What is the probability of living now?
Hey guys,
Imagine the following two population predictions:
Graph 1: Population is booming.
Graph 2: Humanity is not doing so well.
The question(s) goes as follows: In which scenario are we most likely to live? Or rather, can we make a statement about this?
Rationale: If you were to pick a random life from the first graph, there is a larger chance of picking one in the future. If we are to pick a random life from the second graph, there is a pretty good chance you are living today.
My feeling says this is not an argument for having a larger chance that graph two is true, but I am wondering about the argumentation on that. I suspect something in the line of survivorship bias, but I am still curious whether this is an existing thought experiment (I think I saw this somewhere before) and what the arguments/criticisms are.
Looking forward to hearing from you.
Regards,
Jasper
Imagine the following two population predictions:
- In the first, humanity prospers. We venture into space and our population keeps growing steadily. All the humans born until now will be a fraction of all the humans that are to come in the existence of humanity.
- In the second, we go extinct. It doesn’t really matter how it happens, but it happens. We are currently at our peak and 60 years from now there will be no humans alive anymore.
Graph 1: Population is booming.
Graph 2: Humanity is not doing so well.
The question(s) goes as follows: In which scenario are we most likely to live? Or rather, can we make a statement about this?
Rationale: If you were to pick a random life from the first graph, there is a larger chance of picking one in the future. If we are to pick a random life from the second graph, there is a pretty good chance you are living today.
My feeling says this is not an argument for having a larger chance that graph two is true, but I am wondering about the argumentation on that. I suspect something in the line of survivorship bias, but I am still curious whether this is an existing thought experiment (I think I saw this somewhere before) and what the arguments/criticisms are.
Looking forward to hearing from you.
Regards,
Jasper
Comments (123)
The first is why we don't see any evidence for aliens. However, if the reason we don't see any aliens is because technological civilizations are extremely improbable, then there is no Great Filter lying in wait for us. Assuming civilization continues, then eventually we will make super realistic simulations, some of which will be ancestor simulations. The population of simulated people will far outnumber those of non-simulated kind. So therefor, odds greatly favor us living in a simulation.
So either we face extinction soon, or we're simulated. However, I don't really buy these arguments. They seem to be too simple, ignoring potential complications to building ancestor simulations or colonizing the galaxy in a few million years.
Whoever/whenever you are it’s always most likely that yours is the final generation. The rationale being that if the final generation is the largest one, and if a random person is always most likely to be among the largest generation/group, then it follows that you (a random person) are most likely among the final generation.
Quoting Mind Dough
This shows how unlikely it is that we’ll ever expand out into the galaxy, since it would mean we’re all part of a tiny fraction of all humans, rather than the other huge group. Instead it stands to reason that we’re at the top of graph 2’s curve.
Funny that you mention this. I'm writing an article that also references the simulation hypothesis, that's actually the reason I came to ask this question. It is exactly this question, only a substantial part of the first graph being simulated.
Quoting AJJ
From a random person's perspective, this will always be true (if indeed population keeps rising). However, I am wondering if this (and therefor also the simulation hypothesis) is a valid argument to make: Personally I think this is a special case of survivorship bias, in which we simply cannot see (or know) the people that havn't been born yet. A 4 dimensional survivorship bias if you will.
What are your thoughts on that?
I wouldn’t say that bias is in play here. The argument simply acknowledges that it is far more likely we’re at the top of Graph 2’s curve than at the bottom of Graph 1’s. Either situation could be true - indeed because we can’t see or know who is to come - but all that can be said without knowing is that the former situation is more likely.
We also don't have any independent lineage of life existing on earth that we aren't descended from. We also have failed to recreate it even with all the king's horses and men going at it.
It seems likely life is something extremely rare and I don't see why that isn't recognized or taken into account, like ever.
Using that same logic, would it not also make sense to say that we are "far more likely" currently the largest conscious civilization that has ever and ever will exist in existence?
I mean, if over the time of the universe there would be a bigger civilization in existence, it would be more likely to be born as one of them.
Yes, that seems right to me.
Scary thought...But even so, we can still hope to be the one in a billion lottery ticket.
