If i understand it correctly (which is doubtful), in section 2, the cellular automaton conjecture is dismissed because 110 as a computer suffers from exponential slowdown.

>"To prove that 110 is NP-complete, what is needed is to show that Rule 110 allows efficient simulation of Turing machines"

But if the universe is a 'computation', then the efficiency of it doesn't really matter right?

Similar to creating a Blender rendering, it doesn't matter how long each frame takes to render compared to any other frame, as long as the observer sees a smooth sequence of images.

As far as I understand it, his hypergraph based theory we're reading about here is different from the cellular automata ideas in New Kind of Science?

If I understand correctly, condition 4 (see page 104) no longer holds. The new theory, in contrast to the old theory (see bottom of page 100), seems to be a multiway system.