Gerald James Whitrow

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G.J. Whitrow sketch
by Patrick L. Gallegos

Gerald James Whitrow (9 June 19122 June 2000) or G. J. Whitrow, was a British mathematician, cosmologist and historian of science.


  • [Time is not] a mysterious illusion of the intellect. ..It is an essential feature of the universe.
    • The Nature of Time (1961) as quoted by Douglas Martin, "Gerald J. Whitrow, 87, Author Of Philosophic Tomes on Time" The New York Times (June 27, 2000)
  • Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century. In a manuscript treatise, he sought a graphic representation of the Aristotelian forms, such as heat, velocity, sweetness, by laying down a line as a basis designated longitudo, and taking one of the forms to be represented by lines (straight or circular) perpendicular to this either as a latitudo or an altitudo. The form was thus represented graphically by a surface. Oresme extended this process by taking a surface as the basis which, together with the latitudo, formed a solid. Proceeding still further, he took a solid as a basis and upon each point of this solid he entered the increment. He saw that this process demanded a fourth dimension which he rejected; he overcame the difficulty by dividing the solid into numberless planes and treating each plane in the same manner as the plane above, thereby obtaining an infinite number of solids which reached over each other. He uses the phrase "fourth dimension" (4am dimensionem).
    • "Why Physical Space has Three Dimensions," British Journal for the Philosophy of Science, 6 #21 (May 1955)
  • Although the peculiarly fundamental nature of time in relation to ourselves is evident as soon as we reflect that our judgments concerning time and events in time appear themselves to be 'in' time, whereas our judgments concerning space do not appear themselves in any obvious sense to be in space, physicists have been influenced far more profoundly by the fact that space seems to be presented to us all of a piece, whereas time comes to us only bit by bit. The past must be recalled by the dubious aid of memory, the future is hidden from us, and only the present is directly experienced. This striking dissimilarity between space and time has nowhere had a greater influence than in physical science based on the concept of measurement. Free mobility in space leads to the idea of the transportable unit length and the rigid measuring rod. The absence of free mobility in time makes it much more difficult for us to be sure that a process takes the same time whenever it is repeated.
    • Natural Philosophy of Time (1980) as quoted by Suk-Jun Kim, "Time felt and places imagined in my compositions" (2011)
  • Our conscious appreciation of the fact that one event follows another is of a different kind from our awareness of either event separately. If two events are to be represented as occurring in succession, then—paradoxically—they must also be thought of simultaneously.
    • As quoted by Max Jammer, Concepts of Simultaneity: From Antiquity to Einstein and Beyond (2008)

The Structure of the Universe: An Introduction to Cosmology (1949)[edit]

  • Whether the stars were all at the same distance, or whether they were scattered throughout infinite space, or whether they formed a finite system of vast but limited depth, were questions that could not be answered until towards the end of the eighteenth century. Until then, stellar astronomy was a field left to the unaided imagination.
  • Although the classic theoretical foundation of distance measurement in physics is the 'rigid rod', nearly all distances in surveying, whether terrestrial or celestial, are made to depend on the properties of light. The two simplest properties so employed are the principle of propogation in straight lines and the principle that the intensity of light diminishes inversely as the square of the distance.
  • Galileo had raised the concepts of space and time to the status of fundamental categories by directing attention to the mathematical description of motion. The midiaevel qualitative method had made these concepts relatively unimportant, but in the new mathematical philosophy the external world became a world of bodies moving in space and time. In the Timaeus Plato had expounded a theory that outside the universe, which he regarded as bounded and spherical, there was an infinite empty space. The ideas of Plato were much discussed in the middle of the seventeenth century by the Cambridge Platonists, and Newton's views were greatly influenced thereby. He regarded space as the 'sensorium of God' and hence endowed it with objective existence, although he confessed that it could not be observed. Similarly, he believed that time had an objective existence independent of the particular processes which can be used for measuring it.
  • Let us suppose that an explosion occurs on Mars, which is observed by an astronomer on earth, who records the instant when he sees the flash. If light travelled instantaneously with an infinite velocity, this instant would coincide with the time... recorded by the... observer on Mars. In this way a meaning could be attached automatically to absolute time and the simultaneity of events at different places; indeed, the classical theory is now regarded as the limiting form of Einstein's theory when the velocity of light becomes infinite. But as there is a mass of experimental evidence supporting the view that light takes a finite time to travel... the terrestrial observer must correct the time recorded on his watch. This correction... will depend on assumptions concerning the velocity of light and the measurement of distance. Thus the concept of a world-wide simultaneity ceases to be a primitive idea.
  • Consider an event, for example the outburst if a nova... Suppose this event is observed from two stars in line with the nova, and suppose further that the two stars are moving uniformly with respect to each other in this line. Let the epoch at which these stars passed by each other be taken as the zero of time measurement, and let an observer A on one of the stars estimate the distance and epoch of the nova outburst to be x units of length and t units of time, respectively. Suppose the other star is moving toward the nova with velocity v relative to A. Let an observer B on the star estimate the distance and epoch of the nova outburst to be x' units of length and t' units of time, respectively. Then the Lorentz formulae, relating x' to t', are

