Category: Other

Oh My Gosh, It’s Covered in Rule 30s!

A British Train Station

A week ago a new train station, named “Cambridge North”, opened in Cambridge, UK. Normally such an event would be far outside my sphere of awareness. (I think I last took a train to Cambridge in 1975.) But last week people started sending me pictures of the new train station, wondering if I could identify the pattern on it:

Cambridge North train station

And, yes, it does indeed look a lot like patterns I’ve spent years studying—that come from simple programs in the computational universe. My first—and still favorite—examples of simple programs are one-dimensional cellular automata like this:

One-dimensional cellular automata
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Quick, How Might the Alien Spacecraft Work?

[This post is about the movie Arrival; there are no movie spoilers here.]

Arrival trailer image

Connecting with Hollywood

“It’s an interesting script” said someone on our PR team. It’s pretty common for us to get requests from movie-makers about showing our graphics or posters or books in movies. But the request this time was different: could we urgently help make realistic screen displays for a big Hollywood science fiction movie that was just about to start shooting? Continue reading

A Short Talk on AI Ethics

Last week I gave a talk (and did a panel discussion) at a conference entitled “Ethics of Artificial Intelligence” held at the NYU Philosophy Department’s Center for Mind, Brain and Consciousness. Here’s the video and a transcript:

Thanks for inviting me here today.

You know, it’s funny to be here. My mother was a philosophy professor in Oxford. And when I was a kid I always said the one thing I’d never do was do or talk about philosophy. But, well, here I am. Continue reading

Computational Law, Symbolic Discourse and the AI Constitution

Leibniz’s Dream

Computational Law, Discourse Language and the AI Constitution Gottfried Leibniz—who died 300 years ago this November—worked on many things. But a theme that recurred throughout his life was the goal of turning human law into an exercise in computation. Of course, as we know, he didn’t succeed. But three centuries later, I think we’re finally ready to give it a serious try again. And I think it’s a really important thing to do—not just because it’ll enable all sorts of new societal opportunities and structures, but because I think it’s likely to be critical to the future of our civilization in its interaction with artificial intelligence.

Human law, almost by definition, dates from the very beginning of civilization—and undoubtedly it’s the first system of rules that humans ever systematically defined. Presumably it was a model for the axiomatic structure of mathematics as defined by the likes of Euclid. And when science came along, “natural laws” (as their name suggests) were at first viewed as conceptually similar to human laws, except that they were supposed to define constraints for the universe (or God) rather than for humans.

Over the past few centuries we’ve had amazing success formalizing mathematics and exact science. And out of this there’s a more general idea that’s emerged: the idea of computation. In computation, we’re dealing with arbitrary systems of rules—not necessarily ones that correspond to mathematical concepts we know, or features of the world we’ve identified. So now the question is: can we use the ideas of computation, in very much the way Leibniz imagined, to formalize human law? Continue reading

Pi or Pie?! Celebrating Pi Day of the Century (And How to Get Your Very Own Piece of Pi)

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Pictures from Pi Day now added »

This coming Saturday is “Pi Day of the Century”. The date 3/14/15 in month/day/year format is like the first digits of And at 9:26:53.589… it’s a “super pi moment”.

3/14/15 9:26:53.589... a "super pi moment" indeed

Between Mathematica and , I’m pretty sure our company has delivered more π to the world than any other organization in history. So of course we have to do something special for Pi Day of the Century.

Pi Day of the Century with Wolfram: 3.14.15 9:26:53
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A Speech for (High-School) Graduates

Last weekend I gave a speech at this year’s graduation event for the Stanford Online High School (OHS) that one of my children has been attending. Here’s the transcript:

Thank you for inviting me to be part of this celebration today—and congratulations to this year’s OHS graduates.

You know, as it happens, I myself never officially graduated from high school, and this is actually the first high school graduation I’ve ever been to.

It’s been fun over the past three years—from a suitable parental distance of course—to see my daughter’s experiences at OHS. One day I’m sure everyone will know about online high schools—but you’ll be able to say, “Yes, I was there when that way of doing such-and-such a thing was first invented—at OHS.”

It’s great to see the OHS community—and to see so many long-term connections being formed independent of geography. And it’s also wonderful to see students with such a remarkable diversity of unique stories.

Of course, for the graduates here today, this is the beginning of a new chapter in their stories.

I suspect some of you already have very definite life plans. Many are still exploring. It’s worth remembering that there’s no “one right answer” to life. Different people are amazingly different in what they’ll consider an “‘A’ in life”. I think the first challenge is always to understand what you really like. Then you’ve got to know what’s out there to do in the world. And then you’ve got to solve the puzzle of fitting the two together. Continue reading

What Should We Call the Language of Mathematica?

At the core of Mathematica is a language. A very powerful symbolic language. Built up with great care over a quarter of a century—and now incorporating a huge swath of knowledge and computation.

Millions and millions of lines of code have been written in this language, for all sorts of purposes. And today—particularly with new large-scale deployment options made possible through the web and the cloud—the language is poised to expand dramatically in usage.

