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2.27.2007

Probability 

I had a quick look at Andrey Feuerverger's calculations of the probability of the Talpiyot tomb being Jesus's tomb.

First of all, it is extremely important to remember that in the real world, the question "what is the probability of X" is almost always meaningless. Conditional probabilities are the only probabilities that can be calculated, i.e. "what is the probability of X, given that we already know Y".

Feuerverger's method seems to be to calculate the probability of finding the name "Jesus son of Joseph", "Mariamne", "Maria" and "Yose" in the same tomb and obtains a 1/600,000 chance of this. Given that there are about 1000 known tombs of 1st century families in Jerusalem, he concludes that the expected number of tombs with these names is 1/600 (even arbitrarily throwing in a fudge factor of 4 to obtain a more conservative estimate). Given the existence of the tomb we have here, he concludes that that the chance that it belongs to Jesus is 1 / (1 + 1/600), which is 600/601, i.e. there is about a 1/600 chance that it isn't Jesus' tomb.

Now of course we should recognize the conditional assumptions built into this calculation, as Jay noted in Ben Witherington's blog -- we are assuming that we know independently that (1) Jesus's northern Israel-based family would actually be buried in a family plot in Jerusalem, in the southern part of the country, (2) Jesus' tomb would contain a "Mariamne" (and a "Judah" and "Matia", but not have boxes with his other relatives' names on them), (3) Jesus would be identified as "Jesus son of Joseph" (last I checked, he was usually referred to as "Jesus son of Mary" if he was identified as someone's son at all).

Even granting these assumptions, Dr. Feuerverger's calculations still seem to have problems.

The 1/600,000 chance is obtained by taking 1/190 (P(random male is "Jesus son of Joseph)) times 1/160 (P(random female is "Mariamne")) times 1/20 (P(random male is "Joseph") times 1/4 (P(random female is "Mary")) * fudge factor of 4.

The problem here is that the correct way to obtain the probability of this cluster of names is to take P(one of five men in the tomb is "Jesus son of Joseph") * P(one of the four remaining men in the tomb is "Joseph" | P(there is already a "Jesus son of Joseph")) * P(one of two women in the tomb is "Mariamne") * P(the other woman in the tomb is "Mary").

The probability of one of five men being "Jesus son of Joseph" is closer to 5/190 (actually, it's 1 - (189/190)^5, but close enough), or about 1/40.

The probability of one of the four remaining men being "Joseph", given that we already know that there's a "Jesus son of Joseph", is...pretty darned high, as Jay notes. Now if you *assume* that this isn't Jesus's legal father, but another Joseph, then the probability of one of the four remaining men being "Joseph" is (1 - (19/20)^4), or about 1/5.4.

The probability of one of two women being "Mariamne" is (1 - (159/160)^2), or about 1/80.

The probability of the other woman being "Mary" is 1/4.

If we don't assume anything about the Joseph in the tomb, then the probability of a random tomb having these names is (1/40)*(1/80)*(1/4) = 1/12800, making it about a 1/13 chance that this isn't Jesus's tomb (again, assuming that Jesus is buried in a tomb, and that the unusual location and surprise names in the tomb can be reconciled independently with what we know about Jesus, and also discarding Dr. Feuerverger's fudge factor of 4).

If we assume that Joseph is actually not Jesus's father (which means that the presenc of anothe Joseph in Jesus's family tomb needs to be independently reconciled) then the probability of a random tomb having these names is 1/12800 * 1/5.4 = 1/69000, or about a 1/70 chance that this tomb isn't Jesus's tomb. Again, these estimates are conditional upon throwing out a lot of evidence that suggests that this isn't even Jesus's tomb in the first place.

2.26.2007

Dem bones 

So apparently some archeologists found a bunch of ossuaries (boxes used to store dead people's bones) sitting in a tomb. They recently concluded that the inscriptions on the boxes mark them as belonging to Joseph, Mary, Mary Magdalene, and, uh, Jesus and Jesus's son.