    These formulae are... quite general, applying to any event in line with two uniformly moving observers. If we let c become infinite then the ratio of v to c tends to zero and the formulae become
  • Minkowski made a remarkable discovery concerning the Lorentz formulae. He showed that, although each observer has his own private space and private time, a public concept which is the same for all observers can be formed by combining space and time as a kind of 'distance' by multiplying it by the velocity of light, c; in other words, with any time interval we can associate a definite spatial interval, namely the distance which light can travel in empty space in that period. If, according to a particular observer, the difference in time between any two events is T, this associated spatial interval is cT. Then, if R is the space-distance between these two events, Minkowski showed that the difference of the squares of cT and R has the same value for all observers in uniform relative motion. The square root of this quantity is called the space-time interval between two events. Hence, although time and three-dimensional space depend on the observer, this new concept of space-time is the same for all observers.
  • In developing his theory of gravitation, Newton assigned to every material body another property which is called its gravitational mass. Gravitational mass determines the force exerted by the body on other bodies, and so its function appears to be quite distinct from that of inertial mass. Nevertheless, the two are found to be identical in magnitude. Newton made experiments to verify this remarkable equality by swinging a pendulum with a bob which could be made with different materials. The period of the swing depended on the ratio of the inertial and gravitational masses of the pendulum, but in all cases it was found to be the same... In 1890 Eötvös made a much more refined test with the aid of a... torsion balance. Repeated experiments showed that inertial mass and gravitational mass were equal to within one part in 100 million. Einstein suggested that this was because inertia and gravitation are identical.
  • According to the Special Theory of Relativity, the velocity of a moving body is always less than the velocity of light. Since the energy of motion of a body depends on its inertial mass and its velocity, it follows that if the energy of a body is increased indefinitely by the continual application of a force, the inertial mass of the body must be increased too; for, if not, the velocity would ultimately increase indefinitely and exceed the velocity of light. Einstein found that, corresponding to any increase in the energy content of a body, there is an equivalent increase in its inertial mass. Mass and energy thus appeared to be different names for the same thing, the energy associated with a mass M being Mc2, where c is the velocity of light; and the mass M of a body moving with velocity v he found to be given by the following formula
  • Although the Special Theory of Relativity does not account for electromagnetic phenomena, it explains many of their properties. General Relativity, however, tells us nothing about electromagnetism. In Einstein's space-time continuum gravitational forces are absorbed in the geometry, but the electromagnetic forces are quite unaffected. Various attempts have been made to generate the geometry of space-time so as to produce a unified field theory incorporating both gravitational and electromagnetic forces.
  • The philosophical consequences of the General Theory of Relativity are perhaps more striking than the experimental tests. As Bishop Barnes has reminded us, "The astonishing thing about Einstein's equations is that they appear to have come out of nothing." We have assumed that the laws of nature must be capable of expression in a form which is invariant for all possible transformations of the space-time co-ordinates and also that the geometry of space-time is Riemannian. From this exiguous basis, formulae of gravitation more accurate than those of Newton have been derived. As Barnes points out...
  • Space-time is curved in the neighborhood of material masses, but it is not clear whether the presence of matter causes the curvature of space-time or whether this curvature is itself responsible for the existence of matter.
  • Another interesting feature of the Einstein universe is that in principle it could be circumnavigated by a ray of light... it is unlikely that the rays would converge with sufficient accuracy. Nevertheless it is interesting to consider the possibility that some of the stars and nebulae which we see may after all be only optical ghosts.
  • The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity.
    It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties.

"Why the Sun Shines" (18 July 1957)[edit]

The New Scientist

  • By the time of Comte, scientists unanimously rejected the idea that there was any essential difference between celestial and terrestrial matter, but they still had no empirical evidence to support their view any more than had Aristotle to support his, and to the positivist philosopher it seemed that none could ever be obtained. ...The possibility of a solution to this problem appeared shortly after Comte's pronouncement with the rise of the science of astronomical spectroscopy...
  • From a careful determination of the amount of solar heat that which would fall per minute on an area of one square centimetre placed perpendicular to the radiation as it falls on Earth's surface and from a knowledge of the Earth's distance, we deduce that each square centimetre of the solar surface radiates on the average of about the rate of a nine horse-power engine.
  • The solution... was found only after the rise of nuclear physics, and, strange to relate, was not known to Eddington when he developed his celebrated theory of stellar structure between 1916 and 1924. Indeed, it is one of the most intriguing facts in the history of science that the two most influential theories concerning the stars—Newton's theory of gravitation and Eddington's theory of stellar construction—were each developed so successfully although Newton was ignorant of the origin of gravitation and Eddington of the origin of stellar energy.
  • Not until the pioneer work of Rutherford and his colleagues was the possibility of nuclear reactions and transformations as sources of stellar energy envisaged.

