Can we unpack bench gallows? (No.)

This post is very long. A summary is provided at the bottom. The outcome is that I was unable to find an answer.

Bench gallows [ckh, cth, cfh, cph] appear to be combinations of a gallows [k, t, f, p] and a bench [ch]. They also seem to have links with both benches and gallows. The hypothesis that they are a combination of the two is a reasonable suggestion.

There is a further hypothesis that a bench gallows can be “unpacked”. These glyphs contains two features, and bench and a gallows, which can be separated and replaced by other glyphs with the same value. So [ckh] might be the same as [chk] or [kch]. A bench gallows is only an alternative way of writing other glyphs.

To investigate this hypothesis we will look at the text written by Hand 1. Hand 1 uses bench gallows more often than other hands. They also use them in all positions, including word-initial which is rare in other hands. Because [cfh] and [cph] are relatively uncommon through the text and may give unreliable results, we’ll concentrate on [ckh] and [cth].

Bench gallows in hand 1

Hand 1 wrote approximately 11,000 words of text. The glyphs [ckh] and [cth] occurs in 311 and 555, words respectively, or approximately 2.8% and 5% of words. Only three words contain two occurrences of either [ckh] or [cth], and only eight words have the bench gallows word-final. About 45% of [ckh] and 72% of [cth] are word-initial.

For a reason which we’ll discuss in a moment, this article will look at those words with an initial bench gallows. The most common words with initial [ckh] and [cth] in Hand 1 text are:

cthy93ckhy27
cthol52ckhey24
cthor40ckhol18
cthey37ckheey8
ctho19ckhor7
cthody14ckheody5
cthar12ckhody4
cthaiin12ckheol4
ctheey11ckhos3
ctheol9ckham3
cthal6ckhaiin3
cthom5ckho2
ctheody5ckheos2
ctheor4ckheo2
cthain4ckhal2

The two lists are broadly similar, though with different orders and significantly different counts due to [ckh] being less common in this position. The main difference is that two [ckh] words end in [s]. Counterparts with [cth] do occur, but with lower token counts.

The main reason for choosing to look at word-initial bench gallows is the pattern they display depending on line position. Below are the counts of words with initial bench gallows in the first five positions in a line:

Line position12345
[ckh*]040232318
[cth*]367696851

In both cases few to no words occur in the first position of a line. The subsequent positions show that the number should be several dozens, assuming that distribution were smooth.

This present us with the opportunity for an investigation to discover more about the nature of bench gallows. The question is where the words with initial bench gallows went, and what we can learn as a result. Following will be a series of statements potentially explaining the absence of bench gallows in this position, with a discussion about their plausibility.

Line distributions aren’t flat.

The idea that the distribution of words in a line should be flat is an assumption. We have known for a long time, since at least the work of Prescott Currier in the 1970s, that line patterns exist for words and glyphs. Whether they should be flat is not something researchers have been able to establish.

But simply restating the observation that line distributions aren’t flat doesn’t progress the problem. We can acknowledge that the line distributions are a feature and still seek to explain them. Any explanation would take the area of explanation as the difference between flatness and not-flatness, just as irregularities are explained in terms of how they differ from the regular. Assuming flatness, or regularity, is a technique to spur investigation, not an attempt to ignore the text as it is.

Acknowledging the line distribution then choosing not to seek an explanation is the opposite of research. It ignores evidence of the processes which created the text, a point at which they changed, or overlaid, and resulted in an irregularity. Progress on understanding the Voynich manuscript will only be made if the text is not accepted as an inscrutable whole but instead considered a complex outcome from many smaller interlocking processes.

The words were simply moved elsewhere.

The possibility that words with initial bench gallows were simply moved away from the first position in a line seems vaguely plausible. We don’t know what the words are (“word” itself is an assumption used for ease) or why they appear in a sequence. It is easy to assume that they are sequential, as in language, and therefore unmovable.

Even if the text is a written language words could still be flexible in their position. Languages allow for a certain amount of flexibility in how a sentence is phrased. The statistics for [ckh] in the second line position show a larger number than subsequent positions, so could they have been moved there?

The statistics for words with initial [cth] are relatively flat in position 2-5, so there is little chance the words from the first position are to be found there. The wider point about flexibility is reasonable except that line distribution affects many glyphs and words. Some are more common in the first position, others more or less common in the last position, at the end of a line. To create all these patterns would mean that almost every line experiences some amount of reordering to achieve them. At what point does a text become unreadable?

