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The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

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  • [Article] The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026
• The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

• The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

  Torsten > 12-07-2026, 09:34 AM

  The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026
  
  by Torsten Timm
  
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  Quote:In two recent companion papers, Layfield and Davis apply latent semantic analysis (LSA) to the Voynich Manuscript and derive two hypotheses: that the manuscript was conceived as a sequence of single-bifolium quires (“singulions”) later bound out of order, and that the intended sequence of bifolia can be recovered by maximizing textual similarity across page transitions. This review examines both hypotheses against the papers’ own published data. The empirical core of the first hypothesis, an elevated textual similarity within physical bifolia, is real and independently confirmed. The reading-order interpretation built upon it, however, is underdetermined by the data and contradicted by the authors’ own explanation of the herbal section. The second hypothesis rests on the premise that the intended order of a meaningful text maximizes lexical similarity between adjacent pages. This premise is refuted by the authors’ own calibration manuscripts, and the resequencing experiment lacks two controls that would make its reported improvements interpretable: a permutation null distribution and a calibration on deliberately shuffled known text. A similarity-based resequencing of the manuscript is nevertheless methodologically sound under one specific model of the text, namely that page-to-page similarity reflects proximity of production rather than continuity of meaning. Three concrete experiments, each executable with the authors’ existing pipeline, would discriminate between the competing interpretations.

• RE: The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

  Rafal > 12-07-2026, 12:02 PM

  Could you confirm or deny Torsten if I understand one thing correctly?
  I won't get deep deep into statistics and will use a non-statistical language.
  
  Layfield and Davies used "lexical similarity" method in attempt to restore original order of the pages.
  
  This method may work well with a real text telling some continuous story.
  Take Book of Genesis as example. First it is about Adam and Eve, then about Cain and Abel, then about Noah, then about Abraham etc. Each story has its own vocabulary, sets of words are introduced and then disappear.
  In the story of Adam and Eve words like "garden", "fruit", "tree" or "serpent" will appear with bigger frequences. So you may recognize all pages telling this story
  even if it is written in unknown language and unknown script.
  
  On the other hand if you have some dictionary of plants, there won't be any progress of the plot. Each plant description is a separate story which can be placed in any order.
  I believe that's what Layfield and Davies claim - their results show that there is no story progression in herbal section which seams reasonable.
  
  But you mention BAAFU - bifolio as a functional unit.
  
  Is it true that 4 plants appearing on a single bifolio share the same vocabulary that they don't share with other plants from another bifolios?
  
  This would be really hard to explain if the text was a natural language.
  Are there any more articles about BAAFU?

• RE: The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

  LisaFaginDavis > 12-07-2026, 01:40 PM

  That's correct, Rafal, we say quite explicitly that the LSA data are NOT helpful for the herbal section since, although the DHQ article showed that the herbal section seems to have some topical similarity throughout, it also suggests that the text on each herbal page - each plant, that is - is a separate unit. So there may not even BE a "correct" order for that section. We proposed HYPOTHETICAL sequences for Quires 13 and 20 because that was what the data supported. But even there, as we also say explicitly, we cannot know if any of this is truly correct until and unless we can read it.

• RE: The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

  Torsten > 12-07-2026, 08:33 PM

  (12-07-2026, 12:02 PM)Rafal Wrote: You are not allowed to view links. Register or Login to view.Is it true that 4 plants appearing on a single bifolio share the same vocabulary that they don't share with other plants from another bifolios?
  
  This would be really hard to explain if the text was a natural language.
  Are there any more articles about BAAFU?

  
  Rafael, yes, that is essentially correct. Pages on the same bifolium share vocabulary characteristics that they do not share with pages on other bifolia — even adjacent ones in the same quire.
  
  A clear example is the distribution of EVA m in Quires 1–3. On some bifolia 36 and 17/24, EVA-m is used frequently across all four pages. On adjacent bifolia 2/7 and 20/21, m does not appear at all (see You are not allowed to view links. Register or Login to view.). The all-or-nothing pattern follows bifolium boundaries, not page sequence — neighbouring leaves in the bound quire have completely different m usage.
  
  This observation goes back to Timm (2014), where I documented that rare words propagate across consecutive sheets rather than across recto and verso of the same leaf, with a ratio of 37:5 for words occurring seven or eight times (You are not allowed to view links. Register or Login to view., p. 17). You are not allowed to view links. Register or Login to view. coined the term BAAFU (Bifolio As A Functional Unit) in December 2022 in response to a forum discussion of this evidence.

