## December 17, 2010

### The Boyd Orr Centre, or: What is a Severed Horse Leg?

#### Posted by Tom Leinster

Earlier this year I joined the Boyd Orr Centre for Population and Ecosystem Health, at the kind invitation of my friend Richard Reeve in biology. ‘But Tom,’ I hear you say, ‘what do you know about population or ecosystem health?’ Fair question. But the Boyd Orr people are marvellously welcoming, and many of us share an interest in the quantification of biodiversity, so there I am.

I hope to tell you some time about my work on diversity with Christina Cobbold. Right now I want to talk about the incredibly interdisciplinary nature of the Boyd Orr Centre, and how that makes a mathematician feel.

The Boyd Orr Centre does not (yet) have a physical manifestation: it’s a virtual centre within the University of Glasgow, a group of people with common interests. It’s named after the intrepid, idealistic, spectacularly energetic John Boyd Orr. Here are some choice quotes from this potted biography:

John Boyd Orr (known as Popeye to his family) was a visionary researcher, decorated war veteran, Nobel Peace Prize winner, political idealist and activist, and devoted supporter of this University. He was born in Kilmaurs in 1880. He graduated from the University of Glasgow with an arts degree, taught briefly (‘though I liked the children, I hated teaching them’), before enrolling for two further degrees in biology and medicine (‘it would have been exceedingly difficult to get a job with only a science degree…’).

On his Nobel Peace Prize:

Boyd Orr’s work was fuelled by a burning resentment of human injustice, and an intense frustration that the lessons of basic science were so ineffectively applied to the alleviation of human suffering. As the chairman of the Nobel committee observed: ‘The purpose of his scientific work was to find ways of making men healthier and happier so as to secure peace; he believes that healthy and happy men have no need to resort to arms in order to expand and acquire living space.’ Boyd Orr himself wrote ‘We must conquer hunger and want, because hunger and want in the midst of plenty are a fatal flaw and a blot on our civilization.’

[…] it was the appalling living conditions he witnessed in Glasgow as a student, and, later, his observations during his travels for the Food and Agriculture Organization that reinforced to Boyd Orr the necessity of ‘bringing science to politics’.

The Wikipedia article quotes words of his that may provoke a hollow laugh:

His research output suffered from the time and energy he had to devote to fund-raising, and in later life he said, ‘I still look with bitter resentment at having to spend half my time in the humiliating job of hunting for money for the Institute.’

More on fund-raising later in this post…

Unfortunately, the University saw fit to honour Boyd Orr by naming after him its biggest, ugliest building. To generations of students and staff, the words Boyd Orr mean only one thing: this gloomy great hulk of rain-stained concrete that looms over an otherwise rather pleasant neighbourhood. The Boyd Orr Centre has nothing to do with the building; it’s much newer, but more of a credit to his name.

I got involved with the Centre when I went to one of their meetings in May, on diversity. I was amazed by the breadth of people there, all members apart from me, and all with some interest in measuring diversity. Among others, there were field ecologists, genetics and genomics researchers, parasitologists, livestock breeding experts, a microbial engineer, mathematical modellers, and two qualified veterinary surgeons.

Richard Reeve, who invited me, has a background in mathematics and artificial intelligence, and now specializes in vaccines and the diversity of pathogens. Chris Quince, who I got talking to over lunch, knows all about the diversity of the microbes in your gut. Tim Parkin, who I met during the coffee break, is an expert on racehorse injuries, and has therefore spent many hours examining the severed legs of dead horses.

The interdisciplinarity was a big kick. For a mathematician it’s an eye-opener: here are people from at least half a dozen university departments, exchanging serious scientific ideas. It must take good leadership to build a group with such a positive and welcoming culture, where experts in subject A listen to and engage with experts from subject B. We’ve all seen experts on subject A shooting down any outsider who dares to encroach on their territory, or reveals a less than thorough knowledge of A.

Apart from the excitement of the meeting, and what I learned about diversity from it, a couple of things really struck me. Both are about interdisciplinarity.

First there was the simple fact that it was possible to communicate. More than that, it was possible to communicate well. The members of the Centre are probably well-practised at explaining themselves to non-experts, but even so. Take two mathematicians at random, and I’m not convinced that, on average, they’d communicate that well.

