Proof of Immortality III

[Loss Leader]

I have no idea, but I think it would work even better as a drinking game.

I prefer True American myself.

 

[caveman1917]

If the sample space is the set of all possible outcomes of a single roll of a 24-sided, and you roll the die once, you have a single observation.

The sample space of all possible outcomes of a single roll of a 1024-sided die is the same as the sample space of all possible outcomes of batches of 10 rolls of a 2-sided die. Yet in one case it's called a "single datapoint" and in the other "10 datapoints." Why?

 

[jt512]

A simple analogy is that you thoroughly shuffle a deck of 52 playing cards, examine the sequence that was produced, and note that the probability that the shuffle would have produced that sequence if the shuffle were random is 1 in 8 × 10⁶⁷; whereas, if the deck were rigged to produce that exact sequence, then the probability would be 1. Thus, the probabilities overwhelmingly demonstrate that the deck was rigged. The fallacy is that the shuffle had to produce some sequence, and you would have made the exact same remark no matter what sequence was actually produced. Thus the hypotheses that are actually being compared are (1) whether a random shuffle would produce some sequence vs. (2) whether a rigged shuffle would have produced the sequence that was actually observed. The probability of the observation under each hypothesis is 1, so the likelihood ratio is 1, and thus the observation has no power to discriminate between the hypotheses. Of course, in this case, the priors will speak for themselves.

I disagree. Either a result always changes the relative probabilities between hypotheses, including the first time you get it, or it never does. Let S be the sequence produced by the deck, let HR be the hypothesis that the deck is random and HS that it is rigged to produce S. If you keep getting S time and time again then HS increases in probability while HR decreases, therefor if you get S a single time HS and HR also change that way.

In my hypothetical, no number of shuffles will affect the probabilities of the hypotheses. The probability that the shuffle will produce some sequence is 1 whether the shuffle is random or whether it is rigged to produce the sequence that was observed. Thus the observation of a sequence does not discern between the two hypotheses. If you want to extend the hypothesis to multiple shuffles, then to be true to the hypothetical, the subject would claim that the deck was rigged to produce whatever sequence occurred on each shuffle. But, again, some sequence has to be produced on each shuffle under both the rigged and the random hypothesis. Thus no number of observed sequences can discriminate between the hypothesis that the sequences were randomly generated and the hypothesis that they were rigged.

To bring it back to Jabba, rather than have multiple deck sequences, we have multiple individuals (you and me, for instance) that Jabba would say are incredibly unlikely to have arisen by chance. But if you and I weren't here to point to, Jabba would just point to whoever was around. Whether Jabba is right, that there is someone around to point to because of some immortality property, or whether he's wrong, there would be someone around to point to. The probability that there will be somebody around to point to is 1 under either hypothesis. So the fact there are people around to point to doesn't discriminate between the competing hypotheses.

 

[caveman1917]

Don't fight the hypo. Jabba has no information about the game, what any possible outcome is, or why any alien race might play it. Nor does the scene that he is witnessing give him any information.

Then he would be justified in saying "the game is likely rigged."

 

[caveman1917]

That statement is false, because there are sample spaces in which some, but not all, events have the same probability under two competing hypotheses.

An event can not be both discriminating and non-discriminating between hypotheses.

Nonetheless, in my hypothetical no number of shuffles will affect the probabilities of the hypotheses. The probability that the shuffle will produce some sequence is 1 whether the shuffle is random or whether it is rigged to produce the sequence that was observed. Thus the observation of a sequence does not discern between the two hypotheses. If you want to extend the hypothesis to multiple shuffles, then to be true to the hypothetical, the subject would claim that the deck was rigged to produce whatever sequence occurred on each shuffle. But, again, some sequence has to be produced on each shuffle under both the rigged and the random hypothesis. Thus no number of observed sequences can discriminate between the hypothesis that the sequences were randomly generated and the hypothesis that they were rigged.

Let's try this again:

Let S be the sequence produced by the deck, let HR be the hypothesis that the deck is random and HS that it is rigged to produce S. If you keep getting S time and time again then HS increases in probability while HR decreases, therefor if you get S a single time HS and HR also change that way.

There is a sequence S, the sequence produced on the first shuffle. This sequence is also produced on all subsequent shuffles. Let the total number of such S-producing shuffles be n. You must hold either:

1. Irrespective of how large n is, the relative probability of the deck being random vs it being rigged to produce S never changes.

or

2. Starting at some n the relative probability of the deck being random vs it being rigged to produce S changes.

If point 2 is correct, then what is the value of n above which the relative probability changes and below which it doesn't? Why is this value larger than 1?

 

[theprestige]

I prefer True American myself.

