ÿþ<HTML> <HEAD> <META NAME="KEYWORDS" CONTENT= "Jungian analysis, Jungian analyst, Jungian psychology, Carl Jung, dynamic system, self-organization, stable attractor, archetype, psychoanalyst, New York City"> <META NAME="DESCRIPTION" CONTENT="The personality is a dynamic system. A dynamic system assembles itself to express a priori principles of organization (archetypes-as-such). Article is grounded with clinical examples. Clear and lively."> <TITLE> The three gorillas: an archetype orders a dynamic system. Maxson J. McDowell. </TITLE> <STYLE> P {text-indent:30pt; text-align:justify} P.intro {text-indent:0pt; text-align:justify} </STYLE> </HEAD> <BODY> <FONT Verdana> <TABLE ALIGN=center BORDER=0 WIDTH=500> <TR> <TD BORDER=0 WIDTH=500> <H1 ALIGN=center> The three gorillas: an archetype orders a dynamic system</H1> <br><br><br> <H3 ALIGN=center>Maxson J. McDowell</H3> <br><br> <table border=0 width=500> <tr> <td width="100%" valign="middle" align="middle"><SMALL> This article was originally published in<I>The Journal of Analytical Psychology,</I> Vol. 46, 4. October 2001. <br><br><br> Maxson McDowell PhD, CSW is a Jungian analyst in Greenwich Village, New York City. Formerly he was a molecular biologist at M.I.T. </SMALL> <BR><BR><BR> <A HREF="http://home.earthlink.net/~maxmcdowell/index.html">For more information about the author</A> </td> </tr> </table> <br><br><br><br> <H4>Abstract </H4> <P class=intro> The personality is a dynamic system. Like all other dynamic systems, it must be self-organized. In this paper I focus upon the archetype-as-such, that is, upon the essential core around which both an archetypal image and a complex are organized. I argue that an archetype-as-such is a pre-existing principle of organization. Within the personality that principle manifests itself as a psychological vortex (a complex) into which we are drawn. The vortex is impersonal. We mediate it through myths and rituals or through consciousness. In this paper I show that Jung s intuition about the archetype-as-such is supported by recent science. I evaluate other concepts of the archetype. My concept is different from that proposed recently by Saunders and Skar. My concept allows each archetype-as-such to be defined precisely in mathematical terms. It suggests a new interpretation of mythology. It also addresses our spiritual experience of an archetype. Because the archetypes-as-such are fundamental to the personality, the better we understand them the better we understand our patients. The paper is grounded with clinical examples. <BR><br>Key words: a priori, archetype, complexity, dynamic system, mathematical principle, self-organization, spirit.</p class=intro> <br><br> <H4>Introduction</H4> <p class=intro> Rachel s mother was envious and abusive. She criticized Rachel s appearance incessantly. Thus she looked at Rachel with  destructive eyes . Throughout her childhood Rachel had a recurring nightmare:</p class=intro> <blockquote> <p class=intro>My mother was a witch who flew over the neighbourhood, setting fire to the lawns.</p class=intro></blockquote> <p class=intro>There is a related image in Egyptian myth: The lion-goddess, Sakhmet, who breathed fire to incinerate her enemies was also the avenging Eye of Re, the sun god. In this form she flew over the desert and slaughtered the people, reducing them to a lake of blood which she meant to drink (Hart 1986, pp.187- 9). Thus the Eye that consumed with fire was also a mouth that drank blood. Indian myth has a similar image: Shiva burns up the world with his third eye and thus begins a new cycle of creation. When Rachel had her nightmares, however, she knew nothing of Sakhmet, Re, or Shiva. Thus her image, the envious witch/eye that overlooked new life (green lawn) and consumed it with fire, was <i> archetypal</i>. By this I mean that the idea which lies behind the image, the <i>archetype-as-such</i>, was not transmitted by culture but arose spontaneously within her, as it has in others throughout history. As is characteristic of an archetypal image, Rachel s image was highly charged. In a dream such an image may be strangely illuminated. As is also characteristic of an archetypal image, Rachel s witch represented an issue central to her own development: both as a child and as an adult Rachel was injured by envy.</p class=intro> <p> Jung (1936/1968, para. 90) derived his concept of the archetype empirically from observations like the above:</p> <blockquote><p class=intro> There exists a second psychic system of a collective, universal, and impersonal nature which is identical in all individuals ... It consists of pre-existent forms, the archetypes.</p class=intro> </blockquote> <p class=intro> By  pre-existent form Jung meant the archetype-as-such.</p class=intro> <p> Samuels (1985, p. 53) said he spoke for a  post-Jungian ... general move in analytical psychology when he suggested that an archetype-as-such was not an objective reality:</p> <blockquote><p class=intro> The archetypal may be said to be found in the eye of the beholder and not in that which he beholds ... The archetypal is a perspective ... with no pre-existing or prescribed focus ... [The focus] is elected by the individual.</blockquote> <p class=intro> This seems to be a radical departure. For Jung the point of an archetype-as-such was that it was objective: the archetypes constituted the objective psyche. Some of us still find that there is ample clinical evidence for the objective reality of an archetype-as-such. In taking this position I do not imply that an archetype is material or that it has spatial location or extension. I use  real in the sense that a principle is either real or not, true or untrue. To say that a principle is objectively real is not to reify it.