What follows is the English transcript of Andrew Hax’s interview with Stephen Wolfram that resulted in this article: Andres Hax, “Una revolución a la medida de los autómatas,” Clarín, 9 April 2005. Online Spanish version »

Is it correct to say that with your discoveries regarding the behavior of cellular automata you are introducing a paradigm shift in the sciences on par with Darwin?

If there’s an analogy, it’s probably this. Darwin went on voyages around the world and saw all sorts of remarkable biological phenomena—that led him to a new paradigm. I’ve taken a lot of abstract voyages in the computational world, and have seen all sorts of remarkable phenomena there—that have led me to a new paradigm, that I think is going to be important for a lot of science and technology. And in fact, it also happens to have quite a bit to say about some of the foundational questions in biology that Darwin was interested in.

How long will it take for your ideas to become accepted/commonplace?

It’s inevitably a gradual process. But I think it’s off to a very good start. Right now, for example, there’s an average of one or two academic papers per day involving NKS being written. I’m sure that in a decade there’ll be lots of people who have built their careers on NKS, and quite a few organizations built on it. In fifty years I expect that more new technology will be being made using NKS than traditional science. By that time, NKS will be viewed as just another branch of science, like a physics or chemistry. Most of its core conceptual ideas will be commonplace and some of its basic methods will be taught in school alongside basic math. And probably almost nobody will remember that it took any time for NKS to be accepted.

One of the most stunning aspects of your book—at least for a layman—is the absence of mathematics. In the long term will your discoveries make mathematics an obsolete tool for scientific inquiry?

Traditional mathematics will certainly go on being useful for many things. But what NKS does is to let one address all sorts of new questions and areas. And actually, one thing it does is to provide a kind of generalization of mathematics. And like in mathematics, one can use elaborate formalism. It’s just that in writing the book I went to a lot of trouble to polish my ideas so I could describe them just with words and pictures.

Your theory even addresses the concept of free will—has this idea of computational irreducibility changed the way you view your existence? Is this idea as menacing to historical faith traditions as Darwin’s theory of evolution?

I do think that the history of the universe—and everything in it—is completely determined. But the point about computational irreducibility is that it shows that that doesn’t mean it has to be dull. Even though it’s determined, it can still be unpredictable and surprising. And it’s irreducible—so we actually have to live it in order to see what happens. I find that a bit ennobling: to know that our history can’t just be compressed—that we can’t predict its outcome without living it.

NKS brings science into quite a few issues that have only been addressable by philosophy—or theology—before. And one of the things that at first seems troubling is that it makes humans seem less special than we thought. But that’s often the way science advances. The Copernican revolution showed us that we don’t live at a special point in the physical universe. NKS is now telling us that we don’t represent a special point in the computational universe either. Still, it tells us something ennobling too: it tells us that we are just as computationally sophisticated as the physical universe.

Ray Kurzweil says of Class 4 automata, “…they do not continue to evolve into anything more complex, nor do they develop new types of features….They do not evolve into, say, insects or humans, or Chopin preludes….” Is this a damaging critique of the Principle of Computational Equivalence?

Class 4 cellular automata can actually make surprisingly good music! It takes doing a lot of actual experiments to get a good intuition for systems like cellular automata. One of the things I’ve always found is that whenever I think “they can’t do X”, I’m always wrong. It’s just that I can’t imagine how they do “X”. I think that over the next few decades, we’ll see some technological systems with remarkably simple underlying rules do remarkably sophisticated things. And one result of that is that typical people’s intuition will change—and in the end the Principle of Computational Equivalence will seem almost obvious.

How do you see the future of the human race. Will the implications of the Principle of Computational Equivalence, if recognized and adopted, alter the evolution of the human race? If so, how and how soon?

There’s going to be more and more coupling between computers and humans. More and more of our activities—including cognitive ones—will be successfully “outsourced” to computers. Then there’ll be questions about what’s essentially different between computers and humans. And the Principle of Computational Equivalence says there will never be anything fundamentally different. So that means that the difference all has to come from history—it’ll be that thread of history that defines humans.

What is the relation of your theory with chaos and complexity theory. When I try to explain what you discover in your book to someone else they say, “Ah, chaos theory.”

Chaos theory is really about a very specific phenomenon: that sensitive dependence on initial conditions can lead to randomness. And what one finds in the end is that the only way to get randomness out of this phenonenon is just to put randomness in, in the initial conditions. What I’ve found is that simple programs can actually produce randomness—and complexity—without it ever being put it. It’s a much more powerful phenomenon.

Complexity theory has a very confused history, some of which starts with my early work on cellular automata. But to my regret, it’s mostly concentrated on trying to use rather traditional scientific methods to find simple features of complex phenomena—not on understanding the core phenomena and origins of complexity itself, which is what NKS now lets us address.

What is the next step for you? Promoting NKS? Developing practical applications? Continue research based on the Principle of Computational Equivalence?

I’m spending a little time on NKS education, though other people are doing much more on that than me. Right now I’m mostly in a tool-building phase, working on some fairly dramatic new directions for Mathematica, that I think are going to be very important in their own right, but are also going to let me take NKS to a new level. I’m also starting to work on some applications of NKS—mostly in technology—that I think are going to be rather spectacular.

Of the various areas of scientific inquiry which do you think will be first to radically change due to your new kind of science and how.

Two things are already happening. First, there’s a new kind of basic science emerging—”pure NKS”. It’s like a physics, or a chemistry, or a mathematics, but concerned with systems in the computational world. Second, ideas and results from pure NKS are getting applied to lots of other places. Some of them aren’t science at all. Areas like art, music and architecture. Within traditional science, biology looks very promising: trying to understand the operation of cells using NKS ideas—perhaps a bit like understanding ideas of digital information led to the discovery of the mechanism of DNA fifty years ago. There seem to be particularly strong possibilities in areas of science where there’s obvious complexity, but it’s been hard to reproduce. Areas like linguistics, economics, social science and cognitive science. There are very clear and important opportunities in computer science and mathematics too—though my guess is that the applications there will be built on a lot of work in “pure NKS”. In fundamental physics, there’s a possibility of a tremendous breakthrough, but it’s hard to predict when that will happen.

There is an oft quoted phrase of Isaac Newton’s which says he considers himself “to have been like a boy playing upon the seashore and diverting myself and then finding a smoother pebble or prettier shell than ordinary, while the great ocean of truth lay before me all undiscovered.” How would you describe the decades you spent making your discoveries?

It’s been a remarkable experience for me beginning to explore the computational universe. I think Newton’s quote really describes his traditional mathematical approach—studying those “pebbles” that happen to be prettier. I’ve had the advantage of living in the age of computers—and having the tools to explore the computational world in a more systematic way. And in that world, instead of finding pebbles, I’ve found all sorts of remarkable creatures that behave in all sorts of remarkable ways. But there’s still so much more to discover—and so much to do to take what’s out there in the computational world and apply it for our purposes in science, technology and the arts. There are so many lifetimes of exciting things to do.

Finally, the fact that your book is online for free is fantastic news, especially here in Argentina where budgets are very tight. When did you decide to put the book on your website? How important will the internet be for introducing a NKS into the global intellectual community?

I’d planned to put the book on the web, though representing its visual elements there is still a challenge. One thing that’s great about NKS is that once you understand it, all you need to do it is a computer. So that immediately allows it to be a very global enterprise. We’ve been working on inventing some new forms of intellectual interaction on the internet. We’re building a giant atlas of the computational universe. And we’re planning to start live webconferenced computer experiments. NKS is a young field, with tremendous opportunities for a very wide range of people.