>My (ironic) point is that "spiky intelligence" seems rather unhelpful because the "intelligence" part still operates under the rules of "I just know it when I see it."

All intelligence is 'spiky' or 'jagged' or whatever, even human intelligence. We evolved in certain environments and situations and sometimes there's a mismatch and it causes all sorts of wonky things. We just call them funny names like optical illusions and cognitive biases. But it's the same thing. I agree there's no point in call LLMs a 'spiky' intelligence, but for probably the oppoosite reasons as you.

>My calculator solves equations with unknown variables, what makes that insufficiently adaptable? What determines the cutoff-point?

A chess engine can be dropped into a board position it has never encounterd and search over possible continuations, evaluating and selecting actions based on the state it finds itself in.

A calculator solving x+3=7 is doing something quite different. The fact that x can take arbtrary values doesn't make the calculator adaptive; it just means the fixed procedure operates over a range of inputs. Every problem a calculator can solve was effectively anticipated when it was built, and anything outside that grammar produces an error with no partial credit. A chess engine can face positions nobody enumerated, in situations nobody could even dream of and still produce sensible moves.

The core of being intelligent is being able to make decisions independently. That's why we hire smart people - to make better decisions. You can't make decisions if everything is spelt out for you. And naturally, if you can't make decisions, you can't adapt.