Act II, Scene 4

Plato’s Cave – 3D Windows into the Real World

Despite its length (over an hour) the video “IMA Public Lectures: Impossible Objects: The Mathematics of 3D Illusions” of a talk Kokichi Sugihara gave at the IMA, University of Minnesota is really worth watching. A shorter and less mathematical talk by Kokichi Sugihara is here and the screenshot below from his English language website shows some of his “impossible objects” – three dimensional objects that appear impossible when viewed from certain vantage points.

Plato describes a group of people chained to the wall of a cave looking at a blank wall on which they see shadows of the world outside. These shadows are all that they see of the outside world and from the shadows they must build their own model of that world. This video shows how two dimensional projections lead to very distorted views of the three dimensional world.

The world in which live is very high dimensional and our place in it is very small both in extent and time. The people we encounter are complex and multi-dimensional and yet we have very limited interactions with most of them. The quantum phenomena that are transforming our lives even require us to think about things that seem to be in two different places at the same time. Our situation as we try to model the world in which we live is not entirely different from that of the people in Plato’s cave.