Freethought & Rationalism Archive

Christopher Lord · 08-05-2003, 09:39 PM

The Experimenter is limited to a ball existing in both urns because you and I exist in both urns. Doomsday is still ahead of us (regardless of whether it is 10a or 10*e^6a away), so we are in both urns.

Since we are in both 'urns', the numerical value of our particular ball tells us nothing about when doomsday is.

As an alternative analogy, imagine two ticker tapes printing out sequential numbers in parallel. The experimenter decides to mark your existence by making both tapes pause at the exact same time. The number on both tapes is noted as 'you'.

Does the number printed on the ticker tapes at that moment tell you which ticker tape is almost done, and which one will go on for a long time to come?

I think its clear in this case that the answer is no, any guess you make based on the number printed on the ticker-tapes will not help you, leading to a 50/50 chance of guessing which ticker is the short stick.

*edit:
I think its importaint to point out that with the ticker-tape example, it is impossible to avoid the fact that both possibilities are equally probable right up to the present. the future is hidden, and the past is a stream of events leading up to the present.

Jesse · 08-05-2003, 10:24 PM

Christopher Lord:
The Experimenter is limited to a ball existing in both urns because you and I exist in both urns. Doomsday is still ahead of us (regardless of whether it is 10a or 10*e^6a away), so we are in both urns.

I don't think so. Each urn represents a possible world, and I can be only in one of all possible worlds. There are possible worlds where the the human species died out after only one generation--obviously that's not the one I'm in. But the prior probability distribution is just your estimate of the a priori probability of each world, before you modify your probability estimate based on your own birth order. A priori, there's no reason to assign zero probability to the possible world where the human race died after one generation.

Friar Bellows · 08-05-2003, 11:29 PM

Quote:

Originally posted by Christopher Lord
As an alternative analogy, imagine two ticker tapes printing out sequential numbers in parallel. The experimenter decides to mark your existence by making both tapes pause at the exact same time. The number on both tapes is noted as 'you'.

Does the number printed on the ticker tapes at that moment tell you which ticker tape is almost done, and which one will go on for a long time to come?

I think its clear in this case that the answer is no, any guess you make based on the number printed on the ticker-tapes will not help you, leading to a 50/50 chance of guessing which ticker is the short stick.

I think that proponents of the Doomsday Argument would say your analogy was wrong. They might prefer the following analogy:

You stand outside a closed room inside of which is a computer printer. You are told the following facts:

1) The printer was switched on some time ago, some unspecified time ago, at which point it started to print an ordered sequence of numbers, i.e. 1, 2, 3, 4 etc etc.

2) The printer was selected from one of two batches of printers, using the result of a single (unweighted) coin toss: heads, and the printer would be chosen from batch A; tails, batch B.

3) A printer from batch A will stop printing when it reaches the number 10 (ten), while a printer from batch B will stop printing when it reaches the number 1,000,000 (one million).

4) The noise that you are hearing through the door is the noise of the printer printing numbers.

Then, through a small chute on the door, you are passed a small piece of paper, on which is written the most recent number to be printed by the printer. It is the number 7 (seven). From which batch was the printer more likely to have come: batch A or batch B?

I would reason here in the following way. Prior to my being passed the piece of paper and learning that the number was 7, I would have immediately said that the probability of the printer coming from batch A was 0.5, or 50%, and batch B also 0.5, or 50%. Now, the chances of getting a 7 from the batch A printer, i.e. 1 in 10, are much greater than the chances of getting a 7 from the batch B printer, i.e. 1 in 1,000,000. Thus, the fact that I get a 7, suggests to me that it is much more likely that the printer came from batch A than batch B. Precisely how much more likely is calculated via Bayes theorem, described earlier in the thread.

Christopher Lord · 08-06-2003, 06:59 AM

by having 'alternate' printers (only one of which is actually running) the analogy you present fails to capture reality correctly.

All events leading up to *today* will have been the exact same, regardless of when in the future humanity ends. This is why in my ticker tape example I used two printers, one of which will end sooner, the other later.

Basing our observations ONLY on the past (which is all we have, the future is completely opaque) we can only say that we have a 50% chance of going down path a instead of path b.

