First off, I want to publicly thank Torsten for his thoughtful comments, both now and in earlier correspondence. Here is my reply, organized by the theme of Torsten's critique:
1. Scope of the paper and intended claims
Torsten tends to evaluate the Naibbe cipher as if I were proposing the exact historical cipher used to write the VMS or if I were proposing that my cipher fully explains all known VMS properties. However, the paper’s stated goal is narrower: to construct a fully specified, hand-executable substitution cipher, using materials available in early 15th-century Europe, that:
- Preserves the full sequence of plaintext letters in order;
- Produces decipherable ciphertext; and
- Simultaneously reproduces many well-characterized statistical properties of Voynich B when encrypting a range of Latin and Italian texts.
The paper repeatedly disavows the idea that Naibbe is the exact VMS cipher and even takes pains to avoid any declaration that the VMS definitively is a ciphertext. The Naibbe cipher is best understood as a proof of concept. I devote an entire section of the paper, Section 4, to calling attention to several of the cipher’s existing failures, including its absence of long-range correlations, the lack of a mechanism for line-position effects, and incomplete word coverage.
Many of Timm’s most severe conclusions rest on reading the paper as an exacting historical reconstruction, rather than as what the Naibbe cipher is: a feasibility demonstration of what a letter-preserving substitution cipher can do. Under the more modest claim actually made in the paper, most criticisms are either already acknowledged as limitations or point the way toward further tests of this general cipher architecture.
2. “Circular reasoning” and curve-fitting
Torsten’s claim: The tables are populated with VMS words and affixes, table ratios are fitted to Voynich B’s frequency distribution, and the unigram-bigram split is tuned to match common word frequencies. Using these same data to “validate” the cipher is circular.
I agree that it’s important to distinguish between properties that are explicitly targeted and those that are emergent.
The design process of the Naibbe cipher began with an analysis of ensembles of hundreds of randomly generated substitution ciphers that map plaintext n-grams to strings of Voynichese glyphs formed by sweeping across the Zattera (2022) slot grammar. If one attempts to map plaintext letters to Voynichese glyph strings while treating the Voynichese “word grammar” (as defined by Zattera) as a binding empirical constraint, which kinds of glyph-letter mappings and distributions of plaintext n-gram lengths most reliably allow for the replication of the VMS’s observed entropy, token length distribution, and word type length distribution?
This analysis, described in the main text and Supplementary Material 2, establishes that within a verbose substitution scheme—an entropically essential feature of any VMS-mimic cipher encrypting on a letter-by-letter basis—simultaneous and extremely reliable replication of those VMS properties requires a plaintext consisting mostly of unigrams and bigrams. That’s not to say these properties are impossible to achieve while encrypting longer n-grams. But it’s much more probable to achieve these properties
without any fine-tuning of the specific glyph-letter mapping if the unigram-bigram constraint is obeyed. In this setup, the Voynichese word grammar is not “fine-tuning”: It’s an important empirical constraint.
In addition, quasi-Zipfian distributions naturally arise when unigram-bigram plaintexts are encrypted using a homophonic substitution scheme on a letter-by-letter basis. The Naibbe cipher’s specific distribution is fitted to Voynich B; the cipher’s ability to exhibit a quasi-Zipfian distribution is emergent, arising from the general choice to apply a homophonic substitution cipher on a letter-by-letter basis to a unigram-bigram plaintext. The reason I proceeded with constructing the Naibbe cipher at all was because I was surprised to see a quasi-Zipfian distribution appear within Voynichesque ciphertexts, where practically all of the commonest word types encrypted unigrams.
As described in Supplementary Material 3, the Naibbe cipher is fine-tuned to the proportional frequency-rank distribution of Voynich B’s 70 commonest words, under the assumption that all of these words represent standalone alphabet letters under a random respacing scheme. The model used to fit this frequency-rank distribution assumes three inputs: plaintext alphabet letter frequencies; a globally constant number of substitution options per letter; and globally average proportions in which those substitution options are applied (i.e., the commonest option is always chosen X% of the time for every single alphabet letter).
These simplified modeling assumptions led to the six tables and the approximately 5:2:2:2:1:1 proportions in which they are applied on a letter-by-letter basis. This modeling also implied that within this scheme, unigrams cannot make up much more than 50% of the text; if unigrams were 100% of the text, the absolute frequency-rank distribution would overshoot Voynich B's observed one by approximately a factor of 2. If only 50% of the plaintext can be unigrams, Voynichesque (Supplementary Material 2) strongly implies that the other 50% would most likely be bigrams. One natural way to encode a bigram as a Voynichese word type is to split the Voynichese word type down the middle and develop grammatically valid “prefix” and “suffix” inventories, which aligns with the strict glyph sequencing rules observed in Voynichese.
