Source-linked AI summary
Does the Voynich Manuscript Mean Anything? Calibrated Tests Find Little Trace of Language
Xin Zhang, Victor S. Sheng
TL;DR
The paper asks whether Voynich writing is meaningless copying or a real language hidden by a cipher. It compares fitted generators and ciphers under shared conditions, then tests language traces, decipherment, and message recovery. The results favor copying over one-key ciphers but leave a narrow second-key nomenclator possibility.
Problem
The Voynich manuscript resembles writing but has unusual word and glyph statistics, leaving open whether it is meaningless copying or a real language encoded by cipher.
Source: §1 · p. 1Method
The study fits copying programs and ciphers under shared conditions, evaluates held-out statistics, measures recurring word pairs, calibrates decipherment solvers on controls, and plants messages for recovery tests.
Source: §1 · p. 2, §4.1 · p. 6, §6.2 · p. 14Results
The copying process predicts held-out statistics better than one-key ciphers, while second-key or word-class ciphers can match it; the manuscript’s word-pair trace is half that of the weakest of 28 natural texts.
Source: §9 · p. 19, §10 · p. 20Takeaways & Limitations
Word statistics alone cannot decide whether the manuscript means anything, and a second-key nomenclator with heavy miscopying remains unexcluded in 9 of 16 languages.
Source: §9 · p. 19The conclusions apply only to tested programs, codes, and languages; changing-key tables, other transpositions, and plaintexts transformed before enciphering were not tested.
Source: Limitations · p. 20
Abstract
from arXiv · showhide
The Voynich manuscript is a fifteenth-century book in a script that no one can read. One account holds that its text means nothing and that a scribe made it by copying his own words and changing them a little. The other holds that a real language lies hidden behind a cipher. We write each account as a program that fills the pages of the manuscript, fit every program with the same budget, and check it on statistics the fit never saw. The copying process of Timm and Schinner predicts these statistics far better than any cipher with one key. But ciphers that switch keys between the manuscript's two dialects, or that encode only the word classes of a real text, predict them equally well. Word statistics alone cannot decide. We look for a trace of language that needs no decipherment. In 28 texts in 16 languages the same word pairs keep sharing a line. The manuscript shows this pattern at half the strength of the weakest of these texts. A word code keeps the pattern above the manuscript unless its plaintext has a weak pattern or many words are miscopied. Solvers that decipher control texts find no readable text in the manuscript under a letter cipher, a word code or 28 codes with one letter, letter pair or syllable per word. Word codes of abbreviated Latin, the plaintext their fits prefer, show which word follows which more clearly than the manuscript unless two words in five are miscopied. One cipher remains possible, a nomenclator with a second key whose scribe miscopies more than half of the words, and our solvers cannot exclude it in 9 of 16 languages. Most of the structure a solver finds comes from how the end of one word shapes the start of the next, which reflects how tightly glyphs are bound to each other. Planted messages are found reliably only when they are long, each letter always becomes the same word and these words are adjacent, so other messages could hide.
1 Introduction
The manuscript’s unusual writing-like features motivate competing accounts: meaningless copying or a real language hidden by a cipher. The study compares these accounts under shared conditions and tests for language traces, decipherable text, and planted messages.
1 Introduction
- The study asks whether the accounts predict unseen statistics equally well, whether language leaves a decipherment-free trace, and whether short messages could be hidden.Earlier defenses often showed only that a favored procedure reproduced statistics selected for it.Source: §1 · pp. 1–2
- The study measures recurring word pairs across lines in 28 texts spanning 16 languages and in ciphers with known miscopying rates.It uses this pattern as a trace of language that does not require decipherment.Source: §1 · p. 2
- The copying process predicts held-out statistics better than any one-key cipher, while second-key and word-class ciphers perform equally well.The manuscript’s word-pair pattern is also weaker than in natural texts, and a second-key nomenclator with heavy miscopying remains possible.Source: §1 · p. 2
- Programs for both accounts share word shapes, search budgets, and held-out checks; every cipher also has a copying scribe.This design tests whether the accounts predict unseen statistics under comparable conditions.Source: §1 · p. 2
- Control-calibrated solvers find no readable manuscript text under tested ciphers, but cannot exclude a heavily miscopied second-key nomenclator in 9 of 16 languages.Tests also cover one-letter, letter-pair, and syllable-per-word codes.Source: §1 · p. 2
- The message-recovery tests find planted messages reliably only when each letter maps consistently to an adjacent word, and messages are 200 to 5,000 letters long.The study also tests other proposed carriers of meaning, including filler words and zodiac numbering.Source: §1 · p. 2
2 Related Work
Earlier work describes Voynich statistics and proposes generators, ciphers, and decipherment methods, while recent studies increasingly compare accounts using controls. This paper distinguishes its approach through equal-budget fitting, language-trace tests, calibrated solvers, and planted-message searches.
