Jensen’s Great Pyramid

February 2nd, 2012

A painting by Alfred Jensen, reproduced in the catalog for his 2001–2002 Concordance exhibition at the Dia Center for the Arts.

In an article from the catalog, Professor Michael Newman writes, “Jensen’s elaborate diagrams are drawn from various cosmological systems, including the Mayan calendar, the I Ching and other Chinese mathematical systems, the Egyptian number system, Pythagorean mathematics and geometry, and ancient Greek systems of proportion. [For example,] The Great Pyramid (1980) [below] has numbers written in an ancient Egyptian notation, in which a bar stands for the number 1 and a horseshoe for 10, on a pattern that suggests rectangular pyramids seen from above. The panels are set in a progression such that the sum of the top and bottom number of each pair is 13; each contains an even number at the top and an odd one at the bottom—this kind of opposition, echoed in the use of black and white at the cores and edges, is reminiscent of the I Ching” (p78).

The Great Pyramid, 1980, 90 x 360 inches (insert), rotated 90° clockwise to fit this blog’s format. Click for larger, horizontal version.

Critic Peter Schjeldahl writes, “Jensen’s works can be called ‘diagrams’, not because they explicate ideas, but because they delineate them; they are fields united by the purpose of signifying. His is a gesture of communication, rather than of conveyance” (p44).

Asks Newman, “[Jensen] puts the viewer in a position of conflict in relation to the painting: Are we to decipher, turning to books to help us, or are we to look?” (p88).

Dowd on Metaphor

January 16th, 2012

Seven diagrams from movement investigator and trainer Irene Dowd’s 1984 essay, On Metaphor, collected in Taking Root to Fly.

“Studying the history of the eye’s growth… through the depiction… of the developmental process in five arbitrarily determined stages… enabled me to develop a metaphoric model of the activity of ‘seeing’. In each developmental stage, except for the very first one, there is simultaneously both movement outward from the neural core toward the surface periphery of the body and movement inward from the outside toward the neural core. The stages successively provide a more and more complex and elaborate map of precisely how these oppositional streams of moving cells and light waves can travel, grow, and interrelate” (p74).

Each of the five figures below depicts the developmental model on the left and Dowd’s metaphorical model on the right.

Stage 1, 28-day-old embryo: The optic vesicles protrude from the head end of the neural tube toward the surface ectoderm (primitive skin, the interface between the inside and outside world of the embryo) (p72).

Stage 2, 30-day-old-embryo: As the optic vesicles or bulbs continue to grow outward from the neural core, they become concave, cupping as if to receive the outside world they approach (these optic cups are the primitive retina, ground for the light sensitive rods and cones). Stimulated by the approach of the optic cups, surface ectoderm begins to thicken and invaginate into the cups (p72).

Stage 3, 33-day-old embryo: The optic cups continue to enlarge, encircling and grasping the thickened surface ectoderm. As if the optic cups were inhaling it, the surface ectoderm continues to grow into the cups until it has itself inhaled, encircled tiny globes of the outside world (these globes are the primitive lens, which will be able to change shape to accommodate vision from things far to things near in the outside world, just as if still remembering that outer place) (p73).

Stage 4, 42-day-old embryo: Immediately filaments grow to join each optic cup (continuous with the neural core) with each lens vesicle (bubble of outside other). These filaments provide a rudimentary blood supply called the hyaloid artery which nurtures the rapidly differentiating and growing primitive eye (this is gradually replaced by the circulatory system that is fully mature at eight months) (p73).

Stage 5, 100-day-old embryo: Once the hyaloid artery has firmly tied each lens vesicle to its optic cup, the cup releases its suction-like hold on the lens. As the lens floats free, its cells and those of the surface of the skin it moves toward become transparent like windows to the outside, to light. At the same time, nerve cell fibers are growing from the base of the optic cup back through the optic stalk to the developing brain (eventually over one million nerve fibers are formed that pass from eye to brain, making the optic stalk into the optic nerve whose transmissions are finally made vision within the brain itself). All the cells in the eye continue to mature until they are capable of responding in concert to light to create the complex of stimuli the optic nerve feeds back to the brain to produce vision (p73).

