Math for Mystics: From the Fibonacci Sequence to Luna's Labyrinth to the Golden Section and Other Secrets of Sacred Geometry - Softcover

Shesso, Renna

Softcover

ISBN 10: 1578633834 ISBN 13: 9781578633838

Verlag: Red Wheel/Weiser, 2007

Inhaltsangabe

Much of math history comes to us from early astrologers who needed to be able to describe and record what they saw in the night sky. Whether you were the king's court astrologer or a farmer marking the best time for planting, timekeeping and numbers really mattered. Mistake a numerical pattern of petals and you could be poisoned. Lose the rhythm of a sacred dance or the meter of a ritually told story and the intricately woven threads that hold life together were spoiled. Ignore the celestial clock of equinoxes and solstices, and you'd risk being caught short of food for the winter.

Shesso's friendly tone and clear grasp of the information make the math "go down easy" in this marvelous book.

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Renna Shesso has been a student of mystical traditions and spiritual selfdiscovery since the late 1960s. She is the author of Math for Mystics. A longtime resident of Colorado, Shesso follows her calling as shamanic healing practitioner and teacher, professional tarot reader, and priestess of the Craft. Visit her at www.rennashesso.com.

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Math for Mystics

From the Fibonacci Sequence to Luna's Labyrinth to the Golden Section and Other Secrets of Sacred Geometry

By Renna Shesso

Red Wheel/Weiser, LLC

Copyright © 2007 Renna Shesso
All rights reserved.

ISBN: 978-1-57863-383-8

Contents

Introduction: "Math?! Why?"
CHAPTER 0 The Circle of Creation
CHAPTER 1 Counting
CHAPTER 2 The Moon
CHAPTER 3 Measurements
CHAPTER 4 The Days of the Week
CHAPTER 5 The Magical Squares
CHAPTER 6 The Knight's Tour and Templar Codes?
CHAPTER 7 Shapes and Numbers Meditation
CHAPTER 8 Pythagoras
CHAPTER 9 Fibonacci, the Golden Ratio, and the Pentacle
CHAPTER 10 Venus' Pentacle
CHAPTER 11 The Geometric Solids
CHAPTER 12 Individual Numbers
CHAPTER 13 A Tale in Which Gods Do Math
CHAPTER 14 Summing Up
Notes
Bibliography
Index

CHAPTER 1

Counting

"He counts using his fingers." Nowadays, that phrase is generally an unkind one,a snippy way of implying that a person isn't very bright. Once upon a time,though, counting on our fingers had sacred connotations, and to know the numberof things was itself an act of magic. Our word ritual comes from the Indo-Europeanroot ri, which means "to count, to number." The association of ri with"ritual" comes from the use of rites to mark the seasons of the year, back inthe days when a comprehension of time and seasons could be crucial to survival.Clearly, our personal ancestors succeeded in their season-counting and winterfood storage, or we wouldn't be here now. We can take that to mean that we allhave some inherent aptitude for timekeeping and calculating. In other words, weeach have an aptitude for practical math.

Even before the advent of written numbers, people had ways of enumeratingquantities. We could cut or scratch notches on a spare piece of bone (manyexamples of this have survived) or we could line up stones (which would then getscattered), or we could use our fingers. The Sanskrit word for "finger-counting"is mÛdrâ, closely related to mudrâ, the word for the symbolic hand gestures seenin Hindu religious statuary and sacred dance. Maybe you do your own littlefinger dances while you drive, drumming out basslines in time with the radio, asrhythm divides time. Without consciously saying, "One, two, three, and four ...,"you're counting, in the most primal way, as body-knowledge. Forgetmultiplication tables! Give me a turntable!

Zero and Nine

In 773 CE, a diplomatic mission from northern India arrived in Baghdad. FromBaghdad to northern India is roughly 1,500 miles, minimum. As modern humans, wetend to forget our most primal Road Trip roots. Chances are we had distantancestors who spent not hours, but days, weeks, months—or years—physicallygetting to a location that really mattered to them. The Indian delegation madewhat must have been an unimaginably arduous journey.

