[10] · INVESTIGATION
What cipher is it
What is ruled out, what survives, and the one number no model explains.
The central paradox
Everything measured points two ways at once, and any real solution has to explain both halves.
It looks like language
Letter frequencies fit English at the 30th percentile (χ² = 5.01). Index of coincidence, entropy, doubled glyphs, repeated bigrams — all inside the range for 87 characters of real English. Mirrored symbol pairs occur far above chance, so it is not random scribble.
But it does not read as language
No substitution, under any reading order or key motion tried, scores better than the 0th percentile — z between −7.5 and −9.6 — while the same solver recovers a median 87/87 letters on real English controls. Two published studies reach the same conclusion independently.
What resolves it. Frequencies survive a transposition; n-gram order does not. So either a second layer sits on top of the substitution, or the plaintext is not ordinary English — shorthand, phonetics, initials, or another language. Those are the two live branches, and they call for different attacks.
The honest caveat, repeated because it matters: at 87 characters a search free to pick both a substitution and a rearrangement will manufacture English-looking output by chance. Any transposition theory has to arrive with an independent reason for its particular rearrangement — a rule Elgar might plausibly have used — not a rule fitted to make the output look good.
Ruled out
A regular rotating key
Orientation χ² = 26.6, p = 0.0003; key-free. [07]
A plain substitution of English
z −7.5 to −9.6 at matched effort; Wase (2023) and Hauer (2021) agree.
A repeating-key polyalphabetic, period 2–22
No coset-IC peak at any period.
A Wheatstone clock cryptograph
Refuted by three of the five diagnostics in simulation.
Random symbols (a hoax)
Refuted by four diagnostics; and the mirrored pairs are unlikely to be chance.
Still alive
Substitution of a private shorthand
Explains English-shaped frequencies with non-English order — needs no cipher technique at all.
Substitution + transposition
Fits both halves of the paradox; nothing documents Elgar using a transposition.
A text-driven rotating key
Irregular schedules escape the χ² argument.
A two-alphabet polyalphabetic
Survives every diagnostic except the mirror count that no model explains; four alphabets already fail two.
Another language
Latin ranks first in both Hauer's and my language identification. Not tested at full strength.
Which cipher model? — a simulation-backed comparison
The question is not “what could produce 87 symbols” (almost anything can) but “what could a
self-taught amateur plausibly do at a desk in July 1897, that also reproduces every measured property of this
document”. For each candidate model lab/model_prior.py simulates it 320 times on real
English, measures the same five diagnostics, and asks where Dorabella falls in each simulated distribution. A model is
compatible with a diagnostic if Dorabella lands inside the central 90% of what the model produces; refuted if it lands
in the tail. That gives a computed likelihood; combined with an explicitly subjective historical prior, a ranking.
| model | prior | fit | posterior |
|---|---|---|---|
| substitution of a private shorthand | 0.15 | 0.522 | 33.2% |
| substitution + transposition | 0.14 | 0.522 | 31.0% |
| text-driven rotating key | 0.08 | 0.522 | 17.7% |
| 2-alphabet polyalphabetic | 0.06 | 0.522 | 13.3% |
| monoalphabetic English | 0.30 | 0.037 | 4.7% |
| 4-alphabet polyalphabetic | 0.05 | 0.003 | 0.1% |
| Wheatstone clock cryptograph | 0.07 | 0.000 | 0.0% |
| regular rotating key (period 8) | 0.10 | 0.000 | 0.0% |
| random symbols (hoax) | 0.05 | 0.000 | 0.0% |
Read the fit column, not just the posterior. The top four have identical computed fit (0.522): the evidence cannot tell them apart. Their order comes entirely from my priors, which are judgement calls printed so they can be argued with. What the evidence does do is push plain English substitution (the highest prior, 0.30) down to 4.7% and three models to zero.
Why — where Dorabella falls in each model's own output
| model | D1 freq | D2 orient | D3 mirror | D4 distinct | D5 solvable |
|---|---|---|---|---|---|
| private shorthand | 15% | 54% | 99% ~ | 64% | 45% |
| substitution + transposition | 10% | 51% | 98% ~ | 81% | 70% |
| text-driven rotating key | 29% | 89% | 97% ~ | 14% | 78% |
| 2-alphabet polyalphabetic | 45% | 87% | 99% ~ | 20% | 80% |
| monoalphabetic English | 10% | 55% | 98% ~ | 81% | 0% * |
| 4-alphabet polyalphabetic | 26% | 98% * | 99% ~ | 1% | 100% * |
| Wheatstone clock cryptograph | 7% | 100% * | 98% ~ | 0% * | 100% * |
| regular rotating key (period 8) | 4% * | 100% * | 99% ~ | 1% * | 100% * |
| random symbols (hoax) | 2% * | 100% * | 100% ~ | 0% * | 100% * |
Percentile of Dorabella within each model's simulated output. * refutes that model; ~ refutes every model (see below). D1 rank-matched unigram χ² vs English · D2 evenness of the eight directions · D3 consecutive same-ring 180° pairs · D4 how many of the 24 symbols are used · D5 best substitution solve.
Historical note per model
| model | era | tooling |
|---|---|---|
| private shorthand | needs no cipher technique at all — just his own abbreviations | paper only |
| substitution + transposition | columnar transposition was common Victorian knowledge; nothing documents Elgar using one | paper and a ruled grid |
| text-driven rotating key | no standard published cipher does this; an amateur's own idea | a disc turned on a rule he invented |
| 2-alphabet polyalphabetic | Vigenère family, thoroughly published by 1897 | a Saint-Cyr slide or two written alphabets |
| monoalphabetic English | trivial; pigpen ciphers were schoolboy knowledge | paper only |
| 4-alphabet polyalphabetic | the same, with a longer keyword | a slide or a tabula recta on paper |
| Wheatstone clock cryptograph | Wheatstone 1867, English, exhibited in Paris; a literal clock face | a brass pocket device, or a hand-drawn two-ring disc |
| regular rotating key (period 8) | progressive keys known since Trithemius; Elgar drew clock faces | a disc, or careful bookkeeping on paper |
| random symbols (hoax) | requires only mischief | paper only |
The Wheatstone model deserves a word: two geared clock dials of 26 and 27 teeth. You always turn the plaintext hand clockwise to the next letter, so the advance is the alphabetic gap between letters and the tooth mismatch slips the cipher alphabet one step per revolution — text-driven and irregular, exactly the class the orientation test alone cannot rule out. It fails on the other diagnostics instead.
The one number nothing explains
mirrored 180° pairs10chance 5.2 · p = 0.03
models reproducing it0 of 9all at 97–100th pct
Dorabella has ten places where two consecutive glyphs with the same arc count face exactly opposite ways. That count sits outside the central 90% of all nine simulated models, so it was excluded from the posterior: a diagnostic that refutes every model is not evidence between them, it is evidence that every model is incomplete. It is not a tie-breaker. It is a property no candidate mechanism reproduces, and therefore the most interesting single number in the whole analysis.
Hauer et al. used the same pairs to argue against a hoax. Ideas I have for it — a mirrored pair as one unit written in the wrong order, a reflection applied on a schedule — are in the experiments tool and on [11].