# Zitate von Gerald James Whitrow

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## Gerald James Whitrow

Geburtstag: 9. Juni 1912
Todesdatum: 2. Juni 2000

Gerald James Whitrow was a British mathematician, cosmologist and science historian.

### „From this exiguous basis, formulae of gravitation more accurate than those of Newton have been derived.“

The Structure of the Universe: An Introduction to Cosmology (1949)
Kontext: 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...

### „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)
Kontext: 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).

### „Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century.“

"Why Physical Space has Three Dimensions," British Journal for the Philosophy of Science, 6 #21 (May 1955)
Kontext: 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).

### „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)
Kontext: 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.

### „The development of rational thought actually seems to have impeded man's appreciation for the significance of time.“

Time in History: Views of Time from Prehistory to the Present Day (1988)
Kontext: 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.<!--p.22

### „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“

The Structure of the Universe: An Introduction to Cosmology (1949)
Kontext: 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...

### „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 Structure of the Universe: An Introduction to Cosmology (1949)
Kontext: 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.<!--p.46

### „Man must have been conscious of memories and purposes long before he made any explicit distinction between past, present, and future.“

Time in History: Views of Time from Prehistory to the Present Day (1988)
Kontext: Man must have been conscious of memories and purposes long before he made any explicit distinction between past, present, and future.<!--21

### „Language itself inevitably introduced an element of permanence into the world.“

Time in History: Views of Time from Prehistory to the Present Day (1988)
Kontext: 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.<!--p.22

### „It must have required enormous effort for man to overcome his natural tendency to live like the animals in a continual present.“

Time in History: Views of Time from Prehistory to the Present Day (1988)
Kontext: It must have required enormous effort for man to overcome his natural tendency to live like the animals in a continual present.<!--p.22

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### „Another interesting feature of the Einstein universe is that in principle it could be circumnavigated by a ray of light.“

The Structure of the Universe: An Introduction to Cosmology (1949)
Kontext: 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.<!--p.79

### „To obtain a greater degree of permanence the time symbols of oral speech had to be converted into the space symbols of written speech.“

Time in History: Views of Time from Prehistory to the Present Day (1988)
Kontext: 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...<!--p.22

### „He saw that this process demanded a fourth dimension which he rejected“

"Why Physical Space has Three Dimensions," British Journal for the Philosophy of Science, 6 #21 (May 1955)
Kontext: 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).

### „The models of Einstein and de Sitter are static solutions“

The Structure of the Universe: An Introduction to Cosmology (1949)
Kontext: 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 &lambda;, 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.<!--p.82

### „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)
Kontext: 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.

### „Cosmology is peculiar among the sciences for it is both the oldest and the youngest.“

"Theories of the Universe" (10 Apr 1958)
Kontext: 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.

### „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.“

The Structure of the Universe: An Introduction to Cosmology (1949)
Kontext: 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 &lambda;, 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.<!--p.82

### „Minkowski made a remarkable discovery“

The Structure of the Universe: An Introduction to Cosmology (1949)
Kontext: 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.<!--p.64

### „[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)

### „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<nowiki>'</nowiki> units of length and t<nowiki>'</nowiki> units of time, respectively. Then the Lorentz formulae, relating x<nowiki>'</nowiki> to t<nowiki>'</nowiki>, are<center>$x' = \frac {x-vt}{\sqrt{1-\frac{v^2}{c^2}}} ; \qquad t' = \frac {t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}$</center>
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<center>$x' = x - vt ; \qquad t' = t$</center>.
The Structure of the Universe: An Introduction to Cosmology (1949)

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