1.1. Note.

This book was published as "Alfred Russell Wallace. The Story of a Great Discoverer" in the United States.

1.2. Review by: Anon.
The Journal of Education 89 (16) (2226) (1919), 441.

Rarely does a book of today captivate me as has this little book of sixty-four pages on the life and scientific .and social service of Alfred Russell Wallace, who died in 1913 at the age of ninety. Nowhere do we know any such opportunity to know the scientific life and progress of England from 1843 to 1913. Nowhere else does one get the same view of Darwin, with whom he was a co-worker, and than whom no one but Huxley was more nearly his scientific equal. He was two years older than Huxley and fourteen years older than Darwin. He lived twenty-one years after the death of Darwin and eighteen years after the death of Huxley, so that after he was twenty-one he was contemporary with Darwin for nearly forty years and with Huxley for more than fifty years. "The three were closely related scientifically in all those years. No other three men in science have had the same affiliations. Mr Wallace's eighteen years of life after the last of his associates passed away gave him a rare opportunity for public service. No single sentence of his was more characteristic than this: "No one deserves either praise or blame for the ideas that come to him, but only for the actions resulting therefrom."

2.1. Review by: Anon.
The Egoist 5 (5) (1918), 75.

The dedication "to my comrades of the Stepney Herald League" does not arouse confidence, the form is reminiscent and the content mostly meditative; but there is a simple sincerity which strikes out a good line here and there ("When I am old and quite worn out") and which would stand the author in good stead if he would read the right things and work hard.

3.1. Review by: BMJ.
The British Medical Journal 1 (3358) (1925), 886.

In the thoughtful and interesting book to which they have given the title An Introduction to Recent Advances in Comparative Physiology Dr Hogben and Mr Winter have dealt in a clear and pleasing style with a diversity of subjects, such as the fertilisation of the egg, the development of the individual, the sources of vital energy, coordination, behaviour in animals, hereditary transmission, the material basis of inheritance, and the determination of sex. Other subjects of no less interest might be added to this list, such as the blood and circulatory and respiratory functions, the biological action of light and pigment, the production of light by living organisms, the swim bladder and its relation to audition and sense of position and equilibrium. A second volume might deal with such, and would be welcome.

While the attempt by Loeb and others to produce parthenogenesis or virgin birth by experimental means has been crowned with success, we are, say the authors, only on the threshold of a solution of the problem. One factor is proved to be the withdrawal of water from the egg. In dealing with the natural process of fertilisation they point out that the sperm, when shed, becomes active in the presence of a certain degree of alkalinity and that there is a specific attraction emanating from the egg. This attraction is 100 per cent, less in the case of the sperm and eggs of hermaphrodites, and thus self-fertilisation is very rare. The influence of egg extracts on the sperm is specific but not entirely so; it is destroyed by heating above 95º C.

In discussing development of the individual the authors produce evidence that bodily organization may be profoundly altered by external agencies ; thus, the vestigial eyes of the blind cave salamander develop to normal size when the young are reared in red light, and monsters can be produced by acting on embryos with certain concentrations of various salts, by ultra-violet rays, etc. Strange varieties of goldfish are produced thus. Of paramount importance in the production of monsters are initial quantitative differences in cell activity. Susceptibility to external influences varies directly as the rate of metabolism in the parts of an embryo; larvae of a marine worm can be made small-headed by the early action of a cyanide salt and big-headed by the late action. The modern standpoint regards individuation, not as the outcome of a differential distribution of the hereditary determinants through cell division to different regions, but as a result of the reaction to external or internal environment. Thus in the development of the eye the retina is formed from the optic cup, an outgrowth of the brain, and the lens from the skin; if the optic cup is removed in a tadpole no lens develops, while if the optic cup is there any part of the skin grafted over it will form a lens.

3.2. Review by: W C Cullis.
Science Progress in the Twentieth Century (1919-1933) 20 (78) (1925), 364.

This book gives a most fascinating and interesting account of some of the findings of the newer and deeper study of biological problems. The older type of study, classificatory as it was in the main, was based largely on the observation of visible form; but, necessary as it was, it must be admitted that, to the general student of life, it is transcended far in interest by the newer and more physiological way of approach. The authors have written a book which will interest not only those whose lines of scientific investigation and study have followed paths other than the biological, but will have at least an equal appeal to those whose studies have not been in the realms of pure science. The list of chapters giving the subjects dealt with in the book, including as they do matters such as The Development of the Individual, Behaviour in Animals, Hereditary Transmission, and The Material Basis of Inheritance, already promise abundant interest, a promise splendidly fulfilled in the actual reading. This is a book which should be read by all those - and their number is steadily increasing - who wish to have some knowledge of the fundamental facts of biology with their obvious bearing on the understanding of the problems of life. The value of the book is enhanced by the fact that the authors are themselves workers in the field of biological research. Readers will not only gain for themselves much fascinating information, but will secure hours of the keenest enjoyment.

4.1. Review by: J H W.
Science Progress in the Twentieth Century (1919-1933) 19 (75) (1925), 522-523.

Dr Hogben's book deals with an aspect of biology which has hitherto chiefly been the concern of the systematist and speculative evolutionist, but is here approached from the point of view of physiology. It deals with the physiology of colour response in animals.

Most space is devoted to Reptiles, Amphibia, and Fishes. There is also a chapter on Crustacea, and a brief appendix on Molluscs. Great diversity appears to exist in the mechanism of colour response in these different groups. In Reptiles the evidence points to the adrenals as the organs involved. In Amphibians, chiefly through the work of Dr Hogben, the hypophysis cerebri has been shown to be essential to normal colour response. Only in fishes does there appear to be satisfactory evidence that the nervous system takes an essential part. In Crustacea the effectors themselves, and the influences governing them, are much more complex than in the other groups, and our knowledge is chiefly confined to that derived from a study of the responses normally called forth by natural stimulation, an aspect in which Dr Hogben seems to be less interested than in the internal mechanism by which they are effected.

The pigmentary effectors of Molluscs differ totally from those of the other groups discussed in this book in possessing true muscular elements, but our knowledge of their physiology is still very scanty.

Dr Hogben writes in an admirably terse and lucid style, and his book contains some valuable critical discussions on the supposed sympathetic innervation of the receptors in Amphibia and on the supposed analogy between the action of certain drugs on the pigmentary receptors and their possible innervation. The book also contains some interesting suggestions on the light thrown on the nature of receptors in general by these studies on those of the pigmentary system.

4.2. Review by: BMJ.
The British Medical Journal 2 (3315) (1924), 56-57.

The monograph by Dr Hogben deals with the mechanisms by which colour changes are produced in reptiles, amphibia, fishes, crustacea, and molluscs, and it should prove of equal interest to physiologists and zoologists.

The author devotes special attention to the colour changes in amphibia, and the results recorded under this head are based very largely upon his own work. It is interesting to learn from him that the common grass frog possesses greater powers of colour change than the famous chameleon. The frog turns pale under light, warm, or dry conditions, and dark under dark, cold, or moist conditions. These changes are controlled chiefly by endocrine secretions; adrenaline turns the frog pale and pituitary extract turns it dark, and in both cases a small fraction of a milligram is sufficient to produce the effect.
...
An examination of the mode in which colour changes are effected in other classes of vertebrates showed that a surprising variety of mechanisms existed. In all cases the colour changes were produced by expansion or contraction of chromatophore cells, but the mode of control of these cells varied greatly. In reptiles the melanophores are under endocrine control, for adrenaline causes contraction, but pituitary extract appears to be inactive; they may also be affected directly by light. In amphibia the melanophores appear to be entirely controlled by endocrine secretions. In fishes, however, the melanophores are under direct nervous control through the sympathetic neurones; the existence of endocrine control is uncertain, but pituitary extract produces contraction of the melanophores, the reverse effect to that produced in amphibia. Finally, it appears that in crustacea the melanophores are directly stimulated by light.

The results recorded in the monograph certainly make the function of the pituitary more mysterious than ever, for apparently a specific melanophore dilator is present in the pituitary glands of all vertebrates, but only produces an effect on the melanophores of amphibia and fishes, and the effects so produced in these two classes are opposite.

The monograph as a whole is extremely interesting and suggestive and illustrates the great importance of the study of comparative physiology, for it reveals a surprising variety in the mechanisms which exist to produce a single simple physiological reaction. Furthermore, the facts established concerning the endocrine control of the melanophores suggest that a more extensive study of the endocrine systems of lower vertebrates might assist us to understand better the functions of these organs in mammals.

5.1. Review by: BMJ.
The British Medical Journal 1 (3449) (1927), 291.

In contributing a volume on Comparative Physiology to the Textbooks of Animal Biology, Professor L T Hogben has provided both stimulus and means wherewith the zoologist may enrich his knowledge by a vivid glimpse of the experimental methods and results most intimately related to his interests; at the same time it will enable the physiologist to pursue the fascinating inquiries of the last decade in which his methods are applied to problems and material not primarily concerned with an analysis of mechanisms known or suspected in man.

Two hundred and nineteen pages suffice to present an immense variety of phenomena, many of which show unexpected relations between the functions by which lower organisms develop and maintain life and those familiar in the study of mammalia. The diversity of nature is no longer accepted with the resignation of Winterstein, in his comprehensive treatise (1912), as due to "Artverschiedenheiten," but is gradually being woven into a pattern, the significance of which can, at occasional points, be detected. The subjects chosen for discussion, as indicative of such a change, are described in sufficient detail to induce interest and appreciation in readers with little previous specialised knowledge. A high standard of accuracy is reached, and where a particular subject is described at all, few of its recent developments are omitted. The absence of reference to Kato's work on isolated nerves may perhaps be quoted as an exception. The title of the book would suggest that the comparative method had received considerable attention, but it has not yet been applied to any great extent to the data of general physiology. It may be hoped, how ever, that the reorientation of material which is now in progress, and is here described by Dr Hogben, may make the comparative, as contrasted with the experimental, method a more prominent feature of a future edition.

5.2. Review by: W C Cullis.
Science Progress in the Twentieth Century (1919-1933) 21 (84) (1927), 727-728.

During the last few decades physiology has, for many, come to mean human physiology, a conception due in part no doubt to the fact that the chief centres of physiological teaching and investigation to-day are the physiological laboratories of the medical schools. The crowded curriculum of the medical student has inevitably led to a greater and greater stress being laid, in the earlier scientific studies, upon the teaching connected with his ultimate preoccupation, the knowledge and care of the human body. Consequently in these centres comparative physiology is chiefly considered in the light of the knowledge it throws upon human physiology. This being the case, there is every reason to welcome the appearance of books which are devoted to a setting out of some of the findings of those who are primarily concerned with physiology from its more general aspect. In the book under review the author extends the contribution to this subject that he and Winton have already made in their Introduction to Comparative Physiology reviewed in the October issue of last year. The author's aim here is, as he himself puts it, "to consider what are the characteristic properties of animate systems and inquire how far it is possible to interpret each in terms of known physico-chemical laws." In doing this he hopes "to help the student of zoology to appreciate what is achieved by the application of physiological methods to the study of lower animals, and to widen the horizon of the student of physiology who has not been brought into touch with the diversity of problems which are suggested by a consideration of function in a wider range of animals than those with which he has been accustomed to deal in his medical studies."

Comparative Physiology forms the first of a series of Textbooks of Animal Biology edited by Prof Julian Huxley, and is an excellent introduction to the subject. In these days of preoccupation with human physiology it is undoubtedly enlightening to be made to consider for a time results obtained in connection with other forms of activity than those exhibited in man. There are sections devoted to the consideration, from this wider aspect, of studies of movement, secretion, respiration, nutrition, circulation, endocrine coordination, nervous conduction and excitation, behaviour in animals, reproduction, inheritance and development. The author also gives a good bibliography of the subject for the last fifteen years, bearing in mind the encyclopaedic nature of Winterstein's Handbuch der Vergleichende Physiologie, which gives a very complete account of the subject up to the year 1912. At the same time he gives sufficient account of the earlier work to secure the idea of continuity and to inform those who may not be familiar with it. Like its predecessor, the Introduction, it is a very readable and interesting book.

6.1. Review by: BMJ.
The British Medical Journal 1 (3501) (1928), 223.

Dr L T Hogben's book The Comparative Physiology of Internal Secretion is a distinguished contribution to the new series of Monographs on Comparative Physiology, published by the Cambridge University Press. The subject of the chemical co-ordination of function is one of quite recent growth in comparison with that of our knowledge of the complementary phenomenon - the nervous coordination of function. Nevertheless, the growth of endocrinology has been rapid, if sometimes impatient. Now, as the author points out, the practical justification for comparative physiology resides in the fact that some animals provide far more accessible material for the solution of a particular problem than others. This has proved very true in respect of the physiology of the ductless glands, and it has undoubtedly been the comparative point of view which has disciplined the less cautious claims in this field. In a field in which terms are apt to be used with little discrimination,
...
The book is a contribution of real distinction to the literature of endocrinology.

7.1. Review by: BMJ.
The British Medical Journal 1 (3661) (1931), 404-405.

It will probably be admitted, or, at all events, it will probably be found, that the two most momentous fields of work in modern biology are those of the Russian physiologist Pavlov and his co-workers on conditioned reflexes, and of Thomas Hunt Morgan and his compeers on the methods of hereditary transmission. The biological and philosophical consequences and implications of these researches are likely to prove not less revolutionary than those which, in the sphere of physics, have resulted, or are now emerging, from the theory of relativity and from the conception of the structure of the atom. A remarkable and intensely interesting book discussing these biological and philosophical consequences is The Nature of Living Matter, by Lancelot Hogben, professor of social biology in the University of London. The book is even of somewhat wider scope than that indicated. It is the expansion and outcome of the author's contribution to a symposium on the nature of life, arranged by the officers of the Physiological Section of the British Association in the summer of 1929, and a criticism of the philosophical views of General Smuts and Professor J S Haldane, two of the other contributors to the same symposium, who have already set out their ideas in book form. It constitutes a review of the progress of modern biology in its philosophic bearings, and claims that, although so far the physicists have assumed the leading part in the rekindled interest in the relation of science to common sense on the one hand, and the relation of science to moral philosophy on the other, it is essential that the contribution of contemporary biology to such a discussion should be taken into consideration before any assured outcome can be seen or predicted.
...
He proceeds to this examination of the method of evolution, and, among other things, defines the restricted sphere of natural selection, and of the struggle for life and the survival of the fittest. In his third section the author develops the concept of a public world of science which is significant for discussion or discourse as contrasted with, or distinct from, the private world of individual belief with regard to the problems of existence.

This antinomy does not necessarily reside in the system of nature. It arises because our curiosity exceeds our information. Up to a certain point we succeed in pooling our experiences by the method of science. In so doing we construct the public world. But man is pre-eminently interested in himself. So long as science cannot satisfy that curiosity his private and personal values assume a greater importance than the academic hypotheses of science. At every stage in the advance of scientific knowledge a new system has arisen to conserve some fragments from the wreckage of supernatural beliefs.

This line of thought is admirably and lucidly developed. Professor Hogben truly says that "there is no issue which provides more scope for vague, barren, and undisciplined discussion" than the nature of life. His own discussion of that problem, embodied in this volume, deserves epithets the opposite of these. It is clear, suggestive, forceful, and purposive, based upon a fullness of know ledge, and enlivened with delightful touches of humour.

7.2. Review by: J H Woodger.
Mind 40 (159) (1931), 375-381.

This is an extremely clever book, quite one of the cleverest books of its kind that have been written by an experimental biologist. Apart from its forcible and beautifully clear style, and the breadth of interests it shows, its cleverness lies in the extraordinary skill with which the author has succeeded in anticipating and disarming criticism. It would be easy for an unsympathetic and unscrupulous critic to misrepresent the author by quoting extracts without also giving the author's own "antidotes" to them. Consequently it is not easy to give a faithful representation of Prof Hogben's position, still less to convey the peculiar literary merit of the book, in a few words. It is one of the author's merits that he does not fit comfortably into contemporary categories. It would, for example, be a gross misrepresentation to call him a behaviourist, although behaviourists might well claim him as a prophet, and would be hard put to find a better one. The book is dedicated to Mr Bertrand Russell, and the author makes Mr Russell's distinction between "private," and "public," and the notion of "ethical neutrality," the central ideas of the book. If Prof Hogben is to have a label, "Publicist" would perhaps be the best that could be found. The position he wishes to urge has much in common with that of Mr Russell's Outline of Philosophy, the differences between the two works being chiefly dependent upon temperamental differences between their authors, and on the fact that one is a biologist and the other is not. Moreover (and this increases the reviewer's difficulties), the present work does not profess to be a systematic one. It is a collection of essays very skilfully knit together by the central ideas above mentioned.

7.3. Review by: Jas Johnstone.
Journal of Philosophical Studies 6 (21) (1931), 127-130.

Professor Hogben's book has a much wider scope than its title suggests. It contains a connected discussion of controverted biological questions: the conceptions of vitalism and mechanism; the weight of teleology in biological speculation; the possibility of a completely objective study of animal behaviour; the possibility of neglecting consciousness in our descriptions of the public activities of even man himself; atomistic heredity and the application of experimental methods to the problems of eugenics; the biological conception of adaptation; the methodology of evolutionary hypotheses; and, most interesting of all, the author's own concepts of publicity and privacy in relation to investigation to religion, education, humanism, reality, and the "holism" of General Smuts. The book begins by being polemical, but as it proceeds it becomes soundly critical and constructive. It has strong interest for all who are engaged in philosophical studies, and while it may repel some readers, it may not be neglected by them. Professor Hogben tells us that he did not intend to write such a book until he was sixty years of age. This would have been a great pity, for he is a young man who is already well known as a brilliant and successful investigator. Besides. he can always do it again.
...
Enough has been said to indicate the healthily provocative and comprehensive nature of the work. More than any book published for a very long time does it amplify the scope and interest of biology - both for biologists and nonbiological readers. It is most clearly written, so that there is little doubt as to what the author means. It is written in the light of such a personal knowledge of biological researches and their results as to compel one to think again, and more closely, about those parts of the author's conclusions with which he is, at first, inclined to disagree.

8.1. Review by: BMJ.
The British Medical Journal 1 (3652) (1931), 18.

Professor Lancelot T Hogben's recently published book on the Principles of Animal Biology has the merit of living up to its title. It is, in the first place, concerned strictly with the general principles of which the phenomena of living matter are manifestations, presenting no more of the anatomical and physiological facts than are necessary to illustrate these principles; secondly, it deals exclusively with biology - the science of living things - and not, as do many works bearing a similar title, with the architecture of corpses. The author has made a complete break with the traditional "type system" which, introduced by Thomas Henry Huxley, still forms the basis of most English textbooks for first-year students. In this way he not only spares the student the irksomeness of meeting again facts with which his laboratory manual has made him sufficiently familiar, but leaves himself free to develop in a logical manner the principles of scientific method in general and their application to biological science in particular. Wherever necessary he has adopted an historical approach, "in the belief that the student will not attain to a sense of the challenging quality of scientific thought, unless he realises the steps by which our present knowledge has been reached." It is this sense of the profound value of precise and disciplined observation and thinking, of the worthlessness of meta physical speculations not rooted in scientific knowledge, that Professor Hogben succeeds in conveying to the reader throughout this book.

The work falls logically into two parts: the first, in which the elementary facts of comparative anatomy, with strict reference to their physiological significance, are set out in their proper order; the second, in which these facts are used as a basis for the interpretation of the phenomena of living matter. Of special value are the chapters on the machinery of inheritance and on the evolutionary problem, the former presenting a lucid account of the fundamental facts of genetics, the latter a scholarly and philosophical statement of the controversies that have raged about the problem of the origin of species. Professor Hogben, not unmindful of the possibility that "many ... will shake their heads at the introduction of so much new and controversial material into a book of so elementary a character," is ready with his defence. "I have found in teaching," he says, "that young people are not interested in a dead subject, but are attracted to what is - like themselves - in a stage of rapid growth; and in my experience the surest way in which to make dull facts palatable is to make them topical." To the intelligent student, above all to the student who can take pleasure in science in the making, who would rather have his mind stimulated than crammed with sterile facts, this book may be unreservedly recommended.

8.2. Review by: C O'D.
Science Progress in the Twentieth Century (1919-1933) 25 (100) (1931), 722-723.

Zoology and biology are terms of such enormous content that they may be used to cover a multitude of sins, and when in actual practice the task of devising an elementary course in either is essayed, no two people will agree as to the ground it should cover. It is true also that in Britain at any rate there has been a tendency, in some instances strongly marked, to overweight the morphological aspect of the subject. Attempts have been made at various times to break away from this tradition, and the present book is one of them. It does not follow that the new courses suggested in this or any other book are better than the old, but they are different. The present work, in our opinion, swings over to the other extreme and places the weight upon the physiological aspect of zoology, including such a minimum o£ morphology as will help to make the physiological work intelligible, and may perhaps serve as a sop to the older traditions and to those who favour the "polysyllabic aspects of embryology." To this have been added introductory genetics and other interesting topics. Apart from the latter, a book of this type - not, of course, containing the same facts, for many of them were not known then - if it had been written twenty or twenty-five years ago would in all probability have been entitled Elementary General Physiology or something similar.
...
It would be possible, by treating this book in the critical manner adopted by the author in his "Foreword" to pass a number of adverse comments on it, but it is perhaps better to accept it in the spirit in which it is offered. To quote: "I do not claim that my own way of teaching is an ideal one, but I do venture to believe that at a time when methods of teaching zoology are undergoing considerable changes it is worth while that those of us who are trying out new methods should place them at the disposal of others."

8.3. Review by: J P.
Geography 17 (1) (1932), 75.

Professor Hogben is, like many other zoologists, in revolt against the type system of teaching biology, and has written the above work primarily as an elementary textbook for intermediate students in science. There is little doubt that we have adhered to the type system too slavishly in the past, and some deviation from it is both necessary and refreshing. The author has, however, deviated very widely, and the treatment of experimental biology, physiology and genetics has been developed at the expense of elementary morphology. The usual dreary method of describing intimately type after type up the animal scale is replaced by a lively and interesting account of general biological principles, in which the experimental method of approach is put forward vigorously, and the value of the study of genetics is stressed. Indeed, Professor Hogben has struck out on original lines and produced an interesting, well-written and well-illustrated book, but one which is probably of greater value as an introduction to biology for general readers than a rigid guide for the teaching of zoology to the intermediate classes in the University.

9.1. Review by: E B Reuter.
American Journal of Sociology 39 (1) (1933), 115.

This book is an extremely valuable contribution to the social-biological literature. The limited applicability of the experimental techniques in dealing with mankind, together with the facts that human families are very small and the interval between generations is very long, has retarded the advance of objective and verifiable knowledge. Most of the writing on eugenics and the various aspects of human genetics has been without any reasonably sure basis of fact. This body of literature has been for the most part a superstructure erected upon a foundation of wishes, guesses, biases, and analogies. In the present volume the author undertakes to separate the little that is known and demonstrable from the great mass of popular and pseudo-scientific writing. Beyond this he undertakes to present the line of research in this field that may be and is being carried on with the promise of scientific results. The book deserves very careful reading by both the biological and the sociological, students.

9.2. Review by: E M East.
Economica 36 (1932), 235-238.

The two hundred and thirty pages of Professor Hogben's enterprising attempt to show how genetic principles may be applied to social problems are fastened between covers which the discerning eye recognises as an imitation of a crocodilean epidermis. We are not told whether this setting by Messrs Williams and Norgate is purposeful; but it certainly is apt. It forms a cryptographical description of the volume, for which the reader has a choice of interpretations. The sociologist will see his science being engulfed by an irreverent saurian which has no regard for the cloth, which has little respect for accepted tenets like the inheritance of acquired characters. The geneticist, on the other hand, will choose to believe that the somewhat scaly jaw of sociology is having difficulty in swallowing the conclusions of the experimental breeder.

Perhaps this comment may seem to be unduly harsh. The efforts of a man conversant with modern biological facts and with statistical theory to apply rigorous analyses to sociological questions would appear to merit only commendation, for it is a task as desirable to have completed satisfactorily as it is difficult of accomplishment. It is a thankless task, however, for the writer who undertakes to correlate the work in two camps is usually unable to resist the temptation to tell each group just how puerile its isolated labours have been. For this reason he becomes the mark of snipers from each outpost.

In the reviewer's eyes, such weakness on the part of Professor Hogben has seriously marred a book that would otherwise have been very effective.

