A number of people who read my last post have expressed interest in what my opinions on these subjects look like when I remove tongue from cheek. Since those opinions are vaguely related to the ways I have chosen to approach my own research, it seems reasonable to try to respond to these demands. So here we go:
Do I hate math? Am I just afraid of math? Do I really think math is not a useful philosophical tool? No, not usually, and no. I never said otherwise, although I did make my point last time a purposely provocative and sarcastic way, in large part because I wanted to play up this great image by the artist and sometime-Pixar animator Don Shank.
Here’s the straight-talk version: I like math. We are buddies. I often find myself thinking about math while I’m walking to campus or waiting in line at the grocery store. Usually the math I think about is group theory or crystal lattice systems, but sometimes it is the connectedness or orientability of various kinds of manifolds, or homogenization theory, or the simple elegance of bra-ket notation. I am not prejudiced against particular branches of math, although I admit I sometimes find learning completely new branches intimidating. But intimidating in the way I find going on a road trip without a GPS intimidating, not in the way I find getting diagnosed with a terrible disease intimidating. Learning new math is exciting and eye-opening, and often very rewarding, if I can just get comfortable with not knowing where I am or why I am there for a while and have faith that something good will come out at the end.
That last bit, that having faith that something good will come out at the end, that is what I find missing in some very particular styles of philosophy of physics. I have lost faith in the ability of math to do all of someone’s philosophical work for them, and I have read many papers where I feel like I have been duped into believing there is philosophical content, when all there is, is math. It took me a long time to recognize that sometimes—not always, but sometimes—I can’t see a philosophical point through a forest of equations because there is no philosophical point, not because I am too thick to follow an author’s point.
When I am learning math for the sake of learning math, then understanding an equation is its own reward. When I am learning math to try to understand someone’s philosophical point, there had damn well better be a philosophical point at the end of it, and the math had better be necessary to make the point. Otherwise, to return to the road-trip analogy, I’m going to feel like I just blew a tank of gas for nothing. Essays that purport to be philosophical but are really just math lessons, and essays that contain math lessons that have little to do with the paper’s philosophical point, are the ones I find objectionable and mathturbatory.
I have seen more mathturbation in philosophy of physics than elsewhere, but by no means do I believe it is confined to philosophy of physics. Nor do I believe all philosophers of physics either commit mathturbation or endorse mathturbation. Nor do I believe that mathturbators are terrible people who should be branded with a scarlet μ —but I do believe that mathturbation can be damaging to the progress of philosophy, whether it is of physics, of chemistry, of biology, or of law. Philosophers should use math as a tool for making philosophical arguments, not as a shiny distraction from the absence or failure of a philosophical argument.
It is a further point, one I return to frequently in this blog and elsewhere, that I feel an obligation to devote my energies to making philosophical arguments that I believe will make a difference: arguments that will give philosophers, scientists, or lay persons pause for reflection on the best approach to solving a problem whose solution will make a difference to the way science or human life is carried out. This is a deeply Pragmatic-with-a-capital-P view, one that I hope to defend in the dissertation I write as a break from these blog posts. I do not have an airtight defense for it yet, although it is an increasingly popular viewpoint in contemporary philosophy of science. Newly renewed appreciation for the view can be attributed in part, I think, to the feminist-inspired situated-science movement in philosophy of science. Which brings me to the second issue of interest here today.
Did I leave philosophy of physics because I am a woman? My previous post pointed to a sense of alienation from philosophy of physics that has analogues in standard stories of female alienation from various divisions of the natural sciences. Answering the very touchy question of whether philosophy of physics is inherently sexist requires a separation of content and culture, first, so that it will be possible to understand to what extent culture shapes content and vice versa.
So, is the content of philosophy of physics sexist? On one hand, it hard to see how it could be. Unlike research in the life and social sciences, which can actually study things like women and men, physics looks at non-gendered particles, geometries, and fields. It would be crazy to say that reducing the number of degrees of freedom of a system is a chauvinist project, just as it would be crazy to say it is a feminist project.
On the other hand, much of the content of philosophy of physics, at least, largely ignores the broader implications of an argument’s conclusion. For instance, theses refuting some proposed attack on the GHZ theorem rarely frame their discussions in terms of whether or not our inability to recover classically-predicted information from the system should influence experimental design in quantum physics, whether the cryptographic technology that could come out of GHZ is technology that will ultimately endanger communities or societies. Rather, the theses often stop when GHZ has been adequately reinforced against future attacks.
This approach to content, this exclusion of broader discussions of why we should care about the GHZ theorem (or any point of contention in philosophy, much more broadly), has been acknowledged by feminist philosophers of science as problematic. A brief glance at Janet Kourany‘s CV or a Google Scholar search of titles by Sandra Harding offer some suggestions as to why: Feminist views on science are views of science as situated within some larger social context. Harding’s famous standpoint theory is one way of spelling out this cry for socially situated science.
The idea that science and its philosophy needs to pay attention to broader impacts, to use the NSF terminology, came out of feminist philosophy of science because one of the first places where the danger of failing to situate science was recognized was in gender studies in the social sciences. Whether or not that makes situated science inherently feminist, and non-situated science inherently chauvinist, is not a question I am prepared to answer. It is hard to swallow the idea that chauvinism is built into the Standard Model simply because presentations of the Standard Model generally fail to discuss the impact of the (non-)discovery of the Higgs Boson on the economies of Switzerland and France.
So, as I see it, the question of whether the content of some philosophy of physics is sexist remains unresolved. I could probably be persuaded either way. Moving to the second, even thornier question, is the culture of philosophy of physics sexist? Well, based on my experience, I’m going to swing a solid bunt: My best answer is, “Probably yes, but that doesn’t make philosophers of physics terrible people, and most of them seem to mean very well.”*
It is a fact that there are fewer female than male philosophers of physics, by a very non-trivial margin. It is a fact that many of my (male and female) colleagues in philosophy of physics recognize and bemoan this inequity. It is a fact that no one has come up with a really good plan to systematically change the inequity. It is my opinion that the lack of such a plan is attributable in part to the community’s collective failure to figure out what exactly is going wrong.
Spoilers: I’m not going to do that here and now.
I do think the persistence of a mathturbatory culture will not help change things for women in philosophy of physics, and could in fact do more damage. This belief has recently been reinforced by reading a book on efforts to change the culture for women in the School of Computer Science at Carnegie Mellon University. The authors of that book argue that an over-emphasis on particular kinds of technical details of programming languages at the expense of discussion of how those languages could potentially effect positive change was one feature of the culture that was alienating to women trying to enter the field. (Other features included the gender disparity in prior computing experience upon entrance to SCS, the prevalence of single-minded “hacker culture”, and the lack of support systems aimed at encouraging young women in their pursuits.)
The lack of broader applicability of mathturbatory arguments is a problem for philosophy of physics. By analogy from the study at CMU, that lack of broader applicability could be perpetuating gender inequality in the field, over and above holding the field back from its potential to affect the future of physics research.
And that is how I really feel about mathturbation.
*Note: Being terrible is what makes one a terrible person, not being a philosopher of physics. It is unfortunate to confuse the two.