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Psychological Perspectives
A Quarterly Journal of Jungian Thought
ISSN: 0033-2925 (Print) 1556-3030 (Online) Journal homepage: https://www.tandfonline.com/loi/upyp20
Note on Number
C. G. Jung
To cite this article: C. G. Jung (2018) Note on Number, Psychological Perspectives, 61:4,
431-439, DOI: 10.1080/00332925.2018.1536582
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Published online: 28 May 2019.
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Note on Number
C. G. Jung
This article presents a high-resolution copy of C. G. Jung’s Note on Number, tran-
scribed and translated into English, with some notes by Roy Freeman.
1. INTRODUCTION
Marie-Louise von Franz, in her Foreword to Number and Time (von Franz, 1974,p. ix), wrote about C. G. Jung’s Note on Number:
After C. G. Jung completed his article “Synchronicity: An Acausal Connecting
Principle” (Jung, 1969a par. 816ff), he hazarded the conjecture, already
briefly suggested in his paper, that it might be possible to take a further step
into the realization of the unity of psyche and matter through research into
the archetypes of the natural numbers. He even began to note down some of
the mathematical characteristics of the first five integers on a slip of paper.
But about two years before his death, he handed this slip over to me with the
words, “I began to study the individual properties of the whole numbers. I am
too old now to continue this work and therefore I give it over to you.”
In 1992, Marie-Louise von Franz turned the Note over to the History of Science
Collection at the library of the Swiss Federal Institute of Technology in Z€urich (ETHZ)
where it is presently included in the C. G. Jung Archive cataloged as “Hs prov von Franz.”
Shortly after the acquisition, the ETHZ library showcased some of the Jung
material in the archive, including the Note. Roy Freeman (RF), who at the time worked
at ETHZ, noticed this document in passing and recognized its importance. He took a
photograph of the Note to Marie-Louise von Franz and inquired about the significance
of the initial equation. Upon seeing a paper copy of the photograph of the note, she
immediately replied with a brilliant expos�e revealing the deep significance of the open-
ing equation. She encouraged further investigations and, with proper context, future
publication in an appropriate manner. RF is indebted to her unique spirit and personal
engagement in what then evolved into a series of informal interviews on a wide range of
subjects, including her reading of Jung’s Note on Number. Besides Marie-Louise von
Franz, present at most of these sessions were RF and his colleagues Nora Mindell and
David Eldred.
The Marie-Louise von Franz Institute for the Studies in Synchronicity published
the first English translation of Jung’s Note, included in Nora Mindell’s article “In Loving
Memory of Dr. Marie-Louise von Franz” (Kennedy-Xypolitas, 2006, pp. 393–404), which
Psychological Perspectives, 61: 431–439, 2018
Copyright # C. G. Jung Institute of Los Angeles
ISSN: 0033-2925 print / 1556-3030 online
DOI: 10.1080/00332925.2018.1536582
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432 PSYCHOLOGICAL PERSPECTIVES � VOLUME 61, ISSUE 4 / 2018
is reprinted here in the following article. The present translation is essentially identical
to this first version.
RF acknowledges the Foundation of the Works of C. G. Jung and the Paul & Peter
Fritz AG, Literary Agency, Zu€rich, for permission to publish the note here. He also
thanks the late Dr. Beat Glaus for an earlier photocopy of the note and Dr. Yvonne
Voegeli, both at ETH Library Archives, Z€urich, for providing the present high-resolution
digital copy (Figure 1).
2. PROLOGUE
Letter from C. G. Jung to Wolfgang Pauli, October 24, 1953, in Meier (2001),
p. 116:
About a year ago, I actually began examining the characteristics of the
cardinal numbers in various ways, but my work ground to a halt. (Is there
actually no systematic compilation of the mathematical properties of the
numbers 1–9?) The mythological formulations are interesting but
unfortunately call for a great deal of work in comparative-symbolism, and I
cannot afford to get involved in that.
Letter from C. G. Jung to Fritz Lerch, September 10, 1956, in Jung (1975),
pp. 328–329:
In order to see my way more clearly, I tried to compile a list of the properties
of the 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… . Like all the inner foundations of judgement, 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 the 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 unalienable properties of
whole numbers. In this respect, Number proves to be a fundamental element not only
of physics but also of the objective psyche.
