Jabba
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- Thanks, Garrette. That'll get me started.
[Merged] Immortality & Bayesian Statistics
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abaddon
Penultimate Amazing
YOU introduced the brick analogy. Not my issue if you fail to get the literary allusion.
Toontown
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We probably don't read the same books.
Jabba
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Garrette,
- As mentioned before, I find this stuff really difficult to convey effectively. Consequently, I'll try to explain one estimate at a time.
- P(SM|me) = P(me|SM)*P(SM|k)/P(me|SM)*P(SM|k)+P(me|NSM)*P(NSM|k)
- P(me|SM), the "likelihood" of me ever existing (for now, I'll ignore the likelihood of me currently existing), given NR, is either one over a "giganogargantuan" number, or one over infinity.
- I say that because I assume that the number of potential selves is at least giganogargantuan, and probably infinite.
- And, I claim that because I figure that the number of potential selves includes, at least, all the possible combinations of potential but unrealized ova (past, present and future)and sperm cells (past, present and future), and does not preclude evolution. If that doesn't sound infinite, I'm not expressing the idea effectively.
- And actually, I think it's worse than that. I'll explain later.
- Whatever -- I'll leave it at that for now.
- Let me know what you think so far.
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The Pratchett books are highly recommended (at least by me). Once you get over thinking of them as simply humorous books you begin to see the rather wide-ranging and often deeply insightful (and incisive) social, political, and philosophical analysis and commentary. Not in every book, mind you, but in many.
Thanks. Trying to compose a response to your Post 909 while doing myriad other things, too, then will get to this.
godless dave
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I can't speak for Garrette, but here's my problem with your argument in that post:
You haven't demonstrated that the sum probability of your current existence is greater than it is when given the chance/null explanation/hypothesis.
In other words, you haven't demonstrated that the your existence can't be explained by chance. If anything, your math in post #944 shows the opposite.
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Jabba
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Dave,
- Sorry that I haven't expressed my position better. I think I lost you with "Hello." Actually, I think I lost you with the "sum probability" and the "chance/null explanation/hypothesis." I'm now doubting my own choice of words...
- I'll need to think about it more -- but for now, I think I should have just said that the likelihood of my current existence, given the "scientific model" (one finite existence), is MUCH less than the likelihood of my current existence, given that one of the alternative models is true. I think I can validly make such a claim because any alternative model would have my existence being either infinite or multiple.
- Does that help at all?
- Later, I'll try to get to the second part of your objection.
Haven't finished my long response (and maybe there won't be one), but I will jump back in.
No. Godless Dave said what I was thinking, what I have asked more than once, and what Agatha repeatedly asked. We understand what you are saying, regardless if you use a formula or words. We know that you say P(me|NR) < P(me|R). We know that you think you can "validly" say so.
The point is that we disagree, and if you want us to stop disagreeing then you need to show how you arrived at that conclusion (that P(me|NR) < P(me|R)), and simply stating that you think it is valid is vastly insufficient.
godless dave
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It does not.
Still not my intended long response, but that is becoming less relevant as we go.
To start, this is the first, I think, that you have loosened your goal so that it is no longer both infinite and multiple but have instead phrased it so that it is infinite OR multiple.
Just really grasped the part I highlighted. Jabba, I know you think that this is your justification, but it isn't. I will try to explain why I find it insufficient.
No. There are two glaring errors, both of which have been pointed out more than once:
1. You are continuing Toontown's error re: the lottery winner. Any given model is less likely than all the others in combination if chosen prior to its actual existence. What you are saying is that the lottery winner didn't win because it is too improbable for him to have won when in fact it was extremely highly almost but not quite infinitely improbably for him to have won, but now that he has won the new fact is that the probability of him winning is 1. [ETA: You are wrongly comparing IS and WAS.]
2. You are falsely assuming that only one model is possible for a non-unique, non-infinite consciousness. Let me try to explain it this way: The equation is this P(me|NR) < P(me|R).
