Stephen Wolfram

We've got all these real numbers that have infinite numbers of digits.

The universe is not a Turing machine.

Right.

The Turing machines are a small subset that are the things that we make in microprocessors and engineering structures and so on.

So probably, actually through my work in the 1980s, about sort of the relationship between computation and models of physics,

it became a little less clear that there was this big sort of dichotomy between what can happen in physics and what happens in things like Turing machines.

And I think probably by now, people would mostly think... And by the way, brains were another kind of element of this.

I mean, you know, Gödel didn't think that his notion of computation or what amounted to his notion of computation would cover brains.

And Turing wasn't sure either, but although he was a little bit, he got to be a little bit more convinced that it should cover brains.

But I would say by probably sometime in the 1980s, there was beginning to be sort of a general belief that yes, this notion of computation that could be captured by things like Turing machines

was reasonably robust.

Now, the next question is, okay, you can have a universal Turing machine that's capable of being programmed to do anything that any Turing machine can do.

And, you know, this idea of universal computation is an important idea, this idea that you can have one piece of hardware and program it with different pieces of software.

You know, that's kind of the idea that launched most modern technology.

I mean, that's kind of that's the idea that launched computer revolution, software, etc.

So important idea.

But the thing that's still kind of holding out from that idea is, okay, there is this universal computation concept.

thing, but seems hard to get to.

It seems like you want to make a universal computer, you have to kind of have a microprocessor with a million gates in it, and you have to go to a lot of trouble to make something that achieves that level of computational sophistication.

So the surprise for me was that stuff that I discovered in the early 80s, looking at these things called cellular automata, which are really simple computational systems, the thing that was a big surprise to me was that even when their rules were very, very simple,