Carl Jung on the Unconscious and Properties of Whole Numbers
To Fritz Lerch
Dear Herr Lerch, 10 September 1956
Your question, concerns one of those problems that have intrigued me for years: the connection of the psychology of the unconscious with the properties of whole numbers on the one hand and the properties of matter on the other.
I first approached this knotty problem from the purely epistemological angle.
Here I must anticipate by saying that the term “epistemological” has a Psychological flavour because I am obliged by my discipline to answer, or at least bear in mind, the question: What is happening psychologically if I either stop short at the epistemological barrier, or pronounce a transcendental judgment?
Here psychological reactions take place which the epistemologist has hardly considered until now, if at all.
The reason for this is that he does not know of the existence of an unconscious psyche.
If, therefore, my cognitive process comes to a stop at one point or another, this does not mean that the underlying psychological process has also stopped.
Experience shows that it continues regardless.
When the physicist, for instance, can form no picture of the structure of the atom from the data at hand, something suddenly flashes into his mind-a model, perhaps the planetary model-as a product of unconscious associative activity.
This flash or “hunch” must be considered a psychic statement, which is ordinarily called intuition and is a common product of the external data and psychological apperception.
Wherever the inquiring mind comes up against a darkness in which objects are only dimly discernible, it fills the gap with previous experiences or, if these are lacking, with imaginative, that is with archetypal or mythic, material.
In the construction of physical theories you will therefore find the closest analogies with the psychology of the unconscious, since this too is up against the same difficulties.
Our psychic foundations are shrouded in such great and inchoate darkness that, as soon as you peer into it, it is instantly compensated by mythic forms.
When these compensations become too obvious, we naturally try to obviate them and replace them by “logical” concepts.
But this is justified only when these concepts really do give adequate expression to what we have dimly discerned.
Generally they don’t.
Hence the borderline concepts in both sciences are partly mythological.
This would be a good reason for an epistemological-cum-psychological examination of their fundamental concepts.
Unfortunately I am not in a position to demonstrate, from the physical side, facts which have clearly discernible connections or analogies with the facts of psychology.
I can do this only from the psychological side.
Broadly speaking, atoms can be described as the elementary building blocks of physical nature.
Here we have a still very problematical analogy in the psychology of the unconscious, namely in mandala symbolism, expressed in medieval terms as the quadratura circuli.
The model for such configurations is based on the spontaneous self-representation of this archetype in pictorial form.
It is a mathematical structure, which first made me hit on the idea that the unconscious somehow avails itself of the properties of whole numbers.
In order to see my way more clearly, I tried to compile a list of the properties of whole numbers, beginning with the known, unquestionable mathematical properties.
From this it appears that whole numbers are individuals, and that they Possess properties which cannot be explained on the assumption that they are multiple units.
The idea that numbers were invented for counting is obviously untenable, since they are not only pre-existent to judgment but possess properties which were discovered only in the course of the centuries, and presumably possess a number of others which will be brought to light only by the future development of mathematics.
Like all the inner foundations of judgment, numbers are archetypal by nature and consequently partake of the psychic qualities of the archetype.
This, as we know, possesses a certain degree of autonomy which enables it to influence consciousness spontaneously.
The same must be said of numbers, which brings us back to Pythagoras.
When we are confronted with this dark aspect of numbers, the unconscious gives an answer, that is, it compensates their darkness by statements which I call “indispensable” or “inescapable.”
The number 1 says that it is one among many.
At the same time it says that it is “the One.”
Hence it is the smallest and the greatest, the part and the whole.
I am only hinting at these statements; if you think through the first five numbers in this way you will come to the remarkable conclusion that we have here a sort of creation myth which is an integral part of the inalienable properties of whole numbers.
In this respect Number proves to be a fundamental element not only of physics but also of the objective psyche.
It would be a worthy task for a mathematician to collect all the known properties of numbers and also all their “inescapable” statements- which should be quite possible up to 10-and in this way project a biological picture of whole numbers.
For the psychologist it is not so simple.
Apart from the above-mentioned question of epistemology, the possibilities open to him are still on the level of elementary experiences.
They can be formulated as follows: What are the psychic compensations when a task confronts us with darkness?
Here the necessary material on intuitions, visions, and dreams would first have to be collected.
I do not doubt that quite fundamental connections exist between physics and psychology, and that the objective psyche contains images that would elucidate the secret of matter.
These connections are discernible in synchronistic phenomena and their acausality.
Today these things are only pale phantoms and it remains for the future to collect, with much painstaking work, the experiences which could shed light on this darkness.
Yours sincerely,
C.G. Jung
P.S. I have just seen that Rob Oppenheimer has published an article in The American Psychologist (Vol. XI, 3, 1956) on the conceptual data in physics. ~Carl Jung, Letters Vol. II, Pages 327-329.