FIGURE 6.5 Latency to the first response (left) and accuracy (right) in a pair-wise numerical comparison task as a function of numerical disparity. Monkeys (open circles) and humans (closed circles) were required to respond first to the stimulus with the fewer number of elements.

college students and monkeys suggests that a similar representational format and comparison process is used.

In another approach, Hauser et al. (2000) conducted a series of studies on the spontaneous numerical abilities of rhesus macaques free-ranging on the island of Cayo Santiago. In all of these studies Hauser et al. tested a given monkey for a single trial and compared large groups of monkeys in each experimental condition (between-subjects design). This approach is notable because it assesses spontaneous cognition without the extensive training typically required in number discrimination tasks with animals. In one paradigm experimenters successively dropped apple slices into two distinct buckets and determined the percentage of trials on which the monkeys chose the bucket with the larger number of apples (Hauser et al., 2000). The monkeys successfully chose the bucket with the larger number of food items with the comparisons 2 vs. 3 and 3 vs. 4, but were at chance with the comparisons 4 vs. 5 and 5 vs. 6. Surprisingly, the monkeys also failed when presented with the contrast of 4 vs. 8, even though this involved a large ratio. These results differ from those obtained by Brannon and Terrace where rhesus monkeys discriminated values as large as 8 vs. 9 and where the ratio of the values largely controlled performance.

One possible explanation for this discrepancy is that Hauser's paradigm assesses the spontaneous number discrimination abilities of rhesus macaques, whereas Bran-non and Terrace's paradigm shows what a monkey is capable of after extensive training. This explanation may be partly correct; however, it is important to note that the monkeys in Brannon and Terrace's experiments performed above chance on large number contrasts despite the fact that they had no prior training on those particular values. There are two other major differences between these paradigms. First, Brannon and Terrace presented simultaneous visual arrays, whereas Hauser presented items sequentially and sets were not visible. Second, food items were used by Hauser rather than the abstract shapes used by Brannon and Terrace. More work is needed to parse the relative contribution of these three factors to the different performance of rhesus monkeys in these two paradigms.

6.3.2 Addition and Subtraction

Experiments on addition and subtraction have been done with New World monkeys, Old World monkeys, and apes. In perhaps the most impressive demonstration of animal arithmetic, a chimpanzee named Sheba was led around a room to three different hiding places that contained a total of one to four food items. Subsequently, Sheba was led to a platform where she was required to choose the arabic numeral that corresponded to the total number of items. Sheba chose the correct numeral on 75% of trials without any explicit training. Amazingly, Sheba was still successful when the oranges were replaced by arabic numerals (Boysen and Berntson, 1989).

Summation may also be seen in tasks where primates are required to choose the larger of two food quantities. Rumbaugh et al. (1987, 1988) presented chimpanzees with two sets of two food wells, each of which contained some number of chocolates, to determine whether the chimps could choose the set of wells that had the largest cumulative quantity. To choose the set with the largest quantity, the chimpanzees would have to sum the chocolates in each of the two sets and then compare the two summed values. On the critical trials where the largest set of wells did not contain the largest single value, the chimps chose the larger quantity on approximately 90% of trials (see also Beran, 2001; Call, 2000). Olthof et al. (1997) conducted a similar experiment with squirrel monkeys and arabic numerals. The monkeys were first trained to choose the symbol that indicated the larger quantity and then presented with two sets of one to three arabic numerals each. Again, both monkeys reliably chose the set that contained the largest sum, even when this set did not contain the largest individual value.

Hauser et al. (1996) adapted the violation-of-expectation paradigm developed by Wynn (1992) to test arithmetic reasoning in human infants. In this paradigm human infants or monkeys view dolls or food items. A screen is then raised to obscure the items on the stage. A hand then adds or removes an object behind the screen. Finally, the screen is lowered to reveal the expected or unexpected number of objects and looking time is measured. Figure 6.6 illustrates a 2 - 1 = 1 or 2 trial. Hauser et al. (1996) found that monkeys looked longer when the unexpected outcome was revealed for 1 + 1 = 1 or 2 and 2 - 1 = 1 or 2 operations (see also Sulkowski and Hauser, 2001). Uller et al. (1999) also found that cotton-top tamarins look longer at the unexpected outcome of 3 or 1 compared to the expected outcome of 2 when they witness a 1 + 1 operation.

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