Mathological Dialectics (The Evolution of God)



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Ernest Holmes describes how the law of mind, the feed back system that emerges from the realm of Air as it generates Earth, creates the Water element, he calls this aspect of mind “race thought,” Jung called it the collective unconscious.” If Holmes describes the law of mind (this is the Dharma of the East that reacts to the Karma that is the activity of the Fire element), the emergence of the Air Element into Fire, Water, Earth through the Thunder Trigram are described in John Gribbin’s “In Search of the Mulitiverse,” in respect to physical science, and in Bernhard Rensch’s “Evolution above the Species Level,” and in the papers submitted for the Univesity of Chicago Darwinian Centennial, edited by Sol Tax at the life science level, and for the social sciences in Arnold J. Toynbee’s “A Study of History.” There are many references to the processes by which the mind becomes the source of the salt crystallized by the water element and dissolved in the collective unconscious, one of the better discussions of the process by which this salt aspect of the water element relates to the heaven aspect of the earth element can be found in the Quantum Mind by Arnold Mindell.

The expanding circle, sphere that is defined by pi as the infinite curve of the boundless seeking to integrate each infinitesimal monad of the now is the symbol of the realm of Eternal Objects, of the Air Element of the Wind Trigram that penetrates to the core of all things. This sphere is the Sun, as Aton, as the symbol of the One. The symbol “e” represents the natural expansion of the energy released by emergent processes and “i” represents the root that turns inward from the external world of information to the internal world of knowledge, from external energy to internal passion, from external integration and disintegration to internal pleasure and pain, from external time and space to internal dreamtime voices and visions. Hidden in this relationship is what Ernest Holmes calls “Your Invisible Power,” and James P. Carse calls the “Infinite Game.” Just as you cannot know the position and speed of an electron at the same time, so you cannot know the scientific truth about an object in the realm of actual occasions and its relationship to metaphysical and theological truth at the same time. God is hidden in the infinite future and the infinite past and only God’s shadows enter the realm of visible time and space.

Whether God created the world or the world created God, whether God created Man or Man’s brain created

God, are irresolvable questions because they exist in the realm of complementary transcendence, in the realm of the irresolvable complementary relationship of the infinite and the finite, the open and the closed, the simple and the complex, the necessary and the contingent. They cannot be resolved because they are an endless process and the observer and the observed, the knower and the known, the thinker and the thought belong to that endless cycle. This is what Holmes attempts to explain in mystical and theological terms in “This Thing Called You.” Thomas Merton does the same in respect to Catholic Theology, in his “Seeds of Contemplation.”

The Earth Trigram belongs to ordinary arithmetic. Old daughter yin provides the zero point center from which the units of time and space are calculated on a rational basis into the normal curve that is young daughter yin in the individual separate units that are middle daughter yin. Ultimately, science will transform these units into atoms, subatomic particles, quantum events, which can be measure on the axis of time and space that curve into the speed of light defined universe of Einstein’s relativity in the summation of young daughter yin. But the endless progression of thermodynamic energy, its expansion in “e” leads to the thermodynamics that is old son yang. The calculus of its functions and integration in “pi” of the endless curves of everything (middle son yang) is the infinite flux that makes the improbable probable in the imaginary number of the dreamtime monad of subjectivity that is top son yang, generating the creativity and subjectivity of the Heaven Trigram as the complement to the predictable and knowable Earth Trigram. Heaven Trigram is the realm of dreamtime creativity, of the Unknown God that becomes what he/she becomes. This is the realm of the boundless and the immeasurable, of the theology and the metaphysics of the transcendental, of the Eternal Christmas of the Heart. Life is a constant complementary interaction between the meaningless facts of the left hemisphere world of the expanding nothingness of science and the meaningful mystery of the right hemisphere world of the growing significance of the infinite game integration that is the source of love and bliss in the discovery of the circle that endlessly expands to beautify and illumine and include all things in the Buddhamind that is the Aslan Narnia Jesus of the Sufi One Allah Brahman whole.

