Less is More – Arden's Smalltalk Blog

making hard things easy, the impossible, possible

Archive for the month “January, 2016”

Random Musings about “12”

– Why 12 is a good number

By Arden Thomas

 

As computer programmers, software developers and human beings working with numbers, we often take our base 10 decimal system for granted.  But what if, as a society, we were starting over?  If we looked at all the choices and all the advantages and disadvantages of each, would base 10 still be the choice?

Past cultures have indeed used other systems.  We likely settled on base 10 because of the practicality that we have 10 fingers to use in assisting our understanding and manipulation of those numbers.

In this age of computers and computation, it might seem that a computer like base 8 or 16 could be a good choice too.  But the base 12 system seems to have a lot to offer.

Base 12.

The base 12 also known as the duodecimal or dozenal system has a lot of supporters who would support a move to a base 12 system.

For familiarity, we do have some systems that use 12.  We have 12 hours in the day, 12 months in our year, 12 in a dozen, 12×12 (144) in a gross, 12 inches in a foot, etc.  For the musically inclined,  there is 12 TET, twelve tone equal temperament.

What is attractive about the dozenal system?  To start with, the number twelve has 6 factors, namely 1,2,3,4,6,12.  Base 10 has four;  1,2,5,10.  So what does that do for us?  It makes many fractions and divisions simpler and easier.  For example 1/3 in base 10 has a repeating representation of 0.33333…..

1/3 in base 12 is 0.4, ¼ = 0.3.  Of course it is not better in all fractions; 1/5 = 0.24972497…… so it is not better in all ways, just more.

Hold on! You might think.  Base 10 lets us do great things like moving the decimal with great effect!

The good news for base 12 is that this benefit is not unique to base 10, and would work just fine in other systems including the dozenal.

On the practicality of having 10 fingers, dozenal proponents point out that (looking at your palm) your four fingers have 12 segments (phalanxes) in which to work with, which can be indexed by the thumb.

I found the whole idea intriguing and a fascinating idea.

Here are two resources where you can find more information at:

http://www.dozenal.org/drupal/sites_bck/default/files/db38206_0.pdf

http://www.dozenalsociety.org.uk/

http://www.dozenal.org/

 

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