Quotes About Computation

Without the numbers to the right of pi, pi just becomes three,

It's a simple matter of mathematics.

I can multiply. Long divisions start to be a stretch.

The amount of computation necessary for raytracing, we've known for a long time, is many orders of magnitude more intensive than rasterization.

If you understand McCarthy's eval, you understand more than just a stage in the history of languages. These ideas are still the semantic core of Lisp today. So studying McCarthy's original paper shows us, in a sense, what Lisp really is. It's not something that McCarthy designed so much as something he discovered. It's not intrinsically a language for AI or for rapid prototyping, or any other task at that level. It's what you get (or one thing you get) when you try to axiomatize computation.

When a Promise-based asynchronous computation completes normally, it passes its result to the function that is the first argument to then().

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.

Math is one of my favorite subjects.

Computable Numbers' into practice.21 This was

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.

If quantum communication and quantum computation are to flourish, a new information theory will have to be developed.

I have not proved that the universe is, in fact, a digital computer and that it's capable of performing universal computation, but it's plausible that it is.

Computer science is fascinating. As you study computer science, you will find that you develop your mind. It is literally like doing Buddhist exercises all day long.

MATHEMATICIAN

arithmetic.

Some estimate the number of firing patterns of the brain—on/off profiles of total brain activation that are possible—to be ten times ten one million times, or ten to the millionth power. The human brain is thought to be the most complex thing in the universe, artificial or natural.

computer science is the study of "the phenomena surrounding computers"—all the phenomena,

If computers of the kind I have advocated become the computers of the future," he said, "then computation may someday be organized as a public utility, just as the telephone system is a public utility. We can envisage computer service companies whose subscribers are connected to them by telephone lines. Each subscriber needs to pay only for the capacity that he actually uses, but he has access to all programming languages characteristic of a very large system.

What would life be without arithmetic, but a scene of horrors?

The ultimate goal of mathematics is to eliminate all need for intelligent thought.

The question of whether computers can think is like the question of whether submarines can swim.

No sociologist, for instance, 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.

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.

Turing's first goal was to make very concrete this notion of definite procedure. The idea is that, given a particular problem to solve, you can construct a definite procedure for solving it by designing a Turing machine that solves it. Turing machines were put forth as the definition of "definite procedure," hitherto a vague and ill-defined notion.