As a general comment to the thread, saying that we are randomly inserted into the continum is incorrect. This assumes we were 'souls' which poped into a random time in order to pick a random body to haunt. We are actually genetically predispositioned to exist right after our parents, so we are not randomly inserted. There is only one time you or I could come into this world.

Jesse · 08-06-2003, 09:38 AM

Quote:

Originally posted by Christopher Lord
As a general comment to the thread, saying that we are randomly inserted into the continum is incorrect. This assumes we were 'souls' which poped into a random time in order to pick a random body to haunt. We are actually genetically predispositioned to exist right after our parents, so we are not randomly inserted. There is only one time you or I could come into this world.

The self-sampling assumption does not make any claims about us having "souls" which were inserted randomly into the continuum, it just says that if everyone reasons as if they were randomly selected from the set of all observers/observer-moments, then most of them will get correct results. The anthropic-principle.com FAQ addresses this issue:

Quote:

Q3. I have memories of 20th century events, so I cannot have been born earlier than the 20th century.

A3. We have to distinguish two "cannots" here. (1) Given the validity of these memories then I was in fact not born <1900.[true] (2) I could not exist without these memories.[much more doubtful].

It is indeed problematic how and in what sense you could be said to be a random sample, and from which class you should consider yourself as having been sampled (this is "the problem of the reference class"). Still, we seem forced by arguments such as Leslie's emerald example (below) or my own amnesia chamber thought experiment (see my "Investigations into the Doomsday argument") to consider ourselves as random samples due to observer self-selection at least in some cases.

A firm plan was formed to rear humans in two batches: the first batch to be of three humans of one sex, the second of five thousand of the other sex. The plan called for rearing the first batch in one century. Many centuries later, the five thousand humans of the other sex would be reared. Imagine that you learn you�re one of the humans in question. You don�t know which centuries the plan specified, but you are aware of being female. You very reasonably conclude that the large batch was to be female, almost certainly. If adopted by every human in the experiment, the policy of betting that the large batch was of the same sex as oneself would yield only three failures and five thousand successes. ... [Y]ou mustn�t say: �My genes are female, so I have to observe myself to be female, no matter whether the female batch was to be small or large. Hence I can have no special reason for believing it was to be large.� (Leslie 1996, pp. 222-23)

I already know I'm male, so it's not like I "could have been" female--a female Jesse wouldn't be me, it'd be a different person. And yet, if everyone in this experiment reasons as if they were randomly selected from the entire group of 5003 people, and thus believes there's a 5000:3 chance the larger batch is the same sex as themselves (assuming the prior probability of the larger batch being either sex is 50-50), then 5000 of them will be right and only 3 will be wrong.

Do you disagree with the self-sampling assumption in the example Leslie gives above? If not, what's different about the Doomsday argument?

Furby · 08-06-2003, 10:33 AM

Well, I think the analogies of both the urns and the printers are still flawed because you are calculating the probabilities from the perspective of the experimenter, when in fact, you should be calculating them from the POV of the balls.

So, suppose I find myself to be a ball in one of the urns, I have no other information except that urn A has 10 balls and urn B has 10,000 balls.

Now, as mentioned earlier, if every ball guessed that they were in urn B then 10,000 balls would be correct and only 10 balls will be wrong. Hence, I would have good reason to guess that I am in urn B.

Suppose I found out later that I'm actually ball number 7. This new information would cause me to re-evalutate the probability of me being in urn B and would actually cause me to lower my estimate of this probability by a lot. However, since my prior estimate was already so high (10 000 : 10), this would balance out the shift downwards and we would get a 50:50 probability.

Hence, unless you were an alien observing the earth from outer space, you should not be able to conclude whether doomsday for humans would come any sooner or later.

Christopher Lord · 08-06-2003, 11:20 AM

Jesse,
An agent on earth is the Nth imperfect copy of DNA. The agent know nothing about the future, and the past has already happened regardless of whether the world is about to end.

the agent reasons: "Gee, doomsday should be about x years from 0 when N/x=1/2" or some other argument from cosmic popularity of Ns close to his own. this agent is implicitly assuming that x is bounded, and that N is 'probably' in the majority of all possible x.