In determining your numerical value for each side you are being unequal. On the left side you are counting only the characteristic (not unique and not infinite), but on the right side you are counting models (any universe with a consciousness that is either unique or infinite).
Running short on time so I will leave with this last bit:
You still haven't answered my question that got us back on this tack (rephrased from memory here):
Why are the possible consciousnesses that could exist given NR infinite but the possible consciousness that could exist given R are not infinite? And if they are infinite given R, then why does it count only against NR?
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The best example of a good one being?
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It has been a very long time for me, but I suggest both Small Gods and Night Watch. I especially like the latter as I find his exploration of how good but lazy men allow evil to be convincing as do I find his manner of (humorously) demonstrating the culture of a group who have experienced high stress and trauma together.
given the title of the thread, i am going to assume the aim was for a Bayesian argument. and suggest none exists. that none can exist given the details Toontown presented (thanks for those). then i'll suggest we might want to think of this from a freqentist perspective, which is a bit weird but might prove interesting to discuss...
just to be clear, BEFORE refers to the state of affairs prior to the time of the event/non-event and AFTER refers to the state of affairs after the time of the event/non-event.
We agree the probability BEFORE some event is small, call it "p"; and that the probability AFTER the event is, well one, if the event happened and zero if it did not.
from these and other quotes:
as the hypothesis involves you reflecting on the chance of your coming into being, then for the Bayesian this is AFTER and the probability is one. end of argument.
what the probability was BEFORE doesn't enter into it, but reflection regarding it brings the Bayesian no surprise: given that she knows "a sentient experience" can happen. if we are willing to agree that Bayesians are sentient. i am.
so you may have seen this coming. you will no doubt cry foul, but it will not help you if you stay in the Bayesian framework
this is true, (have one or expect one) but in this case "you" are the observation. the entire set up is AFTER. the only probability is one.
none of this changes the Bayesian picture. it seems a bit unfair, of course. but the thread selected the Bayesian framework.
but questions regarding your own existence are NOT obvious in the way questions about the moons existence are obvious. one can ask the probability that the moon does not exist a the moment. or will not rise tomorrow. since the moon is external to the entity forming the question, Bayes is happy.
(there must be threads somewhere on this site discussing the probability that man has never gone to the moon. (interesting that that is an AFTER, but leave it for later).)
so what would a frequentist say? i think you could avoid the BEFORE/AFTER dead end if you dropped the Bayesian perspective (which i do not think has been important to any critical step in this thread) and framed the argument as a frequentist. it may not get you where you want to go, but there is no Bayesian argument that will support you.
I will try and say this more clearly, but you have made it clear your are trying to use the Bayesian framework in a manner it does not allow.
just to be clear, BEFORE refers to the state of affairs prior to the time of the event/non-event and AFTER refers to the state of affairs after the time of the event/non-event.
We agree the probability BEFORE some event is small, call it "p"; and that the probability AFTER the event is, well one, if the event happened and zero if it did not.
from these and other quotes:
it is clear that you are discussing the probability of existing AFTER "someone"/"you"/... exist
as the hypothesis involves you reflecting on the chance of your coming into being, then for the Bayesian this is AFTER and the probability is one. end of argument.
what the probability was BEFORE doesn't enter into it, but reflection regarding it brings the Bayesian no surprise: given that she knows "a sentient experience" can happen. if we are willing to agree that Bayesians are sentient. i am.
so you may have seen this coming. you will no doubt cry foul, but it will not help you if you stay in the Bayesian framework
this is true, (have one or expect one) but in this case "you" are the observation. the entire set up is AFTER. the only probability is one.
none of this changes the Bayesian picture. it seems a bit unfair, of course. but the thread selected the Bayesian framework.
and only people who exist can take the Bayesian way.
but questions regarding your own existence are NOT obvious in the way questions about the moons existence are obvious. one can ask the probability that the moon does not exist a the moment. or will not rise tomorrow. since the moon is external to the entity forming the question, Bayes is happy.
