Right. I think that if we assign measure inverse to the exponent of the shortest description length and assume that the ϵ probability increases the description length of the physically instantiated TM by −log(ϵ) (because the probability is implemented through reality branching which means more bits are needed to specify the location of the TM, or something like that), then this actually has a numerical solution depending on what the description lengths end up being and how much we value this TM compared to the rest of our life.
Say U is the description length of our universe and L−log(ϵ) is the length of the description of the TM’s location in our universe when the lottery is accepted, K−log(1−ϵ) is the description length of the location of “the rest of our life” from that point when the lottery is accepted, T is the next shortest description of the TM that doesn’t rely on embedding in our universe, V is how much we value the TM and W is how much we value the rest of our life. Then we should accept the lottery for any ϵ>2U−TV2−LV−2−KW, if I did that right.
If we consider the TM to be “infinitely more valuable” than the rest of our life as I suggested might make sense in the post, then we would accept whenever ϵ>2U+L−T. We will never accept if U+L≥T i.e. accepting does not decrease the description length of the TM.
Right. I think that if we assign measure inverse to the exponent of the shortest description length and assume that the ϵ probability increases the description length of the physically instantiated TM by −log(ϵ) (because the probability is implemented through reality branching which means more bits are needed to specify the location of the TM, or something like that), then this actually has a numerical solution depending on what the description lengths end up being and how much we value this TM compared to the rest of our life.
Say U is the description length of our universe and L−log(ϵ) is the length of the description of the TM’s location in our universe when the lottery is accepted, K−log(1−ϵ) is the description length of the location of “the rest of our life” from that point when the lottery is accepted, T is the next shortest description of the TM that doesn’t rely on embedding in our universe, V is how much we value the TM and W is how much we value the rest of our life. Then we should accept the lottery for any ϵ>2U−TV2−LV−2−KW, if I did that right.
If we consider the TM to be “infinitely more valuable” than the rest of our life as I suggested might make sense in the post, then we would accept whenever ϵ>2U+L−T. We will never accept if U+L≥T i.e. accepting does not decrease the description length of the TM.