ABSTRACT
A profound shift in thinking about counting comes with the recognition that counting is fundamentally a means of comparing quantities and, in that sense, a measurement tool. Like other forms of measurement, counting requires the choice of a unit. The units are usually taken to be objects—blocks or toy animals or crayons. They can also be parts of objects, like the legs on an insect or the sides of a triangle. In principle, provided we are consistent about what we take as a unit, we can count any sort of discriminable element in any kind of array. But we don’t. There are two things in particular that we don’t customarily do in counting. One is to count aggregates of separate individuals (unless they are grouped). Thus, although it seems natural to count the triads of squares in this row (there are three of them):
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