Imperatives For Unbiased Holistic Education:

The Klein Bottle, A Universal Structure:

An Archetypal Image.

Melanie Purcell, Department of Philosophy, University of Newcastle. 1998

Truth is relative to the perspective of the observer, and the nature of the perception of reality will determine the nature of the truth expressed.. In this presentation I want to explore the relationships between opposed world views and how these oppositional perspectives will determine the nature of truths held. Most models used to describe relationships create an exclusive domain that exteriorizes that which is outside or marginalized by the structure.

The Klein bottle is one structure that creates no exclusive domain as it is a modality that, through a structural twist, unifies the inside and outside surfaces into a continuous surface. Through the use of such a structure, seemingly opposed  perspectives can be illustrated as aspects of the whole where seemingly paradoxical environments necessitate a decisive shift from an “either / or” critique to a pluralistic “and / both” scenario. This structure allows for the relativity of truths to be realized as expressions that are inextricably linked to relative world views, and therefore creates a focus for a holistic approach to information generation.

For educationalists, the imperatives realized through such a model can only  be achieved through a transdisciplinary approach which realizes that seemingly incongruous perspectives and truths can be appreciated sympathetically when  considered pluralistically. Hence the total perception of ultimate reality is viewed through the relativity of  perspectives available through humanities cultural diversity.

At the recent Philosophy, Religion and Science Conference held in Grafton, I heard a presentation by an Aboriginal activist named Graceland Smallwood. She ended her speech with the opening paragraph of her Doctorate Thesis concerning the opposed cultural perspectives of Aboriginal traditional healers and Western allopathic doctors. It was a poignant statement  and relevant to this paper in a number of ways.

1. The two perspectives are antithetical, as are the cultural traditions of these culturally opposed groups of people.

2. Attempts have been made to reconcile these differences in medical perspectives through an understanding of complementarity as have the cultural and social differences through the process of reconciliation, a topical issue in Australia throughout the 1990’s.

3. There have been  deep problems with processes of reconciliation, concerning the structural relationships exhibited by these opposed world views.

The Western dominant perspective is hierarchical or of a vertically ordered nature, where value judgments are perceived as the criteria that results in the ordering from least to highest importance.  It suffers from a patriarchal, supremacist and colonialist foundation which unless addressed has the potential to continue in it destructive path with devastating effects upon the future.

The indigenous perspective is non-hierarchical or cyclic in nature where value judgments are considered as relative perspectives and therefore unable to be ordered in a fashion that sets one above the other. In non hierarchical systems, there is no exclusive domain as every aspect of the reality is seen to be an integral part of the whole.

Graceland’s quote read something like this;

When Aboriginal people pray to their gods and hear them reply they are considered normal and healthy and in contact with the spirit that pervades the universe. When Westerners pray to their god and hear it reply they are considered to be having delusions of grandeur or schizophrenic episodes, as voices in ones head are considered to be an abnormal illusion.

This clearly illustrates the dilemma that prevails when opposing perspectives are confronting each other. Belief systems are relative to the fundamental world view of the group considered, and in this situation, the opposition of two completely different attitudes to human psychology are relative to the different spiritual systems that in turn reflect the philosophy of reality as it is perceived by the groups in question.

Aboriginals believe in a perspective of reality that philosophically may be called Panpsychism, This belief suggest that the universal spirit pervades all of reality, that there is spirit in and around all matter. The basic premises are that energy is conscious, and that thought precedes matter. Whilst the ‘New Physics’ would agree with such a perspective, the predominant materialism that prevails today and is upheld by the dominant culture, goes to great lengths to argue against any spirit, soul or even consciousness. This perspective sees physics taking the meta out of metaphysics and perceives a monist physicality that prevails as Ultimate Reality .

What is curious is that the indigenous cultures and sacred texts could also be considered monistic but that matter is an illusion and all is spirit. I tend to prefer to view this three dimensional reality as an entanglement of both which raises paradox to the fore through the suggestion that both perspectives are true, as each are different vibrational frequencies of the other. The wave particle duality of light also suggests this paradoxical perspective, In fact David Bohm suggests that  matter is revealed as an ocean of energy and light;

“Matter, as it were, is condensed or frozen light ....all matter is a condensation of light into patterns moving back and forth at average speeds which are less than the speed of light...It’s energy and it’s also information- content, form and structure. It’s the potential for everything.”[1]  

I have no doubt however that in higher dimensional existence or in a state of higher vibrational frequency, the matter of the body would cease to be visible, a state which is commonly referred to in Buddhist and many other sacred texts.

