Monday, 23 November 2015

Duodecimal Finger Counting: Counting to 60 on One Hand.

Currently I am reading “The Last and First Men” by Olaf Stapledon. I’ve just reached the section on the third species of mankind. The third species have six fingers on each hand and Stapledon notes that they have a duodecimal mathematical system. By a manifestation of synchronicity I was watching “QI” that very night and a base twelve finger counting system they attributed to the Babylonians was featured. Using this system it was possible to count up to or display numbers of up to 60.

Investigating the topic further I came across a number of websites averring that the Babylonians in fact had a base-60 numerical system. Looking at their numeral system, however, seems to suggest a decimal system. Which of these is true is out of the scope of this blog. I thought it would be handy (pun intended) for readers of this blog to know about a hand signal system that can represent relatively high numbers. Many measurement systems are based on dozens, 24 or 60, after all.

The system is very simple. There are four fingers on your hand and each has three joints. The joint of the first finger nearest the wrist is “1”. The join of the little finger nearest its tip is “12”. By pointing at a joint with the thumb of your other hand you can indicate any number from 1 to 12. If you point with your index finger instead of your thumb the joints are designated 13 to 24. And so the progression goes on up to 60, which would be the tip of your little finger pointing to the last joint of the other little finger. Counting in dozens makes this technique even easier. For example, a count of “three dozen and two” can be easily converted to 38.  The illustration is labelled in “dozenal” notation so the upside down 2 () is “ten” and the inverted 3 () is “eleven” in base-10.

That is the system. Perhaps you may find it of use sometime.

Update.
You can actually count to 144 on your hands! Use the tip of your thumb to touch the finger bones between the joints rather than the joints. You may find it more logical to start with the little finger for the lower numbers. For each dozen you count off you touch the corresponding bone on your other hand with your thumb. 12 x 12 =144. You can also do quick additions using this method. Shifting your thumb from a finger bone to the equivalent fingerbone on the next finger adds three, two fingers adds six and three fingers adds nine. On the other hand skipping a finger adds 36/three dozen. For more on dozenal counting see here.
Using this method you can use your hands as a simple abacus in either base twelve or base ten. For the latter you just ignore the first two sections of your last finger.

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