Quotes About Computation

An algorithm is a finite answer to an infinite number of questions.

So the thing I realized rather gradually - I must say starting about 20 years ago now that we know about computers and things - there's a possibility of a more general basis for rules to describe nature.

Or you could do what is the essence of theoretical science: make a model that gives some kind of procedure for computing the answer rather than just measuring and remembering each case.

Ultimately, every neural net just corresponds to some overall mathematical function—though it may be messy to write out. For the example above, it would be: The neural net of ChatGPT also just corresponds to a mathematical function like this—but effectively with billions of terms.

If you take 200 voxels in this area, and look at which of them are active and which are inactive, you can construct a machine-learning device that decodes which number is being held in memory.

The possibility of incorrect results in the presence of unlucky timing is so important in concurrent programming that it has a name: a race condition. A race condition occurs when the correctness of a computation depends on the relative timing or interleaving of multiple threads by the runtime; in other words, when getting the right answer relies on lucky timing.

You could trust numbers, except perhaps for pi, but he was working on that in his spare time and it was bound to give in sooner or later.

The goal of this book is to highlight the computational beauty found in nature's programs.

There is a button on most calculators that computes the square root for you. It is usually denoted by the symbol "?" and one would normally write things like 3 = ?9. As you can see, the square root is the opposite of squaring, 42 = 16 and ?16 = 4.

A race condition occurs when the correctness of a computation depends on the relative timing or interleaving of multiple threads by the runtime; in other words, when getting the right answer relies on lucky timing.

Calculus, like other forms of mathematics, is much more than a language; it's also an incredibly powerful system of reasoning.

In a nutshell, calculus wants to make hard problems simpler.

Acolyte: Oh machine, would you accept my offer of information so you may run my program and perhaps give me a computation? Priest (on behalf of the machine): We will try. We promise nothing.

In a famous article,8 the physicist Eugene Wigner has written of "the unreasonable effectiveness of mathematics.

A central failure of the "mind as a computational system" theory is that computations, per se, are devoid of meaning.

If you come from mathematics, as I do, you realize that there are many problems, even classical problems, which cannot be solved by computation alone.

All variables are independent.

he presented me with a mathematical conundrum," he said. "It's a famous one, the P = NP problem. Basically, it asks whether it's more difficult to think of the solution to a problem yourself or to ascertain if someone else's answer to the same problem is correct.

No program can say what another will do. Now, I won't just assert that, I'll prove it to you. I will prove that although you might work till you drop, You cannot tell if computation will stop.

algorithms with names such as BigTable, MapReduce, and Percolator are systematically converting the numerical address matrix into a content-addressable memory, effecting a transformation that constitutes the largest computation ever undertaken on planet Earth.

you can build an organ which can do anything that can be done, but you cannot build an organ which tells you whether it can be done."9 "This is connected with the theory of types and with the results of Gödel," he continued. "The question of whether something is feasible in a type belongs to a higher logical type.

The fundamental, indivisible unit of information is the bit. The fundamental, indivisible unit of digital computation is the transformation of a bit between its two possible forms of existence: as structure (memory) or as sequence (code). This is what a Turing Machine does when reading a mark (or the absence of a mark) on a square of tape, changing its state of mind accordingly, and making (or erasing) a mark somewhere else.

That zero and one were sufficient for logic as well as arithmetic was established by Gottfried Wilhelm Leibniz in 1679, following the lead given by Thomas Hobbes in his Computation, or Logique of 1656.

Even Magnifico was put to work on the calculating machine for routine computations, a type of work, which, once explained, was a source of great amusement to him and at which he was surprisingly proficient.