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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"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 world is single and it came into being from the center outwards." Joannes Stobaeus (5th century), Greek anthologist
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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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"To know the order of nature, and regard the universe as orderly is the highest function of the mind." Baruch Spinoza (1632-1677), Dutch philosopher
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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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"This knowledge of ourselves as part of a harmonious whole is now dimmed to everyday awareness, but it can be part of a great vision to be reclaimed."
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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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"It is as if the universe is one single organism, motivated by a single power, developing in many ways to gradually become aware of itself through the awareness of the creatures and forces it produces."
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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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"Number should not be understood solely as a construction of consciousness, but also as an archetype and thus as a constituent of nature both within and without." Marie Louise vonFranz
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"In nature the One circle gives rise to the Many, in the shapes and orbits of the planets, in the roundness of berries, nests, eyeballs, and the cycles of time."
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"Our deepest awareness, the power that motivates all awareness, which we can call the 'Power to Be Conscious,' of which we are not ordinarily cognizant, recognizes its own transcendental nature in the geometry of the circle. For this reason the circle has been a universal symbol of an ideal perfection and divine state that always exists around and within us whether we acknowledge it or not."
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"Men must be aware of the wisdom and the strength that is in them if their understanding is to be expanded." Vauvenargues (1715-1747), French soldier, moralist
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"Numbers keep recurring not because we make them do so but because they are inherent in the proportions of nature that express the timeless mathematical archetypes."
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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 ancient mathematical philosophers probed into the archetypal patterns and found them in nature."
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"Each circle you see or create is a profound statement about the transcendental nature of the uni-verse."
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"It is stirring to realize that each of the physical structures of the universe is a repackaging of the others. We hold the proportions of the solar system in our hands, face, and whole body."
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"Worldwide tradition acknowledges humans as being composed in accord with natural principles and made in the image of the cosmos."
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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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"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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"The mathematical rules of the universe are visible to men in the form of beauty." John Mitchell (b. 1933), English geometer and philosopher
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"We're not separate from the rest of the universe but are literally braided into it; we are a complete whole living in a greater complete whole."
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"A circle [is] the traditional symbol of heaven, wholeness, and unity."
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