Modern examples of background physics

Unpublished Essay by Pauli

June 1948 [Typewritten carbon copy]

MODERN EXAMPLES OF "BACKGROUND PHYSICS"

1. PHYSICAL TERMS AS ARCHETYPAL SYMBOLS

What I understand by "background physics" is the appearance of quantitative terms and concepts from physics in spontaneous fantasies in a qualitative and figurative- i.e., symbolic- sense. I have been familiar with the existence of this phenomenon for about 12 to 13 years from my own personal dreams, which are totally uninfluenced by other people. As examples of physical terms that can appear as symbols, I should like to list the following, without any claim to completeness:

Wave, electrical dipole, thermoelectricity, magnetism, atom, electron shells, atomic nucleus, radioactivity.

As befits my rational, scientific approach, these dreams seemed to me initially offensive- in fact, an abuse of scientific terminology. What is more, I regarded the appearance of this symbolism in my dreams as a personal idiosyncrasy, typical of a physicist, and never even remotely hoped that I would be able to communicate the special experience that manifests itself in dreams of this nature to any psychologists of my acquaintance, for they are certainly not physicists.

Later, however, I came to recognize the objective nature of these dreams or fantasies- i.e., the fact that they are largely independent of the actual person. What first struck me was the similarity of the mood that obtains both in my dreams and in the physical treatises of the 17th century, especially in Kepler, where scientific terms and concepts were still relatively undeveloped and physical considerations and ideas were interspersed with symbolic concepts. Second, I could see certain correspondences between the contents of my dreams and the graphic concepts of scientific laymen, especially those with a poor education and weak critical faculties, who are not hampered by inhibitions οn the part of consciousness that might otherwise affect the naïveté of the fantasies. Thus it was that l gradually came to acknowledge that such fantasies or dreams are neither meaningless nor purely arbitrary but rather convey a sort of "second meaning" of the terms applied. This seems to me today ample proof of the fact that the kind of imagination l call "background physics" is of an archetypal nature. But any attempt to open it up to a psychological interpretation, based οn the idea of the collective unconscious, must not fall into the trap of assuming that the products of background physics are directly comparable with a well formulated doctrine of scientific truths. From the point of view of contemporary science, the form of imagination under discussion is definitely to be seen as a relapse into an archaic stage. Furthermore, my feeling is that the purely psychological interpretation only apprehends half of the matter. The other half is the revealing of the archetypal basis of the terms actually applied in modern physics. What the final method of observation must see in the production of "background physics" through the unconscious of modern man is a directing of objective toward a future description of nature that uniformly comprises physis and psyche, a form of description that at the moment we are experiencing only in a pre-scientific phase. Το achieve such a uniform description of nature, it appears to be essential to have recourse to the archetypal background of the scientific terms and concepts.

In the following outline, l shall attempt to explain how a physicist, as a consequence of this approach, inevitably shifts from this background into the field of psychology. As l regard physics and psychology as complementary types of examination, I am certain that there is an equally valid way that must lead the psychologist "from behind" (namely, through investigating the archetypes) into the world of physics.

2. ΤHΕ SPLITTING OF A SPECTRAL LINE IΝΤΟ TWO COMPONENTS AND ΤHΕ SEPARATION OF A CHEMICAL ELEMENT IΝΤΟ TWO ISOTOPES AS DREAM MOTIFS.

As an example of background physics, l shall discuss a motif that occurs regularly in my dreams- namely, fine structure, in particular doublet structure of spectral lines and the separation of a chemical element into two isotopes.

Let me begin with some explanations for non physicists of the terms used here. The frequencies of spectral lines are characteristic of and specific to the various chemical elements, which can thus be identified by the spectral lines emitted by them- i.e., by the precise values of the frequencies of the light emitted by the atoms of the relevant element. What also happens in spectroscopy is that under coarse observation- i.e., with poor resolution- a spectral line appears singly, whereas in apparatuses with greater powers of resolution it appears as separated, i.e., resolved into two or more components with only slight variation in the number of oscillations. In the last century, spectroscopy introduced the term "fine structure," naming the separated structures "doublet," "triplet," etc., according to the number of components. A well-known example of such a doublet is the yellow "D-line" of the sodium atom, which always appears in the rock-salt flame.