Figure 2. Black and white enlargement of the top lines containing the equation. Jung used a particular way of
writing the sign for “one” here; see text for more details. Two letters from the next line below overprint the
final word bottom right, transcribed here as werden (be). Note and image # 2007 Foundation of the Works
of C.G. Jung.
C. G. JUNG � NOTE ON NUMBER 433
3. TRANSLATION OF C. G. JUNG’S NOTE ON NUMBER
Jung’s Equation
English Translation (Figure 2)
I ¼ 1N – ð1N – IÞ This formula is a petitio principii. I can only be
explained by means of itself.
Note by RF:
A petitio principii is a premise that is assumed to be proven, that is, implicitly
taken for granted.M.-L. von Franz clarified that 1N refers to the pleroma, the
plenitude that contains everything in potentia (see Nora Mindell’s article in this issue).
The pleroma figures in Jung’s Septem Sermones ad Mortuum (see Jung, 2009, p. 509,
footnote 58 in that reference for more amplification).
Jung intentionally used a special notation for “One” (here typed as I) to
emphasize that he is referring to the Unity, the absolute One, and not the counting unit
1 (that appears under “Properties 4” a few lines below). Jung writes:
One, as the first numeral, is unity. But it is also “the unity,” the One, All-One,
individuality and non-duality—not a numeral but a philosophical concept,
an archetype and attribute of God, the monad… . In other words, these
statements are not arbitrary. They are governed by the nature of oneness and
therefore are necessary statements. (Jung, 1968, p. 310)
In his article on the Trinity, Jung also writes:
Unity, the absolute One, cannot be numbered, it is indefinable and
unknowable; only when it appears as a unit, the number one, is it
knowable… [since] the “Other” which is required for this act of knowing is
lacking in the condition of the One. (Jung, 1969b, par. 180)
Properties of the First Five Natural Numbers
� One (Figure 3)
English Translation:
Properties [of the Number 1]
Figure 3. Black and white enlargement of the lines concerning properties (Eigenschaften) of the number
one. Note and image # 2007 Foundation of the Works of C.G. Jung.
434 PSYCHOLOGICAL PERSPECTIVES � VOLUME 61, ISSUE 4 / 2018
1. Cannot multiply itself with itself,
2. and can neither reduce itself by division, nor can it divide itself by any
other whole number.
3. The One in and of itself does not count. The number sequence begins first
with 2.
4. If 1 counts, it is the first uneven prime number.
5. ἕν sὸ πᾶν1N – ð1N – IÞ¼Kenosis
Note by RF:
The German word vermehren used in the first property is often used to mean
“increase through reproduction” as in “to generate,” here specifically meaning “to
generate through self-multiplication.” By “number sequence” in the third property,
Jung is referring to the sequence of natural numbers, that is, the integers without zero.
The Greek phrase, ἕν sὸ πᾶν (h�en t�o p~an), translates as “one is all” and refers to
the “All-One” (see Jung’s text above). Kenosis is a word used in Gnosticism and Early
Christianity meaning emptying or diminishing. In order to become something, the pleni-
tude (the pleroma) has to be diminished. In some Gnostic schools, Christ lived in the
plenitude of the father and was the plenitude of the father. He emptied himself (the
Greek word ek�en�osen is translated in Philippians 2:7 as “emptied”) in order to become
Jesus (in the material world). In other words, God was at first the potential cosmos
(1N, the pleroma) and then emptied himself (1N – I¼Christ) into all creation. In
this process of “diminishing” itself, the Unity remains, paradoxically, the Unity. This is
the statement expressed by the equation at the top of the note. (See Marie-Louise von
Franz’s commentary in Nora Mindell’s article in this issue.)
� Two (Figure 4)
English translation:
2. 1. Can multiply itself by itself, like all other numbers.
2. Can only be divided by itself. 2 � 2 ¼ I, in this respect it is an even
prime number, all other prime numbers [are] uneven.
3. The first number that counts.
4. The sum of IþI ¼ 2�½1N� ð1N�IÞ�¼1N�ð1N� 2Þ.
Note by RF:
In property 4, the square brackets [ ] around the expression1N – ð1N – IÞ are
added for mathematical clarity. Jung did not include them, but clearly intended that the
whole expression1N – ð1N – IÞ should be multiplied by two.
