Philosophers From France

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

"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!"

"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."

"It is interesting to note that Newton was not impressed by Descartes' great argument for God's existence derived from the idea of a perfect Being, nor by other metaphysical arguments that we have mentioned; yet Newton's own arguments for God's existence from the uniformity and suitability of different parts of the universe would not have seemed like proofs to Descartes."

"Despite the disorder observed in Nature, one finds enough traces of the wisdom and power of its Author that one cannot fail to recognize Him."

"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."

"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 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."

"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 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."

"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."

"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."

"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."

"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."

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

"We cannot doubt that all things are regulated by a supreme Being, who, while he has imprinted on matter forces which show his power, has destined it to execute effects which mark his wisdom... Let us calculate the motion of bodies, but let us also consult the designs of the Intelligence which makes them move."

"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."

"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."

"I must now explain what I mean by the quantity of action. A certain action is necessary for the carrying of a body from one point to another: this action depends on the velocity which the body has and the space which it describes; but it is neither the velocity nor the space taken separately. The quantity of action varies directly as the velocity and the length of path described; it is proportional to the sum of the spaces, each being multiplied by the velocity with which the body describes it. It is this quantity of action which is here the true expense (dépense) of nature, and which she economizes as much as possible in the motion of light."

"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."

"Nature always uses the simplest means to accomplish its effects."

"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?"

"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."

"As the reflections of our pride upon our defects are bitter, disheartening, and vexatious, so the return of the soul towards God is peaceful and sustained by confidence. You will find by experience how much more your progress will be aided by this simple, peaceful turning towards God, than by all your chagrin and spite at the faults that exist in you."

"We sleep in peace in the arms of God when we yield ourselves up to His providence, in a delightful consciousness of His tender mercies; no more restless uncertainties, no more anxious desires, no more impatience at the place we are in, for it is God who has put us there, and who holds us in His arms. Can we be unsafe where He has placed us, and where He watches over us as a parent watches a child? This confiding repose, in which earthly care sleeps, is the true vigilance of the heart; yielding itself up to God, with no other support than Him, it thus watches while we sleep. This is the love of Him that will not sleep even in death."

"Commit yourself then to God! He will be your guide. He Himself will travel with you, as we are told He did with the Israelites, to bring them step by step across the desert to the promised land. Ah! what will be your blessedness, if you will but surrender yourself into the hands of God, permitting Him to do whatever He will, not according to your desires, but according to His own good pleasure?"

"Here it is that the Spirit teaches us all truth; for all truth is eminently contained in this sacrifice of love, where the soul strips itself of every thing to present it to God."

"There is but one way in which God should be loved, and that is to take no step except with Him and for Him, and to follow with a generous self-abandonment every thing which He requires."

"O God, the creature knows not to what end Thou hast made Him; teach him, and write in the depths of his soul that the clay must suffer itself to be shaped at the will of the potter."

"If we love Him infinitely more than we do ourselves, we make an unconditional sacr"

"Pure love is in the will alone; it is no sentimental love, for the imagination has no part in it; it loves, if we may so express it, without feeling, as faith believes without seeing."

"If there is any thing that can render the soul calm, dissipate its scruples, and dispel its fears, sweeten its sufferings by the anointing of love, impart strength to it in all its actions, and spread abroad the joy of the Holy Spirit in its countenance and words, it is a simple, free, and child-like repose in the arms of God."

"O Lord! take my heart, for I cannot give it; and when Thou hast it, O! keep it, for I cannot keep it for Thee; and save me in spite of myself, for Jesus Christ's sake."

"True love goes ever straight forward, not in its own strength, but esteeming itself as nothing. Then indeed we are truly happy. The cross is no longer a cross when there is no self to suffer under it."

"If we love Him infinitely more than we do ourselves, we make an unconditional sacrifice of ourselves to His good pleasure, desiring only to love Him and to forget ourselves. He who thus loses his soul shall find it again with eternal life."

"Carefully purify your conscience from daily faults; suffer no sin to dwell in your heart; small as it may seem, it obscures the light of grace, weighs down the soul, and hinders that constant communion with Jesus Christ which it should be your pleasure to cultivate."

"We may be sure that it is the love of God only that can make us come out of self. If His powerful hand did not sustain us, we should not know how to take the first step in that direction."

"Thou lovest like an infinite God when Thou lovest; Thou movest heaven and earth to save Thy loved ones. Thou becomest man, a babe, the vilest of men, covered with reproaches, dying with infamy and under the pangs of the cross; all this is not too much for an infinite love."

"The presence of God calms the soul, and gives it quiet and repose."

"This is the love that does all things; that brings to pass even the evils we suffer; so shaping them that they are but instruments of preparing the good which, as yet, has not arrived."

"As a general rule, those truths which we highly relish, and which shed a degree of practical light upon the things which we are required to give up for God, are leadings of Divine grace, which we should follow without hesitation."

""My Father, it is dark!" "Child, take my hand, Cling close to me; I'll lead thee through the land, Trust my all-seeing care, so shalt thou stand 'Midst glory bright above." Can we be unsafe where God has placed us, and where He watches over us as a parent a child that he loves?"

"God works in a mysterious way in grace as well as in nature, concealing His operations under an imperceptible succession of events, and thus keeps us always in the darkness of faith."

"The kingdom of God which is within us consists in our willing whatever God wills, always, in every thing, and without reservation; and thus His kingdom comes; for His will is then done as it is in heaven, since we will nothing but what is dictated by His sovereign pleasure."

"We must bear our crosses; self is the greatest of them all. If we die in part every day of our lives, we shall have but little to do on the last. O how utterly will these little daily deaths destroy the power of the final dying!"

"This poor world, the object of so much insane attachment, we are about to leave; it is but misery, vanity, and folly; a phantom, — the very fashion of which "passeth away.""

"If we had strength and faith enough to trust ourselves entirely to God, and follow Him simply wherever He should lead us, we should have no need of any great effort of mind to reach perfection."

"A cross borne in simplicity, without the interference of self-love to augment it, is only half a cross. Suffering in this simplicity of love, we are not only happy in spile of the cross, but because of it; for love is pleased in suffering for the Well Beloved, and the cross which forms us into His image is a consoling bond of love."