Thus, I fully agree that:
- The table number, probabilities, and assignment of specific Voynichese strings to table slots are fitted to Voynich B, as described in detail in the paper and its supplementary materials; and
- It is unsurprising that this leads to reasonable agreement on some directly targeted metrics, such as the most common word types.
That said, the paper’s central contribution is not that the Naibbe cipher magically re-discovers that which was explicitly fitted. Rather, it shows that given these fitted components and the Voynichese word grammar, a large bundle of other features—e.g., character entropy, conditional character entropy, glyph and glyph-pair frequencies, token and type length distributions—reliably fall into place as emergent consequences, and that this behavior is stable across multiple, stylistically distinct Latin and Italian plaintexts, tens of thousands of ciphertext tokens at a time. In addition, multiple unmodeled properties of the VMS also emerge, such as the presence of skewed pairs in the ciphertext.
I do not accept the conclusion that the presence of any fitted components renders the exercise “mere curve-fitting” or methodologically invalid. In the context of a singular artifact like the VMS, it is reasonable to ask: Is there any plausible letter-preserving substitution scheme that can reliably reach this statistical regime at all? Naibbe answers that question in the affirmative.
3. Randomness versus scribal “bias”: alleged contradiction
Torsten’s claim: The paper both emphasizes random table selection (via cards) and later speculates that non-random scribal biases and table “bursts” could explain long-range correlations, which Torsten considers to be contradictory.
The paper uses dice and playing cards in two roles:
- As a clean, reproducible baseline for respacing and table selection in modern experiments; and
- As one historically plausible implementation of the required table probability distributions.
Section 2.3 explicitly states that “any random or even non-random source” that yields the same approximate ratios on average would suffice, suggesting letter-based rules as an alternative to playing cards. Cards are historically attested, and I personally found them to be experimentally convenient, but they are not a doctrinal requirement of the cipher. Section 4, in turn, shows that the pseudorandom baseline provided by the card mechanism fails to reproduce long-range correlations. As a result, the paper then proposes non-random deviations (scribal habits, line-by-line reuse, bursts of table use) as candidate mechanisms to add on top of the baseline.
I see no logical contradiction here. The Naibbe cipher is essentially a modeling exercise with a simple pseudorandom core, one provided in this instantiation by drawn playing cards. The cipher’s mismatches with the VMS suggest the need for alternative and/or additional mechanisms. I agree with Torsten that extra mechanisms would need to be implemented to make a more conclusive claim that this class of cipher can generate the VMS, which is why I state in the paper that:
- “...[I]n its current form, the Naibbe cipher fails in several major ways to replicate key properties of the VMS.”
- “The Naibbe cipher cannot be exactly how the VMS was created.”
- “I do not assert that the Naibbe cipher precisely reflects how the VMS was created, nor do I assert that the VMS even is a ciphertext.”
- “...[T]he Naibbe cipher’s incomplete replication of Voynich B’s properties underscores the difficulty of achieving a comprehensive cipher-based model for VMS text generation.”
4. Ambiguity and bigram/unigram collisions
Torsten’s claim: Allowing bigram tokens to coincide with unigram tokens and then managing this ambiguity via collision avoidance and re-encryption is unnecessarily complex and historically implausible.
I agree that the ambiguity-management machinery is not especially elegant. However, ambiguity management is a design compromise, not an oversight, and the paper proposes re-encryption as a way to keep decryptions reliably recoverable. The goal here was not to identify the one true VMS solution; it was to build a fully functional cipher that statistically mimics the VMS with high reliability while encrypting a meaningful plaintext. After experimentally testing the cipher, I found collision avoidance to be a practical solution.
The procedure is invoked only in the specific case where a bigram token accidentally lands on a unigram word type. The paper’s decoding strategy—treat tokens as unigrams if they match, otherwise parse as bigrams—takes advantage of the fact that such collisions are relatively rare, especially if an experienced scribe mitigates collisions during encryption.
The most relevant question here is not whether the design is mathematically pristine, but whether a reasonably trained scribe can reliably decrypt Naibbe ciphertext with the aid of tables. The worked example in Section 2.6, the decoding tables in Tables 7–9, and the decryption exercises posed by Figure 5 and the final line of the paper demonstrate that they can. And for what it’s worth, I am completely open to variants of the cipher that enforce stronger structural distinctions between unigram and bigram tokens, thereby reducing the need for re-encryption. I see this as an area for experimentation, not as a fatal flaw.