According to modern ideas (which are crucial to what now follows), the emission of spectral lines comes about in the transition of the atom from one state to another. Each of these states is also an energy level, and it is a universal law of nature that the frequency of the light emitted is always exactly proportional to the difference of the energy values of the initial and final states of the atom- a fact that cannot be explained in the framework of the older, classical physics. The energy levels are the characteristic states of the atom, and every spectral frequency is assigned both to the energy of a light corpuscle or photon and to the corresponding difference in energy values of a pair of energy levels. The doublets of the spectral lines correspond to the case where one of the two levels assigned to is single and the other one is double (see figure below). The doublet fine structure of a spectral line thus also makes visible the splitting of an energetically defined state into two neighboring states.

In an interesting connection to the universal quantitative assignment of light frequencies to energy levels and their differences, there now exists the situation that in addition to the doublet structure of the spectral lines, isotope separation also appears as a related dream motif. The word "isotope" derives from the two Greek words ίσος = same, and τόπος = place, and it denotes elements that occupy the "same place" in the periodic system of the elements and thus share the same chemical properties. According to the modern concepts of atomic structure, isotopes have the same electric charge of the atomic nucleus and thus have the same distribution of external electrons. Generally they differ physically through their mass (here I can leave aside the possibility of differentiating by means of radioactive properties such as lifetime, since the differentiation through the masses of the atomic nuclei- i.e., the atomic weights, is the usual procedure). This limits their separability to finer physical means, of which the varying detection of electrically charged atoms by external electrical or magnetic fields is the simplest and by far the most well known. The separation of isotopes by this method is brought about by an apparatus known as the mass spectrograph, because the atoms are photographed as lines that look like spectral lines, although of course they have nothing to do with light emission. Isotope separation corresponds here -also externally- to the resolving of a line into two or more neighboring components that correspond to the various values of the mass of the atoms. As mass energy are equivalent, instead of various atomic weights, one can speak of various energy levels of nuclear matter (the structure of which I need not go into at this point). Isotope separation is a relatively difficult procedure (known only since about 1920), and the resolution of the spectral doublets calls for a relatively advanced development of experimental technique.

Now that the way has been prepared with regard to the physical aspects, let me turn to the typical features of the group of dreams to be discussed. In my dreams there usually appears some figure of authority (also regarded subjectively as such by me) or the relevant special field of physics to explain to me that the dispersion of a spectral line into a doublet or-in other cases- the dispersion οf a chemical element into two isotopes, is of fundamental importance. Sometimes the authority goes οn to say that I should proceed with this dispersion or else that I have just completed it; sometimes in the dream I can see clearly before me the spectral line and its dispersion, as i.e. through a spectroscope. Occasionally, the authority also gives the name of the element that emits the spectral line or is to be dispersed into isotopes; but the chemical nature of this element was always changing, and I never found that it had any particular importance. In a much later stage of these dreams, the chemical elements sometimes had fantasy names (based on countries or cities, sometimes numbers). What seems to me important is that generally the two dispersed components are of roughly equal strength; in special cases, one is twice as intense as the other, but it never happens that one dominates and the other is a mere remnant.

Το find the "second meaning" of this group of dreams, what they have to say- their statement- must first be translated into a neutral language, in view of the distinction between the physical and the psychological. A translation of this nature always contains hypothetical elements, and the physical statements should not be regarded as all that important. We shall see how it works with the following "lexicon."

"Frequency" defines a specific energy state on the one hand, and on the other hand-viewed in time- It is a regular repetition.

