Feb. 13, 2011

  • Some people believe that a computational model of reality is the best model.

  • In this model, reality itself is assumed to be a mathematical process. It is a mathematical system sufficient to describe the set of natural numbers.

  • Therefore Gödel's incompleteness theorms apply to this model of reality.

  • Therefore in such a model of reality you can never prove the consistency of the model from within the model.

  • Additionally, there are true statements within this model which are not provable.

  • This means that such a model of reality cannot possibly contain a nested copy of itself, a perfect predictive model of reality/itself, since such a nested model would allow you to break both of the incompleteness theorems.

  • I think that this is proof that any computational or mathematical model of reality paradoxically excludes itself from ever being a perfect model of reality. This probably applies to all mathematical models of our reality, including any Grand Unified Theory.

We can never come up with a mathematical model of reality that is 100% predictive and accurate.