This visiting Indian contingent included an astronomer/astrologer named Kanaka.Though the studies of astronomy and astrology are now firmly separated, theyoriginally evolved together, and the Indians were considered especially skilled.Caliph al-Mansur, the Arabian host, became so impressed with Kanaka's starskills that he had Arabic translations made of the Indian reference works Kanakahad brought along. These translations were avidly shared, copied and recopied(by hand, of course), studied, discussed and mentally digested among Arabianastrologers, and about 50 years later, an original work by Arab mathematicianal-Khuwarizmi appeared. Called Kitab al jam' wa'l tafriq bi hisab al hind("Indian technique of addition and subtraction"), al-Khuwarizmi's text concernedthe still-novel Indian numbers that had so impressed Caliph al-Mansur. Al-Khuwarizmigave a detailed explanation of decimal numeration, the nine Indiannumber symbols and "the tenth figure in the shape of a circle" that was used "soas not to confuse the positions" of the numbers.

That "tenth figure in the shape of a circle" was Zero. One theory of its origin:People counted using pebbles laid in rows on a sandy surface. The Indians' termfor "higher computations" was dhuli-kharma, which actually means "sand-work."Let's put pebbles in rows to represent quantities. To subtract, we removepebbles. What's left? Some pebbles, of course, as well as faint depressions inthe sand. We check our math by looking at the dents left behind by the pebbleswe removed. And the shape of each depression would be a soft-edged circle in thesand, now containing nothing.

But let's get back to ancient Arabia. The al-Khuwarizmi text became popular inthe Arab world and quietly arrived in Europe during the long Moorish presence inSpain. Although the text seems not to have spread into the rest of Europe, itsideas spread readily in other lands, and by the early eleventh century theIndian numerals and the zero were in common use from the borders of central Asiainto northern Africa and Egypt. Undoubtedly, variations on this numericalinformation migrated not just through Indian astrologers, but through otherpragmatic folks as well, since what worked for scholars and astrologers wouldalso be useful to merchants and accountants—to anyone making practical use ofnumbers. Finally, an abridged copy of al-Khuwarizmi's work, now simply calledArithmetic, was translated into Latin in 1126 CE, at which point it quicklybecame influential and controversial throughout Europe.

Why did Arithmetic make such an impact? Because it presented some things Europedidn't have: a consistent and simple way to write the numbers 1 though 9, andthe radically innovative placeholder, zero. What we came to call the "Arabicnumerals"—since they reached Europe through translations from the Arabic—in facthave their roots deeply in India. The legendary brilliance of Indian astronomer-astrologerslike Kanaka was credited to their superior skill in mathematics,skills made easier by their numerical system. Cuneiform and Roman numerals areokay for writing, and pebbles or fingers work fine for counting, but neither ismath-friendly. Astrologers needed writeable math formulae capable of greatercomplexity, and by creatively pushing to discover better and more detailed waysto express numbers, the ancient Indians moved to the forefront in astrology,astronomy, and math.

Not everyone approved of the new-style written numbers. "Quantities" weren't—andaren't—the same as "numbers." The former are visible objects, like sheep orapples, while the latter, those "numbers," are nothing more than weird shapesscrawled on a page. Zeros are especially suspect: Pen a tail on 0 and it becomes6 or 9. Tag on extra zeros, and that bogus 9 becomes 90, 900, 9,000, or worse.Small wonder that eleventh-century monk-historian William of Malmesburyconsidered the newfangled Indian-Arabic numerals, and especially that peskyzero, to be "dangerous Saracen magic."

Back to trustworthy finger-counting. For the record, you can count to 9 on onehand using your five fingers and the spaces between them. The odd numbers landon the fingers, and the gaps get the even num-bers—5...

Details zur Ausgabe

• Verlag: Red Wheel/Weiser
• Erscheinungsdatum: 2007
• Sprache: Englisch
• ISBN 10: 1578633834
• ISBN 13: 9781578633838
• Einband: Taschenbuch
• Anzahl der Seiten: 193
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Buchbär; info@buchbaer.de; ; Weberstr. 67; Osnabrück; 49084; Deutschland