Chapter 1 told where the signs came from. This chapter asks what they are. Why is the same stroke an operation in $12-5$ and part of a number in $-5$? Why did merchants solve the rule of three by memorising where to put each number? Why does $8+4=\square+5$ trip up so many pupils who can add? Why is $\sqrt9$ equal to $3$ and not $\pm3$? And what exactly makes $\frac{dy}{dx}$ an active notation?

To answer, we use the tools of four authors: Saussure (signifier and signified), Morris (syntax, semantics and pragmatics), Peirce (icon, index and symbol) and Duval (registers of representation). The aim is not to fit each formula into a classification, but to learn to ask better questions when faced with a piece of writing.

Texts in this chapter

  1. What is a sign? Saussure, Morris and the minus sign
  2. Peirce: icon, index and symbol
  3. The object and its representations: the case of fractions
  4. The grammar of formulas: brackets, order and space
  5. When place is the algorithm: multiplication and the rule of three
  6. The equals sign is a balance, not an arrow
  7. Square root: the side of the square and the sign that forgot
  8. Formula, table and graph: treatment and conversion
  9. How to read a notation: a guide and a glossary
  10. References and credits