Numerology or, What Pythagoras Wrought

322 Pages·1997·22.335 MB·English

by  Underwood Dudley

NUMEROLOGY
OK, WHAT PYTHAGORAS WROUGHT
UNDERWOOD DUDLEY
© 1997 by
The Mathematical Association of America (Incorporated)
Library of Congress Catalog Card Number 97-74345
ISBN 0-88385-524-0
Printed in the United States of America
Current Printing (last digit):
10 9876 5 4321
SPECTRUM SERIES
Published by
THE MATHEMATICAL ASSOCIATION OF AMERICA
Committee on Publications
JAMES W. DANIEL, Chair
Spectrum Editorial Board
ARTHUR T. BENJAMIN, Editor
DANIEL ASIMOV
KATHLEEN BERVER
DΠ>A CHOUDHURY
RICHARD K. GUY
JEFFREY NUNEMACHER
ELLEN MAYCOCK PARKER
JENNIFER J. QUINN
EDWARD R. SCHEINERMAN
SANFORD SEGAL
SPECTRUM SERIES
The Spectrum Series of the Mathematical Association of America was so named to
reflect its purpose: to publish a broad range of books including biographies, accessible
expositions of old or new mathematical ideas, reprints and revisions of excellent out-of-
print books, popular works, and other monographs of high interest that will appeal to a
broad range of readers, including students and teachers of mathematics, mathematical
amateurs, and researchers.
All the Math That’s Fit to Print, by Keith Devlin
Circles: A Mathematical View, by Dan Pedoe
Complex Numbers and Geometry, by Liang-shin Hahn
Cryptology, by Albrecht Beutelspacher
Five Hundred Mathematical Challenges, Edward J. Barbeau, Murray S. Klamkin, and
William O. J. Moser
From Zero to Infinity, by Constance Reid
I Want to be a Mathematician, by Paul R. Halmos
Journey into Geometries, by Marta Sved
JULIA: a life in mathematics, by Constance Reid
The Last Problem, by E. T. Bell (revised and updated by Underwood Dudley)
The Lighter Side of Mathematics: Proceedings of the Eugene Strens Memorial Confer­
ence on Recreational Mathematics & its History, edited by Richard K. Guy and
Robert E. Woodrow
Lure of the Integers, by Joe Roberts
Magic Tricks, Card Shuffling, and Dynamic Computer Memories: The Mathematics of
the Perfect Shuffle, by S. Brent Morris
Mathematical Carnival, by Martin Gardner
Mathematical Circus, by Martin Gardner
Mathematical Cranks, by Underwood Dudley
Mathematical Magic Show, by Martin Gardner
Mathematics: Queen and Servant of Science, by E. T. Bell
Memorabilia Mathematica, by Robert Edouard Moritz
New Mathematical Diversions, by Martin Gardner
Numerical Methods that Work, by Forman Acton
Numerology or What Pythagoras Wrought, by Underwood Dudley
Out of the Mouths of Mathematicians, by Rosemary Schmalz
Penrose Tiles to Trapdoor Ciphers... and the Return of Dr. Matrix, by Martin Gardner
Polyominoes, by George Martin
The Search for E. T. Bell, also known as John Taine, by Constance Reid
Shaping Space, edited by Marjorie Senechai and George Fleck
Student Research Projects in Calculus, by Marcus Cohen, Edward D. Gaughan, Arthur
Knoebel, Douglas S. Kurtz, and David Pengelley
The Trisectors, by Underwood Dudley
The Words of Mathematics, by Steven Schwartzman
MAA Service Center
P.O. Box 91112
Washington, DC 20090-1112
800-331 -1 MAA FAX [phone]
Contents
1. Introduction................................................................................................ 1
2. Pythagoras.................................................................................................... 5
3. Neopythagoreanism.................................................................................. 17
4. The Pythagoreans Abroad........................................................................ 31
5. Alphabets for Gematria........................................................................... 45
6. The Beast.................................................................................................... 55
7. Beastly Curiosities .................................................................................. 67
8. The Beast is Coming!............................................................................... 75
9. The Law of Small Numbers.................................................................... 81
10. Comes the Revolution............................................................................... 89
11. The Law of Round Numbers................................................................. 95
12. Biblical Sevens.............................................................................................103
13. Thirteens and Squares...................................................................................113
14. The Triangles of Genesis 1:1.....................................................................121
15. Paragrams.......................................................................................................129
16. Shakespeare’s Numbers...............................................................................137
17. Rithmomachy.................................................................................................147
18. Number Forms .............................................................................................159
