Proof of Immortality, the IV league

[jt512]

That doesn't help, because what we want to know is what the "weight of the evidence" is. It can be independent and still be assigned a different weight by different people.

The weight of the evidence for hypothesis H1 vs hypothesis H2 is the likelihood ratio for H1 vs H2. Did you read this post? Please show us how you can calculate any other likelihood ratio in that problem.

ETA: Ugh. Besides, what are you talking about with "doesn't help"? Doesn't help with what? I was responding to the bizarre comment of Nonpareil that somehow I'm "equivocating" about something that involves "evidence for the prior being true," whatever that is supposed to even mean.

 

[Jedi]

As I have repeated and patiently explained, and illustrated using a probability problem that is literally too simple to assign as homework to a high school probability class: To evaluate how an observation affects the relative probabilities of two competing hypotheses, you separately compute the probability of the observation under each hypothesis. The observation increases the probability of the hypothesis (relative to the other hypothesis) under which the observation is more probable. This is really just mathematically formalized common sense.

when did i ever say anything different? you're missing the point i'm making...

your argument is trivial. you're assuming a high prob for the p(live|God)=1 ( the prior is pretty much 0 per jsfisher). i can use your exact same argument to show that a toaster guided people out of the desert.

it's also been pointed out that we don't know how many people get lost and think God is guiding them and don't make it, which you're not accounting for. this would reduce your cond prob by a lot.

if you're just trying to give an example of how to use Bayes in a situation where we have verifiable data that lives were saved due to God, that's fine. but i don't see the purpose of it.

and we're back to the main issue... using anecdotes as evidence is a bad idea.

 

[Garrette]

I calculated that a couple pages back, but looking back, I noticed that I made a decimal place error, so I'll do it again.

Let's say that we are members of an explorer's club. In the history of the club we have sent exactly two explorers into some particular desert. The expeditions were independent, and the explorers did know each other; in fact, let's assume that the second explorer was completely unaware of the first one (and, importantly, that he had know way of knowing that the first explorer claims to have been guided by God). Both explorers returned, both said they had become lost, and both said that God spoke the them and explained where to find water, and in fact, they found water there, and were saved.

We have two hypotheses about how the explorers found water. H1: God told them where to find it. H2: They just got lucky; that is, they found it by random chance. Our data, D, consists of two out of two explorers returning and reporting that God showed them where water would be. We wish to know how much the data supports H1 compared with H2; that is, we wish to know the weight of the evidence in favor of H1 vs H2. Our calculation requires two numbers: the probability of the data on the assumption that H1 is true, P(D|H1); and the probability of the data on the assumption that H2 is true, P(D|H2).
Assume for the sake of argument, that if God guides you to water, you'll get there and live. Then P(D|H1)=1. To calculate P(D|H2) let's assume that we know (for the sake of argument) from our knowledge of the geography and climate, that once lost, the chances of finding water by random chance is 2%. Since two independent explorers each found water, P(D|H2)=.02^2=.0004. The weight of the evidence for H1 vs H2, called the likelihood ratio, is then

P(D|H1) / P(D|H2) = 1/.0004 = 2500.

This says that the evidence is 2500 times more likely if H1 is true than if H2 is true. Or, the weight of the evidence for H1 vs. H2 is 2500.

There are two related things to realize here. The first is that we were able to calculate the weight of the evidence for H2 vs. H1 without considering the prior probability of either hypothesis. As I said earlier, the weight of the evidence is independent of the prior probabilities. Therefore, no matter how much two people disagree on the prior odds of these hypotheses, they should agree on how much the evidence should change the odds. In this case, no matter what your prior odds of H2 vs H1 are, your posterior odds should be 2500 times greater than your prior. (Note that we're using odds* now, not probabilities.)