A "chemical element" is an object that is also recognizable by its specific reactions but also has the aspect of mass, which makes possible a further separation. Thus, the statement of the dream could be understood as follows: "Of fundamental importance is the separation of a specific energy state or an object with specific reactions into two states or two objects with similar but different reactions. This separation comes about not just by watching ('with the naked eye') but through a more delicate form of observation conducted with the aid of a deliberately conscious method." So is the "state" a physical state, the building block of matter, or is it a psychic state, and is the object that is recognized by the specific reactions a material object or is it something psychic- what the psychologists call "contents"?

Does the systematic accomplishment of observation come about through technical construction of apparatuses or by means of a methodically guided imagination (imaginatio vera non phantastica)? It seems to be a characteristic of these manifestations of the unconscious that it leaves open the answers to these questions. For the "standpoint of the unconscious," both are one and the same.

A certain point of reference can be taken from the fact that the dreams select first one and then the other chemical element. Whereas an atom of a specific type- e.g., a hydrogen atom- is a representative of a species of exactly identical objects, this exact likeness does not seem to be present with the psychic objects (contents) alluded to; it is much rather the case that the latter can be regarded as unique.

In the translation of the dreams' statements into a neutral language, the energetic aspect of the frequency concept, which has come to the fore through the new quantum physics, is used more than its original aspect of a regular temporal repetition. As mentioned earlier, the linking of the two concepts is most unexpected- nay, even irrational- from the standpoint of classical physics. (I still vividly recall the tremendous shock I received as a student because of these facts and their implications. Most of the physicists of my generation and the previous one reacted in the same way.) It took science no less than 27 years to set up a system of concepts appropriate to these paradoxical facts and yet logically free of contradiction. It has emerged that the source of the contradictions arising from the linking of energy and frequency with unlimited application of the illustrative images lies in the premise that the energy at any definite moment in time has a quite specific value. It seems pointless to talk about the value of a temporal period in relation to a length of time that is shorter than the period itself. The greater the length of time available to define a period, the sharper is its value defined. A perfectly sharply defined period corresponds to the limiting case of observation during an infinitely long time. The new thing that modern quantum physics has taught us is that something exactly analogous applies to energy. Energy can be measured all the more precisely, the longer the duration of time that is available for that measurement; a perfectly sharp definition of energy would actually, as a limiting case, require an infinitely long duration of measurement. It is pointless to talk about an energy value at a specific point in time. How is that compatible with the conservation, i.e. the indestructibility of energy?

Now physical energy is, without exception, indestructible; it does not change into hidden, nonphysical forms of energy (such as "psychic energy," for example). However, in physics we never deal with the universe as a whole but rather with subsystems that are observed from outside. When these systems are inspected by observation, then they are subjected to the action of the observer or the means of observation itself. What this means is: The more precisely the observation method allows inspection of the temporal processes in the system, the more difficult it will be to detect and determine the exchange of energy between the observer and the system being observed. The laws of nature themselves make it impossible to get away from what the physicists call the complementarity of energy and time. It is true that the energy remains indestructible, but with a measuring setup that makes it possible to determine the temporal progress of a process, one does not know how much of it has entered the observed system from outside or has left the system. The law of conservation of energy applies to closed systems, whereas systems with a definite temporal evolution are never "closed." The two limiting cases of a precisely known energy value with completely unknown time evolution on the one hand and a precisely known time evolution on the other are in practice never wholly realized, but rather we are always dealing with inexact energy values and with imprecisely known temporal processes. Depending on the choice of experiment, one can find oneself closer to one or the other of the above- mentioned limiting cases.

The findings of new physics have accordingly led to a fundamental change in the attitude of modern man toward the archetypal ideas that are at the basis of matter and energy. Since time immemorial, the idea of matter had been closely linked with the Mother archetype. In alchemy, there was an elevating of the status of this idea in that the prima materia was actually assigned the attribute of the Increatum, which orthodox Christianity had assigned exclusively to God, as the masculine spiritual principle. It was C. G. Jung who drew attention tο this, and interestingly enough, he saw in this the psychological basis for the materialism of modern time. When new physics, with its radiation and pair production processes, demonstrated that what had earlier been known as "material substance" was in fact ephemeral, this materialism was deprived of its very foundation. This "substance" has been replaced by the law of conservation of energy by means of which mass and energy are recognized as proportional and hence equivalent (inertia of energy).

