Games, Gods and Gambling : the Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era
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University of Calgary PRISM: University of Calgary's Digital Repository Alberta Gambling Research Institute Alberta Gambling Research Institute 1962 Games, gods and gambling : the origins and history of probability and statistical ideas from the earliest times to the Newtonian era David, F. N. (Florence Nightingale) Hafner Publishing Company http://hdl.handle.net/1880/41346 book Downloaded from PRISM: https://prism.ucalgary.ca Games, Gods and Gambling rc same author: 1 STATISTICAL PRIMER D. E. BARTON, B.Sc., Ph.D.: 2OMBINATORIAL CHANCE Signs of the Zodiac : floor mosaic, Beth-Aleph Synagogue, Palestine (5th century) Games, Gods and Gambling The origins and history of probability and statistical ideas from the earliest times to the Newtonian era F. N. DAVID, D.Sc. (University of London, University College) 1962 HAFNER PUBLISHING COMPANY NEW YORK Copyright 0 1962 CHARLES GRIFFIN & CO. LTD 42 DRURY LANE LONDON W.C.2 First Published in 1962 PRINTED IN GREAT BRpTAIN BY BELL AND BAIN, LTD., GLASOOW [S CONTINUING INTEREST AND ENCOURAGEMENT all we tell you? Tales, marvellous tales and stars and isles where good men rest, evermore the rose of sunset pales, ds and shadows fall toward the West. v beguile you? Death hath no repose and deeper than that Orient sand [ides the beauty and bright faith of those rde the Golden Journey to Samarkand. v they wait and whiten peaceably, mquerors, those poets, those so fair ; ow time comes, not only you and I, whole world shall whiten, here or there : lose long caravans that cross the plain untless feet and sound of silver bells 1 no more for glory or for gain, 8 more solace from the palm-girt wells ; le great markets by the sea shut fast calm Sunday that goes on and on, ven lovers find their peace at last, rth is but a star, that once had shone. Prologue : The Golden Journey to Samarkand JAMES ELROY FLECKER ( 1884- 19 15) Preface TODHUNTERon the " History of Probability " has been and always will be the major work of reference in this subject. He is rarely wrong, always explicit, and has obviously read widely through all available literature. That he stops early in time (with Laplace) and thus does not treat the interesting developments of the nineteenth century is hardly his fault, since he wrote his book in 1864-65 and would have been collecting his material for some years before this. From the point of view of the development of ideas he does not start soon enough. He notes the mathematical arguments; fairly and with precision, but this is like embarking on a river when it has become of respectable size, and paying no attention to the multitude of small streams and tributaries of which it iis the united outcome. The ide,a that one might speculate about the development of the random el lement through references in literature of all kinds- classical, z ~rchaeological,biographical, poetical and fictional-is one which came to me as a student some thirty years ago. Since then, as fri.ends and colleagues learnt of my interest, the number of references to which my attention has been drawn has increased rapidly, ea ~chyear filling many notebooks. It is too much to hope that this li;st of references can ever be completed, but it is, I think, fair to sa)r that many of the most significant have been made known to me. And from these references I have tried to supple- ment Todlhunter on the early development of ideas about chance and to fill in a certain amount of the background of ideas and controversies which attended the creation of the mathematical theory of probability. Writers on the history of science, and in particular on the history of a branch of mathematics, tend to fall into one of two PREFACE categories : they either write severely on the subject-material and leave the men who created it as wooden puppets, or they tell us interesting (and often apocryphal) stories about personalities, with no real attempt to place their achievements. Thus Todhunter will rarely be read for pleasure, although always for profit, by b anyone interested in probability theory, while the potted bio- graphies, always read for pleasure, convey little to us which profits our understanding of theory. I have tried, probably without success, to steer a middle way between the Scylla of Todhunter and the Charybdis of the storyteller. The man creates the mathematical theorem, but the events of a man's life create the man, and the three are indissoluble. Thus I would hold, for example, that it is not enough to remark on and wonder at de P Moivre's analytic genius, but that one should also realise that poverty was his spur, that much of his work might not have been I achieved had he been sure of a post which would have brought him some leisure and about which he wrote so longingly to John Bernoulli. Wherever possible I have gone back to the original documents to check mathematical development.; in the same way, I have tried to check the stories told about great men. The similarity between so many of these latter induces a profound scepticism about all of them, even when told autobiographically, and I have tried to indicate this scepticism in the text. I have tried, not I invariably with success, never to express an opinion without at least adequate information of the relative facts. The documen- tation of one's opinions naturally grows easier as the millennium advances, although the upheaval of the French Revolution led to much of value being mislaid. The lack of information about de Moivre can only be described as startling. When I began work on the history of probability and statistics I had the ambitious aim of covering the whole field from pre- history to the present day and including appraisals of the life and works of such giants as Gauss and Poisson. The accumulation of facts is, however, a slow business, particularly when it is pursued solely as a hobby, and I think I will not achieve my PREFACE original goal. I have in mind to write a monograph on the great triumvirate, James Bernoulli-Montmort-de Moivre, and another on Laplace. An appreciation of the works of Laplace from the modern statistical aspect is long overdue and would lead to the realisation of how many theorems are still being published which are special cases of his general results. At the rate at which I work these two projects will take me beyond my allotted span of years. There is much still to be done. Not only should the history after Laplace be written, but the time is ripe for a mono- graph on inverse probability. It is to be hoped that someone may be stimulated to compile this. So many persons have given me references and have borne with what must have seemed my interminable discussions that space would not permit me to thank them individually. I count myself fortunate in having so many friends. I feel I should add, however, that if it had not been for the continuing interest (and lately the constant prodding) of M. G. Kendall I doubt whether I should ever have stopped collecting information and taken the irretriev- able step of putting it on paper; once something is written it dies a little and one is always reluctant to call a halt. I owe him much both in ideas and stimulus, and it is to him therefore that I would dedicate this book. F. N. DAVID London, 1961 - Contents Chapter Page 1 The development of the random event . 1 2 Divination . 13 3 The probable . 2 1 4 Early beginnings . 27 5 Tartaglia and Cardano . 40 6 Cardano and Liber de Ludo Aleae . 55 7 Galileo . 61 8 Fermat and Pascal . 70 9 The arithmetic triangle and correspondence between Fermat and Pascal . 81 10 Bills of Mortality . 98 11 Christianus Huygens . 110 12 Wallis, Newton and Pepys . 123 13 James Bernoulli and Ars Conjectandi . 130 14 Pierre-RBmond de Montmort and The Essai dYAnal_yse 140 15 Abraham de Moivre and The Doctrine of Chances . 161 ... Xlll CONTENTS Akpendix Page 1 Buckley's Memorabb Arithmetic . 179 Translated by Jean Edmiston 2 Galileo's Sopra le Scoperte dei Dadi . 192 Translated by E. H. Thorne 3 Brother Hilarion de Coste's Life of Father LZlarin Mersenne . 196 Translated by Maxine Merrington 4 Letters between Fermat and Pascal and Carcavi . 229 Translated from Oeuvres de Fermat by Maxine Merrington 5 From The Doctrine oj' Chances by A. de Moivre . 254 Index . .. 269 xiv List of Plates Frontispiece Signs of the Zodiac : floor mosaic, Beth- Aleph Synagogue, Palestine (5th cen- tury) Plate 1 Egyptian tomb-painting showing a nobleman in after-life using an astragalus in a board game . Facing page 8 2 The board game of "Hounds and Jackals " (c. 1800 B.c.), from the tomb of Reny-Soube at Thebes, Upper Egypt Between pages 8 and 9 3 Four views of an astragalus . Between pages 8 and 9 4 Die roughly made on classical pattern Imitation astragalus carved in stone Egyptian carved ceremonial die, with typical astragali . Facing page 9 5 Lorenzo Leombruno's Allegory of For- tune (16th century) . Facing page 24 6 and 7 Excerpt from the manuscript poem " De Vetula " (Harleian MS. 5263) giv- ing the number of ways in which three dice can fall . Between pages 24 and 25 8 Fra Luca Paccioli (National Galleries of Capodimonte, Naples) . Facing page 25 9 Abraham de Moivre-painted by Jos. Highmore, 1736 . Facing page 160 t Acknowledgements I ACKNOWLEDGEMENTSof permission to use quoted matter have in most cases been given in footnotes.