# How many Jesuses were crucified ?

People who argue for the existence of a “historical Jesus” might forget that Israel at that time may have had more preachers called Jesus so that there arises a problem of identification. Perhaps more Jesuses got crucified as well. Perhaps the true Jesus wasn’t crucified but mistaken for another Jesus ? The film Life of Brian mocks about this by inserting the name “Brian” but the question already exists in proper terms when there are more Jesus(s)es.

These issues are known in statistics as Type I and Type II errors. We will explain these below. First though, what is the chance of having preachers called Jesus ?

A google on that question and on the “number of crucified Jesuses” doesn’t give a useful result. To get a rough idea it may be quicker to set up a small model. I suppose that the following exercise has already been done by experts in the field with better data, but let us see how far a bit of reasoning gets us.

The text below is an exercise for mathematics education. We will set up a small model so that students can see that modelling should help answering questions other than geometry too. We will use some missing parameters from modern data that students can verify and relate to. It is unclear how the result relates to ancient Israel. There are difficult questions on this, like what we should take as the territory of “ancient Israel”. Hopefully scholars of New Testament Studies come up with better models and data. For now, back to simplicity.

Question 1: How many boys are called Jesus ? This will differ across time and place. The name may be Joshua and Yehoshua too, see here. The CBS of Israel apparently uses Hebrew for this question, so I cannot use it. We can however find the baby boy names for England and Wales in 2012. Of these 374,346 baby boys 4444 are called Joshua, or 1.2%. There are a few real Jesuses, also Joshua-x combinations, but let us not be misleadingly precise.

Question 2: How many preachers are there in a population ? This appears to be a hornet nest. There are all kinds of functions that might be called “preaching”, while it is claimed that Jesus was a healer too. It also depends upon time and place again. Again, I couldn’t find how many rabbis there are in Israel. Apparently Josephus estimates 6000 rabbis but his numbers apparently may be off by a factor 10. In this case, let us take a look at the USA that is somewhat more religious than the UK. We find the Standard Occupational Classification (SOC) with Religious workers (21-2000): clergy, other and miscellaneous. An overview is given directly by BLS or indirectly by Wolfram Alpha. If we also consider postsecondary teachers in religion, we find a number of 83500 people. When we relate this number to the total US population of 317,493,212 people then we find that the average parish has 3802 people. Half of a parish will be men. In ancient Israel all preachers will be male. Thus 1 in 1901  men will be a preacher.

Can we fully rely on this ? Disaster strikes:

(a) There are also the 2008 Occupational employment projections to 2018. This study is quoted by “faith based jobs” (faith can be a job) and by a university directory:

“U.S. Bureau of Labor Statistics (BLS) figures show that clergy held about 670,000 jobs in 2008. Employment in this field is expected to grow at an average rate compared to other occupations, with a projected 217,700 new clergy jobs through 2018.”

However, in this other BLS study, all Religious Workers in 2008 (SOC 21-2000) add up to 778.8 thousand.

(b) Above study and forecast is confusing. When we look at a standard report of 2008, we find 42040 clergy. In an overview press release we find 14790 “Directors, religious activities and education” and 5640 “Religious workers, all other”. Thus the earlier report for 2013 fits with 2008 but not with the projection study under (a).

I couldn’t quickly determine what causes the difference. I neither checked whether the statisticians measured the number of statisticians different too ….

All this doesn’t quite matter yet. We can use the difference as a range.

Question 3: How many preachers are crucified ? We can use ranges here too. We assume that the properties of preaching and being called Jesus are independent. We assume that being called Jesus is no specific reason to get crucified.

Question 4: How many men were there in ancient Israel ?

This now becomes serious archeology. Wikipedia comes to the rescue with a discussion of life expectancy (LE) in the past. For Classical Rome: LE at birth = LE(0) = 20-30 years. Young children die like flies but the surviving children are stronger: “At age 10, life expectancy [thus LE(10)] was an additional 35 to 37 years (total age 45 to 47).”

The issue is discussed by Sharon Basaraba who refers to gerontologist and evolutionary biologist Caleb Finch in PNAS. The relevant quotes are:

(i) “Despite low survival, half of those reaching age 20 reached 60 (LE(20) of 40 years).” and (ii) “In the ancient Greco-Roman world, demographic reconstructions agree on short LE(0) ranging 20-35 years. [But unreliable]”.

These are some data on LE in Roman Egypt, but it is not clear what the “census” is. The University of Texas has this nice page on ancient Egypt, with also a calculation example. Below I will give a simpler example.

Wikipedia discusses demography in ancient Palestine, and there we find:

“Modern estimates place the population of ancient Palestine at a maximum of around one million. According to Israeli archeologist Magen Broshi, “… the population of Palestine in antiquity did not exceed a million persons.”