After all, this would also raise the chance significantly on being either a Boltzman brain or the rest of humanity being philosophical zombies (I mean, what is the chance of being me in 7 billion?!). A reality I would rather avoid (as if it matters:P).
Yeah, I guess we can.
I’m not sure it raises the chances of being a Boltzmann brain, since for that to be likely the universe would need to have had a much longer past that it’s commonly (to my knowledge) said to have had.
And it seems to me it’s not actually possible for you (anyone) to have been anyone else, since obviously you’d not be you then. I don’t see why you being you makes it likely that everyone else is a zombie, rather than everyone else just being the particular conscious person they are.
It's not a named bias as far as I am aware. It amounts to magical thinking though. It's very similar in that regard to the "fine tuning" arguments. Math (in this case statistics) is used to mask the fact that the argument has no substance. You'll notice that this "doomsday argument" has only a single piece of information as input: that right now, humans exist. It puports to derive from that information a piece of entirely new information - the likelihood of humanities imminent demise.
But how does it get from one bit of information to the other? It does not account for current trends in global politics, the economy or the environment. It simply transforms one piece of information into another. That is, it creates information ex-nihilo, which is impossible.
The interesting question is: How does an application of mathematics that, on it's face, seems valid, lead to an absurd result?
Quoting AJJ
But according to that logic, it stands to reason that everyone who has ever lived was at the top of graph 2s curve, but they weren't. How is that possible?
If we know that someone is not at the top of Graph 2’s curve then obviously they’re not at the top of Graph 2’s curve. But we don’t know where we are, and in that ignorance the probability that we’re at the top of Graph 2’s curve comes into play.
But we're turning that ignorance into a probability without further information. That is impossible. If we're ignorant about what graph we are on and where we are on that graph, we can't magically turn said ignorance into new information using math
No we aren’t, and yes we can.
We don’t know where we are. Mathematical reasoning tells us we’re most likely at the top Graph 2’s curve. We might not be, but what we can say is it’s more likely.
So, which is it? Do we have further information that allows us to make a determination or are we creating information ex nihilo using math?
Just saying "it's mathematical reasoning" is the same as saying "it's magic".
Assume the number I was given is 10. If n is 10 then there would have been a 1/10 chance that I would be given a 10, whereas if n is 100 then there would have been a 1/100 chance that I would be given a 10. Given that a 1/10 chance is greater than a 1/100 chance, it's more probable that n is 10 than n is 100 (and the same is true for any n > 10). This seems to be the sort of reasoning used in your example. It doesn't really work out that way when we play such a game though:
If for each game the range is 1-100 then there's a 5.2% chance that the number I'm given at random is the max. If for each game the range is 1-1000 then there's a 0.7% chance that the number I'm given at random is the max.
All this shows is that the shorter the lifetime of the human race, the more likely that humanity is closer to extinction. But that's a truism.
You’ve blundered here and now you’re trying too hard to disagree with me.
The information we use is the assumption that the final generation will be the largest one. The mathematical reasoning we use is that it’s most likely for a random person to be part of the largest group, assuming we don’t already know where they are.
The notion that there's anything random about you, as the particular individual you are, living at any random time seems flawed, no? Graphs like that would only make sense if you "already existed" somehow, without living, and then the exact year that you wind up living is chosen in a manner akin to selecting lottery numbers. But that's not how it works. So we can't pretend that it's how it works if we want to say anything not purely fantastical about it.
This is misleading. Assume 5 generations with populations like this:
1: 100
2: 200
3: 300
4: 400
5: 500
It's more likely that I'm in generation 5 than in generation 4, and more likely that I'm in generation 5 than generation 3, and so on – but it's more likely that I'm not in generation 5 than in generation 5. The actually probabilities are:
1: 6.7%
2: 13.3%
3: 20%
4: 26.7%
5: 33.3%
If you were blindfolded, so to speak, and told you were part of one of those generations, which would you predict you were a part of?
Your answer wouldn’t be “I’m most likely part the first four”, but rather “I’m most likely part of the last four”. Of those four you’re most likely part of the last three. Of those the last two, and of those the last one.
Is that not right?
Or perhaps this isn't about you and I'm just interested in the topic.
