This maps the credence but I would imagine that the confidence would not be evenly spread around the boxes. With confidence literally 0 it does not make sense to express any credence to stand any taller than another as 1 and 0 would make equal sense. With a miniscule confidence the foggy hunch does point in some direction.
Without h3 it is consistent to have middle square confidence 0. With positive plausibily of h3 middle square is not “glossed over” we have some confidence it might matter. But because h3 is totally useless for credences those come from the structures of h1 and h2. Thus effectively h1 and h2 are voting for zero despite not caring about it.
Contrast what would happen with an even more trivial hypothesis of one square covering all with 100% or 9x9 equiprobable hypothesis.
You could also have a “micro detail hypothesis”, (actually a 3x3) a 9x9 grid where each 3x3 is zeroes everywhere else than the bottom right corner and all the “small square locations” are in the same case among the other “big square” correspondents. The “big scale” hypotheses do not really mind the “small scale” dragging of the credence around. Thus the small bottom-right square is quite sensitive to the corresponding big square value and the other small squares are relatively insensitive. Mixing two 3x3 resolutions that are orthogonal results in a 9x9 resolution which is sparse (because it is separable). John Vervaeke meme of “sterescopic vision” seems to apply. The two 2x2 perspectives are not entirely orthogonal so the “sparcity” is not easy to catch.
This maps the credence but I would imagine that the confidence would not be evenly spread around the boxes. With confidence literally 0 it does not make sense to express any credence to stand any taller than another as 1 and 0 would make equal sense. With a miniscule confidence the foggy hunch does point in some direction.
Without h3 it is consistent to have middle square confidence 0. With positive plausibily of h3 middle square is not “glossed over” we have some confidence it might matter. But because h3 is totally useless for credences those come from the structures of h1 and h2. Thus effectively h1 and h2 are voting for zero despite not caring about it.
Contrast what would happen with an even more trivial hypothesis of one square covering all with 100% or 9x9 equiprobable hypothesis.
You could also have a “micro detail hypothesis”, (actually a 3x3) a 9x9 grid where each 3x3 is zeroes everywhere else than the bottom right corner and all the “small square locations” are in the same case among the other “big square” correspondents. The “big scale” hypotheses do not really mind the “small scale” dragging of the credence around. Thus the small bottom-right square is quite sensitive to the corresponding big square value and the other small squares are relatively insensitive. Mixing two 3x3 resolutions that are orthogonal results in a 9x9 resolution which is sparse (because it is separable). John Vervaeke meme of “sterescopic vision” seems to apply. The two 2x2 perspectives are not entirely orthogonal so the “sparcity” is not easy to catch.