137 - Arthur I. Miller [107]
From these archetypes—of oneness and of opposing pairs—Pythagoreans studied the divisions between even and odd numbers and geometrized certain combinations in the tetraktys, the mysterious equilateral triangle representing the equation 1 + 2 + 3 + 4 = 10.
From whole numbers “emerged such exact abstract concepts” as friendly numbers. In mathematical parlance, a pair of numbers is “friendly” if each of them is the sum of the other’s divisors. He told von Franz a story about “friendly numbers”: “Someone asked Pythagoras whether he had a friend. He replied I have two. He named the friendly numbers 284 and 220.” The numbers 284 and 220 are friendly because the numbers by which 220 can be divided to yield a whole number (1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110) add up to 284; and the divisors of 284 (1, 2, 4, 71 and 142) add up to 220. Friendly numbers may be just another fascinating piece of mathematics, or they may have some use. Presently no one knows.
“From a psychological point of view what does this ‘I have two’ mean to you?” asked Pauli. Plenty, he went on, answering his own rhetorical question, because it is “by no means an easy task to find every pair of ‘friendly numbers.’” (A few hundred friendly numbers were known in the 1950s; with the help of high-speed computers, twelve million have now been found.) Perhaps a clue is that “here is projected a psychological problem connected with numbers.” Pythagoras’s discovery of this pair was rather extraordinary. Apparently it was an inspired mental leap after a great deal of hard work.
The pair of friendly numbers 284 and 220 were well known. In the Middle Ages talismans inscribed with them were worn by a couple to advertise their love for each other. In Genesis Jacob gave 220 goats to Esau on the grounds that one-half of a friendly pair expressed Jacob’s love for Esau. Arab numerologists have written about the practice of carving 220 on one fruit and 284 on another, eating one and then offering the other to a lover as a sort of mathematical aphrodisiac.
Pauli applied this line of reasoning to the dreams about the “strangers,” the lecture, and the Chinese woman, which was still nagging at him: “From my earlier dreams it is to be expected that my unconscious soon will be activated, as soon as I am ‘cranked up’ by means of a suitable lecture.” Perhaps thinking about numbers would activate the proper archetypes in his unconscious which would, in turn, enable him to find all the friendly numbers.
The Piano Lesson
In October 1953 Pauli wrote an “Active Fantasy about the Unconscious,” which he entitled The Piano Lesson. He dedicated it to von Franz. It could be regarded as stream of consciousness, a sort of automatic writing.
He began poetically: “It was a foggy day and for a long time I had been seriously troubled.” In his daydream, Pauli is worried about how to bring together physics and psychology. He searches for a neutral language because both physicists and psychologists need to understand not only words, but their meanings. He visits the house of a friend—von Franz. As he enters, a voice shouts, “Time reversal.” Suddenly Pauli is back in his home in Vienna, in 1913. There is a piano there and a woman—whom he takes to be his anima—is about to give him a lesson. (The woman is actually his maternal grandmother, of whom Pauli had many fond memories.)
He plays the chord C-E-G and he and the woman discuss four variations of it—all on white keys, all on black keys, a combination of the two, or in a major key. When Pauli asks about the opposition of the white and black keys and the many combinations, the teacher replies, “One can play in minor on the white keys and in major on the blacks, it is only a question of knowing how to play.”
In the dream which Pauli had described to Jung, he had been about to give a lecture before an audience of strangers—his “unassimilated thoughts”—who wanted him to speak about psychology. In The Piano