The possibility that Jesus may have wed Mary Magdalene and fathered a son doesn't particularly trouble me, but the resurrection of Jesus is a central tenet of Christianity as I understand it. The apostle Paul claims in 1 Corinthians 15 that 500 people saw him at once. That letter was written around 50-60 AD, within the lifetime of Jesus's contemporaries, so one would think that this claim was falsifiable at the time of Jesus's resurrection and at the time the letter was written. Jesus's followers weren't exactly in a position powerful enough to be able to whitewash history at the time.

Modern theologians have for a while now made the claim that the gospel message is valid even if all of the miraculous elements (including the resurrection) are removed. Paul doesn't buy it, as he wrote later in 1 Corinthians 15:


Now if Christ is preached, that He has been raised from the dead, how do some among you say that there is no resurrection of the dead?

But if there is no resurrection of the dead, not even Christ has been raised; and if Christ has not been raised, then our preaching is vain, your faith also is vain.

Moreover we are even found to be false witnesses of God, because we testified against God that He raised Christ, whom He did not raise, if in fact the dead are not raised. For if the dead are not raised, not even Christ has been raised; and if Christ has not been raised, your faith is worthless; you are still in your sins.

Then those also who have fallen asleep in Christ have perished.

If we have hoped in Christ in this life only, we are of all men most to be pitied.


Assume henceforth that these boxes aren't some sort of cruel hoax, or belong to some other family with the same names, etc. (which of course is a possibility).

It is entirely possible, of course, that the box never actually contained Jesus's decomposed body parts, just a shroud or some other small pieces of tissue.

If the box did once contain Jesus's parts, it is also possible that Jesus's resurrected body was distinct from his crucified one; in the gospels it seems that Jesus's followers didn't quite recognize his resurrected person immediately, and Paul also seems to indicate in 1 Corinthians 15 that a person's resurrected body is distinct from his former body, fully redeemed and heavenly. There would have to be some explanation for why Jesus's tomb appeared to be empty after the resurrection though -- perhaps his old body shriveled away as his new body was resurrected or something like that.

And yes, from a skeptic's point of view this is kind of weaselly. But given all the other miraculous claims in the New Testament, this assumption is hardly in a different league.

Finally, if Jesus never was raised, the most logical thing for Christians to do is probably to hedge their bets by practicing Judaism. Giving up pepperoni and cotton-poly boxers is kind of a drag, but at least I already went under the knife when I was a baby.

EDIT: Paul Maier of the Western Michigan University history department (who I would guess is a Christian, as he has published works with Zondervan and Tyndale) offers a rebuttal, as do some other folks who were interviewed for the film in this TIME article.

EDIT: Here are longer ripostes from Ben Witherington and Darrell Bock, who criticize the findings in the TIME article. In the Witherington entry, read especially the comment by "Jay", who has a few bones to pick with the statistical analysis. Specifically, he notes that the event that a tomb contains a "Jesus son of Joseph" ossuary and the event that it contains a "Joseph" ossuary are likely not independent, and that the presence of boxes marked "Matthew" and "Mariamne" can be interpreted as a strike against the hypothesis that it is Jesus's tomb.

2.20.2007

Coming to America 

Over on my friend Phil's blog, there's a story about the Chinese government attempting to repatriate a schoolgirl who sought asylum with her aunt and uncle in the United States. Yes, she did happen to practice Falun Gong. No gunshots were fired, but it's an interesting read all the same.

That's all Foulke 

Keith Foulke has called it quits. After signing a 1-year $5 million contract with the Cleveland Indians, he decided his knees couldn't take it and retired before throwing a pitch. It should be noted that he easily could have hung on for a little bit longer, qualified for his salary and then bailed, but chose not to do so.

Baseball fans may remember that Foulke threw 100 pitches over 5 innings during the most dire conditions in a span of 48 hours during Games 4, 5 and 6 of the 2004 ALCS against the Yankees. He also pitched four innings in the ALDS against the Angels, and picked up a win and the championship-clinching save in the World Series against the Cardinals. His total line for the 2004 playoffs:

11 appearances, 14 innings, 59 batters, 257 pitches, 7 hits, 1 run, 8 walks, 19 strikeouts, ERA 0.64 over a 14-game postseason.

