Freethought & Rationalism Archive

lpetrich · 12-08-2006, 01:26 PM

As is well-known, the genealogies in Jesus Christ given in Matthew and Luke have almost no names in common; for a more detailed discussion, one may visit Paul Tobin's site, which discusses several additional problems. Between David and Joseph:

Matthew: 28 ancestors
Luke: 40 ancestors

sharing only Zerubbabel and Shealtiel. If they are selections from a single list, then that list must have had at least 66 ancestors.

The probability of Matthew and Luke independently selecting at most two shared ancestors to include in their lists can be calculated for different total numbers of ancestors:

66 - 2.3*10^-16
70 - 7.7*10^-13
84 - 5.4*10^-8
100 - 1.2*10^-5
200 - 0.049

There is the additional problem of generation time. King David likely reigned around 1011 - 971 BCE; Jesus Christ was born a little before 4 BCE, when King Herod died. This is a gap of almost exactly 1000 years, and I will use it to calculate the average generation time:

Matthew: 34 years
Luke: 24 years
Minimum Combined: 15 years

Matthew and Luke are both fairly reasonable, while the minimum combined figure is almost absurdly small.

Therefore, it is extremely unlikely that Matthew and Luke had selected from the same list.

Probability of overlap.

Imagine selecting first n₁ items from a list of n items, placing them back, and then selecting n₂ items. What is the probability that the two selections will share m items? A detailed calculation reveals

$P(n,n_1,n_2,m) = \frac{n_1! n_2! (n - n_1)! (n - n_2)!}{n! (n_1 - m)! (n_2 - m)! (n - n_1 - n_2 + m)!}$

With the help of Abramowitz and Stegun's Handbook of Mathematical Functions, we can find a convenient generating function for the above probability in terms of a Hypergeometric Function:

$G(n,n_1,n_2,z) = \sum_m P(n,n_1,n_2,m) z^m = \frac{(n - n_1)! (n - n_2)!}{n! (n - n_1 - n_2 + m)!} F_{2,1}(- n_1, - n_2; n - n_1 - n_2 + 1; z)$

This generating function can be used to verify that the sum of probabilities is 1, and to find the mean and standard deviation:

$mean = \frac{n_1 n_2}{n}$

$stdev = \sqrt{\frac{n_1 (n - n_1) n_2 (n - n_2)}{n^2 (n - 1)}}$

These are useful in the case of large n, n₁, and n₂, because the probability distribution then approximates a normal distribution.

aa5874 · 12-08-2006, 02:25 PM

Ipetrich, what is the probability that the genealogies are for the same person?

WishboneDawn · 12-08-2006, 04:34 PM

I can't even pretend to understand the equations.

I take it this is an argument for those who don't think Luke and Matthew manufactured their geneologies to support their different views of Jesus but rather somehow think there's consistecncy between the two.

lpetrich · 12-08-2006, 10:53 PM

Oops, I forgot to write in the m! in the probability's denominator:

$P(n,n_1,n_2,m) = \frac{n_1! n_2! (n - n_1)! (n - n_2)!}{n! m! (n_1 - m)! (n_2 - m)! (n - n_1 - n_2 + m)!}$

I could give a detailed derivation, but I wonder who might be interested in seeing it.

Quote:

Originally Posted by WishboneDawn

I take it this is an argument for those who don't think Luke and Matthew manufactured their geneologies to support their different views of Jesus but rather somehow think there's consistecncy between the two.

That's right.

Though one does have to wonder why Matthew preferred Solomon and Luke preferred Nathan as the next one after David.

Matthew's genealogy follow the southern-kingdom line, though it skips the kings between Joram and Uzziah to get his numbers to fit:

14 kings each in:

Abraham to David
- the Davidic dynasty begins
Solomon to Jeconiah
- the Babylonian Exile
Shealtiel to Jesus Christ
- another Big Thing is supposed to happen

By comparison, Luke's names are much more obscure.

Quote:

Originally Posted by aa5874

Ipetrich, what is the probability that the genealogies are for the same person?

