The n-Category Café

It’s also worth remembering that plenty of mathematicians regard this kind of work as perfectly ethical and even patriotic (the NSA has claimed to be the largest employer of mathematicians in the US, for example).

Another aspect of this discussion that I do not think gets as much attention as it deserves is the fact that in general, mathematicians can make a decent living by working for private corporations. This is contrasted with the fact that many jobs in acedemia are adjunct positions.

I don’t really like getting grants, and I’ve managed to survive most of my academic career without them. The pressure to get them has been building, but luckily I’m about to retire.

I’ve gotten a few to help out my grad students. The only military-funded one was not actually a grant, but a ‘subcontract’ from Metron Scientific Solutions, who got money from DARPA to work on their CASCADE (Complex Adaptive System Composition and Design Environment) project. I used this to support my student Blake Pollard and Joe Moeller, and got money from it myself. This project was directly responsible for the discovery of network models, and indirectly for the discovery of the monoidal Grothendieck construction, which we needed for network models. And of course a hefty chunk of the money went straight into the coffers of U. C. Riverside, which is one reason they want faculty to get external funding.

The project started out focused on an innocuous maritime search and rescue mission—saving sailors who went overboard in a yacht race. This is one reason I joined it. But later the focus changed to ‘combat search and rescue’, which made me unhappy. I wouldn’t be surprised if this sort of ‘bait and switch’ is routine.

In the end I quit. One reason was that Joe Moeller pulled out: he wasn’t comfortable working for the military and he actually missed being a teaching assistant. Another reason was my own discomfort with the military. But perhaps the main reason was that I was frustrated. This general kind of DARPA project is aimed at getting results quickly: there was a ‘challenge team’ posing problems to Metron, which had to be solved in months or sometimes hours, and there were software people at Metron whose job was to quickly crank out code to solve these problems. The CASCADE project in particular seemed to be premised on the idea that because David Spivak had written about practical applications of operads, we could just grab those ideas off the shelf and use them to solve complicated problems. In fact the ideas weren’t ready for such complex applications. I wasn’t able to get many people to put time into my own ideas for designing systems using operads. Quite possibly these ideas were impractical, but certainly they were too abstract to apply without some serious work. Everybody except one person, John Foley, was too busy to really think about them. No venue was proposed to get a group of people talking about them and muscling. them into concrete form, and I didn’t have the energy to create such a venue. I’m used to being able to describe something in a very abstract way and be done with it, letting someone else take it from there.

In short, I was a bad match for this line of work, completely independent of whether it involved the military.

It was very interesting nonetheless, and I can’t say I regret it even though it made me ‘lose my purity’ as far as military funding goes. In fact, losing my purity may have been a good thing. It’s very easy to harshly denounce things you’ve never had much contact with yourself, and this applies not just to working with the military but also going to gay bars, or attending a bible study class or a madrassa, or joining the Communist Party or a gun club, or listening to death metal, or becoming a Mormon, or doing various kinds of drugs, or marrying someone of a different ethnic group. Everything seems much more obviously disreputable and scandalous when you associate only with people who don’t do it, and shun those who do. But the conversation is more interesting, to me at least, when you have people with significantly different opinions involved, and not just scolding each other but actually trying to think things through.

Perhaps, at a minimum

This research was sponsored by the National Science Foundation under grant numbers CCF-XXXXXX and Air Force Office of Scientific Research under grant numbers FA-XXXXXX and FA-XXXXXX. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.

could be supplemented by

Conversely, the views and aims of the Air Force Office of Scientific Research [or insert other appropriate body here] are those of the U.S. government and should not be interpreted as representing the position or opinions, either expressed or implied, of the author(s).

The DoD is a department of the executive branch of the US government, and the actions of the DoD are ultimately actions of the US government. So how can a mathematician morally justify accepting funding from the US government but not the DoD? Where do we draw the line?

Tom wrote:

Military involvement in math is particularly an issue in applied category theory, and particularly an issue in the USA.

Maybe all of category theory? For example:

• Saunders Mac Lane, Group Extensions by Primary Abelian Groups, United States Air Force Office of Scientific Research, 1959.

Or in the introduction to Mac Lane’s 1963 book Homology:

For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science.

Or in the introduction to the 1971 edition of his Categories for the Working Mathematician:

I have profited much from a succession of visitors to Chicago (made possible by effective support from the Air Force Office of Scientific Research, the Office of Naval Research, and the National Science Foundation): M. André, J. Bénabou, E. Dubuc, F. W. Lawvere, and F. E. J. Linton.

