The chances of death, and other studies in evolution

Front matter

CORNELL UNIVERSITY LjBRARV

3 1924 097 311 579

Cornell University Library

Preface

The Essays and Lectures contained in these volumes have either been written, or else very carefully rewritten, within the past six years. Of the twelve essays, five — " The Scientific Aspect of Monte Carlo Roulette," " Socialism and Natural Selection," ■'' Politics and Science," " Woman and Labour," and " Eeaction !" have already appeared in print. The first four were originally published in the Fortnightly Review, and for permission to reprint them, as well as the paper contained in the Appendix, I have to cordially thank Messrs. Chapman and Hall. The fifth paper was published as a pamphlet in October, 1895. Of the remaining seven essays, two — namely, "The Chances of Death" and "Woman as Witch" — have been delivered as lectures; two others — namely, "Kindred Group-Marriage" and " The German Passion-Play " — contain material on which papers were read or lectures delivered a good many years ago ; the remaining three, " Reproductive Selection," "Variation in Man and Woman," and "Ashiepattle," are new, except in so far as some of the results of the first two have been communicated in a very different form to the Eoyal Society. I have to thank the Council of that Society for permission to reproduce the plate showing the resolution of the mortality curve in the paper on " The Chances of Death." The volumes, as a whole, contain what the author considers of most value on the more popular side of his work as lecturer and essayist since the publication of his Ethic of Freethought.

To some readers a few words of explanation on the apparent want of unity in the contents of this book may seem desirable. In the first place, the author believes this heterogeneity will be found more in the titles of the several essays than in their contents. There / must always be a unity, interesting at least to the psychologist, if not to the general reader, when a mind with its opinions and methods of investigation reasonably matured approaches even very diverse problems. 1 But the author would be unwilling to admit that this lis the sole unity of his essays. He believes that the isympathetic reader will find in one and all the essays the fundamental note of the author's thought, namely : phe endeavour to see all phenomena, physical and social, las a connected growth, and describe them as such in the briefest formula possible. Without asserting that

PREFACE evolution can explain anything, but accepting it as a most invaluable formula for describing the sequences of phenomena as we have experience of them, the rationalist has at present a quite impregnable stronghold against reactionaries of every type. He is not called upon to show that evolution explains the universe ; he may content himself with the simple challenge to his critics to produce any other formula so useful in describing our experience of the concatenation of phenomena — any other formula which so markedly economises thought, or, differently expressed, which so amply fulfils the piirport of science. From this standpoint the reader wlU find the fourth, fifth, and sixth essays, and the Appendix, are endeavours to defend modern science from recent attacks on the part of the pseudo-scientific, the political, and the theological critic. The remaining essays deal with evolution from either the statistical or the historical standpoint. Into the former, or statistical category fall the first, third, and eighth essays. In this also may be included the second essay^ on " The Scientific Aspect of Monte Carlo Roulette." It originally formed one of a series of popular lectures on chance, of which others on tossing, whist, guessing, etc., may some day be published, and which were especially designed to introduce the audience to those theorems in probability, without a knowledge of which it is impossible nowadays to appreciate the arguments for and against the Darwinian theory of evolution. The essay, on its first publication, appealed to a wider audience than might have been anticipated, and the author stUl receives communications from all sorts of devotees of Monte Carlo. ^ He can only hope they may seek for the reprint in this volume, and that a study of probability will lead them to its more social applications.

Into the second category of essays dealing with the historical aspect of evolution fall the seventh and the last four papers in this series. " Woman as Witch " and " Ashiepattle " are only slight sketches drawn from a much greater mass of collected material, and on this account, perhaps, the reader will be more ready to pardon their imperfections than in the case of the longer and more elaborate studies on " Kindred Group- Marriage" and the "German Passion-Play." These essays, in substantially their present form, the author, according to a well-known recommendation, has put aside for periods of ten and twelve years respectively. Re-writing them during the last few years, he has suffered from the great disadvantage of having no time to thoroughly study the more recent literature dealing

^ One of his latest correspondents reports great successes attending the betting on a disproportionate number of intermittences ! Would the Casino authorities be persuaded of the imperfections of their tables if a majority of the frequenters took to laying on a superabundance of intermittences ?

