Astronomers from France

"On voit, par cet Essai, que la théorie des probabilités n'est, au fond, que le bon sens réduit au calcul; elle fait apprécier avec exactitude ce que les esprits justes sentent par une sorte d'instinct, sans qu'ils puissent souvent s'en rendre compte."

"Said the great and magnanimous Laplace: 'It is India that gave us the ingenious method of expressing all numbers by ten symbols, each receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.'"

""Les questions les plus importantes de la vie ne sont en effet, pour la plupart, que des problèmes de probabilité." Théorie analytique des probabilités, 1812."

"La dernière chose que nous attendions de vous, Général, est une leçon de géométrie !"

"Ce que nous connaissons est peu de chose, ce que nous ignorons est immense."

"L'homme ne poursuit que des chimères."

"Lisez Euler, lisez Euler, c'est notre maître à tous."

"Nature laughs at the difficulties of integration."

"Il est facile de voir que..."

"It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit.But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity."

"On demandait à Laplace quel était selon lui le plus grand mathématicien de l'Allemagne. C'est Pfaff, répondit-il. - Je croyais, reprit l'interlocuteur, que Gauss lui était supérieur. - Mais, s'écria Laplace, vous me demandez quel est le plus grand mathématicien de l'Allemagne, et Gauss est le plus grand mathématicien de l'Europe."

"The most important questions of life... are indeed for the most part only problems of probability. Strictly speaking it may even be said that nearly all our knowledge is problematical; and in the small number of things which we are able to know with certainty, even in the mathematical sciences themselves, the principal means for ascertaining truth—induction and analogy—are based on probabilities."

"Imaginary causes have gradually receded with the widening bounds of knowledge and disappear entirely before sound philosophy, which sees in them only the expression of our ignorance of the true causes."

"Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes. The human mind offers, in the perfection which it has been able to give to astronomy, a feeble idea of this intelligence. Its discoveries in mechanics and geometry, added to that of universal gravity, have enabled it to comprehend in the same analytical expressions the past and future states of the system of the world."

"All these efforts in the search for truth tend to lead it [the human mind] back continually to the vast intelligence... but from which it will always remain infinitely removed. This tendency peculiar to the human race is that which renders it superior... and their progress in this respect distinguishes nations and ages and constitutes their true glory."

"Let us recall that formerly, and at no remote epoch... all the unusual phenomena were regarded as so many signs of celestial wrath."

"The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought."

"It is to the influence of the opinion of those whom the multitude [the populous] judges best informed, and to whom it has been accustomed to give its confidence in regard to the most important matters of life, that the propagation of those errors is due, which in times of ignorance, have covered the face of the earth. Magic and astrology offer us two great examples. These errors... having for a basis only universal credence, have maintained themselves during a very long time; but at last the progress of science has destroyed them in the minds of enlightened men, whose opinion consequently has caused them to disappear... through the power of imitation and habit which had so generally spread them... This power, the richest resource of the moral world, establishes and conserves in a whole nation ideas entirely contrary to those... elsewhere... What indulgence ought we not then to have for opinions different from ours, when this difference often depends only upon the various points of view where circumstances have placed us! Let us enlighten those whom we judge insufficiently instructed; but first let us examine critically our own opinions, and weigh with impartiality, their respective probabilities."

"Whenever I meet in La Place with the words "Thus it plainly appears," I am sure that hours, and perhaps days, of hard study will alone enable me to discover how it plainly appears."

"Laplace made many important discoveries in mathematical physics... Indeed, he was interested in anything that helped to interpret nature. He worked on hydrodynamics, the wave propagation of sound, and the tides. In the field of chemistry, his work on the liquid state of matter is classic. His studies of the tension in the surface layer of water, which accounts for the rise of liquids inside a capillary tube, and of the cohesive forces in liquids, are fundamental. Laplace and Lavoisier designed an ice calorimeter (1784) to measure heat and measured the specific heat of numerous substances; heat, to them, was still a special kind of matter. Most of Laplace's life was, however, devoted to celestial mechanics."

"Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature."

"This is another important dispute in the history of how we think about being wrong: whether error represents an obstacle in the path toward truth, or the path itself. The former idea is a conventional one. The latter... emerged during the Scientific Revolution and continued to evolve throughout the Enlightenment. But it didn't really reach its zenith until the early nineteenth century, when... Pierre Simon Laplace refined the distribution of errors, illustrated by the now-familiar bell curve. ...Laplace used the bell curve to determine the precise orbit of the planets. ...By using the normal distribution to graph... individually imperfect data points, Laplace was able to generate a far more precise picture of the galaxy. ...aggregate enough flawed data, and you get a glimpse of the truth."

"Laplace had taken Newton's science and turned it into philosophy. The universe was a piece of machinery, its history was predetermined, there was no room for chance or for free will. The cosmos was indeed an ice-cold clock."

"With respect to the cohesion and of liquids, I have had the good fortune to anticipate Mr. Laplace in his late researches, and I have endeavoured to show, that my assumptions are more universally applicable to the facts, than those which that justly celebrated mathematician has employed."

"[Sire,] je n'ai pas eu besoin de cette hypothèse."

