If you shared that old McSweeney‘s piece about “physical theories as women”, you can’t complain about Luce Irigaray calling $E = mc^2$ a “sexed equation”.
This is a famous remark by Irigaray that science fanboys like to trot out as proof that gender studies, or sociology of science, or whatever they don’t like at the moment is all bullshit. But when you dig up the source, it’s Irigaray basically spit-balling during a Q&A, taking a question and running with it.
Yet this example of “philosopher’s gonna philosophy” took on a life of its own when Alan Sokal and Jean Bricmont quoted it (incompletely, as we shall see) in their book Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science. Richard Dawkins featured it prominently in his review of Fashionable Nonsense, and it doesn’t seem to have gone out of style since.
The full citation is L. Irigaray, “Sujet de la science, sujet sexué?”, in Sense et place des connaissances dans la société, 3 (Centre national de la recherche scientifique, 1987), pp. 109–110. (This is the third volume in a series; Sokal and Bricmont’s bibliography omits the volume number.) The question begins on p. 109:
Je trouve que beaucoup des choses que tu dis sont tres provocantes, nuancées, originales — comme tout ce que tu as écrit, tout ce que j’ai lu de toi. A d’autres moments, j’ai un malaise : les moments de malaise vienne quand tu fais des extrapolations vertigineuses d’un domaine de réflexion a un autre. Je ne sais pas si c’est seulement le passage du microcosme au macrocosme mais ces analogies me semblent souvent discutables. Pour l’équation $E = Mc^2$ par exemple, on peut bien admettre que cela a conduit aux armes nucléaires mais est-ce que du la décrirais comme une équation masculine?
[I find many of the things you say to be very provocative, nuanced, original — like all that you have written, all that I’ve read of you. At other times, I am uncomfortable : the moments of discomfort come when you make virtiginous extrapolations from one domain of thought to another. I don’t know if it’s just the passage from microcosm to macrocosm, but these analogies seem to be debatable. For the equation $E = Mc^2$ for example, one can well admit that it led to nuclear weapons, but would you describe it as a masculine equation?]
In French, une équation masculine automatically sounds more meaningful than “a masculine equation” does in English; the grammatical gender makes a dose of irony built-in. The audience member follows with another question, and then Irigaray responds.
Sur la premiere question à propos de l’analogie et l’extrapolation, je ne suis pas d’accord avec ces termes. Il ne s’agit pas d’analogie et d’extrapolation et je renverrai la question, comme je l’ai fait dans l’exposé, à son contexte historique : pourquoi philosophie et science sont-elles aujourd’hui la plupart du temps séparées? Jamais il n’aurant été dit à Descartes, Spinoza ou Aristote : “Vous faites de l’analogie ou de l’extrapolation”! Ils faisaient simplement de la science et de la pensée de la science. Je fais de l’expérimentation et je réfléchis sur l’expérimentation. Cela ne revient pas à de l’extrapolation. Mais un des périls de la science actuelle, c’est d’etre tributaire du formalisme et d’être incapable de penser ce qu’elle fait. Hormis, probablement, des gens de la taille d’Einstein, la plupart des scientifiques ne pensent pas la recherche qu’ils sont en train de faire. L’extrapolation, l’analogie : là, je ne suis pas d’accord ou alors il fault dire que c’est toute la science elle-même qui est une extrapolation et une analogie! Parce qu’il y a bien quelqu’un qui l’a produite. Deuxième point : l’équation $E = Mc^2$ est-elle une équation sexuée? Peut-être que oui, Faisons l’hypothèse que oui dans la mesure où elle privilégie la vitesse de la lumière par rapport a d’autres vitesses dont nous avons vitalement besoin. Ce qui me semble une possibilité de la signature sexuée de l’équation, ce n’est pas directement ses utilisations par les armements nucléaires, c’est d’avoir privilégié ce qui va le plus vite et, je crois qu’il y a aujourd’hui pour nous un péril d’excès de vitesse.
[On the first question regarding analogy and extrapolation, I’m not in agreement with these terms. It’s not about analogy and extrapolation. I’ll return the question, as I did in my presentation, to its historical context: namely, why are philosophy and science today separated most of the time? They never said to Descartes, Spinoza or Aristotle, “You’re doing analogy!” or “You’re doing extrapolation!” They were simply doing science and thought about science. I experiment and I reflect upon experiment. That doesn’t come back to extrapolation. But one of the perils of modern science is to be subservient to the formalism while being incapable of thinking what it does. Aside from people the stature of Einstein, probably, most scientists don’t think about the research they are doing. Extrapolation, analogy: there, I’m not in accord, or else we must say that all science is itself extrapolation and analogy! Because there really was a person who produced it. Second point: is the equation $E = Mc^2$ a gendered equation? Perhaps yes. Let us make the hypothesis that it is, to the extent that it privileges the speed of light with respect to other speeds of which we have vital need. That seems to me a possibility for a gendered signature of the equation, one that is not directly its use for nuclear weapons. It’s to have privileged that which goes the fastest, and I believe that today we have a danger of excess speed.]