In a passage written by one of the foremost interpreters of Tibetan Buddhism, Sogyal Rinpoche, a Dzogchen master, describes the first of the four phases of the bardo of dharmata, “Luminosity- the Landscape of Light.”

“In the bardo of dharmata, you take on a body of light. The first phase of this bardo is when “space dissolves into luminosity”: Suddenly you become aware of a flowing vibrant world of sound, light, and colour. All the ordinary features of our familiar environment have melted into an all-pervasive landscape of light. This is brilliantly clear and radiant, transparent and multicolored, unlimited by any kind of dimension or direction, shimmering and constantly in motion.” [2]

The universal spirit of the Aboriginals is symbolically represented as the rainbow serpent and is the primal creator of everything, where everything is an aspect of it. This is a common symbolic motif and can be found in all cultures, both eastern and western and all indigenous cultures. The dragons, feathered serpents and other such composite beasts symbolize this universal energy generally by unifying the various aspects of nature or elements, for example, the fire breathing, winged serpent that can walk on land and as easily swim in the waters unifies all of the elements (earth, air, fire and water) and is an image well known to the mythological past of western and eastern traditions alike. Through a deep investigation of such myths, one becomes aware of the main difference that are apparent with respect to the relationship that each cultures has with the serpent and in turn the environment as the symbolism of this universal serpent is directly connected  with the earth and its riches.

In the West, we find cultures developing complex rituals due to the spiritual complications realised through the act of mining the earths mineral wealth which have lead to myths of the dragon slayer, where the dragon is perceived as a malevolent force that has to be destroyed so as to reclaim the wealth that is considered the possession of mankind. In the East, a similar shedding of guilt is orchestrated with the mythology of the benevolent dragon who gives freely of his wealth be unless contained, will only be in a certain area once in a single time cycle. Hence the necessity to create complex geomantic structures to house the dragon and gain complete access to the mineral wealth of the earth. The Aboriginals in contrast to the Eastern and Western relationships with the universal serpent or dragon, wishes to neither kill nor trap the dragon, nor did they wish to settle and mine the earth as it is  considered that the beginning of mining will bring the end to the dreamtime.

Due to the development and the construction of knowledge in the West, these ancient myths and particularly the mythologies of creation are considered to be humorous fictions born out of uncertain origins that are fraught with confusing and paradoxical relationships leading to perplexing beliefs and dogmatic religions that are ungrounded through logical and rational thought process. For this very reason, Cartesian dualism consolidated the direction away from serious considerations of spiritual problems in an attempt to grasp the very nature of the physical stuff that makes up the world around us as it is at least tangible and real enough to experiment with.

Francis Bacon, Descartes and Newton, have all be criticized for this descent into physical exploration, but it must be remember that each of these great thinkers where deeply spiritual people struggling with many aspects of the phenomenon of reality. Francis Bacon, whilst declaring that nature must be tamed certainly would have rejected a purely material perception of reality, and wrote at length about the nature of the mineral kingdom and plants and animals that would pertain to a panpsychic philosophy. Descartes too was deeply religious yet felt the need to develop a method that might lead into environments of factual knowledge, and of course the climate of the times was fraught with many disturbing problems and restrictions perpetrated by the dogma and political constraints of the church itself.

Newton too, was deeply involved with the more heretical yet deeply spiritual environment of alchemy which he used to explore the problems of physics and in particularly the nature of attraction and repulsion of objects.[3]  Alchemy is a precursor to physics not chemistry. It is wrongly perceived by many scholars of the history of science as the fall into the trap of not seeking to explore that which they do not believe in. The word Alchemy is derived from ‘kmt’ or ‘chem’ that pertains to the original name of Egypt meaning ‘black land’ with reference to the fertile alluvial soils of the land, not as superficial readers have explained as a reference to the Greek ‘chyma’  meaning to cast metals.[4]

The real push into materialism was through the industrial revolution and the faith that the west had developed in technology and progress which forced people into the capitalist framework that  is now so entrenched. There became little or no real space for religious or spiritual values to be upheld and the nature of religious control had been undermined to the extent that Darwin's theory of evolution was able to be grounded without the fear of persecution suffered by the many great minds who were put to death for contradicting the church. Religion had now been forcefully retired and with Carl Marx’s attempt to address the evils of capitalist oligarchies that in the Russian states was effectively a Monarchic totalitarianism supported by the church he effectively crushed spiritual into the subservience of his dialectical materialism. With his credo, ‘religion is the opiate of the masses’, he too influenced the world to  descend into a spiritual dark age.

