The best guess: a procedure

Of the seven explanations of the Voynich text, a procedure is the best guess, not confirmed. A procedure is a fixed set of steps carried out by hand with dice and tables of words. What follows is the guess, not a fact about the book.

The ‘we’ of this page means computer programs. They took the measurements and wrote these pages. No person has checked these numbers by hand. The checking that exists is programs re-running each other's work from the manuscript's own text.

We built three procedures. The first has large tables of 18,000 entries. The second has small tables of a few thousand. An entry is one word or part of a word. The third has rules worked out from the manuscript's own pages. A computer program writes text by the procedure's rule. Text written that way is an imitation. We scored the imitations of both sizes of table on the 23 measurements. A measurement is one thing measured on the text, such as the average length of its words.

Below are the three procedures and the test the second and third fail. The other six explanations are on the page ‘What the tests conclude’.

What would be on the desk

On the scribe's desk lie numbered tables of words. The scribe is the person writing the book. Each word in the tables is an entry with its number. In the imitations the tables hold the manuscript's own words. That is because the scribe's real tables, if there ever were any, are lost. Real tables would be written on parchment. Parchment is prepared animal skin.

Beside the tables lie dice, or lots. Lots are marked slips drawn from a bag. They do the work of dice. There is also a ruler. The scribe lays the ruler along the line just finished. It then shows the word standing directly above the place where the next word will go.

Last there is a working sheet. A working sheet is a list of thirty words. It can be kept on a wax tablet. A wax tablet is a wax-coated wooden slab that can be written on and wiped. The sheet holds words the scribe is drawing on for the page in hand. It changes slowly as the pages go by.

How a word is written

For each word the scribe throws the dice once. The throw decides where the word comes from: the working sheet, the line just finished, or the tables. Some come from the working sheet. Some are copied from the word directly above, with one spelling change. The ruler finds that word. The rest come from the tables. Further throws give a number. The scribe copies the entry with that number.

Not every word from the tables is copied whole. Some are spelled fresh, sign by sign, as the section on the first two procedures says. Counting the throw that picks the source, a word costs about five throws.

Two words in five come from the working sheet, a short and slowly changing list. So a word used on a page tends to be used on it again. The manuscript's words do the same. Text written by chance alone, with no such list, does not. At each new page the scribe strikes out a tenth of the sheet's thirty words. Their places are filled from the tables. A bundle is a set of leaves sewn together as one part of the book. At each new bundle a fifth of them are struck out.

The first two procedures

The first procedure has large tables, of 18,000 entries. Its text matches 21 of 23 measurements. No other explanation's imitation comes as close.

It misses two measurements. One is how much word lengths vary around the average. The other is how much the start of a word tells about the signs that follow. A sign is one letter of the manuscript's own alphabet.

Both misses come from spelling words sign by sign. Not every word from the tables is copied whole. Some are spelled fresh. With the large tables a fresh word is spelled sign by sign. Each sign is chosen from the one before it. Signs can then pile up. So some words come out too long. The manuscript never writes such words.

The large tables have a second fault, their size. Lot books were books of answers picked by dice. The lot books of the time held from 784 to 1,296 answers. The large tables hold 18,000 entries. That is about fourteen times as many as the largest lot book. So we looked for a procedure a scribe could really have owned. Its tables would hold a few thousand entries at most. That is enough to fill about ten sides of parchment. A side is one face of a leaf.

The second procedure, with small tables, is the best of some forty kinds we tried. Among them were lot books, tables read by dice throws, and tables of word parts. A table of word parts holds beginnings and endings of words. A new word is spelled by joining them. We kept the kinds closest to the manuscript on the 23 measurements.

The best small tables match all 23 measurements on the whole manuscript. The smallest of those have 2,870 entries. They fill about ten sides. A word can have more than one entry. That makes the dice pick common words more often. Once repeats are dropped those entries are about a thousand words and word parts.

But those tables were tuned to fit. The procedure has rates. One is how often a word comes from the sheet. Another is how often a word is copied from the line just finished. We set every rate to make the text match the whole manuscript. So matching all 23 measurements on the whole manuscript is partly what the small tables were made to do.

So the smaller tables are not better than the large ones. They are less tested, because we chose them for their fit. Small or large, the tables hold the manuscript's own words. So a match on the whole manuscript shows less than it sounds. Only a test on pages the tables were not built from treats every size alike.

The harder test

The easier test is the one above. Its tables are filled from the whole manuscript. The procedure is then scored on the whole manuscript. The harder test fills the tables from half the manuscript only. So they hold only the words of those pages. The test then asks the procedure to write the other half. Those pages are scored against the manuscript's own.

That is done five times over. Each time is one run. In each run we divide the pages in two a different way. We fill the tables from one half and test on the other. Then we swap the halves and do it again. So each run tests both halves.

We put the small tables and the third procedure through it. The third procedure is described in the next section. Both fail it in the same way. Each writes too few words that appear only once. The shortfall is measured against the manuscript's own wobble. To find it, we cut the manuscript into two halves at random, many times over. We noted how far apart the two halves usually fall on the share of words used only once. That distance is the wobble. A miss of more than three times the wobble is a clear miss.

About two thirds of the manuscript's distinct words appear only once. The manuscript's distinct words are its words with repeats dropped. The procedures do spell new words and not only copy them. Even so, in the pages they write far fewer words appear only once. On most of the five runs the shortfall is a clear miss. That is more than three times the wobble. On the other runs it is short by less.

The procedure worked out from the pages

We built the third procedure another way. Its rules were not chosen for their fit. They were worked out from the manuscript's own pages. We counted which words copy an earlier word and which are spelled fresh, sign by sign. A copied word repeats a word already standing nearby on the page, such as the word directly above. At most one sign is changed. A word spelled sign by sign is built afresh, one sign at a time. Each sign is chosen by the sign before it.

The third procedure copies a nearby word only rarely and has no ruler. That is because the manuscript's pages show fewer copied words than the imitations with large tables do. The large tables copy about fifteen in a hundred words from the line just finished.

The third procedure uses lots, a working sheet and a table of 200 words. Five scribes wrote the book. Their handwriting can be told apart. Each of the five scribes has a table of their own. A new word has its length settled first. It is then spelled to that length. The third procedure's once-used words are closer in shape to the manuscript's than the other procedures' are. But it still writes too few of them.

On the whole manuscript the third procedure matches 22 of 23 measurements. That is one fewer than the 2,870-entry tables. On the harder test it does no better than the small tables. It fails that test as they do, with too few words used once.

Could a scribe of the time have done it?

Yes, with the tools of the time. The manuscript's parchment dates from 1404 to 1438. An ordinary lot book of the decades before held about a thousand answers. The smaller tables hold about a thousand distinct entries. They fill about ten sides. Lot books show dice in use for picking text. A working sheet of thirty words fits on one school wax tablet. Whether the manuscript was written this way is another question. The procedure stays the best guess, not confirmed.

The verdict

So the best guess is the procedure itself, with no size of table picked out. It is not confirmed. The large tables miss two measurements. The smaller ones and the third procedure fail the harder test. The large tables were never given the harder test. So how they would do on it is not known.