Emergent properties in text generation using tables and grilles

Gordon Rugg’s 2004 Cryptologia article showed that using text generation tables combined with modified Cardan grill es can produce text with complexity and structural properties similar to those of the Voynich manuscript. A suggested topic for further work was investigation of the properties arising from tables more highly structured than those used in that article. This article describes our recent work in this area. It: • clarifies some common misunderstandings about the table and grill e method • describes findings from our work on highly structured tables, and • tests some hypotheses arising from this work We conclude that several unusual properties which occur in the Voynich manuscript arise naturally as emergent properties from using highly structured tables in conjunction with modified Cardan grill es. These include the following: • a high proportion of “blank” words, leading to variable line lengths • different frequencies of the same syllable in different parts of the table • sections consisting mainly of long words alternating with sections consisting mainly of short words, and • words which are common in text produced using one grill e being absent from text produced using a different grill e on the same table Some side-effects of this method would, unless corrected, be easily visible in a meaningless hoax document. Correcting these side-effects will i n turn result in different regularities in the output text. One side-effect, mentioned briefly in the Cryptologia article, is that the movement of grill es across a table has to include a significant proportion of random movement, to break up regularities in syllable patterns. A related issue is that the first word on each manuscript page has to be generated in a different way from “normal” text, to obscure regularities which would otherwise be apparent. We are examining the manuscript to see whether these features are present, and will report our findings in a future document. Introduction: some common misunderstandings The Cryptologia article describes how text generation tables can be used in conjunction with modified Cardan grill es to produce text with similar properties to Voynichese. This demonstrated that it was possible to produce text with similar complexity to Voynichese as a meaningless hoax, implying that the Voynich manuscript could have been hoaxed. That is a separate question from whether the manuscript was hoaxed. It is also a different question from whether the manuscript was produced using this method, either as a hoax or as a ciphertext. An argument has been made that if the manuscript were produced using tables and grill es, then it would be possible to reconstruct one or more pages of the manuscript through reconstructing the original tables and gril les. This argument is based on a misunderstanding of how tables and grill es are used in the production of meaningless hoaxes. This section provides a brief summary of the method to clarify this point, and to provide background for some of the points raised below. The table and grill e method produces Voynichese-like text by using a large table of meaningless syllables (about 40 rows by 39 columns) which are combined by using a modified Cardan grill e. The grill e is moved semi-randomly across the table. For simplicity, we have used Stolfi’s breakdown of Voynichese words into three components, namely prefix, midfix and suff ix, although tables can be used with other breakdowns if desired. (We use the term “midfix” rather than “ infix” , with “midfix” referring specifically to the middle slot in Stolfi’s model. There are other models of Voynichese which go beyond the scope of this document, and for which “ infix” would be used differently from “midfix” .) The table fragment below ill ustrates how the method is used. For clarity, we have used different colours to show how each sequence of three columns fits together, with a sequence of prefix, midfix and suff ix columns. For instance, the first column contains prefixes such as “qo” in red, the next column contains midfixes such as “chek” in red, and the third column contains suff ixes in red. This pattern is repeated in the next set of three columns, shown in blue italics, and again in the third set of three columns, in green bold characters. (The tables we actually use are monochrome –we have coloured the cells below to help ill ustrate how the method works.) Some cells are deliberately blank. qo chek ol she dar sol dy she dy qo kee dy she y y k y tee y qo ke dan ol dor y dy k qo t dy or che dy o che dor A grill e is a piece of card, with slots cut in it. Two examples are shown below. Grill e 1 has three slots in a diagonally descending sequence. Grill e 2 has three slots in a “rise and fall ” sequence. If grill e 1 is placed over the red cells of the table fragment, with its prefix slot on the top row, it will reveal the word “qoshey” . If it is now moved to the blue cells it will reveal the word “olkeey” , and if moved straight across to the green cells it will reveal “solshedan”, making the “sentence” “qoshey olkeey solshedan”. When moved to the second row, it produces the words “kdor qotee ke” . If we repeat this with grille 2, the first line we produce is “cheky qoshey y” , and the second is “ yshedor kee qoshe”. At first sight these look like quite different sets of output, but if we put the first line from grill e 1 next to the second line from grill e 2 and tabulate them, then a regularity becomes apparent. grill e1 qo she y ol kee y sol she dan grill e2 y she dor kee qo she Although the grill es have combined the syllables into different words, the midfixes in these two lines are the same in consecutive words (and, li kewise, the prefixes and the suff ixes derived from the same row of the table will occur in the same sequence unless something is done to prevent this). One simple way of breaking the regularities is to introduce some randomness into the grill e’s movement – for instance, by skipping from the red columns directly to the green, without generating a word from the blue columns, or by moving down two rows part-way across the table, or by moving to a completely different part of the table. Other ways include introducing an arbitrary division within the word generated – for instance, breaking “qochedy” into “qoche” and “dy” – and introducing extra words such as “daiin” , or concatenating two successive words. This means that the same table and grill e, used in this way, will produce different output each time they are used. Introducing a random movement two or three times per line would mean that the longest regular sequences would consist of only a few items (for instance, four words containing the same sequence of midfixes). Given the highly repetiti ve nature of Voynichese, it would be very diff icult to distinguish between a “genuine” repetition produced by two different grill es moving across the same section of table, and a “spurious” repetition, where the same sequence of (say) midfixes occurred by chance. A possible exception would be when a very rare character is used, and are currently examining the manuscript for such cases.