Random Thought #131

As I said in my last post, why is it that we view things as having a beginning and an end. Why do we view things hierarchically? Why must there be two sides to a strip of paper? (See Mobius Strip) Why does there have to be an inside and an outside? (See Klein Bottle). Our understanding of things is based on what we observe, learn, and experience. Think about it. Everything that you know to be true today is based on past experiences. Remember the sensation of learning something existed that you never knew before? You've never experienced it before so you never thought it was possible. Imagine you lived in a world where doors always open inwards (I suppose that's relative); let's say in one direction. You would be quite staunch in your approach and would tell someone that doors can only be opened one way. Then imagine you encounter a door that opens the opposite way. How could this be? How are we to understand this strange phenomenon? It so clearly violates the way the world works and yet there is the evidence standing right in front of you. The awesome part is that we now assimilate that experience into our understanding of how the world works and we are now ok with it. Innovators have an uncanny way of pushing the boundaries of their "complete" world and discovering new and exciting things.

This is simply Godel's Incompleteness Theorem. The theorem basically says that a system (your perception in this instance)cannot be both complete and consistent. Everything you know is based on past experiences and they are all true because that's how the world works. We'll say our world is consistent. Everything makes sense and there are no anomolies. We believe that it is complete but then we learn something new that challenges the way our world works and discover our system isn't complete. We could ignore this fact and say that its false and maintain our consistency but then we can't say that our world is complete because there is something new out there that isn't part of our system. Conversely, if we accept this newly learned truth, then we believe that our system is now complete but its not consistent because doors now open in two directions instead of one. So what do we do as humans? We have to change the rules of the game. We have to change our perception and understanding (our system) so that the new information is assimilated and we are again both consistent and complete. Or are we?