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At 10:45 PM 7/07/00 -0400, Eli wrote:

*>a mathematical psychology - one in which the mathematics directly
*

*>describes the psychological events we see, and not just the underlying
*

*>neurons - is a pipe dream, and always will be.
*

I dunno if it always will be, but a truly horrid example of inane and maybe

insane cargo-cultism was French psychoanalyst Jacques Lacan's attempted use

of topology and set theory in understanding the mind, likewise Michel

Foucault's. This stuff still gets trotted out in a usually successful

attempt to dazzle ignorant arts students (and profs). Here's some examples

(from my book THE ARCHITECTURE OF BABEL):

===============

At the same time, there seems now to be a tendency in the non-scientific

disciplines to embrace an obverse of the cautious post-Gödelian

mathematical programme: to write and publish as if undecidables were

everywhere, sanctioned by the formalisms of metamathematics, topology or

group theory (usually, it seems, barely understood).

Carnival! Lévi-Strauss, doyen of structuralism, reportedly swore by this

mantra: `Fx(a) : Fy(b) = Fx(b) : Fa--1(y)'. His commentator Gardner

(1974:269), regrettably, has been `unable to make sense of this formula'.

Loose borrowings from the precise language of mathematics are perhaps more

prevalent in francophone discourses, though they increasingly infect

anglophone post-structuralism. It is hard to resist using the term

`trajectory' as a metaphor for a notional curve marked out by the

sequential intellectual `positions' taken or `constructed' by individuals

or groups. The ballistic graph it embodies is, once noticed, strikingly

overdetermining, as if a scholar's destination and path is set, apart from

the odd buffet, at the moment of `launch'.

Foucault, whose own discourse inveighs against the easy acceptance of

received ways of description and analysis, litters his expositions with

fragments of seemingly ill-digested scientific jargon, which all too often

suffer a weight of explanatory value they cannot bear. One wonders how

many non-scientist readers of the following meditation on power, knowledge

and sexuality recognise the undefined and therefore finally unintelligible

mathematical armature on which they are mounted:

The `distributions of power' and the `appropriations of knowledge' never

represent only instantaneous slices taken from processes involving, for

example, a cumulative reinforcement of the strongest factor, or a reversal

of relationship, or again, a simultaneous increase in two terms. Relations

of power-knowledge are not static forms of distribution, they are `matrices

of transformation'. (Foucault, 1984:99)

This mimicking of the calculi of physics passes within a page to a

straight-faced parody of topology, possibly borrowed from René Thom's then

fashionable schemata of elementary catastrophe surfaces (Zeeman,

1976:65---83):

What is said about sex must not be analyzed simply as the surface of

projection of these power mechanisms. Indeed, it is in discourse that

power and knowledge are joined together. And for this very reason, we must

conceive discourse as a series of discontinuous segments whose tactical

function is neither uniform nor stable. (Foucault, 1984:100)

Jacques Lacan clowned at the carnival with more than one choice item of

dubious algebraisation. In his perhaps most-often quoted essay `The

insistence of the Letter in the Unconscious' (Lacan, 1970) he presents, in

what passes for precise formal notation, the process through which the

elements of a signifying chain manifest themselves as metonymy:

`f(S . . . S1) S = S (-) s'.

According to the key, (-) represents the barrier between signifier and

signified, but this hardly makes the pseudo-formula any more scientific.

The matter becomes more distressing when he presents his formula for metaphor:

`f(S1/S) S--S ( + ) s'.

Now we learn that the plus-sign ( + ) `represents here the leap over the

line--and the constitutive value of the leap for the emergence of meaning.

`This leap is an expression of the condition of passage of the signifier

into the signified . . . although provisionally confusing it with the place

of the subject' (ibid.:123---4)

Sadly, this `mathematisation' of Lacan's, whereby he purports to introduce

the `function of the subject' lacks a basis in any established or defined

mathematical formalism. Opinion is divided about how literally we are

meant to take such Lacanian essays into algebra and topology. Sherry

Turkle (1992:227---40) offers little more than a series of metaphysical

flurries: `There are several ways in which mathematicians might enter a

theoretical discourse about the nature of [human beings]. Mathematics can

be used metaphorically; or it can be used very literally in the

construction of precise and delimited mathematical models. Lacan's use of

topology fits neither of these categories' (ibid.:229).

This seems to me intellectually careless. Perhaps of no other field of

discourse than formal mathematics can it be asserted so categorically that

there is only one valid way to construe its signifying principles, namely,

via the path from arbitrary axioms and transformation rules to provable

theorems, always allowing for Gödelian and computational undecidables.

Of course I am not attempting to rule out of court meta-mathematical

discussion, let alone investigations by sociologists of knowledge into the

sources and uses of mathematical models and procedures. I am insisting,

however, that having once decided on the formalism 1 + 1 = 2, we cannot

(for the sport or mystery of it) decide within the same universe of

discourse to dispute the equality so established. Hence, when Turkle adds

that `Lacan . . . asserted the need for equational science among those who

he feels use poetic justification to avoid the hard and rigorous work ahead

and asserted the need for poetry among those who may be allowing scientific

rigor to narrow their field of vision' (ibid.:238), this seems to me

finally nothing better than self-deception on both his part and hers.

Similar fanciful `borrowing' from mathematics is offered in Stuart

Schneiderman's Jacques Lacan: The Death of an Intellectual Hero (1983),

where, in the spirit of Lacan, we are told that in the notation of set

theory the sound of one hand clapping is the empty set. Schneiderman's

book is also remarkable for its reification of Death and Desire (a category

error not uncharacteristic of psychoanalysis) and its sense of Freud as

divine oracle (ibid.:145, 77---8).

Further evidence for this stern verdict is seen in Martin Thom's paper `The

Unconscious Structured as a Language' (in MacCabe, 1981). The first part

is an edited version of Thom's 1975 account of Lacan, drawing heavily on

Jean Laplanche and Serge Leclaire's `L'Inconsciente: une étude

psychanalytique'. The 1979 revision attempts to correct misreadings of

Lacan now discerned in that paper, especially Laplanche's contribution

(which had been repudiated by Lacan himself). Thom's finger-wagging

discussion of the ills attendant upon treating Lacan's pseudo-algebraisms

literally rather than as graphically heuristic metaphors is unintentionally

amusing, since he (along with many others) was originally enthralled

precisely by what is now seen as a major misinterpretation. It's as if an

early relativity theorist had blindly lauded the formula E=mc^3, retracting

it only after a curt note from Einstein mentioning that what he'd actually

said was E=mc^2. In view of Lacan's clarification, Thom corrects the

formula-- relating such arcana as Name of the Father, Desire of the Mother,

Signified to the subject, and the Phallus--(MacCabe, 1981:41), adding: `As

I understand this formulation, the child's capture in the imaginary order,

as one who has a specular ego, is inseparable from the action of a primal

repression that places him or her within a Symbolic order' (ibid.:42).

What is remarkable is that Thom remains none too confident that he

`understands the formulation' even as he continues to expound it. For such

intellectual obeisance to be justifiable, Lacan would need to be a

transcendental oracle, whose gnomic gifts we must struggle helplessly to

unlock. And that indeed is how he presented himself in his seminars.

Carnival indeed! In 1766 the religious mathematician Leonhard Euler

similarly put the innumerate atheist Diderot to ignominious flight with a

phoney piece of `mathematical logic' (which actually proves nothing):

`Monsieur, (a + bn)/n = X, therefore God exists; respond!' (Hogben, 1967:9).

In the absence of absolute certainty--of `decidability'--must the critic,

too, fall into such blatant (if unintentionally comic) bad faith? Of

course, it is not only literary critics who misplace Ockham's razor on

occasion. Discourse within the sciences, especially those which abut

ideological interests and prejudices most directly, requires the same

vigilance.

==============================

Damien Broderick

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