</p class=intro> <BR><BR> <h4>What is an archetype-as-such?</h4> <P class=intro>The personality is at least an assembly of instinctual impulses, affects, feelings, sensory perceptions, images, thoughts, hopes and the like, together with the memories of all of these. These components are not simply jumbled together: they are organized into a dynamic system which functions adaptively. But from whence comes the organization? Jung s answer was that organization came from the archetypes. From clinical evidence we know something of what an archetype contributes: the mother archetype, for example, contributes containing which leads to security and trust, or devouring which leads to anxiety and mistrust. But what is an archetype-as-such and how does it organize the personality? <P> The field of cognitive neuroscience is new and rapidly growing. It integrates knowledge from dynamic systems theory, neuroscience, cognitive psychology and the clinical disciplines. I show in this paper how cognitive neuroscience may help us to understand the archetype-as-such. For an earlier discussion of archetypes and self-organization see McDowell (1999).</p> <BR><br> <H4>A simple orienting structure? </H4> <p class=intro>Object-relations theorists, for example Bion, Bowlby, Sutherland and Seinfeld (1996, pp. 4-5), have proposed that we inherit a <i>preconception</i> of a good object (mother) and of a bad object (predator). Knox (1999, p. 522) and others have suggested something similar, that we inherit a <i>simple orienting structure</i>, for example one which visually orients an infant towards its mother s face, and that this orienting structure represents an archetypal predisposition or expectation. Experiments by Johnson et al. (1991) suggested that an infant has an innate preference for gazing at a human face. Johnson argued that the corresponding  simple orienting structure is located in pre-cortical regions of the brain. Easterbrook et al. (1999) have obtained results which contradict Johnson s. Further experiments will be needed to clarify the issue. <p> Even if it were proven, however, that a pre-cortical structure helps to establish the initial relationship between mother and infant, such a structure would not account for the phenomenon of the archetype as Jung described it. Because a newborn s repertoire of behaviour is limited, a newborn could inherit only a few such orienting structures. Moreover, while the cortex is a massive system for storing images the pre-cortical system is not. For this reason too, inherited pre-cortical structures could provide for only a few orienting mechanisms. Thus an explanation of the archetype-as-such which rests on newborn behaviour and the anatomy of pre-cortical structures presupposes that there are only a few different archetypes. Yet some of us observe clinically that there are many archetypes. Can a simple orienting structure provide an archetype-as-such for each of the gods, for Inanna, Ereshkigal, Odin, Loki, Zeus, Poseidon, Hades, Ares, Hephaestus, Hermes, Apollo, Dionysus, Athena, Artemis, Demeter, and Persephone? Obviously not. <p> The simple-orienting-structure explanation also fails, I argue, because it operates at the wrong level. It reduces to material terms an issue of spirit, a principle of organization. A principle of organization might incarnate in the infant-mother pair if the mother s face were a  container for the newborn s vision. But that incarnation, if it did occur, would not be the principle.</p> <br><br> <h4>An inherited image in the cerebral cortex?</h4> <p class=intro> Is the archetype-as-such a pattern or generalized image which is hard-wired, not into pre-cortical structures but into the cortex? A hard-wired cortical image would be genetically inherited and hence would be shaped by the process of biological evolution. Within each individual it would be refined by sensory input. Stevens and Price (1996, pp. 9, 26-9) seemed to adopt this view when they cited evolutionary psychologists who described  genetically transmitted ... patterns of behaviour which, the evolutionary psychologists argued, evolved while humans lived as hunter-gatherers. <p> Pietikainen (1998a, p. 335) argued that there is no evidence for the genetic inheritance of archetypes. Pietikainen (1998b, p. 380) suggested instead that archetypes are  culturally determined symbolic forms , that is, that they are transmitted by learning. Hogenson (1998, pp. 367-8) disagreed with both Stevens and Pietikainen. He referred to recent work in cognitive science and suggested, as did Jung, that we inherit not a generalized image but the tendency or the potential to form the image.</p> <br><br> <h4>Genes and self-organization</h4> <p class=intro> Several lines of evidence from biology indicate that images are not inherited in the form of pre- determined connections between cortical neurons (Elman et al. 1998, pp. 25-6, 275-82). <p> One line of evidence concerns the machinery of inheritance. I have only about 32,000 different genes (Baltimore 20001) while a bacterium has 3 to 5,000. But my anatomy is astronomically more complex than that of a bacterium. It has been estimated that the human body contains about 5x1025 bits of information in the arrangement of its molecules while the human genome contains less than 109 bits of information (Calow 1976, pp. 101-3). Again the disparity is of astronomical proportions. These numbers prove that my genes must be used economically. They must code for<i> processes</i> which enable my structure to evolve, but they are too few to form a  blueprint , or image, of my final structure. My body s structure is <i> emergent</i>, that is, my body<i> self-organizes</i> with minimal guidance from the genes. <p> Self-organization is