Physicists From France

"Nicole Oresme introduced the important concept of graphical representations, or geometrical "configurations", of intensities of qualities. ...He proposes to measure the intensity of the quality at each point of the reference interval by a perpendicular line segment at that point, thereby constructing a graph with the reference interval as its base. ...He refers to the reference interval as its longitude, and its intensity at a point as its latitude or altitude there (perhaps adapting these terms from their geographical use). ...Oresme... provided the Merton Rule with a geometrical verification."

"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)."

"Coordinates had been used in astronomy and geography since ... Oresme called his coordinates "longitude" and "latitude," but he seems to have been the first to use them to represent functions such as velocity as a function of time. Setting up the coordinates before determining the curve was Oresme's step beyond the Greeks, but he too lacked the algebra to go further."

"The experimental investigation by which Ampère established the law of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the 'Newton of electricity.' It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics."

"Écoute les savants, mais ne les écoute que d'une oreille!... Que l'autre soit toujours prête à recevoir les doux accents de la voix de ton ami céleste!"

"Either one or the other [ analysis or synthesis ] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion."

"There is synthesis when, in combining therein judgments that are made known to us from simpler relations, one deduces judgments from them relative to more complicated relations. There is analysis when from a complicated truth one deduces more simple truths."

"Great physicists fight great battles."

"For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view."

"... en matière scientifique, on a souvent des prédécesseurs beaucoup plus anciens qu'on ne le pense a priori."

"Le vrai point d'honneur [d'un scientifique] n'est pas d'être toujours dans le vrai. Il est d'oser, de proposer des idées neuves, et ensuite de les vérifier."

"Benjamin Franklin performed a beautiful experiment using surfactants; on a pond at Clapham Common, he poured a small amount of oleic acid, a natural surfactant which tends to form a dense film at the water-air interface. He measured the volume required to cover all the pond. Knowing the area, he then knew the height of the film, something like three nanometers in our current units. This was to my knowledge the first measurement of the size of molecules. In our days, when we are spoilt with exceedingly complex toys, such as nuclear reactors or synchrotron sources, I particularly like to describe experiments of this Franklin style to my students. Surfactants allow us to protect a water surface, and to generate these beautiful soap bubbles, which are the delight of our children."

"A dense film of a conventional surfactant is quite impermeable. On the other hand, a dense film of Janus grains always has some interstices between the grains, and allows for chemical exchange between the two sides; "the skin can breathe". This may possibly be of some practical interest."

"The final lines are not mine: they come from an experiment on soft matter, after Boudin… An English translation might run like this:"

"Lastly, and doubtless always, but particularly at the end of the last century, certain scholars considered that since the appearances on our scale were finally the only important ones for us, there was no point in seeking what might exist in an inaccessible domain. I find it very difficult to understand this point of view since what is inaccessible today may become accessible tomorrow (as has happened by the invention of the microscope), and also because coherent assumptions on what is still invisible may increase our understanding of the visible."

"Il y avait un nombre important de questions que je m'étais posées et, comme vous le savez, lorsqu'on se pose vraiment les questions, on donne de meilleures réponses que si l'on se contente de lire les réponses convenues."

"At the age of 25, not having learnt anything at school nor from book, enthusiastic about science but not about study, Léon Foucault took on the task of making the work of scientists understandable to the public and of passing judgement on the value to the work of leading men of science. From the start he showed great subtlety, good judgement based on more prudence than would be expected. His first articles were remarkable; they were spiritual. He took his duties seriously. Launched, without any experience, into the highest level of science with all its confusion and problems, he was assured carrying out a role in which mediocrity would mean failure, with complete success. … Always polite, yet seeking the truth, Foucault applied carefully considered judgements. Previously an unknown, this young man with no scientific publications nor known scientific discoveries, displayed a quiet authority and frankness which irritated many leading scientists."

