Re: Fwd: Mayan numerals

From: Frédéric Grosshans <>
Date: Wed, 26 Sep 2012 14:44:37 +0200

Le 24/09/2012 20:16, Jameson Quinn a écrit :
> (Resend; last time bounced due to photo attachment)
> So, I see that this thread is heating up again, and a progress report
> is in order.
> I've looked around a bit at ancient uses, insofar as that's easily
> available on the web.
> * In petroglyphs from the classic era, it is far more common to find
> the numbers incorporated into glyphs (such as date glyphs), with
> vertical bars. Also the cloverleaf zero is common in classic
> numbers, and often mixes in the same inscription with the shell zero.
> * In codices (postclassic), usage is more similar to modern.
> Vertical-barred numbers are still present in dates, but the naked
> horizontal-barred numbers, square-spaced numbers are common. I'm
> not enough of an expert to know how the text flow is working, but
> if I'm right that successive digits are alternating colors (red,
> black, red, black) then there are examples of both horizontal
> flow, vertical flow, and 2-by-2 vertical flow. Also, just as in
> modern usage, I haven't seen any cloverleaf zeros.
> * I've seen nothing to suggest to me that the "face" forms of the
> digits are ever mixed with the dots-and-bars forms. I believe that
> for ancient, and certainly for modern, purposes we can ignore the
> "face" forms.
About the ancient use : those numerals have also been used in other
mesoamerican scripts beyond the Maya script. as said here : . So I guess the numerals could
be called "mesoamerican" rather than Mayan:

  * In the Zapotec script, described here . You can clearly see
    some numerals (4 and 8) in the stelae 12 and 13 from Monte Albán :
  * The Epi-Olmec / Isthmian script, described here and here . You have plenty of
    numerals in the few examples I found :
      o stella 6 from Cerro de Las Mesas, with Long Count date of
      o La Mojarra Stela 1 described here . The Long
        copunt dates are easily seen here :
      o a mask seen here : (you see
        a 9 close to the upper right corner)
      o The tuxtla statuette , , whwerw we see a
        long count date and a "vertical 8"
      o The stella C. at tres Zapotes, with a long count date.
      o A LaTeX package and a ad-hoc 8-bit fonts exists for Epi-Olmec.
        It is available here and described here.
  * The Ñuiñe script, briefly mentioned in, where the examples given
    clearly show some numerals (10 and 11).

As far as I understand, there is little agreement over the decipherment
of any of these scripts, and there is probably a long time to wait
before any of it is encoded in Unicode, but given the already encoded
and planned undeciphered scripts (Phaistos disc and Linear A at least),
I wouldn't be surprised to see one of these script being encoded before
the well understood but complex Maya script.

Your initial idea was already to make them multi-script (Maya + Latin),
so adding a few script to your proposal shouldn't be a problem. It might
even ease the situation, since we seem to be in a case similar to the
Aegean Numbers (U+10100–U+1013F ), used in linear A and B. I'm not a
specialist (at all !), but I would be surprised to find the complex
behaviour of the numerals in the Maya script (which seem to scare
Michael Everson) reproduced identically in all the above scripts. In
particular, it seem absent from the Epi-Olmec/Isthmian script.

> * I'm enclosing a picture of the bills
> <> I happen to have around right
> now. There's one of every bill in current use (1,5,10,20,100,200)
> except the 50. As you can see (assuming this comes through on the
> list; otherwise, just google "billetes quetzal"), all 3 of the
> bills with a 0 use noticeably different variations of the "shell
> zero" glyph. The 20 and 100 have two stripes in their zeros, the
> 200 has four of them in its. (The 10 and 50, of course, have no
> zero in base 20)
Good pictures of the bills (including the Q50 one ) can be found her .

By the way, I recently saw a post from an associate professor of
matematics looking at ancient number systems in (Xe)TeX. He says "I’d
love to be able to do something similar with the Mayan numbers. I tried
for a while, but couldn’t get them to work." The reason of his failure
is the lack of unicode encoding.

> Do people think I should include any of this investigation of ancient
> usage in my proposal?
As you've probably guessed by now, I think you should... but I have no
experience at all in the encoding process!

> How many examples of modern usage, aside from currency, are worth
> including in a proposal, assuming that they will take me an hour or
> two each to find distinct uses, or a day or two to go visit the
> publishers and get unlimited examples?

I think it's more the diversity of usages than the number which counts.

Out of pure curiosity, I have the following question :
Do modern Mesoamericans still speak languages using a vigesimal system ?
If yes, how do they write numbers like 127 (especially in informal use
?). 127 ? 6,7 ? In letters ? With Mesoamerican numerals ? As discussed
here (see
e.g. and
answers ), some Inuits have felt the need to introduce a base 20 numeral
system, but I've no idea of their success or failure. If you find some
non-decorative modern everyday use of Mesoamerican numerals, even
handwritten, I think it will be difficult to object the encoding.
Received on Wed Sep 26 2012 - 11:50:33 CDT

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