Exploring “Explorable Explanations”

What they are, what they do, and what’s next

Max Goldstein
6 min readMar 17, 2015


There’s a new type of interactive experience online. You may recognize it by an immediate connection with data or mathematics, coupled with clear visualization of the subject matter. They are called explorable explanations, after Bret Victor’s founding essay. If you’re not familiar with the term, browse some “EEs” at ExplorableExplanations.com.

In this brief essay, I’ll outline what I think are some important concepts and variations on EEs. Then I’ll call for a cohesive community to form out of the proto-planetary disk of interest swirling around the topic.

Although EEs are typically 2D graphics, some use 3D graphics, and the use of sound seems promising. One particularly useful technique is to give the audience control of time, either through a scrubber, or by laying it out in space. EEs need not be entirely software; one could imagine a museum piece with physical controls and motors. This gets closer to Bret Victor’s most recent work, involving physical rooms for thought and learning.

To create a successful EE, regardless of medium, one must understand the subject material (at least well enough to get started), design the visual and interactive presentation, and then implement it. In 2015, implementation usually means writing JavaScript for a browser, but we should recognize that code is just a means to an end.

To wit, explorable explanations are highly multidisciplinary. They draw on, in no particular order, data visualization, information design (and graphic design, and video game design, and user interface design, and design generally), programming, mathematics, journalism, education, nonfiction writing, storytelling, museum studies, and artistic expression. EEs are the confluence of all these previously-independent fields.

Visualization is perhaps the most salient feature of an explorable explanation — you have to show the audience a complex process — but very often the word “visualization” is prefixed by “data”. Data visualization is perfectly legitimate, but not all EEs focus on data.

One can visualize three different subjects. The first is data. Not all visualizations (data or otherwise) are explorable. Turning a Corner is a data visualization, and qualifies as an EE because it is introduced with text examining parts of the data. It also allows brushing, where the user filters the data in one or more dimensions (in this case time); this technique is an important way to give the reader interactivity over existing data. Filtering can go either way: masking and isolation (or mute and solo).

The second subject of visualization is algorithms; the central essay is by Mike Bostock. My own EE debut also falls into this category: Visualizing Melkman’s Algorithm. (You really want to click that link.)

The third subject is simulation — The Parable of the Polygons is a good example. However, simulations have mostly been confined to games, so the public tends to dismiss simulation as a practical tool. Of course, most games are not sufficiently accurate; no one uses SimCity for real urban planning. Simulations may also make use of randomness; one can then abstract over many random trials.

I conceive of simulation lying between data and algorithms. Let me explain. As the audience of an EE or other information presentation, we want to understand a system. In data visualization, the system is complex and empirical, like the stock market or earth’s atmosphere, so we model the system by taking numeric data points, and perhaps some simple statistical regressions. For algorithms, the system is the model; no approximation is necessary. Therefore we have complete knowledge of the system, which will hopefully be communicated to the audience. A simulation uses an algorithmic model of a more complicated, often real-world system. The algorithm itself is usually not focused on, and may be simple enough to not warrant detailed explanation. Therefore, simulation lies between data and algorithms as a subject of visualization.

Explorable Explanations also take on different forms, or structures.

At the simplest and least intrusive, reactive documents are situated directly in the text. The reader’s overhead is minimal. This form can be extended to place sparklines and other word-sized graphics in the middle of sentences.

Alternatively, the interactive pieces may be moved to the side of the text they relate to, much like diagrams that accompany magazine articles. The reader chooses when to break from the text and interact, and for how long. They may return to the same component multiple times. A prime example is Up and Down the Ladder of Abstraction.

Next, the explorable pieces may be interspersed between paragraphs of the text, such that the reader proceeds linearly through both. This form seems popular when the content is not (or only minimally) interactive. Both Learnable Programming and How to Fold a Julia Fractal interrupt the essay with scrubbable videos. However, Explained Visually uses this form with fully interactive demos.

Finally, the prose and graphics may exist on the same surface, typically side-by side. Bret Victor’s “explorable example” (not explanation) of a digital filter is done in this form. The New York Times used it for their buy or rent calculator. The Life and Death of Metadata also occurs on a single surface, as does my visualization of Melkman’s algorithm. This “workbench” form encourages open-ended exploration and backtracking, but also requires the most attention and initiative from the audience.

It’s also possible to stitch many EEs together into a book-like progression, such as this primer on digital circuits, or the essay Exploring Emergence.

No form is inherently superior to any other. Choice of form depends on the model, the author, the intended audience, and the subject matter. As we analyze more examples of EEs — more on that later — we may be able to establish rules of thumb for what often works well.

It’s fair to ask: what differentiates an EE from any other interactive visualization? My answer is that the visuals must be integrated with the author’s prose, meaning that the author must already know (roughly) what the audience will discover. A automatically-updating dashboard, or an exploratory tool like Tableau, provides an interface only to data, not another person. Similarly, algorithms or simulations that are visualized without discussion are insufficient (although providing a sandbox at the end is fine). If numbers in the text auto-update, that might be enough. If entire paragraphs change based on the user’s actions, that’s bonus points.

Of course we will still use other types of visual and informational tools. One of the downsides of EEs is that they take a lot of effort and planning to produce. Fast, exploratory tools have their uses (which may include finding which part of a large dataset is suited to an EE). What makes an EE unique is the combination of purposeful human authorship with verifiable data or other evidence, shown in a cohesive way.

Other times, especially when dealing with factual information in our daily lives, we want simple answers immediately. Bret Victor addresses this in Magic Ink, using examples like airline schedules and digital storefronts. I agree that such information does not benefit from interactivity, and I also feel that the topic of an EE could not be made into a suitably clear static graphic. That is, I think there is a place for both magic ink and explorable explanations.

The field of explorable explanations is still very young. It it but one facet of the computer revolution, the biggest upheaval in media since the printing press. I think it will take decades to figure out how to best use our new technological capabilities, and centuries to build a culture around them. A culture where people demand to see data and models rather than trust rhetoric and authority.

So let’s start now.

Nicky Case has already registered ExplorableExplanations.com, but I’d like to get a forum or wiki going where those interested can collaborate in one place. There, we can gather and categorize not just EEs themselves, but discussions about them (like these blog posts), and other resources and related fields that may be helpful to creators.

I know there are more people out there who have been inspired by Bret Victor and Mike Bostock. If you’re read this far, you’re probably one of them. So let’s get an online community going and see what we can come up with.

If you’re interested, reach out to me on twitter and we’ll find a space to collaborate.



Max Goldstein

Thinks too much, knows too little, and wants to save the world.