"The exchange is reported by Victor Hugo (who in turn was citing François Arago) as:"

"Comment, vous faites tout le système du monde, vous donnez les lois de toute la création et dans tout votre livre vous ne parlez pas une seule fois de l'existence de Dieu !"

"[Sire,] je n'avais pas besoin de cette hypothèse-là."

"Lagrange, also present (or to whom Napoleon repeated Laplace's reply, in another version), then commented: "Ah ! C’est une belle hypothèse; ça explique beaucoup de choses.""

"Wikipedia recounts research about this much-cited episode."

"I was often humiliated to see men disputing for a piece of bread, just as animals might have done. My feelings on this subject have very much altered since I have been personally exposed to the tortures of hunger. I have discovered, in fact, that a man, whatever may have been his origin, his education, and his habits, is governed, under certain circumstances, much more by his stomach than by his intelligence and his heart."

"On certain occasions, the eyes of the mind can supply the want of the most powerful telescopes, and lead to astronomical discoveries of the highest importance."

"The calculus of probabilities, when confined within just limits, ought to interest, in an equal degree, the mathematician, the experimentalist, and the statesman."

"The ancients had a taste, let us say rather a passion, for the marvellous, which caused them to forget even the sacred duties of gratitude. Observe them, for example, grouping together the lofty deeds of a great number of heroes, whose names they have not even deigned to preserve, and investing the single personage of Hercules with them. The lapse of ages has not rendered us wiser in this respect. In our own time the public delight in blending fable with history. In every career of life, in the pursuit of science especially, they enjoy a pleasure in creating Herculeses."

"Let us award a just, a brilliant homage to those rare men whom nature has endowed with the precious privilege of arranging a thousand isolated facts, of making seductive theories spring from them; but let us not forget to state, that the scythe of the reaper had cut the stalks before one had thought of uniting them into sheaves!"

"In the experimental sciences, the epochs of the most brilliant progress are almost always separated by long intervals of almost absolute repose."

"Tel est le privilége du génie : il aperçoit, il saisit des rapports, là où des yeux vulgaires lie voient que des faits isolés."

"The new and the old methods complete one another on numerous points, and their simultaneous use will increase our knowledge of the outer atmosphere of the Sun much more rapidly."

"Ce qui est familier aux savants de profession a grand besoin d'être mis dans le domaine commun."

"It would be easier to endow a fool with intellect than to persuade him that he had none."

"Les esprits partagés, s'égarant dans des routes différentes, perdent l'immense avantage qui résulterait de leurs forces réunies."

"The first step to be taken, is to study carefully the fundamental phenomenon above described, and to examine all the various circumstances under which it presents itself."

"Every measurable thing except numbers is imagined in the manner of a continuous quantity. Therefore, for the mensuration of such a thing, it is necessary that points, lines, and surfaces, or their properties, be imagined. For in them... measure or ratio is initially found... Therefore, every intensity which can be acquired successively ought to be imagined by a straight line perpendicularly erected on some point of the space or subject of the intensible thing, e.g., a quality... And since the quantity or ratio of lines is better known and is more readily conceived by us—nay the line is in the first species of continua, therefore such intensity ought to be imagined by lines... Therefore, equal intensities are designated by equal lines, a double intensity by a double line, and always in the same way if one proceeds proportionally."

"Since money belongs to the community … it would seem that the community may control it as it wills, and therefore may make as much profit from alteration as it likes, and treat money as its own property."

"I am of the opinion that the main and final cause why the prince pretends to the power of altering the coinage is the profit or gain which he can get from it."

"Whenever kingship approaches tyranny it is near its end, for by this it becomes ripe for division, change of dynasty, or total destruction, especially in a temperate climate … where men are habitually, morally and naturally free."

"People marvel at … things only because they rarely happen; but the causes for these are as apparent as for others … For example, at night a fearful man who sees a wolf in the fields, or a cat in his room, will immediately assert and judge that it is an enemy or a devil … because he fixes his imagination on these and fears them. And a person devout and rapt [in ecstasy] will judge that it is an angel … A vigorous imagining of a retained species, then, together with a small external appearance or with an imbalance of some internal disposition … produces marvelous appearances in healthy as well as in sick people."

"God in His infinite grandeur without any quantity and absolutely indivisible, which we call immensity, is necessarily all in every extension or space or place which exists or can be imagined."

"The heavenly bodies move with such regularity, orderliness, and symmetry that it is truly a marvel; and they continue always to act in this manner ceaselessly, following the established system, without increasing or reducing speed and continuing without respite, as the Scripture says: Summer and winter, night and day they never rest."

"It appears that here and there some of our modern ideas were anticipated by writers of the Middle Ages. Thus, Nicole Oresme... first conceived the notion of fractional powers, afterwards, rediscovered by Stevin, and suggested a notation [other than our modern notation]. Since 4^3 = 64 and 64^\frac{1}{2} = 8, Oresme concluded that 4^\frac{3}{2} = 8. Some of the mathematicians of the Middle Ages possessed some idea of a function. Oresme even attempted a graphic representation. But of a numeric dependence of one quantity upon another, as found in Descartes, there is no trace among them."

"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."

"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."

"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 lives very well upon flesh, you say, but, if he thinks this food to be natural to him, why does he not use it as it is, as furnished to him by Nature? But, in fact, he shrinks in horror from seizing and rending living or even raw flesh with his teeth, and lights a fire to change its natural and proper condition. … What is clearer than that man is not furnished for hunting, much less for eating, other animals? In one word, we seem to be admirably admonished by Cicero that man was destined for other things than for seizing and cutting the throats of other animals. If you answer that ‘that may be said to be an industry ordered by Nature, by which such weapons are invented,’ then, behold! it is by the very same artificial instrument that men make weapons for mutual slaughter. Do they this at the instigation of Nature? Can a use so noxious be called natural? Faculty is given by Nature, but it is our own fault that we make a perverse use of it."

"Gassendi, le meilleur philosophe des littérateurs et le meilleur littérateur des philosophes... [Gassendi, the greatest philosopher among literati and the greatest literato among philosophers...]"

"The ancient Greek philosopher, Democritus, propounded an hypothesis of the constitution of matter, and gave the name of atoms to the ultimate unalterable parts of which he imagined all bodies to be constructed. In the 17th century, Gassendi revived this hypothesis, and attempted to develope it, while Newton used it with marked success in his reasonings on physical phenomena; but the first who formed a body of doctrine which would embrace all known facts in the constitution of matter, was Roger Joseph Boscovich, of Italy, who published at Vienna, in 1759, a most important and ingenious work, styled Theoria Philosophiæ Naturalis ad unicam legem virium, in Natura existentium redacta. This is one of the most profound contributions ever made to science; filled with curious and important information, and is well worthy of the attentive perusal of the modern student. In more recent days, the theory of Boscovich has received further confirmation and extension in the researches of Dalton, Joule, Thomson, Faraday, Tyndall, and others."

"Boyle entertains the hypothesis of a universal matter, the concept of atoms of different shapes and sizes, and the possibility of existence of substances that might properly be called elements... The atomic theory as originally conceived by Democritus and Epicurus, developed by Lucretius, and resurrected by Gassendi from about 1647 on, was doubtless the source from which Boyle derived his ideas, ...as he cites both Epicurus and Gassendi. Boyle, however... avoids any dogmatic assertion of these hypotheses. It is plain, however, that these atoms or "corpuscles" as he calls them are a constant element of his thought."

"That Hindu astronomical lore about ancient times cannot be based on later back-calculation, was also argued by Playfair’s contemporary, the French astronomer jean-Sylvain Bailly: “The motions of the stars calculated by the Hindus before some 4500 years vary not even a single minute from the [modem] tables of Cassini and Meyer. The Indian tables give the same annual variation of the moon as that discovered by Tycho Brahe - a variation unknown to the school of Alexandria and also the Arabs.”"

"The Hindu systems of astronomy are by far the oldest, and that from which the Egyptians, Greeks, Romans, and even the Jews derived Hindus their knowledge."

"The motion of the stars calculated by the Hindus some 4500 years before vary not even a single minute from the modern tables of Cassini and Meyer."

"Even before Jones's announcement, Bailly stated that "the Brahmans are the teachers of Pythagoras, the instructors of Greece and through her of the whole of Europe" (51)."

"The astronomer and onetime mayor of Paris, Jean-Sylvain Bailly, in his Histoire de I'astronomie ancienne et moderne (1805), felt that "these tables of the Brahmana are perhaps five or six thousand years old" (53;). Bailly approved of the traditional date of the Kali Yuga, and seemed to have convinced at least some of his colleagues such as Laplace and Playfair of the accuracy of the Indian astronomical claims (Kay, [1924] 1981, 2). This was bitterly opposed by another astronomer, John Bentley ([1825] 1981), with a concern that we have seen was typical for the times: "If we are to believe in the antiquity of Hindu books, as he would wish us, then the Mosaic account is all a fable, or a fiction" (xxvii)."

"These observations must therefore have been made elsewhere, and one can hardly refuse to believe that they were made in India where the Chaldeans seem to have borrowed the first elements of their Astronomy."

"‘It follows, therefore, that the astronomers of Alexandria take from the Indians the primitive and fundamental knowledge of the theory of the moon.’"

"‘Mons. Bailly, the celebrated author of the History of Astronomy, may be regarded as beginning the concert of praises, upon this branch of the science of the Hindus. The grounds of his conclusions were certain astronomical tables; from which he inferred, not only advanced progress in the science, but a date so ancient as to be entirely inconsistent with the chronology of the Hebrew Scriptures. [...] Another cause of great distrust attaches to Mons. Bailly, Voltaire, and other excellent writers in France, abhorring the evils which they saw attached to catholicism, laboured to subvert the authority of the books on which it was founded. Under this impulse, they embraced [...] the tales respecting the great antiquity of the Chinese and Hindus as disproving, entirely, the Mosaic accounts of the duration of the present race of men. [...] The argument [...] by Mons. Bailly, was [...] for a time regarded as a demonstration in form of the falsehood of Christianity.’"