Sunday, April 26, 2009

Putting Odds On Jesus

Suppose several police departments are transferring $10,000 of drug money across country from New York to Los Angeles. Along the way, the money will change hands three times. We have independent evidence that there is corruption in the three police departments that the cops are from. On the whole, the likelihood that a cop from any of those departments is honest is .8. If a corrupt cop gets custody of the money, then he or she will take some. If an honest cop gets custody, they will deliver it to the next leg of the journey without taking any.

Question: What are the odds of all of the money arriving in Los Angeles?

Probability theory says that the answer is .51. Or .8 x .8 x .8. If we 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.

The majority of Americans consider themselves to be Christians. And if you consider yourself to be a Christian, then you believe that Jesus was a real person and he was resurrected from the dead.

Your only source of information about this event is the first four books of the Christian New Testament, Matthew, Mark, Luke, and John. Jesus is alleged to have come back from the grave around 35 AD. Mark was written about 30 years later at 65 AD. The consensus seems to be that Matthew and Luke were written between 70-100 A.D. John was written around 90-100. How many links in the chain of transmission are there between the events in question and when the authors of these books wrote down the story? We don’t know. They were not eyewitnesses; they heard the stories by word of mouth, most scholars believe, and there could have 2, 20, or 200 links between them and the original events. How reliable was each one of those links? We do not know.

We do know this. Eye witnesses are quite poor, especially when they are extraordinary events.
They mix the orders up, the miss important details, they revise, they augment, they embellish, and so on. Even moments after an event, they make serious mistakes.

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)

Other recent work has shown a remarkable level of change and choice blindness in test subjects. Have subjects pick the most attractive person from a group of pictures of people, surreptitiously switch the picture on them, and then ask them to explain why they think the switched picture is of the most attractive person, and they don’t miss a beat. They start explaining why without even noticing the switch. Have shoppers taste a range of tea samples and have them pick their favorite. Then switch it without their knowing and ask them to taste it again and explain why they think it is the best. Even when you replace their favorite, say apple cinamon, with a completely different flavor, 2/3 of the subjects don’t notice the change and the confabulate a justification for why that’s their favorite.

The data in change blindness cases is even more remarkable. Here’s a video of two teams of people passing a basketball, one group in white shirts and one group in black shirts. Watch the video carefully and try to count the number of times that the white team passes the ball. http://viscog.beckman.illinois.edu/flashmovie/15.php

A surprising number of subjects do not notice what should be obvious. In some of these studies, 75% of the subjects do not notice. (Change Blindness)
So robust empirical evidence shows us that change and choice blindness, and overconfidence cast substantial doubt on the reliability of eye witness testimony. Volumes of other studies document the problems with eye witness accounts.

Do we have any way to attach a reliability estimate to the first person in the chain, the individuals who are alleged to have witnessed the resurrected Jesus himself? We do. Every year at the shrine at Lourdes, France, more than 80,000 pilgrims visit. The spring waters there are alleged to have healing powers, after a woman claims to have seen the Virgin Mary. Over the course of a century, then, that is more than 8 million visitors.

The official representatives of the Catholic church have been conservative about the real occurrence of miracles there. They have officially recognized 66. Let’s be generous and grant that 66 real miracles have actually occurred there.

Let’s also be conservative and suppose that of the 8 million visitors, half of them felt that they had observed or felt a real supernatural or spiritual event. This number is conservative because the vast majority of people going there do so with the strong expectation that miracles have occurred there in the past, and that they will be miraculously healed as well.

So for the visitors at Lourdes, what is their reliability for reporting miraculous events? 66/4,000,000 or .0000165. That is, even setting the number of felt miracles low and agreeing with the church about the number of real miracles, the probability that the miracle claim from any given pilgrim is true is .0000165.

