Figure 1.

Aspects of the decimal representation system. On the left side, three powers of 10 are illustrated by means of cylinders of corresponding heights. They correspond to the weights of the simple non-compensatory linear model, which characterizes our number system. In the center of the figure, a simple, fast, and frugal tree describes the quick yet sequential decision procedure we use for number comparison. On the right side, the reader sees a famous illustration of Arithmetic represented through an allegory by Reisch in the Margarita Philosophica, who contemplates with a benevolent smile the “algarist” (image source: Typ 520.03.736, Houghton Library, Harvard University). The algarist performs computations based on the positional system, while the “abakist”, on the other side of the illustration, uses marbles for computation with his abakus. The work of abakists was fundamental during the beginnings of the Renaissance, when businessmen employed them to perform all their computations. The decimal positional system made arithmetic calculations simple, transparent, and thus accessible for everyone.