6.10: A natural cusp

A day after the snail hunt, and almost half way through this story, Hipparchus is taking a constitutional. He carries, and uses, a cane, not that he puts much weight on it. He realises that he is getting old and stiff, and, on rougher ground, likes to be able to feel the terrain through the cane as well as his feet.

Approaching the mid-point of his walk, he sees the newcomer – Fabian the snail – who seems to be running circuits on a piece of sloping ground. Hipparchus waves his cane and Fabian seems to nod very briefly in return but without pausing. 

Hipparchus notices that the snail is running in such a way to climb up a smooth part of the slope, turn right still on a further smooth slope, turn right again to come to a cliff or discontinuity – Hipparchus hypothesises that there is a fold of rock beneath: geology is such a thing! – and bump down that, turn right once more down at the lowest level and then repeat the process. He speculates that going the other way might be impossible, or at least much slower, for the snail. 

Smooth changes at this point of the hill lead to a sudden, albeit modest, cliff. Something about this geometry reminds him of something, but he cannot think what and so continues his walk.