Proof of Immortality III

[Jabba]

jt,
- Again, correct.
- They are, in fact, estimates -- that's how Bayes works. Each of us is free to project our own estimates, and to judge the plausibility of the other estimates.
- Unfortunately, they need to be normalized to the sum of .01, rather than 1.

They are not estimates. In statistics, an estimate is an inference about an unobservable quantity. Your likelihoods are not inferences. Statistical inferences are derived from data and statistical models. Your likelihoods are not implied by any statistical models; they are just numbers you've made up.



Fortunately or unfortunately, they (i.e., the prior weights) need to be normalized to 1. Your "estimate" of P(E|~H) is too low by a factor of 119: a factor of 100 due to failure to normalize and a factor of 19 due to an arithmetic error.

Until now, I had failed to perceive your smugness and your arrogance. Now that I have, adios.

jt,

- Obviously, I disagree. I give two likelihoods -- that of me given H, and that of me given ~H. I accepted your point about the likelihood of the latter, and now agree that my likelihood given ~H is .62.
- Here's my reasoning for the likelihood of my current existence given H.


11.1. Re P(E|H):According to science, I would never exist if
11.1.1. My parents had never met…
11.1.2. They had never had intercourse.
11.1.3. The necessary sperm cell (of the sextillion produced by my dad) had not met up with the necessary ovum (of the 500 carried by my mom).
11.1.4. The same three events (of above) had not occurred for both sets of my grandparents.
11.1.5. And all four sets of my great-grandparents.
11.1.6. Etc., etc., etc.
11.1.7. All the way back to the beginning of life on this planet.
11.1.8. And then, there’s the big bang.
11.1.9. And what if I had been (would have been?) the combination of a particular sperm cell of my dad and a particular ovum of Cleopatra?
11.1.10. How many human sperm cells and ova have existed since the beginning of (just) human life?
11.1.11. And, wouldn’t each potential combination of particular sperm cell and particular ovum represent a different potential person?
11.1.12. And what about all those potential persons of potential but unactualized persons?
11.1.13. However, my particular conscious existence probably doesn’t depend upon a particular sperm cell and particular ovum, anyway…
11.1.14. Rather, a certain organic state must naturally produce the emergent property of consciousness, and each new consciousness must produce its own, brand new, “self.”
11.1.15. IOW, there probably is no limited pool of potential beings – and consequently, the ‘number’ of potential beings is infinite…
11.1.16. Wow!
11.1.17. And then, there’s the anthropic principle.
11.1.18. And, what’s the likelihood that the 14 billion years of apparent universe existence would currently be within the years of my life.
11.1.19. And, what if time is infinite in both directions?

 

[The Sparrow]

This is a restatement, in part, of the essential question Jabba cannot answer: What is the functional definition of a soul? If we don't know what it's supposed to be doing, not only can't we test for it but we can't even say it's necessary to the system.

Never mind of what 'value' it is.
I suppose if one wanted to muse, when I ultimately die and decay, its possible some of the atoms which made me up might end up as part of another human's body at some point.
Ok, cool, and maybe that gives me some sort of.......I dunno.......recognition of my place in the universe, but I wouldn't call that immortality.

Immortality, to be of any value, would involve a seamless continuation of my self awareness, identity, memories etc. Without these, it would be of the same value as some of my carbon atoms becoming part of some other human.

 

[godless dave]

And what if I had been (would have been?) the combination of a particular sperm cell of my dad and a particular ovum of Cleopatra?

Your dad was not alive at the same time as Cleopatra. Your dad's existence depended on the existence of his parents, grandparents, and ancestors all the way back, including his ancestors who were alive at the same time as Cleopatra.

Related:

However, my particular conscious existence probably doesn’t depend upon a particular sperm cell and particular ovum, anyway…

According to science it does.

11.1.14. Rather, a certain organic state must naturally produce the emergent property of consciousness, and each new consciousness must produce its own, brand new, “self.”

A specific brain productes a consciousness, including the self. It's as brand new as the brain. It's produced by the brain.

11.1.15. IOW, there probably is no limited pool of potential beings – and consequently, the ‘number’ of potential beings is infinite…

At any given point in time the number of potential beings is finite. People can only mate with other people who are alive at the same time they are. You could not have been conceived at any point in history, you could only have been conceived when your parents were both alive and of reproductive age.