Many of the neo Marxian Postmodern writings have reacted to this same confusing territory that shakes on paradoxical ground which is reason for the proclamation to be rid of all grand narratives and fictions of origin.[5]   The Western mindset and paradox do not sit well together. Early myths of origin provoke wild manifestations of multiplicity where the father is born simultaneously with the mother, or the son is born before the father, paradoxical problems that I have addressed in “Looking at the Universe Through the Belly of a Klein Bottle”.[6]   

The inability to allow paradox to reign was also the impetus for one of the great attempts to be rid of paradox once and for all, the Principia Mathematica, by Bertrand Russell and Alfred North Whitehead. The problem of the set theoretic was born and further enriched by Kurt Godel’s mathematical explorations as exemplified by his Incompleteness Theorem. The illusive Omega Set was impossible to construct.[7]

Other Postmodern considerations particularly those influenced by anthropological research, accuse the West of supremacist and colonialist persuasions that draw from an hierarchical evolutionary perspective that taken to extremes would see all indigenous peoples eventually inventing complex written languages and technologies if they were given enough time. Hence the hierarchical perspective pushes all others to follow suit into the same narrow passage of technocratic scientistic materialism even though the future of this paradigm has been considered extremely bleak if not outright suicidal for many decades now.

There is so much invested in this paradigm. Even though the neo Darwinian revision sees the process as being cyclic in terms of feedback loops informing the progression of the species, it is extremely difficult to ground these revisions. The machine that we have created, Western materialism,  is in a sense informing itself through its financial and political counterparts that are the faceless heads of the multinational institutions that have been given the freedom to control this planet. Their only concern is the harvesting of funds to realize the debts drawn in from futures markets, where ironically their influence cuts short the future itself. What a paradox we live by. We sell our future to pay for our present. We destroy the natural environment to allow us to make a manmade one. We eliminate our spiritual imperatives to find them manifest in our technologies of global communication and transportation and so on.

Paradox while ever present, has not always been so problematic. The philosophical traditions of the natural sciences, found in alchemy a system that viewed paradox as a fundamental basis of reality. Alchemy provides that linking thread between the Oriental and Occidental traditions, a thread that is common to Islamic, Indian, Chinese, early Greek and Egyptian sacred esoteric schools particularly Buddhist, Hindu, Taoist, and Sufi teachings.

David Hall, an American comparative philosopher, sees the ‘philosophy of presence’ and ‘difference’ particularly Derrida’s ‘logocentrism’ to be central concepts to both Taoism and Confucianism. He argues that premodern Chinese thought is actually Postmodern and contains resources that answer some of the problems represented by the debate over modernity and postmodernity.[8] 

Ironically in our contemporary constructions of Western scientific knowledge paradox plays a central role. Nietzsche's eternal return plagues us. Since the 1920’s with the development of quantum physics, paradox is seen to have primary importance in understanding the nature of physical reality. Particularly with the work of Neils Bohr, his Principle of Complementarity and  Werner Heisenberg's Uncertainty Principle, the wave particle dual nature of light sets a fundamental ground from which all conceptions of reality are built. In the “Re-enchantment of Science, David Ray Griffin proposes

“a positive, revisionary postmodernism. Inspired both by various developments in twentieth century science (e.g. general relativity, quantum theory, the Gaia hypothesis, recognition of mind-body interactions in immunology), and by Alfred North Whitehead’s philosophy of “organism”,..[he] seeks to develop a Postmodern cosmology...[which] denies certain characteristically modern philosophical and scientific notions, especially mechanism, atomism, determinism, and the Cartesian dualism of mind and body. Griffin argues that contemporary science itself, in discarding these modern notions for holistic and indeterminist alternatives, is becoming Postmodern.” [9]

These developments in science, biology and chemistry have given rise to the multitude of books now referred to as the “New Physics”, many of which set out interpretations that are panpsychic or hylozoic and correspond to the philosophy of Leibniz through his notion of monadology and Schopenhauer with Whitehead developing Henri Bergson’s process philosophy which has led into complex formulations of formative causation and morphic resonance. Lyn Margulis, Illiya Prigogine, Francisco Varela and Humberto Maturana are all important figures in this new perception of reality that is being formed.

This perspective of science and reality has brought us head long into a deep and ironic paradox. Whilst contemporary physical theories lean toward a world view that looks far more like that of an indigenous perspective, particularly that informed by Bateson’s anthropology, the prevailing materialist dogma undermines the grounding of a holistic perspective and actually points toward a dilemma which rests with the nature of institutions themselves, that is educational, political, social, and religious.