But that’s not a criticism of mathematicians. The fact is, I have a better understanding of what a severed horse leg looks like than what, say, harmonic analysis looks like, even though I know nothing special about the former and am quite curious about the latter. It’s simply a feature of mathematics that one can have next to no understanding of the research of the person in the office next door. But there are parts of the life sciences about which we all know rather a lot, simply through our daily experience.

And that brings me to the second, depressing, thought. These days—in the UK and, I believe, large parts of the world— there is enormous pressure to be inter/multi/cross/trans-disciplinary. Funding bodies increasingly want to give you money only if you’re joining up subjects in a novel way, rather than drilling deep into the mysteries of some established field. At some point during the Boyd Orr meeting I looked around the room and thought: mathematicians are stuffed. This is what the managers mean when they talk about interdisciplinarity. How can we explain to them the gulfs that separate different parts of mathematics? How can we explain that it might be easier for a commutative algebraist to read a paper on ecology than a paper on non-commutative algebra?

Anyway, I don’t want to finish on that depressing note. I’m happy to have joined the Boyd Orr Centre, I’m optimistic about the opportunities, and I feel lucky to have stumbled into it.

Posted at December 17, 2010 5:11 PM UTC

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### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I have thought often about the difficulty of non-experts to understand mathematics. Imagine, for instance, that you are at a restaurant and overhear a conversation at the next table. I think that if the subject of the conversation were history or philosophy, chemistry or physics, you would recognize this. Now imagine that the next table overhears your conversation about your favorite piece of mathematics (say higher categories in homotopy theory). I would surprised if anyone besides another mathematician or maybe a physicist would recognize that you are talking mathematics rather than gibberish.

However, I’m not sure I agree with the comment about a commutative algebraist having an easier time understanding ecology than noncommutative algebra. This very much depends on what you mean by understand. It is certainly easier to nod my head about ecology than it is to nod my head about Ngo’s proof of the Fundamental Lemma, but I don’t understand and haven’t yet tried to understand either in a serious way. I would guess that, all things considered, ecology is actually far more complicated than the Fundamental Lemma and that I have a better chance of *understanding* the latter. But that’s not to say that one shouldn’t make a good go at ecology.

Posted by: Chris Brav on December 17, 2010 9:24 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

Chris wrote:

However, I’m not sure I agree with the comment about a commutative algebraist having an easier time understanding ecology than noncommutative algebra.

I see what you mean, and while I kind of stand by what I wrote, the risk of being misinterpreted makes me uncomfortable enough that I’ve now changed “understand” [a paper on ecology/noncommutative algebra] to “read”. What I meant was that someone totally untrained in the subject can often pick up a paper in ecology and, in a few minutes, form a rough impression of what it’s about. That’s more than can be said for most mathematics papers outside one’s own area of expertise.

But as you say, it very much depends on what level of understanding we’re talking about. Certainly I don’t mean that there’s nothing deep or difficult about ecology—it was surface understanding I was talking about.

I don’t know whether you’ve tried reading any ecology papers, but if not, you might be pleasantly surprised. Many really are quite accessible to a total outsider. For example, on this page you’ll find a classic paper by Robert Whittaker on the vegetation of the Siskiyou mountains. It’s unusually long (60 pages) and, to be sure, contains some technical words and specialized techniques, but otherwise it’s pretty comprehensible to a non-ecologist. One minute spent with this paper probably tells me more than five minutes spent with a random paper from today’s mathematics arXiv uploads. Again that’s not to say anything negative about mathematicians. It’s just the nature of the subject.

Posted by: Tom Leinster on December 17, 2010 9:49 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

Chris wrote:

It is certainly easier to nod my head about ecology than it is to nod my head about Ngo’s proof of the Fundamental Lemma, but I don’t understand and haven’t yet tried to understand either in a serious way. I would guess that, all things considered, ecology is actually far more complicated than the Fundamental Lemma and that I have a better chance of understanding the latter.

I agree, and I think this isn’t a coincidence.

Cutting-edge research is the hardest to understand in the simplest subjects. Why? Because these subjects have a lot that can be easily understood — but that easy stuff has been understood, and so has the stuff after that, and the stuff after that, and so on. So, it takes a long time to catch up before you get near the cutting edge.

In other words, it’s a lot harder to think of something new to say about adding and multiplying (commutative algebra) than tropical jungles, grasslands, tundras, oceans… and the vast wealth of species doing complicated things in these places.

