Those are both very pertinent questions, tavie. And both are somewhat tricky.
The way I think of h1 and h2 is that they form an entropy fingerprint of a language together. Dividing or subtracting both values is an attempt to integrate both. In my most recent writing about entropy, I preferred to use a scatter plot instead because this just shows both values as they are.
The thing to keep in mind is that texts with a similar h2 but different h1 (or the other way around) can be very different entropy-wise. For example, I have medieval German texts with a similar h1 to Voynichese (even one with a lower h1 than all Voynichese samples). But their h2 is much higher than that of Voynichese, so they are still no good candidate, and trying to map Voynichese to this type of German would fail spectacularly.
Let me try with the tea example. So let's say that I found out that you are observing my tea consumption and I want to mess with your results. Instead of 10 types of tea, I buy 100 different types (this is actually possible). My h0 goes through the roof. If I consume all teas at a similar frequency, h1 will shoot up as well. This in turn may impact my h2 as well.
Now, h0 is an unreliable stat because it doesn't even take frequency into account. Like I said before, adding a single "&"-sign at the end of a 200-page book will impact its h0 the same way the frequent letter "e" does. But h1 tells us a bit more and is a bit more sturdy. If I add a letter and make it frequent, h1 will change more than if I just add a single token of the new type. So we can use h1 and h2 to fingerprint a text's entropy behavior.
Some extreme examples:
Low h1 + low h2: one or few types of tea dominate the selection, and teas are consumed in an ordered manner. If I drink mint and Earl Grey alternatively, you have a good (50%) chance of predicting which tea I will drink even without knowing which tea I drank yesterday (low h1). But if you know which tea I drank yesterday, you have a 100% chance of predicting which one I will drink today.
Low h1 + high h2: a few types of tea dominate the selection, but there is no pattern. In this case, your guess between mint and Earl Grey will always be 50% chance correct. For h1 these are decent odds, but h2 does not help us.
High h1 + low h2: many types of tea are consumed in similar frequencies, in an ordered manner. If I consume all 100 teas in a fixed order, you only have a 1% chance of guessing correctly without prior knowledge. But if you know what I consumed yesterday, you can predict confidently what I will drink today, despite the high h1. In this example and the first example, my odds of predicting today based on yesterday are the same, but the tea consumption landscape is completely different. Same h2 with a different h1 can mean we are looking at a very different text.
High h1 + high h2: many types of tea are consumed in similar frequencies, but there is no pattern. It is hard to predict anything at all.
In summary, when comparing Voynichese to another text, we want to be able to compare the glyph inventory and its use. H1 and h2 together give a more complete picture. And when modifying a Voynich transcription, we want to avoid introducing an absurd amount of different glyphs. But since rare glyphs are not interesting for the "broad" stat of entropy, h1 is a better gauge than h0.
2. Abbreviations: we tested this once, but I'm writing on my phone so I'm going by memory. One might hypothesise that abbreviating reduces entropy, because the same symbol is often found at the end. So the fact that abbreviation symbol is followed by a space is predictable.
Now remember that Voynichese has a lower h1 than most texts. You should now know what will happen if we introduce frequent abbreviation symbols in a regular text: h1 will increase. So even if you do manage to decrease h2 (which is not guaranteed), you will push h1 the wrong way. I didn't realize this yet, but question 2 is actually a good example for question 1
Edit: I forgot to add that some types of abbreviation will increase h2. For example, if you drop common endings, the final letter of words may become more unpredictable. Therefore, abbreviating will always increase at least one of h1 or h2, possibly both. And what we are looking for is a decrease.
The way I think of h1 and h2 is that they form an entropy fingerprint of a language together. Dividing or subtracting both values is an attempt to integrate both. In my most recent writing about entropy, I preferred to use a scatter plot instead because this just shows both values as they are.
The thing to keep in mind is that texts with a similar h2 but different h1 (or the other way around) can be very different entropy-wise. For example, I have medieval German texts with a similar h1 to Voynichese (even one with a lower h1 than all Voynichese samples). But their h2 is much higher than that of Voynichese, so they are still no good candidate, and trying to map Voynichese to this type of German would fail spectacularly.
Let me try with the tea example. So let's say that I found out that you are observing my tea consumption and I want to mess with your results. Instead of 10 types of tea, I buy 100 different types (this is actually possible). My h0 goes through the roof. If I consume all teas at a similar frequency, h1 will shoot up as well. This in turn may impact my h2 as well.
Now, h0 is an unreliable stat because it doesn't even take frequency into account. Like I said before, adding a single "&"-sign at the end of a 200-page book will impact its h0 the same way the frequent letter "e" does. But h1 tells us a bit more and is a bit more sturdy. If I add a letter and make it frequent, h1 will change more than if I just add a single token of the new type. So we can use h1 and h2 to fingerprint a text's entropy behavior.
Some extreme examples:
Low h1 + low h2: one or few types of tea dominate the selection, and teas are consumed in an ordered manner. If I drink mint and Earl Grey alternatively, you have a good (50%) chance of predicting which tea I will drink even without knowing which tea I drank yesterday (low h1). But if you know which tea I drank yesterday, you have a 100% chance of predicting which one I will drink today.
Low h1 + high h2: a few types of tea dominate the selection, but there is no pattern. In this case, your guess between mint and Earl Grey will always be 50% chance correct. For h1 these are decent odds, but h2 does not help us.
High h1 + low h2: many types of tea are consumed in similar frequencies, in an ordered manner. If I consume all 100 teas in a fixed order, you only have a 1% chance of guessing correctly without prior knowledge. But if you know what I consumed yesterday, you can predict confidently what I will drink today, despite the high h1. In this example and the first example, my odds of predicting today based on yesterday are the same, but the tea consumption landscape is completely different. Same h2 with a different h1 can mean we are looking at a very different text.
High h1 + high h2: many types of tea are consumed in similar frequencies, but there is no pattern. It is hard to predict anything at all.
In summary, when comparing Voynichese to another text, we want to be able to compare the glyph inventory and its use. H1 and h2 together give a more complete picture. And when modifying a Voynich transcription, we want to avoid introducing an absurd amount of different glyphs. But since rare glyphs are not interesting for the "broad" stat of entropy, h1 is a better gauge than h0.
2. Abbreviations: we tested this once, but I'm writing on my phone so I'm going by memory. One might hypothesise that abbreviating reduces entropy, because the same symbol is often found at the end. So the fact that abbreviation symbol is followed by a space is predictable.
Now remember that Voynichese has a lower h1 than most texts. You should now know what will happen if we introduce frequent abbreviation symbols in a regular text: h1 will increase. So even if you do manage to decrease h2 (which is not guaranteed), you will push h1 the wrong way. I didn't realize this yet, but question 2 is actually a good example for question 1
Edit: I forgot to add that some types of abbreviation will increase h2. For example, if you drop common endings, the final letter of words may become more unpredictable. Therefore, abbreviating will always increase at least one of h1 or h2, possibly both. And what we are looking for is a decrease.
![[+]](https://www.voynich.ninja/images/collapse_collapsed.png)