Natural Philosophers

"Quaternions came from Hamilton after his really good work had been done, and though beautifully ingenious, have been an unmixed evil to those who have touched them in any way."

"There cannot be a greater mistake than that of looking superciliously upon the practical applications of science. The life and soul of science is its practical application; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind."

"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be."

"In Galileo's time, professors of philosophy and theology—the subjects were inseparable—produced grand discourses on the nature of reality... all based on sophisticated metaphysical arguments. Meanwhile, Galileo measured how fast balls roll down inclined planes. How mundane! But the learned discourses, while grand, were vague. Galileo's investigations were clear and precise. The old metaphysics never progressed, while Galileo's work bore abundant, and at length spectacular, fruit. Galileo too cared about the big questions, but he realized that getting the genuine answers requires patience and humility before the facts."

"The worst that happened to men of science was that Galileo suffered an honorable detention and a mild reproof, before dying peacefully in his bed."

"As a believing scientist [...] it is my deep conviction that it is our task to search nature and the universe, as Galileo Galilei, the father of modern science, did, for the footprints of God."

"How does the world recognizes England, the United Kingdom, as the country that gave birth to the modern age? It was not Newton but Galilei who opened the Moderna age."

"The way in which the persecution of Galileo has been remembered is a tribute to the quiet commencement of the most intimate change in outlook which the human race had yet encountered. Since a babe was born in a manger, it may be doubted whether so great a thing has happened with so little stir."

"[T]he mathematical habit of mind and the mathematical procedure... had to be generated; otherwise Newton could never have thought of a formula representing the force between any two masses at any distance. ...Throughout the middle ages, under the influence of Aristotle, the science was entirely misconceived. Newton had the advantage of coming after a series of great men, notably Galileo... who in the previous two centuries had reconstructed the science and had invented the right way of thinking about it. He completed their work."

"The old Greek philosophy, which in Europe in the later middle ages was synonymous with the works of Aristotle, considered motion as a thing for which a cause must be found: a velocity required a force to produce and to maintain it. The great discovery of Galileo was that not velocity, but acceleration requires a force. This is the law of inertia of which the real content is: the natural phenomena are described by differential equations of the second order."

"To give us the science of motion God and Nature have joined hands and created the intellect of Galileo."

"The allusion to the "puzzling" problem of [the orbit of] Mars shows that Galileo ought not to have been unaware of the great work of Kepler published in 1609: Astronomia nova... in which the first two of Kepler's laws were formulated. Yet he does not mention here at all Kepler's success in solving the problem, nor his laws, nor his name even, which is brought up... only to criticize his belief in the Moon's attraction [effect upon tides], which is quite reasonably presented in the Astronomia nova and founded on astronomical reasons and not on mystical speculations."

"If Galileo had been willing to face the idea of a plurality of worlds, instead of resting on that of the Sun as the natural "centre of things," he might have been impelled to develop his system in the Newtonian sense. ...The position of the satellites in the Copernican scheme proved the existence of a multiplicity of centers. But the way that led from there was fraught with danger."

"Galileo's head was on the block... The crime was looking up for truth... And then you had to bring up reincarnation... How long 'til my soul gets it right... Can any human being ever reach that kind of light... I call on the resting soul of Galileo... King of night vision, king of insight... I'm not making a joke, you know me...I take everything so seriously... If we wait for the time 'til all souls get it right... Then at least I know there'll be no nuclear annihilation... Can any human being ever reach the highest light... Except for Galileo — God rest his soul... Except for the resting soul of Galileo... King of night vision, king of insight."

"How do heavy bodies fall? ...Galileo's investigation of dynamics was physical; Aristotle's was metaphysical. But unlike Galileo, we have the additional convenience of algebraic notation. Had it been invented in his day he would certainly have known it; almost certainly he would have been able to push his development of dynamics much farther."

"It was in Galileo's time that firearms were invented... What is the path of a cannonball? ...Characteristically, Galileo was engrossed with the problem; characteristically, he solved it. The outcome of his ingenuity we know today as the method of superposition."