Educational Institutions are one of the last places to allow a paradigm to ground, even though they have given rise to the seeds of its formation. It is most likely due to the necessity for certainty or at least the hope of certainty that educational institutions hang onto the previous threads that have held the intellectual investments of the past. Perhaps as Max Plank suggested, it is a waiting game, waiting for the old brigade to die out before the new can be fully realized, which is all very well but for the critical nature of the present and the fragility of the planets ecosystems. Political and social institutions are informed by the prevailing philosophical attitudes supported by dominant perspectives of reality as well as the multinational corporations that control the economy and bombard society with the commercial nightmare that we are subjected to 24 hours a day. Religions are actually in hope of the new paradigm to ground a renewal of their own, even though the nature of this revision will shake the very bedrock of their constructions. What is necessary is something that will tie up all of the lacerated threads of the remaining arteries that will be left when the extraction of dogmatic materialism is achieved from the body of knowledge that humanity holds.

In what follows, it will be noted that much of this information is considered of an esoteric nature, certainly heretic and presently finds no academic environment with which to house itself. Departments of philosophy in many institutions have moved from their “Ashmolean” natural philosophical, metaphysical and alchemical base into the philosophy and history of science. Religious Studies have not embraced an overt inquiry into such areas either which usually are discussed in anthropological circles, or squeezed into a  classics thesis or one focusing on English literature. There is a need for diversity that is signaling the rise of institutions particularly in America and Europe, to adopt a more holistic approach to education by offering transdisciplinary studies which recognize the need to open the boundaries of subject areas and appreciate the interconnectedness of all disciplines, a move that can only be positive for education. Not only is there a need for open participation but for less judgmental approaches to the investigations that could lead us into new and invigorating areas. So often I hear one department damming a writer and another upholding them as hero’s. Tensions are prevalent between the sciences and the arts and the economic rationalism that is infecting all decision making processes in educational institutions are generally destroying the humanities and with it the future.

Vocationally driven education will see the rise of shallow inept thinkers that will be devoid of any real understanding of the nature of being human or the expression that humans are driven to create. Waddington’s study of the surprising correlations between painting and the natural sciences in his major work “Behind Appearance” illustrates that the zeitgeist of a time is reflected in the multitudinous efforts of creative thinking that has no boundaries to it.[10]  

Hierarchical structures are driven by the need to judge one thing against another as if it is possible to compare things through some structure of qualitative assessment. I would argue that unless that process of assessment includes the many diverse ways  of approaching problems and perspectives of reality behind that which is to be judged, then the process of judgment is void, and that if all aspects of a perspective are considered judgments are rendered futile as a hierarchy cannot be constructed. The diverse influences that would have to be considered would include temporal, environmental, social, cultural and religious phenomenon.

In his “Dialectics of Inside and Outside”[11], Gaston Bachelard describes the problems faced by structures that set up an exclusive domain simultaneously marginalizing all that isn’t involved with such a space. He also describes the paradox where inside can be outside and visa versa, where shifting perspectives alter the view into oppositional domains. Like a painting by M.C. Escher, that weird twist of a Möebius nature can provide these environments where the same passage traveled can at once be inside and outside simultaneously.

The Klein bottle is one such shape. The Klein bottle is a topological modality that is thought to have been conceived by Felix Klein, a German Mathematician in the later years of the Nineteenth Century. It is a higher dimensional structure that has the peculiar property of being single surfaced.  This attribute is realized through a twist in the topology which is equivalent to passing one end of a cylinder through a hole in its surface and hence into its interior, and then joining the two opposing edges of what was the cylinder, together. See Figure 3. d).

The same topology can be constructed by joining two Möebius strips of opposite chirality. See 3.e). A Möebius strip is simply a rectangle that is joined end to end after initiating a 180 degree twist in the fabric.

Figure 1. Making a Möebius Loop. Join a strip of fabric end to end after twisting it 180 degrees.

If one traces the edge line of a Möebius strip the shape of such a tracing, describes a double circuit, or an infinity symbol in a state of repose. This line is equivalent to the line traced by the midline of a Klein  bottle in the posture of the snake eating its tail. The various postures of the Klein bottle will be discussed below.

Figure 2. The double circuit or edge line of a Möebius strip which is an infinity symbol in a state of "repose". This line is equivalent to a cross sectional edge of a Klein bottle.