That's what I'd attempted to evaluate -- the likelihood that Matthew and Luke had randomly selected from a complete genealogy and got at most two matches between David and Joseph.

spin · 12-09-2006, 02:09 AM

Quote:

Originally Posted by lpetrich

Matthew's genealogy follow the southern-kingdom line, though it skips the kings between Joram and Uzziah to get his numbers to fit

The fact that those names are missing is more evidence that the writer received a defective list rather than that he embarked on the totally illogical effort to impose the fourteens on all three disparate sections. The fact that there are only thirteen generations in the first and last sections is more a matter of lack of skill, rather than manipulation, so gross manipulation such as the omission of those kings seems unlikely.

spin

Doug Shaver · 12-09-2006, 06:53 AM

Quote:

Originally Posted by lpetrich

Therefore, it is extremely unlikely that Matthew and Luke had selected from the same list.

Considering that they don't even agree on who Joseph's father was, I'd say it's impossible.

lpetrich · 12-09-2006, 10:06 AM

Quote:

Originally Posted by spin

The fact that those names are missing is more evidence that the writer received a defective list rather than that he embarked on the totally illogical effort to impose the fourteens on all three disparate sections. The fact that there are only thirteen generations in the first and last sections is more a matter of lack of skill, rather than manipulation, so gross manipulation such as the omission of those kings seems unlikely.

I agree that Matthew had miscounted -- there are 41 names in his list instead of 42. The division I had given earlier was 14 - 14 - 13; here is a 13 - 14 - 14 division:

Abraham to Jesse
- the Davidic dynasty begins
David to Josiah
- the Babylonian Exile
Jeconiah to Jesus Christ
- another Big Thing is supposed to happen

Or had Matthew counted David twice? That would make this nice 14 - 14 - 14 division:

Abraham to David
David to Josiah
Jeconiah to Jesus Christ

And since Matthew seemed fairly familiar with the Old Testament, I do think that his omission of some of the kings is deliberate.

lpetrich · 12-09-2006, 10:09 PM

There is a further puzzle about Luke: why did he agree with Matthew in mentioning Shealtiel and Zerubbabel but not any others between David and Joseph?

And a mathematical note:

Applying a transformation to the probability's generating function yields

$G(n,n_1,n_2,z) = F_{2,1}(-n_1, -n_2; -n; 1 - z)$

This makes it easy to calculate its mean, standard deviation, and other statistics, since they are computed from derivatives with respect to z at z = 1, and since one can use the series definition of this function for that.

Peter Kirby · 12-09-2006, 10:22 PM

Can you identify any and all assumptions made, Loren?

At least one assumption seems to be that different names == different people.

I'm not criticizing the assumption, I just want to have them laid out.

kind regards,
Peter Kirby

spin · 12-10-2006, 01:35 AM

Quote:

Originally Posted by lpetrich

I agree that Matthew had miscounted -- there are 41 names in his list instead of 42. The division I had given earlier was 14 - 14 - 13; here is a 13 - 14 - 14 division:

If you count generations, not names, the generations between Abraham and David are 13, David and Jechoniah are 14, Jechoniah to Joseph are 13. Just count the begats or the "was father of"s.

Quote:

Originally Posted by lpetrich

And since Matthew seemed fairly familiar with the Old Testament, I do think that his omission of some of the kings is deliberate.

I don't think he was that familiar at all, though perhaps would like to have been. I'm still flabbergasted over Jesus on two animals entering Jerusalem, because somebody didn't seem to understand parallelism in Hebrew poetry.

Whoever put the genealogy in the form we have it in the text I think certainly received the king list with the names missing. I think I said in another thread that it was probably a scribal error, a common sort of scribal error called haplography. There is confusion in the Hebrew bible over the son Ahaziah, who gets called Azariah in 2 Chr 22:6. As there is a later king Azariah, the haplography would be overlooking those names from the first Azariah to the second, as though Azariah had only been mentioned once. As this would be a textbook haplography, it's much simpler to think that Matt received a shortened list, rather than the writer jimmying the list to suit a post hoc structure.