"Galileo's comprehension of the concept of acceleration, which he defined as a change of velocity either in magnitude or direction... was an abstract idea that no one seems to have thought much about before. And in using it to test the still accepted Aristotelian precept that a moving object requires a force to maintain it, Galileo easily demonstrated that it is not motion but rather acceleration which cannot occur without an external force. Deliberately rejecting common sense as a prejudiced witness, he let nature herself speak in the form of a "hard, smooth and very round ball" rolling down a "very straight" ideal groove lined with polished parchment, and then rolling up another groove, clocking each roll "hundreds or times"... he showed that, while downward motion (helped by gravity force) makes speed increase and upward motion (hindered by gravity force) makes speed decrease, there is always a "boundary case" in between... where speed remains constant (without any appreciable force)—and that, by reducing friction, this boundary case can be made to approach a horizontal level where gravity has no effect. Similarly testing... he also drafted a law of falling bodies: "that the distances traversed, during equal intervals of time... stand to one another in the same ratio as the odd numbers beginning with unity." And his beautiful analysis of a cannonball's trajectory into horizontal and vertical components... was one day to be of enormous help to Isaac Newton in solving the riddle of gravity."

"History can be helpful in making sense of the world we live in. It can also be fascinating, even fun. How can even the best novelist or playwright invent someone like Augustus Caesar or Catherine the Great, Galileo or Florence Nightingale? How can screenwriters create better action stories or human dramas than exist, thousand upon thousand, throughout the many centuries of recorded history? There is a thirst out there both for knowledge and to be entertained, and the market has responded with enthusiasm."

"He endeavoured to determine the resistance of a beam, one end of which is built into a wall, when the tendency to break it arises from its own or an applied weight; and he concluded that the beam tends to turn about an axis perpendicular to its length, and in the plane of the wall. This problem, and, in particular, the determination of this axis is known as Galileo's problem."

"The first mathematician to consider the nature of the resistance of solids to rupture was Galileo. Although he treated solids as inelastic, not being in possession of any law connecting the displacements produced with the forces producing them, or of any physical hypothesis capable of yielding such a law, yet his enquiries gave the direction which was subsequently followed by many investigators."

"Galileo deduced the laws of freely falling bodies and the parabolic paths of projectiles, initiating an era of applications of mathematics to physics. In his book Two New Sciences, he used indivisible methods to study the motion of a falling body, and he planned, but never wrote, an entire book on indivisibles."

"Galileo's program offers us a dead world: Out go sight, sound, taste, touch, and smell, and along with them have since gone esthetic and ethical sensibility, values, quality, soul, consciousness, spirit. Experience as such is cast out of the realm of scientific discourse. Hardly anything has changed our world more during the past four hundred years than Galileo's audacious program. We had to destroy the world in theory before we could destroy it in practice."

"Copernicus, Kepler and Galileo were ‘revisionists’ in rejecting the geocentric system of Ptolemy (which held sway for some 1500 years) and, against an oppressive and repressive mainstream opinion (and officialdom), reinstated—with improvements—the heliocentric system of Aristarchos of Samos (3rd cent BCE)."

"A light was kindled amongst the investigators of nature when Galilei let balls of a definite weight roll down the inclined plane. For they saw that they only understand what is produced according to a predetermined plan or hypothesis... for otherwise planless observations made according to no ideas could never be brought into the form of a law which reason demands and seeks. ...Thus physics was brought into the position of a certain science after groping about blindly for so many hundred years."

"The beginning of astronomy, except observations, I think is not to be derived from farther time than from Nicolaus Copernicus; who in the age next preceding the present revived the opinion of Pythagoras, Aristarchus, and Philolaus. After him, the doctrine of the motion of the earth being now received, and a difficult question thereupon arising concerning the descent of heavy bodies, Galileus in our time, striving with that difficulty, was the first that opened to us the gate of natural philosophy universal, which is the knowledge of the nature of motion. So that neither can the age of natural philosophy be reckoned higher than to him."

"Galileo was no idiot. Only an idiot could believe that science requires martyrdom — that may be necessary in religion, but in time a scientific result will establish itself."

"It has always hurt me to think that Galilei did not acknowledge the work of Kepler … That, alas, is vanity … You find it in so many scientists."

"Conclusions obtained by purely rational processes are, so far as Reality is concerned, entirely empty. It was because he recognized this, and especially because he impressed it upon the scientific world that Galileo became the father of modern physics and in fact of the whole of modern natural science."

"It is to the Italian astronomer, forced in old age by the Inquisition to turn aside from the more dangerous study of the machinery of the heavens, that we owe the first exposition of many of the problems of mechanics and statics, published... in 1638. Not only did Galileo put together whatever the sixteenth century had learned in the sciences affecting building construction, but from his study of the bending strength of a beam there dates a new branch of science—the theory of the strength of materials."

