[Merged] Immortality & Bayesian Statistics

[Jabba]

Good questions, but I'm still waiting for Jabba to tell us what this "non scientific model" actually is.

Pixel,
- A "non scientific model" in this case is really any (every) theory about individual consciousness that does not hold that each individual consciousness has but one finite existence. Reincarnation is an example.

 

[Jabba]

It wouldn't break my heart if you turned out to be right about that. That would mean I can happen infinitely many times in infinitely many contexts. But each time would seem like the first time.

Because unique is unique, and variable is variable.

- Yeah.

 

[Toontown]

- This is really getting interesting.
- Unfortunately, I'll be babysitting two year olds for most of the day, so won't be able to add much to the discussion today.
- But, I'll do what I can.


Toontown,

- Bak in 651, you said, "But I presume we're not finished yet. You still have that little matter of immortality to prove. Seems to me that accomplishing that goal will require very strongly supporting a specific alternative hypothesis."
- While there is a LOT more to say, your position is sort of confusing and I suspect that I'm not quite understanding it. I say that because
1) The scientific model to which I'm referring holds that we each live but one finite life.
2) If that model is not correct, we are either not finite, or we live more than once.
3) Once we accept that we each live at least twice, where do we stop?

- In other words, it seems to me that (essentially) disproving that scientific model (essentially) proves that we are immortal.

OK, now I have your definition of "immortality". Your definition is not the same as the dictionary definition. Essentially, it's the alternative to uniqueness, whatever that may be.

Here is the Miriam-Webster definition:

im·mor·tal·i·ty noun \ˌi-ˌmȯr-ˈta-lə-tē\
: the quality or state of someone or something that will never die or be forgotten : the quality or state of being immortal

I think your reasoning is valid if we are not unique. I'm not so sure leaving the alternative unexplained will convince many that you've proved immortality.

 

[Jabba]

There is only one way what I specifically described can happen, because it must happen at a specific time in a specific place. That is the scientific definition of a unique object. Given the uniqueness assumption, the size of the universe and how long it lasts matters not. You have one chance, at one time, at one place. And it's not much of a chance.

If you disagree that we are necessarily unique objects, then you are kind of on the same page as Jabba, and I'm kind of on that same page, simply because of the vanishingly small probability the uniqueness assumption gives my observed existence.

What alternative explanations may be is a whole nother discussion.

Toontown,
- I'm glad that you introduced the time aspect instead of me...
- In truth, I suspect that modern science's best guess is that certain physical events create an emergent property of consciousness and each time this happens, a totally brand new self is created, and the number of potential selves is indeed infinite...

 

[Jabba]

What exactly is this so-called "prior probability of the observation"? There is no term in Bayes' Rule with that name. There are just the prior probabilities of the two hypotheses, the likelihoods of the observation under each of the two hypotheses, and the posterior probability of the hypotheses.

Jay,
- I don't remember the proper terminology very well, but why wouldn't you call the "likelihoods of the observation," the "prior probabilities of the observation"?

 

[jt512]

Jay,
- I don't remember the proper terminology very well, but why wouldn't you call the "likelihoods of the observation," the "prior probabilities of the observation"?

Because they are likelihoods; not prior probabilities.

 

[Toontown]

Because they are likelihoods; not prior probabilities.

Your semantics is awesome - but I wasn't actually thinking about the Bayes formula when I said "prior probablity". The concept of prior probability exists independently of Bayes. I don't know what you choose to call the concept.

 

[Jabba]

What exactly is this so-called "prior probability of the observation"? There is no term in Bayes' Rule with that name. There are just the prior probabilities of the two hypotheses, the likelihoods of the observation under each of the two hypotheses, and the posterior probability of the hypotheses.

Jay,
- I don't remember the proper terminology very well, but why wouldn't you call the "likelihoods of the observation," the "prior probabilities of the observation"?

Because they are likelihoods; not prior probabilities.

Jay,

- According to http://www.investopedia.com/terms/p/prior_probability.asp
Definition of 'Prior Probability'
The probability that an event will reflect established beliefs about the event before the arrival of new evidence or information. Prior probabilities are the original probabilities of an outcome, which be will updated with new information to create posterior probabilities.
- I've been assuming that "observation" is just another word for "event" -- and if so, the prior probability of an observation is the same thing as the prior probability of an event, and Toontown's use of the terms appropriate...

- Superficially, at least, "likelihood" seems to be a term used in "normative" statistics rather than Bayes statistics...

 

[jt512]

Jay,

- According to http://www.investopedia.com/terms/p/prior_probability.asp
Definition of 'Prior Probability'
The probability that an event will reflect established beliefs about the event before the arrival of new evidence or information. Prior probabilities are the original probabilities of an outcome, which be will updated with new information to create posterior probabilities.

Exactly. And in Bayes' Formula, the "event" whose probability is going to be updated is the event that the hypothesis is true. The new information that will update that event is the information that you exist. The probability of that new information, given the hypothesis, is called the "likelihood."

- I've been assuming that "observation" is just another word for "event" -- and if so, the prior probability of an observation is the same thing as the prior probability of an event, and Toontown's use of the terms appropriate...