You're probably better off with that than Chardee MacDennis: The Game of Games.

 

[jt512]

An event can not be both discriminating and non-discriminating between hypotheses.

Let's try this again:

There is a sequence S, the sequence produced on the first shuffle. This sequence is also produced on all subsequent shuffles. Let the total number of such S-producing shuffles be n. You must hold either:

1. Irrespective of how large n is, the relative probability of the deck being random vs it being rigged to produce S never changes.

or

2. Starting at some n the relative probability of the deck being random vs it being rigged to produce S changes.

If point 2 is correct, then what is the value of n above which the relative probability changes and below which it doesn't? Why is this value larger than 1?

In my hypothetical, extended to n>1 shuffles, the same sequence s would not be produced under HR (except by coincidence) nor under HS (my HS, not yours). The shuffles would produce sequences s1, s2, ... , sn, and the observer, Gabba, would claim that the probability P(s1, s2, .... , sn | HR) to be 1/(8 × 10⁶⁷)ⁿ and P(s1, s2, .... , sn | HS) to be 1, where HS is the hypothesis that the game was rigged to produce s1, s2, .... , sn.

 

[Loss Leader]

Then he would be justified in saying "the game is likely rigged."

What? Why?

He has no idea what the game is, what the possible outcomes are, what the likely outcomes are, or even if there is a winner. What information about this alien game played by another species does he have?

You previously attempted to give Jabba some information by imposing your own prejudices about games. You pretended this was a game between humans which differentiate between winning and losing. No such information exists. So what information can Jabba possibly used to conclude (based upon knowing nothing of the rules, observing one outcome and never even seeing the game played) that the game is likely rigged?

 

[MRC_Hans]

An event can not be both discriminating and non-discriminating between hypotheses.

The misunderstanding here is in the term 'event' For a statistical 'event' you are right, but for a physical event (which in statistics would be termed a process) it is wrong: A process can produce outcomes ('events') that are either.

Example: We roll a die which may be either six sided or 12 sided (we don't know which).

Results from 1 through 6 are non-discriminating.
Results from 7 through 12 are discriminating.

Let's try this again:

There is a sequence S, the sequence produced on the first shuffle. This sequence is also produced on all subsequent shuffles. Let the total number of such S-producing shuffles be n. You must hold either:

1. Irrespective of how large n is, the relative probability of the deck being random vs it being rigged to produce S never changes.

or

2. Starting at some n the relative probability of the deck being random vs it being rigged to produce S changes.

If point 2 is correct, then what is the value of n above which the relative probability changes and below which it doesn't? Why is this value larger than 1?

Assuming that we examine n shuffles together (you are not stating that clearly):

#1 is false.

vs #2: The probability of the shuffle being non-random falls progressively with increasing n over n=1.

Assuming we examine each shuffle as an individual event (in principle knowing nothing about other shuffles) The probability of S is always the same. We cannot determine whether the deck is rigged from examining any single shuffle.

.... While non-constructive in a statistical process, this is basically the scenario that Jabba is trying to examine. In doing so, he ignores the fact that we have actually got about 100^*) billion shuffles to examine all of which have resulted in an individual, unique human being.

Hans

*) Number of humans ever born according to this: http://www.prb.org/Publications/Articles/2002/HowManyPeopleHaveEverLivedonEarth.aspx

 

[MRC_Hans]

I get it I just think we run too much of a risk of... someone confusing it for agreement.

Perhaps. Then we can confuse 'someone' even furher by telling him we don't.

Hans

 

[Jabba]

jt,
- Assuming, for the moment, that you do agree that your explanation above is another way of describing the Texas Sharpshooter Fallacy...

- I do think that the target was there before the shooting, and I tried to explain that back in #1898.

- But, I also think that there is no need for a target in this situation. What a pre-existing target does is provide a reasonable alternative to "happenstance" (luck of the draw?). Here, IMO of course, we already have a reasonable alternative(s) to OOFLam. There is a reasonable possibility that OOFLam is not correct. We are not stuck with luck of the draw if there is a reasonable alternative to luck. We use Bayes to figure out which side -- H, or ~H -- scores the most points in the formula.
- Given that I exist, which is more probable -- H or ~H? Which is more likely to produce my current existence?