Why can an individual who is also a specific point in a series of copies assume that he is in the statistical majority of all x? He can't. He came in sequence. His number indicates only where in the sequence he is, and not when his particular 'brand' of DNA will no longer exist.

Then, there is the question about bounds. We can not say that humanity will even end before the end of the universe with certainty, because life itself is in theory immortal. it will keep making copies for infinite years given the chance, and so thus will humans.

Jesse · 08-06-2003, 01:43 PM

Christopher Lord:
Jesse,
An agent on earth is the Nth imperfect copy of DNA. The agent know nothing about the future, and the past has already happened regardless of whether the world is about to end.

The past has already happened, but the prior probability distribution should not take into account the agent's knowledge of how many generations have already passed--otherwise it wouldn't be "prior" to his modifying the probabilities based on his own birth rank. That's just how Bayesian reasoning works. So, the agent should not assign zero prior probability to possible worlds where humanity goes extinct after fewer number of people than his own birth rank, as you argued earlier.

Christopher Lord:
the agent reasons: "Gee, doomsday should be about x years from 0 when N/x=1/2" or some other argument from cosmic popularity of Ns close to his own. this agent is implicitly assuming that x is bounded, and that N is 'probably' in the majority of all possible x.

Why can an individual who is also a specific point in a series of copies assume that he is in the statistical majority of all x? He can't. He came in sequence. His number indicates only where in the sequence he is, and not when his particular 'brand' of DNA will no longer exist.

Here you're getting into the "problem of the reference class" that Bostrom mentions, which I already agreed was a major problem for the Doomsday Argument. If the fact that you think it's arbitrary not to include prehuman primates or posthuman intelligences in the Doomsday Argument was your only objection to it, I'd say that's a reasonable objection, but it seems you have more fundamental problems with the self-sampling assumption even in less ambiguous cases. You didn't answer my question about the "two batches of different sexes" problem, which would clarify the exact nature of your objections--please do so if you respond to this post. Also, suppose all the humans in that experiment were going to be created in sequence (so the first three in the sequence would be one sex while the next 5000 in the sequence would be another)--would you then answer differently about how one should reason than if all 5003 humans were created at once? If not, it seems the whole sequential issue is a red herring.

Christopher Lord:
Then, there is the question about bounds. We can not say that humanity will even end before the end of the universe with certainty, because life itself is in theory immortal. it will keep making copies for infinite years given the chance, and so thus will humans.

If that were true, then I'd think all but an infinitesimal fraction of intelligent beings would find themselves arising at a time when the number of intelligent beings before them was so great that the number could not even be compressed into a form they'd be capable of understanding (here I'm talking about 'compression' in the information-theory sense of reducing the number of bits needed to express the number). Thus by the logic of the doomsday argument, since I don't observe this to be true of my own birth rank, I should expect the chance of humanity continuing forever is infinitesimal, unless the prior probability of it lasting a finite time is zero or infinitesimal (although it's possible that I'm actually existing as a simulation performed by a very long-lasting civilization, in which case my true birth rank could be much greater than the 600 billion indicated by historical records, and maybe it would indeed be a number too large for me to comprehend...see Nick Bostrom's other page on the Simulation Argument for the case that there may actually be a high probability we're living in a simulation).

Christopher Lord · 08-07-2003, 10:47 AM

I admit i do not know much about Bayesian reasoning. I have objections on other grounds (which I hope have been made clear), but when it comes to the Bayesian logic behind it I have little grounding.

What sort of university class usually teaches it? math? philosophy?

Mathetes · 08-07-2003, 11:42 AM

I think Friar Bellow's analysis is correct. The big issue with this problem is that we do not know what the unconditioned, "prior" probability is.

Using his terms:

In the urn example, the two models are equally possible, and p(short) = p(long) = 0.5. Is this realistic to refer to humanity? We do not know. It is possible that there is something like p(short) = 0.9 and p(long) = 0.1. Or the other way round.

Without determining what the "prior" probability is, we cannot reliably calculate the conditioned, Bayesian probability of humanity being in the long or the short case.

If the odds were really 50/50 it is very likely that we are doomed. But we do not know what the real odds are.

Interesting puzzle.