"Newton and the Stars" (10 Oct 1957)[edit]

The New Scientist

  • Newton's laws of motion and gravitation achieved their original success when applied to the solar system. The first definite evidence that they were applicable on a larger scale came from the study of binary stars towards the eighteenth century. In recent times the limitations of Newton's theory have become apparent. Even on the scale of the solar system, it has been challenged by Einstein's.
  • As the degree of observational accuracy at which general relativity becomes significantly different from Newtonian theory is far from being achieved in this field, and as stellar velocities are small compared with light, there is no sign yet that any non-Newtonian theory is required.

"Theories of the Universe" (10 Apr 1958)[edit]

The New Scientist

  • Cosmology is peculiar among the sciences for it is both the oldest and the youngest. From the dawn of civilization man has speculated about the nature of the starry heavens and the origin of the world, but only in the present century has physical cosmology split away from general philosophy to become an independent discipline.
  • Einstein's pioneer application in 1917 of his newly developed general relativity to the problem of world-structure ushered in a new phase in the theoretical approach to the subject. Then, some seven years later, Hubble's discovery of Cepheid variables in the Andromeda nebula finally settled the long-debated question concerning this and similar nebulae in the Milky Way.
  • It became clear that our Galaxy is only one system among many, and that the universe is far vaster than the particular stellar system to which the Sun and planets belong. Since then developments have been more rapid than at any time since the days of Copernicus, Digges and Bruno when the geocentric hypothesis of the cosmos received its death-blow.

Time in History: Views of Time from Prehistory to the Present Day (1988)[edit]

  • Man must have been conscious of memories and purposes long before he made any explicit distinction between past, present, and future.
  • The famous palaeolithic paintings found in caves such as that at Lascaux in the Dordogne have been interpreted as evidence that, at least implicitly people were operating 20,000 or more years ago with teleological intent in terms of past, present, and future. It may well be that those responsible for the so-called 'Dancing Sorcerer' ...may have felt that the actual performance of the dance was insufficient, since they were concerned with the magical efficacy of the dance after it ended.
  • It must have required enormous effort for man to overcome his natural tendency to live like the animals in a continual present.
  • The development of rational thought actually seems to have impeded man's appreciation for the significance of time. ...Belief that the ultimate reality is timeless is deeply rooted in human thinking, and the origin of rational investigation of the world was the search for permanent factors that lie behind the ever-changing pattern of events.
  • Language itself inevitably introduced an element of permanence into the world. For, although speech itself is transitory, the conventionalized sound symbols of language transcended time.
  • To obtain a greater degree of permanence the time symbols of oral speech had to be converted into the space symbols of written speech. ...The crucial stage in the evolution of writing occurred when ideographs became phonograms...

Quotes about Whitrow[edit]

  • Most of the illustrations in this book were scanned... from the volumes in which they originally appeared. One of these deserves special mention. It is... from the library of the late Gerald James Whitrow... I was honoured to receive this small book as a gift in 2001 from Professor Whitrow's widow, Magda... I wished to include a copy of this historic image in my own book both as a tribute to Pofessor Whitrow's memory and to express my sincere gratitude to all responsible for the gift.
    • Barbara J. Becker, Unravelling Starlight: William and Margaret Huggins and the Rise of the New Astronomy (2011)
  • Whitrow... proposed an anthropic resolution of the venerable philosophical question Why physical space has three dimensions? (arguing that with a space of different dimensionality there would be no living being to pose the question) and, similarly to [Grigory Moiseevich] Idlis, alluded around 1955 to an anthropic explanation of the size of the observable universe. Anyway, he never published these last ideas, which were developed years later by Wheeler. The only reference to Whitrow’s argument that appeared in print during the 1950s seems to be that due to the philosopher of religion Eric Lionel Mascall, who attributed to the English’s mathematician that

    it may be necessary for the universe to have the enormous size and complexity which modern astronomy has revealed, in order for the earth to be a possible habitation for living beings.

