What Is a Computational Essay?

A Powerful Way to Express Ideas

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:

Simple computational essay example

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Are All Fish the Same Shape if You Stretch Them? The Victorian Tale of On Growth and Form

Is there a global theory for the shapes of fishes? It’s the kind of thing I might feel encouraged to ask by my explorations of simple programs and the forms they produce. But for most of the history of biology, it’s not the kind of thing anyone would ever have asked. With one notable exception: D’Arcy Wentworth Thompson.

And it’s now 100 years since D’Arcy Thompson published the first edition of his magnum opus On Growth and Form—and tried to use ideas from mathematics and physics to discuss global questions of biological growth and form. Probably the most famous pages of his book are the ones about fish shapes:

D'Arcy Thomspon and fish sketches

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It’s Another Impressive Release! Launching Version 11.2 Today

Our Latest R&D Output

I’m excited today to announce the latest output from our R&D pipeline: Version 11.2 of the Wolfram Language and Mathematica—available immediately on desktop (Mac, Windows, Linux) and cloud.

It was only this spring that we released Version 11.1. But after the summer we’re now ready for another impressive release—with all kinds of additions and enhancements, including 100+ entirely new functions:

New functions word cloud Continue reading

When Exactly Will the Eclipse Happen? A Multimillenium Tale of Computation

Preparing for August 21, 2017

On August 21, 2017, there’s going to be a total eclipse of the Sun visible on a line across the US. But when exactly will the eclipse occur at a given location? Being able to predict astronomical events has historically been one of the great triumphs of exact science. But in 2017, how well can it actually be done?

The answer, I think, is well enough that even though the edge of totality moves at just over 1000 miles per hour it should be possible to predict when it will arrive at a given location to within perhaps a second. And as a demonstration of this, we’ve created a website to let anyone enter their geo location (or address) and then immediately compute when the eclipse will reach them—as well as generate many pages of other information.

PrecisionEclipse.com pages
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High-School Summer Camp: A Two-Week Path to Computational Thinking

The Summer Camp Was a Success!

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.

Wolfram Summer Camp 2017 Continue reading

The Practical Business of Ontology: A Tale from the Front Lines

The Philosophy of Chemicals

“We’ve just got to decide: is a chemical like a city or like a number?” I spent my day yesterday—as I have for much of the past 30 years—designing new features of the Wolfram Language. And yesterday afternoon one of my meetings was a fast-paced discussion about how to extend the chemistry capabilities of the language.

At some level the problem we were discussing was quintessentially practical. But as so often turns out to be the case for things we do, it ultimately involves some deep intellectual issues. And to actually get the right answer—and to successfully design language features that will stand the test of time—we needed to plumb those depths, and talk about things that usually wouldn’t be considered outside of some kind of philosophy seminar.

Thinker Continue reading

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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A New Kind of Science: A 15-Year View

Starting now, in celebration of its 15th anniversary, A New Kind of Science will be freely available in its entirety, with high-resolution images, on the web or for download.

A New Kind of Science

It’s now 15 years since I published my book A New Kind of Science—more than 25 since I started writing it, and more than 35 since I started working towards it. But with every passing year I feel I understand more about what the book is really about—and why it’s important. I wrote the book, as its title suggests, to contribute to the progress of science. But as the years have gone by, I’ve realized that the core of what’s in the book actually goes far beyond science—into many areas that will be increasingly important in defining our whole future. Continue reading

Machine Learning for Middle Schoolers

(An Elementary Introduction to the Wolfram Language is available in print, as an ebook, and free on the web—as well as in Wolfram Programming Lab in the Wolfram Open Cloud. There’s also now a free online hands-on course based on it.)

An Elementary Introduction to the Wolfram LanguageA year ago I published a book entitled An Elementary Introduction to the Wolfram Language—as part of my effort to teach computational thinking to the next generation. I just published the second edition of the book—with (among other things) a significantly extended section on modern machine learning.

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

Launching the Wolfram Data Repository: Data Publishing that Really Works

After a Decade, It’s Finally Here!

I’m pleased to announce that as of today, the Wolfram Data Repository is officially launched! It’s been a long road. I actually initiated the project a decade ago—but it’s only now, with all sorts of innovations in the Wolfram Language and its symbolic ways of representing data, as well as with the arrival of the Wolfram Cloud, that all the pieces are finally in place to make a true computable data repository that works the way I think it should.

Wolfram Data Respository Continue reading