Mathematics is much more than computation with pencil and a paper and getting answers to routine exercises. In fact, it can easily be argued that computation, such as doing long division, is not mathematics at all. Calculators can do the same thing and calculators can only calculate they cannot do mathematics.
John A. Van de Walle
Computation, after all, implied a problem not yet solved, insights not yet achieved. There was really only one sort of program for which foreknowledge of the outcome didn't diminish the point of exercise, and Bre¼ks had never been able to find any religious orders that described God as a porn addict.
In almost every computation a great variety of arrangements for the succession of the processes is possible, and various considerations must influence the selections amongst them for the purposes of a calculating engine. One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation.
When the aggregate amount of solid matter transported by rivers in a given number of centuries from a large continent, shall be reduced to arithmetical computation, the result will appear most astonishing to those...not in the habit of reflecting how many of the mightiest of operations in nature are effected insensibly, without noise or disorder.
Upon the present theological computation, ten souls must be lost for one that is saved. At which rate of reckoning, heaven can raise but its cohorts while hell commands its legions. From which sad account it would appear, that, though our Saviour had conquered death by the resurrection, he had not yet been able to overcome sin by the redemption.
Human beings are distinguished by a capacity for experience as well as by their behavior, and homosexuality is as much a matter ofemotion as of genital manipulation.... As we each examine our own sense of identity we realize how much more complex is the question of homosexuality than a mere Kinsey-like computation of orgasms.
Computation, storage, and communications capacity are in the hands of practically every connected person - and these are the basic physical capital means necessary for producing information, knowledge and culture, in the hands of something like 600 million to a billion people around the planet.
I spent 20 years doing research on regular and irregular verbs, not because I'm an obsessive language lover but because it seemed to me that they tapped into a fundamental distinction in language processing, indeed in cognitive processing, between memory lookup and rule-driven computation.
I suppose that Paderewski can play superbly, if not quite at his best, while his thoughts wander to the other end of the world, orpossibly busy themselves with a computation of the receipts as he gazes out across the auditorium. I know a great actor, a master technician, can let his thoughts play truant from the scene ...
Minnie Maddern Fiske
The Saviour said He was going to prepare us a place. How wonderful it will be is beyond human computation. Remember that in six days Christ made the heavens and earth and all that in them is.... If He made so many wonders in six days, then what beauties and marvels He has surely prepared during these 1900 years in which He has been preparing our mansions in the Father's House!
John R. Rice
As a peace machine, it's value to the world will be beyond computation. Would a declaration of war between Russia and Japan be made, if within an hour there after a swifty gliding aeroplane might take its flight from St Petersburg and drop half a ton of dynamite above the enemy's war offices? Could any nation afford to war upon any other with such hazards in view?
John Brisben Walker
We're presently in the midst of a third intellectual revolution. The first came with Newton: the planets obey physical laws. The second came with Darwin: biology obeys genetic laws. In today's third revolution, were coming to realize that even minds and societies emerge from interacting laws that can be regarded as computations. Everything is a computation.
The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.
I've been asked to explain why I don't worry much about the topics of privacy threat...One reason is that these scenarios seem to assume that there will be large, monolithic bureaucracies...that are capable of harnessing computers for one-way surveillance of an unsuspecting populace. I've come to feel that computation just doesn't work that way. Being afraid of monolithic organizations especially when they have computers, is like being afraid of really big gorillas especially when they are on fire.
Computers are good at swift, accurate computation and at storing great masses of information. The brain, on the other hand, is notas efficient a number cruncher and its memory is often highly fallible; a basic inexactness is built into its design. The brain's strong point is its flexibility. It is unsurpassed at making shrewd guesses and at grasping the total meaning of information presented to it.
Ladies are always of great use to the party they espouse, and never fail to win over numbers to it. Lovers, according to Sir William Petty's computation, make at least the third part of sensible men of the British nation; and it has been an uncontroverted maxim in all ages, that though a husband is sometimes a stubborn sort of a creature, a lover is always at the devotion of his mistress. By this means, it lies in the power of every fine woman, to secure at least half a dozen able-bodied men to his Majesty's service.
We couldn't build quantum computers unless the universe were quantum and computing. We can build such machines because the universe is storing and processing information in the quantum realm. When we build quantum computers, we're hijacking that underlying computation in order to make it do things we want: little and/or/not calculations. We're hacking into the universe.
Underlying our approach to this subject is our conviction that "computer science" is not a science and that its significance has little to do with computers. The computer revolution is a revolution in the way we think and in the way we express what we think. The essence of this change is the emergence of what might best be called procedural epistemology-the study of the structure of knowledge from an imperative point of view, as opposed to the more declarative point of view taken by classical mathematical subjects. Mathematics provides a framework for dealing precisely with notions of "what is". Computation provides a framework for dealing precisely with notions of "how to".
Thinking is computation, I claim, but that does not mean that the computer is a good metaphor for the mind. The mind is a set of modules, but the modules are not encapsulated boxes or circumscribed swatches on the surface of the brain. The organization of our mental modules comes from our genetic program, but that does not mean that there is a gene for every trait or that learning is less important than we used to think. The mind is an adaptation designed by natural selection, but that does not mean that everything we think, feel, and do is biologically adaptive. We evolved from apes, but that does not mean we have the same minds as apes. And the ultimate goal of natural selection is to propagate genes, but that does not mean that the ultimate goal of people is to propagate genes.
Why give a robot an order to obey orders-why aren't the original orders enough? Why command a robot not to do harm-wouldn't it be easier never to command it to do harm in the first place? Does the universe contain a mysterious force pulling entities toward malevolence, so that a positronic brain must be programmed to withstand it? Do intelligent beings inevitably develop an attitude problem? (...) Now that computers really have become smarter and more powerful, the anxiety has waned. Today's ubiquitous, networked computers have an unprecedented ability to do mischief should they ever go to the bad. But the only mayhem comes from unpredictable chaos or from human malice in the form of viruses. We no longer worry about electronic serial killers or subversive silicon cabals because we are beginning to appreciate that malevolence-like vision, motor coordination, and common sense-does not come free with computation but has to be programmed in. (...) Aggression, like every other part of human behavior we take for granted, is a challenging engineering problem!