I like your analogy of a convex curve for maturing. :-)
I am not sure if Tolkien ever said, or regarded, history itself as a
"spiral". I know he thought history demonstrated a "long fall".
He did refer to our longing for the Garden of Eden, or rather, the Paradise
that once existed on Earth, and our attempts to regain this earthly paradise,
as a spiral. He said, we will never recover that Eden, but our souls are full
of longing for it.
He says, in letter 96, which is a letter to his son Christopher, who has been
longing for home:
"...but certainly, there was an Eden on this very unhappy earth. We all long
for it, and we are constantly glimpsing it: our whole nature at its best and
least corrupted, its gentlest and most humane, is still soaked with the sense
of 'exile'. ...As far as we can go back the nobler part of the human mind is
filled with the thoughts of sibb peace and goodwill, and with the
thought of its loss. We shall never recover it, for that is not the way of
repentance, which works spirally and not in a closed circle; we may recover
something like it, but on a higher plane. Just as (to compare a small thing)
the converted urban gets more out of the country than the mere yokel, but he
cannot become a real landsman, he is both more and in a way less..."
I can certainly see how this relates to the history of both Elves (who
literally lose Paradise and make little havens for themselves in Middle Earth,
etc) and Men (who keep trying to travel to the light of Paradise, but keep
messing up along the journey, but every once in a while, find the noble and
true). I am just not sure, if the spiral is one continuous movement DOWN. I
don't think, for individuals, it always is. Certainly, we would hope not; we
would hope we are sinning, repenting, and sinning again, but always getting to
higher ground...
ps: what does "sibb" mean, in the above? I have no idea...but I am confident
someone in the RR does!!! :-)
a.s.
Appendix D: "In the New Reckoning the year began on March 25...in commemoration of the fall of Sauron and the deeds of the Ring-bearers. But in honor of Frodo...September 22, his birthday, was made a festival...There is no record of the Shire-folk commemorating either March 25 or September 22."
"A prophet is not without honor except in his own country, and among his own kindred, and in his own house." Mark 6: 4-5