“If all the stages are put together in a single composite picture, they form a complex but consistent pattern of fluid dynamics. As the core moves outward toward surface, it also expands to cover a broader area. Seeping out past the surface membrane, it dissipates even more widely into space. As the outside moves inward through the surface membrane, it coalesces as if compacting the whole of the boundless outside into a tiny enclosed globe. Concentrating even more, it continues to stream into and through the center of the central core itself” (p74).

A composite metaphorical model for the dynamics of ‘seeing’ (p74).

“With abstraction, this model of a developing and ‘seeing’ eye can be used as a metaphor for a way in which any cell, cellular organism, or organism segment with a self-enclosed membrane or skin might interact with its environment or world outside it” (p74).

“This fluid-dynamics metaphor that describes ‘seeing’ serves equally well as a model for the pathways of connection between feet and ground in such activities as standing and walking. The sole of each foot functions like a retina that grows developmentally outward from the pelvis, central core structure of the body, down through the leg to spread the bottom surface of the foot in an ever-widening base of support that is ‘looking’ down and out into the ground. The ground itself is visualized as a transparent cornea through which light passes from the living earth beneath. The light enters the foot which receives the light in the curved space beneath its central dome. The light continues to travel up through the dome and into the central axis of the leg, thrusting the bones—like light beams—straight up into the pelvis they support.

“…I verbally suggest to students that they might visualize their feet (or any other parts of themselves) as if these were eyes ‘seeing’ in the way I have just described…” (p75).

Metaphoric ‘seeing’ with the foot (p75).

“Metaphor can be the fist that breaks through the dark glass between what is already known and what is still mystery.

“Through the vehicle of metaphor, we can participate in that movement from what is to what can be.

“Once in the new land on the other side of the dark glass, we can use the metaphor as a landmark from which to foray into the new world.

“Eventually the metaphor dissipates in explosion outward from its core into the space of new landscape. Finally another metaphor coils around the landscape, coalescing into a new vehicle in which we continue the journey” (p69).

Nine figures from Jonas Salk and Jonathan Salk’s 1981 pictographic essay, World Population and Human Values.

“In this essay, the sigmoidal curve will be used as a ‘thinking tool’ and as a symbol. Its shape reflects a law of nature that governs growth in living systems, and reflects the transformational character of change in our time” (p3).

The sigmoidal curve (p3).

“In this figure, and in those that follow, the horizontal axis represents time and the vertical axis represents number. In the first, upturned portion of the curve, population growth follows a pattern of acceleration; in the second part, growth decelerates and a plateau is reached. The gap in the curve emphasizes the point of inflection—the point of change from accelerating growth to decelerating growth” (p3).

“For thousands of years before agriculture, human population increased very slowly. In response to environmental adversity and population pressures, agriculture emerged, making more food available to support greater numbers of human beings. A pattern of gradual increase thus continued throughout the agricultural period. In the last several centuries, scientific, technologic, and industrial developments have further raised the carrying capacity of the plant, contributing to the recent sharp rise in population” (p27).

Human population trends (p27).

However, rates of human population growth, birth and death rates, fertility rates, population distributions by age and sex, median age, life expectancy, sex ratios, child/woman ratios, and other data suggest that the human population growth curve will follow a sigmoidal pattern. As well, “except for the sun as a constant source of energy, the earth can be seen as  a closed system and, by inference from the examples given [of  animal and yeast population growth in closed systems], we can expect the human population growth curve to follow a sigmoid pattern” (p23).

The following figure “shows the estimated increase in world population size in the period 1750 to 1975, with medium projections to the year 2200. This figure… illustrates the sigmoid pattern of human population growth and the estimated plateau at approximately 10.5 billion people. The high and low variants for the year 2125 are 14.2 and 8.0 billion respectively. The inflection of worldwide growth will become evident at about the turn of the century” (p64).

World population size (medium variant), 1750-2000 (p65).

From a longer-range perspective, the figure below “schematically describes the course of human population growth and population growth rates over a period extending from 8,000 years in the past to 8,000 years in the future. The curve indicates a plateau of world population at approximately 11 billion by the end of the twenty-first century and assumes that this level will remain or slowly decline” (p66).

World population size and rate of growth, 6500 B.C. to 9500 A.D. (p67).