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08-05-2003, 09:39 PM	#31
Christopher Lord Senior Member Join Date: Feb 2001 Location: Toronto Posts: 808	The Experimenter is limited to a ball existing in both urns because you and I exist in both urns. Doomsday is still ahead of us (regardless of whether it is 10a or 10e^6a away), so we are in both urns. Since we are in both 'urns', the numerical value of our particular ball tells us nothing about when doomsday is. As an alternative analogy, imagine two ticker tapes printing out sequential numbers in parallel. The experimenter decides to mark your existence by making both tapes pause at the exact same time. The number on both tapes is noted as 'you'. Does the number printed on the ticker tapes at that moment tell you which ticker tape is almost done, and which one will go on for a long time to come? I think its clear in this case that the answer is no, any guess you make based on the number printed on the ticker-tapes will not help you, leading to a 50/50 chance of guessing which ticker is the short stick. edit: I think its importaint to point out that with the ticker-tape example, it is impossible to avoid the fact that both possibilities are equally probable right up to the present. the future is hidden, and the past is a stream of events leading up to the present.

08-05-2003, 10:24 PM	#32
Jesse Moderator - Science Discussions Join Date: Feb 2001 Location: Providence, RI, USA Posts: 9,908	Christopher Lord: The Experimenter is limited to a ball existing in both urns because you and I exist in both urns. Doomsday is still ahead of us (regardless of whether it is 10a or 10*e^6a away), so we are in both urns. I don't think so. Each urn represents a possible world, and I can be only in one of all possible worlds. There are possible worlds where the the human species died out after only one generation--obviously that's not the one I'm in. But the prior probability distribution is just your estimate of the a priori probability of each world, before you modify your probability estimate based on your own birth order. A priori, there's no reason to assign zero probability to the possible world where the human race died after one generation.

08-06-2003, 06:59 AM	#34
Christopher Lord Senior Member Join Date: Feb 2001 Location: Toronto Posts: 808	by having 'alternate' printers (only one of which is actually running) the analogy you present fails to capture reality correctly. All events leading up to today will have been the exact same, regardless of when in the future humanity ends. This is why in my ticker tape example I used two printers, one of which will end sooner, the other later. Basing our observations ONLY on the past (which is all we have, the future is completely opaque) we can only say that we have a 50% chance of going down path a instead of path b. As a general comment to the thread, saying that we are randomly inserted into the continum is incorrect. This assumes we were 'souls' which poped into a random time in order to pick a random body to haunt. We are actually genetically predispositioned to exist right after our parents, so we are not randomly inserted. There is only one time you or I could come into this world.

08-06-2003, 10:33 AM	#36
Furby Regular Member Join Date: Jul 2003 Location: Southeast Asia Posts: 322	Well, I think the analogies of both the urns and the printers are still flawed because you are calculating the probabilities from the perspective of the experimenter, when in fact, you should be calculating them from the POV of the balls. So, suppose I find myself to be a ball in one of the urns, I have no other information except that urn A has 10 balls and urn B has 10,000 balls. Now, as mentioned earlier, if every ball guessed that they were in urn B then 10,000 balls would be correct and only 10 balls will be wrong. Hence, I would have good reason to guess that I am in urn B. Suppose I found out later that I'm actually ball number 7. This new information would cause me to re-evalutate the probability of me being in urn B and would actually cause me to lower my estimate of this probability by a lot. However, since my prior estimate was already so high (10 000 : 10), this would balance out the shift downwards and we would get a 50:50 probability. Hence, unless you were an alien observing the earth from outer space, you should not be able to conclude whether doomsday for humans would come any sooner or later.

08-06-2003, 11:20 AM	#37
Christopher Lord Senior Member Join Date: Feb 2001 Location: Toronto Posts: 808	Jesse, An agent on earth is the Nth imperfect copy of DNA. The agent know nothing about the future, and the past has already happened regardless of whether the world is about to end. the agent reasons: "Gee, doomsday should be about x years from 0 when N/x=1/2" or some other argument from cosmic popularity of Ns close to his own. this agent is implicitly assuming that x is bounded, and that N is 'probably' in the majority of all possible x. Why can an individual who is also a specific point in a series of copies assume that he is in the statistical majority of all x? He can't. He came in sequence. His number indicates only where in the sequence he is, and not when his particular 'brand' of DNA will no longer exist. Then, there is the question about bounds. We can not say that humanity will even end before the end of the universe with certainty, because life itself is in theory immortal. it will keep making copies for infinite years given the chance, and so thus will humans.

