Chapter 11: The interior of a heart
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Dimmesdale begins to torture himself physically: he scourges himself with a whip, he fasts, and he holds extended vigils, during which he stays awake throughout the night meditating upon his sin. During one of these vigils, Dimmesdale seizes on an idea for what he believes may be a remedy to his pain. He decides to hold a vigil on the scaffold where, years before, Hester suffered for her sin.
These were the usual Catholic routes to purge the soul of sin and guilt. These didn't work because Dimmesdale has yet to take public responsibility for his "sins" before the town and God. In other words, the guy has to let it all out. He decides to do a sort of dry run where he mounts the scaffold of shame and pretends the town is watching his confession.