Both a Klein bottle and a Möebius strip share the property of having only one continuous surface. What is curious is that locally there are clearly two discrete surfaces, but globally there is a continuous whole. It is this property that is one of the most useful aspects of these structures as it beautifully illustrates the paradox inherent in complementary oppositions that belies all aspects of reality, and the relativity of our perceptions.

At the point where the "neck" of the "bottle" passes through the "hole" in the surface of the "body", the structure has a completely zero dimension; it is a singularity. That is, the neck is of no dimension, as is the hole. It is a singularity that marries a black hole with its antithetical counterpart, the white hole.  Singularities are a contentious domain. Hawkins points out that a black hole cannot be unified with a white hole as the force of gravity would not allow the formation of a white hole to be achieved. However, driven by my intuition I feel that it may be possible to unify these opposed structures through a Klein bottle as the interiorisation of the white hole may counteract the force of gravity to such an extent as to allow its formation. This material may not seem appropriate to discuss but as I consider that Alchemy is a precursor to Physics, I believe that Newton was pondering this very material, and that the nature of many of the alchemical drawings by Robert Flood and others actually refer to this central phenomenon which is the complex exchange of antithetical forces.

This shape has often been seen as a topological curiosity and has been  cited in many books and papers dealing with "bizarre" mathematical curiosities  such as the work of Douglas Hoffstadter (1980), Ian Stewart (1989, 1995), and Ivars Peterson (1990), Robert Osserman (1995), and Paul Davies (1994).

The Klein bottle is a shape that by virtue of the zero dimension point, has been considered a mathematical topology that is unable to be created satisfactorily as any material used to pass through the singularity, breaches the possibility of  having zero dimension. For the purposes of this paper and due to the findings from my research that I have outlined below, I have chosen to focus on actual models that simplify the structure so as to illustrate the motion of the whole of its body passing through this zero environment creating a cyclic motion.

The models are made in fabric, and besides the inability to create a singularity or zero point, they are useful as they illustrate some of the Klein bottle properties that have direct relationships with structures that have been consciously used in various schools of thought in many cultures.

Figure 3.Cross-sections 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.

Figure 3. b. i; ii; and iii, illustrates the three main postures that are characteristic of the Klein bottle. 3.b.i, is a cross section of the shape in its classic "pelican" posture. If this shape has the "neck" pulled through the hole,  then it eventually finds the posture of a monopole, as shown in 3.b.ii., and as the process of pulling the shape through itself continued, the following formation is an inside out and upside down classic "pelican" posture. Carry this procedure on and one comes to a point where the structure seems to lock itself up and ceases to flow as depicted by 3.b.iii. This posture I have called the Ouroborus, or snake eating its tail.

This posture echoes the double circuit of the Möebius strip and provides a clue to the reason for Jung's suggestion that both the pelican opening its breast to feed its young and the Ouroborus  or snake eating its tail, seemingly quite different structures, are all symbols of the one thing. This is the Mercurious, and the Mercurious is all things and its antithesis; the divine messenger, the god of revelation, the beginning and the end, the alpha and omega, the Prime Matter and the philosophers stone. As a symbol of duality, Mercurious is the Infinite expanse of everything and nothing, the black and the white, the universal spirit itself.[12] 

Fig. 4. The Python, The Spiritus mercurialis and his transformations represented as a monstrous 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 Mercurious. Illuminated drawing in a German alchemical ms., c. 1600.(from Jung’s, Alchemical Studies.1967.)

The universal spirit has revealed itself to all cultures through their contemplative intuitions. The winged dragons that breathe fire and steal the wealth and young maidens from men is a classic of Western orientation. In this story we have given Saint George and Archangel Michael the Blue sword of Protection with which to slay the dragon and reclaim our wealth. The Mayans have described a great feathered serpent, the Chinese their benevolent dragon, the Aboriginals the rainbow serpent and so on.

The pelican opening its breast to feed its seven young is a symbol that is said to be derived from the mistaken interpretation of the feeding habits of the pelican that often result in bloodied red breasts. It has been considered however to be an archetypal symbol for Christ whose blood redeems mankind. The feeding of the seven young symbolise an manifestation from the mother into a multiplicity, and it is therefore to be considered a symbol of the great origin. The pelican was also a familiar piece of alchemical apparatus, its function being reflux distillation which has the purpose of extracting the essence of whatever fluid is being boiled. The alchemical process was a process of cleansing whereby  through primarily seven stages of sublimation, the materials would become purified into gold. The whole purpose of alchemy was to provide a physical material process that would symbolically echo the desired psychological purification where it was thought that the aura could be turned to gold, and hence a mere mortal could become godlike and as the legend of the illustrious Count Saint Germain would have it, defy the natural process of aging and traverse generations of existence.