“If these estimates and assumptions are valid, we can see that the present extended period of rapid population growth is unique when seen from a long-range perspective; it has never occurred before and is unlikely to occur again” (p66). “Intuitively, we sense from this image that, from a psychological and social standpoint, human beings may be better adapted to conditions associated with less rapid change (like those that existed in the more distance past and that are anticipated in the coming centuries) than they are to those that we presently experience” (p130).

“We use the sigmoid curve not only to represent numbers of human beings but also to provide a frame of reference for discussing the nature of human values, attitudes, and behavior before and after the point of inflection” (p73). “The difference in shape between the two portions of the curve suggests both quantitative and qualitative differences in human life between the two periods of time. It not only indicates differences in population growth patterns but also suggests differences in the characteristics of prevailing conditions and in the quality of human life in the two periods” (p74).

“In this figure, the two parts of the curve before and after the point of inflection have been separated for emphasis. One is designated as A and the other as B. The periods of time prior to and following the point of inflection are referred to as Epoch A and Epoch B, respectively” (p77).

Epoch A and Epoch B (p77).

“From the shape of the A curve, the future would appear to be unlimited in terms of growth and expansion of, for example, population, resources, and availability of energy. To someone born in Epoch B, however, the future would seem to be a time of multiple limitations with a ceiling on growth and expansion. The difference in shape between the two curves thus implies that there will be a fundamental, qualitative difference in circumstances between the two periods of time” (p77).

For example, “during Epoch A, because mortality rates were high at all ages, the control of disease and of premature death were of primary concern. Success in this regard has contributed to the recent sharp increase in population size. As a result of this, the concern in Epoch B can be expected to shift to the control of fertility and to a preoccupation with the enhancement of health” (p80).

Values of health in Epoch A versus Epoch B (p81).

Other changes in values and attitudes discussed by Salk include:

Epoch A Values Epoch B Values
quantity of children quality of children
persistent expansion of societies and industries dynamic equilibrium
extremes in growth and development balance
competition, independence, power collaboration, interdependence, consensus
either/or, win-lose both/and, win-win
present, short-range, parts future, long-range, whole

“This is a change from seeing the world as limitless in terms of growth to seeing it as limited. It is also a change from seeing ourselves in opposition to each other to seeing ourselves in collaboration with one another. It is due not only to a change in perception but to a necessary change in human attitudes and spirit that comes in response to a change in reality, as expressed by the shapes of the curves. The change from A to B can be seen in relationships to nature, our relationships to each other, and in our relationships to ourselves” (p94).

“Human beings possess the capacity for a wide range of attitudes and behavior. The idea underlying the preceding discussion is that those attitudes and behavior that are advantageous and therefore appropriate under one set of circumstances (the reality of Epoch A) may be disadvantageous and inappropriate under another (the reality of Epoch B)” (p101).

“In the region of inflection growth rates are highest, acceleration is changing to deceleration, and values are shifting most rapidly. This period can be expected to be a time of increased conflict” (p101).

The process of inversion of values (p111).

In the above figure, “the relative position of the two lines indicates that Epoch B values exist even in the period before inflection, but are less dominant than Epoch A values. In Epoch B, the relative dominance is reversed… [This] offers an explanation for the tension we feel at this time. It suggests that the conflicts are an inherent part of this developmental and evolutionary process. They are not necessarily a signal of an impending end of the human species but reflect the process of inversion that is now occurring” (p110).

“In the process of adapting to changing conditions, conflict may be most effectively resolved, as symbolized [below], with a both/and approach. For example, completely disregarding the technological and social developments of Epoch A in an effort to immediately halt growth would be inappropriate and unrealizable. On the other hand, attempting to resolve tensions by completely suppressing the tendencies of Epoch B would be equally disadvantageous. With a both/and approach, the developments that have been part of Epoch A can be combined with Epoch B values in order to develop solutions that are appropriate to changing conditions. A specific example of this might be the simultaneous short-term reliance on nonrenewable resources of energy with the long-term goal of reducing consumption and of developing efficient means for using renewable resources” (p112).

Resolution of tensions (p113).

“The patterns revealed in the preceding figures suggest that differing tendencies that have always been present in human beings have diverged in the course of the rapid changes of more recent history” (p134). For example, “at present, the tendency to make decisions based purely on material costs and benefits are in conflict with the tendency to base decisions on human considerations, such as quality of individual health or the quality of the physical environment. In contrast, economic decisions in the future will increasingly take into account both human and material value. The change will affect the nature of economic relationships and organizations in the years ahead” (p138).

