Mathematica 1.0 was released on June 23, 1988—now nearly 19 years ago. And normally, after 19 years, pretty much all one expects from software products is slow growth and incremental updates.

But as in so many things, Mathematica today just became a big exception.

Some people have said that Mathematica 6.0 shouldn’t even be called “Mathematica” at all. That it’s something so qualitatively new and different that it should be given a completely different name.

Well, perhaps I’m just too sentimental. Or too steeped in history. Or too naive about branding. But to me there’s no choice. We owe it to all the foundations we’ve laid these past twenty years to still call what we’ve built today “Mathematica.”

Realistically, I think it took us ten years after Mathematica 1.0 just to realize what a powerful thing we had in Mathematica.

We’d always talked about “symbolic programming,” and how it let us unify a lot of different ideas and areas. But sometime around the mid-1990s it began to dawn on us just what an amazing thing symbolic programming actually is.

And we began to think that there might be a whole new level one could reach in computing if one really did everything one could with symbolic programming.

Well, that was an intellectual challenge we couldn’t resist. So about ten years ago, we embarked on seeing just what might be possible. Continue reading

(This post was originally published on the NKS Forum.)

Last Friday (April 28, 2006) would have been Kurt Gödel’s 100th birthday. I agreed to try to write something about it for publication in a newspaper … which had the dual misfeatures that (a) I had to compress what I was saying and (b) that it didn’t actually get done…

Still, I thought people on the Forum might find my draft interesting … so here it is. Please recognize that this wasn’t polished for final publication…

When Kurt Gödel was born—one hundred years ago today—the field of mathematics seemed almost complete. Two millennia of development had just been codified into a few axioms, from which it seemed one should be able almost mechanically to prove or disprove anything in mathematics—and, perhaps with some extension, in physics too.

Twenty-five years later things were proceeding apace, when at the end of a small academic conference, a quiet but ambitious fresh PhD involved with the Vienna Circle ventured that he had proved a theorem that this whole program must ultimately fail.

In the seventy-five years since then, what became known as Gödel’s theorem has been ascribed almost mystical significance, sowed the seeds for the computer revolution, and meanwhile been practically ignored by working mathematicians—and viewed as irrelevant for broader science.

The ideas behind Gödel’s theorem have, however, yet to run their course. And in fact I believe that today we are poised for a dramatic shift in science and technology for which its principles will be remarkably central.

Gödel’s original work was quite abstruse. He took the axioms of logic and arithmetic, and asked a seemingly paradoxical question: can one prove the statement “this statement is unprovable”? Continue reading

(This post was originally published on the NKS Forum.)

I sent the following today to our NKS mailing list:

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Today [May 14, 2004] marks the second anniversary of the release of A New Kind of Science. And I’m very happy to be able to report that NKS is continuing to develop extremely well.

A wonderful community is forming around the ideas of NKS. The pace of research and applications is steadily building—with an average of about one new paper now appearing every day. NKS classes and courses are being taught. And several times each week we hear about an ambitious new initiative based on NKS—in technology, or art, or business or somewhere else.

We’re trying to do our part to help. Earlier this year we released the online version of the complete book. We launched the NKS Forum. We just sponsored the second annual conference: NKS 2004. And we’re working hard to make wolframscience.com the best possible reference source and meeting place for the NKS community.
Continue reading

(This post was originally published on the NKS Forum.)

At the NKS 2004 conference I did my now-traditional “live computer experiment”. This time the topic I picked came from a question someone asked at the minicourse before the conference: does increasing the “range” of a cellular automaton have a big effect on its behavior?

I decided to investigate a simple version of this question.

In an ordinary r=1 cellular automaton, the new color of a particular cell depends on the previous colors of cells with offsets -1, 0, 1. The question I asked was then: what happens if the offsets are larger?

In the simplest non-trivial cellular automata, the color of a cell depends on the previous colors of two cells. In the ordinary short-range case, the cells have offsets -1, 1. But now we can ask what happens if instead they have offsets -1, m. Continue reading

(This post was originally published on the NKS Forum.)

Today (December 28, 2003) would have been John von Neumann’s 100th birthday—if he had not died at age 53 in 1957. I’ve been interested in von Neumann for many years—not least because his work touched on some of my most favorite topics. He is mentioned in 12 separate places in my book—second in number only to Alan Turing, who appears 19 times.

I always feel that one can appreciate people’s work better if one understands the people themselves better. And from talking to many people who knew him, I think I’ve gradually built up a decent picture of John von Neumann as a man.

He would have been fun to meet. He knew a lot, was very quick, always impressed people, and was lively, social and funny. Continue reading

(This post was originally published on the NKS Forum.)

There’s a certain complexity to many of the characteristic forms used in Christmas images: snowflakes, Christmas trees, frost patterns, etc.

And as in so many other cases, it’s rather easy to capture the essence of these forms using very simple cellular automaton rules.

So that means it’s easy to use cellular automaton rules to make Christmas-like images.

Well, going through some of my archives recently, I was reminded that I did that almost exactly twenty years ago—for Christmas 1983. (The actual file date is November 22, 1983.) Continue reading