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Home , Numerology, Pyramidology, Underwood Dudley

AMS / MAA SPECTRUM VOL 19

UNDERWOOD DUDLEY or

What Wrought Originally published by The Mathematical Association of America, 1997. ISBN: 978-1-4704-5283-4 LCCN: 97-74345

Copyright © 1997, held by the American Mathematical Society Printed in the United States of America. Reprinted by the American Mathematical Society, 2019 The American Mathematical Society retains all rights except those granted to the United States Government. ⃝∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at https://www.ams.org/ 10 9 8 7 6 5 4 3 2 24 23 22 21 20 19 10.1090/spec/019

AMS/MAA SPECTRUM

VOL 19

Numerology or

What Pythagoras Wrought

Underwood Dudley 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 DIPA 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 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 I Want to be a Mathematician,byPaulR.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 Mathematical Circus, by Martin Gardner Mathematical Cranks, by Underwood Dudley Mathematical Magic Show, by Martin Gardner Mathematics: Queen and Servant of Science,byE.T.Bell Memorabilia Mathematica, by Robert Edouard Moritz New Mathematical Diversions, by Martin Gardner Numerical Methods that Work, byFormanActon 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 Senechal 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

Contents

1. Introduction ...... 1 2. Pythagoras ...... 5 3. Neopythagoreanism ...... 17 4. The Pythagoreans Abroad ...... 31 5. Alphabets for ...... 45 6. TheBeast...... 55 7. Beastly Curiosities ...... 67 8. The Beast is Coming! ...... 75 9. TheLawofSmallNumbers...... 81 10. Comes the Revolution ...... 89 11. The Law of Round Numbers ...... 95 12. Biblical Sevens ...... 103 13. ThirteensandSquares...... 113 14. The Triangles of Genesis 1:1 ...... 121 15. Paragrams...... 129 16. Shakespeare’sNumbers...... 137 17. Rithmomachy ...... 147 18. NumberForms...... 159 19. Mrs. L. Dow Balliett ...... 169 20. Numerology Books ...... 185 21. What Numerologists Sell ...... 191 22. ListenforYourNumber...... 199 23. ThePowerofthePyramid...... 205 24. InsidethePyramid...... 219 25. The , Stonehenge, the Malaysian Lottery, and the Washington Monument ...... 229 26. Pyramidiocy ...... 241 27. Are You Gridding? ...... 253

vii viii Numerology

28. Enneagrams...... 263 29. AllthatGlistens...... 271 30. Numbers,NumbersEverywhere...... 281 31. Biorhythms ...... 287 32. Riding the Wave ...... 295 33. Conclusion...... 311 Index...... 313 Index

Agrippa, Cornelius, 52 Cheops, 206 Ahmad, Mabel, ch. 22 Clinton beasted, 46 Ahmad, S. H., 199 Coates, Austin, 253, 262 alphabet , 14–15 Coates, Eric, 255 American Institute of Man, ch. 4 Cunningham, John B., 280 Appolonius of Tyana, 35 Arithmetic (Nichomachus), 17 da Vinci, Leonardo, 209 Artmann, Benno, 157, 158 Dante, 118 Asilo of Wurzburg,¨ 157 De Morgan, Augustus, 57, 62, 88, 117, Athena, 27, 187 119 Der Ablauf des Lebens (Wilhelm Bach and the Riddle of the Fleiss), 288 Alphabet (Ruth Tatlow), 53 DeTemple, Duane W., 280 Ballew, David W., 73 Dow, Charles H., 299 Balliett, Josephine Dennis (Mrs. L. Durer,¨ Albrecht, 67 Dow), ch. 19 dyad, 22–23 Bede, the Venerable, 57 Beesing, Maria, 269 Easter Island, 40–42 Bell, Eric Temple, 3, 4, 9, 10, 11, 16 Eaton, Clara C., 158 Bible, New English,66 Ebin Alexander, ch. 4 biorhythms, ch. 31 Eddy, Mary Baker, 259 Blavatsky, Helena P., 184 Elliott, Ralph , 295, 309 Bobko, D. J., 280 Elliott wave theory, ch. 32 Boissiere,` Claude de, 150, ch. 17 enneagrams, ch. 28 Boletin de Psicologia Cuba, 292 Euxenes, 35–37 Buess, Lynn, 190 Bungus, Peter, 57, 86 Faerie Queen (Edmund Spenser), 140 Falwell beasted, 60 Calise, Lori K., 280 Fibonacci numbers, 70, 72, 297–299, Campbell, Joseph, 95–101 303–305 Carroll, Jon, 252 Finnessey, Arthur, ch. 10 Caruso, Tamara M., 280 Fishler, Roger, 280 Castro, Almerio Amorim, 70, 73 Fleiss, Wilhelm, 287 Cathanus Magus, 53 Fowler, D. H., 280 Chase, A. B., 217 Fowler, Alistair, 137, 145

