Predictions of the Model

A number of consequences fall out as predictions of the accumulator by virtue of the inherent structure and functioning of the model.

1. It predicts that animals (including human infants) should be able to discriminate different numbers of entities on the basis of number per se, not nonnume-rical properties of arrays such as light-dark contrast, configuration, contour complexity, physical magnitude (size, volume, height, etc.), and so on. The accumulator is a mechanism that determines numbers of individual entities; it takes as input discrete individuals, not perceptual information. Moreover, because there is nothing inherent in the structure ofthe accumulator to restrict the kinds of idividuals it can count, we would expect infants and animals to be able to determine numbers of different kinds of entities. From an evolutionary standpoint, there are many kinds of entities it would be advantageous to be able to enumerate; thus, we might expect that a mechanism that evolved specifically for the task of determining the discrete number of things and that has no structural limitations on the kinds of input it can take, beyond the requirement of discrete inividuals, should be able to count different kinds of things.

2. Because of the fact that variance in the fullness of the accumulator increases with numerosity, with larger numbers representation of these numbers becomes more rough and approximate. As a result, discrimin-ability for a given numerical difference should decrease as number increases. Because the variance is additive, the discriminability of two values should rest more on their proportionate difference than on their absolute difference; thus, animals and infants should be able to discriminate larger numbers, provided their proportionate difference is sufficient.

3. Because the representations have a structure in which the magnitudinal relations between different numbers are inherently embodied, we might expect animals and infants to possess procedures for extracting such information, that is, we would expect them to be able to use these representations in numerically meaningful ways.

The following section examines how these predictions bear out in empirical studies of numerical abilities in infants and animals. To preview, a review of the findings shows considerable evidence that this aspect of numerical understanding may form part of the inherent structure of the mind: a sense of numerical magnitude appears to be present early on in infancy and is evident in a wide range of animal species.

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