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The days of the far-off future would toil onward, still with the same burden for her to take up, and bear along with her, but never to fling down; for the accumulating days, and added years, would pile up their misery upon the heap of shame. (5.1)
Hester's punishment isn't to wear the scarlet letter for a year, or even five years: it's to wear it for the rest of her life, and—oh yeah—to be ostracized and shunned until the day she dies. Forgiveness doesn't even enter into it.
Here, she said to herself, had been the scene of her guilt, and here should be the scene of her earthly punishment; and so, perchance, the torture of her daily shame would at length purge her soul, and work out another purity than that which she had lost; more saint-like, because the result of martyrdom. (5.3)
All the magistrates can do is force Hester to wear a scarlet letter: Hester is the one making herself endure the punishment of sticking around in a community that runs on judgment.
On the outskirts of town, within the verge of the peninsula, but not in close vicinity to any other habitation, there was a small thatched cottage. It had been built by an earlier settler, and abandoned because the soil about it was too sterile for cultivation, while its comparative remoteness put it out of the sphere of that social activity which already marked the habits of the emigrants. It stood on the shore, looking across a basin of the sea at the forest-covered hills toward the west. (5.4)
Well, obviously Hester lives on the "outskirts" of town. (Hawthorne must love that word.) She's an outcast; she can't exactly pop over the neighbors every time she wants to borrow a cup of sugar or gossip about that adulteress at the end of the block.