A BEGINNER'S GUIDE TO CONSTRUCTING THE UNIVERSE: THE MATHEMATICAL ARCHETYPES OF NATURE, ART & SCIENCE
Michael S. Schneider
Explores the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, and expressed in the symbolic language of myths and fairytales, in religion, art and architecture.
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"That's why the world is called a UNIverse (Latin for 'one turn'). No other universes exist except within this One, which Plato refers to as the 'whole of wholes'."
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"Geometric construction can be used as a form of meditation. Ponder the point as a seed enfolding a sacred mystery."
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"The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty." Sir D'Arcy Wentworth Thompson (1860-1948), Scottish zoologist, classical scholar
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"Nature itself rests on an internal foundation of archetypal principles symbolized by numbers, shapes, and their arithmetic and geometric relationships."
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"The one Godhead, secret in all beings, all-pervading, the inner Self of all, presiding over all action, witness, conscious knower and absolute….the One in control over the many,… fashions one seed in many ways." Swetaswatara Upanishad
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"Everything seeks unity. The goal of many religions and mythic ordeals is to return to a lost state of Divine Oneness. But we have no need to return to a state of oneness because unity is axiomatic and we already are integrated in it."
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"The ancient mathematical philosophers probed into the archetypal patterns and found them in nature."
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"The archetypal principles of number manifest themselves as forms around us. Circles and spheres, triangles, squares, pentagons, spirals, and the five Platonic volumes represent principles that shape the world."
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"The central secret is to know that the various human passions and feelings and emotions in the human heart are not wrong in themselves; only they have to be carefully controlled and given a higher and higher direction, until they attain the very highest condition of excellence." Vivekananda (1863-1902), Indian spiritual teacher
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"We experience resonance on a very personal level in our rapport with the people we know and meet… Each of us unconsciously broadcasts the energy of our inner life and receives that with which we are in tune."
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"Scientists confirm with formulas what ancient seers knew through revelation: that the world's patterns and cycles are harmonious when seen as mathematical relationships…Where we see 'things', nouns and discrete objects, the ancient mathematical philosophers saw PROCESSES, verbs, transforming patterns meshed harmoniously."
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"I am One that transorms into Two…I am Two that transforms into Four…I am Four that transforms into Eight…After this I am One again." Egyptian (Hermopolitan) creation myth
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"In what way can a mathematical ratio permeate our souls? Through beauty. A deep part of ourselves recognizes in flowers and dancers the beauty of the mathematical infinite and sees in it the endlessness of our own depths. Natural beauty resonates with the archetypal nature within us."
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"The simple beauty of a crystal is, in part, its strict mathematical order. Through the study of number and shape we begin to apprehend the cosmic order."
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"The perfection of mathematical beauty is such that whatsoever is most beautiful and regular is also found to be most useful and excellent." Sir D'Arcy Wentworth Thompson
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"Numbers, as archetypal structural constants of the collective unconscious, possess a dynamic, active aspect which is especially important to keep in mind. It is not what we can do with numbers but what they do to our consciousness that is essential." Marie-Louise vonFranz, Jungian psychologist and writer
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"'Harmony' (from the Greek 'harmonia', signifying 'fitting together') in music, as elsewhere in the cosmos, comes from the reconciliation of opposites by a third element, bringing them all a new unity."
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"There is no man alone, because every man is a microcosm, and carries the whole world about him." Sir Thomas Browne
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"Looking at a circle is like looking into a mirror. We create and respond irresistibly to circles, cylinders, and spheres because we recognize ourselves in them. The message of the shape bypasses our conscious mental circuitry and speaks directly to the quiet intelligence of our deepest being. The circle is a reflection of the world's – and our own – deep perfection, unity, design excellence, wholenes, and divine nature."
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"The orderly process of geometric construction shows us the steps nature metaphorically uses to clothe the archetypal patterns. The geometer gradually learns to see the world of common experience as governed by laws of nature that can be understood as expressions of mathematical archetypes."
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"Polar tension occurs in all natural and human affairs as any opposing relationship, contrast, difference. It is at the root of our pernicious notion of separateness from each other, from nature, and from our own inherent divinity. The paradox of the Dyad (polarity) is that while it appears to separate from unity, its opposite poles remember their source and attract each other in an attempt to merge and return to that state of unity."
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"Our mind divides the world into heaven and earth, day and night, light and darkness, right and left, man and woman, I and you – and the more strongly we sense the separation between these poles, whatever they may be, the more powerfully do we also sense their unity." Karl Menninger (1892-1990), American psychiatrist
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"Intuition is the clear conception of the whole at once." Johann Lavater (1741-1801), Swiss poet, mystic and philosopher
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"The world's material forms are only approximations of ideal, eternal archetypes."
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"God created the universe through the Breath of the Compassionate." Mohammed (ca. 570-632)
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