Can you “formalize” a bit more your reasoning about compressing T and W? I’m generally confused about compressibility: I understand the basics, but I don’t trust myself to judge a hand-wavy discussion about it.
In the particular case of your FMO, the glossing-over of these particulars prevents me from reasoning about the details, like the consequences of simple things like the pigeonhole principle to those of more complex things like the general non-computability of Kolmogorov complexity. (In the latter case, I’m not sure how to justify measuring universes by a non-computable property of theirs, and at the same time considering universes as computing machines.)
I also don’t get your argument for why T is compressible. It feels ridiculously unlikely that the age of the universe (actually, the age of an event) be 3^^^3 (± some humanly useful number); I’d expect rather something like “anything between 3^^^3 and 2×3^^^3”, and most numbers in that range should be very incompressible. (BTW, I’m also confused about up-arrows, but I think 3^^^3 is vastly too large a number to count every particle interaction in the history of the visible universe.)
(I don’t mean you should alter the article, just to comment with more details.)
Can you “formalize” a bit more your reasoning about compressing T and W? I’m generally confused about compressibility: I understand the basics, but I don’t trust myself to judge a hand-wavy discussion about it.
In the particular case of your FMO, the glossing-over of these particulars prevents me from reasoning about the details, like the consequences of simple things like the pigeonhole principle to those of more complex things like the general non-computability of Kolmogorov complexity. (In the latter case, I’m not sure how to justify measuring universes by a non-computable property of theirs, and at the same time considering universes as computing machines.)
I also don’t get your argument for why T is compressible. It feels ridiculously unlikely that the age of the universe (actually, the age of an event) be 3^^^3 (± some humanly useful number); I’d expect rather something like “anything between 3^^^3 and 2×3^^^3”, and most numbers in that range should be very incompressible. (BTW, I’m also confused about up-arrows, but I think 3^^^3 is vastly too large a number to count every particle interaction in the history of the visible universe.)
(I don’t mean you should alter the article, just to comment with more details.)