The second thing to realize is that, since we haven't taken the prior odds of the hypotheses into account, we haven't yet calculated our updated, or posterior, odds. Your prior odds are your own business and based on whatever background information (or baggage) you bring to the problem. Therefore, your posterior odds are your own business as well. This is why I've said to Jabba that I don't care what his prior probabilities are; he can have whatever prior probabilities he wants. However, he cannot have whatever values he wants for the likelihoods (i.e., the P(D|H_) terms). Rather, for each hypothesis there has to be a model that makes a quantitative prediction of the likelihood of the data given the model, as we had in problem.


____________________

*Odds are ratios of probabilities. For example, the prior odds of H1 vs H2 is P(H1) / P(H2).

The paragraph I highlighted is where I take issue because it is where you go wrong. More accurately, it is where you start to go right but get only partially there.

First, why are there only two hypotheses? What about H3 = Experienced Explorers Even in Uncharted Territory Know How to Look for Signs of Water.
Or H4 = The Explorers Lied About Not Being Out There Before.
Or H5 = The Explorers Lied About the God Hallucination Even Though They Found the Water by Chance

Second, and this is the crux of my rebuttal, you use prior experience (or context, as I and others have been saying) in order to determine the chances of H2 but do not allow it for H1, and this is precisely the opposite of what your own hypothetical indicates should be the case. You say that we have sent these two explorers -- and these two explorers only -- to the area in question yet somehow we magically know that the chance of finding water randomly there is 2%. We can leave your internal contradiction aside for the moment and move to H1. If we know 2% from previous experience for H2, then why can we not use chance derived from previous experience for H1? We know about hallucinations; we know about spiritual experiences not being supported by the evidence. Surely we can apply those, too?

Third, as others have said, this same thinking lends itself exactly as well to proving the Jabberwocky was the creature that guided the survivors to water.

Fourth, your method leads to you doing what I have objected to previously, i.e., using Bayes to support an unevidenced claim by using other unevidenced claims.

I am in no position whatsoever to comment on the details of Bayes and the equations, but my lack of expertise there does not prevent me pointing out that GIGO must still apply.

I'll end this post with this hypothetical modification to your hypothetical example: Suppose it wasn't the two surviving explorers who told us God led them to water but rather a patient of a mental institution who had visited there (we have proof of this) and spoke with them (we have proof of this, too). This patient, in fact, is the only one ever to have spoken to these explorers, and his account of their conversation is that each one said a giant flaming doughnut led them to water.

Using the parameters of your hypothetical are we not required to say that the Giant Flaming Doughnut hypothesis is 2500 times more likely than finding water randomly?

 

[marplots]

The weight of the evidence for hypothesis H1 vs hypothesis H2 is the likelihood ratio for H1 vs H2. Did you read this post? Please show us how you can calculate any other likelihood ratio in that problem.

Here is what you said about it in that post:

Our calculation requires two numbers: the probability of the data on the assumption that H1 is true, P(D|H1); and the probability of the data on the assumption that H2 is true, P(D|H2).

Assume for the sake of argument, that if God guides you to water, you'll get there and live. Then P(D|H1)=1. To calculate P(D|H2) let's assume that we know (for the sake of argument) from our knowledge of the geography and climate, that once lost, the chances of finding water by random chance is 2%. Since two independent explorers each found water, P(D|H2)=.02^2=.0004. The weight of the evidence for H1 vs H2, called the likelihood ratio, is then

P(D|H1) / P(D|H2) = 1/.0004 = 2500.

It's the process of assigning numbers that isn't helped by the formalism. What we want to know is how to get those numbers, not what to do with them after we get them. I can assume whatever I like to get whatever answer I want. You weighted the evidence when you assigned the probabilities, that's what changes when people disagree - how should the evidence be assigned a value in the first place. And specifically, what value should an anecdote have?

If I saw bigfoot in my backyard, I must assign the probability that bigfoot exists at pretty damn close to 1. The person I tell my story to is not so bound, but may still assign a probability larger than zero based on what they know about me. Further afield, things will be different still.

All Bayes does here is formalize an expression of belief. Nothing more. Formalizing it does not transform beliefs into facts, the best it can do is aid communication if you are talking to mathematically literate people.