9.3. Review by: Anon.
Charity Organisation Quarterly 6 (4) (1932), 182-185.

Genetic Principles in Medical and Social Science is a title which cannot fail to attract the social worker, and we are very glad that there is a book which purports to give us what no less a personage than the Professor of Social Biology in the University of London has to say on the subject. In addition to that our acquaintances in university circles seem to refer to Professor Hogben almost with bated breath, so transcendent is his ability; and we are very glad to have a chance of studying a sample of his work. There is nothing in the text to suggest that the Professor has ever heard of social case-work or that it would interest him if he had. Quite on the contrary the indications are that he is a mechanistic materialist to whom all forms of social polity except that set up in Soviet Russia are absurdities. If we are right in thinking that social case-work is the only thoroughgoing reply to the Soviet scheme of things, we may assume that the Professor would have no sympathy with it. This does not prevent his including in this volume a very large number of obiter dicta of quite first-class value to us family case-workers.

9.4. Review by: BMJ.
The British Medical Journal 1 (3710) (1932), 293-294.

It is hardly too much to say that Professor Lancelot Hogben's book entitled Genetic Principles in Medicine and Social Science marks the beginning of a new phase in human genetics. Following the rediscovery of Mendel's work, there was a period of intense activity, not only in general animal and plant breeding, but in its applications to man. Soon it became clear that the new science was growing more complex and specialised. The small size of the human family and the slowness of human breeding made it appear that there was little hope of acquiring any full knowledge of human heredity within a reasonable period. During the past few years, however, it has become more generally recognised that statistical methods can be devised by the use of which these difficulties may be largely evaded. There is a new spirit of hopefulness. It is felt that a great store of useful knowledge awaits discovery, and that methods are available or can be made available for the purpose. Various writers, notably in Germany and Scandinavia, have produced important methodological work, and during the short period that has elapsed since he left the field of experimental zoology, Professor Hogben has himself contributed findings of fundamental importance. This book is quite different from any other hitherto produced in this country, and, as far as we are aware, cannot easily be compared with any book produced abroad. There is no exposition of genetic theory and no catalogue of inherited defects. For these the reader is referred to other works. As his title indicates, Professor Hogben is more interested in principles and in methodology. There is a full discussion of the approach to human problems by the study of twin resemblances and by that of the blood groups. The chapter on genetic selection is searching and precise. All who are interested in problems of population growth should read the chapter on that subject, if only to appreciate the strength of the case that can be made against some widely accepted current theories.
...
Professor Hogben successfully sustains his thesis. Genetic principles are not only of value, but can be readily applied both in the field of medicine and in that of social science. The experimental worker, the statistician, and the clinician will realise, if they have not fully realised before, the magnitude of the service they can render to a rapidly expanding and practically important branch of scientific study.

9.5. Review by: A M Carr-Saunders.
The Economic Journal 42 (166) (1932), 304-306.

The extent to which the characteristics and behaviour of men rest upon genetic foundations is a matter of interest to all. To students of the social sciences it is a basic problem which they cannot escape. Not only the explanation of events in past times, but also any long-range proposals for betterment, must be profoundly affected by the view taken as to the part played by the genetic basis of human nature. It was inevitable that men should have speculated concerning a problem of such great and general interest long before there were any means of making a scientific attack upon it. Thus in any case scientific inquiry would have begun in an atmosphere of preconception.
...
The book is not easy reading for those without some knowledge of genetics and of statistical method. In consequence the casual or hasty reader may miss that which is of lasting value-the closely reasoned exploration of particular problems. His attention is likely to be caught by another aspect of the book which is hard to define. It may be put this way. Professor Hogben is not only in revolt against existing pseudo-science, but also against the general conclusions which are based upon it. He is not content, however, to intimate that any general conclusions must be premature. He is emotionally repelled by the doctrine of the importance of inheritance and especially by the superior and condescending outlook to which it sometimes gives rise. It is evident that he is attracted by the opposing point of view; and, while he is far too conscientious a man of science ever to suggest that there is scientific evidence, when it is absent, for that which he would like ultimately to find to be true, he does somehow convey the idea that further knowledge will not tend to support the thesis that inherited differences are of great importance. The careless reader may easily conclude that Professor Hogben has demonstrated this. He has not done so, and it is a pity that he has laid himself open to this misconception.

9.6. Review by: J H Woodger.
Philosophy 7 (27) (1932), 351-352.

Writers on genetics in relation to human affairs are usually more abundantly supplied with missionary zeal than with scientific curiosity. Consequently such scraps of information as we may possess in this field are not submitted to any very searching criticism so long as they can be cited in favour of the views which the author wishes to urge upon his readers in his anxiety for the betterment of mankind. This procedure only impresses readers who share the author's zeal. On a more critical public it has the effect of discrediting the whole movement. The above book by Professor L T Hogben is of quite a different character. The enthusiasms he has displayed in other writings are here successfully held in check, and we are given a much juster estimate both of the difficulties as well as of the achievements of human genetics than the common run of such books would lead us to expect. What distinguishes this author's treatment from that of most others is his far clearer appreciation of the logical aspects of these problems, and his deliberate consideration of the technique of interpretation. As Professor Hogben himself says: "Writers on human genetics have hitherto devoted very little attention to the requirements of a rigorous treatment of genetically determined conditions." This being the case, it is not surprising that our definite information on these topics should be so meagre, and that the exposition of the requirements of a "rigorous treatment" should form the most valuable feature of the above book.

The book is hardly an elementary one, but presupposes a knowledge of the general principles of modern genetics. Nor is it a systematic treatise. In addition to discussing the technique of interpretation of the data furnished by such sources as twinning, serology, and pathology, there is an excellent chapter discussing the bearings of genetical theory on the concept of race as employed in taxonomic biology. It is to be hoped that this chapter will encourage anthropologists to reflect a little on the logic of their own procedure.

The most curious feature of this book which will strike a reader of the same author's Nature of Living Matter, and the one which will most amuse philosophical readers, is the contrast between the author's attitude towards deductive reasoning and its relation to natural scientific theory in the two books. In the earlier work deductive reasoning was covered with ridicule and abuse. In Genetic Principles the same author shows an admirable grasp of its real significance, and it is just this feature which places his work on a plane far above most others of its kind. This paradox is explained when we find that it is correlated with another difference between the two works. Genetic Principles is guided by genuine scientific curiosity and uses the apparatus of reason. The Nature of Living Matter is chiefly inspired by the zeal to convert, and uses with great skill the weapons of propaganda.

10.1. Review by: BMJ.
The British Medical Journal 1 (3822) (1934), 621-622.

Professor Lancelot Hogben has now published, under the title Nature and Nurture, the William Withering Memorial Lectures, which he delivered in the Faculty of Medicine of the University of Birmingham on a subject then described as "The Methods of Clinical Genetics." The original title was not a misnomer, and should attract medical readers, but that now adopted is the more appropriate as indicating the general subject under consideration. No teacher or serious student of genetics, or of subjects such as biology, physiology, medicine, or sociology (of which genetics forms an essential part), will fail to appreciate, on perusal, the learning, research, scientific acumen, and power of exposition which have gone to its making, or the importance of its methods and conclusions with regard to some of the most discussed medical and sociological problems of the day. Much of the book is not easy reading: concentration and logical appreciation are required of the reader throughout; but no one pre pared to contribute these need be debarred should he be unable to follow in all their detail the algebraical expressions and calculations which are a necessary part of the author's complete exposition.

Professor Hogben demonstrates the all-pervading influence of environment in the formation or display of human characters or peculiarities, of the complexities of genetic constitution and methods of transmission, and of the relation of these influences on one another in the manifestation of the end-product. That what are to all intents and purposes the same end-products can be brought about in entirely different ways and by various combinations of contributing factors is clearly shown. The distinction in genetic inheritance between those differences which are recognisable in almost any environment in which the fertilised egg will develop and those manifested only within a fairly restricted range of environment is stressed and usefully illustrated by clinical examples from human disease or abnormality, both bodily and mental. The bearing of this on recent researches on mongolism is well brought out. ...

10.2. Review by: E B F.
Science Progress (1933-) 29 (113) (1934), 175-176.

This book is intended as an introduction to the methods which have so far been devised for the study of human genetics. The investigation of heredity and variation in plants and animals can as a rule be conducted by means of direct experiments. In the human species, however, which is slow breeding, has few offspring, and cannot be mated at will, special methods must be employed. Clearly it is possible only to work backwards, subjecting various family trees to statistical analysis. A knowledge of appropriate statistical methods is thus indispensable to the student of human heredity. Many of those likely to be of value are here presented, together with a discussion of their limitations and cautions as to their use. The advertisement on the dust-cover states that "the author ha« attempted to interpret the new methods of research in human genetics in a way which will be intelligible to readers with little mathematical knowledge." It is to be feared, however, that such readers are not likely to find that the attempt has been entirely successful.

10.3. Review by: C Gini.
Genus 4 (3/4) (1940), 190-191.

This is a good book that any student of human genetics would do well to read. Several important topics are dealt with in a clear and persuasive way and without the hindrance of excessive mathematical apparatus. These are: the distribution of dominant and recessive genes in successive generations in the case of sex-linked traits, the frequency of consanguineous marriages in individuals with rare recessive traits, the lower intra-family variability of the children of relatives compared to the children of non-relatives, the difficulty of distinguishing, in some cases, the recessive characteristics from the characteristics dependent on the complementary action of two independent dominant factors.

The major merit of the work, however, is that it has clearly highlighted how the relative importance of prenatal (nature) and postnatal (nurture) factors cannot be judged, if not in relation to a specific population and environment, as the importance of prenatal factors can be different for different environments and, conversely, the importance of postnatal factors can be different for different genetic constitutions. These are truths, which, once affirmed, seem obvious, but which in reality were not considered and still today are not duly taken into account by the great majority of authors who have treated and deal with the relative importance of innate and acquired characters while taking them into account can exercise a decisive importance in both theoretical and practical questions, as the author opportunely mentions.

10.4. Review by: Anon.
Bios 5 (1) (1934), 28-29.

Can a fuller understanding of the laws of human inheritance disclose a clue to the rise and fall of civilisation? Is such knowledge the only basis for a substantial improvement in the common lot of mankind? Is a critique of such extreme claims justifiable in the light of the broadening scope of genetics?

Doctor Hogben gives us in this book a study of the environmental influence on inherited tendencies. Introductory to his thesis he mentions cases of the inheritance of a certain characteristics in chickens and in rabbits where the appearance of the expected Mendelian ratio can be prevented by changing the diet of the animals. From this he goes to the effect that lack of iodine has on the adult !development of the tadpole and newt and then to the relation of iodine deficiency to cretinism.

The author frankly maintains that more consideration should be given to environmental effects in problems arising in connection with the study of disease and mental defect. He does not ignore the new concepts which have emerged from our newer knowledge of the gene and he handles his discussion admirably from the mathematical standpoint.

He concludes: "The belief that a comparison between observed correlations based upon purely genetical assumptions provide us with a measure of the influence of nurture is not justified, because of the close relationship between the distribution of gene differences and differences due to environment in populations of viviparous animals which live in families, especially when, as with human populations, the environment of different families may differ greatly."

"In so far as a balance sheet of nature and nurture has any intelligible significance, it does not entitle us to set limits to changes which might be brought about by regulating the environment."

11.1. Review by: M F Ashley-Montagu and H T Davis.
Isis 28 (1) (1938), 138-140

This book is probably the best introduction to mathematics that has ever been written. Hereafter there can no longer be any excuse for any one to plead that mathematics is beyond him, for no matter how unmathematically minded the individual may be if he but undertakes to work through this book with no more application than the solution of a crossword puzzle would take he cannot fail to acquire an unusually wide working knowledge of mathematics. The book, which was written during a long illness in hospital, is a remarkable achievement of clear and painless exposition. It is the sort of book for which the Million for whom it was written would have given much if they could have had access to it during the days when they were being "taught" that nightmare - as it became - of all subjects, mathematics, that form of low cunning which made so much of their youthful lives miserable, and their struggles with which put an untimely end, in many cases, to a noble ambition. In the reviewer's day (which is not so long ago) mathematics was taught by gentlemen who seemed possessed of an infinite capacity for giving pain, and to whom it was a positive increase in one's ignorance to listen. The antipathy towards mathematics which may be encountered in many scientists to-day is probably to be traced to unfortunate early experiences of similar kind. The serious retardative effects which such individuals not infrequently have upon the development of certain branches of science is a sufficient reason for taking stock of the manner of our contemporary mathematical teaching. It is a platitude to say that in the laying of good elementary foundations lies the secret of further happy advancement in the understanding and use of mathematics. Such foundations are excellently provided in Professor Hogben's book, and it is perhaps of significance that so good and so humane a work should come from one who is not himself professionally a mathematician, for apparently it takes one who is not a member of the esoteric circle of mathematicians to see the deficiencies in past and present mathematical teaching. Professor Hogben gives reasons for everything, moreover, he gives an operational history of the development of mathematics in its actual socially functioning contexts. This is admirable, but it takes a scientist with a social consciousness to do it. The moral should be obvious: If others are to be admirable they must develop appreciably more of a social consciousness than whatever it is that at present serves them in its place.

11.2. Review by: B W F.
Science Progress (1933-) 32 (125) (1937), 154-155.

This lively and provocative book is a brilliant tour de force. It is intended to remove the inferiority complex of "some of the million or so intelligent people who have been frightened by mathematics while at school." Its theme is that the history of mathematics is the mirror of civilisation, reflecting its progress stage by stage. Its argument is that all fruitful (i.e. socially useful) intellectual activity is limited by the general level of social culture of the time, and beyond that point speculation, even by the cleverest, is bound to end in barren isolation from common life and to become "the plaything of a leisured class." The mathematician and the ordinary man both need each other, and it is therefore of prime importance that we should all know something about mathematics. Its scheme in the author's own words is this: "The customary way of writing a book about mathematics is to show how each step follows logically from the one before without telling you what use there will be in taking it. This book is written to show you how each step follows historically from the step before, and what use it will be to you or someone else if it is taken."

We begin with the earliest attempts at counting and measurement (the beginnings of a "size language"), developed by the Egyptian builders into a system of geometry. The Greeks took this over, and as they became prosperous it degenerated in their hands into a plaything of abstractions. The scene shifts to Alexandria, the world's shipping centre, where trigonometry measured the size of the earth and the distances of sun and moon. Such measurements involved numbers too great for existing counting systems to manipulate, and the next advance came with "the dawn of nothing," the Hindu zero and numerals, developed by the Arabs, spread by the sweep of Moslem civilisation, and brought along the trade routes into Western Europe. With this powerful instrument the treasure box was opened. The great navigations involved more accurate tables of star measurements, and logarithms were invented to calculate them. Mathematicians were now thinking in terms of maps, longitude and latitude. With the invention of mechanical clocks the world was ready for Descartes' new geometry which took count of time and opened the way for the calculus, the measurement of change and the foundation of the modern studies of probability and statistics.

11.3. Review by: Carroll Mason Sparrow.
The Virginia Quarterly Review 13 (3) (1937), 474-480.

Lancelot Hogben's "Mathematics for the Million" emphasises practical utility, giving an outline of elementary mathematics in easily digestible form. A syllabus of the ground covered would show a quite conventional content of algebra, geometry, trigonometry, with the elements of calculus and of statistics. The presentation is less conventional. At times the author shows great skill in leading up to some central concept; at other times the exposition is halted while he slops over into social theory, history made to order, and general irrelevance. Mr Hogben is some sort of Marxist. I hesitate to characterise him more exactly but it were putting it mildly to say that he takes no pains to conceal his antipathy to priests, aristocrats, and capitalists. It is not improbable therefore that I judge his Marxian digressions too harshly; the sauce with which he douses algebra and geometry, and which nauseates my bourgeois stomach, may make his downtrodden millions lick their lips in anticipation. He prefaces the work with a quotation from Dantzig's "Number":

It is a remarkable fact that the mathematical inventions which have proved to be most accessible to the masses are also those which exercised the greatest influence on the development of pure mathematics.

It is indeed a fact, remarkable or not, that the great ideas of mathematics are simple ideas, and hence accessible to all. But Mr Hogben interprets otherwise. He thinks that mathematics has stagnated when it has been the exclusive possession of a few, and that its concepts must become common property before progress is possible. The difficulty with this thesis is that it is unsupported by any facts of history known to us; the facts necessary to support it must be invented for the purpose, or unimportant improvements in notation must be exalted above the insights of men of genius and called "turning points" in the history of mathematics. Professor Bell's biographical sketches, which will be discussed further on, furnish a good corrective to this Marxian mythologizing.

Mr Hogben is no mathematician; there are passages in "Mathematics for the Million" that would make a genuine mathematician shudder. Also there is throughout a failure to distinguish between the abstract logical system which is mathematics proper and the application which interprets it. In taking leave of this book, as a specimen of irrelevance I quote the following gem:

The French language is especially suitable for the exercise of ironical wit. The English language is especially suitable to convey scientific truths concisely. The tortuous prolixity of German diction can be used to befuddle sensible and decent people till they believe that Hegel's dialectic makes sense, and that Jew-baiting makes a nation prosperous.

My insufficient knowledge of French stands in the way of appropriate comment.

11.4. Review by: Ralph Beatley.
The American Mathematical Monthly 44 (9) (1937), 591-595.

Despite the first appeal of this very entertaining and instructive book, "the million" will probably not find it easy reading. By the million the author means the many who have tried to master elementary mathematics through the calculus and have got little out of it. Their experience with mathematics has been one long baffling and bewildering nightmare; they have become more and more discouraged and finally have quit. The author blames their teachers for this. It is the teachers' insistence on technical detail and their failure to reveal the social implications of mathematics which, according to him, have made difficult and obscure that which is obvious and simple. To some extent he is correct in this; but much of the author's material and many of his methods are used by good teachers and still there are pupils who do not understand. Ancient priests and modern teachers are alike, says Hogben, in their reluctance to divulge the mysteries of mathematics. He would emancipate the millions; he would democratise mathematics; the advance of western civilisation, he says, depends upon it. So he offers the downtrodden this fresh treatment of the mathematics they have tried to learn, and gives them a fresh chance to prove themselves. They will appreciate his friendly interest but will probably not really appreciate his book.
...
If the million are bewildered by the ordinary text in mathematics, they will find this book doubly bewildering. They will be fascinated by the clever style, but baffled too. So much good mathematics need not go to waste, however. No matter what the million get from it, teachers and members of mathematics clubs will find it highly entertaining and instructive.

11.5. Review by: David Eugene Smith.
The Mathematics Teacher 30 (5) (1937), 252-253.

To attempt to write a review of this book, condensing it to a dozen pages, would be in the nature of a misdemeanour; to attempt it in a half dozen pages would be a felony; but to limit it to four pages or thereabouts is a crime - a capital crime. The book admits of no worthy summary in the conventional space generally allowed to a review, and to get a real grasp of its contents, its mission, and its distinguishing features is possible only by reading the book itself.

It is not a textbook - far from it. It is not a history although it shows great skill in linking the story of mathematics with the subject as it must be presented by a successful teacher. It is not a book on educational methods, for which many a reader is likely to be truly thankful. It can best be characterised by saying that it represents a holy war, a rebellion against stupidity in the presentation of mathematics in our secondary schools and colleges. It is not a brief rebellion; the warfare map ranges over more than six hundred pages, and the war is not even then completed.

All wars have their beginning either in the desire for gain, for the conquering of the lands or goods of neighbouring peoples; or else, as in the case of civil wars, for the purpose of remedying of wrongs committed by despotism. This book represents no attempt at conquest, it represents a war for the betterment of conditions. In particular, it represents the swing of a pendulum which has gone from the stupid, dull, almost aimless teaching of elementary mathematics, to the equally stupid, dull, and almost aimless efforts of some of our schools of education to banish substantially all of mathematics from our curricula. Between these two swings of the pendulum, Mr Hogben sets up a neutral point in which there remains the best of the past and that of the "pioneers," "shock forces," "forward leaders," and other bands which glory in the childish names of some of our curriculum makers of today. At this point he reveals the riches of the past and the dangers of negation ahead.

11.6. Review by: H E Hawkes.
The Journal of Higher Education 9 (1) (1938), 53-54.

When a book on mathematics appears on the list of "best sellers" month after month, one is curious to discover the reason for so unusual a distinction. In this case the alluring title of the book, which suggests much result for little effort, the fact that many persons who have a defeatist attitude toward mathematics would really like to know what the subject is about, and the desire of others to brush up on some topics to which they were once exposed - each contributes a share of the appeal of the book. The author prides himself on his materialistic outlook in contrast to those persons whose inclinations are sympathetic to an "idealistic world picture." In and out of season he emphasises his social philosophy, minimising the values of contemplation and the urge to discover truth for the reason that it is the truth. For example, he gives Euclid and his like very short shrift, and scarcely mentions the work of Apollonius whose interest in pure ideas resulted in the development of the mathematical theory that Kepler needed for application to what the author considers the "social" problem of determining the form of the orbits of the planets. One becomes somewhat weary with the repetition of comments like the following: "This equation can be used to substitute the socialised information of the sine and cosine for the individual labour of multiplying two numbers," and again "They [the Alexandrians] socialised the achievements of Greek geometry in the new size language of trigonometry." With such an attitude toward the subject it is inevitable that the author sometimes overstates his own case in the interest of making his point. But if a man prides himself on being without ideals, he should not be grudged his delusions, which, perhaps, are the next best thing. Notwithstanding the tendency to sell more than can be produced, the book is interesting, and contains a vast amount of material that is rarely presented in the usual books on mathematics.

11.7. Review by: J L Doob.
Science & Society 1 (4) (1937), 577-579.

Practically everyone is forced to toil through plane geometry and some elementary algebra, although no one seems to know just why this is necessary. School courses reflect this ignorance, and frequently adopt the line of least resistance by offering a (logically) systematic presentation of something which would very probably be useless to the student even if he could be expected to remember it. It is not surprising that so few students find mathematics interesting. Unless they are willing to submit, to enter whole-heartedly into the rules of the game, and to pretend that there is a vital living kernel somewhere, even if it is out of sight, they are unable to think themselves into the sterilised situations to be analysed. Hogben has performed a double service in writing Mathematics for the Million. He has given an historical sketch of the development of mathematics up to about 1700, and at the same time he has written a clear presentation of those parts of the subject which are essential to an understanding of modern society. Mathematics for the Million is not an introduction to higher mathematics, nor is it an attempt to provide an understanding of the general field of mathematics. The book presents an exposition of portions of plane geometry, trigonometry, algebra, calculus, probability, placing each subject its historical setting and development.
...
Hogben's jaunty style is a pleasure to read, even in the technical sections, and it is not surprising that this sparkling book is a best seller in England and the United States. He gallops through the subject, waving his snickersnee with glad abandon, cutting down pet dislikes (usually Hegel) on every side, all the while covering a surprising amount of mathematical territory. The carnage is terrible to behold, although the reader may suspect that some of the victims of Hogben's antipathy to theory were replaced by straw men just before the slaughter. It is unfortunate that the necessary and valuable stress on practice leads to a certain contempt for theory, and it is significant that Hogben's treatment, which follows in part the tradition of Empiricism, although accepting the Marxian historical analysis, is weakest in the most abstract (and powerful) subject studied - the calculus. Hogben evidently wished to avoid a formal definition of the concept of limit, which lies at the base of much of modern mathematics and so has recourse to the evasions popular up to about the middle of the last century. The derivative is defined as the ratio of two immeasurable small quantities, dx2 is dropped as negligible in comparison with dx, etc. But this is meaningless unless one chooses to disregard the qualitative change involved in a passage to the limit (which is one of the distinctive features of mathematics) and to consider mathematics merely as an approximative empirical study of nature. Since the time of Newton much of the power, and indeed of the usefulness, of mathematics has depended upon the direct consideration of abstract mathematical laws.
...
No one reading this book, whatever his disagreements with it, will fail to agree that it is an important social document. Against the exciting panorama of history it traces the development of mathematics in vivid fashion. Without doubt even the expert can derive inspiration and perspective from it. Those intimidated by mathematics are here given their first real chance to see what it's all about. The book provides a clear answer to the question "Why mathematics?"

