[gogoincar]

Can you give some examples? I'm guessing there is a different in definition of understanding here.

As I interpret GP, the claim is you can't describe something in sufficient detail to simulate it, then you don't actually understand it. You may have a higher-order model that generally holds, or holds given some constraints, but that's more of a "what" understanding rather than the higher-bar of "why".

[staticassertion]

I don't think that's what they're saying. We could have the detail and understanding but lack compute.

It seems that they are saying that a simulation is required for proof. We write proofs for things all the time without exhaustively simulating the variants.

[Reelin]

I explicitly called out the case where issues arise solely due to lack of compute in my original comment.

I never claimed that a simulation is required for proof, just that an unexpectedly broken (but correctly implemented) simulation demonstrates that the model is flawed.

[staticassertion]

> (but correctly implemented)

Do you ensure this by simulating it?

[Reelin]

No? It honestly seems like you're being intentionally obtuse. The simulation being correctly implemented is an underlying assumption; in the face of failure the implementer is stuck determining the most likely cause.

Take for example cryptographic primitives. We often rely on mathematical proofs of their various properties. Obviously there could be an error in those proofs in which case it is understood that the proof would no longer hold. But we double (and triple, and ...) check, and then we go ahead and use them on the assumption that they're correct.

[SAI_Peregrinus]

> Can you give some examples? I'm guessing there is a different in definition of understanding here.

I'm not the previous poster, but how about the Halting Problem? The defining feature is that you can't just simulate it with a Turing machine. Yet the proof is certainly understandable.