# Mathematical Proof Jesus Is The Son of God

*From*: "gratis-_+_8_Sum_" <scribio_vide@xxxxxxxx>*Date*: Thu, 20 Aug 2009 20:38:44 -0700 (PDT)

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"He Is Not Here," Or Is He?

A Statistical Analysis of the Claims Made in The Lost Tomb of Jesus

By Jay Cost and Randy Ingermanson1

Introduction

In March, 2007 Emmy-winning filmmaker Simcha Jacobovici presented a

documentary, The

Lost Tomb of Jesus, that proffered a startling thesis: Jesus of

Nazareth, whom most Christians

believe rose bodily from the dead, was actually buried in a tomb in

the present-day East Talpiot

neighborhood of Jerusalem.2

As evidence for the thesis, Jacobovici enlisted the aid of University

of Toronto professor of statistics

Andrey Feuerverger, who, Jacobovici claimed, calculated the odds that

this is the Jesus

family tomb at 600 to 1.3

In the present paper we offer a critique of this statistic and an

alternative estimate. We argue that

Bayes' Theorem is the optimal way to calculate the likelihood that

this tomb belonged to Jesus of

Nazareth. We further argue that the estimate derived from Bayes'

Theorem is fairly insensitive

to a series of assumptions that can be altered as the vital debate

among historians and archaeologists

requires. Finally, making what we believe to be a set of reasonable

assumptions, we offer a

series of estimates of the likelihood that the Talpiot tomb belonged

to Jesus of Nazareth.

1 We are indebted to a number of people for useful discussions on this

topic. We gratefully acknowledge the input of

Steven Avery, Joe D'Mello, Mark Goodacre, Gary Habermas, Michael

Heiser, John Koopmans, Stephen Pfann,

John Poirier, Chris Rollston, James Tabor, David Tyler, and Ben

Witherington, III.

2 See Simcha Jacobovici. The Lost Tomb of Jesus. Discovery Network.

First Aired March 4, 2007.

3 In the aftermath of the documentary's release, Jacobovici and the

Discovery Channel modified their interpretation

of Feuerverger's mathematical computations. It is unclear to us

exactly what Jacobovici now believes that

Feuerverger's number demonstrates. However, it is nevertheless clear

that he believes now, as he did before the

updates made to the Discovery Channel's documentation, that

Feuerverger's number provides some analytical "purchase"

on whose tomb was discovered at the Talpiot site. In other words,

while we are not sure the exact nature of

the inference that Jacobovici draws about the tomb from the number, we

are sure that he is drawing some kind of

inference about the tomb ownership from the number. We disagree even

on this minimal point. We think that this

number is insufficient for any inference about the tomb, and we will

justify this disagreement in the course of this

essay.

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The Talpiot Discovery and the Documentary's Argument

In 1980, the Israeli Antiquities Authority excavated a tomb in East

Talpiot, a Jerusalem neighborhood.

Within the tomb, archaeologists discovered ten ossuaries, or bone

boxes used to intern

the deceased between the first century BCE and first century CE.4 Six

of the ossuaries had

names inscribed upon them - five in Aramaic and one in Greek. The

Aramaic inscriptions, when

translated into English, were "Judah son of Jesus," "Jesus son of

Joseph," "Jose" (a diminutive of

"Joseph"), "Mary" and "Matthew." Kloner (1996), following Rahmani

(1994), translates the

Greek inscription as "Mariamne [also called] Mara."5

In the documentary The Lost Tomb of Jesus, Jacobovici argues that four

of these names correspond

with the family of Jesus of Nazareth. "Jesus son of Joseph" might have

been a way to address

Jesus of Nazareth. Further, Jesus of Nazareth had a brother named Jose

and a mother

named Mary. Jacobovici further speculates that Kloner (1996) and

Rahmani (1994) have mistranslated

the Greek inscription. He asserts that the correct translation is

"Mary [also called] the

Master." He goes on to argue, using the 4th century apocryphal

document called The Acts of

Philip, that this is a name by which Mary Magdalene might have been

known.

It is from this cluster of names that Professor Feuerverger derives

his figure. To date, Professor

Feuerverger has not submitted a formal paper for either public viewing

or scholarly vetting.6

Accordingly, his statistical intuitions must be gleaned from the

popular consumption book, The

Jesus Family Tomb,7 and the documentary's website.8 The formula

offered in the latter is as

follows:

4 See Craig Evans. Jesus and the Ossuaries. Waco, TX: Baylor

University Press, 2003.

5 See Amos Kloner. "A Tomb with Inscribed Ossuaries in East Talpiyot,

Jerusalem," Atiquot 29, 1996, and L.Y.

Rahmani. A Catalogue of Jewish Ossuaries in the Collections of the

State of Israel. Israel: Israeli Antiquities

Authority / Israel Academy of Sciences and Humanities, 1994.

6 Currently, Feuerverger has made an explanation of some of the

assumptions inherent to his calculation available on

line. See Andrey Feuerverger. "The Tomb Calculation, Letter to

Statistical Colleagues. March 12, 2007."

http://fisher.utstat.toronto.edu/andrey/OfficeHrs.txt. Accessed March

26, 2007. Note that Jacobovici and Pellegrino

(2007) indicate that Feuerverger has submitted a paper to scholarly

review, but the above-referenced letter from

Feuerverger indicates that this is not the case. Personal

correspondence between Feuerverger and one of the authors

confirmed that Feuerverger's letter is correct on this point.

7 See Simcha Jacobovici and Charles Pellegrino. The Jesus Family Tomb.

San Francisco: HarperCollins, 2007.

8 See "The Lost Tomb of Jesus: The Discovery Channel."

http://dsc.discovery.com/convergence/tomb/tomb.html.

Accessed March 26, 2007.

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Initial Computation

Jesus Son of Joseph:

1 in 190

Mariamne:

1 in 160

Matia:

1 in 40

Yose:

1 in 20

Maria:

1 in 4

= 1 in 97,280,000

Second Computation

(Matthew Eliminated)

Jesus Son of Joseph:

1 in 190

Mariamne:

1 in 160

Yose:

1 in 20

Maria:

1 in 4

= 1 in 2,400,000

Third Computation

(Unintentional Historical Biases Factored

In)

2,400,00 / 4 = 1 in 600,000

Fourth Computation

(All Potential Tombs Factored In)

600,000 / 1,000

= 1 in 600 = "Probability

Factor"

Critique of the Statistical Method

The above method, as we are able to interpret it, suffers from several

important defects that prevent

any valid inference about the family in the tomb from being drawn.

These defects can be

grouped into two types: theoretical and computational.

Theoretical Defects

This method generally lacks probative value. That is, the "probability

factor" does not speak to

the likelihood that Jesus of Nazareth was buried at this tomb. It is

simply an estimate of the

probability of finding these four names - "Jesus son of Joseph,"

"Mariamne," "Jose" and

"Maria" - in all tombs with exactly four inscribed names. It is does

not speak to whether this

family is actually the family of Jesus of Nazareth. This is because it

fails to consider two important

factors.

It does not consider the unlikelihood of ever finding Jesus of

Nazareth's tomb in the first place.