Statistics of the text
- Prior quantitative work found language-like statistics, glyph predictability, topic structure, and word-length effects, but did not fit a process that produces the text.Studies also describe dialects and scribal hands, and report line-level behavior.Source: §2 · pp. 2–3
Meaningless text and its generators
- Proposed meaningless-text generators include word-part tables, mechanical processes, self-citation, volunteer gibberish, and physical or computational models.Results differ: some signatures are reproduced, while one study found no slot-generator or grille setting matching four signatures together.Source: §2 · p. 3
Ciphers that imitate the manuscript
- Cipher studies found some Latin manipulations approach manuscript statistics, while the Naibbe cipher matches many Currier B statistics but not vocabulary or line effects.No single manipulation in the cited Latin study matched every metric.Source: §2 · p. 3
Decipherment
- Cipher solvers have recovered historical and homophonic ciphers, while earlier Voynich applications proposed Hebrew or recovered nothing from the manuscript.A recent synthetic-cipher attack recovered 74 to 93 percent of keys but found nothing in the manuscript.Source: §2 · pp. 3–4
Calibrated tests of the two accounts
- Earlier calibrated studies tested generators, ciphered texts, and decipherment, but none planted short messages to estimate the length needed for detection.This study also reports solver tests as undecided when controls cannot be read.Source: §2 · p. 4
- This study fits accounts with shared word shapes and copying behavior, calibrates language-trace and solver tests on controls, and plants messages to test recovery.Related methods include simulation-based fitting, predictive checks, and injection–recovery tests.Source: §2 · p. 4
3 Data
The study analyzes two Voynich transliterations and a corpus of historical texts in sixteen languages, with data split into training and held-out documents. Its programs draw on word-shape models, cipher tables, and specified editing or copying rules.
3 Data
- The Voynich data comprise 37,554 ZL tokens and 36,736 IT tokens, with page metadata for dialect, scribe, section, and quire.ZL is the target for every fit; IT serves as a check, and both use EVA conventions for glyph and word segmentation.Source: §3 · p. 4
- The corpus covers sixteen languages, including medieval texts and abbreviated Latin variants, with documents separated into training and held-out data.The Czech corpus is early modern because no medieval Czech text was found; German is excluded from the halves-of-words test for insufficient data.Source: §3 · pp. 4–5
- The programs vary in word shapes and change rules, while the table’s final column counts parameters plus plaintext choice.The three programs at the bottom are fitted to a larger set of statistics.Source: Table 2 · p. 5
4 Two Accounts Under Equal Conditions
Under equal simulation budgets, the Timm–Schinner copying process predicts held-out statistics better than any one-key cipher, but some more flexible ciphers fit them too. Further copying models fail to explain the manuscript’s unusual link between neighbouring words, which remains unexplained.
