Heck, nobody works in Middle-earth, as far as I can tell, least of all immortal
spirits like Tom and Goldberry. The rain does not touch him because it is
Goldberry's rain -- it is her "washing day." Tom is not the master of the
Ring, and yet the Ring is not Tom's master either. Thus just because
someone cannot harm Tom does not mean he is their master.
In "The Shadow of the Past" Tolkien says "Frodo himself, after the first shock,
found that being his own master and the Mr. Baggins of Bag End was rather
pleasant." What does Tolkien mean by that? Note that he divides the
titles: Frodo is (1) "his own master" and (2) "the Mr. Baggins of Bag
End." It is in the latter role that Frodo has servants, although the only
ones we see are the Gaffer and Sam. But when Tolkien calls Frodo "his own
master" he is not saying anything about the relationship between Frodo and
Sam. Instead he is saying that now that Bilbo is gone, Frodo may do as he
please.
Of course in a metaphorical sense that is not true; we will soon learn that
Frodo must serve Someone, and in that sense perhaps Tom serves Someone as
well. But not in the sense that Frodo does when he is on his quest, or
Gandalf does when he is the messenger of the Valar. No, Tom is as free
and easy as Frodo before his quest, or Gandalf after he has handed off
stewardship to King Elessar. Tom is his own master, free and easy.
Far freer, by the way, than he would be if he had servants to look after.
For if we are going to call on medieval traditions, we must remember the
tradition of noblesse oblige. King Elessar was in one sense the master of
all that he surveyed -- but he was not his own master, for he was also
responsible for all that he
surveyed.
“I dislike Allegory - the conscious and intentional allegory - yet any attempt to explain the purport of myth or fairytale must use allegorical language. (And, of course, the more 'life' a story has the more readily will it be susceptible of allegorical interpretations: while the better a deliberate allegory is made the more nearly will it be acceptable just as a story.)” (From Tolkien Letter # 131.)
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