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This page is still incomplete and, to use a term from the earlier days of the WWW: 'under construction'.

Epilogue (part 2) - towards the solution of the MS

Introduction

It is clear that the main unanswered question about the Voynich MS is: "what does it say?". At the same time one can ask: "why has nobody found the solution yet?". Does this mean that the MS could be meaningless after all? Or has someone already found the solution and we simply haven't realised it? Or, alternatively, has everyone been looking in the wrong direction for the last 100 years? That would seem unrealistic, wouldn't it? Well, let's see.

On the previous page I already argued that at least the most common solution approach, namely finding a way to translate the text of the Voynich MS back to plain text, is fundamentally wrong. It could work, but only if several implied assumptions are all valid, most particularly that the MS includes a meaningful text in a language that we still understand. Now I have read and heard many times that, clearly, it wouldn't make sense for such a long MS to be meaningless so there has to be a possible translation. Even though that seems to make sense, still, it is again an assumption, and I dare say that a modern (21st Century) person may not be in the best position (1) to judge what would or would not make sense for someone creating a book 600 years ago.

Many papers have been written about the Voynich MS text. These have presented various tentative conclusions. Some suggest that the text should be meaningful, others that the text shows signs of probably being meaningless, and finally there are those that clearly state that there is evidence for both. What we have is a large corpus of evidence, conclusions, statements, assumptions, opinions, facts, theories, etc. etc., and the true explanation of the Voynich MS text has to fit all of them in the appropriate manner. That means:

When that has been achieved, this true explanation is then capable of telling us which assumptions, opinions, theories, etc. were correct and which were not.

Clearly, it is of critical importance to correctly classify all statements one may find about the Voynich MS into the different categories of:

Facts: what we know, what we think, and what we think we know

It is not only important to be critical about what we know, but also important to keep in mind what we specifically don't know. Most of the factual information we have about the MS concerns the materials it has been made of. There are also some obvious facts, the importance of which is easily overlooked.

The origin of the MS

The parchment of the MS has been radio-carbon dated and gives a consistent time frame when this parchment was prepared. What we don't know anything about is how long the conception and creation of the MS took. This entire process may have taken anywhere between just a few years and, say, thirty years (2), and we don't know if it involved creating a complete draft before making the copy we have, nor do we know at which point in the process the parchment was acquired by the author. It may also have been acquired in batches. The radio-carbon dating of the individual sheets is not precise enough to tell us this.

The conception of the MS may already have taken place during the later part of the 14th Century, while the completion of the MS may also have been as late as ~1450. The handwriting on the last page (f116v), which should coincide with the completion of the MS, or could also be a later addition, is not to be dated after the 15th Century, though.

While everything points to the MS having been created in Central or Southern Europe, nothing should be assumed about the language used for the text (if there is a plain language meaning at all, of course). In fact, it may well be that assumptions that the language should be Latin or one of the main vernaculars in 15th C Europe has contributed to the failure in interpreting the text until now.

The text

It is a fact that no other contemporary document survives that uses the script of the Voynich MS. This has been taken as evidence that the script was specifically created for this occasion. This may well be so, but it is not clear that this makes a big difference for the study of it.

Another important fact is that a consistent character set is used throughout the MS, from the beginning till the end. The same is true for parts of the vocabulary. Many frequent words occur throughout the MS, from the beginning till the end. Therefore, we can state that the entire conception of the MS was a carefully planned and executed activity. It is also true that there are some variations. The meaning of these variations is subject to interpretation.

Counts of the number of different characters that occur one than once in the text has resulted in values between (roughly) 24 and 36. Even if that range is rather wide, it is clear that the script is an alphabetic one. It could be an abjad, in the sense that vowels may not be represented, or only in some cases, though not in the sense that consonants and vowels are combined into composite characters (3). It has to be stressed that this is a property of the script, not the language, and it should not be assumed that the language has to be one that is usually written in an alphabetic manner (again, assuming that there is a plain text language in the first place).

Anything else?

This is quite a short list of facts, and I cannot think of anything else right now. Many of the well known observations about the text of the MS are (or should be) listed under 'features' below.

Features

Summary

Many features of the text have been observed and reported, and a summary of them is presented (4) in the text analysis section, without intending to claim completeness. Some of these features are quite pronounced, and any proposed solution needs to account for, and be able to explain all of them. Following is a list of what I believe are the most important ones.

Now it is tempting to try and find possible explanations for each of these features. For most of them it is not even difficult, with the notable exception of the word structure. (In fact, finding a good explanation for this point should take one a big step closer to a possible explanation of the Voynich MS text. We will come back to this further below.)

