2 Numbers

Brook Danielle Lillehaugen

1. Introduction

This unit is an introduction to the number system in Colonial Valley Zapotec, a form of Valley Zapotec attested in writing during the Mexican Colonial Period.[1]  Zapotec languages (there are many!) belong to the Otomanguean stock and are indigenous to what is now Oaxaca, Mexico. There are probably over 400,000 speakers of Zapotec languages today, and many Zapotec speakers are actively resisting linguistic and cultural threats from deeply embedded discriminatory beliefs and behaviors that deny and devalorize the Zapotec language, people, and knowledge.

The text in Figure 1 is from a grammar about Valley Zapotec, published in 1578, credited to a Spanish friar Juan de Cordova, though many unnamed Zapotec people contributed to it.  This page shows the numbers 1-19.

 

Figure 1.  Cordova 1578a: 102r

2. Learning to read Cordova: Numbers 1-4

Even though this book is printed, you  might find it more challenging to read than modern printed books.  Learning to read older printed books is a skill you can practice! Let’s take a look at Figure 2, which is a close up of the numbers 1-4.

 

Figure 2.  Cordova 1578a: 102r

Exercise 2.1

(a) Transcribe (i.e. write out) what you see in Figure 2. (b) Compare your transcription with a classmate’s.

 

Here’s my transcription:

VNo. Tǒbi. vel. chäga. 1

¶Dos. Tôpa. l. cǎto. 2

¶Tres. Chǒna. l. cäyo. 3

¶Quatro. Täpa. l. tǎa. 4

There’s lots of things to talk about even in these four lines! Let’s go back to just the first line:

VNo. Tǒbi. vel. chäga. 1
  • The book was not printed digitally like today, but with metal casts of individual letters that could be arranged in lines to make a page. This technique is known as .An image of movable type can be found in Figure 3. (You may sometimes find a letter was placed upside down or a similarly shaped letter was substituted for an expected letter– it’s easy to imagine how this could happen!)
Figure 3. Example of moveable type (Blokland 2012)
  • V: The V is in the form of an ornate woodcut.  Sometimes these can be quite elaborate and examples of other woodcuts can be seen in Figure 4. Figure 5 shows how these woodcuts would work– much like the moveable type! (The use of a <v> where we might expect a <u> nowadays is typical.)

 

Figure 4. Woodcut initial capital letters (Heller 2018)
Figure 5. Woodcut Capital “C” (Heller 2018)
  • N: It might be surprising that the <N> is capital, and not lower case, as it is the second letter in the word.  It seems the <V> wood-cut doesn’t “count” and the second letter was capitalized here as well.
  • Notice the period after VNo. In fact there are lots of periods– more than we might expect.  The periods seems to be separating words here.
  • ǒ: There is a caron (or hachek) over the <o> and you might be wondering what it means. Zapotec languages are tone languages, so we might wonder if this (and other accent marks) are marking tone.  However, our current best guess is that they are marking stress, that would mean that in this word the <to> syllable is the stressed one, i.e. the one that is a little louder and a little longer.
  • vel: Vel is the Latin word for ‘or’.  Note that we are only three words into this line and we already have encountered three languages: Spanish, Zapotec, and now Latin!
  • ä: Again, you may be wondering about the diarisis (or umlaut) over the <a>.  You already know that we think the caron is likely marking stress. It turns out we think that any accent mark (caron, circumflex, diarisis, acute, or grave accent) all mark stress.  We are not sure if they were used to mean different things, or if the choice between which mark had more to do with which happened to be available to the typesetter.

Let’s look at the second line now– which will be much easier!

¶Dos. Tôpa. l. cǎto. 2
  • ¶: The pilcrow (paragraph mark) seems to be acting like a bullet point.
  • ô: You already know what we think this means!  (Stress!)
  • l.: l. is an abbreviation for vel ‘or’.

While you might be surprised that it took nearly a page to explain two lines, also look at how much easier this is to read now that you know a few simple things.

Exercise 2.2

Look at lines three and four on your own now.  Are there any printing conventions that remain unclear?

Now that we’ve looked at the form, let’s turn to the content!  Notice that there are two Zapotec words listed for each number. In fact, for the numbers one, two, three, and four only there are two sets of roots, referred to here as Set A and Set B. Set A is the main set. Set B is an alternate set, used only when counting flat things, like tortillas.

