Monday, February 23, 2015

counting and adding

a lot of humor goes into showing how you "add" using Roman Numerals, but actually ancient Romans used a variation of the abacus called a counting board.

 How could anyone calculate with them? Well, how can anyone compute "three hundred and seventy-six times two hundred and thirty-seven". You type these data into you pocket calculator and press the "x" button, that's how. You certainly would not fill page after page with number words. Neither did the Romans: they would load CCCLXXVI and CCXXXVII onto their counting board or abacus and manipulate the pebbles and beads until they had the result.

The counting board shown here is divided into two vertical strips, the right hand one for addition, the other for subtraction. The top number shown on the right is MDCCCCLXV, the lower one is MCCCCXXV. To add them, we just pile everything together into a mess which is shown in third field from the top. To make it readable we have to reduce it: any five beads on a line are converted to one button in the space to the left of that line, any two buttons in a space turn into one bead on the next line over. The answer is MMMCCCLXXXX as shown in the bottom field.
 more about this at Wikipedia.
The Ancient Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of the previousBabylonian abacus. It was the first portable calculating device for engineers, merchants and presumably tax collectors. It greatly reduced the time needed to perform the basic operations of arithmetic using Roman numerals. 

the earliest counting board still in existance is the Salamis Tablet, 300 BC. a series of videos on youtube will show you how to use these ancient counting boards

  Silly me. I assumed the abacus was Chinese, but apparently the Chinese didn't invent it until 600 years ago, during the Ming dynasty
the difference? The Chinese used (ta da!) beads on wires, whereas the earlier types had to move the beads in grooves.

 the first article also notes that Arabic numerals were not picked up when first known until paper was cheap enough to use to scribble on.

headsup Presurfer

No comments: