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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