directed in part by the inherent properties of the component parts (what fits with what). It is also directed in part by information from the environment. Recent experiments on the cerebral cortex demonstrate the latter point. The cortex is highly plastic: individual neurons connect to each other not in predetermined patterns (as a theory of inherited images would suggest) but under the direction of sensory input. In new-born ferrets, for example, visual input was surgically redirected to the auditory cortex. As these ferrets matured the auditory cortex organized itself successfully for vision! (Sharma et al., 2000). <p> Sensory input is translated into neuronal connections in part by the anatomical constraints of the brain. These constraints operate at several levels. At the level of gross anatomy, only the visual area of the cortex receives visual input. At the level of tissue, neurons are arranged in regular patterns: cortical neurons, for example, are arranged in six distinct layers. At the level of cells, the anatomy and physiology of the neuron itself also provide constraints which help to determine connections (Elman et al., 1998, pp. 27-30). <p> While my genes must influence the anatomy of my brain, they are too few to define the detailed wiring between neurons. It follows that they are certainly too few to define the archetypal images which are part of the anatomy of my personality. <p>Not until the year 2000, when the sequence of the human genome was completed, was it known that a human has only about 32, 000 genes. Estimates had been significantly higher. This small number focuses attention on complexity: how does human complexity arise from so few genes? Part of the answer must lie in the archetypes. Because of its familiarity with the archetypes, analytical psychology has a contribution to make here.</p> <br><br> <h4>Genes and behaviour</h4> <p class=intro> Though they cannot<i> specify</i> behaviour, genes must<i> enable</i> behaviour. Here it is helpful to compare the rate of human evolution with the rate at which genes mutate. Our species evolved very rapidly, within about five million years, from an ape which was the common ancestor of both humans and chimpanzees (Mckinney & McNamara 1991, p. 293). But mutations occur in the genes at a slow constant rate, such that only a small number could accumulate in five million years. Humans and chimpanzees differ genetically no more than two different species of mice, or two different species of gibbons (Paabo 1999; Hopkins 1999). Some scientists have suggested that we are separated from a chimp by only a few hundred functional mutations; as few as fifty mutations may be responsible for the difference between our brains (Wade 1998). Certainly the number of mutations is small. These mutations are too few to define the patterns of behaviour by which we differ from a chimp. <p> How can just a few mutations enable a pattern of behaviour? Many human characteristics are due to<i> heterochrony</i>, that is, to changes in the timing of development (Mckinney & McNamara 1991, pp. 291-325). Compared with a chimpanzee, each phase of human growth (gestation, infancy, juvenile phase, and adult phase) is<i> hypermorphic</i> or prolonged. While the juvenile phase lasts about eight years in a chimpanzee, in a human it lasts about 16 years. Our prolonged juvenile phase is due to a simple change in the timing of events in the hypothalamus, a change which would require only a few mutations. (The hypothalamus releases hormones which initiate new phases of growth.) The hypermorphosis of our growth phases makes our body taller, our period of juvenile dependency longer, and our life span longer. <p> The same hypermorphosis of growth phases makes our brain about three times larger than that of a comparable-sized ape. All the neurons in the cerebral cortex are created by mitosis (cell division) between 15 and 18 weeks after conception. In the human brain mitosis is simply prolonged to create about 25% more cortical neurons. Then the phase during which axons grow longer is also prolonged, as are the phases of dendrite growth and glial cell multiplication. These changes account for our large brain. Within the enlarged cerebral cortex there are local disproportions, for example in Broca s area. In an ape s brain Broca s area controls face and mouth movement during feeding while in our brain the same area also controls speech. In our brain it is disproportionately enlarged and more connected to other parts of the cortex. But we know that this local disproportion is mostly determined by information from the environment: Broca s area only enlarges if a child learns to speak. While our brain is larger than an ape s and while some proportions within the brain differ, all of these differences are enabled by a small number of mutations which affect the timing of growth. <p> Our larger brain in turn enables increased fine-motor skills, curiosity, learning, reasoning, imagination, creativity and communication. During our longer juvenile phase we learn more from caretakers. During our longer life span we accumulate more skills, knowledge and judgement. All of the above enables our more complex social and cultural behaviour (ibid. 1991, pp. 292-6). <p> I have explained how a few mutations may enable a complex pattern of human behaviour. Since these mutations are too few to specify the pattern, the pattern must be specified by other means.