[donaldscrankshaw] Donald: A little statistics and the tomb of Jesus
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Sat Mar 3 23:41:01 EST 2007
Posted by Donald:
A little statistics and the tomb of Jesus
http://www.donaldscrankshaw.com/posts/1172965954.shtml
Have you been following the story of the Tomb of Jesus? I haven't been
following it in detail, I'll admit, just reading the odd blog post
[1]here and [2]there. What I'm finding, however, is that a lot is
being read into a rather crude back-of-the-envelope calculation, one
which I'm fairly certain is wrong. Let's put this in perspective.
In a tomb discovered near Jerusalem, there are a number of ossuaries
(bone boxes), inscribed with names. This is nothing unusual. Something
on the order of a thousand tombs have been discovered in the area. The
archeology based on them tells us a lot about the naming conventions
in 1st century Judea. This particular tomb, however, contains
ossuaries inscribed with the names Yeshua bar Yehosef (Jesus son of
Joseph), Yose (an abbreviated form of Joseph), Maria (Mary), and
Mariamne (an odd form of Mary). There were also the names Matia
(Matthew) and Judah the son of Jesus. Now, all of these were very
common names in 1st century Judea. So common, in fact, that 1 out of
every 190 men were named Jesus the son of Joseph. Now Cameron has
produced a documentary, arguing that although the names were common,
the odds of finding this particular combination of names in one tomb
are so miniscule, that this must be the family tomb of the Jesus in
the gospels. To support his argument, there's the aforementioned
"back-of-the-envelope calculation." With a blog called "Back of the
Envelope," I am, as you'd imagine, all for back-of-the-envelope
calculations, especially the crude kind. I do think that if you're a
world class statistician putting your reputation on the line for a
high-publicity documentary purporting to disprove the world's largest
religion, you ought to maybe put a mite more effort into it. So let's
take a look at the calculation involved, conveniently transcribed from
the documentary's [3]flash website by [4]StatGuy:
Click on âEnter the Tombâ, immediately above tomb photo. When the
next page has loaded, click on âSupporting Evidenceâ at the bottom
right of the main window. When the next page has loaded, click on
âStatistical Evidenceâ, the fourth item in the list to the left of
the main text.
This is the full text:
Statistics Overview
Dr Andrey Feuerverger, Professor of statistics & mathematics at the
University of Toronto, has concluded A [sic] high statistical
probability that the Talpiot tomb is the Jesus Family tomb.
In a study, Feuerverger examined the cluster of names in the tomb.
This involved multiplying the instances that each name appeared
during that time period with the instances of every other name.
To be conservative, he then divided the number by the statistical
standard of 4 (or 25%) to allow for unintentional biases in the
historical sources.
He then further divided the results by 1,000 to account for all
tombs that may have existed in First Century Jerusalem.
Taking into account the chances that these names would be clustered
together in a family tomb, this statistical study concludes that
the odds â on the most conservative basis â are 600 to 1 in favor
of this being the JESUS FAMILY TOMB. A statistical probability of
600 to 1 means that this conclusion works 599 times out of 600.
Statistics Tables
Frequency of names:
Jesus Son of Joseph: 1 in 190
Mariamne: 1 in 160
Matia: 1 in 40
Yose: 1 in 20
Maria: 1 in 4
Initial Computation: 1/190 x 1/160 x 1/40 x 1/20 x 1/4 =
1/97,280,000
Second Computation: Eliminating Matia since he is not explicatively
[sic] mentioned in the Gospels:
1/190 x 1/160 x 1/20 x 1/4 = 1/2,400,000
Third Computation: Adjusting for unintentional biases in the
historical sources:
2,400,000 / 4 = 600,000
Fourth Computation: Adjust for all possible First Century Jerusalem
Tombs:
600,000 / 1,000 = 600
Probability Factor = 600 to 1
There are a number of problems with this.
First, much is made that Mariamne is a distinctive form of Mary
referring to Mary Magdalene, and that Mary Magdalene was the wife of
Jesus. Unfortunately for the documentary, this particular belief has
[5]no ancient pedigree. It can't be traced back to the gospels, or any
of the early Christian writings or traditions. Not even the Gnostic
gospels, such as the third century [6]Gospel of Phillip, specifically
make that claim. In fact, it seems to be an entirely modern invention
dating back to the pseudohistorical book "[7]The Holy Blood and the
Holy Grail." It's also questionable whether Mariamne is, in fact, a
distinctive name for Mary Magdalene. The gospels always use Maria or
Mariam, and the use of Mariamne, as a variant of the Hellenized form
Mariamme, doesn't appear until the Gnostic gospels in the late second
century, and even there it doesn't appear to be a unique name for Mary
Magdalene. Further, the name on the tomb is not Mariamne, but
Mariamenou, which [8]Richard Bauckham convincingly argues has a very
different etymology.
The second may be a simple misunderstanding on my part, but several
references point out that Yose is an abbreviated form of Joseph. If
that is the case, is there good reason to believe that the Joseph that
Jesus is the son of is not Yose? If thatâs the case, the presence of
Yose is most definitely not an independent variable, and should not be
included in the probability calculation. Finding Joseph, Jesus the son
of Joseph, and Judah the son of Jesus all in the same family tomb
really only gives us one independent variable, Jesus son of Joseph, to
connect to the Jesus of the Bible. Now, it is true that Jesus's
brother was referred to as Yose in the gospels, so it may be argued
that it is unlikely that Yose and Joseph are the same person. However,
they are still related names, and having a Yose and a Joseph in the
same family are still not independent probabilities.
