Freethought & Rationalism Archive

Friar Bellows · 08-01-2003, 09:25 PM

I place two urns in front of you, and tell you that in one urn there are 10 balls, numbered consecutively from 1 to 10, while in the other urn there are a million balls, numbered from 1 to a million. You don't know which urn has the million balls, and which the 10 balls. I take out at random a ball from the left urn. You see that it is labelled as number 7. From which urn is this ball more likely to have originated: the urn with the million balls, or the urn with the 10 balls? The answer, using Bayesian probability analysis, or alternatively, common sense, is that the ball is more likely to have come from the urn with 10 balls.

Next, instead of two urns, we now have two models of humanity. In one model, humans become extinct after the 100 billionth human has been born, while in the other model, humans become extinct after the 100 trillionth human is born. The act of drawing a ball from an urn is, in this situation, analogous to observing that up to this point in time, some 60 billion humans have existed. Given this information, which model is more likely: the one which has us lasting for quite some time yet, or the one which sees our day of doom not too far off in the future?

The Doomsday Argument says that since the two examples are analogous, then we should reason the same way in the second example as in the first example, and therefore conclude that we are more likely to go extinct sooner than later. Can you spot a flaw in this argument? My meagre brain can't, but maybe some of you can see it. I'm not saying there is a flaw, but at least we'll have an interesting discussion.

Kat_Somm_Faen · 08-01-2003, 09:32 PM

A flaw?

How is this for one - reality trumps, beats, bests probability.

So if that ball come from the million, billion, gazillion ball jar who cares what probability says?

So humanity and its longevity is not in any way determined by this particular thought experiment

Majestyk · 08-01-2003, 09:34 PM

Offhand I'd ask why our extinction would be tied to a specific number of births?

Lobstrosity · 08-01-2003, 09:47 PM

The analogy is complete crap. In the urn example you're drawing a ball at random. It could have any number. In the population example the person you "draw" is anything but random. The number proceeds sequentially. There is nothing random at all about the number 60 billion.

Think of it this way. You have two urns. One contains ten balls numbered one through ten. The other contains a million labeled one through a million. The urns are pre-programmed to release balls in numerical order. Both pop out number one. Then both pop out number two. When you get to number seven, can you tell which urn is the one more likely to have a million balls in it? (Or phrased a different way, say that only one urn started crapping out balls but you knew that the balls had to come out in sequential order. When number seven finally appears after the first six, do you have any reason to conclude the urn is more or less likely to be the one with ten? In actuality it's still a complete toss-up.)

Friar Bellows · 08-01-2003, 09:52 PM

For the more mathematically inclined:

I mentioned Bayesian analysis. You start off with some "prior" probabilities. Then you learn some new information. Next you need to update these probabilities so that they now become "posterior" probabilities. Bayes theorem lets you work these out. Let's apply it to our doomsday example. First we'll assume that the two models of humanity are equally likely, at least as far as our "prior" probabilities go. Let:

p(long) = "Prior" probability of model with 100 trillion humans
p(short) = "Prior" probability of model with 100 billion humans

p(60B | short) = Probability of being at stage 60 billion humans, in the model with 100 billion humans
p(60B | long) = Probability of being at stage 60 billion humans, in the model with 100 trillion humans

What we're after is p(short | 60B) or the probability of the short-lived model being correct, given that we're at stage 60 billion humans. Now we have:

p(long) = p(short) = 0.5
p(60B | short) = 1 / 100 billion
p(60B | long) = 1 / 100 trillion

Bayes theorem applied to this example gives:

p(short | 60B) = p(60B | short) * p(short) / (p(60B | short) * p(short) + p(60B | long) * p(long))

= 0.9990 or 99.90% (approx).

