The sentences

Knowing the letters is not the same as writing with them. The 1446 book, after explaining each letter class, devoted a chapter to assembly: how letters pack into syllable blocks.

This part is gog’s version of that chapter. It moves through six groups, from how words join into a sentence to what a reader does with the finished plot.

First the mechanics. The + operator layers marks in one panel, and the * operator derives a compound mark from a mark and a transform. Where you write a channel then decides whether it binds to the whole plot or to one layer. Second, one pair of operators with two uses. | and / split one plot into a grid of panels, and the same pair places separate plots in an arrangement. Third, two of the transforms that compute a whole picture: flow carries a magnitude through its stages, and cluster builds the tree that puts an axis in order.

Fourth come the coordinate spaces, each a different surface to draw the plot on. space needs only one more vowel, z, to turn a flat plot into a cube. polar bends the same plane into a circle. nest divides a panel into regions, each sized by its measure, that fill it with no gaps. map flattens the earth onto the page, and globe draws it as a sphere. Each of those five takes a sentence you can already write and draws it on a new surface. network is different: its table holds relations, not positions, so a transform, layout, computes where each node goes. Fifth is time, where play cuts the plot into frames and shows them one after another. Last comes selection: with brush, the plot’s reader selects rows with the pointer, and the plot dims the rest.

Every chapter in this part depends on one law, Compositional Invariance: a composed expression means the same thing wherever it appears. What you build in one chapter keeps its meaning when you use it in the next. That is what lets you build a larger sentence from parts you learned in different chapters.