Calculators are an often used example in the philosophy of mind. Sometimes they’re used analogously, to show how computational algorithms can be implemented in a variety of mediums (say, the very different circuitries of the calculator and the human brain). Other times, they’re used metaphorically, as objects that we can attribute intentional states: the calculator ‘knows’ how to add and ‘believes’ that 2+2=4. But how appropriate are comparisons between calculators and humans? Is it a matter of implementing the same (or nearly the same) algorithm? Or is the comparison a mere metaphor? Stanislas Dehaene is the champion of the surprising view that neither of these (caricatured) approaches can be right: calculation is neither a matter of merely attributing intentional states, nor do humans and calculators implement algorithms in the same way.
(Apologies if this topic seems old hat to any – if you are a person already familiar with Dehaene, ‘cultural re-mapping’, number sensing, and the like, the payoff to re-reading this extremely cool and interesting stuff about human mathematical capabilities, is some very exciting and interesting new advances in brain localization and machine-learning)
Dehaene’s view is that our mathematical abilities result from the mixture of two evolved mechanisms, and, importantly, a sprinkling of language. The first of these evolved mechanisms is a capacity to distinguish a certain amount of discrete quantities, or numerosity: the ability to tell apart one, two, three, and maybe four and five. Then, there is the capacity to distinguish differences in quantity: that six is bigger than one, or that twenty is less than sixty. Both of these abilities can be found in animals, and, yes, human children. And it’s easy to understand why such mechanisms might persist over time*: as an organism, it is very handy to have a capacity to determine between alternatives; whether option (a) was better than (b) because more nutrients, or less competition, or what have you. Continue reading “Machine Math?”