The Church-Turing hypothesis I agree could be crisper (ie the definition of effectively computable is a bit complicated/weasely), but it actually says something quite concrete that I can understand and potentially falsify ie that a universal turing machine, the lambda calculus and general recursion can all "effectively compute" the same things. That seems reasonable, and I can check that something I can write in lambda calculus I can compute on a Turing Machine (simulated at least).

Whereas in stating the Principle of Computational Equivalence Wolfram says things like "... the evolution of weather systems can, in principle, compute the same things as a computer."[1]

Well, ... wtf? What does it mean to say the evolution of a weather system can compute something? Where do we even start on understanding this? I pick up a calculator and compute the volume of a cone. It's a sunny day outside. How do I "in principle" use that to check my calculation? It literally makes no sense whatsoever on its face as a claim but it is so slippery because of that "in principle" that it doesn't give me anything to hold onto that I could even test.

And that's before I even get started on the "underpants gnome" logical justification behind the claim, which seems to be:

1. Computers are complex

2. Weather is complex

3. Therefore they are "in some sense" equivalent

4. <don't worry about step 4>

5. Thus weather can "in principle" compute the same things as a computer.

I'm really not trying to misrepresent him, I'm just baffled.

[1] https://mathworld.wolfram.com/PrincipleofComputationalEquiva...