CONVERSATION · Stephen Wolfram 

A New Kind of Something

 May 9, 2003 | STEPHEN WOLFRAM IS EITHER a disappointing — and perhaps disappointed — wunderkind of science or the next Isaac Newton. It's not entirely clear which.

His latest book, self-published and presumptuously titled A New Kind of Science, is a 1,200-page shelf-breaker that purports to reveal a better way to model the universe (and everything in it). The method is based on using short, simple computer programs that he calls "primitives" to describe all phenomena. Identify the right primitives — Wolfram says there are about a trillion of them — turn them on, and watch the universe unfold before you. In fact, he argues, there is no better way to create a true representation of many phenomena.

To make his case, Wolfram has filled page after page with computer-generated patterns. Many of them are quite beautiful and strikingly similar to living systems; others seem merely monotonous variations of a gigantic chessboard. From these pictures, and the short list of simple rules used to make them, he deduces a generalized approach to describing nature.

Most of his ideas are drawn from an arcane branch of computer science called cellular automata, in which Wolfram is an acknowledged pioneer. At the heart of his theory are two concepts:

* Computational equivalence: the idea that all physical phenomena correspond to simple computer programs that are capable of producing great complexity.

* Computational irreducibility: the idea that some systems are inherently unpredictable. Run the programs and wait to see what happens. No differential calculus shortcuts allowed!

This is a bit much for many scientists to swallow. "One could run these automata for trillions or even trillions of trillions of iterations, and the image would remain at the same limited level of complexity. They do not evolve into, say, insects, or humans, or Chopin preludes," writes Ray Kurzweil in a fascinating and generally favorable review of Wolfram's book at

By any account, Wolfram has an extraordinary background. Publishing his first paper on particle physics at age 17, he raced through Eton College and Oxford University, earned his Ph.D. in physics from Caltech at 21, won a MacArthur "genius" fellowship at 22, and spent time at the Institute for Advanced Study at Princeton University. He later founded Wolfram Research in 1986 and got wealthy by writing and selling Mathematica, a popular software package.

For much of the past 10 years, Wolfram spent evenings tucked away in the second floor of his home, writing A New Kind of Science. Clutching the book nervously, he says, "Everything I know is in here." The book has been out for almost a year, to decidedly mixed reviews.

He wins few points for manners. Balding, disheveled, his conversation is always about him and his work. Wolfram is convinced he's discovered a big idea that will change the world. Bio·IT Executive Editor John Russell interviewed him at the O'Reilly Bioinformatics Technology Conference, where Wolfram presented his ideas and their applicability to computational biology.

Q: Why self-publish? Why not present your ideas in a peer review journal, where they could be assessed by other scientists?
A: Well, you just need to go to to see a lot of comments on the book. Most of them are bull____. This is too big a thing to propagate through the standard mechanism of science. As a person who's published a journal for the last 17 years (Complex Systems), I know how that works. Basically, it's a good system for [disseminating] incremental progress in science. It's almost laughably absurd if you're trying to do something as big as what I am trying to do.

Q: What is it you are trying to do? 
A: I've had the experience in my life of trying a couple of sets of ideas and seeing how to plant them in a couple of different ways. One was in the early days of complexity theory, where I developed some intellectual stuff, defined the mission, and then said, 'OK, world, go make this happen.' That didn't work all that well.

Take two was what I did with Mathematica. I basically said, here are a bunch of quite sophisticated ideas, let's package them as a product and have a company propagate it in the world. That seems to have worked pretty well. Two million people around the world use Mathematica.

A New Kind of Science represents a paradigm change. We're referring to the field right now by the acronym NKS. I agonized greatly what to call it — unfortunately, all the nice Greek words were taken for other things. It's a set of concepts that aren't very familiar, so there isn't really a word you can say, 'Oh, it's close to that word.'

Q: How will NKS be applied to solving biological problems? 
A: The basic thing is, we know what the genome looks like. Now the question is, 'How do we go from that to what cells and organisms actually do?' And that question is really, 'What methodology might we imagine [for doing] that?' Many theories in science [have] been based on the idea 'let's make a mathematical equation that describes the question.' But there hasn't really been a framework for making theories about how an organism should look.

The main thing is finding primitives to use to describe biological systems. That is, you string together a few of these primitives and find out what will happen ... you go out in the computational world to see what's there. It's analogous to what naturalists did 150 years ago, going out in the biological world and going around darkest Africa or whatever, trying to find all these funny species.

