Nature, man and mathematics

Summary

Several years ago, when I had brought home a new microscope designed for children's use, we had opportunity to observe the first recognition, by a five-year-old, of the world of size and scale. Or perhaps it was not the first, beginnings are hard to catch; and this fortunate young girl was already deeply involved with fragments of that world, at least – with dolls and furniture to scale, with pictures and maps of her own and others' drafting, and much else besides. But the world of size and scale is something else again, it is a recapitulation and a surmise; a glimpse of generality and of closure. At that young age the eyepiece of a microscope is first a shiny object and then, with luck, a sort of peep-show or television screen in miniature. At any rate we did what we all three, Christa, my wife, and I, called ‘looking at’ various objects. Some, which Christa brought for this new occupation, were ten or fifty times too big to fit between object and stage, and one saw a young child's perceptual unreadiness to make use of what might be called the transitivity of congruences.

But one evening Christa brought to the microscope a tiny bit of lint from the floor. Here for the first time there seemed to be recognition, the lint was seen as lint though transformed a hundred-fold in scale.