Belz...
Fiend God
No, it's not uniform. You could not be born in 1820 because your parents did not exist. And certainly not 6 million years ago or earlier.
Proof of Immortality, VII
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No, it's not uniform. You could not be born in 1820 because your parents did not exist. And certainly not 6 million years ago or earlier.
Evidence?
jond
Illuminator
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Given OOFLam, how could humans exist before the earth was formed? Given OOFLam, how could Jabba exist at any time other than the timeframe in which he does exist?
Says the person that can't figure out if 1/10 is more than 1/100.
RoboTimbo
Hostile Nanobacon
It's also irrelevant to whatever it is your hypothesis is "now".
How can human population not be part of an equation that involves how many lives they have and your current existence?
Seriously, do you give a moment's thought to anything you type?
jt512
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I have applied your argument to valid premises and derived a contradiction, that constitutes a refutation of the validity of your argument. No wonder you keep giving invalid arguments if you don't even understand how refutations of them work.
No. Your premises are not valid. You state that the probabiity that you observe your existence if the wire were live is 1 and likewise for the probability that you observe yourself in a Universe in which no life exists! You then claim that even though the probabilities are 1 under both a hypothesis and its complemet, that the observation can be used to distinguish between them. Thus, not only are your premises false, they don't support the conclusion that you say then do. You only contradict your self. Your supposed refutation of my argument actually refutes itself.
Once again, my argument is simply that
1. if you have two competing hypotheses, H1 and H2, and if H1 is true then you will observe E, and if H2 is true then you will observe E; then observing E cannot possibly help determine which of H1 and H2 are true; and
2. Premise (1) is precisely the case for Jabba's E, H, and ~H.
That's what he's going to do anyways. He will convenitenly take side with your absurd "refuation." But congratulations on now being part of the problem instead of the solution.
Siegfried: How do I know you're not Control?
Maxwell Smart: If I were Control, you'd already be dead.
Siegfried: If you were Control, you'd already be dead.
Maxwell Smart: Neither of us is dead, so I am obviously not from Control.
Shtarker: That actually makes sense.
Maxwell Smart: If I were Control, you'd already be dead.
Siegfried: If you were Control, you'd already be dead.
Maxwell Smart: Neither of us is dead, so I am obviously not from Control.
Shtarker: That actually makes sense.
jt512
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I should add that Premise (1) in my previous post should be uncontroversial: all it says is that if P(E|H1) =1 and P(E|H2) = 1 then the likelihood ratio P(E|H1)/P(E|H2) = 1, and therefore, by Bayes' Theorem, P(H1|E) = P(H1) and P(H2|E) = P(H2). That is, E does not alter the prior probabilities of either hypothesis.
The only room there is for argument is whether Premise 1 applies to Jabba's E, H, and ~H. I think it does, of course, but I wouldn't call it obvious.
The only room there is for argument is whether Premise 1 applies to Jabba's E, H, and ~H. I think it does, of course, but I wouldn't call it obvious.
JayUtah
Penultimate Amazing
No it wouldn't. Probability density is one of the most basic, elementary concepts of probability theory. If you are a "certified statistician," you should be able to immediately give me an accurate tweet-length definition of it without even thinking about it. If that concept is difficult for you, then you have absolutely no business trying to discuss statistical probability. It is the basis of all useful statistics.
Probability density is the class of mathematical constructs expressing in functional terms that not all possible outcomes in a given system are necessarily equally probable.
The above is a bit tilted toward my purpose here, which is to emphasize non-uniform distributions. It's not a textbook definition. Probability is most generally a function of possible outcomes (and other parameters), not a constant across all outcomes. In our simple examples we typically choose devices that have a discrete uniform probability density, where the density function is 1/N. That's to simplify the subsequent concepts. But most practical probability distributions are not uniform, and many are continuous, not discrete. You may have heard of some of them: the normal distribution (i.e., the bell-shaped curve), the Guassian distribution, the Poisson distribution. These are defined by continuous functions of several parameters including possible outcomes. They produce various densities (i.e., y-values to the outcomes' x-values) across all possible outcomes, all of whose integrals (or sums) sum to 1. Then there are distributions that don't have elegant parametric mathematical representations such as those defined by the empirical conditions in each case.
