Gerald James Whitrow's books

One of the interesting features of examining reviews of G J Whitrow's books is that they are equally of interest to philosophers, mathematicians, astronomers physicists, and historians of science. This means that reviews appear in publications with rather different readerships and the reviews obviously reflect this. Another consequence of this wide interest is, of course, that there are many reviews of these books. One problems in listing these books is trying to decide whether a new edition is actually sufficiently different to be listed as a separate work. We make no claim to have a satisfactory solution to this, so the books may not appear in quite the order the reader expects. For each review we give an extract, sufficiently long we hope, to give flavour of the reviewer's thoughts.

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The Structure of the Universe (1949)

The Structure and Evolution of the Universe. Revised edition (1959)

Atoms and the Universe (1956) with G O Jones and J Rotblat

Atoms and the Universe (Second Edition) (1962) with G O Jones and J Rotblat

The Structure and Evolution of the Universe - An Introduction to Cosmology (1959)

The Natural Philosophy of Time (1961)

The Natural Philosophy of Time (Second Edition) (1980)

The Nature of Time (1973)

Time in History: The Evolution of Our General Awareness of Time and Temporal Perspective (1988)

1. The Structure of the Universe (1949), by G J Whitrow.
1.1. Review by: Edmund Whittaker.
Philosophy 25 (95) (1950), 374-375.

This is a lucid and trustworthy account of researches which are highly significant to philosophy. So much new knowledge has accumulated in the last few years that the standard works, such as those of the late Sir James Jeans, can no longer be said to represent the present state of the subject; and a fresh presentation was clearly desirable. Our earth is a dependent of the sun, which is one of the hundred thousand million or so of stars constituting the galaxy: and the galaxy is a member of the vast system of nebulae. Is this in its turn a member of some still larger system? It now seems that this question can be answered in the negative: the world of nebulae is the ultimate background of the physical universe, and occupies the whole of space. Moreover, we are centrally situated in it - that is, the distribution of the nebulae is effectively the same in every direction. This, however, does not imply that we occupy a privileged position: paradoxical though it may sound, every other point in space is also centrally situated with respect to the nebulae. The paradox can be explained by supposing that when very great distances are concerned, the geometry of space is not the geometry we learnt at school, and in fact is such that the total volume of space is finite.
The author gives an instructive history of the dispute between the advocates of the "long" estimate of the age of the universe (over a million million years) and the "short" estimate (two to five thousand million): this has ended in a victory for the latter.

There is, however, much uncertainty regarding some of the most fundamental questions of structure in the universe. For instance, a large proportion of the nebulae have a spiral form. This may mean that the stars composing a nebula are actually arranged in spirals, and many theories of cosmogony have been based on this obvious interpretation. In recent years, however, a considerable amount of evidence has indicated that the spiral structure is shown only by very luminous types of stars, and that the whole space occupied by the nebula is filled more or less uniformly with stars of lesser brightness, so that the appearance of spirality is a luminosity effect rather than the indication of the actual distribution of matter.

The last chapter gives a thoughtful philosophical discussion of the principles :underlying the a priori world-models of Eddington and Milne.

Altogether an excellent book.

1.2. Review by: William Hunter McCrea.
The Mathematical Gazette 34 (308) (1950), 148-150.

This book is the second to be published in the section of Hutchinson's University Library dealing with Mathematical and Physical Sciences. The publishers in their notice of the "Library" state: "The general aim of the whole series is to provide popular yet scholarly introductions for the benefit of the general reader, but more especially for the unprofessional student who wishes to pursue his chosen subject systematically up to something like a University standard. The books are written to be intelligible to those who have made no previous study of the respective subject; .... The books should be of special value to members of Adult Education Classes of all kinds, but it is believed that they will also be serviceable for undergraduates." It is obvious that to achieve this aim in the case of the subject dealt with by the present book is an extraordinarily formidable task. However, no one better qualified than Dr Whitrow could have been found to make a success of it. Dr Whitrow is intimately acquainted with the observational background of the subject. He is a recognised authority on its historical and philosophical aspects, and he has himself also made important contributions to the theories which he describes. In addition he is gifted with a very happy style of exposition for such a work; without appearing to be didactic or unduly terse he contrives to convey an immense amount of information in as few words as possible, and does so in a way which maintains a freshness of interest throughout the whole book. Only those having some acquaintance with the literature of the subject can appreciate what a wealth of scholarship often lies behind a single sentence in Dr Whitrow's presentation. The book is enriched by exceedingly apt quotations from a great array of other authors, including Pascal, Kant, Newton, Bishop Barnes, Edwin Hubble, Eddington and Milne, to mention only a few.

The first two chapters give a comprehensive historical account of the exploration of the universe with the telescope and spectroscope. They present a thoroughly up-to-date account of the observational facts concerning its structure. The next chapter is an historical account of the concepts of space and time, preparing the way for the following chapter on relativity. The latter gives a concise account of Einstein's special and general theories, their physical interpretations and observational tests.

The next two chapters are on "World-Models". The first of them describes those resulting from general relativity, together with results of their comparison with observations. The second of them gives in the first place an account of Eddington's work, culminating in his posthumous work, Fundamental Theory. In a few pages the author conveys a clear impression of the spirit of Eddington's work and its attempt to relate the properties of the universe in the large to those of atomic systems. In the second place it summarises Milne's application of his kinematical relativity to produce a world-model, giving a lucid description of the ideas behind Milne's approach, and finishing with an explanation of Milne's introduction of two scales for measuring time.

The discussion of world-models naturally raises the question of the observational evidence regarding the age of the universe, since this evidence is expected to be an important factor in discriminating between claims of the various proposed models. Dr Whitrow's next chapter gives a summary of the evidence provided by the interpretation of a great many types of astronomical observation. It gives a very clear statement of the existing situation in regard to these interpretations. The "structure of the Nebulae" (meaning by nebulae, the galaxies) is then dealt with. This chapter is an admirable description of the observational results on the distribution of the galaxies, and their dimensions, masses and structure, together with the theories of their dynamics due to Lindblad, Oort and Milne.

The final chapter is entitled "Cosmology and the A Priori", and deals principally with the problems of natural philosophy raised by the approaches to cosmology followed by Eddington and Milne. The author provides a useful bibliography, with brief comments on the items listed. The treatment throughout, except for the quotation of a few simple formulae, is entirely non-mathematical. Many of the ideas have never before been expounded apart from their mathematical developments, and Dr Whitrow has taken the reader very much further than one would have thought possible under this limitation.
Altogether, the book can be recommended unreservedly to all the classes of reader for whom the publishers have designed the series. One can go a good deal further and say that many people who regard themselves as professionals in some parts of the subject will be exceedingly indebted to Dr Whitrow for having produced such an accessible summing-up of the existing observational material and theoretical treatments.

1.3. Review by: William Hunter McCrea.
The British Journal for the Philosophy of Science 1 (1) (1950), 75-76.

Historians and philosophers of science may perhaps look to Dr Whitrow's book to provide an account of the present state of the purely scientific side of his subject, rather than to contribute to their own special fields. It may be said at once that he has given a brilliant description of the astronomical evidence concerning the structure, behaviour and ages of the galaxies and concerning the structure of the whole system of galaxies that constitutes the observable universe. He has given also an extraordinarily able (non-mathematical) description of current general cosmological theory, with special prominence for the ideas of Eddington and Milne, together with some account of more detailed matters such as galactic kinematics and dynamics.

Dr Whitrow is, however, particularly well qualified to write also upon both the historical and philosophical aspects of his subject: readers specially interested in these aspects will be glad to find that his presentation keeps them so well in view. In fact, even the professional historian of science will get a fresh perspective in his own domain from the material brought together by the author in his first three chapters, which give a historical account of the exploration of the universe and of ideas of space and time.
Classical physics was formulated with no explicit mention of the observer. Relativity theory was the first expressly to involve the observer but to no greater extent than that any physical property is regarded as describable only by reference to a specified observer; the property is regarded as uninfluenced by the act of observation. Quantum theory involves the observer much more intimately: its formulation necessitates that the act of observation should have an unavoidable effect upon the system observed. A physical phenomenon becomes a property neither alone of the system observed nor alone of the observer, but of the two taken together. Eddington's theory may be viewed as an attempt to take what appears to be the natural next step and to regard physical phenomena as almost entirely properties of the observer and to credit the system observed with little more than existence. There are admittedly great differences of opinion regarding Eddington's success, but the evolution of ideas, traced so extensively in Dr Whitrow's book, seem to lead almost inevitably to the attempt being made.

