Stephen Wolfram

This evening I took BART into San Francisco to hear Dr. Stephen Wolfram talk about the ideas in his A New Way of Science. I’m about ½” into the book and have found it a relatively easy read for a science book but not that relevant to my interests. The most engaging aspect is Wolfram’s audacious stance, that the rest of the scientific world has been barking up the wrong tree since the Renaissance, if not earlier, and he’s seen what’s been there in plain sight, that everyone else overlooked, and it forces a revision of virtually every scientific discipline from physics to economics.

Wolfram’s doing a whistle stop tour to promote the book and to lay the foundation for his new science. Tonight he spoke at the Herbst Theater across Van Ness Avenue from San Francisco City Hall.

Ron Eisenhart “interviewed” Dr. Wolfram, tossing him a dozen pre-arranged questions. I pulled out my laptop and jotted notes as the conversation progressed. Wolfram is so brilliant that he makes the complex sound simple, so I was actually able to keep up with him most of the time.

If you haven’t heard Wolfram’s story, check the Wired articlefrom June 2002. If memory serves (I read the Wired piece when it came out), Wolfram arrived at Oxford in his early teens, attended one day of first-year classes and decided he’d had enough of that. Next day, he attended second-year classes and found that below him, too. He stopped attending class. When exams came around, young Stephen scored top in his class. Graduated with a PhD in theoretical physics from Cal Tech at the age of 20. Bright kid. You might also check Michael Malone's piece on Wolfram in Forbes ASAP, God, Stephen Wolfram, and Everything Else, which was the first time I'd heard of the guy.

A discussion with Stephen Wolfram

Stephen was making inquiries about cosmology, how structures evolve in our universe, and was surprised to find that particle physics had remarkably little to say about nature. We were using human constructs (Newton’s Laws, Kepler) to interpret nature. That got him started on computer programs.

Were you to look into the world of programs, what would you say these programs really do? It’s like exploring a new part of the world, with new flora and fauna. You start with simple things, you expect to get simple results. In fact, you find that you get very complex behavior.

Here’s his favorite, rule 30:


Click for larger version.

This is really complicated. There’s no easy way to describe it. Statistical methods would tell you a line from the top down would be completely random. And this is the result of a few very simple starting rules.

Stephen looked at cellular automata for a number of years. These are simple little programs built of rules like “when you find a white square, change it to a black square unless there’s black square above it.” He realized that there’s a much larger world of possible programs out there.

One of Wolfram’s rules is that if you really need a better tool, you’d better make it yourself. This is where Mathematica came from. Having developed the tool, he returned to his initial field of inquiry. In 1991, when Mathematica came out, he just sort of “pointed it out there.” He discovered that what he’d found in cellular automata had much broader implications. He looked at physics, biology, chemistry, and so on. He found something wrong with most of these basic areas. What he’d believed simply wasn’t true.

What’s the simple rule that governs the growth of a snowflake? He discovered an explanation. Same for explaining fluid turbulence. Is there some explanation that doesn’t call for outside intervention? Yes. Rule 30 gets you there. Things may look random but they will reliably come out the same again and again. The randomness is built-in, not added on.

Simple rules can lead to extremely complex and random behavior. Add a color and things don’t change. A new rule doesn’t make things more complicated. It’s already as complicated as it ever may be.

Wolfram, speaking rapidly with an Oxford accent, is wearing light gray Nikes, a pink shirt, black chinos and a dark brown tweed jacket. Very much at ease.


If one wants to find complex things in the world, biology is a good place to look. It seems as if natural selection must have been at work over the course of geological time. You assume it took a lot a time to develop complicated things. In reality, human engineers work on things in areas where they better be able to foresee the result. Nature is not under this sort of constraint. Nature’s not just Darwinism.

Take mollusk shells. Something quite similar to the Rule 30 diagram appears on a shell Stephen pulls out of his pocket.

Charles Darwin? There’s come to be a belief that Natural Selection is sort of an all-compelling force. But this is not really where all the complex stuff comes from. Darwin’s belief was more limited and correct than what his interpreters have passed along. One of the most important roles of natural selection is to simplify, not to make things more complex.

