Model comparison
How did the Voynich text come about? Several explanatory models stand side by side here, measured with the same six statistics as the manuscript: a verbose homophonic cipher (Naibbe) with Latin, Italian, Hebrew and German plaintext, Hebrew text through the project’s own character mapping, plaintext without a cipher, and a meaningless generator. The Hebrew reading model behind the lexicon, grammar and translator is one of these models. A model only convinces once it reproduces the manuscript better than the controls.
Findings
- H1, H2 and positional binding do not reveal the plaintext language. Sent through the same verbose cipher, Latin, Italian, Hebrew and German text all land equally close to the manuscript.
- The project’s own mapping does not produce Voynich statistics. Hebrew text encoded into EVA with it stays at H2 3.05–3.23 bit (manuscript 2.12) and reaches only a third to half of the positional binding.
- No model explains the hapax share and Zipf α together. The cipher models produce too few one-off words and too flat a curve; the generator matches the hapax share but misses α by far.
- The readings do not tell the manuscript apart from controls. Meaningless Markov text and Latin ciphertext are “read” as often as the manuscript, and the translated passages do not read as more coherent.
Six statistics per model
| Model | H1 | H2 | Position | Zipf α | Hapax | Mean len. |
|---|---|---|---|---|---|---|
| Voynich (consensus corpus) | 3.863 | 2.116 | 0.696 | 1.011 | 0.669 | 5.00 |
| Verbose cipher (Naibbe v1) | ||||||
| Latin: Pliny, Naturalis historia | 3.867 | 2.007 | 0.689 | 0.913 | 0.413 | 5.24 |
| Hebrew: Mishnah | 3.866 | 2.030 | 0.684 | 0.943 | 0.464 | 5.27 |
| Hebrew: Mishneh Torah | 3.864 | 2.018 | 0.688 | 0.930 | 0.456 | 5.26 |
| Italian: Dante, Commedia | 3.864 | 2.018 | 0.678 | 0.897 | 0.361 | 5.22 |
| Hebrew: Genesis (WLC) | 3.866 | 2.010 | 0.699 | 0.936 | 0.451 | 5.27 |
| Latin: Genesis (Vulgate) | 3.865 | 2.001 | 0.696 | 0.918 | 0.409 | 5.24 |
| German: Genesis (Elberfelder 1871) | 3.839 | 1.977 | 0.683 | 0.947 | 0.430 | 5.41 |
| Hebrew through the project mapping | ||||||
| WLC vocalized: mapping table | 3.829 | 3.162 | 0.260 | 0.802 | 0.654 | 6.38 |
| WLC vocalized: as in the lexicon | 3.984 | 3.231 | 0.262 | 0.817 | 0.634 | 4.75 |
| Targum Onkelos vocalized: as in the lexicon | 4.010 | 3.152 | 0.263 | 0.852 | 0.554 | 4.93 |
| Mishneh Torah unvocalized: as in the lexicon | 3.847 | 3.049 | 0.372 | 0.859 | 0.569 | 4.32 |
| Plaintext without a cipher (Hebrew letters) | ||||||
| WLC unvocalized | 4.232 | 3.896 | 0.265 | 0.816 | 0.621 | 3.92 |
| WLC vocalized (niqqud) | 4.833 | 3.338 | 0.376 | 0.802 | 0.698 | 7.31 |
| Meaningless control | ||||||
| Pseudo-word generator | 3.811 | 2.451 | – | 0.405 | 0.691 | 6.51 |
The cipher models match H1, H2 and positional binding regardless of the plaintext language; between languages, hapax share and Zipf α differ by only 0.05–0.10, from the manuscript by 0.2–0.3. Hebrew through the project mapping stays at least 0.75 bit above the manuscript’s H2 in all 22 variants of the open table choices tested. Plaintext without a cipher is measured in Hebrew letters; its H1 is not directly comparable because of the larger alphabet. The generator was measured without positional binding.