Should we think that the general reliability of the early Christians who spread the Jesus story was greater or less than the pilgrims at Lourdes? I should think it would be much lower. The pilgrims are modern, educated, scientific era people. Many of them are doctors, lawyers, and scientists, people who are trained in making good decisions and being skeptical. They have the benefit of 2,000 years of investigations into the natural causes of allegedly supernatural events. The early Christians, by contrast, would have been largely illiterate, poor, uneducated. They would not have the benefit of the huge body of scientific and empirical knowledge that we take for granted.

But let’s be exceedingly charitable and grant that the early Christians were 10 times more reliable about reporting miraculous events than the modern visitors to Lourdes. And let’s suppose that there are only 3 steps of transmission between the events in 35 A.D. across 30 years to when Mark first wrote the story down. And let’s suppose that those three links were much more reliable than the cops in the story above. What are the odds that the resurrection story is true:

.00165 x .9 x .9 x .9 = .00012

That is, on a vastly charitable estimate, there is a one in ten thousand chance that the story is true.

Should we be that charitable? No. We should not be generous about the 66 miracles at Lourdes. Many of the cases in support would crumble under any serious, objective scrutiny. I would be surprised if 5 of them didn’t have an obvious natural explanation. And I suspect that many more people than 4,000,000 thought they felt or saw something spiritually significant there. If there have been 6 million of them, and 5 real miracles, then the reliability rating of Lourdes pilgrims is 0.00000083333. And the reliability rating for early Christians should be much lower given that they did not have the advantage of 2,000 years of science and a modern education to augment their analysis of miracles. Nor should we grant that all of the tranmission links in the story to Mark would have a .9 reliability. There are too many unanswered questions, too many doubts, and the human propensities to embellish, omit, revise, and confabulate are too great.

Still granting only 3 steps, a more reasonable estimate is:

.000000833 x .7 x .7 x .7 = 0.0000002858

or about 1 in 5 million. According to the U.S. National Weather Service, the odds of your being struck by lightning in your lifetime are 1 in 5,000.

When people take the Jesus stories seriously and make comments like, “Why would the early Christians lie?” or “what incentive could that have for making it all up?” or “how could they have perpetrated such a deception?” they are simply ignoring the strength of the tendency in the human mind to see miracles or events of spiritual or supernatural origin at every turn. We don’t need to have a better, alternative explanation to be quite sure that Jesus was not resurrected from the dead. The reliability of the information transmitted in those stories to us is just too low.

34 comments:

M. Tully said...

“Why would the early Christians lie?”

Why indeed (hmm, I have an agenda I want to sell, is it in my best interest to lie? Looks like a good argument for a peer review process). The question I like to ask is, "If a priest of a new religion today claimed to have cured leprosy by simply touching the person, 'what evidence would you require to accept the healer's claim?'"

And the follow up, "Do you have that same level of evidence for the claims you make about your own particular supernatural healer?"

But to get the heart of probabilities, of all the mysteries in human history that have ever been solved, how many have natural explanations? That would be all of them. Of all the mysteries in human history that have been solved, how many have supernatural explanations? That would be none of them.

So, if we encounter an event that we can't currently understand, what is the probability that it has a supernatural origin?

The math for a natural explanation: all/none=?

No matter how counter intuitive the natural explanation may be, no matter how disconcerting saying, "I don't know" may be; a counter intuitive or reserving judgment answer is, by probabilities...

...infinitely more likely to be correct than any supernatural explanation.

Supernaturalists should not get into probability arguments. The math takes no more than simple algebra, and is "infinitely" stacked against them.

So what is the probability that the constants of physics are what they are by nature's rules alone? What is the probability that something as complex as human intelligence evolved by natural means alone? What is the probability that the human moral sense developed by natural means alone?

The answer to the above questions are, "I don't know (I have no other universes to compare things to.)" But whatever those probabilities may be, they are INFINITELY more probable than a supernatural agent was involved.

What are the odds indeed.

Matt McCormick said...

