15-12-2021, 12:33 AM
Please forgive my ignorance. I taught myself everything I know about Markov chains from Wikipedia, in order to follow some of the good discussions that are happening these days about the statistical properties of the VMs text. My understanding of a Markov model of a dynamic system is one where the probability of any given state depends only on the state immediately prior. By "second-order transitional probability", I understand this to mean the probability of a state transition happening, given the prior two states, in the order they occurred. Do I understand this correctly?
Your idea of an "unmodulated carrier signal" has stuck with me, and I've been trying to think of a good way to model a periodically repeating system where many different paths are possible for each repetition, and each repetition's deviation from the default path can be brought into focus. Some kind of flowchart, where a line's deviation from qokeedy.qokeedy.qokeedy or daiin.chol.daiin.chol.daiin.chol can be meaningfully visualized. One of these days I'm going to start doodling on a whiteboard and come up with something. That said, this is a much easier project when the only state that matters in calculating the probability is the one immediately prior. But as your experiment above shows, taking the last two states into account produces a result that looks and feels much more like actual Voynichese.
Let's say we took the last X states into account when calculating the probability of the next state. I wonder how high a value X could have, before there were no appreciable gains in the similarity to actual Voynichese, to justify the rapid increase in calculation complexity.
A related question I'm wondering about: how many states properly comprise a complete repetition? I don't consider a space a state, as your work has clearly demonstrated that spaces supervene upon state transitions. If [ch] and [sh] are considered a single state each, then it looks like the [qokeedy] loop involves 7 state transitions per repetition, and the [daiin.chol] loop involves 8. I'm curious as to whether lines of Voynichese tend to break down neatly into multiples of 7 or 8 state transitions. I'l going to take a look at some Currier B pages as soon as I get the chance with this filter on my mind, and report back here what I find.
Your idea of an "unmodulated carrier signal" has stuck with me, and I've been trying to think of a good way to model a periodically repeating system where many different paths are possible for each repetition, and each repetition's deviation from the default path can be brought into focus. Some kind of flowchart, where a line's deviation from qokeedy.qokeedy.qokeedy or daiin.chol.daiin.chol.daiin.chol can be meaningfully visualized. One of these days I'm going to start doodling on a whiteboard and come up with something. That said, this is a much easier project when the only state that matters in calculating the probability is the one immediately prior. But as your experiment above shows, taking the last two states into account produces a result that looks and feels much more like actual Voynichese.
Let's say we took the last X states into account when calculating the probability of the next state. I wonder how high a value X could have, before there were no appreciable gains in the similarity to actual Voynichese, to justify the rapid increase in calculation complexity.
A related question I'm wondering about: how many states properly comprise a complete repetition? I don't consider a space a state, as your work has clearly demonstrated that spaces supervene upon state transitions. If [ch] and [sh] are considered a single state each, then it looks like the [qokeedy] loop involves 7 state transitions per repetition, and the [daiin.chol] loop involves 8. I'm curious as to whether lines of Voynichese tend to break down neatly into multiples of 7 or 8 state transitions. I'l going to take a look at some Currier B pages as soon as I get the chance with this filter on my mind, and report back here what I find.