Wow! Not looking good. Now our prior probabilities had no real information content in them. But supposing they did. Suppose that we used all the information at our disposal, from all fields of science and technology, and add a bit of futurology and physical eschatology for fun, and we determined the following priors for our model:

p(short) = 0.01 = 1%
p(long) = 0.99 = 99%

That is, we felt really confident that humanity would last a long time. Now let's see what the fact that we are currently at the 60 billionth human tells us. We plug the new p(short) and p(long) values into Bayes formula and we find that:

p(short | 60B) = 0.9099 = 90.99 % (approx)

Double wow! By itself, the fact that we are at the 60 billionth human has changed our prior probability of 1% to a posterior probability of roughly 91%. Bit of a dent to our confidence!

Kat_Somm_Faen · 08-01-2003, 10:06 PM

Well true if you consider a lifespan of a person.

Probability says nothing about when you will die but as everyday passes you KNOW you have one day less to live

So with every person born we are one person closer to the last human born... that much is true if we assume ( which is pretty much a given ) that lifespan of humanity is finite.

Again you could die tommorow as well as you could die on a 100 years. Reality is the judge on this and probability cant say much about that.

Yeah we are all doomed... everyone dies - but did you really need probability to show that to be true?

Friar Bellows · 08-01-2003, 11:14 PM

Quote:

Originally posted by Kat_Somm_Faen
How is this for one - reality trumps, beats, bests probability.

So if that ball come from the million, billion, gazillion ball jar who cares what probability says?

So humanity and its longevity is not in any way determined by this particular thought experiment

This is not about determinism. This is probability. We don't have all the facts about reality. So, for now, we must stick to probabilities.

Quote:

Originally posted by Majestyk
Offhand I'd ask why our extinction would be tied to a specific number of births?

Because the only two models I allowed in this example involved extinction at a specific number of births. I'm asking which model is more likely, that's all.

Quote:

Originally posted by Lobstrosity
In the urn example you're drawing a ball at random. It could have any number. In the population example the person you "draw" is anything but random. The number proceeds sequentially. There is nothing random at all about the number 60 billion.

Excellent. This is what the shift in probabilities largely hinges on. Can I consider myself a random sample? Well, you say no, but are you correctly calculating "prior" probabilities with respect to the two models? I don't pretend to know the answer to either question. Mathematically, you're saying that:

P(60B | short) <> 1/100 billion

and

P(60B | long) <> 1/100 trillion

("<>" stands for "is not equal to")

That in fact:

P(60B | short) = 1

and

P(60B | long) = 1

In other words, you're saying, "I know we're at 60 billion and so the probability of that is 1, for either model". And so the probability of the long (or short) model being correct is 0.5 or 50%.

I found out about the Doomsday argument after visiting this web site:

http://www.anthropic-principle.com

Possibly the above questions are answered here. Specifically, see:

Question 3 from the Doomsday Argument FAQ, and Investigations into the Doomsday Argument.

Chimp · 08-02-2003, 12:14 AM

What about other factors in the equation, for example, when humans reach a certain level of technological advancement and they are able to guide their own evolution? What would happen if humans are able to increase their intelligence by implanting computer chips?

The many variables in the "life" equation appears to be different that two jars containing the inert matter(numbered balls)?

What about positive feedback? Would it change the outcome in favor, or against, survival?

http://www.lobue.com/enterprise_evol..._feedback.html

Quote:

But there is another type of feedback that may be illustrated with an economics example. Sony was generally credited with having the superior videotape technology with its Beta format and was first to market. However, a larger number of companies came to support the competing VHS videotape format initially developed by JVC. Although the image was not as sharp as the Sony Beta, these decks were less expensive and had a longer playing time, and over time, more and more consumers came to purchase VHS tape decks. When movie videos began to be popular, more tapes were available in the rental stores in the VHS format (because more people had VHS decks), which in turn influenced more people to purchase VHS tape decks because there was more movie selection. This feedback loop of more people wanting VHS tapes leading to more VHS decks being sold continued for several years, and finally Sony ceased making Beta videotape machines altogether.