Quoting AJJ
But as you state, this isn't information, but an assumption. But even if we grant the assumption as essentially correct, it does still not contain any information about humanities demise, so the question of where that information comes from remains.
Quoting AJJ
As an analogy, take the hotel room example. You're in a hotel with 100 rooms, but you don't know which room you're in. If someone asks you whether you are in the first ten rooms, your answer should be no. But if someone asks you whether you are in room 2 or in room 50 your answer should not be fifty just because you are more likely not to be in the first 10 rooms. Because for that specific question, the probability of either is 1/100. This probability doesn't change if you arbitrarily divide the hotel rooms into groups.
So in order to make a meaningful statement, the groups need to be given in advance. Otherwise, just knowing you're "in the largest group" tells you nothing because groups don't actually exist as physical objects.
Say you roll a dice. If it's 2-6 then roll again. Repeat until you roll a 1.
According to your reasoning, your first roll is more likely to be 2-6 than 1 so you're more likely to roll a second time; your second roll is more likely to be 2-6 than 1 so you're more likely to roll a third time; and so on. You're then saying that you're more likely to roll 20 times in a row than to roll once. But of course that's obviously wrong. The chance of rolling just once is 0.167, whereas the chance of rolling 20 times is 0.026.
You're more likely to roll < 20 times than to roll 20 times. You're more likely to be part of generation < 5 than to be part of generation 5.
I would say a reasonable assumption is information. It’s certainly something we can reason from.
No it doesn’t contain information about humanity’s demise. It’s the mathematical reasoning that shows we’re most likely close to that demise.
Quoting Echarmion
The probability does change if you divide the rooms into groups. If I say you’re either in rooms 1 or 2 or in any of the rest, then it’s most likely you’re in the second “any of the rest” group.
Your dice example isn’t analogous to the group situation described. We’re not rolling a dice to find out which group we’re in, but using the amount of people in each group to work out the likelihoods.
A dice analogy would go like this: Imagine you’re a spot on a dice. Which side are you most likely on? You’re more likely on the 2-6 sides than the 1 side. Of those you’re more likely on the 3-6 sides, and so on.
I did that here:
1: 100 people (6.7%)
2: 200 people (13.3%)
3: 300 people (20%)
4: 400 people (26.7%)
5: 500 people (33.3%)
OK, and then of those you're more likely on the 4-6 side, and then of those more likely on the 5-6 side, and then of those more likely on the 6 side? So you're more likely to be on the 6 side than on one of the 1-5 sides? No. There are 21 dots on a dice, and only 6 are on the 6 side. There's a 29% chance that a dot taken at random is on the 6 side and a 71% chance that a dot taken at random is on one of the 1-5 sides.
Doesn’t this prove my point? I think the mistake here is making groups 1-4 one group. You can’t be in multiple generations; since you can only be in one it’s most likely you’re in 5.
I'm not saying that I'm in multiple generations. I'm saying that I'm more likely to be in generation 1 or generation 2 or generation 3 or generation 4 than to be in generation 5.
I have a 33.3% chance of being in generation 5, and so therefore a 66.7% chance of not being in generation 5.
What you’re actually saying is you have more chance of being within generations 1-4. What you actually have to do is pick one; the one most likely for you to be in.
But if I’m blindfolded and asked which one colour you’ve given me then I’m going to say blue. I can’t say “not blue”, because I’ve been asked to pick a particular colour.
Mathematical reasoning, being a deductive process, cannot generate information though.
Quoting AJJ
If those are the groups you are given by some outside source. But if no outside source provides you with any groupings, and you're just standing alone in a room, you cannot reason yourself into rooms 3 to 100 by arbitrarily deciding on these groups. Given arbitrary groups, one can make any sequence of rooms the most likely one. No such thought experiment tells you where you actually are though.
It's even worse when, as is the case with future generations, you don't even know how many rooms there are. If you simply know there are n rooms and you are in one of them, there is no way to tell what number your room is. Yet the logic of the "doomsday argument" would have you believe that you can.
If you're asked to pick a colour then, yes, you should say blue -- although you're more likely to be wrong than right, and so if you're asked if it's more likely to be blue or not-blue you should say not-blue.