19. Mrs. L. Dow Balliett ...................................................................................169
20. Numerology Books.......................................................................................185
21. What Numerologists Sell............................................................................191
22. Listen for Your Number................................................................................199
23. The Power of the Pyramid .........................................................................205
24. Inside the Pyramid .......................................................................................219
25. The Pyramid, Stonehenge, the Malaysian Lottery,
and the Washington Monument..................................................................229
26. Pyramidiocy.....................................................................................................241
27. Are You Gridding?.......................................................................................253
vii
viii Numerology
28. Enneagrams...................................................................................................263
29. All that Glistens............................................................................................271
30. Numbers, Numbers Everywhere..............................................................281
31. Biorhythms...................................................................................................287
32. Riding the Wave.............................................................................................295
33. Conclusion ...................................................................................................311
Index .............................................................................................................313
I
CHAPT6R
Introduction
This book is about numbers. Not about numbers in their workaday role as
counters (send $3.50 plus $4.95 for postage and handling, a total of $8.45), or
as mathematical objects (845 is a sum of two squares in three different ways:
292 + 22, 262 + 132, and 222 + 192), but as things about which can be said,
No, I wouldn’t go so far as some of my fellow calculators and indiscriminately
welcome all numbers with open arms: not the heavy-handed rough-and-tough
bully 8 or the sinister 64 or the arrogant, smug self-satisfied 36. But I do
admit to a very personal affection for the ingenious, adventurous 26, the
magic, versatile 7, the helpful 37, the fatherly, reliable (if somewhat stodgy)
76... [3, pp. xii-xiii]
and
9 is a wonderful being of whom I felt almost afraid, 81 took for his wife, and
there used always to seem a fitness in 9 × 9 being so much more than 8 × 8.
7 again is masculine; 6, of no particular sex but gentle and straightforward;
3 a feeble edition of 9, and generally mean; 2 young and sprightly; 1 a
common-place drudge. [2, p. 253]
For some people, numbers do much more than merely count and measure.
For some people, numbers have meanings, they have inwardnesses, they can
be magic and versatile, or young and sprightly. I am not one of those people,
since I think that numbers have quite enough to do as it is, but for the crowd
of number mystics, numerologists, pyramidologists, number-of-the-beasters,
and others whose ideas and work will be described in the following chapters,
numbers have powers far out of the ordinary.
Number mysticism got its start in ancient Greece, with Pythagoras and
the Pythagoreans in the sixth century b.c. Before that, numbers were just
numbers, things to count with. The Pythagoreans made some discoveries about
numbers—for instance, that the sum of odd numbers starting at 1 is always a
I
≡
Numerology
square,
l+3 = 22, l+ 3 + 5 = 32, 1 + 3 + 5 + 7 = 42,...
which so impressed them that they reportedly came to the mystical conclusion
that “all is number.” If all is number, then numbers are worth investigating,
and that is what the Pythagoreans did to the limit of their abilities, both mathe­
matically and mystically. Both mathematics and number mysticism have been
marching along ever since, though no longer together—they parted company
forever within one hundred years of the death of Pythagoras.
Mysticism is a nonrational method of getting at truth. Ours is a rational
era (even if it seems to become less so every year), and we can lose sight of the
existence of truths that are not arrived at by reason: emotional truths, spiritual
truths, even physical truths. Some truths cannot be described in words, nor
arrived at by reason. Love provides one example. For another, can you describe
a sneeze in words? Or what it feels like? If you can, you are a better wordsmith
than I. Some truths must be. felt.
Number mystics, by feeling properties of numbers, gain mystical insights
into the nature of the universe. Not being a number mystic myself, I cannot
describe them, but I could not describe them no matter how gifted a mystic I
was since, by definition, mystical experiences are ineffable. Those who have
them are fortunate. There is nothing wrong with mysticism.
