Tag Archives: category

There’s only one thing that I know how to do well

Last week I moderated (virtually) a discussion at Stanford between my poetry friend Stephanie Burt and my category theory friend Emily Riehl, on the topic of “identity” — specifically the question of how, in lyric poetry and in mathematics, one addresses the complex topic of what we do when we identify; whether this means “identifying with” a character in a song or poem or story, or identifying two objects which are not equal but which, in Poincare’s phrase, we “call by the same name.”

What I realized after the fact is that, as in so many other matters, the most succinct formulation is in a They Might Be Giants lyric:

There’s only one thing that I know how to do well
I’ve often been told that you only can do what you know how to do well
And that’s be you,
Be what you’re like,
Be like yourself

Surely this points to three different notions that appeared in the discussion:

  • “be you” — to say that you are you is to assert equality
  • “be what you’re like” — that is, have exactly the properties that you have and no others — an assertion of indiscernibility
  • “be like yourself” — this is the assertion of relation (here denoted a “likeness”) between two entities that licenses us, following Poincare, in calling them by the same name — that is, an assertion of equivalence

Here’s YouTube of the discussion:

And here’s YouTube of the They Might Be Giants song, “Whistling in the Dark.” I remember seeing them play this in the fall of 1989, at the Paradise Rock Club, before the album came out, a song nobody had heard. A revelation!

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Tom Leinster on entropy, diversity, and cardinality

You might want to consider reading the n-category cafe even if you don’t know what an n-category is — even if, antique as this view may be, you don’t care what an n-category is!

For instance, it’s the best place to read about the curious case of M. El Naschie, who’s published 322 of his own papers in the journal he edits for Elsevier.

More substantively: Tom Leinster has a beautiful pair of posts (part I, part II) about varying notions of “diversity” in population biology, and a way to capture all these notions as special cases of a general mathematical construction.

Drastic oversimplification: you might start by defining the diversity of an island beetle population to be the number of different species of beetles living there. But that misses something — a population with three equinumerous beetle species is more diverse than one where a single dominant species accounts for 98% of the beetles, with the remainder split evenly between the other two species. Part I of Leinster’s post is devoted to various measures that capture this behavior. In particular, he’ll explain why on the former island the effective number of species is 3 (just as you’d expect) while on the latter the “number” of species is not 3, but about 1.12 — in other words, the second island is very close to having just one kind of beetle.

In part II, Leinster discusses what happens when you take into account that some pairs of species are more similar than others.

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