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uvres & Critiques, XXXIV, 2 (2009)

On Lacan and MathematicsArkady Plotnitsky

Imaginary roots are a subtle and wonderful resort of the divine spirit, akind of hermaphrodite between existence and non-existence (inter Ensand non Ens Amphibio).

Leibniz

As I was, in October of 1997, contemplating the idea of this essay, an e-mailarrived from a physicist friend of mine. The message concerned Lacan andreflected the recent events sometimes referred to as the Science Wars,in the wake of Paul Gross and Norman Levitts book Higher Superstition:The Academic Left and its Quarrel with Science and physicist Alan Sokalshoax article published in the journal Social Text. Sokal and his co-author, aBelgian physicist Jean Bricmont, then just published their book,Imposturesintellectuelles, devoted to the misuse or even abuse (alleged by the authors)of mathematics and science by some among leading French intellectuals.Lacans work appears to be seen by the authors as arguably the most notori-ous case of this alleged abuse, and some of Lacans statements they cite werebound to attract a special attention, which prompted my friends e-mail. Itsaid:

Does Lacan really talks about the penis and the square root of minus 1with a straight face, as reported in Saturdays NY Times article on theSokal and Bricmont book? And if so is there any way to view this asanything but a complete nonsense? I am testing the limits of my open-

mindedness. These seems to go beyond them.I shall, by way of replying to these questions here, sketch an argumentapplicable to Lacans usage of mathematical ideas other than imaginarynumbers (such as the square root of 1), for example, those borrowedfrom topology and mathematical logic, two other prominent areas ofmathematics ventured into by Lacan. I shall deal directly, however, onlywith imaginary numbers and Lacans argument, leading to the statement inquestion, in The Subversion of the Subject and the Dialectic of Desire in

the Freudian Unconscious (crits). It is worth noting at the outset that, asa psychoanalytically informed reader would be aware (my physicist friendwasnt), the erectile organ of Lacans statement is not the same as the penis.

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