The key point to make at this stage, however, is that the vast majority of solutions that have been proposed so far do not even attempt to explain any of these features, and I am not aware of any example that addresses all of them.

Specifically, when a proposed solution includes an alphabet table in which p and f are simply mapped to a plain text character of the alphabet, one can be certain that this solution is incorrect (5).

More about the text

The text exhibits a number of features that suggest it should be language-like or meaningful. Some can be expressed quantitatively, others not. The problem is that none of this evidence is very strong. Zipf's law is followed, there are long-range correlations which are destroyed when the text is scrambled, and there is some numerical correlation between the text properties and the section of the MS. All of these need to be explained in case one proposes a method whereby the MS text is not meaningful, but was instead created using some arbitrary process.

There is one specific feature that needs to be highlighted here. While the many body of the text follows Zipf's law, this is not true for the labels. Specifically for the zodiac labels, the word frequency distribution is almost flat. Some labels do occur up to four times, but the vast majority is unique, and the frequency curve for these words is highly anomalous for a peice of text. It is therefore certain that these labels are 'something different' from the main text. This is again evidence that the text creator (author) was working with a purpose.

Another feature: corrections

The Voynich MS written text shows almost no corrections or erasures. This has been interpreted by some to indicate that the scribe could actually not understand what he wrote, or even that the text was meaningless, but this is not necessarily true. In any case, this is a type of feature that a proposed solution does not need to 'explain'. However, it is a feature one should keep in mind when defining statistical tests, or even a proposed solution. One thing it could mean is that the text has a significant number of errors (since they were not corrected). More in general, one needs to keep in mind that the text, even if it is meaningful, may have significant spelling variations. Comparisons with known plain texts will be biased because of this, as such reference texts are most commonly following a clearly defined orthography and have been fully spell-checked.

Solution tree: a top-level classification of the possible solutions

Introduction

Let me start by repeating some of the key phrases from the previous page:

We don't yet know whether the Voynich MS represents a meaningful text. What we do know for certain, however, is that some time in the past, somebody or some group of people sat down and wrote the Voynich MS using some method. [...] Unfortunately, we don't (yet) know this method. We can only imagine a multitude of different ways how it could have been created.

This text generation method is what we should be looking for, and in the following I will classify some high-level aspects of it using a tree structure. We will then see in which cases the usual 'decoding attempts' could be valid and in which cases they cannot lead to success.

Approach

At various points in the tree structure for the text generation method there are different options. All of these options are numbered. In the following I will avoid going into the question of the likelihood that one or the other option is correct. It is necessary to keep this completely open at this stage. It is in any case very hard to quantify in almost all cases. Instead, I will give what I call examples and challenges.

Examples are ways how a particular option could be explained, without aiming for completeness. They are just there to show that one should not discard any option off-hand.

Challenges are points that might not be easy to explain in case a particular option is chosen.

The total ensemble of all possible solutions is what I called the solution space in the previous page, and it is represented by the entire tree structure developed below. Please note that this tree is not intended to be the only possible way to analyse the problem. The questions about cipher vs. language, or what could be the plain text language are deliberately left out of this analysis. They will only start playing a role in case there is a meaningful plain text. The tree is developed primarily along the branch of meaningful solutions. The other branches are more difficult to develop.

Meaningful or not - Question 1

Whether the text still has a recoverable meaning is addressed as a combination of two different questions. Question 1 is: what did the author intend 600 years ago. Question 2 is: in case he wrote something meaningful, can we still extract this meaning 600 years later?

Option 1a: the author 'encoded' something meaningful

Example(s):
This is the most easily understandable option, and the one that most people tend to assume automatically. The text would be written in any known language of the 15th Century, either well known or more exotic, and represented in a strange alphabet, possibly with some cryptography added as well.

Challenge(s):
There are two main problems that require an explanation in case this option is preferred. The first is how the word structure arises, and the second is why the solution has not yet been found by anyone.

Option 1b: the author 'encoded' something that was meaningful only to him

Example(s):
To explain this option, let's just look at f116v of the Voynich MS. This has text written mostly in plain Roman characters. It is quite possible that this was written by the original MS composer/author. However, it has not been possible so far to make complete sense of it. Now what if the entire MS contains text similar to this? People decoding the text would not even recognise that they solved it, even if they did. Numerous other manuscripts exist that include some magical and nowadays basically meaningless text.

