[Merged] Immortality & Bayesian Statistics

[Jabba]

I haven't been following the thread carefully, but it seems that some posters are objecting to the use of Bayes' Theorem to calculate probabilities retrospectively. However, that is precisely what Bayes' Theorem is for, that is, to update the probability of something (eg, a hypothesis) based on some data. No data, no Bayesian inference. In odds form, Bayes' Theorem is

P(H₁|D)/P(H₂|D) = P(D|H₁)/P(D|H₂) × P(H₁)/P(H₂) .

D in the above formula is the data, and the first term on the right-hand side of the equation is the relative probability of the data under competing hypotheses, H₁ and H₂. I take it that the data in the present problem is something like "Jabba exists." So if Jabba is estimating the probabilities that he would exist under competing hypotheses and using that information to update the prior probabilities of those hypotheses, then that per se does not violate the rules of Bayesian inference.

Jay

Jay,
- Thanks.
--- Jabba

 

[Jabba]

I am still around, and my comment is that your usage of Bayesian statistics is not correct.

Humots,
- But you have agreed upon the formula I'm using -- you just think that the numbers I have inserted are off the wall -- or, out of thin air.
- You probably agree with what Jay said, and I think that what Jay said is all that I'm claiming in regard to "useage."
--- Jabba

 

[shuttlt]

I haven't been following the thread carefully, but it seems that some posters are objecting to the use of Bayes' Theorem to calculate probabilities retrospectively. However, that is precisely what Bayes' Theorem is for, that is, to update the probability of something (eg, a hypothesis) based on some data. No data, no Bayesian inference. In odds form, Bayes' Theorem is
...

The problem as much as much as anything is that Jabba doesn't know the initial probabilities, or the probability of his own existence in either scenario. If he can resolve those issues, I think he could probably use Bayes to answer the question.

 

[MRC_Hans]

dlorde,
- Just to be sure we're talking about the same thing, what I'm calling the "scientific" model, or hypothesis, is that we selves/souls/individual awarenesses have -- at most -- just one short life to live in all of eternity (if there be such a thing as "eternity").
- This is more of an evidentiary description than it is an explanation.
- It describes what appears to be the human "lot." Scientifically, anything more seems to be wishful thinking.
- But, I'm claiming that it's "falsifiable" via Bayesian statistics. If the numbers I've inserted into the formula are correct, this "scientific" model is essentially impossible.
- But, that's where the real issues lie -- are my numbers correct?
--- Jabba

I think your way of ignoring the arguments of others is insulting.

Not only are your numbers likely to be incorrect, but the whole exercise is irrelevant, because it makes no sense to calculate post hoc probability.

How many times must it be said before you notice?

Hans

 

[Squeegee Beckenheim]

I think your way of ignoring the arguments of others is insulting.

Not only are your numbers likely to be incorrect, but the whole exercise is irrelevant, because it makes no sense to calculate post hoc probability.

How many times must it be said before you notice?

Hans

I think it may be easier to understand Jabba's thought processes if we take into account something he said in the Shroud thread - that it was this particular line of reasoning which brought him to have faith as a young man. So if this line of reasoning turns out to be false, then that'll be decades upon decades of belief based on something that's incorrect. He's got a lot invested in this being correct, emotionally. It'll be incredibly hard to let go of it. Add to that the fact that it seems that he's not really encountered critical thinking as it pertains to his beliefs, he's never examined them critically, and I think his behaviour makes a lot of sense.

But that's not to say he's immovable. Actual examination of his views and how they stack up against reality in the Shroud thread has seen him change his views. Very, very slightly and very, very slowly, and it's not actually made him change his conclusions despite his change of heart about the evidence on which those conclusions are based, but I don't think he's utterly unreachable. It's just going to take a looooooong time.

 

[dafydd]

We are going to die, and that makes us the lucky ones. Most people are never going to die because they are never going to be born. The potential people who could have been here in my place but who will in fact never see the light of day outnumber the sand grains of Sahara. Certainly those unborn ghosts include greater poets than Keats, scientists greater than Newton. We know this because the set of possible people allowed by our DNA so massively outnumbers the set of actual people. In the teeth of these stupefying odds it is you and I, in our ordinariness, that are here.

Richard Dawkins

 

[Jabba]

Dafydd,
- Good quote. Dawson agrees with me about the probability of a particular "self" to ever exist. Wonder what he'd say about the probability of a particular self to exist today?
--- Jabba

 

[Humots]

I haven't been following the thread carefully, but it seems that some posters are objecting to the use of Bayes' Theorem to calculate probabilities retrospectively. However, that is precisely what Bayes' Theorem is for, that is, to update the probability of something (eg, a hypothesis) based on some data. No data, no Bayesian inference. In odds form, Bayes' Theorem is

P(H₁|D)/P(H₂|D) = P(D|H₁)/P(D|H₂) × P(H₁)/P(H₂) .

