Experiment 170

“F12.4: a pencil session: K4 written out at widths 7, 8, 13, 14, 21, 24 and 31, six patterns noted by eye, each then tested against 1,000 shuffles”

F12.4. Stein: 'the process of discovery is often intuitive as well as analytic.' Before any search code, K4 was written out at the widths that matter with the known letters marked and looked at; these six patterns were noted and are tested here exactly as written, each against 1,000 letter-preserving shuffles: (1) the most copies of one letter in one column at width 7 (K: 4 of 8 at places 32, 46, 53, 74); (2) K, the commonest letter, in two adjacent width-7 columns (7 of 8: places 3, 32, 46, 53, 74, 87, 94); (3) the number of repeated bigrams (10: HU, SO, FB, GK, SS, QS, EK, KZ, TJ, DI); (4) how many of their spacings share the factor 4 (5 of 10: 20, 28, 32, 44, 48), Kasiski's test; (5) five of the six S's within 12 places (33-44: SSOTWTQSJQSS); (6) one letter three times at a fixed spacing of 2 or 3 (U at 88, 90, 92). An observation outside every shuffle becomes a new item.

revertedstatus
experiment 168parents
3 mintime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

We wrote the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. out in rows of different widths, as Stein did with pencil and paper, and noted what caught the eye: the letter K lining up in sevens, five S's crowded together, three U's two apart, letter pairs that repeat. Each is then checked against a thousand shufflings of the same letters; the eye finds patterns in random lettersa shuffled control The same experiment run on the carved letters shuffled into a random order. too.

Words in the margin are defined on the glossary page.

1.1

The method at work

The carved letters go in at the top; the reading comes out at the bottom.

OBKRUOXOGHULBSOLIFBBWEASTNORTHEASTOTWTQSJQSSEKZZWATJKLUDIAWINFBBERLINCLOCKWGDKZXTJCDIGKUHUAUEKCARIN: THE COPPER, ALL 97 LETTERS, THE 24 KNOWN PLACES IN ACCENT(2) the 8 Ks: in rows of 7, 7 fall in columns 3 and 4; shuffles reach 0.875 too, p 0.004OBKRUOXOGHULBSOLIFBBWFLRVQQPRNGKSSOTWTQSJQSSEKZZWATJKLUDIAWINFBNYPVTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR(5) the 6 Ss: all but one within 12 letters; shuffles 8 to 68, p 0.004OBKRUOXOGHULBSOLIFBBWFLRVQQPRNGKSSOTWTQSJQSSEKZZWATJKLUDIAWINFBNYPVTTMZFPKWGDKZXTJCDIGKUHUAUEKCARplaces 33-44(6) three Us 2 apart, at 88, 90, 92; shuffles 1 to 4, p 0.198OBKRUOXOGHULBSOLIFBBWFLRVQQPRNGKSSOTWTQSJQSSEKZZWATJKLUDIAWINFBNYPVTTMZFPKWGDKZXTJCDIGKUHUAUEKCARthe six patterns, each against 1,000 shufflings of K4's letters: is K4 outside every one?123456inside the shufflings' rangeoutside every onep 0.204, 0.004, 0.04, 0.021, 0.004, 0.198; the two lowest were picked out by eye, so not evidenceOUT: NO READING; WHAT THE EYE FINDS IN K4, THE EYE FINDS IN SHUFFLED LETTERS TOOEASTNORTHEASTBERLINCLOCK
the idea

Stein: 'the process of discovery is often intuitive as well as analytic.' K4 written out in rows of 7, 8, 13, 14, 21, 24 and 31, the known letters marked, and every pattern noted before any code.

the check

Six patterns: the letter K lining up in two columns of seven, five S's crowded together, repeated letter pairs and their spacings, three U's two apart; each counted on a thousand shufflings of K4's letters.

the bound

Nothing beats every shuffling; the strongest two (1 in 250) were picked out by eye among many possible patterns. No new item.

2

Best candidate against the known letters

This experiment produced no candidate: the search ruled everything out before a full text was built. Its product is the bounded negative in section 7.

3

Walkthrough, by hand

Redo the method on a few letters with pencil and paper.

