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Religion and Mathematics

An interview with Dr. Jacques Lacan

Questions by Amadou Guissé, mathematician, and Alexandre Leupin, humanist.

Published in Chair et Métal


The good doctor spoke to the interviewers in French; what follows cannot be called a translation. It is more like a transposition, where the gist of Lacan’s thinking is submitted to the strictures of common English. What we have lost from his Gongorean manner of speech we hope to have gained, on the other hand, in clarity. We can only wish that his English and American translators would be inspired by this example of “infidelity”, which is after all the only way to be faithful to the doctor’s thinking. Saint Jerome already said to saint Augustine that literalism has nothing to do with real translation.

A.G. - Dear doctor, is it at all possible to give religion a mathematical formalization? And, for once, could you please be straightforward and clear? I am asking this question from you, first because you were the first to formalize a relationship between Humanities and science, second because I, as a professional mathematician, have understood the gist of your thinking on psychoanalysis through studying some of your formulas, algorithms and logical tables.

J.L. - The answer is an unequivocal yes, if we restrict ourselves to Judeo-Christianity and Islam, that is the religions of the Book; those three are different, because of their attempt at getting rid of the glue of mythology that entraps all the other religions. But we have to ground our formalization of religion on a more general level. Remember that any religious question is a sub-category of the laws of language.

A.L. - How can this be achieved?

J.L. - Let us go back to the one, in Geneva, who offered scholars the first possibility of a scientific formalization of language in general.A.G. Who is that?

J.L. -I am speaking of Ferdinand de Saussure, of course; he offers us the first possible mathematization of common language, with his formula of the sign. He intuited a possible operation on the sign.

The Doctor goes to the blackboard, chalk in hand, and writes

S/S = S , where
s=signified (any concept or representation, or signification),
S=signifier (any linguistic object),
S=meaning or statement

But we have to correct him; psychoanalysis always has to reformulate others sciences to work. Saussure made an error in putting the signified first; in fact we accede to it (to the signified or signification) through the signifiers. If you have read me, this is what I call the “primacy of the signifier”. We access signification only through the materiality of the signifier.

A.L.- How does this affect the writing of the formula?

J.L. - Here it is:

S /s = S


A.G.- Is your favorite notion, the Real, for the illacani, the unconscious, taken into account by this writing?

J.L. - Absolutely. We can even propose that Saussure was keenly aware of the unconscious’ existence. You know that he turned his interest away from scientific linguistics and tried, with the Anagrams, to remotivate the language he had demotivated, to compensate for the arbitrariness of the sign he had established scientifically. It is really is to prove that the relationship of the signifier to the signified is arbitrary: “Arbre” and “tree” point to the same signified in different languages; hence they are arbitrary. By the same stroke, they are necessary. If we disconnect the relationship, then no speaker will understand another speaker , even if they speak the same language; nobody will even understand oneself. But, after this discovery, Saussure spend the rest of his life trying to find a motivation for signs in Latin poetry. I looked for a hidden word, a crypto- or ana-gram that would harbor the treasure of meaning in Latin poetry, up to the Renaissance. This attempt failed, because Saussure didn’t have Freud at hand. He would have realized that motivation, that is meaning, is always unconscious (like desire) and because of that, essentially form- and figure-less.
However, like all geniuses, he had his intuitions: the unconscious nature of motivation or meaning is already announced in the Cours itself, when Saussure declares he uses the word “sign” to designate the two-faced entity formed by the signifier and the signified for lack of a better word in common language. To me, this is a sure index that he was aware of the unconscious nature of the linguistic operation, whereby meaning comes only at the end of speech, only to be repressed, sublimated, transformed: only to show its unconscious character. But enough about that: anybody who can read can verify that I do not err, on this point as on others.

A.L.- Still, I don’t see how religion can fit in the rewritten formula of the sign…

J.L. - But yes, the formula does relate to religion. First of all, we have to determine how to write “God”; and there are no reasons, here, to stray away from the instructions of thought contained in the Books. In the Old Testament., we are commanded not to fabricate any image of God (Moses’ second commandment); in the Christian tradition, we have a duplication of the second commandment of Moses, in the form of apophatic or negative theology (it is not possible to form for ourselves an adequate notion, or figure, or word of God). Should I prompt you to revisit the Pseudo-Denys or his gifted Irish commentator?

A.G - And what about Islam?

J. L. - What about it, indeed? The Koran doesn't forbid representation, but the Hadith (the Koran's authoritative commentary) is definitely iconoclastic On this point, the three religions of the Book are in perfect harmony; that is why indeed, their faithfuls try so hard – with blood, too often – to differentiate themselves… Anyway, let us begin with my formula for the proper name [1]:


Now
-1 /s = S


Where –1= the signifier of God, because God is not part of the {0,1} that forms the concatenation of the signifier. On a superficial level, the set of the signifier (S) is but a series of binary oppositions (easily, as such, digitalizable).

Pay attention: the bar doesn’t represent a division (it would be psychosis to consider it as such); we are working here in algebra, as I will now demonstrate (the doctor goes to the board again):

In the perfect case were the signified coincides with meaning (s = S), as such unpronounceable (Jewish tradition and the Kaballah have tons of fascinating speculations about this theme), I propose this writing for the name of God:

-1 /S = S, thus SxS = -1, thus S2 = -1, hence S =Ö -1 = i = GOD

Here, you recognize i, the imaginary number of mathematicians, which exists, but cannot be represented.

