We don't pretend here at adequacy to understand the French feminist philosopher and critical theorist Luce Irigaray in any great depth. Since male life expectancy is only 74.5 years in the USA, and what with maintaining this website, keeping up with the newspapers and trying to read some of the classics of Western literature, we frankly doubt that we're ever going to have the spare time to get into her work. Maybe perdida, with the extra five years' life expectancy her gender brings, will give it a crack some time.

Because of our ignorance about what Irigaray actually wrote, we're reduced to getting our information third hand, via people like Alan Sokal and Jean Bricmont. They wrote a book called "Intellectual Impostures" in order to tell us, at mind-numbing length, that Irigaray and other French critical theorists were Very Bad People and Not Worth Reading. Indeed, so many people are of this opinion, and so many of them are folks (like Richard Dawkins and William Safire) who have turned out to be utter arseholes on every other subject, that I at least among the Adequacy staff had come to the conclusion that if literally the entire inflated-self-esteem-hard-science-equals-hard-dick-know-it-all community hated Irigaray enough to write a whole big book about how stupid she was, there was almost certainly something to be said for her.

What I didn't expect was that one of the greatest mathematical geniuses of the last twenty years would prove this view to be crashingly and resoundingly right.

For those of you with better things to do with your time than keep up with the Science vs Sociology wars, the rap sheet against Irigaray boils down to one specific charge; that she did recklessly or with malice aforethought suggest that there might be some connection between

1. the way in which classical mechanics concentrates for the most part on the motions of medium-sized rigid objects, and
2. the fact that most scientists in history have been men, and therefore for the most part obsessed with the motions of a particular kind of object, an object which is often decidedly less rigid and decidedly more medium-sized than its owner would like, but which could charitably be assumed to tend asymptotically toward the Newtonian ideal.

Specifically, the great sin which got Irigaray into the Black Book of Postmodernism was to suggest that mathematics was not as value-independent and Platonic a field of inquiry as one might think. In an attractively adventurous quote, she speculated that things would have been different (specifically, our view of which classes of applied maths problem are easy and which difficult) if women had been in charge of the whole enterprise

The Newtonian break has ushered scientific enterprise into a world where sense perception is worth little, a world which can lead to the annihilation of the very stakes of physics' object: the matter (whatever the predicates) of the universe and of the bodies that constitute it. In this very science, moreover [d'ailleurs], cleavages exist: quantum theory/field theory, mechanics of solids/dynamics of fluids, for example.

Or as American writer Katherine Hayles puts it ...

"The privileging of solid over fluid mechanics, and indeed the inability of science to deal with turbulent flow at all, she attributes to the association of fluidity with femininity. Whereas men have sex organs that protrude and become rigid, women have openings that leak menstrual blood and vaginal fluids... From this perspective it is no wonder that science has not been able to arrive at a successful model for turbulence. The problem of turbulent flow cannot be solved because the conceptions of fluids (and of women) have been formulated so as necessarily to leave unarticulated remainders.

Hard questions

So, to sum it up, male maths is obsessed with hard-ons, while women's maths, if it existed, would be able to solve problems of turbulent flow because women are more interested in it. Not, one might have thought, all that outrageous a piece of speculation about the sociology of mathematicians. But apparently this small mention of our old pal the penis was enough to bring out a long parade of male academics absolutely eager to spell out exactly where Luce Irigaray had gone wrong. So we have ...

• Irigaray, in sum, does not understand the nature of the physical and mathematical problems posed in fluid mechanics," -- Sokal & Bricmont, Fashionable Nonsense
• "You do not have to be a physicist to smell out the daffy absurdity of this kind of argument (the tone of it has become all too familiar), but it helps to have Sokal and Bricmont on hand to tell us the real reason why turbulent flow is a hard problem: the Navier-Stokes equations are difficult to solve." -- Richard Dawkins, Nature ."
• Irigaray's invocations of the sciences concerned may be worse than dodgy" -- John Sturrock, LRB

And so on.

What we are obviously meant to conclude is that there is no sociological reason whatsoever why turbulent flow is generally considered to be an intractable calculation; it has to be intractable, because the only way to model turbulent flow is via the Navier-Stokes partial differential equations, and these have no closed-form solution, so they are intrinsically difficult. Case closed. Irigaray didn't know shit, so let's burn the witch for lying about science. Or is that the end of the story?

OK, we're going to be a bit rude about some scientists here, so sensitive souls should look away ... ....

There is a much easier way to model turbulent flow than trying to solve the Navier-Stokes equations by brute force, and if Sokal, Bricmont, Dawkins and the gang had held themselves to their own intellectual standards and bothered to look up the science before shooting their fucking mouths off, they'd have known about it.

In 1986, Uriel Frisch, Brosl Hasslacher and Yves Pomeau published the paper "Lattice-gas automata for the Navier-Stokes equation" in Physical Review Letters. In this paper, they demonstrated that by modelling a turbulent fluid using the theory of cellular automata as invented by John von Neumann and developed by Stephen Wolfram, one could achieve a step jump in the mathematical tractability of the modelling of turbulent flow. Interestingly, this paper appear some ten years before Sokal and Bricmont published "Impostures Intellectuels", presumably some time after Sokal's knowledge of the field had ossified, but one year after Luce Irigaray set out her views on fluid mechanics in "This Sex Which Is Not One" in 1985.

So what's the big deal? Well, as Stephen Wolfram, the mathematical genius and author of computer program Mathematica, argues in his recent book, "A New Kind Of Science", the theory of cellular automata (the eponymous "new kind of science") is a massively important development in mathematics. By stepping back from the differential equations way of thinking which described classical mechanics so well and allowed us to calculate the trajectories of cannonballs so accurately for so many years, it is possible to use this new method to dissolve all sorts of problems which had previously appeared to be utterly intractable. It gets better. The theory of cellular automata is best illustrated by reference to the famous "Game of Life", in which tiny little cells, which look a lot like ova, propagate themselves by growing, dividing, gestating and increasing in complexity in a way which only someone who was utterly blind or trying to be annoying on purpose could avoid seeing as inordinately analogous to the workings of the female reproductive system.

Cellular automata theory doesn't deal with rigid things which fly around in continuously differentiable trajectories; it deals with things which diffuse outward gradually, then experience sudden unpredictable changes in complexity. The parallels with Irigaray's writings on the feminine as fluid are unarguable:

"continuous, compressible, dilatable, viscous, conductible, diffusable... it enjoys and suffers from a greater sensitivity to pressures... it changes - in volume or in force... it allows itself to be easily traversed by flow by virtue of its conductivity to currents... it mixes with bodies of a like state, sometimes dilutes itself in them in analmost homogenous manner, which makes the distinction between the one and the other problematical: and furthermore that it is already diffuse " in itself ", which disconcerts any attempt at static identification. "

So in other words, Sokal and Bricmont (and later on, their crowd of wannabes), were heaping fun on Irigaray for predicting, one year before the FHP paper, that the problem of fluid mechanics would only be soluble by turning to an area of mathematics which is vastly more suited to the description of female sexuality than male, and being right. We at adequacy think that an apology is probably in order.