Balkinization: If Jesus Had a Child, (Probabilistically) We’re All Jesus' Heirs

If Jesus Had a Child, (Probabilistically) We’re All Jesus' Heirs

Ian Ayres

Christianity should not feel threatened by the possibility that Jesus and Mary Magedline had a child. If Jesus procreated, we are all likely to be Jesus' heirs?

Statisticians are amused when they hear the frequent claim that so-and-so is the direct descendant of Charlemagne. Their amusement isn’t because the claim is wrong, but because virtually everyone of European ancestry is Charlemagne heir.

Here’s the reasoning:

Charlemagne was approximately 40 generations back from the present day. Each person has 2 parents, 22 = 4 grandparents, 23 = 8 great-grandparents, ... and 240, or approximately 1,000,000,000,000 (one trillion), 40th-generation ancestors, which means half a trillion male ancestors. Of course, since the entire male population of Europe at the time of Charlemagne was only about 15 million, these half trillion ancestors cannot all have been different men -- obviously there has been a lot of cross-breeding, and many of our ancestral lines cross and re-cross, eventually ending up at the same person. Let's assume that each of my 40th-generation male ancestors is a randomly-chosen man from eighth-century Europe (this is not really valid, but more on that below). Choosing any one such ancestor, say my father's father's ... father's father, the probability that that particular person is Charlemagne is one in 15 million. Pretty small. To put it another way, the probability that any particular ancestor was not Charlemagne is 1 - 1/15,000,000, or approximately 0.999999933
But now consider the probability that none of my 40th-generation ancestors is Charlemagne. For that to happen, every one of my half trillion male ancestors has to not be Charlemagne, which would be an amazing coincidence. To see how amazing, let's compute the probability. Assuming all of these various not-being-Charlemagne occurrences are independent of each other (more on this below), the laws of probability state that the probability of all these events occurring simultaneously is obtained by multiplying together their individual probabilities:
(0.999999933)·(0.999999933)·...·(0.999999933) =
(0.999999933)500,000,000,000.
This turns out to be an incredibly small number: about one chance in 1015,000. That's a one with 15,000 zeroes after it, a number that's too big even to display in a browser window. This is way more than the number of atoms in the universe (which is estimated to be about 1080). Therefore, if this analysis is even remotely close to correct, it's virtually impossible that Charlemagne is not among my direct ancestors.

The case is even stronger for Jesus (or anyone else who procreated earlier in History) – because the earlier in History the more ancestors we have from a particular generation and the smaller the world population.

This massive overlap of our ancient ancestry means that it in some ways it would be a miracle if any child of Jesus was not our heir. Of course the Charlemagne math crucially assumes that our ancestors are randomly chosen from people living in eighth century. If there is some genetic subgrouping whose ancestors never cross-bred with Charlemagne’s heirs, then people from this subgrouping may have a much lower chance of being Charlemagne’s heirs. Jews are more likely to be Jesus’ heirs than someone from some remote genetic island.

But the orders of magnitude involved in the Charlemagne math suggest that even slight amounts of genetic intermingling may be sufficient to connect subsequent generations.

What’s most improbable about Dan Brown’s narrative is the implication that Jesus has only one living descendant. The suggestion that the virus of humanity survived but never broke out and multiplied (especially with regard to a royal line) is, to put it mildly, implausible.

It’s long been known that we all breathe some of the same molecules that were inhaled by Moses, Buddha, Socrates, Julius Caesar, Mohamed and Jesus. But the Charlemagne math suggests that we’re not just all the figurative sons and daughters of Adam and Eve, we may be the literal (albeit infinitesimal) heirs of Jesus.

Posted 9:01 AM by Ian Ayres [link]

Comments:

This massive overlap of our ancient ancestry means that it in some ways it would be a miracle if any child of Jesus was not our heir.

Two corrections, one linguistic and one statistical: (1) Replace "heir" with "ancestor." It would be a miracle indeed if someone who lived twenty centuries ago was the heir of someone living today. (2) Insert "who has descendants living today" after "any child of Jesus." Some bloodlines do die out, perhaps because someone has no children, or perhaps because their children have no children of their own, or so on. What is incredibily improbable is that a bloodline survives but remains very small throughout many generations.

# posted by

Nobody : 10:42 AM

The mathematical models that play this sort of scenario out are pretty compelling (assuming some semblance of random mating, etc. They've done some work on exactly how random the mating has to be and so on).

What the above post is missing (aside from corrections of a few typos) is some analysis of the possibility that all of Jesus's descendants died out fairly early. The mathematical models don't show that every old organism is the scion of every new organism; they show that they're either the scion of all of them or of none. Given infant mortality rates, etc, it's quite likely that all of Jesus's grandchildren died.

# posted by

Disenchanted Dave : 1:54 PM

Uhh, this analysis doesn't quite fly. As other posters have pointed out in the case of jesus it neglects to take into consideration the possibility that his lineage died out fairly early on. The analysis with charlemagne waves this away by suggesting his early noble descendents are highly likely to survive (and historical records would probably verify this).

Moreover, the analysis misses out on the significant correlations between likelihood to reproduce amoung members of the same family. If your family just happens to have a mutation that makes it immune from the plague it is way more likely to survive than a family that doesn't. Since the incidence of northern europeans with this mutation that provides plague protection is way higher than that of people on other continents some pretty significant gene based selection went on. Even worse members of the same lineage at this time were likely to be geographically concentrated. If people didn't move very far from where they grew up then natural disastors, fire, or even war/genocide might wipe out whole lineages.

The biggest problem though is that the math is simply wrong. Even making the assumption that there are no grouping factors (whether or not person A and person B survive to reproduce are independent events) it simply isn't true that the probability of any of my 40th generation ancestors being charlegmagne is independent.

To illustrate this point let us look at what happens 35 generations back. 2^35 is greater than the population of europe at that time so my 35 generation ancestors can't all be distinct. Thus pick someone who is my 35 generation ancestor in two different ways. This person either is or is not a descendent of charlemagne. Thus it just isn't true that the probability of my 40th generation ancestors traced one way through this individual being charlemagne is independent of my ancestors traced another way through this individual being charlemagne.

In other words this analysis fails to take into account the fact that the same people are going to be my ancestor in more than one way way before we get all the way back to charlgemagne. This is especially serious as it means that it isn't taking into consideration the fact that people of the same nationality or who live in the same region are much more likely to marry each other than to marry outsiders.

I mean surely if you are 100% native american your probability of being descended from jesus is going to be near 0 and while the effect might not be as great for other groupings it should still be present.

Besides even if this argument does work in general it isn't necessarily relevant to the DaVinci code. After all I think the plot (of the movie) is perfectly consistant with the idea that the woman is the only descendent of Jesus with records to prove this fact. The idea presumably being that the Templar's documents tracing jesus's lineage would be supported by DNA tests showing that the woman who the documents claim to be a descendent is indeed related to the woman in the sarcophagus. Other random individuals who aren't documented would only prove that whoever was in the sarcophagus had living descendents but this doesn't say much. Of course at best this only establishes that some people way long ago thought the woman in the coffin bore jesus's child and then protected the lineage nothing more. Since there are plenty of christian sects with strange beliefs why anyone would care is beyond me.

Besides, presumably this family has been hunted by the church for these many years. Presumably the templars could only protect a certain number which would mean the geometric explosions of descendents would be stopped as the church picked off the poorly protected descendents.

Though it isn't like one needs to find more flaws in the DaVinci code.

# posted by

TruePath : 4:03 AM