This is just a side issue. The real issue is that your list of bullet points does not support the numbers you came up with as estimates.

 

[caveman1917]

And yes, statistical modeling is one of many tools mathematics has to offer. But it can't prove anything according to most of the ways we think about proof. Properly used, it can establish the probability of some outcome, and the probability can, in some cases, approach what we would consider enough certainty to bank on that outcome with low risk. But no amount of statistically derived assurance overturns a contrary observation. If everything we can observe about consciousness doesn't start until birth and doesn't persist after death, no amount of statistical mumbo-jumbo can change those observations.

That'll be 5 dollars then.

I cannot use the mathematics to disprove the biopsy.

Of course you can. Keep taking tests n times, each test decreasing the relative probability that you have cancer by a factor of f, then the total decrease in the relative probability that you have cancer will be f^n. At some point - fairly quickly given the exponential growth - it's going to be more likely that those people doing the biopsy had a mass hallucination than that you have cancer.

Obviously so that he doesn't have to keep contending with the qualitative difference between probability and fact.

What qualitative difference? Define qualitative.

 

[JayUtah]

Here's my reasoning for the likelihood of my current existence given H.

And here's where that reasoning fails:

11.1. Re P(E|H):According to science, I would never exist if

That one little letter dooms your argument, for the reasons made abundantly clear. It commits the Texas sharpshooter fallacy. The rest of your bullet points depend on that, so you're done.

 

[JayUtah]

In deciding between two competing hypotheses one data point can be informative, indeed decisive. Consider a classic hypothetical problem. One of two coins has been chosen at random, but you don't know which. One coin is a fair coin; the other has been bent so that it has only a 1% chance of landing heads. [...]

As I have stated in previous posts, I disagree with every number in Jabba's argument along with the myriad untenable assumptions that led to those numbers [...] but, in a very broad sense, the form of his argument is valid. The machinery—Bayes' Theorem—is correct. But his inputs are nonsensical; thus, so are his conclusions.

Indeed, the example you post is well formed. What makes it well formed is the straightforward choice of prior and the explicit givens. You know the fair coin has an equal chance of coming up heads or tails and you're told the quantity of bias in the altered coin. And yes, it illustrates how we can use statistical methods to validate one model over another when presented with data -- even scant data.

When you say the form of the argument is valid, that's the sort of thing Jabba takes and runs with, far beyond what the concession justifies. This is is not unique to Jabba; it's a characteristic of many fringe arguments. The most common misuse of Bayes in fringe thinking is to create the illusion that some proposition plucked out of thin air can somehow be proven as fact via Bayesian inference. Most people will respond at large that Bayes cannot be used this way. Statements such as "The argument is valid in form," can be misinterpreted to imply Bayes can be so used.

I agree; in broad strokes the argument is valid in form. Bayes can be used to show validity in a model, and Jabba is putatively using it (albeit wrongly) in an attempt to determine which of two competing models best explains his existence.

Be that as it may, to bend your example above, I think Jabba's argument is more like being told there are two coins, but being explicitly told that you may not assume whether one or the other coin is or isn't fair. What do you do with one data point? Well, Jabba stacks the deck. He declares, with no evidence whatsoever, that one of the coins is gimmicked. He even goes so far as to assume a certain numerical bias for the presumptively gimmicked coin. Then he can pretend that his one and only data point lets him determine that one coin is definitely fair and the other is definitely gimmicked in the way he claims it was. This is more in line with how fringe arguments typically use statistical methods.

When we say that Jabba's argument is broadly correct in form, it lends unwarranted credibility to his assertion that all he needs is good numbers. This is true only in the sense that he needs numbers that aren't made up, and making up the numbers is a qualitative difference between a valid argument and one that applies a defensibly rational process for arriving at the two numerical models for soul versus no-soul. This is more along the lines of what his critics mean by saying you can't reason this way using Bayes -- you can't use Bayes to convert made-up numbers into facts.

 

[Mojo]

Ok, so Jabba is the coin. So what experiment was then performed on Jabba comparable to a coin flip to get our one observation?

