It's what I said here.

OK... will you deign to share why? — AJJ

Although actually it isn't even what I said earlier. It's just that your argument is invalid.

Premise 1: If you’re plucked out of a history that ends with us having colonised the galaxy and put back in randomly, it’s highly unlikely you’ll wind up in this tiny segment of the total population.

Conclusion: It’s therefore unlikely that (space colonisation) is going to happen.

You're missing a second premise. The only premise that would work is:

Premise 2: Space colonisation is only likely to happen if I am likely to be placed in this tiny segment of the total population were I plucked out of history and put back in randomly.

But then how do you justify this premise?

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.

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

Only if the date of someone's birth is chosen at random, but it isn't as I explained here. I couldn't have been born in China 1,000 years ago. I couldn't have been born on Mars 1,000 years in the future.

But even assuming that the date of someone's birth is chosen at random, let's test your theory.

I've run a computer script to pick a random number between 1 and some number n >= 1. The number it picked is 8,003. You now have to guess the number n.

Using your logic, 8,003 is more likely to be randomly selected if n = 8,003 (1/8,003 chance) than if n > 8,003 (e.g. if it was 16,006, in which case the chance would be 1/16,006).

So are you going to guess that n = 8,003?

Here's a script to test the above:


We play a game 100,000 times. For each game we pick a number between 1 and 100,000 to be the "end". We then pick a number between 1 and this "end". How likely is it that the number we pick is the "end" number? 0.01%. Whereas the likelihood that the number we pick is less than the end is 99.99%.

So even though we're more likely to pick some number r if r = n than if r < n, it is more likely that r < n.

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

The argument doesn’t posit this. That’s just a useful way of visualising it. The fact is we don’t know where we are in history - beginning, middle or end - and the argument shows it’s more likely to be the end. From our perspective where we are in history is somewhat random, because we don’t know.

If you split humanity’s entire population into a group of 1 and then the rest then you have a point here. But we’re not doing that. Since we want to work out what time we’re most likely in, we’re splitting humanity into segments of time: generations.

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

My argument is that, for the purposes of statistical analysis, we cannot treat an unbounded future distribution like a bounded past one. 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.

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.

In order to make the problem solvable, you have to introduce an upper limit and then calculate from there.

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?

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

My argument has never been that we are disembodied souls placed randomly in a human body. That’s just a way of visualising the argument.

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.

The philosophical problem here, is that there is no definite meaning of 'living at a particular date', and we get very different answers to our question depending on whether we are referring to phenomenal aspects of time comprehension, mathematical descriptions of time, or public denotations of time as a network of synchronized clocks and calendars. These relations are very complex, and our theoretical definitions are under-determined.

If we think of time in the traditional realist way, we think of nature as the real calendar of events that we culturally represent and approximate using our calendars; we naturally end up interpreting existential probabilities across time in terms of a linear scatter-plot of calendar-ordered frequencies. Consequently we end up with a philosophically dissatisfying answer to our philosophical question as to the probability of living at a particular time, for all we end up here is with a circular framing of the problem that answers in terms of frequencies, when we were implicitly questioning the relationship between calendar use, physical time, and personal experience.

On the other hand, when trying to understand time directly in terms of personal experience, we run into the problem that the content of personal experience is vague and repeatable without an absolute ordering; I cannot, for instance, distinguish the current appearance of my living room wall from its appearance last Wednesday. So my living room wall does not serve as a calendar.

I am only able to refer to the appearances of my living room wall at different dates by taking it's appearance in conjunction with something else serving as a calendar - for example, other memories I have that are different from one another and that I associate individually with the respective dates. Or if my memory is failing, photographs. But then a similar problem of repeatability resurfaces with respect to the conjunctions of experiences; we can therefore only speak of calendar-like relations as existing between phenomena when they are suitably interpreted, but we cannot phenomenally speak of the existence of absolute calendars - in direct contradiction to realist intuitions.

