Numerical Subtraction in the Pigeon: Evidence for a Linear Subjective Number Scale

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Abstract
When humans and animals compare two numbers, responding is faster and more accurate with increasing numerical disparity and decreasing numerical size. Researchers explaining these distance and size effects often assume that the subjective number continuum is logarithmically compressed. An alternative hypothesis is that the subjective number continuum is linear, but positions farther along it are proportionately fuzzier, that is, less precisely located. These two hypotheses have been treated as functionally equivalent because of their similar empirical predictions. The current experiment sought to resolve this issue with a paradigm originally developed to address the subjective representation of time (time left). In our adaptation, pigeons were required to compare a constant number with the number remaining after a numerical subtraction. Our results indicate that subjective number is linearly, not logarithmically, related to objective number.