[Merged] Immortality & Bayesian Statistics

[Jabba]

This is wierd. You're the only one in the thread who understands anything I say.

- And probably vice versa -- though, I hold out hope that there are a couple more.

 

[Garrette]

- And probably vice versa -- though, I hold out hope that there are a couple more.

I think the number who understand both you and Toontown is greater than you think. It is the number who disagree both with your premise and your conclusion that is the real issue. This is true even accounting for the bits that Toontown calls, in my wording, semantic lockjaw.

There are some errors in your logic that I see, but the one I want to address first is this one, and it is from your Scene2 link. You say

Since P(me|R) is simply indefinable (it isn't .0 or vanishingly small), I can substitute any positive value I want (.01 for instance)...

This is greatly flawed. Just to touch on your conclusion that you can substitute any positive value you want: No. You can't, not if you wish to remain at all objective. You need to explain how you determine that value.

More fundamental, though, is the idea that P(me|R) isn't .0 or vanishingly small. Why not? If P(me|NR) is vanishingly small based on the infinite possibilities of consciousnesses from which to choose, then why does not the same objection apply to R? Does not the deity in R have the same infinite choices of consciousnesses from which to choose?

Forget the rest of your equation. Demonstrate why I should think that P(me|NR) < P(me|R). Everything else flows from that, and merely saying that a deity can choose me is no different than saying a universe without a deity can end up with me.

 

[Jabba]

Garrette,
- Thanks for giving me something to focus upon. Seriously.
- Hopefully, I can provide some effective answers.
- I'll be back.

 

[lenny]

But if every possible outcome is carries a very very low probability, then you expect a low probability outcome, you just don't know which one.

Jabba's angle is you don't expect a particular one.

perhaps not. but i see no angle in that statement inasmuch as you expect which ever particular one does happen to have a vanishingly small probability. and thus is it not at all surprising that the one we observe has a vanishing small probability.

are you suggesting the argument holds even when nothing unexpected happened? when there was no surprisingly low probability event?

 

[jt512]

This is wierd. You're [ie, Jabba] the only one in the thread who understands anything I say.

I agree that it is weird that Jabba is the only one in the thread who understands anything you say, but I have a feeling I interpret that observation differently than you.

 

[jt512]

Go to a race track. Look at the tote board. You will see odds expressed as 3:2, 7:5, 7:2, 1, 2, 3, 4, 5, 6, and so on. Odds are not invarably expressed as "to 1".

And when they are, they are never called "odds to one."

I was talking about 1/p-1, not p/(1-p), and so it was that I said I was talking about "odds to 1" in an apparently impossible attempt to communicate that fact.

If "odds to 1" were a meaningful term, then it would apply equally to 1/p–1 and p/(1–p), since both can always be expressed as a ratio x:1. So the fact that you were referring to the odds against the event cannot be a justification for making up the phrase "odds to 1."

Then jt512 leaped gracefully to the wrong conclusion that I was talking about 0.2/(1-0.2), in spite of my pointed effort to belay any such misunderstanding.

Nope. I knew you were referring to the odds against the event you were talking about because you posted the equation you were using. My point, which you stubbornly refuse to acknowledge, is that having called it "odds to 1," the only reason that I understood what you meant was that you posted the equation. Had you used the actual name, "odds against," I and everyone else would have immediately known what you were talking about.

 

[Toontown]

- Perhaps, my second entry should have been, 'Seven billion over infinity is essentially no greater than one over infinity. So maybe, the fact that there are seven billion of us today instead of just one doesn't make any difference to the proper conclusion here. Though, this probably does deserve more thought.

- I need a nap.

Alternate viewpoint:

The prior probabilities of the other 7 billion do not concern you. You expect them to be present in any case, under any hypothesis that acknowledges what we think we know about reality. What you do not expect, given the assumption of finite uniqueness, is to find your presumably finitely unique self among them, if the hypothesis you are testing is true.

The problem is, your test is unlikely to convince many of them of anything. From Mr. P's perspective, you are just another face in the crowd, to be expected in any case, and Mr. P is the special one. However, all P's can repeat your test on themselves, and arrive at the same conclusion you do, assuming your reasoning is valid. The fact that everyone can do the same test and arrive at the same conclusion hardly makes the answer wrong. OTC, it's strangely evocative of the scientific method.

