Historians Of Science

"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."

"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)."

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

"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."

"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."

"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."

"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."

"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."

"Not until the pioneer work of Rutherford and his colleagues was the possibility of nuclear reactions and transformations as sources of stellar energy envisaged."

"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."

"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."

"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..."

"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."

"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."

"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."

"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..."

"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."

"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 formulaM = \frac {m}{\sqrt{(1 - \frac {v^2}{c^2}}}"

"[Time is not] a mysterious illusion of the intellect. ..It is an essential feature of the universe."

"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."

"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, arex' = \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}}} 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 becomex' = x - vt ; \qquad t' = t."

"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."

"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."

"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."

"Strangely enough, many of the philosophical issues surrounding quantum mechanics are today being used to entice potential students into physics. As quantum computing and quantum communication become a commercial reality, tomorrow’s students may find themselves routinely grappling with the same philosophical questions that challenged their forebears almost a century ago."

"There has never been just one best way to teach quantum mechanics. My goal is neither to sow nostalgia for the philosophically engaged style of Oppenheimer and Nordheim, nor to condemn the pragmatic approach of Fermi, Bethe and Feynman. It is rather to highlight the choices that physicists must always make when stepping into the classroom. Choices of topics to discuss and problems to assign reflect deeper decisions about the ideal type of physicist one seeks to train. Should the new generation be philosophically attuned, concerned with minute details of conceptual interpretation? Or should physicists hone their ability to calculate, pushing Heisenberg’s and Schrödinger’s equations into the service of ever more elaborate problems to solve and phenomena to analyse? Competing ideals have flourished under different pedagogical conditions."

"We see for the first time in al-Jazari's work several concepts important for both design and construction: the lamination of timber to minimize warping, the static balancing of wheels, the use of wooden templates (a kind of pattern), the use of paper models to establish designs, the calibration of orifices, the grinding of the seats and plugs of valves together with emery powder to obtain a watertight fit, and the casting of metals in closed mold boxes with sand."

"A reference framework is required in order to locate events in time and space. With some contractions and omissions, Figure 1.1 shows the conventional divisions for the classical and medieval periods. Even before the birth of the idea of nationality, it is quite acceptable to refer to specific countries, such as Greece and Italy, whose boundaries are well defined. It is also usual to refer to areas in which there is felt to have been some degree of cultural unity —— for example, the Roman Empire and Islam. Sometimes space and time are embraced by one image: the Roman Empire can mean either the first four centuries of our era or the area under Roman dominion. Used with care, these concepts have value for some historical purposes, but they can be very misleading. In the first place, we have to bear in mind the shifting of frontiers; in AD 750, for example, the Iberian peninsula was predominantly Muslim while Asia Minor was Christian — by 1450 the reverse was the case. Also, and this can be more serious, the conventional divisions are associated most closely with political and military realities, and often have little bearing on intellectual or social activities."

"Indeed, in 1998, after the physicist Alan Sokal mocked humanists for delving into physics to support their ideas in a way that seemed ignorant at best and zany at worst – in what has come to be known as “Sokal’s hoax” – historian Mara Beller published an article in Physics Today entitled “The Sokal hoax: at whom are we laughing?”. She cited remarks by Bohr – but also by Heisenberg and Pauli – to make the point that in this respect physicists could sometimes be as zany as humanists, and there is no neat way to distinguish between the two."

"Like the deconstructionist Jacques Derrida, whom Steven Weinberg attacked in his 1996 New York Review of Books article on Sokal's hoax, Bohr was notorious for the obscurity of his writing. Yet physicists relate to Derrida's and Bohr's obscurities in fundamentally different ways: to Derrida's with contempt, to Bohr's with awe. Bohr's obscurity is attributed, time and again, to a "depth and subtlety" that mere mortals are not equipped to comprehend."

"Astonishing statements, hardly distinguishable from those satirized by Sokal, abound in the writings of Bohr; Heisenberg, Pauli, Born and Jordan. And they are not just casual, incidental remarks."

"While Einstein's belief in an objective reality is similar to that of Weinberg and Sokal, his arguments for his conception of reality are not. In fact, Einstein was no "naive realist," despite such caricaturing of his stand by the Copenhagen orthodoxy. He ridiculed the "correspondence" view of reality that many scientists accept uncritically. Einstein fully realized that the world is not presented to us twice-first as it is, and second, as it is theoretically described-so we can compare our theoretical "copy" with the "real thing." The world is given to us only once - through our best scientific theories. So Einstein deemed it necessary to ground his concept of objective reality in the invariant characteristics of our best scientific theories."

