Invertebrates discuss geometry
Ant: Here I am, ant-ing my way along the ground, and I've hit an obstacle which blocks my path. How do I make sense of this problem? Well, first question: What shape is the obstacle that I see before me? This will help determine my solution. Answer: It is a long, straight line with two end points. There is a dyadic relationship going on here. Therefore the solution must be one dimensional. That's how I will think about it as I envision what I can and can't do next.
Worm: Wrong! I am underground, beneath the shape, looking up at it. It is a triangle. There is not one straight line, but three sides, and three points. Lift your gaze, lowly ant! You see only one edge of it. There is a triadic relationship going on here. The solution must be two-dimensional.
Spider: Incorrect, both of you! I am hanging by a thread, above the shape, looking down on it. It is a tetrahedron, or a triangular pyramid. It is resting on the ground, you dummies! One of you sees only an edge, and the other sees only the base. In fact, there are four, triangle-shaped sides, and four points. So there is a quadratic relationship going on here. What are you, blind? The solution is three dimensional.
Slug: Wrong, all of you! I have shlurmed my way to the very top of the pyramid. At its apex is a single, sharp point. And now I am stuck on it! From my perspective and as far as I am concerned, there is very monadic relationship going on here. And it is very uncomfortable! The solution has zero dimensions! Just get me down from here!
posted by TiR at 7:01 AM
