In The Tempest, analyze how is the experience of exile "alienating" for Prospero? How is it "enriching"?

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The benefits of exile for Prospero are clear from Miranda's description of his magic art at the beginning of Act I scene 2. Prospero has had all the time in the world to focus his efforts and energies on studying his magic books and mastering the arcane arts that seem to be so much a part of him. Note what Miranda says about his ability:

If by your art, my dearest father, you have

Put the wild waters in this roar, allay them.

The sky, it seems, would pour down stinking pitch,

But that the sea, mounting to th'welkin's cheek,

Dashes the fire out.

Miranda recognises that it is Prospero's skill that is causing the tempest to break, and the way he is able to manipulate nature is explored through her description of the severity of the storm. This level of knowledge in the magical arts would only have been possible after serious study and effort, which is precisely what Prospero's exile has enabled him to do.

However, at the same time, although the play does seem to stress the positives of exile for Prospero more than the negatives, being in exile has meant that Prospero has been cut off from humanity, which is a matter of concern for him now that his daughter is reaching marriagable age, and he has to think of her future. Although Prospero is clearly much more interested in his magical arts and skill, because of his daughter, he is not able to forget them completely, and this is the major negative of exile for him.