Explorable explanations

ciechanow.ski has no about page. The site offers a name in the header, a blog, an archive, and links to Patreon, X, Instagram, e-mail, and RSS, and that is the whole of the author’s self-presentation. The archive splits into two eras: seventeen interactive articles published between 2019 and 2024, and five “earlier articles” from 2014 about iOS and graphics programming (Mesh Transforms, Exposing NSDictionary, Exposing NSMutableArray, Drawing Bezier Curves, Exploring GPGPU on iOS). Maggie Appleton, in A Collection of Design Engineers, lists him tenth and describes the work in one line: “Creates interactive explanations. Not a Design Engineer as a profession, but a good example of blending design and engineering for educational content.” That is the genre this section is about, usually called explorable explanations: articles where the reader operates the subject instead of reading about it.

Every one of the seventeen opens the same way. Within the first paragraph or two there is a working model and an instruction to touch it. In Mechanical Watch (May 2022): “You can drag the device around to change your viewing angle, and you can use the slider to peek at what’s going on inside.” In Moon (December 2024): “You can drag it around to change your point of view, and you can also use the slider to control the date and time.” The hero demo comes first and the explanation comes after, and the explanation is always framed as a ramp from simple to real. GPS promises “we’ll step-by-step improve upon it”; Cameras and Lenses will “build a simple camera from first principles”; Bicycle starts with “much simpler objects” (a plain wooden box and a force slider); Exposing Floating Point says “let’s start at the shallow end of the pool.” He is explicit that the model is not the thing. Sound admits “this visualization simplifies things a little”; Bicycle says “In the magical world of these simulations I removed all friction or air resistance”; Lights and Shadows keeps a flawed ray analogy because “despite its flaws, it will serve us as a valuable tool.”

What the reader is asked to do varies by subject, and the variety is the craft. In Gears (February 2020) you control a desk fan’s speed with a slider, then scrub time back and forth on a spinning disc while painted points “leave a trace of the path they followed,” which is how he shows that points at different radii have different velocity. In Curves and Surfaces you drag control points, and you can tap a point to see its influence: “the redder the section of the curve the more influenced it is by that control point.” In Airfoil you can click or tap anywhere in a flow to drop a marker, in any demo that shows a little hand symbol. In Moon’s “cosmic playground” you drag a planet and its velocity arrow, then press a button to let it go, with ghost trails and predicted trajectories drawn so you can plan. In Sound you play notes on little keyboards with the mouse or the W, E, and R keys, after a warning to check your volume. In GPS you grab a yellow figurine and move it around a landscape with three landmarks, and the uncertainty of your position is drawn as a yellow area whose size grows with the guesswork, on the way to trilateration. He even refuses the textbook opening on principle: Color Spaces begins, “A dry definition of a color space is not a good way to kick things off.”

The range of subjects is part of the lesson. The interactive run starts in January 2019 with Exposing Floating Point (a companion to his tool float.exposed), then Color Spaces, Alpha Compositing, Earth and Sun, and Tesseract in the same year. 2020 brings Gears, Lights and Shadows, and Cameras and Lenses; 2021 Internal Combustion Engine, Naval Architecture, and Curves and Surfaces; 2022 GPS, Mechanical Watch, and Sound; 2023 Bicycle; 2024 Airfoil and Moon. The first three are the concerns of a graphics programmer, as the 2014 posts were; by Earth and Sun, Tesseract, and Gears the subjects have become physical machines, natural phenomena, and geometry. The method does not change. A mechanical watch and a colour space get the same treatment: a model you can hold, a promise of scope, and a slow build.

Why do they work as explanation? Read his own sentences about the reader. The demos are built so that your hands do the noticing: “Notice that as soon as you let go of the arbor by releasing the slider, the mainspring will turn the arbor right back.” Legibility is engineered rather than assumed. In Airfoil he scales arrow lengths to stop them overlapping but keeps them proportional, “if one arrow is twice as long as the other, then the flow at that location is also twice as fast.” Moon offers a toggle between real and ten-times-larger body sizes, Sound slows time and flashes colliding particles red, and the numbers are frequently waved away (“the numbers aren’t particularly important here”). He respects the reader’s machine and attention: animations can be paused globally “if you find them distracting, or if you want to save power,” units switch between imperial and metric, copy swaps between click and tap, and geolocation in Moon runs only “If your browser allows it.” Each article ends in a Final Words section that hands the subject back to daily life: “Perhaps the next time you’re on a bicycle, you’ll be able to conceptualize some of those invisible forces.” Airfoil closes with the claim that justifies the whole genre: “by seeing how all the pieces fit together, you’ll find the whole thing even more magical.”

Gears is the article to start with if you want to see the method small. It opens on a personal fascination with “the way their teeth come together to create a fluid, unified motion,” promises to show “how gears affect the properties of rotational motion,” and builds from angular velocity through transmission and torque to the shape of a tooth. The figure below is this book’s own small homage in that spirit, not a reproduction of his work: two gears, two tooth counts, one input speed. Drag the tooth sliders and watch the ratio follow the counts, then give the driven gear fewer teeth than the driver and see it outrun the input. The spoke on each gear marks one revolution so you can count.

A diagram of two gears with an arrow between them tells you that the ratio is a fact. The figure lets you find the fact. That difference is the lesson for anyone who builds interfaces for a living, and it is the reason this book is built the way it is: its figures are meant to be operated, and the prose around each one tells you what to do and what to notice, the way his articles do. When you next need to explain a behaviour to a colleague, a reader, or a user, notice whether you are drawing a picture of the answer or handing them the controls. A slider, a draggable handle, and a number that responds will teach things a paragraph cannot, and the work of building that slider is design engineering in its purest form: a model, a set of controls, and a promise that what you see is true enough to learn from.