11.8. Review by: Albert A Bennett.
Science, New Series 86 (2232) (1937), 330.

The title might suggest that here is another "mathematics made easy," a short-cut course in technical tricks for the apprentice computer. On the contrary, this is a reasoned appeal for common sense and understanding on the part of educated readers for the application of the mathematical discoveries of the race toward the solution of present-day problems. The earlier British edition stirred wide interest. For the wealth of historical and social contacts, for the pervasive philosophical motivation, for the breadth of sympathy and vigour of attack upon entrenched apathy this book is outstanding. It is not designed to inform the specialist, since it contains little material on pure mathematical theory with which any competent instructor in college mathematics is not already familiar. No brief list of its twelve chapters can do the work justice. Perhaps the most unusual are Chapter III - "The Grammar of Size, Order and Number, or Translating Number Language," and Chapter XII - "Statistics or the arithmetic of Human Welfare," which strike notes that traditional text-books seldom suggest. Undoubtedly even the little mathematical technique assumed will discourage or repel many scholarly persons. Yet the lively, informative and gracious style and suggestive illustrations will maintain the average reader's interest through its six hundred and fifty pages, leaving him eager for more, and thrilled with a new sense of the power and flexibility of mathematics as a method of thinking.

11.9. Review by: S E Rasor.
Educational Research Bulletin 17 (6) (1938), 171.

This is not another "mathematics made easy" or a short-cut course in technical tricks for the apprentice computer. On the contrary it is "a reasoned appeal for common sense and understanding on the part of educated readers for the application of the mathematical discoveries of the race toward the solution of everyday problems." This entertaining and instructive book is really outstanding in its many historical references and its social contacts, its wide sympathies, and the vigorous manner in which it attacks one's entrenched apathy. Its philosophical motivation is quite refreshing. While it is not designed to inform the specialist, "the million" will not find it easy reading. The author, however, would emancipate the millions; he would make mathematics quite democratic; he even asserts that the advance of western civilisation depends upon it. The book will possibly be most appreciated by, not "the million," but the thousands of teachers in secondary schools and colleges. Of course one would expect the sacrifice of rigour in a book of this kind. The author's treatment of mathematics thus becomes discursive and casual. It is hardly even a history of mathematics. It might be better called socialised mathematics.
...
The average reader will be fascinated by the clear style of the book and perhaps baffled, too, but his interest will be challenged throughout its 650 pages, leaving him eager for more and perhaps thrilled with a new sense of the power and flexibility of mathematics as a method of thinking.

11.10. Review by: G Waldo Dunnington.
National Mathematics Magazine 12 (3) (1937), 157-158.

This book demands attention because in a short time it has become a best seller in England and America. As in most popularising books, the attempt is made to show that it is "easy" to master mathematics. We are told that mathematics is the language or grammar of size, and also the "mirror of civilisation". If a grammar, one wonders whether it represents the phonology, morphology, or syntax. As a "mirror of civilisation" it depends directly on social and physical environment. The reader will naturally raise the question, "Has every discovery resulted from the need of social progress?" The entire treatment of the book is from the social, statistical and political point of view, which probably explains in part why it has appealed to such large masses of readers.

Copious historical material is woven in rather loosely, along with many statements in conversational familiar tone of personal opinion, etc., which aid in maintaining the reader's interest. The closely scrutinising reader may question some of these interpretations and alleged historical facts, but one must keep in mind that the volume is written "for the million". The danger in this type of book is that the author is too easily led to broad generalisations without qualifying such statements.

Various chapters treat arithmetic, algebra, geometry, trigonometry, spherical triangles, graphs, logarithms, calculus and statistics. There are many figures, graphs and diagrams by J F Horrabin; at the end of each chapter there are questions and problems for the reader to solve. It would be interesting to learn what results might occur from the use of this book in a course in general mathematics. Each subject is developed from its historical origins and this method may prove fruitful in the future, provided it does not require too much time on the part of pupil and teacher. There is a strong tendency today to stress in elementary work the practical (and social) aspects or values of mathematics even more than formerly.
...

11.11. Review by: H F M.
The High School Journal 21 (5) (1938), 186-187.

This book is the most peculiar combination of the history of mathematics, the practical uses of mathematics, and pure mathematics that has recently been published. It is written for the layman, not for the mathematician. The claim is made for it that anyone with ordinary ability who will take paper and pencil and study this book will be able to work through the material contained in it. This material embraces the elements of arithmetic, algebra, geometry, calculus, statistics, and plane and spherical trigonometry.

There are many unique features about the book. In the first place the author is English and, because of this, one finds many expressions and view-points that are flavoured by an English setting. This many readers would find intriguing. The rich historical background which has been used to stimulate the reader to want to know something about mathematics, to enrich his store of knowledge, and to give him an insight into the causes for certain phenomena as we find them is a real contribution to the literature in this field. The peculiar ways and devices which have been used to promote an understanding by the reader of those fundamentals of mathematics which are usually thought of as the special province of the college student or university professor are worthy of note. The audacity of the author in leading the reader into mathematical waters which are usually considered troubled or beyond their depths is unusual. There are many diagrams which are splendid aids to the reader's imagination in developing an understanding of the principles involved. Then too, one finds a bit of humour from time to time which is refreshing.

The book should be read by those who would lay claim to a cultural background of the world of knowledge. It should be read also by the teacher and student of mathematics who desires to enrich his notions of the value of mathematics to mankind and the part it has played in the development of our present state of civilisation. The book is a real contribution to the literature of mathematics, and will no doubt do its part in allaying certain criticisms of mathematics which have been prevalent in recent years.

11.12. Review by: Anon.
Journal of the Royal Society of Arts 85 (4411) (1937), 693.

This brilliant, eminently readable book begins with an anecdote about Diderot and ends with a page of logarithms. The first sections are mainly historical, and the succeeding pages are also illustrated with a wealth of historical matter drawn from a quite astonishing fund of learning. There are many diagrams, and excellent drawings by Mr J F Horrabin. From measurement and observation of the sun and stars we pass to the language of Number: to the uses of geometry and trigonometry to that Hindu invention of Nought which "liberated the human intellect from the prison bars of the counting-frame": and so on to logarithms and the calculus. The last chapter is called "Statistics, or the Arithmetic of Human Welfare."

It ought to be possible to learn a great deal from the book. Even a cursory reading would make the subject seem alive and fascinating, yes, though one's schooling had set one as much against figures as it did Thackeray against the Parthenon. Not that the problem of making mathematics palatable for children is solved - only, a boy or girl with exceptional general knowledge would understand the allusions which make it attractive to grown-ups. Nor of course are we of the adult Million going to find this a broad and easy path to Einstein. We shall perhaps at last grasp how Achilles beat the tortoise which had a start of him, but we are going to have cudgel our brains between page 89 and page 647. But at least we now know there could be many worse ways of spending leisure.

12.1. Review by: J H, Jr.
The Journal of Philosophy 35 (2) (1938), 51-53.

This significant and stimulating lecture by the versatile author of Mathematics for the Million now appears under two American imprints. "The outlook of the scientist when he turns his attention to the problems of social organisation," says Professor Hogben, "is essentially constructive, though sometimes, and perhaps usually, naive." Mr Hogben is an English biologist convinced with Huxley that "the great end of life is not knowledge but action." In this closely-packed little book he uses the potentialities of biological knowledge to throw out a multitude of suggestions in satirical criticism of the existing pattern of things, and pointing toward a new order based on a genuinely scientific humanism in education. Like the best British popular lecturers on science, he manages to convey the impression of brilliant conversation, as well as the further reflection, "This will bear a good deal of thinking over." His point of view has much in common with the Technocrats, though as the advocate of biotechnology rather than of engineering he does not, like that adventure in ideas, evade the problems of social science and action. Since he thinks he has attained a little skill in it, he devotes himself largely to "the art of making your opponents look silly." His opponents include the social scientists in general and the Austrian school of economists in particular, whose verbal logic, untouched by any suspicion of scientific method, is one of the astrologies of the machine age; the Liberals, whose pre-scientific view of human nature has always been inimical to the objective study of human behaviour, and to finding out how men must be educated if a stable social pattern for industrialism is to be achieved; the Marxists, who are particularly silly in forcing the unscientific and extraordinary jargon of the Hegelian dialectic upon empirically-minded Englishmen, in believing the out-of-date and crude propaganda of class war in an age of plenty the most effective way of remedying the irrationalities of our social arrangements, and in appealing to the small depressed section of the proletariat rather than to the growing salaried classes; the internationalists, who do not realize that national economic self-sufficiency has been made possible by science and inevitable by nationalism, that collective police-action is a light-hearted and light-headed invitation to the total destruction of war, and that their sentimental views will produce a universal cataclysm and dictatorship unless science is used to make Britain progressively more isolated from Europe and the Empire; and finally, all those who aim at the anarchic production of a variety of goods rather than the satisfaction of basic human needs, who are unwilling to undertake a far more drastic repudiation of laisser-faire than socialists have been willing to countenance. and who do not see that tolerance is a mere makeshift until we have found out how to deal with an issue in a rational way and know the right thing to do. These ideas are all provocative; some are admirable. They are obviously food for thought rather than for immediate assimilation.

13.1. Review by: W D R.
The Mathematics Teacher 30 (7) (1937), 348.

This is a textbook edition of an earlier edition which has been a best seller in both England and in this country. This special edition has a very interesting introduction written by Professor David Eugene Smith who wrote a review of the earlier edition in the May number of The Mathematics Teacher. There is no question that the appearance of this book has accelerated the interest in mathematical education in this country and the fact that this edition is sold at a lower cost to teachers will make the book all the more helpful.

13.2. Review by: C O Tuckey.
The Mathematical Gazette 21 (243) (1937), 166-173.

This is a remarkable book. It is original, it contains a great deal of mathematics, and most of this is set out in such a way as to be highly interesting. It is a book which at any rate all teachers of mathematics should take very seriously for it will obviously be of great use on the shelves of the classroom available for lending to pupils of certain types.

Whether it will be equally successful as a self-educator is another question. The non-mathematical (or failed-mathematical) reader is certain to find an increased interest in the subject if he follows the author's instructions to "read the whole book through once quickly"- which will for this type of reader imply skipping very many pages containing meaningless symbols - "to get a bird's-eye view of the social interconnections of mathematics".

It is in the "reading it for the second time" and "working on the detailed contents" that it seems likely there may be many failed self-educators.

The author "wrote this book in hospital for his own fun", but his real excuse for writing it and a general idea of its character may be given in two quotations from the first chapter.

"As mathematics has been taught and expounded in schools no effort is made to show its social history, its significance in our own social lives, the immense dependence of civilised mankind upon it. Neither as children nor as adults are we told how the knowledge of this grammar (the grammar of size and order) has been used again and again throughout history to assist in the liberation of mankind from superstition. We are not shown how it may be used by us to defend the liberties of the people. Let us see why this is so."

"This book will narrate how the grammar of measurement and counting has evolved under the pressure of man's changing social achievements, how in successive stages it has been held in check by the barriers of custom, how it has been used in charting a universe which can be commanded when its laws are obeyed, but can never be propitiated by ceremonial and sacrifice.

As the outline of the story develops, one difficulty which many people experience will become less formidable. The expert in mathematics is essentially a technician. So his chief concern in teaching is to make other technicians. Mathematical books are largely packed with exercises which are designed to give proficiency in workmanship. This makes us discouraged, because of the immense territory which we have to traverse before we can get insight into the kind of mathematics which is used in modern science and social statistics. The fact is that modern mathematics does not borrow so very much from antiquity. To be sure, every useful development in mathematics rests on the historical foundation of some earlier branch. At the same time every new branch liquidates the usefulness of clumsier tools which preceded it. Although algebra, trigonometry, the use of graphs, the calculus, all depend on the rules of Greek geometry, scarcely more than a dozen from the two hundred propositions of Euclid's elements are essential to help us in understanding how to use them."
...
In conclusion, it may be asked how far the author succeeds in proving his main thesis that all valuable discoveries in mathematics are due to the demands of the social environment of the discoverers.

In endeavouring to prove this he certainly raises to the nth power the method of the Bellman ("what I tell you three times is true") and does so with such a variety of language that his argument might almost be praised, as is the Scherzo of the Choral Symphony, "a miracle of repetition without monotony".

It must be admitted that he makes very effective play with the importance of the invention of the sign for zero, and of course he reduces the difficulty of his thesis very much by insisting as a matter of definition that, to be valuable, a discovery in mathematics must react on the real world and affect the social environment of the discoverer. This gets him into difficulties once or twice, as when Mendel's laws provide a use for Fibonacci series or the discovery of the mechanical equivalent of heat "gave the methods of the integral calculus much greater practical importance than its inventors could have realised", but on the whole helps him to make a good case, and one which will probably be regarded as conclusive by his non-mathematical readers.

May he have as many of them as his title demands! If they don't all succeed as self-educators, perhaps the demand for private tuition will help the professional teacher; and anyhow he has been benefited by the production of a book which should provide him with many new ideas and dodges for teaching, much valuable historical information, and a good deal of amusement.

14.1. Review by: A L.
Journal of the Royal Society of Arts 86 (4482) (1938), 1144-1145.

This work is from the same pen as Mathematics for the Million, acclaimed as the most remarkable publication of 1936. The author postulates that science is an essential part of a citizen's education, and with this conviction, emulating the eloquent literature of Faraday and Huxley, he has written another noteworthy book; an average citizen's introduction to science without tears. Most frequently an encyclopaedia of science is an unconnected corpus of knowledge written by various experts and lacking any attempt at design. But the original purpose of this book as a preliminary course of lectures to students pre-ordained a structural framework. The author complies with Schoedler's definition of "the natural philosopher to whom the whole extent of nature belongs."

The compendious volume of 1,120 pages comprises five parts, each divided into major topics in separate chapters under intriguing titles, treating the origin, history and development of the particular aspect of scientific knowledge. The titles of the parts run consecutively: The Conquest of Time Reckoning and Space Measurement; The Conquest of Substitutes; The Conquest of Power; The Conquest of Hunger and Disease; The Conquest of Behaviour. Thus a glance at the titles indicates a historic development of scientific research from the primitive observation of natural phenomena to the investigation of the human mind, "how infinite in faculty." In an epilogue serving as a summary, entitled The New Social Contract, the theme is expounded that "scientific knowledge gives us the means of planning for plenty and also helps to free us from habits which prevent us from doing so."
...
Science for the Citizen further disproves the tradition that scientific books must be didactic, dull and deterrent. The volume is well written, has a good bibliographical appendix to each part, a workmanlike index and very clear illustrations by J F Horrabin. It reveals abundant proof that the sciences are lock-stitched, or parts of a great research plan, under which a change in one of these can alter the system of others. Nevertheless, Professor Hogben has not over-popularised his work so that the explanations cease to be scientific, whilst he has left the reader pondering over Pope's couplet:

"One science only will one genius fit,
So vast is art, so narrow human wit."

14.2. Review by: Dirk J Struik.
Science & Society 3 (4) (1939), 544-548.

The special value of this sequel to Mathematics for the Millions lies in its emphasis on the social background of scientific discovery. Early in the book the author writes:

Whether we chose to call it pure or applied, the story of science is not something apart from the common life of mankind. What we call pure science only thrives when the contemporary social structure is capable of making full use of its teaching. furnishing it with new problems for solution and equipping it with new instruments for solving them. Without printing there would have been little demand for spectacles: without spectacles neither telescope nor microscope; without these the finite velocity of light, the annual parallax of the stars, and the microorganisms of fermentation processes and disease would never have been known to science.... Without the dynamics of the pendulum and projectile. no Principia. Without deep-shaft mining in the sixteenth century. when abundant slave labour was no longer to hand. there would have been no social urge to study air pressure, ventilation, and explosion .

This theme is developed throughout the work. The many examples given and the constant references illustrating the social content of a discovery will certainly be an eye-opener to all those readers who have been ignorant of the, social forces which influence scientific research. Hogben has done a great service to the history of science in relating it so clearly to the affairs of the market place. Most historians of science still ignore the role of economic forces in determining the fate of science. "Representative men" working in a social vacuum are still worshiped in textbook and classroom. Persons reared in this tradition are here confronted with an overwhelming amount of evidence which shows the effect of society on science and invention.
...
Yet, in spite of all shortcomings, the book remains an astonishing piece of work. One cannot take it up without a feeling of admiration for the author's encyclopaedic knowledge, his talent for popularisation, his witty style, his originality, his boundless energy. We are shown some of the instruments which are already in existence to create a rational social order, an "age of plenty." We are led to see the necessity for a planned economy and the possibility of a tremendous increase in material wealth for all. We can heartily agree with Hogben in drawing the moral that we have social responsibilities as citizens to help bring about this new social order.

14.3. Review by: E N.
The Journal of Philosophy 36 (2) (1939), 54-55.

Mr Hogben himself formulates succinctly the thesis which his book supports: "Science is not a photographic picture of the real world which exists independently of our views about it, and will continue to exist when we are no longer part of it. It is an ordnance map which guides us in finding our way in it." Like its predecessor Mathematics for the Million, it is written with verve, with many asides roundly damning "pure science" and "logic," and with an emphasis upon the possibilities residing in science as an instrument for achieving a happier social order. It ranges from astronomy to physiology, but avoids rather conspicuously themes with no obvious social use however great their theoretical import; and it brings together much fascinating material on the social background of many of the great scientific innovations.

The book as a whole is by no means easy reading, for Mr Hogben does not try to fool his readers by pretending that his material does not require careful study; and one wonders how many of those who purchase it do succeed in acquiring an education from its pages. Mr Hogben's enthusiasm for the methods of science is contagious and his faith in them as liberators from social and intellectual bondage is heart-warming. There is all the more reason for regret, therefore, that he underestimates the role in the history of science of theoretical inquiries whose direct contributions to social welfare may be negligible. No understanding of the function of abstract theories can be obtained by simply ignoring the indispensable part which as a matter of fact they have. Does not Mr Hogben's policy of fostering an undiscriminating contempt for the "pure scientist" succeed only in widening, rather than narrowing, the distance between those who engage in scientific inquiries and those who are the potential consumers of their fruits?

14.4. Review by: M Ashley-Montagu.
Isis 31 (2) (1940), 467-469.

Before, while, and after reading this book I had the opportunity to peruse with much interest somewhat in the vicinity of a score of reviews of it. I do not, as a purely cautionary practice, place much faith in reviews, not even in my own, for a review is after all merely one man's opinion of a book judged by such standards as he has managed to gather to his horizons. I have often found that even the most reliable of reviewers have upon occasion either completely belied the work which they have reviewed, done it scant justice, or judged it uncritically; that is, in my opinion. I speak not only of the reviews which appear in the better literary journals, but also of those which appear in first-rate scientific journals.
...
The reviews which I have seen of this latest popular work to come from Hogben's pen have unexceptionally been laudatory. The English reviews led me to expect that when at last a copy of Science for the Citizen did reach my hands it would really be a delightful experience. The American reviews were, interestingly enough, a little calmer, though still laudatory. At any rate, when eventually I did get to the book itself and had read the first few score of pages my disappointment was extreme. This feeling of disappointment was not greatly reduced by the time I had arrived at the last pages of this enormous work. What was the reason for my disappointment? Had I been led to expect too much? It is possible. Was the style wrong? No, the style is good. Too many errors of fact? No, there are relatively very few. Then what? Well, I know this: When I was a boy there was a work called The Popular Educator, it was issued in parts (once a month, I think), the complete work formed two volumes, and as I remember it, it made much more interesting reading and certainly much easier reading than Hogben's latest volume, and it covered a great deal more ground. My feeling of disappointment is due to the fact that I do not find Hogben's book as good as my popular educator was. Undoubtedly Hogben's book is in many ways sounder and certainly more humanely balanced than my educator was. Hogben's emphasis on the historical and social aspects of the subjects with which he deals was absent from my educator, but if I had to choose between my old educator and Hogben I would unhesitatingly plumb for the earlier not-so-learned work because it was easier to read and to learn from. Surely, if we are to make science attractive to the citizen, (and it is, of course, open to question whether that is desirable), our first essential must be the realisation that our citizen hasn't much time; that what science he is going to acquire in his spare time he will want to acquire as painlessly as possible. This he could have done with my old educator, but with Hogben's book he will have to take a stool and apply the seat of his trousers to it very very hard, and concentrate, and furrow his brows, and work, and get a headache because he has tied himself all in knots, and the consequence will be that Science for the Citizen will look very nice on the bookshelf in its pretty jacket, while other things will suddenly occur to our citizen as of more urgent importance while the dust gently gathers upon the blue-black top of science. If this diagnosis is correct then the purpose for which Hogben wrote this book is defeated. It is devoutly to be hoped that my diagnosis is incorrect.

14.5. Review by: William Fielding Ogburn.
American Journal of Sociology 44 (4) (1939), 584-585.

Mr Hogben's thousand-page history of Science for the Citizen has special interest for sociology. More so than most such histories. The reason is that he correlates the development of science with the sociological conditions of the times. We have heard it said that necessity is the mother of invention, but extremely little has ever been written on what are the social conditions that give rise to inventions and scientific discovery. The author doesn't attack the problem from an analytical point of view, but his book gives a very good descriptive account. We see, for instance, the Egyptian's concern with astronomy, the calendar, and geometry-all needed for their religious, agricultural, and constructional activities in these times. Similarly the interest of the world in navigation was closely related not only to practical navigation but to celestial mechanics.

This relationship of sociology and science leads the author to give emphasis to what is sometimes called practical or applied science. It is true he stresses this aspect of scientific development more than most writers, but I wonder if this doesn't help to redress the imbalance in previous writings. The role of practical issues in the development of science is a somewhat disputed question. The natural sciences, particularly mathematics, are thought to grow as a sort of symmetrical structure out of the logical attributes of the mind, stimulated by curiosity without much reference to practical matters. Hogben's analysis would seem to discount this theory, for he seems to stress so much the practical interest of science. This is of importance to the social scientist for the reason that practical demands for solution of social questions play such a big role in directing his energies. Insistence on the solution of practical questions in the social field has often been held as a hindrance to the development of a fundamental social science. The inference from Hogben's discussion would be that these practical questions are an asset rather than a liability. His book therefore is encouraging and leads to the pragmatic attitude of making the best in a scientific way of the contemporary social questions in the field of the social sciences.

I don't dwell on the author's vivid style and attractive illustrations because the reader will assume, and correctly so, that the author of Mathematics for the Million has done a swell job of popularising the development of science.

14.6. Review by: John Case.
Science Progress (1933-) 33 (132) (1939), 801.

Today there is great danger of science degenerating into the naïve mysticism of a Jeans or an Eddington, or the wish-fulfilment "science" of National Socialism, which has prompted M Planck to state "the importance of a scientific idea is often due not so much to its truthfulness as to its inner value" (Weltanschauung - world outlook). This attitude has, for political ends, actually produced a new racial "science" advancing such theories as: "No person of Jewish blood can think German. Therefore, when a Jew writes German he lies," and that Einstein's Theory of Relativity must be denounced because a Jew can only produce non-Aryan and therefore false scientific theories!

If man is to enjoy the fruits of science this nonsense must be exploded, and Hogben's book could leave no reader in danger of deception, for it shows science as a whole, as one unit in the complete structure of human culture, not as a number of isolated cells. It shows science and technology developing side by side, as determined by the social structure of society and the technical level of production appropriate to that structure, thus teaching us how we can ensure that science is used to enlarge and not destroy life.

Even if the reader skips the "harder" passages, the clear exposition, helped by Horrabin's excellent diagrams, will equip him well to understand contemporary thought. All teachers of science who wish to bring reality into their instructions should read the book. On particular points I can only criticise in my own field; and here I think it a pity to have used the word poundal in mechanics, and that the author has not given sufficient credit to the early engineers of Sumer, Egypt, India, Crete, who laid the foundations upon which the Greeks could build.

15.1. Review by: P K Whelpton.
American Journal of Sociology 47 (5) (1942), 768-770.

This book consists of a "Prolegomena" by Hogben and twelve articles by seven of his associates in the department of social biology. The "Prolegomena" is an indictment of armchair philosophising in the absence of facts and a plea for the development of a true "science of society."
...
Unquestionably, each chapter adds significantly to our fund of factual information regarding the problems dealt with. The data presented are worth while, and the conclusions sound. Bringing such material together in a readily accessible form is an important step toward the scientific goal for which Hogben pleads.

15.2. Review by: A M Carr-Saunders.
The Economic Journal 48 (192) (1938), 707-708.

This volume includes seven papers grouped together under the title of "The Survival Minimum" to form Part I, and five papers under the title of "The Recruitment of Social Personnel" to form Part II. They are preceded by an introduction contributed by the editor; it was during his distinguished tenure of the Chair of Social Biology at the London School of Economics that they were written by members of his department.
...