4.1 Programs
- Programs share ZL’s page and line layout; copying models reuse and alter earlier words, while ciphers encode plaintext units and add a scribe who can locally repeat or miscopy words.Copy-T applies Timm and Schinner’s glyph-group changes and other word edits; Cipher-C instead encodes plaintext word classes.Source: §4.1 · pp. 5–6
4.2 Fitting and checking
- The programs are fit on 22 statistics and checked on 15 held-out statistics, using 4,000 simulations per program and predictive checks against the manuscript.The statistics cover copying, vocabulary, word length, word order, glyph sequences, word-pair reuse and dialect differences; the statistics were fixed before fitting.Source: §4.2 · p. 6
4.3 Results
- Copy-T misses no held-out statistic by more than 5 standard deviations, unlike Cipher-W (>100) and Cipher-N (about 200); Cipher-C and Cipher-M2 also pass held-out checks.Cipher-W2 covers 13 of 15 held-out statistics in both searches; Cipher-C covers all 15, and Cipher-M2 comes within 1.6 standard deviations of all 15. No program passes the joint check over all 37 statistics.Source: §4.3 · pp. 7–8, Table 3 · p. 7
4.4 Three more copying programs
- Copy-H, Copy-L and Grille reproduce only 0–3 of 15 held-out statistics and fail their checks; each also misses or distorts the cross-word link.Copy-H’s link is 0.107 bits versus 0.204 in the manuscript; Grille overshoots it by nearly a factor of three.Source: §4.4 · pp. 8–9
4.5 The link between neighbouring words
- HABIT and SPACE reach the cross-word link but fail predictive checks; the manuscript’s 1.39-bit glyph bond when spaces are reset by word length points to glyphs, not spacing alone.The manuscript’s real spaces loosen that bond to 15 percent, about the plaintext average; neither program passes checks on fitted or held-out statistics.Source: §4.5 · p. 9, Table 4 · p. 10
5 Traces of Language That Need No Decipherment
Word statistics alone leave both accounts standing, so the section tests recurring word pairs as a trace of language that needs no decipherment. It also compares natural texts in invented scripts and calibrates a gibberish classifier against enciphered texts.
5 Traces of Language That Need No Decipherment
- Words that belong together tend to share lines repeatedly across a meaningful text, whereas copying-generated local pairs need not recur elsewhere.A word code retains this pattern unless its plaintext has weak replication or many words are miscopied.Source: §5.1 · p. 10, §5 · p. 10
5.1 Word pairs in a line
- 0.071 in ZL and 0.053 in IT fall below all 28 natural texts, whose word-pair replication ranges from 0.139 to 0.411.The manuscript also falls below the natural texts on pairs at least two words apart and on overdispersion.Source: Figure 2 · p. 10, §5.1 · p. 11
- At fitted miscopying rates, word and syllable codes retain 52% to 84% of the pattern on average, usually remaining above ZL.Codes approach ZL mainly with weak-pattern plaintexts or at high miscopying rates.Source: §5.1 · p. 11
- The second fit of Cipher-M2 matches ZL’s word-pair pattern with ordinary plaintexts, but its scribe miscopies more than half the words.Its predictive texts have a median distance of 0.74 from the manuscript, with the closest at 0.58.Source: §5.1 · pp. 11–12
- Copying programs produce word-pair replication near ZL but fail the joint check because they do not match pair overdispersion on lines or pages.Their average replication ranges from 0.022 to 0.065; the joint check separates every fit (p = 0.01).Source: §5.1 · p. 11
- The replication pattern persists across Currier dialects and page-selection variants, while every plaintext except abbreviated Latin lies above ZL in every view.Removing near-copy words does not change the result.Source: §5.1 · p. 12
5.2 Natural languages in invented scripts
- No tested script makes a natural text resemble the manuscript; the 64 texts fall outside its range on 11 of 55 statistics.The manuscript also exceeds their range on several measures, including repetition of the previous word and differences between Currier A and B.Source: §5.2 · p. 12
5.3 A gibberish classifier, calibrated
- The calibrated classifier calls the manuscript gibberish with probability 0.71, but also labels 53 of 54 enciphered meaningful texts as gibberish.It therefore cannot distinguish gibberish from a cipher.Source: §5.3 · p. 12
6 Decipherment With Calibrated Controls
The section tests cipher families with solvers calibrated on controls whose plaintext is known. The tests find no readable text under most tested ciphers, while leaving a second-key nomenclator unresolved in some languages.
