All Quotes

"The one book that turned out to be perhaps the most influential in guiding Newton's mathematical and scientific thought was none other than Descartes' La Géométrie. Newton read it in 1664 and re-read it several times until "by degrees he made himself master of the whole." ...Not only did analytic geometry pave the way for Newton's founding of calculus... but Newton's inner scientific spirit was truly set ablaze."

"By... confounding the properties of matter with those of space he arrives at the logical conclusion, that if the matter within a vessel could be entirely removed the space within the vessel would no longer exist. In fact he assumes that all space must be always full of matter."

"The primary property of matter was indeed distinctly announced by Descartes in what he calls the "First Law of Nature": "That every individual thing, so far as in it lies, perseveres in the same state, whether of motion or of rest.""

"Descartes... fell back on his original confusion of matter with space—space being, according to him, the only form of substance, and all existing things but affections of space. This error... forms one of the ultimate foundations of the system of Spinoza."

"The first and typical example of the application of mathematics to the indirect investigation of truth, is within the limits of the pure science itself; the application of algebra to geometry, the introduction of which, far more than any of his metaphysical speculations, has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences. Its rationale is simple. It is grounded on the general truth, that the position of every point, the direction of every line, and consequently the shape and magnitude of every enclosed space, may be fixed by the length of perpendiculars thrown down upon two straight lines, or (when the third dimension of space is taken into account) upon three plane surfaces, meeting one another at right angles in the same point. A consequence or rather a part of this general truth is that, curve lines and surfaces may be determined by their equations."

"As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition."

"Noli turbare circulos meos. or Noli tangere circulos meos."

"How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!"

"Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible."

""Do you know who first explained the true origin of the rainbow?" I asked. "It was Descartes," he said. After a moment he looked me in the eye. "And what do you think was the salient feature of the rainbow that inspired Descartes' mathematical analysis?" he asked. "Well, the rainbow is actually a section of a cone that appears as an arc of the colors of the spectrum when drops of water are illuminated by sunlight behind the observer." "And?" "I suppose his inspiration was the realization that the problem could be analyzed by considering a single drop, and the geometry of the situation." "You're overlooking a key feature of the phenomenon," he said. "Okay, I give up. What would you say inspired his theory?" "I would say his inspiration was that he thought rainbows were beautiful." I looked at him sheepishly. He looked at me. "How's your work coming?" he asked. I shrugged. "It's not really coming." I wished I was like Constantine. It all came so easily to him. "Let me ask you something. Think back to when you were a kid. For you, that isn't going too far back. When you were a kid, did you love science? Was it your passion?" I nodded. "As long as I can remember." "Me, too," he said. "Remember, it's supposed to be fun." And he walked on."

"Descartes ... is distinguished from Bacon in respect of the thoroughness of his education in the Scholastic philosophy and in the profound impression that geometrical demonstration had upon his mind, and the effect of these differences in education and inspiration is to make his formulation of the technique of inquiry more precise and in consequence more critical. His mind is oriented towards the project of an infallible and universal method or research, but since the method he propounds is modelled on that of geometry, its limitation when applied, not to possibilities but to things, is easily apparent. Descartes is more thorough than Bacon in doing his scepticism for himself and, in the end, he recognizes it to be an error to suppose that the method can ever be the sole means of inquiry. The sovereignty of technique turns out to be a dream and not a reality. Nevertheless, the lesson his successors believed themselves to have learned from Descartes was the sovereignty of technique and not his doubtfulness about the possibility of an infallible method."

"I would inquire of reasonable persons whether this principle: Matter is naturally wholly incapable of thought, and this other: I think, therefore I am, are in fact the same in the mind of Descartes, and in that of St. Augustine, who said the same thing twelve hundred years before. ...I am far from affirming that Descartes is not the real author of it, even if he may have learned it only in reading this distinguished saint; for I know how much difference there is between writing a word by chance without making a longer and more extended reflection on it, and perceiving in this word an admirable series of conclusions, which prove the distinction between material and spiritual natures, and making of it a firm and sustained principle of a complete metaphysical system, as Descartes has pretended to do. ...it is on this supposition that I say that this expression is as different in his writings from the saying in others who have said it by chance, as in a man full of life and strength, from a corpse."

"Descartes subscribed to the doctrine of instantaneous propagation, but with him something new emerged: for his was the first uncompromisingly mechanical theory that asserted the instantaneous propagation of light in a material medium... Indeed, mechanical analogies had been used to explain optical phenomena long before Descartes, but the Cartesian theory was the first clearly to assert that light itself was nothing but a mechanical property of the luminous object and of the transmitting medium. It is for this reason that we may regard Descartes' theory of light as legitimate starting point of modern physical optics."