Corresponding to the transition from static to dynamic laws of nature, the attribute of indestructibility (Increatum) was now linked with a concept that had come originally from the archaic view of "mana," which was totally different from the idea of matter.

In this connection, it seems significant that according to quantum physics the indestructibility of energy on the one hand- which expresses its timeless existence- and the appearance of energy in space and time on the other hand correspond to two contradictory (complementary) aspects of reality. In fact, both are always present, but in individual cases the one or the other can be more pronounced. The "non illustrative" mathematical functions used by modern physics take on the role of symbols that unite opposites. (Such symbols are always of an abstract nature in psychology, too, whereas "illustrative" in old physics would be analogous to "concretistic" in psychology. Incidentally, for me the term "illustrative" is largely a relative one and is simply a question of habit.) The opposition that emerges here is nο longer that between matter ('mater') and dynamics ('mana'), but rather that between indestructibility (energy) and time. The former seems to belong to a timeless form of existence that is contrasted with time as a feminine principle, similar to the way in which, at an archaic level, material substance and the physis stand in contrast to the spirit and the psyche. The ancient idea of polar opposites, such as the Chinese Yang and Υin, is thus replaced in modern thinking by the idea of the complementary (mutually exclusive) aspects of phenomena. Because of the analogy of microphysics, I feel that one of the most important tasks for the Western mind is to translate the ancient idea into the new form in psychology as well. We shall return frequently to this viewpoint.

Complementarity in physics, as I have indicated elsewhere, has a very close analogy with the terms "conscious" and "unconscious" in psychology, in that any "observation" of unconscious contents entails fundamentally indefinable repercussions of the conscious on these very contents. An "ego with total consciousness" (claimed by Eastern philosophy- and probably with justification- to be possible only in death) or, on the other hand, an objective psychic one, not observed by any subjective consciousness (and hence influenced), corresponds to two limiting cases that in reality can never be achieved. The universality of the objective- psychic and the uniqueness of contemporary consciousness are both ever present. The symbolic images uniting this opposition are known to manifest themselves in myths. With this pair of opposites, the "objective- psychic" (known in Eastern philosophy as "consciousness" but in Western psychology as "the collective unconscious") acquires- as a result of being so widespread- a sort of timeless reality, whereas the "individual ego" ("consciousness" in our Western terms) and the usual way of looking at time are essentially linked together.

Βy bringing in this general analogy of the epistemological situation in physics and in psychology, an attempt will be made to acquire further reference points for the (hitherto somewhat vague and ill-defined) "second sense" in the group of dreams discussed. Note should be taken of my immediate associations with the dreams (context), as well as material from other sources as a basis of comparison.

3. FREQUENCY SYMBOLISM AND LEVEL OF CONSCIOUSNESS

Even with the very first dreams, the ones dealing with a separation into two components (be they spectral lines or chemical elements), the following type of idea immediately and ingenuously occurred to me. A birth is a division of a body into two parts; as it is a form of separation that can only be perceived by subtle methods, it could mean a "psychic birth." The child or embryo plays an important role in yogin meditation; when the "child" rises above the head of the yogin in a later stage of meditation, this "detachment from the spirit body into an independent existence" could justifiably be described as a "doublet splitting" of the psyche of the yogin meditation as a conscious activity would be analogous to the manufacture and application of the spectrograph in physics. In this case, the "child" is a graphic representation of the previously mentioned "spirit body" or "adamantine body" or the "corpus subtile"-a concept that has been very familiar in the West since late antiquity (especially to the Gnostics). This is linked to the idea of a "superior personality part'', which is more constant than the ego, can outlive it, and is said to express itself by appearing as a specter or ghost. In accordance with the Gnostic idea of the light sphere (pleroma), in which the psyche- before and after birth- has an existence free of the dark physis, this corpus subtile would be closer to the light sphere than the ordinary ego trapped in the body. But this corpus subtile, as its name suggests, would have not only a psychic existence assigned to it but also a physical one (the latter, it seems to me, in a way that would be very unclear to us).

