"What are the relationships between Infinity and Zero? The Implications of A Cyclic Universe and the Diagonally Woven Single Joined Thread Klein Bottle."

Melanie Purcell

Department of Philosophy, Newcastle University. 1998

Abstract:

This paper looks at a structure created by Shiela Morgan that has over the past few years been presented as a model of space-time for discussion at the University of Newcastle. Through an excursion into alchemy, Jungian psychology, crosscultural cosmologies and isomorphic symbols it is suggested that this model may be useful for understanding paradox, the reconciliation of opposites and the nature of a structural metaphor that a cyclic universe might require. It presents what the author believes is a far more satisfactory model of a monopole than the torus and reveals a complex process of transformation which relies on an exchange of oppositional intensities. The relationships of these "postures" are recognised as a reference to the primary symbols of transformation of alchemical traditions.

Figure One: The Diagonally Woven Single Joined Thread Klein Bottle made by Shiela Morgan

The Diagonally Woven Single Joined Thread Klein Bottle is constructed with a diagonally woven thread of copper wire that meets beginning to end after negotiating a repeated motif that completes the construction. The Motif has been called a double circuit as it is a motion that circumscribes the Klein bottle configuration twice, the second circuit being a completely mirrored representation of the first circuit. It is a single sided four dimensional modality which means that locally a differentiation of sides is discernable, but globally the surface is continuum. There is a singularity located where the neck passes through the body of the bottle which is the reason it has been considered an impossible construction to make, as the singularity signifies an absolute zero point.

Figure 2. The double circuit as it navigates the higher dimensional modality of the DWSJTKB.

The double circuit is repeated a number of times to make up the structure and illustrates the archetypal symbol that it is. Later in the paper it will become apparent that the structural aspects of the DWSJTKB are identical to those depicted in the yin yang symbol.

Before I begin this presentation, I feel that it is appropriate to outline a brief history concerning the direction that has brought me to this line of enquiry.

In 1990 I was working on a paper concerning the reconciliation of opposites. I came to consider the nature of a structure that would illustrate the relationships between oppositional binaries and I realised that as there was no common centrality to the extremes of such binaries, a spherical structure would be unsatisfactory. I attempted a sketch as seen in the following illustration and asked the question? What is this structure? When I first met Shiela, she was giving a seminar on the Klein bottle, and I immediately saw the correspondence between my simple sketch and her structure. Soon after we came to collaborate on this work and as we come from such different backgrounds we have been able to extend the interpretation of this structure into some surprising arenas.

Figure 3. This diagram was an attempt to illustrate the relationship between oppositional binaries.

Having worked as an artist with a language of symbols for some years I realised that as time went by, the interpretations that I gave my paintings changed and seemed to have a life of their own reflected through mine. It became quite clear that there were many levels from which an interpretation could be considered and that the viewer’s ability was affected by their various experiences and education. Locally, the imagery would have connections to events, places, relationships and objects around me and through a global perspective, the analogue of mythic dramas and archetypal narratives tied the symbolism to deeply universal themes. The research into creativity, symbolism and mythology by such authors as Joseph Campbell, Mercia Eliade, Robert Graves, Sir James Frazer and Carl Jung have acknowledged such relationships, and in the words of Joseph Campbell has given “Confirmation...of the unity of the race of man, not only in its biology but also in its spiritual history, which has everywhere unfolded in the manner of a single symphony, with its themes announced, developed, amplified and turned about, distorted, reasserted, and today, in a grand fortissimo of all sections sounding together, irresistibly advancing to some kind of mighty climax, out of which the next great movement will emerge”. (Campbell 1968.)

It seemed that there could be no study of creativity without relating its process to other similarly symbolic procedures or rituals, so I began to study comparative religion and mythology, cross cultural cosmologies, esoteric mysticism, Jungian psychology, and the creative work of the ‘mentally insane’.

The strong connections that all of these fields had with creativity seemed obvious but the theory of art and its practice as taught in art schools, suffered from an inadequate lack of depth and diversity amongst the programs offered which mainly concentrated on a fairly superficial historical analysis. There was an overriding sense that art itself was indefinable and that the study of creativity was too overwhelming a field to become involved with theoretically. Lack of critiques concerning problems of meaning and interpretation that could explore symbolism, crosscultural correspondences, and local and global relationships would shed light at least on the breadth of the field that Art encompasses could only provide an impoverished environment.

Art itself is a territory that whilst being so rich with attitudes and philosophical perspectives remains ultimately undefined, with differences of world views effecting the very nature of one’s perception of art practice. Most world views share fascinating correspondences but are contrary to the contemporary world view of our dominant civilisation that has built its truths upon a structure of scientific rationalism that is in itself in a state of revision. (See Johnson 1996, Horgan 1996, and Elvee 1992.)

Can we find a science that will enable us to realise the nature of creation itself? Why have institutions that specialise in art education and professional training been so unsympathetic to strong research? Can we find within our own cultural constraints a satisfactory understanding of creativity that may resolve these problems?

In answer to the above questions, it may be possible to find a science that can describe reality, but it is most likely to be a science that is not only physical, but a collaboration of human as well as physical sciences. The nature of process is perhaps the unifying element that will allow for this type of approach, and the alchemical process is one analogue that can provide the bridge between science, art, psychology and mysticism. An understanding of art can only be explored through analysis of symbols and the nature of meaning and interpretation, where the explorations of myth, ritual, and religions that are both esoteric and exoteric provide the ground from which an extension of our understanding of these matters may be developed. Without understanding the correspondences between crosscultural cosmology of both literate and preliterate cultures, we are unable to decipher the nature of our creative expressions and their effect.

I hesitate to suggest that we may well have an understanding of reality already found in physics, there are certainly many theories that have attempted to provide the answers many of which have turned to eastern mysticism as a comparative support for their theories, but as was the case with David Bohm’s physics of reality, his association with mysticism as exemplified in his interviews with Krishnamurti, and Rene Weber(See Bohm and Edwards, 1991, B.J.Hiley and F. David Peat 1995, Weber, 1990? and Weber in Williams 1992), are arrogantly considered to be a descent into the mystical of an aging physicist.

Whilst many consider his work with such high regard it is difficult to ground such mystical associations that see paradox as primary and fundamental, in the contemporary environment of rationalist materialism. Here the primacy of paradox disturbs the western mind to the point of overruling one choice above another, reducing the complexities into a heirarchical and value laden structure, as it is inherent in the choice of one perspective above another, or the weighing up of odds, and the necessity for solutions. 

Isaac Newton’s alchemical work has been ill considered by biographers who in some instances were unable to even set eyes on his alchemical papers as they were lost for some decades. (See Dobbs 1975.) There seems to be a problem of condemnation of that which is not understood, an egotistical self-preservation of the authors perception. It was also recently brought to light by Einstein's daughter in an article published in The New Scientist, that he frequently consulted Helena Blavatsky’s “The Secret Doctrine” which he kept upon his desk at all times. There are many more examples concerning strong correspondences with sacred traditions, all of which consider Heisenberg's Principle of Uncertainty, Bohr’s Principle of Complementarity and Alain Aspect’s experiments concerning non-locality as a fundamental ground from which to speculate.. (See Capra, 1984. Capra, 1997. Kauffman, Steven E. 1997. Laszlo, Ervin, 1993. Wilkins, M.H.F. 1995. Kafatos and Nadeau, 1990 and many others, there is certainly a rich tradition of such perspectives.).

Many theorist have suggested that one of the main problems facing such an enquiry, is the inability to embrace both an objective and subjective analysis of reality. For example in Anne Klein’s “Meeting of the Great Bliss Queen, Buddhists, Feminists, and the Art of the Self.” (Klein 1995) the author has focussed upon this problem of duality that opposes the subject to the object as it does male to female, and self to other, and with an extremely detailed analysis and juxtaposition of the Buddhist question of whether enlightenment can be realised through a process of development of the self, or whether one must be born enlightened, with the problem of identity that has been raised in contemporary feminist debates, for example is a woman born a woman or is the identity of gender culturally determined. Klein overcomes this problem of dualism through the analyses of Taoist Buddhist tradition that is rooted in the alchemical literature of both India and China. This model realises a triadic process that corresponds to the Taoist cosmological description and process of a cyclic universe, and realises a resolution to the oppositional duality through a synthetic tradition.

