The M3gic -44% Numbc Martin Gardner The . Magic Numbers The . Mag~c Numbers Martin Gardner Prometheus Books Buffalo, New York Published 1985 by Prometheus Books 700 E. Amherst Street, Buffalo, New York 14215 Copyright @ 1985 by Martin Gardner Material previously published in Scientific American, copyright @ 1960,1961,1963,1964,1965,1966,1967, 1968,1969,1971,1972,1973,1974,1975,1976, 1977, 1978, 1980 Scientific American. All rights reserved No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photo- copying, recording, or any system now known or to be invented, without permission in writing from the publisher, except by a reviewer who wishes to quote brief passages for inclusion in a magazine, newspaper, or broadcast. Portions of this book appeared as The Numerology of Dr. Matrix and The Incredible Dr. Matrix Printed in the United States of America Library of Congress Catalog Card No. 84-43183 ISBN 0-87975-281-5 cloth ISBN 0-87975-282-3 paper For Tom, my number two son Contents Introduction 1. New York 2. Los Angeles 3. Sing Sing 4. Lincoln and Kennedy 5. Chicago 6. Miami Beach 7. Philadelphia 8. Pi 9. Wordsmith College 10. Squaresville 11. Left \'ersus Right 12. Fifth Avenue 13. The Moon 14. Honolulu 15. Houston 16. Clairvoyance Test 17. Pyramid Lake 18. The King James Bible 19. Calcutta 20. Stanford 21. Chautauqua 22. Istanbul Answers and Commentary Introduction Myfriendship with the late Dr. Irving Joshua Matrix and his daughter Iva spanned a period of some twenty years. I first wrote about him in my column on "Mathematical Games" in Scientific American, January 1960. With enormous sadness, and echoes of Watson's famous tribute to his friend Sherlock Holmes, my column for September 1980 recorded all I could learn about his untimely death. This is the third collection of my columns about Dr. Ma- trix. In 1967 Simon and Schuster brought together the first seven columns in a small book called The Numerology of Dr. Matrix. Reverse the digits of 67 and you get the date of The Incredible Dr. Matrix, a Scribner's book that contained the previous one. After another lapse of nine years, Prome- theus has now allowed me to assemble all my Dr. Matrix columns in one volume, from my first meeting with him in Manhattan to his violent end in 1980 on the banks of the Danube. Over the years, mathematicians and others who have fol- lowed my accounts of Dr. Matrix's remarkable predictions, analyses, and play with words and numbers have asked me to provide the doctor's curriculum vitae. I will do the best I can. The information that follows is based almost entirely on what has been disclosed to me over the years by Iva. The reader should understand that, except for a few isolated facts, this information has not been otherwise verified. 4 THE MAGIC NUMBERS OF DR. MATRIX Dr. Matrix was born on February 21, 1908, in Kagoshima, on the Japanese island of Kyushu. His father, the Reverend William Miller Bush, was a Seventh-Day Adventist missionary from a small town in Arkansas called Figure Five. In 1908 he was in charge of the Adventist mission in Kagoshima. Young Irving Joshua Bush, who later took the name of Matrix, was the eldest of seven children, all but the youngest three born in Kagoshima. He grew up a devout believer in the biblical prophecies of his parents’ faith, and, owing to a natural bent in mathematics, was particularly intrigued by the numerical aspects of those prophecies. At the age of seven he surprised his father by pointing out that there are 1 God, 2 testaments, 3 persons in the Trinity, 4 Gospels, 5 books of Moses, 6 days of creation, and 7 gifts of the Holy Spirit. “What about 8?” his father had asked. “It is the holiest number of all,” the boy replied. ‘The other numbers with holes are 0, 6, and 9, and sometimes 4, but 8 has two holes, therefore it is the holiest.” At the age of eight young Bush devoted most of his spare time to investigating the numbers that occur in various bibli- cal passages. For example, 1 Chronicles, chapter 20, verse 6, says that the giant of Gath had six toes on each foot and six fingers on each hand. It is no coincidence, the boy insisted, that 20, the number of the chapter, gives the normal allot- ment of toes and fingers to a man, and 6, the number of the verse, describes the abnormality of each hand and foot of the man of Gath. Moreover, said the boy, if we assign numbers to each letter in Gath, letting a equal 1, b equal 2, c equal 3, and so on, the numbers add to 36, the square of 6. At the age of nine the budding numerologist applied a sim- ilar technique