But it is impossible to close any mention of a book, which is evidence of the great value of the work and methods of Professor Hogben and his collaborators in the field of social study, without expressing regret that he should attack other workers in this field in a manner which can only result in damage to himself.

15.3. Review by: Frank Alexander Ross.
American Sociological Review 4 (2) (1939), 287-288.

The various chapters of this volume are the work of members of the staff of the Department of Social Biology of the University of London. Being the product of nine different authors, and confessedly but a fragmentary set of reports on researches so far pursued under an ambitious program of progressive study, it lacks cohesion and system. Each chapter, however, considered as a separate document, is a definite contribution.

15.4. Review by: Robert K Merton.
Isis 30 (3) (1939), 555-557.

This noteworthy symposium signalises the coming-of-age of political arithmetic, now rounding out its third century of growth. It is a credit to the Department of Social Biology of the University of London where the researches here reported were conducted. It is difficult to choose among the twelve chapters in point of excellence. Each represents a notable contribution to its particular field. In a typically vigorous introduction, Professor Hogben announces his intolerance of economic mysticism and scarcity dialectics and presents a case for factual social studies rather than home-spun verbalistics.

15.5. Review by: R A Fisher.
Science Progress (1933-) 33 (131) (1939), 611-613.

This book, edited by Prof L Hogben, who contributes two introductory essays, is a collection of research papers from his department of Social Biology at the London School of Economics. Much has already appeared in the appropriate journals; the publishers state that about half the material is presented for the first time.

It is to be regretted that both publisher and editor appear to give a misleading impression of the scope of the book. On the cover we are told that "The individual chapters ... deal both with the quantitative and qualitative aspects of population growth"; and again, "The first part contains an analysis of the ... differential fertility of social classes." The editor in the Introduction to Part II says, "The significance of differential fertility with respect to occupation, locality, and income has been dealt with in the introduction to the first part and in Chapters III and IV." He adds further, "The ensuing chapters are primarily concerned with one of two differential issues involved in the qualitative aspect of differential fertility." The reader might reasonably expect from these statements that he would find, if not original researches, at least some account of what has been established on this important subject; but it should be explained that the statements quoted are almost entirely unwarranted. Differential fertility with respect to income and its qualitative effects seem both to be topics studiously avoided. Both the make-up of the book and the prevalent style of the writing are expressive of the Editor's personality. Readers of his previous books will anticipate that his estimable capacity for personal conviction is liable to express itself in hasty and superficial judgments; and that his verbal facility, uncontrolled by self-criticism, falls too readily into prolixity.

15.6. Review by: G O'B.
Studies: An Irish Quarterly Review 27 (106) (1938), 346-348.

This collection of papers, embodying the result of researches undertaken by the Department of Social Biology in London University, deals with quantitative and qualitative aspects of the growth of population. The introductory essay by Professor Hogben contains an account of the relations of the three founders of British demography - Graunt, Petty and Halley, all original fellows of the Royal Society - to the intellectual life of their time, which was an age when scientific research and social practice were closely linked together. A contrast in this respect is drawn between the seventeenth century and the present day, very much to the detriment of our contemporary economists in general and in particular of some of Professor Hogben's colleagues in London University. While it cannot be denied that the impact of scientific progress on society is neglected in some schools of economic inquiry, the criticism of economists and their methodology is overstated by Professor Hogben, who seems to have been in a very bad temper when he was writing his "Prolegomena to Political Arithmetic," as he entitles his highly controversial introduction. Disapproval of the tone or disagreement with the matter of this introduction should not deter the reader from proceeding to the essays themselves, all of which are valuable and some of which are excellent.

15.7. Review by: BMJ.
The British Medical Journal 2 (4055) (1938), 661.

This volume opens with an introductory essay by Professor Lancelot Hogben, stated (by the publishers) to be "a challenging critique of contemporary economics and an eloquent appeal for realistic research on social institutions."

15.8. Review by: Anon.
Copeia 1939 (1) (1939), 58.

Though this volume deals almost entirely with the sociological aspects of changes in human population, it should be of interest to those studying any population problems. The book is a collection of papers dealing with population changes in England and the sociological consequences.

15.9. Review by: William O Brown.
Science & Society 3 (2) (1939), 264-266.

The materials in part two represent something of a new departure in population analysis. Hogben's contributors here deal with the somewhat elusive problem of factors in social selection. The studies seem to show that educational training and economic opportunity are only partially associated with ability; that economic and social arrangements tend to penalise both the average and exceptional individual within the lower economic strata, while giving great rewards and exceptional support to mediocrity in the upper classes. In short, the distribution of ability is indifferently associated with the distribution of opportunity, a fact which eugenists might ponder.

15.10. Review by: Frank Lorimer.
The Annals of the American Academy of Political and Social Science 203 (1939), 241-242.

The symposium begins with a heady cocktail by the editor, Lancelot Hogben, Fellow of the Royal Society. Its base is the idea of useful, quantitative knowledge about man and the conditions of human life-distilled by Petty (author of the Politicall Arithmitick) and his fellows of the original Royal Society. This is seasoned with erudition and bitters, the latter from the decomposed fruits of Malthus and the classical economists. Hogben's particular thesis of a social technology in terms of thermodynamics strikes this reviewer as fantastic, but it is a stimulating idea.

16.1. Review by: C Delisle Burns.
Ethics 50 (3) (1940), 348-349.

Professor Hogben is at present professor of natural philosophy or the biological sciences in the University of Aberdeen, Scotland. He is well known as the author of two books - one on science and the other on mathematics - which are in the best sense of the word popular. His "dangerous thoughts" are expressed in the book under review in the form of fifteen essays and addresses, largely concerned with the position of science in education. There are three historical essays on John Wilkins, one of the original fellows of the Royal Society, on Sir William Petty, and on Havelock Ellis. Other essays deal with the necessity of increasing the birth-rate in highly civilised countries, on the right kind of education for an age of plenty, on Marxism and the middle classes, and on Marxism as a theology of violence. The book is full of the most amusing sentences and pointed criticism. But the most important general idea, which connects all the essays, is that science arises out of the needs for some social advantage and that science will progress best when it is closely connected with the social uses to which its discoveries may be put. The author's chief attacks are directed against forms of thought which appear to him to have no immediate bearing upon action. And indeed he explains the tendency of the younger generation to swallow Marxist dogmatism as a result of the false distinction between useful knowledge and pure thought. He writes: "The pitiable predilection for action without thought is the legitimate offspring of thought divorced from action." He explains the peculiar phenomenon of a scientist of the status of J B S Haldane accepting Marxism by an amusing reference to Sir John Napier, who invented logarithms in the seventeenth century but also spent most of his time making mathematical calculations to prove that the "number of the beast" in the Book of Revelations referred to the Church of Rome: not every scientist is always scientific. Professor Hogben's final essay in this book is a devastating analysis of the Marxist dialectic; but, as he says in his Preface, he is "more anxious to be right than to stay Left."

The most important issue for students of ethics and political philosophy, which is raised by Professor Hogben's general argument, is the question of what he calls the social uses of knowledge. Clearly the phrase ''social use" implies an estimate of value and not a mere perception of facts. But, whenever specialists in the physical sciences deal with the social uses of science, they seem to avoid any attempt to analyse what is meant by an estimate of value. They assume that what is thought to be useful in their circles is actually useful. It may be so. But no one who has read Professor Hogben's own description of the history of science can avoid noticing that the conceptions of what is socially useful differ in different generations and sometimes in different circles of society in the same generation. The truth is that the estimate of value changes and develops just as much as knowledge of facts. Early astronomers, for example, thought it socially useful to find out from the position of stars when the local king would die. Indeed, much of what we regard as the socially useful discoveries of science were the accidental results of attempts to obtain knowledge which we should now regard as quite useless. The admiration of contemporary scientists for the rather crude conceptions of social utility accepted by Francis Bacon and the earliest fellows of the Royal Society would perhaps be modified if they had a clearer historical knowledge of the growth of the estimates of value in more recent times. It may also be pointed out that it is "socially useful" to free the mind from superstition and fear, even if the knowledge that gives this freedom has no result in the making of machinery or in the curing of disease. But perhaps our more revolutionary scientists do not understand what is meant by "pure" knowledge. Thinking is action of a kind.
...
Professor Hogben's thoughts will be "dangerous" enough if they lead to the restriction of all science within the fields that Professor Hogben at present thinks are socially useful. But he intends them to be dangerous only to obsolete forms of education.

16.2. Review by: F H S.
Journal of the Royal Society of Arts 88 (4569) (1940), 846-848.

The title of this book is wrong. Professor Hogben's thoughts arc not in the least dangerous; but they are challenges to most people and sources of irritation, doubtless, to some. We are bound to take account of the fact, already noted by an enlightened daily journal, that Hogben has become the great populariser of ideas. For this he is well equipped, for quite beyond the borders of his own specialism, biology, he has wide scientific knowledge and great literary gifts. He writes in the most lucid fashion, can be as epigrammatic as anyone, is a master of irony, and is a most polished, as well as, usually, a sincere dialectician. Whatever we do we must take notice of him, for he (a biologist) has written a book on Mathematics of which 15°,000 copies in English have already been sold at a high price, and on Science for the Citizen, which has already had a sale of 50,000 copies.

What then, has Professor Hogben to say? The present book is principally a collection of addresses delivered to various Societies and gatherings during the last two or three years, together with some fugitive writings. Hogben, in thought, belongs to the Left. But neither the Communist Party (if there still is one) nor the Labour Party command his allegiance. He pours scorn on the out-of-date gospel of Karl Marx, and scarcely conceals his contempt for the intellectual make-up of the Labour Party, particularly as exemplified by its political leaders. In this volume he lays about him vigorously, dealing lusty blows at the Eugenists, at politicians of all parties, at the University of Oxford, and especially at the "Greats" school, at Universities (including his own Cambridge) as cultural institutions, at the great mass of teachers, the present form of parliamentary democracy, and a host of other things.

But the mass of this book is not merely destructive, and often wickedly effective criticism. The author preaches a gospel. His creed he calls "Scientific Humanism." Of the many passages in which he defines or advocates this creed, perhaps this from his first essay should be quoted:

The social contract of scientific humanism is the recognition that the sufficient basis for national cooperation between citizens is scientific investigation of the common needs of mankind, a scientific inventory of resources available for satisfying them, and a realistic survey of how modern social institutions contribute to or militate against the use of such resources for the satisfaction of fundamental human needs.

We may object that this creed, regarded as a programme, is impracticable, and that Professor Hogben furnishes us with no clues as to how it should be undertaken. But few of us would deny that the purpose so set out is "a good thing." This gospel the author preaches or supplements in almost all of these essays, whether the chapter is on Sir William Petty's Political Arithmetic, on The Teaching of Mathematics, or on Education for an Age of Plenty.

The reader need fear no dullness. There is not a page in the book which is not brilliantly written. The book sparkles with epigram and (to resort to well worn metaphor) with rapier thrusts and winged barbs.

16.3. Review by: S A Nock.
The Sewanee Review 48 (4) (1940), 572-576.

Mr Hogben, while not quite so urbane and charming as Sir Arthur Eddington [he has just reviewed The Philosophy of Physical Science], is equally entertaining and somewhat spicier. More than most of his colleagues he makes a particular effort to approach whatever subject he is discussing in the scientific manner; that is, he endeavours to discover all relevant facts, to deal with them operationally, and to present the results of his inquiry as a basis for further investigation.

Mr Hogben states his hypotheses as hypotheses, and suggests how facts may be investigated in the light of these hypotheses. He makes clear that his notions and peculiarities are his notions and peculiarities; so that although he is fully as crotchety a human being as Sir Arthur, all his crochets are merely that and nothing more. It is incredible, for instance, that anyone who writes as well as Mr Hogben and delights in as many activities as he does, should show such appalling incomprehension of the fine arts as he does in Dangerous Thoughts. It is incredible that any one who writes so well should have no remote notion of the function of literature; yet Mr Hogben states his shortcomings so very plainly that there is no mistaking them. Equally plainly he states his superstitions and personal prejudices. Yet always when dealing with a subject - and he deals with a variety of subjects - he makes every effort to leave personal whim and fancy out of his calculations.

Especially when he discusses economic matters, we feel that the scientific approach is unusually fortunate. For although there is a good deal of Marxism that Mr Hogben quite obviously would like to take stock in, he is just as obviously unable to put any faith in it. He feels apparently that Marxism is better religion than most, but that no religion with its faiths and shibboleths is going to do us any good in facing problems which have to be solved. The way to solve problems, Mr Hogben feels, is to get all relevant facts and investigate them in the light of hypotheses, and then abide by the results of the inquiry. Consequently it is a matter of no particular interest to him whether volition is objective or subjective, or whether other consciousnesses exhibit the same structure as his own, which is the structure imposed on them and the physical world by another consciousness.

16.4. Review by: Harry Alpert.
American Sociological Review 5 (5) (1940), 808-810.

Hogben's Dangerous Thoughts - dangerous refers to their non-endorsement by a church-is a collection of essays and addresses with no particular unity other than the author's implicit social philosophy. This creed, called scientific humanism, is given its most explicit, albeit not too precise, formulation in the first essay. Its cardinal tenet is the implementation of the age of plenty for all the people by the fullest development of the social and human potentialities of scientific knowledge. It is part technocracy, part socialism, part scientist, part common sense, with the whole liberally seasoned with some independent Hogbenism. It is not unlike Lynd's Knowledge For What? and may be taken as the credo of modern liberal intellectuals trained in the scientific tradition. "The social contract of scientific humanism is the recognition that the sufficient basis for rational cooperation between citizens is scientific investigation of the common needs of mankind, a scientific inventory of resources available for satisfying them, and a realistic survey of how modern social institutions contribute to or militate against the use of such resources for the satisfaction of fundamental human needs". The essays include studies in the social history of science, analyses of the place of science in the school and in the education of citizens, and of the impediments to scientific inquiry in contemporary society, critical remarks on the Marxian theory of class struggle and the relations between Marxism and the middle classes, and discussions of the problems of eugenics, prejudice, fertility trends, and adult education. Teachers will find especially valuable Hogben's numerous shrewd observations on how to teach even dry subjects with interest and enthusiasm. A brilliant essayist, a trained natural scientist, a teacher of amazing pedagogical prowess, with broad social consciousness, and sensitive to the social functions and obligations of science and education, Hogben represents in many respects the modern ideal intellectual. The reviewer has exercised great self-control in resisting the temptation to quote the many keen witticisms contained in this collection of essays.

17.1. Review by: Dorothy W Douglas.
American Sociological Review 7 (1) (1942), 151-153.

In Author in Transit Mr Hogben has tried, and sometimes succeeded, in giving us an amusing picture of a writer making the best of a bad bargain in a forced trip nearly around the world to get back to England from Norway after the Nazi occupation. He likes Norway, Sweden, and Denmark, he dislikes the Soviet Union, he loves Japan, he likes the United States - this is about the way his impressions read. One gets some interesting comments on language structure (Mr Hogben is a biologist and language with him is a hobby), but the rest of his comments appear naive. For instance he tells us "I suppose that about fifty percent of my most intimate friends are Jews"; he refers to his bee-line trip across Russia on the Trans-Siberian Railroad, plus three days waiting for the train at Moscow, as "My nearly three weeks travel across the Soviet Union away from the beaten track", and he assures us regarding Japan that, "A few hours in the country" suffice to show that Japan is not seriously exhausted by "the China incident".

18.1. Review by: BMJ.
The British Medical Journal 2 (4155) (1940), 258.

The second edition of Professor Lancelot Hogben's Principles of Animal Biology is to a large extent a new book. It is primarily a textbook for the upper forms of secondary and public schools and for students at universities and technical colleges; but it may well be used by any intelligent and serious reader who wishes to gain a basic understanding of animal life and some knowledge of recent developments in the subject. The first edition was published in 1930 and has been out of print for some time. In this second edition the original and most admirable plan remains, but throughout the chapters have been most carefully revised and extensively rewritten. The illustrations are an attractive and effective feature of the work. All those in the earlier edition have been redrawn by Mr J F Horrabin, and many new ones have been added or substituted. Here, as in other well-known and remarkable volumes from the same hands, the cooperation between author and illustrator adds materially to the value of the book. Here, too, both the general plan and the exposition of the subject-matter in each section or chapter demonstrate the excellence of Professor Hogben both as a teacher and as a writer. His clearness and accuracy are beyond question, and the development of his impressive technique is manifest throughout. The book deals with principles and is not a manual directing the dissection of types. This is just what is needed and is most useful both to the medical student and to others. It is in two parts, the first dealing with the vertebrate body as a going concern, including reproduction, development, and the machinery of inheritance: and the second dealing with the diversity of animal life under a unity of type, classification, and evolution. Its reading requires, as it should. close and progressive attention on the part of the student, and at the end of each chapter there are admirable questions or exercises as "topics for home study." Altogether this revision of his work has resulted in the production by Professor Hogben of as satisfactory a textbook as could be reasonably desired.

18.2. Review by: J L M.
Man 41 (1941), 67.

In this new edition the object of the book remains, to supplement laboratory work with a general introduction based on evolutionary principles with emphasis on function throughout. The chapter in which the vertebrate skeleton is used to illustrate the principles of geological succession by reference to the fossil record takes full account of recent discoveries of early types of man. The new illustrations are not only clear but pleasant to the eye. While much of the matter is of interest mainly to zoologists, the chapters on the 'Machinery of Inheritance' and on 'Evolutionary theory to-day' are commended to anthropologists who make use of 'evolutionary' and 'functional' phraseology. Not that the risk of perversion is all on one side. As Professor Hogben says "biologists do not use the word living in the same sense as lawyers or metaphysicians," and it was a pity that they let themselves be called 'biologists'; but that is ancient history. There are some sound remarks about 'homology' and 'convergence' on 'race', and on 'conscious behaviour' as they appear to a biologist.

19.1. Review by: Mario A Pei.
The Modern Language Journal 28 (7) (1944), 633-639.

As for Interglossa, its primary merit is to call attention once more to the ever more imperative need for a vehicle of international communication, and that, despite all his subjectivisms, is the spirit in which Hogben offers it.

19.2. Review by: L J D R.
The Journal of Hellenic Studies 63 (1943), 138-139.

The growing babel of artificial languages perhaps shows at least one merit denied to the natural babel, that of an improvement on broad lines by evolution as this or that feature is progressively jettisoned as cumbrous or unnecessary, and as the aims and claims of an auxiliary language become more modest. Not that 'interlinguistic' research can ever hope to combine all the good points of various systems in one. Mr Ogden's Basic English made the important contribution that in vocabulary the ideal is not facility in unlimited word-building, as was hitherto assumed, but a rigid restriction to a minimum of words. So, too, Mr Hogben's Interglossa, which posits a somewhat larger number (880) of 'essential words' than Basic (850), now emphasises a truth which was being largely overlooked and which is of special interest to Hellenists. It is a paradox that this technological age, now only in its infancy, is falling back more and more on Greek for its terminology. Newer coinages like microphone, megacycle and allergic rapidly achieve the universal currency already won by the telegram, photograph and elastic of an earlier vintage. A wireless mechanic's apprentice is as much at home with heterodyne as Mr Jackson Knight is when expounding the rhythms of Virgil. Furthermore, these words soon leave the laboratory for the market-place, and, as Mr Hogben remarks, of the many persons who associate the element micro- with 'small', how few know that parvus means the same. The earlier advocates of an interlanguage looked to Latin, whether Classical, 'Church,' 'botanical' or in some reduced form such as Latino sine flexione or else simply as the foundation of Romance vocabulary (as does Occidental in especial). Some words of Greek provenance were usually included, the result of an illogical compromise, such as the rather surprising kaj of Esperanto. But the great majority of the words of Interglossa, being based on roots which now belong to the international vocabulary of science, are of Greek origin, with, however, a fair sprinkling of Latin derivatives when these are supplied by technical usage.
...
Mr. Hogben's venture is frankly experimental, a basis for further development; but it without doubt marks a step onward in the search for an agreed medium of global intercommunication. And, as already stated, there is something here which those who wish to promote Hellenic studies would do well to consider.

20.1. Review by: Albert Guérard.
Books Abroad 18 (4) (1944), 355-356.

Mathematics for the Million, in the same series, actually teaches you Mathematics. This book is a methodology rather than a primer: it teaches you how to learn. Although it gives you, in the first part, a good survey of linguistics, its chief interest lies in two ideas, a) Language is an instrument that man is free to improve at will - and the way to improvement is simplification, b) The task of learning foreign languages is made easier by their family resemblances. The first is a return to the Enlightenment (which was enlightened, after all): for a whole century, the romantic-historical - organic - obscurantist conception of unconscious growth prevailed. Bodmer is a "planner," not to say a New Dealer.

20.2. Review by: Harry Hoijer
Language 21 (2) (1945), 100-108.

The Loom of Language is the third in a series of books which have as their principal purpose the interpretation of science to the layman. Mathematics for the Million was the first of these; in it Lancelot Hogben attempted to describe the practical origins of mathematics as well as to present in non-technical language the essentials of mathematical procedures. Science for the Citizen, also by Hogben, had the same objective in regard to the natural sciences.

It should be noted that these books, as well as the work under review, are neither simple popularisations nor mere 'self-help' manuals. They seek rather to steer a middle course. Mathematics, the sciences, and linguistics are to be presented as accurately as possible but in a language wholly free from merely academic technicalities, and from the point of view of the practical, everyday citizen rather than the cloistered scholar. In The Loom of Language, Hogben states this general purpose as follows: 'First and foremost The Loom of Language is a book which adults can use as a basis for sustained study, and a book from which teachers alert to new techniques of instruction to meet the needs of the ordinary citizen can get helpful suggestions with a direct bearing on their daily task. Its design is based on the conviction that in the past the orientation of studies in many of our schools and universities has not provided a sufficient equipment for the constructive tasks of the society in which we live, that radical changes in the scope and methods of education are a necessary condition of continued social progress, that such educational reforms will not come about unless there is a vigorous popular demand for them'. And later: 'Because this book is a successor to Mathematics for the Million and Science for the Citizen, its motif is social and its bias is practical'.

20.3. Review by: Grace Kurz.
The French Review 18 (2) (1944), 121-123.

This book of almost seven hundred pages is the result of happy collaboration between author and editor. Mr Hogben, who wrote Mathematics for the Million, disclaims in his editorial foreword any linguistic scholarship that would entitle him to co-authorship, but assumes unblushing responsibility for passages that attempt to "strew flowers in the path of knowledge." The reader accordingly guesses that certain amusing diagrams, reminders to the Million of adventures in mathematics, are due to his influence.

20.4. Review by: Harold Whitehall.
The Kenyon Review 6 (4) (1944), 672-676.

Whatever else may be said of him, Lancelot Hogben is undoubtedly one of our more brilliant pedagogues. The Loom of Language, written under his eye and apparently at his prompting by the Swiss linguist Bodmer, completes a trivium for the adult education of our times. Like Mathematics for the Million and Science for the Citizen, the Loom is social in motif, practical in bias. Like them it is designed to cover a great area of information virtually ignored by the conventional systems of education. The real precursors of this book are not the various works on general linguistics with which it will be inevitably compared ... . Within its tradition, The Loom of Language, although it may infuriate the professional linguist, horrify the classicist, and startle the semanticist, is a timely, perhaps a genuinely important book.

In overall purpose, the Loom exploits a thesis familiar to readers of the various manuals on Basic English: language diversity results from geographical barriers that interrupt human communication; scientific invention has now nullified these barriers; the close-knit world commodity of tomorrow will need widespread facility in foreign vernaculars a practical international auxiliary language, some understanding of language as a human institution. This facility, this auxiliary, this understanding the Loom attempts to provide. ...

