The n-Category Café

Size and scale. Michael Reed memorably observed that the American Mathematical Society is about the same size as the American Society for Nephrology, “and that’s just the kidney”. Simply put: not many people care about mathematics.

The British Ecological Society (BES) meeting had 1200 participants, which is about ten times bigger than the annual international category theory meeting, and still only a fraction of the size of the conference run by the Ecological Society of America. You may reply that the US Joint Mathematics Meetings attract about 7000 participants; but as Reed pointed out (under the heading “Most of Science is Biology”), the Society for Neuroscience gets about 30,000. Even at the BES meeting in our small country, there were nearly 600 talks, 70 special sessions, and 220 posters. In the parallel sessions, you had a choice of 12 talks to go to at any given moment in time.

Concision. Almost all talks were 12 minutes, with 3 minutes for questions. You cannot, of course, say much in that time.

With so many people attending and wanting to speak, it’s understandable that the culture has evolved this way. And I have to say, it’s very nice that if you choose to attend a talk and swiftly discover that you chose badly, you’ve only lost 15 minutes.

But there are many critiques of enforced brevity, including from some very distinguished academics. It’s traditionally held that the most prestigious journals in all of science are Nature and Science, and in both cases the standard length of an article is only about three pages. The style of such papers is ludicrously condensed, and from my outsider’s point of view I gather that there’s something of a backlash against Nature and Science, with less constipated publications gaining ground in people’s mental ranking systems. When science is condensed too much, it takes on the character of a sales pitch.

This is part of a wider phenomenon of destructive competition for attention. For instance, almost all interviews on TV news programmes are under ten minutes, and most are under five, with much of that taken up by the interviewer talking. The very design favours sloganeering and excludes all points that are too novel or controversial to explain in a couple of sentences. (The link is to a video of Noam Chomsky, who makes this point very effectively.) Not all arguments can be expressed to a general audience in a few minutes, as every mathematician knows.

The pleasure of introductions. Many ecologists study one particular natural system, and often the first few minutes of their talks are a delight. You learn something new and amazing about fungi or beavers or the weird relationships between beetles and ants. Did you know that orangutans spend 80% of the day resting in their nests? Or that if you give a young orangutan some branches, he or she will instinctively start to weave them together in a nest-like fashion, as an innate urge that exists whether or not they’ve been taught how to do it? I didn’t.

Interdisciplinarity. I’ve written before about the amazing interdisciplinarity of biologists. It seems to be ingrained in the intellectual culture that you need people who know stuff you don’t know, obviously! And that culture just isn’t present within mathematics, at least not to anything like the same extent.

For instance, this afternoon I went to a talk about the diversity of microbiomes. The speaker pointed out that for what she was doing, you needed expertise in biology, chemistry, and informatics. She was unusual in actually spelling it out and spending time talking about it. Most of the time, speakers moved seamlessly from ecology to statistics to computation (typically involving processing of large amounts of DNA sequence data), without making a big deal of it.

But there’s a byproduct of interdisciplinarity that troubles my mathematical soul:

The off-the-shelf culture. Some of the speakers bowled me over with their energy, vision, tenacity, and positive outlook. But no one’s superhuman, so it’s inevitable that if your work involves serious aspects of multiple disciplines, you’re probably not going to look into everything profoundly. Or more bluntly: if you need some technique from subject X and you know nothing about subject X, you’re probably just going to use whatever technique everybody else uses.

The ultimate reason why I ended up at this conference is that I’m interested in the quantification of biological diversity. So, much of the time I chose to go to talks that had the word “diversity” in the title, just to see what measure of diversity was used by actual practising ecologists.

It wasn’t very surprising that almost all the time, as far as I could tell, there was no apparent examination of what the measures actually measured. They simply used whatever measure was predominant in the field.

Now, I need to temper that with the reminder that the talks are ultra-short, with no time for subtleties. But still, when I asked one speaker why he chose the measure that he chose, the answer was that it’s simply what everyone else uses. And I can’t really point a finger of blame. He wasn’t a mathematician, any more than I’m an ecologist.

The lack of theory. If this conference was representative of ecology, the large majority of ecologists study some specific system. By “system” I mean something like European hedgerow ecology, or Andean fungal ecology, or the impact of heatwaves on certain types of seaweed.

This is, let me be clear, not a bad thing. Orders of magnitude more people care about seaweed than $n$-categories. But still, I was surprised by the sheer niche-ness of general theory in the context of ecology as a whole. A group of us are working on a system of diversity measures that are general in a mathematician’s sense; they effortlessly take in such examples as human demography, tropical forestry, epidemiology, and resistance to antibiotics. This didn’t seem like that big a deal to me previously — it’s just the bog-standard generality of mathematics. But after this week, I can see that from many ecologists’ eyes, it may seem insanely general.

Actually, the most big-picture talks I saw were very unmathematical. They were, in fact, about policy and the future of humanity. I’m not being flippant:

Unabashed politics. Mathematics is about an idealized world of imagination. Ecology is about our one and only natural world — one that we happen to be altering at an absolutely unprecedented rate. Words like “Brexit” and “Trump” came up dozens of times in the conference talks, and not in a tittery jocular way. The real decisions of people with real political power will have real, irreversible effect in the real world.

Once again, this brought home to me that mathematics is not like (the rest of) science.

It’s not just that we don’t have labs or experiments or hypothesis testing (at least, not in the same way). It’s that we can do mathematics in complete isolation from the realities of the world that human beings have made.

We don’t have to think about deforestation or international greenhouse gas treaties or even local fishery byelaws. We might worry about the applications of mathematics — parasitic investment banks or deadly weapons or governments surveilling and controlling their citizens — but we can actually do mathematics in lamb-like innocence.

On the other hand, for large parts of ecology, the political reality is an integral consideration.

I saw some excellent talks, especially from Georgina Mace and Hugh Possingham, on policy and influencing governments. Possingham was talking about saving Portugal-sized areas of Australia from industrial destruction. (His advice for scientists engaging with governments: “Turn up. Have purpose. Maintain autonomy.”) Mace spoke on what are quite possibly the biggest threats to the entire planet: climate change, floods and heatwaves, population growth, and fragmentation and loss of habitats.

It’s inspiring to see senior scientists being unafraid to repeat basic truths to those in power, to gather the available evidence and make broad estimates with much less than 100% of the data that one might wish for, in order to push changes that will actually improve human and other animal lives.