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By convention sweet, by convention bitter, by convention hot, by
convention cold, by convention color, but in reality: atoms and
void.
-Democritus of Abdera I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the 'Law of Frequency of Error.'* The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement amidst the wildest confusion. The huger the mob and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of unreason. -Francis Galton *In modern terminology this is known as the central limit theorem. We see that the theory of probability is at bottom only common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by a sort of instinct, often without being able to account for it...It is remarkable that this science, which originated in the consideration of games of chance, should become the most important object of human knowledge...The most important questions of life are, for the most part, really only problems of probability. -Pierre Simon Marquis de Laplace If controversies were to arise there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, and say to each other: Let us calculate. -Gottfried Wilhelm Leibniz about his attempt at formalizing all reasoning Chance favors the prepared mind. -Louis Pasteur I would rather discover a single fact, even a small one, than debate the great issues at length without discovering anything new at all. -Galileo Galilei Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. -Paul Halmos The theory of computation has traditionally been studied almost entirely in the abstract, as a topic in pure mathematics. This is to miss the point of it. Computers are physical objects, and computations are physical processes. What computers can or cannot compute is determined by the laws of physics alone, and not by pure mathematics. -David Deutsch The whole is always more, is more capable of a much greater variety of wave states, than the combination of its parts. ... In this very radical sense, quantum physics supports the doctrine that the whole is more than the combination of its parts. -Hermann Weyl In mathematics you don't understand things. You just get used to them. -John von Neumann It is a profoundly erroneous truism, repeated by all copybooks, and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments. -Alfred North Whitehead In our acquisition of knowledge of the Universe (whether mathematical or otherwise) that which renovates the quest is nothing more nor less than complete innocence. It is in this state of complete innocence that we receive everything from the moment of our birth. Although so often the object of our contempt and of our private fears, it is always in us. It alone can unite humility with boldness so as to allow us to penetrate to the heart of things, or allow things to enter us and take possession of us. This unique power is in no way a privilege given to "exceptional talents" - persons of incredible brain power (for example), who are better able to manipulate, with dexterity and ease, an enormous mass of data, ideas and specialized skills. Such gifts are undeniably valuable, and certainly worthy of envy from those who (like myself) were not so "endowed at birth, far beyond the ordinary". Yet it is not these gifts, nor the most determined ambition combined with irresistible will-power, that enables one to surmount the "invisible yet formidable boundaries" that encircle our universe. Only innocence can surmount them, which mere knowledge doesn't even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child's play. -Alexander Grothendieck I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." -Godfrey Hardy on Ramanujan While walking along the street one day, the notoriously absent-minded mathematician David Hilbert encountered the physicist James Franck. "James," he asked, "is your wife as mean as mine?" Franck, taken aback by the question, asked poor Hilbert what his wife had done. "It was only this morning that I discovered quite by accident," Hilbert replied, "that my wife does not give me an egg for breakfast. Heaven knows how long that has been going on!" Back to Stephen Jordan's homepage. |