Proof of Immortality, VII

[caveman1917]

Probability is most generally a function of possible outcomes (and other parameters)

No, the domain of a probability function is a sigma-algebra, which contains the possible outcomes but is larger than that.

More importantly, a probability function does not depend on other parameters. Again, the domain of a probability function is a sigma-algebra. Sometimes interesting classes of probability functions are grouped and indexed by parameters (such as the normal distribution with parameters mean and variance) but the class of such functions is not a probability function itself. Each individual instance of such a class (for example the normal distribution with a specific value for mean and variance) is a probability function, but the class (group) itself isn't.

In our simple examples we typically choose devices that have a discrete uniform probability density, where the density function is 1/N.

Which reminds me, since nobody took the bait: 3 points for anyone proving that, given the definitions and assertions in my post:

1. P can not be uniform.
2. That hence the 3rd Venn diagram is actually impossible to draw given the assertion at the start of the post of each pixel representing an outcome, and that I tried to pull a fast one with it.

 

[jt512]

Prove it. Show that it was impossible for Jabba to not have existed, that there does not exist even a single possible alternate history of the universe that wouldn't have resulted in Jabba existing.

What is impossible is for Jabba to observe his non-existence, ~E. Since he is doing the observing, his existence, E, is a foregone conclusion whether H is true or ~H is true. Thus his observing E, the only thing he can possibly observe under either H or ~H, provides no evidence for either H or ~H.

 

[caveman1917]

Since he is doing the observing

1. Who cares who is doing the observing?

2. Even if we assume that your argument is correct, then why doesn't it apply to my example with the wire? Why does it suddenly stop applying if only I do this:

What is impossible is for Jabba caveman to observe his non-existence, ~E. Since he is doing the observing, his existence, E, is a foregone conclusion whether H L is true or ~H ~L is true. Thus his observing E, the only thing he can possibly observe under either H L or ~H ~L, provides no evidence for either H L or ~H ~L.

Answers in spoiler:

1. Nobody cares. As we have seen above, conditioning on an event is asserting a certain predicate to be true on the universe. It doesn't matter who utters the predicate, what matters is that we consider it true and proceed to condition on it. Whether it is Jabba saying "I exist" or someone else saying "Jabba exists" has no bearing on the result. Same probability space, same predicate, same result.

2. It never applies. The complement of "Jabba exists" isn't "Jabba observes his own non-existence" but "Jabba doesn't exist". You've basically stumbled upon the right answer (that the problem is P(E|H) = P(E|~H)) but by incorrect reasoning (arbitrarily declaring that P(E) = 1 and hence trivially P(E|X) = 1 for any X). You probably came up with an argument, checked that you had the right conclusion, but failed to check whether you actually had a right argument. It's basically going "The moon is made of cheese therefor the sky is blue", then checking that the sky is indeed blue, and proceeding to think you've made an insightful argument with the notion of the moon being made of cheese.

 

[Belz...]

1. Who cares who is doing the observing?

Well, it's a bit important since he couldn't observe anything if he weren't alive, making his question quite silly.

 

[caveman1917]

No, the domain of a probability function is a sigma-algebra, which contains the possible outcomes but is larger than that.

Come to think of it, technically it doesn't even contain any outcomes, it contains sets of outcomes (subsets of the universe). So for any outcome p P(p) isn't defined, but P({p}) is. Huh, outcomes don't have probabilities, funny that

 

[jsfisher]

1. Who cares who is doing the observing?

You are correct. It doesn't matter who is observing Jabba (or anyone else for that matter). The point is, though, that whomever is being observed, the observer should not be surprised that the observed exists.

 

[caveman1917]

the observer should not be surprised that the observed exists.

Formalize this. You are probably wrong but it depends on what exactly you mean by this.

 

[caveman1917]

Formalize this. You are probably wrong but it depends on what exactly you mean by this.

Here's why you're probably wrong. I'm assuming you're going to come up with some sort of "but it's not surprising that someone exists", in the same vain as "I am the lottery winner" is not surprising since someone is going to win the lottery. Basically that Texas Sharpshooter Fallacy thing. Here's why it's wrong:

Let LR be the likelihood ratio: P(E|H) / P(E|~H). As I said earlier to JayUtah, P(E) is irrelevant, what matters is LR. Now let's start varying our E from specific to broad (ie successive E's are supersets of preceding E's).

1. E = "Jabba exists". P(E) is very small, so we should be surprised of E. LR = 1.

2. E = "Some male person exists". P(E) is somewhat larger now, so we shouldn't be all that surprised of E. LR = 1.

3. E = "Some person exists". P(E) is even larger now, so we shouldn't be surprised at all of E. (someone's going to win the lottery). LR = 1.

Note how it doesn't matter how we vary E as long as we hold LR constant. Your argument would basically be the assertion that E must be the E in case 3, but you have no basis for demanding that. This was already argued earlier in the thread in terms of getting a specific hand of cards from a deck and comparing "was randomly drawn" with "was drawn on purpose", in a response to jt512.

 

[jt512]

You are correct. It doesn't matter who is observing Jabba (or anyone else for that matter). The point is, though, that whomever is being observed, the observer should not be surprised that the observed exists.

Formalize this. You are probably wrong but it depends on what exactly you mean by this.

He's correct. And, in fact, when I first started posting about Jabba's fundamental error, I concentrated on cases where the the observer was not the observed, since I thought that was the more straightforward situation. But it is difficult to define what it means to observe that Jeff is my next-door neighbor. Exactly how do we define "Jeff"? It's an unnecessary complication: since Jabba is using his own existence as his data, it suffices to restrict a refutation of his argument to precisely that case.

 

[caveman1917]

He's correct.

1. How can you know whether he's correct if his assertion is ambiguous?

2. If you believe it's so correct then why aren't you formalizing the claim and supporting it?

And, in fact, when I first started posting about Jabba's fundamental error, I concentrated on cases where the the observer was not the observed, since I thought that was the more straightforward situation. But it is difficult to define what it means to observe that Jeff is my next-door neighbor. Exactly how do we define "Jeff"? It's an unnecessary complication: since Jabba is using his own existence as his data, it suffices to restrict a refutation of his argument to precisely that case.

There's too much to pick apart here[*], but for 5 points: Prove that we don't need an exact definition of "Jeff" or "Jabba" or indeed any such E in this case.

A hint in the spoiler costing you 3 points if used:

Do we need an exact definition of E or can we use a certain symmetry between the H and ~H half of the universe so that our argument holds true for any suitable definition of E? Add 1 point (so lose only 2) for also making the notion of "suitable" precise.

ETA:
* well it isn't actually too much, the other thing is basically that those cases aren't distinct and hence there is nothing to restrict your refutation too. Your refutation is simply incorrect, it only happens to stumble on one instance of the refutation (P(E|H) = P(E|~H)) by accident. Only one instance since it only works for the case where P(E) = 1 anyway, and that's the trivial case (since for any X, Y: P(X) = 1 => P(X|Y) = 1 is trivially true).

 

[The Norseman]

Should we mention that the are 10⁷⁰ particles in the universe?

You probably shouldn't. According to this website at least, there are 3.28 x 10⁸⁰ particles in the universe.

So... close but no cigar!

 

[Jabba]

- I think I was wrong again. The human population variable should be involved in the prior probabilities -- not the likelihoods.
- Caveman, what do you say?

 

[Jabba]

You probably shouldn't. According to this website at least, there are 3.28 x 10⁸⁰ particles in the universe.

So... close but no cigar!

Norseman,
- What, specifically, are "particles"?

 

[Belz...]

Norseman,
- What, specifically, are "particles"?

Stick to the topic.

 

[Belz...]

Formalize this. You are probably wrong but it depends on what exactly you mean by this.

Something cannot observe itself when it doesn't exist. Do you really need formalising for this?

 

[JayUtah]

I think I was wrong again. The human population variable should be involved in the prior probabilities -- not the likelihoods.

More importantly you need to define "now" in a way that supports your math. You said "now" is a uniform random variable across all time. But that is not the natural meaning of "now," nor is it what you mean when you say "What are the chances that the century corresponding to my life would occur now."

Most of your arguments in this forum revolve around you foisting new definitions for common words, or leaving your intended meaning unclear so that it's guaranteed to be misinterpreted and equivocated. This is evidently what you're doing again. Your proofs never have much to do with math. They tend to have everything to do with you playing a shell game with ordinary human language. As soon as we finally arrive on a serviceable definition for one of the concepts in your argument, you declared there to be a "communication problem" and change all the words again.

Please reconcile the definition of "now" with your usage of the word in your proof.

Caveman, what do you say?

For someone nearly obsessed with the notion of friendliness in debate, you seem oddly deferential to a poster well known for being pompous and condescending. Would you care to explain your double standard?

 

[JayUtah]

Something cannot observe itself when it doesn't exist. Do you really need formalising for this?

We seem to have lost sight of the fact that the observation in this case is necessarily subjective. It is not merely Jabba's existence that is observed, but the fact that he is self-aware. I cannot observe that Jabba is self-aware. Only he can. Jabba is the one claiming there is distinction, uniqueness in the nature of that observation.

 

[RoboTimbo]

- I think I was wrong again. The human population variable should be involved in the prior probabilities -- not the likelihoods.

You think you've arranged the deck chairs incorrectly on your Titanic argument?

I say you should concentrate on the numerous major flaws to your argument, each of which is individually fatal to it.

 

[Jabba]

More importantly you need to define "now" in a way that supports your math. You said "now" is a uniform random variable across all time. But that is not the natural meaning of "now," nor is it what you mean when you say "What are the chances that the century corresponding to my life would occur now."...

Jay,
- Per usual, I don't understand your objection. Try again?

 

[Belz...]

- Per usual, I don't understand your objection. Try again?

Out of everyone in this thread, no one's put more effort into educating you as Jay has. He's made a great number of long posts explaining, in detail, where you go wrong, and instead of listening to him and responding to his points, you ignore him rudely time and time again. I don't understand why Jay's wasting so much of his life trying to educate you, but you've got some nerve asking him for an extra after all this.