Computation Quotes

The more we learn about AI and about how the brain works, the more amazing the brain seems. Just the sheer amount of computation it does is truly incredible, especially for a couple of pounds of meat. ~ Stuart J. Russell

That which occasions so many mistakes in the computations of men, when they expect return for favors, is that the giver's pride and the receiver's cannot agree upon the value of the kindness done. ~ Francois De La Rochefoucauld

In accordance with the law of accelerating returns, paradigm shift (also called innovation) turns the S-curve of any specific paradigm into a continuing exponential. A new paradigm, such as three-dimensional circuits, takes over when the old paradigm approaches its natural limit, which has already happened at least four times in the history of computation. In such nonhuman species as apes, the mastery of a toolmaking or -using skill by each animal is characterized by an S-shaped learning curve that ends abruptly; human-created technology, in contrast, has followed an exponential pattern of growth and acceleration since its inception. ~ Ray Kurzweil

The reason that I have concentrated on non-computability, in my arguments, rather than on complexity, is simply that it is only with the former that I have been able to see how to make the necessary strong statements. It may well be that in the working lives of most mathematicians, non-computability issues play, if anything, only a very small part. But that is not the point at issue. I am trying to show that (mathematical) understanding is something that lies beyond computation, and the Godel (-Turing) argument is one of the few handles that we have on that issue. It is quite probable that our mathematical insights and understandings are often used to achieve things that could in principle also be achieved computationally-but where blind computation without much insight may turn out to be so inefficient that it is unworkable (cf. 3.26). However, these matters are much more difficult to address than the non-computability issue. ~ Roger Penrose

When you zap things with light to build quantum computers, you're hacking existing systems. You're hijacking the computation that's already happening in the universe, just like a hacker takes over someone else's computer. ~ Seth Lloyd

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

But biology and computer science - life and computation - are related. I am confident that at their interface great discoveries await those who seek them. ~ Leonard Adleman

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. ~ Laurence Sterne

Consider an AI that has hedonism as its final goal, and which would therefore like to tile the universe with "hedonium" (matter organized in a configuration that is optimal for the generation of pleasurable experience). To this end, the AI might produce computronium (matter organized in a configuration that is optimal for computation) and use it to implement digital minds in states of euphoria. In order to maximize efficiency, the AI omits from the implementation any mental faculties that are not essential for the experience of pleasure, and exploits any computational shortcuts that according to its definition of pleasure do not vitiate the generation of pleasure. For instance, the AI might confine its simulation to reward circuitry, eliding faculties such as a memory, sensory perception, executive function, and language; it might simulate minds at a relatively coarse-grained level of functionality, omitting lower-level neuronal processes; it might replace commonly repeated computations with calls to a lookup table; or it might put in place some arrangement whereby multiple minds would share most parts of their underlying computational machinery (their "supervenience bases" in philosophical parlance). Such tricks could greatly increase the quantity of pleasure producible with a given amount of resources. ~ Nick Bostrom

The term, information at your fingertips, is to remind people what a broad role the personal computer will be playing. It's not a computation device, it's not a word processing or a spreadsheet device. It's a window onto the world of information. ~ Bill Gates

Consider a cognitive scientist concerned with the empirical study of the mind, especially the cognitive unconscious, and ultimately committed to understanding the mind in terms of the brain and its neural structure. To such a scientist of the mind, Anglo-American approaches to the philosophy of mind and language of the sort discussed above seem odd indeed. The brain uses neurons, not languagelike symbols. Neural computation works by real-time spreading activation, which is neither akin to prooflike deductions in a mathematical
logic, nor like disembodied algorithms in classical artificial intelligence, nor like derivations in a transformational grammar. ~ George Lakoff

One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation. ~ Ada Lovelace

Whew, this might be getting a bit confusing. I hope you are following me so far. This is the point in every Theory of Computation course at which students either throw up their hands and say "I can't get my mind around this stuff!" or clap their hands and say "I love this stuff!"

Needless to say, I was the second kind of student, even though I shared the confusion of the first. ~ Melanie Mitchell

Q5. Have not I merely shown that it is possible to outdo just a particular algorithmic procedure, A, by defeating it with the computation Cq(n)? Why does this show that I can do better than any A whatsoever?

The argument certainly does show that we can do better than any algorithm. This is the whole point of a reductio ad absurdum argument of this kind that I have used here. I think that an analogy might be helpful here. Some readers will know of Euclid's argument that there is no largest prime number. This, also, is a reductio ad absurdum. Euclid's argument is as follows. Suppose, on the contrary, that there is a largest prime; call it p. Now consider the product N of all the primes up to p and add 1:

N=2*3*5*...*p+1.

