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On 4/9/2018 1:37 PM, Alex Fink wrote:
> On Sun, 8 Apr 2018 22:23:42 -0400, Tim Smith <[log in to unmask]> wrote:
>
>> I got the idea for this from the system used by the ancient Mayans to
>> write their vigisimal (base-20) system.
Well, obviously what I should have said was, "I got the idea for this 
from my vague memory of something I read years ago about the system used 
by the ancient Mayans," which I thought I remembered well enough that I 
didn't have to look it up before spouting off about it.  Evidently I was 
wrong.  Thanks, Alex, for pointing out my errors and omissions.

But this doesn't affect the Nenyuvai system, which, if anything, has a 
"look and feel" even more like the Mayan system than I thought it did, 
now that I see that the Mayan number glyphs also had horizontal lines 
and horizontal rows of dots.  (Actually, although the examples shown in 
the Wikipedia article are horizontal, the article mentions that they 
could be either horizontal or vertical.)  Although one thing I forgot to 
mention about the Nenyuvai system is that it does use a vertical line 
for a sexagisimal point.

And it does still appear that my use of a single horizontal line for 
"zero" is unusual, maybe even "un-naturalistic", although the Mayan 
precedent shows that at least it doesn't always mean "one".

-- Tim
>> Theirs was also a positional
>> system, but without any symbol for zero, which meant that numbers could
>> be ambiguous, especially when taken out of context.  It, too, consisted
>> of lines and dots, but unlike the Nenyuvai system, the lines were
>> vertical and the dots were arranged in a vertical row to the right of
>> the rightmost line. (But their writing system was vertical, and the
>> Nenyuvai system is horizontal.)  Each line meant five, and each dot
>> meant one; a "digit" could be anything from one dot, meaning one, to
>> three lines and four dots, meaning nineteen.
> Oh, yes, I forgot about the Mayan system.
>
> The Mayans did have a glyph for zero!  It's the shell-looking glyph displayed e.g. at the top right here:
>    https://en.wikipedia.org/wiki/Maya_numerals
>
> But here's the under-reported thing: the lines-and-dots Mayan numerals are *never* textually attested to write anything other than dates or lengths of spans of time.  What follows is from chapter 9 of Chrisomalis' _Numerical notation: a comparative history_.
>
> When the Mayans wanted to write a count of general objects, they combined the bars and dots with a logogram for 'moon' to denote 20, so that 21 would be moon and a dot, ..., 39 would be moon, three lines, four dots.  That doesn't reach very far, and it's thought that to count forty or more objects the strategy was to use a measure word denoting a larger unit: e.g. we seem to have '40000 cocoa beans' written as "5 pi" where a _pi_ is a unit of 8000 cocoa beans.  However, even expressions like this are scant: "One is struck, upon comparing Maya inscriptions to those of any other civilization, by the virtual absence of phrases indicating large quantities of captives taken in war, goods paid in tribute, wealth owned by individuals, or any other noncalendrical quantity."
>
> Dates were written with a sequence of these measure words: _b'ak'tun_ '20^3*18 days', _k'atun_ '20^2*18 days', _tun_ '20*18 days' (thus, loosely, a year), _winal_ '20 days', _k'in_ 'day'.  And when writing a date, the standard was to leave all the measure words in.  Leaving them out is a reasonably-well attested variant, but that by itself doesn't make a positional notation system any more than writing today's date as "9/4/2018" does.  One would like at least to see usage of figures written this way in calculation vel sim., but we have no evidence of this.
>
> Myself, I suspect we have math education in the "new math" style to blame for the pervasion of the idea that the Maya had a general-purpose base 20 system of written numerals.  Computing in other bases was a pillar of that scheme, and its proponents would surely have devoured any historical precedent they could point to to argue that this wasn't all inapplicable abstract nonsense, including running with incautious statements about the bars-and-dots system that ignore its highly circumscribed position within Maya numeration as a whole.
>
> Alex
>