The Pirahã Controversy: Numbers (part 2)
In the previous post, I’ve described one experiment designed to shed some light on the number words in Pirahã and their use. But many more experimental studies add food for thought and fuel to the debate.
One such study was conducted by Dr Peter Gordon, a psycholinguist at Colombia University, and published in 2004 addressed the following question: Can speakers of Pirahã appreciate larger numerosities without the benefit of words to encode them? According to Prof. Gordon,
“numerical cognition is clearly affected by the lack of a counting system in the language. Performance with quantities greater than three [is] remarkably poor, but [shows] a constant coefficient of variation, which is suggestive of an analog estimation process.”
As the first part of the study Peter Gordon replicated the “ten spools” experiment, where the Pirahã had to name the number of objects and use fingers to supplement oral enumeration, but this was highly inaccurate even for four. The results are schematized in the table on the left. As you can see, not only the use of words like hói ‘one’ and hoí ‘two’ was not consistent with their interpretation as “number words”, but the confused showing of fingers seems to indicate that the Pirahã have trouble appreciating numerosities larger than 3. Gordon also notes that “there [is] no recursive use of the count system—the Pirahã never used the count words in combinations to designate larger quantities.”
In addition, Gordon conducted a series of experiments in which the number of objects presented by the experimenter (Gordon himself) had to be matched by the same number of objects laid out by a Pirahã speaker. Instead of thread spools, AA batteries and ground nuts were used. A stick was laid out in the middle of the table, separating the experimenter’s array (below the line) and the participant’s attempt “to make it the same” (above the line). Tasks A through D required the participant to match the array presented by the experimenter using a line of batteries (the picture above illustrates task C: Orthogonal Matching). Task E involved an unfamiliar task of copying lines drawn on paper. Task F was a matching task where the participant saw a numerical display for only about one second before it was hidden behind the screen. Task G involved putting nuts into a can and withdrawing them one by one; the participants responded after each withdrawal as to whether the can still contained any nuts or was empty. Task H involved placing candy inside the box with a number of fish drawn on the lid; the box was then hidden and brought out again with another box with one more or one less fish on the lid, and participants had to choose which box contained the candy. As can be seen from the associated graphs, the Pirahã did well only with numerosities smaller than four, and failed on harder tasks even with three. Gordon concludes:
“The split between exact enumeration ability for set sizes smaller than three and analog estimation for larger set sizes parallels findings from laboratory experiments with adults who are prevented from explicit counting; studies of numerical abilities in prelinguistic infants, monkeys, birds, and rodents; and in recent studies using brain imaging techniques.”
In the following post, I will describe one such study in which MIT students were effectively “turned into Pirahã”.
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