"The phenomenon develops calmly, but it is invisible, unstoppable. One feels, one sees it born and grow steadily; and it is not in one's power to either hasten it or slow it down. Any person, brought into the presence of this fact, stops for a few moments and remains pensive and silent; and then generally leaves, carrying with him forever a sharper, keener sense of our incessant motion through space."

"To contribute usefully to the advance of science, one must sometimes not disdain from undertaking simple verifications."

"May those men who are animated by the true scientific spirit cease to believe that they are obliged to consider only subjects of public utility; ...because, one must not hide it, the field of applications, so rich and fertile today, would not take long to be blighted by sterility if it ceased to be fertilized and revivified by the beneficial light which theoretical research radiates and pours incessantly upon it."

"Above all, we must be accurate, and it is an obligation which we intend to fulfill scrupulously."

"You are invited to come to see the Earth turn, tomorrow, from three to five, at Meridian Hall of the Paris Observatory."

"Ceux qui passent toujours par les mêmes chemins, voyent ordinairement toujours les mêmes objets; il est rare qu'à force de suivre différentes routes, on ne découvre de nouveaux sujets dignes de nos attentions les plus sérieuses. De même les différentes tentatives nous font avoir un plus grand nombre de connaissances. En essayant donc différentes clefs, on peut espérer d'en rencontrer enfin qui nous ouvriront les passages assurés, courts et faciles pour arriver aux richesses de la Physique."

"The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict with quantum mechanics and with facts established by experiment."

"Science doesn’t give authentically access to the Real in the ontological meaning of the word, but only to the links between phenomena."

"Si on veut faire quelque chose, il faut donc s'occuper d'éducation."

"History of science played a very important role for me. Before I knew well how to do an experiment, I knew why Joliot has missed the neutron, why his wife missed the fission, why they succeeded in having artificial radioactivity, and even why they almost missed the other things, by doing very nice experiments, but didn't come to the conclusion. That is science. Science is doubt, is research. It is not something which is – and that is the danger of teaching – which is too academic and which the people explain you it is like the logic thing that comes out of the computer, which is not true. You have intuition, you have passion."

"When a change occurs in Nature, the quantity of action necessary for that change is as small as possible."

"The quantity of action is the product of the mass of the bodies times their speed and the distance they travel. When a body is transported from one place to another, the action is proportional to the mass of the body, to its speed and to the distance over which it is transported."

"After so many great men have worked on this subject, I almost do not dare to say that I have discovered the universal principle upon which all these laws are based, a principle that covers both elastic and inelastic collisions and describes the motion and equilibrium of all material bodies. This is the principle of least action, a principle so wise and so worthy of the supreme Being, and intrinsic to all natural phenomena; one observes it at work not only in every change, but also in every constancy that Nature exhibits. In the collision of bodies, motion is distributed such that the quantity of action is as small as possible, given that the collision occurs. At equilibrium, the bodies are arranged such that, if they were to undergo a small movement, the quantity of action would be smallest. The laws of motion and equilibrium derived from this principle are exactly those observed in Nature. We may admire the applications of this principle in all phenomena: the movement of animals, the growth of plants, the revolutions of the planets, all are consequences of this principle. The spectacle of the universe seems all the more grand and beautiful and worthy of its Author, when one considers that it is all derived from a small number of laws laid down most wisely. Only thus can we gain a fitting idea of the power and wisdom of the supreme Being, not from some small part of creation for which we know neither the construction, usage, nor its relationship to other parts. What satisfaction for the human spirit in contemplating these laws of motion and equilibrium for all bodies in the universe, and in finding within them proof of the existence of Him who governs the universe!"