In a scholarly analysis titled “The Foundations of Newton’s Alchemy or The hunting of the Green Lyon” written by Betty Jo Dobbs, (Dobbs, 1975) we become aware of the damming attitude that has been expressed concerning the practice and misrepresentation of what are extremely obscure and difficult alchemical texts. Through Carl Gustav Jung’s brilliant scholarship many of these have been returned to a psychological interpretation where the ‘symbols of transformation’ as he calls them are considered to be of psychic origin. They primarily concern the reconciliation of opposites realised again by triadic transformative processes where “the body was to be changed into the spirit and the spirit into the body until each joined with the other to form a new and more valuable entity” which Jung referred to as the process of individuation. (Dobbs 1975 and Jung 1980,1976 1977, 1946.)

Added to this, in “Science Meaning and Evolution, The Cosmology of Jacob Boehme” Basarab Nicolescu, a leading theoretical physicist in Paris at the Centre National de Recherches Scientifique calls for a ‘new dialogue between the knowledge of science and a deeper, older way of understanding, so that a real evolution of the human spirit can take place. The discovery of the laws of correspondence can develop only by a new cultural approach - one that is transdisciplinary- in which all branches of knowledge, both the so-called exact sciences and the so called human sciences as well as art and tradition must co-operate’ (Nicolescu, 1991). Nicolescu sees Boehme’s  Cosmology as an alchemical description of self organising systems where “threefoldness concerns the inner dynamics of all systems.”

“Like the modern physicist, Boehme is haunted by the idea of the invariance of the cosmic processes and by the paradoxical coexistence of unity and diversity. All is movement, in a continual creation and annihilation, in a perpetual genesis where nothing is stable and permanent, but this movement is not chaotic or anarchic; it is structured, organised by virtue of an order that is certainly complex and subtle, but nevertheless perceivable. As Boehme says to us continually, “even God is begotten by this movement, he is born not in the world but with the world.” (Nicholescu 1991)

All of the above examples can locate for us a common descendent that extends to Egypt. The word Alchemy is thought to refer to the ancient Egyptian’s name for their country, chem which meant Black Land, which was also associated to the later Greek word chyma that refers the act of fusing or casting metal), and consequently this practice is visible in all alchemical traditions from which our science was born. However in a true oedipal contest, alchemy has been dispossessed by western knowledge as being incomprehensible mutterings of misdirected contemplations. In this light, the tendency for contemporary scientists to seek out origins for their interpretations of reality in the sacred books of the East, gives us a passage into the history of our own scientific pursuits.

There have been a great number of contemporary artists who have attempted to bring forth a dialogue concerning spirituality and creativity, particularly through the international exhibition at the Pompedoe Centre in Paris titled, “Magicians of the Earth”, but Joseph Beuys would certainly figure as perhaps the most influential voice of the humanist and spiritual artists. For Beuys, it was the nature of alchemy that provided the essential schema of the creative process. He emphasised the analogy that humans are transceivers and all individuals have the potential to realise freedom through self exploration and individuation where art provides the process for the internal and external exchange between the self and its external machinations in reality. (See Beuys 1979, Tisdall, 1980, Wilson 1980) These ideas correlate with the perception of the universe as having a ‘holographic’ paradigm where an interconnectedness of all things are unified as a whole. David Bohm and Carl Pribram both arrived at this metaphor for the universe and human consciousness respectively. (Talbot, 1991. Weber, 1982)

The main symbols of transformation seem at first glance to be extremely diverse. The reason for this Jung explains is due to the contemplative nature of observation where information is derived psychically from meditative states and dreamscapes.  (Jung 1980, 1976, 1977.) What this means is that alchemists where dealing with a symbolic language that was based on correspondences where the possibility for interpretation was limited only by the experience and education of the interpreter.

Much has been made of the desire to protect the sacred information of the alchemists particularly due to the nature of condemnation inflicted upon the alchemists throughout the ages. It was common that expulsions, jail and even death were the sentences offered by the establishment mainly because of the heretical nature of the texts and imageries that mostly perceived the ultimate god as being self sacrificed so as to come into manifestation as all that is in existence. Added to this, there were great fears concerning the danger associated with individual power, thought to be accessible through the meditation of the alchemical process. For these reasons it has been suggested that the complexity of the symbolism was overtly used as a cipher, protecting the true and hidden meaning for those who were able to understand them.

However through Jung’s analysis and subsequent studies of alchemy we realise the source of the symbolism as psychic (Jung 1980, 1977, 1976., Westman 1986.). These images were not drawn to conceal meaning from others, these images came to the pen, and came in dreams and contemplations as they were, virtually indecipherable and extremely complex even to many adepts. They were the subject of contemplation and interpretations were of many levels. Because these images could be considered immensely disturbing struggles between good and evil with dragons being trampled underfoot and fierce lions poised to devour each other, they were considered to be conjourings of evil and heretical magicians conscious of and in complete control of their visualisations. This certainly is a possibility, but as Jung has illustrated extensively through his field work these images still flood into the creative mind through dreams and nightmares, drawings and paintings, poetry and prose, music and dance, causing him to consider the nature of these images as archetypal. It is this psychic nature of the creative process that is the main reason for artist Joseph Beuys’ correspondence between the artist and the alchemist/shaman and the notion of the human as transceiver where possible transcendence could be realised through the individuation and personal empowerment of the species.

Alchemy sees correspondences in all things- ‘as above so below’, where the macrocosm and the microcosm are seen as reflections of each other unified as a system in a state of perpetual process where nothing is perceived as dead or static. In “Blueprints, Solving the Mystery of Evolution”, Maitland Edey and Donald Johanson tackle the vast question of our origins. In a particular chapter titled “The Dual Nature of DNA”, they describe how in 1956, Arther Kornberg, an American biochemist,

“identified an enzyme - a “sort of” organic thing that could turn stray nucleotides-not quite organic things - into a DNA sequence, a blueprint for life. As the Nobelist George Beadle has said, “He knocked the final prop out from under the comfortable assumption of mankind that ‘life’ is inherently different from ‘non-life’.  When we get that close, right on the edge between life and non-life, we find that Beadle was right. There is no edge, only a grey area, a continuum. The slide over from the nonliving to the living is not sudden. It is plaguingly gradual, and it is noticed in chemistry by the coming together of certain elements that are labelled- for definition’s sake- organic molecules, although they are far from being alive. However they are the precursors. Life appears to depend, not on some magic elixir, but on the organisation of those chemicals in new ways, in slightly more complex ways in which atoms would not ordinarily glue themselves together. They do so when they have picked up bits of energy to hold them together in those unusual ways- and even attract to them other units. In that sense, a nucleotide, the building block of DNA, might be said to be the nearest to a living thing that exists among the chemical compounds on earth....Life, it may be said, starts with odd chemical assemblages and is kept in business by supplies of raw materials and energy to hold those assemblages together”. (See Edey and Johanson 1989.)

Art and Music were seen as corresponding with the physical world through the geometries of proportion. The nature of matter, sound and light was considered to differ from each other only in vibrational frequency, therefore the spectrum of existence was considered in terms of energy and the frequency of its coherence which determines the nature of its density. These ancient ideas are echoed in contemporary string theory where Joel Scherk proposed that ‘particles are not particulate at all but strings that spin and vibrate in space. All known phenomena of physical nature would be built from different combinations of these vibrations, much as the music of a string quartet is built from the vibrations of the strings of the four musical instruments.’ (See Laszlo 1993) Superstring theory introduced supergravity into the equations, hence its name, and considers that particle-strings vibrate in a higher-dimensional superspace. (Laszlo 1993 and Kaku 1994) Also in considering present field theory David Bohm suggests that,

“the fundamental fields are those of very high energy in which mass can be neglected, which would be essentially moving at the speed of light. Mass is a phenomenon of connecting light rays which go back and forth, sort of freezing them into a pattern. So, matter, as it were is condensed or frozen light. Light is not merely electromagnetic waves but in a sense other kinds of waves that go at that speed. Therefore all matter is a condensation of light into patterns moving back and forth at average speeds which are less than the speed of light. Even Einstein had some hint of that idea. You could say that when we come to light we are coming to the fundamental activity in which existence has its ground, or at least coming close to it.” (See Williams, 1992)

What is of importance is that alchemy describes the process of a system. It describes the emergence of the universe as a process of transformation from a nonspatial nontemporal void into the physical spacetime reality of a cyclic universe. This process of transformation is common to all things. The interconnectedness of all things is realised through the structural transformations of process and like the effect of a bootstrap or in Sheldrake’s terminology a morphic resonance (see Sheldrake 1987) of formative causation, the very act of creation itself binds everything together as one, and provides access to the relationships between things.

