My prayers have been answered: the Discovery Channel has posted up a PDF file summarising the evidence that the supposed "Lost Tomb of Jesus" really did belong to the Biblical Jesus. It reveals the methodology used in the statistical analysis which previously made me so uneasy.
The numbers are, to say the least, unconvincing.
The analysis begins by looking at the frequencies with which the names "Jesus son of Joseph", "Mariamne", "Maria", and "Yose" (Joseph) appear. One can express these as the number of occurrences of the name in question divided by the total of all inscribed names, to give the fraction of inscribed names represented by each of the four in question. (A full quarter of all names were Maria!) Then these fractions are all multiplied together and a fudge factor is thrown in, to give what is supposed to be the probability of any one tomb containing this collection of names. The analysis then assumes there were 1000 tombs in Jerusalem from the appropriate period (twice as many as I supposed, and, as far as I can tell, nothing but a guess), and multiplies the probability by 1000 to give the odds, 600 to 1, that this tomb belonged to the Holy Family.
I remain unconvinced that this figure is in any way meaningful. Suppose the average tomb contains six ossuaries, and thus six names. The chances of the tomb containing "Jesus son of Joseph" will--naively, at least!--jump from 1 in 190 or .005 (as given in the PDF, as a probability of occurrence among names) to 1-(189/190)6=0.031 or only about 1 in 32 (as a probability of occurrence among tombs), a substantial increase. Analyse the data like that and you'll get totally different results, and the coincidence of names will start to seem a lot less significant.
Do I think this 1 in 32 figure is more meaningful than the 1 in 190 used in the analysis? Not really. Without more data on how many ossuaries one finds in the average tomb and how various names tend to be correlated within a tomb (names are often handed down through families, after all; it wouldn't be too surprising at all if a Jesus son of Joseph named his son after his father) and how many tombs there actually are or were in Jerusalem, none of these numbers means a gosh darned thing.
A Canadian documentary filmmaker will reveal at a news conference Monday that he has strong evidence a group of burial boxes unearthed in Jerusalem belonged to Jesus Christ and his family.The discovery could have profound implications 2,000 years after the boxes were placed in the ground, shaking the foundations of modern faith and raising Da-Vinci-Code-like speculation that Jesus had a child with Mary Magdalene.
"It's mind boggling. It's an altered reality," Toronto documentary director Simcha Jacobovici told the Star last week.
...Except that, when you read the rest, it all starts to sound a bit flimsy. They found a grand total of ten ossuaries and three skulls. Six of the ossuaries had names on them, including a "Jesus son of Joseph" and a "Mariamne", a Grecified form of Mary. The filmmakers claim that DNA tests indicate that this Jesus and this Mary were unrelated; they presume that they must have been married, and that this Mary was the Biblical Mary Magdalene. So far, so good, yes? But...
"The names that are found on the tombs are names that are similar to the names of the family of Jesus," [skeptical Bar Ilan University archaeologist Amos Kloner] conceded. "But those were the most common names found among Jews in the first centuries."
And yet...
In The Lost Tomb, however, University of Toronto statistician Andre [actually Andrey] Feuerverger calculates that while the names are common, the chances of them being found together are 600 to one.
What is a gender-unspecific colloquial term for person to think?
Don't answer that, because I'm going to tell you what to think right now.
The quotation here is ambiguous, and without a certain familiarity with probability theory it's easy for the average reader to become confused. Until Dr. Feuerverger reveals more about his methodology, the figure is meaningless. Are these odds supposed to represent the probability that, purely by random chance, this combination of Biblical names would occur together in any given tomb? Or are these odds supposed to represent the probability of finding these names together in any tomb anywhere in Jerusalem? These are very different quantities, and since I'm a mathematician I'd like to explain how and why this is so.
Let's suppose that this quote has its plainest English meaning, that the odds of finding this combination of (very common!) names together in a tomb is 600 to 1. If there were exactly one tomb in all of Jerusalem, and you popped it open to find these names, you'd be gobsmacked (lit. "punched in the mouth by the jewelled hand of Surprise"). "Mehercule!" you'd exclaim, "my mouth is bleeding like a bitch in heat. I hate you, Surprise. Oh and by the way that's pretty crazy, that whole Jesus thing, you know? Wow, man. Like, wow. Far out. I think you loosened a tooth. I need a Valium."
"But wait!" you'd hear as the sandy plains of Metaphor resonated to my firm and commanding (yet paradoxically high-pitched and piping) call. "There was more than one tomb in Jerusalem. Come, o person of indeterminate age and gender identity. Come and seek ye Truth in my transcendent Temple of Basic Mathematics."