"By using only simple analogies and intuitively appealing, yet misleading, metaphorical images, Bohr established supposedly necessary connections between acausality, wave-particle duality and the impossibility of an objective unified description in the quantum domain. One needed no technical knowledge of quantum mechanics to read Bohr's operational analysis of mutually exclusive experimental arrangements consisting of bolts, springs, rods and diaphragms. While publicly abstaining from criticizing Bohr, many of his contemporaries did not share his peculiar insistence on the impossibility of devising new nonclassical concepts-an insistence that put rigid strictures on the freedom to theorize. It is on this issue that the silence of other physicists had the most far-reaching consequences. This silence created and sustained the illusion that one needed no technical knowledge of quantum mechanics to fully comprehend its revolutionary epistemological lessons. Many postmodernist critics of science have fallen prey to this strategy of argumentation and freely proclaimed that physics itself irrevocably banished the notion of objective reality."

"In an exchange several months after his New York Review of Books article, Weinberg admitted that the founders of quantum theory had been wrong in their "apparent subjectivism," and declared that "we know better now." What exactly do we know better now? Do we know better that one should not infer from the physical to the political realm and if yes, why? Or do we know better that the "orthodox" interpretation of quantum physics the one that confidently announced the final overthrow of causality and the ordinary conception of reality is not the only possible interpretation, and that, ultimately, it might not even be the surviving one?"

"The opponents of the postmodernist cultural studies of science condude confidently from the Sokal affair that "the emperors ... have no clothes." But who, exactly, are all those naked emperors? At whom should we be laughing?"

"We find ourselves in agreement with most of the points made in Mara Beller's article "The Sokal hoax: At whom are we laughing?". … Beller is right to point out that this quasi-religious attitude can arise in any field, even in physics. Thus, many physicists have for years blindly repeated Bohr's and Heisenberg's views on the foundations of quantum mechanics, without having a clear idea of what they meant. We are pleased to note that the grip of the so-called Copenhagen orthodoxy is weakening and that physicists are beginning to consider alternative views on foundational questions with an open mind."

"I read the Beller article in Physics Today. In fact, I’ve read several of her articles before: she writes very well. She of course has a point about Bohr’s intractable language; I’ve spent many hours myself trying to make some sense of it all. To the people with less patience than I, I’m sure it’s not obvious that they should struggle to find some meaning there. That’s exactly why someone has to get in and say something reasonable about (a modernday version of) the “Copenhagen interpretation” before things get out of hand."

"Shapin’s admirable essay misses, however, the point of Mara Beller’s piece in Physics Today (1998). Beller is not urging a more thoughtful attitude on physicists by pointing out that the wisdom of Bohr would sound like nonsense if it came from sociology or cultural studies. Quite the opposite. She is denouncing the great icons of quantum physics for uttering what she takes to be nonsense, and she is urging scientists to clean up their own act before they get on with the business of mocking others."

"Mara Beller has probably succeeded in making what may well be the first truly penetrating assessment of the Copenhagen interpretation of quantum mechanics. Physicists have been too much in awe of the mystique of their topic to have done anything comparable. [...] I am sorry if this role reversal of old and new is an anticlimactic answer to three quarter century of Copenhagen riddle. Mara Beller made me do it!"

"Kuhn had the genius to find the words and sketch the concepts that made important old philosophical problems relevant to the public and newly discussable by philosophers. He had the strength of mind and commitment to lead the discussion. He could speak the truly incommensurable languages of physics, philosophy, and history, all necessary to frame and advance his epistemological quest. He wrote, as one of his admirers, Margaret Masterman, put it, in a "quasi-poetic style," sometimes veiled, sometimes with "rhetorical exaggeration," but always after careful and even painful thought. Or, to switch metaphors, he drew the portrait of science in the manner of the Impressionists. At a distance, where most viewers stand, the portrait appears illuminating, persuasive, and inspiring; close in, where historians and philosophers stare, it looks sketchy, puzzling, and richly challenging."

"Kuhn's revolution was not yet a Kuhnian revolution, although he dated his intention to write the book that became Structure to the time of his wrestle with Aristotle. What he needed was a historical exemplar. He found it in the Copernican revolution."

