[split] Volvelles or Disks

[DG97EEB]

It's a nice idea, but one that has been tested extensively. In my experience, even with a drift mechanism, the mechanical coupling can't simultaneously produce the high autocorrelation, low repetition, Zipfian distribution, and entropy profile that VMS exhibits.

Hi Ed,

I'm really intrigued by the tests you mentioned. Would you mind sharing any links or specific thread titles from the forum where this was discussed? (From the forum or any other source please)

The high autocorrelation isn't a linguistic choice. It’s a physical one. If the rings are interlocked, the state of the first glyph (the Gallow) forces the starting position of the next. 

About the Zipf’s Law and Entropy, in a natural language, you have infinite ways to combine letters. In a machine/volvelle, you only have a finite number of ''gear teeth''. This 'limited menu' is exactly what creates the low entropy and the flattened Zipfian curve that Mr René Zandbergen and Mr Jorge Stolfi identified.

If we assume the author was simply aligning rings and writing down the result instead of writing sentences, those "impossible" patterns become the natural result of using a tool like that.

Alicia

Hi Alicia,

I'm working on a couple of papers and haven't published anything yet, but below is a summary of where we get to.. I'm sure others will challenge the exact numbers, but that's not really the point of my reply.

The autocorrelation issue in VMS isn't character-to-character, it's word-length-to-word-length. Adjacent words tend to have similar lengths (AC1 around +0.16). A geared ring constrains which glyph follows which, but for it to produce word-length clustering you'd need something controlling how many rings engage per word, and that's a separate mechanism sitting on top of the volvelle. Once you need that, the volvelle isn't really doing the explanatory work any more.

On the Zipf point, a finite mechanism with a limited number of gear positions actually predicts the opposite of what we see. If each position is roughly equiprobable you get a flat distribution, not a Zipfian one. Zipf requires that some outputs are massively more frequent than others, which in natural language comes from the fact that common words carry common meanings. VMS has a robust Zipf distribution. That's one of the stronger arguments that something language-like is going on, not something mechanical.

The entropy is indeed lower than most European languages, you're right, but the pattern of how it varies, by position within a word, by position on a line, by position on a page, and by manuscript section, looks linguistic rather than mechanical. A volvelle would give you roughly uniform entropy across all those dimensions. VMS doesn't do that. First-line words differ systematically from mid-page words, Herbal-A sections differ from Biological sections, and there are at least two scribal hands with different frequency profiles. Each of those needs a separate bolt-on to the volvelle model, and at some point the bolt-ons are doing all the work.

What you're really getting towards is constrained Markov chains, drift mechanisms over lookup tables, coupled ring simulations etc, and the consistent result is that you can match some VMS statistics but not the full package simultaneously. Tight coupling gives you the autocorrelation but produces about 14% repeated words (VMS has around 2%). Loosening the coupling fixes repetition but kills autocorrelation. There's a narrow statistical zone where VMS sits that none of the mechanical models reach without becoming circular.

None of this means the idea is worthless, by the way. If you strip away the physical metaphor, what you're really proposing is a state-dependent generation system with constrained transitions, which is a perfectly reasonable computational model. The question is whether calling it a volvelle adds explanatory power or just dresses up the problem in hardware. I'd say Rob's challenge still stands: What specific configuration of rings and teeth produces the observed frequency distributions? If you can answer that concretely, with numbers, you'd have something genuinely new.

Looking forward to seeing where you take this.

Thanks,

Ed