Sokal and Bricmont (p. 109 of the 1998 Picador edition) start quoting at “is the equation…” without any indication that this was a reply to a question, that several sentences precede that point, or that “is the equation…” was not the beginning of that sentence. The elided portion (most of the paragraph) makes a couple points worth discussing. Irigaray underlines that her concern is why science and philosophy are separate activities in the modern age; this is a reasonable question to ask. She then goes on to say that apart from the rare cases like Einstein, scientists do science without thinking about what they’re doing. This is an unkind cut, but when it comes either to philosophical implications or social consequences, we do engage in cheerful neglect rather too often.
In the omitted portion, then, we have a legitimate question, followed by a harsh but not unwarranted judgment. The quoted portion has a rapid-fire sequence of qualifications: perhaps, let us make the hypothesis, to the extent that, seems to me a possibility. Sokal and Bricmont’s translation trails off with an ellipsis before the last of these, downplaying the speculative character of the passage and excising the gendered signature part entirely. But this is the whole point of the question-and-response: If you take away the trite observation, does some aspect of gendering yet remain? Well, gosh, it’s not like society makes any associations between masculinity and the need for speed, right?
An interesting fact about special relativity is that it is founded on principles, rather than specific equations. The axioms come first, the formulae second.
1. Inertial observers Alice and Bob can come to agree on the laws of physics.
2. Alice and Bob cannot agree on which is “really moving” and which is “really standing still”, no matter what experiments they perform — even measuring the speed of light.
I would not try to express the essence of special relativity by writing any equation, not even the Lorentz transform. And in the development of the mathematics, $E = mc^2$ arrives late. A formula closer to the heart of the subject would be a jocular equation, $c = c’$.
(If you know the subject, you’ll get the joke.)
$E = mc^2$ also feels faintly old-fashioned in some respects. It’s not just that the hepcats all work in “natural units” and set $c = 1$, measuring length and time in the same units, so that we’d have $E = m$. It’s also that modern treatments would say
$$ E^2 = p^2 c^2 + m^2 c^4 \, , $$
where the letter $m$ is reserved for the rest mass. It’s the more basic concept, and so it gets the simplest symbol (while “relativistic mass” gets a subscript or something). So, the act of quoting $E = mc^2$, and especially bringing it to the forefront as the mascot of the theory, harks back to an earlier age. And relics from the old days do have a gendered-ish atmosphere, just because of the time we’re peering back into. When we look up old textbook problems, the physicists in them are always dudes, etc.
It’s like being shown one of those ghastly recipes for tuna salad in lime Jell-O and being asked, “Is this gendered?” Well, it casts me back into the days of Bert the Turtle, when cooking in the home was even more “women’s work” than it is now, so yes, it carries that effluvium of gendering (in a way that has nothing to do with the rigidity or fluidity of the material itself). The question isn’t whether the equation exists in some Platonic realm and has carnal intercourse with other equations there in ways that obey or transgress some hypothetical sexual binary of mathematical entities. This is a matter of the way humans use an idea, the freight we burden it with. A shot of whisky exists, as a physical object, without intrinsic gender, yet we socially invest it with gender significance (no umbrella here!). So, what if we take the question posed to Irigaray and consider this adjacent form of it: “Can the equation $E = mc^2$, or the foregrounding of it in expositions of relativity, be seen as gendered in the way that an umbrella cocktail or a soy latte or a jug of motor oil has gender baggage?” Perhaps the answer is ultimately no, but the question is evidently more legitimate than originally advertised!
To say it another way: We can easily imagine a physics exam problem that is overtly sexist, for example, asking the student to integrate the total momentum transfer involved in a husband beating his wife. It is also easy to conceive of problems that incorporate social standards in more subtle ways: questions that presume all marriages are between a woman and a man, that cooking dinner is women’s work, that everyone lives their adult life as the gender they were assigned at birth, and so on. If every astronaut in our textbook is a man, that says something about what we take as default, at the very least. We would like all examples of this kind to be peripheral, to be outside the shining empirical core of physics stricto sensu. But where exactly, then, is this boundary between core and periphery, and what is its character?
(Questions about boundary-drawing tend to become more complicated the longer one dwells upon them. When is thermodynamics chemistry instead of physics? When is a stochastic-process model physics and when is it mathematical biology? We tend to think that conventions of units are outside the essence of a physical theory, outside the bright shining core of the physics, but without making some choice of unit system, we cannot do the work of comparing predictions to data. No one speaks without an accent!)