to his last name, Bush, obtaining the numbers 2, 21, 19, and 8. They coincided exactly with his birth date, the twenty-first day of the second month of the year 1908—an astonishing correlation, which he took to be a favorable omen about God’s plans for him as a laborer in the Adventist cause. In 1920, when Bush was thirteen, those plans were suddenly shattered. He found hidden in a dark comer of his father's study a copy of D. M. Canright's explosive book Life of Mrs. E. G. White, Seventh-Day Adventist Prophet: Her False Claims Re- futed (Cincinnati: Standard publishing, 1919). Shaken and dis- enchanted by the disclosures of this book, and finding himself in hopeless conflict with the fundamentalist views of his par- ents, he ran away from home, eventually making his way to Tokyo. He spoke, of course, fluent Japanese as well as English. In addition to his early interest in numbers, young Bush had also made a hobby of magic and juggling. An elderly Japanese friend of his father, who had once been in show business, had taught him some elementary juggling and sleight of hand. In Tokyo he supported himself for several years by juggling and doing magic tricks on street corners. A famous Japanese magician named Tenkai saw him work and hired him as an assistant. Later, in his twenties, Bush traveled throughout Japan performing a mind-reading act under the stage name of Dr. Matrix. In 1938 he married his assistant, Miss Eisei Toshiyori, whose father was a Japanese foot juggler and trick bicycle rider. Their only child, a daughter, was born the following year. Mrs. Matrix was killed in April 1942, during the bombing of Tokyo. After the war with Japan came to its abrupt end, Dr. Matrix took up residence in Paris, where, on the Left Bank, he quickly achieved a considerable reputation as an astrologer and numerological consultant. It is said, although I cannot vouch for it, that Charles de Gaulle once sought his advice on whether he should make AndrC Malraux his information minister, and re- ceived a convincing affirmative answer based on a careful analysis of the birth dates and full names of the two men. It was while he was in Paris that Dr. Matrix became a personal friend of the world- renowned French mathematician Nicolas Bourbaki. Although Dr. Matrix had no formal schooling beyond the sixth grade at the mission school in Kagoshima, he had managed to teach himself a surprising amount of number theory. From the great 6 THE MAGIC NUMBERS OF DR. MATRIX Bourbaki he acquired even deeper insights into this funda- mental branch of mathematics. I would have liked to include in this book a photograph of Dr. Matrix and Iva, but alas, they would never allow me to take a picture of either of them. As for Iva, I have not heard from her since her father was killed. Perhaps she will read these words and get in touch with me. Hendersonville, N.C. 1. New York Numerology, the study of the mystical significance of numbers, has a long, complicated history that includes the ancient Hebrew cabalists, the Greek Pythagoreans, Philo of Alexandria, the Gnostics, many distinguished theo- logians, and those Hollywood numerologists who pros- pered in the 1920s and 1930s by devising names (with proper "vibrations") for would-be movie stars. I must confess that I have always found this history rather boring. Thus when a friend of mine suggested in late December 1959 that I get in touch with a New York numerologist who called himself Dr. Matrix, I could hardly have been less interested. "But you'll find him very amusing," my &iend insisted. "He claims to be a reincarnation of Pythagoras, and he re- ally does seem to know something about mathematics. For example, he pointed out to me that 1960 had to be an un- usual year because 1,960 can be expressed as the sum of two squares-142 and 422-and both 14 and 42 are mul- tiples of the mystic number 7." I made a quick check with pencil and paper. "By Plato, he's right!" I exclaimed. "He might be worth talking to at that." I telephoned for an appointment, and several days later 8 THE MAGIC NUMBERS OF DR.MATRIX a pretty secretary with dark, almond-shaped eyes ushered me into the doctor's inner sanctum. Ten huge numerals from 1 through 10, gleaming like gold, were hanging on the far wall behind a long desk. They were arranged in the triangular pattern made commonplace today by the ar- rangement of bowling pins, but which the ancient Py- thagorean~viewed with awe as the "holy tetractys." A large dodecahedron on the desk had calendars for each month of the new year on each of its twelve sides.