LACAN JACQUES: (1901-1981) French psychoanalyst & psychiatrist. An extraordinary illustrated A.L.S., Lacan, two pages, 4to, Rue de Lille, Paris, 18th October 1946, to Raymond [Queneau], in French. Lacan writes regarding a challenging puzzle of logic, in greater part, ´Pardonnez-moi, mon cher Raymond, de vous avoir importuné hier soir: mais pris entre ma paresse et le tourment de l’effort inaccompli, j’avais besoin, comme on dit, de me faire mettre les points sur les i. Voici donc ce que j’ai trouvé en rentrant de chez les amis d'où je vous fis mon appel. 1ere pesée. Vous mettez les pièces dans chaque plateau de la balance. Deux cas: a) Les plateaux s’équilibrent. Donc la mauvaise pièce est dans les 4 restantes. Il est clair qu'en deux autres pesées vous détecteriez facilement la mauvaise pièce entre 4. (Je précise: vous comparez 2 pièces. 2 cas: ∝) elles s’équilibrent. Alors en comparant l’une d'elles à l’une de 2 que vous avez laissées de côté: où bien elles s'équilibrent et c’est la dernière qui est la mauvaise. Ou elles ne s'équilibrent pas et la mauvaise est cette pièce même que vous venez de prendre pour la dernière pesée. β) elles ne s'équilibrent pas. Dans ce cas vous prenez par exemple la pièce lourde et vous la comparez à l’une des 2 autres. Si elle l’emporte encore, c’est elle la mauvaise. Si elle s’équilibre, c’est l’autre pièce de la 2e pesée qui est la mauvaise.b) Les plateaux ne s'équilibrent pas. Ceci est le cas intéressant. Posons bien la situation pour la résoudre. Vous avez donc trois groupes. Un groupe de 4, où vous avez la mauviase pièce, Si elle est la plus lourde. Un groupe de 4 où elle se trouve Si elle est la plus légère. Un groupe de 4, sûrement “sain”. 2eme pesée. Voici comment procéder. [A ce stade de la lettre, Lacan a ajouté une rapide esquisse pour illustrer sa théorie] Vous allez substituer dans le plateau lourd 3 pièces saines (prises dans le 3ᵉ groupe) à 3 pièces de ce plateau. Puis placer ces 3 dernières pièces dans le plateau léger, d'où vous sortez bien entendu 3 pièces. La figure ci-dessus signifie cette double translation. Alors 3 cas a) le plateau lourd reste le plus lourd: donc c’est que l’une des deux pièces qui n'ont pas bougé (appelons-les ∝ et β) est la mauvaise pièce —pièce plus lourde si c’est∝, plus légère si c’esf β. Point qu’éclaircirait de la façon la plus facile une 3eme pesée. (Je n'ai pas besoin, je pense, de préciser. Car il faul que je parte pour l’hôpital et on vient de me déranger par la petite employée de la librairie ... qui vient de “tourner de l’œil”). b) les 2 plateaux s'équilibrent: alors la mauvaise pièce est parmi les 3 que j’ai fait passer d'un plateau (lourd) dans l’autre (léger): groupe∝ et elle est ne pièce lourde......3eme pesée. Qu´il s´agisse de trouver une pièce lourde ou légère parmi 3 autres, cette 3e pesée le résoudra aussi facilement. Que les deux pieces que nous comparerons entre elles s´équilibrent ou se manifestant inégales. Merci beaucoup, mon cher, de m´avoir donné ce petit sujet de tracas et d´amusement´ (Translation: ´Forgive me, my dear Raymond, for having bothered you last night: but caught between my laziness and the torment of unaccomplished effort, I needed, as they say, to dot the i's and cross the t's. So here is what I found when I returned from the friends' house from where I made my call to you. 1st weighing. You put the coins on each pan of the scales. Two cases: a) The pans balance each other out. So the wrong coin is among the remaining 4. It is clear that in two more weighings you would easily detect the wrong coin among the 4. (I specify, you compare 2 coins. 2 cases: ∝) they balance each other out. So by comparing one of them to one of the two that you left out: either they balance each other out and the last one is the wrong one. Or they do not balance each other out and the wrong one is the very coin that you just took for the last weighing. β) they do not balance. In this case, you take the heavy piece, for example, and compare it to one of the other two. If it is still heavier, it is the wrong one. If it balances, the other piece from the second weighing is the wrong one. b) The trays do not balance. This is the interesting case. Let's set out the situation in order to solve it. So you have three groups. A group of 4, where you have the lousy piece, If it is heavier. A group of 4 where it is If it is the lightest. A group of 4, surely ‘healthy’ 2nd weighing. Here's how to proceed. [At this stage of the letter, Lacan added a quick sketch to illustrate his theory] You are going to substitute 3 good coins (taken from the 3rd group) for 3 coins on the heavy tray. Then place these last 3 coins on the light tray, from which you will of course remove 3 coins. The figure above represents this double translation. So 3 cases a) the heavy tray remains the heaviest: so one of the two pieces that have not moved (let's call them ∝ and β) is the wrong piece - heavier piece if it is ∝, lighter if it is β. A point that would be clarified most easily by a third weighing. (I don't think I need to explain. Because I have to leave for the hospital and I have just been disturbed by the little employee from the bookshop... who has just ‘taken a nap’).b) the 2 trays balance each other out: so the wrong coin is among the 3 that I have moved from one (heavy) tray to the other (light): group a and it is a heavy coin.........3rd weighing. Whether it is a question of finding a heavy or light coin among 3 others, this 3rd weighing will solve it just as easily. Whether the two pieces that we will compare are balanced or unequal. Thank you very much, my dear, for giving me this little subject of hassle and fun´). A wonderful letter; although Lacan was sometimes accused of obscurity, even of extravagance, this letter proves that his intellectual constructions were based on an impressive capacity for analysis.VGRaymond Queneau (1903-1976) French novelist, poet, critic and editor.Queneau and Lacan had known each other since the 1930s, when they attended the famous Kojève seminar on Hegel's philosophy together. Another bond united them; Sylvia, Jacques Lacan's wife, was a childhood friend of Jeannine, Raymond Queneau's wife. But what fundamentally brought them together was the same interest in language games (which they each used in a different way) and problems in mathematics and logic, the present letter being a perfect example of this.It is understandable that Jacques Lacan, while he was at a friend´s house, found himself confronted with some mathematical or logical problem. Lacan evidently telephoned Queneau, who undoubtedly replied and submitted another brainteaser for his consideration. It is a classic puzzle. There are 12 coins that are absolutely identical in appearance. One of them is fake, and of a different weight (but it is not known whether it is heavier or lighter). To find out which is the fake coin, all you have is a set of scales with two pans and three weights. Taken in by the game, Lacan began to think about the problem on his way home from his friend´s house and the very next day he wrote this long letter that brilliantly resolved the question. In a playful way, it is a striking illustration of his power of reasoning, his logical rigour and his agility of mind.
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