Bakersfield, CA. Allan Ralph Andrews, May 4th 2012

Now let us consider Euler’s “e” to the “i” x pi power plus 1 = 0. If we look at the cube of personality disorders and I Ching trigrams, the imaginary number, square root of -1, is the young son yang, schizoid personality disorder and the = sign is its dependent personality disorder young daughter yin opposite. The number 1 is the narcissistic personality disorder that is middle daughter yin, with pi as the avoidant personality disorder middle son yang opposite, the circle drawn according to pi is forever avoiding the straight path, while the number one is forever asserting itself as the only on. The imaginary number is endlessly withdrawing into its imaginary complex inner roots, while the equal sign sets out measurable parameters in the public world of relative time and space, a world where we are dependent upon public measurements to find our way. Finally zero describes the compulsive personality disorder world of old daughter yin that continues to add measurements until there is nothing left at all but the measuring stick. The opposite of the compulsive world of old daughter yin is the antisocial personality disorder of old son yang that continues to expand itself in the natural log base “e” regardless of its effects upon other entities around it. It is irregular and refuses to conform to all rational rules and conventions.

The numbers set out the trigrams. The realistic trigram of Earth and science belongs (the realm defined by middle daughter yin 1 and oldest daughter yin zero and youngest daughter yin and the system of equivalent (=) ratios, the natural numbers) to arithmetic and the coordinate systems and measurements described by natural real numbers. This is finite realm inhabited by realism and the depressive personality disorders. Its opposite is the realm of calculus and the schizotypal personality disorders, a realm ruled by curves lines in middle son yang pi and progressions in old son yang “e” and the imaginary number plane in young son yang.

Emerging from this realm of magic is the Wind Trigram that belongs to metaphysics and penetrating necessity in imaginary numbers and pi rooted in the zero point axis of the wheel of all things. This is the realm of Higher Algebra, of Euler’s Formulas, of Mathematical Proofs and systems, and the Classical basis of Mathematical Idealism, the Eternal Objects of Alfred North Whitehead.

This kingdom is ruled by the paranoid personality disorders. The opposite of this kingdom is the realm of histrionic personality disorders and pragmatism, of business and economics. This is the realm of probability and statistics. It is ruled by narcissistic middle daughter yang number one and dependent youngest daughter rational number equivalents, as well as oldest son yang “e” progressions that generate the principles of probability and statistics and rule the realms of contingency. If Heaven Trigram is magical and romantic, and Wind is classical, if Earth is realistic, this the realm of expressionism (particularly the histrionic variety).

Running counter to this axis, the axis of God in Heaven Trigram, Eternal Objects and the Form of the Good in Wind Trigram, actual occasions and measurable objects in Earth Trigram, and their shadows, expressions, continent aspects in Thunder Trigram (note the similarity to Alfred North Whitehead and Plato’s Divided Line).

Flame (or Fire) Trigram takes old son yang and young son yang to the narcissistic excess of middle daughter yin. This is the opening in all systems, the realm of art and design, of the mathematics of topology, this is cubism in art and the sadistic personality disorder in behavior. It is competition and natural selection and extinction in the realm of biology. The opposite of this realm of the open is the Baroque realm of the mechanical and the closed, of Water Pit Abysmal Trigram. It is the realm of absolutistic government and law, of the police. It is the masochistic personality disorder as the complement to the sadistic personality disorder. It is rational numbers and set theory and logical proofs in mathematics. It is ruled by old daughter yin zero and the young daughter yin = sign integrated and turned on itself by the middle son yang circles ruled by pi. Mountain trigram is the realm of trigonometry and analytic geometry, set out by the imaginary number plane, by middle daughter yin in 1 and old daughter yin in 0, extended into imaginary numbers by young son yang. It is the realm of philosophy and logical debate and empiricism, of negativism in personality disorders and impressionism and formalism, of conceptualism and abstraction in art. It is the realm of the simple.

Its opposite is the Lake Trigram, the realm of group theory in mathematics, of complexity, set out by the progression in e of old son yang, in equivalent relations and series of young daughter yin, and the inclusive circles defined by pi in middle son yang. This is the realm of literature, of Marxist and Hegelian dialectic, of religious dogma and ideology. It is syncretism, post-impressionism, symbolism in art. It is the Jungian collective unconscious and the complement to the empirical mind of Mountain Trigram. In biology it is syngamy, recombination, and population genetics. In behavior it is the borderline personality disorders (in which personality lacks good boundaries and generates complex fusions and dependencies).