Challenge(s):
The main problem that requires an explanation in case this option is preferred is whether anyone could really write more than 200 pages in such a manner. How the word structure arises in this case would also require an explanation.

Option 1c: the author intentionally created something that has no meaning

Example(s):
While the exact method given by Gordon Rugg does not work, the idea he proposes is a good example in general how this could be done with 15th Century means. The method proposed by Torsten Timm also fits into this category. Other methods could include generating / picking words from an existing text that has been written in a language or script unknown to the author.

Challenge(s):
One of the main problems that require an explanation in case this option is preferred is why the labels in the MS follow completely different word statistics than the main text. This cannot be the result of an arbitrary process.

Question 1 summary

This question relates to what the composer/author of the MS intended. Although the boundaries between the three proposed options may not be very precise, all possibilties can be associated to one of the three, even when it is a matter of taste. Anyone looking for a translation of the text should realise very clearly that he is choosing option 1a, and there are some points that require an explanation. Anyone proposing an alternative option similarly has some questions to answer.

Meaning lost? - Question 2

This question further qualifies the case 1a above, that the original author intended to write something generally understandable. The question is whether this meaning is still recoverable now. Again, the boundary between 'yes' and 'no' may not be very precise.

Option 2a: meaning still recoverable

Example(s):
Again, this is the most easily understandable option, and the one that most people tend to assume automatically. 'Recoverable' should be understood as 'in principle'. It should not necessarily be easy.

Challenge(s):
The main two challenges of option 1a are still valid: the first is how the word structure arises, and the second is why the solution has not yet been found by anyone.

Option 2b: meaning no longer recoverable

Example(s):
The loss of the original meaning would happen, for example, in case a meaningful text has been encoded using an irreversible method. A variation of this is the so-called 'ignorant scribe' scenario, where a scribe unintentionally makes an inaccurate copy of the original, thereby eliminating critical information or introducing large errors. Anonther possibility for a loss of the original meaning is in case the original language is no longer known.

Challenge(s):
The main problem that requires an explanation in case this option is preferred is not a very strong one. It seems hard to imagine that the MS author or composer would make the mistake of using an irreversible method, and also the 'ignorant scribe' theory seems difficult to accept. A lost language is likely to still have cognates in modern times.

Questions 1 and 2 summary

In the end we have two options: either there is a recoverable meaning or there is not. In the negative case, we have identified three high-level possibilities how this could have happened. Assuming that the MS has a meaning therefore implies that one assumes none of these three options applies.

Are word spaces significant? - Question 3

We are now ready to further explore the case where the MS text still has a recoverable meaning, and one of the first questions that arises is related to the spaces we see between groups of characters. In the analysis section we called these groups of characters 'word tokens'. Here, for brevity, I will just call them 'words'. The question is whether the spaces are really meant in the sense that these character groups indeed represent words, which is something that most people will almost automatically assume.

Also this question is addressed as a combination of two different questions. Question 3 is: are the word spaces as we see them real separators between units of information. Question 4 is: in case not, can we still (re-)introduce such spaces / separators in a (more-or-less) simple manner?

Option 3a: word spaces are significant

Example(s):
This is the most easily understandable option, and the one that many if not most people tend to assume.

Challenge(s):
The main two challenges of options 1a/2a are still valid: the first is how the word structure arises, and the second is why the solution has not yet been found by anyone.

Option 3b: word spaces are not meant as separators

Example(s):
In this case there are several possibilities. For example, it could be that some spaces are 'real' while others are dictated by orthography, as in the arabic script where there are breaks following characters that cannot be 'connected' to the next one. It should also be noted that many of the spaces in the MS are difficult to judge. They have highly variable width, leading to significant doubt in many places in the MS whether there is a space or not. Thus, the main two cases in this option are, on the one hand, that many or most of the spaces may be real but some may not be, or may be missing missing. In the other case, spaces could be completely arbitrary. Furthermore, the 'words' may not not represent complete words, but only parts of words (e.g. syllables) or even only single characters.

Challenge(s):
The main problem that requires an explanation in case this option is preferred is the observation that the label words in the MS, which are definitely single units, do occur most frequently in the running text separated by spaces (6). This is a very strong indication that the spaces do function as 'separators' of some sort.

Question 3 summary

The main purpose of this question is to make people realise that one should not necesarily assume that the 'words' in the MS really represent words in the way they are usually understood.

Can we figure out word spaces anyway? - Question 4

This question further qualifies the case 3b above, that the spaces we see in the Voynich MS are not (always) word separators.