 

[Nonpareil]

Sorry, but there is just no excuse for making a statement like that at this point in the conversation. I have said, and shown, over and over again, that the weight of the evidence is independent of the prior.

No. Read before responding, please.

As I literally just said, "your chances of drawing a royal flush are much higher if you cheat than if you play fair" is true, but it is not evidence that a given royal flush is the result of cheating. You trying to label that statement as evidence does not actually make it so.

Because you still seem to have trouble grasping this, I will rephrase: if you use a magic spell to alter probability so that your chances of drawing a royal flush are one hundred percent, then you have a much higher chance of drawing one than if you just draw five cards from the top of the pack.

This does not make a given royal flush evidence of probability-altering magic.

 

[Mojo]

As I literally just said, "your chances of drawing a royal flush are much higher if you cheat than if you play fair" is true, but it is not evidence that a given royal flush is the result of cheating.

What if the royal flush is drawn by the cousin of the controller of a lottery?

 

[Slowvehicle]

What if the royal flush is drawn by the cousin of the controller of a lottery?

How many legs does the cousin have?

How many legs does the flush have?

 

[Jabba]

Mojo,
- Say that a patient claims that he saw something occur in a room down the hall while he was being resuscitated. Actually during the resuscitation, witnesses in the room down the hall reported the (same) incident to a nurse. Prior to telling the nurse what the patient had claimed, staff asked her what had happened. The nurse provided the same story in detail. The particular event was quiet, had nothing to do with the patient and was not something that anyone would expect to occur in a hospital.
- Wouldn't you agree that such would be at least weak evidence for immateriality?

1. It's just another anecdote.
2. At this point you don't need to provide "weak evidence" of anything, you need to prove that the immaterial soul is part of the hypothesis you are trying to disprove. Otherwise, if your factor of seven billion over infinity belongs anywhere, your existence is infinitely less likely under your preferred hypothesis than it is under the hypothesis you are trying to disprove.

Mojo,
- It is an anecdote.
- As you know, my claim is that anecdotes can provide evidence.
- Here, I'm trying to provide evidence for immateriality and claiming that this particular anecdote would provide such evidence.
- It's always possible that there is a flaw in the claims and/or logic, but the info we have supports the belief that something immaterial is going on -- and, if mainstream science hadn't pretty much dismissed the possibility of immateriality, this anecdote would clearly be some evidence for it.

 

[Jabba]

Well, you probably shouldn't give a hypothesis a prior probability of exactly 0 unless the hypothesis is logically impossible...which is not to say you can't give it a really, really small non-zero probability. A serious calculation of whether something supernatural could have occurred should take into account the fact that it is possible, no matter how unlikely, that physics has actually gotten everything wrong.

jt,
- How about that physics is missing a major piece (or dimension) of the puzzle?

 

[Squeegee Beckenheim]

- As you know, my claim is that anecdotes can provide evidence.

And, as you know, this is not the case, for all the reasons which have already been outlined for you over the last month or so.

- It's always possible that there is a flaw in the claims and/or logic, but the info we have supports the belief that something immaterial is going on -- and, if mainstream science hadn't pretty much dismissed the possibility of immateriality, this anecdote would clearly be some evidence for it.

Nope. The current scientific model includes dark matter, despite none having been directly observed. Someone saying that they found some dark matter in their armpit but dropped it behind the fridge and couldn't find it again would not be evidence for dark matter.

 

[Nonpareil]

As you know, my claim is that anecdotes can provide evidence.

And it's wrong.

Here, I'm trying to provide evidence for immateriality and claiming that this particular anecdote would provide such evidence.

And you're wrong.

It's always possible that there is a flaw in the claims and/or logic, but the info we have supports the belief that something immaterial is going on

No, it doesn't.

and, if mainstream science hadn't pretty much dismissed the possibility of immateriality, this anecdote would clearly be some evidence for it.

No, it wouldn't.

You have failed on every count.

 

[Belz...]

jt,
- How about that physics is missing a major piece (or dimension) of the puzzle?