Allan Ralph Andrews, Bakersfield, Ca. May 5th 2012

The narcissistic one, the middle daughter yang, becomes the verbal ego, the fact and language oriented area of the left hemisphere of the cerebrum and the avoidant pi, becomes the middle son yang, that bends everything into circles of meaning and integration, this is the myth generating right hemisphere of the cerebrum. The square root of minus one, the imaginary number plane, is generating out of the future predicting planning areas in the executive areas of the frontal lobe, the centers for young son yang. Young daughter yin, the rational number association scales, belong to the cerebral association areas of temporal lobe (sound), occipital lobe (vision) and parietal lobe (space) in posterior area of the cerebral cortex. Zero point old daughter yin, central point in the information axis is in the hippocampus of the cerebral cortex, old daughter yang, and the progression of attention is in the amygdale, thalamus, hypothalamus and brain stem areas, underneath the cerebral cortex of the brain. Thus, the axial nodes of the brain correspond to the axial nodes of the world. Here is another complementary relationship between observer and observed, knower and known that involves process, where neither element is superior or prior to the other.

Consider some of the typical trinities. For example those of Buddhism. The trinity of suffering, flux, and no-self, or the suffering coming from the narcissism of 1 and the flux coming from the greed of e progressions and the no self coming out of the = of all attached things, for which the solution is the Sanga, or community of all (=) dependence in the Dharma (zero) compulsive adherence to the Buddha of nirvana-buddhamind compassion in the inclusive circle of pi. Or the trinity of the dance of Shiva in antisocial destruction in the progress of “e” as Karma, and the boundless inclusiveness of that in Vishnu as the Brahman One in the boundless circle of pi and finally Brahma as the creativity of the square root of minus one in the complex number/ imaginary number plane. Atman is that imaginary number root discovering itself as part of the Dharma zero axis of the wheel of all flux that belongs to the ever inclusive pi curve of the Brahman One. The imaginary number is the logos mind of Christ in the Christmans manger and Aslan in Narnia as part of the information potential of the Whole Spirit in Zero and the inclusive circles of God as inclusive love in pi. The trinity system of Ernest Holmes in the science of mind is the trigonometry of 1 as the narcissistic ego body and zero as the blank information mirror on which it is reflected as a shadow of the activity of imaginary and complex numbers in the creative spirit of complex and imaginary numbers, as described in Quantum Mind (see above). In a sense, Buddha is the schizoid discovery of the pure sattva guna of the imaginary number root within the antisocial karma activity of rajas guna in e progressions and the tamas of the body in 1 narcississim. Following the Zero path focal compulsion Dharma of the pure law, Buddha sees the pure compassion of the ever expanding Nirvana pi circle of love that extends out endlessly gone gone gone utterly beyond in to avoidance of all desire and attachment to the world.

May 5th 2012 Allan Ralph Andrews, Bakersfield CA.



Arnold Mindell develops these ideas in Quantum Mind. On p.36, he discusses counting, the middle daughter yin of our system as 1 and the younger daughter yin as a rational system of numbers. This sets up the Earth Trigram realm. “Consensus reality” is what Mindell calls it. It was called “Actual Occasions” in the terminology of Alfred North Whitehead. The negative number field that Mindell discusses on page 82, opens us up to the realm of Mountain Trigram, the mind as the observer, what Alfred North Whitehead calls “prehensions.” The complex number field, on page 99 opens up the Wind Trigram, the realm of Alfred North Whitehead’s “Eternal Objects.” The imaginary number belongs to the root of minus one, to what we call youngest son yang. Youngest son yang rules four sectors, the Heaven Trigram that belongs to Alfred North Whitehead’s “God” and is the realm of Arnold Mindell’s dreaming, “the dreamtime” of African and Australasian aboriginal thought, the Wind Trigram, equivalent to Plato’s Form of the Good, and the Mountain and Fire/Flame Trigrams that are the equivalent of the Pneuma/Psyche/Soma and Sattva/Rajas/Tamas trinities that rule the mind and will. On page 101 Mindell shows how a + ib = complex number shows the object perceived by the mind and made a part of its Non-Consensus Reality. In Alfred North Whitehead terms, the Actual Occasion is “a” and its perhension (perception in Mountain Trigram mind) is “b” and its subjective (Heaven Trigram imaginary element) is the first part of “ib.” The “+” element is activity in the rajas guna, in old son yang mathematical development (what we call Fire/Flame Trigram) and the ideal form of this is the entire equation a + ib = which is pure Eternal Object, pure algebra, pure Wind Trigram mathematical idealism rooted in the complex field coordinates rooted in the zero point that is the core, the central axial point of old daughter yin, the systems and law giver, the Dharma order, the pure law of mind, the Psyche core of rational subjective mind (see Science of Mind, by Ernest Holmes, where the charts in the appendix show the pure trigonometry of these relationships). On page 125, Mindell begins to chart the death of Nature, of the Earth in Earth Trigram, as a result of her separation from Non Consensus reality in Heaven Trigram (the imaginary number and complex number field, the dreamtime self). The uncertainty and complementary relationships described in the chapter that begins on page 203 are the Flame Fire Trigram aspect of our system, where old son yang “e” generates progression that pull the novel from imaginary numbers and complex number fields in “dreamtime” Heaven Trigram to generate the observations, the prehensions, the trigonometric calculation and analytic geometry of Mountain Trigram. With calculus and pi comes the interconnectedness of all things that allows the realms of set theory and group theory to generate the collective order of things in Water Pit Abysm Trigram and Lake Trigram water element, the synchronicity of Jung’s system. This is the realm ruled by middle son yang and the Brahman Nirvana Sufi Allah One, the God of Spinoza’s Ethics.