</p> <br><br> <h4> The image</h4> <p class=intro> Jung pointed out that the archetype-as-such is an underlying constant, while the archetypal image is a particular image which has been chosen to represent that constant. The image is derived from the natural environment or from the cultural environment. It elaborates the archetype-as-such with learned information. The archetype-as-such of the individuation journey, for example, is sometimes expressed in my dream by the image of riding a bicycle. Obviously I do not inherit the image of a bicycle in my genes; I take it from the environment. Before there were bicycles I might have dreamt of a knight s quest on horseback and, millennia before that, I might have dreamt of Gilgamesh s journey. Thus the source of the image is not in question. But what is the source of the underlying archetype-as-such? </p class=intro> <br><br> <h4> A geometrical principle</h4> <p> Jung (1938/68, para. 155) said that the archetype-as-such: <blockquote><p class=intro> might perhaps be compared to the axial system of a crystal, which ... determines only the stereometric structure but not the concrete form of the crystal ... [Amongst different crystals of the same substance] the only thing that remains constant is the axial system, or rather, the invariable geometric proportions underlying it. The same is true of the archetype. In principle it can be named and has an invariable nucleus of meaning - but always only in principle, never as regards its concrete manifestation [or image].</blockquote> <p class=intro> Thus Jung said that an archetype-as-such is like a geometrical principle. <p>Pythagoras principle may serve as an example:<i> for any right-angled triangle a<font size=-1><sup>2</sup></font> = b<font size=-1><sup>2</sup></font> + c<font size=-1><sup>2</sup></font>, where a is the length of the hypotenuse and b and c are the lengths of the other two sides.</i> The geometrical principle (archetype-as-such) is always and everywhere true. A particular right-angled triangle, however, whether it be formed in stone, or on paper, or in the cerebral cortex, is located in time and space; it corresponds to an archetypal image. <p> Jung s idea had great explanatory power but it was confused by the suggestion, which he made in the same passage, that an archetype-as-such is inherited. A principle is not inherited, nor does it evolve. It is<i> inherent</i> to our universe. <p> It is clear from Jung s writing (1936/68, para. 99; 1943/66, para. 109) that he did not understand the mechanism of evolution, nor the mechanism of inheritance. Jung s understanding was sometimes based on Lamarck rather than Darwin and Mendel. Jung said that an archetypal form of behaviour would, if it were rehearsed often enough, be inherited. We now know that only genes are inherited and that genes are not altered by behaviour but by random mutation. An individual whose behaviour is, by chance, better-adapted reproduces more and so perpetuates his or her own genes.</p> <br><br> <h4> Dynamic systems</h4> <p class=intro> While a triangle is static, the personality is a<i> dynamic system</i>. Here I discuss several dynamic systems which are more transparent than the personality. I use these systems not as analogies but to explain a homology, a single property which is true of all dynamic systems.</p class=intro> <br><br> <i>A stream</i><br><br> <p class=intro> Imagine a mountain stream.<i> It is a dynamic system because it only exists while energy flows through it</i>, in this case the water s kinetic energy. Sometimes the stream forms a whirlpool and sometimes it takes the serpentine form (the latter is seen most clearly in an aerial photograph of a river delta). Each of these forms represents a pre-existing mathematical principle or possibility, characteristic of rivers and streams everywhere. A whirlpool is not caused by the bed of the stream because it may also form in the ocean or in the atmosphere. Even the stars of a galaxy sometimes form a whirlpool (Hildebrandt & Tromba 1996, pp. 12-13, 246). A stream organizes itself but the ways it can do so are constrained: only certain pre-determined forms are possible. <p> The whirlpool is<i> robust</i> or<i> homoeostatic</i>. It is called a<i> stable attractor</i> (Kauffman 1995, p. 187) because it is a stable form into which a dynamic system is attracted. Imagine a whirlpool around the drain in your tub. Interrupt the whirlpool by putting your hand in it and the water continues to drain, but not as a whirlpool. Remove your hand and the whirlpool reforms. Besides the whirlpool and the serpentine form, there are many other forms that a stream could assume but most of them are unstable. Whatever form the stream is placed into, it slides spontaneously into one of its few stable attractors and remains there.</p> <br><br> <i>A living creature</i><br><br> <p class=intro> In biology we can trace the evolution of a dynamic system. Evidence comes both from the fossil record and from existing plants and animals. Because it only exists while energy flows through it a living creature is a dynamic system<font size=-1><sup>1</sup></font>. Like the evolution of a mountain stream, the evolution of a living creature leads to forms which represent principles of organization. This is proven by <i>convergence</i> in evolution. The snake is an example. Not all snakes are related because, at different times, several different groups of reptiles evolved the snake-form (Zug 1993, p. 119). It is an adaptation for penetrating through narrow apertures. A snake-like body-form also evolved independently in earthworms, in fish (the eel) and in mammals (the ferret). Thus the snake body-form is a principle of organization which has been rediscovered again and again by evolution. The wing is another example. It evolved independently in insects, reptiles, birds, and mammals. Holland (1995, pp. 27-8; 1998, pp. 229-31) discussed a further example, the principle of the camera-eye, which was discovered independently in the evolution of vertebrates and of squids and octopuses. <p> Holland is perhaps the foremost authority on the mathematics of self-organization and emergence. He warned against teleology. Different organisms do not evolve along convergent lines<i> in order</i> to attain the same end-point. Evolution is by chance. <blockquote><p class=intro> Convergence refers to the similarity of agents occupying similar niches. With some knowledge of the niche, we can say something of the form of the agent that will occupy it (Holland, 1995, p. 169).