Good ideas, MT. But there's a problem. Increasingly, believers have taken to portraying naturalists or non-supernaturalists as being in the grips of a circular ideology. They protest because it appears that we are insisting that no explanation except a natural one is ever possible or necessary, and our grounds for thinking that are that no non-natural explanation is ever necessary. If you set this problem up like you're doing, then it appears that you're just defining "acceptable explanation" as meaning "natural explanation." And that appears to be circular. We want to allow for the possibility that a supernatural explanation could be called for or it could be the best account of what is going on in some circumstances. The problem is, I am arguing, that the substantial burden of proof has not been met in the Jesus case. We can allow that miracles could happen in principle. But in the case of the single most important miracle to the Christian religion, the likelihood that a real magical event happened is vanishingly small.

Nevertheless, I share your sentiments. I am placing the odds at 5 million to one on the basis of some liberal assumptions. The real likelihood is probably much smaller, if that's possible.

thanks.

MM

Reginald Selkirk said...

the first four books of the Christian Biblethat would be the first four books of the Christian New Testament.

Matt McCormick said...

Right, RS. Thanks. Fixed.
MM

M. Tully said...

"They protest because it appears that we are insisting that no explanation except a natural one is ever possible or necessary, and our grounds for thinking that are that no non-natural explanation is ever necessary."

Good point. I'll have to rework it. The funny thing is that if supernaturalism gave better explanations of observations and made better (as far as I know it doesn't make any) verifiable predictions, I would jump on the supernaturalists' train in a heart beat. My base assumption for naturalism is in fact based on probabilties.

Maybe I just need to state that premise at the outset?

Steve Martin said...

The tendency in the human mind would be to save their own skins.

They ran away from Him at the cross.

But after He appeared to them again after His crucifixtion, they willingly went to their deaths rather than to deny Him.

M. Tully said...

Steve,

You continue to repeat the same old canards.

"But after He appeared to them again after His crucifixtion..."

In keeping with the probability theme of this post. What is the probability that a man who was clinically brain dead returned to life (take the number of clinically demonstrated resurrections and divide that by an estimate of the total number of people who have died). The probability is staggeringly low. So what level of evidence should I require for an event that has such a low baseline probability?

Well, what level of evidence would you require if someone reported that it happened to the Great Wiki in the forests of the Amazon only 100 years ago? Would you accept a book put together by Wiki accolades, with no provenance of authorship, first transcribed approximately 50 years after the event happened? Even if the book had written in it, "Wiki appeared to thousands after his death?"

Or would you ask, "Who were these thousands? Did a number of them go on record as being skeptical about Wiki before the event? Did they record what they saw soon after the event? Out of thousands, were there at least a score of real time reports?”

Can you produce contemporary, non-accolade source citations of said appearances of Jesus after proven clinical brain death?

And even if the Wikifarians could produce such documents, would you say then that Wiki must have come back from death? Or would you ask, “What standards of evidence did these people of the Amazon use? How do I know Wiki was actually brain dead? Did they have EEG technology? How do I know Wiki did not have a twin brother or use doubles as actors and heads of state have been known to use?

So, really Steve, when commenting on a post about statistical probability, using an example about a single sourced, accolade produced, five decade post-event testimony about an alleged happening with an extremely low baseline probability is, quite frankly, a way to show that your position is in fact most improbable.

M. Tully said...

OK Matt,

I've rethought it.

"They protest because it appears that we are insisting that no explanation except a natural one is ever possible or necessary, and our grounds for thinking that are that no non-natural explanation is ever necessary."

No, I'm not insisting that a non-natural explanation is never possible. I am only asserting that based on probabilities that a natural explanation is, by a large magnitude, more likely. If the supernaturalist wants to put forth the evidence, that contrary to probabilities, the event still has a supernatural origin, I am willing to entertain that (quantum mechanics shows that improbable events do in fact happen all the time). However, if they are making a probability based argument for their assertions (i.e. supernaturalism is the most probable explanation for the event) then my argument stands as written.