Figure 5. This image shows the relationship between the symbol of the pelican opening its breast and the alchemical vessel itself which is certainly a Klein bottle structure which illustrates the base as a stoppered orifice.

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 and is followed by Figure 6, depicting the structural relationships of the vessel.

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.”

Figure 6. Depiction of the structural relationships of the alchemical vessel called the Pelican. “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.”

“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.”

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 realized as we pursue this archetypal image.

Figure 7. 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 Ouroborus (1) is half velvet and half plain fabric denoting the inside and the outside. (2) is the pelican and is all velvet externalized. (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.

In figure 7. the structural relationships of the postures are shown as they flow from one to the other, illustrating how the structure turns itself inside out and upside down.

The patterns made as the structure rotates have an uncanny resemblance to a series of images denoted in a text concerning “Rosicrucian’s”, by Hargrave Jennings shown below.[13]

Figure 8. A curious sequence of motifs found in Hargrave Jenning’s “Rosicrucian’s” 1966, which has unfortunately no explanation.

In chapter seven of Lewis Caroll’s Mien Herr, there is a description of the making of a Purse of Fortunatus, and instructions showing how one can be constructed out of three square napkins.

Figure 9. Napkin two is twisted and placed on top of napkin one where the edge DC is sewn to the edge CD. The corners at AA and BB and sewn and the space between them becomes the bags opening which usually given a draw string, unless worn as a Cap Of Fortune in which case this was the hole in which the head would sit. The third napkin is sewn as follows, edge WX is sewn to edge AC of Napkin Two, XZ is sewn to edge DB of napkin one, ZY is sewn to ZY is sewn to BD of napkin two and the final edge YW is sewn to edge CA of napkin one.

Topologically this shape is a Klein bottle  and where the bag has its draw string opening of the purse would be the opening of the Cap of Fortune as it is placed upon the head. The purse was seen to contain not only all of ones personal riches on the inside but also it contained the universe outside through the nature of its  single surfaced structure, so anything on the outside is also on the inside.

The purse is also considered to be a cap of fortune, as I have mentioned above, and it is here that we find connections to the Phrygian cap which was given to released prisoners. It was a symbol of the reclamation of themselves and their inner life with the external free world.[14]

Figure 10. The Phrygian cap and Greek War Helmets.

We can also see interesting correspondences in the construction of early Greek war Helmets that twisted and curled at the nape of the neck, reminiscent of the Cap of Fortune also shown in Hargraves’ “Rosicrucians”.

All of these Klein bottle structures are associated to the Cornucopia, known also as the Horn of Plenty, perceived as the infinite source of all things, as the structure turns in on itself. The open end meets the beginning. These structures are unifying symbols of opposition, and in this sense are fertile sexual images of copulation as the horn bends around for the opposing extensions the point of the male aspect and the opening of the female aspect, to meet and couple. These opposed extensions have explicit male and female sexual connotations and in Hindu thought particularly, are referred to as the lingum and yoni. They are primary dyadic aspects of the one universal energy of all that is. [15]

 a) b) c)

d)   e)

Figure 11. Diagrams of a) horn of cornucopia showing male aspect as the curling tail and female aspects as the "life giving orofice" b) A masonic goats horn vessel, C) Lingum in a Yoni , and d) the Maypole, a staff (phallus crowned by a garland wreath, virgina, usually with ribbons of the seven colours of the rainbow woven down the sheath and in reverse opening up, the whole dance sugnifying the sexual act of divine union, the ultimate statement on the coming into existence of all that is, from a primary union of opposities.; e) the complete maypole after the dance, with diagonally woven coloured ribbons covering the staff.

The correspondence between complements is also apparent in the symbolism of the maypole, as the erect phallus or lingum is capped by the virgina or yoni, from which the multiplicity of rainbow colored ribbons are born and through the dance of virgins around the phallus, two opposing serpentine movements, weave the ribbons down the staff and reverse to undo the weave, repeating this in a copulatory motion.

In early depictions of the Yin Yang symbol we meet the serpent again and find that all of these constructions refer to the oppositional aspects of the primordial manifestation of everything that is in existence.

