People are used to producing prose—and sometimes pictures—to express themselves. But in the modern age of computation, something new has become possible that I’d like to call the computational essay.
I’ve been working on building the technology to support computational essays for several decades, but it’s only very recently that I’ve realized just how central computational essays can be to both the way people learn, and the way they communicate facts and ideas. Professionals of the future will routinely deliver results and reports as computational essays. Educators will routinely explain concepts using computational essays. Students will routinely produce computational essays as homework for their classes.
Here’s a very simple example of a computational essay:
How far can one get in teaching computational thinking to high-school students in two weeks? Judging by the results of this year’s Wolfram High-School Summer Camp the answer is: remarkably far.
I’ve been increasingly realizing what an immense and unique opportunity there now is to teach computational thinking with the whole stack of technology we’ve built up around the Wolfram Language. But it was a thrill to see just how well this seems to actually work with real high-school students—and to see the kinds of projects they managed to complete in only two weeks.
I originally expected my book’s readers would be high schoolers and up. But it’s actually also found a significant audience among middle schoolers (11- to 14-year-olds). So the question now is: can one teach the core concepts of modern machine learning even to middle schoolers? Well, the interesting thing is that—thanks to the whole technology stack we’ve now got in the Wolfram Language—the answer seems to be “yes”! Continue reading
“In the next hour I’m going to try to make a new discovery in mathematics.” So I began a few days ago at two different hour-long Math Encounters events at the National Museum of Mathematics (“MoMath”) in New York City. I’ve been a trustee of the museum since before it opened in 2012, and I was looking forward to spending a couple of hours trying to “make some math” there with a couple of eclectic audiences from kids to retirees.
People usually assume that new discoveries aren’t things one can ever see being made in real time. But the wonderful thing about the computational tools I’ve spent decades building is that they make it so fast to implement ideas that it becomes realistic to make discoveries as a kind of real-time performance art. Continue reading
Computational thinking needs to be an integral part of modern education—and today I’m excited to be able to launch another contribution to this goal: Wolfram|Alpha Open Code.
Every day, millions of students around the world use Wolfram|Alpha to compute answers. With Wolfram|Alpha Open Code they’ll now not just be able to get answers, but also be able to get code that lets them explore further and immediately apply computational thinking. Continue reading
Computational thinking is going to be a defining feature of the future—and it’s an incredibly important thing to be teaching to kids today. There’s always lots of discussion (and concern) about how to teach traditional mathematical thinking to kids. But looking to the future, this pales in comparison to the importance of teaching computational thinking. Yes, there’s a certain amount of traditional mathematical thinking that’s needed in everyday life, and in many careers. But computational thinking is going to be needed everywhere. And doing it well is going to be a key to success in almost all future careers.
Doctors, lawyers, teachers, farmers, whatever. The future of all these professions will be full of computational thinking. Whether it’s sensor-based medicine, computational contracts, education analytics or computational agriculture—success is going to rely on being able to do computational thinking well.
I’ve noticed an interesting trend. Pick any field X, from archeology to zoology. There either is now a “computational X” or there soon will be. And it’s widely viewed as the future of the field.
I’m excited today to be able to announce the launch of Wolfram Programming Lab—an environment for anyone to learn programming and computational thinking through the Wolfram Language. You can run Wolfram Programming Lab through a web browser, as well as natively on desktop systems (Mac, Windows, Linux).
But a little while ago, I realized there was another book I had to write: a book that would introduce people with no knowledge of programming to the Wolfram Language and the kind of computational thinking it allows.
For as long as I can remember, my all-time favorite activity has been creating ideas and turning them into reality—a kind of “entrepreneurism of ideas”. And over the years—in science, technology and business—I think I’ve developed some pretty good tools and strategies for doing this, that I’ve increasingly realized would be good for a lot of other people (and organizations) too.
So how does one spread idea entrepreneurism—entrepreneurism centered on ideas rather than commercial enterprises? Somewhat unwittingly I think we’ve developed a rather good vehicle—that’s both a very successful educational program, and a fascinating annual adventure for me.
Twelve years ago my book A New Kind of Science had just come out, and we were inundated with people wanting to learn more, and get involved in research around it. We considered various alternatives, but eventually we decided to organize a summer school where we would systematically teach about our methodology, while mentoring each student to do a unique original project.
From the very beginning, the summer school was a big success. And over the years we’ve gradually improved and expanded it. It’s still the Wolfram Science Summer School—and its intellectual core is still A New Kind of Science. But today it has become a broader vehicle for passing on our tools and strategies for idea entrepreneurism.
This year’s summer school just ended last week. We had 63 students from 21 countries—with a fascinating array of backgrounds and interests. Most were in college or graduate school; a few were younger or older. And over the course of the three weeks of the summer school—with great energy and intellectual entrepreneurism—each student worked towards their own unique project. 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
Last week I wrote about our large-scale plan to use new technology we’re building to inject sophisticated computation and knowledge into everything. Today I’m pleased to announce a step in that direction: working with the Raspberry Pi Foundation, effective immediately there’s a pilot release of the Wolfram Language—as well as Mathematica—that will soon be bundled as part of the standard system software for every Raspberry Pi computer.
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):
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
The long-term goal is to have an assistant app for every major course, from elementary school to graduate school. And the good news is that Wolfram|Alpha has the breadth and depth of capabilities to make this possible—and not only in traditionally “computational” kinds of courses.
The concept of these apps is to make it as quick and easy as possible to access the particular capabilities of Wolfram|Alpha relevant for specific courses. Each app is organized according to the major curriculum units of a course. Then within each section of the app, there are parts that cover each of the particular types of problems relevant to that unit. Continue reading
Our 2007 NKS Summer School started about two weeks ago, and one of my roles there was to show a little of how NKS is done.
In the past, it would have been pretty unrealistic to show this in any kind of live way. But with computer experiments, and especially with Mathematica, that’s changed. And now it’s actually possible to make real discoveries in real time in front of live audiences.
I’ve done a few dozen “live experiments” now (here is an account of one from 2005). My scheme is as follows. Sometime between a few hours and a few minutes before the live experiment, I come up with a topic that I’m pretty sure hasn’t been studied before. Then I make sure to avoid thinking about it until I’m actually in front of the live audience.
Then, once the experiment starts, I have a limited time to discover something. Just by running Mathematica. Preferably with a little help from the audience. And occasionally with a little help from references on the web.
Every live experiment is an adventure. And it seems like almost every time, at around the halfway point, things look bad. We’ve tried lots of things. We’ve opened lots of threads. But nothing’s coming together.
But then, somehow, things almost always manage to come together. And we manage to discover something. That’s often pretty interesting. (There are still papers coming out now based on the live experiment I did at our very first Summer School, back in 2003).
I usually make my first live experiment at each Summer School be a piece of “pure NKS”: an abstract investigation of some simple program out in the computational universe.
This year I decided to take a look at an “old chestnut” that I’d recently been reminded about: a simple program (though it wasn’t thought of that way then) that was actually first investigated all the way back in 1920. Continue reading