Generally speaking, Milne's work may be regarded as another such attempt. Dr Whitrow gives an illuminating analysis of its difference from Eddington's and tentatively suggests that the two 'may provide complementary perspectives of the physical universe', and ascribes this, even more tentatively, to the fact that 'Eddington's concept of physical measurement is associated with the idea of the ruler, Milne's with the idea of the clock'. This apparently simple comment seems to the reviewer to penetrate very deep; for the concepts of measurement associated with the two ideas are fundamentally different and a satisfactory physical theory must depend upon adequate analyses of both concepts. Such analyses may well prove to be much like those formulated by Eddington and Milne. But it also seems to the reviewer that the two ideas may not correspond, as Whitrow suggests, to the spatial and to the temporal aspects of the universe but rather to the material and to the spatio-temporal aspects, respectively. This view is somewhat borne out by the fact that Eddington's analysis led him to discuss the fundamental properties of matter, whereas Milne's led in the first place to a discussion of the universe in the large. The view does not depend, however, upon the correctness or otherwise of these discussions.

Whatever the possibilities of what Whitrow classes as a priori theories, their present limitations are emphasised by an hypothesis advanced (in definite form and in accessible accounts) only after his book was written. It is that of the continuing creation of matter as formulated by Jordan, Bondi and Gold, and Hoyle. The hypothesis may not be 'true', but it represents a conceptual possibility about which it is exceedingly difficult to see how these theories can make any pronouncement. This is not to criticise Whitrow's analysis: indeed it seems merely to underline many of his arguments.

Sufficient has perhaps been written to show that Dr Whitrow's book, modest though it be in appearance, is a quite exceptional piece of work.

1.4. Review by: M W O.
Science Progress (1933-) 38 (150) (1950), 358-359.

The aim of the series is to provide "popular yet scholarly introductions for the benefit of the general reader, but more especially for the unprofessional student who wishes to pursue his chosen subject systematically up to some- thing like a University standard." While a university standard of cosmology may be an ill-defined concept, it is difficult to believe that a text which contains less than a score of equations could fulfil this aim. But in attempting the impossible it is not surprising that the author falls short of the ideal - in fact, it is surprising that he has succeeded in conveying so much difficult matter in a lucid manner.

The treatment develops three interdependent themes. Modern observation of the extragalactic nebulae is approached by an historical survey, where the difficulty of interpreting "crude" observational data is emphasised. General relativity and its associated cosmologies lead to the second theme, the theoretical foundations of science. In the conflict between the Baconian and Kantian approaches to natural philosophy, the reader is not long left in doubt as to the opinions of the author as a member of the Oxford school of Kinematic Relativists. This philosophical discussion is a necessary prelude to the third topic, the Eddington and Milne theories of the constants of nature. The treatment of these a priori epistemological approaches to cosmology is the most important, if the most exacting, task of the author, and it is a pity that an impartial critical faculty so evident throughout most of the text should at this point be partially eclipsed by personal enthusiasm.

A gallant attempt has been made to satisfy both the layman and the serious student. If the former finds much that is incomprehensible, and the latter only enough to whet his appetite, this is due to the inherent difficulties of the subject, and not to any shortcomings of authorship. Broad in outlook, and up-to-date in technical content, it can be recommended as a useful elementary introduction to one of the most fascinating realms of scientific speculation.

1.5. Review by: Fred Hoyle.
Nature 166 (1950), 574.

Dr Whitrow is to be congratulated on this survey of the cosmologies of essentially the pre-1939 period. The remarkable achievements of Hubble and his colleagues are described in detail - distance measurements, the velocity-distance law, and the large-scale uniformity of the distribution of matter in space being fully and adequately treated. Then follow two chapters that deal with space-time and the theory of relativity. These are written in a fluent, expert style and should prove of great value to the lay reader. They provide an excellent introduction to the difficult problems of cosmology that are treated in the last part of the book.

In cosmology more significance is attached to a few observational results than in any other branch of science. At first the uniformity of space and the red-shifts of the spectra of the extra-galactic nebulae formed almost the only evidence available to cosmologists, and it was perhaps natural that some men of science should have come to regard this as a somewhat flimsy basis for the support of such weighty matters. But, as Einstein himself has pointed out, it is difficult to gainsay the orthodox interpretation of the red-shifts without undermining the whole structure of physical science. Nevertheless, it is of the first importance that our store of observational knowledge on this subject should be extended to the maximum degree, and it is for this reason that such great efforts have ben made by Hubble to obtain crucial information from nebular counts. ...

Dr Whitrow discusses the age of our galaxy at length, and directs attention to the discrepancy between the four thousand million years given by astrophysics and the very short age of the universe - no more than two thousand million years - demanded by many systems of cosmology. Perhaps even greater weight might have been attached to this discrepancy, especially in the case of Milne's kinematical theory. Milne was able to avoid many of the difficulties of other cosmologies by means of his dual time-scale. But this no longer suffices to explain away the ages of the stars, which are now determined by a method that uses the physical time-scale. ...

... the book is eminently readable and is packed with a fund of interesting historical details. It cannot fail to be a great success with all those who are interested in the fascinating problems of cosmology.
2. The Structure and Evolution of the Universe. Revised edition (1959), by G J Whitrow.
2.1. Review by Dennis Willam Sciama.
Mathematical Reviews MR0122530 (22 #13254).

This book is a revised version of The structure of the universe [Hutchinson, London] which was published in 1949. It takes account of two major advances in cosmology, one observational and one theoretical. The observational advance is the coming into operation of the 200-inch telescope. The theoretical advance is the realisation by Bondi, Gold and Hoyle that the universe may be in a steady state.

The present text gives a good non-technical account of cosmology up to the end of 1958, although some of the statements about the steady-state theory are incorrect.

2.2. Review by: W B B.
Science Progress (1933-) 48 (190) (1960), 358-359.

In the last forty years cosmology has ceased to be a part of speculative philosophy and has become a branch of science. This has happened partly through the appearance of a theoretical framework capable of dealing with the motion and evolution of the universe as a whole, and partly because of the construction of telescopes powerful enough to survey the universe to depths previously thought quite inaccessible.

The development of both these sides of cosmology is admirably described by Dr Whitrow in The Structure and Evolution of the Universe. Although the book is largely non-mathematical, the ideas and predictions of the theories are described with great clarity, and, as cosmologists would wish, special emphasis is placed on those features which can be checked by observation. The nature and results of the observations themselves are presented in a detailed, yet interesting, manner, and the material throughout is absolutely up to date.

It is almost certain that during the next few years new observations, especially from radio telescopes, will decide between rival cosmological models, notably those based on general relativity, and that of the steady-state theory. Whichever way the decision goes, an exciting new phase in cosmology will open. Dr Whitrow's book provides a first-rate basis of knowledge for those, whether professionals or non-specialists, who will wish to understand these future developments.
3. Atoms and the Universe (1956), by G O Jones, J Rotblat and G J Whitrow.
3.1. Review by: C A Haywood.
The Mathematical Gazette 41 (338) (1957), 304-305.

The rapid advance of modern science in recent years has made it increasingly difficult for the layman to have even a sketchy understanding of the subject. This is particularly true of Nuclear and Relativistic Physics, where the fundamental concepts are so difficult. Many popular expositions are doomed to failure because emphasis is laid on parts of the subject which permit of a spectacular result, regardless of whether it could possibly be understood. The layman today does not want to be amazed; he wants to be reassured that science is at least rational, even though it is becoming more and more complicated.

