# Counting by 10s vs. 20s

Benjamin Barrett gogaku at IX.NETCOM.COM
Thu Aug 22 20:36:09 UTC 2013

```That's an interesting question. I have no idea, but I took a look at Wikipedia and the internet and found what might be an explanation.

Saying that Yuki and Pamean have octal because they count the spaces between the fingers, the octal Wikipedia page (http://en.wikipedia.org/wiki/Octal) implies that the decimal system arose from humans having ten fingers, which is a common enough explanation. http://en.wikipedia.org/wiki/Sexagesimal#Origin uses a similar explanation for duodecimal and sexagesimal. http://en.wikipedia.org/wiki/Base_27 has a similar explanation for septemvigesimal.

Perhaps such explanations are sufficient to hypothesize that counting systems are based on the fingers and/or other body parts. Children to this day count using their fingers--whether taught or innate, it seems that fingers are a natural way for humans to abstract when counting.

Fingers and toes are used to explain the vigesimal systems: http://www.mayacalendar.com/mayamath.html, http://bit.ly/14n3Ma3, http://wikipedia.qwika.com/pt2en/Sistema_vigesimal, though an explanation along the lines of the sexagesimal system seems just as reasonable. For example, it might have come about by counting all your fingers twice; doing so three times risks losing track, but doing so twice is doable.

See http://en.wikipedia.org/wiki/Decimal#Other_bases and the box at the top of that page, which includes http://en.wikipedia.org/wiki/Quaternary_numeral_system, http://en.wikipedia.org/wiki/Base_32 and http://en.wikipedia.org/wiki/Pentadecimal.

http://en.wikipedia.org/wiki/Duodecimal#Origin says that the evidence of eleven and twelve in English for a vestigial duodecimal system is demonstrated with reconstruction to be incorrect.

Benjamin Barrett
Seattle, WA

On Aug 22, 2013, at 12:57 PM, Joel S. Berson <Berson at ATT.NET> wrote:

> At 8/22/2013 03:47 PM, Geoffrey Steven Nathan wrote:
>
>> It is vestigial in modern French,
>
> Otherwise known as the vestigial vigesimal, of course.
>
> My question is not really about how pure it is in
> French, nor where it arose and spread to.  But
> rather, *why* did it arise?  Lost in prehistory,
> but that has never discouraged speculators.

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