And if you're asked to pick a generation then, yes, you should say the last generation -- although you're more likely to be wrong than right, and so if you're asked if you're more likely in the last generation than not in the last generation then you should say not in the last generation.
Well sure, I guess reasoning doesn’t generate information, but it does discover it.
Quoting Echarmion
The groups we’re using in the thought experiment are real though: Generations, with the assumption that each is larger than the last, which so far has actually been the case.
Quoting Echarmion
That we don’t know how many generations there will be is entirely the point though. If we knew there’d be no room for the probabilities we’re establishing.
I don't have to pick one. It is true that I'm more likely of being within generations 1-4 (66.7% chance) than being in generation 5 (33.3% chance). Therefore it's less likely that my generation is the last generation.
So are you claiming that information concerning the timing of the end of humanity is encoded in a) the fact that humans exist right now and b) the assumption that the living human population will be highest shortly before it's demise?
Quoting AJJ
Generations aren't real. they are more or less arbitrary groupings of people who were born in the same time period. But regardless, the generations are the rooms in the hotel. You want to know which room you're in.
So let's set up a proper thought experiment: The entire human population that will ever have lived is grouped into 100 hotel rooms. Every room represents the same amount of time between humanity's evolution and it's demise, but you don't know how long that is. Every room is an incredibly vast extradimensional space, and it is completely dark, so you don't know how many other people are in your room and you have no way of communicating with them.
Now a voice tells you that you will go to heaven if you can guess which room you're in. You can choose any range of 5 rooms as your guess, as long as you're in any one of them, you win. Which range do you choose?
Quoting Michael
You seem to be saying you’re more likely to be in a generation other than the one you’re in.
Once you’re in a generation there is no chance you’re in the other four. So the question is which particular generation is yours, and the best answer is “the last one”.
Assuming population growth (and an abrupt rather than gradual end), you're more likely to win if you select the last 5 rooms (assuming the rooms are numbered according to the time period).
But you're more likely to be wrong than right (unless >= 50% of humanity lived during the final 1/10th of humanity's total time). This is where I think AJJ is going wrong.
No I'm not. I'm saying that if you have to pick a generation then you're more likely to be right if you pick the final generation, but that you're more likely to not be in the final generation than to be in the final generation.
Consider again the example with 1 red ball, 2 orange balls, 3 yellow balls, 4 green balls, and 5 blue balls.
If you have to guess which ball you will be given your chances of winning are:
1. Guess red - 6.7%
2: Guess orange - 13.3%
3: Guess yellow - 20%
4: Guess green - 26.7%
5: Guess blue - 33.3%
Guessing blue gives you the best odds, but you're more likely wrong (66.7% chance) than right (33.3% chance).
There's a difference between an answer being the best answer and that answer being more likely right than wrong. The best answer has < 50% chance of being right, so it's wrong to say that we're most likely in the last generation. We're most likely not in the last generation.
Yes.
Quoting Echarmion
Sure, but those arbitrary groupings are real and that’s what we’re using.
Quoting Echarmion
Whatever the last five are, because that will be the range with the most people in it. That’s assuming we go extinct quickly, but whatever the choice you’d choose a range towards the end of all the rooms.
Quoting Michael
I haven’t said the answer is more likely right than wrong. For whichever generation we might be in you can say we’re most likely not in that generation, but we can’t not be in whichever generation is ours so I don’t see why that’s a factor.
So the question I’ve been answering is which generation carries the best likelihood of being ours. And the answer is the last one; the last one is the most likely to be ours; of all the generations we can be in we’re most likely (but not more likely than not) to be in the last one. It seems to me that last part is only a contradiction if you allow the chance that we are not in whichever our generation is.
What you originally said is "Whoever/whenever you are it’s always most likely that yours is the final generation. The rationale being that if the final generation is the largest one, and if a random person is always most likely to be among the largest generation/group, then it follows that you (a random person) are most likely among the final generation." That's wrong. I am not most likely among the final generation. Just as in my example with the coloured balls you're not most likely to have a blue ball.
You're most likely to not have a blue ball and you're most likely to not be among the final generation.