How about you're making things up and requiring science to explain the stuff you make up?

 

[JayUtah]

As you know, my claim is that anecdotes can provide evidence.

No. Your claim was that a few anecdotes provide evidence for life after death. You used a venue-changing stunt to widen those goalposts but it didn't work. Now you're back to this specific claim. "Men can rob banks" is not the same proposition as "This man robbed that bank."

Here, I'm trying to provide evidence for immateriality

No. You said you would prove immortality. As much as you want those goalposts to widen, they will not. "Immateriality" is not the same as immortality.

...and claiming that this particular anecdote would provide such evidence.

No. As with all your other anecdotes, you tell a story and then attribute a cause or mechanism to it. The story is not proof that the attribution is correct.

It's always possible that there is a flaw in the claims and/or logic, but the info we have supports the belief that something immaterial is going on -- and, if mainstream science hadn't pretty much dismissed the possibility of immateriality, this anecdote would clearly be some evidence for it.

No. The problem with your proof is not that your critics are closed-minded.

 

[JayUtah]

How about that physics is missing a major piece (or dimension) of the puzzle?

Well, make up your mind. Yesterday you're telling us that quantum mechanics provides the mechanism for all your woo. Today you're telling us physics has it all wrong, in the form of missing a major piece. As always, if you claim that some hypothesis has fallen short, then you must show observations it does not account for. But you cannot do that. In fact, you all but insist that your soul would be invisible to scientific inquiry. So no matter how much you attempt to disguise it, your claim is still that there exists a soul for which you have no evidence, and which satisfies no observable need. And this is your "proof."

 

[Filippo Lippi]

How about you're making things up and requiring science to explain the stuff you make up?

Or rather, he's making stuff up, saying science can't explain it*, and then claiming the stuff he's made up proves eternal life.

Following on from that, sotto voce, we have, therefore, Jebus.


*science is probably really bored now and just puts everything Jabba claims down to mendacity

 

[JoeMorgue]

Jabba you really need to decide if "science" (either real science or your nonsense strawman version of it) is on your side or not and stop invoking it out of one side of your mouth and condemning it out of the other.

 

[JoeMorgue]

Or rather, he's making stuff up, saying science can't explain it*, and then claiming the stuff he's made up proves eternal life.

Following on from that, sotto voce, we have, therefore, Jebus.

This really is Woo distilled down to it's most basic level and it's really sad that people can get so much mileage out of something that is so obviously just playing with the language and nothing else.

1. Define thing as "outside" of science.
2. Use the fact that it is outside of science, which it only is because you defined it as such, as proof of itself.

That's it. That's all 99% of Woo is at the end of the day and it's just silly word games.

 

[Nonpareil]

silly word games.

That, sir, is my line.

 

[Mojo]

- It's always possible that there is a flaw in the claims and/or logic...

You think?

...but the info we have supports the belief that something immaterial is going on -- and, if mainstream science hadn't pretty much dismissed the possibility of immateriality, this anecdote would clearly be some evidence for it.

You have conceded that even if it is considered evidence it is very weak evidence.

Your 'proof' of immortality relies on shoehorning a factor of seven billion over infinity into the expression of the likelihood of you existence under the model you are trying to disprove. To include this factor you need to establish that immaterial souls are part of that model. You have to overcome the burden of proof. Weak evidence won't achieve this.

And, incidentally, you also need to prove that the hypothesis under which you are immortal doesn't include immaterial souls, otherwise we can just stick that hypothesis into your formula and prove that immortality is impossible.

 

[JoeMorgue]

And, if mainstream science hadn't pretty much dismissed the possibility of immateriality, this anecdote would clearly be some evidence for it.

I love how Woo Slingers keep trying to come up with new ways of trying to make the fact that science doesn't recognize things that don't exist sound like a flaw.

"If (dramatic pause and/or scare quotes) mainstream science hadn't pretty much dismissed the possibility of impossible silly evidence-less nothing, this anecdote would clearly be some evidence for it."