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OLDEST NUMBERS IN THE WORLD

The fact that humans have been recording tallies with sticks and bones for 30,000 years is impressive, but the critical issue is this: what cognitive abilities enabled them to encode quantities in the first place? To identify the inherent constraints on humans’ ability to process numerical information, it is helpful to consider the evolutionary history of numerical thought. We can look for clues to the evolutionary precursors of numerical cognition by comparing human cognition with nonhuman primate cognition. The degree to which humans and nonhuman primates share numerical abilities is evidence that those abilities might derive from a common ancestor, in the same way that common morphology like the presence of 10 fingers and toes in two different primate species points to a common morphological heritage.

So far, there is evidence that nonhuman primates share three essential numerical processing mechanisms with modern humans: an ability to represent numerical values (Brannon and Terrace, 1998; Nieder, 2005; Cantlon and Brannon, 2006, 2007b), a general mechanism for mental comparison (Cantlon and Brannon, 2005), and arithmetic algorithms for performing addition and subtraction (Beran and Beran, 2004; Cantlon and Brannon, 2007a). These findings compliment and extend a long history of research on the numerical abilities of nonhuman animals [see Emmerton (2001) for review].

Representation

When adult humans and monkeys are given a task in which they have to rapidly compare two visual arrays and touch the array with the smaller numerical value (without counting the dots), their performance reliably yields the pattern shown in Fig. 16.1: accuracy decreases as the ratio between the numerical values in the two arrays approaches 1 [Cantlon and Brannon (2006); see Dehaene (1992) and Gallistel and Gelman (1992) for review]. The explanation of this performance pattern is that both groups are representing the numerical values in an analog format (Fig. 16.2).

In an analog format, number is represented only approximately, and it is systematically noisy (Dehaene, 1992; Gallistel and Gelman, 1992]. More precisely, the probability of noise (i.e., the spread of the distributions) in the subjective representation of a number increases with the objective number of items that are coded by that representation. Consequently, the probability of confusion (i.e., the overlap between distributions) between any two objective numbers increases as their value increases. This means that the probability of having an accurate subjective representation of a numerical value decreases with its objective value. This relationship can be succinctly quantified by the ratio between the numerical values being



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