What also occurred to me in this division into two was the neutralizing of an unconscious identity of two people who are connected emotionally. All these associations to my dreams were related to a raising or multiplying of consciousness.

Now the doubling of a psychic content as it develops consciousness is a motif that is well-known in psychology. It can be explained by the fact that the new consciousness content indicates a different mirror image in the unconscious. This motif is equally common in mythology as the saga of two brothers, one of whom is immortal (spiritual), while the other is mortal (material) and bound to life on earth.

In connection with this, I also recalled the existing symbol consisting of alternating light and dark stripes, which was very familiar to me at the time, a symbol that arises from the image of the "doubled content" by means of multiplicatio. This symbol often appears linked to what is known in psychology as "anima"and is also found in Indian temples. It seems to represent a series of complementary-opposite situations, one of which is presented as spiritual-timeless (aion), the other as material-temporal (chronos). The question remains open as to whether the "series" is thought of in temporal terms or as a simultaneous juxtaposition.

In the former case, it seemed to me to express that archetypal concept which is at the base of the doctrine of the transmigration of souls; according to this doctrine, the timeless reality of the life of the psyche is repeatedly being interrupted by a temporal sequence of material earth lives.

In the second version of the simultaneous juxtaposition of the "series," the stripes could also be related to the "multiple luminosity" of the unconscious psyche, a luminosity represented by separate sparks of light.

The ideas that struck me with regard to the group of dreams under discussion were both immediate and vivid, but at first my dreams were not in any way influenced by them, and they carried on producing their spectral doublets and isotope separations. Today I understand why. At the time, I was firmly of the opinion that the dreams were a "misuse" of physical concepts; for that reason, I searched frantically for purely psychological interpretations and explanations just so that I could get the physics out of the way; I did my utmost to cling to my conviction that this was all "just" psychology. But as dreams are compensatory to the conscious attitude, they insisted that the physical terminology should be taken for what it was. This forced me to accept it as an essential part of what was being represented.

I could not draw any further conclusions from this alone, but later I had the opportunity to establish further proof of the "frequency- degree of consciousness" connection. First, I came across the book by C. N. Hsieh "Quantum Physics and I Ching" (Shanghai, l937). The author is Chinese, a private scholar with a somewhat inadequate background in mathematics and physics. (There is nο translation of this book from the Chinese; it was Chinese colleagues in the U.S.A. who made it accessible to me.) What is of interest to us is that the author makes a direct link between the physical emission of light and the previously mentioned psychological phenomenon of the multiplicatio, with the physical concept of the light wave being derived from the Taoist symbol of the Tsi-Gi. Once again I was struck by the similarity between the tone and mood of this book and that of my "physical dreams," as well as that of the writings of Kepler. This was the first time that it had occurred to me that this might be an archetypal background for the physical concepts.

Moreover, in the essay of Jung's quoted earlier, "Der Geist der Psychologie" [The Spirit of Psychology], there is a parallel between spectral frequency and degree of spiritualization, in that the "psychic" drive processes are compared with the ultra red part of the spectrum, and the archetypal images of the drive consciousness, which belong to the spiritual sphere, are compared with the ultraviolet part. At first one might think that this is a rationally constructed analogy, but I feel that Jung's specific arguments about the colors red, blue, and violet indicate an already existing symbolism. It is probably not possible to deduce anything more definite from the actual text of the essay.

Μy knowledge of "background physics" in general and "frequency symbolism" in particular was, however, developed in a quite unexpected and fundamental way by S. Ε. White's unusual book, "The Unobstructed Universe". The author seems to have only a superficial knowledge of physics, has nο great critical faculties, nor is he particularly well educated; his mentality is very much that of an engineer, clinging to practical matters and not given to the formulation of general concepts. Compensating for this conscious attitude is his "anima," which has the utmost difficulty in getting him to think in abstract terms. The spiritualistic side of the book is of no interest to us and for our purposes can be regarded as an engineer's dream. The "anima" dictates to the author ideas that purport to be those of natural philosophy, and characteristically the anima is accepted by the author as an authority in this field, with its ideas being viewed as scientific truths.