Suppose that there were two tombs in Jerusalem, and that the odds of any one tomb containing this combination of names was indeed 600 to 1, or 1/600. Then the odds of finding any other combination of names, even no names at all, will be 599/600: the probability of finding something is exactly 1. 599/600 is, we can all agree, a very, very large probability. But if we want to compute the odds or probability of finding this particular combination of names in either of our two tombs (and we don't care which), how shall we proceed? Call this probability P. Now let Q be the probability of investigating both of our tombs and finding that neither has this desired combination of names inscribed in it. We must have that P+Q=1, since we must find something, and either we'll find the names we want somewhere or we won't. Each tomb is independent; the odds of finding certain names in one tomb, we can assume, are independent of the odds of finding any other names in any other tombs. (This is a reasonable assumption of randomness in the overall layout of the tombs.) Now, if we have two tombs, the probability is 599/600 that each tomb separately does not contain our names. The probability Q that both do not contain our names will be (599/600)2, which is still quite large, but--and this is the important bit!--not nearly so large as it was. Multiplying together numbers that are all less than 1 will always give you something even smaller. Which means that P, the probability that one or the other of the tombs will contain by random chance our names, will be more than the 1/600 we naively expected, when we have a sample of two tombs to investigate. In fact, we'd have P=1-Q=.003, or about 330 to 1. The more tombs there are in Jerusalem, we see at once, the more likely it is that purely by random chance one of them will contain this particular collection of names. In order to truly estimate P, we need a rough estimate of how many tombs there are to search.
According to the State of Israel, there are "hundreds" of tombs known in Jerusalem dating from the 2nd century BC to the 1st century AD, which is the historical period from which the supposed tomb of Jesus dates. These typically contain ossuaries and bones, like the tomb in question. In fact, "thousands" of ossuaries have been found. We can assume that many more tombs did at one time exist, but over the last 2000 years some have been lost or destroyed. Let's be incredibly conservative. Let's assume there are only 300 tombs from the correct period in all of Jerusalem. The probability Q that none of these contain our collection of Jesuitical names is (599/600)300=.61. This means that the probability of finding these Biblical names together purely by random meaningless chance is P=1-Q=.39=39/100, or only about 2.6 to 1! And when you put it like that, that's not so unlikely at all, is it? Unlikelier things happen all the time and we never bat an eye. And this was a conservative estimate. If there are 500 tombs in Jerusalem to examine, the odds rise to P=.57 or about 1 to 1.77, which is better than even. In this case we should be more surprised not to find these names than we would be to find them!
In plain language, no matter how improbable any desired outcome to any given event (like reading the names in a tomb) may be in isolation, if you repeat the event often enough it is quite likely that improbable things will happen purely by chance, with no deeper meaning whatsoever. As the poet once said, "It's a funny old world, innit?"
Consider too the other possible interpretation of the quote. Suppose the statistical analysis in question already considered this point, and that the odds of finding these special names in any given tomb are much, much wilder, to give an honest 600 to 1 chance of finding them by chance in any tomb in all of Jerusalem. Pretty improbable, eh? Now consider though that there is more to Biblical Judea than just Jerusalem. I can find no estimate (without unduly exerting myself) for the number of burial sites in all the region dating from the correct period, but similar reasoning must apply. While the odds of finding these names in Jerusalem may be high, the more sites one considers, the lower the odds will get. It's much more likely that the names will be found together somewhere, and if it happens to be in Jerusalem..."It's a funny old world, innit?"
Thus, much as I would like to have the bones of Jesus Himself to throw into Christians' metaphorical fa(e)ces with a sarcastic "This guy isn't looking so hot; you may have to pray a little louder to get his attention," I must regretfully conclude that, unless the investigators have some really whiz-bang evidence that hasn't leaked yet, this is all probably a load of fuss over nothing.
Like most of religion...
(26-02-07) More today on this from the Guardian, following a press conference. It all sounds like a lot of fuss over nothing. Apparently the only DNA testing done was mitochondrial, which only shows that this Jesus and this Mariamene were unrelated through the maternal line. She could've been his wife, but she could also have been his half-sister, or the wife of someone else buried in that tomb, or...anything, really. The 600-1 odds get repeated again, still no more clearly or helpfully. Journalists are so useless when it comes to covering numbers...
(27-02-07) More details emerge, and I remain dubious.
...by Steely Dan...
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This is the day You call me a fool [Chorus] My back to the wall I crawl like a viper [Chorus] This is the night [Chorus] |