20.5. Review by: Mario A Pei.
The Modern Language Journal 28 (7) (1944), 633-639.

Hogben's sweeping condemnation of all language-teaching methods but the one he favours is paralleled by an extremely long list of subjective, personal statements on all sorts of matters, linguistic and otherwise. It is not merely linguists in general and Indo-European linguists in particular who come in for a sound drubbing. Roman Catholics will not care for his assertion that "Latin is still the language in which the Pope invokes divine disapproval of birth control or socialism," and even less for the one to the effect that "many hundreds of Arabic words bear witness to what Spain owes to a civilisation vastly superior to its Catholic successor." Jews may not approve of the charge that "Zionists encourage the difficulties of existence for Jews by trying to revive Hebrew as a living tongue." Philosophers may be at variance with the statement that "I think, therefore I am" is "Cartesian claptrap." Lovers of French will resent the remark that their claims for French as a language of clarity or as an international tongue are "nonsense," and that though French "still has ostentation value as a female embellishment in well-to-do circles, unfamiliarity with French no longer stamps a person as an ignoramus among educated people." German grammarians will not like the labelling of the rules of German grammar as "representative exhibits of speech deformities or evolutionary relics". Latin scholars will he angry at "the grammar of Latin is mainly concerned with social ritual. ... The use of Latin case-forms is a social habit, like eating asparagus with the fingers". Russian is not merely said to have "a large number of archaic and useless grammatical devices", but to be "a tower of Babel"; the editor's sole advice to those wishing to learn Russian is "to take the precaution of being born and brought up in Russia"; even the Soviets, to whom he is quite partial in other respects, are severely taken to task for continuing to inflict on their citizenry "a hang-over from a church-ridden past," the Cyrillic alphabet, which is again described as "a cultural handicap", despite its manifest phonetic advantages. Indeed, few tongues escape the editor's personal disapproval: the grammar of the Semitic languages is called "a load of grammatical ballast", and Icelandic "a surviving fossil language, like the duckbill of Tasmania".

21.1. Review by: Edward C Colin.
The American Biology Teacher 9 (9) (1947), 283-284.

In a brief Foreword the author of this book states his aim, as follows: "Since the pioneer work of Jennings on systems of mating, there has been a steady output of publications elucidating the statistical implications of the theory of the gene. Theoretical investigations of this sort have practical applications in agriculture and furnish the only satisfactory basis for a scientific approach to the problems of human inheritance. So they are of general interest to all students of genetics. To many students of genetics the original sources are still a closed book, because the mathematical reasoning relies on methods which have as yet no place in the early stages of mathematical teaching. This volume aims at making some of the outstanding results of mathematical genetics intelligible to readers who need assistance before they can consult the original publications with profit and understanding. It is based on a course of lectures delivered to postgraduate students in the Genetics Department of the University of Wisconsin in the winter of 1940."

The headings of the eight chapters and the two appendices follow: Gene frequencies, genotypic frequencies, and systems of mating; Basic types of algebraic series in genetical theory; First steps in the calculus of finite difference; Binomial series; Non-assortative mating in the absence of selection or mutation; Selection; Assortative mating and consanguinity; Mutation pressure and isolate effects; Significance tests for Mendelian ratios; The estimation of linkage and determination of variance formulas for gene-frequency analysis by the method of maximum likelihood.

A knowledge of the fundamentals of genetics is assumed. The book consists primarily in the derivation of mathematical equations for certain genetic principles. It will, no doubt, be useful chiefly to professional geneticists and to graduate students in genetics. ...

21.2. Review by: Carl L Hubbs.
The American Naturalist 81 (800) (1947), 382.

Although fairly comprehensive in regard to the analysis of simple gene actions, this treatise is defective in that it does not cover gene systems. Furthermore, the valuable and widely used chi-square test is neglected and no attention is given to Fisher's treatment of selection or to Wrights work on population genetics. For these reasons the book is inadequate for a student of evolutionary genetics.

21.3. Review by: C W Cotterman.
Journal of the American Statistical Association 42 (237) (1947), 184-185.

The author of Mathematics for the Millions here lends a helping hand to the hundreds of geneticists who have experienced difficulty in understanding the mathematical writings of a few of their colleagues. The subject of the present volume is the mathematics of Mendelian populations - an extension of those probability relationships which hold for single families to more complex problems involving whole populations. This specialised form of statistics provides a framework for mathematical theories of evolution, such as those developed by Sewall Wright, R A Fisher, and J B S Haldane, and has already found many practical applications, notably in the genetic analysis of human populations and livestock herds. In large part, this material has not previously been summarised in book form in the English language.

The book is an expansion of a series of lectures presented to graduate students of genetics at the University of Wisconsin in 1940. It has the logical arrangement of a mathematics text and is provided with numerous exercises and answers which increase its usefulness as a manual for self-teaching. Particularly valuable in this respect are three introductory chapters on basic algebraic series, first steps in finite differences, and binomial series, in which the author gathers together various algebraic devices that have been found to be most useful in statistical genetics.
...
It is unfortunate that the author did not apply his skill to the exposition of a wider variety of statistical methods from the works of other authors. For example, he sets forth a method which he devised for the correction of ratios derived from selected human families, but he does not correctly state its limitations, nor does he describe a more generally serviceable method due to Fisher. Indeed, none of the latter author's important contributions to statistical genetics are mentioned in the very inadequate lists of references which are provided at the ends of chapters. Metrical characters are not discussed, hence the general problems of analysis of variance and correlations between relatives are not developed. However, the very simple and widely useful coefficients of relationship and inbreeding due to Wright should at least be mentioned in an introduction to mathematical genetics, and their use would have simplified the sections on assortative mating and consanguinity.

21.4. Review by: W Feller
The American Mathematical Monthly 54 (7.1) (1947), 423-424.

Genetical theories and various breeding practices lead to pleasing mathematical problems. They have intrigued abstract algebraists to construct special "genetic algebras," and some of the recurrence relations and functional equations describing the genetical structure of succeeding generations have not yet been solved. Readers of this Monthly will be more interested in the fact that genetical theories provide perhaps the easiest and best accessible examples illustrating how even very elementary mathematical reasoning leads to interesting insights and applications. It is a fairly common practice to use the Mendelian laws as a first application for the elementary rules of combining probabilities. The equally elementary and intuitive applications of simple difference and, other recurrence equations, of matrix computation, and so forth, are less known. Mathematicians, and in particular mathematics teachers, will, therefore, greet a book on mathematical genetics with great interest.

Unfortunately, the book under review will disappoint them inasmuch as it is clearly not intended for them. It is written for students of biology and practical breeders who have difficulties with simple fractions but wish to understand the results of a quantitative analysis of breeding systems, of mutations, selection, and so forth. Accordingly, the choice of material, though natural and justified, is not ideal from the peculiar point of view of the mathematician. The mathematical tools and ideas are hidden so far as possible and the access to the book is made difficult by the standard practice in genetics of using as many technical terms as possible and not defining a single one. It is possible that students of biology would be acquainted with these terms long before they desire to consult Hogben's book. Nevertheless, one page of explanations would have opened the book to many other readers.

21.5. Review by: Kenneth Mather.
Science, New Series 106 (2741) (1947), 45-46.

[New] mathematical developments are especially associated with the names of Fisher, Haldane, and Wright; but many others have contributed, and the literature is both extensive and scattered. Prof Hogben, in a book which is based on a course given to postgraduate students of the University of Wisconsin, has brought many of these results together and attempted to make their derivation intelligible even to those geneticists whose mathematical background is limited.

The book falls into three parts. In the first the author lays the foundation, both genetical and mathematical, for his later treatment. He considers certain basic genetical conceptions, such as those of gene frequencies and mating systems, and illustrates them and their applications by reference to models made with playing cards. The mathematical introduction is more elaborate and includes accounts of certain algebraic series and their manipulation, the calculus of finite differences as used in handling these series, and the binomial expansion, both complete and incomplete.

These foundations having been laid, attention is turned in the second part to the effects of selection, assortative mating and inbreeding, mutation, and isolation. This section is prefaced by some remarks on what the author calls the limitations of mathematical genetics. They are concerned with the principles of gene expression and their effects on the validity of the mathematical findings. The treatment is most comprehensive in regard to the types of selection and systems of mating covered, but their consequences are considered only as they apply to single genes. Systems of genes are not dealt with. As we might expect from the author's own interests, the special problems of human genetics are well to the fore in both treatment and example.

The third part consists of two appendices, one on tests of significance and the other on statistical estimation. These topics are dealt with in a more mathematically thorough than a practically comprehensive way.

21.6. Review by: Sewall Wright.
The Quarterly Review of Biology 22 (2) (1947), 149-150.

Mathematical genetics is a term which might be interpreted in widely different ways. Geneticists often have occasion to use the ordinary statistical methods in describing the populations with which they deal and in testing the significance of differences. The author very properly excludes all of this, except for cases of peculiar interest to geneticists. Significance tests for Mendelian ratios are discussed in Appendix One, which includes a derivation of the normal probability curve and discussion of the probability integral. Appendix Two deals at some length with the estimation of linkage and determination of variance formulas for gene frequency analysis by the method of maximum likelihood. The body of the book deals with the genetic properties of simple populations. Genetics provides as satisfactory illustrations of the principles of a priori probability as do the traditional coins, dice, and decks of cards. The application of elementary probability theory to the interpretation of Mendelian ratios is presented at some length in the first chapter.
...
Summing up, the book gives a good introduction to the use of the elementary theory of probability and of the calculus of differences in determining the frequencies of alleles in simple populations under various conditions; but it does not penetrate far into the problem that must be considered in dealing with complex characters in populations with the complexity of structure encountered in nature, in human races, or even in breeds of livestock.

21.7. Review by: C P Winsor.
Mathematical Reviews MR0019906 (8,478f).

An elementary presentation of mathematical methods and genetic results, intended for geneticists without mathematical training. The first four chapters deal with the probabilities (called throughout "proportionate possibilities") arising in various genetic situations, with elementary finite difference equations, and with the binomial frequency distribution. The later chapters consider gene-distribution problems under random (called "non-assortative") mating, the effects of various types of selection, the effects of assortative mating and inbreeding and the effects of mutation and selection. The genetic problems are confined to those involving a single gene substitution, on the ground that "it is relatively simple to extend" the results to any number of substitutions.

22.1. Review by: C R Fay.
The American Economic Review 38 (4) (1948), 648- 649.

The maps and pictures are excellent, though thrown together in somewhat chaotic form, but I can say nothing for the scholarship of the book except to regret that one so well known in this country should take such liberties with his reputation. In no sense is there a British background for this book. It is a jumble of matter thrown together with little regard for sequence and no regard for balance. No doubt in isolation most of the facts are true or near-true, but they tell no story. They are merely endless tips and tags joined together by a rather foolish affection for the pseudo-history of certain natural scientists.

23.1. Review by: Bentley Glass.
The Quarterly Review of Biology 25 (2) (1950), 200.

In his Conway lecture a year ago Lancelot Hoghen warmed to his subject by directing a number of savage thrusts at C D Darlington, Conway lecturer of the preceding year. The New Authoritarianism, which many a scientist today views with apprehension, is in Hogben's eyes an outcome, perhaps an inevitable outcome, of large-scale enterprise. The very growth of scientific knowledge makes it impossible any more for us to identify "the scientific outlook with refusal to take propositions about external or human nature on trust." In higher levels of education and investigation the diminution of

... concern for rational grounds of confidence is evident on all sides. The constant pressure of foundations which finance research, diverts the eager curiosity of the young investigator by speeding up publication of results in any field of inquiry with an aura of novelty. The policy of our institutions of higher learning penalises honest effort devoted to the exposition of science to students or public alike by allocating academic promotion solely on the basis of mileage covered by repetitive reprints. In universities or Government research stations, heads of departments ostensibly appointed by reason of capability to do original scientific work soon discover that they are paid to be super-salesmen of problems nobody can solve ... the temper of science itself in this context becomes increasingly more authoritarian ... the pity of it is the complacency we have in common with every pre-existing culture in its decline. ... Increasingly elaborate techniques call for expenditure on a scale which necessitates the support of either the State or of private foundations; and the new patronage imposes a new discipline on the process of discovery, reshaping the outlook of its personnel. To justify the newer and more costly techniques it is necessary to show results. Accordingly, a memoir in a scientific journal is less now, as once in my own life-time, the announcement of a new discovery than a progress report on a cash advance. ... He who pays the piper calls the tune.

Hogben concluded by quoting the Nobel Prize speech by H J Muller, which emphasised that continued growth in the freedom of the human spirit in inquiry and communication must be paralleled by "the bringing of the benefits of modern techniques to all, the raising of the standard of living of the broad masses everywhere, not exclusive of any groups or races ... so as to make high culture and free criticism not the unstable possession of a limited sector of society, as among the ancient Greeks, but a part of the accepted inheritance of all humanity."

23.2. Review by: Martin Wight.
International Affairs (Royal Institute of International Affairs 1944-) 26 (3) (1950), 385-386.

This is a very good lecture on the dangers inherent in the present organisation of scientific work, its specialization and its divorce from humanistic studies. The temper of all large-scale enterprise is authoritarian, scientific work included. Since the logical instruments for coordinating the growing accumulation of facts are far more various and exacting than a hundred years ago, the modern scientific worker is disposed 'to take more and more on trust with less and less concern for rational grounds of confidence'. Universities and research foundations encourage quick results at the expense of original work and honest teaching: 'a memoir in a scientific journal is less now ... the announcement of a new discovery than a progress report on a cash advance'. 'To sustain the morale of a team it is necessary to invest its work with a sense of disproportionate urgency; but such auto-suggestion is inconsistent with the reflective reserve which holds authority in check'. Pure mathematics 'will soon be the only field in which conformity to authority, a shrewd eye for novelty, and an accommodating committee-technique of man-management will count for less than a craving for intellectual adventure regardless of social advancement'. The psychological conflict between this kind of opportunism and scientific honesty 'helps to explain why creeds such as racialism and Communism, inviting violent and destructive measures, have a peculiar appeal to scientific workers who realise, if through a glass darkly, some of the implications of living in society'. Professor Hogben demolishes Dr Darlington's defence of Soviet genetics and attacks the Mandarins and Fellow Travellers of science with bland authority, himself the most elegant literary mandarin in the field.

24.1. Review by: Lorus J Milne and Margery J Milne.
The Quarterly Review of Biology 25 (2) (1950), 264.

If man is unique, concludes the author, it is because he is "the only picture-making animal which has ever lived on our planet." Nothing else about him is more than an extension of features found in other animals. With copious and excellent illustrations, the pictorial strand is followed from some 30,000 years ago to the present day. Careful consideration is given to the relationships of totemistic signs, zodiacal portents in relation to agriculture, alphabets and modes of counting, paper-making, playing cards, and movable type. Hogben traces the shift of centres of civilisation northward and shows how cloudy weather plus winter cold make understandable the new interest in the technology of glass-making - and its products, such as clear window glass, lenses, and eyeglasses. He points to the standardisation of spelling and grammar which followed the introduction of printing, and to the development of the international symbolisms that have grown up in electronic circuit representations, in floral diagrams, and atomic detail. As a culmination in this direction, Hogben praises at length the universal picture language begun by Otto Neurath in 1925 in Vienna, and called "Isotype"; - the present "book is a tribute to his memory." Printers' ink, vanishing points, map making, colour printing, and improvements in press design bring the subject to modern times and a carefully documented analysis of the American comic strip, with the frustrations of everyday life found to be the clue to its appeal. The book ends with a plea for early adoption of an international language and for an acceleration in the training of world citizens through wall charts, motion pictures of improved types, and other visual aids ...

24.2. Review by: Paul S Wingert.
American Anthropologist 53 (3) (1951), 403-404.

For those acquainted with Hogben's Mathematics for the Million and Science for the Citizen, it should be said that his present book is again a popular exposition, brilliantly written, of a subject of the first importance. The subtitle, "A Kaleidoscope of Human Communication," makes clear the content of From Cave Painting to Comic Strip. Techniques of "human communication" are traced from prehistoric cave painting, through the invention of the calendar, alphabet, and computation systems, to the development of printing, graphic representation, photography, and, finally, the comic strip, movies, radio, and television. The major historical facts are usually presented accurately, but in most cases without documentation, in keeping with Hogben's often declared disdain of "cloistered" scholarship. Throughout this book, in fact, there are constantly recurring minor motives made up of his favourite convictions, such as the importance of the fight against illiteracy and the role standardisation should play in it, the necessity for world government, so that mankind may survive, and the great importance of visual education in bringing about a world where ideas can be interchanged understandably. These ideas finally emerge as a major theme in the concluding and most important chapter of the book. No one can deny the urgency of the ideas that bear upon the present state of the world. And no one would deny that popularisation is important, if rooted in solid scholarship. But the blending of facts, hypotheses, and suppositions is dangerous and undesirable, even if in support of worthy ideals.

24.3. Review by: Mario A Pei.
The Modern Language Journal 34 (4) (1950), 326-327.

The distinguished author of "Mathematics for the Million" and editor of "The Loom of Language" has teamed up with Marie Neurath, Director of the Isotope Institute, to give us a fascinating book on visual communications, to which Mrs. Neurath contributes the pictures (231 of them) and Professor Hogben the running commentary. The former constitute an absorbing pictorial history of civilisation. The latter is vast and all-embracing, deep in spots, shallow in others. Where Hogben knows, he tends to become technical, as in the chapter on the Calendar (II) and that on Photography and the Motion Picture (IX). Where he does not know, he is glibly inexact (this is particularly true of the linguistic sections). At all times he is earnest, persuasive, inspired by an idealism which he vainly tries to conceal beneath a crust of scientific materialism.
...
But these shortcomings, both factual and subjective, must not blind us to the many things of value Hogben has to offer. In addition to the many truly excellent chapters replete with authentic information (for instance, the one on the History of Printing), Hogben is an effective advocate of the most desirable of social reforms: the abolition of illiteracy; the widespread use of visual aids in education; the creation of an auxiliary international language; the standardisation of weights and measures; the abolition of war and the creation of a federal world government, all described in his closing chapter.

It is particularly this closing chapter that should be carefully read and pondered by every educator, whatever his field, for Hogben supplies a keynote that is too often forgotten by too many of us. Civilisations, he reminds us wither away because their means of communication are inadequate to integrate community effort in the advancement of knowledge, which simply means that the role of education in the preservation of Civilisation is paramount.

Hogben's final, eloquent plea is for a world government in which representation shall be based on ever-expanding literacy, an idea which is no less excellent because it was previously advanced in a supposedly materialistic America ...

24.4. Review by: A C S.
The Burlington Magazine 93 (576) (1951), 99-100.

Professor Hogben's latest volume is a history of man's techniques of visual communication. With his usual brilliance and clarity he shows how the growth of cultures has depended on the development of these techniques, and he argues with great force that on their further development and use must depend not solely the future development, but even the continued existence of civilisation.

Though not in any sense a history of art, it is a history which touches that of art at many points. In the palaeolithic cave paintings, art is not separable from religion or science or magic. In the subsequent formation of those basic elements of civilisation, the calendar and the alphabet, the artist was closely involved, since it was he who drew the zodiacal signs with which the heavens were charted; he, as architect, built the temple-observatories by means of which movements of sun and planets were brought to the knowledge of man; and he, as scribe, influenced by his craftsmanship the forms of letters. The central theme of Prof Hogben's history is therefore one which it is essential for the historian of certain phases of art to consider.

Even in the later chapters of the story, dealing with the development of mathematical notation, the invention of paper, printing, etc., the artist is never far from the surface.

24.5. Review by: I Bernard Cohen.
Scientific American 182 (2) (1950), 58-59.

Lancelot Hogben, who has a high reputation as a populariser of science, especially in his Mathematics for the Million, here undertakes a history of communication - how men since prehistoric times, by pictures, signs, symbols and printed words have expressed and exchanged their ideas. He concludes that, although we have travelled far since Cro-Magnon man first made his magnificent paintings on cave walls in France and Spain, we have scarcely begun to exploit visual aids in education as well as politics. He believes that such methods are essential if we are to preserve our culture by raising the level of mutual international understanding to the point where another world war would be impossible. Unfortunately Hogben himself has difficulty communicating his ideas in a hastily written book that strains after effects on almost every page.

24.6. Review by: H M Kallen
Social Research 18 (1) (1951), 122-125.

Mr Hogben's book's ... subtitle is A History of Human Communication. It contains 230 illustrations. Each signalises a step in this history, and all together give an overall view of the sequence and a suggestion of the next step. With their rubrics, they fascinate. Although designed to exemplify and illustrate the ideas of the text, their effect on me has been to take my attention away from the text and to make return to it an effort. And the text has an interest all its own, by no means small. Perhaps this experience is one more confirmation of Mr Hogben's idea that man is the sole picture maker among animals, that pictures are his first and last means of communication; that all his enduring signs and symbols begin as pictures of pictures of pictures; that pictures thus are the primal vehicles of numbers and letters and words, the first beginnings of the religions, the arts, the sciences in the economy of human cultures. ...

The pictures bring it home independently of the text; the text would tell the tale even if there were no pictures. Perhaps, then, they ought not to have been interleaved as they have. Their span stretches from the cave paintings of Altamira to the colour-prints of the daily press. They tie communication in with basic instinctual need-first the need for food and shelter and safety, as these are postulated by cave images and by the totemic animals which primitive imagination projected upon the constellations that mark the places of the earth's seasonal turns, and instituted as "signs" of the Zodiac; again, the need for measuring time which is served by such structures as the pyramids of Egypt, the Downtor in Devon, the Sun Tower in Peru ...

For in the past, Mr Hogben believes societies have failed because communication failed to keep up with development. Communication fails wherever it is a monopoly of an elite or wherever it is inadequate to the "day-to-day cross fertilisation of theory and practice." It is failing today because. also in democratic societies. under the present conditions of research "the temper of science becomes daily more authoritarian" and a "new authoritarianism of the campus and of the laboratory" is joining that of the churches: To stop this we must undertake "an all-round and intensive speed-up of the educational process from the cradle to the grave." And this calls for media of communication common to all mankind. Mr Hogben argues for an international language auxiliary to the national ones, and a sort of "pictorial esperanto" which can present, for the eye to see and the mind to understand instanter. abstract relational configurations whose verbal or mathematical explication might require the mandarin-like equipment of the occupational elite.

24.7. Review by: Grace E Oehser.
The Scientific Monthly 70 (2) (1950), 134-135.

Hogben's From Cave Painting to Comic Strip (subtitled "A Kaleidoscope of Human Communication") contains enough excellent material for half a dozen books, but as one book it reminds us of Stephen Leacock's Lord Ronald, who "flung himself upon his horse and rode madly off in all directions." It is in many ways a fine book, reflecting the author's enormous knowledge and his amazing ability to make lucid what he knows, but it seems to lack viewpoint. Hogben seems to try to write the history of art, of illustration, and of the printed word in one volume. There are excellent chapters on symbols, hieroglyphics, the calendar, numerals and mathematics, and on all the techniques of mass production of visual communicative media, tracing the evolution of the tools involved in visual education. Early in the book the author describes it as a "picture-book about picture-making," and so, when he includes a chapter, however interesting, on the invention and use of the cipher in mathematics and another on the internationalism of free speech (including a denunciation of modern educational methods), we wonder, like Alice, how we got from the cucumber frame to the Mad Hatter's party. The illustrations (230 of them) were selected by Marie Meurath, and she did a fine job staying within yoohooing distance of Hogben. They are pertinent, varied, and often beautiful.

But Mr Hogben, having traversed the historic field of illustration as an educating method, comes to the close of his book with some concrete suggestions about what social applications can and should be made. As is often stated, man is heading toward more and more learning about less and less. This rightly is of concern to Hogben. He fears there will be a breakdown of bonds of understanding among peoples. General education, he says, can and should be speeded up in the cause of international understanding. He stresses the use of a modern tool developed by the Isotype Institute of London and the late Otto Neurath as likely to help greatly in bringing about a literate, understanding world populace. The tool is a system of standardised printed symbols used with great effect in statistical and factual illustration and, according to Hogben, not yet fully exploited. These are the visual aids that could make possible speedily a universal used secondary language. This speed-up of general education is necessary, he thinks, because the body of scientific knowledge is so great and so increasing. The aim is the attainment of world government, world harmony, world peace. We believe that the widespread use of these visual aids to factual education would help to fulfil the hope for peace, and Hogben's efforts are praiseworthy and deserving of support. But we could ask, Can we ever assimilate this snowball of facts as fast as it rolls up? Will the individual break, mentally and physically, under the strain of the speed-up? Isn't it a slowing-up we need instead of acceleration? ...

25.1. Review by: A M Mood.
Econometrica 20 (2) (1952), 342-343.

This book is an introduction to probability and statistics; it is the first volume of a projected two volume work. The ten chapter headings are: Figurate Numbers and Fundamental Approximations, Calculus of Choice, Hypothesis and Expectation, Recognition of a Taxonomic Difference, Significance and Confidence, Interlude on the Method of Moments, Recognition of a Mean Difference (for Large Samples), Correlation and Independence, The Nature of Concomitant Variation, Preview of Sampling Systems.