Here it is depicted as a crowned roosters head that has a body of snake which is an interesting feminization of the snake usually seen to have masculine attributes as the extension and therefore the head is considered to be male and the origin from which the Logos of intellect has been extended, is the female counterpart. The original yin yang symbol was a simple ridgepole depicting the relationship of six aspects to any extension or line, that is the point at either end, in front and behind, above and below.[16]  As a correspondence to the dynamic depiction of opposite complementarities it is possible to consider the Yin Yang symbol to be a two dimensional depiction of the Klein bottle.[17]

Figure 12. The Chinese symbol of Yin Yang: hermaphrodite, as the cock is male and the snake female.

If one traces the surface of the Klein bottle in the posture of the pelican with their finger, the curious single sidedness of the structure is revealed, and in doing so one becomes aware of the four environments. These are the inside of the inside, the outside of the inside, the inside of the outside and the outside of the outside. The logic of inside and outside is stretched somewhat with the associational parameters of the Klein bottle.

The great narratives of origin are based as I have mentioned earlier, upon confusing and paradoxical ground that has been perplexing to the Western mentality, yet considered fundamental in Eastern traditions. In that introduction to the Hermetica and the Aschlepias, it was noted that such a contradiction as having two fundamental primary aspects, was considered untenable and as recently as the 1950’s, commentaries were suggesting that the Aschlepias could not be one book as it was presented but two as it contained a book of evil moral values and one of good[18] . The work of God and the work of the devil. The primary dyads are separated and the god removed to an external and exclusive domain that is impossible to reach, but an example to aspire towards. Such concepts as original sin allows mankind the privilege of roaming the domain of evil, an existence where purging oneself of the temptations that the devil places before us is an ongoing trial to be relieved through the redemption of Christ's dying on the cross, and the judgment of our usually damned souls to a purgatory of sustained condemnation make our chosen beliefs a violent vehicle through which control can be manipulated.

The mythic image of the primordial expansion describes the rising infinitude that is a masculine principle hence the phallus, rising and expanding exponentially with the desire to become. In desiring to be whole, it seeks out its antithesis to which its attraction is a natural phenomena of the force that exists between opposites. Its antithesis is the nothing or void out of which it has sprung, hence the many references to the primordial mother that is veiled and hidden in the waters of that which came before, the origin which was both there prior to the rising out of it, and formed by the rising itself. [19]

This very motif is the source of perhaps the most confusing phenomena of the books of origin as the father is born as the first primal entity but realizes through the natural force of attraction to its opposite, the bride, the mother, that she was there all along and she is in fact the origin of he. The mother simultaneously gives birth to the son which is the father and groom, as she is the mother daughter and bride herself.

Divine paradox is born out of the primal urge to be in existence.

The three male aspects of the father and the three female aspects of the mother are the one event and perhaps the cause of so much confusion concerning the critique of such paradox. The star of David symbolizes the union of triadic male and female aspects, and through the history of the Seal of Solomon, the union is of the sexes is explicit in the joined pentangles that are realized by drawing the diagonal lines illustrated in the middle of the three drawings below. With the three axis in place, the image of cube is suggested and on the right, if a Gestalt is shifted from two to three dimensions, the Seal of Solomon can be seen as a diamond where two pyramids are joined at the square. This diamond formation is symbolic of the alpha and omega point united.[20]

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.

These structural relationships are echoed in Yeats’ Vision, in the Sufi cosmological doctrines of Alchemy and Robert Floods Alchemical Papers.[21]

All myths of origin struggle to explain this phenomena, and many cultures, particularly the western dominant culture, have had great difficulty allowing the paradox to be. Consequently, the hierarchical office of the grand male aspect as the First one and only one god, bears the fruit of separation, where the difference allows the primal material of the female womb to be construed as the evil dark waters that lurk behind the veil of reality. 

The antithesis is seen to be extreme, and the brilliant light of the primordial infinite father is seen to be supremely distant from the opposite entity infinitely removed in comparison, and hereby defined as the duality of evil and good, through the separation of the sexes.

Again, the unifying structure of the Klein bottle allows us to see more clearly the revelation of complementarities where opposition allows the extremes of infinity and zero to be entangled upon the same environment, where alpha and omega are united in a primordial explosion and consequent entanglement of unity, and the diamond of this extraordinary singularity, becomes the energetic powerhouse of manifestation within the centre of all centers of this extraordinary universe.

I believe that the Klein bottle is a universal symbol and a symbol of the universe. It allows us to comprehend the dynamics of oppositional relationships and the relativity of our perspectives. The curious and far reaching connections that I have made necessitate a strong transdisciplinary and non hierarchical approach to institutional learning and the expansion of courses opened up to provide unrestricted and unbiased exploration of seemingly heretical and inconsequential environments that are often misconstrued as worthless fragments of primitive thinking.