The God of Spinoza’s Ethics is pi and the monad of the Monadology is the imaginary number root of minus one. Cartesian analytic geometry contributes the zero point coordinates and the result is the Form of the Good, the mathematical ideal in Euler’s formulas and equations. Old daughter yin is the wisdom, the Santa Sophia, the Dharma, the perfect rational order potential in all systems and all things, the psyche and the nous of platonic philosophy. Young son yang is the creative element of the complex number field that generates the stimulus, the Atman of Atman, Dharma, Brahman, the Sattva of Sattva, Rajas, Tamas, the Pneuma of Pneuma, Psyche, Soma. This is Brahma as the Creative Spirit.

Pi is Vishnu as the Brahman one that integrates all of this in the boundless curves of calculus. Old son yang is the mathematical progressions that develop all of this out of the infinite flux that makes the improbable probable to base “e.”

Allan Ralph Andrews, May 5th 2012, Bakersfield, California.

On page 20 of Roger Penrose, “The Road to Reality,” you will see the basic trigonometry of this system where zero in oldest daughter yin represents the “Platonic mathematical world,” and the imaginary number square root of minus one in youngest son yang represents the “mental world” and 1 in middle daughter yin represents “the physical world.” Everything in “The Road to Reality” is simply an expansion of this system into the Tamas Guna of the physical, the Soma of the physical, that expands the Wind and Mountain Trigram into the Earth Trigram through the progressive activity of base “e” and old son yang in the Heaven, Fire/Flame, and Thunder Trigram to generate the order and synchronicity of water element in Water Pit Abysmal and Lake Trigrams. It is one and the same with the “Perennial Philosophy” of Aldous Huxley and the Platonism and Stoicism of Cicero, Epictetus, Marcus Aurelius and Plotinus. The One of Plotinus is the pi of integration and middle son yang. The mind and reason of Plotinus is the zero axial point and the coordinate fields and systems of old daughter yang and the phenomenological observer, the monad soul, is the imaginary subjective element, the complex number field rooted in the square root of minus one creativity of the private monadology and phenomenology that is the dreamtime self. The Road to Reality is simply the emergence, the development of the calculus of progressions in “e” into the Earth Trigram and the Thunder Trigram of the natural world. Through the trigonometry in the appendix to Ernest Holmes, Science of Mind, and the coordinates and trigonometry of physics in the Road to Reality and the mathematical extensions of the equations of Euler in “Dr. Euler’s Fabulous Formula,” we see the Mountain Trigram, Earth Trigram, Wind Trigram systems that is extended Water Pit Trigram and Lake Trigram to generate the order shown in “Cosmos and Psyche” by Tarnas.

May 6th 2012, Allan Ralph Andrews, Bakersfield, CA

Somewhere I have the reference to a website that discusses the different kinds of immortality, none, pantheistic, weak pagan, reincarnation (strong pagan), philosophic (platonic and Pythagorean, East Asian), and finally Christian (resurrection, etc.). No immortality is the immortality of narcissism, everything is the number 1 as the proud body ego, which must finally die and is the source of Buddhist suffering in its death. The solution for the Buddhist and the Hindu is pi, is the calculus of the boundless curves that include everything in the ultimate compassion of the gone gone gone utterly beyond nirvana that is (in Christianity and Hinduism and Islam) the God of endless love and bliss, and is also the pantheistic God of Spinoza’s Ethics, this is pantheistic immortality, or its Buddhist Hindu Platonist equivalent. So mortality in middle daughter yin finite time span is opposed to boundless space time infinity in middle son yang pi curve calculus integration of all possibilities.