The book is a strange combination of advanced mathematics and very elementary statistics. The author's intention is to fill the gap between the cook books on statistics and the advanced treatises of Wilks and Kendall. His interest is in applied statistics, not mathematical statistics, but he is very concerned that his readers really understand statistical techniques and does not hesitate to use mathematics when it seems needed. The presentation, however, is generally intuitive; one works through numerous specific numerical examples and thereby "sees" how things go in general. This method will probably annoy mathematically trained readers.

Unfortunately enough, one must be mathematically trained to read the book.
...
Hogben has a semiphilosophic turn of mind and is much concerned about the foundations of probability theory, noncircular definitions of probability, the meaning of randomness, the implications of Bayes' theorem, and the like. Although he is no authority on these matters, he writes at considerable length about them and in a very authoritative vein. Much of this comment is downright naive. His main difficulty in these excursions seems to be that he has not clearly differentiated in his own mind the proper roles of pure and applied mathematics. The reviewer enjoyed Hogben's prose even though the book was a failure; he has a vast vocabulary and employs it with enviable dexterity and discrimination.

25.2. Review by: Donald C Williams.
Philosophy and Phenomenological Research 12 (3) (1952), 434-436.

This is doubtless the world's most sumptuous statistics book. The title and some of the earlier material are reminiscent of W A Whitworth's Choice and Chance, An Elementary Treatise on Permutations, Combinations, and Probability (1878), but these topics are promptly integrated into a quite ambitious modern textbook of statistical inference, blown up to atlas size and illustrated by attractive red and black diagrams of pertinent arrays of playing cards, urns of balls, and similar aleatory devices. Leaning appropriately on M G Kendall, R A Fisher, Egon Pearson, and Jerzy Neyman, it presents the fundamental methods and mathematics of hypothesis testing, estimation, and rules of significance and confidence. It works up to the theory of sampling distributions for correlations and promises similar treatment of more elaborate methods in Volume Two.

A student of philosophy with little mathematics may be helped by this book and its diagrams to understand the arithmetical ideas of combinations, probability, and statistics, but like the author's famous Mathematics for the Million it is nowhere near so perspicuous as the pictures and sprightly captions make it look, and this time it looks much harder. Conversely, it may bring a certain amount of philosophical and logical enlightenment to the student of professional statistics. (I do not attempt to judge how much statistics it will teach him, though it strikes me as a better job in this respect than most duller texts.) Not only is the style a little more philosophical and folksy than is usual; the very diagrams forbid that the formulas be used as mere implements without thought of the real relations which validate them, and Professor Hogben's asides and even his evasions make him philosophically more stimulating than most of his peers.

25.3. Review by: George W Snedecor.
Journal of the American Statistical Association 46 (254) (1951), 255-257.

This is a challenging book. As may be indicated in the title, one purpose of the author is to "start, as Pascal started, with some preliminary theorems not commonly dealt with in modern text books" in an attempt to "recapture the thought of those who laid the foundations of the theory of chance in the seventeenth and eighteenth centuries." A second purpose is to emphasise exact statements based on discrete distributions (chiefly the binomial) in contrast with approximate solutions derived from continuous distributions such as the normal. Another purpose is to exploit a "new educational technique" which (if I read aright the second paragraph of the Foreword) is the use of rather elaborate visual aids. These consist of numerous diagrams, many in red and black, depicting arrangements of cards, dice, and balls. Quoting from page 58: "Difficulty in dealing with problems of choice, i.e., sampling, arises less in connection with the solution of the mathematical problem than with the selection of the mathematical operation appropriate to its verbal formulation. It is therefore desirable at the outset to define in explicit terms conditions relevant to the enumeration and specification of samples. Also at the outset, it is well for the beginner to realise that difficulties which beset the verbal formulation will be less than otherwise forbidding, if study of the visual aids keeps in step with reading of the text."

In the title, the use of Whitworth's alliteration in reverse (in the text, it regularly appears in its original order) should not lead one to assume that the present treatment is similar to that of the earlier writer. Professor Hogben's book is strictly up-to-date. The cardpack and chessboard are made to rub elbows with all the rubrics of modern mathematical statistics. Not even the controversial topics are avoided, Bayes' theorem and fiducial probability being among the subjects discussed.
...
Chance and Choice is not for cursory reading. The lack of an index penalises skipping. Numerous cross references to numbered sections require thumbing through the pages because neither the chapter nor section number is indicated in the headings. With few exceptions conventional terminology is displaced by new, the technical terms being introduced casually in chapter headings, in tables and examples, as well as in the text. The arguments are drawn out over scores of pages with more or less relevant intercalations.

The book is not addressed to any one audience. For the beginner, there are the visual aids and several introductory passages which are models of exposition. The mathematician will find convenient summaries of the idioms of earlier days. But these need not hamper the layman because the verbal logic is adequately developed in parallel. The professional statistician will be interested in the polemics as well as in the originality of the viewpoint. There are few, I think, who will not find their wits sharpened and their ideas marshalled in more orderly ranks by Professor Hogben's meticulous insistence on fine distinctions. Chance and Choice might well be included in any list of required reading for students of statistics at the first or second year of graduate study (in American colleges).

25.4. Review by: R L P.
Journal of the Royal Statistical Society. Series A (General) 113 (4) (1950), 580-582.

Professor Hogben states in his Foreword that "... less than 1 per cent of research workers clearly apprehend the rationale of statistical techniques they commonly invoke ..." and he therefore hopes "... that an attempt to present the elements of statistical theory by exploiting a new educational technique will commend itself to the sympathetic consideration of statisticians who are also interested in education".

This volume, he continues, avoids "... issues of rigour which the author is not competent to arbitrate upon ..." and "... deals only with statistical methods for which it can offer the reader a rationale en rapport with the rules of algebra and differential calculus nowadays included in the higher school leaving syllabus, if supplemented by a few less accessible theorems set forth in the introductory chapter".

The book is sub-titled An Introduction to Probability in Practice by Visual Aids, and is illustrated by 84 Figures, many of which detail, by suitable combinations of hearts, clubs, diamonds and spades, all the possibilities which occur when sampling a binomial or multinomial population. Others use red and black balls or dice. This set of figures must represent the "new educational technique", as the remainder consist largely of histograms. All are excellently drawn by Miss Gladys Haines from designs by the author, and are obtainable from the publishers as a 2-colour complete set of 84 wall charts. They are likely to prove useful in helping the reader, or a class of students, to realise how the sampling distributions and tests for multinomial populations are derived. One minor criticism of these illustrations is that the accompanying numbers are sometimes almost illegible at ordinary reading distance.

The scope of the book, considered more fully below, is broadly speaking that of Yule and Kendall, introducing the reader to probability and the standard distributions, large sample tests for means and differences between means, confidence interval estimation and correlation. Multinomial distributions predominate throughout, and continuous distributions, such as the normal and Pearson series, are derived as limits from them, so that anyone new to the subject may receive a misleading impression of their importance in practical statistics, considerable though this is. There are plenty of illustrative examples and 354 well-chosen exercises, but no index, which is rather inconvenient in a work of this size. The book can scarcely be recommended for student use, considering its price, but the more mathematically inclined research worker will undoubtedly find much to dispel his ignorance, and a little to increase it.

For the most part the exposition is clear, but there is a tendency to hammer away at a topic for too long (in Chapters 4 and 5 in particular), and confuse the reader without making any real progress, while the mathematics could be abbreviated in several places without leaving the level set by the author in his Foreword, and which he successfully maintains. Those who are acquainted with other statistical texts cannot fail to notice that Professor Hogben uses standard terminology as though he had found the words lying about with no meanings attached to them.
...
There are also signs that the book has been hastily written .... Finally, it is impossible to review the work without reference to Professor Hogben's style, which, although largely scientific discourse, is characterised at times by the use of artificial expressions.

25.5. Review by: B C Brookes.
The Mathematical Gazette 35 (312) (1951), 129-131.

As Professor Hogben rightly claims, there are already many useful text- books which describe the techniques of statistical analysis for the student who is prepared to accept the recurring phrase: "it can be shown that ... ". There are also available some excellent textbooks for the reader with a good mathematical training. Many of those who have to use statistical methods in their work, however, are not equipped to benefit from the mathematical texts, and yet need more insight into statistical reasoning than is provided by the books of recipes. The purpose of this volume is to provide those whose specialist work lies in the fields of medicine, the biological sciences, agriculture, or sociology, with a detailed exposition, complete as far as it goes, of large sampling theory. All the necessary pure mathematics, from the binomial theorem to beta and gamma functions, is adequately developed as required. If, however, the sub-title "An Introduction to Probability in Practice by Visual Aids " suggests that it is suitable as a first book on statistical method, it misleads. A reader without some previous knowledge of statistical method would lose all perspective.

25.6. Review by: R E B.
Journal of the Institute of Actuaries (1886-1994) 77 (1) (1951), 151-152.

The proper training of the student who will require to make use of statistical methods in his future occupation is a topic that has recently received careful consideration by the Institute in connexion with the revision of the examination syllabus, and the appearance of a new textbook will be of interest to those concerned with this problem. Prof Hogben, Professor of Medical Statistics in Birmingham University, has clearly been dissatisfied with the position regarding training and has accordingly set to work to develop what he considers to be a suitable approach. The present work represents the first of two volumes on statistics. It has become apparent that the rigorous formulation of some modern textbooks goes well beyond the equipment needed for many practical problems. On the other hand without an appropriate mathematical background the proper appreciation of statistical problems becomes difficult and the question of training is largely reduced to establishing a proper balance between practical application and theoretical formulation. Broadly speaking, Prof Hogben has developed an approach which may be described as parallel to that of the Institute and his first volume covers similar ground to that of Vol. 1 of Johnson and Tetley's Statistics, i.e. large-sample technique. The second volumes will apparently each cover roughly the same ground. The important difference is that the Institute textbook relies on considerably more mathematics, though similar standards are assumed of the student.

25.7. Review by: I Bernard Cohen.
Scientific American 184 (2) (1951), 70.

From its title and its author's reputation as a populariser of science, one might suppose this volume to be a layman's guide to the theory of probability. It is in fact a presentation for the fairly advanced student of the mathematical basis of statistical procedures, illustrated with many colour charts and other graphic devices favoured by Hogben in his broad program to renovate the teaching of science and other subjects by the use of fresh visual methods. Unusual and interesting but not for the innocent amateur.

25.8. Review by: A Chapanis.
The Quarterly Review of Biology 27 (2) (1952), 247.

This, the first of a 2-volume set dealing with statistical theory, covers what may be called the classical treatment of large samples in both its aspects - the sampling of attributes and the sampling of measurements. There are 10 chapters, as follows: Figurate Numbers and Fundamental Approximations; The Calculus of Choice Hypothesis and Expectation; The Recognition of a Taxonomic Difference; Significance and Confidence; Interlude on the Method of Moments; The Recognition of a Mean Difference [for large samples]; Correlation and Independence; The Nature of Concomitant Variation; and Preview of Sampling Systems. The book is ingeniously illustrated with drawings showing various aspects of probability theory applied to familiar examples of card games and chess problems. Despite the pedagogical cleverness used by the author in presenting his material, this is a high-level text well beyond the average student in the biological sciences.

25.9. Review by: A J H M.
The Incorporated Statistician 1 (2) (1950), 29-30.

To those familiar with Whitworth's Choice and Chance, the title of Professor Hogden's book will suggest a treatise on probability. It is actually a highly-original and somewhat elaborate introduction to a limited field of statistics, chiefly sampling and correlation. The author's aim is to bridge the gap between the highly-mathematical textbook like Kendall's Advanced Theory of Statistics and the book that merely prescribes certain techniques without attempting to justify them. This he succeeds in doing with the aid of examples taken from games of chance, copiously illustrated with diagrams in black and red, which no doubt account largely for the price, as well as the value, of the book.

25.10. Review by: E Grebenik
Economica, New Series 19 (74) (1952), 221-223.

This is the first volume of a treatise which sets out to cover the main fields of statistical theory and method. Small-sample theory and most of the analysis of variance and covariance will be treated in the forthcoming second volume; the present instalment covers moments, correlation and the ordinary tests for large samples.

In the recent past a large number of textbooks on statistics have been published in this country and the United States, and an addition to their number should therefore justify itself either by appealing to a new group of students or by different methods of presentation. The present book would qualify on the second of these points only. The audience to whom it is addressed consists of those students who, whilst not being expert mathematicians, have reached a standard in that subject in which they are acquainted with the calculus and the properties of the simpler series. The mathematical level is therefore slightly higher than that demanded by Yule and Kendall's well known Introduction, but is approximately the same as that of Professor Weatherburn's textbook.

It is, however, in presentation that Professor Hogben differs most from the orthodox textbooks. He has for long been an advocate of visual aids in education, and in this textbook his ideas are applied to the teaching of statistics. The book is illustrated by 84 handsomely designed and beautifully printed colour charts which have, however, one drawback which is probably due to unavoidable technical reasons: some of the figures are printed in such small type that it is difficult to read them without the aid of a magnifying glass. The colour charts illustrate the properties of a number of simple probability models. Professor Hogben spends considerably more time on a discussion of these models than do other textbook writers. This is due to his anxiety to bring out clearly the logical assumptions which underlie the statistical tests in common use. In his view it is best to discuss the simplest models first and then to generalise from them to the more complex. His discussion of these logical bases is important and will be of benefit to all students of the subject. But the method has disadvantages. The mathematical argument is often unnecessarily prolix and involved. Moreover, the charts are not perhaps as universally helpful as Professor Hogben believes. There must be many people (the present reviewer is one of them) to whom a study of the charts adds singularly little illumination. I cannot help feeling that some of the more elegant and general proofs which can be achieved by using a little more mathematics are intellectually more satisfying than the process of arguing from simple models which Professor Hogben uses, and I do not think that the limitations of the procedures need necessarily be forgotten when slightly more sophisticated methods are used.

25.11. Review by: F N David
Biometrika 39 (1/2) (1952), 213.

It is claimed that 'Choice and Chance' aims to make the logical basis of statistical theory, that is the theory of probability, accessible to any college student who has the intellectual equipment to make use of statistical methods or to benefit from a practical course, and the author claims that this is done against the background of the new theory of logical inference developed in America by Neyman's School (!). What Professor Hogben has done is to write a textbook of statistical methods in which the proofs of probability theorems are magnificently illustrated by coloured pictures.

Among the subjects covered are permutations and combinations, expectations and moments, distribution of a proportion, confidence intervals, and correlation. The approach to the subject is not particularly novel, and once the statistician has grasped Professor Hogben's nomenclature and symbolism he will find that there is little here which he has not read before. Statisticians appear, broadly speaking, to be divisible into two categories - those who find a diagram helpful and those who do not. The former class are appreciative of R A Fisher's geometrical approach to sampling distributions and are undoubtedly in the majority. This being so there will be many who will like to read this book, and possibly be stimulated by it.

While Prof Hogben may stimulate the professional statistician by his book, it is to be doubted whether he will succeed in teaching the biologist and non-mathematical workers generally. Euclid is reported to have remarked that there is no royal road to learning and any non-mathematician who has patience to puzzle out Prof Hogben's diagrammatic approach would probably find his time better employed with an old and tried classic such as Yule and Kendall's Introduction to the Theory of Statistics. The style of writing is irritating and at times unnecessarily florid.

25.12. Review by: D G Champernowne.
The Economic Journal 60 (240) (1950), 785-787.

This textbook of statistical theory employs unusual methods of presentation in accordance with the vigorous views set out in the author's foreword. He points out that "less than 1 per cent. of research workers clearly apprehend the rationale of statistical techniques they commonly invoke" and that "the experts themselves disagree on fundamental issues: ... One therefore hopes that an attempt to present the elements of statistical theory by exploiting a new educational technique will commend itself. ..." The book is intended for students who have covered the higher school-leaving syllabus in mathematics, and whilst avoiding issues of rigour always offers a rationale - i.e., a vague proof of validity - for the statistical methods advocated.
...
Any attempt to apply new techniques to the teaching of statistics deserves a welcome, and it will be interesting to discover what type of student finds this book to his taste. The chief qualities required seem to be a powerful visual memory, intense curiosity and ingenuity, and immense capacity for taking pains.

26.1. Review by: Otto Struve.
Scientific American 187 (2) (1952), 71-72.

A third, revised edition, with numerous amendments of the earlier text, corrections, and an additional chapter on atomic energy. The treatment of the latter subject, described as "novel," is scarcely satisfactory, no attempt being made to carry the story beyond 1939. One may, in fact, question more broadly the merits of this book as a "self-educator:" It covers a wide ground, is full of sound information and is strongly supported by James F Horrabin's excellent illustrations; on the other hand it is much more difficult to read than its title would lead anyone to suspect, and the instruction is uneven, with disproportionate emphasis on details that Hogben considers essential to bringing out his theories of social and intellectual evolution. The result is a survey that, because of its gaps, falls considerably short of the requirements of a good textbook - though it contains valuable material not to be found in any school text - yet is very likely to overtax the ability of all but a few of the "alert" citizens to whom it is addressed.

27.1. Review by: Anon.
Science Education 38 (1) (1954), 116.

In early days every man was an explorer, following hunting animals into strange countries. Travel was often by river roads - first on a log but finally in modern boats. Herdsmen crossed the continent - China, India, Europe, Africa, America. Changing roads have changed the speed of travel and transportation. Ships sailed into unknown oceans. Finally exploring man found a flat earth to be really round. Exploration and the search for treasure continued-across oceans, across plains and deserts, to the equator, and to the poles and back. Man's exploring continues on and one wonders where it will finally end. Much of man's exploration is now in science and disease. Such briefly is the content oi this book-suitable for elementary science students of the intermediate upper grades. Coloured illustrations by Marie Neurath add to the understanding and attractions of the book.

28.1. Review by: James R Newman.
Scientific American 186 (3) (1952), 79.

Third edition of an immensely, and deservedly, successful popularisation of mathematics, with a new chapter on the "algebra of the chessboard and the card pack." The information contained in the additional chapter, while both instructive and interesting, will not, it should be noted, improve the reader's mastery of the Queen's Gambit Declined, Pinochle, Bridge or Old Maid.

29.1. Review by: Vera Sanford.
The Arithmetic Teacher 3 (4) (1956), 174-175.

This book is a delight. In it, Professor Hogben tells "how the growth and development of civilisation is also the story of the growth and development of mathematics as a science." Professor Hogben's skill in presenting specialised subject-matter to the layman is well-known to us through his Mathematics for the Million. In The Wonderful World of Mathematics, the text is coupled with superb pictures and maps in colour, the publishers say over 250 of them. The page size is large and the arrangement of illustrations and text is varied and skilful.

The end papers are an integral part of the book. Here on a double spread is a summary of the text in pictures. These take you from the use of fingers to indicate numbers to counter reckoning and to numerals; from observing the Great Dipper to Galileo and his telescope; from the rope stretchers of Egypt to a surveyor with a theodolite; and, at the lower left, separated from the rest by a body of water, a Mayan developing his numerals in Central America. Spend some time with these pages before going to the book itself, and when you have finished the text, use the end papers for review. You will be surprised to find how much new material they contain.

The organisation of the book is one of its strong points. The story is close knit. It moves fast. The treatment is chronological. The illustrated summary is excellent.

The book will be useful to teachers and to their pupils. It will intrigue the general reader.

30.1. Review by: F N David.
Biometrika 43 (1/2) (1956), 236.

This is the continuation of the first volume which appeared in 1950. The subtitle to this, as to the first, is 'An Introduction to Probability by Visual Aids', but this, in the reviewer's opinion, is not an accurate description. What Prof Hogben has done is to write two textbooks about statistical methods, illustrating with diagrams at intervals the various facets of the finite fundamental sets from which probability is calculated. As the statistical methods become more complicated the diagrams become more infrequent, and in this second volume Prof Hogben has to come down to algebra like everyone else, and begins with a chapter on expectation techniques. This is followed by bivariate models, simple analysis of variance, moments, sampling distributions, significance tests, regression, covariance and factor analysis, and an awkward chapter on sampling in a finite universe. The book is completed by a chapter entitled 'Second Thoughts on Significance', which reveals a certain naivety of outlook on the part of the author.

It is certain that these two books will be of little use to the research worker in other fields who wishes to learn a little statistical method. In spite of the attractively produced diagrams the mathematical approach is there and must be mastered, and this mathematical approach is not rendered less formidable than that of any other statistics textbook by the author's delineation of it. Serious students of mathematical statistics will undoubtedly prefer something more definite, such as, for example, Prof Kendall's two volumes. They will find in Prof Hogben's two volumes, however, a certain freshness of exposition which will possibly help them when they come to revise what they already know.

30.2. Review by: N L Johnson.
Journal of the Royal Statistical Society. Series A (General) 118 (4) (1955), 485-486.

This second volume follows the same method of treatment as the earlier part of the work. There is the same lavish use of illustration, the same extensive algebraic development, and the same use of somewhat over florid language. The reviewer unfortunately finds none of these features helpful to an understanding of the subject, so his comments must, to some extent, be biased.

The present volume contains a varied selection of topics. The first chapter is on "The Algorithms of Summarization" and contains a number of formulae in preparation for the welter of algebra to follow. This chapter includes an introduction to the algebra of expected values, variances etc. The operator E( ) is introduced, however, not as an "expected value" but as "the operation of extracting the grand mean of the cell-scores." The opportunity of emphasising the distinction between sample value and population parameter is lost. The second chapter applies the methods developed in the first chapter to certain 'Models of Bivariate Universes' including the important Lexis models. In this chapter the "Cardpack and Chessboard" of the title are supplemented by a lottery wheel and the familiar urns.

The next chapter is on "Assumptions underlying the Analysis and Synthesis of Variance." This chapter is a good example of both the virtues and the shortcomings of the book. The author makes crystal clear the necessity for an adequate appreciation of practical conditions, and a corresponding caution in building up a theoretical model. On the other hand, the logical development of the analysis leaves much to be desired.

The next two chapters ("More about Moments" and "Sampling Distributions") develop, somewhat circuitously, the "Significance Tests for Analysis of Variance" which constitute the Subject matter of the sixth chapter. This is followed by two chapters on multivariate analysis ("Simple Regression and Discrimination" and "Elements of Analysis of Covariance and Factor Analysis") and a rather oddly placed chapter on multinomial distributions and the "so-called chi-square statistic." ...

There is a final chapter with the title "Second Thoughts on Significance" which contains a rapid survey of more recent developments in statistical theory - naturally translated into the author's own inimitable language - and finishing with a section ("The show must go on") which expresses rather grave doubts on the present status of the subject, but concludes that "if convinced that a transvaluation of statistical theory is overdue, accept what limitations intellectual rectitude imposes on its claims with cheerful resignation."

The book provides stimulating reading, but the reviewer cannot recommend it as a text-book to persons seeking an introduction to statistics or probability theory. Rather is it a book to be read after having attained some mastery of these disciplines. The non-mathematical scientist will find the algebra heavy; the mathematician will find the logical development unsatisfying. But it is a book of character and one that cannot be ignored.

30.3. Review by: B C Brookes.
The Mathematical Gazette 40 (332) (1956), 156-158.

In this volume Professor Hogben completes his tremendous task of patiently exploring in detail all the assumptions and implications of statistical techniques commonly used in biological research. ... The second volume broadly covers analysis of variance, regression, factor analysis, and tests of significance.

The sub-title of the book is "An Introduction to Probability in Practice by Visual Aids" and it is as an introduction to statistical method that it must be considered. For what kind of readers then is it intended to be an introduction? The profusion of elaborate black and red diagrams of cards, dominoes, coins and urns, together with the excellent but painstaking exposition of all the elementary mathematics required (including in Vol. I the binomial theorem) suggests that the intended readers are not expected to be well-versed in mathematics or statistics, but may need to use these subjects as ancillaries when their work in medicine or biology yields numerical data to be analysed. Such readers are usually reluctant to devote to an ancillary subject any more effort than is necessary to enable them to grasp the techniques that seem appropriate to their needs and which are commonly accepted in the specialist journals; they scour the books of recipes for the appropriate formulae, apply them forthwith to their own data, and leave any arguments about the validity of the recipes to the statistical experts who understand them. Professor Hogben rightly deplores this ready acceptance of recipes and disregard of implicit assumptions. In this book his purpose is to expose to the reader all the assumptions and all the mathematical tricks that underlie the statistical methods commonly used. In this task he is eminently successful; everything is taken to pieces and logically displayed in the minutest detail. ...

