Nicholas, suppose Eliezer’s fictional universe contains a total of 2^(10^20) star systems, and each starline connects two randomly selected star systems. With a 20 hour doubling speed, the Superhappies, starting with one ship, can explore 2^(t36524⁄20) random star systems after t years. Let’s say the humans are expanding at the same pace. How long will it take, before humans and Superhappies will meet again?
According to the birthday paradox, they will likely meet after each having explored about sqrt(2^(10^20)) = 2^(510^19) star systems, which will take 510^19/(365*24/20) or approximately 10^17 years to accomplish. That should be enough time to get over our attachment to “bodily pain, embarrassment, and romantic troubles”, I imagine.
Nicholas, suppose Eliezer’s fictional universe contains a total of 2^(10^20) star systems, and each starline connects two randomly selected star systems. With a 20 hour doubling speed, the Superhappies, starting with one ship, can explore 2^(t36524⁄20) random star systems after t years. Let’s say the humans are expanding at the same pace. How long will it take, before humans and Superhappies will meet again?
According to the birthday paradox, they will likely meet after each having explored about sqrt(2^(10^20)) = 2^(510^19) star systems, which will take 510^19/(365*24/20) or approximately 10^17 years to accomplish. That should be enough time to get over our attachment to “bodily pain, embarrassment, and romantic troubles”, I imagine.