We have to consider probabilities, not just for where the pieces are, but also for how they are moving.
I completely omit that because, well, it’s hard, but also I don’t think it’s necessary here. This approach doesn’t work even if you consider only positions and assume uniformly random momentum. It doesn’t work even if the microstate is “is this pixel more red or more blue” in the paper’s experiment!
But thank you for the comment, I’m glad I didn’t completely butcher entropy with my weird nonrigorous internal model I developed based PBS Space Time videos lol
Lol I got so tripped up by him later saying “this is no longer clearly 0 or 1 so it doesn’t exist” and decreasing N that I missed he does the reverse thing when encoding the message.
This is like the ontological argument. He creates a virtual entity from words alone and then treats it as a physical thing storing energy. And then once it no longer fits the words of the definition, poof, gone it is, oh look, total entropy decreased.