Thursday, December 10, 2009

Relearning to Count - Zero, One, Many

I have been thinking about the methods we use to count with.  What method of counting is most appropriate to the task at hand (pardon the pun).  A smart friend of mine told me that developers need to relearn to count.  As a software developer the appropriate method of counting is, zero, one, many.
Little 1 by Ann & Paul Rand

The first time we learn to count we use our fingers in the simplest technique.  Some time early in childhood we learn to show fingers for our age, "I'm this many (shows two fingers)".  Then we actually learn to count, 1, 2, 3.  Later taking it up to 10.  So a base-10 number system seems like a natural human number system.  But is this true?

I've been wondering why we used a sexagesimal number system (base-60) for time.  A hour has 60
minutes and 60 seconds in the minute.  Why use this system when it would appear a base-10 system would have been more natural?

Babylonian sexagesimal symbol set
These two facts perplexed me.  We learn to count in base-10, yet our fundamental unit of measure is base-60.  Reading about the Babylonian number system may lead to a plausible explanation.  We adopted the Babylonian system for time.  And perhaps the Babylonian children learned a different method of counting, not counting fingers - but instead counting finger joints.  If one counts all the finger joints on the fingers one can count to 12 just using the four fingers.  That is much more efficient.  So using the left hand to count in base-12 and the right hand to count the multiples of 12 one arrives at a combined base-60 system of counting.  A bit more complex than counting to 10 on the fingers.  But the Babylonian's were not children.

Compare the simplicity of a base-60 system to a base-10 system when one is in a shop counting baskets of grain.  There is a high chance that there will be more than 10 baskets, but lower chance that there will be over 60 baskets before someone wants to start marking on clay tablets.  Perhaps the shop keepers relearned to count in base-60 because it afforded fewer trips to the clay tablet.

For non-developers you may continue to think in base-10. As a software developer you need a slightly more abstract system.  That system is Zero, One, Many.  Simple.  All you need.  Zero is used to mean the empty set, nothingness, the absence of quantity.  Zero has an interesting history.  One is used to mean the unique thing, unity, not Zero and not Many.  Many is used to mean a collection of like things.  Modern programming languages have allowed this abstraction level with many types of objects to represent Many.  We have Collections frameworks all designed to represent a specific constraints on Many, but the abstract concept is still Many.

Is there an anatomical representation of this system (Zero, One, Many)?  How about the closed fist for Zero, the raised index finger for One, and the open palm held horizontally ready to hold the collection for Many.

See Also:
The History of Zero:  How Ancient Mesopotamia Invented the Mathematical Concept of Nought and Ancient India Gave It Symbolic Form
Linguistics of Numerals - guess what a duodecimal system uses as it's base?
Post a Comment