Misconceptions about Me, Baye's, Rigor, Exodus, Evolution

[Phil153]

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(Thus Pair The Board's comment that I base my probability of a miracle on its non occurence so far, is wrong. I also base it on the strong suspision that it can't occur. A subtle but important difference.)

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What's the strong suspicion based on? Observed non occurrence? [img]/images/graemlins/laugh.gif[/img] [img]/images/graemlins/laugh.gif[/img] [img]/images/graemlins/laugh.gif[/img]

Personally I take a different approach. If you run Baye's Theorem on the ratio of (claims of miracles) to (verified miracles), any claim of a miracle is instantly an incredible long shot to be true. This goes all the way from the guy performing magic tricks on the street to the flood myth in Genesis.

And there's another approach as well - anything that holds humans in a privileged position is a massive underdog to be true, as a huge number of privileged position claims have been shown to be false, and none shown to be true. In fact it's so unreliable, that the utterances of those who believe in privileged position have about the same usefulness as cow farts.

[David Sklansky]

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Ok, I got over my disgust at the first sentence. On to serious question(s) for David:

What do you assess is the probability of there existing some event that occurs exactly once throughout the duration of the universe? Or is it even possible to assess this quantity?

Is it sensible to talk in the language of physics about these events, if they exist?

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You can't mean what you are asking. Someone getting eight royals in a row might be favored to happen exactly once.

As for my disbelief in miracles, it does not stem from the fact that I think their probability is so low that it is favored that they will never happen. It is because I believe that there is a high probability that their probability is zero. The answers come out the same but their is a difference. Sort of like the difference between my saying a baseball team is 60% to win and a sprinter is 60% to win. In the second case I am actually saying that there is a 60% chance that the sprinter is (virtually) 100%.

[borisp]

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Ok, I got over my disgust at the first sentence. On to serious question(s) for David:

What do you assess is the probability of there existing some event that occurs exactly once throughout the duration of the universe? Or is it even possible to assess this quantity?

Is it sensible to talk in the language of physics about these events, if they exist?

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You can't mean what you are asking. Someone getting eight royals in a row might be favored to happen exactly once.

As for my disbelief in miracles, it does not stem from the fact that I think their probability is so low that it is favored that they will never happen. It is because I believe that there is a high probability that their probability is zero. The answers come out the same but their is a difference. Sort of like the difference between my saying a baseball team is 60% to win and a sprinter is 60% to win. In the second case I am actually saying that there is a 60% chance that the sprinter is (virtually) 100%.

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I understand the difference between those two notions, far better than you give me credit for, I believe. But let me try to repeat what you have said in a very different way.

You are saying that you have a planned a way to measure a property of a sprinter, and likewise of a baseball team. When you take this measurement the answer will take one of two values, say "win" and "lose." There is a physical process that happens in between, and it is called a "game," and each has its own game (= "event") description.

There is a key difference between these two events. Your knowledge of the sprinter that you have now is, in principle, all of the knowledge that is needed to completely determine the outcome of the sprinter's game. This is because the sprinter's state will not change in a relevant way between now and the time of measurement; i.e., the game is very nonrandom and has virtually no extreme occurrences.

But...your present knowledge of the baseball team is easily corruptible by completely random events that happen during the baseball game, and it is easily known that the game itself can take on very extreme configurations (no hitters, 10 run innings, etc.) Hence, you will admit that in principle you CANNOT determine the outcome now.

Or, to quote the greatest author ever on how to make 100k a year gambling, "baseball is the only sport in which a college team could conceivably beat a pro team."

Anyway, when you are announcing the probability of an event, namely the measurement taking a particular value, you are announcing the numeric value of an integral; you are "adding up" the probabilities of all the paths that lead to "win." This amounts to an integral of integrals, and that is where tricks of language can confuse even the most careful reader of 2+2.

The sprinter has two paths that lead up to the measurement, "going to win," and "not going to win," since his state will not change between now and the measurement. (There are a few "quantum" paths where he (or his opponent) pulls a hamstring or tests positive for steroids and he suddenly jumps from one path to the other.) Your assessment of his probability to win is your assessment that he is on one of these two paths. You perform two integrals, and you are done.

The baseball team has many paths leading up to the measurement, the totality of which is impossible to describe. Now there is randomness in your knowledge of the state, and you cannot escape it. So you integrate over a much larger state space, and you "average out" a lot of extreme events that cancel. For every walk off grand slam, there are so many no hitters, for every blown save, there are so many 9th inning ending double plays, etc. Your knowledge of these cancelling factors, largely a series of estimates, determines your overall success.

At the end, you announce the likelihood that the baseball team is on one of the infinitude of paths that happen to land on "win."

Now to the point:

You don't say that no paths lead to miracles.

You don't say that the integral over the space of all paths to all miracles produces zero.

You do say that any meaningful integral over those paths that do lead to a SPECIFIC miracle must produce zero.

Correct?

Then Bayes theorem allows two conclusions. The probability that there are miracles, given the physics that we know, is zero. And the probability that the physics we know will ever be a complete understanding of the universe, given a miracle, is also zero.

In other words, Bayes theorem has allowed the mutual exclusion of these two states, "miracle" and "modern physics." You choose the non miracle side, because in your view, modern physics is more useful to you than belief in miracles.

