Immortality & Bayesian Statistics

[Jabba]

- I seem to have written an 8 page paper virtually proving -- through Bayesian statistics -- that we are immortal (or something similar). Obviously, I must be doing something wrong...
- The paper is essentially all 1) math, 2) my logic otherwise and 3) a couple of claims about scientific opinion (that, from my searches, no scientist has written directly about).
- Consequently, I'd like someone who knows what they're doing, re Bayesian statistics, to tell me if, and where, I've gone astray.
- I can post it in relatively small pieces, and could be that one page would be enough.

- Any objections?

- Thanks.

 

[Dason]

Post away.

 

[Jabba]

Dason,
- Thanks.
- I'll be back.

 

[Jabba]

Re: Immortality & Bayesian Statistics/First Page

- First page:

One Finite Life?​

THE BASIC IDEA


1. I think I can virtually prove that the "well-educated" belief that
we each have but one, finite, life to live is incorrect.
2. I call this belief "well-educated" because most of those who hold
it are well educated.

3. But, just to be perfectly clear, when talking about "life," I am
not referring to a body - I'm referring, instead, to a "self."

4. Unfortunately, "self" is a difficult concept to convey -- "personal
consciousness" might be the best, simple, term to use.
5. "Soul" might work better - but, only if we can drop its built-in
connotation of "immortality"...
6. Not to deny immortality, but neither should it be snuck in as an
implied given.
7. Perhaps, the best example of the kind of self I'm addressing is the
self that keeps coming back if reincarnation is real.
8. (If those don't work, try Wikipedia.)
9. Take your time - this stuff isn't easy.

10. I think that I can virtually prove that this well-educated belief is
false because simple deduction applied to science's possible explanations
for different selves leads to the conclusion that the probability of my,
current, personal existence - given our well-educated belief -- is virtually
zero...
11. In other words, if our well-educated belief is true, I really
shouldn't be here.
12. And, since I am here, that deduction has significant - negative --
mathematical implications regarding the truth of our well-educated belief.
13. In fact, my current existence is so unlikely -- given our
well-educated belief -- that the negative mathematical implications
regarding this belief are virtually "irresistible."
14. In other words, I'm claiming that my own personal existence virtually
proves that our well-educated belief is wrong...
15. I'll elaborate.

16. For statisticians:
a. The likelihood of drawing a particular sample from a particular
population has mathematical implications re the probability that a
particular sample was, in fact, drawn from that population...
b. In this case, I (the sample) was very likely not drawn from a
hypothetical population of people having just one, finite, life to live.

17. For dummies:
a. The likelihood of a "red state" to elect Candidate X is 10%.
b. State A elects Candidate X.
c. State A is probably not a "red state."

18. Take your time...

 

[Dason]

Assume that X is a random variable with a standard normal distribution. Lets say you observe a draw from this variable (call the observed value x). Do you know what P(X = x) is? Regardless of the observed value the probability is 0. So just observing a small probability doesn't mean that something is impossible.

 

[bryangoodrich]

I like a good philosophical debate, but I think this was easily squashed by Dason on the exact same thing I was thinking: P(X=x) = 0. This argument is also not that different to me than the anthropic principle in that it tries to use limited information (observations) to infer global principles about things to which the observation provides no basis for. In this case, P(X=x) = 0, therefore the entire domain (support) must have 0 probability! That wouldn't make sense ...

 

[Jabba]

Assume that X is a random variable with a standard normal distribution. Lets say you observe a draw from this variable (call the observed value x). Do you know what P(X = x) is? Regardless of the observed value the probability is 0. So just observing a small probability doesn't mean that something is impossible.

Dason,

- I'm 72, been out of school for a long time -- so, could be that I'm just not recognizing (or, remembering) your terminology...
- In the Bayesian terminology I remember, I'm claiming that P(x|X) = ~0. I.e., the probability ("likelihood") of my current existence -- given the hypothesis that we each have but one, finite, life to live -- is (virtually) zero.

- Hopefully, that helps.

- Also, I'm not claiming that the likelihood of x given X is just small -- I'm claiming that it's infinitesimally small.

- Thanks.

 

[Jabba]

I like a good philosophical debate, but I think this was easily squashed by Dason on the exact same thing I was thinking: P(X=x) = 0. This argument is also not that different to me than the anthropic principle in that it tries to use limited information (observations) to infer global principles about things to which the observation provides no basis for. In this case, P(X=x) = 0, therefore the entire domain (support) must have 0 probability! That wouldn't make sense ...

bryangoodrich,

- I'm a terrible typist -- is it ok to address you as "Bryan"?

- Yeah, my conclusion here and the math behind it are similar to those of the anthropic principle. But so far, I think that the anthropic principle is very interesting, and probably correct.

- Also, if a hypothesis X claims that x cannot occur, but x does occur -- the hypothesis X must be incorrect...

- Thanks.

 

[Dason]

In the US men's heights have a mean of 69.1 inches and standard deviation 2.9 inches. Let's for the sake of argument assume that heights are normally distributed. My height is 64 inches. If was to randomly select somebody from the population that has a normal distribution with mean 69.1" with a standard deviation of 2.9" then the probability of selecting somebody 64" is exactly 0. Obviously though I am part of the population so it is possible for this to happen. You can make this argument for *every* person in the population. Does that mean that no height is actually possible?

 

[bryangoodrich]

if a hypothesis X claims that x cannot occur, but x does occur -- the hypothesis X must be incorrect...

