Computational Theory Quotes

Some years ago, I wrote a book called the Emperor's New Mind and that book was describing a point of view I had about consciousness and why it was not something that comes about from complicated calculations.

The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.

You can't *discover* that the brain is a digital computer. You can only *interpret* the brain as a digital computer.

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

What I realized is that if we're going to be able to have a theory about what happens in, for example, nature there has to ultimately be some rule by which nature operates. But the issue is does that rule have to correspond to something like a mathematical equation, something that we have sort of created in our human mathematics? And what I realized is that now with our understanding of computation and computer programs and so on, there is actually a much bigger universe of possible rules to describe the natural world than just the mathematical equation kinds of things.

Is the human race a universal constructor?

Alan Turing gave us a mathematical model of digital computing that has completely withstood the test of time. He gave us a very, very clear description that was truly prophetic.

The question you raise, 'How can such a formulation lead to computations?' doesn't bother me in the least! Throughout my whole life as a mathematician, the possibility of making explicit, elegant computations has always come out by itself, as a byproduct of a thorough conceptual understanding of what was going on. Thus I never bothered about whether what would come out would be suitable for this or that, but just tried to understand - and it always turned out that understanding was all that mattered.

My work was fairly theoretical. It was in recursive function theory. And in particular, hierarchies of functions in terms of computational complexity. I got involved in real computers and programming mainly by being - well, I was interested even as I came to graduate school.

Trying to explain Turing's work in encryption and decryption? It's complicated.

I would suggest, merely as a metaphor here, but also as the basis for a scientific program to investigate the computational capacity of the universe, that this is also a reasonable explanation for why the universe is complex.

'You might think of combinatorics as a machine too', the major says. 'A different sort of machine, though. Have you heard of Babbage's analytic engine? He never built it. ... I have an analytic machine of my own-right here.' He taps his own skull.

I remember that mathematicians were telling me in the 1960s that they would recognize computer science as a mature discipline when it had 1,000 deep algorithms. I think we've probably reached 500.

Thinking of the universe as a computer is controversial.

In this metaphor we actually have a picture of the computational universe, a metaphor which I hope to make scientifically precise as part of a research program.