Letter from René Thom to Michel Magnen

Letter from René Thom published by the IHÉS

Introduction

René Thom nurtured a philosophical ambition in the branch of mathematics in which he excelled: that of changes of form. He received in 1958 the Fields Medal for findings in this domain. He was then able, crowned by this success, to develop his thought further, by making excursions outside his discipline of origin. Biology and linguistics interested him in particular. He remained, however, faithful to the question of the nature of form, which was that of his mathematical works. Since it is the human mind that thinks the forms apprehended in reality by it, Thom finds himself led to treat the question of the forms of the mind, starting from that of geometric forms, and so becomes directly a philosopher, uniting two objects within a single question. He starts from geometric forms — and so rather from the object findable in the world. He arrives at the forms of the mind — and so concerns himself rather with the thought that thinks this world.

The tangle of social determinations meant that my parents were linked to the great mathematician through the Protestant parish of Palaiseau. I was thus easily put in contact with him about the first part of “Meaning and Distance”. One may consult here the letter — which, moreover, I do not entirely approve of or understand — that he sent me on this occasion, a letter that the directorship of the IHÉS published in 2003 in the scholar's complete works.

Michel Magnen

Letter from René Thom

Bures-sur-Yvette, 21 December 1994

M. Michel Magnen

Dear Sir,

Your dispatch «Meaning and Distance» — of which I am far from having absorbed all the riches — has fascinated me. Let me say at once, to reassure you, that I have not detected any gross error in it. But I am far from having mastered all the notions of a luxuriant terminology. I am no logician, and I am not assured of the perfect consistency of your numerical evaluations. What truly attracted me in your work is this effort to envisage a «space of signifieds» in which one could define a distance d(p, q) between two signifieds (p) and (q). In itself, this project is in no way unreasonable. I no longer recall which analytic philosopher (W. V. Quine?) observed that for any phonetically correct expression of a language (F) (such as, in French, Abracadabra), one can find a context in which it makes sense. (For example, if Abracadabra is the password for entering a citadel.) From then on, the Saussurean distinction between signifier and signified loses much of its importance. One should rather say that, for every signified in use in a language, there is a finite set of «generic» contexts in which each context engenders a specific sense. And the sense is all the more usual the larger the set of associated contexts is, the less preparation it demands, the lower its codimension in this functional space of contexts. One may even believe that for a usual expression, the set of associated contexts forms a relatively thick set in the general space of contexts (which inherits from spatio-temporal spatiality a topology). In this sense your attempt to define numerically a distance d(a, b) between two signifieds (a, b) appears reasonable; one may perhaps hope to verify in it the triangle inequality d(a, c) < d(a, b) + d(b, c) — which would be the case for the distance defined by the number of «cases». In any event, your evaluations of semantic distance can claim only «qualitative» validity (in the sense of Rutherford's maxim: «Qualitative is nothing but poor quantitative...»). They are not physical laws! Let us go a little further into your Analysis of «the poetic». A poet I knew told me that, in his view, one must distinguish poetry from «the poetic». Whereas «the poetic» in general translates, is preserved from language to language — compare the text of Genesis in French, in German, in English… — poetry itself is in general untranslatable from one language to another. I do not know whether you would agree with this distinction: what do you think? Reflecting on your method of analysis, I recalled an astonishing passage from Aristotle: at the beginning of De Generatione Animalium (G.A., 734 a, 15–20), Aristotle evokes an Orphic poem in which it is said that the formation of an embryo is similar to the making of a fisherman's net. This metaphor, transposed to your case, would say that the poem is constituted in the mind of the poet — or of his reader — as the embryo within his mother. Using the analogy of the Orphic poem (unfortunately unknown!), I should like to visualize your attempt thus: the poem is in principle a text (I thus set aside some (post-)modern attempts which I prefer not to qualify). It comprises therefore words charged with meaning, linked by grammatical relations. These relations constitute a great graph (in the manner of Tesnière) (G), whose edges are constituted by those extremely solid «valencies» that are the syntactic links. This is the basic skeleton that will constitute the «weft» of the net, your «buffer» (?). Then appear the phonological links formed by alliterations, from line to line, or internal to a line. There it would seem to be a wave-like phenomenon of resonance that must be invoked: an identification between a sound of one phoneme and a harmonic of another, allied phoneme. Finally, onto the fabric — warp and weft — of the net thus constituted, will be added the semantic resonances aroused by the (total or partial) intelligibility between fragments of lines, long threads of connection (threads of «pick») of the tissue. The fabric constituted by the warp and the weft would belong to the domain of «the poetic»; to add to it the effect issuing from the confluence of the first resonances with the poetic resonances between significations would belong to the domain of poetry properly so called (cf. «La vitre aux veines de pensée», P. Éluard). I should readily see the fish caught in the net as an «attractor» of a dynamics issuing by resonance from this triple origin. Your method of analysis consists in distending, by deformation, a knot of the net: one perturbs an association (u, v), by replacing (v) with v_ and evaluating the «stability» of (u, v_). In general the effect of resonance weakens. One conceives that, having dismantled enough knots, you find that finally the net is empty, and that all life, all poetry, has escaped from it. Such is the sad fate of every reductionist technique, in Poetics as in (experimental) Biology. In this sense, «Meaning and Distance» is indisputably a scientific work, almost a Laboratory protocol. I want to hope that the technicians of the hard sciences (Physics and Biology) will know how to recognize its nature, and that at least some will be sensitive to the strange and powerful spirit that animates it. And that the technicians of Poetry will know how to appreciate the merits of the effort you have made to identify, in this domain, the sources of Beauty…

René Thom
Emeritus Professor at the I.H.É.S.

With my warm regards to your parents

Transcription of the letter, taken from the complete works of René Thom published in 2003 by the Institut des Hautes Études Scientifiques (IHÉS) on CD-ROM, in the Correspondence section for the year 1994: «Letter to M. Magnen, 21/12/94.»

The Editors of the Internet Journal LALIF

The online journal LALIF takes stock of current contributions to linguistic knowledge in the field of French and related languages. It came into being within the University of Toulouse II — Le Mirail.

The editors of the journal offered to publish the first part of „Meaning and Distance“ in the issue of 10 January 2002: Publication-Michel Magnen. The following year, they also agreed to insert a note about our essay in another issue: Post-publication-Michel Magnen.