Stephen Wolfram Q&A

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Some collected questions and answers by Stephen Wolfram

Questions may be edited for brevity; see links for full questions.

April 26, 2013

From: Interview by Patrick Tucker, IEET

Your seminal book, A New Kind of Science, is ten years old. You recently wrote a blog post on the anniversary. Can you talk a little bit about the future of science?

The main idea of A New Kind of Science was to introduce a new way to model things in the world. Three hundred years ago, there was this big transformation in science when it was realized that one could use math, and the formal structure of math, to talk about the natural world. Using math, one could actually compute what should happen in the world—how planets should move, how comets should move, and all those kinds of things.

That has been the dominant paradigm for the last 300 years for the exact sciences. Essentially it says, Let’s find a math equation that represents what we’re talking about, and let’s use that math equation to predict what a system will do. That paradigm has also been the basis for most of our engineering: Let’s figure out how this bridge should work using calculus equations, and so on. Or, Let’s work out this electric circuit using some other kind of differential equation, or algebraic equation or whatever.

That approach has been pretty successful for lots of things. It’s led to a certain choice of subject matter for science, because the science has tended to choose subject matter where it can be successful.

The same is true with engineering. We’ve pursued the particular directions of engineering because we know how to make them work. My goal was to look at the things that science has not traditionally had so much to say about—typically, systems that are more complex in their behavior, and so on—and to ask what we can do with these.

It’s a great approach, but it’s limited. The question is, what’s the space with all possible models that you can imagine using?

A good way to describe that space is to think about computer programs. Any program is [a set of] defined rules for how a system works. For example, when we look at nature, we would ask what kinds of programs nature is using to do what it does, to grow the biological organisms it grows, how fluids flow the way they do—all those kinds of things.

I’ve discovered that very simple programs can serve as remarkably accurate models for lots of things that happen in nature. In natural science, that gives us a vastly better pool of possible models to use than we had from just math. We then see that these may be good models for how nature works. They tell us something about how nature is so easily able to make all this complicated stuff that would be very hard for us to make if we just imagined that nature worked according to math.

Now we realize that there’s a whole different kind of engineering that we can do, and we can look at all of these possible simple programs and use those to create our engineering systems.

This is different from the traditional approach, where I would say, I know these things that work. I know about levers. I know about pulleys. I know about this. I know about that. Let me incrementally build the system where I, as an engineer, know every step of how the thing is going to work as I construct it.

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