The sentences

Letters are not yet writing. The 1446 book, after explaining each letter class, devoted a chapter to assembly: how letters pack into syllable blocks, blocks into words, words into sentences.

This part is gog’s assembly chapter, and it moves through five groups.

First the mechanics. The + operator layers marks in one panel, and the * operator derives a new statement from a mark and a transform. Position in the sentence then decides which layer a channel binds to. Second, the two partitions, which are one pair of operators doing two jobs: | and / split one plot into a disciplined grid of panels, and the same pair arranges separate plots on a page.

Third come the four coordinate spaces. space stands a flat plot up by adding a single vowel, z. polar bends the same plane into a circle. nest packs a panel into regions, and map lays the plane on the earth. None of the four asks anything new of the sentence. Fourth is time, where play cuts the plot into frames and runs them in order. Last is the reader’s own hand: brush picks rows out with the mouse, and the plot dims what you did not choose.

The rule that holds this part together is Compositional Invariance: a composed expression means the same thing wherever it appears. What you build in one chapter can be carried into the next without changing under you, which is exactly what makes sentences worth building.