Your example of the grid of rooms does not quite work. Unlike height (but somewhat like birthday), which column you are in follows a uniform distribution, with no mode near the middle. You are in fact more likely to find yourself in column {A or Z} than to find yourself in column M, for instance. Same for the rows.
Generally speaking, we expect a priori to be part of the typical set of any given distribution, not near the middle per se. In fact, even for Gaussian distributions, as the dimensionality of the space increases, the typical set actually recedes away from the mode/center and towards a hyperellipsoidal shell around it (https://arxiv.org/abs/1701.02434).
This is just something to keep in mind. I haven’t yet thought through how this caveat may apply to doomsday timelines, but it’s probably important.
I probably should have clarified that in the case of raws, I count as “middle” everything which is not on the border, that is not first or last raw.
This caveat actually plays in the situation of the universe anthropic fine-tuning by many parameters. The number not-perfectly-fine-tuned universes is much larger than the set of fine-tuned ones. This means lower concentration of civilizations in space compared with “optimal universe”. Seems to be solution of the Fermi paradox.
Your example of the grid of rooms does not quite work. Unlike height (but somewhat like birthday), which column you are in follows a uniform distribution, with no mode near the middle. You are in fact more likely to find yourself in column {A or Z} than to find yourself in column M, for instance. Same for the rows.
Generally speaking, we expect a priori to be part of the typical set of any given distribution, not near the middle per se. In fact, even for Gaussian distributions, as the dimensionality of the space increases, the typical set actually recedes away from the mode/center and towards a hyperellipsoidal shell around it (https://arxiv.org/abs/1701.02434).
This is just something to keep in mind. I haven’t yet thought through how this caveat may apply to doomsday timelines, but it’s probably important.
I probably should have clarified that in the case of raws, I count as “middle” everything which is not on the border, that is not first or last raw.
This caveat actually plays in the situation of the universe anthropic fine-tuning by many parameters. The number not-perfectly-fine-tuned universes is much larger than the set of fine-tuned ones. This means lower concentration of civilizations in space compared with “optimal universe”. Seems to be solution of the Fermi paradox.
Thank for the link.