Figure 4. Black and white enlargement of the lines concerning properties of the number two. Note and image
# 2007 Foundation of the Works of C.G. Jung.
C. G. JUNG � NOTE ON NUMBER 435
� Three (Figure 5)
English translation:
3. 1.) Can only divide itself by itself like the 2.
2.) Is the first uneven prime number aside from the 1.
Prime numbers¼ aperiodic intervals in the number sequence.
3.) First prime number. Appears in the number row in aperiodic intervals
and discontinuously
3.) Sum of 2þ I¼ capable of increase, divisible only through itself,
¼ prime numberþ incapable of multiplication and
indivisible.
Note by RF:
Concerning property 2, Jung writes: “What exists in the pleroma as an eternal
process appears in time as an aperiodic sequence, that is to say, it is repeated many
times in an irregular pattern” (Jung, 1969b, par. 629).
� Four (Figure 6)
English translation:
4. 1. The first self-multiple, namely, 22.
[1.]. 4 points ¼ 3-sided pyramid. First body.
2. Equations of the 5th degree can no longer be solved 6¼ ½?� property of 4.
Figure 5. Black and white enlargement of the lines concerning properties of the number three. Note and
image # 2007 Foundation of the Works of C.G. Jung.
Figure 6. Black and white enlargement of the lines concerning properties of the number four. Note and image
# 2007 Foundation of the Works of C.G. Jung.
436 PSYCHOLOGICAL PERSPECTIVES � VOLUME 61, ISSUE 4 / 2018
3. Sum of the first two prime numbers Iþ 3, i.e. that which is not capable
of multiplication by itself and is indivisibleþ that which is capable of
multiplication and is divisible by itself.
[(dup]lication 2�þ 2�Þ¼ Axiom of Maria 3þ I o.[r?] 4 – I [?]
Note by RF:
Concerning property 2, Jung writes:
It is a property of the number four that equations of the fourth degree can be
solved, whereas equations of the fifth cannot. The necessary statement of
the number four, therefore, is that, among other things, it is an apex and
simultaneously, the end of a preceding ascent. (Jung 1963, p. 310).
Due to the note being slightly frayed at the very bottom, the transcription of the
last line concerning the number 4 is uncertain. On the left side, Jung may be referring to
the mathematical property that 2� 2¼ 4 and also that 2þ 2¼ 4; that is, multiplication of
2 by itself gives the same result (¼ 4) as the duplication of 2 (¼ 4). On the right side,
Jung refers to “the axiom of Maria,” about which he wrote in several places, for example:
Maria Prophetissa, also called Mary the Jewess, was probably an historical
alchemist of the Alexandrian period (4th cent. BC to 7th cent. AD). Her axiom,
one of the most influential in alchemy, runs: “One becomes two, two becomes
three, and out of the third comes the one as the fourth.” (Jung, 1975, p. 412,
footnote 4. See also Jung, 1968, par. 26, 209f.)
The theme of counting backwards (retrograde counting) to then go forward is
discussed in Number and Time (von Franz, 1974), for example, on page 65f.
� Five (Figure 7)
English translation:
5. 1.) Prime number.
2.) Whole number 4 þ I.
Sum of the divisibles 3 þ 2.
Note by RF:
Since the numbers 3 and 2 are prime numbers, Jung is probably referring to
the property that these numbers can only be divided by themselves (see properties of
2 and 3 above).
4. GERMAN TRANSCRIPTION
I ¼ 1N – ð1N – IÞ Diese Formel ist eine petitio principii. I Kann nur
durch sich selber erkl€art werden.
Eigenschaften:
1. Kann sich nicht durch sich selber vermehren.
Figure 7. Black and white enlargement of the lines at the top of the backside of the note concerning the
number five. Note and image # 2007 Foundation of the Works of C.G. Jung.
C. G. JUNG � NOTE ON NUMBER 437
2. " " " nicht " " " theilen auch nicht durch eine andere Zahl.
3. Das Eine zahlt an u. f€ur sich selber nicht. Die Zahlenreihe beginnt erst
mit 2.