That, however, is archeology, genealogy, and etymology, and I promised
you a little statistics. You'll have to bear with me, as I explain the
problems with the back of the envelope calculation above, but the
basic problem is that the expert, Dr. Feuerverger, treats as a
permutation what should really be a combination. Okay, those terms are
not entirely mathematically accurate here, but let me try to explain:
([9]show very long explanation)
Suppose you have a bag with an infinite number of marbles, one-third
of which are red, one-third of which are green, and one-third of which
are blue. Now draw three of them. What are the odds you get a red, a
green, and a blue one? Well, calculating it the way Dr. Feuerverger
has, it'd be 1/3*1/3*1/3, or 1/27, right? Except that this is wrong.
Those are the odds that you'd draw a red marble, then a green marble,
than a blue marble. What if you drew a blue marble first, then a red,
then a green? You'd still have all three. There are a couple of ways
of calculating it: one is just to sum up all the possible ways you can
get all three marbles, then multiply the possibility of each. There
are six different possibilities that give you all three: RGB, RBG,
BGR, BRG, GRB, GBR. So the odds are 6/27, or 2/9. Now let's make the
problem more interesting. Suppose you draw four marbles. What are the
odds that in that draw you'll have at least one red, one blue, and one
green marble? Well, now it's 1/3*1/3*1/3*1/3 = 1/81, right? Well, no,
that's the possibility of each permutation, but now there are more
permutations that work. A lot more:
RRGB RRBG RBGR RBRG RGRB RGBR
RGGB RGBG RBGG RBBG RBGB RGBB
GRGB GRBG GBGR GBRG GGRB GGBR
GRRB GRBR GBRR GBBR GBRB GRBB
BRGB BRBG BBGR BBRG BGRB BGBR
BRRG BRGR BGRR BGGR BGRG BRGG
That's a total of 36 possible outcomes, so 36/81 give 4/9. So how do
you perform this calculation without listing every possible
permutation? You start by determining how many you're interested in.
Although we draw four marbles, we only care about three, or we
calculate the odds to be 1/3*1/3*1/3*1 = 1/27 for each combination,
since we don't care about what the final marble would be. Now, we
decide how many possible ways we can distribute them and still get the
red, green, and blue. In this case, there are four different positions
where our red marble might be (we might draw it first, second, third,
or fourth), there are three different positions where our green marble
might be (since we've already decided where the red one will be), and
there are two different positions left for the blue, and finally, the
one we don't care about goes wherever is left. That's 4*3*2, or 24.
Wait a minute, that gives 24/27, or 8/9 and that's clearly not right.
Well, that's because we counted twice. Our fourth marble is going to
be red, green, or blue, meaning that whether we have RGBX, or XGBR, if
X=R, they're actually the same permutation. This sort of caveat is
what makes probability so dang difficult, so let's divide by two and
get 4/9, which is the result we got before. Note that this factor of
two can get smaller if the fourth marble chosen is not necessarily a
match for any of the others, approaching one when there's only a
slight possibility that more than one marble in the group will have
the same color (which is what we assume when we're talking about names
below).
([10]hide)
If you read the hidden explanation (hidden mainly because it's pretty
long), I think you see where this is going. If not, well, the bottom
line is that Dr. Feuerverger's calculation gives the correct result
for computing the odds that a man named Jesus son of Joseph has a
mother named Maria, a brother named Yose, and a wife named Mariamne,
respectively, whereas the archaeological find doesn't indicate what
their relationship is. The proper way of formulating the question is
if four people, at random, are buried together, what are the odds that
their names would be Jesus son of Joseph, Maria, Yose, and Mariamne,
which is the odds calculated (1/2,400,000)/2^4*(4*3*2*1). Wait a
moment, you ask. Where does the 2^4 come from? That's a normalization,
assuming that the odds are one in two that the person is either male
or female. In this formulation, you only improve the odds slightly, to
(1/1,600,000). Ah, but I'm not done yet. You see, there were more than
four ossuaries there: there were at least six, probably 10, and
possibly as many as thirty-five. Now the odds start to look better.
With six, the odds of finding this combination of names is 1/107,000,
with 10, it's 1/7,600, and with 35, it's 1/31. In other words, if you
find 1000 tombs (as Dr. Feuerverger assumes), each with 35 names on
ossuaries (which he does not), then there is a 99.9999999999994%
chance that one of them will contain this combination of names. There
should, in fact, be 30 tombs with this combination of names inside.
(The one thing that keeps this from happening is that most of the
tombs don't have that many names.)
Now, if you want to prove something, show me that these people are
connected in the way proposed by this presentation. Then, the odds
start to work out the way they suggest.
References
1. http://parablemania.ektopos.com/archives/2007/02/the_lost_tomb_o.html
2. http://magicstatistics.com/2007/03/01/our-bulging-how-not-to-do-statistics-file-just-filled-up-and-burst/
3. http://dsc.discovery.com/convergence/tomb/tomb.html
4. http://magicstatistics.com/2007/03/01/our-bulging-how-not-to-do-statistics-file-just-filled-up-and-burst/
5. http://en.wikipedia.org/wiki/Mary_Magdalene
6. http://en.wikipedia.org/wiki/Gospel_of_Philip
7. http://en.wikipedia.org/wiki/The_Holy_Blood_and_the_Holy_Grail
8. http://www.christilling.de/blog/2007/03/guest-post-by-richard-bauckham.html
9. file://localhost/var/www/powerblogs/donaldscrankshaw/posts/1172965954.html
10. file://localhost/var/www/powerblogs/donaldscrankshaw/posts/1172965954.html
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