It’s very easy to point to Marie Curie, as Sokal and Bricmont do on page 109, and say that she provides a proof by example that physics is not masculine, in some essential and absolute sense. But that lone data point says very little about whether modern society construes the pursuit of physics as a masculine profession. It says even less about whether physics, or any given topic within physics, falls on the side of a dividing line that one could metaphorically call male.
Sokal and Bricmont quote N. Katherine Hayles, a literary critic and theorist who commented upon Irigaray. In her summary of Irigaray’s argument, Hayles writes, “In the same way that women are erased within masculinist theories and language, existing only as not-men, so fluids have been erased from science, existing only as not-solids.”
I’d say “erased from science” is a gross overstatement, but “erased from the undergrad curriculum” would be fair.
If gender has to do with power dynamics, with social advantages, with the presumptions of who gets to be the default and who is seen as the exception, then it is plainly valid to “gender” the subjects within physics, at least analogistically. I majored in physics at MIT, and I could begin a reminiscence about the courses there by saying, “Quantum mechanics wore the pants in the curriculum.” I could expand on that by saying that we had three whole semesters of it, that the vision of the department was pretty clearly to raise the next generation of quantum field theorists.
Now, a certain audience would feel a bit of a barb within that joke, a hint that the selection of what topic predominated in the curriculum was arbitrary or capricious, or at least very historically contingent.
Nonlinear dynamics, it so happens, was shunted off into a single elective that wasn’t even formally taught within the physics department proper — it was a co-registered course with mathematics and with atmospheric/planetary sciences, taught by a professor outside our department. When it came to nonlinearity, we failed the Bechdel test.
“When it came to nonlinearity, we failed the Bechdel test.” That’s another pretty decent line for a magazine interview or an after-dinner speech. I could say that, and people would get it and chuckle.
The equations in Strogatz’ Nonlinear Dynamics and Chaos aren’t any harder than those in Griffiths’ Introduction to Quantum Mechanics. The arduous character of the Navier–Stokes equations does not enter into the question, any more than undergrad quantum concerns itself with the labor of calculating six thousand Feynman diagrams to compute a tenth-order correction to the electron magnetic moment. It’s all down to interest and tradition.
Sokal and Bricmont extend Hayles a measured compliment, opining that “Hayles’ exegesis of Irigaray’s ideas is clearer than the original.” They add, “Hayles, for her part, rejects Irigaray’s reasoning on the grounds that it is too distant from the scientific facts […], but tries to arrive at similar conclusions by a different route.” Hayles herself, meanwhile, wrote the following:
Although I think it can be demonstrated that deep cultural assumptions are replicated in hydraulics, I do not agree that fluids have simple or unified gender identifications.
I am dubious that readers of Sokal and Bricmont would appreciate this rather important point from the summary they give.
(In footnote 136 on page 111, Sokal and Bricmont quote Hayles incorrectly by omitting her mention of continuity principles without indicating so by an ellipsis. The full passage, including the examples she gives in the part they do ellipsis away, is better than the abbreviated version, in that it is more clear Hayles is aiming to describe situations where assumptions are not useful or not applicable. If one studies only systems with a lot of friction, then the guy saying “well, actually motion in a vacuum is frictionless” is not being a big help. They also call Hayles’ discussion of the history of calculus “rather confused” without explaining why. It’s a standard story of Newton and Leibniz, Berkeley’s jab about “ghosts of departed quantities”, and a gloss on Boyer.)
[EDIT TO ADD (21 October 2025): I agree with Gabriel Stolzenberg that Sokal and Bricmont whiff their discussion of how Irigaray treats boundaries. Irigaray raises the problem of sets whose edges are fluctuating or ill-defined, sets that are too cloudy to delineate. Sokal and Bricmont riposte with a remark about manifolds with boundary, which are completely beside the point, because their boundaries are sharp. They chastise Irigaray for using “vague” phrases and then drop in technical terms like algebraic topology without even a gesture at a definition. Inserting scary yet irrelevant technical terms for rhetorical effect: Sokal and Bricmont writing seriously do the same thing as Sokal writing a parody.]
Jorge Luis Borges, in his short story “Averröes’ Search”, has Averröes speak thusly: “In Alexandria there is a saying that only the man who has already committed a crime and repented of it is incapable of that crime; to be free of an erroneous opinion, I myself might add, one must at some time have professed it.” I find myself wondering if only a person who found Fashionable Nonsense the funniest book ever when they were a young physics student can be truly underwhelmed by it, all these heavy years later.