Exactitude Quotes (8 quotes)
Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.
Art and science encounter each other when they seek exactitude.
I do not believe there is anything useful which men can know with exactitude that they cannot know by arithmetic and algebra.
It is better to teach the child arithmetic and Latin grammar than rhetoric and moral philosophy, because they require exactitude of performance it is made certain that the lesson is mastered, and that power of performance is worth more than knowledge.
Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.
The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wilderness lies in wait.
The theory of probabilities 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 have become the most important object of human knowledge.
We debase the richness of both nature and our own minds if we view the great pageant of our intellectual history as a compendium of new in formation leading from primal superstition to final exactitude. We know that the sun is hub of our little corner of the universe, and that ties of genealogy connect all living things on our planet, because these theories assemble and explain so much otherwise disparate and unrelated informationnot because Galileo trained his telescope on the moons of Jupiter or because Darwin took a ride on a Galápagos tortoise.