Quotes About Mathematical

According to one story, Von Neumann was asked to assist with the design of a new supercomputer, required to solve a new and important mathematical problem which was beyond the capacities of existing supercomputers. He asked to have the problem explained to him, solved it in moments with pen and paper and then turned down the request. Von

in the arena of economic policy, the citizens of today's democracies have learned altogether too much modesty. We have been advised that these are matters for experts: that economics and its policy implications are far beyond the understanding of the common man or woman—a point of view enforced by the increasingly arcane and mathematical language of the discipline.

Numbers were originally abstractions, invented just to quantify things, to count rocks or people or grapes or whatever. The fact that dust floating in the air & the price of stock options behave according to the same mathematical principles, the fact that everything in the universe apparently can be described or predicted with a mathematical equation-a radical idea when Pythagoras suggested it- is probably the most startling coincidence in the history of mankind.

Dullards would have you believe that once you have eliminated the impossible, whatever remains, however improbable, must be the truth... but to a mathematical mind, the impossible is simply a theorem yet to be solved. We must not eliminate the impossible, we must conquer it, suborn it to our purpose.

Perhaps the rivers of ink that have been expended discussing the nature of the "continuous" over the centuries, from Aristotle to Heidegger, have been wasted. Continuity is only a mathematical technique for approximating very finely grained things. The world is subtly discrete, not continuous. The good Lord has not drawn the world with continuous lines: with a light hand, he has sketched it in dots, like the painter Georges Seurat.

Our entire current technology is founded on the use of a physical thing-electromagnetic waves-that was not discovered empirically: it was predicted by Maxwell, simply by searching for the mathematical description accounting for the intuition Faraday got from bobbins and needles. This is the outstanding power of theoretical physics.

Loop theory describes this atomic and granular quantum structure of space in a precise mathematical form. It is obtained by applying the general equations of quantum mechanics written by Dirac to Einstein's gravitational field. In particular, loop theory specifies that volume (for example the volume of a given cube) cannot be arbitrarily small. A minimum volume exists. No space smaller than this minimum volume exists. There is a minimum "quantum" of volume: an elementary atom of space.

In quantum mechanics no object has a definite position, except when colliding headlong with something else. In order to describe it in mid-flight, between one interaction and another, we use an abstract mathematical formula that has no existence in real space, only in abstract mathematical space.

Performance cannot be based on one assessment. You cannot determine the slope of a line given only one point, as there is no line to begin with. A single point in time does not show trends, improvement, lack of effort, or mathematical ability.… Sincerely,

Performance cannot be based on one assessment. You cannot determine the slope of a line given only one point, as there is no line to begin with. A single point in time does not show trends, improvement, lack of effort, or mathematical ability….

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

Steenrod was a careful, methodical man who chose his suits and sports coats according to a mathematical formula and had a mania for thinking up highly logical, if impractical, solutions to social problems like crime.

Other mathematical geniuses, Einstein and Bertrand Russell among them, recount similarly revelatory experiences in early adolescence.

I did what I could to inflate the rumor I was on my way to stardom. What I was on my way to, by any mathematical standards known to man, was oblivion, by way of obscurity.

Her concentration was gone, and last night she had had a nightmare about discovering a formalism that let her translate arbitrary concepts into mathematical expressions: then she had proven that life and death were equivalent.

Her concentration was gone, and last night she had had a nightmare about discovering a formalism that let her translate arbitrary concepts into mathematical expressions: then she had proven that life and death were equivalent. That was something that frightened her: the possibility that she was losing her mind. She was certainly losing her clarity of thought, and that came pretty close.

I've always had a more spatial mind, mathematical, than literal.

If you had to give a name to the whole apparatus, what would you call it?" "Hmmm," Waterhouse says. "Well, its basic job is to perform mathematical calculations—like a computer." Comstock snorts. "A computer is a human being." "Well . . . this machine uses binary digits to do its computing. I suppose you could call it a digital computer." Comstock writes it out in block letters on his legal pad: DIGITAL COMPUTER.

Nowadays he is best remembered for the Fibonacci sequence of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21 . . .), in which each successive number is the sum of the previous two, and the ratio between a number and its immediate antecedent tends towards a 'golden mean' (around 1.618). It

trade. They wrote down their history and had discovered a 365-day calendar that was more accurate than its European counterparts. One particular society—the Mayan—had also managed to come up with that beautiful concept of zero to which I alluded earlier, and without which mathematical computation is very difficult. It may

from the idea of nature as a "fixed" and harmonious order that can be subjected to classification and mathematical description to an idea of nature that is run through with continual transformations, something that is living and historicized even while it works according to recognizable laws and is animated by recognizable forces.

Cold calculation, random spots of color, mathematically exact construction (clearly shown or concealed), drawing that is now silent and now strident.... Is this not form?"

I studied space dynamics, in all its phases, Gaean economics, the mathematical basis of trans-dimensional propulsion. I am familiar with Handbook to the Planets and Gaean Cosmography. In short, I am not just another dilettante! I am anxious to apply my knowledge to useful purposes.

the new discipline of physics could not proceed until Isaac Newton appropriated words that were ancient and vague—force, mass, motion, and even time—and gave them new meanings. Newton made these terms into quantities, suitable for use in mathematical formulas. Until then, motion (for example) had been just as soft and inclusive a term as information.