313 314 Numerology

Frazer, James G., 95, 96 Kancil, Sung, 240 Freud, Sigmund, 287 Keith, Michael, 64, 66, 71, 73 Frost, Albert John, 301, 310 , 206 King Lear, 105 Galton, Sir Francis, 4, 163–165, 168 Gardner, Martin, 239, 240, 242, 288, Law of Small Numbers, 23, 25, 77, 291 ch. 9, 232, 239, 244, 245, 246, Gates beasted, 55 276, 278, 305 Gattei, Pierino, 280 Ley, Willy, 205, 217 Gaunt, Bonnie, 229, 240 Lincoln’s Gettysburg Address, 107, gematria, 21, ch. 5, 93 116–117 Gettysburg Address, Lincoln’s 107, Locks, Gutman G., 53 116–117 lottery, Malaysian, 233–235 Godel,¨ Kurt, 309 Goldberg, Oscar, 119 Magnificent Numbers of the Great golden section, ch. 29 Pyramid and Stonehenge, The Graves, Gypsy, 211 (Bonnie Gaunt), ch. 25 Greek alphabet, 47 Malaysian lottery, 233–235 Gurdjieff, George Ivanovich, 264–265 Markovsky, George, 271, 280 Guy, Richard, 37, 81–82, 87 Masters of (Charles Portis), 16 Hale, William Kendrick, 60–61, 66 McCarthy, Joseph R., 6 Harper’s,66 Menninger, Karl, 53 Hebrew alphabet, gematria, 48, 203 Midonick, Henrietta, 217 Henderson, Janice A., 16 Moessner, Alfred, 73 Henrici, Christian Friedrich, 133 monad, 20–21 Heraclitus, 6 Muller,¨ R., 86,87 Herodotus, 206, 217, 279 Herz-Fischler, Roger, 279 Napoleon beasted, 61 Heston, Charlton, 211 navels, measured, 273–274 Hipparchus, 41, 100 Neopythagoreans, ch. 3, ch. 4 Hippocrates, 263 New English Bible,66 Hitler beasted, 70 Newsweek, 269 Høeg, Peter, 280 Nichomachus, 17 Holmes beasted, 59 Nixon, Richard, 260–261 Hopper, Grace Murray, 27–28, 30 number forms, ch. 18 Hornbrook, Adelia, 167–168 , ch. 6–8 Huffman, Carl, 6, 12, 15, 16 “Numero”, 190 Hume, D. D., 184 numerological short story, 181–182 Huntley, D. E., 274, 280 Numerology (Austin Coates), ch. 27 Numerology (E.T.Bell),3 Iamblichus, ch. 3 Nunnaly, Tiina, 280 Indianaopis Star, 210 Irenaeus of Lyon, 56 Ondrejka, Rudolf, 68–69, 73 Ouspensky, P. D., 265 Johnson, Alan William, Jr., 69, 73 O’Leary, Pat, 269 Index 315