The particular claim of yours which is wrong is "a random person is always most likely to be among the largest generation/group". This is only true if there's > 50% chance of being in the largest generation. In our example there's a 33.3% chance of being in generation 5, so you're not most likely to be among the largest generation. You're most likely to be among one of the other generations (even though no individual generation is more likely than the largest).
It seems to me what you’re doing is selecting an option and reasoning that you’re most likely not to have selected that option. You’ve chosen a ball but you’re most likely not to have chosen that ball. You’re in a generation but you’re most likely not in that generation.
And if you have to bet on a generation then bet on the last because it has the best odds, but if you can choose to not bet then don’t because you’re more likely to be in an earlier generation and lose than to be in the last generation and win.
Quoting AJJ
So, the argument here is the last five presumably have the most people, and presumably we're in the largest group.
But we're assuming population growth as well. So if humanity stays around after us, the chance that we are in the last 5 rooms drops dramatically. So to answer the last 5 rooms is presuming - and not proving - that humanity's demise will come relatively soon. If the demise isn't soon - and we have no prior information on that - the chances might be completely different.
Our ignorance here is such that even betting on being in the largest (and therefore last) group doesn't work, because the way we've set the thought experiment (assuming population growth and a rapid decline) the question we are asking is actually "are we in the largest group". The argument thus ends up circular.
Quoting AJJ
That seems to me an utterly fantastical claim. It would imply that the laws of physics somehow base humanity's demise on the first person who is formulating this doomsday argument in their heads.
If the chances are 3-1 and you’re getting 3-1 on your money then you can bet all you want since you’ll break even. Does “best odds” not mean most likely to win?
You’re still in check as far as I’m concerned. What you’re doing it picking a ball and saying, “whatever ball this is, it’s more likely another one.”
I don’t think it is. The only presumption is population growth until an abrupt demise. It then follows that the final X years will have a greater population than any earlier X-year range, and so therefore that betting on the final X years will give us the best odds of winning.
However, contrary to AJJ’s claim, unless more than half of humanity lives in the final X years then it doesn’t follow that we’re most likely living in the final X years.
If the chances are 3-1 then you’re not most likely to win (be in the last generation). You’re 3 times more likely to lose (not be in the last generation). This discussion has nothing to do with payouts.
No I’m not. I’m saying “I’m going to bet that it’s blue but it’s more likely not blue” - which is true if there are 15 balls and only 5 are blue. Two-thirds of the time I lose. It’s better odds than betting on any other colour, but it’s still losing odds.
That is if we are in fact living in the final years. If we're not, then betting on the last rooms gives you no better chance of winning. Your position in the rooms is determined by time, not population number, so you can only be in the largest group (given continuous population growth) by being in the last group. So, the question ends up circular.
If the 3-1 is the best chance available then the 3-1 is the most likely to win. Most likely to win is what “best odds” means right? Payouts come into this if you say you shouldn’t bet in a spot; payouts are essential to consider there.
Quoting Michael
But of all the balls blue is the most likely one you’re holding. You can say it’s more likely to not be that colour about any of them, but it has to be one, and one of them is going to be most likely.
That’s not right. Take my example with the coloured balls. 1 red is given out at T1, then 2 orange at T2, then 3 yellow at T3, then 4 green at T4, and then 5 blue at T5. There’s nothing circular in saying that if I have to bet on which Tn my ball was given to me then T5 gives me the best odds (1/3). It doesn’t make sense to say that if I was given my ball at T4 then T5 doesn’t give me the best odds. That’s like saying that if my ball is red then betting on blue doesn’t give me the best odds. That’s not how probabilities are calculated.
That's true, but in your example, you know you're already after T5. That is to say all balls are in the game. With the doomsday argument, this is not the case. In your example, you'd have to account for the probability that there are no blue balls at all yet.
Sorry if I wasn't clear. I'm just told the rules and then given a hidden ball. I don't know if my ball is blue and I don't know if the time I was given the ball (say 12:00pm) is T5.
Quoting AJJ
This is ambiguous, so perhaps this will better explain what I'm saying:
Let's say 98 people have 1 lottery ticket and you have 2 lottery tickets. Of everyone playing, you have the best chance of winning (1/50 compared to their 1/100). However, it is most likely that someone other than you wins (98/100).