No. In Bayesian terminology, the prior probability is the probability of the hypothesis that you want to update with new information. The updated probability of the hypothesis is the posterior probability.

- Superficially, at least, "likelihood" seems to be a term used in "normative" statistics rather than Bayes statistics...

Superficially doesn't count in mathematics. Rigorous definitions do. A likelihood in statistics is a function with the same form as a probability density or mass function, but with unknown parameters whose values are conditional on the values of some observation(s). Thus in Bayes' Formula the terms that have form P(Data | Hypothesis) are likelihoods.

 

[Toontown]

No. In Bayesian terminology, the prior probability is the probability of the hypothesis that you want to update with new information. The updated probability of the hypothesis is the posterior probability.

I get what you're saying.

I should have said "the likelihood of the observation, assuming the hypothesis" instead of "the (prior) probability of the observation". Because "prior" is reserved, and may only be used in reference to "the prior probability of the hypothesis".

 

[godless dave]

- Bak in 651, you said, "But I presume we're not finished yet. You still have that little matter of immortality to prove. Seems to me that accomplishing that goal will require very strongly supporting a specific alternative hypothesis."
- While there is a LOT more to say, your position is sort of confusing and I suspect that I'm not quite understanding it. I say that because
1) The scientific model to which I'm referring holds that we each live but one finite life.
2) If that model is not correct, we are either not finite, or we live more than once.
3) Once we accept that we each live at least twice, where do we stop?

- In other words, it seems to me that (essentially) disproving that scientific model (essentially) proves that we are immortal.

2 doesn't follow from 1. Even if the current model of reality turns out to be wrong, the correct model might still involve single , finite lives.

 

[Toontown]

2 doesn't follow from 1. Even if the current model of reality turns out to be wrong, the correct model might still involve single , finite lives.

In which case the "correct model" would be identical to (1), and also wrong. Which is illogical.

 

[Garrette]

In which case the "correct model" would be identical to (1), and also wrong. Which is illogical.

How so? Identical in one aspect does not mandate identical in all aspects.

 

[Toontown]

How so? Identical in one aspect does not mandate identical in all aspects.

Identical in the aspect in question - the assumption of finite uniqueness.

This is not a Grand Unification Theory.

 

[Toontown]

delete

 

[Garrette]

Identical in the aspect in question - the assumption of finite uniqueness.

This is not a Grand Unification Theory.

Doesn't matter. Jabba is basing his equation on the Scientific Model (the key aspect of which is mortality), but comparing it to "any other possible model." I think that particular concept is correct, but only if the set of "any other possible model" actually includes any other possible model. What you are suggesting is that the set is actually "any other possible model that doesn't include mortality."

That's a mistake.

 

[godless dave]

In which case the "correct model" would be identical to (1), and also wrong. Which is illogical.

Not at all. Human consciousness could be created by a god rather than evolving naturally like our other traits. And that god could have created us with single, finite lives.

 

[Toontown]

Not at all. Human consciousness could be created by a god rather than evolving naturally like our other traits. And that god could have created us with single, finite lives.

How likely do you consider this god-of-the-one-offs hypothesis? LIkely enough to be considered as a reasonable alternative to the so-called scientific hypothesis?

In the absence of any specific knowledge or evidence about the god-of-the-one-offs' completely imagined modus operandi, I could treat this evidence-unencumbered hypothesis probabilistically as well. From my less-than-all-knowing perspective, the god-of-the-one-offs hypothetical decisions would be as random as the quantum chaos at t=0+10^-43. So I wouldn't see my presumed unique atheistic existence as any more likely under that hypothesis. So I would reject the god-of-the-one-offs hypothesis on the same grounds as Jabba rejects the so-called scientific hypothesis.

At any rate, as I see it, what is actually being questioned is the uniqueness assumption, irrespective of the mechanism or interpretation behind it.

 

[godless dave]

How likely do you consider this god-of-the-one-offs hypothesis?

Exactly as likely as the god that creates immortals hypothesis - not likely at all.

LIkely enough to be considered as a reasonable alternative to the so-called scientific hypothesis?

No.

 

[Garrette]

How likely do you consider this god-of-the-one-offs hypothesis? LIkely enough to be considered as a reasonable alternative to the so-called scientific hypothesis?

In the absence of any specific knowledge or evidence about the god-of-the-one-offs' completely imagined modus operandi, I could treat this evidence-unencumbered hypothesis probabilistically as well. From my less-than-all-knowing perspective, the god-of-the-one-offs hypothetical decisions would be as random as the quantum chaos at t=0+10^-43. So I wouldn't see my presumed unique atheistic existence as any more likely under that hypothesis. So I would reject the god-of-the-one-offs hypothesis on the same grounds as Jabba rejects the so-called scientific hypothesis.

At any rate, as I see it, what is actually being questioned is the uniqueness assumption, irrespective of the mechanism or interpretation behind it.

You are discounting alternatives based on how you feel about them. There is no less evidence for the one-off god than for the others. Even if not, non-scientific models need not be god-based to allow mortality as opposed to immortality.