The other problem is, to really understand the test, we need to grasp what is actually being tested, which is, IMO - is eternal nothingness the corollary to this particular finite, unique brain (one organization, one time, one place, or bust), which is generating this particular sentient experience?

If the all-knowing bird's eye answer to the seemingly obvious question is yes, then I have beaten arguably infinite odds because this brain has come into existence against arguably infinite prior odds. My frog's eye question then becomes

'Should I believe I've beaten infinite odds?'

If any of you can come up with a consistent hypothesis which makes my observed sentient existence significantly more than infinitely unlikely, then I will prefer that hypothesis - until your hypothesis dies or I find a better one. Until then, my answer is

But none of you can do it. You ain't got the chops.

 

[Garrette]

Alternate viewpoint:

The prior probabilities of the other 7 billion do not concern you.

Quibble I had intended to point out to Jabba earlier: The 7 billion should be much more than that, unless you are restricting this to consciousness existing right now. Not that 1 trillion over infinity is any further from zero than 7 billion over infinity.

You expect them to be present in any case, under any hypothesis that acknowledges what we think we know about reality.

Well, we might expect some 7 billion to be present but not necessarily those specific 7 billion.

What you do not expect, given the assumption of finite uniqueness, is to find your presumably finitely unique self among them, if the hypothesis you are testing is true.

Yes, but we also do not expect to find ourself among them even with other hypotheses, re the recent discussion about definition of "self." (Might be remembering terms incorrectly, but as you are adamantly not hung up on those, I gather I'm safe there).

The problem is, your test is unlikely to convince many of them of anything. From Mr. P's perspective, you are just another face in the crowd, to be expected in any case, and Mr. P is the special one. However, all P's can repeat your test on themselves, and arrive at the same conclusion you do, assuming your reasoning is valid. The fact that everyone can do the same test and arrive at the same conclusion hardly makes the answer wrong. OTC, it's strangely evocative of the scientific method.

I think I'm with you here.

The other problem is, to really understand the test, we need to grasp what is actually being tested, which is, IMO - is eternal nothingness the corollary to this particular finite, unique brain (one organization, one time, one place, or bust), which is generating this particular sentient experience?

Why is that what is actually being tested? It is of interest, yes, but I see no requirement for its involvement in the question to hand.

If the all-knowing bird's eye answer to the seemingly obvious question is yes,

To me, at least, the "seemingly obvious question" is not obvious at all. Clarification, please?

then I have beaten arguably infinite odds because this brain has come into existence against arguably infinite prior odds.

I'll leave out discussion of whether you are using "prior odds" correctly, because I don't know the answer, but your questions seems rather intentionally tautological, i.e., if there were infinite odds against my being, does my being mean I beat infinite odds? I would think the answer is, yes, of course, but that is only a valid argument, not necessarily a sound one.

My frog's eye question then becomes

'Should I believe I've beaten infinite odds?'

Surely it is the same question?

If any of you can come up with a consistent hypothesis which makes my observed sentient existence significantly more than infinitely unlikely, then I will prefer that hypothesis - until your hypothesis dies or I find a better one. Until then, my answer is

I actually agree with your answer, but not your premise. Leaving aside the definition of "beat" in regard to the odds, the odds weren't infinite. The use of the word "significantly" in your request ("significantly more than infinitely unlikely") is misleading. Anything at all that is more than infinitely unlikely is "significantly" so, even if virtually vanishingly small. Infinite possibilities is not the equivalent of infinite impossibilities.

But none of you can do it. You ain't got the chops.

And I should bow down before you now? I've little trouble accepting that I fall far short of many here, and probably even you, in the philosophical realm, among others. Doesn't mean I have no place in the race, particularly when the back of the runner in front of me seems more like the guy in high school who was a bit quicker than I am but was not Usain Bolt by any means. You aint Usain, Toontown.

 

[Toontown]

perhaps not. but i see no angle in that statement inasmuch as you expect which ever particular one does happen to have a vanishingly small probability. and thus is it not at all surprising that the one we observe has a vanishing small probability.

By that reasoning you should not be surprised at all if you win the lottery after finding a ticket on the sidewalk, simply because other lottery winners exist.

