teaching machines

Triangular Colors

Last week I was trying to think of boolean predicates that I could use for exercises in an introductory programming class. I remembered the triangle inequality, which states how the lengths of three line segments must relate if they are to be formed into a triangle. In short, each segment must be shorter than the […]

Power Set of Venn Diagrams

In our introductory programming class, I try to reframe abstract logic into concrete spatial thinking. One way I do this is through the game Trux Falsy. Another way is through Venn diagrams. I want students to see how the AND operator creates an intersection, how the OR operator creates a union, and how DeMorgan’s Law […]

Terra’s Theme

I’m not exactly sure what Deltaphone is for, but this afternoon, it was for analyzing the structure of Terra’s Theme from Final Fantasy VI. (Thanks to 8-bit of 8-bit Music Theory, who did all the work.) The melodic line consists of a phrase repeated three times, and this phrase is expressed in the prefix function […]

New Geometry

What do you call a portion of the shaded area between two arcs? A sharc. The figure above was created in Twoville, a little language for drawing vector art. Here’s the complete program:

Little Notebooks

The best days are the days in which I write in a little notebook. The things I write are myriad: 20 drafts of a haiku, big goals for a project, a TODO list for the day, an outline for a lecture, a draft of a talk, a humorous thought, a record of a dream, an […]


Several months ago Microsoft started wrapping all URLs in my university email. Now, when I click on a URL, I first go to a web service that checks to see if the page has malicious intent or unsafe content. The problem with this safety feature is that I can no longer read the destination URL. […]

Interpolants in Twoville

Shapes in Twoville are animated across time by interpolating their properties between keyframes. Time is a first-class concept in the language, with assignment statements storing values across a timeline rather than in a static memory cell. Here’s a rectangle that oscillates left and right using this keyframe-sensitive assignment syntax: The animation above uses linear interpolation. […]

VOICES 2019: Learning Music Theory through Code with Deltaphone

Follow is a draft of my talk for VOICES 2019, a virtual conference on the use of music in STEM learning. This is the first virtual conference I have attended. No flight, no badge, no bag of unwanted promotional materials. Just people talking about music and learning from the comfort of their homes and offices. […]

Starring Matariki

During our last week in New Zealand, we attended the Matariki Festival at my sons’ school. Matariki is the Māori name for one of the stars that becomes visible in June, marking the start of a new growing season. The school celebrated with song and dance and an art show. For the art show, one […]

Triadic Chords in Deltaphone

When non-pianists approach a piano, they will strike random keys—but often just one key at a time. If they play more than one, the sound is likely to be unpleasant. But that’s only because they don’t know which keys to strike at the same time. Let’s work out in Deltaphone a system of notes that […]

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