Here two precautions are in order; first, I am taking literally an algorithm (thus diverting it to appropriate it to a psychoanalytic use); the bar of the quotient is not really a division; it functions like a real border, in borderline topology): an abstract limit and relationship between two sets. Second, you cannot use the algorithm mechanically. You have to use it in accordance to the singularity of a human subject (even when you apply it to God) [2]

A.G. - I thought religion was in direct opposition to rationality, precluding any form of rigorous formalization.

J.L. - What can I say? Like many, you have bought into the masses’ opinions, which are very often on the wrong side of any equation. Remember that Galileo was a good Christian. He never claimed otherwise, but, at his time, the Church’s official thinkers were in the grips of scholasticism: that is, pure thinking of Antiquity, in its Aristotelian form accommodated to the Christian taste by the Ox of Aquinas (“When he will moo the whole world will hear him!” – we heard him…) The Church, because of Thomas of Aquinas, was indeed, still in the XVIth cent., wholly Pagan).

A.L. - What if we apply the writing of God’s name to Christianity?

J.L. - Then we have to consider the Incarnation, its only authentically original dogma. If not we will fall into syncretism à la Joseph Campbell, of which we can say, in the least, that it doesn’t advance thinking in any way. Christianity’s claim to have the only incarnated god in all history: “In the beginning was the Word, and the Word was with God, and the Word was God (…). And the Word was made flesh, and dwelt among us, full of grace and truth.”). This seemingly crazy claim will be validated because a church (not a sect) will be grounded upon it, and therefore became, as Hegel says, “a real world in which men live”, may be written thus (Christ being the exact representation of God):


j (i) = X, where j =faithful representation, i=God, X =Christ (as exact representation of God)


A.G. - As a mathematician, I have a problem with these formulas: can they be developed? Opinions are on this point controversial; some say your mathematical writings are only local, and do not support further development; others presume that they should be furthered, hence giving them some more generality. More specifically, what is the impact of these formulas?

J.L. - It has become obvious to me that, from the formula of the Incarnation, we can infer the radical singularity of every human subject. It should work like that:


X (Christ) = j (i) = j’ (i) + ij’’ (i) where j’ (i) is the real part, and j’’ (i) is the imaginary part.


Remark: j (i), the image of i by the representation, is not a number, rather a relation (function) between numbers. The properties verified by j (i) are transported to j’ (i) and j’’ (i) by simple algebra.

A.L. - Any consequences on symbolic sexuality?

J.L. - What is interesting here is that the Christian discourse, as I formalize it, has an impact on sexuality; and, dialectically, my little formulas have an impact on how we should think about theology and religion.

First of all, if any subject is completely distinct from any other, there is no sexual rapport:

x R y where x = any man, and y = any woman, and R = symbolic relation (not physical, they work more or less; that is why I say rapport, not sexual relation; I told you I was coherent). The proof reside in the fact that the relation is faithful, hence any two distinct objects having the same image by the representation would by identified as identical. And vice versa, any two distinct representations would be coming from two distinct objects.


On the level of (symbolic) sexuality, love is convinced that there is a rapport. What my writing shows is that this conviction (or cunt-viction) is no less than an illusion. Any x , says love, is in relation with an y, and vice-versa. But this happens only through a representation that masks the fact that the relation itself is not faithful to its object. In psychoanalysis, we call that projection and identification, without which you would be literally impotent.

The modern subject (that is, a subject which is not a particularity, associated to a community as a part of it), but an unconscious singularity (which of course brings all kinds of dejection with it) can be said to have been born in the cradle of Christian discourse.

A.G. - You spoke about consequences for religion?

J.L. - What is fascinating about the Book (the New Testament in that case), is that it inverts the logical chain, if we adhere strictly to its letter. The Book says:


1. (Cause)There is no sexual rapport (between Mary and Joseph, it is litteral)
2. (Consequence) Hence there is an incarnated God.


Logic and psychoanalysis say:


1. (Cause) There is an Incarnated God
2. (Consequence) Hence, there is no sexual rapport.


What my formulas show is that the Incarnation is the cause of the absence of sexual rapport, whereas, as you have learned in Sunday school, the Bible literally makes of this absence (Joseph and Mary didn’t sleep together) the cause of the Incarnation. This absent sleep is a slip.

Of course, humanity has known about the absence of sexual rapport since it began to speak; witness Leroi-Gourhan’s work. But Christianity is the first religion to make this absence the epicenter of its discourse.

Having other things to think about, this a bone I throw to theologians; it is up to them to extract the marrow from it, and I reckon they are pretty good at that.

Slowly, the Doctor fades away.

The Doctor, wherever he disappeared, is to busy thinking to answer your questions or register your reactions to this interview. However, Alexandre Leupin (general problems) and Amadou Guissé (mathematical formulas) will gladly respond to your queries.

 

Notes

[1] For the illacani, p. 819 in the French edition of the Ecrits (footnote by the interviewers).

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[2] See Écrits, p. 821.

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