Please see my other reply here. Yes, value is finite, but the number of possible states of the universe is enormously large, and we won’t explore it in 8000 years. The order of magnitude is much bigger.
(Incidentally, our galaxy is ~ 100,000 light years across; so even expanding to cover it would take much longer than 8000 years, and that would be creating value the old-fashioned way by adding atoms, but it wouldn’t support continued exponential growth. So “8000 years” and calculations based off the size of the galaxy shouldn’t be mixed together. But the order-of-magnitude argument should work about as well for the matter within 8000 light-years of Earth.)
In much the same way, estimates of value and calculations based on the number of permutations of atoms shouldn’t be mixed together. There being a googleplex possible states in no way implies that any of them have a value over 3 (or any other number). It does not, by itself, imply that any particular state is better than any other. Let alone that any particular state should have value proportional to the total number of states possible.
Restricting yourself to atoms within 8000 light years, instead of the galaxy, just compounds the problem as well, but you noted that yourself. The size of the galaxy wasn’t actually a relevant number, just a (maybe) useful comparison. It’s like when people say that chess has more possible board states than there are atoms in the observable universe times the number of seconds since the Big Bang. It’s not that there’s any specifically useful interaction between atoms and seconds and chess, it’s just to recognize the scale of the problem.
Please see my other reply here. Yes, value is finite, but the number of possible states of the universe is enormously large, and we won’t explore it in 8000 years. The order of magnitude is much bigger.
(Incidentally, our galaxy is ~ 100,000 light years across; so even expanding to cover it would take much longer than 8000 years, and that would be creating value the old-fashioned way by adding atoms, but it wouldn’t support continued exponential growth. So “8000 years” and calculations based off the size of the galaxy shouldn’t be mixed together. But the order-of-magnitude argument should work about as well for the matter within 8000 light-years of Earth.)
In much the same way, estimates of value and calculations based on the number of permutations of atoms shouldn’t be mixed together. There being a googleplex possible states in no way implies that any of them have a value over 3 (or any other number). It does not, by itself, imply that any particular state is better than any other. Let alone that any particular state should have value proportional to the total number of states possible.
Restricting yourself to atoms within 8000 light years, instead of the galaxy, just compounds the problem as well, but you noted that yourself. The size of the galaxy wasn’t actually a relevant number, just a (maybe) useful comparison. It’s like when people say that chess has more possible board states than there are atoms in the observable universe times the number of seconds since the Big Bang. It’s not that there’s any specifically useful interaction between atoms and seconds and chess, it’s just to recognize the scale of the problem.