It might be a unique occurrence to find these four names, but the

uniqueness of this occurrence

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must be understood in the context of the uniqueness of finding Jesus

of Nazareth at all. For instance,

if there were a 1 in 1 billion chance that we would find Jesus of

Nazareth's ossuary, the

probative value of the unadjusted probability in the above table,

which shows a 1 in 2.4 million

likelihood, would be severely diminished. Thus, this other probability

must be taken into account

before any inferences can be drawn. To fail to do so is to commit what

is known as the

prosecutor's fallacy. The unlikelihood of finding the particular

evidence that has been found

must be weighed against the unlikelihood of making the match that the

documentarians wish to

make.

Second, it assumes that there is no doubt that Jesus of Nazareth - if

he was buried in a tomb -

would certainly be buried with these individuals. The implication here

is that this is a "unique"

match with the family of Jesus of Nazareth. However, this hypothesis

is underdetermined. Even

if we accept the uniqueness of the names, and there is good reason not

to, there are reasons to

expect Jesus of Nazareth to be buried with another cluster of names.

This estimation, further,

cannot be taken in the context of the four matches. It must, rather,

be taken in the context of all

six matches - for this "Jesus son of Joseph" was not interned with

three other known people. He

was interned with five. Thus, we should inquire whether there is

reason to expect that Jesus of

Nazareth would be interned with these five names.

Computational Defects

The calculation itself also suffers from four computational problems.

First, there are six inscribed ossuaries in the tomb. If the intention

is to discover the probability

of finding these four names in a given tomb of this type, it should be

calculated with a mind to

the number of inscribed ossuaries in the tomb and not to the number of

"matches" that one

wishes to make. For instance, if there are six inscribed ossuaries,

the chances of finding these

four names should be calculated not as the chance of finding the four

names in four attempts, as

is the case here, but of finding these four names in six attempts.

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Second, the factor that "adjust[s] for unintentional biases in the

historical record" seems to be ad

hoc. This, it is explained in Jacobovici and Pellegrino (2007), is

intended to account for the

family members who might have been placed at the tomb but are in fact

not there - namely the

brothers James, Simon and Jude. However, it is unclear to us why a

factor of four is sufficient

for dealing with the "absences" from the tomb. It seems more

appropriate to include the factor

we mentioned above - an evaluation of the likelihood that Jesus of

Nazareth would be interned

with this particular cluster of names. Hopefully, at a future date

Professor Feuerverger will have

the opportunity to clarify his justification.

Third, the documentarians hypothesize that Mary Magdalene was interned

in one of the ossuaries,

and that "Mariamne [also called] Mara" is a mistranslation that, when

corrected, points toward

her. However, they do not offer a convincing argument as to why this

is expected to be the

case. At best, they provide a potential connection between the two.9

This connection should be

critically evaluated before the name "Mariamne [also known as] Mara"

is included in the computation.

Absent this inquiry, the statistical computation should be limited to

the three known

matches between the tomb and Jesus of Nazareth's family. Including

"Mary Magdalene" in the

statistical analysis heavily biases the probability estimate toward

the hypothesis.

Fourth, the computation fails to account for the potential bias that

occurs with the consideration

of the name "Jose," which Jacobovici takes as a rare and highly

significant reference to Jesus of

Nazareth's brother. It fails to consider that "Jose" has been found

given the discovery of a reference

to "Joseph." It is reasonable to believe that "Jesus son of Joseph"

and "Jose" might not be

independent events - namely, that "Joseph" might have generally been a

family name. Accordingly,

when a Joseph is found in a family, one is more likely to find another

Joseph, or a person

with a variant of the name, such as "Jose." Thus, we should expect P

(Jose|Joseph) > P(Jose).

Unfortunately, the historical record is not sufficiently detailed to

offer conditional probabilities

such as the one that we have in mind. However, this is not to say that

the computation's incorporation

of "Jose" is optimal. While it might be impossible to estimate the

precise difference be-

9 For this argument, they rely upon the research of François Bovon.

However, in a recent article, Bovon argues: "I

do not believe that Mariamne is the real name of Mary of Magdalene.

Mariamne is, besides Maria or Mariam, a possible

Greek equivalent, attested by Josephus, Origen, and the Acts of

Philip, for the Semitic Myriam." See François

Bovon. "The Tomb of Jesus." The Society of Biblical Literature Forum.

http://sblsite.

org/Article.aspx?ArticleId=656. Accessed March 26, 2007.

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tween P(Jose|Joseph) and P(Jose), it seems intuitive to expect that

the former is greater than the

latter. Thus, Jacobovici and Feuerverger are likely wrong to take the

name "Jose" to occur with

less frequency than the name "Joseph" (which they do). They should,

instead, expect a "Jose" or

some variant to occur in a tomb like this, i.e. one that was used by a

family known to have a "Joseph"

within it, with a greater likelihood than a "Joseph" would in the

general population.

Even with these critiques, the above figure represents an important

step in calculating the probability

that this tomb belongs to Jesus of Nazareth. Jacobovici and

Feuerverger are to be credited

for astutely recognizing that the other names in the tomb are the key

components in determining

whether the Talpiot tomb once held the remains of Jesus of Nazareth.

Building upon their intuition,

we propose a different, more comprehensive approach than they have

adopted.

Bayes' Theorem and the Jesus Tomb

Introduction

We propose the use of Bayes' Theorem to evaluate the likelihood that

this tomb belongs to Jesus

of Nazareth. Indeed, it is our intuition that Bayes' Theorem offers

the most direct way to answer

the question at hand. We also believe that Jacobovici's argument is

fundamentally Bayesian.

Jacobovici is interested in the extent to which the other names in the

tomb provide a clue to the

person interned in the "Jesus son of Joseph" ossuary. In other words,

his endeavor is to find a

conditional probability: given the other names in the tomb, what is

the likelihood that Jesus of

Nazareth is interned in the "Jesus son of Joseph" ossuary, what we

define as P(J|T). Meanwhile,

it is Jacobovici's intuition that the Talpiot tomb provides a close

match with what we would expect

in Jesus of Nazareth's tomb. That is, he believes that what we define

as P(T|J) is very large

- i.e., if we were assuredly to find Jesus of Nazareth's tomb, we

would expect many of these

names within it.

What Jacobovici has done, then, is define one conditional probability,

P(J|T), in terms of another,

P(T|J). This is a Bayesian argument. Unfortunately, as the last

section makes clear,

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Feuerverger's statistical analysis does not speak to this. It suffers

from two theoretical problems:

(i) any inferences drawn from his number will run afoul of the

prosecutor's fallacy;

(ii) it implicitly assumes an artificially high value of P(T|J).

What is required, then, is a reformulation and formalization of what

we take to be Jacobovici's

accurate intuitions.

Statement of the Problem

A tomb has been found in East Talpiot, Jerusalem, containing ten

ossuaries. Six of these were

inscribed with names, while four were not. The excavating

archaeologists estimated that the

tomb might have held up to 35 bodies. This was not based on any count

of bones within the

tomb. Rather, it was an estimate based on many similar tombs around

Jerusalem dating from the

same era, the first century.10

Two of the ossuaries are special and indicate a rudimentary family

tree. One is inscribed "Judah

son of Jesus" and the other is inscribed "Jesus son of Joseph." While

there is no proof that the

"Jesus" in these two inscriptions is the same man, that is the general

assumption, since a tomb

like this generally contained extended families over several

generations.

The immediate question to ask is whether the ossuary inscribed "Jesus

son of Joseph" might

have contained the bones of Jesus of Nazareth. The ossuary dates to

the first century and the

tomb lies within a few miles of the crucifixion site of Jesus of

Nazareth. What is the probability

that Jesus of Nazareth might be the Jesus of the tomb?