Unfortunately, however, for the non-specialist reader, the three chapters leading to the first discussion of the analysis of variance occupy 150 pages of this quarto volume. Certainly, if he works through them the reader will see all the bits and pieces which this minute dissection displays, but it is doubtful whether the reader for whom this book is intended would succeed in putting the bits and pieces together again. The sheer bulk and detail of these chapters (and of the two quarto volumes) is forbidding except to those who already know their way about the subject. Moreover, though one must admire the intellectual honesty of Professor Hogben's final comment on analysis of variance and his last chapter on " Second Thoughts on Significance " in which he admits doubts about the validity of his exposition in the light of recent critical work on statistical inference, this note of doubt is likely only to convince the inexperienced statistician that the intellectual effort Professor Hogben demands of him is more than he can spare for ancillary statistics.

30.4. Review by: P G M.
Journal of the Institute of Actuaries (1886-1994) 81 (3) (1955), 318-319.

Now that both volumes of this work are available it is possible to view it as a whole and to discern the underlying threads. Leaving aside for the moment the last chapter, the work as a whole hangs together. The subject matter discussed is closely akin to what would be expected of a book written just prior to the last war with the heavy emphasis on attributes, moments and frequency curves. Comparing the book with some pre-war works one sees how Professor Hogben has tried to reinforce his argument with the diagrammatic representation of problems and set-ups. This representation of the problems is undoubtedly forceful but it is noteworthy that the volumes depend largely on heavy, though not unduly difficult, algebra which underlines the fact that in statistics there is no royal road to success save through mathematical theory followed by example. Diagrams may help the reader to appreciate what theory is applicable or needed but they do not eliminate entirely the need to understand the theory involved. Undoubtedly many students learn more easily from diagrams than from mathematics and this book will help them but they will not thereby avoid studying the mathematics necessary for a full understanding of the techniques. It is perhaps a pity that in the discussions on regression and discrimination there are few diagrams although these two topics are open to vivid portrayal with their aid. The author does not hesitate to use pungent words when he feels them necessary. Thus he talks of the 'hypnotic influence of Pearson's apothesis of measurement as an end in itself' when castigating other authors for the misuse of Latter's well-known data concerning cuckoos' eggs. Or again we find the author coming down severely on those who would use the mean and variance outside the Gaussian case, stating that they can claim no 'special semantic status in preference to other parameters more or less usefully invoked'. In view of this and other similar remarks it is unfortunate that there is not more discussion of appropriate estimators in non-normal cases.
...
Summing up one may say that any would-be student of statistics who reads and digests the two volumes of this work would gain a really solid grounding of statistical theory, although he would not be an up-to-date practical statistician without a great deal more work of both a theoretical and a practical nature. He would probably find that even with these volumes there would still be difficulty in following the pages of modern statistical journals, but his groundwork would be sure and solid.

30.5. Review by: Corrado Gini.
Genus 12 (1/4) (1956), 284.

Known not only for his biology works, but also for the popular volume Mathematics for a million, also translated into Italian under the title La matematica nella sioria e nella (Hoepli, Milan, 1948), the author wishes to adopt in these two volumes the same approach for probability theory and its applications. To illustrate and better understand the problems of mathematics, he also makes extensive use of figures, in particular those of playing cards and the chessboard which are therefore expressly mentioned in the title.

The first volume refers specifically to the mathematical theory of probability; the second to its applications to statistics and in particular to sampling, significance tests, regression, variance and co-variance analysis.

The method is certainly to be recommended, but, if it can facilitate understanding, and above all better fix the results of the demonstrations or observations in the reader's mind, I do not think it is enough to make reading accessible to those who have not already acquired practice with the mathematical treatment of problems of probability or statistics. The author has not escaped the temptation to give a new name (electivity) to an old concept, thus believing that he can overcome the difficulties inherent in its definition, vain hope - I believe - and an approach not to be recommended because there are already too many poorly defined words in the theory of probability so there is no need to add others.

30.6. Review by: W R.
The Incorporated Statistician 6 (1) (1955), 45-46.

Professor Hogben's second volume, beautifully printed and lavishly illustrated with diagrams in two colours, is no book for those who seek a short compendium of what he scathingly calls "cookery book recipes." At every stage in the development of the argument, attention is drawn in great detail to the assumptions which are being made, two particularly valuable chapters being those which deal with the assumptions underlying the analysis of variance and with the rationale of significance tests in general, with special reference to the Neyman-Pearson approach. At the same time the book succeeds in covering the elementary theory of regression and covariance, and also devotes chapters to the calculation of moments and the Pearson distributions. What is so valuable to the student in all these is the freshness of approach and the emphasis on what it all means; the mathematics is always the servant, never the master. No better indication of the nature of Professor Hogben's attack on his subject can be given than the following quotations from his chapter on the analysis of variance:

"No statistical technique is an adequate substitute for common sense, alertness to the nature of the problem on the part of those who ought to be clear about it or for ingenuity directed to the removal of irrelevant variables in an experimental set-up. Indeed, it is well to remind ourselves that experimental science, in its assault on problems most successfully attacked by experimental methods to date, had advanced far towards its present stature without recourse to statistical principles of any sort."

"In the last resort, any statistical technique referable to a system of many classes will be more or less useful to the extent that the investigator exercises good judgment of his materials in the initial task of classifying them."

A clear exposition of the underlying assumptions and a warning against the all too ready belief that these are necessarily satisfied in application to sociological problems runs like a thread throughout this volume. The exposition is sufficiently detailed to be of great value to private students, and as in the first volume, no very advanced knowledge of mathematics is assumed. It should not be assumed, on account of this, that the book is easy reading ...

30.7. Review by: R L Plackett.
Journal of the Royal Statistical Society. Series C (Applied Statistics) 5 (1) (1956), 68.

Professor Hogben has now completed his enterprising venture in the field of statistical education. His object has been to clarify the basic assumptions and expose the theoretical structure of many techniques important in applied statistics, without exceeding the level of mathematical knowledge represented by the Advanced papers of the General Certificate of Education. In this volume he is largely concerned with analysis of variance, regression, and goodness of fit; but he also offers an introduction to methods not so widely accessible, such as factor analysis and sequential tests. The pattern of his approach is the same as in Volume 1. He begins with situations where all the probabilities can be enumerated, illustrating them by coloured diagrams of cardpacks and other gaming devices; and he then proceeds to more difficult problems involving continuous variation.

His account of the analysis of variance can be taken as a fair sample of the advantages and shortcomings of his presentation. He distinguishes between random and systematic models, examines the partition of sums of squares, and derives distribution theory for the appropriate significance tests; these operations take several chapters to complete, and perseverance is a necessary adjunct to survival. The limitations of the technique as an instrument of biological research are brought out by a devastating section on cuckoos, their eggs, and the non-existence of their nests; and he emphasises that the principles were developed for small adjustments due to errors of observation, where unknowns are linearly connected, and that similar assumptions in other problems should be made with caution. He does not discuss the power of the F-test to detect departures from the null hypothesis, its robustness under non-normality, or its sensitivity to differing variances. Such matters are undoubtedly part of the rationale of the test, which is what he claims to explain, and their omission may possibly be due to the mathematical restrictions he has imposed; but as far as the question of power is concerned, internal evidence suggests that he was simply unaware of its existence until most of the book had gone to press.

What he does discuss, however, is carefully argued with a wealth of vivid terminology and numerical illustration; he always writes well, and his individual outlook is continually refreshing.

30.8. Review by: D G Champernowne.
The Economic Journal 65 (260) (1955), 692-693.

The second volume of Professor Hogben's treatise on statistics mainly deals with regression and correlation, the analysis of variance and covariance, factor analysis, curve fitting and a variety of significance tests and estimation procedures. A number of text-books have appeared in the last decade which cover this field, but Chance and Choice offers something new to the research worker and the teacher in statistics.

As in the first volume, the sampling procedures and concepts are explained by exhaustive discussions of simple games with cards, dice and counters: these are illustrated by ingenious and elaborate pictures. Although only the exceptional pupil is likely to be able to plough through these explanations with understanding, lecturers in statistics should find here some useful assistance in teaching their subject. Unfortunately, when the author is dealing with the branches of the subject which involve the normal distribution of errors, games with cards and dice prove to be less apposite, and he falls back on more orthodox examples about experiments on animals.

Those who do not know the subject matter already will find this a difficult book. This is partly because of the author's ingenious choice of new methods of proof and new notations, for example in the chapter on "The Algorithms of Summation," and partly because of his employment of elaborate words, and sentences such as this one: "Through Bowley the new evangel of correlation spread to the social sciences, expounded against a background of geometrical concepts which defy any attempt to make explicit the manifold circumstances in which co-variation may arise."

31.1. Review by: Norman T J Bailey.
The British Medical Journal 1 (5118) (1959), 347-348.

Professor Hogben starts this book by scenting out a crisis in current statistical theory, and ends it by reaching pessimistic conclusions about the value of statistics that make him feel isolated from the bulk of his intellectual contemporaries. While we may admire the courage and approve the sincerity of his views, we may yet deplore the unnecessary despair. Much controversy about principles and foundations there certainly is in mathematical statistics, and there is often disagreement as to the appropriateness and interpretation of various practical procedures. Nevertheless, it would be unwise to reject methods found by experience to be rewarding if cautiously applied. Professor Hogben's analysis of statistical theory leads him to believe that most "cookery-book" statistics is virtually useless. While dissenting from such extremism, most statisticians would agree that care and common sense are required. A statistically significant result is, as Hogben implies, a clue for further exploration, not a final achievement. But the fact that some unimaginative investigators seize on statistical analysis as a substitute for genuine scientific research is no ground for discarding an extremely useful tool of proved worth.

This book is not an elementary introduction to statistical theory for beginners, nor is it a comprehensive philosophical analysis of current controversy such as might interest professional statisticians. Nevertheless, it does contain a great deal of shrewd criticism, with much of which I am inclined to sympathise. The chief value of the book lies in its skilful and persuasive presentation of the sort of criticisms apt to be made by highly intelligent and mathematically minded scientists who contemplate the use of statistical methods. Professional statisticians should know how to handle these objections, which Professor Hogben puts forward with great force and clarity. Statistical examiners may also find the book useful as a source of quotations on which to base essay and discussion questions.

31.2. Review by: Cedric A B Smith.
Journal of the Royal Statistical Society. Series A (General) 121 (2) (1958), 234-236.

The title of this book is rather misleading. It is not an introduction to statistical theory for beginners, but rather a criticism of some standard theory and methods. In fact, it is a further consideration of some doubts and queries raised by the author in his earlier book Choice and Chance by Cardpack and Chessboard, Vol. 2.

Statistics is now applied in many fields - biological, physical and social sciences, commerce and industry. Nevertheless, repeated discussion at Royal Statistical Society and other meetings of the topic of statistical inference shows that statisticians are still somewhat uneasy about the basis of the methods used and the interpretation of the results, and any reasonable review and criticism in this field is welcome. Prof Hogben has the advantage of being a trained biologist and experimenter as well as a statistician, and he is noted for his emphasis on intellectual honesty. He observes that in the past statistical theory has gone badly astray, e.g., by uncritical and inappropriate use of inverse probability.
...
... one would expect Prof Hogben to suggest in his book a plan for a thorough reform of either statistical theory itself or else of its teaching. Instead one finds doubts expressed about certain points in statistical theory and practice as they stand at present. But the author does not put any coherent alternative system in their place, and suggests pessimistically at the end of the book that there may be no such system.

The first three-quarters of the book are mainly concerned with the calculus of probability and its "direct" applications, which the author terms the calculus of error, of exploration and of aggregates, together with an historical review of how these came to occupy their present position. On the whole there is little here that the professional statistician could seriously dispute. Prof Hogben's style of exposition is well known: the subject is illustrated by simple (but often artificial) examples, which require only simple algebra for their treatment, but the vocabulary is highly unusual, and a bit disconcerting to those used to standard terminology. In this way he hopes to bring some appreciation of the assumptions and principles underlying statistical methods to the user who may not have any advanced mathematical knowledge. The author seems to consider that statistics is generally taught at present in too authoritarian a manner, and those who need to use it ought to have a better knowledge of the background so as to apply it in a critical and understanding way. However, in 1958 very few statisticians would want to seem in any way authoritarian, and an understanding of statistical principles by the scientist is a great help to the statistician, both as regards the advice he gives, and reciprocally in enabling him to understand better just what the scientist is looking for. Any book which promotes this critical appreciation is helpful. But often the experimenter is not much interested in the statistical details (not unnaturally, for it is not his subject) and is grateful for a collection of simple recipes without bothering about finer points. Unfortunately the reviewer feels doubtful as to how well the present book will fulfil its purpose. The long discussion of elementary points will repel the professional, while the beginner will hardly know what the argument is about, and will get more enlightenment from some more suitable introductory text, such as Choice and Chance by Cardpack and Chessboard, if that is to his taste. This is a pity, since there are many important and shrewd comments scattered about the book, and a number of statistical sins are roundly and rightly condemned. Most of these result from insufficient cooperation and mutual understanding between experimenter and statistician.

31.3. Review by: H W H.
Journal of the Institute of Actuaries (1886-1994) 84 (1) (1958), 114-116.

Professor Hogben is well known as a biologist. He has also spent much of his time over many years in studying mathematical statistics. He has written two large volumes Chance and Choice by Cardpack and Chessboard, which are virtually textbooks (of a rather novel kind) on statistics, and for a long period he was editor of the British Journal of Social Medicine. He has now travelled the full circle. Having taken up statistics with some doubts and reached a stage when he apparently considered that the methods were of great value - why otherwise write two large volumes on the subject - he has now written another large book which is extremely critical of recent statistical techniques, and which concludes that these techniques are of little, if any, use to biologists and social scientists.

One must admire Professor Hogben's courage. He admits that he has reached these conclusions 'with all the mental discomfort of discarding a weighty incrustation of prevalent custom-thought .... It is not agreeable to cherish opinions which isolate one from the bulk of one's intellectual contemporaries ...'.
...
Professor Hogben has written an interesting and valuable book, but it is marred by the author's narrow definition of the concept of probability. Scientists and laymen use the word in the same sense, namely, to qualify assertions. Decisions on the basis of probability can be and are made by scientists and practical men of affairs without their being able to state the probabilities in precise quantitative terms. Closed models are used in situations which are essentially open, and the deductions from these models do help men to come to decisions about the actions to be taken in given circumstances. If we dismiss these procedures because the actual situations are open then we dismiss a large part of the present-day application of mathematics to the social sciences, including economic science, as worthless. It is doubtful if any sociologist or economist would accept this conclusion.

31.4. Review by: R L Plackett.
The Mathematical Gazette 42 (341) (1958), 244-245.

Many statistical techniques in current use embody a mathematical model, a calculus of probability and a theory of uncertain inference. Statisticians agree about the calculus of probability, but there is no general agreement on the other two aspects. Professor Hogben contends that this represents a crisis and he sets out to examine the way by which mathematics enters statistical theory, mainly in the context of the biological sciences and social studies, and to pass judgement on the several schools of statistical inference. His approach is elementary at the mathematical level but a general knowledge of statistical ideas is most desirable in order that the reader may be stimulated without being overwhelmed - this is not a textbook.

Hogben begins by asserting an objective outlook, which requires all statements to be verifiable, and which he describes as behaviourist. He thus rejects theories of probability which are concerned with degrees of rational belief, and limits the use of inverse probability to experiments carried out in two stages. He considers that probability is meaningful only as a frequency ratio in an infinite random sequence, but he strongly and repeatedly objects to the widespread convention of conferring stochastic properties on natural phenomena by claiming that statistical data represent a random sample from some infinite hypothetical population. He shows how the normal law, in a close historical connection with the method of least squares, was translated from the field of error distributions to an all-embracing description of natural variation by Quetelet, seen as the skeleton in the cupboard of contemporary statistics. The resulting applications of regression are examined, and considered valid in physics, often unjustifiable in biology, and limited to classification in social studies. He disagrees with Fisher's ideas on significance tests and prefers, like Neyman and Pearson, to operate a rule which keeps the probability of incorrect decisions below a specified level.

31.5. Review by: Morris Kline.
Scientific American 198 (5) (1958), 143-146.

Lancelot Hogben, who is a biologist and might be expected to rejoice in this powerful tool, has come to bury and not to praise it. He wants to halt the mushrooming of the theory and its applications, and to have us re-examine their value. He is not only critical of what statistics and probability are purportedly accomplishing; he is also convinced that the current generation of research workers has relinquished the obligation to examine the mathematical credentials of the principles it uses. In their frantic haste to get on with research they take on trust the procedures recommended by a few leaders and perform meaningless calculations. More and more they rely upon methods which they understand less and less. Though Hogben would not drive social scientists out of the paradise they have discovered, he would have them make themselves worthy of it.

The central theme in Hogben's attack is that statisticians have become so attracted by tidy mathematics that they have overlooked the major reason for the existence of their subject, namely, its value in deriving knowledge of real phenomena and in giving power to biological, social and psychological investigations. Hogben does not decry the intellectual activity of mathematicians seeking to perfect abstract systems of thought. But he is not concerned with it. His book examines the value of statistical theory in enlarging our understanding of living organisms and social systems. His harsh conclusion is that the theory is not successful in the solution of practical problems.

In view of the widespread use of statistics, and the weight given to the results of statistical investigations, one must pay attention to Hogben's criticisms. He believes that he can make these criticisms clearer, and show how the weaknesses in the current theories arose, by dividing the applications of statistics into four domains. These divisions are not concerned with statistics in its original meaning, in which simple arithmetic yields helpful summaries of unemployment, birth rate, death rate and so on. Rather he devotes his attention to statistical theory which invokes the theory of probability.

31.6. Review by: Pietro Gennaro.
Il Politico 24 (4) (1959), 864.

Albeit belatedly, the applications of sample theory have been spreading in more recent years in Italy. It seems, therefore, particularly important to point out this book by a biologist who, with uncommon preparation and clarity, re-examines the logical foundations of statistical procedures that have become fundamental tools for scientific researchers in all countries over the last fifty years. Starting from the historical origins of the probability calculus, the author examines the basic hypotheses that support the normal law, the least squares method, point estimation, stochastic models, factorial analysis and statistical inference in general. The conclusions lead to a serious re-examination of all the statistical tools that are often used uncritically today. ... Overall, a work that stimulates the re-examination and perhaps the reconstruction of most of the statistical tools necessary for modern scientific research.

31.7. Review by: Stanley Alderson.
Journal of the Royal Society of Arts 106 (5022) (1958), 462-463.

Let it be explained at once that Professor Hogben's latest book is not statistics for the million, nor yet for the citizen. It is, on the contrary, statistics with tears, not least for the statisticians. When Professor Hogben says he writes as a biologist, statisticians will laugh hollowly. Yet there is a sense in which it is strictly true. In this book he is concerned to assert the paramountcy of induction over deduction - to assert the ultimate right of the scientist to overrule the mathematician in any dispute 'about the relevance of the common calculus to the world of experience'. Suppose a hundred people each choose any number between 0 and 9. It might be assumed that every number will be chosen ten times more or less. Testing has shown that 3 and 7 are chosen much more frequently than the other numbers. This very simple example of the difference between deduction and induction has a bearing on the 'crisis' in statistical theory. It casts considerable doubt on the assumption that mental decisions made in complete ignorance are random occurrences. Research workers rely on statistical theory. They assume that it has been shown to be a logical necessity and that its application to the world of experience has been justified pragmatically. Professor Hogben questions both these assumptions. He points out that there are several statistical theories (in the sense of theories invoking the calculus of probabilities): not all of them can be both right and of universal application unless they can be reconciled. He also points out that the effective application of statistical theory to experimentation shows it has its uses but does not define them.

31.8. Review by: F N David
Science Progress (1933-) 47 (185) (1959), 133-134.

This book is divided into four parts. Part I consists of gambling, randomness and probability, and uncertain inference in the guise of inverse probability with Thomas Bayes and Pierre-Simon de Laplace. In Part II we have the normal curve, least squares, point estimation, regression and factor analysis. Physics and Genetics in relation to statistics follow in Part III, while in Part IV we have the design of experiments, the inference to be drawn from experiments, what statistical decisions mean, and the soi-disant inductive processes which statisticians perform. Appendix 1 containing a proof (!) of the central limit theorem is surprising.

It should be said emphatically that no-one should buy this book under the impression that he is going to learn any statistical theory from it. It is not Statistics for the Stupid or even Statistics for the Savant. What Professor Hogben has done is to write a critique of the logic of present-day statistical methods setting out its inadequacies, which are manifold, but without being adequately constructive in his turn. The bitter criticism of Karl Pearson, now twenty-three years dead, is a testimony to the power of Pearson's personality and the vigour of his ideas. The criticism of R A Fisher is no less forceful and, in the writer's opinion, antiquated.

Workers in the field of logic who are conversant with modern statistical techniques may perhaps find this book useful in that it sets out the flaws, real and imaginary, which are contained in the accepted corpus of statistical theory. Those who merely wish to learn and who have to make the best of an imperfect world would be well advised to leave this book on one side. Both Pearson and Fisher, bitterly opposed personally as they were, had the same central thread running through their teaching. It is not enough to destroy, it is necessary to construct as well. This, in the reviewer's opinion, Professor Hogben signally fails to do.

32.1. Review by: Robert R Wilson.
Scientific American 199 (6) (1958), 149-150.

Hogben's story of man's conquest of power presents some of the highlights of physics and chemistry. He describes the early use of simple machines such as the slope and sledge; the principle of the lever, pulley and capstan; the introduction, in different forms, of water power; the discoveries of Galileo and Torricelli; the history of clocks; the invention of the steam engine and locomotive; the work of Guericke, Franklin, Galvani, Volta; applications of the chemical, magnetic and heating effects of electric current; the foundations of modern chemistry; the advances of Boyle, Charles, Avogadro, Gay-Lussac, Faraday; the rise of atomic energy. His account is a little too ambitious and diffuse, but there is much in it to give pleasure and to prompt further reading.

33.1. From the Publisher.

Traces the development of man's attempts to preserve and communicate information from prehistoric cave paintings to present day use of machines such as telephones, computers, and television.

34.1. Note.

This is the American edition of The Signs of Civilisation.

35.1. Review by: J Ravetz.
The British Journal for the Philosophy of Science 12 (48) (1962), 344-346.

Back in the innocent 'thirties (when, in the words of the New Yorker cartoon, all we had to worry about was where our next meal was coming from) Lancelot Hogben amused himself in hospital by writing his Mathematics for the Million, and was astonished when first a publisher and then the public liked it. Now the amateur is displaced by Team Research, and Hogben has directed the production of a glossy lithographed volume, full of multi-colour diagrams and the most enchanting plates. The purpose remains the same as in the earlier book: to help in the understanding of mathematics through an acquaintance with its history.

Hogben knows quite well what he is and is not doing, so it would be pointless to criticise the book as a self-contained essay in the social history of mathematics. The work is sufficiently well done, within its own terms of reference, for the question of its programme to be considered seriously. In brief, what can the history of mathematics teach us about mathematics? First, it can teach us that mathematics has a history, that each theorem and technique was invented by someone. This helps to dispel the impression gained when studying mathematics at any but the most advanced level, that it is an impersonal and eternal monolith of abstract truths. Moreover, by showing that the mathematics pursued at any period was in some fashion related to the applications of mathematics, Hogben may help to break down the distinction between 'basic' mathematics (what the schoolmaster learned when young) and 'frills' (introduction to modern techniques, such as computers).

But there remains the question of how much use is the historical approach in the comprehension of modern elementary mathematics. Hogben knows the problem here, but I am not sure that he realises its implications. The course of history is tortuous; the calculus was not invented in neat stages following the chapters of a modern text. Many techniques, such as logarithms, were so swaddled in outworn concepts and special techniques by their inventors, that the form they first took is entirely unsuitable for teaching. Hogben does not lose sleep over this, any more than he has patience for (or interest in) the difficulties in the concept of infinity. Given a topic he sketches the social-historical background, and then sails into an abbreviated sketch of the modern elementary theory. I found this (to my dismay) when I first read Mathematics for the Million; each chapter was neatly divided into two, one half fascinating, the other incomprehensible. The division persists in the present book; the uniform scattering of illustrations does not mitigate it.

Hence the title of the book is misleading, and the aim of 'bringing a new humanistic approach' succeeds only partially. The brute fact is that mathematics, like any other discipline, physics, history, or playing the piano, requires hard, concentrated work for mastery at any level. To ignore this fact, and to attempt to 'bridge gaps' by historical talking-around a subject, is to achieve little more than sugar-coating the pill.