"Structure joins the evocative concept of paradigm, a disarmingly simple dialectic of scientific change (long periods of paradigmatic "normal science" punctuated by short "revolutions"), and the apparent authority of historical example to show that major conceptual shifts in the natural sciences are effected not by logical argument alone but also by appeals to worldviews, religion, metaphysical commitments, notions of simplicity and order, and so on. The view that science, like other thought systems, advances or retreats through rhetoric and persuasion, not by logical necessity, was a revelation to people who had never practiced it or studied its history. The book comforted social scientists who wanted to assimilate their discipline to physics, Luddites who blamed social problems on scientists and engineers, and everyone who rejected authority. It repelled the philosophers of science at which it was aimed for the good reason that it undercut their belief that scientific knowledge advances by the application of rational criteria to the products of observation and experiment."

"The physicists of Gilbert's time had recourse to mechanism infrequently, and its effective explanations touched only a few disconnected phenomena. The virtuosity, inventiveness, and optimism of Descartes, however, and the counter-example of latter- day hermetists like Robert Fludd, persuaded many that mechanical models offered the only hope for a precise and comprehensible physics. Expectations rose. Physicists demanded more from models, perhaps even a complete fit with phenomena, with little or no negative analogy. Gilbert's countrymen , diplomat and philosopher, and Thomas Browne, physician diplomat and literateur, freed his watery humor objections of Cabeo by concocting it into an unctuous, elastic vapor. Such a vapor could allow Cabeo's rebounds, occasion the reattractions of ricocheting that Digby noticed, and — in its elastic contractions — draw the electric as well as the chaff. This last inference was first made about 1660, by the unconventional Cartesian fellow traveller , S.J., 'a veritable giant in science' and a liberal and candid physicist whenever his Society's obligation to combat Copernicans did interfer."

"In writing Newton's biography, I have attempted, in accordance with my understanding of biography as a literary form, to avoid composing an essay on Newtonian science. At the same time I have sought to make Newton the scientist the central character of my drama."

"The fact that the tragic story of Évariste Galois, the mathematical genius who burned brightly but all too briefly, is not as unusual as one might think among mathematicians of his and subsequent generations. It is, rather, the most famous and dramatic of an entire genre of mathematical stories that originated in the early decades of the nineteenth century but is still going strong today. Consider, for example... Niels Henrik Abel.. János Bolyai... Srinivasa Ramanujan... John Nash... Kurt Gödel... Alexander Grothendieck... Grigory Perelman... Among modern mathematicians, it seems, extreme eccentricity, mental illness, and even solitary death are not a matter of random misfortune. They are, rather... reserved only for the most outstanding members of the field."

"Catholics... believed that the grace of God was bestowed upon sinners only through the holy Church and its sacraments, enacted by an ordained priest. Protestants, conversely, believed in a "priesthood of all believers," meaning that God would bestow his grace directly upon them. Catholics believed that Christ was physically present in the bread and wine during the sacrament of the Mass. Protestants believed that Christ was either present everywhere (Luther) or that the Mass was a mere commemoration of his sufferings (Zwingli). Catholics believed that God would take into account a man's good works in this world in determining whether be saved or lost. Protestants believed that only faith and divine grace mattered. Catholics believed that the Bible required interpretation by the hierarchy and the traditions of the Church. Protestants believed that the Bible was a clear guide for righteous behavior, accessible to anyone. What these arguments had in common were that they were entirely inconclusive."

"Where the Jesuits insisted on clear and simple postulates, the new mathematicians relied on a vague intuition of the inner structure of matter, whereas the Jesuits celebrated absolute certainty, the new mathematicians proposed a method rife with paradoxes, and seemed to revel in them; and whereas the Jesuits sought to avoid controversy at all cost, the new method was mired in intractable controversies... It was everything that the Jesuits thought mathematics must never be, and yet it flourished... It was known as the method of indivisibles."

"...the whole point of studying and teaching mathematics was that it demonstrated how universal truth imposed itself upon the world—rationally, hierarchically, and inescapably. Ideally, the Jesuits believed, the truths of religion would be imposed on the world just like geometrical theorems, leaving no room for avoidance or denial by Protestant or other heretics and leading to the inevitable triumph of the Church."

"It was clear to Clavius that Euclid's method was successful in doing precisely what the Jesuits were struggling so hard to accomplish: imposing a true, eternal, and unchallengeable order upon a seemingly chaotic reality."

"Theological and philosophical disputes could rage forever, he Christopher Clavius] believed, because there was no universally accepted way to decide who was right and who was wrong. ...But mathematics was different: with mathematics, the truth forces itself upon its audience whether they like it or not. One could dispute the Catholic doctrine of the sacraments, but one could not deny the Pythagorean theorem; and no one could deny the correctness of the new calendar, based as it was on the detailed mathematical calculations."