The feedback loop described in the Sony example is technically known as positive feedback. As the example discusses, the output from one state of the system (the number of VHS tape decks and the number of videotapes) is fed back into the system, which then leads to more VHS tape decks and more VHS video tapes, which then lead to more VHS tape decks and more videos, and so on. Positive feedback loops are an important characteristic of many complex systems, and constitute one of the interaction processes that contribute to nonlinearities and emergence in complex systems.

Furby · 08-02-2003, 01:25 AM

Suppose we were to present this Doomsday Argument several thousands years back where the number of humans that have existed was only one hundred thousand.

Now, we again have two models of humanity. In one model, humans become extinct after the 1 millionth human has been born, while in the other model, humans become extinct after the 60 billionth human.

So, according to the argument, it is far more probable that the first model is true rather than the second one. But hey, here we are with 60 billion humans having been born and we still exist!

Hence, given the sheer improbabilities that we are still alive, I have to conclude that some divine hand is guiding and helping us.
Atheism is thus an insupportable position, please go to your nearest church and convert now.

Tenpudo · 08-02-2003, 02:33 AM

Taken to extremes, wouldn't this formula indicate that humanity is most likely to go extinct before another single person is born?
*checks watch*
Oop-- too late!
Back to the drawing board...

08-01-2003, 09:25 PM	#1
Friar Bellows Veteran Member Join Date: Apr 2001 Location: arse-end of the world Posts: 2,305	We're doomed! Doomed I tells ya! I place two urns in front of you, and tell you that in one urn there are 10 balls, numbered consecutively from 1 to 10, while in the other urn there are a million balls, numbered from 1 to a million. You don't know which urn has the million balls, and which the 10 balls. I take out at random a ball from the left urn. You see that it is labelled as number 7. From which urn is this ball more likely to have originated: the urn with the million balls, or the urn with the 10 balls? The answer, using Bayesian probability analysis, or alternatively, common sense, is that the ball is more likely to have come from the urn with 10 balls. Next, instead of two urns, we now have two models of humanity. In one model, humans become extinct after the 100 billionth human has been born, while in the other model, humans become extinct after the 100 trillionth human is born. The act of drawing a ball from an urn is, in this situation, analogous to observing that up to this point in time, some 60 billion humans have existed. Given this information, which model is more likely: the one which has us lasting for quite some time yet, or the one which sees our day of doom not too far off in the future? The Doomsday Argument says that since the two examples are analogous, then we should reason the same way in the second example as in the first example, and therefore conclude that we are more likely to go extinct sooner than later. Can you spot a flaw in this argument? My meagre brain can't, but maybe some of you can see it. I'm not saying there is a flaw, but at least we'll have an interesting discussion.

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08-01-2003, 09:32 PM	#2
Kat_Somm_Faen Veteran Member Join Date: Jun 2001 Location: Boulder, Colorado Posts: 3,316	A flaw? How is this for one - reality trumps, beats, bests probability. So if that ball come from the million, billion, gazillion ball jar who cares what probability says? So humanity and its longevity is not in any way determined by this particular thought experiment

08-01-2003, 09:34 PM	#3
Majestyk Veteran Member Join Date: Mar 2003 Location: Northeast Ohio Posts: 2,846	Offhand I'd ask why our extinction would be tied to a specific number of births?

08-01-2003, 09:47 PM	#4
Lobstrosity Senior Member Join Date: Feb 2003 Location: San Diego, California Posts: 719	The analogy is complete crap. In the urn example you're drawing a ball at random. It could have any number. In the population example the person you "draw" is anything but random. The number proceeds sequentially. There is nothing random at all about the number 60 billion. Think of it this way. You have two urns. One contains ten balls numbered one through ten. The other contains a million labeled one through a million. The urns are pre-programmed to release balls in numerical order. Both pop out number one. Then both pop out number two. When you get to number seven, can you tell which urn is the one more likely to have a million balls in it? (Or phrased a different way, say that only one urn started crapping out balls but you knew that the balls had to come out in sequential order. When number seven finally appears after the first six, do you have any reason to conclude the urn is more or less likely to be the one with ten? In actuality it's still a complete toss-up.)

