The previous chapters dealt with letters and signs written in a line. This one deals with what is written on the plane: crossing circles, curves, bars, arrows, points joined by lines. A diagram is not read from left to right; it is read with the eye, all at once or in any order.
Peirce said that the diagram is the most powerful sign in mathematics, because it is an icon of relations: the shape of the drawing repeats the shape of what it represents. Two nested circles do not say that one set is inside the other; they show it. That is why a good diagram makes conclusions appear by themselves. And, for the same reason, a bad diagram makes false conclusions appear: the scale of a chart, a drawing out of proportion or a line that looks straight convince the eye before reason can check.
Texts in this chapter
- Euler’s circles and Venn diagrams
- From Oresme to the graph: drawing a quality that varies
- Charts that saved lives: Playfair, Snow, Nightingale and Minard
- The scale of a chart: when the drawing lies
- Argand’s plane: the imaginary number that found a place
- Graphs and maps: the drawing in which only connections matter
- Proofs without words
- The fourth dimension: drawing what cannot be seen
- How to read a diagram: a guide and a glossary
- References and credits