It is a dangerous stance to take that perpetuates the separation of opposites and the hierarchical order of the dominant culture. The Faustian dilemma as expressed by contemporary writers poignantly sees the entanglement of these two worlds of oppositions where our technologies provide the domains of good and evil in such a way as to render judgment impotent. Everything has an equally positive and negative attribute. Are we selling our souls and environment to gain knowledge of both, and if so where does this lead us?  We are poised in the web of divine paradox, and unless this is felt through the heart of humanity, the future remains as bleak as the nuclear winters of our science fiction intuitions.

Whilst this essay seems to be damming of all that it is provided through the materialist, technocratic Western mindset, on the contrary, there is as I have stressed above a positive and negative attribute to all things. Whilst I have found it extremely difficult to search for a profoundly positive perspective of technology, I believe that I have done so. This perspective was influenced by a conversation that I have had with a local Aboriginal elder from the Mindaribba Community, Rick. I had gone to Rick in one of my commonly frustrated moods and asked him how it was possible for Aboriginal's who hold such a deeply powerful belief system that finds mining completely untenable, how was it that they could be such peaceful protesters against the destruction of not only their peoples but their earth as well? He looked at me and said that every stone that had been upturned by the western peoples, had a desire to be moved in such a way. There was a purpose behind everything, even though our perspective found it hard to understand it.

So I struggled to find the purpose of our destructive ways and played on the words Art, Science and, Being, Knowledge, Technology and Ontology, a nice sextuplet. After returning to the dictionary to define Art, I realised what I had never seen before, and that was the notion of art as being, as in the religious context. So I considered that if Art is Being and Science is Knowledge, then the Art of science: Technology, and the Knowledge of Being: Ontology had a curious entanglement. That is the being of knowledge, technology can provide us with the alchemical analogue that is the physical matter from which we can draw metaphorical associations enabling us to understand the knowledge of being, ontology.

The table below shows comparatively some of the differences between the materialist, the holistic panpsychic paradigms of indigenous and ancient cultures, and the holographic paradigm as perceived by the Bohmian, Pribramian theory which is in itself holistc. It seems at first that the differences between the indigenous and ancient cultures and the materialist hierarchical culture of the contemporary Western dominant perspective are irreconcilable, that each is determined by a complex understanding of reality that is the basis of the belief. As is made apparent by the table, the holographic paradigm corresponds well with the holistic one and is therefore seen as the means through which reconciliation between such opposed groups as the western culture is with the aboriginal can be effected. The essential axiom of the hierarchical paradigm is that matter precedes thought. The opposite axiom is the foundation of both the indigenous, panpsychic perspective and the holographic paradigm, that consciousness precedes matter.  

Holistic                                                Hierarchical                                      Holographic Paradigm

Cyclic- the extremes, Alpha        Hierarchical- extremes are                      Holographic; innterco-and Omega converge on the         considered to be infinitely                 nnection of all things;           

same point.                                removed from each other.              Torus Moebius or Kleinbottle                                                                                                      HD cyclic in shape.

Evolution is seen to be cyclic                Evolution is seen to be a                 Evolution is informed by

where development a spiral                   linear progression into superior              feedback loops.

motion.                                                developments.                              

Panpsychism-everything                        Materialism-everything is                Matter, sound, light are

has  consciousness.                             matter or dependent upon              different vibrational

                                                            matter, consciosuness                    frequencies of one

                                                           is emergent.                                    universal energy.

Holistic- everything is                        Individualistic- Everything                   Everything innterconec-

considered to be equally                       is considered as a separate      ted, holographic, fractalised

mportant aspects of the whole.            entity and judged accordingly.        non-local, consciousness universal                                                                                                              is primary.

Holistic Medicine, considers                  Allopathic Medicine,                      Formative causation.

the etheric, astral, mental and                considers the physical body            Both allopathic and

causal bodies as integrated                    alone and attempts to treat             holistic medicine are

aspects of the whole, each              the psychological (mental)              complementary.                   affecting the other.                                    and energetic (astral and

                                                            etheric) bodies through

                                                            tweating the physical chemistry

                                                            in the body.

NB: The holographic paradigm uses the hologram as a metaphor as it has the unique property of containing all necessary information to generate an image of the entire hologram contained in any small fragment of the structure, i.e. if a chip of a hologram was broken off it would still be able to generate the full image.

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