In the alchemy of Newton we see that his interest was not only spiritual in inclination as he was fascinated by the properties of metals using alchemy to “‘probe the internal structure of its particle’, to find those “certain forces by which the particles of bodies...are either mutually impelled towards one another ... or are repelled and recede from one another”, for that, he said, “was the burden of philosophy’”(see Dobbs, 1975).

With the source of alchemical symbology originating in the psyche, we can therefore understand why the interpretations of symbols are considered to be relative to the inquirer and the knowledge base that the inquirer has. The nature of meaning is not constrained by anything but the limitations of the minds ability to interpret the symbol. The ultimate aim of full comprehension of any symbol is to be able to realise the relationships between things through which one realises not only local but global and universal correspondences. Alfred North Whitehead considered these correspondences to be so far reaching that any given event is impossible to grasp, conceptually, in its totality, and that any contemplation of an object ‘contains everything that you can find in it and that try as you will, you will never exhaust what it contains’ (See Waddington 1969). In this sense the depths of interpretation of art may reveal far greater insights to the viewer than are recognisable by the artist herself and the interpretation of symbols will always remain open to the infinite potential of universal associations. It is interesting to note that Abner Shimony, in his response to Penrose in “The Large The Small And The Human Brain” suggests that Penrose should look at Whitehead’s philosophy of organism “From a modernised Whiteheadian standpoint, what is missing inadvertently or deliberately in Rogers theory of mind is the idea of mentality as something ontologically fundamental in the universe” (See Shimony in Penrose 1996).

In alchemical literature such extended correspondences are realised yet the connections seem obscure, however this obscurity is relieved somewhat through an understanding of the Klein bottle. The most common and interrelated symbols of transformation are the Ouroborus or snake eating its tail; the pelican opening its breast to feed its seven young; the Hermaphrodite, the Caduceus, the serpent and cobra.

The Ouroborus is generally seen as a serpent, snake or winged dragon biting its own tail and it symbolises the closed cycle of development. At the same time this symbol enshrines the ideas of continuity, motion, self-fertilization and the eternal. It is often depicted as being half black and half white, and therefore bears the meaning of a marriage of opposing principles.

Jung considered the Ouroborus to be a complex symbol of transformation that related to the winged dragon, the pelican, Mercurious, the divine winged Hermes, and the hermaphrodite. With all of these images we begin to see an extraordinary complexity of interconnectedness and deeply profound area of contemplation that will be further elucidated from the perspective of a Klein bottle.

“The dragon symbolises the visionary experience of the alchemist as he works in his laboratory and “Theorises.” The dragon in itself is a monstrum- a symbol combining the chthonic principle of the serpent and the aerial principle of the bird. It is.. a variant of Mercurious. But Mercurious is the divine winged Hermes manifest in matter, the god of revelation, lord of thought and sovereign psychopomp. The Liquid metal, argentum vivum- “living silver,” quicksilver- was the wonderful substance that perfectly expressed the nature of that which glistens and animates within. When the alchemist speaks of Mercurious, on the face of it he means quicksilver, but inwardly he means the world-creating spirit concealed or imprisoned in matter. The dragon is probably the oldest pictorial symbol in alchemy of which we have documentary evidence. It appears as the tail eater, in the Codex Marcianus, which dates to the tenth or eleventh century, together with the legend: the One, the All. Time and again the alchemists reiterate that the opus proceeds from the one and leads back to the one, that it is a sort of circle like a dragon biting its own tail. For this reason the opus was often called circulare  (circular) or else rota (the Wheel). Mercurious stands at the beginning and the end of the work: he is the prima materia, the caput corvi, the nigredo; as dragon he devours himself and as dragon he dies, to rise again as the lapis. He is the play of colours in the cauda pavonis and the division into four elements. He is the Hermaphrodite that was in the beginning, that splits into the classical brother-sister duality and is reunited in the coniuntio, to appear once again at the end in the radiant form of the lumen novum, the stone. He is metallic yet liquid, matter yet spirit, cold yet fiery, poison and healing draught- the symbol uniting all Opposites.” (See Jung 1963).

Figure 4. This drawing from Rosarium philosophorum, depicts the filius or rex in the form of an hermaphrodite. He/She acts as the mediator uniting the one with the three (the axiom of Maria). In the background the pelican is depicted opening its breast to feed its young. Standing on a writhing serpent that has three heads, the hermaphrodite rises out of the triadic process of emergence as He/She unites the four in a conjiunctio tetraptiva, whereby the four are joined as the union of persons.

When scrutinised closely the Ouroborus becomes far more than a serpent biting its tail. As with the Codex Marcianus, and other’s that depict the dual black and white aspects, the Ouroborus clearly is devouring itself but it is devouring what has been turned inside out. Some depictions of the Ouroborus show a dual relationship between two loops, an inside and an outside and others actually depict this duality as two separate dragons eating each other. These correspondences are often related to the fact that snakes shed their skin. Serpents are central images in alchemy and the various depictions describe quite different motions, spirals, serpentine “S” shapes, and various triple headed and five headed snakes are littered throughout alchemical literature.

Fig. 5. The Ouroborus as depicted in various manuscripts. Top left, from the Chrysepaeia of Cleopatra; top right, the Ouroborus as symbol of the aeon, Selecta heiroglyphica 1597; bottom Crowned dragon as tail-eater, then dragons froming a circle and, in the four corners, signs of the four elements- Eleazar. Yralies Chymisetres 1760.

The Ouroborus is a continuum that is the union of internal and external polarities. To understand how such a union may be effect, it is useful to consider the oddities of the Möebius strip. If you take a single strip of paper and join the ends after negotiating a 180 degree twist, you will find that what was originally two separate and discrete surfaces have become one continuous surface, and if you trace the edge with your finger, what was originally two discrete edges has become one.

Figure 6. Making a Möebius Strip and the double circuit that traces the continuous single edge line.

Fig 7. The Ouroboros left, Paris MS and right, St Marks MS showing  two distinct circular motifs, one within the other.

The unification of the originally discrete sides and surfaces realises a continuous relationship between the local and the global. Locally there is a distinction between the surfaces which when considered globally is lost. Hence our reading of the ouroborus, particularly those from the Paris and St Mark’s manuscripts can be seen as a double circuit of a continuous single sided shape..

Fig.8. One of the original depictions of the Chinese symbol of Yin Yang: hermaphrodite, as the crowned cock is male and the snake female.

An early version of the Chinese symbol of Yin Yang shows that is also depicted as the snake, in this case the duality is shown in the opposites as male cock and female snake. It is interesting to note here that the male aspect is the head of what usually is a masculine entity; the snake. This refers to the origin of the rising logos (male aspect) being female which has correspondences with the male phallus or lingum rising out of the yoni, the original point from which the logos is given form. Here also we see the serpentine feature and the twisted loop of the infinity symbol whose significance will become clearer as we explore these structures further.

Fig. 9. The serpent-enclosed ithyphallic Osiris, suggestive of the rising logos, as an infinite expanse that is attracted to its antithesis, the origin of its initial expansion.

The union of these opposites is often depicted through the personification of sexuality and here the phallic central image of Osiris is the central figure situated between what seems to be two overarching and opposed snakes. There is in fact one snake which serpentines about the central axis which is seen as the nexus of fertilisation, suggesting a copulation that prepare for the new birth.

Fig. 10. The serpent here contains the four cardinal points which are also associated to the four elements of earth air fire and water. The fire breathing winged dragon of Western mythology is also a creature that through its very form, unifies the quadration.

Fig. 11. This image shows the relationship between the symbol of the pelican opening its breast to feed its young, known as the Pelican Christus and the alchemical vessel- the pelican flask which is certainly a klein bottle structure, here showing a stoppered base.