If that were all the information we had, then the answer would be

fairly easy to compute. Suppose

there were

EURO

NJ men in Jerusalem named "Jesus son of Joseph." The probability of

choosing

any one of these at random is clearly 1/

EURO

NJ .

10 See Kloner (1996).

8

We note that Jesus of Nazareth is not a randomly selected "Jesus son

of Joseph" from ancient

Jerusalem. We have more information about him than we do about the

other men named "Jesus

son of Joseph."

Most scholars accept the New Testament account that Jesus was buried

immediately after his

crucifixion in a tomb owned by Joseph of Arimathea, roughly three

miles from the East Talpiot

location of the alleged "Jesus family tomb." Nobody believes Jesus of

Nazareth is still in this

original resting place.

Christians generally believe that Jesus was physically resurrected

about a day and a half after his

death and that he eventually ascended to heaven. If that is not the

case, then he was instead reburied

elsewhere (perhaps a tomb such as this, or a common burial pit, or

something else). Conceivably,

he could have been transported some three miles away to the East

Talpiot tomb, but

that is not a sure thing. But neither is it a sure thing that he was

not.

The question of whether Jesus ascended to heaven is a faith-question,

which will be answered

differently by different people. The question of whether Jesus might

have been transported three

miles to East Talpiot for reburial is a historical question, which

will be answered differently by

different historians. In either case, there is a subjective element.

This appears to put us at an impasse. But does it really? We argue

that it does not. The subjective

element introduces uncertainty into the calculations, but science has

well-defined ways for

dealing with numerical uncertainties. Thus, while we might not be

capable of identifying an expected

probability value, we might nevertheless be able to identify the range

of values that this

probability might take.

There are several points in this calculation at which we will run into

"judgment calls" that depend

on subjective elements. We will encapsulate each of these points in a

"fuzzy factor" that is

strictly bounded. We will then carry out the calculations and show

that the final range of probabilities

is still bounded. We will now define the first "fuzzy factor."

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Define

EURO

F1 = "the probability that the body of Jesus of Nazareth was

transported to a tomb of the

type found at East Talpiot and featured in the documentary The Lost

Tomb of Jesus."

Obviously,

EURO

F1 is a subjective factor. Those who believe with certainty in a

physical resurrection

and ascension of Jesus will assign

EURO

F1 a value of zero. Those who believe with certainty that Jesus

was reburied in a trench grave near the site of the crucifixion will

likewise assign

EURO

F1 a value

of 0. Those who are willing to consider the possibility that he was

transferred a few miles away,

and that he might have ended up in a family tomb, will assign

EURO

F1 a non-zero value. Those who

consider the tomb a bad demographic or socio-political "match" for

Jesus of Nazareth's family -

for instance because the tomb might be a "middle class" tomb, etc -

would assign a low non-zero

value. Those who see the Talpiot tomb as a good potential match would

assign it a higher number.

EURO

F1 cannot be less than 0 or greater than 1, since it is a probability.

So

EURO

F1 is a bounded parameter,

and it is likely to have only limited effect on our calculations. We

can run calculations

with different values of

EURO

F1 when we complete our analysis to see what is the range of effects

it

can have.

We asked earlier for a first estimate of the probability that Jesus of

Nazareth is buried in the East

Talpiot tomb. We need some notation. Define:

J = The event that Jesus of Nazareth was buried in the East Talpiot

tomb.

~J = The event that Jesus of Nazareth was not buried in the East

Talpiot tomb.

P(J) = The probability that Jesus of Nazareth was buried in this tomb.

P(~J) = The probability that Jesus of Nazareth was not buried in this

tomb.

Obviously, since J and ~J are exclusive events, P(J) and P(~J) add up

to 1.

Then we have the following naïve estimates of P(J) and P(~J):

EURO

P(J) =

F1

NJ

P(~ J) =1- P(J)

We note that

EURO

NJ has been estimated by different scholars to be anywhere from a few

hundred up

to about 1,000.

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If this were all the information we had, then the tomb would not be

interesting since P(J) is very

small. However, the tomb also contains ossuaries bearing the names

"Mary," "Mary," "Matthew,"

and "Jose." We know that Mary was the name of the mother of Jesus of

Nazareth and the

name of several other women in the close circle of Jesus (including

Mary Magdalene, Mary of

Bethany, and probably others). Furthermore, one disciple of Jesus was

named Matthew and one

of his brothers was named Jose. These factors tend to strengthen the

case that the tomb might

belong to Jesus of Nazareth.

However, there is also some counter-evidence. One ossuary in the tomb

bears the name "Judah

son of Jesus." No record tells us that Jesus of Nazareth had any

offspring at all, much less a son

named Judah. We should note that no historical records explicitly deny

that Jesus had children,

but we would expect to have heard of progeny if they existed. Three

leaders in the earliest Jesus

community were his brothers James and Judah and his cousin Simon. This

indicates that the

family of Jesus played an important role in the early community. A son

would have played a key

role in this community had he existed. If Jesus had a son, history is

stunningly silent about it, for

no apparent reason.

So the problem then is the following: In light of these additional

five inscriptions, how does the

naïve estimate P(J) change? Will the "pro" evidence outweigh the "con"

evidence?

We will use a few simple techniques from statistics and probability

theory to estimate a revised

probability. A key element will be Bayes' Theorem. We will briefly

review Bayes' Theorem

next.

Bayes' Theorem

In probability theory, one often needs to compute a conditional

probability of one event, given

that another has occurred. This allows one to make inferences based on

partial information.

As an example, suppose two dice are thrown. The odds of rolling a 12

are quite low: 1/36.

However, if we are given information on the state of one of the dice,

we can make a revised es11

timate. If we are told that one of the two dice came up a six, then

the odds of having rolled a 12

are now revised to 1/6. However, if we are told that one of the dice

came up a three, then the

odds of having rolled a 12 are now revised to 0.

Let

EURO

E1and

EURO

E2be two events. We are interested in the probability that

EURO

E1 has occurred, given

that

EURO

E2 has occurred. This is called the conditional probability

EURO

P(E1 | E2) and is defined to be:

EURO

P(E1 | E2) =

P(E1 & E2 )

P(E2 )

One formulation of Bayes' Theorem then follows immediately:

EURO

P(E1 | E2)P(E2) = P(E1 & E2 ) = P(E2 | E1)P(E1)

We can rewrite this as:

EURO

P(E1 | E2) =

P(E2 | E1)P(E1)

P(E2 )

This is a powerful form of the theorem, but we will expand the

denominator by noting that either

EURO

E1 will occur or it will not. So it is easy to prove that

EURO

P(E2) = P(E2 | E1)P(E1) + P(E2 |~ E1)P(~ E1)

Then we get the fairly complicated-looking equation:

EURO

P(E1 | E2) =

P(E2 | E1)P(E1)

P(E2 | E1)P(E1) + P(E2 |~ E1)P(~ E1)

This is useful when we already have a naïve estimate

EURO

P(E1) and we want to improve it in view

of the observation of a second event

EURO

E2. Bayes' Theorem tells us how to make this improvement.

In the previous section, we made a naïve estimate

EURO

P(J) and we then asked how to improve this

estimate based on a set of other observations from the tomb. We will

denote the collection of

these other observations by the event T:

T = "All the rest of the information about the other five ossuaries".