The authors of Atoms and the Universe give the general reader this reassurance in a highly commendable way. Typical of their concern for the reader's difficulties, is that they point out that a distant nebula, the size of our own galaxy, receding at the "fantastic" speed of 40,000 miles per second nevertheless takes about half a million years to pass through a distance equal to its own diameter. The reader is never expected to accept a result without a reasonable indication of the justification for it and at no time does the eminence of the authors obtrude into the text. The concepts of "light horizon" and "curvature of space" are hardly mentioned, without detracting much from the cosmological arguments except that the distinction between the Milne and Eddington interpretations of the expansion of the universe are then not really apparent. The general reader is however, less likely to be troubled by this than by the concepts themselves.

The book is divisible into two sections: Nuclear Physics and Stellar structure and Cosmology. There is a connecting chapter concerning extranuclear structure and the solid state. The brevity of this chapter, compressing as it does, everything between nuclei and stars into about ten pages, may seem a little out of balance unless the title of the book be taken literally.

3.2. Review by: Uli W Steinlin.
Publications of the Astronomical Society of the Pacific 69 (409) (1957), 370.

This book gives a coherent and understandable account of modern physics and astronomy. It begins with the physics of the atom (5 chapters) and of solids and liquids (1 chapter), then considers briefly the theory of relativity and the quantum theory (1 chapter), continues with a description of the solar system and the Galaxy (2 chapters), and closes with a discussion of the problems of cosmology (2 chapters). The unity of all of the relevant sciences and the universal validity of the laws of nature are stressed.

The book also attempts a brief examination of the philosophical implications of the modern developments of physics. This, however, seems to be too delicate and weighty a subject to be considered within the framework of such a volume, or in such short fashion.

Clear diagrams, good photographs (many of them from the Mount Wilson and Palomar Observatories), an index, and a well-chosen list of books for further reference complete this attractive volume, which can be highly recommended.

3.3. Review by: H Spencer Jones.
Science Progress (1933-) 45 (177) (1957), 138-139.

To provide a survey of modern physics, from the smallest known objects to the largest, within the compass of a moderate -sized book might appear to be an impossible task. But that is the task attempted by the three authors who have collaborated in the writing of this book and a task which, it must be admitted, they have succeeded in accomplishing with marked success. They are, of course, authorities in their respective fields ; they write with authority but also in clear and simple language, suitable for the general reader without any special training in science. At the same time, since so wide a field is covered, there are few scientists who could fail to derive interest and profit from reading this book. The guiding thought throughout is that the methods of science, whether dealing with the smallest particles of matter, or with the world of familiar everyday phenomena, or with the stars and galaxies, possess a uniformity and lead to a continuous body of knowledge.

The first section of the book is concerned with the world of the atom and of the fundamental particles of matter. The phenomena of radioactivity, nuclear disintegration, fission and fusion are dealt with; the practical utilisation of atomic energy and the nuclear reactions in the Sun and stars are then discussed. A chapter is devoted to cosmic rays and to an account of the various speculations about their origin.

The second section deals with the properties of matter in bulk, the gaseous, liquid and solid states, and the properties of ordered matter in the form of crystals. Some account is then given of the transition from classical to modern physics, resulting from the changes in view-point following upon the development of the theory of relativity and the quantum theory.

The third section is devoted to matter on the large scale as studied by the astronomer. The solar system, the Milky Way and other galaxies, the size of the Universe as revealed by modern astronomical observation, its origin, evolution and possible time-scale are considered. It is commented that the Copernican revolution, despite its shattering impact on human thought, was merely a rearrangement of the same pieces on the same chess-board. This seems to me to underrate the significance of the work of Copernicus for, having brought the sphere of the fixed stars to rest, it was no longer necessary to suppose that they were all at the same distance, nor that the stars were fixed, nor that there was a centre to the Universe. Though Copernicus did not commit himself on these matters, they were quickly noted and the possibility that the Universe, instead of being small and compact, might be infinite in its extent was first opened by his doctrine.

3.4. Review by: A W Haslett.
The British Medical Journal 1 (4979) (1956), 1345.

The origin of this book was a series of university extension lectures. Its purpose is to give a general outline of the physical universe, beginning with the fundamental particles of matter, taking in atomic energy by the way, and proceeding via the properties of matter in bulk - those of ordinary, solid materials - to some of the wider problems of astronomy and cosmology. A further object is to illustrate the methods of science, "showing that it is a continuous body of know ledge and not merely a collection of unrelated subjects"; and, for good measure, there is an appendix which deals with what has come to be known as the philosophy of science and the organisation of research. With so ambitious a programme, it is hardly to be supposed that the authors could have been as successful as, apparently, they hoped in catering for "the general reader," who is defined as one without any special training in science. But for the reader who has once done some physics, and retained even a small foundation of knowledge, it should be another matter. The authors write pleasantly and by no means formally. Where necessary, they are prepared to say roundly that something either is not known or must be taken on trust. For anyone who wants to learn, for example, the distinction between fission, fusion, and thermonuclear reactions - about the greater difficulty, in terms of first principles, of the properties of quite ordinary solids - or on what grounds of observation the universe is now thought to be twice as old, or more, than it used to be thought - this book can be warmly commended as entirely genuine in its approach.
4. Atoms and the Universe (Second Edition) (1962), by G O Jones, J Rotblat and G J Whitrow.
4.1. Review by: C J Smith.
Science Progress (1933-) 51 (201) (1963), 126.

The excellence of the first edition of this work has been maintained in the new edition and nothing more can be added to the praises which so many distinguished reviewers have given it. From a purely pedagogic viewpoint, however, I should like the authors to consider the following remarks or suggestions. Since the book is most likely to be read by undergraduates and those already engaged in school teaching, only words and phrases which are strictly correct should be used. Thus, in several places, weight and mass are confused and on p. 17 we find the statement that hydrogen and oxygen atoms can be separated by passing an electric current through water; according to Debye there is complete ionisation of the acid in the water! On p. 29 the statement is made that the mass of the electron is always the same and yet on p. 30 the variation of mass with velocity is mentioned, so that the first statement must refer to rest mass. Again, is it not somewhat archaic to speak of ultraviolet light instead of ultraviolet radiation? Also, do α-particles have a charge which is twice that carried by an electron, and what are electric forces?
5. The Structure and Evolution of the Universe - An Introduction to Cosmology (1959), by G J Whitrow.
5.1. Review by: William Hunter McCrea.
The Mathematical Gazette 44 (350) (1960), 314.

This book is a thoroughly revised and appreciably extended version of Dr Whitrow's Structure of the Universe (1949) reviewed in the Gazette (XXXIV, p. 148). The new edition is called for on the one hand because of the deserved popularity of the first edition and its translations into three other languages, and on the other hand because of the great amount of observational and theoretical work in the field during the past ten years. Dr Whitrow has incorporated into the re-writing of his book a survey of the most significant features of recent work in a remarkably clear and concise fashion. As the modification of the title implies, the extension of the book has mainly to do with the evolution of stars and stellar systems on which only the latest researches have shed any fairly certain light. All the commendation that one felt bound to give to the earlier book can now be transferred to the new one. But the reader must be advised to read the work as a whole, for the book as well as its subject has a structure and the significance of each part can be properly appreciated only with reference to its place in the general development of the whole account.

5.2. Review by: William Persehouse Delisle Wightman.
The Philosophical Quarterly (1950-) 12 (47) (1962), 189-190.

If there is any substance in the view that philosophy consists only of the study of those parts of experience which science has so far been unable to explain, cosmology is likely to be one of the last "sciences" to free itself from "philosophy"; for its basic concepts "beginning", "end", "time", "space", "infinite", "continuous", and the like are unlikely ever to become "empirical", even to the extent that "atom" and "electron" are "empirical". It is highly desirable, therefore, that philosophers should keep a watchful eye on such epistemological puzzles as "expanding universe" and "continuous creation". But it will be to no purpose unless they are prepared to make themselves thoroughly familiar with the context in which such expressions occur. It is as a guide to this highly complex and rapidly changing context of data referred to a source outside the solar system that notice of this book may suitably find a place in the Quarterly.

