Wednesday, February 25, 2009

Resurrection? Probably not.

Suppose there’s a big drug bust in New York City and the police impound \$10,000 in drug money. Later there’s a trial at a Federal court house in California and the money needs to be taken to Los Angeles. (Don’t ask why.) Let’s suppose that between NYC and Los Angeles the money will be in police custody, but it will change hands between several escorts as it travels. Suppose there will be three different cops in charge of the money for different legs of the journey. And let’s suppose that we have independent evidence that there is some degree of corruption in the police departments that are providing the escort cops. Suppose that when considered on the whole, the likelihood that a cop from any of those departments is honest is .8. Maybe there are 100 cops in each department, and 80 of them are honest, while 20 are corrupt. If a corrupt cop gets custody of the drug money, he or she will take some. If an honest cop gets custody, he or she will deliver it to the next leg of the trip without taking any of it. We don’t know anything more about which cop will get the duty except the .8 probability information about their honesty.

Here’s a question: what are the odds that the money will arrive in Los Angeles without any of it missing?

Probability theory tells us that we should calculate the odds this way for 3 cops: if the P that each one is honest is .8, then we multiply. .8 x .8 x .8 . So the odds of the money all arriving in L.A. are .51. If you add two more cops at the .8 honesty rate it goes down to .32! And that’s despite the fact that majority of cops in each department are honest.

(Thanks to Randy Mayes and Jonathan Baron—Thinking and Deciding, for making the basics here clearer to me.)

Now let’s change the example. Suppose that instead of travelling across the country, the item in question is moving across time. And instead of money, the thing that is in custody is a story. That is, suppose that many different people tell and retell a story across many centuries of time.

What do we know about testimony? We know that when a person testifies that some claim is true and all we have to evaluate is the testimony, we can attach a value to the probability that what they are saying is true. In general, when people assert that x is true, and they mean it, we can and should ask, what is the probability that it is true, given that Smith, for instance, asserts that it is. For most of us, it would mean something for Smith to say it earnestly. And if Smith says he is utterly convinced of its truth—he says he’s 100% certain that it is true—then that should count for a lot in my assessment of whether or not x actually is true.

What do we know about people’s confidence levels and the real accuracy of their claims? In general, people are over-confident. They will claim to be accurate and certain more often than they are. In one study, subjects were asked to spell a word and then indicate how confident they were that they had spelled it correctly. When they were “100% certain” in fact they only spelled the word correctly 80% of the time. You’ve had this feeling of certainty many times about a spelled word. When you have it, it would be very hard to dissuade you without substantial proof, that you were wrong. But there are the real rates. (Adams and Adams, “Confidence in the recognition and reproduction of words difficult to spell,” American Journal of Psychology, 73, 544-552)

It is alleged that Jesus was resurrected from the dead. The chain of custody for that story (think of it like the money above) goes something like this. 30-60 years after the alleged event, the author of Mark wrote down the story as it had been told to him. We do not know how many tellings and retellings the story went through between the alleged event and when Mark recorded it. Matthew and Luke were written later still, but they were lifted for the most part from Mark and another source that is now lost known as the Q source. We don’t have that source, nor do we know its history. John is written a few decades later still. All four accounts differ significantly in detail and emphasis. All of them have significantly different accounts of the resurrection.

We don’t have those original written accounts. What we have today are some copies of copies of copies of those original written accounts that were written on the basis of decades old tellings and retellings of the original story. The oldest copies of the gospels that we have today are from roughly 200 years later than when they are generally thought to have been written.

So the point here should be clear. If people who avow that something is true (like the correctly spelled words) insist that they are “100% certain,” we have good reason to attach, at best, a .8 probability to the claim. And this is about something as simple and obvious as spelling. If a story goes through multiple people’s custody, like cops carrying money, then we apply the multiplication rule to determine what will come out the other side. It only takes a few generations, or links in the chain of custody for the overall probability to drop to very low levels.

Even if every single one of the people that the resurrection story passed through retold it with as much care as they could muster, and even if each one of them was completely certain that the resurrection happened, it is highly improbable that the story that they are passing on is true.

This is granting more than we should grant in this case. We do not know who the story passed through between the alleged events and us, we don’t know what sort of motives or goals they had, we don’t know if they were corrupt, or liars, or delusional. We don’t know how many times it was retold or by whom before Mark heard it. And we don’t know what happened between the original Mark story and the surviving copies of it that we have.

Suppose that it passes through 10 people and we assign a .9 reliability to each of them, the likelihood of an accurate story arriving at the other side is around .3. If just one of those people is only 50% reliable because he exaggerates, or lies, or gets enthusiastic, or is guilty of wishful thinking, or sincerely wants the world to believe in Jesus or whatever, the overall likelihood that the story is true drops to .15.