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We are interested to know how this new information T changes our naïve

estimate P(J). In other

words, we want to know the probability that Jesus of Nazareth is

really the Jesus of the tomb,

given all the other information we have from the other ossuaries. That

is, we want P(J|T).

Bayes' Theorem then tells us that:

EURO

P(J |T) =

P(T | J)P(J)

P(T | J)P(J) + P(T |~ J)P(~ J)

Bayes' Theorem takes a bit of getting used to, but it corresponds to

Jacobovici's and our intuition.

For example, if Jesus of Nazareth were really buried in this family

tomb, we would expect

the other names in the tomb to correspond to his family members. That

is, we would expect

P(T|J) to be rather high. Whereas if Jesus of Nazareth were not buried

in the tomb, we would

expect the names in the tomb not to correspond well with his family

members. That is, we would

expect P(T|~J) to be rather low.

Bayes' Theorem tells us how to weigh the two cases against each other

to make the best decision

we can in light of the information we have. If new information were to

come to light, that would

change the calculation.

We have already shown in principle how to compute P(J) - the initial

naïve estimate that Jesus

of Nazareth is in the tomb. From that, we immediately get P(~J). So it

remains only to compute

the two conditional probabilities P(T|J) and P(T|~J). These are not

hard, and we will spend the

bulk of this article estimating these.

First, however, there are a few preliminary issues to work through.

Preliminaries to P(T|J) and P(T|~J)

First, we will deal with the issue of the ossuary "Judah son of

Jesus." If the Jesus of the tomb

were some randomly chosen man on the street, he would have a high

probability of having a son.

Most Jewish men of the period were married and did their best to obey

the commandment to be

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fruitful and multiply. We do not know the exact probability that any

given man would have a

son, but it is likely to be near 1.

That is not the case for Jesus of Nazareth. In all of history, nobody

seems to have ever postulated

that Jesus had a son. Dan Brown, in the DaVinci Code, followed a long

and hazy tradition

that postulates a daughter. Did Jesus of Nazareth have a son? We do

not know for sure. What

we can say is that he might conceivably have had a son but that he is

not more likely than a randomly

chosen man of Jerusalem to have had a son. So we can define another

"fuzzy factor" here

to incorporate this range of possibilities. Define

EURO

F2 as follows:

EURO

F2 = the relative probability that Jesus of Nazareth had a son

By "relative probability" we mean the ratio of the probability that

Jesus had a son to the probability

that any other man of Jerusalem had a son. We expect

EURO

F2 to be between 0 and 1. Different

historians will assign different values to

EURO

F2. We will see at the end of this calculation

whether it makes much difference what value you assign to

EURO

F2.

We also define

EURO

Pson-Judah to be the absolute probability that a randomly chosen man

of Jerusalem

would have had a son named Judah.

Then, by definition, the probability that Jesus of Nazareth had a son

named Judah is

EURO

F2Pson-Judah .

We will never actually need to compute

EURO

Pson-Judah . It will factor out of our equations completely,

leaving us with only the fuzzy factor

EURO

F2, which is nicely bounded between 0 and 1.

It is worth defining exactly what we mean by the event T. What we

really care about is the set of

all possible events like the set of names observed in the tomb. That

is, we want to consider all

sets of names that would generate the same level of surprise. We have

already dealt with the

surprises of two of the ossuaries. There remain four, containing two

women and two men.

What is surprising is that two of these had the names of members of

the immediate family of Jesus.

We found a Mary and we found a Jose. Each of those coincides with

names of known

members of the family of Jesus. We also found a second Mary, who is

known by DNA analysis

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not to be a member of the immediate family of Jesus. We also found a

Matthew, who is not in

the known immediate family of Jesus.

If we opened a random tomb in Jerusalem and found two women and two

men, what are the odds

that at least one of the women would be a Mary and at least one of the

men would have the name

of a brother of Jesus? That is the question that P(T|~J) will answer.

Likewise, if we had opened the actual tomb of the family of Jesus and

found the names of two

women and two men, we must also ask what are the odds that at least

one of the women would

be a Mary and at least one of the men would have the name of a brother

of Jesus. Neither of

these is a sure thing, even in the family tomb of Jesus. That is the

question that P(T|J) will answer.

In order to answer these questions, we need to know the probability of

drawing the names of

close family members of Jesus if we choose people from ancient

Jerusalem at random. We need

census data, and we do not have it. But we do have two surveys of

names from Israeli scholars,

Rachel Hachlili and Tal Ilan.11 Their numbers do not agree perfectly,

but they are reasonably

close to each other.

In the following table, we summarize the relevant data. Note that

names took many forms in ancient

Israel. We consider all variant forms to be essentially the same. So

the Hebrew/

Aramaic/Greek names Miriam, Mariam, Maria, Mariame, Mariamme,

Mariamne, Mariamene,

Mariamenon, etc., all count as Mary. Likewise, the variant forms

Yosef, Yehosef, Yosi,

Yoseh, Yosah, etc., all count as Joseph.

We will also assume that the probability of finding a "Jesus son of

Joseph" is obtained by multiplying

the probability of finding a "Jesus" by the probability of finding a

"Joseph". Note that

Jesus had four brothers, James, Simon, Judah, and Jose. Jose is a

variant form of Joseph.

11 See Rachel Hachlili. "Names and Nicknames of Jews in Second Temple

Times," Eretz Israel 17, 1984, and Tal

Ilan. Lexicon of Jewish Names in Late Antiquity: Part 1, Palestine 330

BCE-200 CE. Tubingen, Germany: Mohr

Siebeck, 2002.

15

Here are the probabilities that we will need:

Name Probability (Hachlili) Probability (Ilan)

Jesus 0.09 0.0411

Joseph 0.14 0.0921

Jesus son of Joseph 0.0126 0.0038

Simon 0.21 0.1024

Judah 0.10 0.0713

James 0.02 0.0179

Joseph 0.14 0.0921

Any Brother of Jesus 0.47 0.2837

Mary 0.214 0.254

Since we have two choices for the probability distributions of names,

we will need to run our

calculations twice, once for Dr. Hachlili's numbers and once for Dr.

Ilan's numbers.

We can now estimate the number of men in Jerusalem who might be named

"Jesus son of Joseph."

Suppose there were N people in Jerusalem, and suppose the practice of

burial in ossuaries

continued for g generations. The practice went on for about 90 years,

so g will be more than 1

but less than 3. Since half the inhabitants of Jerusalem were males,

we estimate the number of

men named "Jesus son of Joseph" to be:

EURO

NJ =

1

2

NgPJesusPJoseph

Estimating N = 80,000, g = 2, we find a value roughly between 300 and

1000.

We are now ready to compute P(T|J) and P(T|~J). The second of these is

a bit easier to compute,

so we will do it first.

Computing P(T|~J)

16

If we know for sure that the ossuary labeled "Jesus son of Joseph" did

not contain Jesus of Nazareth,

what are the odds of observing the other five ossuaries in the tomb?

That is quite easy to compute. There are three factors:

1) The probability of the "Judah son of Jesus" ossuary, which is

EURO

Pson-Judah

2) The probability of finding at least one "Mary" ossuary out of two

ossuaries containing

randomly chosen women.

3) The probability of finding at least one ossuary with the name of a

brother of Jesus,

out of two ossuaries containing randomly chosen men.