That Dr Whitrow is likely to be a reliable guide may be reasonably inferred from the fact that the present work is a thoroughly revised and enlarged version of his book, The Structure of the Universe, which, published in 1949, rapidly achieved translation into several other languages. His long association with the late E A Milne, architect of an important version of relativistic cosmology, gives him a special familiarity with the new scene in which one of Man's earliest intellectual adventures is now being undertaken. His recently published book on the Natural Philosophy of Time has filled a gap in recent philosophical literature.

The book is conveniently divided into four pairs of chapters together with an important appendix entitled "Why physical space has three dimensions". In the first two chapters the galactic and extra-galactic "depths of the universe" are respectively studied; the third and fourth deal with the problem of space and time in the "classical" and "relativistic" formulations respectively. The fifth and sixth are concerned with "world-models", the division being based on a methodological rather than a strictly historical criterion; for whereas the former set may be regarded as to a considerable extent "inductive" in approach, the model being inferred from the assumed gravitational law of General Relativity, in the latter a more definitely axiomatic approach is made, in which purely theoretical assumptions are postulated, "hypotheses or principles appropriate to local phenomena, e.g. General Relativity, are not always invoked and may even be discarded". To the former belong the "classical" relativistic models of Einstein, Lemaitre and de Sitter; to the latter the models due to Eddington (revised cosmical constant of General Relativity), Milne (kinematic relativity), Bondi and Gold (continuous creation). All these bristle with philosophical difficulties, which are clearly brought out in the discussion. One may note in passing that although "continuous creation" involves no logical difficulty, to accept it as an "explanation" would imply a complete break with the philosophical tradition of science since the rejection of the Aristotelian astral intelligences, prime movers, and "perfect figures" - none of these are solutions, but at best reformulations of the problem, perhaps now, as in the dawn of science, unavoidable. The "break" therefore is not to be rejected as "irrational"; equally it is not to be surreptitiously smuggled in with no clear recognition that it has been made.

The last two chapters provide speculative interpretations of the latest results accruing from the use of the 200-foot reflector and radio "telescope" - the literature up to 1957 being cited.

Neither space nor the competence of the reviewer permit of any critical assessment of Dr Whitrow's own criticism of rival theories. In my view, however. some of his historical judgments bear the marks of too great a reliance (inevitable of course for all of us at some stage) on secondary sources. I do not cite instances, since they nowhere affect the main argument.

One curious error (not Dr Whitrow's) might be of interest to those concerned with the texts of the Critique of Pure Reason. In the Preface to the 2nd edition in Meiklejohn's translation (Everyman edition, 1942), quoted on p. 51, occurs the extraordinary statement "... when Stahl changed metal into lime, and lime back again into metal Kant used the German word 'Kalk' (which is of course correctly translated as 'lime' in any ordinary context) to designate the chemical entity 'calx' which has nothing to do with lime, but refers to the "earthy" character of the product of metals "burnt" in air. All this would be of little consequence, but for the fact that Kant is using it to refer to the emergence of the experimental method, whereas the translation makes it appear like pure magic.
6. The Natural Philosophy of Time (1961), by G J Whitrow.
6.1. Review by: H D.
Science Progress (1933-) 50 (199) (1962), 512-513.

Any attempt to review a book of this type in a small compass is of necessity misleading. It covers such a vast field and deals with so many aspects of what is perhaps the most fundamental of all intellectual problems that a reference to any one of them inevitably presents it out of due proportion to the whole. Dr Whitrow has classified his subject under six headings: Universal Time, Individual Time, Mathematical Time, Relativistic Time, Space -Time and Cosmic Time, and the Nature of Time. These indicate at once the multiform character of the subject and the impossibility of analysing it into wholly self-contained components. What first strikes the reader's attention is the extent of the ground covered and the enormous amount of reading which the result must have entailed. No such conspectus could be complete, but very little seems to have escaped notice. But the book is not a mere catalogue. All aspects of the subject are reviewed critically, and although not all the criticisms will meet with universal approval, they are all very much to the point and help to bring the problems more clearly into focus.

Dr Whitrow wisely does not attempt to define Time. He does, however, refer to "the hypothesis which we shall adopt in this book: that there is a unique basic rhythm of the universe." It is perhaps not an unfair question, considering the scope of the treatment, to ask what is meant here by "the universe" and if - as some passages suggest - this "unique basic rhythm" is equivalent to the "cosmic time" associated with mathematical-physical theory, one requires evidence, which is not forthcoming, that this unique physical time has any unique psychological meaning - whether, for instance, Blake's "eternity in an hour" is "just poetry" or corresponds to an actual psychological possibility. But there is no end to the questions which such a book as this arouses. It fills a distinct gap in literature remarkably well, is invaluable as a work of reference, and is most stimulating to original thought.

6.2. Review by: Max Black.
Scientific American 206 (4) (1962), 179-185.

It is admirable to find a knowledgeable scientist (Whitrow teaches applied mathematics at the University of London) taking the pains to become thoroughly familiar with the long history of philosophical speculation on time. A quick glance at Whitrow's excellent index is enough to show the extent of his erudition and the amount of sustained work that must have gone into making this valuable book.

Whitrow's choice of a title indicates that he is unwilling to accept the currently fashionable view that physics and philosophy are irrevocably divorced. He is not afraid to draw a metaphysical moral from a scientific tale. This makes his book at once more interesting and more controversial than if he had stayed on solid scientific ground. Whenever he speaks as a philosopher of science rather than as an expert in cosmology and the theory of relativity, his claims will have to be judged by philosophical rather than scientific criteria.

The preliminary account that Whitrow gives of his purpose is somewhat misleading. He implies in the preface that he will develop "that part of science which deals with the concept of time with the same wide scope as 'geometry' deals with space," and he welcomes a suggestion of J L Synge's that the subject be called "chronometry." If chronometry were to time as geometry is to space, one might expect Whitrow's work to result in an improved system of axioms for space-time in the manner of the German mathematician David Hilbert. (Valuable studies of this sort have already been made by Alfred A Robb and Hans Reichenbach.) Whitrow does provide some rather stiff technical discussion of certain relevant mathematical questions, but he suggests that readers with limited mathematical knowledge can skip this and other mathematical sections without detriment to the main argument. As the design of his book quickly shows, Whitrow's main concerns are with the philosophy of time.

A long first chapter entitled "Universal Time" is partly directed against the tradition that "temporal flux is not an intrinsic feature of the ultimate basis of things." (Whitrow agrees with common sense that time is objective.) Whitrow may be right, following Bergson, in maintaining that philosophers and scientists have had a "tendency to subordinate the temporal to the spatial." But it might be better to say that theoretical science is committed, for excellent reasons, to what could be called the mathematisation of time (and everything else); that is, the reduction of the layman's concept of time, in all its complexity, irregularity and roughness, to a smooth and idealised concept answering to the physicist's symbol t.

Had Whitrow seen this point sufficiently clearly, I doubt that he would have described a chemical equation as an "expression of a principle of identity, of preservation, of time-elimination-in short a statement that, despite appearances, basically nothing has happened." There is something perverse about the notion that the discovery of a chemical or physical invariant shows that "basically nothing has happened." Imagine saying that to a man whose house has just burned down, with a murmured reference to the conservation of matter! It is one thing to say that science searches for invariants; it is quite another to add the misleading gloss that so far as science has anything to say nothing really happens.

Whitrow's rapid historical sketch whets the appetite, but he has a short way with philosophers. His discussion of Zeno is one of the least satisfactory sections of the book. It is startling to find Aristotle described as "an empiricist whose exclusive concern was the actual physical universe as he conceived it" - a remarkable verdict on a great thinker who was a rationalist through and through, deeply convinced that scientific knowledge must come by the intellectual apprehension of necessary truth.

