1.”Y=AX/((AX)+(B(1-X))” How have you got this formula? Sorry, my probability math is a bit rusty, so maybe I’m missing something obvious.
2.I find it a poor choice to use two islands as your example. In context of this problem we deals with two sets, and each set >1. Even more, such example biases us to think that an observer to be moke likely to belong to a set of worlds where catastrophe hasn’t happened, as there are only two islands. It doesn’t need to be the case. While each world that experienced catastrophe is less populated, combined population of post-catastrophe worlds can be still greater than population of no-catastrophe worlds if there is too many of post-catastrophe worlds and too few no-catastrophe worlds. IMHO, it would be better to use set A (islands where volcanic eruption happened) and set B (islands where were no volcanic eruptions).
3.”So the probability of being on an island that has had a volcanic eruption is 1⁄3 ” Why would we want to know this? I think that calculation of risk of catastrophe (i.e. share of ruined worlds/islands) is much more relevant.
4.It’s unclear to me how you select worlds among which M.A.D. either happened or didn’t. For an example, in my comment I limited myself to all worlds where I was born. If you don’t do the same, then you will run into problems. Consider this. There are parallel worlds where Roman civilization never crumbled. Where they had time to achieve everything that current Western civilization achieved + several addtional centuries to go beyond this. In 2022 there would be Roman worlds that colonized several planets of Solar system, maybe even terraformed them and found ways to sustainably support much bigger population than 8 billions. It seems plausible for population to be distributed heavely in favor of Roman worlds in current year 2022. Yet you and me aren’t is a Roman world. Curious, don’t you think?
The formula is just the fraction of people who live in a world where a given event happened. You take, (the number average number of persons in a world where an event took place * the probability of the event taking place), and divide it by, (the number average number of persons in a world where an event took place times the probability of the event taking place + the average number of persons in a world where the event didn’t take place * the probability of the event not taking place) Math is admittedly not my strong suit.
the two island example is just to give the simplest possible example, this is why there are only two. You are correct that there could be more people in post-catastrophe worlds.
Yeah, certainly we might rather know the percentage of worlds where the catastrophe occurred. The formula is useful because it lets you convert between the percentage of worlds in which a thing happens and the percentage of persons that thing happens to(if you know the average populations of worlds where the thing both happens and doesn’t)
I imagine the set of worlds to be identical up until the precise moment of the trinity test(July 16th, 1945 5:29 AM), however, this is just a narrative choice, and ultimately it’s kind of arbitrary. My suspicion is that the doomsday argument is valid due to space colonization being logistically impossible(or at least so implausible that it basically never happens/when space colonization does happen very few people actually live off-world due to logistical complications), and this is why we don’t find ourselves in a roman world. We might also just be in an unlikely circumstance.
1.”Y=AX/((AX)+(B(1-X))” How have you got this formula? Sorry, my probability math is a bit rusty, so maybe I’m missing something obvious.
2.I find it a poor choice to use two islands as your example. In context of this problem we deals with two sets, and each set >1. Even more, such example biases us to think that an observer to be moke likely to belong to a set of worlds where catastrophe hasn’t happened, as there are only two islands. It doesn’t need to be the case. While each world that experienced catastrophe is less populated, combined population of post-catastrophe worlds can be still greater than population of no-catastrophe worlds if there is too many of post-catastrophe worlds and too few no-catastrophe worlds. IMHO, it would be better to use set A (islands where volcanic eruption happened) and set B (islands where were no volcanic eruptions).
3.”So the probability of being on an island that has had a volcanic eruption is 1⁄3 ” Why would we want to know this? I think that calculation of risk of catastrophe (i.e. share of ruined worlds/islands) is much more relevant.
4.It’s unclear to me how you select worlds among which M.A.D. either happened or didn’t. For an example, in my comment I limited myself to all worlds where I was born. If you don’t do the same, then you will run into problems. Consider this. There are parallel worlds where Roman civilization never crumbled. Where they had time to achieve everything that current Western civilization achieved + several addtional centuries to go beyond this. In 2022 there would be Roman worlds that colonized several planets of Solar system, maybe even terraformed them and found ways to sustainably support much bigger population than 8 billions. It seems plausible for population to be distributed heavely in favor of Roman worlds in current year 2022. Yet you and me aren’t is a Roman world. Curious, don’t you think?
The formula is just the fraction of people who live in a world where a given event happened. You take, (the number average number of persons in a world where an event took place * the probability of the event taking place), and divide it by, (the number average number of persons in a world where an event took place times the probability of the event taking place + the average number of persons in a world where the event didn’t take place * the probability of the event not taking place) Math is admittedly not my strong suit.
the two island example is just to give the simplest possible example, this is why there are only two. You are correct that there could be more people in post-catastrophe worlds.
Yeah, certainly we might rather know the percentage of worlds where the catastrophe occurred. The formula is useful because it lets you convert between the percentage of worlds in which a thing happens and the percentage of persons that thing happens to(if you know the average populations of worlds where the thing both happens and doesn’t)
I imagine the set of worlds to be identical up until the precise moment of the trinity test(July 16th, 1945 5:29 AM), however, this is just a narrative choice, and ultimately it’s kind of arbitrary. My suspicion is that the doomsday argument is valid due to space colonization being logistically impossible(or at least so implausible that it basically never happens/when space colonization does happen very few people actually live off-world due to logistical complications), and this is why we don’t find ourselves in a roman world. We might also just be in an unlikely circumstance.