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And that’s a crucial part of what’s great about computational essays. If you read an ordinary essay, and you don’t understand something, then in the end you really just have to ask the author to find out what they meant. In a computational essay, though, there’s Wolfram Language input that precisely and unambiguously specifies everything—and if you want to know what it means, you can just run it and explore any detail of it on your computer, automatically and without recourse to anything like a discussion with the author.

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There’s something satisfying about both writing—and reading—computational essays. It’s as if in communicating ideas we’re finally able to go beyond pure human effort—and actually leverage the power of computation. And for me, having built the Wolfram Language to be a computational communication language, it’s wonderful to see how it can be used to communicate so effectively in computational essays.

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I like writing textual essays (such as blog posts!). But I like writing computational essays more. Because at least for many of the things I want to communicate, I find them a purer and more efficient way to do it. I could spend lots of words trying to express an idea—or I can just give a little piece of Wolfram Language input that expresses the idea very directly and shows how it works by generating (often very visual) output with it.

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Traditional computer languages are about writing code that describes the details of what a computer should do. The point of the Wolfram Language is to provide something much higher level—that can immediately talk about things in the world, and that can allow people as directly as possible to use it as a medium of computational thinking. And in a sense that’s what makes a good computational essay possible.

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One feature of the Wolfram Language is that—like with human languages—it’s typically easier to read than to write. And that means that a good way for people to learn what they need to be able to write computational essays is for them first to read a bunch of essays. Perhaps then they can start to modify those essays. Or they can start creating “notes essays”, based on code generated in livecoding or other classroom sessions.

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So what can go wrong? Well, like English prose, Wolfram Language code can be unnecessarily complicated, and hard to understand. In a good computational essay, both the ordinary text, and the code, should be as simple and clean as possible. I try to enforce this for myself by saying that each piece of input should be at most one or perhaps two lines long—and that the caption for the input should always be just one line long. If I’m trying to do something where the core of it (perhaps excluding things like display options) takes more than a line of code, then I break it up, explaining each line separately.

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But it was only in 1986, when I started documenting what became Mathematica and the Wolfram Language, that I started seriously developing a style close to what I now favor for computational essays:

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It’s so nice when I get something sent to me as a well-formed computational essay. Because I immediately know that I’m going to get a straight story that I can actually understand. There aren’t going to be all sorts of missing sources and hidden assumptions; there’s just going to be Wolfram Language input that stands alone, and that I can take out and study or run for myself.