Thank for the interesting sequence so far! While reading, I had a question about the mathematics here:
A digital abstraction layer is a way of grouping the low-level configurations of a system together such that knowing which group the system’s current configuration is in allows you to predict which group the system’s next configuration will be in.
This sounds to me like the high-level configurations partition the low-level configurations of the system into disjoint classes. In particular, the high-level configuration is a (deterministic) function of the low-level configuration.
If this is the case, does the mutual information between the two not simply become the entropy of the high-level configuration? This already feels like it's missing the mark (a similar objection was raised in the last post under "Perfect self-knowledge").
Thank for the interesting sequence so far! While reading, I had a question about the mathematics here:
This sounds to me like the high-level configurations partition the low-level configurations of the system into disjoint classes. In particular, the high-level configuration is a (deterministic) function of the low-level configuration.
If this is the case, does the mutual information between the two not simply become the entropy of the high-level configuration? This already feels like it's missing the mark (a similar objection was raised in the last post under "Perfect self-knowledge").