The alternative is the eternal monads of the Monadology and the eternal souls of Pythagoras and Plato and Plotinus in the complex number field centered on the youngest son yang of the square root of minus one, its opposite is the weak reincarnation of paganism in which these souls complex together in various number fields to control their connection to bodies in space and time in younger daughter space time relativity yin (it is the reincarnation of Chinese Daoist folk belief). The final opposite is the Karma, the cycles of reincarnation and samsara that are standard theology in Eastern Religion and philosophy as a old son yang turning of the Dharma wheel. The opposite is the wheel itself as the perfection of pi and the curve of love. This reincarnation is the Classical Idealism of Dante in his Divine Comedy and the Christian home of the Narnia series, and the descriptions of Heaven and Hell in the works of C. S. Lewis, and other Ideal visions of the like. Included here would be the ever coming Kingdom of the theology of Wolfhart Pannenberg in which the ultimate Christian Father and Logos appears to sleep till the final days as a potential, a seed hidden in the Zero point that is divine rational potential in the oldest daughter yin, waiting for his/her awakening at the end of all “e” flux time in oldest son yang.

Allan Ralph Andrews, Bakersfield, CA, Sunday May 6th 2012

Now here is an interesting point. Oldest daughter yin is the compulsive point, she is the ever faithful Virgin Mary Queen of Heaven, she is holy wisdom, Santa Sophia, she is adherence to the true law, the true Dharma, the true Koran, the true Vedas, the true Holy Scriptures, the true law of Moses. She is the faith of all faiths, “In my house are many mansions” that adherence to the law of God will bring his kingdom, according to Wolfheart Pannenberg, will bring the existence of his Kingdom, allow him to exist in the visible world out of the potential of the Infinite Future. Remember how this works, infinite flux in old son yang and middle son yang makes the improbable probable in young son yang. This is the true Brahma as the creative logos word, the ultimate hope made flesh.

The idea of a written law for the Jewish community to keep them pure and holy probably goes back to the expansion of the Persian and Carthaginian Empires, described by Arnold J. Toynbee, on page 238 if Volume 5, part one of his “A Study of History.” It is probably the Phoenician alphabet and their practice of writing on scrolls that is the source of the Jewish idea of a holy book that contains God’s prophecy. The idea of a single God over a single divine king (David, Christ, etc.) may come out of the older Egyptian Empires. The notion of a war between Heaven and Hell, between God and Satan, seems to come out of Persia. The notion of the ever coming kingdom embodied in the trinity and the Christian Church is an attempt to accommodate these Syrian area civilization to the Hellenic notions of the Roman Empire. Even so, these symbols, however pale, are still shadows of the eternal wisdom potentials stored in the kernel of old daughter yin and drawn out by the “Infinite Game” (James P. Carse) danced out by “e” extensions in old son yang. The Jewish, Muslim, and modern Hindu traditions, even Buddhism, simply provide different version of this ancient dreamtime storyline.

Allan Ralph Andrews, May 6th Sunday, 2012

Arnold Toynbee in his “Study of History” discusses these points of view in respect to the great civilizations. He points out that Western Civilization has always been seen as focused on the technical and the scientific. It contrast, its Hellenic roots were focused on the aesthetic, and the Hindu traditions, further East, were basically religious. We have discussed elsewhere how this can be symbolized as a great tetrahedron of symbolic elements with China as the Lake that dissolves all things in its blood red water generating a dialectic of young daughter yin Confucianism, old son yang Daoism, and middle son yang Buddhism. In contrast India is more Wind Trigram and air element in a trinity of young son yang Atman, old daughter yin Dharma, and middle son yang Brahman One. This is a civilization of caste, of the dominant elite and elitist caste riddled aristocratic classical idealism. This is an air element filled with the golden light of the Sun as the symbol of aristocratic power. The Flame Trigram and Fire element belong to what survives of the Greek militarism of Alexander in the Moslem Middle East, a Flame Trigram and Fire element filled with war for the Green Islands it forms in the desert. It belongs to the raiding external proletariat, but its color is Green for the green oasis that is the goal of its plunder. The utilitarian trigram is the Earth Trigram and the Earth element, democratic and practical, it has made the entire blue planet its empire and therefore its color is sky and ocean blue. All metaphysics and religion, and philosophy as well, is a war between these four elemental tempers and the separate ideological kingdoms they have generated. The positions they represent, complex water against simple salt, necessary air against contingent thunder, infinite sky against finite earth, opening burned by flame against resisting predetermined water courses, they were long ago shown as complementary by the Critique of Pure Reason of Immanuel Kant. The attempt to resolve their differences in favor of one or the other is as empty as the attempt to resolve the position and speed of an electron, the particle and the wave.

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