Hi Ed,
Please don't worry about the exact numbers. I completely understand the context of your argument, thank you for raising the level. It is great that you are working on a paper, if you have a pre-print or draft ready at any point, I would be delighted to offer a detailed review from the mechanical perspective.
Now, let's address the core of your critique. You argue that a simple machine would produce flat distributions and uniform entropy, and that to fix this, we have to add "bolt-ons" until the model becomes circular.
I believe this conclusion comes from viewing the Volvelle as a Random Number Generator, when in reality, we should be viewing it as a State Machine with Physical Interference.
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''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''
This is only true if every tooth on the gear is unique. But think about Hardware Redundancy. Imagine a gear with 24 teeth (or positions or whatever).
If I paint the syllable "ol" on 12 teeth. And I paint the syllable "daiin" on 1 tooth.
Even if the wheel spins with perfect random probability (flat distribution of movement), the result will be strictly Zipfian. "ol" will appear 12 times more often simply because it occupies more physical surface area on the Volvella. The Zipf curve in the VMS isn't proof of "common meaning", it is a map of repetition in the manufacturing of the wheel.
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Adjacent words tend to have similar lengths... 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.
You don't need a separate mechanism. You just need Nulls (Empty Teeth) and Gear Interference. If the third ring (Suffixes) has a cluster of 5 blank slots (empty teeth), whenever the gear hits that patch, the words generated are shorter (Root only).
About the Interference: If the rings have coprime tooth counts (Let's say that: Ring A has 17 teeth, Ring B has 19 teeth), they create a Moiré Pattern or "beat frequency": You are not allowed to view links.
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The "Blank Patch" on Ring B will align with Ring A for a sequence of turns, creating a "cluster" of short words, then drift away to create a cluster of long words. The autocorrelation is just the mathematical interference pattern of two mismatched gears spinning together.
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First-line words differ systematically from mid-page words... A volvelle would give you roughly uniform entropy across all those dimensions.
A volvelle gives uniform entropy only if it never stops. But a scribe has to physically stop at the end of a line.
This creates a Reset Cycle. If the machine is mechanically reset to a "Home Position" (using the Gallow as a lever) at the start of every line, the first word is drawn from a highly constrained set (Low Entropy). As the gears turn and "drift" away from the start, the possible states expand (Higher Entropy), until the Carriage Return resets it again. The positional variation isn't linguistic. It’s the tension and release cycle of the return mechanism.
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I'd say Rob's challenge still stands: What specific configuration of rings and teeth produces the observed frequency distributions?
To answer this concretely, the specific configuration isn't a language simulation. It is a 3-Ring Stack configured as follows:
1. High Redundancy on the Middle Ring: Painting frequent roots like "chol" on 50% of the teeth solves the Zipf/Frequency issue.
2. Coprime Tooth Counts (Like 17 vs 19): Mismatching the rings solves the Length Autocorrelation/Clustering issue.
3. Line-Start Mechanics (Reset): Resetting the lever at the margin solves the Entropy/Positional issue.
I don't need "bolt-ons." I just need friction, geometry, and a scribe who resets the lever when he hits the margin.
Alicia from Sicily