6.3. Review by: Geoffrey Thomas Kneebone.
Philosophy 39 (147) (1964), 86-88.

The notion of time is an all-pervading constituent of our thought, involved in one way or another in every form of rational activity. Consciousness itself is in time; the world as known to common sense is a world of happenings and processes; natural science presupposes throughout its domain a mathematically idealised counterpart of intuitive time; and theology raises fundamental questions of the relation between the temporal and the eternal, and of a possible beginning and end of time. Profound reflection on many different aspects of time is to be found in the writings of thinkers as diverse as Aristotle, Augustine, Kant, Einstein, and Whitehead; but most of what has been written on the subject of time is essentially fragmentary, dealing with specific problems or with single aspects of the temporal rather than attempting to bring together in a single discussion the many ways in which the notion of time manifests itself. The task which Dr Whitrow has undertaken is that of preparing the ground for such an eventual synthesis. His object is a limited one, however, since he does not go much beyond critical appraisal of each separate line of inquiry that he retraces; and his immediate purpose appears to be to make a map of this hitherto neglected territory and to give an initial survey of what is at present known about it.

Whitrow's book consists of six chapters, each of which is devoted to a more or less loosely organised group of related topics or problems, the discussion being supported throughout by a wealth of historical information. The first main topic is the historical development of the idea of time in relation to the physical world; and here Whitrow sets out from the antithesis between Archimedes, who was 'the prototype of those whose philosophy of physics presupposes the "elimination" of time, that is, of those who believe that temporal flux is not an intrinsic feature of the ultimate basis of things', and Aristotle, who was 'the forerunner of those who regard time as fundamental, since he insisted that there are real "comings-into- being" and that the world has a basic temporal structure'. In Chapter I, 'Universal Time', Whitrow then goes on to deal with such matters as the reversibility of time in classical physics and its irreversibility in statistical mechanics, the reality or ideality of time, and the absolute and relational conceptions of the temporal structure of the phenomenal world. In Chapter II, 'Individual Time', a new beginning is made with the psychological origin of the idea of time; and there then follows a factual account of what is known concerning physiological mechanisms that may underlie our awareness of the passage of time, and a discussion of such psychological elements as the mental present, memory, and personal identity. The argument begins afresh yet once more in Chapter III, 'Mathematical Time', for we are concerned here with the conceptual schemes that have been evolved for the abstract handling of temporal structure. The development of the infinitesimal calculus is, of course, a crucial step in this evolution; and Whitrow outlines the ideas of Barrow and Newton on time and motion, following up this account with a detailed discussion of Zeno's paradoxes and their significance.

The first three chapters of the book are thus devoted to ideas of time which are unaffected by the theory of relativity, or which took shape before that theory had been propounded. The remaining three chapters, on the contrary, are directly concerned with the theory and its consequences. These chapters are 'Relativistic Time', 'Space-Time and Cosmic Time', and 'The Nature of Time'. Some of the argument in them is rather technical, although most of what is said presupposes little knowledge of either relativity or mathematics. Many philosophically important ideas that have been advanced by Einstein and his followers are discussed -for example the view that reference to time in a physical theory is only significant when it is made clear how this time is to be measured, and the contention that time is more fundamental than space in astronomy, since the only spatiotemporal measurements that an astronomer can make directly are measurements of time-and an account is given of the extent to which space and time have been absorbed, in the theory of relativity, in a single four-dimensional continuum. An interesting point which Whitrow also makes in this connection is that, although Einstein had to reject Newton's uniformly-flowing absolute time in favour of the 'proper time' peculiar to the observer who measures it, universal time has nevertheless been reintroduced, in a modified sense, in the cosmic time which is used by cosmologists.

It will be seen from this indication of the scope of Whitrow's book that a unified treatment of the multifarious ways in which time enters into our thought is long overdue; and it is very much to be hoped that this first attempt at giving such a treatment will now be followed up, perhaps by Whitrow himself, more comprehensively and more systematically. Whitrow has certainly made out a prima facie case for the undertaking of such a full-scale investigation, and he has already done much valuable work in sketching various parts of the outline of the treatise that urgently needs to be written.

6.4. Review by: Rom Harré.
The Mathematical Gazette 48 (363) (1964), 128-129.

In this comprehensive study of the role of time in the sciences three different areas of time involved in science are considered, against a particular philosophical background. They are "time" as an all-pervading feature of the physical sciences, "time" as an ingredient in the biological and psychological sciences, and "time" as it appears as the parameter t in mathematical analyses of phenomena. The general philosophical thesis of the book is that time is a necessary concept in all the sciences and the various ways in which time elimination is attempted are unsuccessful.

In the sections of special interest to mathematicians the author makes the following points: mathematical time is a form of notation only, and no important philosophical conclusions can be deduced from the fact that the temporal continuum has a model in the points in a line; the various combinations of continuity and discontinuity of space and time, which are canvassed for instance in Zeno's paradoxes, do not count against the logical independence of temporal concepts, provided that we distinguish between the properties of the temporal continuum and the properties of the spatial model.
No doubt for mathematicians the focus of attention must be on the discussion of the mathematical analysis of temporal facts, but this should not imply that the other parts of this excellent book would not be of the greatest interest to them.

6.5. Review by: Richard M Gale.
Philosophy and Phenomenological Research 23 (2) (1962), 279-281.

Whitrow's book fills a serious gap in the literature on the problem of time; for the first time the voluminous writings of both ancient and modem scientists and philosophers on time in psychology, physiology, mathematics, physics, cosmology, and epistemology are brought together and intelligently collated. For this prodigious feat of scholarly exposition we are in Whitrow's debt. His book should become the secondary source and do much to raise the level of discussion concerning the time-problem.

His own position is developed in a number of cursory critical comments interspersed throughout the book. He defends the significance of time as an ultimate and irreducible feature of the world against the a temporal "block universe" theory, whether in the form of the Parmenidean Being or the four-dimensional Being of Einstein-Weyl, in which becoming is a subjective illusion due to the "movement" of consciousness up a world-line. The mind comes upon pre-existent physical events one after the other. In regard to this theory Whitrow asks:
... if events are eternally 'there' and we merely come across them, how do we get the illusion of time without presupposing time as its origin? On the contrary, we have the faculty for temporal apprehension of successive phases of sensory experience because our minds are adapted to the world we live in, and this is a constantly changing world with a universal basic rhythm (p. 311).
I agree with Whitrow's naturalistic account of our consciousness of becoming; for if the physical events upon which consciousness is dependent are "always" there why am I not always conscious? The Einstein-Weyl view must involve a non-naturalistic account of mind in which it is a ghost in space-time, since it claims that only mental events become but not the physical events with which they are correlated and upon which they are causally dependent. Whitrow's thorough analysis of the physiological factors involved in our psychological awareness of time shows the difficulties with such a view. He also shows how the physicists' geometrisation of time is a theoretical construction from the empirical data of the specious present of consciousness.

In the same spirit as Milne, but avoiding the pitfalls of his rationalism, Whitrow sketches a program for deriving spatial measurements from temporal ones. The significance of time on a cosmic level comes out in his treatment of the natural origin of time based on the assumption of the uniform expansion of the universe. The fundamentality and primitiveness of the concept of time is seen in his claim that it cannot be derived from any non-temporal concept, such as thermodynamics or causality.

When he is not discussing technical issues in science, his comments sometimes are oversimplified and lack sufficient precision. For example, he claims that the mind and body "can interact only in time, and therefore this interaction must occur mentally" (p. 113). Is this saying any more than that, if we accept an analysis of causality based on temporal conjunction of events, then mental and physical events which are temporally conjoined can be said to causally interact? Another example is his claim that "strict causality would mean that the consequences pre-exist in the premisses. But, if the future history of the universe pre-exists logically in the present, why is it not already present?" (p. 295). This is a confusion between causal connections between events in time and the relation of logical entailment between propositions, in which it is nonsense to speak of a temporal relation between them.

6.6. Review by: John Lighton Synge.
The British Journal for the Philosophy of Science 13 (50) (1962), 177-180.

Dr Whitrow is Reader in Applied Mathematics in the University of London at the Imperial College of Science and Technology. He is the author of The Structure of the Universe (1949), revised under the title The Structure and Evolution of the Universe (1959), and of a considerable number of papers on the philosophy of science and various aspects of relativity. The book now under review has six chapters: Universal Time, Individual Time, Mathematical Time, Relativistic Time, Space-Time and Cosmic Time, The Nature of Time. The style is clear and imaginative. Mathematical symbolism is introduced where required, but the greater part of the book is open to the non-mathematical reader. In the text, and particularly in the footnotes, there is a wealth of information culled from many sources, ancient and modern. There is an excellent index. The volume is well and carefully produced - I noticed only a few trivial misprints.