Material value versus human value (p139).

“At this point, innovation in the area of human development and social relationships is as important as the advent of agriculture 10,000 years ago, or the understanding of microbes and machines in the past century. Just as some of the brightest minds of recent years turned their attention to the advancement of science and technology and to the prevention and cure of disease, many of the brightest minds of coming generations will turn their attention to the phenomenon of the human mind and the improvement of the quality of human life” (p164).

Klee on Pluralism

July 14th, 2011

A diagram by James Klee from his 1982 Points of Departure.

“The use of the word ‘dimension’ creates a peculiar difficulty in that it is not clearly pluralistic in nature. When we analyze we also unwillingly tend to objectify. So if a whole is analyzed into four parts one is tempted to think of ending up with four different entities. But if the analysis merely stresses four aspects we have not an objective pluralism but rather an existential pluralism. We have made the analysis and taken responsibility for the selective emphasis but the whole is not considered as disturbed. Rather we have paid attention to something less than the whole. We have restricted ourselves. The whole is not cut up into a multitude of fragments now independent of each other and of the whole” (p162).

Definitions of Body, Mind and Soul from a Phenomenological Point of View, p154. I have reoriented labels and legend to better fit this format.

The diagram “intended to show body, mind, soul, and matter as four differend [sic] questions or contexts about the whole instead of the resynthesis of four discrete entities. The yang-yin form was to show the ever changing relationships among the various aspects. One saw the aspects in different contexts so as to selectively emphasize mind or body or soul… If it had been a motion picture it could have emphasized the temporal dimensions even more than the yang-yin does although as a static symbol it tries hard and is occasionally successful” (p162, n*).

Nicholas on Cogito

April 4th, 2011

A diagram by J. W. Nicholas, from an appendix of his 1977 Psience (see previous post).

Cogito means ‘I think,’ but I interpret Descartes’s famous dictum as a contraction of, ‘I think about the I which thinks, therefore I am.’ Thinking requires an object. To think at all, one must think about something. The mystal no-mind is not achieved by suspending mental process but by eliminating mental content. The cogitating Descartes thought about thinking in a way that proved his existence as a thinker. I believe he thought about the I which thinks.

“Philosophers know the syllogistic conjunction ergo/therefore requires two premises to balance a conclusion, but Descarte presented only one premise—‘I think.’ His statement either fails as logic or transcends logic. I believe it transcends.

“The view that all knowledge is logically derivable gets one into a limitless proliferation of prior premises, an infinite regress, a reverse martingale, unacceptable to the practical cogitator. We need some premises that are not prior conclusions, or there will be no base on which to build the logical structure. I judge Descartes’s sum/I-am to be one such fundamental premise, needing no antecedent. As Ouroboros swallows his tails, so:” (p65)

Two diagrams from J. W. Nicholas’ 1977 Psience: A General Theory of Existence.

Self-realization of the universe (p59)*. Click for larger version.

“Psience posits four frames of reference [as shown in the figure above], two real and two imaginary. (If it were not for mathematical convention, these might be called the material and immaterial.) One real and one imaginary frame of reference are linear; I call them spaces; their dimensions are of interval. The other two frames are non-linear; I call them fields; their dimensions are of regular recurrence, here called frequence” (p13).

“The real and imaginary frames are formally orthogonal… Thought, spirit, the immaterial or massless in general exist as recurrent pattern in the imaginary field. The imaginary pattern induces its realization in the real field, which is reflected in turn in the real space. Symbols existing in the real field have a magical power to affect the phenomenal world, or real space, in a manner that recalls the power the three-dimensional beings to produce miracles in Flatland. The geometric inversion of linearity is held to be a closed loop, that is, a regular recurrence; induction between imaginary and real fields takes places between closed loops, as with electric current and magnetic flux. The real field (and perhaps also the real space) has more than three dimensions; the imaginary field and space have unlimited dimensions.” (p15).

“As the unlimited dimensionality of temporal interval is disclosed by the statistical independence of different relative likelihoods, so the unlimited dimensionality of temporal frequence is disclosed by the harmonies of recurrent pattern. Though the pattern is imaginary, it may still be useful. For example, we could define the structure of a chord in such a schema without reference to the key in which the chord were played… what Globus (1976) called ‘relatedness per se’. Such a pattern is perpetual rather than eternal, qualitative rather than quantitative, imaginary rather than material. It is defined by its own harmonies” (p27).