5. Word-type coverage and combinatorial morphology
Torsten’s claim: The Naibbe cipher produces only ~45% of Voynich B word types and, with effectively free prefix–suffix combination, generates many non-VMS types. This suggests a mismatch between Naibbe’s combinatorial freedom and the VMS’s constrained morphology.
I agree that this is a genuine limitation of the Naibbe cipher, and I already say as much in the paper. Section 4 notes that limiting valid plaintext n-grams to only unigrams and bigrams necessarily bounds the generable word-type space, especially for producing especially rare long word types. Relaxing this cap could expand coverage but would also increase ambiguity. This is already framed as a tunable tradeoff.
On the “free combination” point, it is important to emphasize that Naibbe does not treat prefixes and suffixes as fully unconstrained:
- All affixes must be valid under a Zattera-style slot grammar;
- Certain glyphs are confined to either type-1 affixes or type-2 affixes, which correspond roughly with Zattera’s slots 0-5 or slots 6-11;
- Nearly all prefixes are type-1 affixes, and nearly all suffixes are type-2 affixes, which meaningfully reduces the effective morphological design space; and
- Table selection probabilities are strongly skewed, further concentrating realized combinations.
I freely concede that the combinatorial space is not perfectly aligned with VMS’s observed word types and agree that this deserves more quantitative treatment, as I say in the paper. I deliberately did not go too far down the path of quantitatively optimizing the grammar or the specific affix-letter assignments, as doing so felt far too uncomfortably like a decryption attempt that assumed—almost certainly incorrectly—that the VMS was not only a ciphertext and but also that I had found the VMS’s exact cipher architecture.
Again, Naibbe is not positioned as a generative model for all VMS properties. We must remember that the Naibbe cipher is focused on a more modest claim: demonstrating the existence of a class of substitution cipher whose ciphertexts can live within the statistical neighborhood of Voynich B when encrypting real plaintexts.
6. Long-range correlations
Torsten's claim: The Naibbe cipher fails to reproduce well-documented long-range correlations in the VMS; this may falsify the entire Naibbe class of ciphers, not just the current implementation.
I fully agree that the current Naibbe implementation does not reproduce long-range correlations. I discuss this failure at length in Section 4, reporting it explicitly using random-walk analysis and highlighting it as a major limitation. Where I disagree is the leap from:
“This particular version of the Naibbe cipher, which uses random respacing and independent table draws, fails when encrypting a compound plaintext made of diverse Latin and Italian sources”
to
“This entire class of verbose homophonic substitution ciphers is incompatible with long-range correlations across all possible plaintexts.”
Torsten does not prove general incompatibility. Section 4 of the paper sketches out several candidate mechanisms that could potentially introduce correlations that operate on top of the cipher’s existing structure. I see implementation and testing of such mechanisms to be fruitful avenues of future research. Generally, I think it would be fascinating to see whether and how a Naibbe-like cipher could be hybridized with the rules explored in the self-citation algorithm, such as line-by-line reuse. One important thing to look at in the testing of such a hybrid cipher would be the nature of the modeled plaintext. Is there any configuration that can reliably accommodate a plaintext written in prose, or does the only probabilistically favored type of plaintext read as gibberish? Let’s go out and test it!
7. Line-level structure and position-dependent effects
Torsten’s claim: Because Naibbe is position-agnostic at the line level, it cannot reproduce observed line-initial and line-final effects, gallows distributions, and related positional phenomena, which are “fundamental VMS properties.” Torsten also characterizes the paper’s gesture at line-initial <p> glyphs and line-terminal <m> glyphs as “superficial and inaccurate.”
The paper calls attention to the cipher's inability to replicate positional effects, and my suggested modifications are deliberately modest. I did not and do not claim to reproduce the full suite of positional phenomena documented for the VMS. Fully enumerating and grappling with these properties was beyond the scope of an already dense first paper. In addition, nothing in Naibbe’s design prevents positional behavior being layered on, though as I note in the paper, it would be inelegant to bolt many additional rules onto the current Naibbe cipher to force this outcome.
If the VMS does represent a ciphertext, the encoding method must naturally produce line-position effects, a property that the Naibbe cipher currently lacks. So I agree with Torsten in spirit that positional effects are important to study further. I disagree that these effects’ current absence from the Naibbe cipher proves broad structural incompatibility with a Naibbe-class verbose homophonic cipher.