  Set A                              Set B

    1. tobi                            chaga
    2. topa                           cato
    3. chona                        cayo
    4. tapa                           taa

3. Putting together higher numbers

Let’s jump ahead now to some bigger numbers.  Just like in languages that you already know, most higher numbers in Zapotec are composed of building blocks based on the lower numbers. Think about the English number fifteen which has two parts: the fif part which is related to ‘five’ and the teen part that is related to ‘ten’. In Zapotec, most higher numbers are also built from pieces related to words for small numbers, but maybe not in the same way that you’re used to!  Let’s look now at Figure 6, a close up for the words for 11-15.

 

Figure 6.  Cordova 1578a: 102r

I’ve pulled out the Zapotec words and transcribed them below leaving out any accent marks for now.  You may recognize tobi at the end of ‘11’ from above– it is the word for ‘1’.  Chij is the word for ‘10’ and bi is a piece that can be used in bigger numbers to mean ‘and’ or ‘plus’, though it isn’t the regular word for ‘and’ in other contexts– it’s a special ‘and’ for numbers only.  So ‘11’ in Zapotec is ten plus one, which makes sense, of course!  ‘12’ is ten and two as shown below, though there are two different ways to say it– one uses the set A number for ‘two’ and one uses the set B number for ‘two’.  We don’t have many examples, but we would expect that chijcato ‘12’ would be used to count flat things, since it has the B-set form for ‘two’ in it.

11. chij-bi-tobi

     10-and-1        [=11]

12. chij-bi-topa

      10-and-2      [=12]

or

12. chij-cato

     10-2(B)          [=12]

Let’s skip now to ‘15’.  The first form for ‘15’ is chino.  While this might look like it could start with the word for ‘10’, it doesn’t have anything that looks like ‘five’ in it.  So we’ll say that this word on it’s own means ‘15’. There is another, longer way, to say ‘15’ as well, which seems to mean ‘another 5 will walk to 20’.  What could that mean? In this case, it looks like 15 is being calculated based on its relationship to 20– that you’re 5 away from 20 and that if you go another 5 you’ll arrive at 20.  That makes sense, too!

15. chino  [=15]

or

15. cecaayo quizaha calle

      ce-caayo     qui-zaha   calle

      another-5   IRR-walk   20         [=15]

      ‘another 5 will walk to (arrive at) 20’

4. Building blocks for numbers

You almost know everything you need to know to start doing some Zapotec math on your own! Here we listed all the parts you’ll find in the numbers 1 – 24,000, including the prefixes ‘and’ and ‘another’ (a) – (b); the verb ‘will walk to’ that we just saw (c); and number roots (1) – (16,000).  Use these as your reference to figure out the higher numbers in 4.1.

a) bi-[number] ‘and [number] more, plus [number]’ (like in 11)

b) ce-[number] ‘another [number] until’ (like 15)

c) quizaha ‘will walk to’ (like in 15)

Conjunto A Conjunto B
1 tobi chaga
2 topa cato
3 chona cayo
4 tapa taa
5 cayo
6 xopa
7 cache
8 xono
9 caa
10 chij
13 chijño
15 chino
20 calle, lalle
40 toua
60 cayona, quiyona
80 taa
100 cayoa, quioa
200 chija
300 chinoa
400 ela
8,000 çoti
16,000 topa

Exercise 4.1

Your turn!  Figure out the composition of the following Zapotec numbers.  They are already segmented for you. Then explain how they mean what they mean.

16. chino-bi-tobi

17. chino-bi-topa

or chino-bi-cato

or ce-chona qui-zaha calle

18. chino-bi-chona

or ce-topa calle

or ce-topa qui-zaha calle

19. chino-bi-tapa

or ce-tobi calle

or ce-tobi qui-zaha calle

20. calle

21. calle-bi-tobi

22. calle-bi-topa

or calle-bi-cato

23. calle-bi-chona

or calle-bi-cayo

24. calle-bi-tapa

25. calle-bi-cayo

26. calle-bi-xopa

27. calle-bi-cache

28. calle-bi-xono

29. calle-bi-ga

30. calle-bi-chij

Exercise 4.2

What do you notice about the way that these numbers are built up?  In what ways is it similar to English and other languages you know?  In what ways is it different?

Exercise 4.3

Ready for a challenge?  In the numbers below you’ll notice that there are no hyphens that divide the words into their meaningful parts.  This time, figure out what the parts are and analyze them as you did in (4.1). (While we stop here at 24,000, the Zapotec number system could be used to count higher, of course! There is no reason it couldn’t continue to count infinitely high.)