"I am certainly interested in a tribunal in which, for having used my reason, I was deemed little less than a heretic. Who knows but men will reduce me from the profession of a philosopher to that of historian of the Inquisition! But they behave to me in order that I may become the ignoramus and the fool of Italy..."

"After the publication of my dialogues, I was summoned to Rome by the Congregation of the holy Office, where, being arrived on the 10th of February 1633, I was subjected to the infinite clemency of that tribunal, and of the Sovereign Pontiff, Urban the Eighth; who, notwithstanding, thought me deserving of his esteem."

"I cannot sufficiently admire the eminence of those men's wits, that have received and held it to be true, and with the sprightliness of their judgments offered such violence to their own senses, as that they have been able to prefer that which their reason dictated to them, to that which sensible experiments represented most manifestly to the contrary. ...I cannot find any bounds for my admiration, how that reason was able in Aristarchus and Copernicus, to commit such a rape on their senses, as in despite thereof to make herself mistress of their credulity."

"Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows all. But with regard to those few which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty, for here it succeeds in understanding necessity, beyond which there can be no greater sureness."

"The sun, with all those planets revolving around it and dependent on it, can still ripen a bunch of grapes as if it had nothing else in the universe to do."

"Among all the great men who have philosophized about this remarkable effect, I am more astonished at Kepler than at any other. Despite his open and acute mind, and though he has at his fingertips the motions attributed to the earth, he nevertheless lent his ear and his assent to the moon's dominion over the waters, to occult properties, and to such puerilities."

"In the long run my observations have convinced me that some men, reasoning preposterously, first establish some conclusion in their minds which, either because of its being their own or because of their having received it from some person who has their entire confidence, impresses them so deeply that one finds it impossible ever to get it out of their heads. Such arguments in support of their fixed idea as they hit upon themselves or hear set forth by others, no matter how simple and stupid these may be, gain their instant acceptance and applause. On the other hand whatever is brought forward against it, however ingenious and conclusive, they receive with disdain or with hot rage — if indeed it does not make them ill. Beside themselves with passion, some of them would not be backward even about scheming to suppress and silence their adversaries."

"If you could see the earth illuminated when you were in a place as dark as night, it would look to you more splendid than the moon."

"If what we are discussing were a point of law or of the humanities, in which neither true nor false exists, one might trust in subtlety of mind and readiness of tongue and in the greater experience of the writers, and expect him who excelled in those things to make his reasoning most plausible, and one might judge it to be the best. But in the natural sciences, whose conclusions are true and necessary and have nothing to do with human will, one must take care not to place oneself in the defense of error; for here a thousand Demostheneses and a thousand Aristotles would be left in the lurch by every mediocre wit who happened to hit upon the truth for himself. Therefore, Simplicio, give up this idea and this hope of yours that there may be men so much more learned, erudite, and well-read than the rest of us as to be able to make that which is false become true in defiance of nature."

"I cannot without great astonishment — I might say without great insult to my intelligence — hear it attributed as a prime perfection and nobility of the natural and integral bodies of the universe that they are invariant, immutable, inalterable, etc., while on the other hand it is called a great imperfection to be alterable, generable, mutable, etc. For my part I consider the earth very noble and admirable precisely because of the diverse alterations, changes, generations, etc. that occur in it incessantly. If, not being subject to any changes, it were a vast desert of sand or a mountain of jasper, or if at the time of the flood the waters which covered it had frozen, and it had remained an enormous globe of ice where nothing was ever born or ever altered or changed, I should deem it a useless lump in the universe, devoid of activity and, in a word, superfluous and essentially non-existent. This is exactly the difference between a living animal and a dead one; and I say the same of the moon, of Jupiter, and of all other world globes. The deeper I go in considering the vanities of popular reasoning, the lighter and more foolish I find them. What greater stupidity can be imagined than that of calling jewels, silver, and gold "precious," and earth and soil "base"? People who do this ought to remember that if there were as great a scarcity of soil as of jewels or precious metals, there would not be a prince who would not spend a bushel of diamonds and rubies and a cartload of gold just to have enough earth to plant a jasmine in a little pot, or to sow an orange seed and watch it sprout, grow, and produce its handsome leaves, its fragrant flowers, and fine fruit. It is scarcity and plenty that make the vulgar take things to be precious or worthless; they call a diamond very beautiful because it is like pure water, and then would not exchange one for ten barrels of water. Those who so greatly exalt incorruptibility, inalterability, etc. are reduced to talking this way, I believe, by their great desire to go on living, and by the terror they have of death. They do not reflect that if men were immortal, they themselves would never have come into the world. Such men really deserve to encounter a Medusa's head which would transmute them into statues of jasper or of diamond, and thus make them more perfect than they are."