Population hypotheses

We might be on the safe side by assuming a mature population of age 20+ with a size of T = a half million men and women. We don’t have to look into the birth & death of children. For display only, our graph starts at an arbitrary cohort 25000 at age 0. We assume two age-groups: 20-50 and 50-70. When we also assume that the final cohort at age 50 still has f = 10000 remaining then we get fairly nice numbers with a life expectancy LE(20) = 35, i.e. to a total of 55 years. The latter calculation result is coloured red below.

You can run your variants with HypotheticalSurvivalGraph-xls.The key parameters are T = 500000, f = 10000, and ages x = 50 and d = 70. From this we can calculate the distribution and the median age of death starting from age 20. The trick is to recognize the triangles and C and the rectangle A in the graph.

Hypothetical survival graph for Israel in 20-75 CE (own hypothesis)

We can now try to determine the total number of men in Israel in antiquity. Conventionally, we would look at around 30 CE and there would be some 15000 men and women around age 30. However, the story of Christ is surrounded with uncertainty. The destruction of Jerusalem in 70 CE can be judged to have an impact, see my earlier review of the book by Maurice Casey. Thus, let us use a time window of 20-75 CE. Let us also look at men in the age-group 20-50, including either young revolutionaries or fitting with stories that Jesus actually died in his 50s. Now, we should not double-count people. People who are alive already in 20 CE may be counted once, and this is the group A + B. To this we add the new faces given by the new cohort additions over the period till 75 CE. This results into 658333 men (and one woman who cannot find a man).

Hypothetical number of men in Israel in 20-75

Combining the hypotheses

When we combine these various assumptions, we arrive at some idea how many Jesuses were crucified in Israel in that period 20-75 CE.

With 1.2% of boys called Jesus, we find a total of 7815 Jesuses in that period.

The number of men per parish ranges from 204 to 1901. This gives a range for the number of preachers, as low as 346 or as high as 3230. (All lower than Josephus’s 6000.) Applying the 1.2% again, we find 4 to 38 preachers called Jesus.

Hypothetical number of Jesuses in Israel in 20-75 CE

If there is only 1 preaching Jesus who was also crucified then the percentage of being crucified ranges from 2.6% (out of 38) to 25% (out of 4) of all preachers called Jesus.

If we accept this range of uncertainty, then the application of 25% to the total of 38 preaching Jesuses gives 10 preaching Jesuses who were also crucified.

The last column arises from applying the crucifixion percentages to the Males column. When the lower percentage of 2.6% is applied to all 658333 males, then this gives some indication of 17170 Israelites who would have been crucified in 20-75 CE, regardless of their name or employment. And 1.2% of those would be called Jesus, i.e. 204. They are likely to be followers rather than preachers themselves, and their real percentage need not be 2.6%. We found the latter percentage by assuming at least one crucified preacher called Jesus, but for the rest it hangs in the air.

Error of Type I and Type II

Of course, it is also possible that there isn’t a “historical Jesus” so that the true parameter is 0%.

Even in the case that there are 10 preaching and crucified Jesuses, it isn’t guaranteed that one of these is the true and proper Jesus that the gospels report about.

Given that there is no evidence that Jesus really existed, the null-hypothesis H0 is that he did not exist indeed. The alternative H1 is that he actually existed. We only accept his existence if there is proof. Thus:

H0 = Jesus Christ is a myth = He doesn’t exist (until proven)
H1 = There did exist a person who is associated with the gospels.

Pr[ Reject H0 | H0 is true ] = probability of error of Type I = Alpha = α
Pr[ Not reject H0 | H0 is false ] = probability of error of Type II = β

Given the discussion above 2.6% ≤ α ≤ 25%. Given that the gospels were created for other reasons (see here), and discuss a Jesus who preached and got crucified, there still is an independent probability that there are 1 or 10 such Jesuses. The existence of those random Jesuses cannot be taken as evidence for the “historical Jesus” (who the gospels call Christ). Those 1 to 10 Jesuses exist purely because of the random chances of being called Jesus, becoming a preacher, and getting crucified. As long as there is no evidence that links one of these Jesuses to the activities reported in the gospels, there is no base to speak about a “historical Jesus”.

As so often, it is harder to calculate β. I will not try it now. Say, “I will leave this as an exercise” ?

Conclusion

Commonly an argument is made for a “historical Jesus” that runs like: “We only know that there was a Jew called Jesus (Christ) who preached and was crucified. For the rest we have no evidence. What one believes from the gospels is precisely that: a belief.” (no quote)

This kind of argument however confounds the uncertainty that is inherent in the label “Jesus, preached, crucified” (omitting the “Christ” because that is part of the gospels).

If you look at the numbers above, there may be 0 – 10 of those Jesuses. There is no evidence that links any of those Jesuses to the gospels.

The probability of error type I (alpha) of accepting a “historical Jesus” while there is only a myth could fall in the range 2.6% ≤ α ≤ 25%.

It would be great if someone could show a study that has already looked at this issue in similar manner, with much better data. It would also be useful to get more clarity on the question whether statistics really is a good tool to deal with this question.