Statistics and The Jesus Family Tomb
(March 3, 2007) This past week, Simcha Jacobovici and Charles Pellegrino launched a new book titled "The Jesus Family Tomb: The Discovery, the Investigation, and the Evidence That Could Change History." They'll follow it up with a documentary to be shown on the Discovery Channel.
It's a fascinating book. I grabbed it as soon as I could and read it carefully to see what the case is. I'll say right away that I came to like Simcha Jacobovici very much while reading the book. His intellectual curiosity launched this investigation, and he clearly loves a great puzzle.
There are folks who want to make Simcha the bad guy here, as if he somehow set out to demolish Christianity by cooking up some evidence. I don't get that impression from reading his story or watching him on video. He's clearly passionate about this story and interested in getting at the truth.
This is a BIG story! A bone-box was found in Jerusalem with the name "Jesus son of Joseph!" Right nearby were nine other bone-boxes. Five of them had names on them, and those names included Mary twice, Joseph, Judah, and Matthew. We know that Jesus had two brothers named Joseph and Judah and his grandfather was named Matthew. Furthermore, two of his disciples were also named Judah and one was named Matthew. Isn't that an awfully big coincidence? What if this Jesus is the REAL Jesus of Nazareth? Why didn't the archaeologists pursue this with a little more interest?
After reading the book carefully, I believe there are some serious problems with the case that the authors have made. I will not comment much here on the archaeological or lingustic issues. Those have been discussed already by various scholars. I'll refer you to Prof. Ben Witherington's blog. Dr. Witherington is a noted Jesus scholar who coauthored a book just a few years ago on another major archaeological find -- the alleged bone-box of James, the brother of Jesus.
In this article, I'll focus on the statistical analysis described in the book The Jesus Family Tomb. There, the authors explain why they believe that the odds are 600 to 1 that the tomb they found contained the bone-boxes of Jesus of Nazareth, his mother Mary, his "wife" Mary Magdalene, his "son" Judah, his brother Joseph, and one other person named Matthew who might be either a disciple or a family member. The book describes a "Jesus Equation" that defines this probability.
I believe that the statistical calculations need to be done differently. I am not here to cast aspersions on Mr. Jacobovici or Mr. Pellegrino or the statistician they asked to do their calculations, Dr. Andrey Feuerverger. Name-calling solves nothing. What I want to do is to redo the calculation in a way that I believe answers the fundamental question more accurately.
And what is the fundamental question? That's very important. In science, getting the right answer is a whole lot easier when you start with the right question. Years ago, when I wrote my book on the alleged Bible code, I found time after time in which the Bible coders had asked the wrong question and then answered it correctly. They concluded that they had found powerful evidence that God encoded secret messages in the Bible. But I believe they were wrong, because they asked the wrong question.
The Fundamental Question
Here is the fundamental question: We have found a bone-box containing a man named "Jesus son of Joseph." We have found with it five other bone-boxes containing two women named "Mary" and three men bearing the names of brothers or disciples of Jesus of Nazareth. One of the bone-boxes contains the son of the Jesus of the tomb. Based on this information, what is the probability that the Jesus of this tomb is Jesus of Nazareth?
I'll explain later why this is the correct question to ask. I'll also explain why it's a better question to ask than the ones that Simcha Jacobovici and Charles Pellegrino asked their statistician.
First, let me show how to answer the question. As much as possible, I'll use the same numbers as those used in The Jesus Family Tomb, because part of their calculation is quite reasonable.
Those numbers, in fact, can be found in another book that appeared a few years ago, The Brother of Jesus, by Hershel Shanks and Ben Witherington III. Hershel Shanks is the editor of Biblical Archaeology Review. Ben Witherington III is a noted scholar of the historical Jesus, and is the author of Jesus The Sage, among other books.
On page 56 of The Brother of Jesus, a table is listed showing how common various men's names were in first-century Jerusalem. The table is based on data from Rachel Hachlili's article, "Names and Nicknames of Jews in Second Temple Times," published by the Israel Exploration Society in 1984 in volume 17 of Eretz-Israel.
Here is the table, using the usual English equivalents for the Hebrew and Aramaic names:
The interpretation of this table is the following. If you were in ancient Jerusalem and walked up to some randomly chosen man on the street, the probability is 14% that his name would be the Hebrew or Aramaic equivalent of Joseph. The probability is 9% that his name would be the Hebrew or Aramaic equivalent of Jesus in one of its forms. (There are several different forms for many Hebrew names, just as there are for English names. For example, Robert, Rob, Robby, Bob, and Bobby are all different forms of the same name.)
So if you walked up to a random man in Jerusalem, the probability that his name would be Jesus and that his father's name would be Joseph is about 1.26%. You get this number by multiplying 9% by 14%.
