What is Space?

Drum Teacher teaches rhythm; this one teaches linear algebra — specifically, the one idea that unlocks the whole subject: a space is something you build. Seven short steps, each just a sentence or two, walk you from a single glowing point to all of 3-D space: add an arrow v₁, multiply it by a number α ∈ ℝ and sweep α through every number to paint a line, add a second arrow to slide that line into a plane, add a third to fill space itself. Every idea happens visually, inside a live hand-rolled 3D scene you can orbit — no libraries, just a canvas and a projection matrix. The camera starts zoomed in on the lonely origin and pulls back as the universe grows.

The math notation is deliberately minimal but honest: α ∈ ℝ chips in serif italic, a small aside that the rationals ℚ (any field) work too, and a live column-vector line where the slider values stream into α·[1 0]ᵀ + β·[0 1]ᵀ and out the resulting column.

And then there’s the easter egg. Double-click the 3D space itself — on any step — and it becomes a full-screen arcade: your arrow w = αv₁ + βv₂ + γv₃ steered by three sliders, a life bar that’s always draining, beating hearts as the only medicine, and stars to catch for a hall-of-fame leaderboard. Score thresholds rebuild the universe stage by stage, and the ± power-up literally teaches span: catch one and your arrow goes double-sided, catch two and a whole plane catches for you, catch three and — span of three independent vectors — everything on screen is yours. Reaching the third dimension turns on a permanent star magnet, because by then you’ve earned it.

Like its siblings, the whole thing ships as one self-contained HTML file in the same seaside palette, which is why you can play it right here.