But there’s a problem. And it’s a problem that—embarrassingly enough—I’ve been thinking about for more than 20 years. The problem is: what should the language be called?

Usually on this blog when I discuss our activities as a company, I talk about progress we’ve made, or problems we’ve solved. But today I’m going to make an exception, and talk instead about a problem we haven’t solved, but need to solve.

You might say, “How hard can it be to come up with one name?” In my experience, some names are easy to come up with. But others are really really hard. And this is an example of a really really hard one. (And perhaps the very length of this post communicates some of that difficulty…)


Let’s start by talking a little about names in general. There are names like, say, “quark”, that are in effect just random words. And that have to get all their meaning “externally”, by having it explicitly described. But there are others, like “website” for example, that already give a sense of their meaning just from the words or word roots they contain.

I’ve named all sorts of things in my time. Science concepts. Technologies. Products. Mathematica functions. I’ve used different approaches in different cases. In a few cases, I’ve used “random words” (and have long had a Mathematica-based generator of ones that sound good). But much more often I’ve tried to start with a familiar word or words that capture the essence of what I’m naming. Continue reading

Welcome, National Museum of Mathematics

I was just in New York City for the grand opening of the National Museum of Mathematics. Yes, there is now a National Museum of Mathematics, right in downtown Manhattan. And it’s really good—a unique and wonderful place. Which I’m pleased to say I’ve been able to help in various ways in bringing into existence over the past 3 years.

Museum of Mathematics logo

Of all companies, ours is probably the one that has been most involved in bringing math to the world (Mathematica, Wolfram|Alpha, Wolfram Demonstrations Project, MathWorld, Computer-Based Math, Wolfram Foundation, …). And for a long time I’ve thought how nice it would be if there were a substantial, physical, “museum of mathematics” somewhere. But until recently I’d sort of assumed that if such a thing were going to exist, I’d have to be the one to make it happen.

A little more than 3 years ago, though, my older daughter picked out of my mail a curious folding geometrical object—which turned out to be an invitation to an event about the creation of a museum of mathematics. At first, it wasn’t clear what kind of museum this was supposed to be. But as soon as we arrived at the event, it started to be much clearer: this was “math as physical experience”. With the centerpiece of the event, for example, being a square-wheeled tricycle that one could ride on a cycloidal “road”—a mathematical possibility that, as it happens, was the subject of some early Mathematica demonstrations. Continue reading

A .data Top-Level Internet Domain?


There’s been very little change in top-level internet domains (like .com, .org, .us, etc.) for a long time. But a number of years ago I started thinking about the possibility of having a new .data top-level domain (TLD). And starting this week, there’ll finally be a period when it’s possible to apply to create such a thing.

It’s not at all clear what’s going to happen with new TLDs—or how people will end up feeling about them. Presumably there’ll be TLDs for places and communities and professions and categories of goods and events. A .data TLD would be a slightly different kind of thing. But along with some other interested parties, I’ve been exploring the possibility of creating such a thing. Continue reading

Music, Mathematica, and the Computational Universe

This week I’m giving a talk at a conference on Mathematics and Computation in Music (MCM 2011)… so I decided to collect some of my thoughts on such topics…


How difficult is it to generate human-like music? To pass the analog of the Turing test for music?

Though music typically has a certain formal structure—as the Pythagoreans noted 2500 years ago—it seems at its core somehow fundamentally human: a reflection of raw creativity that is almost a defining characteristic of human capabilities.

But what is that creativity? Is it something that requires the whole history of our biological and cultural evolution? Or can it exist just as well in systems that have nothing directly to do with humans?

In my work on A New Kind of Science, I studied the computational universe of possible programs—and found that even very simple programs can show amazingly rich and complex behavior, on a par, for example, with what one sees in nature. And through my Principle of Computational Equivalence I came to believe that there can be nothing that fundamentally distinguishes our human capabilities from all sorts of processes that occur in nature—or in very simple programs.

But what about music? Some people used their belief that “no simple program will ever create great music” to argue that there must be something wrong with my Principle of Computational Equivalence.

So I became curious: is there really something special and human about music? Or can it in fact be created perfectly well in an automatic, computational way?

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Talking about Computing and Philosophy

Wolfram|Alpha, A New Kind of Science, and even Mathematica all have aspects that are philosophy projects. Each of them, in different ways, informs questions in philosophy—and are themselves informed by philosophical ideas and discoveries.

Indeed, the very fact that I decided Wolfram|Alpha might be a possible project was the result of what amounts to a philosophical realization that I learned from A New Kind of Science: there is no bright line that identifies “intelligence”; it is all just computation.

I don’t get to talk much about philosophy. But here is a recording of a keynote speech I was recently asked to give about “computing and philosophy”.

Launching a New Era in Large-Scale Systems Modeling

Over the past 25 years, we’ve been fortunate enough to make a mark in all sorts of areas of science and technology. Today I’m excited to announce that we’re in a position to tackle another major area: large-scale systems modeling.

