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.
(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 pőgbi”
(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 epacuńap”
(“our fingers the next one”), etc. He again stops at ten, which he successively
calls “xep xep pőgbi” (two hands) and “soat pu” (all fingers). He finally
counts on his left foot, again naming the successive toes: 11 is “wuy eu’
axiri 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.
(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 “ta” excepts for what seem to be more conceptual number words
such as five which already incorporates the classifier for fingers “bi” (“pũg pőgbi”). 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 pőgbi”). 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 pőgbi” (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.
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 pőgbi” 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).
We are
grateful to Association Pussuru, its president Jose Crixi, Valdemar Manhuary and Zenildo Saw for
their help in interpreting those data.