• RE: The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

  Torsten > 12-07-2026, 09:02 PM

  (12-07-2026, 01:40 PM)LisaFaginDavis Wrote: You are not allowed to view links. Register or Login to view.we say quite explicitly that the LSA data are NOT helpful for the herbal section

  
  This applies to the resequencing experiment, where the herbal section was excluded. However, the herbal quire data in Table 8 of your paper is central to the singulion hypothesis itself. The paper reports conjoint/facing differentials for all seven herbal quires — for instance Quire 6 shows conjoint 0.448 versus facing 0.166, and Quire 7 shows conjoint 0.336 versus facing 0.138. These herbal quire measurements are the primary evidence for the conclusion in paragraph 56 that "there is very strong evidence that the Voynich was not meant to be nested and bound in quires at all." Without the herbal data, the singulion argument rests on only two quires.
  
  This is in tension with the statement in paragraph 35: 'The results for the Herbal section suggested that each page is a distinct botanical topic (as also inferred from the illustrations, which change with each page).' If each herbal page is a distinct topic, that explains why facing pages are dissimilar — they depict different plants. But it equally predicts that conjoint pages should be dissimilar, since they also depict different plants.

• RE: The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

  Pointless.. > 15-07-2026, 05:54 PM

  (12-07-2026, 08:33 PM)Torsten Wrote: You are not allowed to view links. Register or Login to view.A clear example is the distribution of EVA m in Quires 1–3. On some bifolia 36 and 17/24, EVA-m is used frequently across all four pages. On adjacent bifolia 2/7 and 20/21, m does not appear at all (see You are not allowed to view links. Register or Login to view.). The all-or-nothing pattern follows bifolium boundaries, not page sequence — neighbouring leaves in the bound quire have completely different m usage.

  
  Is a comparable phenomenon observable with f, and, albeit to a lesser degree, with g?

• RE: The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

  LisaFaginDavis > 15-07-2026, 06:17 PM

  (12-07-2026, 09:02 PM)Torsten Wrote: You are not allowed to view links. Register or Login to view.

  (12-07-2026, 01:40 PM)LisaFaginDavis Wrote: You are not allowed to view links. Register or Login to view.we say quite explicitly that the LSA data are NOT helpful for the herbal section

  
  This applies to the resequencing experiment, where the herbal section was excluded. However, the herbal quire data in Table 8 of your paper is central to the singulion hypothesis itself. The paper reports conjoint/facing differentials for all seven herbal quires — for instance Quire 6 shows conjoint 0.448 versus facing 0.166, and Quire 7 shows conjoint 0.336 versus facing 0.138. These herbal quire measurements are the primary evidence for the conclusion in paragraph 56 that "there is very strong evidence that the Voynich was not meant to be nested and bound in quires at all." Without the herbal data, the singulion argument rests on only two quires.
  
  This is in tension with the statement in paragraph 35: 'The results for the Herbal section suggested that each page is a distinct botanical topic (as also inferred from the illustrations, which change with each page).' If each herbal page is a distinct topic, that explains why facing pages are dissimilar — they depict different plants. But it equally predicts that conjoint pages should be dissimilar, since they also depict different plants.

  
  That exactly right, Torsten. The data for the herbal section alone does NOT support interpreting the herbal bifolia as singulions. As we wrote, however, the data for the herbal section suggests that each herbal page is its own micro-topic, AND, as shown in the DHQ article, the whole herbal section shows a general topical coherence. The illustrations crossing the gutters of several herbal bifolia DO support the singulion hypothesis, especially since there is so much evidence elsewhere in the manuscript supporting the idea: we have made a case for quires 13 and 20 being singulions; the astrological/astronomical and Rose bifolia already are singulions; and the missing bifolia 91|92 and 97|98 also were singulions. There is quite a lot of evidence supporting the hypothesis.

• RE: The Singulion and the Sequence: A Methodological Review of Layfield and Davis 2026

  Torsten > 15-07-2026, 07:14 PM

  (15-07-2026, 06:17 PM)LisaFaginDavis Wrote: You are not allowed to view links. Register or Login to view.As we wrote, however, the data for the herbal section suggests that each herbal page is its own micro-topic.

  
  Lisa, could you point me to where in the DHQ paper the herbal micro-topic finding is presented? Paragraph 35 of the Digital Medievalist paper attributes this to the DHQ paper, but I can only find the per-page topic conclusion for the Cosmological and Astronomical sections (DHQ, Section 5, point 2). For the herbal section, the DHQ paper attributes the decreased scores to the A→B transition (Section 5, point 1). I may be overlooking something, but I would like to verify the reference.
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