4. Wenn 1 z€ahlt, ist es die erste ungerade Primzahl.
5. ἕν sὸ πᾶν: 1N – ð1N – IÞ ¼ Kenosis
2. 1. Kann sich durch sich selber vermehren wie alle anderen Zahlen.
2. Kann sich nur durch sich selber theilen 2� 2¼ I; ist also insofern eine
gerade Primzahl, alle €ubrigen Primzahlen ungerade.
3. Die erste Zahl, die z€ahlt.
4. Summe von Iþ I¼ 2�½1N�ð1N� IÞ� ¼ 1N�ð1N� 2Þ
3. 1.) Kann sich nur durch sich selber theilen wie die 2.
2.) Ist die erste ungerade Primzahl ausser der 1. Primzahlen¼ aperiod.
Intervalle in derZahlenreihe
3) Tritt in der Zahlenreihe in aperiodischen Intervallen auf und
discontinuirlich auf
3.) Summe von 2þ I¼Vermehrungsf€ahig, nur durch sich selber theilbar
¼Primzahlþ nicht vermehrungsf€ahig u. untheilbar.
4.) 1.) Der erste Selbstmultipel n€amlich 22.
[1.] 4 Punkte¼ 3 seitige Pyramide. Erster K€orper.
2.) Gleichungen 5ten Grades k€onnen nicht mehr aufgel€ost werden 6¼ ½?�
Eigenschaft der 4.
3. Summe der zwei ersten Primzahlen Iþ 3. D. h. der nicht durch
sich selbst Vermehrungsf€ahigen und der Untheilbarenþ der
Vermehrungsf€ahigen und durch sich Theilbaren.
[(dup]lication 2�þ 2�Þ¼Axiom der Maria 3þ I o.[der?] 4� I [?]
5. 1.) Primzahl.
2.) Ganzzahl 4þ I.
Summe der Theilbaren 3þ 2.
Roy Freeman has a diploma in physics and a PhD in geophysics from the Swiss
Federal Institute of Technology in Z€urich (ETHZ). He also studied at the C. G.
Jung Institute in Z€urich, where Dr. von Franz was his supervising analyst after
he passed the Propaedeuticum exams. Since 2008 he has been working on the
English translation of the first volume of von Franz's and von Beit's monumen-
tal work, Archetypal Symbols in Fairytales.
FURTHER READING
Jung, C. G. (1963). Memories, dreams, reflections. A. Jaff�e (Ed.), & R. C. Winston (Trans.).
New York, NY: Vintage Books.
Jung, C. G. The collected works of C. G. Jung. H. Read, M. Fordham, G. Adler, & W. McGuire (Eds).,
R. F. C. Hull (Trans.). Princeton, NJ: Princeton University Press. Vol. 8.
(1968). Psychology and alchemy. (2nd ed.).
(1969a). The structure and dynamics of the psyche (2nd ed.).
(1969b). Psychology and religion: West and East (Vol. 11, 2nd ed.).
Jung, C. G. (1975). Letters, Vol. 2: 1951–1961. G. Adler & A. Jaff�e (Eds)., R. F. C. Hull (Trans.).
Princeton, NJ: Princeton University Press.
438 PSYCHOLOGICAL PERSPECTIVES � VOLUME 61, ISSUE 4 / 2018
Jung, C. G. (2009). The red book, liber novus: A readers’ edition. S. Shamdasani (Ed.), M. Kyburz,
J. Peck, & S. Shamdasani (Trans.) New York, NY: Norton.
Kennedy-Xypolitas, E. (2006). The fountain of the love of wisdom: An homage to Marie-Louise
von Franz. Wilmette, IL: Chiron.
Meier, C. A. (2001). Atom and archetype: The Pauli/Jung letters 1932–1958. London & New York:
Routledge.
von Franz, M.-L. (1974). Number and time: Reflections leading toward a unification of psychology
and physics. London: Rider & Company.
C. G. JUNG � NOTE ON NUMBER 439
	mkchap1536582_artid
	Introduction
	Prologue
	Translation of C. G. Jungs Note on Number
	Jungs Equation
	Properties of the First Five Natural Numbers
	German Transcription
	Further reading