What it is in actual fact is a spontaneous manifestation of the archetypal background of physical concepts, whose objective tendencies- especially that of aiming for a uniform description of nature- emerge very clearly. The conditions for the materialization of what I call "background physics" were in this case absolutely ideal.

Particularly relevant for our purposes is the chapter on "frequency" (pp. 44-46). Here the author says that frequency measures the "degree of consciousness," the "potentiality of life or evolution," hinting at a continual progression; he goes on to say that this is also what produces this life and that the "quality of what is produced is contained therein"; frequency is "the unity of consciousness in motion," and every consciousness finds itself in motion. What seems to me important here is the author's remark that in English the adjective "frequent" (in contrast to the noun "frequency") also has the meaning of "habitual" and "persistent." For him, he says, frequency has the naive- illustrative meaning of a series of "go-stop" actions. On the other hand, "constancy" for him does not have the meaning of unchangeability but is rather a continuous- i.e., uninterrupted- extension; in other words, "constant" means an unending continuum as a whole. For this author, too, the image of "frequency" does not psychologically presuppose the concept of time. Ordinary physical time is much rather just a representation of real (orthic) time in the higher level of "consciousness" and, just like space and motion, establishes the connection between real ("orthic") time and what he calls the "obstructed" aspect of "consciousness." But there is just one single universe, and it has these two aspects: the obstructed and the unobstructed.

What can be clearly recognized here is an analogy between these ideas and the associations that occurred to me in connection with the dreams about doublet splitting and with the archetypal periodic symbol consisting of alternating light and dark stripes. Here, too, frequency is a characteristic of a stable state and its "degree of consciousness"; and here, too, a distinction is made between two aspects of the one universe, an unobstructed "higher," spiritual, timeless one and an obstructed one, rooted in the physical world and ordinary time.

Obviously, there is a lot of criticism that can be leveled at the way in which S. Ε. White uses these concepts. The term "consciousness" in particular is used in a way that is hardly acceptable to the Western scientific mind. An essential part of the definition of this concept for us is that a perceiving subject is confronted with an object that is different from him and is that which is perceived. That is why it strikes us as pointless to apply the term "consciousness" to the whole cosmos. And that is also why the term "degree of consciousness" is rather unclear; I would prefer to replace it with "degree of spiritualization or desubstantialization." Subjective ego consciousness, by way of contrast, seems to me to be standing on the side of matter and ordinary time, with the timeless, objective psyche standing οn the other (complementary) side.

Furthermore, although I have no objection to accepting the existence of relatively constant psychic contents that survive the personal ego, it must always be borne in mind that we have no way of knowing what these contents are actually like "as such." AII we can observe is their effect on other living people, whose spiritual level and whose personal unconscious crucially influence the way these contents actually manifest themselves. The author's critical admiration for the manifestation and the utterances of his "anima" may well be the reason why he gets bogged down with the triads and never makes it as far as the quaternity.

Regardless of any justified criticism, however, we can once again ascertain from the spontaneous manifestation of this author's unconscious that the concept of "frequency" can be psychologically brought into association with the pair of opposites conscious- unconscious, although the ordinary concept of time will not automatically be taken for granted. Of course, rationally it is difficult to understand why frequencies or masses should have any connection with level of consciousness. And there is certainly no direct connection between the physical data of frequency or mass and consciousness: A rapid physical process runs without consciousness just as a slow one does, and a heavy atom has just as little consciousness as a light one. But these associations of ideas between level of consciousness and frequency, between doublet splitting of spectral lines or isotope separation and doubling of a psychic content with developing consciousness, all appeared directly and spontaneously; this is similar to the way in which the connection between frequency and energy level in physics, which could not be understood rationally a priori, was simply found to be existing in nature.