Outward and inward departures from Origin (p39).

“…As the point of access to 3d space, τ space, r field, or ψ field, Origin displays four respective facets: Here/Now/Everywhere/Always. [The figure above] depicts outward departures from Here and Now, inward departures from Everywhere and Always. Unlike Here and Now, which serve as zero points for quantification, Always and Everywhere confound and nullify all measurements. Qualitative rather than quantitative, the ψ and r fields disallow direct measurements but still provide a frame of reference in which to consider relatedness per se” (p38).

“Psience proposes an inductive coupling between the orthogonal ψ and s fields—between the domain of imaginary, immaterial pattern and the domain of its symbolic representation. What is symbolically represented is relatedness per se. We can label the two arcs of this interactive feedback loop ‘expression’ and ‘communication’ [as figured above] (p58)”.

Hence “creation is the self-realization in the real field of relatedness per se in the imaginary field” (p62).

* I believe the top figure mislabels linear to the left of u-space, implying that both u-space and s-field are linear, whereas it is u-space and τ-space that are linear (as dimensions of interval). Perhaps a correct label would be spatial, as opposed to temporal, though this blurs the denomination of dimensions of interval as -spaces.

Three diagrams from Nahum Stiskin’s 1972 The Looking-Glass God.

“The principle of dualistic monism is based on the intuition common to all men that things, phenomena, and beings are in a dynamic state of change and that life is process. Plants, men, and ideas all bloom in their season and wither in their season. Day changes into night, and night returns to day; the seasons run their course; Time, the enumeration of this change, stops for no man. In daily life we find no constant.

“The course of this change, however, is not erratic. We find ourselves living in a world of extremes. From midnight to midday, from the heat of summer to the cold of winter, from joy to sadness, all movement is along a continuum from one extreme to its opposite. Judging from our experience, we deduce that the universe is constructed on a plan of polarity: beginning and end, male and female, expansion and contraction, ascent and descent, life and death. Process occurs as movement between these poles of the universe.

“Although at first view nature’s poles present themselves as opposite and mutually antagonistic, on closer inspection we realize that they are complimentary; one cannot exist with the other… If movement in either direction were to stop, life would cease… The universe and our knowledge of it are therefore constituted of the endless to-and-fro movement of life from any pole to its complimentary opposite…

“Let us devise a practical language to use in discussing the structure and inner workings of polarity within the universe… that of yin and yang, derived from ancient China. But this is not to say we are simply expropriating that ancient philosophy as it was defined and used by Fu Hsi some five thousand years ago. We can and must redefine this terminology in such a way that modern man can make rational sense of it. This ancient principle of relativity is not a mysticism but a paradoxical logic of the universe.

“We shall designate as yin all phenomena, beings, and things that are dominated by centrifugal force, and as yang those dominated by centripetal force. Centrifugality can be most easily imagined as the tendency to move from a center toward a periphery; centripetality is movement from a periphery toward a center” (p20-21).

Yang centripetality and yin centrifugality (p21).

“Using our newly defined principle, we will categorize density as a yang phenomenon in comparison to expansive airiness, which we shall consider a yin phenomenon. By extension, a proton, having weight and density, will be classified as yang in comparison to an electron, which, having relatively little weight and density, will be classified as yin. Movement away from the center of the earth would express the yin tendency; movement toward the center, the yang. Verticality with reference to the earth may be considered an expression of yinness, horizontality an expression of yangness. Based on this latter concept, colors may be classified as a series of changes along the continuum from red to violet. Red describes an electromagnetic wave of low amplitude and frequency that may be said to be dominated by centripetal force. Violet describes a wave of much higher amplitude and frequency and, in comparison, may be said to be dominated by centrifugal force [see the figure below]. Heat and light are ‘centered’ phenomena: their existence presupposes a point of concentration in space and thus may be said to be yang. Cold and darkness are ‘dispersed’ phenomena: they originate at a peripheral nowhere and permeate space, and therefore may be said to be yin. Fire is yang; water, its antagonist, is yin. Shapes, too, may be classified. Shapes like △ contain their greatest bulk toward the bottom. Their movement is downward, and they are thus dominated by the yang tendency. Shapes like ▽ express a centrifugal movement upward and are dominated by the yin” (p21-22).