Based on all the evidence we have to date, a supernatural explanation is infinitely (if you must assign a number, I like 6.6 x 10^-34) less probable than a natural one.

Consequently, I am not saying that supernatural explanations should be rejected out of hand. I am only saying that a supernaturalist argument that is based on probabilities, is by all available data, wrong. If a supernatural explanation is put forward that argues that despite the probabilities, the evidence dictates a hearing, that argument deserves consideration (and for that matter our assent if that is what the evidence dictates).

I am not making a circular argument that supernaturalism is wrong by definition. I am only making the argument that supernaturalism by probability is wrong by data.

Matt McCormick said...

Agreed. The non-believer, if they are serious about all of these demands they make for evidence, must always be prepared to allow that some sort of evidence would be convincing, if only hypothetically. Otherwise, they are just being dogmatic.

MM

dillinger916 said...

Hello, I'm a friend of Gamaliel (no last name needed, I'm sure he's the only student you had with that name), he was a student of yours, showed me this blog, found it interesting. I'm agnostic myself, but definitely lean more towards atheism. Anyway, early Christians would lie because most of the people making up these stories probably used the stories to tell the aforementioned uneducated, poor folk back in the day that if they didn't fly right they'd end up in hell, so don't do anything stupid to ruin your chance in getting into heaven (i.e, challenging authority, etc...). This is my thought at least, I could be wrong, I am about most things after all. XD

Samphire said...

Steve Martin said...

”The tendency in the human mind would be to save their own skins.

They ran away from Him at the cross.

But after He appeared to them again after His crucifixtion, they willingly went to their deaths rather than to deny Him.

Who were “they”? And what contemporary evidence do you have that any were executed?

feeno said...

5 million to 1 odds? Those are better odds than the Cincinnati Bengals winning a Superbowl?

Steve Martin, You are a wild and crazy guy. But you are right.

People die for a lie all the time, when they think it's the truth. But Jesus' disciples died for what they actually saw.

Peace out, feeno

feeno said...

5 million to 1 odds? Those are better odds than the Cincinnati Bengals winning a Superbowl?

Steve Martin, You are a wild and crazy guy. But you are right.

People die for a lie all the time, when they think it's the truth. But Jesus' disciples died for what they actually saw.

Peace out, feeno

Samphire said...

feeno said...

"People die for a lie all the time, when they think it's the truth. But Jesus' disciples died for what they actually saw."


feeno, I ask you the same question I asked Steve. Harry McCall made a similar statement a month or two ago at Debunking Christianity but, despite some offensive and ridiculous bluster, he too was unable to answer the question which is: What were the names of the disciples who were martyred shortly after the crucifixion and what contemporary (secular or biblical) evidence do we have of these supposed deaths?

feeno said...

Hello Samphire

Did you mean Harry asked the question and Steve couldn't answer it? 'Cause I think Harry would agree with you about this?

The only death mentioned in the Bible for any Apostle was that of James.(Acts 12:1-3). Unless you count Judas' death?

I would like to take the time to share what I believe is a really cool story about the other James in the Bible.

Jesus had a brother named James. This James thought his brother Jesus was nothing more than that, his brother. (John 7:5). And In all 3 gospels it mentions that "Only in his hometown and in his own house is a prophet without honor." (Matt 13:53-58). But later one of these same brothers not only writes a book that almost mirrors Jesus' sermon on the mount, but was thrown off the top of the Temple, and then when he didn't die, they beat him to death. Why? because he refused to denounce Christ.

Something changed with James. He went from skeptic to martyr. What changed? I think it was the fact that he witnessed his Brother after he was crucified, died and buried.

Now most fundies like me get most of our facts on the deaths of the Apostles from an old book called Foxe's book of Martyrs. Written by Foxe. (First name escapes me.) But you can check out all of his resources in the back of that book. You can probably find a copy on line for 5 or 10 bucks.

