OK... will you deign to share why? — AJJ
The idea is just that it’s unlikely for a random person to be at the beginning of a history like that, and way more likely they’re at the end of one. — AJJ
<?php $max = 0; $min = 0; for ($i = 1, $g = 100000; $i <= $g; ++$i) { $n = mt_rand(1, 100000); $r = mt_rand(1, $n); if ($r == $n) { ++$max; } else if ($n > $r) { ++$min; } } echo 'r = m: ' . $max / $g * 100 . PHP_EOL; echo 'r > m: ' . $min / $g * 100 . PHP_EOL;
The issue with the puzzle is that we're not disembodied souls that are randomly placed in one of any of the human bodies which will ever live. — Michael
It's true that we can only calculate the probabilities if we know the distribution, but the questions being posed in this discussion are in the form "if the human population over time is distributed like this then what is the probability that we will live during this time period" in which case we have a known distribution from which to calculate a probability.
Obviously in real life we don't know how the human population will be distributed. We don't know the rate at which the population will grow or decline or stabilise over time, which is why I answered that we can't know when humanity will end. The only thing I've been trying to argue is that if the human population grows at a steady rate until an immediate end such that the last generation is the largest it doesn't follow that we are probably the last generation – that's only true if the last generation contains more than half of all humans who will ever live. — Michael
The argument doesn’t posit this. That’s just a useful way of visualising — AJJ
The argument doesn’t posit this. That’s just a useful way of visualising
— AJJ
Didn't you tell me earlier that this was, in fact, your argument? — Echarmion
In fact I didn’t even say that. I said the thought experiment involves abstracting yourself from history then putting yourself back in. I didn’t mean that is literally something that happens. — AJJ
Consider this example: There is a machine that, when you press a button, produces a random ball from it's inventory. Balls are either red or blue. The machine starts with 10 red balls. Every hour, a blue ball is added. You find this machine an unspecified amount of time after it has begun operating. Are you more likely to receive a red or a blue ball?
The way I see it, the logic of the doomsday argument would have you pick blue. After all, there are potentially many more blue balls than red ones. I say that the question has no answer. You cannot calculate any meaningful probability without further information. That is despite the fact that you know the exact distribution of balls for every hour of operation. — Echarmion
For example, you have to consider the possibility that humanity survives until the heat death of the universe. A priori, that scenario is as likely as humanity disappearing tomorrow. Since the scenario is possible, it must have an effect on your calculation. So you'd have to first assign a probability to that scenario and every other possible end point until you could make a meaningful calculation. — Echarmion
The Doomsday argument only works because we have information about the past (the number of people who have already lived) whereas in your analogy we don't, so they're not comparable. — Michael
In other words, we could assume that we could be 95% certain that we would be within the last 95% of all the humans ever to be born. If we know our absolute position n, this implies an upper bound for N obtained by rearranging n/N > 0.05 to give N < 20n. — Michael
This seems backwards. These arguments are being used to suggest how probable the above scenarios are; e.g. the Doomsday reasoning is used to assign a low probability to humans surviving until the heat death of the universe. — Michael
Well, yes. My point is that the doomsday argument is essentially circular reasoning. If you already know the probability you don't need the doomsday argument. — Echarmion
But in fact the question is: Is the green ball more likely to be the green ball in the second case than in the first case?
I think we are asking something like: Is there a smaller chance of you being you when there are more people in existence. — Mind Dough
I think we are asking something like: Is there a smaller chance of you being you when there are more people in existence. — Mind Dough
Well if that's the question, the answer pretty clearly has to be no. The chance that you will be born is not related to how many people exist afert you were born. — Echarmion
True. It still makes me wonder whether we can say anything at all about the graphs though. From a mathematical point of view, yes. But I wonder if there is more to it.
Found this video about the subject btw. Nick Bostrom explains the doomsday argument very clearly: — Mind Dough
Seems well put. There seems to be some problem with the doomsday argument, but it's not a simple mathematical problem but one that has to do with more basic considerations. You can probably say that the problem is not that the math is wrong, is that the math doesn't provide a good model for reality in this case. So if we were just talking about the graphs as graphs, it might be fine to conclude that graph 2 is more likely. — Echarmion
fdrake pointed that out back on page one. — SophistiCat
Of course, the matter is not so cut and dried as to be dismissed out of hand, as evidenced by decades of arguments over The Sleeping Beauty, Doomsday, Simulation, etc. And the issue is not confined to abstract philosophical puzzles either: it lies at the heart of some conundrums in modern cosmology as well (typicality, fine-tuning).
For more on the general form of the issue look into self-locating beliefs. — SophistiCat
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