"According to Du Bois Reymond, Maupertuis's teleological tendencies showed themselves early in his career in speculations as to what grounds the Creator could have had for preferring the law of the inverse square to all other possible laws of attraction. ... Maupertuis read to the Paris Academy on the 20th of February, 1740, a memoir entitled: "Loi du Repos des Corps." He began by remarking that demonstrations a priori of such principles as that of the conservation of vis viva "cannot apparently be given by physics; they seem to belong to some higher science." ... Maupertuis's first enunciation of the law of the least quantity of action was in a memoir read to the French Academy on April 15th, 1744, entitled "Accord de différentes Loix de la Nature qui avoient jusqu'ici paru incompatibles." The laws in question appear to be those of the reflection and of the refraction of light. When a ray of light in a uniform medium travels from one point to another, either without meeting an obstacle or with meeting a reflecting surface, nature leads it by the shortest path and in the shortest time. But when a ray is refracted by passing from a uniform medium to one of different density, the ray neither describes the shortest space nor does it take the shortest time about it. As Fermat showed, the time would be the shortest if light moved more quickly in rarer media, but Newton proved that, as Descartes had believed, light moves more quickly in denser media. Maupertuis's discovery was that light neither takes always the shortest path nor always that path which it describes in the shortest time, but "that for which the quantity of action is the least.""

"After having worked in the theory of light and gravitation, he announced, in 1744, a new minimum principle, the Principle of Least Action, from which he claimed he could deduce the behavior of light and masses in motion. The principle asserts that nature always behaves so as to minimize an integral known technically as action, and amounting to the integral of the product of mass, velocity, and distance traversed by a moving object. From this principle he deduced the Newtonian laws of motion. With sometimes suitable and sometimes questionable interpretation of the quantities involved, Maupertuis managed to show that optical phenomena, too, could be deduced from this principle. Hence, to an extent at least, he succeeded in uniting the optics of the eighteenth century and mechanical phenomena. ... Maupertuis advocated his principle for theological reasons. ...He ...proclaimed his principle to be not only a universal law of nature but also the first scientific proof of the existence of God, for it was "so wise a principle as to be worthy only of a Supreme Being."

"Research into motion was not to the liking (or perhaps not within the scope) of the ancients, so that we may consider it as a completely new science. How could the ancients have discovered the laws of moiton, given that some philosophers reduced all their speculations about motion to sophistic disputes, whereas others denied that motion existed at all?"

"Maupertuis really had no principle, properly speaking, but only a vague formula, which was forced to do duty as the expression of different familiar phenomena not really brought under one conception. ...Maupertuis' performance, though it had been unfavorably criticized by all mathematicians, is, nevertheless, sort of invested with a sort of historical halo. It would seem almost as if something of the pious faith of the church had crept into mechanics. However, the mere endeavor to gain a more extensive view... was not altogether without results. Euler, at least, if not also Gauss, was stimulated by the attempt of Maupertuis."

"A true philosopher does not engage in vain disputes about the nature of motion; rather, he wishes to know the laws by which it is distributed, conserved or destroyed, knowing that such laws is the basis for all natural philosophy."

"The elements that make up all other bodies, these must be bodies that are perfectly inelastic, undeformable and unchangeable."

"The supreme Being is everywhere; but He is not equally visible everywhere. Let us seek Him in the simplest things, in the most fundamental laws of Nature, in the universal rules by which movement is conserved, distributed or destroyed; and let us not seek Him in phenomena that are merely complex consequences of these laws."

"One should not be deceived by philosophical works that pretend to be mathematical, but are merely dubious and murky metaphysics. Just because a philosopher can recite the words lemma, theorem and corollary doesn't mean that his work has the certainty of mathematics. That certainty does not derive from big words, or even from the method used by geometers, but rather from the utter simplicity of the objects considered by mathematics."

"Everything is so arranged that the blind logic of mathematics executes the will of the most enlightened and free Mind."

"It is only mental habit that prevents us from realizing how miraculous it is that motion can be passed from one body to another. Once our eyes have opened, nothing is so striking. For those who have never thought about it, it doesn't seem mysterious; by contrast, those who have meditated on it may despair of ever understanding it."