N is certainly larger than p, but it cannot be divisible by any of the prime numbers 2,3,5...,p (since it leaves the remainder 1 on division); so either N is the required prime itself or it is composite-in which case it is divisible by a prime larger than p. Either way, there would have to be a prime larger than p, which contradicts the initial assumption that p is the largest prime. Hence there is no largest prime. The argument, being a reductio ad absurdum, does not merely show that a particular prime p can be defeated by finding a larger one; it shows that there cannot be any largest prime at all. Likewise, the Godel-Turing argument above does not merely show that a particular algorithm A can be defeated, it shows that there ~ Roger Penrose

Amos and I called our first joint article "Belief in the Law of Small Numbers." We explained, tongue-in-cheek, that "intuitions about random sampling appear to satisfy the law of small numbers, which asserts that the law of large numbers applies to small numbers as well." We also included a strongly worded recommendation that researchers regard their "statistical intuitions with proper suspicion and replace impression formation by computation whenever possible. ~ Daniel Kahneman

The purpose of computation is insight, not numbers. ~ Richard Hamming

Our human intelligence is based on computational processes that we are learning to understand. We will ultimately multiply our intellectual powers by applying and extending the methods of human intelligence using the vastly greater capacity of nonbiological computation. So to consider the ultimate limits of computation is really to ask: what is the destiny of our civilization? ~ Ray Kurzweil

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. ~ Rudy Rucker

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations. ~ David Hilbert

Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance. ~ Nassim Nicholas Taleb

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. ~ Paul Dirac

Thirty years ago, we used to ask: Can a computer simulate all processes of logic? The answer was yes, but the question was surely wrong. We should have asked: Can logic simulate all sequences of cause and effect? And the answer would have been no. ~ Gregory Bateson

Lately I've been working to convince myself that everything is a computation. ~ Rudy Rucker

The history of the universe is, in effect, a huge and ongoing quantum computation. The universe is a quantum computer. ~ Seth Lloyd

Theory is relevant to you because it shows you a new, simpler, and more elegant side of computers, which we normally consider to be complicated machines. The best computer designs and applications are conceived with elegance in mind. A theoretical course can heighten your aesthetic sense and help you build more beautiful systems. ~ Michael Sipser

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. ~ Joseph Addison

Mathematics is no more computation than typing is literature. ~ John Allen Paulos

He did not believe in luck at all, good or bad. Gamblers believed in luck, and he was not a gambler. Never had been, never would be. John Henry Holliday believed in mathematics, in statistics, in the computation of odds. Fifty-two cards in a deck. Make it easy. Say it's fifty. Any card has a 2 percent chance of being dealt from a full deck. Keep track of what's out. Adjust the probabilities as the hand progresses. ~ Mary Doria Russell

Keep computations to the lowest level of the multiplication table. ~ David Hilbert

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. ~ Dennis Altman

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. ~ Steven Pinker

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

Excuse my wandering.
How can one be orderly with this?
It's like counting leaves in a garden,
along with the song-notes of partridges,
and crows.
Sometimes organization
and computation become absurd. ~ Rumi

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. ~ Yochai Benkler

But real-world questions aren't like word problems. A real-world problem is something like "Has the recession and its aftermath been especially bad for women in the workforce, and if so, to what extent is this the result of Obama administration policies?" Your calculator doesn't have a button for this. Because in order to give a sensible answer, you need to know more than just numbers. What shape do the job-loss curves for men and women have in a typical recession? Was this recession notably different in that respect? What kind of jobs are disproportionately held by women, and what decisions has Obama made that affect that sector of the economy? It's only after you've started to formulate these questions that you take out the calculator. But at that point the real mental work is already finished. Dividing one number by another is mere computation; figuring out what you should divide by what is mathematics. ~ Jordan Ellenberg

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? ~ Seth Lloyd

University of California, Irvine, Professor of Art and Engineering, Codirector of Arts, Computation, and Engineering (ACE) Program
Kavita Philip University of California, Irvine, Associate Professor of Women's Studies, Anthropology, and Arts, Computation, and Engineering (ACE) Program
Todd Presner University ~ Cathy N. Davidson

When the idea of any pleasure strikes your imagination, make a just computation between the duration of the pleasure and that of the repentance that is likely to follow it. ~ Epictetus

Dividing one number by another is mere computation ; knowing what to divide by what is mathematics. ~ Jordan Ellenberg

What's needed now are software technologies that interconnect computing systems, people and data to produce more rapid answers to the questions of science, and to help researchers use computation in the most effective manner. ~ Bob Muglia

A third position has been called "strong Al." When the Mind As Computer metaphor is believed as a deep scientific truth, the true believers interpret the ontology and the inferential patterns that the metaphor imposes on the mind as defining the essence of mind itself. For them, concepts are formal symbols, thought is computation (the manipulation of those symbols), and the mind is a computer program. ~ George Lakoff

I've always been very interested in the question of how computation can fundamentally advance the things that we can see. This led me to have a fascination with medical imaging, especially things like MRI and scanning, and eventually computer graphics. ~ Ren Ng

Superfluous focus on accounting and other procedural details is preventing U.S. industry from competing with rough-and-ready rivals in Asia that can build thousands of factories and skyscrapers while the United States dithers with environmental-impact litigation, re-computation, and backup of accounting reports. ~ George Gilder

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. ~ Bruce Sterling

To me quantum computation is a new and deeper and better way to understand the laws of physics, and hence understanding physical reality as a whole. ~ David Deutsch