Of each generation, you have the best chance of being in generation 5 (1/3 compared to 1/15 for generation 1, 2/15 for generation 2, 1/5 for generation 3, and 4/15 for generation 4). However, it is most likely that you're in some other generation (2/3).
So this really depends on what you're trying to say. If it's "you're probably in the final generation" then you're wrong. That would be like saying "you're the most likely to win the lottery, therefore you're probably going to win the lottery" – which is wrong; you're probably going to lose even though you have better odds of winning than any other individual.
So what are the probabilities P(it is at most T4) and P(it is T5 or later)? If they aren't equal, this changes the probability to have a blue ball.
P(T1) = 1/15
P(T2) = 2/15
P(T3) = 1/5
P(T4) = 4/15
P(T5) = 1/3
So, if we have to bet on a time then betting on T5 gives us the best odds. This is where I agree with AJJ. However, given that P(T1-T4) = 2/3, it's most likely not T5. This is where I disagree with AJJ.
And, as I said before, there's no circular reasoning here, and it's the same reasoning as used in the case of which time period we're living in (it's just "people being born at time" rather than "balls being given out at time").
The likelihood to live now...compared to living in history or in the future is very low. Now if we assume humans have been around for 100 000 years, it's totally possible for us to be around for another 100 000 year. No, we won't go extinct in a couple of decades or continue on an upward trend (as Peak Human Population) will come likely in 100 years or so. Yet if there are 10 billion people for the next 100 000, do the math.
(Actually demographics is something that is very precise. The simple fact is that those who will have children 20 years or so from now have already been born. I've seen some very accurate forecasts made of population growth and demographic change done in the early 1900's, which predicted correctly the next 100 years.)
What is your distinction between “best chance” and “most likely”?
Whichever generation you bet on is going to be against the aggregate probability of you being among the others. So the way to distinguish between them is to say which ones are against a lower aggregate, which it makes sense to call the more/most likely of the options.
I haven’t been saying this is probably the last generation; only that a random person is always most likely to be part of the last generation, compared to other individual generations.
It seems to me then that the best answer in your view to the question, “which generation are we most likely to be a part of?” is “a one other than the one you bet on”, which is really to say none of them.
It was what you said in your first post:
Quoting AJJ
Ignoring the actual dates and population figures and just assuming that it's a projection of how the human population will change throughout its history, it's more likely that 2019 is somewhere in the first 2/3rds than somewhere in the last 1/3rd. That's the proper way to approach this issue.
That’s assuming we expand out into the galaxy, which I figure would involve a huge increase in population (through the occupation of other planets) that would dwarf our population up until now.
But it seems to me that it should make a difference that it's possible that not all balls are in the game. The chance that there is one red ball is 100% (as we have been given a ball, so it must be at least T1). The chance that orange balls are in the game must be less than 100%, since it could still be T1. Similarly, the chance that there are yellow balls in the game must be less than 100%. Doesn't the probability that each "stage" of the game has already happened decrease linearly? It's more likely that at least 2 stages have elapsed than it is that all 5 stages have elapsed. Isn't it like the room problem? I don't know which room I am in, but I am more likely to be in room 1-4 than in room 5.
If you agree with AJJ's take on the basic probabilities, then do you also agree that we can somehow deduce the timing of humanity's demise based on just the information outlined in the thought experiment?
Is this not the same question in essence? Only instead of asking it for all humanity (or conscious beings) over time, we are asking the question for all humans currently alive.
If indeed the chance of you being you is one, then it also answers my original question. In such a case the chance of me being someone else in a different time is also zero. (Assuming that me being me is connected to me being me in the time I live in).
Yes, you're right. The chance that current time T >= 1 is 1, the chance that T >= 2 is 14/15, the chance that T >= 3 is 4/5, the chance that T >= 4 is 3/5, and the chance that T >= 5 is 1/3. But that works out as exactly the same odds I gave above:
P(T = T1) = 1/15
P(T = T2) = 2/15
P(T = T3) = 1/5
P(T = T4) = 4/15
P(T = T5) = 1/3
Quoting Echarmion
I agree with that if there are more people in rooms 1 - 4 than there are in 5.
Quoting Echarmion
No.