#1898:

1. Toontown doesn’t agree with me, but I think I, basically, agree with him…

2. Why my existence isn’t just dumb luck:
3. Whereas, very unlikely things do happen (e.g. winning the lottery), they are unlikely given (based upon) specific hypotheses, or models.
4. And -- re the lottery -- were it not for the rules, the oversight, the results and the media (including the Internet), we wouldn’t be so sure that luck was the answer.
5. If, for instance, we discovered that the winner was secretly the 2nd cousin of the person most in charge of the lottery, we’d have 2nd thoughts…
6. Which is the point -- if we have a reasonable alternative to luck, we don’t have to assume that it's luck…

7. And here, what can be counted as “reasonable” doesn’t need to be very probable at all – in fact, it can be extremely improbable.
8. That’s because the likelihood of what it is being compared to, weighed against (my existence, given OOFLam) is virtually zero.
9. IOW, we have an alternative hypothesis which is much more probable – given my existence – than is OOFLam.
10. The posterior probability of OOFLam – given me -- is much smaller than the posterior probability of ~OOFLam.

11. But, the ultimate question is, “In which case am I more likely to be here – OOFLam, or ~OOFLam?”
12. The obvious answer is “~OOFLam”…

13. And then,
14. I’m the only “thing,” “process” or “illusion” that I know exists.
15. I don’t know what I am -- but, I know I am.
16. Everything else could be my imagination

17. We humans take our personal existence (selves) totally for granted.
18. We act as if we had to exist.
19. Though scientifically speaking, that’s the very last thing we should take for granted.
20. Again, according to modern science, the likelihood of my (and your) current existence is virtually zero.
21. Yet, I’m the only thing, process or illusion that I actually know exists. 22. And, you’re the only thing, process or illusion that you actually know exists (if you’re not a robot)). 23. The rest could be our imagination.24. So, we don’t know what we are, but we do know we are.
25. And again, we know we are – even though the scientific likelihood of each of our current existences is hardly more than zero…

26. But further, if I didn’t exist it would be as if there were nothing – there might as well be nothing.
27. And, if I never existed, there might as well never be anything.
28. And, what if you never existed?

29. And then, if you think about it, nothing really makes sense, anyway.
30. Once there is something, reductive materialism (the basic axiom of science) just doesn’t work…
31. Now, if there were nothing, that would make sense!

32. There’s something wrong here…
33. There’s something “magical” here.
34. Science seems to be missing a serious piece of the puzzle…
35. Again, there’s something magical here…

Narcissism isn't an explanation or proof...

Jay, is it that you disagree with 21-23 above?

 

[Jabba]

Jabba,

This is what you just said:

"If I'm walking along the street and I see a quarter face up, I can create two hypotheses: a) the quarter landed with a 50% chance of being face-up; or b) this quarter is gimicked by weight or it has two "heads" sides."

You then go on to say, "If the quarter has two heads or is influenced to land on heads, the chance of it showing heads is 100%. If it's a regular quarter, the chance is 50%. Since 100% is so much larger than 50%, I must conclude that this is a rigged quarter."...

LL,
- It would depend upon the prior probability of the quarter having two heads or being influenced to land on heads -- starting from scratch, that prior probability, here, would be roughly zero, and we would not conclude that the quarter had two heads or was influenced to land on heads.

 

[John Jones]

#1898:


Jay, is it that you disagree with 21-23 above?

Do you think you could stop regurgitating your entire litany of nonsense?
We've seen your regular fringe resets for 4 years now.

You could have just quoted lines 21-23.

 

[caveman1917]

What? Why?

He has no idea what the game is, what the possible outcomes are, what the likely outcomes are, or even if there is a winner. What information about this alien game played by another species does he have?

I asked you what information he has, you said he has none. That's exactly why he would be justified in stating "the game is likely rigged". Given no information the priors for "the game is rigged" and "the game is not rigged" are equal (no information = equal priors).

You previously attempted to give Jabba some information by imposing your own prejudices about games. You pretended this was a game between humans which differentiate between winning and losing. No such information exists.

That the game can be won is pretty much the only information there is, as you provided it with the "I won! I won!" response of the alien.

So what information can Jabba possibly used to conclude (based upon knowing nothing of the rules, observing one outcome and never even seeing the game played) that the game is likely rigged?

Denote the game as G. We know that there is at least one possible outcome, namely a win, denote it as W. Hence we know that the universe of possible outcomes is some superset of {W} and let's denote the universe as U. Denote with O the other possible outcomes, such that O = U \ {W} remembering that O may or may not be the empty set. Define G as "rigged" if G always produces W and "not rigged" if G at least sometimes does not produce W. Denote the hypothesis "G is rigged" as HR and "G is not rigged" as HF. We have no information, therefor P(HR) = P(HF). We also have P(W | HR) = 1 and P(W | HF) < 1. Then we calculate P(HR | W) > P(HF | W).

