03 Number systems

But what if we leave the pure numbers and number words we know and move into other place value systems? If we no longer count to 10 as in our decimal system (which does not happen to harmonise with the number of our fingers), but perhaps to twenty, as in the vigesimal system. Or to sixty, as in the sexagesimal system.

A variant of this often used by cachers is the Mayan numerals or the numbers of the Babylonians.

Number system of the Maya

Perhaps the Maya counted with fingers and toes. Anyway, they divided into four blocks of five digits each, with a dot counting as 1 and a dash counting as 5. Everything was nicely sorted, the dashes, meaning the 5s at the bottom, the dots, meaning the ones at the top. All the numbers that were larger were simply written higher, i.e. on top of the blocks of numbers up to 19. This is called the place value system, where the second block from the bottom is multiplied by 20, the one above is multiplied by 400, then comes 8000,…

But watch out: for calendar dates, the place value system has been changed a bit with a view to the 360 days of a year 😉

Numbering system of the Babylonians

The number system used by the Babylonians was a sixties system with only 59 (there was no separate symbol for zero !) different digits, all composed of two wedge symbols.

Numbers were written digit by digit, as they are today, from left to right, with the more significant digits on the left.

You will see, the world of number systems is diverse. Look closely. A wiring diagram for a telephone socket with the common designations La, Lb, W, E, b2,a2 stands for the connection terminals with the numbers 1 to 6. Add to this the 0 and you have the 7 system. Now all that remains is conversion.