Now that he's specified his existence as an event so unlikely it disproves something or other, we just need to wait and see if the event occurs. In the four plus years these threads have been running, it hasn't.

 

[Loss Leader]

Of course you can. Keep taking tests n times, each test decreasing the relative probability that you have cancer by a factor of f, then the total decrease in the relative probability that you have cancer will be f^n. At some point - fairly quickly given the exponential growth - it's going to be more likely that those people doing the biopsy had a mass hallucination than that you have cancer.

You contradict yourself within this paragraph. First you say that "of course" statistics can be used to prove a proposition mathematically. Then your example only shows an increasing probability. Even the most overwhelming of probabilities do not prove mathematically that some proposition is true. They only provide information about the likelihood it is true. That likelihood may be great enough to base human decisions on, but it isn't mathematical proof.

 

[caveman1917]

First you say that "of course" statistics can be used to prove a proposition mathematically.

A biopsy is not a proposition. Try again.

 

[Loss Leader]

A biopsy is not a proposition. Try again.

Any attempted statement of fact is a proposition. "You have cancer," is the proposition. The biopsy is the test of that proposition. Repeated biopsies may strengthen or weaken our confidence in that proposition. But they will never, through statistics alone, mathematically prove the proposition one way or another.

This is really, really basic stuff. I'm surprised to even be debating it.

 

[caveman1917]

Any attempted statement of fact is a proposition. "You have cancer," is the proposition. The biopsy is the test of that proposition.

Then what exactly does it mean to "disprove a biopsy"?

I cannot use the mathematics to disprove the biopsy.

 

[caveman1917]

I mean, I know how to prove a proposition. So I just went ahead and proved the proposition: "you can use Bayesian inference - apparently known as "the mathematics" - on a sequence of tests to arrive at a probability that the biopsy is wrong being higher than you having cancer". You know, as one possible interpretation of the notion of "disproving a biopsy" in context of what had gone before. Here's the full quote for reference:

But going back to my test above, if it comes up negative then the small false-negative rate combines with the small prior cancer rate to produce a very small posterior probability that I have cancer. But that's still only a probability. It may be one that I can reliably use to plan the rest of my life, but it's qualitatively different from a biopsy that shows cancer cells under the microscope. The observable fact of having cancer is not the least concerned with the extremely low probability suggested by mathematics. I cannot use the mathematics to disprove the biopsy.

But apparently I'm missing some really really basic stuff, so what exactly does it mean to "disprove a biopsy" if not that which I argued?

 

[jt512]

Fair enough, I'm not even sure exactly what Jabba is calculating there.

Jabba's hypothesis "~H" is a composite hypothesis comprising nine simple hypotheses, let's call them (~H)_i, i=1...9, which he enumerated in a previous post. P(E|~H) should then be calculated as a weighted average of the P(E|(~H)_i)'s, that is, the probability of the evidence under each simple hypothesis, where the weights are the conditional prior probabilities of the (~H)_i's given ~H. These prior weights need to sum to 1. But Jabba's summed to .01. Thus his P(E|~H) was erroneously too small by a factor of 100 (plus a bit due to an arithmetic error).

 

[jt512]

Be that as it may, to bend your example above, I think Jabba's argument is more like being told there are two coins, but being explicitly told that you may not assume whether one or the other coin is or isn't fair. What do you do with one data point? Well, Jabba stacks the deck. He declares, with no evidence whatsoever, that one of the coins is gimmicked. He even goes so far as to assume a certain numerical bias for the presumptively gimmicked coin. Then he can pretend that his one and only data point lets him determine that one coin is definitely fair and the other is definitely gimmicked in the way he claims it was. This is more in line with how fringe arguments typically use statistical methods.

It seems to me that Jabba's argument is that the probability that "he" would be created by a random process, where "he" is some exactly identifiable entity (maybe down to the molecular level) is infinitesimal; whereas, if "he" always existed, in some sense, the probability would be 1 (well, .62, anyway). Therefore, the probabilities overwhelmingly favor the latter hypothesis.

The fallacy is that we are living in a Universe that produces things. Even if we assume that these things are produced randomly, and the probability that any specific one of them, defined on a molecule by molecule basis is infinitesimal, no matter what happened to have gotten produced, it would be what we would look at and ask "What are the odds of that?"

