AMS / MAA SPECTRUM VOL 19 UNDERWOOD DUDLEY Numerology or What Pythagoras 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. ⃝1 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 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,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 Martin Gardner 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 Gematria . .................... 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 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. 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 mysticism, 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 Number 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 Nelson, 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 Khufu, 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 Atlantis (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 Number of the beast, 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 pyramidology, 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