It is difficult to form any further definitive conclusions from the material given. Yet everything seems to point to a deeper archetypal correspondence of the complementary pairs of opposites:

From the psychological point of view, physical laws seem to be a "projection" of archetypal associations of ideas, whereas seen from outside, even the microphysical occurrence could be interpreted as archetypal, albeit with its "reflection" in the psychic being a necessary condition for the possibility of perception.

In summary, we can interpret the material given as follows: The unconscious spontaneously executes a projection of the one complementary pair of opposites onto the other, with the energy level or the mass number on the one side symbolically corresponding to the level of consciousness on the other.

What is it that lies at the essence of the situation described by the term complementarity that makes one have to limit oneself to perceiving the compatibility of the two aspects of reality that initially seem contradictory, without any consideration of things or processes in space and time, which are objective- i.e., independent of the method in which they are observed? This is possible only through unifying symbols, the role of which in physics is played by abstract mathematical functions.

4. ΤHΕ ACTIVE CONTRIBUTION OF CONSCIOUSNESS AND ΤHΕ APPEARANCE OF QUATERNITY SYMBOLISM.

According to the point of view presented here, the quaternity would not be effective in physics, but a quaternity would certainly be assigned to the wholeness made up of physics and psychology insofar as the complementary pair of opposites of physics reappears reflected in the psychic sphere. It would be conceivable, and in fact seems to me plausible, that there might be phenomena in which the whole quaternity plays a crucial role, and not just the physical and psychic pair of opposites. With such phenomena, it would not be possible to give a meaningful definition to conceptual distinctions such as that between "physical" and "psychic" (as is also the case with atomic phenomena, where the distinction between "physical" and "chemical" frequently loses its meaning).

I am not yet in a position to say anything that could be adequately substantiated, but nevertheless, both by way of summing up and looking ahead I would like to give two dreams that belong together, in which the quaternity features prominently. The dreams occurred within an interval of four days in the middle of March this year, when my work on Kepler had more or less come to an end. I shall now describe these dreams in detail:

Dream 1.

Μy first physics teacher appears and says: "The change in the splitting of the ground state of the H-atom is a fundamental one. Brass tones are engraved on a metal plate." Then I go to Gottingen.

Dream 2.

(Seven pictures in a row. Νo words are spoken until right at the end and I am the one speaking.)

Picture 1. A woman comes with a bird, which lays a large egg.

Picture 2. This egg divides itself into two:

Picture 3. I go closer and notice that l have in my hand another egg, with a blue shell.

Picture 4. I divide this last egg into two. Miraculously, they remain whole, and l now have two eggs with blue shells.

Picture 5. The four eggs change into the following mathematical expressions:

Picture 6. This gives the formula

Picture 7. I say, "The whole thing gives e^iδ, and that is the circle." The formula vanishes, and a circle appears.

[This is an example of the complex unit circle which is missing from the original text. Here, the letter δ is replaced by the letter t without any loss of generality.]