Different words were chosen.

Similar to the statement above, a dedicated author in English can avoid the letter “e”, so why not words containing [ckh]? All languages have some degree of synonymy within their vocabulary/lexicon/wordhoard, so avoiding certain words is very possible.

The arguments against this statement are much the same as above, though with further problems. It is unlikely that every word will have a synonym yet there are no words with initial [ckh] in the first position.

The words were deleted without replacement.

This statement proposes a text which is literally missing words every single line. Information and meaning would undoubtedly be lost. It is hardly credible that such a process created the line patterns which we observe.

The bench gallows were removed from the words.

As above, removing the whole glyph could result in a serious loss of information from the text. But if the rest of the word remained then the lost information could be supplied by the reader. This statement can be tested with statistics.

We know the most common words with initial [ckh] and [cth]. Removing the initial bench gallows supplies a list which can be checked against actual occurrences, as in the table below:

Line Position12345
[y]16161888
[ol]131814119
[or]17151386
[ey]01000
[o]137895
[eey]00110
[ody]00131
[eody]00000
[ar]05162
[aiin]087410

Only [o] shows an increased occurrence in the first position of a line. Yet for the hypothesis to be correct all such words would need to show a similar increase. We can say that the statement of bench gallows being removed from words in this position is almost certainly wrong.

Initial bench gallows is moved to an internal position.

The absence of initial bench gallows in the first position of a line could be due to the bench gallows moving position within a word. This could be the glyph moving in relation to others, or through additional glyphs being added before an initial bench gallows. Either way, this too should be easy to test with statistics.

Below is a table showing the number of words with non-initial bench gallows in different line positions.

Line Position12345
Non-initial [ckh]1925392220
Non-initial [cth]2228221925

The statistics show no increase in occurrences in the first line position, which would be expected if words with initial bench gallows had been altered in this position.

The gallows feature has been removed.

As bench gallows seem to be composed of two features – gallows and bench – it could be suggested that one feature is removed in the first line position to account for their lack of presence there. A bench gallows would become an ordinary bench. So the word [ckhy] becomes [chy], and so on.

The table below shows the line position statistics for the most common words with an initial bench gallows if the gallows were removed.

Line Position12345
[chy]119221315
[chol]1267545021
[chor]1056361611
[chey]01820148
[cheey]09641

The distribution statistics for words with initial [ch] do not suggest that bench gallows have been replaced with [ch] in the first position. All of the words are much less common in first position, as all words with initial [ch] are. In some cases – [chy], [chey], and [cheey] – the numbers are so low that there is no way to argue that additional words could have been added. Yet, for the hypothesis to be true, all such words should show an increase to accommodate the alternate words which previously had an initial bench gallows.

The bench feature has been removed.

As above, the bench feature could be removed to leave a gallows. So the word [ckhy] would become [ky], and so on.

The table below shows the line position statistics for the most common words with an initial bench gallows if the bench were removed.

Line Position12345
[ky]01514
[ty]00032
[kol]23643
[tol]101110
[kor]22431
[tor]51110
[key]00401
[tey]00010
[keey]04123
[teey]00211

The word [tol] shows exactly the kind of increase expected if [cthol] had become [tol]: an increase in the first position which is clearly above the normal distribution. [Tor] could be argued as having the same pattern, but we expect to see all words have this pattern, not only two. Words with initial [to*] are more common in the first position, with 50 occurrences against a normal 4-5, though that could be caused by any number of line patterns which affect the distribution of words.

An interesting result, but not the outcome we’re looking for.

Bench gallows are unpacked into a bench followed by a gallows.

In this case the bench gallows [ckh] would become [chk]. So the word [ckhy] becomes [chky].

Another table is unnecessary in this case: the words mostly don’t exist in any position. The words are valid, but so uncommon throughout the text. We would expect maybe 10 occurrences of [chty] in the first line position, but only 7 occur in the whole of Hand 1.

The hypothesis is defintiely wrong.

Bench gallows are unpacked into a gallows followed by a bench.

In this case the bench gallows [ckh] would become [kch]. So the word [ckhy] become [kchy].