08-06-2003, 01:43 PM	#38
Jesse Moderator - Science Discussions Join Date: Feb 2001 Location: Providence, RI, USA Posts: 9,908	Christopher Lord: Jesse, An agent on earth is the Nth imperfect copy of DNA. The agent know nothing about the future, and the past has already happened regardless of whether the world is about to end. The past has already happened, but the prior probability distribution should not take into account the agent's knowledge of how many generations have already passed--otherwise it wouldn't be "prior" to his modifying the probabilities based on his own birth rank. That's just how Bayesian reasoning works. So, the agent should not assign zero prior probability to possible worlds where humanity goes extinct after fewer number of people than his own birth rank, as you argued earlier. Christopher Lord: the agent reasons: "Gee, doomsday should be about x years from 0 when N/x=1/2" or some other argument from cosmic popularity of Ns close to his own. this agent is implicitly assuming that x is bounded, and that N is 'probably' in the majority of all possible x. Why can an individual who is also a specific point in a series of copies assume that he is in the statistical majority of all x? He can't. He came in sequence. His number indicates only where in the sequence he is, and not when his particular 'brand' of DNA will no longer exist. Here you're getting into the "problem of the reference class" that Bostrom mentions, which I already agreed was a major problem for the Doomsday Argument. If the fact that you think it's arbitrary not to include prehuman primates or posthuman intelligences in the Doomsday Argument was your only objection to it, I'd say that's a reasonable objection, but it seems you have more fundamental problems with the self-sampling assumption even in less ambiguous cases. You didn't answer my question about the "two batches of different sexes" problem, which would clarify the exact nature of your objections--please do so if you respond to this post. Also, suppose all the humans in that experiment were going to be created in sequence (so the first three in the sequence would be one sex while the next 5000 in the sequence would be another)--would you then answer differently about how one should reason than if all 5003 humans were created at once? If not, it seems the whole sequential issue is a red herring. Christopher Lord: Then, there is the question about bounds. We can not say that humanity will even end before the end of the universe with certainty, because life itself is in theory immortal. it will keep making copies for infinite years given the chance, and so thus will humans. If that were true, then I'd think all but an infinitesimal fraction of intelligent beings would find themselves arising at a time when the number of intelligent beings before them was so great that the number could not even be compressed into a form they'd be capable of understanding (here I'm talking about 'compression' in the information-theory sense of reducing the number of bits needed to express the number). Thus by the logic of the doomsday argument, since I don't observe this to be true of my own birth rank, I should expect the chance of humanity continuing forever is infinitesimal, unless the prior probability of it lasting a finite time is zero or infinitesimal (although it's possible that I'm actually existing as a simulation performed by a very long-lasting civilization, in which case my true birth rank could be much greater than the 600 billion indicated by historical records, and maybe it would indeed be a number too large for me to comprehend...see Nick Bostrom's other page on the Simulation Argument for the case that there may actually be a high probability we're living in a simulation).

08-07-2003, 10:47 AM	#39
Christopher Lord Senior Member Join Date: Feb 2001 Location: Toronto Posts: 808	I admit i do not know much about Bayesian reasoning. I have objections on other grounds (which I hope have been made clear), but when it comes to the Bayesian logic behind it I have little grounding. What sort of university class usually teaches it? math? philosophy?

08-07-2003, 11:42 AM	#40
Mathetes Senior Member Join Date: Jun 2003 Location: Spaniard living in Silicon Valley Posts: 539	I think Friar Bellow's analysis is correct. The big issue with this problem is that we do not know what the unconditioned, "prior" probability is. Using his terms: In the urn example, the two models are equally possible, and p(short) = p(long) = 0.5. Is this realistic to refer to humanity? We do not know. It is possible that there is something like p(short) = 0.9 and p(long) = 0.1. Or the other way round. Without determining what the "prior" probability is, we cannot reliably calculate the conditioned, Bayesian probability of humanity being in the long or the short case. If the odds were really 50/50 it is very likely that we are doomed. But we do not know what the real odds are. Interesting puzzle.

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