D in the above formula is the data, and the first term on the right-hand side of the equation is the relative probability of the data under competing hypotheses, H₁ and H₂. I take it that the data in the present problem is something like "Jabba exists." So if Jabba is estimating the probabilities that he would exist under competing hypotheses and using that information to update the prior probabilities of those hypotheses, then that per se does not violate the rules of Bayesian inference.

Jay

Humots,
- But you have agreed upon the formula I'm using -- you just think that the numbers I have inserted are off the wall -- or, out of thin air.
- You probably agree with what Jay said, and I think that what Jay said is all that I'm claiming in regard to "useage."
--- Jabba

I do agree with what Jay said. But it is not just that the numbers that you use are off the wall.

As I said before, Bayes' Theorem is not a syllogism. It is a mathematical equation that is meaningful only with things that are defined well enough to be assigned a probability.

True scientific hypotheses and data are very specifically defined. Newton's original hypothesis about gravity contained a specific mathematical formula detailing exactly how gravity behaved. And the data used to verify the hypothesis consisted of precise measurements.

I believe that your terms "NR" and "R" and "k" are not precise enough to be included as either hypotheses or data in the Bayes' formula.

Let me try to illustrate what I mean. Suppose we hypothesize "All crows are black". Using pure logic, we can verify this statement by either:

1. Determining that every crow in the world is black, or
2. Determining that every non-black object in the world is not a crow.

Suppose we try (2), and we find an albino raven? This is a non-black object that is not a crow, so it would seem to support the hypothesis.

But a raven is genetically related to a crow, so an albino raven implies that an albino crow could exist. So here is a non-black object that is not a crow that implies that not all crows are black.

In the real world, "crow" and "raven" are not completely distinct. They overlap.

Jabba, I am trying to give an example of how your hypotheses are "fuzzy" in a logical sense that prevents them from being treated as you are treating them.

 

[Jabba]

I think it may be easier to understand Jabba's thought processes if we take into account something he said in the Shroud thread - that it was this particular line of reasoning which brought him to have faith as a young man. So if this line of reasoning turns out to be false, then that'll be decades upon decades of belief based on something that's incorrect. He's got a lot invested in this being correct, emotionally. It'll be incredibly hard to let go of it. Add to that the fact that it seems that he's not really encountered critical thinking as it pertains to his beliefs, he's never examined them critically, and I think his behaviour makes a lot of sense.

But that's not to say he's immovable. Actual examination of his views and how they stack up against reality in the Shroud thread has seen him change his views. Very, very slightly and very, very slowly, and it's not actually made him change his conclusions despite his change of heart about the evidence on which those conclusions are based, but I don't think he's utterly unreachable. It's just going to take a looooooong time.

Squeegee,
- You're right. This is important to me.
--- Jabba

 

[wollery]

Dafydd,
- Good quote. Dawson agrees with me about the probability of a particular "self" to ever exist. Wonder what he'd say about the probability of a particular self to exist today?
--- Jabba

 

[Jabba]

I do agree with what Jay said. But it is not just that the numbers that you use are off the wall.

As I said before, Bayes' Theorem is not a syllogism. It is a mathematical equation that is meaningful only when things that are defined well enough to be assigned a probability.

True scientific hypotheses and data are very specifically defined. Newton's original hypothesis about gravity contained a specific mathematical formula detailing exactly how gravity behaved. And the data used to verify the hypothesis consisted of precise measurements.

I believe that your terms "NR" and "R" and "k" are not precise enough to be included as either hypotheses or data in the Bayes' formula.

Let me try to illustrate what I mean. Suppose we hypothesize "All crows are black". Using pure logic, we can verify this statement by either:

1. Determining that every crow in the world is black, or
2. Determining that every non-black object in the world is not a crow.

Suppose we try (2), and we find an albino raven? This is a non-black object that is not a crow, so it would seem to support the hypothesis.

But a raven is genetically related to a crow, so an albino raven implies that an albino crow could exist. So here is a non-black object that is not a crow that implies that not all crows are black.

In the real world, "crow" and "raven" are not completely distinct. They overlap.

Jabba, I am trying to give an example of how your hypotheses are "fuzzy" in a logical sense that prevents them from being treated as you are treating them.

Jay,
- Do you agree with Humots?
--- Jabba

 

[dafydd]

Dafydd,
- Good quote. Dawson agrees with me about the probability of a particular "self" to ever exist. Wonder what he'd say about the probability of a particular self to exist today?
--- Jabba

Right over your head and splat against the wall. I suspect you of trollery and deliberate obtuseness.

 

[dafydd]

Jay,
- Do you agree with Humots?
--- Jabba

No, the point is do you agree with Humots?