Anything new that someone has to say about addition and multiplication is almost certain to be incomprehensible to someone who hasn’t devoted their lives to thinking about $+$ and $\times$. Of course, still occasionally someone will prove a theorem about $+$ and $\times$ whose statement can be understood without vast amounts of training: like, “you can find arbitrarily long arithmetic progressions of primes”. But people win Fields Medals for this. And the proofs of these results are not easy to understand.

On the other hand, there’s a lot of interesting stuff close to the surface in ecology.

In even more difficult subjects, like politics and ethics, the gap between expert and non-expert knowledge is even less.

Posted by: John Baez on December 18, 2010 2:03 AM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I’m sure that there’s something to the difficulty of thinking up new ideas, but one of the other big reasons that, at least in non-preprepared communication, is the way that certain subjects have a very dense, specialised terminology whilst others are using words that are already understood, even though the complexity of the argument may be similar in both fields. One thing that makes this really hard when talking to academics in other disciplines (who have an appreciation for study in general), and I think is a historical mistake in mathematics, is that some of its standard terminology is named after the people who discovered important things (eg, Hausdorff, Banach, Kan, Frobenius, Givental, etc) rather than attempting self-description. This has the consequence that even if someone gives me a verbal glimpse of what’s key about, say, a Frobenius manifold, I’m likely forget the association between the term and the concept quickly. If I’m talking to you and you mention a fractional-linear transformation I can probably connect that with some vague memory I have of functions which were fractions, whereas to do that with Mobius transformation I have to remember exactly. (Of course it fulfills the role of both honouring people and coming up with a snappy name for a concept.)

I’ve seen mathematicians, and in particular what I consider “pure mathematicians working in computer science” communicating very effecitvely in pre-preapred communication of sophisticated ideas because they’ve painstakingly figured out how to word things so that the audience has to do as little figuring out what the words they’re saying mean as possible and can concentrate mostly on piecing together the ideas.

Posted by: dave tweed on December 18, 2010 3:38 AM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I agree with John, the principal difference is that to understand a lot of modern mathematics you have to have had a layered learning experience: learn the basics, then the stuff after that and then the stuff after that etc. I think the reason for this is the level of abstraction. To understand why abstraction is necessary and powerful, you need to have understood the situations which are unified by this abstraction.

In studying philosophy, I get the same feeling. I recently tried to dig into Derrida’s “Spectres of Marx”, and I had the same difficulties as I had when I first glanced at Ngo’s work. There are layers of knowledge that are needed, and I think this is because of the level of abstraction in which Derrida thinks and argues.

Posted by: Ryan Mickler on December 20, 2010 3:39 AM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I’m so glad you’re getting into this biodiversity stuff, Tom! It sounds vaguely like my own experience dipping my toes into the waters of climate science.

You wrote:

… it was the appalling living conditions he witnessed in Glasgow as a student, and, later, his observations during his travels for the Food and Agriculture Organization that reinforced to Boyd Orr the necessity of ‘bringing science to politics’.

Heh. There’s something exquisitely Scottish, or British, or something, about how you wanted to include that comment.

At some point during the Boyd Orr meeting I looked around the room and thought: mathematicians are stuffed.

There is another breed of mathematician, the applied mathematician, who can thrive in this ecosystem. Often just a little mathematical know-how can accomplish things that nonmathematicians will find very impressive and useful. But the requirement is a willingness to learn about the mess and murk of the world, where not everything is definitions, theorems and proofs.

Right now I’m trying to learn about the El Niño. Nobody knows what causes it, but there are a lot of really fascinating theories — and a lot of cool math, ranging from Hopf bifurcations to stochastic differential equations, delay-differential equations, orthogonal functions, principal component analysis, and more. It’s exciting! It’s like opening a door and seeing a big new world out there. I don’t know what I’ll do yet, except explain this stuff, but someday I may get a good idea.

Posted by: John Baez on December 18, 2010 2:39 AM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I think Tom is referring more to presentation rather than content in the “being stuffed” sentiment. One of the things about UK grant awarding bodies, in my opinion, is that they’re much, much more interested in the scope and grandeur of what you propose to do than in what you are likely to actually acheive at the end of things (if indeed they follow up at all). It’s not the pure vs applied issue as much as the “that sounds cool” vs “that sounds dull” issue. Unfortunately being very precise and using words that the listener doesn’t instantly know both increase the feeling of “it’s dull” in listeners.