Define

EURO

PMary to be the probability of a randomly chosen woman being named

Mary. We can estimate

this using either Rachel Hachlili's data or Tal Ilan's data, given in

the table above.

Then the probability of a randomly chosen woman not being a Mary is

EURO

1- PMary. Likewise, the

probability that neither of two randomly chosen women will be a Mary

is

EURO

(1- PMary )2. Therefore,

the probability that at least one of two randomly chosen women will be

a Mary is

EURO

1- (1- PMary )2 .

Likewise, define

EURO

PBrother to be the probability of a randomly chosen man having a name

that

matches one of the brothers of Jesus of Nazareth. Again, we can

estimate this probability by

using either the Hachlili or the Ilan data. In either case, we

likewise compute the probability that

at least one of two randomly chosen men will have a name that matches

one of the brothers of

Jesus is

EURO

1- (1- PBrother )2.

Now we can put all this together to get what we are after:

EURO

P(T |~ J) = Pson-Judah[1- (1- PMary )2][1- (1- PBrother )2]

Computing P(T|J)

If we know for sure that the ossuary labeled "Jesus son of Joseph" did

contain Jesus of Nazareth,

what are the odds of observing the other five ossuaries in the tomb?

This is again fairly easy to

compute. As before, there are three factors:

1) The probability of the "Judah son of Jesus" ossuary, which is

EURO

F2Pson-Judah

17

2) The probability of getting at least one "Mary" ossuary out of two

ossuaries chosen

randomly from women in the extended family of Jesus.

3) The probability of getting at least one "brother" ossuary out of

two ossuaries chosen

randomly from men in the extended family of Jesus.

A new wrinkle comes in here. Since this is definitely the family tomb

of Jesus we are considering,

we need to make sure that the family of Jesus is actually in it. This

means that we should

ensure from the beginning that the tomb contains:

1) Mary, the mother of Jesus, plus a number of other unknown women

2) James, Simon, Joseph, and Judah, the four brothers of Jesus, plus a

number of other

unknown men

This should be obvious. When we say "this is the family tomb of

Jesus," what we mean is that

his immediate family is in it, plus his (unknown) extended family. The

intuition here is that all

immediate family members, except the father Joseph, would be expected

to be buried here.

However, as is the case with all family tombs - some family members

receive inscriptions while

others do not. Thus, our interest here is in estimating the

probability that the known family

members of Jesus of Nazareth's family would receive inscriptions in a

family of size 2n+2.12

Assuming that the extended family members have names that are

distributed according to Ilan or

Hachili, let us work out the consequences of all this. Besides "Jesus

son of Joseph" and "Judah

son of Jesus," we will assume that the tomb contains n men and n

women, but the distribution of

names will be slightly distorted, because we have stipulated a few

names. We can work out the

new distribution of names quite easily.

The expected number of women named Mary is now:

EURO

E(Mary) =1+ (n -1)PMary = nPMary + (1- PMary )

12 Implicit in this is the assumption that a named member of Jesus of

Nazareth's family is just as likely as a nonnamed

member of the family to receive an inscription. This assumption may or

may not correspond with reality.

However, the extent to which it does not would only be insofar as we

would expect the named family members to be

more likely to receive an inscription. If that is the case - if, say,

Simon is more likely than this "Matthew" to receive

an inscription - the probability that this is Jesus of Nazareth's tomb

will drop because it becomes more and

more unlikely that only 2 members of the known family would have an

inscription. Thus, this assumption - insofar

as it fails to correspond to reality - is favorable to Jacobovici's

thesis. This is important to note. We are offering a

critique of the hypothesis, but the critique itself is not predicated

on any assumption we have made. On the contrary,

our assumptions, where and when we are forced to make them, favor

Jacobovici's thesis and thus do not diminish

the analytical power of our critique.

18

This implies that the new probability for finding a Mary within this

family tomb of n women is:

EURO

PMary

* (n) = PMary +

(1- PMary )

n

This confirms what we intuitively expect. Within the family tomb of

Jesus, it is more likely to

find a woman named Mary. But the "Mary-enrichment" effect decreases as

the number of

women in the tomb increases.

Likewise, the expected number of men having names of the brothers of

Jesus is

EURO

E(Brothers'names) = 4 + (n - 4)PBrother = nPBrother + 4(1- PBrother )

This implies that the new probability for finding a man with the name

of a brother of Jesus

within this family tomb of n men is:

EURO

PBrother

* (n) = PBrother +

4(1- PBrother )

n

Again, this is intuitively clear. Within the family tomb of Jesus, it

is more likely to find a man

with the name of one of his brothers, but this "brother-enrichment

effect" decreases as the number

of men in the tomb increases.

We can now put all this together to compute the term we wanted all

along:

EURO

P(T | J) = F2Pson-Judah[1- (1- PMary

* )2][1- (1- PBrothers

* )2 ]

At this point, it is natural to ask about the practice of naming sons

after fathers. Isn't it more

likely to have a son named Joseph in a family that already has a

Joseph as the father?

The answer is yes, it does appear that families did quite often name

one of their sons after the

father. This is certainly true in the family of Jesus - he had a

brother Joseph who was named

after his father. The New Testament calls this brother both

"Joseph" (Matthew 13) and "Joses"

(Mark 6).

19

Will this effect change our calculation somehow? Will it enrich the

number of expected Josephs

in the family tomb of Jesus?

The answer is no, it will not. We already knew that Jesus had a

brother named Joseph, so we

have already enforced that fact above. So there is no "tendency" to

account for in the family of

Jesus. We enforced it already as a fact.

However, this issue does suggest that we should revisit our previous

calculation for P(T|~J) and

account for the "Joseph enrichment factor" there. We will turn to that

now.

Revised Computation of P(T|~J)

If we know that our tomb does not contain the family of Jesus of

Nazareth, we need to account

for the "Joseph enrichment factor" which will increase the probability

of finding a son of Joseph

named after him in this tomb. But there are actually two effects to

account for.

In a family tomb with a "Jesus son of Joseph," there is a fairly high

probability that the father

Joseph of this Jesus will also be buried in the tomb. We need to

account for that, too.

It may be, of course, that we are barking up a wrong tree and that

neither of these really matter.

In that case, there will be no increase in the expected number of

Josephs in this family tomb.

That is one extreme.

On the other hand, it may be that we should always expect to find both

the father Joseph and a

son named after him, in which case we would find two more Josephs in

such a tomb than in an

ordinary one.

Neither of these is a likely scenario. The answer is probably

somewhere between these extremes.

20

Let us define a new "fuzzy factor"

EURO

F3 to account for our lack of knowledge.

EURO

F3 will be a number

between 0 and 2 that represents the increase in the expectation value

of the number of Josephs in

a family tomb that contains the name "Jesus son of Joseph".

Since the expectation value in a tomb with n men was already

EURO

nPJoseph , it should be clear that the

enhanced probability of finding a Joseph in such a tomb is exactly:

EURO

PJoseph

+ = PJoseph +

F3

n

When

EURO

F3 is set to 0, there is no enhancement at all. That is the value we

should choose in societies

where families are neither more nor less likely to name one son after

the father and where the

father of a man named "Jesus son of Joseph" is never buried in the

family tomb with him.

EURO

F3 should be set to 2 in societies where the probability of naming a

son after the father is 1 and

where the probability of a father being buried with his son is also 1.

