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REFERENCE

Title:A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science
Type:Book
Author:Michael S. Schneider
Listed by:Joann K - Sun, May 27, 2007
Publisher:HarperPerennial
Date:1995
Description: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.

QUOTES
All quotes from this reference

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1 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

2 View "The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal." William James (1842-1910), American psychologist and philosopher A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

3 View "The ancients were aware of nature's geometric language and purposefully employed it in their arts, crafts, architecture, philosophy, myth, natural science, religion, and structures of society from prehistoric times through the Renaissance. The world today needs scholars and researchers who give the ancients credit for their intelligence and understanding, to view their art and entire cultures in light of its mathematical symbolism." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

4 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

5 View "A circle [is] the traditional symbol of heaven, wholeness, and unity." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

6 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

7 View "The ancient mathematical philosophers probed into the archetypal patterns and found them in nature." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

8 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

9 View "Islamic tradition holds that there are one hundred names of God but only ninety-nine are knowable and speakable, and they are called the 99 Beautiful Names of Allah. The highest pronounceable name is 'The Compassionate.'" A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

10 View "God created the universe through the Breath of the Compassionate." Mohammed (ca. 570-632) A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

11 View "The manifest cosmos is an approximation of its mathematical ideal." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

12 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

13 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

14 View "Cognizance of harmony in nature and mathematics attunes us to harmony at our own core." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

15 View "The mathematical rules of the universe are visible to men in the form of beauty." John Mitchell (b. 1933), English geometer and philosopher A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

16 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

17 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

18 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

19 View "There is no man alone, because every man is a microcosm, and carries the whole world about him." Sir Thomas Browne A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

20 View "Worldwide tradition acknowledges humans as being composed in accord with natural principles and made in the image of the cosmos." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

21 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

22 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

23 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

24 View "The One underlies the Many." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

25 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

26 View "At the center of our Self, deep within our consciousness, is a calm 'I.' Like the calm 'eye' within a storm, our center is untouched by psychological turbulence. Peaceful, it observes all from the vantage of wisdom. Placid, it is unmoved by the turbulent weather of the surrounding psyche. When you're feeling connected with your center it seems very familiar. It feels like the Self you know best, like who and what you know your Self to be, calm in knowing without thinking. To be centered is not the same as being 'self-centered' or selfish. Instead, it is identity with the deep, divine power that motivates us." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

27 View "'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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

28 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

29 View "A common theme in worldwide mythology is the human as microcosm, a miniature model of the whole universe…this view was long considered a key to the understanding of the Self. The ancient philosophers saw their inner lives arranged according to nature's own harmonies, for in nature, geometry, and their spiritual lives they discovered the same principles." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

30 View "What nature creates has eternity in it." Isaac Bashevis Singer (1904-1991), American author A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

31 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

32 View "The world's material forms are only approximations of ideal, eternal archetypes." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

33 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

34 View "Intuition is the clear conception of the whole at once." Johann Lavater (1741-1801), Swiss poet, mystic and philosopher A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

35 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

36 View "Thou, nature, art my goddess; to thy laws my services are bound." William Shakespeare A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

37 View "Even the seasons form a great circle in their changing, and always come back again to where they were…. and so it is in everything where Power moves." Black Elk, Native American elder A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

38 View "Geometric construction can be used as a form of meditation. Ponder the point as a seed enfolding a sacred mystery." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

39 View "Traditionally, the center is the most honorable place, known to the Greeks as 'the keep of Zeus.' Protector of hearths and boundaries (centers and circumferences) and the source of moral order, Zeus dispensed judgment from the center." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

40 View "The world is single and it came into being from the center outwards." Joannes Stobaeus (5th century), Greek anthologist A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

41 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

42 View "Each circle you see or create is a profound statement about the transcendental nature of the uni-verse." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

43 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

44 View "The eye is the first circle, the horizon which it forms is the second: and throughout nature this primary figure is repeated without end." Ralph Waldo Emerson (1803-1882), American essayist and poet A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

45 View "Everything an Indian does is in a circle, and that is because the power of the world always works in circles, and everything tries to be round." Black Elk (1863-1950), Native American elder A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

46 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

47 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

48 View "Only a self-imposed illusion of separateness keeps us from recognizing our own center of awareness and identity with the One" A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

49 View "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." A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)

50 View "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 A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art & Science (Michael S. Schneider)


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