Scroll to the end if you just want the answer. I give a detailed explanation of how I reached it.
First, I hypothesized that the permutation has two cycles: one of length 9, and one length 17. The length-17 one contains T and R, and the length-9 one contains E. How did I get there?
Look at the string JR.
at the start of the second paragraph. That's a peculiar two-letter abbreviation. It could be "Mr." or "Ms." or "Dr.". It tempting to thing that the R maps to itself. If so, it must be in a cycle whose length is a factor of 340, its position. That's 340=2*2*5*17
.
I was also struck by the three-letter words TXE
and OHE
. Wouldn't it be cool if they were THE
? The positions are T: 187=11*17
, H:323=17*19
, and E:324=2*2*3*3*3*3, 189=3*3*7
. Isn't the number 17 showing up a lot? It's not a common prime factor.
To check the theory, I took every 17th letter of the ciphertext
LADRHSONEATIHOGYPDHREPIANNFCEYWMOKRIAWDIATTYOKATNLTDMAHCDLRNCPR
Those sure are nicer letters than usual. Which makes sense, since if there were a cycle of 17, then all 17 letters in that cycle would map to themselves in every 17th position, and so take on their natural frequencies.
And taking every 9th letter,
ETQSJUNXUUREDZISEYVUEQZLSABUSWTRYDDEXIITDVNBHRJDSAFSTMMCRSVJEUXCEYNIJSEGAIQIENHNMDCYOITJEWOIIMIEXETIQAJEEOGCOGCRUECERYRA
13.3% of the letters are E, which is totally consistent with the 12.7% in English
In fact, this suggests a general method to find the cycle sizes. To test a cycle-length n, take every n'th letter, and see how well those letters correspond to the English distribution. Here, I measured this by taking the average English-letter frequency of each letter appearing.

As you can see there's peaks at 9 and 17. There are other "overtones" of 9 in its factors or multiples. 18 has the same peak because those letters are a subset of every ninth letter. Every multiple of 3 (shown as vertical gridlines) has 1/3 the peak because 1/3 of those letters are multiples of 9.
Next, I determined approximately what the nine-cycle is. I'm lucky to know the nine-cycle to contain the letter E
, the most common letter in the English alphabet. This means that in positions that are 1 mod 9, E is mapped to the next letter in the cycle, and that letter is likely to be the most common letter. It turns out that letter is P
. Likewise, the most common letter in positions 2 mod 9 is likely to be two after E in the cycle, and so on.
The gives the claimed cycle EPDKBIDWF
. They're similar to the letters in richardb's analysis But they can't be totally right: D
appears twice. Though E
is the most common letter in English, that might fail to be the case in a random sample of letters, so some of these will be wrong. I guessed that the second D
is wrong and replaced it with the filler character *
.
Knowing the nine-cycle let me decrypt all the letters that are part of it. This gave:
---- --E FE---E-K I----I-- -----D --E ---
---WED ---- -----I-- ---- KW*-------- --D ------*D
---- --E -K--- D-------. --- P----E P---E--ED -- I----E
--E ---F-KI-- -KW*--- -F --E --KE,
--D --* WI--EEKEK --- -FF -- - ---- W--.
K- --E -EP--- II-ED --D F------E- I- --E ----I-E- -E-F KI-P--
"D----ED," B-- I- --K B----: I-----
--D K--- -W--, ---I-- -- --K- -- --E -I--
W-E-E -- -E--ED - ---K* --D -E-FED --E ---FE-.
"---- -I-E --. -I-*E" --* -EI--B--K ----ED,
-E-E- D-E--I-- ---- --E ----, -EEPE---B-E E-I-
----E--ED ---K ---- --D --------ED ---E -I---
--- ---- ---K- K-D, DEFE--ED *-E- --D ---E
-------*D --E K--. --D --- -- ---D --E-
--E- W---D ---* ---WE-ED W--- - K----ED,
-----W-E-E-DI-- K---E.
--, -E ----- --- DIK---P --EI- -E-- F---- ---DE;
-E- --- -IE B--*K I-KIK-*D ---- --IK W-- - ----IB-E -IE---E:
B--- W-K -E D-D-- --I-- I- - E-B---?
--- --E -E-I-K -- --E -E-- F---
-- --E -IDD-I-- K-----E -F --E -*-E-- ---E--ED?
--D -I----- I----K P--P-K -IK B---D
--D D-I-- I- -IK B--*E--P, -----I-K ---EF---- D--W-,
---K-----K E---- BI--E --D --IEK -- F--
-- --- -I---I-- FI----E -- --E -EI-D--:
--I-K E-E-- -I-E --D ---*K -I-K--F F-- ---I--.
-E --- ------- -D-EE-F - -E--, --D ---E- ----I-----,
--D D-E--- -- -IK F---, --E ----D- F--- -F --E -E--;
B-- --W -IDEK ------*- ---I-K,
K*--EK -- ------K ----I--EEK,
--D W-K-EK -E --D D--W-ED.
-- I----K, B- EDW--- FIE-D
So, there's clearly many things wrong; the K
's look off in particular. But, there's segments of recognizable text. Particular useful is the last line, which contains "B- EDW--- FIE-D", which I guessed was "By Edward Field." Perfect, that's the name of a poet! It also means the letters EDWFI
are right.
I looked for a word that had lots of those. There was the third word "FE---E-K". The K
is surely wrong, and plugging the pattern into a regexp matcher gave the very plausible word "FEATHERS".
Finally, Googling "edward field feathers" was enough to take be to the poem Icarus whose text clearly matched.
Only the feathers floating around the hat
Showed that anything more spectacular had occurred
Than the usual drowning. The police preferred to ignore
The confusing aspects of the case,
And the witnesses ran off to a gang war.
So the report filed and forgotten in the archives read simply
“Drowned,” but it was wrong: Icarus
Had swum away, coming at last to the city
Where he rented a house and tended the garden.
“That nice Mr. Hicks” the neighbors called,
Never dreaming that the gray, respectable suit
Concealed arms that had controlled huge wings
Nor that those sad, defeated eyes had once
Compelled the sun. And had he told them
They would have answered with a shocked,
uncomprehending stare.
No, he could not disturb their neat front yards;
Yet all his books insisted that this was a horrible mistake:
What was he doing aging in a suburb?
Can the genius of the hero fall
To the middling stature of the merely talented?
And nightly Icarus probes his wound
And daily in his workshop, curtains carefully drawn,
Constructs small wings and tries to fly
To the lighting fixture on the ceiling:
Fails every time and hates himself for trying.
He had thought himself a hero, had acted heroically,
And dreamt of his fall, the tragic fall of the hero;
But now rides commuter trains,
Serves on various committees,
And wishes he had drowned.
Icarus, by Edward Field
Horton, ?? George Moses
,??????, BT Walter Scott
$\endgroup$ – leo Dec 16 '14 at 10:21