“What is a number that a man may know it?” (Warren McCulloch). A wave model can determine “numerosity” (number of identical items) for small numbers of items. Identity and numerosity can be explained through similar mechanisms. Can there be a biology of number? Imaging studies find a topographic map of number magnitude in the human brain. Higher mathematics is based in part on refined perception. Classic mathematical philosophy—Platonism and formalism—may be usefully extended with perceptual components both learned and unlearned. Perceptual involvement suggests why mathematics is surprisingly good at dealing with the physical world. We find perceptual involvement even in simple integer multiplication. We can use “active” perceptual-based nets to program elementary abstract mathematical operations. A “brain-like” program is described for the “greater-than” program done by a digital computer in Chapter 4
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