Pacioli, Luca, 209 Singmaster, David, 246–252 Palmer, Helen, 269 Smith, David Eugene, 158 Panin, Ivan, 104–105 Smith, Stephen B., 4 paragrams, ch. 15 Sommers, Paul M., 280 Parthenon, 274 Spenser, Edmund, 140 Patrick, G. T. W., 165–167, 168 squares, biblical, 114–115 Penning, P., 73 Star, Indianapolis, 217 phi, 42, 208, 209, ch. 29, 297 Stewart, Basil, 219, 227 pi, 216, 282–283 Stifel, Michael, 50, 130 Piazzi Smyth, Charles, 209, 217, 230 Stonehenge, 222, ch. 25 Picander, 133 Stueben, Michael, 59 Pickover, Clifford, 72, 73 Swoboda, Hermann, 291 Poll, Michael, 131 Portis,Charles,16 Tatlow, Ruth, 53, 135 Prechter, Robert Rougelot, 301, 310 Taylor, John, 62, 208, 217, 279 pyramid inch, 221 Tennessean, Nashville, 119 pyramid, great, ch. 24, 25 The Astronomical Almanac, 101 , ch. 23 The Spice of Torah—Gematria (Gutman Pythagoras, passim Locks), 53 Pythagorean opposites, 13, 175 The Phoenix and the Turtle (Shakespeare), 140 Randi, James, 291 The Great Pyramid (Basil Stewart), Reagan beasted, 59 208, ch. 24, 279 Relfe, Mary Stewart, ch. 8 The Divine Proportion (D.E.Huntley), Revolution, American, ch. 10 274 Rhind papyrus, 212–216 The Merry Wives of Windsor Rhodes, 41 (Shakespeare), 141 Richards, John F. C., 158 Theology of Arithmetic (Iamblichus), Riederer, Johann Friedrich, 132 ch. 3 rithmomachy, ch. 17 thirteens, biblical, 113 Robins, Gay, 217 Thom, David, 62 Round numbers, ch. 11 Tolstoy, War and Peace, 61–62 Tompkins, Peter, 242, 252, 306 Sabiers, Carl, 112 Tribune, Chicago, 66 Sadat, Anwar, 79 Trigg, Charles W., 73 Schiffman, H. R., 280 Triumphal Forms (Alistair Fowler), 137 Schimmel, Annemarie, 66, 86, 88 Twain, Mark, 184 Secrets of the Great Pyramid (Peter Tompkins), ch. 26 Universal product code, 63–65, 78 , 213 Urdang, Lawrence, 88 sevens, biblical, ch. 12 Sheakespeare, sonnets of, ch. 16 Visa beasted, 75 Shute, Charles, 217 Von Fritz, Kurt, 16 Singer, Astuter, 63 Singh, Chanchal, 72, 73 Walker, Kenneth, 269 Singleton, C. J. R., 69 War and Peace (Tolstoy), 61–62 316 Numerology

Waring, Edward, 84 world ends in 2037, 66 Washington, George, 93 Wren, Sir Christopher, 258–9 Waterfield, Robin, 18, 30 Weger, R. C., 73 Zerger, Monte, 69, 73, 277, 280 Woodrow, Ralph, 66 Zhmud, Leonid, 15–16 AMS / MAA SPECTRUM

Recreational Mathematics Numerology is about numerology, which is the delusion that numbers have power over events. Numerology is a descendent of number mysticism, which is the belief that the contemplation of numbers can give mystical and non-rational insights into their nature and the nature of the universe. Number mysticism (e.g., 2 is wet, and cold) originated with Pythagoras 2500 years ago, and has continued to this day. Numerology is applied num ber mysticism (e.g., if your number is 2, you tend to be wet, and cold), and is a recent invention. Underwood Dudley received his PhD from the Numerology gives an outline of the history of number in 1965 and taught briefl y at mysticism and numerology and gives many examples, before accepting a position at past and present. It includes the Elliott Wave theorists, DePauw University where he has taught since 1967. who explain the movements of the stock market with He has been active in the publications program of Fibonacci numbers, the biorhythmists, who explain The Mathematical Association of America (MAA) for our good and bad days using properties of 23,28, over fi fteen years as an Associate Editor of Mathematics and 33, or perfect squares in the bible-numberists, Magazine, Collaborating Editor of the Problem the Pyramidologists, who see all of human history Section of the American Mathematical Monthly, and in numbers derived from measurements of the great as Chair of the New Mathematical Library Editorial pyramid of , the number-of-the-beasters, who view Board. His other publications include, Mathematical with alarm those who bear the number 666, the eminent Cranks, The Trisectors, and Readings for Calculus, scholar who asserts that Shakespeare wrote his sonnets published by the MAA, as well as Elementary Number keeping triangular numbers in mind, the researcher who Theory published by W.H. Freeman. fi nds 57s throughout the American Revolution, the entre- preneurs who would sell you your personalized numerological profi le, and others.

The message of the book is that numbers indeed have power, but the power is not over events, it is over human minds. It is intended for anyone interested in human folly and requires no mathematical knowledge beyond arithmetic to understand.

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