The continuum from yang red to yin violet (p22).

“If, then, the operation of yin and yang is at the core of nature, what fundamental shape will all entities and processes share? A symbolic representation of the principle of dualistic monism would have to fulfill the following seven requirements: first, it must display a polar structure of the relative world by indicating such things as beginning and end, above and below, periphery and center; second, it must link the two poles of existence indissolubly by showing them to be but the two complementary ends of one continuum; third, it must indicate the stages of change; fourth, it must show the variations of yin and yang within each stage; fifth, it must indicate the change of velocity within the process of change itself; sixth, it must demonstrate the potentiality for simultaneous movement in opposite directions between any two antagonistic poles; and seventh, it must indicate the original source of evolution and show that all evolved entities ultimately return to that source. In so doing, it must reveal the connectedness of the absolute and relative worlds, thereby demonstrating that all dualities are only modifications of an originally unified essence” (p28).

The logarithmic spiral (p29).

“The only pictorial symbol that can fulfill all seven conditions is the logarithmic spiral and its three-dimensional analogue, the helix. The spiral is a two-dimensional structure; the helix is its three-dimensional extension into space. The coils that curve along the ordinary screw exemplify helical structure. Thus, [the figure above] may be viewed in depth, with the periphery near to and the center far from the eye.

“We see in [this figure] that the polarities of both beginning-end and above-below are clearly expressed. We further note that in a logarithmic spiral the center is dense compared to the expanded periphery. The movement from beginning to end within any process follows the line of the spiral from periphery to center. The coils are thus the continuum. All things, phenomena, and beings begin at the periphery and move toward the center.

“The spiral may be portrayed with six or seven coils; each represents either a different stage from inception to conclusion of a process or different elements in the structure of an entity. Analysis into seven or eight parts is usually sufficient for an adequate explanation of the structures and processes within nature… By drawing a line through the spiral and dividing it in half, we see the variation of yin and yang within each stage.

“Since the distance between coils decreases logarithmically, it requires less time to travel from points C to D than from points A to B. This is equivalent to saying that processes speed up toward their conclusion or, in terms of entities, that density is a characteristic of center.

“If we take the empty space between the spiral’s coils to constitute another spiral—this one originating at the center and moving toward the periphery—we shall have indicated the simultaneity of antagonistic tendencies. We shall have also shown the dialectical identity of beginning and end, for the end point of one spiral is the origin of the other.

“Finally, the empty space surrounding and leading into the spiral may be conceived to be the invisible, infinite sea of energy. The world of polarity splits into being at the first point along the periphery of the coil and returns to its origin along the inner spiral” (p28-30).

The Double-Triadic Hexagram

September 30th, 2010

Eight glyphs from Barbara Walker‘s The I Ching of the Goddess whose sequence derives the hexagram.

Figure 1 (p17).

“The original triangle stood for the Goddess’s trinity of Creator, Preserver, and Destroyer, she of a thousand names, such as Maya the birth-giving Virgin, Durga the preserving Mother, and Kali Ma the death-dealing Crone. Her primary symbol was a downward-pointing triangle, the Yoni Yantra, sometimes called Kali Yantra. This represented a vulva (Sanskrit yoni), and femaleness in general: by extension, a womb, motherhood, female sexuality, the life spirit embodied in menstrual blood, or the world-activating power of the Goddess herself. The same symbol stood for ‘woman’ and ‘Goddess’ among ancient Egyptians, pre-Hellenic Greeks, Tantric Buddhists, and the gypsies who migrated westward from Hindustan. The primordial female triangle became a male-female hexagram by eight stages, graphically represented as follows.

“At first there was only the Goddess alone, containing within herself all the elements in a fluid, unformed state (Fig. 1)” (p16-17).

Figure 2 (p17).

“With the passage of ages and by her will, eventually a spark of life was formed within her core, represented by a dot (Fig. 2). Tantric sages called this spark the bindu, and one of the Goddess’s titles was Bindumati, Mother of the Bindu. Among Cabalists it became Bina, the Womb of Earth” (p17).

Figure 3 (p17).