If MLB awarded just a playoffs MVP trophy instead of LCS and World Series trophies, Foulke certainly would have been the winner.

Baseball fans may also remember that he blew several saves and pitched poorly during the first couple months of 2005, earning him the wrath of the Fenway faithful. Foulke cantankerously replied that


I'm more embarrassed to walk into this locker room and look at the faces of my teammates than I am to walk out and see Johnny from Burger King booing me.


That did not go over so well.

In retrospect, it is clear that he had significant physical problems during the last few years he pitched, and that pitching overtime during the 2004 playoffs exacerbated his problems. It may not have been completely clear during the first half of the 2005 season, but most Red Sox fans I know suspected that something was wrong. I sincerely hope that the fans who booed Foulke feel ashamed of themselves.

Below is a picture of Foulke just after recording the final out of the 2004 World Series. Thanks for the memories, dude.

2.17.2007

Epiphany 

After arguing with a bunch of people on a bulletin board, I have come to a realization that I am pretty sure I have made several times in the past:

Discussing politics (or economics, or sports, or pretty much anything else other than TV shows) with people who don't have a rudimentary understanding of statistics is completely futile.

2.14.2007

Somebody please YouTube this 

I got this email in my Harvard inbox recently:


Dear Harvard Mathematics Department:

It has recently come to my attention that our colleagues at the MIT
Mathematics department do not think much of our collective dance abilities.
In fact, they don't think we're any good at all. This is unacceptable.

My counterpart at MIT and I have decided to settle this dispute, by
holding the:

****First Annual, Harvard-MIT Mathematics Department Valentine's Day Dance
Dance Revolution Competition****

To the winner goes bragging rights for a year. The loser goes home. The
winner also goes home, presumably.

Specifics:

When: Valentine's Day, 2/14, around 5.00 PM
Where: MIT student center, arcade room
What: Dance Dance Revolution competition
Who: You
Why: Because this aggression will not stand, and it will be fun.

For the uninitiated, Dance Dance Revolution is a dancing video game, best
described by video --
http://www.youtube.com/watch?v=uWmgBKTmXvQ

We will have a team of 10 from each department (comprised of graduate
students, postdocs and faculty) face off against each other one at a time.

If you're interested in being on the team -- please send me an email by
Friday. This will not be a big time commitment (just an hour or two next
Wednesday) and it will certainly be fun. No experience on DDR necessary.
No physical coordination necessary. Just an ability to laugh with/at
oneself.


UPDATE: Articles from The Crimson and Globe here.

2.12.2007

Too little, too late 

The Police are back, and they've announced their reunion tour. I don't know why they're playing only a handful of dates, or if they have more planned. In addition, Sting now has problems hitting the high notes, as was evident at their performance at the Grammys.

I like The Police, but I think I'll have to pass on paying $700+ and driving 6 hours to see them. I will, however, admit to being jealous of those folks in Boston who get to see them at Fenway Park, which is pretty much the perfect place for a concert (due to the combination of small crowd and open-air stadium, as well as Fenway's general awesomeness).

EDIT: Apparently dates for LA (as well as a bunch of other major cities that aren't up yet) are in the works.

2.05.2007

Worst Super Bowl EVAR 

Ugh. Not only do the Colts win, but I miss out on $300. Also, the game itself wasn't very well played at all.

The only bit of actual insight I can offer is this: it became obvious during the second half that Bears coach Lovie Smith had zero faith in Rex Grossman's ability to throw the ball downfield. If that's the case, and you need to mount a comeback, why keep him in at all? Why not put in Brian Griese or Kyle Orton?

Every columnist I've read so far says that the Bears defense is mostly to blame for the loss, but I completely disagree. Holding the Colts to 22 points is pretty good for any defense. If Chicago had been able to mount an actual offensive drive here and there, the defense could have rested. Instead, the Colts were able to keep the ball for 38 minutes, and the Bears defense eventually wore down as the game went on.

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