Chimeric plants: why botanists see different species on the same page

The argument about the Voynich plants has been running for a hundred years and always to the same pattern: a specialist looks at a page and names a species. Another specialist looks at the same page and names a different one. Both are confident, both are competent. Some see European henbane, others a Mexican sunflower.

We decided not to take part in the argument but to explain it. The hypothesis is simple: the problem is not with the experts but with the way the drawings are built.

What we measured

If an artist draws from life, the features of a plant are connected to one another: from the type of leaf one can predict, with some confidence, the type of root, and from the flower the structure of the stem. Nature does not combine them arbitrarily.

If, on the other hand, a drawing is assembled from ready-made parts, that connection weakens: any leaf may end up attached to any root.

The connection between features is measured by mutual information. This is not a judgement of "looks like it" or "doesn't", it is a number.

How the experiment was set up

The plan was written down in advance, before any coding, so as to exclude fitting. The coder was a person who did not know which hypothesis was being tested and worked blind: he was given a deck of 64 cards with plant drawings from three sources shuffled together, and marked the type of leaf, the type of root and the type of flower on each card.

The three sources:

• the Voynich manuscript - the object of study;
• Dioscorides - the classical herbal, whose drawings go back to drawing from life;
• the herbal of Manfredi - a stylised herbal of the Voynich period. This is the key control: it shows what the connection between features looks like in a conventional, crude, schematic drawing of the same time.

The result

The difference between Dioscorides and the Voynich is significant at p = 0.0068. The difference between Manfredi and the Voynich is significant at p = 0.0254.

The second number matters more than the first. It closes off the main objection, that the Voynich has a low connection simply because its drawings are conventional. Manfredi is conventional too, and his features are still more than twice as strongly connected. The low connection in the Voynich is not an artefact of crude drawing but a sign of combinatorial assembly.

What follows from this

First, the century-old argument about species gets an explanation. Under combinatorial assembly, every specialist completes the whole from the parts he recognises and sees the flora he knows best. The argument is unresolvable, and not through any fault of those arguing. The same applies to the Aztec version with its 37 Mexican plants: the identification there rests on the same unreliable channel.

Second, the botanical route to a reading is closed. If the species of a plant cannot be established reliably, then its name cannot be used as a hint to the text either: see Bax's route.

Third, and this is the most interesting part, the structure of the drawings turns out to be the same as the structure of the text. Three quarters of Voynich words are assembled to the scheme "prefix plus root plus suffix" out of a small set of elements. The plants are assembled the same way: out of a small set of leaves, roots and flowers. One and the same combinatorial principle in two different materials.

What we do not know

Here we are obliged to stop and name the open question.

A low connection between features is explained equally well by two different things:

1. A defence against identification. The drawing is deliberately made so as not to serve as a hint to the enciphered text. 2. The modelling of crossings. The artist was depicting not existing plants but combinations - for example, ideas about where cultivated varieties came from.

They can be told apart: breeding predicts clusters of recurring combinations of "parental" features, while a defence against identification predicts uniform independence. We have the data for such a test, but not much of it - the 64 cards include only 20 Voynich pages, and the power of the check is low.

We state the caveats on the whole piece of work plainly: there was one coder, the significance passes a strict correction for two comparisons only marginally, and the coding noise is around half. This is a result at the level of "supported", not "proved".

Why we value it

Out of the whole recent wave of our checks this is the one positive result. Everything else consists of honest zeros: versions rejected, routes closed, our own conclusions retracted. That proportion is what research looks like when the answer is not being fitted.

No decipherment of the Voynich manuscript exists, and we claim none: a coincidence is not a reading.

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