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M Quotes

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All M Quotes

“Mathematically speaking, the probable (that in 6,000,000,000 throws with a regular six-sided die the die will come up proximately 1 ,000,000,000 times) and the improbable (that in six throws with the same die the one will come approximately up six times) are not different in kind, but only in frequency, whereby the more frequent appears a priori more probable. But the occasional occurrence of the improbable does not imply the intervention of a higher power, something in the nature of a miracle, as the layman is so ready to assume. The term "probability" includes improbability at the extreme limits of probability, and when the improbable does occur this is no cause for surprise, bewilderment or mystification. Cf. Ernst Mally's Probability and Law, Hans Reichenbach The theory Probability, Whitehead and Russell's Principia Mathematica, von Mises' Probability, Statistics and Truth”

“Mathematicians are beginning to view order and chaos as two distinct manifestations of an underlying determinism. And neither state exists in isolation. The typical system can exist in a variety of states, some ordered, some chaotic. Instead of two opposed polarities, there is a continuous spectrum. As harmony and discord combine in musical beauty, so order and chaos combine in mathematical [and physical] beauty.”

“Mathematicians are proud of the fact that, generally, they do their work with a piece of chalk and a blackboard. They value hand-done proofs above all else. A big question in mathematics today is whether or not computational proofs are legitimate. Some mathematicians won't accept computational proofs and insist that a real proof must be done by the human hand and mind, using equations.”

“Mathematicians call it “the arithmetic of congruences.” You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o’clock, and you add 9 hours, what do you get? Well, you get five o’clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ≡ 5 (mod 12), pronounced “eight plus nine is congruent to five, modulo twelve.”

“Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.”

“Mathematicians have sought knowledge in figures, Philosophers in systems, Logicians in subtleties, and Metaphysicians in sounds. It is not in any nor in all of these. He that studies only men, will get the body of knowledge without the soul, and he that studies only books, the soul without the body.”

“Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.”

“Mathematicians need proofs to keep them honest. All technical areas of human activity need reality checks. It is not enough to believe that something works, that it is a good way to proceed, or even that it is true. We need to know why it's true. Otherwise, we won't know anything at all.”

“Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.”

“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don't happen to have all the data. In mathematics we have all the data, brought together in the full light of demonstration, and yet we don't understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”

“Mathematics and thought are ontologically the same thing. Have you understood? You are a thinking entity inhabiting a world created from thought. “God” doesn’t make the world out of nothing. God makes the world out of thought, his own thought. God is himself thought, and you yourself are an eternal, necessary node of God. This reality is just “God”, in all of his different monadic nodes, thinking about things and calculating the best answer to everything.”