Or in 2014, on the Homotopy Type Theory blog:

We are pleased to announce that a research team based at Carnegie Mellon University has received a $7.5 million, five-year grant from the US Air Force Office of Scientific Research, as part of the highly competitive, DoD Multidisciplinary University Research Initiative (MURI) program. The MURI program supports teams of researchers that intersect more than one traditional technical discipline, and our effort will focus on mathematical and computational aspects of HoTT. The team consists of Jeremy Avigad, Steve Awodey (PI), and Robert Harper at CMU, Dan Licata at Wesleyan University, Michael Shulman at the University of San Diego, and Vladimir Voevodsky at the Institute for Advanced Study. External collaborators are Andrej Bauer (University of Ljubljana), Thierry Coquand (University of Gothenburg), Nicola Gambino (University of Leeds), and David Spivak (Massachusetts Institute of Technology).

In order to encourage collaboration and development, the funds will be used to provide support for students, postdoctoral researchers, visiting junior and senior researchers, meetings, and conferences. We are delighted about the opportunities that the grant provides to build infrastructure and lay the foundations for this exciting research program.

The technical portion of the grant proposal can be found here: MURI proposal (public).

In 2017, an Army Research Office Broad Agency Announcement for Fundamental Research wrote:

Modeling frameworks are desired that are able to eschew the usual computational simplification assumptions and realistically capture … complexities of real world environments and phenomena, while still maintaining some degree of computational tractability. Of specific interest are causal and predictive modeling frameworks, hybrid model frameworks that capture both causal and predictive features, statistical modeling frameworks, and abstract categorical models (cf. Homotopy Type Theory).

and later:

Homotopy Type Theory and its applications are such an area that is of significant interest in military applications.

The examples could be multiplied.

The DoD does not need help to fight against low-tech adversaries from mathematicians. Mathematicians might be useful in dealing with highly sophisticated threats from authoritarian highly sophisticated countries like China and Russia.

As bad as one thinks the US military has been, I don’t think it’s defensible to refuse to cooperate against hostile authoritarian adversaries. It all sounds nice to try to be above the fray, but we should really consider exactly what we are really doing when we try to lock the military out from mathematics.

Thanks for sharing!

One topic that hasn’t been brought up– at least I didn’t see it– is the secretivity of the US Military.

If your work, which we will assume is open to the public, is used by the US government in applications that are top secret, then any new findings will be top secret as well.

Thus, not only can your work be used to do bad things, it can also be advanced in an anti-scientific way, that is, in secrete! Thus preventing science from being a product for all.

In fact, there are entire secrete government journals.

This is one of many big reasons I will not work with the US military. I feel our work belongs to the world not to my government.

I do take money from the NSF, but I don’t see this as directly working with the US military.

The article is ridiculous and naive.

The DoD doesn’t _care_ about gaining access to your mathematical community. A very few people like me see promise in “applied applied” category theory and struggle to get others in our orbits to drink the Kool-Aid. Like me, they are in the von Neumann camp, not the Grothendieck one. If y’all want to lecture in the forests to prove a point then go for it. Your perceived adversaries in DoD have nothing to lose from your disengagement because you’ll have produced nothing of value to them.

Your math _is_ too abstract to be useful. Your ideas will not be “applied applied” until they are mature, and they are uniformly not yet. People like me make them mature enough, with considerable effort, given a good enough reason. But I have had enough trouble applying my own very specific and concrete forays into ACT. If you want anyone to make your ideas mature enough to be applied, then you should come to terms with the fact that applications will inevitably be out of your hands, for better or worse. I believe it will mostly be for the better. Grothendieck left IHES and became a hermit. Are any of you glad that he did? Von Neumann helped usher in computer science and much of modern economics. I for one am glad that he did. I know which of these two had a bigger net positive impact on the world (and even more certainly in their own productive span).

The DoD doesn’t care about normalizing themselves. The DoD is normal: you are not. You can decry it, but I don’t think you can honestly deny it: it is a fact. And I’m sure that some of those who have met me can vouch for my utter lack of concern about what others think of me personally. There is no conspiracy at NSA or DARPA about seducing applied category theorists. I have been in closed door funding meetings (mostly for quantum computing) as a government participant. There is no man behind the curtain. There are only other mathematicians with different research interests and ethical stances than yours, and I have never encountered a Teichmuller. (If any of you think I am one, I suggest you ask me privately about my positions and actions outside of mathematics: you will be quickly disabused of this notion.)

The DoD will not lie to you. But neither will they assume that you are naive enough to think that you have an exclusive right to ideas that you put into the open, or to think that they are not actually a military organization that is necessary in some form (for sad but inevitable reasons) so long as humans are just slightly evolved chimps. DoD funding agencies frequently dual-track applications: I’ve seen many examples of this and produced slightly nontrivial mathematics of my own this way. But again, I’ve been in the funding meetings. I’ve never known anyone to lie. The idea that people like me live on a different moral plane from “you” is ultimately false and self-defeating. Many of you are collectively arguing from the privilege of a position (whether youth or tenure) that frees you from the obligation to actually grapple with work that might actually be useful out of the box.