I like the ball example, but as I am a simple man, the ball abstraction is the only abstraction I want to make, so let's use real numbers:
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?
It is a question I believe not only of math, but also one of consciousness. I actually liked the answer of . Even though I don't completely understand it, I think he is thinking in the right direction here.
I don’t think so: We know who we are among everyone currently alive, but we don’t know where in human history we all are, except that we’re currently heading it.
Which begs the question how we are supposed to calculate such a probability in the first place if we lack information on it.
Quoting Michael
Ok, so this is how I think the probabilities look when we don't know what "stage" we are in. Since we don't have information on the length of the stages, we should assume we are equally likely to be in each one.
T1: 1/5
R: 1/1 -> 1/5
T2: 1/5
R: 1/3 -> 1/15
O: 2/3 -> 2/15
T3: 1/5
R: 1/6 -> 1/30
O: 2/6 -> 2/30
Y: 1/2 -> 1/10
T4: 1/5
R: 1/10 -> 1/50
O: 1/5 -> 1/25
Y: 3/10 -> 3/50
G: 2/5 ->2/25
T5: 1/6
R: 1/15 -> 1/75
O: 2/15 -> 2/75
Y: 1/5 -> 1/30
G. 4/15 -> 4/75
B: 1/3 -> 1/15
This neatly reverses the probabilities. Because red is always in the game, it has a total probability of 1/3, and we should now always bet red.
Have I made some grave error here?
Let's ignore the future for a bit.
Why would it be ok to think we would had a probability of being born (as someone else) in the past (just a high one now, hence the graphs), but not ok to have the probability to have been born as someone else in the present?
I don’t think either is OK, since we can’t be anyone else. The thought experiment involves abstracting yourself from history then putting yourself back in randomly. We find that the last generation is the most likely one for us to wind up in, so that’s what makes sense for us to think, even though it’s not unlikely we’re somewhere else.
That's not quite how the argument goes. If we exited history and then randomly re-entered it, we might indeed be justified in reasoning we'd enter somewhere nearer the end of humanity. But the argument had been whether or not probability theory tells us there is an increased probability we are close to the end right now.
Well it’s how the argument I’ve been making goes.
That's wrong. When the experimenter is deciding who to give the red ball to at T1 there's only a 1/15 chance that he picks me. Therefore there's a 1/15 chance that when he gives me a ball it's red, and so a 1/15 chance that when he gives me a ball it's T1.
One of the criticisms of the Doomsday argument can apply to your example:
Simply put, the fact that we're more likely to pick 2019 from graph 2 than from graph 1 is countered by the fact that an extinction level event in the near future isn't very likely.
Sometimes physical possibility trumps a mathematical puzzle.
In that case your conclusions on the first page:
Quoting AJJ
Don't follow from your argument.
Quoting Michael
Uh, what do you mean "who to give the ball"? It was never mentioned that the balls are distributed among 15 people. This is all based on the assumption that you get one ball out of a pool of 15 balls.
Given that whether or not the other 14 balls are lying in a box somewhere or in the hands of 14 other people is irrelevant from the perspective of the "player", I also don't see how you arrive at different probabilities here. If it's T1 and you have a ball, the ball must be red. It's not possible for it to be T1 and the red ball being in some other person's hands, because you have a ball.
Quoting Michael
While the argument is mathematically different, it's the same kind of statistical analysis. So the same criticism would apply: how could we generate information (in the form of a probability) about the end of humanity based on the input information?
In memory of the discussion we had a while back on the Sleeping Beauty problem, say you're going to be put to sleep. A scientist will select one of the coloured balls at random. If it's red then you'll be woken on Monday; if it's orange you'll be woken on Tuesday; and so on.
Before you're put to sleep you're asked about the probability that you will be woken on Monday. That probability is 1/15. You're put to sleep and then woken up on your randomly selected day. What's the probability that it's Monday? It's still the same 1/15 it was before you were put to sleep.
It's described in the argument:
"If Leslie's figure is used, then 60 billion humans have been born so far, so it can be estimated that there is a 95% chance that the total number of humans N will be less than 20 × 60 billion = 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1140 billion humans will be born in 9120 years"
That's correct.