Phenomenal time therefore isn't linearly ordered and non-repeating as suggested by calendars; and the psychological past isn't immutable and separable from the psychological future, rather they are both mutable and inseparable aspects of present experience. Therefore any empirical attempt to conceptually reduce physical time to a phenomenal foundation must abandon the linear-ordered-time orthodoxy; Cartesian notions of time are merely practically convenient, without a phenomenally legible basis.

On the surface, the law of entropy sound appealing as a justification for absolute temporal ordering. However, entropy cannot serve as a justification for an absolute temporal order; for the notion of increasing disorder is relative to the labeling conventions we use for describing a system, and in science our labeling conventions are deliberately chosen so as to maximise the information we get from an experiment. Entropy is therefore an epistemological notion as opposed to a physical or metaphysical notion. From an omniscient perspective, there is no absolute 'law' of entropy.

The assumption of time symmetric microscopic laws is a big give-away that entropy isn't real; for any microscopically time-symmetric system that is observed to decrease in order, there exists an alternative labeling of it's micro-states in which it is described as increasing in order; to see this, simply imagine a simulation of a deck of cards being shuffled. At the end of the simulation, identify the top three cards on the shuffled stack and give them an identical label. Then replay exactly the same simulation from the beginning, remembering the cards we previously labelled. When re-interpreted with respect to this new labeling convention, the card shuffle increases in order. Therefore entropy isn't a phenomenal intuition and neither is it a physical concept. Entropy refers purely to epistemological uncertainty; to state it mathematically: Given a random assignment of labels to micro-states, the average entropy change of a time-symmetric system is zero.

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

If that's not literally what happens, how can we use the thought experiment as evidence that a particular scenario is more or less likely?

We can't "put ourselves back into history" since we don't know the extent of history. So what we end up doing is assuming that our lives represent a random spot in a bounded distribution. This, however, is also not accurate since our position in time is not a random point on humanity's timeline. Since we already exist we occupy a fixed position on that timeline, and the timeline is not finished so we can't run statistical analysis on it.

Look, my first post explains the argument clearly enough. If you don’t get it, then I guess you don’t get it.

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

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.

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

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.

I have a feeling that adding time is making the argument more complex than it should be.
Breaking it down, the real question is something like: How big is the chance of you being you in a set of N people.

In the first graph, N is simply bigger than in the second.

This might not be a question of probability, as the change of you being you is 1. Saying there are more people alive in graph 1 doesn't really matter.



As for the balls:

I read somewhere that in our past, 100 billion people have lived (black balls). with roughly 8 billion currently alive (green balls):

so let's say graph 1:
100 black balls
8 green balls
1 million yellow (future humans) balls

and graph 2:
100 black balls
8 green balls

Now indeed, the chance of getting a green ball is a lot higher in the case of graph 2. I think no one is denying that.

But that's not really the question.

From the perspective of our balls, every single one of them has had a life. So basically I am not removing one ball from each bag. I am removing all balls from the bag.
The green ball knows not about the yellow balls, so when I ask him the question, he will assume graph 2 is more likely (which is true). Yet graph 1 can also be true.

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.

If you would not exist, you would not be asking this question. Hence the survivership bias I mentioned. But i'm not sure it's applicable.

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

I don't think it's that easy. The actual claim that the doomsday argument makes is the following:

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

That is to say humanity will likely end before more than 20 times the number of humans that have lived so far will have lived. That statement remains the same for any point in time you do this calculation, so for the ancient Egyptians it would have been the same formula as for us. This is the part that purports to generate information, and it does so without reference to the past.

Putting in the numbers is merely reformulating the result.

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.

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

That's not right. The exact wording (from the Wikipedia article) is:

"Denoting by N the total number of humans who were ever or will ever be born, the Copernican principle suggests that any one human is equally likely ... to find themselves at any position n of the total population N, so humans assume that our fractional position f = n/N is uniformly distributed on the interval [0, 1] prior to learning our absolute position."

Nothing is circular here. From this it then follows that "there is a 95% chance that f is in the interval (0.05, 1), that is f > 0.05" and so that there is a 95% chance that N < 20n.

