Discover the most popular and inspiring quotes and sayings on the topic of Computations. Share them with your friends on social media platforms like Facebook, Twitter, or your personal blogs, and let the world be inspired by their powerful messages. Here are the Top 100 Computations Quotes And Sayings by 91 Authors including Donna K. Fitch,Niklaus Wirth,Isaac Asimov,Guido Van Rossum,Raymond Louis Wilder for you to enjoy and share.
The program operates on facts, and extrapolates from those facts using a complex series of stochastic functions.
In the practical world of computing, it is rather uncommon that a program, once it performs correctly and satisfactorily, remains unchanged forever.
All that had been done in the mid-twentieth century on "calculating machines" had been upset by Robertson and his positronic brain-paths. The miles of relays and photocells had given way to the spongy globe of plantinumiridium about the size of a human brain. She
There was a project at Lawrence Livermore National Labs where many years ago they went down this path for scripting and controlling very large numerical calculations.
Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.
In accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.
Computable Numbers' into practice.21 This was
Nobody ever looks in the mirror and says, "Let's face it, I'm smarter than Gauss." And yet, in the last hundred years, the joined effort of all these dummies-compared-to-Gauss has produced the greatest flowering of mathematical knowledge the world has ever seen.
By all means, have you give great attention to your arithmetic, as its advantages are so many and important.
A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.
All physical systems can be thought of as registering and processing information, and how one wishes to define computation will determine your view of what computation consists of.
A new, a vast, and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible.
Numbers instill a feeling for the lie of the land, and furnish grist for the mathematical mill that is the physicist's principal tool.
The unreasonable efficiency of mathematics in science is a gift we neither understand nor deserve.
I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.
Pure mathematics, may it never be of any use to anyone.
It took me 1057 pages to describe the hundreds of mathematical equations, algorithms and programming techniques that I invented and used.
The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation.
The implied methods would permit construction of entirely new computers reduced in size and basic complexity by a factor of at least a thousand.
But we must not underestimate the potency of the mathematical process of abstraction. A surprising variety of things happen to have both magnitude and direction and to combine according to the parallelogram law; and many of them are not at all reminiscent of journeys.
As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise - by what course of calculation can these results be arrived at by the machine in the shortest time?
To DNA, our most complex programming projects are like pocket calculators.
Fake Math owes its existence to a number of things and people who have inspired and assisted this book on its way into the world.
Programmers are not mathematicians, no matter how much we wish and wish for it.
In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself, and for others, the most complicated issues of formulas and concepts.
Mathematicians come to the solution of a problem by the simple arrangement of the data, and reducing the reasoning to such simple operations, to judgments so brief, that they never lose sight of the evidence that serves as their guide.
I wanted to figure out how long to cook things. I did some experiments and then wrote a program using Mathematica to model how heat is transferred through food.
Transcendental [numbers], They transcend the power of algebraic methods.
People tend to think that mathematicians always work in sterile conditions, sitting around and staring at the screen of a computer, or at a ceiling, in a pristine office. But in fact, some of the best ideas come when you least expect them, possibly through annoying industrial noise.
Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.
It seems to be expected of every pilgrim up the slopes of the mathematical Parnassus, that he will at some point or other of his journey sit down and invent a definite integral or two towards the increase of the common stock.
Mathematics is not a careful march down a well cleared highway, but a journey into a strange wilderness, where the explorers often get lost.
A state-of-the-art calculation requires 100 hours of CPU time on the state-of-the-art computer, independent of the decade.
Lisp ... made me aware that software could be close to executable mathematics.
Among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other, and continues to fascinate me, is the structure hidden in mathematical things.
Mathematics takes us still further from what is human into the region of absolute necessity, to which not only the actual world, but ever possible world, must conform.
We cannot forbear suggesting one practical result which it appears to us must be greatly facilitated by the independent manner in which the engine orders and combines its operations: we allude to the attainment of those combinations into which imaginary quantities enter.
The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying.
Mathematical discoveries, like springtime violets in the woods, have their season which no man can hasten or retard.
Computing technology started out as number-crunching.
What promotes math progress even more than new ideas are new technical tools and habits of thought that encapsulate existing ideas, so that insights of one generation become the instincts of the next.
'You might think of combinatorics as a machine too', the major says. 'A different sort of machine, though. Have you heard of Babbage's analytic engine? He never built it ... I have an analytic machine of my own-right here.' He taps his own skull.
The purpose of computing is insight, not numbers.
This splendid subject [mathematics], queen of all exact sciences, and the ideal and norm of all careful thinking ...
If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.
Algebra applies to the clouds.
Pascal and C are special-purpose languages for manipulating the registers and memory of a von Neumann-style computer.
In the hands of Science and indomitable energy, results the most gigantic and absorbing may be wrought out by skilful combinations of acknowledged data and the simplest means.
One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.
When the difficulty of a problem lies only in finding out what follows from certain fixed premises, mathematical methods furnish invaluable wings for flying over intermediate obstructions.
[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.
Her calculations have always held the utmost accuracy, but mathematics alone will not be enough to guide her; she must learn to trust in chance and, if need be, in accident.
Computers are the central access; information processing based on a spiral network, similar to that which is the chaos of existence itself, the analysis of systems, the interlocking lokas.
I never calculate. That is why those who do, calculate so much less accurately than I.
The more progress physical sciences make, the more they tend to enter the domain of mathematics, which is a kind of centre to which they all converge. We may even judge the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.
Mathematical high culture collides with pop culture and all hell breaks loose! Harris takes us on a wild ride
never a dull moment!
One does not learn computing by using a hand calculator, but one can forget arithmetic. Perlis 1982
Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.
The Analytical Engine weaves algebraic patterns, just as the Jacquard loom weaves flowers and leaves.
The mathematical phenomenon always develops out of simple arithmetic, so useful in everyday life, out of numbers, those weapons of the gods: the gods are there, behind the wall, at play with numbers.
True technique will know how to maintain the illusion of liberty, choice, and individuality; but these will have been carefully calculated so that they will be integrated into the mathematical reality merely as appearances!
I can show you that the art of calculation has to do with odd and even numbers in their numerical relations to themselves and to each other.
I wish to God these calculations had been executed by steam,
After growing wildly for years, the field of computing appears to be reaching its infancy.
There is a largeness about mathematics that transcends race and time; mathematics may humbly help in the market-place, but it also reaches to the stars.
The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede.
To contribute usefully to the advance of science, one must sometimes not disdain from undertaking simple verifications.
Nets, grids, and other types of calculus.
Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.
A calculating engine is one of the most intricate forms of mechanism, a telegraph key one of the simplest. But compare their value.
Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.
The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
The aim of Mathematical Physics is not only to facilitate for the physicist the numerical calculation of certain constants or the integration of certain differential equations. It is besides, it is above all, to reveal to him the hidden harmony of things in making him see them in a new way.
At the present time there exist problems beyond our ability to solve, not because of theoretical difficulties, but because of insufficient means of mechanical computation.
It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50.
It is the mark of a great man that he puts to flight all ordinary calculations. He is at once sublime and touching, childlike and of the race of giants.
I have heard myself accused of being an opponent, an enemy of mathematics, which no one can value more highly than I, for it accomplishes the very thing whose achievement has been denied me.
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.
The object of the engine is in fact to give the utmost practical efficiency to the resources of numerical interpretations of the higher science of analysis, while it uses the processes and combinations of this latter.
Bill Frindall has done a bit of mental arithmetic with a calculator
The worst class of sum worked in the every-day world is cyphered by the diseased arithmeticians who are always in the rule of Subtraction as to the merits and successes of others, and never in Addition as to their own.
Courage is not a quality one normally associates with mathematicians. Yet it should apply to people who work in their attics in secret for seven years without cease on a problem that has eluded the greatest mathematical minds since first proposed in 1637.
An algorithm must be seen to be believed.
The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.
The mere formulation of a problem is far more essential than its solution, which may be merely a matter of mathematical or experimental skills. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science.
Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.
Do many calculations lead to victory, and few calculations to defeat
Mathematics is no more computation than typing is literature.
In order to make a perfect and beautiful machine, it is not requisite to know how to make it. All the works of human genius can be understood in the end to be products of a cascade of generate-and-test procedures that are, at bottom, algorithmic and mindless
One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems.
All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
Method is the arithmetic of success.
Examples ... which might be multiplied ad libitum, show how difficult it often is for an experimenter to interpret his results without the aid of mathematics.
This is a question too difficult for a mathematician. It should be asked of a philosopher(when asked about completing his income tax form)
Mathematics is not yet ready for such problems.
When modern physics exerts itself to establish the world's formula, what occurs thereby is this: the being of entities has resolved itself into the method of the totally calculable.
Over the centuries, monumental upheavals in science have emerged time and again from following the leads set out by mathematics.
The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.
Keep computations to the lowest level of the multiplication table.