The pelican is a most curious symbol. There is a direct reference in the “Tractatus aureus Hermetis” found in Jung’s Mysterium Coniunctionis, concerning the nature of the vessel used in the various processes.

“Let all be one in one circle or vessel. For this vessel is the true philosophical Pelican, nor is any other to be sought after in all the world.”

This is followed by Figure 12, depicting the structural relationships of the vessel and the following explanation is given :

“BCDE represent the outside, A is the inside, “as it were the origin and source from which the other letters flow, and likewise the final goal to which they flow back,” FG stands for Above and Below. “Together the letters ABCDEFG clearly signify the hidden magical Septenary.” The central point A, the origin and goal, the “Ocean or great sea,” is also called circulus exiguus, very small circle, and a “mediator making peace between the enemies or elements, that they may love one another in an meeting embrace.”

Fig. 12. Depiction of the structural relationships of the alchemical vessel called the Pelican.

It is clear from this description that the pelican is in fact a Klein bottle  and that the connection between them is more than a simple comparison of form. A is the centre from which and through which everything must flow. BCDE are the four directions that expand outward and intersect at the centre, while F and G signify above and below. These structural relationships will become more fully realised as we pursue this archetypal image.

This may become clearer after we look at the actual Klein bottle. One way of making a Klein bottle, (there are many ways of creating one) is by taking a cylinder twisting one end down to meet itself half down its length, passing through a hole into the interior and joining the cylinder end to end. The formation of the Klein bottle may also be described realised as a sphere extending at one point outward, twisting to loop back on itself, plunging through its self, and reforming through the base, or perhaps a rising expanse  in all directions that embraces its point of origin and reforms at a singularity in the interior, as in Fig. 14.

Figure 13. a) Cross-section of a Klein bottle cut where the seam of two joined Möebius strips of opposing chirality would occur if constructed in fabric. b) The three main postures of the Klein bottle. i) the pelican, ii) the monopole, iii) the Ouroborus. The monopole and the Ouroborus are inversions of each other and the space between the beginning and the end of the line is representative of the very small hole, which signifies a singularity. c) A classic Klein bottle. d) Making a Klein bottle out of a material cylinder. e) By joining two Möebius strips, one left handed and the other right handed, along the side edge, (there is only one continuous edge on a Möebius strip), a Klein bottle results.

Fig. 14. A possible Kleinbottle formation from an elongated sphere.

Fig. 15. A possible formation that rises out of a singularity, expands in all directions and whilst enclosing its origin, reforms at the singularity.

As can see from Figure 14. above, there are three main areas considered as positive “+”, negative “-” and neutral “o”. The positive and negative relationships refer to the extremes of the interior and exterior aspects that have both become externalised and are the dual aspect that locates a neutral position at the centre. The completion of this process is the negotiation of positive and negative with and through a zero point to be reformed as a Klein bottle. It presents us with a four dimensional spacetime geometry, which may correspond to the “3” “4” relationship that has been called the axiom of Maria. In figure 15 these corresponding relationships would be the “x” centre as a neutral point, a singularity, the rising as a positive and the point of origin as a negative, which is also the central position prior to conjunction.

The relationship between three and four has caused considerable consternation amongst alchemical theorists which Jung suggests ‘is due to the polemical attitude to the Axiom of Maria (figure 4) and to the relation of the Quaternity to the Trinity’ (Jung, 1963), where he considers the fourth as the ‘Microcosmic mortal man, who compliments the upper triad’. More importantly he continues with the following quotation:

Here we find explicit references to space, the body, and time. As the original non-being was considered as existing with no space or time in an absolute zero  dimension, a void or plenum, the action that we are considering is likened to a feedback loop, where the two opposites, the infinitude of the rising logos and the zero point from which it sprang are attracted to each other and realise their neutral central axis which as the third aspect of the self, signifies the conjunction of opposites, creating the individuated whole.

It is the desire or potential for  emergence to come into existence itself which has bootstrapped the extension  from absolute nothing to an extension of infinitude. The loop is realised as the self, often considered in the literature of origins as a masculine extension of the logos rising and expanding to infinitude, uniting with  the complementary opposite of the self, the feminine from which this extension sprang or the zero point which is its origin. It is united through the power of the attraction of opposites. In this sense, this primary motive of original motion into existence, will never recur again as the process of recreation is  instigated through the structure of this initial singularity. It is the absolute singular deity, the “meta potential” which in alchemical terms is self sacrificed to come into existence. It realises itself as a male extension and female origin and in a process of coupling ("god" fertilises itself) the birth of the universe is actuated.

This copulatory action is recognised as the union of the son with the mother who is simultaneously the bride and daughter as the son is equally the father and groom. Robert graves, Joseph Campbell , Marie Louise von Franz and Jung have all discussed this phenomenon that recurs in the myths of origin. Again, to use the alchemical metaphor further in terms of the process of numbers, "zero" has become the "one" that existed prior to the infinitude of everything which was and is a process of oppositional attraction and conjunction between complementary aspects of the whole. The whole is both all and nothing (a very ‘Bohmian’ notion) as each is an insideout and upsidedown, or complete inversion of the other. The Klein bottle, through the structural aspect of its singularity, is always therefore in a process of creation and recreation, as a dynamic dance of oppositional intensities that allow such a paradox as being and non-being to coexist.

The arrow of time has been given direction through a process of formative causation and the expansion is realised as a process of coming to know oneself which is revealed through the reflection of the self in its opposite, the "not self", in this case everything and nothing. The process of complete inversion allows for the qualities of time reversal without actually reversing the arrow of time. It is a structural inversion not a reversal of direction that assumes this phenomenon.

The desire for the reclamation of the whole self, is actuated through the process of attraction of opposites, where the self is transformed minute by minute, and the process of individuation is the evolution of self through the assimilation of the

experience of otherness.

Symbolically the feedback can be associated to the motion of flow like the convection patterns of a Bernard cell and the process of formation that occurs with the development of the blastopore in complex organisms. Whilst the latter is a torus, it is interesting to note the similarities of cosmological design between the torus and klein bottle when the klien bottle is in the posture of a monopole, in which case the singularity is placed within the interior. Many of the conjectures that postulate the shape of space as a torus, actually describe such an internal singularity, a postulation that I would argue could infer the  more appropriate topology of a  Klein bottle.

The twisting of inversion where the distinction between these states of opposition, that is inside and outside, become globally unified, raises the topology into the fourth dimension (remember we are dealing with the shape of a four dimensional spacetime continuum). This twist provides the powerhouse of transformation, a singularity which  structurally allows for the transformation of opposites to their complementary states to occur. For example all matter as it approaches a singularity is densified to a point of zero. This density is equivalent to an infinite intensity of energy. The point of transformation becomes the actualisation of the release of the tension between such opposites which are seeking to be released into complementary states as the tension builds. This tension explodes into a white hole, however it has been noted by Hawkins and others that such a formation out of a singularity is constrained by the force of gravity which would disable such a unification of black hole and white hole, through a singularity; the gravity would not allow the explosion to actualise.

However, it could be possible that the geometry of a Klein bottle may well enable such a process to actualise as the force of gravity may be counteracted by the interiorisation of the womblike space in the inner regions of the bottle structure. This is purely intuitive speculation. I am aware that making such assertions is treading into environments that are certainly outside of my field of enquiry, however, my research shows that alchemy is a precursor of physics, and that the numerous illustrations focusing on triangulations that overlap each other and are centralised in a macrocosmic microcosmic diagram of the nature of the universe, are intuitive contemplations concerning the process of transformation which may well illuminate some of the vexing puzzles that contemporary cosmological theory has contrived.

Spacetime is here perceived as a spiralisation of a basic primal motif of motion and ‘Emotion’ where the interconnectedness of all things is realised as the projections of a conscious desire to become. The infinity of consciousness and   finitude of matter are entangled in a realm where paradox is primary. Here the life that we are now involved with is the projection of all that is spiralling into an epoch of transcending godhead; possible the reunification of consciousness that will find itself as one once again to expand into a recursion of experience once more.

