How multi-character substitution might explain the voynich’s strange entropy

[obelus]

I measured n-gram entropy per word

I am following the discussion with interest... and concern about the numerical values calculated for high-order conditional entropies (if I understand your methods correctly).

Consider an infinitely long Cuva text sample with its characters randomly scrambled.  The first-order entropy remains 3.85 bits, as calculated from the character frequencies.  Because all correlations between characters have been removed, all conditional entropies of higher order are also 3.85 bits.  The true "Entropy vs n-gram order" curve in this case is a flat line at 3.85 bits, out to n=14 and beyond.

Already at n=4, however, the value calculated from a character-scrambled version of the complete but finite-length Cuva text is only 3.39 bits, and by n=14 it will be approaching zero.  So in this case at least, tailing off of an "Entropy vs n-gram order" plot would be a numerical artifact. As mentioned elsewhere in these pages, the geometric increase in possible n-mers requires geometrically longer text samples in order to obtain quantitatively correct values.  Shorter text samples will tail off sooner.  And a correct monotonic decrease, acting in concert with a steeper numerical decrease, can potentially create a qualitative bump in the curve.

It is tempting to assign "entropy" to a single text sample (which I might call a "micro-message").  But the sequence of characters is known, so all of the probabilities are unity;  insofar as it can be said to have an entropy, the value is exactly trivially zero.  The meaningful entropy that we discuss here should be attributed to the text generator ("macro-messenger"), as a logarithmic measure of how many different micro-messages it is capable of producing.  Approximate values at various orders can be calculated from one micro-message, but the accuracy of approximation depends on its length.  I expect that there are formulas in the literature that relate n-mer order, sample size, and systematic error.  The only way to evaluate high-order conditional entropies of the VMS author is to discover more text that it produced.

I look forward to new experiments!