[Walter even gave the tortoises a mock-biological name, Machina speculatrix] because they illustrate particularly the exploratory, speculative behavi… - William Grey Walter

Simon, always a fool for simplicity, accepted. Punch took an envelope out of his pocket and scribbled on the back of it. He said, 'This has a simple arithmetical proof but no rational explanation of the paradox.' He gave it to Simon. Simon read it, looked at Punch with raised eyebrows, hunched his shoulders, shook his head sadly, and got up and left the room without a word.

Rapidly going over what I could recall of Jim Bursley's information about pathological curves confirmed the conjecture. The snowball curve, derived from an equilateral triangle, is a perimeter of infinite length enclosing a finite area. The angles or points of the perimeter are uncountable. An equilateral triangle projected integrally in the third dimension is a triangular pyramid of equal surfaces. The three-dimensional snowflake derived from this pyramid--hence its diamantine appearance--is a finite volume enclosed in a surface of infinite area. The convolutions of such a surface, to be gathered around its defined content extrude a number of discrete angles or points beyond all possibility of computation. The pressure on each point is infinitesimal, unmeasurably small; the total external pressure exerted on any part of the surface is an aggregate of infinitesimal values, itself infinitesimal.

Not in looks, but in action, the model must resemble an animal. Therefore it must have these or some measure of these attributes: exploration, curiosity, free-will in the sense of unpredictability, goalseeking, self-regulation, avoidance of dilemmas, foresight, memory, learning, forgetting, association of ideas, form recognition, and the elements of social accommodation. Such is life.