The Socratic Snake That Eats Itself

I had a wonderful IM discussion with the author of Within/Without this morning which, through caffeination of an idle mind, got me thinking about the Socratic cave - a theoretical construct of Socrates. When one leaves this cave and returns, nobody believes anything you say because their own points of reference are only within the cave. And, based on the conversation between Neha and myself, was considering how this works when one leaves one Socratic cave to enter another. And then another. And then another. And then another. And then... Hopefully, you get the point.

But then, one does end up returning to the original Socratic cave, only there's a difference. One can look in from one's new perspective, but through the refraction and reflection inherent in the walls of the cave from the inside - a concave surface - the people inside cannot see out. So there's this border, a border which frustrates the person jumping up and down on the convex surface of the outside of the cave as they look in. Because of the nature of the cave, the ability of a convex surface to maintain under pressure, the cave is not likely to break from the outside. But with enough pressure exerted, people in the cave might be forced out. And when they are forced out, they are not likely to go in the direction of the pressured surface - rather, they would go perpendicular to that pressure (if the pressure is exerted around the surface - picture a tube of toothpaste). Those that leave the Socratic cave end up in another cave, and so on - and like a snake it eats itself. Infinity in one aspect, and growth in another - the circumference of the snake eating itself increases.

And so, a cross section of this Socratic snake which eats itself might look like something to the right - with that simple rule: Outer layers may view inward, but inward layers may not view outward.

It might even be fun to consider the circumference as k in Lorenz curves for a number of Pareto distributions... as it eats itself and grows, the center changes as it digests itself.

But the joke is that there are a lot of interconnected snakes eating themselves, like rollercoasters circling through a really dense network. We could delve into quantum mechanics, philosophy, or the nexus of the two. Consider - for those of you geeky enough - Holodynamics and Quantum Computer Models and Orbital Data Confirms Dynamic Fractal Firework Universe Having 3D-spiral Code (pdf, 704 kb).

It's a fun model to play with in one's mind, if you have space for it. Or maybe I'm just squeezing a tube of toothpaste. Or more likely, I'm in the tube of toothpaste. :-) I think that this thought, or a similar thought, has existed for quite some time in older cultures in China and India, as well as others.

It's when the Socratic snake gets indigestion that we have to worry. It probably ate something bad...