On the other hand, everything is wrong with numerology. Numerologists
purport to apply number mysticism. That is, they take mystical properties of
numbers—2 is cold, say, and wet—and attach them to things and people. If
your number is 2 (numbers can easily be assigned to people, in many different
ways), then you are cold and wet, whether you know it or not.
This is standing mysticism on its head. For a number mystic, numbers are
tools, means of gaining understanding. For a numerologist, numbers are the
masters, dictating the nature of the world. Numerologists assert that numbers
tell you where it would be best to live, who you should marry, even at what
time you should arrive for an appointment. Numbers do not do this. It is not
their job. Numbers have power, but not that kind of power.
This is a thread that runs through numerology, pyramidology, and the many
other misuses of numbers that are described in this book. What they have in
common is the belief that things happen because numbers make them happen.
The pyramidologist measures his pyramid and says that the world will end on
August 20,1953 because of his measurements (chapter 25). A neo-Pythagorean
says that Greeks carved the Easter Island statues because his numbers tell him
so (chapter 4). A distinguished Oxford University scholar asserts that one of
Shakespeare’s sonnets is irregular because 28 is a triangular number (chapter
Introduction 3
17). The stock market behaves as it does because Fibonacci numbers make it
go up and down (chapter 33).
Another thread is the numerologists’ refusal to believe that patterns can
occur by accident. Human beings are very good at seeing patterns, and some­
times they see patterns that no one made but exist only by chance. The Bible is
full of 7s, one author tells us, while another finds 13s. Yet another finds squares,
and a fourth finds triangular numbers. Each of the four says that the numbers
are there because God put them there. It is possible that God takes delight in
confounding poor, limited humans with obscure puzzles, and it is possible that
the Bible is full of 17s or 23s that were put there on purpose and that no one
has noticed yet, but I doubt it. The 7s, 13s, squares, and triangular numbers are
all there by chance. Like numbers, chance has power.
Others find that people they dislike bear the number of the beast, 666.
They are thus bad, because of the number. Or, they think that they find 666
in the bar code that is on almost everything that we buy and, because of the
number, deduce the existence of a vast conspiracy. Biorhythmists say that we
are all oscillating in cycles of lengths 23, 28, and 33 days and act as we do
because of the numbers. There is something about numbers that can turn the
head.
What follows in this book is a description of these and other manifestations
of number mysticism and numerology. The lessons to be learned are that
numbers have power
but
numbers do not control events
and
coincidences happen.
These facts are so obvious that they hardly need stating; so the question
is, why read any further? The answer is that by so doing you can learn about
something that you may not be aware of, the world of number mysticism and
those infected by it: the pyramid-measurers, bible-numberists, Elliott Wavers,
and so on. It is, I think, a colorful and interesting world, and worth knowing a
little about.
There is, by the way, no other book devoted to this subject. Numerology
by E. T. Bell [1] contains nothing on modem numerology, and other books
with that word in their titles tend to be written by numerologists. Since this
book covers more than numerology, a more descriptive title for it would be its
subtitle, What Pythagoras Wrought, but that would be less informative. Also,
4 Numerology
it is my hope that copies of it will turn up on the New Age shelves of used
book stores, where they may fall into the hands of those expecting something
different. The shock may do them good.
I wish to thank those who provided me with material or other help, in
particular Arthur Benjamin, James Bidwell, I. J. Good, Richard Guy, Michael
Keith, David Singmaster, Diane Spitler, Ian Stewart, Michael Stueben, and
especially Martin Gardner, who allowed me to inspect his wonderful files. I
am also indebted to the Fisher Fund of DePauw University, which provided a
semester free of teaching duties.
References
1. Bell, E. T., Numerology, Century, New York, 1933, reprinted by Hyperion Press,
Westport, Connecticut, 1979.
2. Galton, Francis, Visualised numerals, Nature 21 (1879-1880), 252-256.
3. Smith, Stephen B., The Great Mental Calculators, Columbia University Press, New
York, 1983.