I feel like you could just add some noise or randomness to the LLM and start approximating the leaps that the human mind uses to solve and understand unrelated things. Maybe that’s naive, it’s just coming from my organic computer in my skull.

Technically true, but the counter argument would be that the probability of this working would be ~ 2^(-(entropy_of_leap)) for an LLM (presumably intractable) and a human would succeed at a higher probability.

Hahaha you just derived temperature from first principles.

Turns out temperature is pretty bad too, you can find ways to sample from deeper in the distribution without distorting it. Great example is XTC (exclude top choices), In a few weeks/months it'll also have a proper scholarly paper with peer review.