6.1 Letter ciphers
- Under 15 readable language models, ZL and IT fall below both same-language letter-cipher controls, and the solver finds no readable text in ZL.The solver reads controls in 15 of 16 languages; Hebrew is undecided because its controls are not readable.Source: §6.1 · p. 13, Table 6 · p. 14
- The letter solver’s signal mostly comes from the end of one word linking to the start of the next, a boundary coupling stronger in ZL than in controls.Keeping those adjacent glyphs preserves 78% of ZL’s gap; forcing Copy-T to match the link reaches about half that gap.Source: §6.1 · p. 13
6.2 Word codes and miscopying
- All 64 fitted-rate word-code controls have higher word gaps than the manuscript, but many approach its value as miscopying rises.At 60% miscopying, 50 controls reach the manuscript’s best value, while those controls are at least 0.73 away on the 22 fitted statistics.Source: §6.2 · p. 14, Figure 4 · p. 15
- A word code of abbreviated Latin matches the manuscript’s word order only when two words in five are miscopied.At the fitted rate, 11 of 12 controls remain above ZL; the solver recovers only 4% of words with the codebook unknown.Source: §6.2 · p. 15
- Word codes of herbals and recipes produce larger solver gaps than prose, and none of the 24 ingredient-list texts reaches the manuscript’s level.One of six medical-work texts reaches it at 40% miscopying.Source: §6.2 · pp. 15–16
6.3 Nomenclators
- The second fit of Cipher-M2 remains open in 9 of 16 languages, while the tests exclude one-key nomenclators in many languages.At the fitted miscopying rate, the word solver recovers at most 8% of any nomenclator’s code words.Source: §6.3 · p. 16
6.4 One word, one unit
- The tests exclude every readable plain code with up to 10% nulls, but leave codes with many nulls, homophones, or several letters per word undecided.Across 1,144 decisions, 596 are excluded, 429 undecided, and 119 not excluded.Source: §6.4 · pp. 16–17, Table 7 · p. 16
- Tests of one-unit-per-word codes have little power in several cases where the manuscript exceeds the ceiling only slightly or the codes are poorly read.For page-group and line-position tables, texts without plaintext already gain a median of 0.28 bits, and codes are read correctly for only one token in ten.Source: §6.4 · p. 17
7 Other Ways to Carry Meaning
The section tests whether meaning could be carried by filler, split words, notation, or labels. These tests find no supported link to a hidden text, though they do not rule out every possibility.
7 Other Ways to Carry Meaning
- Removing 16% of words that copy nearby words raises ZL’s replication by 0.034, but the manuscript fails the prespecified test for revealing a hidden text.Copy-H texts without real text rise by up to 0.09, and padded plaintexts rise by 0.012 to 0.071.Source: §7 · p. 17
- Splitting words and rejoining neighbouring halves does not describe ZL: its 2.3% gain falls within the 0.4% to 14.0% range of Copy-L.Natural texts under the simplest scheme lose 14% to 54% of distinct units, while plain natural texts gain 19% to 229%.Source: §7 · p. 17
- The tested notation hypotheses find no support: glyph substitutions show no pitch-step preference, and glyph-run lengths do not point to a count.The pitch-step preference is 0.000 in the manuscript; ZL’s run measure lies just below copying texts and IT lies within their range.Source: §7 · p. 17
- Labels show no link to their page’s text or to the herbal page of the depicted plant, despite forming a vocabulary of their own.The labels occur on their own page about as often as labels moved to random pages do (0.144 versus 0.123 to 0.146; p = 0.09).Source: §7 · p. 17
8 Could a Short Message Hide in the Text?
The section tests whether short messages could be hidden in scribal choices or selected text positions. The planting tests detect messages reliably only under restricted conditions, so other messages could escape them.
8 Could a Short Message Hide in the Text?
- Scribe choices carry 7.4 to 8.3 bits per word, enough for a message two-fifths to three-quarters as long as a plaintext, so capacity rules nothing out.The parser recovers the generator’s true choice for only 38% of words, and planted messages are found in 10% to 50% of cases.Source: §8 · p. 18
- Planted messages are reliably bounded mainly when each letter maps to one word type in consecutive positions, with required lengths varying by channel.For example, messages among paragraph-first words are found in all 17 plaintexts at 500 letters; most other patterns are found less consistently or not above chance.Source: §8 · p. 18
- ZL shows no sign of a planted message, but most tested message forms escape detection or require long messages to be found.The best readings are scattered letters without words, and the manuscript exceeds shuffled references in only 12 of 119 combinations.Source: §8 · p. 18
9 Discussion
Copy-T predicts held-out word statistics better than one-key ciphers, but two-key and word-class ciphers remain competitive. Word-pair recurrence and calibrated decipherment tests constrain the language-cipher account, while a second-key nomenclator remains open.