This is a panpsychic perspective of life's collective existence from the humble wave/particle to the universe itself, where the possibility of releasing ourselves from the enslavement of the maya of physicalisation may well be perceived as the ancient books of the East suggest, through the convergence of vibrational frequencies where we may experience the interconnectedness of every thing, as one. This is an extremely alchemical notion, and is the meaning of the Greek letters depicted in the  Ouroborus serpent from the Chrysopoeia of Cleopatra shown above in figure five.

Fig. 16. Described as “Another Synthetic Emblem of the Great Work, this image is taken from the Viridarium Chymicum, Stoleius, 1614.

There are a few images that are clues to unravelling the meaning and relationship between three and four for example in “Another Synthetic Emblem of the Great Work” a drawing from Viridarium Chymicum, Stoleius, 1614, where the hermaphroditic Regent balances upon a fire breathing winged dragon that is resting on a winged globe that contains  a geometric sketch of a central point out of which two axis form a cross or quadration about which a three dimensional drawing of a pyramid structure with the numerals 4 3 drawn on it.

The actual structure depicted, is most like a pyramid that is joined to another of equal proportions at the square of the base. The Star of David and the double pyramid have interesting correspondences and are again some of the most commonly used symbols in Alchemy. These correspondences can be realised through a simple shift from the two dimensional perspective to that of three dimensions. The star of David is now seen as a pyramid construction like that which was just described.

Figure 17. The Star of David or Seal of Solomon, showing how the pentangle of solomon can be traced through a gestalt shift from two dimension to three dimensions.

The Star of David, one of the most common symbols found in alchemy, contains within it the expression of all of the numbers from one to ten. The two dimensional Star, is a construction of two equilateral triangles, one pointing down and the other pointing up signifying the female and male aspects respectively. Seen however from a higher dimension it becomes a construction of eight equilateral triangles that are position to form a double pyramid as above so below. There are three axis that can be considered as the six directions of north south east west up and down. There is the square of the union of the two pyramids, as their bases touch, and particularly visible in the central motif, the two triangles can also be seen as two pentangles joined in copulative union about the central point.

The relationship between three and four corresponding to the three dimensions of time becoming the four dimension of spacetime, bound together as the number seven is of significance as the addition of the three and the four as entwined numbers. Many of the processes were of a seven fold nature and the emergence into four dimensions that is procured at that pivotal point between two triads signifies the midpoint of the procedure from which the five is born. Nine similarly is a number derived out of associations, and in this sense can be seen to refer to the dimensionality as each side of the primary triads meets the side of another triad, hence a triangle being formed out of the negative space of three triangles touching each other at the points.

In an etymological analysis of the word Pyramid it is suggested that the derivation from Greek sources as referring to wheat and measure, and from Coptic roots, signifying pyr, division; met,: ten. Furthermore Jennings (1966)” suggests that

“It signifies product or growth  or elimination, in other words, and in the symbolic sense, it means ‘sun-begotten’. ....Thus we obtain another reason upon which we rely as the real interpretation of the name of the pyramid, or obelisk, or great original alter or upright, raised in the divinity working secondarily in nature. IIup is fire (or the Division produced by fire); METpov is Ten (or measures or spaces numbered as ten). The Whole word ..and the entire object bearing this name means, the original Ten Measures of Parts of the Fiery Ecliptic or Solar Wheel, or the Ten Original Signs of the Zodiac. Therefore the Pyramids are commemorative alters raised to the divinity Fire.”

It is also of interest that the diamond refers to the alpha and omega point, that is the beginning and end point of the journey of transcendence symbolised in the intense density and clarity that the diamond has, having reached a state of maximun perfection and order. (See Jill Purce 1980)

R.A. Schwaller de Lebruz was a student of Henri Matisse in the first decade of this century. Interested in art, science and metaphysics, Paris became became for him an intellectual nexus and alchemy a central process which unified his interests. He wrote a series of articles concerning such metaphysics that were given as lectures to the Theosophical Society in 1913-14, and carried out extensive research into Egyptian Mathematics which resulted in quite a number of books concerning sacred science, symbolism and esoteric knowledge of the Ancient Egyptians. “A Study Of Numbers, A Guide To The Constant Creation Of The Universe” was published in 1917 and in the translators note written by Robert Lawler we are told that Schwaller’s subsequent studies into Egyptology would necessitate a revision of this particular work as he became aware that

“the entirety of Egyptian philosophical mathematics was based on the notion that the primary expression of being is not the philosophical “point” but a three dimensional volume. Hence he wrote in Le Temple de l’Homme, “Everything that exists is a volume.... therefore a point is the apex of a volume, a line is the edge of a volume, and the surface is the face of a volume.” These three components (point, line and plane), when considered by themselves, are abstract concepts expressive only of mental ideation with no basis in the three-dimensional world of physical embodiment. By accepting the “original state” as volumetric, the physical world, which is also exclusively three-dimensional, then reflects the essential nature of its creative origins.” (See Schwaller, 1986.)

The entire conception of the natural numbers he believes, corresponds to the process of becoming and continuation of a cyclic universe. The first sequence of numbers from 0 to ten are considered to correspond with the original formation or coming into existence. It is through the dimensionality of numbers and corresponding shapes and forms that the allows us to perceive the Star of David as that which embodies the essence of the process of creation. The following tables describe the process through which the numbers are generated from zero being formless and timeless, to ten the beginning of a the next process and the first of the cycles that are informed by the original coming into existence.

Fig. 18. Tables taken from “A Study Of Numbers, A Guide To The Constant Creation Of The Universe” by R.A Schwaller De Ledruz.

This process of coming into existence of the first cause is the ideation of the logos, and it is the Prima Materia, the original matrix from which all has sprung with the imprint of this ‘becoming’ being the very agent through which this process occurs. As exemplified by the Klein bottle, it is a feedback loop of archetypal proportions. It is the original genesis, that rises to realise full selfhood at the forth stage and just as it is mirrored in our own process of life and death the cycle continues powered by the exchange that occurs in the singularity, the centre of the universe, the eye of god or the transitory “fiat” of absolute zero that signifies the death life of a whole new cycle.

“The accentuation of the centre is again a fundamental idea in alchemy. According to Michael Maier, the centre contains the “indivisible point,” which is simple, indestructible, and eternal. Its physical counterpart is gold, which is therefore a symbol of eternity. In Christianos the centre is compared to paradise and its four rivers. These symbolise the philosophical fluids which are emanations from the centre. “In the centre of the earth the seven planets took root, and left their virtues there, wherefore in the earth is a germinating water.”.... it is the “house of fire” or “Enoch”.......therefore the centre is “an infinite abyss of mysteries.”” (Jung 1983.)

There is a common phrase that is found everywhere in alchemical and now in post modern literature, “the centre is everywhere and the circumference nowhere”. The Klein bottle passes the entirety of itself through itself at the singularity and in doing so the zero centre contains the infinitude of the totality. In this sense that centre is everywhere and the circumference nowhere. In the work of Shiela Morgan, her tables that describe the nature of the weaving patterns of the DWSJTKB actually show a run of the infinite number sequence at a point zero.

In one of my many attempts to track the actual transformative process that the Klein bottle achieves as it moves constantly through its postures, I sought to maintain the centre or mouth of the structure in a fixed position, so as to track the motion of the central axis of the structure, that is the seam that would exist if two material Möebius strips of opposing chirality were sewn together. I simulated this action by fixing a loose string either end to two nails situated fairly close to each other. Then by positioning the string in the formation of the Ouroborus, I began the process to document the patterns which are illustrated as follows.

Figure 19. Having fixed two nails to a piece of wood with a strings attached either end to each nail the motion of the postures is able to be defined. These line drawings correspond to material models that are able to be manipulated. the Ouroboros (1) is half velvet and half plain fabric denoting the inside and the outside. (2) is the pelican and is all velvet externalised. (3) The monopole is half velvet and half plain, and (4) a pelican is the complete inverse of (2) showing all plain fabric on the outside. (5) and (1) are the same. The dotted lines on 1 and 5 correspond to the flipping motion that occurs to the outside part as the structure motions into the next phase of its process.

These line drawings correspond to material models that are able to be manipulated. The Ouroborus (1) is half velvet and half plain fabric denoting the inside and the outside. (2) is the pelican and is all velvet externalised. (3) The monopole is half velvet and half plain, and is the complete inversion of the Ouroborus (4) a pelican is the complete inverse of (2) showing all plain fabric on the outside. (5) and (1) are the same. These postures correspond to the primal duality of the pelican and the snake shown clearly in the Python.