The surprising part (if you are fully aware of the staggering odds against your ticket being the winning one), is not that lottery winners exist. That's inevitable. What is not inevitable, and in fact deeply surprising, is when you win.

Don't hold your breath.

are you suggesting the argument holds even when nothing unexpected happened? when there was no surprisingly low probability event?

Something quite unexpected has happened if you find your finitely unique self among the living, against giganogargantuan odds. But stop insisting on being so finitely unique, and your existence stops being so unexpected.

It is not the observation that is being tested, it is the hypothesis that gave rise to the prior probability that is being tested. A probability, in this sense, is a degree of certainty. When this degree of certainty is utterly ravaged, it is justified to be surprised, and then to question the hypothesis which gave rise to the ravaged degree of certainty.

 

[Garrette]

By that reasoning you should not be surprised at all if you win the lottery after finding a ticket on the sidewalk, simply because other lottery winners exist.

The surprising part (if you are fully aware of the staggering odds against your ticket being the winning one), is not that lottery winners exist. That's inevitable. What is not inevitable, and in fact deeply surprising, is when you win.

Don't hold your breath.



Something quite unexpected has happened if you find your finitely unique self among the living, against giganogargantuan odds. But stop insisting on being so finitely unique, and your existence stops being so unexpected.

It is not the observation that is being tested, it is the hypothesis that gave rise to the prior probability that is being tested. A probability, in this sense, is a degree of certainty. When this degree of certainty is utterly ravaged, it is justified to be surprised, and then to question the hypothesis which gave rise to the ravaged degree of certainty.

No. The surprise if one wins with a lottery ticket found on the sidewalk is no greater than the surprise if one wins with a lottery ticket purchased, and neither surprise is anything but an emotional response. Objectively, it is no more surprising if I win than if the little old lady from Pasadena whom I have never met wins or if you win or if any of a million other winners win.

Regarding the ravaging of certainties, (1) such things happen all the time and are to be expected without resort to anything else, and (2) it hasn't been ravaged; that would only happen if a particular low probability outcome were reliably predicted; that has not been shown to happen. Not even the attempt to show it has been made.

Your dismissal of finite uniqueness may be correct, but nothing you have said or shown here supports the idea.

 

[Toontown]

Quibble I had intended to point out to Jabba earlier: The 7 billion should be much more than that, unless you are restricting this to consciousness existing right now. Not that 1 trillion over infinity is any further from zero than 7 billion over infinity.

It doesn't matter how many of anything exists. You might as well be counting grains of sand on Mars.

If you hypothesize that a unique brain is the only way to experience sentience, then the probability of experiencing sentience is exactly equal to the probability of that unique brain coming into existence, in that unique organization, in those unique spacetime coordinates, or it's nothingness forever.

Well, we might expect some 7 billion to be present but not necessarily those specific 7 billion.

In which case your imagined substitutes would be the 7 billion. No matter.

Yes, but we also do not expect to find ourself among them even with other hypotheses, re the recent discussion about definition of "self." (Might be remembering terms incorrectly, but as you are adamantly not hung up on those, I gather I'm safe there).

I don't know what hypotheses you're referring to, but if they make my sentient experience equally unlikely, then I will reject them with equal certainty.

I guess I'm just odd that way. I tend to be skeptical of hypotheses that can't account for my existence. I might even prefer a hypothesis that seems less parsimonious in other respects if the alternative stacks giganogargantuan odds against my primary observation.

Why is that what is actually being tested? It is of interest, yes, but I see no requirement for its involvement in the question to hand.

If the presumed prerequisite to my sentient experience does not occur, then what is the alternative?

To me, at least, the "seemingly obvious question" is not obvious at all. Clarification, please?

Sorry, I forgot what the "seemingly obvious question" was. But take my word for it. It was seemingly obvious.

I'll leave out discussion of whether you are using "prior odds" correctly, because I don't know the answer, but your questions seems rather intentionally tautological, i.e., if there were infinite odds against my being, does my being mean I beat infinite odds? I would think the answer is, yes, of course, but that is only a valid argument, not necessarily a sound one.

You need to remember what gave rise to that IF. That IF was brought about by assuming a hypothesis to be true for testing purposes. Your sentient experience means you beat infinite odds ONLY IF the presumed hypothesis is true. But the presumed truth of the hypothesis is an IF, not a fact. What you know is, the hypothesis says what you are experiencing is far too unlikely to maintain any confidence in the hypothesis.

I actually agree with your answer, but not your premise. Leaving aside the definition of "beat" in regard to the odds, the odds weren't infinite. The use of the word "significantly" in your request ("significantly more than infinitely unlikely") is misleading. Anything at all that is more than infinitely unlikely is "significantly" so, even if virtually vanishingly small. Infinite possibilities is not the equivalent of infinite impossibilities.

I don't insist that the odds are infinite. But an argument could be made. I do insist that the odds are giganogargantuan. It's just that infinite is quicker to type, and doesn't change the issue at hand.

The bottom line is, I would prefer a consistent hypothesis that makes what I see more likely over an otherwise consistent hypothesis that makes what I see less likely. I'm just odd that way sometimes.

And I should bow down before you now? I've little trouble accepting that I fall far short of many here, and probably even you, in the philosophical realm, among others. Doesn't mean I have no place in the race, particularly when the back of the runner in front of me seems more like the guy in high school who was a bit quicker than I am but was not Usain Bolt by any means. You aint Usain, Toontown.

Yes. You must bow down before Zarg.

Or come up with a consistent hypothesis that makes what I see more likely than the alternatives.

 

[jt512]

By that reasoning you should not be surprised at all if you win the lottery after finding a ticket on the sidewalk, simply because other lottery winners exist.

The surprising part (if you are fully aware of the staggering odds against your ticket being the winning one), is not that lottery winners exist. That's inevitable. What is not inevitable, and in fact deeply surprising, is when you win.

Don't hold your breath.

So, you're surprised. What's your point? You're not going to throw out the hypothesis that you were just lucky, are you?

Something quite unexpected has happened if you find your finitely unique self among the living, against giganogargantuan odds. But stop insisting on being so finitely unique, and your existence stops being so unexpected.

It is not the observation that is being tested, it is the hypothesis that gave rise to the prior probability that is being tested. A probability, in this sense, is a degree of certainty. When this degree of certainty is utterly ravaged, it is justified to be surprised, and then to question the hypothesis which gave rise to the ravaged degree of certainty.

So you're surprised. What's your point? You're not going to throw out the hypothesis that you were just lucky, are you?

 

[Toontown]

No. The surprise if one wins with a lottery ticket found on the sidewalk is no greater than the surprise if one wins with a lottery ticket purchased, and neither surprise is anything but an emotional response. Objectively, it is no more surprising if I win than if the little old lady from Pasadena whom I have never met wins or if you win or if any of a million other winners win.

Objectively, it is a great deal less likely that your ticket wins the lottery than it is that one of all the others does -of which the old lady's ticket would be an unspecified member, unlike your ticket, selected by the fact that you have it, and it is the sole determinor of your lottery destiny. And that's why you will be surprised if you do win, and that's why surprise is an appropriate response. Because it's not going to happen for you, even if there is 1 chance in 15 million that it will.

Trust me. Don't hold your breath, and don't dismiss odds stacked to the moon against you as if they're nothing.

Regarding the ravaging of certainties, (1) such things happen all the time and are to be expected without resort to anything else, and (2) it hasn't been ravaged; that would only happen if a particular low probability outcome were reliably predicted; that has not been shown to happen. Not even the attempt to show it has been made.

And what if an extremely high predicted probability failed to materialize? Such as a giganogargantuan probability predicted by a certain hypothesis that you would never have a sentient experience? That wouldn't mean anything?

So, if Bernie Madoff guaranteed you a 99.99% chance of doubling your money, and you took the shot and came up cold, your confidence in Madoff's promises would remain unshaken?

Your dismissal of finite uniqueness may be correct, but nothing you have said or shown here supports the idea.

Nothing you've said indicates you wouldn't call an all in bet with your entire stack to draw to a gutshot straight on the turn against a one-suited board.

 

[Toontown]

So, you're surprised. What's your point? You're not going to throw out the hypothesis that you were just lucky, are you?

Red herring.

The point is I should be surprised, because Garrette's assertion was bogus. If Garrette believes that assertion, then Garrette should not be surprised at anything.

So you're surprised. What's your point? You're not going to throw out the hypothesis that you were just lucky, are you?

