A hand procedure of the period

Walk-through pages, on which the reader can run the procedures described here: ‘Writing Voynich with the Large Tables’.

The question. This test asks whether a scribe of the years 1404 to 1438 could have written a text with these properties using only what was on a desk of the time. The devices allowed were tables written out on parchment, lots or dice or playing cards to draw from them, a ruler, and the page in front of the writer. The Cardan grille of 1550 and the cipher disk of 1467 are later than the parchment, so neither was allowed. The generators above are computer models. This test instead builds a procedure a person could follow step by step, simulates it with every random act counted, and scores its output on the same battery (the set of 23 statistics) as everything else.

The procedure. It has six steps and two sets of tables, one for each Currier regime (one of the two writing styles Prescott Currier identified, A or B). The tables hold the commonest 600 words of the regime, laid out in 1,500 cells in proportion to their frequency, so that a common word occupies several cells and a rare one none. Six further rows hold the words that follow a word ending in y, in n, in r, in l, in s, d or o, and in anything else. Two further tables hold the words that begin a line and the words that end one. A table of 200 spelling changes holds the commonest ways a rare word differs from a common one, such as "drop d after e" or "write sh for ch at the start of the word". A small table of glyph successions serves the few words in a hundred that are built glyph by glyph. A working sheet of 30 cells lies on the desk, and at each new page the writer strikes out a tenth of the sheet, a fifth at a new gathering, and refills the struck cells from the tables. Then, for each word, one draw picks the source. In 15 cases out of 100 the writer copies a word from the line above, found with a ruler, or from the last four words written, and changes its spelling with one rule. In 40 the word comes from the sheet, and in 45 from the row that matches the last glyph just written. Two words in five drawn from the sheet or the rows are changed by a rule, and some of those by a second rule. The first word of a line comes from the line-head table, and the last from the line-end table. Throughout, the writer has to remember nothing beyond the last glyph written. The rates were fitted to twelve statistics and the recurrence profile, and everything else the procedure produces is a prediction. In all it takes 17,976 table cells written once and about five random acts per word, 177,000 for the whole book. A companion page, Writing Voynich with the Large Tables, lets a reader throw the lots word by word and watch a line of this text take shape under these rules.

What it reproduces. The full procedure lands within tolerance (the range a statistic wanders over between random halves of the text's pages) on 9 of the 23 statistics and within three tolerances on 21, with a total misfit of 33. The procedure without the working sheet reaches 11 and 22, with a misfit of 32, but it has no clustering beyond three lines. No other generator comes close on the same footing. The slot template of this examination reaches 10 and 15, the drifting-state generator 3 and 11, the copying generator of Timm and Schinner's kind 3 and 4, and the table and grille 3 and 3. The procedure gives the open vocabulary, with 6,609 distinct words against 6,983 and the same share of words used once, and it gives the line rules. It also gives the near-copying of neighbours, the word-order information at the word level (0.101 bits against 0.113) and a page burstiness of 1.82 against 1.96. The renewed sheet gives the recurrence of words across the page, the leaf and the gathering at the measured strength, which is what the drifting state of the generator below supplies. Each device is needed, because removing any one of them loses something the text has. Without the spelling rules the text has 1,026 distinct words, and without the boundary rows the word-order information vanishes. Without the line tables the line-edge rules go, without copying the near-copying goes, and without the sheet the page-scale clustering goes.

What it does not reproduce. The spread of word lengths is 1.87 against 1.79, and the information in the start of a word is 0.43 bits against 0.48. Both misses come from the spelling rules, which see one glyph of context and can stack, and so write words the manuscript never writes, such as qqokeedy. Of the distinct words the procedure produces, only 27 in 100 occur in the manuscript, though its rare words are as close to its common words as the manuscript's are. Words come back on the neighbouring line too often (5.96 times chance against 4.58) and two to three lines away too rarely (2.86 against 3.55), because a ruler reaches one line. The dependence across the word boundary is right at the word level and under half the measured strength at the glyph level. Two table sets, one for each regime, give the difference between Currier A and B with the right sign on every measure but not the right size. The glyph-level difference is too large, the gap in glyph predictability is half the measured one, and the sharing of vocabulary is too low, while one table set for both regimes gives no difference at all. Three limits of the test need stating. The tables were filled from the manuscript's own words, so the test shows that such tables suffice, and it does not show how a scribe would have composed them. The procedure, likewise, was only simulated and was never carried out by hand. And the apparatus is large. About 18,000 cells, some 60 page sides at 300 entries a side, is more than a scribe is likely to have written out. Whether a far smaller set of tables and devices can do the same work is the question the next subsection answers. Two further faults come from reading the manuscript's own pages, as the subsection after that describes. The ruler step is not supported by the page evidence. When a word in the text has an exact copy on the line above, the copy stands within one position of it 1.24 times as often as chance. This procedure's copies stand there 1.37 times as often. The derivations of inner words from the line above sit within two positions of the word 0.196 of the time in the text, against 0.838 here. And the two table sets give the two regimes different vocabularies, where the page evidence gives the hands different rates of new words. Hand 2 writes a word used nowhere else 0.100 of the time and hand 3 0.146 (hands 2 and 3 being two of the five scribal hands), while this procedure writes 0.125 and 0.126 for the two. The companion page shows the procedure as fitted, ruler included.

What it means. No property in the battery, the recurrence profile or the regime comparison needs a language behind the text. The reason is that a writer with these tables and a die produces all of them within three tolerances except two, and those two are traces of the rule mechanism. That does not show that the manuscript was made this way, since the identity of the rare words is not reproduced and the section vocabularies were not tested, so the account stays the best guess, not confirmed.

Earlier work. Rugg (2004) proposed a table and a Cardan grille as a hand method, and Rugg and Taylor (2017) proposed that it reproduces the text's statistical features, though the grille dates from 1550 and so falls outside the period. Timm and Schinner (2020) proposed a self-citation method, in which each new word is copied with changes from a word already on the page, and that method can be carried out by hand. Zandbergen (2021) described rotating wheels of word fragments. The procedure here takes Rugg's tables without the grille and Timm and Schinner's copying with a ruler, and it adds the boundary rows, the spelling rules and the renewed sheet. What is new is the restriction to devices in use before 1400 and the count of random acts per word. New too are the scoring on the full battery beside the published generators, the removal of each device on its own, and the test of the two regimes with two table sets.