Fifty years ago today there was a six-year-old at a kindergarten (“nursery school” in British English) in Oxford, England who was walking under some trees and noticed that the patches of light under the trees didn’t look the same as usual. Curious, he looked up at the sun. It was bright, but he could see that one side of it seemed to be missing. And he realized that was why the patches of light looked odd.
He’d heard of eclipses. He didn’t really understand them. But he had the idea that that was what he was seeing. Excited, he told another kid about it. They hadn’t heard of eclipses. But he pointed out that the sun had a bite taken out of it. The other kid looked up. Perhaps the sun was too bright, but they looked away without noticing anything. Then the first kid tried another kid. And then another. None of them believed him about the eclipse and the bite taken out of the sun.
Edited transcript of a talk given on March 4, 2016, at the Computer History Museum, Mountain View, California.
I normally spend my time trying to build the future. But I find history really interesting and informative, and I study it quite a lot. Usually it’s other people’s history. But the Computer History Museum asked me to talk today about my own history, and the history of technology I’ve built. So that’s what I’m going to do here. Continue reading
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
In a few weeks it’ll be 25 years ago: June 23, 1988—the day Mathematica was launched.
Late the night before we were still duplicating floppy disks and stuffing product boxes. But at noon on June 23 there I was at a conference center in Santa Clara starting up Mathematica in public for the first time:
I have four children, all with very different interests. My second-youngest, Christopher, age 13, has always liked technology. And last weekend he and I went to see the wild, wacky and creative technology (and other things) on display at the Maker Faire in New York.
I had told the organizers I could give a talk. But a week or so before the event, Christopher told me he thought what I planned to talk about wasn’t as interesting as it could be. And that actually he could give some demos that would be a lot more interesting and relevant.
Christopher has been an avid Mathematica user for years now. And he likes hooking Mathematica up to interesting devices—with two recent favorites being Arduino boards and quadricopter drones.
And so it was that last Sunday I walked onto a stage with him in front of a standing-room-only crowd of a little over 300 people, carrying a quadricopter. (I wasn’t trusted with the Arduino board.)
Christopher had told me that I shouldn’t talk too long—and that then I should hand over to him. He’d been working on his demo the night before, and earlier that morning. I suggested he should practice what he was going to say, but he’d have none of that. Instead, up to the last minute, he spent his time cleaning up code for the demo.
I must have given thousands of talks in my life, but the whole situation made me quite nervous. Would the Arduino board work? Would the quadricopter fly? What would Christopher do if it didn’t?
I don’t think my talk was particularly good. But then Christopher bounced onto the stage, and soon was typing raw Mathematica code in front of everyone—with me now safely off on the side (where I snapped this picture):
(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
One day I’m sure everyone will routinely collect all sorts of data about themselves. But because I’ve been interested in data for a very long time, I started doing this long ago. I actually assumed lots of other people were doing it too, but apparently they were not. And so now I have what is probably one of the world’s largest collections of personal data.
Every day—in an effort at “self awareness”—I have automated systems send me a few emails about the day before. But even though I’ve been accumulating data for years—and always meant to analyze it—I’ve never actually gotten around to doing it. But with Mathematica and the automated data analysis capabilities we just released in Wolfram|Alpha Pro, I thought now would be a good time to finally try taking a look—and to use myself as an experimental subject for studying what one might call “personal analytics”.
Let’s start off talking about email. I have a complete archive of all my email going back to 1989—a year after Mathematica was released, and two years after I founded Wolfram Research. Here’s a plot with a dot showing the time of each of the third of a million emails I’ve sent since 1989:
I got started with science quite early in my life… with the result that I got my PhD (at Caltech, in physics) when I was 20 years old. Last weekend a young woman named Catherine Beni (whom I had met quite a few years ago) sent me mail saying she had just received her PhD from Caltech (in applied math)—also at the age of 20.
Needless to say, we were both curious who had the record for youngest Caltech PhD. Catherine said she was 20 years, 2 months and 12 days old when she did her PhD defense. Well, I knew I’d finished my PhD in November 1979—and I was born August 29, 1959. So that would also have made me around 20 years and 2 months old.
I quickly searched the OCR’ed archive that I have of my paper documents, and found this:
The month was confirmed, but frustratingly, no day was filled in. But then I remembered something about my PhD defense (the little talk that people give to officially get their theses signed off). In the middle of it, I was having a rather spirited discussion (about the second law of thermodynamics) with Richard Feynman, and suddenly the room started shaking—there was a minor earthquake. Continue reading
For nearly a quarter of a century, one of the responsibilities that I’ve taken most seriously is the shepherding of the design of Mathematica. Partly that has involved establishing foundational principles, and maintaining unity and consistency across the system. But at some point all the capabilities of Mathematica must get expressed in the individual built-in functions—like Table or NestList—that ultimately make up the system.
Each one of those functions encapsulates some piece of repeated computational work—often implemented by some deep tower of algorithms. And each one of those now 3000 or so functions requires a name.
We’re currently in the closing weeks of a (spectacular!) new version of Mathematica, and I spent part of last week doing final design reviews for some fascinating new areas of the system. And as part of those design reviews, we were confirming and tweaking some of the names we’re going to use for new functions.
The naming of functions is a strange and difficult art—a bit like an ultimately abstracted form of poetry. The goal is to take the concept and functionality of a function, and capture the essence of it in one, or two, or perhaps three, words (like Riffle, or DeleteCases, or FixedPointList)—chosen so that when someone sees those words, they immediately get the right idea about the function. In even the most succinct forms of ordinary poetry, you get at least a handful of words to communicate with. In function names, you typically get at most perhaps three.
It’s not easy to make a big software system that really fits together. It’s incredibly important, though. Because it’s what makes the whole system more than just the sum of its parts. It’s what gives the system limitless possibilities—rather than just a bunch of specific features.
But it’s hard to achieve. It requires maintaining consistency and coherence across every area, over the course of many years. But I think it’s something we’ve been very successful at doing with Mathematica. And I think it’s actually one of the most crucial assets for the long-term future of Mathematica.
It’s also a part of things that I personally am deeply involved in.
Ever since we started developing it more than 21 years ago, I’ve been the chief architect and chief designer of Mathematica‘s core functionality. And particularly for Mathematica 6, there was a huge amount of design to do. Actually, I think much more even than for Mathematica 1.
In fact, I just realized that over the course of the decade during which were developing Mathematica 6—and accelerating greatly towards the end—I spent altogether about 10,000 hours doing what we call “design reviews” for Mathematica 6, trying to make all those new functions and pieces of functionality in Mathematica 6 be as clean and simple as possible, and all fit together.
At least the way I do it, doing software design is a lot like doing fundamental science.
In fundamental science, one starts from a bunch of phenomena, and then one tries to drill down to find out what’s underneath them—to try to find the root causes, the ultimate primitives, of what’s going on.
Well, in software design, one starts from a bunch of functionality, and then one needs to drill down to find out just what ultimate primitives one needs to support them.
In science, if one does a good job at finding the primitives, then one can have a very broad theory that covers not just the phenomena one started from, but lots of others too.
And in software design, it’s the same kind of thing.
If one does a good job at finding the primitives, then one can build a very broad system that gives one not just the functionality one was first thinking about, but lots more too. Continue reading