STEPHEN WOLFRAM

The most important precedents deal with the whole idea of symbolic programming - the notion of setting up symbolic expressions that can represent anything one wants, and then having functions that operate on both their structure and content.

What I realized is that if we're going to be able to have a theory about what happens in, for example, nature there has to ultimately be some rule by which nature operates. But the issue is does that rule have to correspond to something like a mathematical equation, something that we have sort of created in our human mathematics? And what I realized is that now with our understanding of computation and computer programs and so on, there is actually a much bigger universe of possible rules to describe the natural world than just the mathematical equation kinds of things.

There are a few very small incompatible changes - I really doubt most people will ever run into them.

So the thing I realized rather gradually - I must say starting about 20 years ago now that we know about computers and things - there's a possibility of a more general basis for rules to describe nature.

...All the wonders of our universe can in effect be captured by simple rules, yet ... there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold.

You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.

Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today.

People have been trying to do kind of natural language processing with computers for decades and there has only been sort of slow progress in that in general. It turned out the problem we had to solve is sort of the reverse of the problem people usually have to solve. People usually have to solve the problem of you're given you know thousands, millions of pages of text, go have the computer understand this.

The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?

The fact that the same symbolic programming primitives work for those as work for math kinds of things, I think, really validates the idea of symbolic programming being something pretty general.

The most important precedents deal with the whole idea of symbolic programming - the notion of setting up symbolic expressions that can represent anything one wants, and then having functions that operate on both their structure and content.

The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?

You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.

The fact that the same symbolic programming primitives work for those as work for math kinds of things, I think, really validates the idea of symbolic programming being something pretty general.

There are a few very small incompatible changes - I really doubt most people will ever run into them.

So the thing I realized rather gradually - I must say starting about 20 years ago now that we know about computers and things - there's a possibility of a more general basis for rules to describe nature.

Well, the first thing to say is that we've worked hard to maintain compatibility, so that any program written with an earlier version of Mathematica can run without change in 3.0, and any notebook can be converted.

Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today.

People have been trying to do kind of natural language processing with computers for decades and there has only been sort of slow progress in that in general. It turned out the problem we had to solve is sort of the reverse of the problem people usually have to solve. People usually have to solve the problem of you're given you know thousands, millions of pages of text, go have the computer understand this.

What I realized is that if we're going to be able to have a theory about what happens in, for example, nature there has to ultimately be some rule by which nature operates. But the issue is does that rule have to correspond to something like a mathematical equation, something that we have sort of created in our human mathematics? And what I realized is that now with our understanding of computation and computer programs and so on, there is actually a much bigger universe of possible rules to describe the natural world than just the mathematical equation kinds of things.

...All the wonders of our universe can in effect be captured by simple rules, yet ... there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold.