[Merged] Immortality & Bayesian Statistics

[jt512]

We agree that the probability of Jabba's existence is 1. That would be P(Me) = 1.

Again, briefly, you are confusing the term P(me) in Bayes' formula with P(me|me). To put it another way, the probability that you are saying is 1 is the probability of Jabba's existence given that we know he exists. But such a probability does not appear in Bayes' formula. Rather (and Toontown is basically correct on this), the term P(me) in Bayes' formula is the weighted average of the conditional probabilities that "me" would be observed under each hypothesis, where the weights are the prior probabilities of those hypotheses. If Jabba's model "A" is that "me" is a random event, then P(me|A) is not 1, but some small number. That, in turn, implies that P(me) is less than 1.

The problem with Jabba's analysis (well, one problem) is that neither P(me|A) nor P(me|~A) belongs in the analysis, because "me" is not what either A or ~A predicts. Rather, what A (to the extent that it has been defined) predicts is that the population of humans at any particular moment in human history will be a ragtag assortment produced by more-or-less random sperm–egg pairs, and what ~A (to the extent that it has been defined) predicts is that the population (the entire population, not just "me") had been somehow pre-selected.

In my view the data are in better agreement with A than ~A.

 

[PixyMisa]

Again, briefly, you are confusing the term P(me) in Bayes' formula with P(me|me).

Yes, but there is something unusual going on with this type of argument: The argument and the arguer are effectively both variables in the argument itself. If we define me as someone who makes Jabba's argument or its equivalent (rather than Jabba's exect genes or molecules) then P(me|my argument) = 1 - the argument implies the arguer. And the probability of my argument is 1, because it's the topic at hand.

To put it another way, the probability that you are saying is 1 is the probability of Jabba's existence given that we know he exists.

But he must exist to present the argument. So the anthropic principle comes into play: If the argument is being made, the arguer and the universe in which he or she exists must be such that the argument could be made.

The problem with Jabba's analysis (well, one problem) is that neither P(me|A) nor P(me|~A) belongs in the analysis, because "me" is not what either A or ~A predicts.

Yes, I'd say that's the single biggest problem. But the point that P(me) = 1 is also valid, if from a philosophical rather than purely mathematical perspective.

 

[Toontown]

Yes, but there is something unusual going on with this type of argument: The argument and the arguer are effectively both variables in the argument itself. If we define me as someone who makes Jabba's argument or its equivalent (rather than Jabba's exect genes or molecules) then P(me|my argument) = 1 - the argument implies the arguer. And the probability of my argument is 1, because it's the topic at hand.

1. The probability of any argument is 1.

2. The primary prerequisite to questioning the genesis of any observation is the actual existence of the observation.

But he must exist to present the argument. So the anthropic principle comes into play: If the argument is being made, the arguer and the universe in which he or she exists must be such that the argument could be made.

My analogy, which you gave short shrift, demonstrates your error here. In the analogy, the player is not allowed to play unless a white bead is drawn. A white bead is the prerequisite to being allowed to guess which urn the bead came from.

To make your argument here, show how it is impossible for the player to guess the genesis of the white bead to a high level of confidence.

...But the point that P(me) = 1 is also valid, if from a philosophical rather than purely mathematical perspective.

The constant repetition of an irrelevant tautological mantra is not valid from any perspective.

the probability that I exist is 1 - nam myoho renge kyo
the probability that I exist is 1 - nam myoho renge kyo
the probability that I exist is 1 - nam myoho renge kyo

......

 

[Akhenaten]

1. The probability of any argument is 1.

<stuff>

Cool. So that essentially proves immortality, does it?

I thought there'd be more to it than that.

 

[jsfisher]

Again, briefly, you are confusing the term P(me) in Bayes' formula with P(me|me). To put it another way, the probability that you are saying is 1 is the probability of Jabba's existence given that we know he exists.

Not quite.

Borrowing the example from Wikipedia, a randomly selected person is under consideration. Is the person female? Does knowing the person has long hair help us improve our probability estimate of gender? Yes, Bayes' inference comes to our aid.

But that does not parallel what Jabba is doing. Jabba has selected an existing person then asked is the person mortal. Does knowing the person exists help us improve our estimate of mortality? No, it does not. Existence was already determined as part of the background information.

 

[Jabba]

Jabba, would you agree that there are an infinite number of possible grains of sand in the universe?

Dave,
- No.

 

[Akhenaten]

Oops.

 

[jt512]

Yes, but there is something unusual going on with this type of argument: The argument and the arguer are effectively both variables in the argument itself. If we define me as someone who makes Jabba's argument or its equivalent (rather than Jabba's exect genes or molecules) then P(me|my argument) = 1 - the argument implies the arguer. And the probability of my argument is 1, because it's the topic at hand.

It doesn't matter if the person making the argument also happens to be a data point. The term P(me|my argument) does not appear in Bayes' Formula. If fact, you've just concocted an unnecessarily complicated way of stating P(me|me), which, as I've said, is also not in Bayes' Theorem. In fact, it would make no difference if "me" were replaced by "Leonard Nimoy." Leonard Nimoy isn't making the argument, yet the argument would be formally, and presumably numerically, the same. P(me|A) is presumably the same (the number 1/4e17 has been proposed) regardless of whether "me" is the person making the argument or someone else.

The relevant terms involving "me" are P(me|A) and P(me|~A), which is to say the only thing that matters is the relative probability that "me" would have come into existence under model A (whatever that is) vs its complement (whatever that is). The fact that "me" exists, or that "me" is the one doing the analysis, doesn't matter. The question is, which model of the Universe better explains the observed data, in this case, "me."

But he must exist to present the argument. So the anthropic principle comes into play: If the argument is being made, the arguer and the universe in which he or she exists must be such that the argument could be made.

It doesn't matter, because the question is which model of the universe is more likely to have produced the observed data. Professional cosmologists can ask questions about the relative likelihoods of models of the universe they live in. Why can't Jabba?

Yes, I'd say that's the single biggest problem. But the point that P(me) = 1 is also valid, if from a philosophical rather than purely mathematical perspective.

So P(me|A) is one thing mathematically and another philosophically? I doubt it; rather, I'd say that the probability that you've made a philosophical mistake is pretty close to 1.

 

[jt512]

Not quite.

Borrowing the example from Wikipedia, a randomly selected person is under consideration. Is the person female? Does knowing the person has long hair help us improve our probability estimate of gender? Yes, Bayes' inference comes to our aid.

But that does not parallel what Jabba is doing. Jabba has selected an existing person then asked is the person mortal. Does knowing the person exists help us improve our estimate of mortality? No, it does not. Existence was already determined as part of the background information.

It seems to me that we can take any piece of information that we already know, treat it as the data rather than background information, and use it to calculate a posterior probability. Consider your example from wikipedia: We want to calculate the probability that a person's sex is female. Our background information suggests a prior probability of .5. Now we learn that the person has long hair. We plug that data into Bayes' Theorem, and we find that our posterior probability is, say .9.

Now, a variation on the above example. We know that a person has long hair and we ask ourselves, how does that knowledge (ie, that data) affect the probability that that person is a female? We start by ignoring the data, giving us, again a "prior" probability of .5, we plug the data into Bayes' Theorem, and voila, we find that the posterior probability is, .9, just as before. This is, of course, as it must be since the priors and the likelihoods were the same in both cases. The only difference was the timing of the analysis. In the first case, we decided to do the analysis before we knew the hair length; in the latter case, after.

Another example. I have a real dataset, and I do a thorough exploratory analysis of it followed by some frequentist hypothesis testing. The data, clearly exist, and by the time I am done with my analysis, I am thoroughly familiar with it. A year goes by and I have become a Bayesian. According to your line of reasoning, I cannot use the dataset as data in a Bayesian hypothesis test because the dataset already exists and I know its content; therefore, it is background information, not data. WTF?

 

[Jabba]

Again, briefly, you are confusing the term P(me) in Bayes' formula with P(me|me). To put it another way, the probability that you are saying is 1 is the probability of Jabba's existence given that we know he exists. But such a probability does not appear in Bayes' formula. Rather (and Toontown is basically correct on this), the term P(me) in Bayes' formula is the weighted average of the conditional probabilities that "me" would be observed under each hypothesis, where the weights are the prior probabilities of those hypotheses. If Jabba's model "A" is that "me" is a random event, then P(me|A) is not 1, but some small number. That, in turn, implies that P(me) is less than 1.

The problem with Jabba's analysis (well, one problem) is that neither P(me|A) nor P(me|~A) belongs in the analysis, because "me" is not what either A or ~A predicts. Rather, what A (to the extent that it has been defined) predicts is that the population of humans at any particular moment in human history will be a ragtag assortment produced by more-or-less random sperm–egg pairs, and what ~A (to the extent that it has been defined) predicts is that the population (the entire population, not just "me") had been somehow pre-selected.

In my view the data are in better agreement with A than ~A.

Jay,
- Again, this won't bring closure, but it could be a step in the right direction. I am talking about the entire population... I'll rethink how I should try to phrase all of this.

 

[godless dave]

Dave,
- No.

What limits grains of sand that doesn't limit observers?

 

[jt512]

Jay,
- Again, this won't bring closure, but it could be a step in the right direction. I am talking about the entire population... I'll rethink how I should try to phrase all of this.

It would be a step in the right direction for you to consider the probability of the entire human population in your calculations, rather than just you; but, please, don't try and convince us that that was what you meant by "me" all along.

 

[John Jones]

What limits grains of sand that doesn't limit observers?

This.

 

[Giordano]

What limits grains of sand that doesn't limit observers?

Good question. Is it because Jabba really means "selves" and not observers as you and I define it? Because for Jabba, "selves" are magical and grains of sand aren't?

But again, Jabba, aren't grain of sands extrinsically finite like VWs? So aren't grains of sand, VWs, and selves proven to be reincarnated by your formula? Am I not understanding here? Tell me if so.

Oh, I forget, you and Dave are having a private conversation and the rest of us are currently ignored. Sorry to barge in!

 

[Giordano]

Jay,
- Again, this won't bring closure, but it could be a step in the right direction. I am talking about the entire population... I'll rethink how I should try to phrase all of this.

Great! I am truly glad to have you realize this. But remember, if as the SM declares, the "self" or "observer" is an emergent property of having a physical human brain, then the probability of having a "self" is nearly equal to the probability of having a physical human brain. So your calculation will have change to predict the probability of a human fetus successfully forming and having a physical brain. Given there are an average of about 2 children for each couple, and the vast majority of them have brains, I don't think the chance of a "self" is 1/infinity as you have claimed!

 

[abaddon]

What limits grains of sand that doesn't limit observers?

This.

I will have a stab at the likely response. Grains of sand are not significant, but selves are. Yet another evidential mountain to climb, and for what? Another ten years of prevarication?

 

[abaddon]

What limits grains of sand that doesn't limit observers?

Observers are special. Here begineth the inevitable circular argument.

 

[PixyMisa]

It doesn't matter, because the question is which model of the universe is more likely to have produced the observed data. Professional cosmologists can ask questions about the relative likelihoods of models of the universe they live in. Why can't Jabba?

Cosmology is still based on methodological naturalism.

Your post deserves a more complete answer; I'll come back to this later today.

 

[pakeha]

Well spotted, Giordano.
"...your calculation will have change to predict the probability of a human fetus successfully forming and having a physical brain. ..."

That's limiting the calculation to humans on our own planet, I dare say?

 

[Jabba]

It would be a step in the right direction for you to consider the probability of the entire human population in your calculations, rather than just you; but, please, don't try and convince us that that was what you meant by "me" all along.

Jay,
- I may be misunderstanding your point, but I've always said that as long as you guys aren't androids, immortality applies to you guys (and everyone else) also.