The Sign

Abstract

Arithmetic, the art of counting from 1 to 8, is what the cryptic exercises in pronunciation represent. They concern figures, digits, and numbers, with la le li lo lu lyl being another way to say two hundred and ninety-nine thousand five hundred and ninety-three. In October 1718, during the construction of the canal known as Karls Grav (‘Charles’s Ditch’) outside Vänersborg, Swedenborg wrote his proposal for an octal numeral system, a new arithmetic with base eight, entitled En ny räkenkonst. The full title in English translation is ‘A new system of reckoning which turns at 8 instead of the usual turning at the number 10 whereby everything respecting coinage, weights, dimensions, and measures, can be reckoned many times more easily than in the ordinary way’ (1718). This was an attempt to reform our way of counting, a task that seems to have amused both himself and the man who assigned it to him, Charles XII. The work is dedicated to Charles XII, yet not to a king but to ‘a profound Mathematicus’. Whether it should be 64 or 8 instead of 10 was the question. Which number is best suited as a base for counting coins, weights, and measures, while simultaneously being geometrical? An advantage of the number 8 is that it is ‘geometrical’, unlike the number 10, in that 8 is equal to the cube of 2, and can be halved all the way down to 1 with no need for fractions. Moreover, octal arithmetic would correspond better to the way of counting and dividing coinage, weight, volume, and dimensions, all of which—with a few exceptions—could be derived from base 8.