Fig. 20. The Python, The Spiritus mercurialis and his transformations represented as a montrous dragon. It is a quaternity, in which the fourth is at the same time the unity of the three, the unity being symbolised by the mystagogue Hermes. The three (above) are (left to right): Luna, Sol and coniunctio Solis et Lunae in Taurus, the House of Venus. Together they form the Mercurius. Illuminated drawing in a German alchemical ms., c. 1600.(from Jung’s, Alchemical Studies.1967.)

 The patterns made as the structure rotates has an uncanny resemblance to a series of images denoted in a text concerning “Rosicrucians”, by Hargrave Jennings shown below. (See Jennings 1966.)

Fig. 21. A curious sequence of motifs concerning ancient cosmographs from the Chaldeans and found in Hargrave Jenning’s “Rosecrucians” 1966, which has unfortunately no explanation.

The Ouroborus is a “locked up” posture which means that the entire object is fully extended before it begins another cycle, and also suggests that at this position there is one less axial dimension.

Figure 22. The left of these line drawings is the depiction of an elongated torus in cross-section. Imagine this form as a cross section of a snakes body. If we were to “swallow the lips and shit out the intestines”, we would become aware that the inside and out side are actually the same side and there is concealed with in the structure an enclosed interior that is discrete from the outside. The central sketch shows a simple manipulation of the “mouth” that provides access to the interior of the interior. The result is that the Ouroborus extends the original interior as a part of the exterior and the new interior has now become accessible. Consequently if you made the snake so that the velvet side of the fabric corresponded to the inside and the outside of the torus, the externalisation of the true interior is found to occur with posture no (4) of the previous illustration and is half externalised in both the monopole and the Ouroborus.

The left of these line drawings is the depiction of an elongated torus in cross-section. Imagine this form as a cross section of a snakes body. If we were to “swallow the lips and shit out the intestines”, we would become aware that the inside and out side are actually the same side and there is concealed with in the structure an enclosed interior that is discrete from the outside. The central sketch shows a simple manipulation of the “mouth” which provides access to the previously concealed interior. The result is that the Ouroborus extends the original interior as a part of the exterior and the new interior has now become accessible. Consequently if you made the snake so that the velvet side of the fabric corresponded to the inside and the outside of the torus, the externalisation of the true interior is found to occur with posture no (4) of the previous illustration and is half externalised in both the monopole and the Ouroborus.

The following illustration, figure 23, we see a succession of images that depict a five fold correspondence to the main posture as described above. As it refers the original genesis, the first of the images hold all of the key elements necessary to effect emergence.

With the crowned pelican, beak plunging into its breast situated upon the egg that contains the virtual self to be born, we are reminded of the significance of the potential for the original formation of the Klein bottle. In the second image, the humble servant of god is depicted clothed in black as the complete antithesis of this divine vision, and hence the realisation of opposing aspects, the volatile and the passive. The third image in the centre of the motif is inscribe with a name for the divine and depicts that momentary flash or “fiat” that signifies the exchange of opposites with each other. The forth image depicts the pelican as if a phoenix rising and the egg now contains the regent lion surrounded by a firmament. The final image is the hand of god reaching out to the new born offering passage into the calm of the dimensions of material reality.

What happens at this central point of exchange between opposites? It must be remembered that a Klein bottle is a geometric shape that has been considered a curiosity that can be described mathematically but cannot be perfectly constructed from any material real surface, because the Klein bottle is required to be a continuous closed surface with no hole for anything to go through. The hole that the neck passes through and the neck at that point become a singularity, that is they have zero dimensions. (See Stewart (1991,1995); Osserman (1995);Peterson (1990); Davies (1994).).

Fig 23. The Prima Materia: the opening of the great Work

The following diagrams , Part A,B and C correspond to the Chaldaic mysteries. Part A refers to the Astronomical and Astrological relationships, Part B to the Natural and Supernatural, Light and Dark, and the “Mysteries of their interchange” and Part C  to the production of the “Worlds- Visible” or the “Generation” of the “Microcosmos”. All of these diagrams refer explicitly to the transformative nature of the centre which is the area of the Klein bottle where the neck passes through its body at a singularity of Absolute Zero which since the first grand cycle of formation, is the momentary “Fiat” of the Eye of God that glimpsed between the destruction and re-creation of the new.

Figures 24. These are diagrams taken from Hargrave Jenning’s book on the Rosicrucians. Part A, Part B and Part C, all of which describe cosmographs from the Astrological and Astronomical Chaldaic Mysteries.

Figure.25 When we consider the relationship that a cyclic structure has with geometrical axis we can sketch a passage that illustrates these relationships and find that we are tracing that very shape that is indicative of the Klein bottle as depicted in the inset.

The centre is now able to be viewed for what it really is, a singularity where the oppositional aspects of the quadration of infinities, that is the infinitely small the infinitely large, the negatively infinitely small and the negatively infinitely large. The numbers 1 and -1 can be considered as the “Architectural Principle” about which the singularity drives the process. One, and therefore -1, is considered particularly in Indian Mathematics as being the fundamental concept. It is seen as the midpoint between the infinitely large and the infinitely small and likewise the midpoint of the negative infinities is -1. To the atomistic school of Indian philosophy, unity alone is an objectively real quality inhering in substances. Indian Physics as it proceeds from Samkhya doctrine, teaches that all objects are evolved forms from the same ultimate energy. (See Kramish (1962; Suzuki 1962)

It is often considered that they are moving against each other, but if they are both seen the be the opposing complementarities of a single entity, then the exchange must be related to an extreme exponent of oppositions where each “desire” to realise the state of the other, which is where the “infinities” return or pass through the centre, the absolute yet momentary zero. With the singularity of a black hole, the tension between the infinite densification of the matter and the infinite intensification of the energy encapsulated within the matter is an example of such a desire for exchange. The intensification of the energy rises to breaking point necessitating a release from the constraints and pressures surrounding it as the matter too requires the same release. This is able to realised at the instant of passing through the hole in the Klein bottle where the neck has now become internalised and may be considered as a white hole.

There have been some extremely interesting developments in contemporary physics, many that correspond quite clearly to the ideas mentioned above. According to Ervin Laszlo, “one of the boldest and most exciting hypotheses of cosmology to be put forward this century” is to found in “Beyond the Big Bang, Ancient Myth and the Science of Continuous Creation, written by Paul Laviolette who is the president of the Starburst Foundation. Laviolette explores what he considers to be ‘astonishing parallels between the vanguard of scientific thought and creation myths from the dawn of civilisation.’ Drawing from modern systems theory and theories of process, he finds direct correspondences with the traditions particularly of ancient Egypt. (See  Laviolette, 1995)

Added to this, there have been a few expressions concerning the state of the universe prior to the Big Bang, particularly those of Illya Prigogine, and Li Xin Li.

In the original formation of the Klein bottle, the original feedback onto itself corresponds with Prigogine’s hypothesis concerning the “Meta Universe." In fact both Illya Prigogine (see Prigogine 1997)  and Li-xin Li (See Li 1998) have suggested recently that prior to the Big Bang or Spacetime as we know it, there was a loop that expanded and became unstable causing it to feed back onto itself and consequently intersecting itself from which the new posture is reformed into a continuous chaotic and indeterministic, self organising, non equilibrium system. In this meta universe time is seen as an expansion and instability with consequent feedback and intersection.