Quoting AJJ
In that case I'm afraid we have had a miscommunication and have both been talking about something else :P
I think I know where we are talking past each other. You are looking at this from the perspective of the experimenter, who decides in advance what ball to give to the player, knowing the sequence of colours. So from you perspective, all balls are always in the pool.
I am looking at this from the perspective from the player who just receives a ball. The ball can be drawn from a machine. The machine draws from a pool of balls that changes over time in the manner outlined above. In that case, we have to account for the fact that the machine will more likely than not have drawn from a limited pool.
What I want to illustrate is that, if the pool of balls is not fixed in advance, the probabilities can change quite drastically. In such a case, merely assuming to have drawn from the largest group is mistaken. This is the case for the argument made in this thread. There is no "experimenter" that knows the sequence in advance and has assigned you a slot in the history of humankind. You simply know you "drew" a slot, but not whether or not the pool is limited. In that situation, you need further information.
Quoting Michael
Sure, that's what happens mathematically. But since we're on a philosophy forum, let's look at it from an epistemological perspective. It's not actually possible to compute the (likely) end of humanity based on the input information here, would you agree? If so, then what does that probability actually mean?
This is exactly the name I was looking for, thanks!
One thing I don't understand from the quoted text though (still have to read the wiki): Why is the conclusion that there is a 95% chance there will be still 1140 billion humans to come? As I understand it, the chance is 5% sure that there is a 95% chance of 1140 billion humans still to come.
Still, the mathematical puzzle is interesting. I think it's worth the discussion. The physical facts do not apply to the puzzle itself :)
From the standard realist perspective, averaging over all possible futures that are consistent with current cosmological information makes the probability of living at this moment of time vanishingly small, i.e. undetermined but convergent towards zero.
I think it's an interesting point.
The graph is discriminating towards humans. What about all other conscious beings that ever existed/will ever exist in the universe (that might ask the same question). I think they should also be plotted on the graph. ;)
Then indeed the possibility either way will probably be close to zero...
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.
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. I just am this particular physical body (and its emergent consciousness), and this particular physical body (and its emergent consciousness) isn't equally likely to have been born at any point in human history. It could only have been born to my parents, who in turn could only have been born to their parents, and so on. There's some degree of latitude (e.g. I was born premature, but it's possible that I could have been born late), but it's limited (e.g. I couldn't have been born in China 1,000 years ago).
The puzzle is like asking for the probability that of the countless animals that have ever lived on Earth, what is the probability that only members of the human species will have the ability to speak – and asserting that each member of every species is equally likely to have this ability. Given this assertion we would expect that most speaking animals wouldn't be human as most animals aren't human, but the ability to speak isn't something that is just randomly assigned to a species at birth, just as being born in 1988 isn't something that was just randomly assigned to me.
They do though. 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. It’s therefore unlikely that space colonisation is going to happen.
Your conclusion doesn't follow.
OK... will you deign to share why?
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.
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?
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 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.
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.
Quoting AJJ
Didn't you tell me earlier that this was, in fact, your argument?
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.
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.
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.
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.
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.
I don't think it's that easy. The actual claim that the doomsday argument makes is the following:
Quoting 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.
Quoting 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.
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.
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.
Quoting 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.
Quoting 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:
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.
@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?
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.
Quoting 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?
I had the impression you thought that criticism applied only to AJJ's version of the argument. But yes, I think that is at least the right track. Since @SophistiCat pointed out this problems similarity with other problems, like "Sleeping Beauty", I wonder if we can apply the same kind of criticism there.
In the Sleeping Beauty problem, the question can be rephrased as whether you are more likely to be an observer in a world that has more observers in total. The result of the view that this is the case (i.e. Sleeping Beauty is more likely to have been woken twice) interestingly enough runs directly counter to the result of the Doomsday argument, since the more humans will ever exist, the more possible observers "you" have to choose from.
But your criticism applies either way, since again assuming that you are more likely to be an observer in a world with more observers assumes "you" are a disembodied spirit that is the randomly assigned an observer "slot". It therefore seems that in these kinds of problems, the copernican principle does not apply.
Very nice explanation. Also didn't know about the sleeping beauty problem, very nice thought.
Thanks guys, I've learned a lot :)
As did I.