If I believed Garrette's assertion was correct, then I would not be surprised. But I would be surprised. And I would be correct to be surprised. Because Garrette's assertion is bogus.

 

[jt512]

Red herring.

The point is I should be surprised, because Garrette's assertion was bogus. If Garrette believes that assertion, then Garrette should not be surprised at anything.



If I believed Garrette's assertion was correct, then I would not be surprised. But I would be surprised. And I would be correct to be surprised. Because Garrette's assertion is bogus.

Let me try again. Is surprisal supposed to have some relevance to Jabba's argument? If so, what is that relevance?

 

[lenny]

The surprising part (if you are fully aware of the staggering odds against your ticket being the winning one), is not that lottery winners exist. That's inevitable. What is not inevitable, and in fact deeply surprising, is when you win.

Don't hold your breath.

That is sorta the point, isn't it.

After you have the data, the probability of your winning is one. Breath holding need only be avoided before you have the data.

 

[Toontown]

Let me try again. Is surprisal supposed to have some relevance to Jabba's argument? If so, what is that relevance?

Why should it, when it was a rebuttal to an assertion which itself had no relevance to Jabba's argument?

 

[jt512]

Why should it, when it was a rebuttal to an assertion which itself had no relevance to Jabba's argument?

I didn't say it should have relevance to Jabba's argument. Since you say it doesn't, I won't bother trying to figure out what your point is.

 

[xtifr]

Would you say "The odds are 3"? Three to what? They could be three to two. Quite often they are, at the racetrack.

No, I wouldn't say that, and thanks for helping make my point for me. If the odds aren't three, then saying "the odds to one" makes no sense when you're talking about the odds being three to one, because "to one" is part of the odds!

The odds might not be "to 1".

You mean the odds might not include "to one". Saying they wouldn't "be to one" makes no sense.

In any case, that's only partly true. Any odds can be expressed with "to one". 5 : 2 is 2.5 : 1. But if you're going to suggest that there's something special about odds which include the term "to one", you should say that instead of coining nonsensical phrases which only confuse your readers.

They're distinct from odds to 2.

There's no such thing as "odds to 2" either. If you mean odds which include "to 2", well, that's different. In any case, even if I overlook your bizarre phrasing, you're still wrong. The only distinction is a cultural convention. We tend to say "five to two" instead of "two point five to one", but they're not distinct.

I was talking about 1/p-1, not p/(1-p), and so it was that I said I was talking about "odds to 1" in an apparently impossible attempt to communicate that fact.

The thing that made it impossible to communicate was your firm insistence on sticking with the bizarre phrase "odds to one". If you'd tried communicating in standard English instead of inventing eccentric and counterintuitive coinages, I think you would have gotten a lot farther.

So, now that we've gotten this far, and maybe are both on the same page, what, exactly, is it that's so special about odds where the numerator is one?

 

[Toontown]

That is sorta the point, isn't it.

After you have the data, the probability of your winning is one. Breath holding need only be avoided before you have the data.

No, that's not the point at all. That's the antithesis of the point.

In the case of the hypothesis in question, The only reason you would be (figuratively) holding your breath at all is if you believe the hypothesis gives you very little chance of every drawing one. So if you are (figuratively) holding your breath, you're assuming the conclusion.

After you have the data, you have a means of testing the hypothesis, because you have an observation. It just happens, in the case of the particular hypothesis in question, that the observation is vanishingly unlikely by the available means, which would almost certainly not exist if the hypothesis is correct. If, OTOH, the hypothesis strongly predicted the observation by the available means, you would have no reason to doubt it. It is the fact that the hypothesis rules heavily against the specific observation, indeed the observer himself, that you have cause to doubt the hypothesis. Hypothetically, is there a better reason to doubt a hypothesis?

Before you have the data, you literally have no means at all, no chance to test the hypothesis, and almost certainly never will, if the hypothesis is correct. Again, it is the fact that you have the opportunity at all which casts doubt on the hypothesis.

It's always that way when observations are used to test a hypothesis. You must test by an available means. You can't test the hypothesis before you have an observation. After you have the observation, the probability that the observation exists is 1, whether it agrees with the hypothesis or not. That's why you use the prior probability of the observation as predicted by the hypothesis, to test the hypothesis.