Posted by: dave tweed on December 18, 2010 4:03 AM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

Unfortunately being very precise and using words that the listener doesn’t instantly know both increase the feeling of
“dull” in listeners.”

Fortunately, when I applied for renewal of my Marshall Scholarship for a 3rd year, they granted it on the basis they had been unable to find anyone able to referee it properly! (here belongs a quote from WS Gilbert)

Posted by: jim stasheff on December 18, 2010 1:59 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

By “stuffed” I meant “in trouble”. It occurred to me that that might not be an internationally understood colloquialism. (Dave, I can’t tell from your comment whether you understood me—at first I thought not, but now I think you did. If not, my fault.) The only decent alternatives to “stuffed” that I could think of at the time were not… decent.

Posted by: Tom Leinster on December 18, 2010 7:28 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I did get the meaning you intended, Tom. I was basically making a point that it’s easy to think it’s because pure mathematics “isn’t applied” (at least according to some people) that’s the problem, but I don’t think that’s the problem. My experience, for whatever it’s worth, is that if you can come up with a reasonably understandable grand vision in pure mathematics that’ll be favourably received. On the other hand, being “realistic” about what you’re going to achieve, even in an applied area, doesn’t get a look in. And typical mathematical communication looks a lot like the latter.

Posted by: dave tweed on December 18, 2010 11:58 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I see. Yes, I agree with you—both on this point and on your earlier point that British funding bodies tend to focus almost entirely on initial proposals rather than final reports.

I have seen grant proposals suffer by being (according to reviewers) unrealistic. But more often they suffer by being insufficiently ambitious.

Posted by: Tom Leinster on December 19, 2010 4:48 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I should add that I’ve generally been reassured and impressed by the people I’ve had contact with at EPSRC, the main UK funding body for mathematics. As an academic one’s immediate fear is that people in that position would be purveyors of the particular brand of academic management bullshit that many of us are familiar with. But actually, my experience has been that they listen to mathematicians and take seriously what our priorities are. For example, I was once at a meeting at which grant proposals were being ranked, and we put a proposal in pure finite group theory very near the top of the list. None of the EPSRC staff said “you can’t do that, it’s not interdisciplinary enough”, and there would have been uproar and probably a mass walk-out if they had.

On the other hand, it seems clear which way the wind’s blowing.

Posted by: Tom Leinster on December 18, 2010 9:42 AM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

These days—in the UK and, I believe, large parts of the world— there is enormous pressure to be inter/multi/cross/trans-disciplinary. Funding bodies increasingly want to give you money only if you’re joining up subjects in a novel way

This trend certainly extends to the US. At the risk of introducing excessive glibness into a serious discussion…

Posted by: Mark Meckes on December 18, 2010 2:42 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

When I saw the URL, I thought the link would be to this one.

Posted by: Tom Leinster on December 21, 2010 5:39 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

I think that Tom is too negative about how stuffed (or worse!) mathematicians are. Having left maths to join this interdisciplinary mess/wonderland many years ago, these last couple of years since we formed the Boyd Orr Centre have been the first time that I’ve found a community where we care more about finding out what we have in common rather than we focus on what divides us. It may sound a bit fluffy to talk about what we care about rather than what our research area is or what we say we’re doing, but it really matters - even having got to this stage we often struggle to communicate even basic concepts.

It is hard to find interesting areas of conceptual overlap between different fields which have practical and not just theoretical implications, and this applies just as much to Ecology, Microbiology, Veterinary Medicine and Epidemiology as it does to different areas of Mathematics. It is certainly the case that the problems in mathematics are more abstract and that the low-hanging fruit has been more rigorously harvested, but the conceptual and (even worse) the language barriers are just as high in both cases.

Advances in research certainly require focussed attention in very specialised areas, but they also require people trying to translate advances in one area to another or to generalise from similar advances/problems in several areas. These attempts are often futile and always hard to achieve but it’s really fun to try, and that applies just as much to maths as it does to the life sciences. I’m frankly delighted to have got Tom involved.

Posted by: Richard Reeve on December 20, 2010 2:38 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

Hi Richard!