Having thus discharged the prime duty of a reviewer (describe the book), I now feel free to look around a bit, perhaps to pat the author on the back for giving us a most scholarly book on a most interesting and important subject, and perhaps to pick a few quarrels with him.

Dr Whitrow is a polymath, but definitely, and that is what gives charm and richness to his book. After the Contents, he salutes the reader with seven quotations ranging from St Augustine through Lewis Carroll and Samuel Butler to Whitehead, including a very apposite one from C D Broad: 'Our knowledge of time as of space owes more to the labours of mathematicians and physicists than to those of professed philosophers.' Yet it seems to me that in this book it is the philosophical strand which dominates.

Nevertheless the balance is well maintained, and we see the author in turn as physicist, historian, biologist, psychologist, mathematician, relativist, and cosmologist. The range of his reading is enormous. I cannot resist the mischievous temptation to censure his omission of reference to the supply of candles of equal length used by the great King Alfred (cf. M Bloch, Feudal Society, p. 73).

Dr Whitrow combines with his erudition a refined sense of diplomacy. The semantic undertones of his chosen title are calculated to seduce both the philosopher (natural? well, not unnatural surely) and the physicist who recalls dimly that certain venerable chairs of mathematical physics carry the name 'natural philosophy'. So Dr Whitrow gallops into the ring with one foot on the saddle of Rozinante and the other on the back of Sancho's honest and reliable ass. By changing from one mount to the other, he is ready to tilt against windmills or to jog along the quiet ways of scientific common sense.

6.7. Review by: Richard Schlegel.
Isis 54 (3) (1963), 410-411.

Dr Whitrow's book has the great virtue of presenting, in one volume, a scholarly and lucid treatment of the salient material from various sciences that is relevant to the characterisation of time. In the opening chapter, "Universal Time," aspects of time that seem to obtain for phenomena throughout the natural world are discussed, and there is a return to these topics in the sixth and concluding chapter on "The Nature of Time." In between, there is first (Chapter II) Whitrow's impressive and highly interesting review of biological and psychological temporal phenomena. Chapter III is devoted to "Mathematical Time," with discussions of time in Greek geometry and in the calculus, and of the mathematical expression of time as serial order. Also in this chapter, in a discussion of Zeno's paradoxes, we see one topic where the problem of time has for more than two millennia shown itself in an effective interlocking with a definite problem. Chapter IV, "Relativistic Time," is concerned with a formulation of special relativity theory. Dr Whitrow's thorough knowledge of general relativity theory and cosmology is manifest in his discussion, in Chapter V, of space-time and of the time aspects of various cosmological models.

Some mathematics is used in the book - enough, I would say, to give a proper rigour and definiteness where equations are appropriate - but the non-mathematical reader will by no means be confronted by complete unintelligibility. Readers of Isis will appreciate the interest in historical development, with adequate citation of sources, that Dr Whitrow brings to almost every topic which he discusses.

It is to be expected that readers, probably both the expert and the not-so-expert, will find points of disagreement in a book, as this one, which involves many speculative matters. Thus, to cite a few instances, the solution that is given for the celebrated clock paradox of relativity theory is along the lines of distinguishing between the "rest" and "moving" clocks by reference to all the other matter in the universe. This is a possible and even a reasonable solution, but it is one that does involve some deviation from the pure relativity principle, and it is not likely to be a last word on the subject. I could not accept Whitrow's conclusion (page 32) that "An elapsed infinity of acts is a self-contradictory concept." One wonders what is meant by the statement (page 211) that Einstein's theory involves only apparent changes. (And, on page 212, the number of oscillations of electromagnetic waves emitted from a source is erroneously identified as the number of photons emitted from the source.) The hypothetical elementary unit of time, the chronon, is more seriously regarded by the author, I would judge, than is justified by its role in current physical theory.

One might complain of a certain lack of unity in this work: one does not gain a sense of seeing relations between the different approaches to the study of time. And yet, this lack may be as much a commendation as a criticism. We perhaps are in a period of transition from speculation on the mystery of Time to the study of temporal aspects of all natural phenomena; as, somewhat analogously, we have already passed from concern with a hidden entity, Life, to the study of the properties of living organisms. In any event, the reader of Dr Whitrow's book will be well rewarded in the knowledge that he gains therefrom about time in the vigorous natural philosophy of our day.

6.8. Review by: John Jamieson Carswell Smart.
The Philosophical Review 72 (3) (1963), 405-407.

This is an extremely interesting book. The second half of it (especially the discussions of time in relativity and cosmology) is particularly admirable. The first part of the book contains a good many loose and unconvincing arguments, and it also seems overburdened with excursions into the history of philosophy, which while interesting in themselves do not seem to advance philosophical understanding.

Whitrow seems to hold that not only the relations of earlier and later but also the notion of passage are essential to the concept of time. It is true that on page 270 Whitrow agrees that it is misleading to talk of time "flowing in a definite direction," but it is hard to reconcile this with the emphasis on passage elsewhere in the book. Thus on pages 227-228 he rejects the view that "the passage of time ... is to be regarded merely as a feature of consciousness with no objective counterpart." Nowhere does Whitrow take account of the recent literature, e.g., Donald Williams, "The Myth of Passage" (Journal of Philosophy, XLVIII [1951], 457-472), which argues the passage of time is an illusion - and equally that acceptance of what Whitrow calls the "block universe" of Minkowski does not involve the correlative confusion of consciousness crawling up world lines. If it is accepted that the passage of time and the advance of consciousness are illusions, then some of Whitrow's arguments are seriously weakened. Thus on page 32, accepting one side of Kant's first antinomy, namely the proof that the world cannot have existed for an infinite time, Whitrow says, "An elapsed infinity of acts is a self-contradictory concept." Now if we journey through time, the journey must start somewhere. But if we reject the correlative myths of the passage of time and the journey through time, then we have no more reason to object to an infinite sequence of past events than we have to object to an infinite sequence of future ones. Similarly I would be prepared to argue against Whitrow's objection to the purely mathematical (or Russellian) treatment of Zeno's puzzle about Achilles and the tortoise: I suspect that his objection rests partly on the myth of passage, as when on page 148 he contrasts "a static or completed infinite" with "an indefinitely growing, dynamic, or uncompleted infinite."

On pages 157-169 there is an ingenious section concerned with the logical construction of instants out of the data of consciousness (overlapping durations). This is based partly on the work of Russell, Wiener, Walker, and Robb. However, the procedure is pointless to those of us who reject an operationalist point of view: if we are prepared to accept space-time instants either as postulated theoretical entities or as definable in terms of these, then there is no need to construct them out of the data of consciousness. I suspect that Robb's theory of time and space, which is discussed on pages 198-200, is also motivated by a too operationalist point of view.

There is an excellent discussion of the so-called clock paradox on pages 219-222 and on pages 231-232. Whitrow is quite clear that the paradox should be cleared up within special relativity itself - that it is unnecessary to bring in the general theory. An interesting contribution to the discussion, based on an earlier paper written in collaboration with E A Milne, is the analysis of the case of a clock which moves uniformly in a straight line in a space of uniform positive curvature, and which thus leaves and returns to a stationary clock without undergoing acceleration. I particularly like Whitrow's elucidation of the clock paradox in terms of a Minkowski space-time diagram. ...
7. The Natural Philosophy of Time (Second Edition) (1980), by G J Whitrow.
7.1. Review by: Michael Heller.
The Review of Metaphysics 37 (2) (1983), 432-434.

J L Synge argued that "Euclid put us on the wrong track by taking space as the primary concept of science and relegating time to a poor second." This situation, however, has changed nowadays by reason of the influence of recent developments of Einstein's relativity theory. Whitrow himself has taken a significant role in promoting time studies. The book now under consideration is the second, completely revised edition (first edition 1961); its goal is to give a general framework for the study of time. Let us have a closer look at the book's content.

