Axial Symmetry in Lines

In this study I am exploring the hypothesis that the red line of text on f67r is a model or template for other lines of Voynich text. 

Specifically, in a previous post, I exposed the symmetries of this red text. It is this palindromic pattern that might – in this hypothesis – form a basic pattern of lines. 

Here is the pattern:

There is a central axis of the line and features of the text are mirrored either side of this axis.

In the red text line we find a word duplicated at this midpoint, and we find symmetries either side of them. 

What we are looking for, then, are cases where a word (or similar words) are duplicated at the midpoint of lines – how common is this? – or, more broadly, any case where we find symmetries around a central axis.

The proposal is that lines of text are organized around an axial point. 

Much research has been done on line starts and line ends. This is a different approach to the study of lines, suggested by the red text on page f67r. 

* * *

In the first instance, we will search by just counting words in a line and going to the midpoint. If there are ten words, the midpoint is the space after the fifth. And so on. 

Such is the case in the first line on the first page:

fachys.ykal.ar.ataiin.shol.shory.cthres.y.kor.sholdy-

We have ten words. The axis is between [shol] and [shory]. 

Thus we find two similar words either side of the axis. 

fachys.ykal.ar.ataiin.shol.shory.cthres.y.kor.sholdy-

It is hard to detect any further symmetries, but there are some important ones. 

[ykal] and [y.kor] offer a symmetry involving the gallows [k]. 

Then we notice the same symmetry in the glyph [t] – there is a [t] glyph either side of the axis. 

Thus we have this palindromic pattern:

K   T  shol – shory  T    K

Moreover, note how the glyph [a] is only found on the left side of the axis (i.e. the first half of the line:

fachys.ykal.ar.ataiin.

shol.shory.

cthres.y.kor.sholdy-

This is exactly the same type of pattern that we find in the red text line. 

Again: the method is simple. Find the axis of the line and then be sensitive to any symmetries around that axis. 

* * *

Another example:

Line 4 from f30v:  

chotchol.daiin.cthol.doiin.daiin.chokeor.dal.chtoithy-

Eight words. The axis is after [doiin]. 

Here we find the symmetry of [doiin] and [daiin]. 

From this point another pattern emerges. The initial glyphs of words run in alternations of [ch] and [d]:

chotchol.daiin.cthol.doiin.

daiin.chokeor.dal.chtoithy-

In this case there is no obvious pattern to the gallows glyphs, but there is to word initial glyphs. Thus:

CH  D  CH  DOIIN – DAIIN CH D CH

* * *

How widespread is this phenomenon? I don’t have the facilities or the inclination to undertake detailed statistics – but it is probably easily done. 

We learn more – and avoid all the pitfalls of global statistics – by looking at particular cases. 

It does not take long to find lines that do not conform. 

Some lines clearly do. 

Here is a line that presents our paradigmatic word QOKEEDY as the axis:

dol.sheey.qol.olkshey.qokeedy.olkeedy.qol.okaiin.oly-

Line 16, f79v.

There are nine words, so the axis is the fifth. 

dol.sheey.qol.olkshey.

qokeedy.

olkeedy.qol.okaiin.oly-

There is mirroring around this axis. This line is palindromic. 

In other cases the symmetry is harder to see and, although there, is not obvious or pronounced. 

See this line, line 25 from f83r:      

qokeedy.qolchey.qokeey.qokedy.chedy.otal-

Six words. The axis is after [qokeey]:

qokeedy.qolchey.qokeey.

qokedy.chedy.otal-

There is axial symmetry between [qokeey] and .[qokedy].

Otherwise the points of symmetry are the [che] and the [l], with these found either side of the axial line:

qokeedy.qolchey.qokeey.

qokedy.chedy.otal-

The only palindromic pattern is:

L  CH  QOKEEY – QOKEDY – CH – L

In some cases we find duplicated words at the line midpoint but little symmetry beyond that:

Line 16, f84r:

sor.ol.olaiin.oqol.yqor.or.ckhedy.chkedy.

okain.shedy.qokolchedy.olain-

Twelve words. The axis falls between [ckhedy] and [ckhedy]. Thus:

sor.ol.olaiin.oqol.yqor.or.

ckhedy.

chkedy.

okain.shedy.qokolchedy.olain-

But what symmetries are there beyond two versions of the word [olaiin]?

* * *

Nevertheless, I conclude that the pattern we find in the red text line on page 67r is at least one pattern upon which Voynich text lines are modelled. 

Importantly, it alerts us to the midpoint of the line as the axis for patterns and symmetries. It suggests a method worth pursuing. Let us divide lines in half. 

R.B.