    1. callebichijbitobi
    1. callebichijbitopa
    1. callebichijbichona
    1. callebichijbitapa
    1. callebichino
    1. toua
    1. touabitobi
    1. touabichij
    1. touabichijbitobi
    1. cayona
    1. Cayoa
    1. Xopalalle
    1. Xopalallebichij
    1. Cachelalle
    1. Chija
    1. Tobiela
    1. Tobiela cayoa
    1. Tobiela chija
    1. Topaela
    1. Catoela chija
    1. Tapaela
    1. Cayoela
    1. Chijela
    1. Chagaçoti

or tobiçoti

    1. Chonaçoti

(Although we stop at 24,000 here, the Zapotec numbering system can obviously be used to count larger numbers. There is no reason why we could not continue to count infinitely large numbers.)

Exercise 4.4

Figure 7 is the first few lines from a 1666 last will and testament from San Miguel Etla, accessible on Ticha at: https://ticha.haverford.edu/en/texts/SME666/. These lines include the year 1666 written out in Zapotec: tapa ella chela cayona bixopa. Can you find that phrase?

 

Figure 7. The first two lines of a 1666 last will and testament from San Miguel Etla

 

Explain how tapa ella chela cayona bixopa means 1666.  (Some words may be spelled slightly differently than you saw above!)

 

Exercise 4.5

Ready for a challenge?  Based on the pattern you figured out in Ex. 4.1, 4.3, and 4.4, how do you think you would express the following numbers in Colonial Valley Zapotec?

74

86

97

124

136

402

5. Number systems and bases

Number systems in the world’s languages can use different bases.  English uses a base-10, as numbers over 10 are built on 10 and powers of 10 are specially named: e.g. ten, hundred, thousand.

Exercise 5.1

Can you figure out the bases used to count in Zapotec?  Hint: there are three bases! One used for 10-14, another for 15-19, and another for 20 and above!

Zapotec has a long history of writing and shares a system for representing numbers with other languages in the Mesoamerican cultural area.

Exercise 5.2

Do some research on the Mesoamerican representation of numbers using bars and dots. Does this system reflect the structure of the number system and the bases as you analyzed in (5.1)?  If so, how?

6. Zapotec numbers today

Listen to the numbers in Zapotec as spoken today in the same town where the text in Figure 1 was written nearly 500 years ago, San Jerónimo Tlacochahuaya.  Maestro Moisés García Guzmán has a playlist of the numbers 1-100 on his YouTube channel, available here: https://www.youtube.com/watch?v=aajhujTUL20&list=PLh7FCBo-wt5uJWS89HvgSv5DP-UTgJrsr

(For more on the differences between counting in Colonial Valley Zapotec and Modern Valley Zapotec, see Lesson 3: Language Shift.)

 

Exercise 6.1

What similarities and differences do you notice between numbers as written in the Colonial period and how they sound today?

Exercise 6.2 How does it work in your language?

6.2 What are the numbers like in your language? What is similar and and what is different between the numbers in your language and in Colonial Valley Zapotec?

Exercise 6.3

Search the internet for more examples of Zapotec counting.  Compare them to the numbers in Tlacochahuaya.

7. Works Cited

Blokland, Frank E. 2012. On the origin of Patterning in Movable Latin Type. Online: https://www.lettermodel.org/.

Heller, Steven. 2018. Initial Caps: The Birth of Illustrated Typography. Design Observer. Online: https://designobserver.com/feature/initial-caps-the-birth-of-illustrated-typography/39885.

Munro, Pamela & Aaron Huey Sonnenschein. 2007. Four Zapotec Number Systems. Bernard Comrie Festschrift: ms.

 


  1. This chapter is a work in progress and can be cited as follows:

    Lillehaugen, Brook Danielle. In preparation. Numbers. In Caseidyneën Saën – Learning Together: Colonial Valley Zapotec Teaching Materials, ed. by Flores-Marcial et al. Online: http://ds-wordpress.haverford.edu/ticha-resources/modules/chapter/unit-2-numbers/.

    The volume can be cited as:

    Flores-Marcial, Xóchitl, Moisés García Guzmán, Felipe H. Lopez, Broadwell, George Aaron, May Helena Plumb, Mike Zarafonetis, and Brook Danielle Lillehaugen, (eds.). In preparation. Caseidyneën Saën – Learning Together: Colonial Valley Zapotec Teaching Materials. Online: http://ds-wordpress.haverford.edu/ticha-resources/modules/.

    We appreciate feedback and suggestions from anyone who teaches or learns with these materials.

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Caseidyneën Saën - Learning Together Copyright © by Brook Danielle Lillehaugen. All Rights Reserved.

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