In two introductory chapters the author looks at the time problem from two distinct, and in a sense opposite, points of view: "universal time" (Chapter 1), with its cosmological origin and cosmic scale, its thermodynamic and evolutional "arrows," and its absolute (Newtonian) or relational (Leibnizian) character, is confronted with the "human time" (Chapter 2) as rooted in the mind, and as laboriously developed in the course of history, closely connected with psychology of the conscious self. Although the first chapters of the book are rather a review of current theories, their criticism leads Whitrow to reveal his own standpoint. He asserts that "our 'sense' of time is neither a necessary condition of our experience, as Kant thought, nor a simple sensation, as Mach believed, but an intellectual construction. It depends on processes of mental organisation uniting thought and action. It is a late product of human evolution, in all probability closely related to the development of language."

A chapter on "biological time" (Chapter 3) follows in a natural way. The chapter is rich with information concerning empirical works on time in biology. It is interesting to note that most probably it is a clock mechanism that lies at the origin of life: "oscillations were necessary to keep cells alternating between extreme physiological states, anabolic processes predominating in the one and catabolic in the other."

In chapter 4, the book's character changes from a review of opinions to a monographic study. Whitrow's approach to a geometrisation of time by modern mathematics and physics certainly deserves more attention than it is possible in a short review. But to sum up briefly, the object of the mathematical physicist's one-dimensional continuum of instants, isomorphic with the axis of real numbers, "has not been to establish the 'reality' of point-like instants but instead to analyse the principles underlying their theoretical construction from the empirical data of consciousness."

The next two chapters (Chapter 5: "Relativistic Time"; and Chapter 6: "Space-Time and Cosmic Time") are a deep study of time in the theory of relativity within a broad philosophical context. Analyses presented here bear evidence of the author's work done, as early as the thirties, on Milne's cosmological theory; they are, in fact, "kinematic considerations" transferred from Milne's vision of the world to the conceptual frame of the theory of relativity. Perhaps one would like to have here more about developments in the space-time structure study made in recent years; nevertheless the originality of the approach is very illuminating.

In the last chapter (Chapter 7: "The Nature of Time"), Whitrow deals with problems such as: physical irreversibility and time asymmetry; the causal theory of time; the transitional nature of time; and the dimensionality of time. He expresses the view that Boltzmann's attempts "to invert the Second Law of Thermodynamics so as to provide a statistical explanation of time's arrow" and a refinement of this theory by Reichenbach are "evidence for believing that time cannot be derived from more fundamental concepts that involve no implicit appeal to it." This leads to a kind of final conclusion: "The essence of time is its transience. ... time does not exist independently of events, but it is an aspect of the nature of the universe and all that comprises it."

In my opinion, this book is indispensable for any philosopher who wants to speculate on time or temporality. He may not share Whitrow's opinions but he certainly cannot ignore views and polemics presented by him.

7.2. Review by: Clive William Kilmister.
The British Journal for the Philosophy of Science 34 (2) (1983), 200-201.

It is twenty-one years since the first edition of Whitrow's comprehensive study of time. It is scarcely fanciful to see that book as instrumental in starting the widespread increased interest in time, including of the foundation of the International Society for the Study of Time, and the various international colloquia. In taking account of two decades of thought, this one comes quite a long way towards being a new book, but does retain enough of the original to be truly a second edition. The Preface concludes, as did the former, with a page of quotations, and once again Broad's 'Our knowledge of time as of space owes more to the labours of mathematicians and physicists than to those of professed philosophers' occupies a central position and gives the key to the spirit behind the book. But in pride of place at the top of the page St Augustine is replaced by Lucretius: 'Similarly, time by itself does not exist; but from things themselves there results a sense of what has already taken place, what is now going on and what is to come.' Perhaps this change typifies the way in which time ideas have advanced since 1960.
Whitrow himself finishes the book with a section (longer than in the first edition and substantially different) on Conclusions. He contrasts relationists (with Kant as the exemplar) for whom time belongs to the perceiving mind with idealists (McTaggart) who see an essentially non-temporal series endowed with temporality by varying consciousness. Whitrow's position elegantly bridges these; for him, conscious awareness of time is not a necessary pre-condition of experience but an intellectual construction which is both environment and culture dependent. Moreover unlike McTaggart, perception is based on an objective factor - physical time - which correlates with physiological processes. (But in keeping with McTaggart and against the 'scientific reductionists', the essence of time is its transience, not to be explained in terms of anything more fundamental; time is a mode of activity.) This perception is a complex process, and one for which experimental investigation is important. So also perhaps for the mathematical measurement of time, where there is no evidence in nature for a continuum of instants, where Zeno's paradoxes still imply indivisible instants but where experiment does not yet provide the size.

This is not exactly a philosophical book; neither is it only a scientific one. Indeed, its title is just right; into the bargain, there is a generous measure of history and background material. It is essential reading for anyone concerned with time, and it combines this with being highly enjoyable reading. There is an excellent index.

7.3. Review by: Lawrence Sklar.
Mathematical reviews R0122530 (22 #13254).

This is a second edition of the author's well-known treatise on time, originally published in 1962 [Nelson, Thomas, Camden, N.J., 1962]. While some attention is paid to philosophical work on time subsequent to the publication of the original edition, the bulk of the changes consists in additions and revisions based on scientific results in recent years.

The scope of the book is vast, perhaps too vast, with chapters entitled: "Universal time", "Human time", "Biological time", "Mathematical time", "Relativistic time", "Space-time and cosmic time" and "The nature of time".
The book is a major repository of information, scientific and philosophical, about time. It is stimulating and informative and should be read by anyone seriously interested in time. In its more philosophical sections it does suffer from a tendency to leap about in a hectic manner from topic to topic, and, in its attempt to be compendious, subtle positions and arguments are sometimes given in merely sketchy, and sometimes misleading, outlines. The author's own philosophical arguments frequently take the form of provocative brief paragraphs or even single lines, stimulating to thought but rather less successful in disentangling complex issues and throwing clarifying light on problems notorious for leading even more careful thinkers into conceptual confusion. It is certainly, though, a major contribution to the literature on time, and this updated edition is most welcome.
8. The Nature of Time (1973), by G J Whitrow.
8.1. Review by: James Fucini.
The Science Teacher 40 (7) (1973), 52.

The author is in applied mathematics at Imperial College, London. The book is an expansion of lectures given over the BBC.

... ultimately time must be regarded cosmologically and is a fundamental property of the relationship between the universe and the observer which cannot be reduced to anything else." This represents the author's conclusion.

The origins of the idea and nature of time from various viewpoints are the subjects of the opening chapter. Many ancient civilisations believed time to be a linear progression measured by some form of calendar.

Among animals, only man has a sense of past and future. But is there a sense for time? The fascinating subject of biological clocks involves this question. "... navigational achievements of birds cannot be understood unless we assume that animals possess some form of internal time-keeping mechanism such as a rhythmic process whose pace is maintained by external rhythmic events." The actual measuring of time by astronomical events, mechanical and atomic clocks is treated in another chapter. Two chapters deal with Einstein's ideas of space time. Starting with Galileo's idea of time as a geometrical straight line, the contributions of Newton, Locke, and others are examined. Their concepts are well presented and their comprehension is of great value to those wishing to get a background for relativity. The thermodynamic, historical, and cosmological time arrows and the significance of time are treated in the final chapter. For general high school use.
9. Time in History: The Evolution of Our General Awareness of Time and Temporal Perspective (1988), by G J Whitrow.
9.1. Review by: Carlene E Stephens.
Isis 81 (2) (1990), 312-313.

Time, in all its physiological, cultural, and cosmic aspects, has been the focus of much research in the past two decades. Biologists, physicists, geographers, anthropologists, psychologists, and historians have joined philosophers in identifying temporal factors in their areas of specialisation. Interdisciplinary studies, once non-existent, now attempt to synthesise the myriad answers to the question: What is time? These studies point to time as the fundamental organising principle - the abstraction that regulates every human community, regardless of geography or historical period, and the periodicity that underlies the natural world, from the smallest subatomic particles to the edges of the universe.

