Le compte est bon: Carl Jung’s couch arithmetic

Le compte est bon

In Carl Jung’s 1910 paper “On the Significance of Number Dreams“, the famous Swiss psychiatrist, psychoanalyst and founder of so called “analytical psychology” attempts the description of a peculiar type of arithmetic applied to the interpretation of dreams. The result is an impressive pseudoscientific piece of sheer nonsense. The process is the psychoanalytical version of the arithmetic quiz in Armand Jammot’s “Des Chiffres et des Lettres”, a TV programme that since 1965 has been entertaining generations of viewers. In Jammot’s game the contestants are given six numbers chosen at random from these alternatives: 1 to 10, 25, 50, 75, 100 and then a three digit target number is generated. The players are allowed to think for one minute and produce the target number by addition, subtraction, multiplication or division and using at most once each of the chosen numbers. The winner is the player that first arrives at the target number, in which case the phrase “le compte est bon” (the total is right) confirms the success, or to the nearest possible number. It is a quite entertaining game for a lot of people and anyone with some ability in arithmetic can be successful or be given the impression that can be successful. In Jung’s paper a similar “number game” is proposed, only much simpler from arithmetic point of view, as one may choose any initial numbers from a subject’s life, including ages of relatives, dates of birth, various amounts of money, street numbers, numbers of children etc. In case the numbers at hand have more than one digit, it is allowed to first break them in any conceivable way to proceed with calculations. Moreover one may employ in the calculations as many initial numbers as desired and no time limit exists. Under these conditions the question addressed in the paper is whether one can produce at some point a specific “target number” seen by the subject in a dream. In the (quite likely) case the process is successful and “le compte est bon”, a deeper meaning is supposedly revealed. To make his point, Jung considers the example of a specific “middle-aged man whose conflict of the moment was an extramarital love affair“. For simplicity, this man will be referred to here as “John” and his mistress as “Jane”. Three specific dreams of John are described in the paper.

Carl Jung (1875 – 1961)

Couch arithmetic

In the first example, John has a dream of himself holding some ticket:  “… the dreamer shows his season ticket to the conductor. The conductor protests at the high number on the ticket. It was 2477.“

A first possible explanation given in the paper is this: maybe John is worried about the financial cost (in francs) of his affair. So, the idea goes, let’s calculate the total cost of the affair and see if the exact sum matches 2477. Jung reports that “A rough estimate of the expenses so far involved led to a number which in fact approached 2477 francs“. Though such a calculation could be rather vague, it is quite favorable for a “player” of Jung’s number game as one may continue adding up the expenses until the desired target number is reached. At this point the effort of trying to remember any further expenses may comfortably come to an end. However Jung reports that, despite efforts, John’s expenses could not be stretched enough to reach the target number and a “careful calculation” gave 2387 francs, i.e. 90 francs short, “which could only arbitrarily be translated into 2477“.

The second attempt to explain 2477 is then left upon John. He suggests that it could be a telephone number. In a “Bouvard and Pécuchet” manner, Jung bluntly reports that “This conjecture proved incorrect“.

The third attempt is actually a plunge into “couch arithmetic” for which some extra attention and a lot of patience is required. John was born February 26 from which date one can make the number 262. Jane was born on August 28. John’s wife was born on March 1st, his mother on February 26, his two children on April 29 and on July 13. From these dates Jung similarly got the numbers 288, 13, 262, 294, 137. February 1875, the month and year of John’s birth, produces the number 275. For Jane August 1885 is the month and year of birth from which date Jung similarly produced the number 885. Then John’s age is 36 while Jane’s is 25. Adding up all these numbers together he got the much desired result 2477:

262+288+13+262+294+137+275+885+36+25=2477

It is interesting that though the birth date of John’s mother was included in the calculation the birth date of John’s father was comfortably excluded from this numerical hocus-pocus because he was “long dead” (or because he simply spoiled the total). According to Jung, this result “…led to a deeper layer of the dream’s meaning. The patient was greatly attached to his family but on the other hand very much in love with his mistress. This caused him severe conflicts.“

Sadly calculated

In the second example, John sees in another dream his own psychoanalyst: “The analyst asked the patient what he actually did when he was with his mistress. The patient said he gambled, and always on a very high number: 152. The analyst remarked ‘You are sadly cheated’.“

Again Jung makes a first brief remark about the possible (this time) monthly expenses of the affair, which was “close to 152 francs“. But then he moves towards a quite different interpretation based upon the fact that Jane, as Jung reports, claimed that she was deflowered by John. Yet John was convinced that there was at least one man in Jane’s life before him. The word “number” associates, according to Jung’s line of thinking, “size in gloves” or “caliber“. “From there” Jung remarks, “it was but a short step (sic) to the fact that he had noted at the first coitus a remarkable width of the opening instead of the expected resistance of the hymen.“

Then, following an even more extraordinary line of reasoning, Jung returns to the heavyweight machinery of “couch arithmetic”. The number 152 “proved refractory at first to further analysis” he reports. This in simple terms means that the “players” of this “number game” had a really hard time with adding, subtracting and multiplying various numbers, actually any numbers from John’s life, and get the target number 152. But then it was discovered that when John “first knew her the lady lived at 17 X street, then at 129 Y street, then at 48 Z street“. Unfortunately the sum of these numbers, which is 194, “had already gone far beyond 152“, so one of them must go. It then occurs that “for certain reasons” Jane had left 48 Z street at John’s instigation “so the total must be 194-48=146“, which is still not good. But Jane was now living at 6 A street. As we all know 146+6=152. Quod Erat Demonstrandum.