  • The point at issue between the two theories [A and B theory] is whether 'time' really is, in some deep ontological sense, differentiated into past, present and future. ...Reichenbach and Whitrow propose that there is indeed such a type of event and this is the 'becoming', or 'coming into being' of factual states-of-affairs in the physical world. ...Whitrow expressed ..."The past is the determined, the present is the moment of 'becoming' when events become determined, and the future is as-yet undetermined.
    Although neither Reichenbach nor Whitrow developed their thesis at any length, the general purport of what they meant is clear: there is a basic chance element in nature, at least at the micro-level, and the moment of 'becoming', which they identify with 'the present', is marked by a tranisition from what is merely possible to what is factual. However... this important attempt to provide a physical basis for the A-theory is by no means immune from criticism.
    • K. G. Denbigh, Three Concepts of Time (2012)
  • While at Oxford, he was much influenced by cosmologist, E. A. Milne. ...Whitrow is... remembered for his very loud voice which could be heard 'from miles away.'
    • Hannah Gay, The History of Imperial College London, 1907-2007 (2007)
  • Remarks on the concept of simultaneity may mislead the reader to believing that only modern physicists and philosophers recognize the crucial importance of this notion. ...this concept has occupied the attention of philosophers and scientists throughout the whole history of human thought and played an important role in the writings of such intellectual giants as Aristotle, St. Augustine, Leibniz, and Kant.
    It would be a serious mistake to associate the concept of simultaneity exclusively with philosophic or scientific reasoning. In fact it was at the level of prescientific apprehension, a fundamental ingredient in the process of human apperception and conception of time. As Gerald Whitrow rightly pointed out, "our conscious appreciation of the fact that one event follows another is of a different kind from our awareness of either event separately. If two events are to be represented as occurring in succession, then—paradoxically—they must also be thought of simultaneously."
    • Max Jammer, Concepts of Simultaneity: From Antiquity to Einstein and Beyond (2008)
  • One of the few authors to have explicitly connected the physical issue of the expansion of the universe with the philosophical topic of the metaphysical status of space is Gerald James Whitrow.
    • Giovanni Macchia, "Philosophy of Space and Expanding Universe in G. J. Whitrow" (2014) Abstract
  • Whitrow's stance... is probably the first attempt to introduce such a philosophical approach in modern cosmology... it could be the a stimulus for new insights and a better comprehension of the physical foundations of cosmology itself.
    • Giovanni Macchia, "Philosophy of Space and Expanding Universe in G. J. Whitrow" (2014)
  • By combining prodigious scholarship from the ancient Greeks to modern physicists, he argued persuasively in more than 100 academic papers and a string of books that an integrated, interdisciplinary understanding of time should be possible.
    • Douglas Martin, "Gerald J. Whitrow, 87, Author Of Philosophic Tomes on Time," The New York Times (June 27, 2000)
  • Much of Dr. Whitrow's work is concerned with problems in cosmology and relativity. ...He has been editor of The Observatory Magazine and the Monthly Notices of the Royal Astronomical Society.
    • The New Scientist (18 July 1957) Contributors List
  • Perhaps the most important of Whitrow's books was The Natural Philosophy of Time. He showed that time can be studied independently of its magnitude. ...Whitrow's historical work included a paper on Robert Hooke.
    • Virginia Trimble, Thomas R. Williams, Katherine Bracher, Richard Jarrell, Jordan D. Marché, F. Jamil Ragep, Biographical Encyclopedia of Astronomers (2007)
  • The shift toward a linear time conception, a confutation against (instead of a development from) the age-old cyclic time conception, did not occur suddenly and lasted well into the nineteenth century. ...Attention had clearly drifted away from seeking an eternally valid order toward a focus on change; truth had now ceased to lie in an unchanging order of things—rather, it tended to be regarded as dependent on process. Gerald Whitrow has put the matter succinctly, that in the nineteenth century " interest was transferred from the 'thing completed' to the genetic process, that is, from 'being' to 'becoming.' "
    • Sean Yung-hsiang Wang, Lost in Time: The Concept of Tempo and Character in the Music of Brahms (2008) pHD Dissertation
  • Professor Gerald Whitrow, who has died aged 87, wrote The Natural Philosophy of Time (1960) a tour de force that examined the subject from every side—mathematical, cosmological, historical, biological and psychological. ...As an opening for his talks, he would sometimes recount one of his favourite stories on time. It concerned the Russian poet Samuel Marshak, on a visit to London before 1914. Marshak's English was not too good and when he asked a man in the street "Please, what is time?", he received the surprised response, "But that's a big question. Why ask me?"
    • "Professor Gerald Whitrow," The Telegraph (15 June 2000)

External links[edit]

  • New Scientist Vol. 2, No. 35 (Jul 18, 1957) includes "Why the Sun Shines" by Dr. G.J.Whitrow
  • New Scientist Vol. 2, No. 47 (Oct 10, 1957) includes "Newton and the Stars" by Dr. G.J.Whitrow
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