A Math Magic God Problem

[David Sklansky]

I want to pin down Pair The Board and others as to what exactly their contention is regarding using probability to measure the likelihood that an event was caused by God or some other supernatural power.

Consider this scenario.

A man bursts upon the scene proclaiming that he was sent by God to convert people to his religion. As evidence, he does something astonishing and seemingly unexplainable. It doesn't matter what. Perhaps he makes the sun appear purple or he puts random books into his briefcase and then takes them out five seconds later and they are translated into Chinese. For months, no one can think of any way he could do this demonstrtion via trickery, and sceptics reluctantly come to the conclusion that he is probably telling the truth.

Then one day a famous magician duplicates the "trick". And he explains how he did it. Sceptics breathe a sigh of relief. But the guy doesn't change his claims. He simply admits that this brilliant magician figured out a non supernatural way to do the same thing. But it isn't how he does it. He does it with God's powers.

My question is whether it makes sense at this point to try to rigorously come up with a number that captures the probability that the guy is a fraud. Commonsensically almost everyone would be virtually certain he was, once a magician duplicated what he did. But is there a RIGOROUS mathematical or statistical argument that would agree with common sense and perhaps even help assign a precise probaility to him being a fraud. My guess is yes. How bout some mathmeticians and statisticians weighing in.

[Shine]

call a feat X "irrational" if it was done using supernatural powers.
call a feat X "rational" otherwise

Irrational feats have probabilities roughly similar to the probability of the existance of supernatural powers, Q. Rational feats have roughly high probabilities.

So we now see this SPECIFIC feat X (a SPECIFIC event.) What's the probability that it is irrational?
Bayes: P(X irrational | X) = P(X | X irrational)P(X irrational)/P(X)

P(X) = 1 (we just saw it.) The probability of X given that X is irrational is roughly Q.

So P(X irrational | X) = Q * P(X irrational)

Now that X is shown to be possible to be rational, P(X irrational) decreases substantially*, and thus P(X irrational | X) = the probability of X being accomplished by supernatural powers also decreases.

(*More on this complicated first sentence "Now that... substantially" later.)

[Shine]

To complete my discussion, let me now go over my bolded claim in the previous reply.

"Given X can be performed rationally, P(X irrational) decreases."

Well, again, assign Q the probability that supernatural powers exist. Say X can only be performed irrationally with probability 1-Z.

IF X CAN BE PERFORMED RATIONALLY OR IRRATIONALLY (prob. Z):
Then 1-Q of the time, X can ONLY performed rationally.
Q of the time, X was performed rationally (say probability R) or it was performed irrationally.

IF X CAN ONLY BE PERFORMED IRRATIONALLY (probability 1-Z):
Then X is always irrational.

So given that X can be performed rationally, then we have restricted our sample space. The probability of X being irrational, is (1-Z) + ZQ(1-R). This is also "essentially" Q, since P(X irra) and Q are obviously directly correlated.

But by being given that Z = 1, it clearly drops. If you believe that Q is very low, like most atheists, then the majority of the argument that the person doing X had over you, was that Z was believed to be very low, and thus "essentially" Q = (1-Z)/(1-Z+ZR) was very high. This argument falls over fast once it is shown Z = 1.

[Piers]

No. Probabilistic estimates can only exist within a model. Whether such a model applies to reality is purely subjective. With something as obscure as religious belief you are not going to get a generally acceptable model with more refinement than the obvious trivial one.

Some probabilistic reasoning might appear to be applicable to a god existence. But really they are being applied to an as yet undefined probability space. ‘However you set it up this will be true’ sort of arguments. But if it’s not practical to use a non-trivial model encompassing a god’s existence, such reasoning is just hot air.

Besides tackling a god’s existence directly is going too far in one step. First look for evidence and understanding of an environmental framework that could support a god. It’s a big step from imposable things happening to a god exits and its important not to read too much into your experimental evidence.

[ QUOTE ]
A man bursts upon the scene proclaiming that he was sent by God to convert people to his religion . As evidence, he does something astonishing and seemingly unexplainable.

[/ QUOTE ]

The fact that the man clams the astonishing thing is due to god is of no significance. Many if not most people seeing such an imposable event are likely to attribute to god, just because it’s so astonishing. Its 'conceivable' that he has been deluded into believing the truth, but that would just be a coincidence.

[Phil153]

I think David is coming from this angle: It's obvious that duplication of magic lowers the probability of that event involving real magic to almost zero. It's so obvious that there should be some way to model it mathematically.

Here's my take. The argument is a historical one. All of human history is full of extraordinary supernatural claims for ordinary events, many of which stood for years or centuries. The vast majority were later proven to be frauds, delusion, or simple tricks, and there is no compelling evidence for the ones that were indeterminate.

It's no different to the argument that the sun will come up tomorrow. Imagine you lived 2000 years ago with no knowledge of what the Sun was. Now imagine you're 40 years old, and someone offers you a prop bet for $10 at 1 to 100,000 odds that the sun won't come up tomorrow. You'd be mad not to take it. The more trials we have of something we don't understand, but which always point in one direction and never in another (despite excitement to the contrary), the more obvious it becomes that that there is some underlying process at work which is causing that direction. On the other hand, if we'd arrived on this Earth today, with no knowledge of the laws of physics or human psychology, the numbers would be vastly different. Maybe around 50/50.

And when there are strong psychological reasons (think fraudster or NotReady) to believe in the other direction which is constantly being postulated and shot down , it become even more of a slam dunk.