PREFACE with their topics. This will no doubt offer a wide field to specialists to point out the enormity of the blunders committed. At the same time, the renewed study of these papers has convinced the writer that much in them is probably correct, and that, if what is correct be well known to the select few, it has certainly not yet made itself a part of current thought. The idea that mediaeval western Christianity was a product neither of Jewish nor Greek minds, but of the Teutonic folk-spirit, is certainly not general, and yet it illustrates one of the most important axioms of comparative religion, e.g. that neither the propounder nor the dogma, but the convert, makes a religion what it is. The principle that the noblest characteristics of man must have developed from animal instincts under the pressure of natural selection may be commonly accepted in theory, but a study of the Aryan words for kinship and sex shows in an almost startling manner this evolution in progress.

Beyond the one chief helper to whom the author dedicates this book, he has to express his keen sense of gratitude to Mr. Francis Galton, F.E.S., Professor W. F. E. Weldon, F.K.S., Professor George Thane, Mr. G. U. Yule, Miss Alice Lee, and Dr. E. J. Eyle for friendly assistance in a variety of ways.

KAEL PEAESON.

December 1896.

CONTENTS OF VOLUME I

PAGE

1. The Chances op Death ... 1

2. The Scientific Aspect of Monte Carlo Roulette . 42

6. Reaction ! A Criticism of Mr. Balpouk's Attack on

Rationalism . . . . 173

8. Variation in Man and Woman . 256 Appendix — Sectarian Criticism . .379

ILLUSTRATIONS IN VOLUME I

PAGE

The Beidge of Life . Frontispiece

Heidelberg Block-Book 4

Ghoss-Basel Dance of Death . 5

Holbein's DajStces op Death . 9

Games of Chance . . . .13

Frequency Curve . 16 Cephalic Index op Long-Headed Population in Eow-Graves 20

Distribution of Enteric Fever Cases . . .22

Frequency of Target Hits . .23

English Male Mortality . . . to face 26

Scarlet Fever and Diphtheria . 33

BouLETTE Diagram . 46

Curve of Fertility in Man — Anglo-Saxons . . 71

Curve op Fertility in Man — Danes . .87

Diagram of equal range Frequencies . .275

United States Recruits • 277

Cephalic Index of Bavarians . 279

Typical Skulls . 288

Male and Female Variation • 373

ERRATA

Vol. I

P. 169, footnote, for throu read through.

For footnote, p. 283, read, "The probable error of a coefficient of variation

is approximately •6745 x — ^ of its value," etc.

THE CHAITCES OF DEATHS

'I see a bridge,' said I, 'standing in the midst of the time.' 'The bridge thou seest,'said he, 'is Human Life; consider it attentively.' . . . 'But tell me farther,' said he, ' what thou discoverest on it.' 'I see multitudes of people passing over it,' said I, 'and a black cloud hanging on each end of it.' As I looked more attentively, I saw several of the passengers dropping through the bridge into the great tide that flowed underneath it. — Vision of Mirsa.

There is an old German proverb : " Death has no calendar," which taken in conjunction with our English, " Death is no respecter of persons," strongly marks the folk-conception of Death as of one who obeys no rule of time, or of place, or of age, or of sex, or of household. This idea of Death as the lawless one, the one who strikes at random, arose early in mediaeval tradition, and is represented in the well-known Dances of Death, from the primitive block-book to the finished designs of Holbein. Parallel with this notion of the random character of Death's aim, has run in the mind of the folk a vague idea of Chance as that which obeys no rule and defies all measure and prediction. The two conceptions cross one another in the mediaeval representa-

^ Delivered as a lecture before the Leeds Philosophical and Literary Society, January, 1895.

VOL. I B tion of Death seizing the gambler's dice-box and casting the dice with him for his life.-'

Almost the earliest medigeval conception of Chance is associated with the idea of dice — the origin of the word itself is very possibly related to the falling of the dice from their box, — and certainly the first attempts at a theory of Chance arose from the general interest in gambling with dice. It is indeed in a fifteenth century commentary on the lines of Dante —

When from their game of dice men separate, He, who hath lost, remains in sadness fix'd, Revolving in his mind, what luckless throws He cast —

that we find the first attempt to rise above the folk-conception of Chance as the chaotic, to the modern notion of Chance as obedience to law. Let us bear these points in mind, the association of Death and Chance, the notion of both as chaotic in their action, and their embodiment in a great artistic ideal — the Dance of Death — which gave so much colouring to mediaeval thought and life. We find this sombre notion everywhere — on the church walls, on the bridges, in the engravings and broadsides, but as well in the sermons, the poetry, and the very turn of folksentiment.^ That the reader may realise more clearly

1 Death to the Gamblek.

Fuessaier Todtentanz.

- Even medals or coins were stamped with the death's head upon them as mementoes of times of plague and death.