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

You first need to define what makes each ball unique. What makes one green ball different from another green ball? Do the green balls each possess essential and intrinsically individuating properties, or is their individuation a holistic property of the set they belong to?

If you have children who are identical twins, they will always at least possess geographical uniqueness. But if you yourself are part of an identical twin, any conceptual notion of uniqueness here is unrelated to the former notion.

Suppose you were one half of a pair of Siamese twins and you experience pain. Does it necessarily make sense to attribute your pain sensation to only one of the bodies? It is conceivable that your opinion might be irreconcilable with those of onlookers, in virtue of irreconcilable notions of sameness.

Sure, the mathematical operation itself isn't circular. If it were that obvious people would have realized long ago. It's actually quite difficult to find an argument against it, and my argument is probably pretty muddled at this point.

I think there is a hidden assumption in treating the entire future human population as an already existing and closed sequence of persons that you can then find you place in via statistical analysis. Perhaps applying the Copernican principle is actually wrong here. Your viewpoint is privileged, as you are already born. You can no longer be considered a random element.

Anyways, I was hoping my examples would make it easier to understand what I meant, but you don't seem interested.

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.

What exactly do you mean? I think even if the balls are exactly the same, the question holds. However, all viewpoints will also be the same.

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:

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.

I believe you hit the nail on the head.

We don't even know how to define our perspective, our consciousness. Who is to say that it is a random pick from existence at all (no god/fate references intended).

You have better chances of survival on scenario I (modern medicine, less accidents, no wars), but you might have a shorter but better life in scenario II because of higher standards of living caused by a drastically decreased population.

This might be true, however the point of the argument is that other probabilities do not matter. Therefor these observations are irrelevant for the argument.

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.

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.

Probability (YOUR birth in year x)= P(you) = (Y or all births that can be identified as YOU)÷(T or total number of births) = Y/T

T is increasing exponentially i.e. T = A × r^t where A is the startibg population and t is particular year

Y is also increasing exponentially i.e Y = S × R^t where S is the initial number of people that can br you.

P(you) = Y/T = (S/A) × (R/r)^t.

If 0 < R/r < 1 then P(you) will decrease with time paradoxically. If R/r > 1 then we could agree that there's an increased likelihood that you're living in the higher population region of the graph.

My math ain't so good. See anyrhing wrong in it?

fdrake pointed that out back on page one. — SophistiCat

I also pointed out that I think there is a problem with the doomsday argument on page one. I then spent the remaining pages trying to come up with a convincing argument, but unfortunately this seems to have driven off the remaining participants.

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

I agree it's a very thorny problem. Likely one for which there will never be a convincing purely mathematical solution (or one including formal logic). I was kind of reminded of the "Monty-Hall Problem". That one is considered solved, but it continues to baffle people.

I think my initial response, one page one, is still sound insofar as the problem of all these "self-locating" problems is that they apparently create new information ex-nihilo. The difficulty lies in properly explaining how a valid application of statistical principles leads to an invalid result. I earlier suspected that it has something to do with considering all future humans to have already lived when assuming one is a random observer. This would not directly apply to, say, the Sleeping Beauty problem. Both do, however, share the issue of whether or not the observer is privileged and can therefore not be considered to be randomly selected.

I think the issue with the Doomsday argument is its claim that each of us is equally likely to find ourselves at any position n of the total population N. As I said here, we're not disembodied souls that are randomly placed inside any one of the human bodies which will ever live.

If we consider the notion of the self, does it make sense to suggest that you could have lived my life and that I could have lived your life? Are we each some transcendent thing that only incidentally has the body we have, born in the time and place that we were? Or is it the case that any human born 1,000 years ago in China, or 1,000 years in the future on Mars, is necessarily not me?

In my opinion, the sleeping beauty problem and the doomsday argument aren't meaningful epistemological problems, and merely serve as reductio ad absurdums against the conceptual atrocities of Bayesian epistemology and it's accomplice Set Theory, which together confuscate the empirical foundation of reason.