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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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2048 Contest!

The folks at Cincom have put together a fun challenge for developers, the Cincom Smalltalk 2048 contest.  It involves implementing or improving the recent popular game called 2048.

I have put together an example running 2048 application that you can use as a starting point, if you like;  we have 2048 running in both our Smalltalk products (ObjectStudio and VisualWorks).

New to the Smalltalk computer language?  (I encourage you to find out about it; it will make you a better programmer no matter what language you use).

  • You can download a personal use license version of our commercial IDE  here
  • Contact athomas@cincom.com for tips on getting started, and for code examples
  • I am happy to answer questions and give pointers to new or novice Smalltalk developers

See all the Contest details including prizes.

Regards

Arden

athomas@cincom.com

 

Building a Business with Cincom Smalltalk

Last month I gave a presentation at the STIC conference with one of our engineers (Dirk), on how to build software to support a business, using Cincom Smalltalk.  It went very well and we got some very good feedback.  I think the demo shows pragmatically how CST can be used to build robust software.  I’ll post links when the video is available.  For now, the slide as available:

http://www.cincomsmalltalk.com/main/2012/03/cincom-smalltalk-speakers-shine-at-a-very-successful-stic12/

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