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Old Today, 10:30 AM   #3361
Belz...
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Originally Posted by Jabba View Post
Dave,
- For now, at least, I think you're right.
And he leaves it at that! Marvelous.
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Old Today, 10:48 AM   #3362
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Originally Posted by Belz... View Post
Ten points? That's a weak bet. What happened to that trillion dollars you owe me?
If he can't tell the difference between 1/10 and 1/100 then why would you expect him to know the difference between ten points and a trillion dollars?
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Old Today, 12:22 PM   #3363
caveman1917
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Originally Posted by JayUtah View Post
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.

Quote:
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.
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Old Today, 07:29 PM   #3364
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Originally Posted by caveman1917 View Post
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.
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Old Today, 07:55 PM   #3365
caveman1917
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Originally Posted by jt512 View Post
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:
Quote:
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.
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"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin

Last edited by caveman1917; Today at 07:57 PM.
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Old Today, 08:07 PM   #3366
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Originally Posted by caveman1917 View Post
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.
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Old Today, 08:24 PM   #3367
caveman1917
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Originally Posted by caveman1917 View Post
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
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"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin

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Old Today, 08:34 PM   #3368
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Originally Posted by caveman1917 View Post
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.
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Old Today, 08:53 PM   #3369
caveman1917
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Originally Posted by jsfisher View Post
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.
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"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin
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Old Today, 09:16 PM   #3370
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Originally Posted by caveman1917 View Post
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.
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"Ideas are also weapons." - Subcomandante Marcos
"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin

Last edited by caveman1917; Today at 09:18 PM.
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Old Today, 09:21 PM   #3371
jt512
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Originally Posted by jsfisher View Post
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.
Originally Posted by caveman1917 View Post
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.
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Old Today, 09:42 PM   #3372
caveman1917
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Originally Posted by jt512 View Post
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?

Quote:
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).
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"Ideas are also weapons." - Subcomandante Marcos
"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin

Last edited by caveman1917; Today at 10:02 PM.
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Old Today, 10:05 PM   #3373
jt512
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Originally Posted by caveman1917 View Post
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?



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).
In the unlikely event that you rephrase your questions without your condescending, insufferable poposity, I'll consider actually answering them.
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Old Today, 10:09 PM   #3374
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Originally Posted by jt512 View Post
In the unlikely event that you rephrase your questions without your condescending, insufferable poposity, I'll consider actually answering them.
No, ain't going to happen. I'll consider your position refuted.
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"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin
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Old Today, 10:16 PM   #3375
jt512
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Originally Posted by caveman1917 View Post
No, ain't going to happen. I'll consider your position refuted.
Since you're such a stickler for logical rigor, how does your refusal to post in a respectiul manner entail the conclusion that you have refuted something?
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Old Today, 10:21 PM   #3376
caveman1917
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Originally Posted by jt512 View Post
Since you're such a stickler for logical rigor, how does your refusal to post in a respectiul manner entail the conclusion that you have refuted something?
It doesn't. Pretty obvious, wouldn't you think?

ETA: I was already considering your position refuted because of, well, refuting it. I was just open to being shown wrong, but since you refused to argue your case no such change will occur and I will hence keep considering your position refuted (ie "I'll consider your position refuted.")
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"Ideas are also weapons." - Subcomandante Marcos
"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin

Last edited by caveman1917; Today at 10:22 PM.
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Old Today, 10:22 PM   #3377
jt512
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Originally Posted by caveman1917 View Post
It doesn't. Pretty obvious, wouldn't you think?
Thus you have no justification for this statement: "No, ain't going to happen. I'll consider your position refuted."
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Old Today, 10:23 PM   #3378
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Originally Posted by jt512 View Post
Thus you have no justification for this statement: "No, ain't going to happen. I'll consider your position refuted."
Your arguments from ignorance are unappealing.
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"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin
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Old Today, 10:24 PM   #3379
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Originally Posted by Dancing David View Post
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!
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Old Today, 10:38 PM   #3380
jt512
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Originally Posted by caveman1917 View Post
Your arguments from ignorance are unappealing.
Caveman, if there is a flaw in my argument, then, honestly, you are the most likely person to detect it. And if I am wrong, I'd really like to know. But I'm not so eager to know that I will put up with your arrogance, pomposity, and condescension to find it out.

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Old Today, 10:52 PM   #3381
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Originally Posted by caveman1917 View Post
It doesn't. Pretty obvious, wouldn't you think?

ETA: I was already considering your position refuted because of, well, refuting it. I was just open to being shown wrong, but since you refused to argue your case no such change will occur and I will hence keep considering your position refuted (ie "I'll consider your position refuted.")
Not in this thread. At least, I haven't seen any evidence you are open especially considering several other posters who have taken the time and effort into demonstrating your misapprehensions.
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