“For many physicists, the acceptance of the big bang theory as the origin of our universe means that time must have a beginning, and perhaps an end. It seems more likely to me that the birth of our universe was only one event in the history of the entire cosmos, and that we therefore have to ascribe to that so-called “meta-universe” a time prior to the birth of our own......we consider the big bang an irreversible process par excellence. We suggest that there would have been an irreversible phase transition from a preuniverse that we call the quantum vacuum. This irreversibility would result from an instability in the preuniverse induced  by the interactions of gravitation and matter. Clearly we are at the edge of positive knowledge, even dangerously close to science fiction. Nevertheless, we argue that irreversible processes associated with dynamical processes have probably played a decisive role in the birth of our universe.  From our perspective, time is eternal. We have an age, our civilisation has an age, our universe has an age, but time itself has neither a beginning nor an end. This brings closer two of the traditional views of cosmology: the steady state theory introduced by Herman Bondi, Thomas Gold, and Fred Hoyle, Which may apply more precisely to the unstable medium that generates our universe (the meta- or preuniverse), and the standard big bang approach.” (See Prigogine 1998)

I am certainly not in any position to comment upon the theoretical assumptions of such work, but I do believe that there are some striking correspondences with such ideas, which throw up some complex questions such as “Are our intuitions gleaned from the contemplations of the many esoteric traditions that we have explored able to shed light on the origins and nature of the universe?” “Is the ‘coincidence’ of such similarities due to a contemplation of the structure of the universe, where the initial fiat of thought is considered the only truths.” “Is the Klein bottle a universal symbol or a symbol of the universe itself.”

If we are to run with the similarities further we may be able to effectively understand the nature of our origins and in turn the origins of the universe. Many scientists wince at the thought of metaphorical associations being used to explain things as is the language of science and maths is somehow a purer analog than other languages. Analogs and isomorphic associations shouldn’t be seen to denigrate the “truth” as our science itself is confirming the interconnectedness of all things. It simply depends on whose “truths” one considers to be more honest than others. For systems of contemplation, there is no question of the nature of truth, simply the question of how it is discerned and whether the subject is able to ascertain the difference between it and the illusion of the analytical mind interfering with the information. This is in fact the nature of training for subjects who are involved in remote viewing, that is where the mind is able to gain information of a particular spacetime position from a remote place.

Through all of these various correspondences that I have made, the Yin and Yang symbol can now too be seen for what it is. In a previous illustration we see an ancient depiction of this opposition as a writhing snake. It is not simply a dynamic depiction of opposite complementarities, but is described as having the three main aspects that are seen as axis. Hence it is possible to consider the Yin Yang symbol to be a two dimensional depiction of the Klein bottle.

“The original Tao is conceived as the supreme emptiness from which the one, which is none other than the primordial breath, emanates. This gives birth to the two, embodied by the two vital breaths of yin and yang. By their interaction , yang, as the active force, and yin, as receptive softness, govern the multiple vital breaths that animate the ten thousand existents, the three has its place.

The three represents the combination of the vital breaths of yin and yang and the median emptiness ...(‘Ten thousand existents carry yin and embrace yang. Harmony is born with the breath of median emptiness’.)....This median emptiness , itself a breath, issues from the original emptiness, from which it draws its power. Median emptiness, is necessary for the harmonious functioning of the yin-yang pair: it attracts the two vital breaths and draws them into the process of reciprocal becoming. Without it, yin and yang would be in a relationship of frozen opposition. They would remain static substances and be formless. It is clearly this ternary relationship between yin and yang and the median emptiness that gives birth to, and also serves as a model for, the ten thousand existents. For the median emptiness that resides at the heart of the yin-yang pair also resides at the heart of all things. Imbuing them with the breath and life, it keeps all things in relationship to supreme emptiness, enabling them to enter into internal transformation and harmonious unity. Thus Chinese cosmology is dominated by two intersecting movements, which can be represented by two axes: a vertical  axis representing the coming and going between emptiness and fullness, in which fullness originates from emptiness and emptiness continues to act within fullness; and a horizontal axis representing the interaction within fullness of the complementary poles of yin and yang.” (see Cheng 1994)

Again there seems to be a problem of dimension as consideration of a horizontal, and vertical only brings to light two of the three spatial dimensions. If however we consider the vertical and horizontal as three axis; where yin and yang is associated to the horizontal in terms of a plane, being the four directions north, south, east and west, and the fifth and sixth direction emptiness and fullness or above and below- this allows us access to an extension of cosmological consideration as perceived by many indigenous cultures. (See Peat, (1996), Suzuki & Knudtson  (1992)). Above and below signifies the union of the macrocosmic and microcosmic through the identity of self and all that is above as anchored to all others through that which extends into the depths of the earth itself.

The Tao can now be perceived as a relationship between three axis;  one axis, the vertical signifying the coming and going, emptiness and fullness and the two axis of four directions of the horizontal plane signifying the interaction within fullness yin and yang, darkness and lightness, the quadration of infinities.

The original inception of the Yin Yang symbol was thought to be the ridgepole, a simple line which was thought to develop into a line between a left and right handed crescent. (See Wilhelm 1974, Paul Hargrave 1998.)

“With this line, which in itself represents oneness, duality comes into this world, for the line at the same time posits an above and below, a right and left, a front and back, in a word, the world of opposites.” (See Introduction to the I Ching. 1974.written by Richard Wilhelm).

Figure26. The central singularity, has been depicted as a line between two crescents 

The central singularity, has been depicted as a line between two crescents. As it is a singularity and signifies a zero point, we can see that a circle with a cross in it corresponds equally well.

Fig 27, the classic Klien bottle figure.

The same motif that has been called the double circuit is woven through-out to create the complete DWSJTKB. The Klein bottle and the “Yin Yang symbol are one and the same.

The origins of the infinity symbol were derived by looping the extremities of the cross. If the double circuit were joined end to end the symbol realised is an infinity contained by a zero.

When researching ideas on creativity, I returned to the dictionary to find an understanding of the various definitions considered and realised that in the many years that art and creativity have been my central focus  I had for various reasons  ignored the first entry that treats the word “art” in the biblical context of being. ‘Thou art here in existence.’ ‘ Who art in heaven’ etcetera. Art in this sense refers to "isness" or being itself. Upon further enquiry I found that the Hebrew symbol that denoted the word art was in fact a circle (See Drucker 1997) .

So whilst the circle has connotations of continuous motion, a structure that has no beginning or end, wholeness and entirety, it also had significant etymological relationships with art, creation, being and isness. An eternal nothing of timeless spaceless existence; that is pure consciousness, has to feedback on itself to realise the antithesis of the singular existence of the non existence of the metauniverse, and as if being turned on, twists and unifies the local and global relationships of inside and outside realising a hyper-dimensionality.

The demand for diversity of interest to be realised academically has necessitated the genesis of interdisciplinary and transdisciplinary academic departments. This signifies  a rise from the fine tuned focus of the specialist to the diffuse terrain of comparison and association, interpretation and isomorphism. We are poised on the edge of the Millennium looking deeply into our past as it signifies a nexus for emotion. We have proven that we can create things by the labours of our hands, the knowledge of our sciences and the resources of the planet but we have constrained our perspective of reality to the world of substance and aborted the project of spiritual transcendence. Our technologies have replaced the transcendent object of humanities collective desire. We are groping in the darkness of our separateness to see reason for this material nightmare that we have created. The Universalism that we have transcended into is a technological fabrication. Humanities project has been aborted for the very physical manifestation of human potential realised in our global communications networks, a poor excuse for the unlimited infinite and universal hyper-reality of the humanity that we have hoped to realise.

The stage has been prepared for a final catastrophe. As we have wagered our existence for the proof of the first cause, and while we are arguing about which world view we base our assumptions on, our view of the world  and its future gets bleaker.

Consider this- If science can be seen as knowledge and art as being then the art of science is the being of knowledge: technology and the science of art is the knowledge of being: ontology, therefore our art of science is enabling us to realise our science of art. The critical problem is however whether humanity can realise this dilemma and alchemical use the material of technology to realise our ontology before the destruction that technology has caused obliterates our potential reside in the material form that we are currently accustomed to.

We should hit the bottle for some serious cosmological considerations.

References.

Beuys, Joseph. “Und Die Medizine.” S. Coppenrath Velag, Muster, 1979.

Beuys, “Multiples.” N.Y. University Press 1980.

Campbell, Joseph. “The Way Of The Animal Powers, Times London 1984.

Campbell, Joseph, “The Masks Of God, vols. 1 to 4 , Primitive Mythology, Oriental Mythology, Occidental Mythology,   Creative Mythology.” Penguin 1968.

Capra, Fritjof. “The Tao of Physics”, Bantum Books 1984.

Capra, Fritjof. “The Web of Life”, Flamingo, 1997.

Cheng, Francois. “Empty And Full; The Language of Chinese Painting”,  Shambala 1994.

