People know, or dimly feel, that if thinking is not kept pure and keen, and if respect for the world of mind is no longer operative, ships and automobiles will soon cease to run right, the engineer's slide rule and the computations of banks and stock exchanges will forfeit validity and authority, and chaos will ensue.
Quotes about computations (14 Quotes)
If we suppose that many natural phenomena are in effect computations, the study of computer science can tell us about the kinds of natural phenomena that can occur.
It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
I am ashamed to tell you to how many figures I carried these computations, having no other business at the time.
I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.
GNOME, n. In North-European mythology, a dwarfish imp inhabiting the interior parts of the earth and having special custody of mineral treasures. Bjorsen, who died in 1765, says gnomes were common enough in the southern parts of Sweden in his boyhood, and he frequently saw them scampering on the hills in the evening twilight. Ludwig Binkerhoof saw three as recently as 1792, in the Black Forest, and Sneddeker avers that in 1803 they drove a party of miners out of a Silesian mine. Basing our computations upon data supplied by these statements, we find that the gnomes were probably extinct as early as 1764.
We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road we want to understand the idea of the proof, the deeper context.
No sociologist should think himself too good, even in his old age, to make tens of thousands of quite trivial computations in his head and perhaps for months at a time.
Computations are everywhere, once you begin to look at things in a certain way.
What we're saying is it's too close to call. There were a handful of tickets left, and we're trying to figure out where they were, if they were singles. Obviously, the computations, we want to make sure we're accurate. There were a handful of seats here and there.
I have just gone over my comet computations again, and it is humiliating to perceive how very little more I know than I did seven years ago when I first did this kind of work.
The theory of computation has traditionally been studied almost entirely in the abstract, as a topic in pure mathematics. This is to miss the point of it. Computers are physical objects, and computations are physical processes. What computers can or cannot compute is determined by the laws of physics alone, and not by pure mathematics.
The desire to economize time and mental effort in arithmetical computations, and to eliminate human liability to error is probably as old as the science of arithmetic itself.
One of the things that I've been doing recently in my scientific research is to ask this question: Is the universe actually capable of performing things like digital computations?