We expect that

EURO

F3 should be somewhere between 0 and 2, but we do not really know

where it

should be for the society of ancient Jerusalem. When we run

calculations, we will be interested

to know whether

EURO

F3 makes any difference or not, so we will run calculations over a

range of values

for

EURO

F3.

There is a corresponding enrichment in the probability that a randomly

drawn man in the tomb

will have one of the names of the brothers of Jesus of Nazareth. This

probability is now:

EURO

PBrother

+ (n) = PBrother +

F3

n

The net effect of all this is to change our previous estimate of P(T|

~J) slightly:

EURO

P(T |~ J) = Pson-Judah[1- (1- PMary )2][1- (1- PBrother

+ )2]

Final Computation

21

Now we can put all our results together. Recall that we are trying to

compute:

EURO

P(J |T) =

P(T | J)P(J)

P(T | J)P(J) + P(T |~ J)P(~ J)

We have estimated the following:

EURO

P(J) =

F1

NJ

P(~ J) =1- P(J)

EURO

P(T | J) = F2Pson-Judah[1- (1- PMary

* )2][1- (1- PBrother

* )2]

EURO

P(T |~ J) = Pson-Judah[1- (1- PMary )2][1- (1- PBrother

+ )2]

where:

EURO

NJ =

1

2

NgPJesusPJoseph

EURO

PMary

* (n) = PMary +

(1- PMary )

n

EURO

PBrother

* (n) = PBrother +

4(1- PBrother )

n

EURO

PBrother

+ (n) = PBrother +

F3

n

Note that the completely unknown probability

EURO

Pson-Judah factors out of the calculation, since it is a

factor in both the numerator and denominator of the Bayes' Theorem

equation.

The resulting equation is computable as a function of n and the

various fuzzy factors

EURO

F1,

EURO

F2,

and

EURO

F3. The first two of these fuzzy factors are required to be between 0

and 1, and the last is

required to be between 0 and 2 so the fuzziness is nicely bounded.

22

Results

In this section, we will compute the results of P(J|T) for a variety

of choices of the input parameters.

Again, the final results will vary depending upon the choices made

with regard to the

fuzzy factors we have delineated. Rather than provide our own estimate

of the probability,

which would require us to engage in a historical/archaeological

discussion that is beyond our

purview, we choose rather to offer five estimates that differ in the

choices of the fuzzy factors

and, accordingly, P(J|T). We also choose the most and least optimistic

values for each fuzzy

factor, which as we have discussed will vary individually over a

bounded range, so as to provide

a bounded range of potential values that P(J|T) might take.

Readers who would like to check our calculations (or run new ones with

different assumptions)

can download our spreadsheet from the following page:

http://www.ingermanson.com/jesus/art/stats2.php

The spreadsheet allows you to set six variables:

(a) The number of people in Jerusalem

(b) The number of complete generations during which ossuaries were in

use

(c) Use Rachel Hachlili's population statistics or use Tal Ilan's

(d) F1: The relative probability that Jesus had a son

(e) F2: The relative probability that Jesus was interred in a tomb

like the one at Talpiot

(f) F3: The number of "extra Josephs" one would expect in a family

tomb containing a

man named "Jesus son of Joseph"

23

Case 1: Advocate who wants the tomb to belong to Jesus of Nazareth

The numbers are chosen to be as favorable as possible to the "tomb

hypothesis." This is the case

no matter how absurd the assumptions might be from a historical

perspective. The intention here

is to make P(T|J) as high as possible, regardless of rationality:

(a) N = 30,000 (Number of inhabitants of Jerusalem. Set as low as

possible.)

(b) g = 1 (Number of generations in Jerusalem using ossuaries. Set as

low as

possible.)

(c) Tal Ilan's probabilities for names

(d) F1 = 1.0 (Relative probability that Jesus had a son. Jesus was

just as likely as

any man to have a son.)

(e) F2 = 1.0 (Relative probability that Jesus could be buried in

Talpiot. Jesus was

just as likely as any man to be buried in Talpiot.)

(f) F3 = 0.0 (Expected number of extra Josephs in a tomb with a "Jesus

son of Joseph"

ossuary. No extra men named "Joseph" are to be expected.)

The results are plotted for a number of bodies in the tomb ranging

from 10 up to 36:

P(J|T) vs. Number of bodies in tomb

0

0.01

0.02

0.03

0.04

0.05

0.06

0 10 20 30 40

P(J|T)

P(J|T)

Conclusion: The probability that the tomb belongs to Jesus of Nazareth

could conceivably be as

high as 1 in 18 if all factors are made as favorable as possible,

irrespective of historical plausibility.

24

Case 2: "Indifferent" historian

The numbers here are chosen with the concept of indifference in mind.

That is, the historian in

this instance does not have a relatively strong opinion on any of the

fuzzy factors. This is not to

be taken as our estimation of the average scholarly response, which is

probably better modeled as

being somewhere between this and Case 4.

(a) N = 50,000 (Number of inhabitants of Jerusalem)

(b) g = 2 (Number of generations in Jerusalem using ossuaries)

(c) Tal Ilan's probabilities for names

(d) F1 = 0.01 (Relative probability that Jesus had a son)

(e) F2 = 0.5 (Relative probability that Jesus could be buried in

Talpiot)

(f) F3 = 1.0 (Expected number of extra Josephs in a tomb with a "Jesus

son of Joseph"

ossuary)

The results are plotted for a number of bodies in the tomb ranging

from 10 up to 36:

P(J|T) vs. Number of bodies in tomb

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0 10 20 30 40

P(J|T)

P(J|T)

Conclusion: The probability that the tomb belongs to Jesus of Nazareth

is less than 1 in 19,000,

with a choice of parameters likely to be made by a historian

indifferent to the outcome.

25

Case 3: Historian inclined toward theory

The numbers are chosen to be quite favorable to the "tomb hypothesis,"

but staying within the

bounds of historical reasonableness:

(a) N = 50,000 (Number of inhabitants of Jerusalem)

(b) g = 2 (Number of generations in Jerusalem using ossuaries)

(c) Tal Ilan's probabilities for names

(d) F1 = 0.1 (Relative probability that Jesus had a son)

(e) F2 = 0.8 (Relative probability that Jesus could be buried in

Talpiot)

(f) F3 = 1.0 (Expected number of extra Josephs in a tomb with a "Jesus

son of Joseph"

ossuary)

The results are plotted for a number of bodies in the tomb ranging

from 10 up to 36:

P(J|T) vs. Number of bodies in tomb

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0 10 20 30 40

P(J|T)

P(J|T)

Conclusion: The probability that the tomb belongs to Jesus of Nazareth

is less than 1 in 1,100,

even when choosing relatively liberal values of parameters so as to

favor the tomb hypothesis.

26

Case 4: Historian disinclined toward theory

The numbers are chosen to be unfavorable to the "tomb hypothesis"

while still being defensible

from a historical perspective. Based upon an informal survey of most

responses to the documentary's

hypothesis - it seems that many scholars would place themselves here.

That is, they

are inclined to assign low values to the "fuzzy factors":

(a) N = 80,000 (Number of inhabitants of Jerusalem)

(b) g = 2 (Number of generations in Jerusalem using ossuaries)

(c) Rachel Hachlili's probabilities for names

(d) F1 = 0.001 (Relative probability that Jesus had a son.)