Option 4a: there should be word spaces and they can be (re-)introduced

Example(s):
This is only likely to be possible if some large part of the spaces we see in the MS is real. Another option would be that word spaces are to be ignored altogether, and another character is meant as a word separator.

Challenge(s):
There are several problems that would require an explanation in case this option is preferred. If a large fraction of the spaces are to be ignored because they are not real word spaces, this will have a negative impact on the word length distribution, as the average word length will increase significantly. In case word spaces are considered arbitrary, a reconstruction would be possible if another character should represent the word space. The big problem here is that no other charater is sufficiently frequent to take up this role. In general, this option would require a lengthy analysis and explanation.

Option 4b: it is not possible to (re-)introduce word spaces

Example(s):
This option just confirms the idea that word spaces are completely arbitrary, and it is not possible with easy means to identify the real ones.

Challenge(s):
The challenge for option 3b still applies here: it would need to be explained why or how the label words appear in the running text separated by spaces.

Questions 3 and 4 summary

In the end we have two options: either we can identify the words in the text with 'units of meaning', or we cannot. Beside the examples given above, the negative case could also arise in very different scenarios (that have occasionally been proposed). These include suggestions that the text, as we see it, is not meaningful text but more like a 'background', against which we need to extract the real meaning from geometrical means, or by selecting individual characters using a grid, etc. etc.

The units of meaning could represent (in the plain text) words, syllables, characters, or other, as indicated by the codes W, S, C, O in the above figure.

Is a word-for-word translation possible? - Question 5

Having reached a point in the tree where the written words in the MS are representing units of meaning, the next logical question is, whether each word type we see in the MS is a consistent rendering of the same unit of meaning in the original or plain text. We need to keep in mind that we are looking at the process of writing the text by the author/scribe (whether translation or encryption or something else). The easiest case would be if one plain text word would be uniquely represented by one word in Voynichese, i.e. there is a one-to-one mapping. Another possibility would be that a plaintext word is represented by different Voynichese words (one-to-many). As long as each Voynichese word derives from only one original plain text word, we would still be able (in principle) to reverse this process and retrieve the plain text. A third possibility is a many-to-one mapping. Here, several different plain text words would map onto the same Voynichese word. This is in principle irreversible (7). Finally, many-to-many mappings could exist, which would equally be irreversible.

Option 5a: there is a one-to-one or one-to-many mapping of plain text to Voynichese

Example(s):
To deal with this question, we should imagine that there exists a 'dictonary' from plain text to Voynichese. It is not necessary that this dictionary physically exists. In the one-to-one mapping case, this dictionary has one entry for every plain text word, and it translates to one Voynichese word. If we had this dictionary, we could translate the text back. One possibilty is, of course, that this is how the MS text was written. The author created such a dictionary and used it. Another possibility is, that the plain text words were encrypted using a well-defined cipher that generates different cipher words for different plain text words. Finally, the text could be a rendition of an 'unusual' language in an invented alphabet, executed consistently.

The one-to-many mapping means that our (imaginary) dictionary has one entry for each plain text word, and this can translate to several different Voynichse words. If we had this dictionary, we could still translate the text back, assuming that there is no overlap in the Voynichese words from different plain text words. (In that case we should call it a many-to-many mapping). One possibility for ending up in such a situation is in case the author encrypted the text using a poly-aphabetic cipher, or added null characters.

Challenge(s):
A dictionary or look-up table to encrypt the MS text would not be a very practical manner. If it were a simple cipher, it is hard to understand why the MS text has not yet been deciphered. For a true one-to-many encoding, the word frequency distribution, which now follows Zipf's law, would be significantly disturbed.

One other challenge that exists in case this option is preferred is that we lack an explanation for the (relatively) many word repetitions, in particular also for the high-frequency words like daiin, and for the relative lack of repeating seqeunces.

Option 5b: there is no (clear) mapping from plain text to Voynichese words

Example(s):
This situation is a bit more difficult to imagine. It could be that the text is a very inaccurate rendering of an 'unusual' language, with loss of unique representation (several sounds mapping to the same character). It could also be that a cipher has been used that maps many to one. Finally, the text could include a great number of mistakes. In these cases, we are basically in the situation of option 2b above: meaning has been lost. This depends on the level or amount of redundancy that has been created.

Challenge(s):
It is also not easy to come up with challenges for this option. It remains to be seen whether the Zipf law would still be followed by a text that was generated using a many-to-one or many-to-many mapping, but it remains entirely possible.