Realize that this is a choice, and mathematics was only useful in determining that it was a choice. Physics does not "prove" this choice, it is what shaped your gut feeling about how you made the choice.

Mathematics has only made it obvious that you are either willing to discuss miracles with an open mind, or you are not. You should admit to yourself that you have chosen the latter and move on.

Or, you can admit that there actually may exist miracles, and that the methods of probability are obviously useless for predicting these miracles, by definition. It is still reasonable to go about recognizing when they happen, or even asking others about their efforts to do the same. Try church, I guess, I dunno.

Personally, looking for miracles seems stupid and boring, and I much prefer trying to predict and asses things that the tools of mathematics allow me to predict and assess.

[mrick]

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What do you assess is the probability of there existing some event that occurs exactly once throughout the duration of the universe?

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Actually, this is supposed to be an event that happened once during the lifetime of our Earth. Events unique in the life of this planet would be considered quite routine for the cosmic observer, eg large comet hitting the planet. Kapow.

Notice that if we accept the biblical version of the Earth's age, the uniqueness of the event becomes less improbable.

[borisp]

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You can't mean what you are asking. Someone getting eight royals in a row might be favored to happen exactly once.

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By the way I meant exactly what I was asking. Your point with the royals translates to:

"What is the probability that intelligent life evolves on some planet, they go on to invent exactly the game of poker, and then one day someone gets some absurdly crazy sequence of hands, and furthermore they die off before it happens again?"

I'd call this a miracle. Hence, probability zero.

"Now, GIVEN that humans HAVE invented poker, what is the likelihood that some crazy sequence occurs exactly once?"

Well, here we already believe in a miracle, since we have actually witnessed humans invent poker, and we see it all around us. So now the answer is probably 1.

My point was ultimately that probability is useless with respect to the likelihood of miracles. What is the chance of all of New York City turning out exactly the same, given that the conditions in the year 10000 BC were exactly as they were, except for some "irrelevant" differences? Zero. But this doesn't change the fact that we do actually observe an actual New York City, and it is the way it is.

Who woulda thunk it?

[Max Raker]

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boris---

Wait, are you saying that patience/dedication + high-but-not-genius-IQ can achieve non-trivial results in math/science?

I honestly did not know this was possible. (No sarcasm.) My impression had always been that essentially all important work was done by a few transcendent geniuses. Confirm/deny?

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I remember something a math professor told us once. He said it is very hard to tell the difference between a real genius and just a really smart person who has spent alot of time on a particular subject. As an undergrad I thought all my professors where genius level but many of them where probably not that much smarter than the top 5% of students in the class. Doesn't make their achivements any less great though.

[Crane]

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Slightly tougher one. There are ten coins in a jar. One is heavily weighted towards heads. 90%. You pick a coin and flip three heads. The total chances that could happen is 1/10 x .729 plus 9/10 x .125. DUCY .0729 + .1125 = .1854. So the the chances we picked the bad coin is .729/.1854

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Poor math student here. I follow this except for the last part .729/.1854. This equals 3.93. Aren't the chances of plucking the bad coin 1/10 x.729=.0729. Shouldn't it be.0729/.1854=.393%?

Thanks

[RJT]

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2. Any eight year old can understand Baye's Theorem. I explain it in a few pages in Getting The Best Of It. Anyone who hasn't read that book has no right to have an opinion about anything.

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I love this statement. It's so David. Probably should be a sticky.

[uDevil]

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Looking back at my original response to this question, I should have written specifically "high IQ," not "genius IQ," as I wasn't really distinguishing.

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What is the threshold for "high IQ"? According to James Gleick, R. Feynman had an IQ ~125, above average but not exceptional. Despite that, he made the David Sklansky Top 10, clearly a nontrivial achievement.

[Praxising]

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BUT WAIT. Guess what. There really is at least one person who had this physical ability. They called him the Flipper. Now deceased. This changes everything. It shows that there is one example AND it shows that it is not an impossibility.....
Just like I'd totally change my thinking about religion if I ever heard of ANY sort of CLEARLY supernatural event.

I don't have time to get to Evolution and Exodus and Absence of Evidence right now but I will shortly.

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Hi there. Stumbled across this while waiting for my new copy of SoP to arrive. I don't know nuthin' 'bout no math.

I know a LOT about miracles. Here's the thing. Define please "CLEARLY supernatural" in terms of an event. I'm asking for parameters. But then, I'd like to know how anyone who had experienced such an event could "prove" it to anyone. Sort of like, you can't prove the Flipper could do what you claim.

The problem with the miracle discussion online is, well, anyone can say anything online. So, if I describe to you an event that fits your definition of "clearly supernatural" I doubt it will change your present position.

It isn't really that "supernatural" events do not occur - it is just that the understanding of what is, well, natural, keeps changing. Things thought impossible become just something we didn't understand before.

I used to teach evolutionary theory and genetics. I used to work in a museum. I get science. But, the miracles are real enough. Someday, we will understand how these things happen in that quantum physics or physical chemistry or some other discipline or more likely many of them will make this graspable.

Then when we see or hear miracles, we won't tie oursleves into knots "explaining them away" but we won't think of them as miracles anymore. Just like we look at the inside of a human body without cutting it open and think: cool.

Not having read the whole thread, this may make zero sense.

Off to read Sklanky on evolution, etc., while waiting to learn about Razz....

-prax-