(e) F2 = 0.01 (Relative probability that Jesus could be buried in

Talpiot)

(f) F3 = 1.5 (Expected number of extra Josephs in a tomb with a "Jesus

son of Joseph"

ossuary)

The results are plotted for a number of bodies in the tomb ranging

from 10 up to 36:

P(J|T) vs. Number of bodies in tomb

0

0.000000002

0.000000004

0.000000006

0.000000008

0.00000001

0.000000012

0.000000014

0.000000016

0.000000018

0.00000002

0 10 20 30 40

P(J|T)

P(J|T)

Conclusion: The probability that the tomb belongs to Jesus of Nazareth

is less than 1 in 5 million

if all factors are made unfavorable.

27

Case 5: Christian who insists that Jesus' body ascended to heaven

Only one number matters:

(e) F2 = 0.0 (Relative probability that Jesus could be buried near

Talpiot)

The results are plotted for a number of bodies in the tomb ranging

from 10 up to 36:

P(J|T) vs. Number of bodies in tomb

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40

P(J|T)

P(J|T)

Conclusion: If Jesus' body ascended to heaven, then the probability

that this is his tomb is 0.

Assigning a Range to P(J|T)

Finally, it is worthwhile to assess the range of values that P(J|T)

might take. Unfortunately, we

have six factors that vary, which makes graphical representation

impossible. Thus, let us vary

two factors, F1 and F2, simultaneously. Recall that F1 is the relative

probability that Jesus of

Nazareth had a child and F2 is the relative probability that Jesus of

Nazareth could be buried at

Talpiot.

The remaining factors will be held constant according to the

assumptions in the "indifferent historian"

case. Thus, N = 50,000, g = 2, F3 = 1 and Tal Ilan's probabilities are

used. With these

conditions, we obtain the following results:

28

F2

0.001 0.01 0.9 1.0

F1 0.001 0.0000000105 0.0000002092 0.0000094574 0.0000105138

0.01 0.0000001046 0.0000010459 0.0000945656 0.0001051276

0.9 0.0000094124 0.0000941210 0.0084398749 0.0093737827

1.0 0.0000104583 0.0001045778 0.0093688530 0.0104044776

The rows represent the different values for F1, the columns for F2 and

the cells are the calculations

of P(J|T) for every given F1 and F2. Two observations stand out

immediately. First, while

it is the case that varying F1 and F2 have a large relative effect -

that is varying from the lowest

F1/F2 to the highest amounts to a 1 million-fold increase - the

absolute effect is minimal. That

is, varying the factors from the least optimistic to the most

optimistic only "purchases" a single

percentage point. Second, the numbers are consistently low. Regardless

of the value of either F1

or F2, the likelihood that this tomb belongs to Jesus of Nazareth is

consistently small. Even assuming

that he is as likely as any man to have a son and to be buried at

Talpiot - one still can

find only a 1.04% probability that the Talpiot tomb belongs to him.

Discussion

Our analysis thus points in a very different direction than the

conclusion of Jacobovici. Why is

this the case? The answer to this question can best be seen by

computing a simple estimate of

P(T|J). Let us, in this instance, remove all of the fuzzy factors. In

other words, let us say that

Jesus of Nazareth is just as likely as any man to have had a son (i.e.

F1 = 1) and just as likely as

any man to have been interned at Talpiot (i.e. F2 = 1). Let us also

say that we expect no extra

Josephs in the tomb (i.e. F3 = 0). Additionally, let us take the rest

of the assumptions made by

our "indifferent historian" in Case 2 above. Thus, we assume a

population of Jerusalem of

50,000 people and the total number of generations interned in

ossuaries is two. We also use Tal

Ilan's demographic data. Finally, we assume only 10 people were

interned in the tomb.13

13 All of these have the effect of maximizing the value of P(J|T)

while retaining reasonable assumptions about demography.

29

We still use our basic Bayes' Theorem formulation. That is:

EURO

P(J |T) =

P(T | J)P(J)

P(T | J)P(J) + P(T |~ J)P(~ J)

With the stated assumptions, we obtain:

P(T|J) = 0.687

P(T|~J) = 0.216

P(J) = 0.005

P(~J) = .995

Returning to our equation, we obtain:

( | ) .014 1.4%

..218

..003

( | )

0.687 0.006 0.216 .995

0.687 0.005

( | )

= =

=

× + ×

×

=

P J T

P J T

P J T

This is far from the 600 to 1 chance hypothesized by Jacobovici. The

reason should be clear

when we recall the fundamental intuition of Bayes' Theorem. We are

interested in defining

P(J|T) in terms of P(T|J). This requires us to consider two factors,

neither of which Jacobovici

considered.

The first is the unlikelihood of ever finding Jesus of Nazareth in the

first place. This value -

even under these very optimistic assumptions - is quite low, just

0.5%. Relatedly, the likelihood

that we have not found Jesus of Nazareth is a very sizeable 99.5%.

This must be considered in

any evaluation of the tomb. To fail to do so is, again, to commit what

is known as the prosecutor's

fallacy. One cannot focus solely upon the uniqueness of the evidence

gathered. Its uniqueness

must be weighed against the uniqueness of the claim. While Talpiot

might have some

unique evidence that points to Jesus of Nazareth, its descriptive

power is necessarily diminished

when we consider just how unlikely it is that we would ever find his

tomb in the first place.

30

The second is the extent to which the names in the tomb provide a clue

to which Jesus was interned

there. The good news for Jacobovici's hypothesis: we can expect with

68.7% likelihood

that Jesus of Nazareth would be buried with at least one Mary and at

least one brother. The bad

news: we can also expect 21.6% of all people named "Jesus son of

Joseph" who are not Jesus of

Nazareth to be buried similarly. In other words, Talpiot does not

provide all that unique a clue at

all. Why is this the case? It is for the reason that historians,

archaeologists and New Testament

scholars have been stating since the day the film was announced: these

names are common.

Thus, while it is true that finding four particular common names in a

cluster is uncommon, as

Jacobovici and others have responded, this is beside the point. The

point is that the names in Jesus

of Nazareth's family were not sufficiently unique such that a tomb

that matches two of them

decisively points toward Jesus of Nazareth. Indeed, the difference

between P(J|T) and P(T|~J) is

far from decisive. Many men named "Jesus son of Joseph" can be

expected to have been buried

with at least one woman named Mary and at least one man with a name

that follows the names of

Jesus of Nazareth's brothers. Common names mean that the names

themselves do not take us

very far in terms of identifying the owner of the tomb.

Thus, it should be clear that Jacobovici's inferential errors had a

sizeable and beneficial effect on

his hypothesis. The failure to consider P(J) and P(T|J) dramatically

inflated the estimate of

P(J|T), biasing it (in the statistical sense of the term) from its

expected value and toward the conclusion

of the documentary. Factoring in the miscellaneous computational

errors we also reviewed,

it should be clear why our figure is dramatically lower.

When we begin to consider the fuzzy factors, the value of P(J|T)

begins to drop even further. It

is important to note that it can only fall from this value of 1.4%.

Jacobovici implicitly assumed

F1 = 1, F2 = 1, and F3 = 0. All are unrealistic assumptions. If we

adjust them to be more realistic,

P(J|T) will fall below 1.4%. Much of the "damage" will be done by F1,

the fuzzy factor that

assigns a relative probability to Jesus of Nazareth having a child.

Given the unanimous and

deafening silence of the historical record, it seems to us unlikely

that this value could be taken

above 0.05 without resort to a tendentious and error-filled argument.