The ability to reckon a proper probability distribution for the problem being modeled is an absolutely crucial first step.
In fact, the implied probability density in the Texas sharpshooter illustration is not uniform. In normal sharpshooting, even a novice shooter is expected to cluster his shots in the vicinity of a predesignated bullseye, not uniformly over the whole barn wall. Over many shots, in a frequentist sort of way, a two-dimensional density plot should appear on the barn wall in the general vicinity of the target. Precision versus accuracy, yes I know. The Texas sharpshooter, in contrast, wants his grouping to be defined by one shot, and he wants that grouping, or distribution, to center on a "predesignated" target. It's not so much part of the illustration that he draws the circle around the bullet hole as it is that he draws a very tiny circle that just circumscribes the hole such that the presumed normally distributed shot grouping doesn't seem like it would account for such results.
That's part of the problem, which is odd coming from someone who purports to teach others about statistical reasoning. But no, you don't know the right concepts. And you show absolutely no interest in learning them, or at least understanding how they affect your claims. Shoving your head in the sand does not make those facts go away, Jabba. You don't get to disregard them just because you can't figure out how they work in your model, or because they give you a different answer than you'd hoped for.
That's not what I asked you for. I asked you for a simple discussion of what a probability density is, in your own words, such as the one I gave above. I didn't ask you to just invoke the words while rambling further about your argument.
Gibberish.
It's the essence of the tautology you're being accused of to say that now must fall within an interval defined around now. You're presently alive and having a discussion. Any time you say "now" in this discussion, it must necessarily occur during the period of your lifetime that contains the discussion. That's what "now" means. The period 1942-2042 and the concept of now are both defined from the same parameter -- Jabba's lifetime. The probability that they will coincide is therefore 1 by virtue of that definition.
The probability that some random timepoint will fall within one of 140,000,000 centuries is governed by 1/140,000,000. But "now" is not some random timepoint in the sense of being uniformly distributed. When you or I say "now" it does not have an equal probability of referring to any timepoint from the Big Bang until the heat-death of the universe. As usual you're simply trying to ambiguously define your way to victory.
You may disagree. But you've been asked several times to define "now" as it applies to your argument. Specifically, to define "now" in such a way as to satisfy the mathematical rigor your argument would need in order to prove what you expect it to prove. You assiduously refuse to do so, which leads most of us to conclude you are planning to maintain it -- as you almost always do -- as an ill-defined concept in your argument so that you can equivocate over many possible meanings of it in order to evade refutation.
It's pretty much required by your givens, if you want the ensuing calculation to have any relevance to your specific proof for immortality. Immortality has no relevance outside the domain of human existence. The question is not whether there exists some abstract concept of "immortality." The question is whether humans are immortal, and therefore the question is only defined for when there have been humans, not for all of time. The probability of human existence, immortal or otherwise, is not uniformly distributed across all centuries. You've made it abundantly clear via your solipsism that the overriding question is whether Jabba is immortal, which further narrows the field. (The unstated generalization is that if Jabba is immortal then all humans must be immortal.) Most importantly, you've suggested that the period when someone exists, among all existing time periods, is probabilistically related to whether he is immortal. Under those conditions it's simply not possible to construct a valid statistical inference regarding human mortality without respecting the factors that apply to human existence in general, irrespective of mortality.
Probability distributions change according to how they are sampled, how the outcomes are made to arise in the underlying system. Consider a container filled with 10 wooden balls and 10 steel balls, all of identical size and shape and all mixed up. What's the likelihood of drawing a wooden ball if you reach in with a pair of kitchen tongs to grab a ball at random? What's the likelihood of drawing a wooden ball if you extract the ball using a magnetic probe? Different distributions arise based on different biases in the selection method as the underlying system implements them. (Science again!)