"To apply oneself to great inventions, starting from the smallest beginnings, is no task for ordinary minds; to divine that wonderful arts lie hid behind trivial and childish things is a conception for superhuman talents."

"It always seems to me extreme rashness on the part of some when they want to make human abilities the measure of what nature can do. On the contrary, there is not a single effect in nature, even the least that exists, such that the most ingenious theorists can arrive at a complete understanding of it. This vain presumption of understanding everything can have no other basis than never understanding anything. For anyone who had experienced just once the perfect understanding of one single thing, and had truly tasted how knowledge is accomplished, would recognize that of the infinity of other truths he understands nothing."

"I tell you that if natural bodies have it from Nature to be moved by any movement, this can only be circular motion, nor is it possible that Nature has given to any of its integral bodies a propensity to be moved by straight motion. I have many confirmations of this proposition, but for the present one alone suffices, which is this. I suppose the parts of the universe to be in the best arrangement, so that none is out of its place, which is to say that Nature and God have perfectly arranged their structure. This being so, it is impossible for those parts to have it from Nature to be moved in straight, or in other than circular motion, because what moves straight changes place, and if it changes place naturally, then it was at first in a place preternatural to it, which goes against the supposition. Therefore, if the parts of the world are well ordered, straight motion is superfluous and not natural, and they can only have it when some body is forcibly removed from its natural place, to which it would then return by a straight line, for thus it appears that a part of the earth does [move] when separated from its whole. I said "it appears to us," because I am not against thinking that not even for such an effect does Nature make use of straight line motion."

"Whence do you have it that the terrestrial globe is so heavy? For my part, either I do not know what heaviness is, or the terrestrial globe is neither heavy nor light, as likewise all other globes of the universe. Heaviness to me (and I believe to Nature) is that innate tendency by which a body resists being moved from its natural place and by which, when forcibly removed therefrom, it spontaneously returns there. Thus a bucketful of water raised on high and set free, returns to the sea; but who will say that the same water remains heavy in the sea, when being set free there, does not move?"

"Philosophy is written in this grand book, which stands continually open before our eyes (I say the 'Universe'), but can not be understood without first learning to comprehend the language and know the characters as it is written. It is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these one is wandering in a dark labyrinth."

"I would say here something that was heard from an ecclesiastic of the most eminent degree [probably Caesar Baronius]: "The intention of the Holy Ghost is to teach us how one goes to heaven, not how heaven goes.""

"I do not feel obliged to believe that the same God who has endowed us with senses, reason, and intellect has intended us to forgo their use and by some other means to give us knowledge which we can attain by them."

"Nature … is inexorable and immutable; she never transgresses the laws imposed upon her, or cares a whit whether her abstruse reasons and methods of operation are understandable to men. For that reason it appears that nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called in question (much less condemned) upon the testimony of biblical passages which may have some different meaning beneath their words. For the Bible is not chained in every expression to conditions as strict as those which govern all physical effects; nor is God any less excellently revealed in Nature's actions than in the sacred statements of the Bible."

"Copernicus never discusses matters of religion or faith, nor does he use argument that depend in any way upon the authority of sacred writings which he might have interpreted erroneously. ... He did not ignore the Bible, but he knew very well that if his doctrine were proved, then it could not contradict the Scriptures when they were rightly understood."

"To this end they make a shield of their hypocritical zeal for religion. They go about invoking the Bible, which they would have minister to their deceitful purposes. Contrary to the sense of the Bible and the intention of the holy Fathers, if I am not mistaken, they would extend such authorities until even in purely physical matters — where faith is not involved — they would have us altogether abandon reason and the evidence of our senses in favor of some biblical passage, though under the surface meaning of its words this passage may contain a different sense."

"Persisting in their original resolve to destroy me and everything mine by any means they can think of, these men are aware of my views in astronomy and philosophy. They know that as to the arrangement of the parts of the universe, I hold the sun to be situated motionless in the center of the revolution of the celestial orbs while the earth revolves about the sun. They know also that I support this position not only by refuting the arguments of Ptolemy and Aristotle, but by producing many counter-arguments; in particular, some which relate to physical effects whose causes can perhaps be assigned in no other way. In addition there are astronomical arguments derived from many things in my new celestial discoveries that plainly confute the Ptolemaic system while admirably agreeing with and confirming the contrary hypothesis."