35.2. Review by: Carl B Boyer.
Science, New Series 135 (3503) (1962), 522.

The name Hogben was known chiefly in connection with zoology until, in 1936, its bearer demonstrated conclusively that books about mathematics can break into the lists of "best sellers." The phenomenal success of Mathematics for the Million prompted the subsequent appearance of Science for the Citizen and The Wonderful World of Mathematics; and now we have, in much the same tradition, Mathematics in the Making. The motive again is to "elicit intelligent understanding" on the part of the non-specialist, and once more the exposition is built on a historical matrix.
...
Mathematics in the Making is not a history of mathematics, despite the fact that it contains much history. Where historical development fails to take the same direction as the exposition, the latter assumes the upper hand. Historians will be less upset by such cavalier adaptation of their discipline than by the occasional failure of the author to indicate where evidence stops and conjecture takes over. Mathematicians, too, will find cause for some displeasure in that their subject has been presented from the point of view of the consumer rather than of the devotee. Eschewing modern tendencies to equate mathematics with abstract deductive thinking, Hogben proceeds from the position that "Mathematics is the technique of discovering and conveying in the most economical way possible useful rules of reliable reasoning about calculation, measurement and shape."
...
The layman who wishes to find out quickly and easily why mathematics is so useful will be charmed by the author's facile style and by the publisher's artistry. Here he will find no precise definitions, no tedious proofs, no dull exercises. One who wishes to go further and to learn what mathematics is really about should be reminded once more that, visual aids notwithstanding, to the achievement of this austere goal there is no royal road.

35.3. Review by: Henry W Syer.
The Mathematics Teacher 55 (7) (1962), 596-599.

First, let it be admitted that this is one of the most beautiful books on mathematics ever produced. The stunning use of colour; the ingenious types of visual presentation of mathematical ideas; the unusual and pertinent mathematical diagrams, maps, and photographs; the paper, type, and binding; all contribute to a splendid book. Unfortunately, it is one of the most confusing attempts ever made to explain the subject to the general public.

The following seven adverse criticisms will be substantiated by definite references to the book:

1 The book shows a lack of understanding of the real spirit of mathematics and of its content and purpose.

2 The sole interpretation of mathematics which is presented is that of the physical world, and the only mathematical concepts which appear to have any meaning are those with immediate, physical uses or analogues.

3 Some explanations contain mathematical errors.

4 The style of writing is confusing and tends to conceal meaning rather than illuminate it.

5 Many explanations do not explain.

6 Symbolism and vocabulary are often original, awkward, and not as suitable as the conventional usage.

7 There are a few examples of poor editing and poor bookmaking.
...
There is real danger that this book will fall into the hands of people who do not know mathematics and will frighten them away from other books which give clear and helpful explanations of the subject. To many it will confirm the view that the subject is hopelessly involved and beyond the reach of the common man, and that it is, therefore, of little purpose to teach it in schools to any except the very top students. If the present book had been more modest in the breadth of coverage of topics, and had tried to use the same fine, high level of pictures to explain simple and basic things well, it might have succeeded. But there would always remain the style of writing - perhaps it is just best to cut out the pictures and throw the text away.

35.4. Review by: R L G.
The Mathematical Gazette 45 (353) (1961), 259-260.

The use of the historical method in the teaching of mathematics takes many forms, from a slavish imitation of the development of the concepts, to a judicious side-glance at the historical setting in which the concept evolved; at one extreme the student is denied the simplification which time brings to the presentation of new ideas and at the other extreme the historical details are merely an additional burden on the memory. Hogben avoids both these dangers and has succeeded in producing an account of the development of elementary mathematics which makes interesting and important contacts at many points with world history. The great feature of the book is the huge collection of magnificent diagrams, visual aids of a quality that has never been surpassed. One can but envy the author the service his artists and Editor have given him. Unhappily the text does not always achieve the same high standard. Aside from technical mistakes, ... there is a marked failure to appreciate the importance of work like Euclid's theory of proportion and his invention of the axiomatic method, and the mathematical significance of such theorems as the impossibility of trisecting an angle by ruler and compass constructions, a failure that is a product of the author's preoccupation with the social significance of mathematics.

35.5. Review by: A Rupert Hall.
Scientific American 205 (6) (1961), 186-187.

With Mathematics for the Million Hogben broke new ground in the popularisation of the subject. There had, of course, been other good simplifications long before his time. In the 18th century, for example, the great Leonhard Euler broke open the mysteries of algebra in his Letters to a German Princess; in the 19th century Adolphe Quetelet wrote charmingly (for a duke) about the meaning of statistics, and Augustus De M organ published several first-rate mathematical primers; in this century Silvanus P Thompson's celebrated little Calculus Made Easy and Alfred North Whitehead's Introduction to Mathematics were among the books which helped the student and general reader to grasp mathematical concepts and to taste the intellectual excitement of the foremost science. Hogben, however, made his own distinctive contribution, not only in the range of topics with which he dealt, the detailed treatment and the skilful use of illustrations, but also in style and interpretation. In Hogben's view mathematics is and always has been a tool, an instrument, a means of communication. While he is not indifferent to its elegance and beauty, nor insensitive to mathematics as a form of art, his primary concern is with its service to man in achieving understanding of and control over the physical world. Man made mathematics to help him as an accountant, surveyor, architect, explorer, carpenter, merchant, stargazer, bridge builder, physicist, biologist, gambler, underwriter, soldier, clockmaker, economist - and as a student of human affairs and human behaviour. This view of the subject strongly flavoured Mathematics for the Million and continues to flavour, though perhaps somewhat less strongly, the present volume. What is now offered is a "humanistic" account of the growth of mathematics, an attempt to describe by selected major achievements "a facet of the history of the technique of human communications." In a text strongly supported by a variety of visual aids - ingenious diagrams, photographs, facsimiles, coloured illustrations - Hogben spans the development of mathematical ideas from the beginnings of counting and measurement to the sophistications of Gödel's proof. This is not always an easy book for the beginner or even the beginner-over-again. It compels concentration and presses the reader to work through the methods and examples. It is also opinionated and designed to affront orthodox opinion; he says, for example, that Aristotle was pre-eminent in stifling human inventiveness, and that if he and Plato were truly representative of the intellectual achievements of Greek civilisation, "we might reasonably write off the Greek contribution as a prolonged setback." But Hogben naughty is still Hogben, which is to say an able scientist and a lucid populariser, with a gift for illuminating mathematical ideas, tracing their origins and exhibiting astonishing relationships between apparently unrelated concepts . For teenagers and adults.

36.1. Review by: J Knowelden.
The British Medical Journal 1 (5238) (1961), 1517-1518.

A problem common in medical research is that records, kept primarily as an aid to treatment of the individual patient, have subsequently to be subjected to statistical analysis. Whereas highly mechanised processes are available for such analysis their use is possible only when the original manuscript data have been transcribed into suitable numerical codes, and it is in this transcription stage that time and effort are easily wasted and errors most commonly arise. The authors have provided an introduction to such coding procedures, and from a discussion of the principles lead on to the design of record forms, which reduces effort and minimises the risk of ambiguity and error. By the use of properly designed records the clinician is aided in his task of providing complete and accurate data, while the transcription and analysis can be entrusted to clerical.

The principal method of analysis considered is by punched cards and electrically operated sorting and tabulating machines. Nevertheless, the authors have valuable advice to give in the situations where hand sorting is appropriate. Examples of documents and codes designed by the department of medical statistics for the Birmingham Teaching Hospitals occupy over half the book. One disadvantage of this is that for beginners these are both too detailed and too confined to a specific application of the techniques. No mention is made of electronic computers requiring tape feed, or of the use of codes to the base 2, instead of to base 10 as in punched cards, yet these are being increasingly used in medical research.

37.1. From Chapter 1.

In the mid seventeenth century the British Royal Society and French Academy each followed the lead of Italy's Lincei by adopting the national vernacular for learned communication. The Latin lingua franca was lost. In 1664 the Royal Society commissioned an inaugural member, Bishop Wilkins, to seek a remedy. Leibniz devoted his leisure in later years to this end. Their published efforts were harder to learn than Latin and less flexible to later development. Linnaeus, Lavoisier and scientists generally for 200 years produced only piecemeal moves toward a world language of science. The vast growth of mails and movements in the 19th century increased the need for a global code. Leibniz proposed comparative language study as a useful next step. Several schemes emerged. Pirro devised Universal-Sprache before German Catholic priest Schleier produced Volapük that was actually spoken and promoted by scientists and societies. Zamenhof's 1887 Esperanto soon eclipsed it, and several schools taught it briefly after World War I. More than 300 alternative schemes have been published since but none with such broad and persistent following as Esperanto. All are put forward as a second, bridging, helping/ auxiliary, not a dominant or sole language or replacement for mother tongues. Only after World War I did the US emerge as predominant in science and technology developments. Proposed auxiliaries then took words from predominant technical speech communities, mostly Romance and Teutonic. They discarded irregularities and grammatical quirks (as e.g. English, alone among Indo-European and Semitic languages, has discarded grammatical gender).

38.1. Review by: Michael Scriven.
Philosophy of Science 31 (2) (1964), 184-186.

Lancelot Hogben is an important totem figure for the Bicultural tribe. Totem objects associated with him are to be found on the bookshelves of all young men and elders of the tribe, and rituals in his honour are frequently performed in the review section of the tribal publications. Let the ceremony begin again, for Hogben is indeed a worthy father of the tribe, and it may be we shall not again be able to honour him.

The present volume is a collection of addresses and papers of his recent retirement years, whose topics do not readily group, (our ancestor has great virtue, for he is Versatile) and hence are listed in full: The Race Concept; the Origins of Species; Whewell's Dilemma (an essay on taxonomy); The Nature-Nurture Issue in a Contemporary Curriculum of Medical Studies; The Assessment of Remedies; The Present Crisis in Statistical Theory; Science and Its Social Functions; Astraglossa or First Steps in Celestial Syntax; The New Authoritarianism. Our ancestor has again performed mighty feats of valour, attacking many live dragons, unlike the false gods who achieve much fame with lesser tribes, who choose only dead ones.

Hogben is notable for redoubtable scholarship and his passionate concern with the human aspects and applications of science; (the book is redolent with references to the social history of science) and his powerful blend of the two. His best known works obviously illustrate this: Mathematics for the Millions, Science for the Citizen, The Loom of Language, Essential World English. Even in the weightier Statistical Theory and in Mathematical Genetics, he is clearly a humanist and not just a formalist. An absolute necessity for success in these terms is clarity of expression. Unfortunately, the present volume contains a great deal of virtually incomprehensible prose. While it is addressed more to the academic's leisure hours than the proletariat's, the obscurity is needless and unfortunate.

Hogben raises interesting and central questions about the grave defects in Darwin's theory of evolution which have only partially been patched up while the flood of uncritical enthusiasm has kept the great craft spinning along.

39.1. Review by: D M Jones.
The Classical Review 17 (3) (1967), 393-394.

The purpose of this book is to show how the task of learning certain foreign languages can be simplified for speakers of Anglo-American (i.e. English) by utilising the diverse linguistic material available in their native tongue as aids to memory and understanding. The diligent reader who does not neglect the quizzes (i.e. exercises) will have a number of rewards for his trouble - an introduction to some aspects of comparative and historical linguistics, an acquaintance with some of the basic vocabulary and grammar of Germanic and Romance languages, and an elementary knowledge of Old and Middle English. There are a number of errors, which it would be pointless to correct in a journal unlikely to be seen by many of those for whom the book appears to be intended.

40.1. Note.

This is a 97 page novel whose most surprising quality is that it is written entirely in words of one syllable.

41.1. Review by: E A Maxwell.
The Mathematical Gazette 52 (380) (1968), 201-202.

This edition of a very well-known work comes "extensively revised with additional material and completely re-illustrated". One feels that if ever a book lived up to its title, this must be such. The subject matter remains classical: one searches the index in vain for sets (except square), mappings (except terrestrial and celestial), Venn and company. But here, in compensation, are Agricola, mining technology; American revolution; Calculus of Founding Fathers; Algebra of the Chessboard; Gas integral; Money-lending; Vanishing triangles - and proper names innumerable. And the passing of 24 years, with 23 editions, preceding this revision serves to emphasise what most people know, that the exposition is that of a master.

42.1. Review by: T A A Broadbent.
The Mathematical Gazette 53 (385) (1969), 332.

This is an excellent item for the school library or for a middle-school prize. The pictures are numerous, pleasing and almost always relevant. The text is concerned mainly with beginnings: counting and measurement in Egypt, India, Mesopotamia, the Greek revolution which insisted on logical proof, the needs of travel, mapping, commerce. There is a little about the 17th century, and a little about the demands of modern technology. Professor Hogben writes in good simple English, with, as usual, force and clarity. To cover a wide field in a slim volume, brevity is essential and sometimes statements need qualification; to say that "the Greeks had studied only the curves one can draw using compass and ruler" could be misleading. The transfer of terms in an equation is illustrated on p. 74 by three positions of a balance, but is wrecked by a misprint. A volume so well organised and produced can hardly fail to stimulate the young reader.

43.1. Review by: Ernest Rubin.
Monthly Labor Review 91 (12) (1968), 66.

This book appeared in 1957 and has been reissued without any changes. Much has been written about statistical theory since the original publication date. It is regrettable that the present volume did not incorporate some of the pertinent discussions of the ensuing decade or take into account some of the reasoned criticisms voiced by the professional reviewers of 1957-58. That a commercial publisher would reissue this book, which at most received rather reserved praise from the profession when it first appeared, comes as a surprise. Further, it would appear that the demand for this volume is quite modest.

Dr Hogben's tome is primarily concerned with the divergent views statisticians hold regarding statistical inference and with the possible misapplication of statistical methodology in the social and biological sciences. This book sketches statistical theory, beginning with «the historical roots of probability arising from gambling problems, and carries the discussion through to the developments of R A Fisher, J Neymann, and E S Pearson. Unlike the author's popular Mathematics for the Millions, the style here is difficult to follow and Dr Hogben's unique terminology is generally not recognisable by most statisticians. Because it is concerned with substantive issues this book may be of some value, despite its scepticism and pessimism of statistical theory, to professional statisticians and to teachers of the subject.

44.1. Note.

The first of Lancelot Hogben's "Beginnings of Science".

44.2. From the Publisher.

Explains what archaeology has revealed about each step of man's progression from a nomadic search for survival to the earliest beginnings of civilisation.

44.3. From the Introduction.

This book is primarily for children in the 11-plus group; but some of them may wish to discuss its contents with their parents or teachers.

44.4. Review by: Anon.
Bulletin of the Center for Children's Books 25 (1) (1971), 8.

A good survey of the development of early civilisation from the first tool-making activities of prehistoric man. The first of four volumes on science, history, and understanding, this is written in straightforward, quite staid, style but is well-organised in a sequential and comprehensive text which unfortunately lacks an index. The author stresses man's ability to communicate, and the living patterns that changed as tools improved, animals were domesticated, and diversification led to trade and cultural exchange. The book ends with the building of the first cities.

45.1. Review by: Ffrangcon Roberts.
The British Medical Journal 3 (5716) (1970), 215.

This book is described in the blurb as a "crash course in the nearest thing to a world-wide auxiliary language." It is intended to help biology students "who have little or no Latin and Greek to gain in a few weeks more than a nodding acquaintance with the overwhelming majority of Latin and Greek words which occur as components of internationally current technical terms."

Like Gaul this book is divided into three parts. Part One describes in full detail the whole history of scientific language from the pre-Christian era to the present time, taking us from the East through the Moslem empire and the different countries of Western Europe - truly a philological tour de force - all in 57 pages.

Part Two consists of a long list of words divided into sections covering all aspects of human life from the four elements to parts of buildings. The English words are on the left; it is not clear why the reader who knows little or no Latin and Greek should want to know the classical equivalent, nor why for instance the biology student should want to know the foreign word for barn. Part Three continues this process to words of medicine and biological terms. Here Greek and Latin words are in separate lists with curious results. Thus we read the Latin vulpus (fox), but the Greek alopex which is of greater importance is omitted. An epilogue returns to the philological quest in even greater detail than in Part One, for there are now included Spanish and Welsh words. An appendix consists of Latin and Greek vocabularies. Latin nouns are given in the ablative singular. It is difficult to imagine what a student with "little or no Greek" will make of the Greek vocabulary.

In spite of or perhaps because of its profound erudition this book completely lacks the human touch. It entirely ignores the romance of words; the fact, for instance, that many words are immortal though the ideas they originally connoted are long-since dead. The word artery means air carrier and perpetuates the Greek idea of the function of the arteries. Trachea is an adjective meaning rough. It followed artery in arteria trachea, rough artery. Melancholia means black bile.

A defect is that it is not easy to find one's way about. The teeming cross-references are difficult to find. Greater variety in type would have helped. Though its aim is to provide a "crash course" this book seems a singularly roundabout way to initiate a student in a few weeks to "more than a nodding acquaintance" with his verbal heritage.

45.2. Review by: Philip Morrison.
Scientific American 224 (1) (1971), 120.

As combative, lively and blunt as ever, Professor Hogben here seeks to bring the classics to the tens of thousands, that is, to give the student of natural science a minimum reasonable knowledge of those Latin and Greek forms that make up the international language of the scientist, particularly, of course, in medicine and biology. The late-Renaissance decline of Latin as the lingua franca of Europe was followed by an explosion in the need for new terms. The acronyms of our day - a target of Hogben's scorn - are neither reasonable nor in any degree international; such contrivances were not used in those times. The speech of the period felt the long legacy of Latin, and there was already a clear pattern in English and French, and evidently in Italian as well, for adding newcomers of Latin origin. Lavoisier invented a scheme for the chemist's logical use of the words and affixes of Latin, and men who spoke English used a language that still shows the hybrid vigour brought in by the Normans. Thus English and French led the way as vernacular making full use of the classical sources. Indeed, scholars such as Carl Friedrich Gauss still wrote in Latin at a time when Latin papers from Thomas Young or Faraday or Ampere would have been astonishing. The entry of Greek roots was easy because the old Latin tongue already knew them. It was Linnaeus, anxious for a rich source of new words for his thousands of new classifications, who explicitly set out rules for the assimilation of Greek roots in the botanical volume of his Systema Naturae, published in 1737.

The latter two-thirds of Hogben's book, after a few "hints" about the grammar of the old tongues, offers an interesting glossary of Latin and Greek words and roots, classified by subject matter and then indexed alphabetically. There are about 2,400 terms listed, roughly half of them Greek and half Latin. Strobeo means "I spin" in Greek. "Belomancy" must mean divination by the use of missiles; it is a word not much encountered (possibly because it usually occurs in classified documents?). The lists are not complete; for example, mantis, the Greek for seer or prophet (invoked in belomancy ) does not occur. The book is nonetheless good reading and a reference tool of utility and pleasure, although it is auxiliary to a good dictionary.

46.1. Review by: Anon.
The Junior Bookshelf 36 (1972), 402.

The second of the author's "Beginnings of Science" roughly covers the period from 3500B.C. to the death of Eudoxus and Aristotle in the 4th century B.C. Although it is printed in large clear print it is not suitable for the average primary school child being closely reasoned and demanding some familiarity with mathematics and astronomy for a full understanding. Its unstuffy approach would also be better appreciated by an older reader.

47.1. Note.

The third of Lancelot Hogben's "Beginnings of Science". This book highlights the history of science from 300 B.C. to Columbus' voyages. Hogben assures his readers that there was no science whatever during the Middle Ages and that scholasticism is nonsense.

47.2. Review by: Anon.
Appraisal (1974), 22.

The third volume in the author's Beginnings of Science series covers the period 350-500 B.C. to 1500 A.D. with emphasis on the achievements of the Alexandrian school. The scope is limited largely to astronomy and mathematics, with attention given also to physics, mechanics, and geography. The Alexandrian scientists are dealt with at length, and the author then jumps into the time of Prince Henry the Navigator and the great age of exploration, holding that Christianity and the doctrines of Plato and Aristotle were inimical to science and that the first 1400 years of the Christian era were truly the Dark Ages, when no scientific advances were made.

48.1. Note.

The fourth volume in the author's Beginnings of Science series.

48.2. Review by: Anon.
The Junior Bookshelf 39 (1975), 197.

The author of Science and the Citizen continues to write with lucidity and total grasp of his subject matter which made that and its companion bumper books a nine years' wonder, although his talents are now being revealed in the type of limited area treatise that makes for less cumbersome reference sources and spread cost. The Columbus of the title signifies the advances in navigation which arose out of and partly made possible voyages round substantial arcs of a world proved to be round; the Cannon Ball is the basis of a link with the laws of motion; and the Common Pump embraces the human heart as well as the technicalities of introducing a vacuum (to put it briefly if not precisely).

49.1. From the Publisher.

Hogben escaped from a background of religious bigotry by the academic ladder and gained a major scholarship at Cambridge and graduated in 1916. During a noteworthy academic career, he found time to be active in the Fabian Society and in the London Labour Party. He also founded the Journal of Experimental Biology along with Julian Huxley and J.B.S. Haldane. He is most widely known for Mathematics for the Million and Science for the Citizen, and he played a big part in creating The Loom of Language.

49.2. Review by: John Edwards.
Journal of Medical Genetics 35 (11) (1998), 966-968.

Unauthorised autobiographies are rare, but the title is arresting rather than accurate. After Hogben's death Professor G P Wells, who wrote an extensive obituary in the Biological Memoirs of the Royal Society, attempted to get a mass of papers, which was clearly an unfinished autobiography, published. Ten years ago I met Hogben's elder son, Adrian, who had retired to near Bar Harbor, and made an equally unsuccessful attempt to interest Oxford University Press. This unfinished and extensively annotated manuscript had limitations as a profitable venture unless extensively edited, when I feared it would lose more than could be gained. However, it has been edited without losing the forceful elegance of his prose and the various repetitive sections have been welded into a seamless narrative. Additions include many photographs taken by Adrian, although only a small representation of his extensive collection after, when a child, he had been given a camera by Frank Bodmer, coauthor of The Loom of Language. It also includes an essential, but all too brief, appendix of the cast.
...
Readers of reviews need to know if the book is worth reading, buying, or advising a librarian to buy. The answer must be yes, yes, and sometimes. It is essential for libraries of Departments of English, Modern History, and the History of Science. It is a fine work of English prose, and a fine document to the political, social, and academic environment of the period. But it has limited claims on a library of a Department of Genetics or a hospital. The publishers are to be congratulated on both their standard of production and their price. It should create a need for a second edition with more photographs, a more extended appendix, maps of the "grand tour" from Oslo to Aberdeen, some facsimile pages of the original, and more details of the several centres of excellence he visited in the USA en route from Aberdeen to Birmingham.

49.3. Review by: Milo Keynes.
Notes and Records of the Royal Society of London 53 (3) (1999), 361-369.

On his death in 1975, Lancelot Hogben left behind two unedited versions of an autobiography that have now been combined and published by his son, Adrian, Emeritus Professor of Physiology and Biophysics at the University of Iowa. ' Lancelot Hogben, whose first name derived from that of a Methodist missionary prominent at the time of his birth, came from a non-conformist Kentish family, the son of "poor but intellectually dishonest parents". (Throughout this paper all the quotations taken from Hogben's autobiography' are placed between double quotation marks.) His strong and unrelieved Methodist upbringing influenced him all his life, but he escaped early from the doctrine that the fate of the unsaved is in everlasting hellfire. On the way to losing his religious faith and becoming an evangelical atheist-later he liked to say "I'm an atheist, thank God"-he joined the Society of Friends, renouncing any intention of becoming the Methodist missionary that his parents wanted him to be.

At sea in a storm in a small boat, he and a research student, the future scientific journalist, Maurice Richardson, "joined in prayers to Darwin, Marx and Bernard Shaw", with invocations that apparently succeeded. However, he soon turned against Marx and "found Marxist dogma dished out as dialectical materialism deeply distasteful and wholly incompatible with my own criteria for intellectual integrity. Having off-loaded one brand of religious fanaticism, I had no inclination to submit to another."

49.4. Review by: Timothy M Boon.
Social History of Medicine 13 (3) (2000), 575-576.

At a time when deterministic genetic explanations of human social characteristics - of a type repudiated by Lancelot Hogben - are so very fashionable, we could all do well to consider the first and only Professor of Social Biology at the LSE. His on and daughter-in-law have therefore done a great service by editing together here, from archive sources, his autobiography, Look Back with Laughter and his Professional Reminiscences. Hence the good joke about it being an "unauthorised autobiography".