(09-07-2026, 08:37 AM)Aga Tentakulus Wrote: You are not allowed to view links. Register or Login to view.Almost certainly a case grid
That's very interesting. I haven't seen case grids being used in the early 1400s.
Furthermore, I have never encoutered a grid from medieval times where the symbols are binary
Why would they even do that?
No way this is a cipher, it must have something to do with calendar calculations. The page is all about the length of days and the moon etc.
There are 30 "digits" in the sequence
Is the bit at the end "Cristē 1"? i.e. maybe Christen?
Is that supposed to explain what 1 means?
15 1s; 15 0s...
EDIT:
It's explained here
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Search for 110111000001100111101000100110
I understand that 1 stands for Christians in a killing game against Muslims.
That's the optimal arrangement so that all Christians survive.
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Some people apparently couldn't even imagine a mathematical puzzle without xenophobic fantasies intruding
"A binary representation of a theoretical counting problem" in a medieval manuscript sounds like what an AI would come up with as a Voynich solution. But that's definitely it!
I'd be interested to know whether the use of zeros and ones was common in Europe during the late Middle Ages, or whether it was introduced only by mathematicians like von Gmunden. Does anyone know anything about this?
(09-07-2026, 02:20 PM)bi3mw Wrote: You are not allowed to view links. Register or Login to view.I'd be interested to know whether the use of zeros and ones was common in Europe during the late Middle Ages, or whether it was introduced only by mathematicians like von Gmunden. Does anyone know anything about this?
I remember a letter in Kircher's Carteggio (from the 1600s) where a Cardinal friend of his explains to him the binary number system as if it were a novelty. So it maybe was hardly common knowledge in the 1400s.
The novelty of the Arabic number system was not the fact that it expressed a number as the sum of powers of 10 times digits 1 to 9. The Etrusco-Roman number system already did that. It was not even using a single symbol for each digit 1-9. The Greek number system already did that.
The novelty was using the same symbols for the 9 digits in any position, which required a zero symbol to make the position unambiguous. (The Babylonians and Mayans already did that, but using other bases; and one had been forgotten for many centuries, and the other would not be known in Europe for many centuries to come.)
Thus the adoption of the Arabic number system by Europeans in the late Middle Ages did not automatically suggest to them that one could use other bases, like 2. The base was still 10 as they had been using since the finger-counting days.
Some people may have figured it out, but it probably seemed to them to be just a curiosity, like it apparently did to that Cardinal.
The English measurements of liquid volume are a base-2 system, which apparently developed between the 13th and 15th centuries. However its use has been limited to measuring liquids, not numbers in general. It also uses specific names for each position (gallon, pottle, quart, pint, etc.) so that it spans only a small range of values; and it has no symbolic notation like true binary. People would surely say "five pints" rather than "one pottle, no quarts, and one pint".
All the best, --stolfi
I have an idea. What if the person who found the Voynich manuscript, did not understand it, so they wanted to ssk someone who is expert. And Gmunden had teacher who worked with Oresme. Maybe they thought he could help, because the illustration in The Voynich manuscript is also copy from Oresme?
A bit of binary, Anne McLaughlin, 23 August 2022
Note: An early introduction of zero and one (MS/47, Tractatus de Arithmetica, ca. 1200).
Quote:MS 47, in introducing the new numbers, echoes exactly this definition: ‘1’ is the ‘unit’ (unitas), an object, something present and countable, while ‘0’, ‘has nothing of significance’ (cum nulla significatio), and only functions to define the absence of another figure.
So this number system was already known in the High Middle Ages. There was enough time for the possible development of a binary number system ( in the sense of a two-character code ) in the late Middle Ages. However, nothing on this subject could be found online.
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Edit: Here is another identical sequence from a different 15th-century manuscript. An astrological-medical compendium with a calendar,, BSB Clm 4394
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That's interesting; it shows different sequences. The topic is the rules for determining Septuagesima and Easter.
edit:
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