So the way you chose your century is a parameter in the density function that governs the likelihood of each century being a winner, which in turn amplifies or attenuates the likelihood in the inference. It matters. If you choose your century according to the criterion that it contain a life that might possibly be immortal, the probability distribution skews heavily toward the last 200,000 years. You're more likely to get a century in that late stage than in the early Hot-Mess eons just after the Big Bang. More recent centuries are more likely to satisfy the criterion that potentially immortal life occur in them, just as steel balls are more likely to satisfy the criterion that they be attracted to a magnet. If you choose your century according to the criterion that it be your lifetime -- which is what you said you did -- then the distribution curve is flat-zero until it gets to 1942-2042. Only one century satisfies the parameter, and in this case it will be guaranteed to come up every time we sample the space given that parameter.
But while that's an interesting topic for debate, it's not really the most fatal error you're making here. The most fatal error is the one I discussed in the previous section -- that both of your supposedly independent variables are, in fact, both conditioned on a third variable. They don't vary independently and your proof assumes they can. The coincidence of two variables that cannot vary independently is not significant.
What's really hilarious is that this is all supposed to be a proof for immortality, and nothing about your proof is even remotely concerned with it. That is, you say the likelihood of your existence in a purely materialistic way is governed by the probability of one century arising from among 140 million of them. But you don't say how having an immortal soul would change that in any way.
jt512 told you that your model actually produced probabilities, not likelihoods. That's because your formulation at the highest level covers all possible conditions disjointly. Let's leave aside for now the many ways your model is wrong. The union of H and ~H is the universe, and H and ~H are distinct. So P(H|X) and P(~H|X) for some event X are, in fact, probabilities. In your argument they must be, because you don't compute P(~H|X). You reckon it must be 1-P(H|X), a property that holds only for probabilities.
A different use of Bayes theorem -- and the one more suited to your proof -- compares the posteriors P(A|X) and P(B|X), where the union of A and B is not the universe (i.e., there are hypotheses we don't test), and A and B may not necessarily be independent events, or hypotheses. That's where likelihood gets interesting and useful. When we consider A and B as events, the "event" would be the "observation" that the hypothesis is true. And in the world of likelihoods those are not mutually exclusive, black-and-white events.
We apply event X Bayesianly to both A and B. It doesn't matter that the posterior probabilities don't sum to 1, because we're looking at likelihoods in a partially defined system. Trust me, there's a hypothesis C in the wings. If we observe P(A|X) = 0.20 and P(B|X) = 0.25, we can note simultaneously that while both are small numbers, the normalized difference between them (i.e., the ratio of one to the other) may be quite significant and tell us a great deal of information about A and B. This would be especially true if C were some third hypothesis and completely independent from A and B. If P(C|X) is 0.005, then clearly either A or B is a vastly superior hypothesis even if their absolute likelihoods are small on the [0-1] scale for probability. If A and B are partially dependent, we can further hypothesize that the mechanism common to A and B is clearly more predictive than C's, but B's refinement may be additionally preferred. The takeaway is that the absolute numbers of likelihoods in a given system is not as important as their relative likelihoods.
So to bring this back home, you're telling us that P(materialism|your existence) is very small because of your present existence versus 140 million centuries. You haven't told us why P(immortality|your existence) will be a different number, if your present existence is still up against 140 million centuries. If 1/140,000,000 is the governing term in both cases -- as it appears to be -- I don't see where asserting immortality changes the likelihood. If you can't propose and test some mechanism of immortality that exerts a stronger influence than 1/140,000,000 then at best all you've proven is that your current existence is unrelated to whether materialism or immortality is true -- the point jt512 has just made in far fewer words. It seems like your endeavors here have gone fully over to simply trashing your critics' hypothesis with no regard for whether it helps your proof along. You're just obsessed now with proving skepticism wrong on some topic; it doesn't matter what.
If it doesn't involve modeling human population factors then it has dubious if any relevance to your proof for human immortality. It would degenerate into convolving of two meaningless random variables with no context or relevance. Gee, here's a random century out of 140,000,000. Here's a random point in time out of that same 14 billion years. What is the probability they coincide? Oooh, very small. Cool story, bro. That doesn't prove anything. All you've done is demonstrate the algebra of convolution. You can't give the arithmetic the significance you want it to have for your proof without incurring the baggage that comes with that significance. You're cherry-picking only the parts of the model that give you the "right" answer.