We all know about the fundamental unifying theory of physics. Laughter in the audience. (“I learned about it when I was a kid,” says Wolfram).

For instance, space. We usually think of space as background. But if you really want to understand space, you’ve got to look at it as something by itself. (Missed a couple of sentences here.) The collective effect of these things sort of reflect what we feel about things like space and time. (Huh? Those must have been important sentences; this makes no sense.)

If one believes the rule for the universe is really simple, it changes the way you look at the universe. If you start by asking, rule by rule, “Is this a rule for the universe?”, you usually find, “No, this is not a rule for the universe.” The universe has had a long time to go through its calculations.

Determinism? If I think, “I’m choosing to be yellow or black,” but in reality the model is dictating it… There are these issues outside of the realm of science. The concept of mathematical irreducibility, as with the predictability of the behavior of robots, doesn’t really constrain the eventual results. Remember, a few simple rules can generate randomness. Logic is but one of many modalities.

Implications for technology? If you are trying to do mechanical things, you get a tool, e.g. a hammer to pound in nails. But in the realm of intellect, the computer can go after it. It’s odd that this has had little impact on the foundations of natural science. Making a universal computer, millions of gates and lots of work in Silicon Valley, you might think this takes an amazing amount of effort. Actually, it may not be so tough. A molecule might implement these rules. That’s one direction.

Stephen sees himself producing new ways of making things. These are fundamental new elements you could use in growing new morphologies.


Stephen just spent 10 years (and 100 mouse-miles) writing the book. The guy’s into measuring things. He knows that a 40,000 keystroke-day is a good day, a 10,000 keystroke-day hasn’t been very productive.

There isn’t a “Journal of Big Ideas” where one publishes these rather rare happenings. Hence, he squirreled away for ten years to produce his book. It was probably the biggest project he’ll ever do.

The first thing Stephen is doing is recovering. Next will come building more tools. He needs them for studying other fundamental questions.

This has been sort of a one-person operation this far. How do you grow a science? He’s building a community. Lots of enthusiasm. 15,000 inbound email messages. Stephen would like to architect the new science.


Q&A. Math is simple. The axioms take but two pages in his book. The axioms are simple but the explanations are lengthy.

In the early nineteenth century, the belief was that any math issue could be shown to be true or false. Godel disproved this. His stating point was “This statement cannot be proved.”

I tried to ask a question but couldn’t get the attention of the people carrying the remote microphones in the auditorium. (I was sitting in seat A-1, the closest box seat to the stage, apparently undesirable but great as far as I was concerned.)

Had I the opportunity, I intended to ask Dr. Wolfram’s thoughts on today’s news that 96% of the universe is “dark matter.” Tough to identify those laws of the universe if most of it is invisible.

90 minutes after things kicked off, the audience applauded and Wolfram disappeared from sight.


So, is Wolfram a genius or a very confused individual? Probably the former although only a few results of his findings generalize to my work.

1. Simple things can have complex outcomes.
2. Random can arise without outside intervention.
3. Human concepts make scientific explanations overly complex.

Maybe I’ll wake up with new insights in the morning. Perhaps playing with Wolfram’s software will clear things up. Or maybe you’ve got this figured out. If so, please make a comment below. Thanks.

Ray Kurzweil's not convinced:

    Some of the phenomena in nature (e.g., clouds, coastlines) are explained by repetitive simple processes such as cellular automata and fractals, but intelligent patterns (e.g., the human brain) require an evolutionary process (or, alternatively the reverse-engineering of the results of such a process). Intelligence is the inspired product of evolution, and is also, in my view, the most powerful "force" in the world, ultimately transcending the powers of mindless natural forces.

    In summary, Wolfram's sweeping and ambitious treatise paints a compelling but ultimately overstated and incomplete picture. Wolfram joins a growing community of voices that believe that patterns of information, rather than matter and energy, represent the more fundamental building blocks of reality. Wolfram has added to our knowledge of how patterns of information create the world we experience and I look forward to a period of collaboration between Wolfram and his colleagues so that we can build a more robust vision of the ubiquitous role of algorithms in the world.

some of the historical notes from the book


Posted by Jay Cross at February 12, 2003 11:34 PM | TrackBack
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