George ended by looking at the larger picture. He said that computation at present is still parasitic on us, but it probably is in the process of becoming part of life itself
it's just another system of genetics. Evolution, after all, is massively parallel computation, and now the world of code is evolving, perhaps to reshape the tree of life itself. ~ Stewart Brand

Computer scientists have so far worked on developing powerful programming languages that make it possible to solve the technical problems of computation. Little effort has gone toward devising the languages of interaction. ~ Donald A. Norman

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. ~ Howard Aiken

Imagination is actually a form of computation. Imagination gives calculated and instinctive solutions for the future. ~ L. Ron Hubbard

Ethics is the restraint by which the individual organism affects computation in the ecosystem, creating moral position. What is "right" produces the least amount of disturbance to the individual in the ethical habitat. ~ James Eicher

Quantum computation is ... a distinctively new way of harnessing nature ... It will be the first technology that allows useful tasks to be performed in collaboration between parallel universes. ~ David Deutsch

I lost it in the bathroom. Sitting on the toilet, I started to panic when I noticed the graveyard of empty toilet paper rolls. The brown cylinders had ostensibly been placed vertically to form a half oval on top of the flat shiny surface of the stainless steel toilet paper holder. It was like some sort of miniature-recycled Stonehenge in the women's bathroom, a monument to the bowel movements of days past. Actually, it was sometime around 2:30 p.m. when my day exited the realm of country song bad and entered the neighboring territory of Aunt Ethel's annual Christmas letter bad. Last year Aunt Ethel wrote with steady, stalwart sincerity of Uncle Joe's gout and her one - no, make that two - car accidents, the new sinkhole in their backyard, their impending eviction from the trailer park, and Cousin Serena's divorce. To be fair, Cousin Serena got divorced every year, so that didn't really count toward the calamitous computation of yearly catastrophes. I ~ Penny Reid

When physicists create a mathematical model of a physical process, they rely on the mathematical framework that can represent that process as closely as possible. When Newton developed a model of forces and motion, the appropriate mathematical framework was calculus. When Einstein developed a model of wave-particle motion, he relied on the mathematics of wave equations and eigenvalues. For many models in scientific computation, the computational framework that best aligns with our need is object orientation. ~ Anthony Scopatz

The achievements of willpower are almost beyond computation. Scarcely anything seems impossible to the man who can will strongly enough and long enough. ~ Orison Swett Marden

ALGEBRA is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpose, and found convenient. ~ Colin Maclaurin

On learning. - Learning is discovery, the discovery of the cause of our ignorance. However, the best way of learning is not the computation of information. Learning is discovering, uncovering what is there in us. When we discover, we are uncovering our own ability, our own eyes, in order to find our potential, to see what is going on, to discover how we can enlarge our lives, to find means at our disposal that will let us cope with a difficult situation. And all this, I maintain, is taking place in the here and now. ~ Bruce Lee

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations. ~ G.H. Hardy

Long live transfinite mountains, the hollow earth, time machines, fractal writing, aliens, dada, telepathy, flying saucers, warped space, teleportation, artificial reality, robots, pod people, hylozoism, endless shrinking, intelligent goo, antigravity, surrealism, software highs, two-dimensional time, gnarly computation, the art of photo composition, pleasure zappers, nanomachines, mind viruses, hyperspace, monsters from the deep and, of course, always and forever, the attack of the giant ants! ~ Rudy Rucker

It's always seemed like a big mystery how nature, seemingly so effortlessly, manages to produce so much that seems to us so complex. Well, I think we found its secret. It's just sampling what's out there in the computational universe. ~ Stephen Wolfram

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! ~ Steven Pinker

What would it be like if, right in the midst of this busyness, we were to consciously take our hands off the controls? What if we were to intentionally stop our mental computations and our rushing around and, for a minute or two, simply pause and notice our inner experience? ~ Tara Brach

The computational paradigm for the universe supplements the ordinary mechanistic paradigm: the universe is not just a machine, it is a machine that processes information. The universe computes. The computing universe is not a metaphor, but a mathematical fact: the universe is a physical system that can be programmed at its most microscopic level to perform universal digital computation. Moreover, the universe is not just a computer: it is a quantum computer. Quantum mechanics is constantly injecting fresh, random bits into the universe. Because of its computational nature, the universe processes and interprets those bits, naturally giving rise to all sorts of complex order and structure (Lloyd, 2006). ~ Paul Davies

- we no longer live in the Age of Reason. We don't have reason we have computation. We don't have a tree of knowledge; we have an information superhighway. We don't have real intelligence; we have artificial intelligence. We no longer pursue truth, we seek data and signals. We no longer have philosophers, we have thinking pragmatists. We no longer have morals, we have lifestyles. We no longer have brains which serve as the seat of our thinking minds; we have neural sites, which remember, store body signals, control genes, generate dreams, anxieties and neuroses, quite independent of whether they think rationally or not. So starting from reason, where did we get? ~ Malcolm Bradbury

If you think of your life as a kind of computation, it's quite abundantly clear that there's not going to be a final answer and there won't be anything particularly wonderful about having the computation halt! ~ Rudy Rucker