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Roman numerals and entropy

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• Roman numerals and entropy

• Roman numerals and entropy

  Koen G > 05-05-2022, 10:06 AM

  Several people expressed their interest in the entropy behavior of Roman numerals. I decided to run a few preliminary tests to get a first basic idea of the numbers. These are just experiments, they do not represent any reality found in real manuscripts.
  
  First I made a list of numbers from 1 - 3500 and placed them in a random order. Then I used Excel's ROMAN function to convert these to roman numerals. I made a second version of the roman numerals file where they use additive notation (XIIII instead of IX). Then I made versions of each of these where final letters are replaced with swooped versions (IIJ instead of III). This resulted in five files to test:
  
  01: randomized list of numerals 1-3500
  02: list (01) converted to Roman numerals
  03: list (02) with additive notation
  04: list (02) with swoops
  05: list (03) with swoops
  
  I compared the h1 and h2 numbers to those of some Voynichese sections and a normal text (Chaucer). The green dot in the square is a minimally modified EVA version. I drew some arrows from the "best performing" Roman numeral version to modified EVA to Chaucer, just to make the graph a bit easier to read.
  
     
  
  As we see, a randomized list of Roman numerals has significantly lower h1 and h2 than Voynichese, as we probably could have expected. After all, Roman numerals only have seven characters, which can be increased to a dozen or so if some swooped versions are added. This lack of character variety explains why especially h1 is lower.
  
  These numbers are pretty far off, but there may still be room for improvement. Apparently there were medieval practices that included additional symbols for some numbers, like O for XI. (See for example You are not allowed to view links. Register or Login to view.). There is also mention of a system of lines or "brackets" to make numbers larger, for example | I | would be 100,000 or something like that. Or "( ( I ) )" is a way to write 10,000. If a bracket system is used to enlarge numbers, it might explain benched gallows. But testing this would require some more thought, time and planning than this initial experiment allowed.

• RE: Roman numerals and entropy

  Bernd > 05-05-2022, 11:52 AM

  Excellent, thank you!
  
  This is what I wanted to see, the VM falls in the middle between the entropy of pure numerals and pure text.
  Now we need some real world examples containing a high amount of roman numerals contemporary with the VM.
  If we assume such documents do not only consist of numbers but also operators / descriptions we might be getting somewhere.
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