But okay, let's stipulate, arguendo for this section, that we disregard the probability density of human population. It doesn't fix your argument because the most egregious failure in your latest proof is still that the two variables you convolve are not independent.
You tie the choice of century to your lifetime. That's not a uniform random variable. The parameter "must be Jabba's lifetime" results in a degenerate likelihood with a probability of 1 for the century 1942-2042 and zero for all the other centuries. Similarly "now" is not a uniformly distributed time point among all possible time points. You tie the operative timepoint to times when you can use the word "now" -- you tie it to your lifetime.
Regardless of human population factors, that is still not a "gee-whiz" coincidence. If Jabba's lifetime is the third variable that both of your "independent" variables are conditioned on, then they cannot vary independently. They must be coincident under that parameter. You're trying very hard to make two obviously dependent events seem independent. And as with all your other arguments, it comes down to silly word games, not actual math. You don't know math. You only know sophomoric word-play style debate tricks.
That wasn't really the issue. Your negligence toward probability density affects your choice of century if the selection criterion requires human life, which your proof seems to suggest. If it does, you don't get to ignore the baggage that comes along with that asserted significance. Human population factors don't affect the other event as much. That's a going concern, but a worse concern is that you up and admitted you chose the century because it represented your lifetime, which is ongoing because you're not yet dead. "Coincidentally" that's also the time when "now" has relevant meaning. The variables from whose convolution you want to derive your itsy-bitsy probability for materialism are not as independent as you claim. They are defined together, in fact, in terms of a third variable: Jabba's lifetime.
The Texas sharpshooter fallacy illustrates an underlying conditioning error that can just as easily be illustrated by stacking a card deck. The dealer says, "I'm going to deal the eight of spades from the top of the deck." He shuffles and presents the deck to another to cut. Then lo and behold, he deals the eight of spades.
We state as a premise that the dealer has cheated. Using any of various sleight-of-hand techniques, he has arranged for the eight of spades to be at the top of the deck after the shuffle and cut. That he chose the eight of spades out of all the possible ranks and suits to be his target is immaterial. He could have chosen the king of hearts, the three of diamonds, or whatever. That much is purely arbitrary, and the abstract probability (p=1/52) of choosing any given card is computable but irrelevant.
His announcement of what card he would produce is meant to seem like a uniform random variable. "I'll draw, oh, I guess, the eight of spades." But that announcement is conditioned on his prior decision to draw that specific card, not because that card sprang to mind arbitrarily as he was working the crowd. This is admittedly a contrived plot point. I separate mens rea and dictus rea to underscore the conditioning, not to be pedantic.
The shuffle is meant to seem like it creates another uniform random variable. But it's a ruse, because the criterion by which the top card is determined is unrelated to the shuffle. The dealer has sequestered the eight of spades via sleight-of-hand, to plant it surreptitiously as the top card after all the irrelevant display. The decision of which card to sequester was not random either. It derived inexorably from -- again -- the prior decision to use the eight of spades as the show card, not from the disposition of any of the other cards. p=1/52 does not apply once a decision is made.
The trick appears to convolve the 1/52 probability of any card being the one announced with the 1/52 probability of a designated card being dealt from the top, resulting in a presumed likelihood of 1/52 that the trick will succeed. (I.e., the likelihood that a designated card will be on top, given a designation.) But neither of those variables was random or independent. At the outset the dealer thinks, I'm going to use the eight of spades as my target today. Based on that decision, he sequesters the eight of spades (one event -- the identity of the top card -- conditioned strictly on that prior thought) and announces "I'm going to deal the eight of spades from the top" (another variable -- the prescient identity of the target -- conditioned just as strictly on that same prior thought). You can certainly quibble about the contrived way I've described the three-way dependence, but it's only important to see a clear dependence that you know shouldn't be there. At this point in the trick neither the probability of a specific card being on top nor the probability of a specific card being the target is really up for grabs, probabilistically speaking. The target is the given, but yeah -- the top card is foisted as the given. Just as in the selection of the century, the card trick has collapsed to a degenerate distribution that guarantees success.