“The bindu grew and slowly became a separate being within the Mother (Fig. 3), though it still lay wholly inside her borders. At this early stage of the divine creation, the sages said, darkness (the god) was still enveloped in a greater Darkness (his Mother). The god was still one with the author of his being, Maha-Kali, the Great Power” (p17).

Figure 4 (p17).

“At the fourth stage, the god was born. Represented by an upward-pointing triangle—which often symbolized the masculine principle of fire—the god broke through the boundaries of the primordial maternal triangle (Fig. 4). Here, at the moment of ‘birth,’ the idea of the male deity was conveyed by three solid lines, while that of the female deity became three broken lines. Thus was the design taken apart, and its components utilized as trigrams and hexagrams in the I Ching” (p17).

Figure 5 (p19).

“In allowing her boundaries to be penetrated from within by an emerging Other, the Goddess demonstrated her true creativity. She became the universal Mother. This crucial moment of birth was synonymous with creation, according to the ancient concept. This was the moment when the Goddess (not the emerging God) said, ‘Let there be light,’ because the eyes of her newborn first perceived the light of existence, as he himself might become the light of fire or the sun. In the classical world, the Goddess had names like Juno Lucina or Diana Lucifera, the Bringer of Light. From her the biblical Yahweh copied his Fiat lux.

“The god’s birth was celebrated each year at midwinter. The nocturnal festival was known as the Night of the Mother to pre-Christian Britons, which may explain why Christmas Eve (the time of the actual birth) carried even more significance in Old England than Christmas Day. In Alexandria, the god’s birth was hailed by joyful shouts: ‘The Virgin (Kore) has given birth! The light grows!’ The naked image of the divine birth-giving Virgin was decorated with gold stars and carried seven times around the temple.

“Just as, in pagan belief, creation was a birth, so every birth was a new creation. Each year the Aeon or year-god was reborn from the eternally virgin, eternally maternal Goddess. Thus, at the mystic point of creation itself, the graphic symbol of the Mother became three broken lines, while that of her son-spouse was three solid lines.

“Male and female triangles, one separated, came together again in a very ancient figure that later rounded off to the mathematical symbol of infinity in so-called Arabic numerals, which were actually Hindu in origin. The two tangential circles or teardrop shapes of this sign meant the same as two tangential triangles: the two sexes in contact (Fig. 5). The female triangle above now took on the aspect of a nourishing breast, while the male received her nourishment.

“This was also taken as a sexual sign, in unconscious but nevertheless real recognition of the connection between adult sexuality and bond between mother and infant. According to Tantric symbolism, the female triangle was placed above the male, who then assumed all forms of relationship with her: offspring, twin, spouse, and eventually sacrificial victim, as he became the eternally dying-and-reborn god, similar to Osiris, Attis, Dionysus, Adonis, Orpheus, Yama, and so on. Therefore Tantric yogis and their shaktis (priestesses) favored female-superior sexual positions, which Vedic and Confucian patriarchs condemned because of their association with the Old Religion that they wanted to erase. Though this style of lovemaking was instituted by Shiva as Universal God and the original ‘daughters of the sages’ (shaktis), patriarchal Brahman priests insisted that it was a perversion” (p17-18).

Figure 6 (p19).

“However, Tantric yogis continued to hold that sexual union in true love was an intimation of divinity, giving the partners a sense of merging ‘like pouring of water into water’ (Fig. 6). Similarly in Egypt, the Goddess and her god were represented by vessels of water, their conjunction by a combination of the two waters, as in the sacred talisman known as menat. In the Middle East, a sacrificial god was preceded by a vessel of water in procession to his place of execution, a tradition that was followed even in the story of Jesus (Mark 14:13). Like Shiva, the Christian God also was born of the same Mother on whom, as a divine spouse, he begot himself” (p18-19).

Figure 7 (p19).

“By penetrating each other to the farthest boundary, god and Goddess formed between them the ancient Tantric symbol of the world and also the yoni: a diamond (Fig. 7), flanked by four new triangles that were assimilated to the elements, the four directions, the four corners of the earth (when the earth was supposed to be square), the four winds, the four divisions of the zodiac, the four Sons of Horus, or the Norsemen’s related spirits of north, east, south, and west that upheld the heavens. Sometimes this symbol represented a family or clan. All these ideas could be expressed in a simple glyph of six lines” (p19).