It’s a huge and important area, long central to engineering, and increasingly central to fields like biomedicine. To do it right is also incredibly algorithmically demanding. But the exciting thing is that now we’ve finally assembled the technology stack that we need to do it—and we’re able to begin the process of making large-scale systems modeling an integrated core feature of Mathematica, accessible to a very broad range of users.

Lots of remarkable things will become possible. Using the methodology we’ve developed for Wolfram|Alpha, we’ll be curating not only data about systems and their components, but also complete dynamic models. Then we’ll have the tools to easily assemble models of almost arbitrary complexity—and to put them into algorithmic form so that they can be simulated, optimized, validated, visualized or manipulated by anything across the Mathematica system.

Making models computable

And then we’ll also be able to inject large-scale models into the Wolfram|Alpha system, and all its deployment channels.

So what does this mean? Here’s an example. Imagine that there’s a model for a new kind of car engine—probably involving thousands of individual components. The model is running in Mathematica, inside a Wolfram|Alpha server. Now imagine someone out in the field with a smartphone, wondering what will happen if they do a particular thing with an engine.

Well, with the technology we’re building, they should be able to just type (or say) into an app: “Compare the frequency spectrum for the crankshaft in gears 1 and 5″. Back on the server, Wolfram|Alpha technology will convert the natural language into a definite symbolic query. Then in Mathematica the model will be simulated and analyzed, and the results—quantitative, visual or otherwise—will be sent back to the user. Like a much more elaborate and customized version of what Wolfram|Alpha would do today with a question about a satellite position or a tide.

OK. So what needs to happen to make all this stuff possible? To begin with, how can Mathematica even represent something like a car—with all its various physical components, moving and running and acting on each other?
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Touch Press: The Second Book

“Someone has to make the first great ebook publishing company; it might as well be us.” So I said a few weeks before the iPad was released this April. And a little while later Touch Press was formed. The iPad was released, and simultaneously, Touch Press’s first book The Elements was released. The book has been on the iPad bestseller list ever since—in addition to being featured in all sorts of iPad television commercials and the like.

Well, it’s good for a publishing company to have a successful first book.  But for me it’s been getting a little old telling people that I’m a partner in a new publishing company, but so far we’ve only published one book. So it’s exciting to be able to say that as of this week, Touch Press has a second book: Solar System.


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Welcome to the Blog

I like to write.  And most days I actually do write a lot.  But most of it is not visible to the world at large.  Hundreds of internal emails and documents.  Pieces of content inside Wolfram|Alpha or Mathematica.  The occasional unsigned public webpage or other document.

My purpose in this blog is to have a visible outlet for a little more of what I do, and what I think about.

I’m constantly thinking about new things.  Coming up with new ideas. Getting new perspectives.  Thinking of new possible projects to do.

Usually I don’t talk much about things until or unless I’ve actually done something real with them.  Which can take years, and sometimes decades—if it happens at all.

But I’ve decided it’s time I started writing a little more about what I’m thinking about—rather than always waiting to have a complete, finished, project or product.

I’d also like to write about some of the things that happen in my life.  In some ways my life is delightfully simple and ordinary.  But in others I’ve chosen to make it pretty far out on the curve.

Some of the wildest and juiciest things that happen I won’t be able to write publicly about, typically because they’re someone’s corporate or personal secrets.  Or because, frankly, I don’t want to tell the world about some things I’m doing before I’m ready.

I’m a great believer in the value of history, not least because I think it’s the best way to have an informed view about the future.  I’ve also been a collector of stories—often as a participant.  Sometimes the stories aren’t appropriate for public consumption, at least at the time.  But I’ve now been around long enough that it’s beginning to be OK to tell pretty much any of the earlier ones.  So I hope to have a chance to do that on this blog.

There’s a lot that I could write—about all sorts of topics.  Some of it is timely; some of it I just think I should write down sometime.

I’ll enjoy writing whatever I end up writing.  But if people want to request particular topics, please contact me. I suspect there are a lot of things where I might have something interesting to say, but I’ve never realized it.  So ask me!

The Space of All Possible Bridge Shapes

(This post was originally published on the Wolfram Blog.)

When I hear about something like Wednesday’s bridge collapse, I immediately wonder whether any of the science I’ve worked on can be of any help.

Bridge design is one of the classic—almost iconic—successes of traditional mathematical science.

And when I first talked about A New Kind of Science, a not uncommon reaction was precisely, “But can it help build better bridges?”

Well, as a matter of fact, I rather suspect it can.

Bridges have a long history. Early on, only a few types seem to have been used. But with the arrival of iron structures in the 1800s there was a kind of “Cambrian explosion” of different types of truss bridges:

Bridge structures

But what is the very best bridge structure, say from the point of view of robustness? There’s a huge universe of possibilities. But so far, only a tiny corner has been explored–and that mostly in the 1800s.

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