With F1 = .05, F2 = 1 and

F3 = 0, the value of P(J|T) drops to 0.08%. When F2 is lowered and F3

is raised to correspond

better with our expectation of reality, P(J|T) will drop even further.

31

Conclusion: Statistics above All?

Rather than conclude by recapitulating our hypothesis, we feel we

should take the opportunity to

respond to an insightful argument offered by Professor James Tabor,

who has been a thoughtful

supporter of the theory of Jacobovici. On his Jesus Dynasty Blog,

Tabor writes:

A statistician, as statistician, is not primarily focusing on

prosopography, that is,

matching ancient names to known historical characters. That is the

task of the

historian who then seeks to determine if there is any potential "fit"

between this

cluster of names, with its configurations, and that of any

identifiable persons/

family in our records...

I am not optimistic that more advanced statistical models can be

effectively applied

to questions of historical prosopography since the kinds of

identifications

and subtle correspondences used are not easily quantified. Is

Mariamene an appropriate

name for [Mary Magdalene]? How could you put a number on it? Is it

significant that her ossuary is decorated and her inscription is in

informal Greek?

How is that quantified? Does it matter that the name Yeshua bar

Yehosef is

written in a very messy graffiti style while the others are elegant

and block? How

do you put a number on that? What of how the ossuaries were placed in

the various

kokim, and with names grouped in twos and threes? Are there hints of

potential

relationships implied? I have about 25 other factors of this sort that

I am considering

in formulating my own prosopographic proposal, including the symbol

on the tomb that comes from contemporary temple gate imagery. As far

as I can

tell many of these factors can not be quantified.14

This raises an interesting question: does statistical analysis such as

the kind that we have outlined

here preclude historical and archaeological analysis?

While we find ourselves agreeing with Dr. Tabor on several important

points, we believe that the

answer is no. To clarify our position, it is valuable to outline what

we believe we have and have

not delineated in this article.

At a fundamental level, statistical analysis is a formalization of the

proper manner of descriptive

inference. Thus, we would argue that the first accomplishment we have

made in this essay is

formally to outline how analysis of the Talpiot tomb should proceed.

This is the case even if one

14 James Tabor. "Probabilities, Statistical Theory, and the Talpiot

Tomb." March 19, 2007.

http://jesusdynasty.com/blog/2007/03/19/probabilities-statistical-theory-and-the-talpiot-tomb/.

Accessed March 26,

2007.

32

ultimately decides that a formal probability is incalculable. Even if

it is impossible to assign actual

values to the sundry variables that we have delineated - one

nevertheless must take these

variables into account. This is, as we indicated above, the

fundamental methodological mistake

of Jacobovici. He failed to consider P(J) and P(T|J). Even if he had

chosen a non-quantitative

route for his argument, the failure to consider these factors would

still invalidate his conclusions.

The reason is that, even if one chooses to avoid the mathematics

behind statistical analysis, one

must still obey the rules of descriptive inference it delineates. When

one fails to do this, one runs

the risk of committing an inferential fallacy of some sort - just as

Jacobovici has committed the

prosecutor's fallacy.15

In addition to outlining the proper manner in which an argument about

Talpiot should proceed,

we also would argue that we have here delineated a range of values

that the final P(J|T) can

take. In other words, we are in full agreement with Dr. Tabor that the

job of the "statistician"

does not preclude the job of the historian or the archaeologist. This

is why we have delineated a

series of "fuzzy factors" and have demurred from assigning final

values to them. We are not

formally trained in either history or archaeology. It is not our

business to assign values to these

numbers. What we have done, however, is identify where the historical

and archaeological debates

can influence the final outcome. While we might lack the scholarly

background in history

to predict the results of the sundry debates that are ongoing, we

nevertheless have the capacity to

identify where, how and why those results will affect the final

estimate of P(J|T). For instance, a

prosopographical discussion of the family of Jesus of Nazareth, above

all a serious investigation

of the likelihood that he had a son named "Judah," will influence P(T|

J). An archaeological/

historical discussion about whether one might expect Jesus of Nazareth

to be interned in a

15 Dr. Tabor, in arguing for the more simple method advanced by Dr.

Feuerverger and explicitly against our method

(which he calls "a more Bayesian model"), asserts that the measure of

Feuerverger embodies what he calls "the

Ockham's razor of probability theory." As it is, however, any argument

about the ownership of this tomb that relies

upon Feuerverger's figure without reference to the other factors we

have delineated will be guilty of the inferential

errors we have also delineated. And while, following Ockham,

simplicity is a virtue in any argument, it is not the

highest virtue: simple arguments with inferential errors are not to be

preferred to (slightly) more complicated arguments

that lack such errors. We would also note that while we discussed our

basic hypothesis with Dr. Tabor, we

did not give him an advance copy of this essay. Accordingly, we are

not sure that his knowledge of our methodology

was sufficient for this critique, which predates the public release of

this essay. See James Tabor, "Statistical

Clouds, Fuzziness, and Ockham's Razor." March 25, 2007.

http://jesusdynasty.com/blog/2007/03/25/statisticalclouds-

and-fuzziness. Accessed March 26, 2007.

33

tomb like the Talpiot tomb, placed in the particular ossuary in

question, and so on, will influence

P(J).

These debates are therefore embodied in our "fuzzy factors," which

each vary over a small

range. While we cannot predict what their particular values will be,

and while we recognize

(following Dr. Tabor) that it is possibly the case that their expected

values cannot be quantified

because it would require placing numbers on what are essentially non-

numerical concepts, we

can nevertheless vary these factors between 0 and 1 to see how this

variation affects P(J|T). It is

in this manner that we can offer a range of values for P(J|T). This is

what we have done.

What we have not done is delineate an expected value for P(T|J), which

we would agree with Dr.

Tabor might in fact be incalculable. This would require us to take

positions on matters which are

beyond our purview, namely the historical/archaeological debate that

is now ongoing, and to

quantify what is possibly not quantifiable.

Thus, we find ourselves in both agreement and disagreement with Dr.

Tabor. On the one hand,

we think that statistical analysis cannot stand as a substitute for

the historical/archaeological debate

- and that, at some point, certain unquantifiable elements might

preclude the assignment of

an expected value. On the other hand, we think that statistical

analysis can be taken further than

Dr. Feuerverger has taken it, and further than Dr. Tabor believes it

can be taken.

Specifically, we think that our model possesses the right combination

of flexibility and clarity

not only to allow for the prosopographical debate Dr. Tabor rightly

wishes to see commence, but

also to indicate where the results of that debate will have an effect

and what kind of effect that

might be. Generally, we believe that it can offer two valuable

services: (a) the methodological

outline of how any argument - quantitative or non-quantitative -

should proceed; (b) a range of

values for P(T|J).

34

About the Authors

Jay Cost is a doctoral candidate in political science at the

University of Chicago. His scholarly interests include

contemporary American political parties, congressional elections, and

the media's role in politics. He is also a

regular contributor for RealClearPolitics.com, a Chicago-based

organization that provides a daily digest of the best

commentary and analysis of American politics.

Randy Ingermanson earned his Ph.D. in physics from the University of

California at Berkeley. He has worked for

many years as a computational physicist. Randy is the author of six

award-winning novels, and he also authored a

nonfiction book, Who Wrote the Bible Code?, which applied statistical

methods to debunk the alleged "Bible code."

He is currently working on a novel about Jesus. His web site is at

http://www.Ingermanson.com.

.

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