[Shine]

[ QUOTE ]
No. Probabilistic estimates can only exist within a model. Whether such a model applies to reality is purely subjective. With something as obscure as religious belief you are not going to get a generally acceptable model with more refinement than the obvious trivial one.

Some probabilistic reasoning might appear to be applicable to a god existence. But really they are being applied to an as yet undefined probability space. ‘However you set it up this will be true’ sort of arguments. But if it’s not practical to use a non-trivial model encompassing a god’s existence, such reasoning is just hot air.

[/ QUOTE ]

The italicized parts of what you said, I agree with, the bolded parts, I don't.

I think the rest of your response dodges the question. Here, Sklansky asks for an argument that reflects the common sense opinion that, given the events in the story, one is much more likely to believe that the "feat" was a fraud.

Here, my argument is not "hot air." I've shown a direct relationship, for example in the latest post, between the existence of supernatural powers and whether it is possible to perform the feat that we saw, without supernatural power. This confirms conclusively what we already knew from common sense.

[PairTheBoard]

[ QUOTE ]
No. Probabilistic estimates can only exist within a model. Whether such a model applies to reality is purely subjective. With something as obscure as religious belief you are not going to get a generally acceptable model with more refinement than the obvious trivial one.

Some probabilistic reasoning might appear to be applicable to a god existence. But really they are being applied to an as yet undefined probability space. ‘However you set it up this will be true’ sort of arguments. But if it’s not practical to use a non-trivial model encompassing a god’s existence, such reasoning is just hot air.

Besides tackling a god’s existence directly is going too far in one step. First look for evidence and understanding of an environmental framework that could support a god. It’s a big step from imposable things happening to a god exits and its important not to read too much into your experimental evidence.

[ QUOTE ]
A man bursts upon the scene proclaiming that he was sent by God to convert people to his religion . As evidence, he does something astonishing and seemingly unexplainable.

[/ QUOTE ]

The fact that the man clams the astonishing thing is due to god is of no significance. Many if not most people seeing such an imposable event are likely to attribute to god, just because it’s so astonishing. Its 'conceivable' that he has been deluded into believing the truth, but that would just be a coincidence.

[/ QUOTE ]


PairTheBoard

[Shine]

Why the run around? What is wrong with my argument?

[PairTheBoard]

[ QUOTE ]
Why the run around? What is wrong with my argument?

[/ QUOTE ]

To begin with you say this:

[ QUOTE ]
Irrational feats have probabilities roughly similar to the probability of the existance of supernatural powers, Q.

[/ QUOTE ]

You're making the prior assumption,

P(Existence of Supernatural Powers) = Q

On what Probability Space does that probability live? That's the whole point. You have none. That is a subjective probability statement not a rigorous one. The OP is asking for Rigor here.

[ QUOTE ]
My question is whether it makes sense at this point to try to rigorously come up with a number that captures the probability that the guy is a fraud.

[/ QUOTE ]

Furthermore, your notation here,

[ QUOTE ]
P(X irrational | X) = P(X | X irrational)P(X irrational)/P(X)


[/ QUOTE ]

makes no sense. I suspect this is not your area of expertise.

PairTheBoard

[PairTheBoard]

Your arguments are certainly reasonable and persuasive. I think what they boil down to is that the Working Assumption of Physics - known laws of Physics apply continuously in the past present and future - has proved so reliable for making accurate predictions of Events, past and future, that it only makes common sense to adopt the Assumption as our Best Working Hypothesis. I find this compelling common sense and therefore find your argument reasonable and persuasive.

Therefore, I would need extraordinary evidence to become convinced of the occurrence of an Event that did not conform to that Assumption. The evidence I have when this man first performs his Feat is His Word for it, And the fact that we've searched and could not see how laws of physics explain it. That evidence is only good enough to get me curious about it. After it's been explained, the only evidence left is the Man's Word for It. I would not generally find that compelling extraordinary evidence to discard the Working Assumption of Physics that has proved so reliable in the past. The Man may be a fraud, he may be deluded, or he may be speaking in symbolic language and trying to communicate something entirely different than the literal interpretation his words indicate.

Here's the thing. In all that discussion, which I see as a reasonable way to look at it, nowhere did I need to resort to the authority of some phony claim to mathematical rigor involving use of psuedo-math and psuedo-probability statements. I object to such sophomoric appeal to phony authority on more than just principle. I also see it producing faulty inferences.

For example, DS insists that every time we encounter a Freak Event that stumps us, where we can't see how known laws of physics can explain it, and even more vaguely can't see how even "yet to be discovered" laws of physics could possibly explain it, we must pump up the psuedo-probability that maybe God Did it. That's the kind of absurd inference Sklansky gets with his little pretend games with psuedo-probability statements.

As I look into a hopeful future for the human race, where we may have billions of years to explore and discover new things about our Universe, I fully expect us to encounter one such Freakish Event after another. Sklansky would throw us back into the superstituous attitudes of the past whereby everytime they encoutered something they couldn't understand they attributed it to God! Sklansky would not do as they did and give it a 100% probabilility. Just a pumped up partial probability. But it is the same superstitous attitude. Sklansky just puts a psuedo-probability face on it.

I believe this perspective of mine is important for people to consider. Whatever the word "God" might meaningfully point to, our approach to it is not by way of such Freak Events that puzzle known laws of physics. This perspective offends everybody. Athiests don't like it, even though it defends an Atheist perspective, because it pulls one of their rugs out from under them. Many Religious people don't like it, even though it defends approaching "God", because it pulls one of their rugs out from under them. Thus is the way of a new paradigm.

PairTheBoard