</blockquote> <p class=intro> That is to say, given the air as an ecological niche, we can predict that many of the life-forms which colonize that niche will develop wings. Wings, therefore, are a pre-existing (predictable) principle. <p> In a dynamic system a principle of organization is not a static form like a triangle. Rather it is a dynamic, an ordered way for energy to flow. The whirlpool orders the energy of a stream, the snake- form organizes sinuous movement, the wing-form organizes flight, and the camera-eye organizes light to form an image. <p> The snake, the wing, the camera-eye, and many other examples of convergence prove that evolution fulfils pre-existing principles of organization. That the same possibilities are realized again and again at different times also proves that the total number of such principles is limited. Principles of organization are specific, unchanging, and limited in number. <p> You may object that there is no principle of organization, only an interaction between components the outcome of which is determined by their properties and by inherent constraints. Thus in the evolution of birds the properties of bone, muscle, feather, air and gravity interacted according to inherent constraints and the wing emerged from these interactions. But this objection misses the point. Insects and birds evolved independently. In the insect different components with different properties interacted under different constraints to evolve the same structure, the wing. The number of ways in which such components might interact is very large. Most of the structures formed, however, would not be functional. The few structures which could potentially function in movement represent the pre- existing principles of organization. These include wings, legs, the snake-form, tail-and-fin, and several others.</p> <br><br> <i>The brain</i><br><br> <p class=intro> The brain is a dynamic system because it too only exists while energy flows through it. Like every other part of the body, the brain is self-organized. I explained earlier that the brain s self-organization is directed both by the properties of the component parts (what fits with what) and by information from the environment. But self-organization is also directed by the inherent tendency of a dynamic system to adopt organized forms. Here I focus on this last factor. <p> Elman et al. (1998) are authorities in the field of cognitive neuroscience. They examined the factors which determine how neurons are interconnected during the brain s development. I quote them at some length here because their words elucidate self-organization: <blockquote><p class=intro> Useful self-organization may occur in the absence of explicit guidance from the environment. Certain problems have a <i>natural solution</i>; all that may be required are a few gentle nudges in the form of pre- wired biases and constraints (ibid. p. 16; italics mine).</blockquote> <p class=intro> Elman et al. (ibid., pp. 111-12) use the hexagonal honeycomb to explain their concept of  natural solution . <blockquote><p class=intro> Since each cell contacts just six other cells, the surface tension of the wax and the packing pressure of the bees will force each sphere into a hexagonal shape. The hexagonal shape maximizes the packing of the hive space and the volume of each cell and offers the most economical use of the wax resource.... The bee doesn t need to  know anything about hexagons.</blockquote> <p class=intro>Concerning the development of an embryo (a dynamic system): <blockquote><p class=intro> [When the timing is right] certain interactions between structures inevitably occur. There is no need for genes to encode and control these interactions directly. Instead they follow from the laws [principles] of physics, geometry, topology - laws of great generality, but laws that have very specific consequences for the actors on that stage ... If this is so demonstrably true for the embryogenesis of simple organisms, why should things be different for the embryogenesis of the human mind? (ibid., pp 41-2). </blockquote> <p class=intro> Concerning computer simulations of a self-organizing nerve network (a dynamic system): <blockquote><p class=intro> Certain problems may have intrinsically good (or sometimes unique) solutions. For example, the logical function  Exclusive OR readily decomposes into two simpler functions,  OR and  AND . Given a range of possible architectures, networks will typically  choose this solution without being explicitly instructed to find it ... The solution [does not] need to be internally specified ... [Such] outcomes are immanent in the problems themselves. (ibid., p. 34) </blockquote> <p class=intro> No component of the developing brain contains a design for the final form. The role of the genes is only to provide the components and a few  pre-wired biases and constraints . Elman et al. s experiments showed that, when the  Exclusive OR problem is posed to a developing nerve network, then the available components and the environmental constraints will interact to form new connections which incarnate the  OR and  AND solution. These interactions do not determine the solution: the solution is a pre-existing mathematical abstraction. The interactions of