You may be right that I’m too gloomy about the prospects for mathematicians. Certainly that feeling is born partly out of the current British government’s enthusiastic vandalism of the university system.

What I’m worried about is the future of support for pure mathematics. To be clear: I view anything interdisciplinary—e.g. the work I’ve done with you—as applied mathematics. (There’s a traditional interpretation of the term “applied mathematics”, over-narrow in my opinion, as meaning something like “analytical methods applied to a physical problem”. But I’d say that combinatorics applied to computer science, for instance, has as much of a claim to being applied mathematics as PDEs applied to solid mechanics.)

As long as there continues to be funding for pure mathematics, I have every reason to hope that those who administer that funding will do so reasonably (as I think they do now, on the whole). But given what’s happened to funding for arts subjects, mathematicians who don’t have some claim to interdisciplinarity may be in for a tough time.

Posted by: Tom Leinster on December 20, 2010 7:28 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

Hi Tom,

I quite understand your concern for pure maths funding. And I certainly prefer your definition of applied maths to the one often found hanging around by default. However, I am concerned by the idea of defining something by what it is not. You say “I view anything interdisciplinary — e.g. the work I’ve done with you — as applied mathematics.” This appears to leave pure mathematics as those things which are not interdisciplinary. As I’ve pontificated about before elsewhere, I think this is a dangerous place to leave yourself — you back yourself into a corner where you exclude yourself from many funding sources simply by your definition of your subject area, irrespective of what you actually do.

Why would you choose to do that? Surely something is either interesting to you or it isn’t? Does it have to have no possibility of application before it becomes interesting? If not, why make that a prerequisite? It may well be the case that pure mathematics tends to not have any obvious applications, but to define it as those things which have no application seems to be actively unhelpful, as well as often being untrue in the longer term…

I suppose what I’m really trying to say is that for better or for worse funding may be moving towards more interdisciplinary projects, but my feeling is that the consequences of that movement are subject-specific, and maybe in pure mathematics even being willing to contemplate applications for your research is so far beyond where most people are that it is easily a big enough step for the foreseeable future. Or maybe I’m just being desperately naive!

Posted by: Richard Reeve on December 21, 2010 2:50 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

Well, I actually have little desire to draw a line between pure and applied mathematics. I don’t think it’s a very helpful distinction. At the moment I’m on a bit of a mission to get people to revise their opinions about which parts of mathematics can be used outside mathematics, which is why I’ll grab the ear of anyone passing and tell them that I think their definition of applied mathematics is too narrow.

Many people who call themselves pure mathematicians had the experience, when undergraduates, of going to applied lectures and being put off by the lack of rigour. Or, quite simply, they don’t like differential equations. I suspect that there are many pure mathematicians in the world whose view of applied mathematics is more or less characterized by those two things: differential equations and a lack of rigour.

But as soon as you think about it, it’s obvious that applied mathematics doesn’t have to mean either thing. For example, there’s a long history of category theory applied to computer science, which is both scrupulously rigorous and (for the most part) miles away from any kind of analysis.

So I don’t really think it’s a fruitful distinction to make. Frankly, I’ll call my work on diversity either pure (because it springs from a traditionally very “pure” subject, category theory) or applied (because it’s applied to biology) depending on what will get more money.

There will—I hope—always be pure mathematicians, in the sense of people who are unconcerned with applications. There may be applications of their subject, but they don’t happen to be interested in them. It seems likely that at some point in the near future, we’ll have to make a vigorous argument for why these people are important. Most of the time I’d count myself as such a person, so it’s something that concerns me.

On the other hand, I’ll willingly take your advice on anything to do with funding, because you seem to be exceptionally good at getting it. You have, as they say, detailed knowledge of the funding landscape.

Posted by: Tom Leinster on December 21, 2010 4:56 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

Apologies, I may have got a bit carried away there. I think we fundamentally agree - my only concern is to make pure maths a positive choice because it’s valuable in its own right rather than a negative one of not being applied…

Posted by: Richard Reeve on December 21, 2010 11:16 PM | Permalink | Reply to this

### Re: The Boyd Orr Centre, or: What is a Severed Horse Leg?

The Boyd Orr Centre now has its own blog.

Posted by: Tom Leinster on May 19, 2013 5:50 PM | Permalink | Reply to this

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