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.

The summer school is part idea incubator, part course, part hackathon and part mentoring event. And it’s become a tradition for me to open it with a concentrated burst of idea entrepreneurism: a live experiment in which over the course of an hour or so I try—live and in public—to discover or invent something new.

Realistically, what makes this—and indeed much of what’s done at the summer school—possible is what’s now the Wolfram Language, with all its built-in knowledge and automation, as well as immediate presentation capabilities.

My rule for live experiments is that apart from spending a few minutes beforehand coming up with a topic (sometimes just by opening A New Kind of Science at random), I don’t think at all about what I’m going to do. The experiment is always fresh and spontaneous—and quite an adventure for all concerned. It’s a strange kind of intellectual performance, and it takes quite a bit of concentration. But I think it’s pretty educational to watch—not least because most people have never seen something done from scratch in real time like this.

There are always ups and downs in the course of a live experiment—and sometimes it seems that all is lost. But so far, in dozens of live experiments I’ve done, I’ve always found a way to navigate them to some kind of success. And seeing this always seems quite empowering to people; and makes this kind of idea entrepreneurism feel like something close at hand, that they can do too.

This year I actually did two live experiments. My first one was a piece of pure science that involved numbers. The idea is pretty elementary: just take a number, write it in base 2, manipulate its digits, then add it to the original number. Then iterate this many times. Here’s the little piece of Wolfram Language code I wrote during the live experiment to do this:

In A New Kind of Science, I did a version of this where the digit manipulation consisted of reversing the whole sequence of digits. But now I wanted to try something simpler: just rotating the digits by some number of positions. I wasn’t sure this would do anything interesting. But in the spirit of the live experiment, I wrote a little piece of code to find out:

What happened was quintessential NKS (New Kind of Science). Even though the underlying rule was incredibly simple, the behavior was far from simple—and in many ways looked quite random.

Here’s the whole notebook from the hour or so of live experiment:

It’s got quite a few interesting results. And indeed—like many previous summer school live experiments—it’s got the core of what would make a nice research paper.

In addition to this pure science experiment I decided this year to do a second—more practical—live experiment. In a sense it was a meta experiment. Because it consisted of analyzing code of pretty much the type used to do live experiments. Specifically, I read in lots of code from the Wolfram Demonstrations Project, then started doing statistics on it.

At first I looked at the general distribution of functions used, and started analyzing correlations and so on. But then, following a suggestion from the audience, I decided to focus on one simple example, and just started looking specifically at the use of named colors. The result was this bar chart, showing that (for whatever reason) red and black are the most common named colors in this corpus of code:

It’s always important to get visualizations at every step along the way. And in this particular live experiment, we quickly decided to visualize correlations between colors, generating bar charts showing what the distribution of colors is if one already knows that a certain color (shown as the background) appears:

My original idea for the live experiment was to look for repeated patterns of code that might suggest functions we’d want to name and implement. But we never quite got there—and when we ran out of time we were instead looking at how one could use “code corpus analysis” to develop good color palettes: a quite different, but interesting, direction that emerged from the experiment.

Doing live experiments in a sense provides a way to illustrate the spirit of idea entrepreneurism—as well as letting one introduce some specific methodologies and tools. But another important element of successful idea entrepreneurism is choosing a direction to pursue. And it’s become a tradition at our summer school that after I do my live experiment, I talk about the directions we’re currently pursuing—and about what science and technology I’m currently most excited about.

After that we launch into the most important business of the summer school: defining a project for each student. Over the years we’ve developed and steadily refined a whole process for doing this. I’m always accumulating lists of interesting problems and projects. And students often come in with definite ideas for projects. But I’ve found the best results come from pure real-time creativity: from learning about each student and then creatively coming up with a project that matches their skills and interests.

And this year, over the course of three fairly long days, we did that 63 times, defining a unique original project for each of our students.

There’s quite a bit of structure to the summer school. For example, there’s always “homework” done during the first week. Usually we pick some previously unexplored area of the computational universe, and ask students to find something interesting in it. This year lots of students found lots of interesting things—that are actually now being assembled into a paper.

Every day there are a few hours of lectures. About how to do a good computational experiment. About the types of systems studied in A New Kind of Science. About computational techniques. About implications for philosophy, music, engineering and more. About perception. About natural language. About what’s worked in previous student projects. About principles that emerge from A New Kind of Science. About all sorts of other things.

Being an instructor at the Wolfram Science Summer School has become a favorite activity for some of our top R&D employees. And as it happens, this year all the instructors were also summer school alumni from previous years (yes, we’ve done a lot of recruiting from the summer school). For three weeks they worked with students, bringing to bear on each project the kind of idea entrepreneurism that we’ve taught at the summer school—and practice at our company.

This year—not least because we’d just finished launching Wolfram Programming Cloud days before—I had the pleasure of spending plenty of time at the summer school, getting to know all the students (by the end, I knew everyone by name!), and watching lots of projects take shape. I’ve been involved with my share of hackathons and incubators. But the summer school is something different. It’s really about entrepreneurism of ideas: about the process of creating ideas and turning them into reality.

And at the end of three weeks, there were 63 projects to present—and lots of interesting things discovered and invented:

Over the years at the Wolfram Science Summer School, there have been many hundreds of great projects done, as well as many careers launched.

There’s a lot to say about education. But I think for many people, doing a unique original project is the single most powerful and useful form of education there is. Doing this successfully is quintessential idea entrepreneurism. And I think that in the long run the most important achievement of the Wolfram Science Summer School may just be the framework it’s developed for spreading entrepreneurism of ideas.

The Wolfram Science Summer School is just one of a growing constellation of education initiatives that we’re involved in. (Another that runs alongside the summer school is our two-week Mathematica Summer Camp for high-school students—that directly uses ideas from the summer school.) And particularly with all the new technologies that we’ve been developing, there are vast new opportunities for education. For me the Wolfram Science Summer School is an important and fascinating success story about innovation in education—and an encouragement for us to do more.