Reading tests against controls
The same reading pipeline (lexicon, CUT decomposition, word-by-word glosses) applied to the manuscript and to texts without a Hebrew message. A reading model only carries weight once it reads the manuscript clearly better than the controls.
| Measure | Voynich | Markov-2 | Naibbe (Latin) | Generator | Glyphs shuffled | Random |
|---|---|---|---|---|---|---|
| Confident CUT reading (TopGap > 20) | 45.2 % | 43.6 % | 43.3 % | 15.7 % | 13.1 % | 7.0 % |
| Lexicon hit | 59.0 % | 57.7 % | 50.7 % | 4.2 % | 12.3 % | 5.0 % |
| Coherence of the translation (1–5) | 2.20 | 2.30 | 1.97 | – | – | – |
| Judged “real text” | 23 % | 10 % | 7 % | – | – | – |
Word level: 2,000 tokens each; the 95 % bootstrap confidence intervals of Voynich, Markov-2 and Naibbe overlap. Sentence level: 30 passages of 12 words, shuffled and unlabeled, rated by three people; rule fixed in advance (one-sided permutation test, Voynich must beat both controls at p < 0.05). Result: Voynich vs. Markov-2 p = 0.68, vs. Naibbe p = 0.24.
Test register
Each test with its question, decision rule and result. For pre-registered tests, design, plaintexts and rule were fixed before measuring and frozen by a hash.
| Test | Question | Result | For the Hebrew reading model |
|---|---|---|---|
| Encoding test | Does Hebrew or Aramaic text, encoded into EVA with the project’s own mapping, produce Voynich statistics? | No. H2 2.87–3.46 bit instead of 2.12; positional binding 0.19–0.41 instead of 0.70; Zipf α stays at the Hebrew level. | counts against |
| Method test, word level | Does the pipeline read the manuscript better than texts without a Hebrew message? | No. Markov-2 and Naibbe ciphertext get almost as many confident readings and lexicon hits as the manuscript. | counts against |
| Blind test, sentence level | Do the translated Voynich passages read as more coherent than translated controls? | No. Mean coherence Voynich 2.20, Markov-2 2.30, Naibbe 1.97; not distinguishable under the rule fixed in advance. | counts against |
| Verbose cipher: Hebrew vs. Latin | Does Hebrew plaintext, sent through the same cipher, reproduce the manuscript better than Latin? | Equivalent. Hebrew is closer on three of six statistics and further on one; the cross-check (Mishneh Torah vs. Dante) agrees. | does not discriminate |
| Verbose cipher: Genesis in three languages | Is the small Hebrew lead on Zipf α and hapax share specific to Hebrew? | No, or unclear. With the same content, German shows the lead on Zipf α even more strongly; on hapax share it lies between Latin and Hebrew. | does not discriminate |
Method: all six statistics use the same definitions as the entropy and Zipf checks: H1/H2 word-internal, positional binding as mutual information between glyph and word position, Zipf α as the slope over ranks 1–1000 (types with at least two occurrences only). Cipher models: Greshko’s Naibbe cipher, version 1, with the original tables; Hebrew letters take over the table fields of the Latin letter with the same frequency rank (no free parameters). 52,641 letters per plaintext, 10 seeds, measured on the first 34,000 cipher tokens; Voynich reference: 10 random samples of 34,000 tokens from the consensus corpus (39,144 tokens). The reference checks use their own base, because hapax share and Zipf α depend on text size and each check compares texts of equal size: the entropy check measures the H-layer with certain readings only (about 37,900 tokens; H2 2.122 instead of 2.116 bit), the Zipf check the whole consensus corpus (39,144 tokens; its hapax share is about 0.005 lower). As the Latin Naibbe text, the entropy, Zipf and word-length checks use Greshko’s published Pliny ciphertext (one encoding, 34,764 tokens) instead of the mean of ten own encodings; the values differ by less than 0.01 (H2 2.001 instead of 2.007 bit, Zipf α 0.922 instead of 0.913, hapax share 0.409 instead of 0.413).