From Scott Aaronson, quoted in @2022viteri:
[A] step-by-step logical deduction tends to be seen as merely the vehicle for dragging the reader or listener, kicking and screaming, toward a gestalt switch in perspective—a switch that, once you’ve succeeded in making it, makes the statement in question (and more besides) totally obvious and natural and it couldn’t ever have been otherwise. The logical deduction is necessary, but the gestalt switch is the point. This, I think, explains the feeling of certainty that mathematicians express once they’ve deeply internalized something—they’re not multiplying out probabilities of an oversight in each step, they’re describing the scenery from a new vantage point that the steps helped them reach (after which the specific steps should be modified or discarded).
Question #concept-question What does the last part mean, to modify or discard specific steps—information compression that only preserves the feeling of confidence?