One of the frustrating things with the way Stephen Wolfram works is because he never actually defines anything it’s very hard to pin down what is actually interesting empirical science and what is data visualisation buggering around.

Here, before he starts, how do we know that the bugs in the Turing machine implementation of f(n)=n+1 are in any way representative of bugs in a normal computation? He seems to be generating random state machines and then evaluating them and picking ones which are nearly but not quite correct implementations of f(n)=n+1. Is that like a normal “honest” software bug? Is it like a deliberate software sabotage like you might look for when evaluating a software supply chain risk? Is it like the sort of vulnerability you might see when fuzzing? As far as I can see, there’s no reason to think it’s like any of these.

More broadly, since the “Principle of Computational Equivalence” and “computational irreducibility” are referred to as touchstones but are never actually defined or properly established how are we supposed to treat them? Interesting conjectures? Actual axioms? Something in between?