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.

To bring this back to Jabba, Jabba could point to anything in the Universe and ask, What is the probability of that exact thing if it were produced randomly? He happens to be pointing to himself, but he could just as well point to you, me, Mt. Sinai, or my grandfather's Edsel, and ask the same question. But if that thing wasn't there to be pointed to and asked about, something (or someone) else would be. And so the probability that something (or someone) would be there to point to is 1, whether the thing was produced randomly or purposefully, and so the observation that the thing exists does nothing to discriminate between the two hypotheses.

 

[Loss Leader]

A simple analogy is that you thoroughly shuffle a deck of 52 playing cards, examine the sequence that was produce, 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.

And the playing card analogy gives Jabba's ideas far too much credit to begin with. We know how many playing cards there are and exactly what they are. We only have the first clues as to what the universe is made of or how it works. Playing cards can also be shuffled and dealt again and again - each one a separate test. The universe is a single test. It can't be run again to see how (or even whether) things would be different.

But from the beginning, Jabba has liked the playing cards. He has written about how one might suspect cheating if one walked into a casino and was dealt a royal flush on the first hand. This ignores that fact that the royal flush was designated as having meaning before the cards were dealt. He believes his existence has the same meaning. Instead, he's holding a 2, 4, 5, 7 and 9 of varying suits and yelling, "I won! I won!"

 

[JayUtah]

he could just as well point to you, me, Mt. Sinai...

Mt. Ranier is the preferred geological formation in this thread. But yes, I agree entirely with your analysis. Jabba has an answer for the Immortal Soul vs. Mt. Ranier conundrum. It painfully begs the question.

 

[MRC_Hans]

I'm not comparing it to a single toss. Suppose you have 10 datapoints in the space of binary sequences of length 1 (ie H or T in this case), you call this 10 datapoints yet it is the same as 1 datapoint in the space of binary sequences of length 10.

Suppose you have a special coin that can only be tossed in batches of 10. Your datapoints are hence binary sequences of length 10 and suppose you have 1 datapoint. You make an inference on the distribution of H and T in those sequences of length 10. Suppose someone then asks "but what if we could toss it only a single time, what would we expect?" Then you can calculate that and the answer will be the same as if you had thought of it in terms of 10 datapoints of single tosses from the start.

Hence my claim that there's no inherent difference between a single datapoint and multiple datapoints.

I disagree. You are just describing different ways of collecting 10 datapoints.

Hans

 

[JoeMorgue]

Oh for Pete's sake can we stop nitpicking the exact probability metaphors being used?

You can't prove immortality with probability. Period end of discussion.

 

[Jabba]

It seems to me that Jabba's argument is that the probability that "he" would be created by a random process, where "he" is some exactly identifiable entity (maybe down to the molecular level) is infinitesimal; whereas, if "he" always existed, in some sense, the probability would be 1 (well, .62, anyway). Therefore, the probabilities overwhelmingly favor the latter hypothesis.

The fallacy is that we are living in a Universe that produces things. Even if we assume that these things are produced randomly, and the probability that any specific one of them, defined on a molecule by molecule basis is infinitesimal, no matter what happened to have gotten produced, it would be what we would look at and ask "What are the odds of that?"

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.

To bring this back to Jabba, Jabba could point to anything in the Universe and ask, What is the probability of that exact thing if it were produced randomly? He happens to be pointing to himself, but he could just as well point to you, me, Mt. Sinai, or my grandfather's Edsel, and ask the same question. But if that thing wasn't there to be pointed to and asked about, something (or someone) else would be. And so the probability that something (or someone) would be there to point to is 1, whether the thing was produced randomly or purposefully, and so the observation that the thing exists does nothing to discriminate between the two hypotheses.

jt,
- This seems to be another way of expressing the Texas Sharpshooter Fallacy. Do you agree?

 

[caveman1917]

I disagree. You are just describing different ways of collecting 10 datapoints.

What if you get a single integer between 0 and 1023? Is that a single datapoint or 10 datapoints? There's the obvious identification of integers in [0,1023] with binary sequences of length 10.