Tuesday, July 16, 2019

Children, Dialectics, and Topology

"One of the curious things about our educational system, I would note, is that the better trained you are in a discipline, the less used to dialectical method you're likely to be. In fact, young children are very dialectical; they see everything in motion, in contradictions and transformations. We have to put an immense effort into training kids out of being dialecticians." -- David Harvey, Companion to Marx's Capital: The Complete Edition. Verso (2018).

I do not have children, and I am not sure I understand Harvey's claim. But one writer I liked was Jean Piaget. (I also want to mention Seymour Papert.)

I take from him that children think in a way that can be described by advanced mathematics. I think, in particular, of topology and modern algebra. The idea is children take time to learn certain invariants and conservation laws that many of us now take for granted. In topology, one asks what can be said about sets and functions when one does not have a distance function? If you rotate a disk, suppose, for example, the distance between two points cannot be assumed the same when you look in the east-west and north-south direction. Algebra investigates certain abstract structures, with as little as possible assumed about the properties of operations. A difference between mathematicians and children, however, is that the mathematicians (better than me) learn how to articulate and characterize such structures.

I do not think I am necessarily contradicting Harvey. J. Barkley Rosser, Jr. has a paper that perhaps can be used to draw connections between Piaget and Harvey's ideas about how children think.

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