Sorry that my last comment up was posted twice, I still stumble around the computer.

Have a great weekend, I'll be checking back by.

Peace out, feeno

Samphire said...

Thanks for the reply, feeno.

I do have the Book of Martyrs. As far as I know (please correct me if I am wrong) James was not a disciple and, in any event, was not martyred for at least 30 years after the resurrection and so I don’t think he qualifies.

So, which of the 11 original disciples who witnessed the resurrection went out into the world to spread the Gospel in fear of their lives and were soon martyred?

After asserting something similar Harry McCall couldn’t answer the question either but told me to go and get an education. I’m not making any point here other than it is a claim I have heard made for 50 years as a proof of the historicity of the resurrection and yet nobody seems able to back it up with even a couple of names.


Anonymous said...

You may have noticed, Professor, that John Loftus is making fun of your proabability argument over at this Debunking site.

Why you would use his book to study atheism is beyond me...first, because is is not really about how he became an atheist and second because he only argues for atheism in the last couple of chapters; making egregious errors in the process.

The book itself is misleadingly superficial, as it covers over 40 arguments in some 400 pages; this leaves some with the impression that they are then knowledgable about the those arguments when he has spent as little as a dozen pages on subjects like the Resurrection or Biblcial Archaeology.

More later...

DebunkingLoftus.blogspot.com

feeno said...

Hello again Samphire

I'm not sure why you haven't been able to get a response, it's a reasonable question.

I know that according to the Ecclesiastical Antiquity The apostle Paul, again not an original Disciple was beheaded by Nero around 67or68 A.D.

Matthew killed by a sword in Ethiopia.

Peter again probably killed by Nero. Crucified upside down?

John was boiled in a vat of oil, somehow he managed to live.

I personally don't think any Disciple necessarily were "soon" killed after the resurrection. But they seemed to be in constant danger of prison, persecution or the threat of death.

I'm sorry this is such a lame response, it's all I got. I will re-fresh myself with Foxe's book.

Later, feeno

eheffa said...

Feeno,

What were Foxe's sources for all this information?

If his primary source was the Early Church & you accept that, then I trust you are quite happy accepting the infallibility of the the Pope & any other ancient assertions made by the Catholic Church & her oh-so honest minions....

-evan

eheffa said...

Addendum,

Just for the record; the edict declaring that the Pope is infallible is not really that ancient. (Formally declared in July 18, 1870)

Nevertheless, the reality is that the Church has a pretty checkered past & a history of exaggeration & falsehood that makes it a singularly unreliable source of information.

-evan

Samphire said...
This comment has been removed by the author.
Samphire said...

feeno said:

”I know that according to the Ecclesiastical Antiquity The apostle Paul, again not an original Disciple was beheaded by Nero around 67or68 A.D." 
But Paul was neither a disciple nor a witness to the resurrection nor a biblical or historical martyr. Also, he is unknown to secular history.

”Matthew killed by a sword in Ethiopia.”



Again, neither biblical, immediate nor historical.

”Peter again probably killed by Nero. Crucified upside down?”
Ditto





”John was boiled in a vat of oil, somehow he managed to live.”



Ditto. And which John?

 


"I personally don't think any disciples necessarily were "soon" killed after the resurrection. But they seemed to be in constant danger of prison, persecution or the threat of death."



Where is your evidence? The ancient world seems to have been awash with itinerant preachers (the 1st century equivalent of American evangelical TV channels) who, away from orthodox Jewish fundamentalism, were free to preach whatever they wished. Where was the danger?

”I'm sorry this is such a lame response, it's all I got.”
That’s OK. It seems that the truth is that the disciples were not actually under immediate threat of death for their beliefs. This does not reflect on the historicity of the physical resurrection (which I deny) but simply kills the argument that the disciples were putting their lives at risk by preaching their Jewish version of the “gospel”.


Perhaps Steve has something to add.

Bill Pieper said...