A calculus of pregnancies

John sees in another dream the bill he has to pay to the psychoanalyst: “He received a bill from the analyst charging him interest of 1 franc on a sum of 315 francs for delay in payment from the 3rd to the 29th September.” 

Maybe it would be reasonable to assume that there was a conflict inside John about the amount of money he was probably paying to his psychoanalyst for all this nonsense. Yet the explanation provided in the paper is quite different, involving again all the equipment of first grade arithmetic combined with pure crackpottery. The analysis is based upon the assumption that John felt “a strong unconscious envy” towards his analyst because “the analyst had lately had an addition to his family” while John’s perturbed relation with his wife “permitted no such expectation in his case“. Jung explains that it was some tendency of John to begin with weird additions, yet he himself goes along, seems excited by the extraordinary results and even makes his own contributions. The result is a delirium of nonsense:

• First the meaning of the digits of number 315 is explained. Digit 3 is the number of the analyst’s children (excluding the recent addition) . John has 2 children. Adding the 3 stillborn children we get 5. This is the number of the children John would have if all of them survived. This explains the digit 5. Then subtracting the number of the children that survived from the number of the stillborn children we get 3-1=2. This explains digit 1. “But these associations were far from exhausting the number symbolism of the dream“.
• The period from the 3rd to 26th September comprised 26 days. The sum of 26 days plus 1 franc plus 315 francs is the number 342 (adding days to francs does not seem to bother anyone at this point). The analyst had 3 children, now has 4 while John has only 2. This explains all three digits of 342 at once. “The patient, who had discovered this explanation for himself without my help, declared himself satisfied. His analyst, however, was not; to him it seemed that the above revelations did not exhaust the possibilities determining the unconscious products“.
• Of the 3 stillborn children, Jung continues, 1 was born in the 9th month and 2 in the 7th month. John’s wife had had in the past 2 miscarriages, 1 in the 5th week and 1 in the 7th week. Adding the number of weeks we get 5+7=12 weeks which is approximately 3 months. Adding to this number the months of the three stillborn children mentioned above we get 3+7+7+9=26. This is equal to the period for which John had to pay interest to his analyst in the dream. It is also equal to his wife’s lost periods of pregnancy. Moreover, during the time in which John knew his analyst, the analyst got ahead by 1 child and therefore 1 franc in the dream may mean 1 child. John’s wife had two successful pregnancies which gives 2 x 9=18 months. Now Jung adds 26 and 18 to get 44. Then he observes that the digits of both these numbers give a sum equal to 8 while the sums of the digits of both 315 and 342 give a sum equal to 9. As 9-8=1 Jung remarks that “it seems as if the thought of the difference of 1 were asserting itself.” Then he notes that 3 x 1 x 5 = 15 and 3 x 4 x 2 = 24. Subtracting these products he gets 24-15=9. And he concludes that “once more we come upon the significant figure 9, which fits very aptly into this calculus of pregnancies and births“.

A sea of uncertainties

After cracking the mysteries of John’s dreams, Jung proceeds in examining the dreams of his wife, as “It is particularly interesting to see how the problems of the patient were mirrored in the unconscious of his wife.” A small passage, indicative of the line of thinking, is the following:

“… she dreamed – and this is the whole dream – Luke 137. Analysis of this number showed that she associated as follows: the analyst has got 1 more child. He had 3. If all her children (counting the miscarriages) were living, she would have 7; now she has only 3-1=2. But she wants 1+3+7=11 (a twin number, 1 and 1), which expresses her wish that her two children had been pairs of twins, for then she would have had the same number of children as the analyst.“

Repeatedly in the paper Jung mentions that he is aware of the fact that this kind of analysis may not be considered by others as valid or scientific but rather seem to be “floating in a sea of uncertainties” instead. Yet he claims that this  by no means obliges us to pass over in silence what has happened and been observed, simply from fear of being execrated as unscientific. There must be no parleying with the superstition-phobia of the modern mind, for this is one of the means by which the secrets of the unconscious are kept veiled.” Taking this thought even further, he even declares that passing on this “couch arithmetic” to future investigators is actually a scientific duty, as they may “be able to put them in the right perspective, as we cannot do for lack of adequate knowledge.“