Critchlow, Keith., Lawler, Robert., Macaulay, Anne., Raine, Kathleen., Zajonc, Arther. Edited by Chris Bamford (1986) “Rediscovering Sacred Science, Form  Number, Architecture, Light, Colour, Music, Poetry”, Floris Books.

Danielou, Alain. “The Gods Of India,” Inner Traditions Press, 1985.

Davies, P.C.W., and Brown, J. “Superstrings.” Canto Series, Cambridge University Press, 1995.

Davies, P.C.W. “The Edge of Infinity:beyond the Black Hole”. Pelican Books. 1994.

Dobbs, Betty Jo Teeter, “The Foundations of Newton’s Alchemy or The Hunting of the Greene Lyon”, Cambridge University Press, 1997.

Drucker, Johanna. “The Alphabetic Labyrinth, The Letters In History and Imagination.” Thames and Hudson. 1995.

Fabricius, Johannes. “Alchemy: The Medieval Alchemists And Their Royal  Art.” The Aquarian Press, 1976.

Feynman, P.  “QED: The Strange Theory Of Light And Matter.” Penguin, 1985.

Hagger, Nicholas. “The Universe And The Light: A New View Of The Universe And Reality.” Element 1993.

Hargrave, Paul, Unpublished Paper concerning the I Ching. 1998.

Heisenberg, Werner. “Quantum Theory And Its Interpretation” in “Neils  Bohr,” North-Holland Publishing Company. 1964.

Hofstadter, Douglas R. Hofstadter. “Godel, Escher, Bach: An Eternal Golden  Braid; A Metaphorical Fugue On Minds And Machines In The Spirit Of  Lewis Carroll.” Penguin. 1980.

Horgan, John, “The End Of Science”, 1996, Little, Brown and Company.

Huntington Moore, Douglas. J. “Generic S cience and the Foundation of   Mathematics, Matter and Mind- Generic Synchronic Structure”, 1997,  Internet.

Kelso,J.A. Scott. “Dynamic Patterns; The Self Organisation of Brain and Behaviour.” 1995, M.I.T.Press.

Edey, Maitland.A. and Johanson, Donald. C., “Blueprints-Solving the Mystery of Evolution.” Little, Brown and Co. 1987

Elvee, Richard Q., editor, “The End Of Science? Attack And Defence.” Nobel   Conference Number xxv, 1992.

Johnson, George. “Fire In The Mind”, Viking, 1996.

Jung, Carl Gustav. “Alchemical Studies”. 1967, Princeton 1983.

Jung, Carl Gustav. “Psychology and Alchemy.” Princeton,1980.

Jung, Carl Gustav. “Symbols of Transformation”. 1956, Princeton, 1976.

Jung, Carl Gustav, “Mysterium Coniunctionis,” 1963,  Princton, 1970.

Jung, Carl Gustav, “The Psychology of the Unconscious.” Keagan and Paul, 1946.

Kaku, Michio. “Hyperspace, A Scientific Odyssey Through Parallel Universes, Time Warps, and The Tenth Dimension”. Oxford University Press. 1994.

Kafatos, Mena. Nadeau, Robert. “The Conscious Universe: The Part And  Whole In Modern Physical Theory.” Springer 1990.

Kauffman, Steven E. “The Dynamic Structure of Space” and “The Relational Matrix Model of Reality”, “Unified Reality Theory” 1997 (Internet).

Kramisch, Stella. “Natural Science and Technology in Relation to Cultural Patterns and Social Practices in India.”,  in Philosophy and Culture,  East-West Philosophy in Practical Perspective, ed. Charles A. Moore.  1962.

Krauss, Lawrence M. “The Physics Of Star Trek”, TSP Press. 1996.

Laszlo, Ervin, “The Creative Cosmos-A Unified Science of Matter, Life and Mind”, Cromwell Press, 1993.

Laviolette, Paul. A. “Beyond The Big Bang, Ancient Myth and The Science Of Continuous  Creation.”, Park Street Press, 1995.

Lerner, Eric, J. “The Big Bang Never Happened, A Startling Refutation of the Theory of the Origin of The Universe,” Simon and Schuster, 1991.

Li-Xin Li, “A Loop Of Time”, New Scientist, 1998.

Morgan, Shiela, “A Candidate for Reality: The Klein Bottle Woven With One Single  Straight Line Thread.” published in “Dialectic 1994: Women Philosophers And  Their Work”., Journal of the Newcastle University Philosophy Club.) 

Osserman, Robert. “Poetry Of The Universe: A Mathematical Exploration of   The Cosmos.” Weidenfeld & Nicholson. 1995.

Peat, F. David. “Blackfoot Physics, A Journey Into The Native American Universe”. Forth Estate, 1996.

Peterson, Ivars. “Islands Of Truth: A Mathematical Mystery Cruise.” W.H.Freeman and co. 1990.

Pribram, K.H. “The Implicate Brain” in “Quantum Implications, Essays in  Honour of David Bohm, Edited by B.J.Hiley and F. David Peat. Routledge,     1995.

Prigogine, Ilya. “The End Of Certainty; Time Chaos, and the New Laws of  Nature.” The Free Press 1997.

Purcell, Melanie “A Point In Time As We Create The Future.” Masters Thesis 1990.

Purcell, Melanie. “The Reconciliation of Antithesis” Unpublished Notes. 1990.

Purce, Jill. “The Mystic Spiral, Journey of The Soul.” Thames And Hudson, 1980.

Rucker, Rudy. “Infinity and the Mind; The Science And Philosophy Of The Infinite.” Paladin, 1982.

Sarfatti, Jack. “Post Quantum Cosmology”, Star Quest- Internet. 1997.

Schwaller, R.A. de Lubricz, “A Study of Numbers, A Guide To The Constant  Creation Of The Universe.” Inner Traditions, 1986.

Sheldrake, Rupert. “A New Science of Life”, Paladin 1987.

Smolin, Lee. “Life of the Cosmos”, Weidenfeld and Nicholson,1997

Stapp, Henry. “Light as Foundation of Being.” in “Quantum Implications", B.J.Hiley and F. David Peat, “Essays in Honour of David Bohm", Routledge, 1995.

Stewart, Ian. “Nature’s Numbers: Discovering Order and Pattern In The Universe.” 1995, Science Masters.

Stewart, Ian. “Game, Set and Math, Enigmas And Conundrums.” Penguin,  1989.

Suzuki, Daisetz.T. “Basic Thoughts Underlying Eastern Ethical And Social  Practice.”  in Philosophy and Culture, East-West Philosophy in Practical  Perspective, ed. Charles A. Moore. 1962.

Suzuki, David & Knudtson, Peter. “Wisdom Of The Elders”, Allen and Unwin, 1992.

Talbot, Michael. “The Holographic Universe.”, Harper Collins. 1991.

Tisdall, Caroline. “Joseph Beuys Coyote.” Schirmer/ Mosel 1980.

Tzu, Lao. “Tao te Ching”, Translated by Arther Haley, Wordsworth Classics, 1997.

Vickers, Brian editor “Occult And Scientific Mentalities in the Renaissance”, Cambridge University Press 1986.

Waddington, C.H., “Behind Appearance- A Study of the Relations Between Painting And  The Natural Sciences In This Century.” Edinburgh University Press. 1969.

Weber, Rene, “The Enfolding-Unfolding Universe: A Conversation With David Bohm,” in  “The Holographic Paradigm”, ed. Ken Wilber. (Boulder, Colo.: New Science Library, 1982.

Westman, Robert S. “Nature, Art, and Psyche.”, found in “Occult And Scientific Mentalities in the Renaissance”. ed. Brian Vickers, Cambridge University Press,     1986.

Williams William E.(Edited by), (1992) 'Unbounded Light, The Inward Journey.' Published by Nicholas-Hays Inc, York Beach Maine.

Wilkins, M.H.F., “Complementarity and The Union Of Opposites”, In “Quantum Implications, Essays in Honour of David Bohm, Edited by B.J.Hiley and F. David Peat. Routledge, 1995.

Wilson, Colin, “Joseph Beuys- In Memorium”: “Joseph Beuys- Obituaries, Essays, Speeches. Internation Bon 1980.

Zajonc, Arthur. “Catching the Light, The Entwined History of Light And Mind.” Oxford University Press 1993.