Figure 8 (p19).

“Finally, the ultimate interpenetration was shown by the full hexagram (Fig. 8). Male and female principles extended even beyond each other’s boundaries, becoming ‘one’ in sixfold symmetry. This was the union proposed by cabalists as well as Tantric sages: the symbol of eternal conception and re-creation. This was the hidden reason for the rabbinic traditions claiming that the Ark of the Covenant contained male and female images sexually joined, ‘in the form of a hexagram,’ and that the triple six of Solomon’s golden talents (1 Kings 10:14) represented the king’s sexual union with his goddess, who gave him his great wisdom.

“This explains also the early Christian’s horror of the sixfold symbol of Aphrodite, similarly united with Hermes as the first ‘hermaphrodite,’ and their insistence that three sixes made a devilish number (666) and six was the ‘number of sin.’ However, such sexual joining was envisioned for the male-female Primal Androgyne common to ancient India, Persia, Greece, and Rome. Even Jewish patriarchs declared that Adam and Eve were androgynously united in one body until God separated them.

“The ultimate absorption of the god into the Yoni Yantra (Goddess) was his immolation, usually conceived as a voluntary sacrifice of his life for salvation of the earthly world, which needed the life-force inherent in divine blood. As Kali the Destroyer, the Goddess devoured her consort and returned to the original solitary female form of the Yantra (Fig. 1). Thus the cycles of creation and destruction were carried on throughout the life of universe” (p19-20).

A diagram from Odhams Press’s 1955 The Wonderful Story of You: How Your Body Works, How Your Mind Works.


Mind a mere by-product of body


Body a mere precipitate or condensation of mind


Mind and body on parallel lines, but no connection between them whatever


Mind and body two aspects of the same reality


Body alone exists. Consciousness is merely a physiological process


Mental processes alone exist


The view of Common Sense. Mind and body both exist and act and react one with the other

“Obviously mind and body influence each other to a very great extent, and many theories have been put forward to explain how they are related. Some of the most important of these theories are illustrated in diagram form above” (p197).

Various Forms in Play

June 23rd, 2010

A diagram from Rawson’s The Art of Tantra (see previous post) delineating “the essential process… whereby man’s world of reality is developed… as it is conceived in the… Sankhya philosophy of Tantra” (p181).

“Sankhya Tattva diagram, illustrating the manifestation processes of creation” (p182), cf. earlier post on the three gunas. Click for larger version.

“Many Hindu Tantrik images represent the first division of the creative urge into male and female, white and red… Without the division there can be no love, no activity or field of action, no puja can be made… Since the time of the oldest Upanisads, subject and object have been called ‘I’ and ‘This’… equated with male and female, Siva and Sakti, male and female dancer…

“The lower levels of the Sankhya diagram define all the various sub-functions and categories through which the original flow of Being-energy is channelled and subdivided to make up the experienced world of forms and time. It is, in fact, a full phenomenological ‘synthetic a priori‘ system, and it matches the pattern of the subtle body remarkably… An important point has always to be remembered. In every experience of every objective ‘This’ by every experiencer the female quantifier is absolutely necessary; but so too is the male reservoir of energy, which supplies the ‘Being’ from the side of the objective, the unitary consciousness of self from the side of the experiencer. Within every yoni, every active world-as-woman, is buried the lingam, the phallus, without which there would be no energy to inflate her pattern. To a primary male spark of Being (Prakasa) the Goddess offers Herself as the ‘Pure Mirror in which He reflects Himself’ (Vimarsa). There are innumerable icons in India which represent the Divine Pair either as a male and a female, He with erect organ, She holding a mirror, or as a single double-sexed being, divided down the centre, the right half male, again with an erect organ, the left half female.

“Philosophy, however, must not be allowed to delude itself with its own constructions. Whilst it may theoretically assume an original spark within the reflection, the moment it seeks to attribute to that spark any character or form it falls into delusion. For: ‘Whatever power anything possesses, that is Goddess… Into the hollows of her hair-pores millions of cosmic eggs constantly disappear… She grants the desires of sadhakas by assuming various forms in play.’ But ‘She who is absolute Being, Bliss, and Consciousness may be thought of as female, male or pure [neuter] Brahman; in reality she is none of these.’ Even these are simply forms She assumes to make sadhana possible” (p181-183).