Nearly thirty years ago G J Whitrow pioneered such an interdisciplinary approach in The Natural Philosophy of Time (1961; 2nd ed., 1980), in which he examined the occurrences of time-related phenomena in the physical world. In his most recent book he has collected his afterthoughts on this early work.

The result is a useful but disjointed book. The initial chapters, the book's best, summarise our present understanding of time awareness. The author draws from a broad range of specialised works in science, literature, and history and defines the human sense of time in its various aspects. Human time consciousness can take several forms: as tyrant in charge of our daily schedules, as feeling of duration, as learned experience in childhood, as distinction between past, present, and future. Whitrow also relates time to the way we express it in language and numbers. These chapters deftly weave together both the unconscious biological and the external natural and cultural factors that influence the way humans reckon and experience time.
There are no ordinary men and women in this volume, only great men, great ideas, and great civilisations. Whitrow's twentieth-century chapter, for example, with its discussion of Einstein, cosmic time, and the outer boundaries of astrophysics, is most remote from the everyday schedules that he maintains are driving us frantic. Also, despite his historical look at Japanese, Indian, Islamic, and Mayan civilisations, his frame of reference is western European. He discusses past civilisations in terms of their impact or lack of impact on present-day Western timekeeping.

Because the book is a synthesis, there are few surprises. Whitrow's survey reminds us succinctly that ideas about time and time reckoning, far from being absolute, are entirely relative to the civilisation devising them. Predictably, he places special emphasis on the invention of the mechanical clock, an event that shifted the social organisation from the calendar to the clock. Even the half dozen clockwork illustrations have previously appeared elsewhere. New material does appear in a miscellany of mathematically based appendixes devoted to leap years, the Athenian astronomer Meton's calendar cycle, and the calculation of Easter.

9.2. Review by: Francis C Haber.
The American Historical Review 95 (4) (1990), 1156.

In his influential Natural Philosophy of Time (1961, 1980), G J Whitrow presented an analytical survey of modern Western theories of time. His Time in History supplements that work by expanding the survey of views of time through the course of history and across cultures. The general theme that lies behind Whitrow's selection of materials is that, although the human capability to have an idea of time probably has its origins in our psychological and physiological evolution, the form the idea of time takes is a cultural product, shaped by the nature of temporal awareness present in a given society. These particular notions of time in a society are a product of its mode of existence, but the notions have a reciprocal relationship, influencing in turn that mode of existence.

Although we are now obsessed with living by the clock, Whitrow is concerned to show that the different experiences of societies throughout history have led to various attitudes and ideas about time unlike our own. On the whole, from prehistory down to the Renaissance in the West, in the Islamic world, the Far East, and Mesoamerica, he argues, the view of temporality was mostly negative. Although timekeeping had its practical side, time awareness was subservient to religious or other prepossessions about the nature of things that valued a static permanence above temporal change. As a result, temporal change was viewed as non-progressive, being perceived largely as the endless repetition of cycles or the manifestation of some higher order of permanence. Only with the acceptance of the processes of change as desirable was the emergence of modern time awareness possible.

One of the main threads that Whitrow follows as he moves through ancient cultures to contemporary society is methods of time measurement. Throughout the book Whitrow relies on the scholarship of others, but his coverage of time measurement, though brief, is comprehensive, interesting, and illuminating. His own interest in this subject has resulted in the garnering of many curious insights whose inclusion is only loosely connected with his more general theme, but they do help in anchoring timekeeping with the practical experience of earlier societies. The reciprocal relationship, however, of the awareness of time and the mode of existence in a society is exceedingly complex, as Whitrow recognises, and the development of technique in time measurement does not necessarily result in a break with traditional awareness of time. He suggests that there was such a break in the West, but that it occurred later than is often supposed.

Although the West was indebted to the ancient cultures for techniques of timekeeping, a new turn was taken with the invention of the mechanical clock around the end of the thirteenth century. In the long run, the mechanical clock had a decisive influence on the modern awareness of time, but he concludes that it was first adapted to traditional attitudes of time. The break in time awareness came not through this method of timekeeping alone but in conjunction with social and cultural changes that fostered an appreciation of temporality, as evidenced in the emergence of ideas of history, progress, and evolution. This change of values, to the acceptance of temporality as being good, he attributes to the Western perception of the importance of time in the transactions of practical life, markedly so with the growth of industrialisation, and to the growth of science and critical reason, which broke the hold of tradition on intellectual attitudes.

The idea of the reciprocal action between views of time and cultural experience presents difficulties in historical causation and explanation that Whitrow does not address in any depth. He has read widely in history, but, within the compass of so small a book, his treatment of history is necessarily summary and hurried. Still, he does convey the range of time awareness present in the development of the modern sense of understanding in terms of temporal process.

9.3. Review by: James Arthur Bennett.
The British Journal for the History of Science 23 (2) (1990), 252.

After an introduction stressing the social determination of our sense of time and the conventional nature of systems of time reckoning, the book settles down to a broad history of two time-related themes: time measurement and ideas about both the passage of time and the nature of history. These two themes are not easily held together and the attempt to combine their histories over a period longer than civilisation is ambitious indeed.

After speculations on the awareness of time in prehistory, the story begins with ancient Egyptian calendars and time reckoning, moves through Babylon and ancient Iran to classical antiquity, and so on to medieval Europe, Islam and the East. From the watershed of the mechanical clock and the conceptual and technical developments of the Renaissance and early modern periods, Professor Whitrow presses on to the quickening pace of perceived time after the Industrial Revolution and the fundamental changes in the concept of time and in its measurement characteristic of the twentieth century. This ambitious synthesis ranges widely not only chronologically, but also geographically and culturally. The result is bound to be somewhat anecdotal and episodic, and becomes more fragmented in later chapters. This is particularly so of the attempt to weave into one account the technical determination of time and concepts of history and of progress.

But once the reader comes to terms with the synthetic, wide-ranging character of the book, there is much to be learnt from it, presented in a clear and entertaining manner. The erudition is impressive. Your reviewer was intrigued to learn, for example, the origins of 'noon', of 'daisy', of 'influenza', to discover that certain Greek monks still use the Julian calendar and even reckon sunrise as twelve o'clock, and to know that restrictive Sunday legislation can be traced to social taboos of the Babylonians. Not least, he now understands, at last, why each month has its allotted number of days.

9.4. Review by: King J Dykeman.
CrossCurrents 39 (2) (1989), 225- 228.

Different philosophers and different physicists over history have presented a number of persuasive accounts on the nature of time. For over forty years, G J Whitrow, an Emeritus Professor at the University of London and Senior Research Fellow of the Imperial College of Science and Technology, has studied, written and lectured on the notion of time. His most significant work and one of the great contemporary books on time, is The Natural History of Time, first published in 1961 and republished in a second edition by Oxford's Clarendon Press in 1980. Whitrow considers his work distinct from that of Stephen Toulmin, Jane Good field, and Rudolf Wendorff, because, as superb as their works have been in terms of general intellectual history, only his understanding of time takes direct account of the technical development of chronology and chronometry and their social and ideological consequences as a central supporting argument. Whitrow's second book The Nature of Time, published in 1972, discusses the different points of view concerning the nature of time and clarifies our contemporary scientific view by raising consciousness about the mistaken notions of cyclical (v.g. Greek), absolute (v.g. Newtonian), and outer determined (v.g. common sense) time that appear in most cultures. Whitrow believes the correct understanding of time is only 300 years old.

Now Whitrow, has brought together the power of these two major works in a third book, Time in History. Here he calls upon the scholarship of the many who have in the last forty years made time a topic equally significant for the philosophic, the scientific and general reading public. I can find no important historical, philosophical, technological, or literary discussion of time that is not alluded to in this book of under 200 pages. As the title proclaims, Time in History, is a his tory of our present scientific awareness of time as well as of how this temporal perspective has become the basis from which all history should be told. Whitrow maintains that there is now a settled and single contemporary understanding of time. This book traces science's realisation of this proper understanding of time.

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