08-01-2003, 09:52 PM	#5
Friar Bellows Veteran Member Join Date: Apr 2001 Location: arse-end of the world Posts: 2,305	For the more mathematically inclined: I mentioned Bayesian analysis. You start off with some "prior" probabilities. Then you learn some new information. Next you need to update these probabilities so that they now become "posterior" probabilities. Bayes theorem lets you work these out. Let's apply it to our doomsday example. First we'll assume that the two models of humanity are equally likely, at least as far as our "prior" probabilities go. Let: p(long) = "Prior" probability of model with 100 trillion humans p(short) = "Prior" probability of model with 100 billion humans p(60B \| short) = Probability of being at stage 60 billion humans, in the model with 100 billion humans p(60B \| long) = Probability of being at stage 60 billion humans, in the model with 100 trillion humans What we're after is p(short \| 60B) or the probability of the short-lived model being correct, given that we're at stage 60 billion humans. Now we have: p(long) = p(short) = 0.5 p(60B \| short) = 1 / 100 billion p(60B \| long) = 1 / 100 trillion Bayes theorem applied to this example gives: p(short \| 60B) = p(60B \| short) * p(short) / (p(60B \| short) * p(short) + p(60B \| long) * p(long)) = 0.9990 or 99.90% (approx). Wow! Not looking good. Now our prior probabilities had no real information content in them. But supposing they did. Suppose that we used all the information at our disposal, from all fields of science and technology, and add a bit of futurology and physical eschatology for fun, and we determined the following priors for our model: p(short) = 0.01 = 1% p(long) = 0.99 = 99% That is, we felt really confident that humanity would last a long time. Now let's see what the fact that we are currently at the 60 billionth human tells us. We plug the new p(short) and p(long) values into Bayes formula and we find that: p(short \| 60B) = 0.9099 = 90.99 % (approx) Double wow! By itself, the fact that we are at the 60 billionth human has changed our prior probability of 1% to a posterior probability of roughly 91%. Bit of a dent to our confidence!

08-01-2003, 10:06 PM	#6
Kat_Somm_Faen Veteran Member Join Date: Jun 2001 Location: Boulder, Colorado Posts: 3,316	Well true if you consider a lifespan of a person. Probability says nothing about when you will die but as everyday passes you KNOW you have one day less to live So with every person born we are one person closer to the last human born... that much is true if we assume ( which is pretty much a given ) that lifespan of humanity is finite. Again you could die tommorow as well as you could die on a 100 years. Reality is the judge on this and probability cant say much about that. Yeah we are all doomed... everyone dies - but did you really need probability to show that to be true?

08-02-2003, 01:25 AM	#9
Furby Regular Member Join Date: Jul 2003 Location: Southeast Asia Posts: 322	Suppose we were to present this Doomsday Argument several thousands years back where the number of humans that have existed was only one hundred thousand. Now, we again have two models of humanity. In one model, humans become extinct after the 1 millionth human has been born, while in the other model, humans become extinct after the 60 billionth human. So, according to the argument, it is far more probable that the first model is true rather than the second one. But hey, here we are with 60 billion humans having been born and we still exist! Hence, given the sheer improbabilities that we are still alive, I have to conclude that some divine hand is guiding and helping us. Atheism is thus an insupportable position, please go to your nearest church and convert now.

08-02-2003, 02:33 AM	#10
Tenpudo Regular Member Join Date: Jul 2002 Location: Bellingham WA Posts: 219	Taken to extremes, wouldn't this formula indicate that humanity is most likely to go extinct before another single person is born? checks watch Oop-- too late! Back to the drawing board...

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