components and environment merely enable the emergence of a physical incarnation of that natural solution. <p> Elman et al s  natural solution is precisely what I mean by  principle of organization'. </p><br><br> <i> Business</i><br><br> <p class=intro> The concept of principle-of-organization is subtle and you may be tempted to dismiss it:  A thing exists, so it is possible. Isn t that an empty tautology? Or  Doesn t the concept only restate the obvious, that the manifest world obeys the laws of mathematics? The concept may be more clear if you look at it in a non-biological system. In the world of business, every business opportunity represents an as-yet- unrealized principle of organization. <p> This country has no overnight mail service. I could provide it. Business would reorganize to take advantage of the speed. I would prosper . Here the country s business economy is a self- organized dynamic system. The  hub-and-spoke principle of overnight delivery (all mail is flown in the evening to one central location, sorted that night, and delivered by air next morning) changes the behaviour of one component of the system, that is, it changes the behaviour of the entrepreneur who recognizes it. Hence it induces a reorganization of the whole system.</p> <br><br> <i> The personality</i><br><br> <p class=intro> I said earlier that the personality is an assembly of instinctual impulses, affects, feelings, sensory perceptions, images, thoughts, hopes and the memories of all of these. But the personality only exists while psychological energy flows through it: it depends, for example, on mirroring, challenge and companionship. Psychoanalytic writers have concluded that the personality is a self-organizing dynamic system (Sander 1985, pp. 23-4; 1987, pp. 340-1; Beebe & Lachmann, 1988, p. 307). Because my personality is a dynamic system it follows that, like all other dynamic systems, it must self-organize to express a principle of organization. This confirms Jung s intuition that an archetype-as-such is a principle of organization. <p> I have shown that biological evolution has made manifest the principle of the snake, that is, the principle of penetration through a narrow aperture from one area to another or from one level to another. But my personality may also manifest that principle. Then I may dream of a snake or perhaps of someone descending a spiral staircase. Both of these images suggest Hermes who journeys to and from the underworld. Kundalini yoga uses the image of the snake to suggest a similar movement. <p>You may object that the dream image is only an ephemera. But that ephemera represents a principle of organization. Clinical evidence shows that when I dream of being bitten by a snake my analysis may be taking hold at a deeper level. Thus the principle of the snake catalyses change in the personality. I do not inherit the principle. What I inherit is a dynamic system, my personality, which may be gripped by the principleb<font size=-1><sup>2</sup></font>. <p> Related to the snake is the principle of the spear which is seen in an airplane s body, a fish s body, a ship s hull and ice skates. The spear is a mathematical solution to the problem of moving through a resistant medium. In the personality it seems obvious that the same mathematical principle is expressed as penetrating phallic power. <p>Reflection will show that any archetype-as-such can be described as a mathematical principle. A <i>mathematical set</i> is a group of numbers enclosed within a boundary. The archetype-as-such of Aphrodite is the principle that, when two sets intersect, they create a third set which includes components of the first two. Imagine a fenced-in field of beets which partially overlaps a fenced-in field of cabbages. In the area of overlap they create a new fenced-in field of intermingled beets and cabbages. This is the essence of sexuality, the sharing of genes, the sharing of bodies, and the sharing of psychological qualities. The archetype-as-such of the father is the principle that new organization can be injected into a set (fertilizing), or can be imposed upon it (law-giving). The archetype-as-such of the Self is the principle that several sets may be integrated to form a unity (see McDowell 1999, pp. 25-7,  The Self , for a discussion). <p> By my use of biological examples, I do not mean to suggest that an archetype-as-such is biologically based, or that it is based in the body. An archetype-as-such is<i> mathematically</i> based. Biology is one medium in which it may be expressed, the personality is another. Subjectively I may associate the archetype-as-such of  containing with the body because I first encountered that archetype in my mother s arms. But her holding was not the archetype-as-such. Her holding was an incarnation of a pre-existing possibility. <p> My psyche organizes itself spontaneously around a pre-existing principle. The organizing force is entirely impersonal, not specific to me as an individual nor even to my species. I am drawn into it inexorably as though into a vortex. Images of that organization thrust themselves upon me. Normally the organizing force is mediated, contained and translated into human form, by the rituals and myths of my collective. When collective means fail then I must contain that impersonal force in consciousness.