| 12, 24, 60 are all used because they are cipherable using one's fingers. To cipher on 12, pick a hand and assign the values 1 to 12 to each finger joint so that the tip of the index finger is one, the middle joint of the index finger is 2 ... the base joint of the little finger is twelve. Use the thumb as pointer to a number. Add and subtract by moving your thumb as you count. Cipher on 24 by using each joint on both hands. Cipher on 60 by using one hand to cipher on 12. The other to cipher on 5 in the traditional way but value each finger as 12. Example: Base joint of pinky on right hand and ring finger of left hand is 48. To get the full Babylonian number system allow the exponent to float based on context. It's really just an extension of the move from ciphering on 12 to ciphering on 60. Exercises: 1. [M05] Where are the indexes after adding 13 and 8? 2. [10] Change the system to use natural numbers. 3. [50] Is abandoning sexigisimal ciphering for decimal ciphering the oldest case of changing a computational system so as to make it easier for beginners at the expense of vastly reduced expressive power? http://en.m.wikipedia.org/wiki/Babylonian_number_system |