Matt-- You pick a pretty easy target when you go after just the Christian god. Not that I disagree,but there's so much implausibility and internal contradiction to the Jesus story, plus the the really bad fit of the Old Testimate with the New, that the wonder is they've been able to sell it at all. I'd rather buy a new Chrysler Imperial, even now.
But a brave man you are in vowing to prove the negative, something usually conceded to be impossible.
Moving beyond Cristianity, though I still wouldn't take Pascal's wager (basic to it is that the god in question is so human-centric as to care whether one believes or not), I nonetheless ascribe to there being a god of some sort, but utterly beyond human ken. In fact we have photographs, and better ones than have ever been shot of Bigfoot.

I'm talking about the star-birth/ star-death panoramas beamed back by the Hubble telescope. Something genuinely awesome is going on out there, and whatever it is or how it works, it holds sway over everything you or I could conceivably conceive of. So why not call it God.

SwimmerBoy84 said...

The reason not to call it God is that God actually means something more than our awe at the beauty of the stars. If you're going to call that God, why not call it Zeus, or Quetzalcoatl?

Bill Pieper said...

As a reply to SwimmerBoy, who weighed in on the comment from me just prior to his, I believe he misinterpreted me on two points.

I said nothing about the beauty (in the fireworks sense, that is, of the Hubble photos, though it's an interesting question as to why most viewers seem to see them as beautiful)being my reason for suggesting that God is a fit name for the process on display. It is the pure power to create something out of nothing and nothing out of something that warrants the name God.

Moreover, my use of God in that context is as an all-enveloping term which would incorporate Zeus and all other specific but more limited conception of supreme power. To be supreme, in other words, means to include and supercede all others.

Carbon Based said...

"It is the pure power to create something out of nothing and nothing out of something that warrants the name God."

But the singularity is not "nothing" So your premise seems to be quit simple minded and wrong.

And at the oppisite end we have never seen "nothing" in our universe. Nothing as far as I know does not exist.

Nothing if it exists at all may be unstable. Just a thought. :)

Anonymous said...

I like this odds game. I agree there was a lack of witnesess for a historical jesus. But what about all the testimonies of religious experience in general involving jesus throughout history? I mean the odds must be in favor of at least one account panning out?

eheffa said...

Anonymous said: I like this odds game. I agree there was a lack of witnesess for a historical jesus. But what about all the testimonies of religious experience in general involving jesus throughout history? I mean the odds must be in favor of at least one account panning out?The evidence would suggest that rapturous religious experience is a neurologically based phenomenon common to many otherwise incompatible religious belief systems. The Mormon's experience the "Holy Spirit" but reject the Divinity of Christ. The Pentecostal or Charismatic Christian experiences the "Holy Spirit" too but would reject the notion that the heretic Mormon is worshiping the same god. They both can't be right.

Recent studies using enhanced MRI or PET scans ( I don't recall which) demonstrate that Catholic Nuns & Buddhist Monks when praying & meditating deeply will light up the same part of their brain when this happens.

The most likely explanation for these varieties of religious experience is that this a physiological / neurological phenomenon without any supernatural implications & certainly unconnected to the veracity of the belief that spawned the experience.

Anonymous said...

eheffa I am all for science explaining supernatural experiences. Possibly a religious experienced marked as a supernatural is in fact natural but yet explained by science. But wouldnt this lend credibility to religious experience? As something actually tangible and not just a product of human imaginiation? I think the age of enlightement brought men who worked hard to understand religious experience as an explainable phenonmenon.

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Anonymous said...

This is one of the most biased arguments I have ever read. The math used to back up the authors claims is absurd. The relationship the writer trys to establish between people's memories when pictures are switched and seeing someone "RISE FROM THE DEAD" should be argument enough to establish this story is written by an idiot, for idiots.

macroman said...

feeno et al: I think there is some evidence that James the brother of Jesus was killed for saying Jesus was the Messiah, not that Jesus was raised from the dead. Not the same thing?