We know that these bone-boxes were used in Jerusalem for only a short stretch of time in history -- roughly from 20 B.C. to A.D. 70. One can then estimate the total number of men in Jerusalem who lived during that time. That number is estimated in the book The Brother of Jesus, page 58, to be about 80,000 men. This is a reasonable number and we'll use it in our estimates.
So now we can estimate the number of men in Jerusalem who would have been named "Jesus son of Joseph". The number is 1.26% of 80,000 men, which works out to 1008. Remember, this is an estimate. How good is this estimate?
That is easy to answer. We would expect the true number of such men, using the usual laws of statistics, to be between 900 and 1100 men. (We compute the "standard deviation" of our estimate to be the square root of 1008, which is about 32. With extremely high probability, the true number of men should be within 3 standard deviations of our estimate of 1008. So, in round numbers, we can be VERY confident that there were between 900 and 1100 men in Jerusalem named "Jesus son of Joseph" or some variation of that name.
The next step is a little more complicated. We know that all 1008 of those men died and were buried somewhere. Some were put in bone-boxes, some were tossed to the wolves, some were laid to rest in other ways. We know that at least one of them ended up in a tomb in Jerusalem in the company of five other named bone-boxes, and those bone-boxes bore some extremely interesting names. There were two women named Mary! (Of the women close to Jesus of Nazareth, three were named Mary: his mother, Mary Magdalene, and Mary of Bethany.) Three of the bone-boxes bear the names of brothers or disciples of Jesus of Nazareth. Coincidence or not?
The standard way to answer this question in statistics is as follows: Let's imagine that all 1008 of the men named "Jesus son of Joseph" were buried with 2 women and 3 men. Compute the probability that the 2 women would both be named Mary AND that the 3 men would have names of Jesus' brothers or disciples.
The first part of the question is very easy. Mary was an extremely common name in Jerusalem. Approximately 21.4% of all women in Jerusalem bore some variation of this name. So if a man were buried with two female relatives, the probability is about 4.6% that BOTH would be named Mary. (We get this number by multiplying 21.4% by 21.4%, once for each of the two Marys.) So of the 1008 men named "Jesus son of Joseph" whom we are burying with 2 females, we would expect that 46 of these men would be buried with two Marys.
Now we have to calculate the second part of the question. If we ALSO bury all 46 of those men with 3 males, how many of them will be buried with 3 men whose names are either the brothers of Jesus of Nazareth or one of the twelve disciples? This is a little more complicated, and we can actually ask it in three different ways. Two of the three men in the tomb bore names of the BROTHERS of Jesus (Judah and Joseph). Two of the three men in the tomb bore names of the DISCIPLES of Jesus. (Judah and Matthew). All three of the men in the tomb bore names that were EITHER brothers of Jesus OR disciples of Jesus. What are the odds of each of those three cases?
Let's make some tables that add up the probabilities for the names of Jesus' brothers and for his disciples:
What this means is that if you went up to a random man on the street in ancient Jerusalem, the odds are 47% that his name would be the same as one of the four brothers of Jesus!
|Other disciples||Very low|
What this means is that if you went up to a random man on the street in ancient Jerusalem, the odds are 48.2% that his name would be the same as one of the twelve disciples of Jesus!
|Disciple or Brother||Percentage|
|Other disciples||Very low|
So if you went up to a random man on the street in ancient Jerusalem, the odds are 62.2% that his name would be the same as one of the twelve disciples of Jesus or one of his brothers!
Now let's return to our questions. We'll answer them each in turn. (The calculations use the "binomial distribution" from probability theory, and I am not going to explain that here. I'll just say that any statistician would apply this distribution to solve this problem when it's set up this way.)
- If we have 3 men in bone-boxes, what is the probability that at least 2 of those 3 men have names of the brothers of Jesus? Answer: 45.5%. (The odds are 35.1% that 2 of them match, and the odds are 10.4% that all 3 match.)
- If we have 3 men in bone-boxes, what is the probability that at least 2 of those 3 men have names of the disciples of Jesus? Answer: 47.3%. (The odds are 36.1% that 2 of them match, and the odds are 11.2% that all 3 match.)
- If we have 3 men in bone-boxes, what is the probability that all 3 men have names of either disciples of Jesus or brothers of Jesus? Answer: 24.1%.
Now we can answer our main question. Remember, we had 46 men named "Jesus son of Joseph" who are buried with a pair of Mary's. If we bury all of those with 3 randomly chosen male family members and friends, we expect the following:
- About 21 will be buried with at least 2 men whose names match the brothers of Jesus.
- About 22 will be buried with at least 2 men whose names match the disciples of Jesus.
- About 11 will be buried with 3 men whose names match either the disciples of Jesus or the brothers of Jesus.
The conclusion then is that one would expect at least 11 men to be buried with a set of other people that meets or beats the "amazing coincidence" found for the Jesus of the tomb. [Click here to read the rest of the article ...]