</p> <br><br> <h4> An archetype-as-such organizes a complex</h4> <p class=intro> The god Ares is associated with slaughter and war- madness. He personifies another principle of sets, that a set can be cleaved into smaller sets by a divisor. When a soldier in wartime holds a weapon in his hands, that possibility impresses itself upon his mind. It may induce him to commit terrible acts. When I pick up a hammer, or a sword, or a loaded rifle I feel a rush of adrenalin as I am gripped by the archetype. This is why boys like to play with toy weapons. <p> Ares is connected to dismemberment. If an infant is not adequately held then the infant may fear that his or her body will disintegrate, that is, dismember itself. When she was four my patient, Louise, would watch her mother dismember a side of lamb with a cleaver. Since the carcass was as big as Louise s own body she imagined herself being dismembered in the same way. She feared that she might be dismembered by her mother s aggression. At the same time Louise felt more connected to her mother than to anyone else. <p> Louise formed an  Ares complex or a  cleavage complex , that is, a group of images, ideas, memories and the like became organized together around the principle of cleavage to which she had been traumatically exposed. In adult life whenever Louise formed a connection with another she would compulsively sever it. Connection was a challenge to which Louise s personality had to respond. Guided by its associations, it responded according to its Ares complex. <p>Louise met the principle not as an abstraction but in concrete form, as an act of cleavage. This generated associations which led her in adulthood to further concrete acts of cleavage. But the sequence of external events had form and meaning: above it all hovered the god Ares. Louise and her Ares complex represent clinical evidence for Jung s contention that a complex is organized around an archetype-as-such. <p> When Alexander cut the Gordian knot with his sword he found a simple and compelling solution (Ares) to a complex problem. The simplicity of a principle of organization is part of its power. We know that in politics a simple idea has the power to organize the populace, which is a dynamic system. That Alexander acted impulsively suggests archaic organization. (There is other evidence for this in his biography.) An archaic personality structure, a borderline for example, or narcissistic, or addictive structure, may result when the personality is gripped excessively by one principle of organization. A narcissistic personality may be gripped excessively by the possibility of being central.</p> <br><br> <h4>Two other dynamic-systems views of the archetype </h4> <p class=intro> After this paper was first submitted for publication, Saunders and Skar (2001) published a paper which also proposed that complexes are self-organized. Our concepts of the archetype are different. Saunders and Skar (ibid., pp. 312, 318-20) suggested that an archetype is not an<i> a priori</i>, but a  property of the dynamic which emerges as a category or  equivalence class of complexes . Their concept is broad and somewhat unclear: it seems likely, for example, that all members of an equivalence class would have in common an<i> a priori</i> principle. I argue that an archetype-as-such is an<i> a priori</i> principle of organization. An archetype-as-such, therefore, can be defined precisely in mathematical terms (for example, cleavage in mathematical terms is division). Since my concept is precise it may prove fertile for future research. I show below that my concept suggests both a new interpretation of mythology and an explanation for our spiritual experience of an archetype. <p> Michael Conforti (1999, pp. 41-2, 127) has drawn connections between complexes, dynamic systems and  replicative patterns . Conforti postulated an  a-causal archetypal field which creates complexes in the personality. But there is no objective evidence for such a field. The concept of principle-of-organization substitutes for Conforti s field and is to be preferred for several reasons: it is supported by much objective evidence, it is a more economical concept, and it is causal. As Jung (1952/60, para. 967) himself insisted, we must chose a causal explanation whenever it will suffice.</p> <br><br><h4> Numinosity</h4> <p class=intro> When I dream of a principle of organization its image tends to be charged and mysterious. Sometimes such an image is strangely highlighted as shown by the halo in religious painting. In literature, likewise, an archetypal image is charged. Why? <p> A principle of organization is eternal and unchanging. It is a foundation stone upon which my personality forms itself. If my conscious personality tries to divorce myself from one of its fundamental principles then an image of that principle will thrust itself forward to compensate. My conscious personality will be threatened by the particular force which it has denied (McDowell 1999, pp. 23-7,  The Anima ,  Thor , and  The Self ).</p> <br><h5>Clinical illustration </h5> <p class=intro> In his mid-thirties Jack was unable to claim his own authority and was unrelated or alienated, both from himself and from others. He dreamt that <blockquote><p class=intro> I was lying sick on a cot in a jungle hut. Three gorillas came into my hut and sat around my cot, looking at me.</p class=intro> </blockquote> <p class=intro>Jack s image of the gorillas was highly charged. The numbers in his dream suggested that <i>individuation</i> was at issue. (Because four sides complete a square the number four suggests completion or wholeness. Individuation is the overall maturation and unification of the personality, a process which may become more conscious in the second half of life.) Jack s sickness in the dream, together with the primitive cot and hut, suggested that his ego structure needed to develop. By virtue of their weight and strength gorillas suggest authority. Since they are intelligent and highly social they also suggest relatedness. Both authority and relatedness are principles of organization. In sum, the dream suggested that Jack s ego was weakened and that if he was to develop further he would have to attend to the issues of authority and relatedness. In part because he was gripped by this dream Jack came to me to begin his analysis. Our interpretation of the dream was confirmed by the ensuing decade of treatment: authority and relatedness were central issues. <p> The charge or highlighting of the gorillas in his dream suggested, in the language of the unconscious, that they represented principles of fundamental importance to Jack.