Oh

PLATE II.

GROSS-BASEL.

the significance of the old Dance of Death, I will place before him the development of the artistic side of the mediaeval idea of death during the space of more than a century.

The earliest Dance of Death, of which fragments are still preserved to us, appears to be that on the wall of the cloister of a former nunnery at Klingenthal, near Klein-Basel. The cloister has long been used as a barn, and but for the pious pencil of a good old master-baker of Basel, who copied the Dance in 1773, but little would have been preserved to our day. The language and costume of the designs suggest the first quarter of the fourteenth century ; but they have certainly been renewed twice, if not more often — once towards the end of the fifteenth, and once in the beginning of the sixteenth century. In 1480 the nuns of Klingenthal were dispersed, and probably in this year the Dominicans reproduced the nuns' Dance on the wall of the cemetery of their own church in Gross-Basel. This is the dance of death so famous through several centuries. I give in facsimile the pictures of Empress and Cripple in the Gross-Basel Dance as reproduced by Massmann from the drawings of the old master-baker. That the monks copied the nuns' Dance is as clear from the baker's drawings as that Holbein was afterwards influenced by the Gross-Basel Dance. As both the Basel Dances have only reached us after several restorations, I add a reproduction of the Empress and Cripple from a block-book in the Heidelberg Library, scarcely later than 1450, and belonging to the very infancy of woodcutting. During the fifteenth century we find Dances of Death at Liibeck, Luzern, Bern, Strasburg, and other towns, painted in public places, and at the end of this century and during the whole of the next, many woodcuts, engravings, and other forms of representation were published. The artistic value of the Dance of Death has been usually supposed to culminate in the Holbein cuts published first at Lyons in 1538 (see our figures, reproducing the Empress and the Old Man), but throughout the sixteenth, and even in the seventeenth century, we still find vigorous productions dealing with the same central idea, and illustrating how widespread and deeply-rooted this traditional representation of the random action of death remained for more than four centuries. Nor was this folk-idea of death — even if it arose in a time when men were face to face with the terrible mortality of the plague, and heard almost daily the shriek of the wounded and the cry of the condemned — without a healthy lesson for later ages. It taught in public places and in symbols, which the mass of the people could interpret, features of human life common to all classes and to all ages. The shadow of death, more strongly even than blood or nation, maketh mankind akin ; it arouses sympathy and understanding, which surmount all the barriers of caste and station. The old Dances of Death supplied what fails so much in our modern life — an artistic representation appealing to all classes of at least one experience common to the whole of humanity.

Standing in 1875 on the well-known wooden bridge at Luzern, with its pictures of the Dance of Death, it struck me that something might be done to resuscitate the medieval conception of the relation between Death

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V^^S. ^?illW^\ '■C^iurTirr-'-^y / iiiiiSSa^^^^^ gjig^ and Chance, and to express it in a more modern scientific form. It is only within the last year that I have reached such a generalisation of the theory of Chance, that I have been able to work out my idea of 1875, and my aim in this essay is to place before the reader a modern conception of the Dance of Death. To achieve this, however, I must ask the reader first to follow me in the statement of one or two general principles of the theory of Chance, and some apparently dry statistics derived from the Census and Kegistrar - General's returns.

In the first place, we have to recognise that our conception of Chance is now utterly different from that of yore. Where we cannot predict, where we do not find order and regularity, there we should now assert (as in the case of the Monte Carlo roulette returns) that something else than Chance is at work. "What we are to understand by a chance distribution is one in accordance with law, and one the nature of which can for all practical purposes be closely predicted. Let me exemplify this by some experiments on throwing dice, the particular game of Chance in which our ancestors were so interested. Twelve dice were thrown together 26,306 times,^ and on each occasion the number of dice having 5 or 6 pips on their upper faces was recorded. Eeduced to a diagram we at once see a certain order in the distribution. The most frequent occurrence — 6100 odd times — is 4 fives and sixes in the throw of 12 dice. "We may term that occurrence, which happens not necessa/rily a majority of times, but more frequently