Question 5 summary

At the end of this question we end up with basically two options. Either the text that we have in the Voynich MS could be translated back to a plain text using a consistent word-for-word substitution, or it cannot. Again, my feeling is that people naturally tend to assume the former, but the present analysis should show that this involves a number of unconscious assumptions.

Does the word 'dictionary' have a system? - Question 6

We have now reached the point where there exists (in theory) a dictionary that would allow a word for word translation of a plain text into Voynichese and vice versa. We may compare the plain text words and the Voynichese words, and see if there is any relationship between the two. There are various possibilities. Such a relationship may exist and be straightworward, it may exist and be more complicated, or it may in fact not exist. These three options are now compared.

Option 6a: there exists a simple relationship between plain text and Voynichese words

Example(s):
This is again very easy to imagine, for example if the plain text is a language which is simply rendered by an invented alphabet, or in case it was a written text that had been encrypted using a very simple cipher, such as a simple substitution. In such a case, the dictionary would not be needed, but one would just have to remember the 'rule' to convert one to the other.

Challenge(s):
While this option is automatically assumed by most newcomers to the MS, the big problem is that in this case the solution should have long been found. The character entropy values of the Voynich MS text also preclude that the text is one of the well known languages just converted by simple substitution.

Option 6b: there exists a more-or less complicated relationship between plain text and Voynichese words

Example(s):
This is a variety of the first option, and it would still have allowed the author to create the text without actually consulting a long dictionary. It is hard to come up with good examples for the precise form of this relationship. It could be a moderately complicated cipher, or some as yet unforeseen way to turn plain text into Voynichese.

Challenge(s):
It is equally hard to come up with specific difficulties related to this option. It seems one way in which the problem could have remained unsolved for such a long time. A very complicated cipher would be anachronistic, though.

Option 6c: there is no identifiable relationship between plain text and Voynichese words

Example(s):
In this case, the plain text words would indeed have been written in a dictionary, or rather a code book, with in principle arbitrary entries for the resulting 'code'. This is one way in which the word pattern would not be a big problem, since this could have been part of the design. The 'code' could even have been generated in the form of a number system, although such a system has not been identified so far, and there are many exceptions to the word pattern.

Challenge(s):
The obvious problem in case this option is selected is that it would have been quite inconvenient to generate the text in this manner, unless the author had a remarkable memory. In practice, it would have required the author to look up (almost) every word before writing it down. This would have been in a draft, to be copied as a fair copy later.

Question 6 summary

These three options are not fundamentally different, but one or two of them would have been far more practical to implement than the third. All three only play a role in case a word by word translation of the text is possible, which is far from certain.

The complete tree structure

Taking all questions and options together, we may draw a simplified version of the tree structure as shown below. In this tree, I have split the entire 'solution space' into two parts. The part A (in green) concerns the case where the text has a meaning, and a word by word translation of the text is possible. Part B (in red) concerns all other cases.

It is now possible, for any proposed solution, to identify the 'box' or the category into which it falls. As an example, the solution of Newbold is one where the text is meaningful (branch 1a), the meaning is still recoverable after 600 years, at least according to him (branch 2a), but words are not units of meaning (branch 3b and 4b), since he reads the text from the fragmented edges of the characters.

Another use of this tree structure is the demonstration that anyone who starts working on a 'solution' of the MS, by substituting Voynich characters into plain text letters in some language, is immediately jumping into the lower left box above (under the green A boundary), meaning that a whole array of hidden or subconscious descisions has been made.

Finally, one may wonder what is the likelihood that the 'truth' is in part A or in part B. This question cannot be answered, except that neither of the two probabilities are zero. I believe that the main 'divider' is the question whether the words in the MS are units of meaning. Analysing the words (both the word types and their frequency) should be able to tell us if they are, or are not, units of meaning.

To be continued.

Notes

1
I.e. without having any background (dedicated education) in this area.
2
The higher value of 30 years is taken from the time it took the author (Lambert de St.Omer) to create the 'Liber Floridus'. The very short time (less than a year) proposed by Gordon Rugg applies to making a copy of the MS and excludes the processes of conception and preparation of the MS.
3
Such as for example in Korean.
4
Though unfortunately still incomplete.
5
More specifically, if the characters p and f are proposed to be the only characters to represent certain plain text characters. This, by the way, is also true for the Voynich characters q and m, and in my opinion even y.
6
This was verified early September 2016 by Marco Ponzi. The result of his analysis will be included in the analysis section in the (near) future.
7
Though scenarios could exist in which the meaning could be recovered, for example if the plain text turns out to be one known from other manuscripts.

 

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