(there must be threads somewhere on this site discussing the probability that man has never gone to the moon. (interesting that that is an AFTER, but leave it for later).)
so what would a frequentist say? i think you could avoid the BEFORE/AFTER dead end if you dropped the Bayesian perspective (which i do not think has been important to any critical step in this thread) and framed the argument as a frequentist. it may not get you where you want to go, but there is no Bayesian argument that will support you.
Toontown
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Bayes, schmayes. I simply stated the question as I see it, per your request. A simple statement of the question by any other name would smell as sweet.
We will see what Mama will and will not allow.
At this point, I'm not sure you know that probability can be used to test a hypothesis. You seem to be denying the validity of data as a statistical test because it already exists.
Perhaps the following links may help shore up your confidence in the validity of comparing probabilistically expected states to observed states as a means of testing hypotheses.
Below is a demonstration of the Chi-square test. I can vouch that I used the method for a semester in Genetics I class to compare probability 1 existing fruit fly phenotypes to their hypothetical expected frequencies. The method was 100% efficient in numerous tests. It never failed to accept a true hypothesis, and never failed to reject a false one.
It is notable that the various phenotypes of these flies were only probabilities before their parents met. These were the "expected" probabilities. These expected probabilities slowly increased over time, finally reaching 1 when they hatched.
http://www.colby.edu/biology/BI17x/freq.html
Below is a Chi-squared calculator. The upper one calculates the probability of chance of a given X2 value and degrees of freedom. The lower one calculates the corresponding X2 value for a given probability of chance and degrees of freedom.
http://www.fourmilab.ch/rpkp/experiments/analysis/chiCalc.html
I bring this up only to prove the principle involved. It is tried and tested. Not suitable for testing a single observation, but also not necessary for such. The probability of chance of a single observation is identical to the expected probability.
Dude. the question is not "Do I exist or not?" The question is "Should I believe the unique brain hypothesis, given that it rules massively against my specific existence, which, given my specific existence, almost rules it out?" Yes, it's a quandary. Maybe there is something wrong with the way we think the universe works.
However, if you insist on asking the "Do I exist or not?" question instead - well, it's like this:
Your existence is the probability 1 side, and your nonexistence is the probability 0 side. Both possibilities are fully accounted for in their own distinct ways. It's just that you don't directly observe one of them. Not observing yourself existing IS the observation of not existing.
Wierd how that nonexistence stuff works, isn't it. Not surprising that you don't know anything about it, never having had any dealings with it.
Yes, I did see it coming, and I do cry foul.
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Jabba
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Garrette,
- I think you're wrong. Can you find a quote? If I said "infinite and multiple," I shouldn't have.
I'll take your word for it, so long as we're clear on it now.
Jabba
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Garrette,
- I still claim that "friendly" debate tends to be much more constructive than does "unfriendly" debate. A lot of the time, you (in particular) do seem to be friendly when addressing my arguments. Above however, when you say, "No. There are two glaring errors, both of which have been pointed out more than once:" you don't sound very friendly.
- In trying to be friendly, I would have said, "I think that there are actually two errors, and that both have been claimed previously." -- or, something like that. I would add "I think," drop "glaring" and change "pointed out" to "claimed." I think that would have given your respondent (me) more (at least subconscious) incentive to be open-minded about your claim...
- Using Bayesian terminology, the probability of an event occurring based upon the existing model (here, one finite life) -- before the event occurs -- is called the "likelihood." I'm claiming that the likelihood -- before I occur -- of me actually occurring -- based upon the existing model -- either "approaches zero," or is just unimaginably small.
- That's a lot to say in one gulp. Hopefully, it doesn't just further confuse the issue.
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Jabba
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Garrette,
- Good. I'm sure we're clear.
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