Q: Who is looking for these primitives, and how long will it take before we see tools that are based on them?
A: Not long at all. There are people working on it right now. You can just search in the space of all possible simple programs because there just aren't that many of them. There might be a trillion of them. It's not hard to search a space of a trillion simple programs. Whereas with a traditional mathematic model there are an infinite number, and that's much harder to search.

There are going to be quite a lot of cases in biology where there's a bunch of data that are known and they look very complicated, but by doing the appropriate kinds of searches or whatever, one will find that there's an extremely simple program that describes what's going on.

Q: You've said the conventional idea of natural selection is wrong. What do you mean? 
A: People have tended to think there can't be a predictive theory of biology because they say, 'Well it's all governed by natural selection and adaptation. You know, the way we are today is due to some accident that happened to some trilobite 200 million years ago.'

But I don't think that. I think actually there's good evidence that in many kinds of traits, what one is seeing is all of the possible random choices that could be made. So for example, in the case of mollusk shell patterns, what one is seeing is all possible cellular automata rules being played out in each of these species. So that means that one can start to have a predictive theory of biology because one says, given what we know is out there in the computational world, that maps into what we'll then see in biology.

Q: In practical terms, researchers want tools that they can actually use and don't wish to spend their time searching computational space. Where will they find the right primitives? 
A: One project that's not specifically about computational biology [that we are doing is] building an Atlas of simple programs and what they do. My idea is [similar to] organic chemistry databases that have developed over many years — in them, you have this or that chemical, and explain what it does and where it might be useful and so on. For these simple programs, one can ask the same kinds of questions using the Atlas.

We have had considerable success with public information Web sites. MathWorld is by far the most visited math site in the world. So that emboldens us to think about similar kinds of things in other areas, and this Atlas of simple programs is one example. We're also trying to formulate the right strategy for how to do those kinds of things in the context of computational biology.

I think it's important to get an intuition about what simple primitives actually lead to. That's the thing in NKS Explorer (software accompanying the book) and the Atlas of simple programs, that's the place where one starts to get an intuition of just how simple the primitives have to be to achieve such and such a solution.

 Illumination or illusion? Wolfram argues that simple computer programming rules, such as rule 30 shown here, can produce complex patterns and account for most of what we observe in nature—from mollusk shell patterns to complex chemical synthesis pathways. 

Q: When will the Atlas be out? 
A: I would guess [in the next month] or so. Right now we have a large lump of data that we can put into the repository as the initial conditions, so to speak. But our great interest is having other people contribute. The hope is, and the expectation is, a lot of other people will contribute.

Q: One unsettling aspect of NKS is computational irreducibility — the idea that you can't predict what will happen with a program. Can you define what you mean? 
A: Well, [let's say] you want to predict where the earth is going to be a million years from now. We don't have to follow each orbit a million times. We just have to plug a number into a formula, and immediately we can work out where the earth will be in a million years from now. The question is: Can we do that kind of thing in general? The principle of computational equivalence says no, in fact, you can't. A system like this will be computationally irreducible in the sense that to work out what some bit will be down here, you really can't do that any more efficiently than by just running each step explicitly to see what happens.

Q: Most of the examples in your book look at things easily represented by images, such as leaf patterns. Can NKS be used to model other tasks, such as biochemical pathways? 
A: The things I've studied in great detail are large-scale morphological features like, for example, shapes of leaves. So when it comes to looking up mollusk pigmentation, I look at a pattern and it's very easy to see what class of programs [are appropriate]. It turns out you can also look at networks with simple programs. You might end up with [a visual pattern] that represents some operation such as phosphorylation or some other biochemical pathway. I'm talking about networks of chemical reactions rather than about morphological layout of things.

Q: What are you doing to spread the word about NKS? 
A: The first step is this [book]. Also, I've given 25 talks at most of the major research universities in the U.S. So that's a start. Right now, we know of about 20 courses being taught using this book. There are probably lots more that we don't know about. We're also having a conference in Boston in June. After the conference, we're doing a summer school for graduate students at Brown University.

One of the nice things about this approach to science is that it's possible for people at very low levels of the educational system to actually get to the frontiers without having to learn a lot of elaborate calculus or whatever else. It's a young enough field that it's possible for a high school kid to make a discovery.

Q: Are there problem areas in which the ideas and techniques of NKS are not applicable? 
A: Who knows? It's hard to answer that question until you've tried them all. *