1 I owe these returns to the kindness of Professor W. F. R. Weldon, F.R.S.

than any other the "mode." The "mode" in this case is 4 dice in the 12 thrown with 5 or 6 pips. Now the reader will notice on examining the diagram that the frequency of other casts does not distribute itself symmetrically round the "mode." For instance, casts of 2 and casts of 6 both deviate by 2 from the mode 4, but their frequencies are in the ratio of about 16 "5 to 14 '15. The whole system of frequencies, however, forms a fairly smooth polygon, which conveys at once the notion of law and regularity in chance distributions. Now, suppose we were to consider every possible combination of the faces which could be thrown with our 12 dice, and count up in all these possible combinations the number of those with no fives or sixes, then the number of those with one five or six, then with two, three, four, etc., fives or sixes, and suppose we then distributed our actual total of 26,306 throws according to the frequency of these various possible combinations.^ I will not enter into the mathematics of it, but the result is indicated on the diagram by the dotted line. We see that the two lines are in very close agreement.' We may therefore conclude that all the combinations mathematically possible in tossing 12 dice together do actually occur in their due proportions when we throw 12 dice several thousand times. This is not a result which we have any right to assume beforehand ; that the mathematically possible actually does occur in

^ Those who are acquainted with the elementary theory of Chance will know that it is expressed by 26,306 x (| + J)^^.

" Not such close agreement as occurs in the case of card-drawing and tossing for dice are never theoretically perfect, and a persistent bias has been observed in them.

experiment is demonstrated and can only be demonstrated by actual experience.

Now this conclusion is so important tbat it ought

Games of Chance.

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(1) COUNTER DRAWING A h&g contained loo counters, 25 each of red. black, yellow

12) CARD DRAWING 10 cards from a pack: the luniiljer of hearts in each draw recorded.

once c recorc ud the number ed. 9,148 drawing

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number of^fives

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(Weldon) ogether and the Si sixes recorded throws.

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to be supported by still further evidence, and I accordino-ly draw your attention to one or two other results of a like character.

In the first place, we have on the same diagram a figure for the drawing of ten cards together 18,600 times^

1 For these experiments I am indebted to members of my audience at Gresham College, and for the counter experiments to Miss Whiteley.

out of a pack of 52, and then one for the drawing 9148 times of 10 counters out of a bag containing 25 counters each of four different colours. Again, we see a very close approximation between the mathematically possible sets of combinations and the frequencies given by actual experiment. Here, however, there is a fundamental distinction between dice and cards or counter-drawing. In the former case each die gave its own result, uninfluenced by what its fellows might give. But if we draw ten cards in a set from a pack, or ten counters at once from a bag, it is clear that the cards or counters are not each independent ; if, for example, we take the ten cards successively out of the pack, the first draw will influence the chances of all that succeed it, the first and second all that foUow both, and so on. This is of vital importance for the consideration of mortality curves, the frequency of death at later ages must depend on the incidence of death at earlier ages.

But to return to the results we have already reached, we may sum them up as follows : —

First, the chances of the single event, 2 : 1 in our dice, 3 : 1 in our cards, 1 : 1 in tossing (or 36 : 1 in roulette), may be any whatever.

Secondly, the single events may or may not be independent of each other.

Thirdly, when we take a large number of experiments, we see that, however unable we may be to predict the result of a single trial, the frequencies of many trials distribute themselves round the mode in a perfectly orderly manner, and that the law of distribution is precisely that whicli we obtain by considering all the combinations which might possibly occur.

It is not theory, but actual statistical experience, which forces us to the conclusion that, however little we know of what will happen in the individual instance, yet the frequency of a large number of instances is distributed round the mode in a manner more and more smooth and uniform the greater the number of individual instances. When this distribution round the mode does not take place — as, for example, at Monte Carlo — then we assert that some cause other than chance is at work. Our conception of chance is one of law and order in large numbers ; it is not that idea of chaotic incidence which vexed the mediaeval mind.

The reader will now, I think, be prepared for the next stage in our argument, the conception of a generalised frequency curve. Taking all the individual results or observations, let us sort them into groups by their deviations from the mode, each group containing all the deviations falling within a certain small range, this small range being the same for each group, and corresponding in many cases to a unit change of deviation. Now, taking a point on a horizontal line to represent the mode, measure the deviations from the mode along this line — deviations in excess to the right, and deviations in defect to the left, of the point. Then place at the centre of each small range or unit a vertical line, proportional in length to the number or frequency of observations having a deviation falling within that range. If the tops of all these verticals be joined we have a polygon which approximates more and more i6 closely to a curve the smaller the range of deviation corresponding to each group be taken. This curve is the so-called frequency curve. It gives us by its height at any point, or, to speak more accurately, by its area, the frequency of the corresponding range of deviations from the mode.

c

^a Mode ^

bb Mean •^cc Median ^ b

—

I c b

FiQ. 2.

We cannot now stay to discuss the mathematical properties of this curve, but attention must be drawn to one or two of its characteristic features.