PS–for those who have been concerned about my personal involvement in your orbit, I am no longer at BAE, but at another DoD contractor (that I am not naming, much less representing here) doing the same sort of stuff. I look forward to engaging many of you in conversations in the flesh down the road.

Thank you Jade for raising such an interesting issue, and thank you Tom for inviting everyone to reflect about it.

I posted my two cents on the issue on my blog.

Let me ask a very simple question to those of you who think it’s just math: would you feel the same if I go and present in North Korea, Iran, and other sanctioned countries work that is just pure category theory, or even ACT? What about if that conference was sponsored by the Iranian intelligence service? Or the North Korean military? Is it then just a matter of me presenting useless information to disinterested but generous funders?

I am proud that my work is funded by the US military, and I am happy if it can be of use to them. I believe that despite its many failings and mistakes (which include some truly terrible ones, and all of which we can and should criticize and work to reform), the US military is one of the greatest forces for good in the world today, and has been for most of the past century. Often this is less because of what it does than because of what it prevents others from doing. I find it extraordinary that anyone could spend a few minutes imagining a world without the US military and not conclude that by and large, its effect on the world is positive. Note, for instance, that after the US, China spends more on its military than the next four countries put together — and two of those next four are Russia and Saudi Arabia.

I do not want to have an argument here about the military, and I will do my best not to respond to further discussion on that subject. But given how difficult it can be for academics (especially younger ones) to dissent from progressive orthodoxy, I don’t want any readers to get the impression that there is unanimity among Cafe hosts on this issue.

Really pleased to see this excellent post of Jade Master promoted on here. I don’t intend to comment much on the topic for reasons that may be more or less obvious to at least some of the people on this thread (so I will not be responding further to the thread), but I will just say the following:

1) I want it on the record that while I have immense respect and regard for my colleague Mike Shulman, I disagree almost entirely with what he has said in this thread and find it shocking & disturbing in some respects. I do appreciate the welcoming attitude to dissenting points of view, however — something I frequently must take advantage of.

2) I think that while it is admirable to want to disengage from military funding, there may be some who underestimate the level of integration in the imperialist system: almost any source of grant funding in advanced capitalist-imperialist countries, whether it is private or public, is in essence tainted in the same way (and I am not referring to morals or purity, but rather in the sense of contributing materially to the evil imperialist project).

The military is only but one weapon wielded by imperialism to sow misery and cause trouble around the world, and works hand-in-hand with finance capital (that quant job some people planned to take when they get burned out of the academy), large corporations (Facebook, etc.), the charity/philanthropy sector, NGO industrial complex. Not to mention the destruction of human living environments by large industry — a trend that disproportionately affects the masses of countries under the boot of imperialism.

I applaud Jade’s post and much of Tom’s discussion of it. But I think we need to move toward a discussion of what scientists in mathematics can do to actively attack the foundations of imperialism, this demon that enslaves humanity for the sake of super-profits, and veer away from too much emphasis on individual actions that may have less factual impact than intended.

About military exploitation of mathematical result, I recommend Roger Godement’s preface in his first book on analysis : Analysis I Convergence, Elementary Functions. For example this ferocious judgment : “And I do not see why being opposed to the military exploitation of mathematics and science should be considered as a more political stand than for instance, helping Los Alamos or Arzamas to develop their “weapons of genocide” was.” But not only, the preface (and other parts in the treatise) is about relations between science - in particular mathematics - and weaponry.

Grothendieck’s decision was also motivated by other issues than the military ones. He talks about it in his conference at Cern in 1972 : “Je voudrais préciser la raison pour laquelle au début j’ai interrompu mon activité de recherche : c’était parce que je me rendais compte qu’il y avait des problèmes si urgents àrésoudre concernant la crise de la survie que ça me semblait de la folie de gaspiller des forces à faire de la recherche scientifique pure” (Excuse my french..)

I’m unclear what this discussion is hoping to achieve. Presumably the logic behind disengagement with DoD has the form:

The political situation is X. If the political situation is X, then you should do Y and refrain from Z. Therefore, you should do Y and refrain from Z.

I very much doubt anyone’s value of X is going to be changed by a blog discussion such as this, and that’s surely where the variation of opinion will be. The hypothetical seems straightforward enough.

One point to raise: It’s very difficult to find a permanent job in the academic field of your choice. Foregoing certain funding sources may lessen your already slight chances. But, then, who didn’t realise this?

This thread has required some active moderation and there are other things I need to pay attention to for a while, so I’m closing comments now. Thank you, everyone, for the discussion.