8. Historical plausibility and practical burden
Torsten’s claim: Naibbe is far more complex than known 15th-century ciphers, imposes a heavy operational burden (especially if used for an entire book), and is therefore historically implausible. In addition, the paper’s stepwise evolution sketch is “just-so.”
I agree that Naibbe sits at the high end of plausible complexity; the paper says as much. Section 4 explicitly notes that Naibbe “would represent a major leap in complexity over known 15th-century ciphers.”
However, several points mitigate the charge of implausibility:
Survival bias in the cipher record. Our surviving corpus of 15th-century ciphers is
small and heavily weighted toward diplomatic and mercantile use
and thus cannot represent the long tail of all ciphers designed or used within medieval Europe. By all appearances, the VMS is a one-off, as is its exact method of text generation, regardless of whether it’s meaningful or meaningless.
Matching effort to artifact. The VMS itself clearly represents a substantial investment of time and resources. It is reasonable to explore the upper edge of what a determined person—or group of people—could have done over a span of months to years. What’s more, the more than century of failed VMS decipherments strongly suggest that if the VMS contains meaning in the form of an encoded message, the cipher must deviate from mainstream cryptographic history in a serious and fairly elaborate way. Otherwise, the VMS would have been cracked by now.
Collective effort. I know that Torsten prefers the solo-author hypothesis, but his “encrypting 57,000 letters alone” scenario does not jibe with the recent paleographic suggestion of multiple scribes. Naibbe-style encryption could have been distributed across several people. And having written in the cipher myself, my personal suspicion is that a single experienced scribe could pull off a VMS-length ciphertext in several months of full-time work, on the order of but probably longer than Gordon Rugg’s (2004) suggested timeline with Cardan grilles. In both cases, using external physical objects to facilitate affix selection—grilles and tables in Rugg’s case, tables and playing cards in my own—makes the procedure much less of a cognitive burden than one might initially suspect.
I agree that the stepwise evolutionary sketch in Section 4 is speculative; it is labeled as such and is not offered as direct historical evidence. I do not claim to have documentary proof of Naibbe-like systems existing in the 15th century. Having said that, I find it at least interesting that my modeling efforts preferred a substitution scheme acting on a unigram-bigram plaintext, and advanced ciphers of the approximate time and region of the VMS’s creation are attested to substituting the same plaintext units, albeit with far less systemization.
From the standpoint of the paper’s core question—“are substitution ciphers in principle capable of producing VMS-like text under 15th-century constraints?”—it is appropriate, in my view, to push into ambitious territory. If an elaborate system straining the upper limits of historical plausibility could not even partially match the VMS, that would be strong evidence against the ciphertext hypothesis. The fact that it can is therefore informative.
9. Paper's own criteria and actual contribution
Torsten concludes by evaluating the Naibbe cipher against the criteria mentioned in the paper, based on my own criteria and those of Lisa Davis. I believe Naibbe meets more of these criteria than he credits:
- Uses a known 15th-century cipher type (homophonic substitution): Yes.
- Can be done with 15th-century materials (tables, cards, dice, wax tablets): Yes.
- Derivation is reproducible and fully specified: Yes.
- Preserves the plaintext letter sequence in order: Yes (a strict requirement I built in by design).
- Reliably yields minimally ambiguous decryptions: I would say yes, with caveats and explicit procedures; Torsten regards this as more problematic. (There are two decryption exercises in the paper itself, for those who want to try it for themselves.)
- Historically plausible: Unquestionably on the high end of complexity but arguable.
- Replicates VMS properties: Many, but not all, with clear acknowledgment of several key missing ones (notably long-range correlations and positional effects).
It’s also worth noting that Torsten summarizes the paper’s main takeaway accurately and fairly:
“Demonstrating that a verbose homophonic substitution cipher can simultaneously satisfy multiple VMS constraints (entropy, token length, word grammar) is intellectually interesting. It shows that these properties are not individually impossible to replicate.”
That is precisely the level of contribution I intended Naibbe to make: not a definitive solution to the VMS, but an existence proof that a letter-preserving, hand-doable substitution cipher can live deep inside the VMS’s statistical envelope.
In summary, I agree with Torsten where he identifies genuine limitations of Naibbe 1.0. I disagree with his conclusions that frame these open issues as proof of the VMS’s fundamental incompatibility with Naibbe-class ciphers. If anything, going out and testing these open issues could place very tight constraints on how a substitution cipher specifically could or could not generate fully VMS-like text. I also disagree with readings of the paper that treat Naibbe as anything more than a demonstration of feasibility.