(1) The mode is not necessarily the same as the mean. For example, suppose we set about counting buttercup petals, then we should find that five petals occur most frequently, but that there are buttercups to be found with ten and even more petals. The mean will be found to lie nearer to six than five petals, and after selection and cultivation may even difi'er by as many as two petals from the mode. The amount by which the mean differs from the mode gives us a conception of the amount of asymmetry or skewness of the frequency curve — the greater length of tail, so to speak, on the mean side of the mode.

(2) Experience soon shows us that very large devia-

THE CHANCES OF DEATH ly

tions have little or even no frequency ; that the great bulk of the frequency is contained in a comparatively limited range round mode and mean. Now we require some standard by which the degree of concentration of the frequency can be measured. We can realise such a standard in the following manner : — We know that if a body be swinging about an axis, both its energy and momentum will be less the more its mass be concentrated along this axis. Hence we might take the distance from the axis at which all the mass should be concentrated in order to have the same momentum and energy as the actual body, as a good measure of the concentration of its mass. This conception can be applied to our deviations. Suppose a uniform metal disc, or template, to be cut out in the form of the frequency curve, and swung on the vertical through the mean as an axis. Then the distance from this vertical or mean at which the mass of the template must be concentrated, in order to have the same energy and momentum, would not only measure the concentration of mass, but the concentration of frequency (which is proportional to the mass of the template) about the axis or mean. This measure of the concentration of frequency is termed the standard deviation. The distance from the axis at which we must concentrate the mass of a swinging body in order to get the same energy or momentum is termed its swing radius, and we accordingly see that the standard deviation of a frequency curve is nothing else than its swing radius about the mean. There are various methods used by physicists and statisticians for finding the swing radii or standard VOL. I c deviations of curves,^ but we must be content for our present purposes with the recognition that a good measure of concentration exists, without entering into details of calculation, which would carry us too far from our present quest. I may, however, remark that whatever be the degree of skewness of the frequency curve, practically the whole of the frequency falls within a range of three times the standard deviation taken on either side of the mean.

Scientifically, we take the ratio of the deviation of the mean from the mode to the standard deviation as the actual skewness. To sum up then, we have these two conceptions with regard to a frequency curve : —

(1) The skewness, measuring the amount of asymmetry, or the way in which the mean or average differs from the mode.

For example, in house property the mode is in England a value of about 2s. per week, but the mean is about £15 per year — over 5s. 9d. a week.

(2) The standard deviation, measuring the concentration of frequency round the mean.

For example, in tossing twelve coins, and counting the number of heads in each throw, the mean being six heads, the standard deviation is about 1 -4 heads, but in throwing twelve dice, and counting the fives and sixes in each set, the standard deviation is about 1 "6. There is thus greater concentration in such coin-tossing than in the dice-throwing experiment.

The reader will be curious, however, to learn what

' In a, whole range of important oases, a piece of uniform card, a pair of scissors, and a fairly delicate balance, e.g. a, good letter-balance, \vill suffice.

frequency curves deduced from coin -tossing and dice experiments have to do with mortality ? The answer is this : If the laws of frequency we are here dealing with hold very generally for the distribution of artificial frequency in cases where we have no knowledge of how the individual instance will turn out, but only statistics of what happens in the mass, may we not reasonably assume that they are essentially the laws of all large numbers, and that even the frequency of death, its distribution with age, will obey the same laws? Is it not likely that the regularity and order of chance will be manifest even in the apparent chaos ^ which at first impresses us, as it impressed our mediaeval ancestors, in the incidence of death ?

Let us try and grasp how wide is the field to which results such as these we have deduced from cards and dice apply, and in doing this let us turn to frequencies more directly the product of Nature and less influenced by the hand of man.

In the first place, Mr. Galton has shown by numberless measurements on man, and Professor Weldon by thousands of measurements on crabs and shrimps, that the apparently random sizes of living things have a frequency closely corresponding to our theoretical curves. Personally, I have found skull measurements give good "fits," and I illustrate by a diagram the frequencies of the several cephahc indices for 540 dolichocephalic German skuUs found in the Eow- Graves of the fifth to the ninth centuries. Theory and observa-

^ Addison, indeed, considered a bill of mortality " an unanswerable argument for a Providence," since "chance could never hold the balance with so steady a hand." — Essay on the Bills of Mortality.

tion here agree with a closeness comparable with that given by counter or card drawing experiments.

The frequency of the various barometric heights is again an instance of the same characteristic type of

CEPHALIC INDEX OP LONC-HEABED POPULATION IN ROW- GRAVES