Homotopy and the tearing off of a drop from a hard surface
No. 248, 1987
(Topology, hydrostatics, and geometric intuition)
India ink and pencil on paper, 34 x 50 cm.
Suspended in space, floating before a crystalline complex in the background, is a globule of viscous fluid, dripping from one of its appendages. As a whole, the image shows the very beginning of a drop forming, as the heavy viscous liquid hangs from a hard surface. Shown too, the beginning of a homotopy of a geometric object, which begins as a rigid shape and then softens into a pliable, resilient form that begins to deform continuously. Such images play a critical role in certain areas of mathematics, since many deep proofs have their basis in visually intuitive ideas. Often a formal algebraic proof comes to mind only after one formulates a clear geometric picture of some complex problem. Thus geometric imaginings themselves come to have practical value often in nonobvious, sometimes mysterious ways.
