To the extent boltzman brains can be understood as a classical process then I think they are or can be viewed as pseudorandom phenomena. For quantum I do not really know. I do not know whether the paper intends to invoke quantum to get them that property.
The claim in the paper that they are “inaccesible by construction” is very implicit and requires a lot of accompaning assumptions and does a lot of work for the argument turn.
Numerology analog:
Say that some strange utility function wants to find the number that contains the maximum codings of the string “LOL” as a kind of smiley face maximiser. Any natural number when turned into binary and turned into strings can only contain a finite amount of such codings because there are only a finite amount of 1s in the binary representation. For any rational number turned to bianry deciaml there is going to be a period in the representation and the period can only contain finite multiples. The optimal rational number would be where the period is exactly “lol”. However for transcendental numbers there is no period. Also most transcendental numbers are “fair” in the sense that each digit appears approximately as likely as any other and additionally fair in that bigger combinations converge to even statistic. When the lol-maximiser tries to determine whether it likes pi or phi more as numbers, it is going to find infinite lols in both. However it would be astonishing if they contained the exact same amount of lols. The difference in lols is likely to be vanishingly small ie infinidesimal. But even if we can’t computationally check the matter, the difference exists before it is made apparent to us. The utility function of the lol-maximiser over the reals probably can’t be expressed as a real function.
While the difference between boltzman histories might be small if we want to be exact about preference preservation then the differences need to cancel exactly. Otherwise we are discarding lexiographic differences (it is common to treat a positive amout less than any real to be exactly 0). There is a difference between vanishingly different and indifferent and distributional sameness only gets you to vanishingly different.
To the extent boltzman brains can be understood as a classical process then I think they are or can be viewed as pseudorandom phenomena. For quantum I do not really know. I do not know whether the paper intends to invoke quantum to get them that property.
The claim in the paper that they are “inaccesible by construction” is very implicit and requires a lot of accompaning assumptions and does a lot of work for the argument turn.
Numerology analog:
Say that some strange utility function wants to find the number that contains the maximum codings of the string “LOL” as a kind of smiley face maximiser. Any natural number when turned into binary and turned into strings can only contain a finite amount of such codings because there are only a finite amount of 1s in the binary representation. For any rational number turned to bianry deciaml there is going to be a period in the representation and the period can only contain finite multiples. The optimal rational number would be where the period is exactly “lol”. However for transcendental numbers there is no period. Also most transcendental numbers are “fair” in the sense that each digit appears approximately as likely as any other and additionally fair in that bigger combinations converge to even statistic. When the lol-maximiser tries to determine whether it likes pi or phi more as numbers, it is going to find infinite lols in both. However it would be astonishing if they contained the exact same amount of lols. The difference in lols is likely to be vanishingly small ie infinidesimal. But even if we can’t computationally check the matter, the difference exists before it is made apparent to us. The utility function of the lol-maximiser over the reals probably can’t be expressed as a real function.
While the difference between boltzman histories might be small if we want to be exact about preference preservation then the differences need to cancel exactly. Otherwise we are discarding lexiographic differences (it is common to treat a positive amout less than any real to be exactly 0). There is a difference between vanishingly different and indifferent and distributional sameness only gets you to vanishingly different.