"In the theory of the state of the seventeenth century, the monarch is identified with God and has in the state a position exactly analogous to that attributed to God in the Cartesian system of the world."

"Descartes is rightly regarded as the father of modern philosophy primarily and generally because he helped the faculty of reason to stand on its own feet by teaching men to use their brains in place whereof the Bible, on the one hand, and Aristotle, on the other, had previously served."

"Descartes may have made a lot of mistakes, but he was right about this: you cannot doubt the existence of your own consciousness. That's the first feature of consciousness, it's real and irreducible. You cannot get rid of it by showing that it's an illusion in a way that you can with other standard illusions."

"Modesty was not a condition from which Descartes suffered."

"Descartes's so-called dualism is often taken to represent a fundamental revolution in ideas and the starting point of modern philosophy. ...but in substance his work is... better understood as an attempt to conserve the old truths in the face of new threats. His dualism was in essence an armistice... between the established religion and the emerging science of his time. ...isolating the mind from the physical world... ensured that many of the central doctrines of orthodoxy—immortality of the soul, the freedom of will, and, in general, the "special" status of humankind—were rendered immune to any possible contravention by the scientific investigation of the physical world. ... For men such as Descartes, Malebranche, and Leibniz, solving the mind-body problem was vital to preserving the theological and political order inherited from the Middle Ages... For Spinoza, it was a means of destroying that same order and discovering a new foundation for human worth."

"Descartes... clearly understood the power of algebraic methods in geometry. He wanted to withhold this power from his contemporaries, however, particularly... Roberval... La Géométrie was written to boast about his discoveries, not to explain them. There is little systematic development, and proofs are frequently omitted with a sarcastic remark such as, "I shall not stop to explain... because I should deprive you of the pleasure...""

"[E]arly analytic geometers—Descartes in particular—did not accept that geometry could be based on numbers or algebra. Perhaps the first to take the idea of arithmetizing geometry seriously was Wallis..."

"Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance."

"Algebra had already been applied to geometry by other writers, as we have seen. The wholly new contribution made by Descartes was in importing the idea of motion into geometry. It is said that the idea came to him while lying in bed and watching the movements of a fly crawling near an angle of the room. He saw that its position at any moment could be defined by its perpendicular distance from the ceiling and two adjacent walls. Thus he saw a curve as described by a moving point, the point being the point of intersection of two moving lines which were always parallel to two fixed lines at right angles. As the moving point described the curve, its distances from the two fixed axes would vary in a manner characteristic of the curve, and an equation between these distances could be formed which would express some property of the curve. Algebraical transformations of this equation would then reveal other properties of the curve."

"How you picked your hypotheses (he argued) was of no importance whatever... even if picked at random. ...[A] hypothesis was to be judged by its fruits. ...Descartes' analogy between code-breaking and theory-making is excellent."

"It was left up to Newton to compute the detailed implications of the vortex-theory... and the result demolished the foundations of Descartes' cosmology."

"Houston, we have a problem"

""Kismet Hardy / Kiss me, Hardy" – British Vice Admiral Horatio Nelson"

""The only thing necessary for the triumph of evil is for good men to do nothing" – Edmund Burke"

""We don't need no steenking badges!" – Bandit in The Treasure of the Sierra Madre"

"Spare the rod, spoil the child"

""Crisis? What crisis?" – British Prime Minister James Callaghan"

"Sometimes a cigar is just a cigar."

"Show me a young Conservative and I'll show you someone with no heart. Show me an old Liberal and I'll show you someone with no brains."

"I woke up this mornin' and I got myself a beer."

"Hold you in his armchair, you can feel his disease."

"Let them eat cake."

"You want the truth? You can't handle the truth!"

"Hello, Clarice."

"Well, here's another fine mess you've gotten me into"

"I'm out of order? You're out of order! This whole court's out of order!"

"I am the devil, and I have come to do the devil's work."

"Music hath/has charms to soothe the savage beast."

"Only the Dead have seen the end of War."

"A rose by any other name smells just as sweet."

"Where art thou Romeo?"

"If you build it, they will come"

"'Step into my parlor,' said the spider to the fly."

"Brain: An apparatus with which we think we think"

"Nul points"

""Mirror, mirror, on the wall..." – The Queen in Snow White and the Seven Dwarfs"

"Fe-Fi-Fo-Fum, I smell the blood of an Englishman, Be him alive or be he dead, I'll grind his bones to make my bread."