Today I’m excited to be able to announce that our company is moving into yet another new area: large-scale system modeling. Last year, I wrote about our plans to initiate a new generation of large-scale system modeling. Now we are taking a major step in that direction with the release of Wolfram SystemModeler.
SystemModeler is a very general environment that handles modeling of systems with mechanical, electrical, thermal, chemical, biological, and other components, as well as combinations of different types of components. It’s based—like Mathematica—on the very general idea of representing everything in symbolic form.
In SystemModeler, a system is built from a hierarchy of connected components—often assembled interactively using SystemModeler‘s drag-and-drop interface. Internally, what SystemModeler does is to derive from its symbolic system description a large collection of differential-algebraic and other equations and event specifications—which it then solves using powerful built-in hybrid symbolic-numeric methods. The result of this is a fully computable representation of the system—that mirrors what an actual physical version of the system would do, but allows instant visualization, simulation, analysis, or whatever.
Here’s an example of SystemModeler in action—with a 2,685-equation dynamic model of an airplane being used to analyze the control loop for continuous descent landings:
Today ten years have passed since A New Kind of Science (“the NKS book”) was published. But in many ways the development that started with the book is still only just beginning. And over the next several decades I think its effects will inexorably become ever more obvious and important.
Indeed, even at an everyday level I expect that in time there will be all sorts of visible reminders of NKS all around us. Today we are continually exposed to technology and engineering that is directly descended from the development of the mathematical approach to science that began in earnest three centuries ago. Sometime hence I believe a large portion of our technology will instead come from NKS ideas. It will not be created incrementally from components whose behavior we can analyze with traditional mathematics and related methods. Rather it will in effect be “mined” by searching the abstract computational universe of possible simple programs.
And even at a visual level this will have obvious consequences. For today’s technological systems tend to be full of simple geometrical shapes (like beams and boxes) and simple patterns of behavior that we can readily understand and analyze. But when our technology comes from NKS and from mining the computational universe there will not be such obvious simplicity. Instead, even though the underlying rules will often be quite simple, the overall behavior that we see will often be in a sense irreducibly complex.
So as one small indication of what is to come—and as part of celebrating the first decade of A New Kind of Science—starting today, when Wolfram|Alpha is computing, it will no longer display a simple rotating geometric shape, but will instead run a simple program (currently, a 2D cellular automaton) from the computational universe found by searching for a system with the right kind of visually engaging behavior.
(This is the second of a series of posts related to next week’s tenth anniversary of A New Kind of Science. The previous post covered developments since the book was published; the next covers its future.)
“You’re destroying the heritage of mathematics back to ancient Greek times!” With great emotion, so said a distinguished mathematical physicist to me just after A New Kind of Science was published ten years ago. I explained that I didn’t write the book to destroy anything, and that actually I’d spent all those years working hard to add what I hoped was an important new chapter to human knowledge. And, by the way—as one might guess from the existence of Mathematica—I personally happen to be quite a fan of the tradition of mathematics.
He went on, though, explaining that surely the main points of the book must be wrong. And if they weren’t wrong, they must have been done before. The conversation went back and forth. I had known this person for years, and the depth of his emotion surprised me. After all, I was the one who had just spent a decade on the book. Why was he the one who was so worked up about it?
And then I realized: this is what a paradigm shift sounds like—up close and personal. Continue reading
After 20 years of research, and nearly 11 years writing the book, I’d taken most things about as far as I could at that time. And so when the book was finished, I mainly launched myself back into technology development. And inspired by my work on the NKS book, I’m happy to say that I’ve had a very fruitful decade (Mathematica reinvented, CDF, Wolfram|Alpha, etc.).
I’ve been doing little bits of NKS-oriented science here and there (notably at our annual Summer School). But mostly I’ve been busy with other things. And so it’s been other people who’ve been having the fun of moving the science of NKS forward. But almost every day I’ll hear about something that’s been being done with NKS. And as we approach the 10-year mark, I’ve been very curious to try to get at least a slightly more systematic view of what’s been going on.
A place to start is the academic literature, where there’s now an average of slightly over one new paper per day published citing the NKS book—with that number steadily increasing. The papers span all kinds of areas (here identified by journal fields):