Where would the fourteen generation framework come from otherwise? Hmmm, I could leave out the names from here to here and count wrongly here and here and get three series of fourteen generations. Make sense to you? It doesn't to me.

spin

12-08-2006, 01:26 PM	#1
lpetrich Contributor Join Date: Jul 2000 Location: Lebanon, OR, USA Posts: 16,829	Matthew vs. Luke Genealogies As is well-known, the genealogies in Jesus Christ given in Matthew and Luke have almost no names in common; for a more detailed discussion, one may visit Paul Tobin's site, which discusses several additional problems. Between David and Joseph: Matthew: 28 ancestors Luke: 40 ancestors sharing only Zerubbabel and Shealtiel. If they are selections from a single list, then that list must have had at least 66 ancestors. The probability of Matthew and Luke independently selecting at most two shared ancestors to include in their lists can be calculated for different total numbers of ancestors: 66 - 2.310^-16 70 - 7.710^-13 84 - 5.410^-8 100 - 1.210^-5 200 - 0.049 There is the additional problem of generation time. King David likely reigned around 1011 - 971 BCE; Jesus Christ was born a little before 4 BCE, when King Herod died. This is a gap of almost exactly 1000 years, and I will use it to calculate the average generation time: Matthew: 34 years Luke: 24 years Minimum Combined: 15 years Matthew and Luke are both fairly reasonable, while the minimum combined figure is almost absurdly small. Therefore, it is extremely unlikely that Matthew and Luke had selected from the same list. Probability of overlap. Imagine selecting first n₁ items from a list of n items, placing them back, and then selecting n₂ items. What is the probability that the two selections will share m items? A detailed calculation reveals $P(n,n_1,n_2,m) = \frac{n_1! n_2! (n - n_1)! (n - n_2)!}{n! (n_1 - m)! (n_2 - m)! (n - n_1 - n_2 + m)!}$ With the help of Abramowitz and Stegun's Handbook of Mathematical Functions, we can find a convenient generating function for the above probability in terms of a Hypergeometric Function: $G(n,n_1,n_2,z) = \sum_m P(n,n_1,n_2,m) z^m = \frac{(n - n_1)! (n - n_2)!}{n! (n - n_1 - n_2 + m)!} F_{2,1}(- n_1, - n_2; n - n_1 - n_2 + 1; z)$ This generating function can be used to verify that the sum of probabilities is 1, and to find the mean and standard deviation: $mean = \frac{n_1 n_2}{n}$ $stdev = \sqrt{\frac{n_1 (n - n_1) n_2 (n - n_2)}{n^2 (n - 1)}}$ These are useful in the case of large n, n₁, and n₂, because the probability distribution then approximates a normal distribution.

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12-08-2006, 02:25 PM	#2
aa5874 Contributor Join Date: Feb 2006 Location: the fringe of the caribbean Posts: 18,988	Ipetrich, what is the probability that the genealogies are for the same person?

12-08-2006, 04:34 PM	#3
WishboneDawn Veteran Member Join Date: Dec 2005 Location: Nova Scotia, Canada Posts: 4,287	I can't even pretend to understand the equations. I take it this is an argument for those who don't think Luke and Matthew manufactured their geneologies to support their different views of Jesus but rather somehow think there's consistecncy between the two.

12-09-2006, 10:09 PM	#8
lpetrich Contributor Join Date: Jul 2000 Location: Lebanon, OR, USA Posts: 16,829	There is a further puzzle about Luke: why did he agree with Matthew in mentioning Shealtiel and Zerubbabel but not any others between David and Joseph? And a mathematical note: Applying a transformation to the probability's generating function yields $G(n,n_1,n_2,z) = F_{2,1}(-n_1, -n_2; -n; 1 - z)$ This makes it easy to calculate its mean, standard deviation, and other statistics, since they are computed from derivatives with respect to z at z = 1, and since one can use the series definition of this function for that.

12-09-2006, 10:22 PM	#9
Peter Kirby Veteran Member Join Date: Jul 2001 Location: the reliquary of Ockham's razor Posts: 4,035	Can you identify any and all assumptions made, Loren? At least one assumption seems to be that different names == different people. I'm not criticizing the assumption, I just want to have them laid out. kind regards, Peter Kirby

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