I will answer these comments in order:—
There is no more cleverness in a child drawing a curve than in the pendulum of the harmonograph doing so; in both cases alike an implement has been set moving according to a certain law, and beauty has resulted, not from understanding but from obedience. As for any strain to the brain, stitching a curve from its tangents is not more straining to the brain and nerves than stitching round a printed outline, not nearly as much so as working the fine cross-stitch samplers of our grandmothers. The difference is that working a sampler and following a ready-drawn outline cultivate only neatness and dexterity, but the act of evoking a curve 'out of the everywhere into here,' by simple obedience to a rhythmic law, lodges an impression on the unconscious mind which will be ready to surge up in ten years' time, and perhaps make some class-teacher at College wonder why this boy or girl, though not very studious and full of all sorts of interests outside the curriculum, never had the least difficulty in grasping the idea of the differential calculus. As for the implied suggestion that there can be no other alternative except either conscious understanding or else dishonest 'show-off,' let us notice this: If the child had grown some cress in his garden, no one would have asked