Both this contrived example and the Texas sharpshooter example illustrate how one can misstate the true dependence of variables and deceptively purport that a system is governed instead by an implied or assumed probability distribution that is not factually the case.
caveman1917
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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.
Prove it. Take the example in my post with the Venn diagrams above, and show that S|H is a subset of U.
ETA:
I've done the same with most of yours.
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caveman1917
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10 points for anyone presenting proof that, given a sigma-algebra F in a probability space, there does not generally exist an event A|B \in F for A, B \in F. This theorem was proven in the 1970's showing that, indeed, conditional probabilities aren't probabilities. One requires extensions to standard probability spaces (specifically embedding F in a larger algebra and defining an extended P) in order to make this work.
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Belz...
Fiend God
Jabba
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- The likelihood of now being between 1942 and 2042 -- given only that now has to be between the big bang and 2042 Gregorian time is approximately 1/140,000,000. That likelihood does apply to the posterior probability of OOFLam -- given my current existence.
- And, if no other information is attached/considered in P(H|E), the posterior probability of OOFLam is extremely small. Unfortunately, I now think that by including the given of my current existence, I introduce more info...
- It's like betting on a football team based only on the won/lost records of the two teams, when you know that the star quarterback of the team your betting on is injured, and won't be playing...
- So, for now at least, it seems like I do need to add whatever scientific evidence I have that bares on the likelihood of my own current existence. Knowing that the world population of humans this century has included a lot more humans than any other century does increase the likelihood of my current existence -- even given OOFLam.
- Fortunately (for me) there is at least 2 more ingredients that need to be added to the likelihood: 1) time probably isn't limited to 14 billion years (it could be infinite) and 2) if I don't have to ever exist, the amount of possible time is meaningless anyway -- what is the likelihood of existing now if time is limited to 14 billion years, but I don't have to ever exist?
- And, if no other information is attached/considered in P(H|E), the posterior probability of OOFLam is extremely small. Unfortunately, I now think that by including the given of my current existence, I introduce more info...
- It's like betting on a football team based only on the won/lost records of the two teams, when you know that the star quarterback of the team your betting on is injured, and won't be playing...
- So, for now at least, it seems like I do need to add whatever scientific evidence I have that bares on the likelihood of my own current existence. Knowing that the world population of humans this century has included a lot more humans than any other century does increase the likelihood of my current existence -- even given OOFLam.
- Fortunately (for me) there is at least 2 more ingredients that need to be added to the likelihood: 1) time probably isn't limited to 14 billion years (it could be infinite) and 2) if I don't have to ever exist, the amount of possible time is meaningless anyway -- what is the likelihood of existing now if time is limited to 14 billion years, but I don't have to ever exist?
Belz...
Fiend God
Was it possible for you to be born before the Earth existed? Before humanity existed? Before your parents were born? You did have parents, correct?
Jabba
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Dave,
- For now, at least, I think you're right.
Dave Rogers
Bandaged ice that stampedes inexpensively through
Bad analogy. It's more like betting on the probability that a certain team went 13 and 3 last season after looking at the end of season won/lost records that show that they went 13 and 3.
Dave
JayUtah
Penultimate Amazing
Neither now nor your century is a random variable in your argument, so no. Now cannot be any timepoint between the Big Bang and 2042. That's not what now means. If you disagree, define "now" as you're using it in your argument.
Not via any mechanism you've established, nor any mechanism that applies to materialism. Your argument is "Here is one number divided by another, therefore materialism is false." The only way your argument makes those numbers relevant to your existence establishes a tautology.
Science isn't concerned with the likelihood of any one organism's likelihood of existence. You're playing a statistical shell game and trying to call it science.
And we're back to you trying to backfill a pseudo-rational explanation for infinity being your Big Denominator. An infinite number of "potential nows" is no more a thing that your infinite number of "potential selves." Unless you can explain how it was possible for you to exist under materialism before the Big Bang.
Gibberish. The problem with your argument is that you define both its supposedly independent variables in terms of a third, making it a tautology.
Belz...
Fiend God
And he leaves it at that! Marvelous.
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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