We can anticipate these objections: but we have independent corroboration of the events in the New Testament. We have thousands of documents that back the stories up. We have no reason to doubt the honesty or integrity of the people in the chain of custody. The followers of Jesus would not have lied or put their lives in danger for the sake of something so important. And so on, blah, blah, blah. . . .

We don’t have thousands of documents to back up the custody chain being considered here. We can have as many copies or corroborations of the story as you want later on, but if it’s a corrupted story, copying it over and over doesn’t make it true. You can put as many honest cops on the guard detail of the money when it gets to the court house in LA as you want. That won’t insure that someone didn’t pilfer some of it before it got there. The period from the alleged resurrection to the first written record is almost a complete mystery for us now. And the period from when the gospels were written until the copies that we have today were written is mysterious too. “But we know that the Jewish oral tradition was highly accurate.” Maybe. If the resurrection story is being used as part of that tradition, then this is begging the question. The Jewish oral tradition was people telling and retelling stories. And we have mountains of evidence from carefully constructed, double-blind testing of thousands of subjects about people’s unreliability, even when they are trying really hard. We can’t really atest to the integrity of the custodians of the story if the only information we have about the custodians integrity is part of the story itself. How can I know that Smith is a reliable witness? I asked him and he insists that he is. Furthermore, we don’t need to have any concrete explanation or alternative account here. I don’t need to know what motivated the people in the study above to misspell the words. I don’t need to why they did it, or what mistake they made exactly. It’s enough to know that even when they claim to be 100% certain, their real accuracy is .8.

M. Tully said...

Matt,

I think you are being quite kind with your 0.15 probability for the telling of the resurrection story.

Throw in a little Bayesian inference into the equation. Out of all the observed human deaths in the written and archeological history of the earth, how many confirmed resurrections have occurred? Then multiply that number by the 0.15.

Matt McCormick said...

Yeah, that's right M. Tully. I'm being absurdly generous here. There are a hundred considerations, including the one you raise about the overall likelihood of a resurrection, that reduce the odds effectively to zero.

Without getting too Bayesian here, what's interesting, I think, is just the impact of the multiplication rule. Once an extraordinary story has passed through a couple levels of hearsay, we should all say, "Unreasonable--Multiplication Rule!!" and move on.

Thanks.

MM

Toby said...

Once again you've wrote an amazing post. I think the typical religulous response is to say God protected the integrity of the documents through out it oral and written transmission. In one debate where Bart Erhman eloquently pointed out the numerous mistakes that are undeniable in the New Testament his opponent said that yes that are errors, but none that affected the heart of the story.

So apparently God in unconcerned with stopping thousands of small errors from creeping into the texts, but stops all of the larger ones...

Bryan Goodrich said...

I think your measure of Pr("tells an accurate story")=0.90 is a bit low. Unless someone really screws up 1/10th of what they say, then we can expect the details that get muffled are much smaller. It would be like a small amount of noise, but overtime that noise accumulates as each message gets transmitted in a linear fashion with the same static. Consider Pr(X)=0.99. Over the 10 times the accuracy rate is down to 90%. Over 20 transmissions it is down to about 80% (22, actually).

Of course, I shouldn't have to point out the massive amount of assumptions that go into this, and the linearity in the methodology (which many things can be nonlinearly dynamic). That doesn't imply it isn't a good thought experiment to test our notions of accuracy with small margins of error over numerous trials.

Steve Martin said...

You and I had better pray that tiny probability be true.

It is our only hope in a world that leads all to the graveyard.

Carbon Based said...

"It is our only hope in a world that leads all to the graveyard."

And as far as we KNOW that is where it ends.

Teleprompter said...

Why should it matter that it "leads to the graveyard"?

Why can't we just appreciate this life for what it is while we have it?

And doesn't that preciousness, that scarcity, cement its value?

Death is part of life - in many cases, death enables life: why should we tremble? Why should we not celebrate it?

Within your body: apoptosis, programmed cell death. Death as the maintenance of life.

We play our small part in the cosmos, and then we surrender it.

Steve Martin said...

That sounds like Christianity.

At least the Christian faith that I know.

Out of death, comes life.

ChrisAC said...

That sounds like Christianity.

At least the Christian faith that I know.

Out of death, comes life.

Only if you take an absurdly egotistical look on things, where the only life that matters is human life, or even worse, yours.

If you would like, I could probably dig up a copy of The Lion King's circle of life clip if you would like a more colorful explanation of Teleprompter's point. It seems a cartoon would be suiting for you.

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