It's exactly because we have no information that we use equal priors and arrive at that conclusion. The same thing holds for the coin you find lying heads-up. If you have no other information you conclude that the coin is likely biased towards showing heads. If you observe a single outcome of a system and you have no other information whatsoever about it then you should assume that the system will keep producing that same outcome. In this sense there can be something said for Jabba's claim that the universe is biased towards producing him - assuming that he has no other information about the universe, which is false and requires ignoring basic science - but then by the same argument it can be said that the universe is biased towards producing that pile of manure lying on the farm down the street. So how useful such a conclusion is is quite another question.

I'm guessing that in your examples you are implicitly using information, such as things that I specified earlier about the alien game or, in the case of the coin, your previous experience with coins.

 

[Loss Leader]

LL,
- It would depend upon the prior probability of the quarter having two heads or being influenced to land on heads -- starting from scratch, that prior probability, here, would be roughly zero, and we would not conclude that the quarter had two heads or was influenced to land on heads.

This is marvelous news. Now, pretend you're the quarter. Do we have nearly as much information about you as the quarter? Do we know how many "sides" or possibilities there were to create your neurosystem? Can we run experiments over and over on fair quarters with expected outcomes? Do we know the probability of a random system over a designed one?

You took all of that for granted with the quarter. Now you seem to be taking it all for granted in order to speculate about immortality. But do you know how the system works through careful experimentation? Do you know when it's working or cheating? How do you know any of this?

Remember also that we have plenty of evidence that ]two-headed quarters exist. We can describe their properties and even flip them to compare them to regular quarters.

Do we have any evidence that your immortal "soul" even exists?

 

[caveman1917]

The misunderstanding here is in the term 'event' For a statistical 'event' you are right, but for a physical event (which in statistics would be termed a process) it is wrong: A process can produce outcomes ('events') that are either.

An event is an element of a sigma-algebra, that's the definition in probability theory and is the one I am using.

Assuming that we examine n shuffles together (you are not stating that clearly):

#1 is false.

vs #2: The probability of the shuffle being non-random falls progressively with increasing n over n=1.

Assuming we examine each shuffle as an individual event (in principle knowing nothing about other shuffles) The probability of S is always the same. We cannot determine whether the deck is rigged from examining any single shuffle.

This is incorrect, formalize your argument. Let G be the generator of sequences, the set of all such sequences be U and the sequence we receive be S \in U. Let HR be the hypothesis that G always produces S and HF the hypothesis that G does not always produce S. Let C be the relative posterior probability of HR vs HF, A be the relative prior probability of HR vs HF and B the relative conditional probability of S given HR vs S given HF and n the number of times we get outcome S. Then

C = A * B^n

Define the probability as "changing" if C / A != 1. Then

C / A != 1 <=> B^n != 1 <=> B != 1

Hence for all n >= 1 (also for the first one, this is the important bit, it doesn't magically start changing only at the second time you get it) the probability changes.

Either an event discriminates between two hypotheses, and it does so from the very first time you get the event, or it doesn't and it never does no matter how many times you get the event. This is fully determined by whether B = 1 or not.

 

[JayUtah]

Jay, is it that you disagree with 21-23 above?

Why don't you go back and see what I wrote at the time and address that. Now that you've demonstrated that no technical error has prevented you from viewing my posts, and that you've just been deliberately ignoring them all along, please repent of your rudeness and address the many points I've made in rebuttal to you since you made that monumental fringe reset. It's not as if I've been coy in my assessment of your beliefs and methods.

 

[godless dave]

Or just read the part you quoted that explains why 21-23 are irrelevant:

Narcissism isn't an explanation or proof.

 

[JayUtah]

Or just read the part you quoted that explains why 21-23 are irrelevant:

I would also have accepted "solipsism" as an answer. "It's remarkably special to be this way because I know I am this way and I can't know that about anyone else," is essentially the argument he's trying to warp his latest fringe reset into. Loss Leader is finally making some headway getting Jabba to notice the big Texas sharpshooting elephant in the room. Jabba desperately needs to show that he is a priori special and that the salience of his special outcome by scientific means enlivens his false dilemma.

 

[Jabba]

Why don't you go back and see what I wrote at the time and address that. Now that you've demonstrated that no technical error has prevented you from viewing my posts, and that you've just been deliberately ignoring them all along, please repent of your rudeness and address the many points I've made in rebuttal to you since you made that monumental fringe reset. It's not as if I've been coy in my assessment of your beliefs and methods.

Jay,
- I would really like to address your questions and comments -- you easily provide the most challenges to my argument -- but I can't keep up with them. Please give me one q/c at a time. And also, please answer my singular questions directly -- I just don't have time to look for, and sort out, your previous answers.
- If you can slow down, I'll try to keep up.