Compute Quotes (14 quotes)
Computed Quotes, Computing Quotes
Computed Quotes, Computing Quotes
First you guess. Dont laugh, this is the most important step. Then you compute the consequences. Compare the consequences to experience. If it disagrees with experience, the guess is wrong. In that simple statement is the key to science. It doesnt matter how beautiful your guess is or how smart you are or what your name is. If it disagrees with experience, its wrong. Thats all there is to it.
For me, the first challenge for computing science is to discover how to maintain order in a finite, but very large, discrete universe that is intricately intertwined. And a second, but not less important challenge is how to mould what you have achieved in solving the first problem, into a teachable discipline: it does not suffice to hone your own intellect (that will join you in your grave), you must teach others how to hone theirs. The more you concentrate on these two challenges, the clearer you will see that they are only two sides of the same coin: teaching yourself is discovering what is teachable.
In a library we are surrounded by many hundreds of dear friends, but they are imprisoned by an enchanter in these paper and leathern boxes; and though they know us, and have been waiting two, ten, or twenty centuries for us,some of them,and are eager to give us a sign and unbosom themselves, it is the law of their limbo that they must not speak until spoken to; and as the enchanter has dressed them, like battalions of infantry, in coat and jacket of one cut, by the thousand and ten thousand, your chance of hitting on the right one is to be computed by the arithmetical rule of Permutation and Combination,not a choice out of three caskets, but out of half a million caskets, all alike.
It may be true, that as Francis Thompson noted, Thou canst not stir a flower without troubling a star, but in computing the motion of stars and planets, the effects of flowers do not loom large. It is the disregarding of the effect of flowers on stars that allows progress in astronomy. Appropriate abstraction is critical to progress in science.
Mathematics, like dialectics, is an organ of the inner higher sense; in its execution it is an art like eloquence. Both alike care nothing for the content, to both nothing is of value but the form. It is immaterial to mathematics whether it computes pennies or guineas, to rhetoric whether it defends truth or error.
Of habitable worlds, such as the Earth, all which we may suppose to be of a terrestrial or terraqueous nature, and filled with beings of the human species, subject to mortality, it may not be amiss in this place to compute how many may he conceived within our finite view every clear Star-light night. In all together then we may safely reckon 170,000,000, and yet be much within compass, exclusive Of the Comets which I judge to be by far the most numerous part of the creation.
One may be a mathematician of the first rank without being able to compute. It is possible to be a great computer without having the slightest idea of mathematics.
Only six electronic digital computers would be required to satisfy the computing needs of the entire United States.
The human brain became large by natural selection (who knows why, but presumably for good cause). Yet surely most things now done by our brains, and essential both to our cultures and to our very survival, are epiphenomena of the computing power of this machine, not genetically grounded Darwinian entities created specifically by natural selection for their current function.
The object of geometry in all its measuring and computing, is to ascertain with exactness the plan of the great Geometer, to penetrate the veil of material forms, and disclose the thoughts which lie beneath them? When our researches are successful, and when a generous and heaven-eyed inspiration has elevated us above humanity, and raised us triumphantly into the very presence, as it were, of the divine intellect, how instantly and entirely are human pride and vanity repressed, and, by a single glance at the glories of the infinite mind, are we humbled to the dust.
The purpose of computing is insight, not numbers. [But] sometimes the purpose of computing numbers is not yet in sight.
The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didnt bother to remember things. He computed them. You asked him a question, and if he didnt know the answer, he thought for three seconds and would produce and answer.
Two of his [Eulers] pupils having computed to the 17th term, a complicated converging series, their results differed one unit in the fiftieth cipher; and an appeal being made to Euler, he went over the calculation in his mind, and his decision was found correct.
We [Irving Kaplansky and Paul Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free , but when the chips are down we close the office door and compute with matrices like fury.