 

[Jabba]

In the time you took to tell us that you'd eventually get round to answering the criticisms of your post #215, you could have posted the remainder of your supposed proof of immortality, and also answered some of those criticisms.

Honestly, Jabba, do you have any idea how damaging it is to your credibility that you act like this? It was bad enough that you took two weeks to post what should have been in the first post, but now you are doing what you have done in the shroud thread. Instead of answering people, you waste post upon post in telling us that you intend to answer at some indeterminate time in the future, instead of just answering.

Despite your attempt to inject a little levity, you don't have 2^64 questions to answer. You just have five.

1) Where did you get your numbers from?

2) Do you agree with Humots that your maths shows the probability of the non-religious hypothesis to be much more likely than the religious hypothesis?

3) Do you understand that you are calculating the probability of 'you' existing in 2012 as if you were performing the calculation 20,000 years ago?

4) Do you understand why this is a foolish thing to do, given that we are in 2012 and all the things that had to happen to produce you (or any of the 7 billion people in the world) have already happened?

5) Do you understand what people are getting at when they give you analogies such as a puddle thinking the hole is made for it, or the wine thinking the glass is made for it?

It takes one post to answer those five questions. It takes one post to lay out the rest of the argument (again, you should have put your entire argument into your first post). One post. In the words of Nike, just do it.

Agatha,
- Re #2: no.
- Re #3: no.
- Re #4: no.
- Re #5: no.
--- Jabba

 

[dafydd]

Agatha,
- Re #2: no.
- Re #3: no.
- Re #4: no.
- Re #5: no.
--- Jabba

You do realize that you are admitting that you do not understand?

 

[Humots]

Agatha,
- Re #2: no.
- Re #3: no.
- Re #4: no.
- Re #5: no.
--- Jabba

OK, let's have some specifics.

 

[Jabba]

Jabba, you are saying:

1. P(NR|me) = P(me|NR)P(NR)/(P(me|NR)P(NR)+P(me|R)P(R)), and

• P(NR) = .99
• P(me|R) = .05
• P(R) = .01

(2. - 5.) P(me|NR) approaches 0.

So, P(NR|me) approaches 0.

I wonder, what is P(NR|k), the probability that the Non-Religious Hypothesis is true given all background knowledge? Well,

P(NR|k) = P(k|NR)P(NR)/(P(k|NR)P(NR)+P(k|R)P(R))

From your own argument:

• P(NR) = .99
• P(R) = .01

Then for k = all background knowledge:

• P(k|R) = .01 or less, since if the Religious hypothesis is true, most background knowledge (including evolution) is false
• P(k|NR) = .99 or more, since P(NR) + P(R) = 1.0, again from your own argument that R and NR are a binary partition

We obtain
P(NR|k) = 0.99 * 0.99/0(.99 * 0.99 +0.01 * 0.01) = 0.9801 / (0.9801 + .0001) = 0.9999

What about P(R|k), the probability that the Religious Hypothesis is true given all background knowledge?

Using P(R|k) = P(k|R)P(R)/(P(k|R)P(R)+P(k|NR)P(NR))

we get, using the same values,

P(R|k) = .01 * .01 / (.01 * .01 + .99 * .99) = .0001

which is consistent with P(NR) + P(R) = 1.0.

So, what’s wrong with this picture?

Humots,
- I'm going to give my quick answer. If you find something wrong with it, I'll re-think.
- I think that what is wrong with your picture is that you're counting k twice in each probability. I'm saying that the k is already counted in P(R) and P(NR).
--- Jabba

 

[carlitos]

Dafydd,
- Good quote. Dawson agrees with me about the probability of a particular "self" to ever exist. Wonder what he'd say about the probability of a particular self to exist today?
--- Jabba

Dawson?

You do realize that you are embarrassing yourself here, right?

 

[shuttlt]

Humots,
- I'm going to give my quick answer. If you find something wrong with it, I'll re-think.
- I think that what is wrong with your picture is that you're counting k twice in each probability. I'm saying that the k is already counted in P(R) and P(NR).
--- Jabba

I still don't get why we care about P(Jabba) or why it would make any significant difference to any of these theological claims about the existence and perminance of the soul. Am I the only one who thinks the entire discussion can be reduced to a proper answer to this question. Why is P(the soul is eternal | Jabba) different to P(the soul is eternal), or however this is being phrased?

 

[Humots]

Humots,
- I'm going to give my quick answer. If you find something wrong with it, I'll re-think.
- I think that what is wrong with your picture is that you're counting k twice in each probability. I'm saying that the k is already counted in P(R) and P(NR).
--- Jabba

What do you mean by "counting k twice in each probability"?

What do you mean by "the k is already counted in P(R) and P(NR)"?

For that matter, what do you mean by "counting" and "counted"?

In addition, please indicate where I do these things in my argument.