3. The Coming of Age of Arithmetic

This chapter “The Coming of Age of Arithmetic” traces the tedious journey from the tally stick, through the bead frame, to the smartphone. To this day the importance of the Ishango bone discovered in Africa is puzzling. The tally stick was a digital memory with which falsification was hardly possible. Among popular calculating aids was also the (digital) quipu. Since time immemorial the fingers have served for counting and calculating. An (digital) abacus utilizes either lines and counters (counting board) or staffs with beads (bead frame). Unlike the Roman number system, the use of the Roman hand abacus is simple. Although there was no symbol for zero, one could represent this number on the “pocket calculator” along with ones, tens, hundreds, etc. Once widespread logarithmic analog calculating devices, such as the slide rule, circular slide rule, and cylindrical slide rule, disappeared 50 years ago, as did mechanical desktop calculators. The difference between numerical and graphical computation is also described. A special form is nomography. The omnipresent portable smartphone is regarded as an extremely versatile tool. The evolution of certain mathematical instruments is illustrated in the form of lines of development.