It is perhaps a little humbling to discover that we as humans are in effect computationally no more capable than cellular automata with very simple rules. But the Principle of Computational Equivalence also implies that the same is ultimately true of our whole universe.
So while science has often made it seem that we as humans are somehow insignificant compared to the universe, the Principle of Computational Equivalence now shows that in a certain sense we are at the same level as it is. For the principle implies that what goes on inside us can ultimately achieve just the same level of computational sophistication as our whole universe.