Are you the Isaac Newton of the 21st century?

Who knows? I think I've discovered some big and important things. But I'm more interested in what I've discovered than where it puts me in the world. Sometimes I think I might be happier just to figure things out and keep them to myself. I've put a lot of effort into getting ready to share them. And if people actually start to understand what I've figured out, then I think I'll be forced to be a very famous scientist. I have mixed feelings about that. But I think it's important to the ideas that I don't try to avoid it too much.

What's the story behind this new kind of science? How did it all begin?

Around 1980, I had become interested in several really different questions--galaxy formation and how brains work. They all seemed to be getting stuck in the same kind of way. I began to realise that the real problem was with the basic infrastructure of science. For about 300 years, most of science has been dominated by the idea of using mathematical equations to model nature. That worked really well for Newton and friends, figuring out orbits of planets and things, but it's never really worked with more complicated phenomena in physics, such as fluid turbulence. And in biology it's been pretty hopeless.

If equations aren't the right infrastructure for modelling the world, what is?

Simple programs. If you're going to be able to make scientific theories at all, systems in nature had better follow definite rules. But why should those rules be based on the constructs of human mathematics? In the past, there wasn't any framework for thinking about more general kinds of rules. But now you can think of them as being like computer programs. About 20 years ago, I decided to try to work out what kind of science you could build from these more general kinds of rules. The first big question was what do these rules typically do? What do simple programs typically do?

Did you carry out experiments to find out?

Yes. I started with very simple programs called cellular automata. The version that I used began with a row of cells, each either black or white. Then you make a new row underneath. You use a definite rule to work out the colour of each cell, by looking at the colours of its neighbours on the row above. And then you repeat this over and over again. It's a simple set-up. There are just 256 of these kinds of programs. The question is what happens when you run them, say just starting with a single black cell. You would guess it should always be something simple. The remarkable thing I discovered--almost 20 years ago--is that this intuition is completely wrong. You see, of the 256 possible cellular automata, several make incredibly complicated patterns that look almost completely random and that you'd never imagine came just from repeatedly applying a simple rule to a single black square.

So your experiments convinced you that nature uses simple programs to generate the complexity we see around us...

Yes, I think it's the main secret of nature. It's what lets nature come up with things that look so much more complex than anything we've been able to invent does. Some people say complexity in biology can't just be coming from natural selection. They're right, but the point is that nature uses tools we didn't expect. That's what I've discovered.

How did you follow up on this?

I worked out lots of details and published lots of papers. And I got lots of other people interested. The whole topic of complexity got very popular. I even began a journal and a research centre. But people understood only part of what I'd done. The rest required a big conceptual leap. And if you want to pursue those things, history says you pretty much have to go it alone.

And a new science needs a new tool--was that why you invented Mathematica?

Partly. I needed to be able to build programs then find out what they do as efficiently as possible. It required big new ideas about setting up software systems to do that. It turned out that the very fact that I could figure out how to build all the complexity of Mathematica from quite simple "primitives" was an important inspiration. It made me realise that I might work out what primitives nature uses for its rules. So Mathematica was both a tool and an inspiration.

What exactly does Mathematica do?

It's a complete environment for technical computing. It lets people do a huge range of calculations, and creates graphics and documents, interacts with the Web, and so on. It's all based on a language that lets you build complex programs far more easily than before. A few million people use it.

Did that make you a multimillionaire?

Yes, I've made a lot of money, but I've always wanted to put my energies into the things that I find most interesting. What motivates me most is discovering new things and building new ideas.

Tell me about your 10 years of silence...

It began in 1991 after I'd built up a terrific team at my company. I began to split my time between management and basic science. I wanted to finish building the new kind of science I'd begun in the early 1980s. I had no idea it would take so long. I kept on discovering more and more things. Every time I turned over a rock there was a huge new universe underneath. It's been exciting, but there's been a huge amount to do and it's taken immense focus to get it all done. I always used to like lecturing and travelling, but to get this project done, I've had to shut those kinds of things down.

And talking to journalists?

Right. I'm going to have to get used to that again now.

So, what have you discovered?

Enough to fill hundreds--maybe thousands--of scientific papers. I've amassed a huge amount of evidence for my idea that simple programs--like the cellular automata--are the key to lots of important phenomena in nature. In physics, for instance, I can finally explain why the second law of thermodynamics works--that is, why many physical systems tend to become irreversibly more random as time progresses. In biology, I now know how a lot of the complexity arises. I've discovered that many things we might have thought were special about life and intelligence, for example, can also emerge in all kinds of physical systems. Consequently, I don't believe "anthropic" arguments that say that for us to be here it's necessary for there to be stars, galaxies and so on. There can be things just as complex as us without any of that.

Why haven't you published any of this?

Because it's all part of a big picture that can be communicated properly only by showing everything together. I guess if someone else had been paying for my work, I might have had to give progress reports. Fortunately, I've been able to concentrate on putting everything together in a nice coherent way, as a book called A New Kind of Science. It's been a huge project. I've devoted about 100 million keystrokes to it. I've taken a lot of trouble to polish my ideas so they're as clean as possible. Usually, new directions in science begin far more gradually, with lots of people involved. But the things I'm doing now are different enough that I've had to build up a whole new intellectual structure by myself.

Who's the book aimed at?

Everyone. It's completely new so there aren't any specialists. It may turn out that people who have good intellectual discipline but perhaps don't know so much about science will have an easier time.

Have you discovered the simple program that is generating the Universe?

Not yet. But I have found increasing evidence that it exists. It could be as simple as a few lines of Mathematica code. I think before too many years it'll be possible to find it.

So is Stephen Hawking right about scientists being close to discovering a "theory of everything"?

Well, the things I've been thinking about are very, very different from the usual quantum field theory and string theory approach. There's some very basic intuition that's different when you think about simple programs instead of equations and so on. One big issue is that getting a fundamental theory of physics doesn't mean physics is finished. That'd be like saying that computing is finished once you have a computer. Suppose that the program for the Universe is four lines long. There's no room in those four lines to put in all the familiar stuff we know about space-time having four dimensions, the muon being 206 times the mass of the electron, and so on. Almost nothing from the everyday world will be obvious in the program. These things will have to emerge when the program runs. Figuring out how that works, and exactly what can emerge, can be arbitrarily difficult.

Could it be that the Universe-generating program will only produce what we see around us after it's run for 13 billion years?

Yes, I think that will be partly true. But even though the evolution of the Universe as a whole may be what I call computationally irreducible, there will still be patches that are reducible--where we can figure what the Universe does faster than it does it. And actually almost all of what traditional equation-based science has been doing is looking just at those computationally reducible parts.

So there's no mystery in Einstein's famous observation that the most incomprehensible thing about the Universe is that it's comprehensible?

Well, I think that's really much more a statement about the practice of science than about our Universe. One of the clear lessons from history is that fields of science tend to get defined according to whatever their methods allow them to study successfully. What I've discovered is that there's lots of other stuff out there that you can see if you think in terms of programs.

So if the Babylonians had invented computer programs before geometry, might science have been more effective?

Well, quite a bit of what I've discovered could have been found by the Babylonians. If you know what to look for, you could just find it by arranging pebbles with a simple rule. Young kids today could certainly do it. If my kind of science had been around for ages, perhaps only now would a Newton have invented calculus.

A New Kind of Science is due to be published by Wolfram Media in January 2002