The table below shows the distribution of words with initial bench gallows altered in this way.

Line Position12345
[kchy]07563
[tchy]12265
[kchol]26731
[tchol]21232
[kchor]65122
[tchor]103120
[kchey]20231
[tchey]03102
[kcheey]01100
[tcheey]01120

The word [tchor] alone appears to show the kind of distribution we might expect. The others definitely do not. And, as above, either all the word show signs on the correct distribution or the hypothesis should be considered false.

For the sake of completeness I also ran the statistics for replacing a bench gallows with a gallows followed by [sh] rather than [ch]. So [ckh] would become [ksh]. While [tshor] and [tshol] show promising signs of the correct distribution, not other words did.

Some more complex change happened.

This statement is really a final catchall possibility. A free pass for me to look for some possible set of words which could, be regular alterations, represent word initial bench gallows in the first position of a line. The only criteria are that the transformations must be regularly applied to all such words and they must all have the correct line distributions: common in the first position and less common (or rare) thereafter.

Where to look for these missing words, if we can look anywhere? Hand 1 contains 140 and 398 word with word initial [ckh] or [cth]. Line lengths vary but (accounting for labels which have a line length of 1) the typical line might have 8 words. So the numbers of words with initial bench gallows should be about 1/7 higher: 20 [ckh] and 57 [cth], or 60+ in total if we allow a margin of variability.

Perhaps the most promising are words with initial [o] or [qo]. Both are more common in the first line position, and much of the difference in both cases is due to words containing gallows, as the table below shows.

Line position12345
[ok*]10358815958
[ot*]9542435551
[qok*]8739737046
[qot*]8029323132

In general, these are the kinds of distributions we would want to see. There is plenty of “excess” words in the first position where bench gallows could exist. Although these words rarely contain bench gallows, they could be combined with another alteration. The most likely is having the bench gallows unpack to a gallows followed by a bench. So in these cases the word [ckhy] would become either [okchy] or [qokchy].

The next table will show the distributions of words with initial bench gallows altered in the way of [ckhy] to [okchy].

Line position12345
[okchy]31312
[otchy]40530
[okchol]11202
[otchol]102044
[okchor]33310
[otchor]62204
[okchey]31302
[otchey]22320
[okcheey]10000
[otcheey]00010

The distributions of most these words show no sign of additional occurrences in the first position. Only [otchol] shows a marked increase. This cannot be the correct hypothesis.

The table below shows the distributions of words with initial bench gallows altered in the way of [ckhy] to [qokchy].

Line position12345
[qokchy]127834
[qotchy]149294
[qokchol]23321
[qotchol]21222
[qokchor]52010
[qotchor]90110
[qokchey]10020
[qotchey]20221
[qokcheey]01000
[qotcheey]10000

Although the results are marginally better, with several words showing increased occurrences in the first position, none are very strong and all words should show a consistent pattern.

Summary

The nature of bench gallows is an unresolved question. Specifically whether or how they can be “unpacked” into constituent parts.

The start of lines in the Hand 1 text provides an opportunity to investigate this question, as word initial bench gallows occur far less in this position than they should. By finding what replaces such words we should gain an insight into the nature of bench gallows.

Multiple sets of words were proposed by regularly altering those words with initial bench gallows. However, there is no set of words which have a matching distribution for the missing words in the first line position.

This environment still has the potential for research into bench gallows, but the most obvious investigations provide no answers.

2 thoughts on “Can we unpack bench gallows? (No.)

  1. Why did you not mention Grove words, given that this is a mechanism that would interfere with pretty much all of your tables here?

    Incidentally, I had a quick look at tchor (which you incidentally flagged here). When tchor appears at the start of a line, it almost always appears at the start of a paragraph: however, when chor appears at the start of a line, it never appears at the start of a paragraph. Perhaps there are other patterns for which this kind of thing holds true, if you want to try to understand Grove words.

    Like

    • Hi Nick, I did consider whether to mention Grove words, but I knew it would complicate things even further. I excluded [cph] and [cfh] knowing that it meant the impact of Grove words would be smaller.

      But the main reason I didn’t mention Grove words is simply that I wouldn’t accept a single word as a positive match, but really sought a complete set of words with the correct distribution.

      (I’m also not totally convinced that all Grove words are unusual. Some must genuinely begin with a gallows.)

      Like

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