  1. Write K4 in rows of 7 and find the Ks: four sit in the fifth column, three in the fourth.
  2. Write K4 in a line and mark letter pairs that occur twice: ten of them; measure the distances between the two copies.
  3. Mark the S's: five fall between places 33 and 44. Mark the U's at 88, 90, 92.
  4. Shuffle the 97 letters and count the same things; repeat a thousand times; a pattern is real only if no shuffle matches it.
the worksheet: the first steps by hand, on squared paper
K4 IN ROWS OF 7, THE KS AND THE SS MARKEDOBKRUOXOGHULBSOLIFBBWFLRVQQPRNGKSSOTWTQSJQSSEKZZWATJKLUDIAWINFBNYPVTTMZFPKWGDKZXTJCDIGKUHUAUEKCARSeven of the eight Ks fall in the thirdand fourth columns; five of the six Sssit between places 33 and 44. Each looksstriking; a thousand shufflings reacheither one time in 250.
4

Worked example, generated

The same steps run by the code on the real letters.

K4 in rows of 7 (K in capitals, everything else lower case):

  o b K r u o x
  o g h u l b s
  o l i f b b w
  f l r v q q p
  r n g K s s o
  t w t q s j q
  s s e K z z w
  a t j K l u d
  i a w i n f b
  n y p v t t m
  z f p K w g d
  K z x t j c d
  i g K u h u a
  u e K c a r

K at places 3, 32, 46, 53, 74, 78, 87, 94
5

Hypothesis, for a cryptanalyst

Family, key space, the constraint under test, and the clues it reads.

Stein 1999 (knowledge/sources/stein-1999-cracking-the-courtyard-crypto.txt): looking before attacking; F12.2 (0168) measured the fixed battery. These six are by-eye findings, so their selection is post hoc: the multiple-comparison count is the number of patterns a reader could have noticed, larger than six; a pattern counts only if outside every shuffle. Statistic definitions are in the method and fixed before the run.

6

Prediction

Written before the run; the result decides it.

None of the six lies outside every shuffle (eye-found patterns in 97 letters are usually chance). Zero candidates.

7

Method

  1. Statistics: (1) max over letters and residues mod 7 of the letter's count in that residue; (2) for the commonest letter, its largest count in two adjacent residues mod 7, as a share; (3) repeated bigrams (occurrences beyond the first); (4) repeated-bigram spacings divisible by 4; (5) for each letter with at least 6 copies, the shortest window holding all but one (smaller is more clustered); (6) the most equal letters in an arithmetic run with step 2 or 3.
  2. 1,000 shuffles (seed 1614); one-sided p in the direction observed.
8

Result and bounds

The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.

0candidates returned
0passed every gate
0/24known letters, best
–lowest loss
nonechampion before

(1) most of one letter in one width-7 column: K4 4, p 0.204; (2) commonest letter's share in two adjacent width-7 columns: K4 0.875, p 0.004; (3) repeated bigrams: K4 10, p 0.04; (4) repeated-bigram spacings divisible by 4: K4 5, p 0.021; (5) shortest window holding all but one copy of a 6-copy letter: K4 12, p 0.004; (6) most equal letters at a fixed step of 2 or 3: K4 3, p 0.198

What was searched, as the harness recorded it.

family
observation: six by-eye patterns in K4 against 1,000 shuffles
observations
  1. observation
    (1) most of one letter in one width-7 column
    k4
    4
    shuffles min
    2
    shuffles max
    5
    p one sided
    0.204
    outside every shuffle
    no
  2. observation
    (2) commonest letter's share in two adjacent width-7 columns
    k4
    0.875
    shuffles min
    0.375
    shuffles max
    0.875
    p one sided
    0.004
    outside every shuffle
    no
  3. observation
    (3) repeated bigrams
    k4
    10
    shuffles min
    0
    shuffles max
    14
    p one sided
    0.04
    outside every shuffle
    no
  4. observation
    (4) repeated-bigram spacings divisible by 4
    k4
    5
    shuffles min
    0
    shuffles max
    7
    p one sided
    0.021
    outside every shuffle
    no
  5. observation
    (5) shortest window holding all but one copy of a 6-copy letter
    k4
    12
    shuffles min
    8
    shuffles max
    68
    p one sided
    0.004
    outside every shuffle
    no
  6. observation
    (6) most equal letters at a fixed step of 2 or 3
    k4
    3
    shuffles min
    1
    shuffles max
    4
    p one sided
    0.198
    outside every shuffle
    no
outside every shuffle
none
note
selected by eye, so post hoc; only an observation outside every shuffle would become an item
controls
1000 letter-preserving shuffles (seed 1614)

How this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.

Rendered from the record on 2026-10-18 12:26 UTC; updated after every experiment.
view on GitHub