</p> <br><br><h4>Mythology</h4> <p class=intro> What I have argued in this paper changes my view of mythology. Because a god represents a principle of organization, myths about the gods say that such principles create and regulate the world. But science says the same thing. Natural structure, whether it be an atom, a living organism, a brain, or a galaxy, is created and regulated by self-organization. Self-organization is guided by principles of organization. It follows that a polytheistic myth is an accurate, though metaphorical, description of the process by which the world is created and regulated. Mythology seems to have intuited the process of self-organization which science is only now beginning to explain. The congruence here between myth and science is too great to be coincidental. All of this supports Jung s emphasis on mythology. </p class=intro><br><br> <h4> The archetypal viewpoint</h4> <p class=intro>In clinical terms, why is the archetypal viewpoint important? Recall Rachel who dreamt that a witch burned up the lawns. A personalistic or reductive psychology might interpret Rachel s image too narrowly as referring only to her personal experience of her mother. Such an interpretation would deny Rachel s creativity and hence would injure her sense of self. It would also miss the healing potential of the principles which her image represents. <p>Rachel could have dreamt that her mother was cruel to her and made her cry. She did not. She dreamt of a witch. Her witch was like Sakhmet, Re and Shiva, gods with penetrating eyes who both destroyed and created. Thus Rachel s witch suggested the principles of vision, destruction and creation. <p> As mother, Rachel s witch also represented the principle of the vessel. As Rachel became conscious of the devouring aspect of the vessel she also became conscious of its implied opposite. The envious  bad witch implied a  good witch who would admire her. In part she needed to find the  good witch in the person of her analyst. In part the  good witch was consciousness itself which also contained her. Because Rachel was contained, both by her analyst and by consciousness, she experienced the healing aspect of the vessel. The grip of Rachel s old organization was thus loosened and her personality could re-organize itself. <p>Thus the archetypal viewpoint encompasses not only personal experience but also the principles of organization which structure that experience. These include principles of balance and integration.</p> <br><br><h4> Conclusion</h4> <p class=intro> Jung (1940/84, para. 296) did not argue that the spiritual was fact but that our subjective sense of it was recurrent psychological fact. Hence the discipline of psychology had to address our experience of the spiritual. <p> Though what I have said in this paper hews closely to Jung s own thought, never-the-less you may think it reductive:  An archetype is nothing but a principle of organization . But a principle of organization is no small thing. It is one of the guidelines by which the universe was created. When I am conscious of a principle of organization, then I am conscious that in the course of my brief life I incarnate a timeless spiritual possibility. Even an unconscious or somatic enactment is an attempt to express a spiritual possibility. Perhaps this is why I experience the psyche as having  purpose which transcends my own.</p> <br><br><h4> Notes</h4> <p class=intro>1.<br><br> The term  dynamic system is used inclusively. It refers equally to three successive levels of organization: A simple dynamic system is a singular system like the whirlpool. A complex dynamic system is a group of dynamic systems, each interacting with the others. A complex adaptive system, for example a multicellular organism, represents the third level of organization. An organism s body comprises a hierarchy of successive layers of complexity. Each layer is formed from an assembly of simpler systems, that is, each layer is itself a complex dynamic system. Thus an assembly of chemical systems forms a cell (a complex dynamic system) and then an assembly of cells forms an organ (also a complex dynamic system). For example, immune cells form a functioning immune system and nerve cells form a functioning brain. Organs, in turn, form an organism. Organisms, in their turn, form an ecosystem. This hierarchy of layered complex dynamic systems is the basis for emergence in life (Holland 1998, pp. 225-31). <p>The argument I make in this paper applies equally to a simple dynamic system, a complex dynamic system, and a complex adaptive system: each of these organizes itself according to pre- existing principles. <p>Of the three successive levels of organization described above, the personality seems to occupy the middle level. Each complex is a singular dynamic system while the personality seems to be an assembly of interacting complexes, that is, a complex dynamic system.</p class=intro> <br><p class=intro> 2.<br> <br>Note the difference in time scales. A mountain stream reorganizes itself in seconds but an economy takes years to reorganize and biological evolution takes much longer. My personality is like a stream in that it may reorganize in seconds. 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