Planted messages
- Table 8 organizes planted-message results by the number of plaintexts with reliable recovery and the corresponding message-length ranges.Its caption also distinguishes consecutive placements from messages spaced every second or third position.Source: Table 8 · p. 19
What the word statistics say
- Copy-T’s learned glyph-group swaps, prefix changes, and word joins reproduce held-out word patterns, but two-key and word-class ciphers perform equally well.The competing programs share a scribe who builds many words from visible words, so these statistics reveal more about writing than meaning.Source: §9 · pp. 18–19
What the trace of language says
- The manuscript’s recurring line-pairs are half as strong as those in the weakest tested text, and ordinary word codes retain more unless many words are miscopied.Abbreviated Latin with a second key comes close and predicts held-out statistics, but its controls show more word order unless two words in five are miscopied.Source: §9 · p. 19
- A second-key nomenclator matches the manuscript’s word-pair pattern and passes the held-out check, but its scribe miscopies more than half its words.In 9 of 16 languages, neither solver can exclude it.Source: §9 · p. 19
The boundary between words
- The end-to-start glyph link across word boundaries carries much of the solver’s structure, yet no tested program reproduces it together with the manuscript’s spaces.Neighboring glyphs depend on each other twice as strongly as neighboring letters in tested plaintexts; programs that add the link place spaces incorrectly.Source: §9 · p. 19
Calibration
- A solver that cannot read controls made by its assumed cipher says nothing about the manuscript; readable controls followed by no manuscript reading count against that cipher.Twin texts show that flexible codes can generate substantial solver signal even without language.Source: §9 · pp. 19–20
10 Conclusion
The paper compares copying programs and ciphers under equal conditions, tests language traces and calibrated decipherment, and finds one cipher family it cannot exclude. The strongest remaining structure is a cross-word glyph link that tested programs do not reproduce alongside the spaces.
10 Conclusion
- The copying process predicts held-out statistics better than one-key ciphers, while second-key and word-class ciphers perform equally well, leaving word statistics inconclusive.The manuscript’s recurring word-pairs are half as strong as those of the weakest of 28 natural texts in 16 languages.Source: §10 · p. 20
- Calibrated solvers find no reading for letter ciphers in 15 languages, word codes in 16, or 28 one-unit-per-word codes in 17.The letter solver could not read Hebrew controls.Source: §10 · p. 20
- A second-key nomenclator remains possible: it matches the manuscript’s word-pair pattern, and solvers cannot exclude it in 9 of 16 languages despite more than half its words being miscopied.Abbreviated Latin word codes require two words in five to be miscopied to reduce word order to the manuscript’s level.Source: §10 · p. 20
- The strongest residual structure links neighboring words and reflects glyphs bound twice as tightly as tested-language letters, but no program reproduces it with the manuscript’s spaces.No tested account passes the joint predictive check.Source: §10 · p. 20
- Across nearly all languages, planted-message tests rule out only one fixed word per letter in consecutive positions, generally from lengths of 200 to 5,000 letters onward.Messages using several words per letter or letters spaced apart could still remain hidden.Source: §10 · p. 20
Limitations
The conclusions are bounded by the tested programs, codes, languages, solver designs, and transliteration conventions. The statistics section defines its measures and explains two comparison terms.
Limitations
- The conclusions cover only tested programs, codes, and languages; several changing-key, transformed-plaintext, and transposition schemes were not tested.Copy-T’s rules and Copy-H’s tables draw on manuscript-derived knowledge unavailable to the ciphers.Source: Limitations · p. 20
- The solvers use bigram models, and the word solver’s limited vocabulary cannot reliably identify language or recover many abbreviated-Latin words.The letter solver cannot read Hebrew controls or most controls for second-key nomenclators.Source: Limitations · p. 20
- Short-message bounds apply only to the simplest code, while homophones or gaps between letters can prevent reliable detection.Both transliterations use the same word-break and glyph conventions, which affect several statistics; no program passes the joint predictive check.Source: Limitations · p. 20
A Statistics
- Table 9 defines the Section 4 statistics and reports both transliterations; “near” means one glyph changed, inserted, or deleted, while “shuffled” texts reorder each page’s words.The passage does not provide the table’s statistic values.Source: A Statistics · p. 23
B Priors and Fitted Parameters
The fitted-parameter account reports priors and medians from each program’s best simulations, along with parameter-bound behavior and the most frequent plaintexts.
