says a lot about me. Usually, when I meet people socially, our jobs are some of the first things that come up. This job-first introduction is like saying $\pi \approx 3$. It doesn’t say everything, it’s sort of stupid, but it’s the start of a conversation.

Thanks, Statistics Canada! ↩︎

Identity and Approximation

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