Counting in an old Mundurukú man

This is a description of movies available on http://video.rap.prd.fr/videotheques/cnrs/grci.html

 

As described in our study (Pica, Lemer, Izard and Dehaene, Science, 2004), the Mundurukú system of number words stops at 5. Furthermore, the Mundurukú typically do not use their numbers words in a counting sequence. However, an old man, seen in Sai Cinza during the first pilot trip, claimed that he had a counting system above 5. He was therefore asked to demonstrate how he counts.

First movie

(http://video.rap.prd.fr/cnrs/grci/MundurukuFingerCounting.ram)

 

In the first movie, the man demonstrates the counting sequence, which is accompanied by pointing on fingers and toes. Note how he hesitates, even on the word for 5. He first stops there, then recounts, at which point he first says “soat bu” (all fingers) then “cinco” (five in Portuguese), and finally, after being corrected by his son, “pũg põgbi” (one hand). 

 

He then goes on to count on the left hand. The expressions that he uses designate his fingers. 6 is “bu axiri ku” (literally “finger thumb here”), 7 is “wuy bu epacuñap” (“our fingers the next one”), etc. He again stops at ten, which he successively calls “xep xep põgbi” (two hands) and “soat pu” (all fingers). He finally counts on his left foot, again naming the successive toes: 11 iswuy euaxiri eju” (“our foot toe here”), 12 is “wuy eu’ipidase at” (our foot the toe that one can see”), 13 is (“our foot the middle toe”) etc. Note that some expression such as “all fingers” or “soat pu” are ambiguously used for five, ten or fifteen.

 

The rest of the tape shows him and his son checking the sequence of numbers again.

Second movie

(http://video.rap.prd.fr/cnrs/grci/MundurukuSeedCounting.ram )

 

The second movie shows the same old man and the ‘paje’ (medecine man) of the village successively attempting to count some seeds. The old man first counts 10 seeds (successfully), then both men successively attempt to count 13 seeds (unsuccessfully).

 

The first set comprises ten seeds. Counting is slow but correct, based on a clear strategy of separating the seeds that have already been counted and those that remain to be counted. The old man (sometimes corrected by his son) counts “one seed, two seeds, three seeds, four seeds, five”. Each numerical expression is associated with the classifier for seeds “taexcepts for what seem to be more conceptual number words such as five which already incorporates the classifier for fingers “bi” (“pũg põgbi”). Note how the man stops when reaching a first group of five, and says two different expressions for the same number (“cinco be” and “pũg põgbi”). He then goes counting by naming the successive fingers, up to ten. Note again how “ten” is again expressed in two different ways, with a clear stop before enunciating the final result “xep xep põgbi” (two hands).

 

The second set comprises thirteen seeds. The ‘paje’ (the man with the white T-shirt) is the first to attempt to count. He counts only up to “two”, with the lexical unit for “two” (“xep xep”) associated with the classifier for seeds “ta”. He then repeatedly says “another, another”, roughly aligning the seeds. The count stops at five with a gesture of an open hand, but no word is said.

 

The ‘paje’ tries again. This time, he repeatedly says “two” and vaguely groups the seeds by two’s. Again he says no numerical expression above “two”.

 

On the fourth scene, the old man tries to do better. He says the correct number words up to five. He makes a pause there, saying and showing “one hand”. He then goes on counting, but erroneously stops after 9 and shows his two hands. Finally, for the remaining four seeds, he uses the words “one”, “two”, “three”, and then again erroneously says “one hand” after the fourth seed. None of these errors are corrected by his son.

 

The movie thus illustrates a surprising variation in counting performance and even in vocabulary among two subjects. The ‘paje’, who is the least in contact with the Western world, shows no evidence of using any numerical expressions above “two” in this situation.  The old man, who entertains more contacts with the Western world (through his son), has a greater vocabulary, and the words that he uses above five show the rudiments of what could be called a “base five” system, clear imposed by finger counting. Yet even he occasionally makes gross errors.

Discussion of the two movies

 

Altogether, although anecdotal, the movies nicely illustrate how difficult counting is for the Mundurukú. Counting is not a routine activity. Rather, it is a slow and effortful process, based primarily on finger movements, with the names mostly serving as descriptors of the pattern of fingers. When the fingers are used to move seeds, they can no longer be used to count, and hence counting frequently fails.

 

Crucially, there is no routinized sequence of count words in Mundurukú, unlike our ability to recite “one two three four…” very fast. Rather, the number words are always expressed with a classifier: “one finger, two fingers, three fingers…” or “one seed, two seeds, three seeds…”. Furthermore, the numerical expressions can be redundant: three different words “soat pu”, “cinco”, “pũg põgbi” are uttered for five. Conversely, they can be ambiguous: “soat pu” (all fingers) is used for five, ten or fifteen fingers depending on the context. Thus, counting does not seem to be based on a recitation of a rigid series of unique count words, each paired one-to-one with the objects to be counted.

 

Yet we do not think that these counting difficulties provide any evidence for a conceptual limitation in the Mundurukú. The old man at least seems to understand what he is trying to do, and to spontaneously obey the fundamental principles of counting (such as the necessity of not counting the items twice). However, most Mundurukú have very little training in counting. Therefore they make many errors, and they rarely count spontaneously, even when solving simple exact arithmetic problems such as six minus four (see our main article).

Acknowledgement

We are grateful to Association Pussuru, its president Jose Crixi, Valdemar Manhuary and Zenildo Saw for their help in interpreting those data.