A bit pedantic, but isn’t superexponential replication too fast? Won’t it hit physical limits eventually, e.g. expanding at the speed of light in each direction, so at most a cubic function of time?
Also, never allowing followers to catch up means abandoning at least some or almost all of the space you passed through. Plausibly you could take most of the accessible and useful resources with you, which would also make it harder for pursuers to ever catch up, since they will plausibly need to extract resources every now and then to fuel further travel. On the other hand, it seems unlikely to me that we could extract or destroy resources quickly enough to not leave any behind for pursuers, if they’re at most months behind.
Naturally it doesn’t go on forever, but any situation where you’re developing technologies that move you to successively faster exponential trajectories is superexponential overall for some range. E.g. if you have robot factories that can reproduce exponentially until they’ve filled much of the Earth or solar system, and they are also developing faster reproducing factories, the overall process is superexponential. So is the history of human economic growth, and the improvement from an AI intelligence explosion.
By the time you’re at ~cubic expansion being ahead on the early superexponential phase the followers have missed their chance.
I agree that they probably would have missed their chance to catch up with the frontier of your expansion.
Maybe an electromagnetic radiation-based assault could reach you if targeted (the speed of light is constant relative to you in a vacuum, even if you’re traveling in the same direction), although unlikely to get much of the frontier of your expansion, and there are plausibly effective defenses, too.
Do you also mean they wouldn’t be able to take most what you’ve passed through, though? Or it wouldn’t matter? If so, how would this be guaranteed (without any violation of the territory of sovereign states on Earth)? Exhaustive extraction in space? An advantage in armed space conflicts?
A bit pedantic, but isn’t superexponential replication too fast? Won’t it hit physical limits eventually, e.g. expanding at the speed of light in each direction, so at most a cubic function of time?
Also, never allowing followers to catch up means abandoning at least some or almost all of the space you passed through. Plausibly you could take most of the accessible and useful resources with you, which would also make it harder for pursuers to ever catch up, since they will plausibly need to extract resources every now and then to fuel further travel. On the other hand, it seems unlikely to me that we could extract or destroy resources quickly enough to not leave any behind for pursuers, if they’re at most months behind.
Naturally it doesn’t go on forever, but any situation where you’re developing technologies that move you to successively faster exponential trajectories is superexponential overall for some range. E.g. if you have robot factories that can reproduce exponentially until they’ve filled much of the Earth or solar system, and they are also developing faster reproducing factories, the overall process is superexponential. So is the history of human economic growth, and the improvement from an AI intelligence explosion.
By the time you’re at ~cubic expansion being ahead on the early superexponential phase the followers have missed their chance.
I agree that they probably would have missed their chance to catch up with the frontier of your expansion.
Maybe an electromagnetic radiation-based assault could reach you if targeted (the speed of light is constant relative to you in a vacuum, even if you’re traveling in the same direction), although unlikely to get much of the frontier of your expansion, and there are plausibly effective defenses, too.
Do you also mean they wouldn’t be able to take most what you’ve passed through, though? Or it wouldn’t matter? If so, how would this be guaranteed (without any violation of the territory of sovereign states on Earth)? Exhaustive extraction in space? An advantage in armed space conflicts?