The way we write numbers today seems natural because it is the only one we learned. But other cultures solved the same problem, writing quantities and calculating with them, in different ways, and each solution left its mark on what those cultures were able to think. Chinese counting rods For almost two thousand years, Chinese mathematicians calculated with rods: little sticks of bamboo, bone or metal laid out on a board divided into columns. Each column was a decimal place, and a digit from 1 to 5 was made with the same number of rods; from 6 to 9, with one rod worth five plus a few more. So that neighbouring columns would not be confused, the rods alternated position: upright in the units, lying down in the tens, upright again in the hundreds.
The oldest surviving piece of written mathematics is a scratched bone. The Ishango bone, found in 1950 on the shore of Lake Edward, on the border between the Democratic Republic of the Congo and Uganda, is about 20,000 years old and carries groups of parallel notches carved in three columns. Nobody knows for sure what they counted. But the idea is clear: one mark for each thing. The Ishango bone, with the groups of notches carved along the handle. Museum of Natural Sciences, Brussels.Joeykentin · Wikimedia Commons · CC BY-SA 4.0 In the language of chapter 2, the notch is an icon: five marks look like five sheep, at least in number. That is why this writing does not need to be taught. You only have to look. The price is size: to write a thousand, a thousand marks.