I find it suspect that the hypothesis denies x from occurring, which is basically what I was getting at about the anthropic principle. You want to apply some global principles from observations that provide no basis for them. In this case, your point 10 is supposed to be true by "simple deduction applied to science's possible explanations for different selves." This entire point needs to be unpacked

1. What system of logic are you referring to by "simple deduction" because if you think propositional logic can say anything about reality, you're mistaken. It's like saying Connect Four has real consequences.

2. Which scientific explanations? What about the ones that science doesn't have because the "self" is a complicated topic we haven't mastered here.

3. What is the "self" to begin with?

All of these beg important questions you haven't addressed and expect us to take for granted. You want the proof to rest upon probability theory as if mathematics provides any substance to something empirical: it doesn't. Even if you were on the right track, the explanandum is still empirical, not resting on the laws of probability theory. Therefore, your hypothesis in this mathematical exercise, to be relevant, need to fully and adequately represent the phenomena. This is why modeling in statistics is so important. Frankly, everything you've talked about are just loose and fluffy concepts that I don't think refer to anything real.

 

[Jabba]

In the US men's heights have a mean of 69.1 inches and standard deviation 2.9 inches. Let's for the sake of argument assume that heights are normally distributed. My height is 64 inches. If was to randomly select somebody from the population that has a normal distribution with mean 69.1" with a standard deviation of 2.9" then the probability of selecting somebody 64" is exactly 0. Obviously though I am part of the population so it is possible for this to happen. You can make this argument for *every* person in the population. Does that mean that no height is actually possible?

Dason,
- At 64 inches, you're within 2 standard deviations. The probability of selecting someone of your height, or shorter, is about 21% (if I remember my math).

 

[Jabba]

I find it suspect that the hypothesis denies x from occurring, which is basically what I was getting at about the anthropic principle. You want to apply some global principles from observations that provide no basis for them. In this case, your point 10 is supposed to be true by "simple deduction applied to science's possible explanations for different selves." This entire point needs to be unpacked

1. What system of logic are you referring to by "simple deduction" because if you think propositional logic can say anything about reality, you're mistaken. It's like saying Connect Four has real consequences.

2. Which scientific explanations? What about the ones that science doesn't have because the "self" is a complicated topic we haven't mastered here.

3. What is the "self" to begin with?

All of these beg important questions you haven't addressed and expect us to take for granted. You want the proof to rest upon probability theory as if mathematics provides any substance to something empirical: it doesn't. Even if you were on the right track, the explanandum is still empirical, not resting on the laws of probability theory. Therefore, your hypothesis in this mathematical exercise, to be relevant, need to fully and adequately represent the phenomena. This is why modeling in statistics is so important. Frankly, everything you've talked about are just loose and fluffy concepts that I don't think refer to anything real.

bryangoodrich,
- I was vaguely thinking that anyone on this thread would be familiar with my earlier conversation with Dason -- sorry about that...
- In that conversation, I had told Dason that I had an 8-page paper I would like to have reviewed -- suggesting that I would post one page at a time. That first page is meant as an introduction. Hopefully, I'll provide what you need (in order to make sense of my claim) in the next seven pages.

 

[Dason]

Dason,
- At 64 inches, you're within 2 standard deviations. The probability of selecting someone of your height, or shorter, is about 21% (if I remember my math).

Any why are you doing that calculation instead of looking at the probability of the actual observation? In your argument aren't you just looking at the probability of the observation?

 

[bryangoodrich]

bryangoodrich,
- In that conversation, I had told Dason that I had an 8-page paper I would like to have reviewed -- suggesting that I would post one page at a time. That first page is meant as an introduction. Hopefully, I'll provide what you need (in order to make sense of my claim) in the next seven pages.

A whole 8 pages to explain this and unpack what is meant by the "self"? Impressively concise! I'm sarcastic, but of course you can make certain assumptions for the sake of argument about how you're defining this integral concept. However, if the argument is weak because it rests upon weak assumptions, then you're basically digging yourself a hole.

Even if you had a solid definition to which we can refer, I still find your statement "science's possible explanations for different selves" being used to justify your claim is trying to sneak in some broad statements about what science is possible of doing. Are you resting the "self" on a definition that is not scientifically explainable and then going "see, science can't explain it" or is my suspicion incorrect?

 

[hlsmith]

Yeah, this is not my type of debate. Not good enough with logic concepts/bayes concepts.

This may fall under BG's missing definition of self or be irrelevant, but the number of people countinually fluctuates. During our life times, increases, meaning self is not finite. However, how would any of this function in the face of a catastrophy when the population becomes smaller than the current population? Where would those self units with a limited number of vessels be under the immortality hypothesis (zero-sum?)?

 

[Jabba]

Any why are you doing that calculation instead of looking at the probability of the actual observation? In your argument aren't you just looking at the probability of the observation?

Dayson,
- Yes. I probably misunderstood your intent in the previous post.
- But, why do you say that the probability of selecting somebody 64" is exactly zero?

 

[Jabba]

Any why are you doing that calculation instead of looking at the probability of the actual observation? In your argument aren't you just looking at the probability of the observation?

Dason,
- Yes. I probably misunderstood your intent in the previous post.
- But, why do you say that the probability of selecting somebody 64" is exactly zero?

 

[Dason]

Because mathematically that is what it is.

 

[bryangoodrich]

Dason is full of tact.

What he meant to say was "Calculus."

 

[bryangoodrich]

Specifically when a = b

\( \int_{a}^{b} p(x) dx = F(b) - F(a) = 0\)