B Priors and Fitted Parameters
- Abbreviated medieval Latin is the most frequent plaintext among Cipher-W’s 100 best simulations in 97% and 100% of the two searches, and among Cipher-W2’s in 56% and 70%.Other frequent plaintexts vary by cipher and search, including Middle French, Italian, and Middle English.Source: B Priors and Fitted Parameters · p. 23
- Second-search best fits of Cipher-W, Cipher-W2, and Cipher-S have median W sharpening values from 16.5 to 19.4 and come about as close to the manuscript as Table 3.The median sharpening of W remains near its upper bound in four fits.Source: B Priors and Fitted Parameters · p. 23
- Copy-W, Copy-T, Copy-N, and Cipher-N use narrower priors, while other ciphers use wider priors after initial fits reached their bounds.Median code-word counts for Cipher-M and Cipher-M2 lie near the 2,000-word upper bound in three of four fits.Source: B Priors and Fitted Parameters · p. 23
C All Predictive Checks
The predictive checks show similar results across transliterations, while word-pair replication remains markedly weaker in the manuscript than in natural-language texts. Corpus controls also show that solver performance varies between edited historical texts and machine transcriptions.
C All Predictive Checks
- IT and ZL differ on at most three in-range statistics and 1.6 in Mahalanobis distance, and the ordering of programs remains the same.Tables 11 and 12 report ZL z-scores under predictive samples for each program and search.Source: C All Predictive Checks · p. 23
D Corpora
- For Italian and Middle French, the solver reads 77% and 84% of solved control tokens, versus 47% and 62% on machine transcriptions; the control gaps rise to 0.41 and 0.45.The tests use 6 Italian and 16 Middle French edited-text and early-print documents from 1300–1500.Source: D Corpora · p. 23
E Word Pairs by Language
- With pairs at least two words apart, ZL reaches 0.028 versus 0.055–0.325 in natural texts; with frequent types, ZL reaches 0.069–0.070 versus at least 0.138.ZL’s line overdispersion is 0.731, compared with 0.895–2.133 in natural texts; page replication is 0.021–0.024, near the natural-text low of 0.021.Source: E Word Pairs by Language · p. 23
F Implementation
The implementation fixes decision rules before experiments and specifies how fitted, held-out, and layout statistics are used. The accompanying passages document exploratory reading routes, model priors, predictive-check tables, and corpus resources.
F Implementation
- Every decision rule was fixed in code before its experiment, and simulations are cached by program, parameters, and seed.The programs, statistics, and solvers use Python with NumPy; code and decision rules are slated for release with the published version.Source: F Implementation · p. 23
- Fitted statistics enter distance D, held-out statistics are used only for checks, and layout statistics are reported except in Sections 4.4 and 4.5.Table 9 lists the 41 statistics.Source: Table 9 · p. 24
- The earlier word-rewriting and word-meaning routes are exploratory; neither establishes a manuscript reading, and the second route did not reliably recover known word-by-word ciphers.Pages guided development of both routes; the first route recovered known substitution ciphers, but its manuscript rule tables failed fixed criteria and often assigned shared meanings.Source: F Implementation · p. 24
- Cipher-N uses narrower first-round priors, including 0–0.3 for miscopied words and 1–400 for look distance; Cipher-MN applies homophone parameters only to code words.Tables 11 and 12 report ZL z-scores under predictive samples for the listed programs, with bold values outside the central 95% of the sample.Source: Table 10 · p. 25, Table 11 · p. 26, Table 12 · p. 27
- Table 13 covers texts in 16 languages and abbreviated Latin, while Table 14 lists public collections; Table 15 reports word-pair replication and gives ZL as 0.071.The project corpus includes texts from 1300–1500, and the larger abbreviated-Latin models use 5 million additional words from 144 Latin manuscripts dated 1200–1500.Source: Table 13 · p. 28, Table 14 · p. 28, Table 15 · p. 28