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
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
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