Games, Gods & Gambling: A History of Probability and Statistical Ideas

295 Pages·1962·9.04 MB·English

by  F. N. David

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,
more solace from the palm-girt wells ;
8
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
TODHUNTEoRn 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 ii s 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,b iographical, 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 ~cyhe ar filling many notebooks. It is too much to hope
that this li;s t 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 Todlh unter on the early development of ideas about chance
and to fill in a certain amount of the background of ideas and
controversi es 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