With regard to Dream 1, it evidently belongs to that group of dreams dealing with a splitting of a spectral line or an energy level into a doublet. But it has certain features that were not present in other dreams of this kind. First of all, there is a change in the splitting, which in physics is possible only by means of existing electromagnetic fields of force. What this corresponds to in the psychic sphere is an intervention of consciousness (which Dream 2 confirms). The H-atom is the simplest one of all, since the positively charged atomic nucleus is only encircled by one single negative electron. Thus it also represents the simplest "polar opposite." Moreover, the "proton," being the lightest atomic nucleus, is the building block for all other heavy nuclei. Hence "p," which of course means "the first," points cosmogonically to the beginning. Cosmogonical pictures are always connected with the process of developing consciousness. The metal plate is not in itself a symbol and represents the material physical world (physis) in a relatively stable form. It was originally assumed that there were 7 metals (as well as 7 planets); in Dream 2 there are 7 pictures. The tones, by way of contrast, serve very well as symbols; with their connection to music, they represent feeling- the very thing that physics cannot express. With their connection to the music of the spheres (I was very involved with Kepler at the time), they have a cosmic character. As an acoustic phenomenon, they also belong to physis, so they are a symbol uniting physis and psyche. Το me they appear to be exactly what is meant by "archetypes". If we interpret "brass" as aere perennius, i.e., indestructible- timeless, the dream is saying that the archetypes also imprint their stamp on matter, so that physis and psyche form an indivisible connection. But this seems to be a consequence of the change in the splitting of the ground state (initial state). An attempt will be made to assert the point of view that psychic contents, and hence archetypes, too, only alter because they are being observed, i.e., as the result of an intervention οn the part of human consciousness. In relation to the archetypes, this is the "secular displacement of the unconscious world picture, " which C. G. Jung has been referring to for a long time. (Cf. here what is said at the end of section 2 about the alteration of the concept of energy.) Το add to this a spontaneous alteration of the archetypes seems to me neither very satisfactory nor essential. The objective (independent of the personal) statement of Dream 1 seems to indicate, therefore, that the development of human consciousness, particularly through the convergence of microphysics towards other archetypal concepts, has led to a situation in which physis and psyche are indivisibly linked "archetypically." So I go to Gottingen, a place where not just physics but a lot of important work in mathematics is being done.

The close link between Dream 1 and Dream 2 is obvious, in that Picture 2, with the spontaneously produced two eggs can be interpreted as the "ground state" οf which a "fundamental" change is brought about through the intervention of the "ego" in Pictures 3 and 4- This change consists in the appearance of the quaternity, which comes about through the reflection of the duality. With this outcome, Dream 2 goes beyond Dream 1. In fact, Dream 2 corresponds fully to the ''Axiom of Maria Prophetissa": One becomes two, two becomes three, and out of the third comes the One as the fourth. The last mentioned typically comes about for me through mathematics. The formula

is mathematically correct, and in the representation of complex numbers through distances e^iδ is a number that always lies on the "unit circle" (the circle with the radius 1); if δ is taken as any size desired, e^iδ actually represents a circle.

The imaginary unit i = √-1 is a typical symbol since it is not contained under the ordinary numbers; the introduction of this symbol gives many mathematical theorems a simple and distinct form. In this dream it has the irrational function of uniting the pairs of opposites and thus producing wholeness.

Without going into mathematical detail, I should nevertheless like to stress here that I cannot acknowledge an antithesis between a mathematical and a symbolic description of nature, since for me the mathematical representation is a symbolic description par excellence.

Far be it from me to presume to be able to give an "interpretation" of the two dreams; in fact, I have the feeling that any such interpretation would call for further progress in all the sciences. The decisive role played by mathematical signs in the production of the ''One'' in Dream 2 also seems to suggest that the unifying power of mathematical symbolism is far from being exhausted; in fact, I would venture to say that it goes further than physics does in this respect.

According to its own definition, physics has to represent regularity in nature in conceptual terms and thus has to focus its attention on that which can be reproduced and quantitatively measured. As a consequence of this limitation that is at the very essence of physics, anything that is feeling- toned, judgmental, and emotional lies οn the opposite side-the psychological one- and what is more, from this root there springs the statistical nature of its statements, a nature which, especially with atomic processes, must basically dispense with any consideration of individual cases (apart from special ones). This is not a question of any shortcomings of the quantum theory within physics but a shortcoming of physics within life as a whole.

Mathematics, οn the other hand, has not only a quantitative side but also a qualitative one, which comes to the fore, for example, in the theory of numbers and in topology. Concepts created by mathematics, such as Riemann's surfaces, lend themselves very well to a symbolic representation of the relativization of the concept of time that is linked to the developing consciousness of the new focal point described as the "ego." It is, however, beyond the scope of this essay to delve into the problems involved in the symbolic union of the unique with the general.

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From the standpoint of the tendency to unify our world picture, it seems pleasing that connections are starting to be formed in a sphere that has already become so broad that it includes the Dioscuri myth οn the one hand and doublet splitting of spectral lines and isotope separations on the other.