"Having discovered the true principle, I then derived all the laws that govern the motion of light, those concerning its direct propagation, its reflection and its refraction. I reserve for particular members of our Assembly the geometrical demonstration of my theory. I know the distaste that many mathematicians have for final causes applied to physics, a distaste that I share up to some point. I admit, it is risky to introduce such elements; their use is dangerous, as shown by the errors made by Fermat and Leibniz in following them. Nevertheless, it is perhaps not the principle that is dangerous, but rather the hastiness in taking as a basic principle that which is merely a consequence of a basic principle."

"The refraction of light agrees with the grand principle that Nature always uses the simplest means to accomplish its effects. From this principle, can be derived whenever light passes from one medium to another, the ratio of the sine of the angle of refraction to the sine of the angle of refraction equals the inverse ratio of the speeds at which light moves in each medium. But this "budget", this expense of action that Nature minimizes in the refraction of light, is it also minimized in the direct propagation and reflection of light? Yes, it always has the smallest possible value."

"Let us calculate the motion of bodies, but also consult the plans of the Intelligence that makes them move. It seems that the ancient philosophers made the first attempts at this sort of science, in looking for metaphysical relationships between numbers and material bodies. When they said that God occupies himself with geometry, they surely meant that He unites in that science the works of His power with the perspectives of His wisdom. From the all too few ancient geometers who undertook such studies, we have little that is intelligible or well-founded. The perfection which geometry has acquired since their time puts us in a better position to succeed, and may more than compensate for the advantages that those great minds had over us."

"After meditating deeply on this topic, it occurred to me that light, upon passing from one medium to another, has to make a choice, whether to follow the path of shortest distance (the straight line) or the path of least time. But why should it prefer time over space? Light cannot travel both paths at once, yet how does it decide to take one path over another? Rather than taking either of these paths per se, light takes the path that offers a real advantage: light takes the path that minimizes its action."

"Now I have to define what I mean by "action". When a material body is transported from one point to another, it involves an action that depends on the speed of the body and on the distance it travels. However, the action is neither the speed nor the distance taken separately; rather, it is proportional to the sum of the distances travelled multiplied each by the speed at which they were travelled."

"On the 15th of April 1744, I described the principle upon which the following work is based, in the public assembly of the Royal Academy of Sciences of Paris, as reported in the Acts of that academy. At the end of the same year, Professor Euler published his excellent book Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes. In a supplement to his book, this illustrious geometer showed that, in the trajectory of a particle acted on by a central force, the velocity multiplied by the line element of the trajectory is minimized. This observation gave me great pleasure, as a beautiful application of my principle to the motion of the planets, which is determined by this principle. From the same principle, I will now try to derive higher and more important truths."

"The most beautiful discoveries since the Renaissance, indeed since the beginnings of all science, are the laws governing light, whether moving through a uniform medium, or being reflected from an opaque surface, or changing direction upon entering another transparent medium."

"May we not say that, in the fortuitous combination of the productions of Nature, since only those creatures could survive in whose organizations a certain degree of adaptation was present, there is nothing extraordinary in the fact that such adaptation is actually found in all these species which now exist? Chance, one might say, turned out a vast number of individuals; a small proportion of these were organized in such a manner that the animals' organs could satisfy their needs. A much greater number showed neither adaptation nor order; these last have all perished.... Thus the species which we see today are but a small part of all those that a blind destiny has produced."

"The ancient Greeks knew the laws that govern the propagation of light in a uniform medium and upon its reflection. However, the law governing the refraction of light as it passes from one transparent medium to another was unknown until the last century. Snell discovered it, Descartes tried to explain it and Fermat criticized his explanation. Since then, many great geometers have researched the problem, although no one has yet found a way of harmonizing the law of refraction with more fundamental laws that Nature must obey."

"The first law is the same for both light and material bodies; they both move in a straight line, as long as they are not deflected by an outside force. The second law is also the same as that governing the reflection of an elastic ball from an impenetrable surface. Mechanics shows that such a ball is reflected from such a surface so that its angle of reflection equals its angle of incidence, as observed for light. But the third law still requires a plausible explanation. The passage of light from one medium to another exhibits behavior that is totally different from a ball moving through different media."