Messiah vs. Virgin Birth
Offline I hear a lot of terribly convincing arguments on here, but it occurred to me that there's one I have a problem with. I hear a lot of people talking about how Jesus being both descended from King David through Joseph and also being born of a virgin is incompatible. Of course it is. I'm also not saying any of these propositions are true, but just for the sake of argument:
Let's say it is absolutely true that Joseph was descended from David AND it is also absolutely true that Mary was a virgin. I can't see how any believer would possibly care that Joseph was not Jesus' biological father. Out of all the billions of people on the planet the mother of the son of god (who could just as easily have been a Chinese woman or an Eskimo) could have chosen to associate herself with, for it to have been THIS guy, Joseph, is almost statistically impossible. Even if you look to her, Mary, personally, and compare only the people she came in contact with in the years of her life before the pregnancy with how many thousands of people in her part of the world might have been also descended from David, it's still extremely unlikely to have been one of them...I'd say a one-in-50,000 chance, at best.
I realize this is only one of many, many quite valid arguments, but I think this is one that ought to be retired.
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Actually, assuming for the sake of argument that King David actually existed, and Joseph actually existed, and Joseph actually was a descendant of King David, then the odds are much better than 1 in 50,000 that any random Jew would have been a descendant of King David.
This may take some background reading, so here are a few links:
http://blog.case.edu/mxs24/2006/10/02/realistic_calculation_of_the_date_of_our_most_recent_common_ancestor
http://en.wikipedia.org/wiki/Most_recent_common_ancestor#Time_estimates
http://humphrysfamilytree.com/ca.html
This assumes tracking the ancestry through both the mother and father. However, even if you only track through the father, the odds are still good that King David had many many male descendants if he had any at all.
First let's examine it as if we're tracking both male and female descendants, as the links above use.
The trick is that genealogical ancestry is an exponential thing. You have 2 parents, 4 grandparents, 8 great-grandparents, etc. Very quickly, the number of your genealogical ancestors grows far bigger than the total population of the planet. Go back only 10 generations, and that's 2^10 or 1024 ancestors. 20 generations and it's about a million. 30 and it's a billion.
Clearly, that's not possible because there were less than a billion people alive 30 generations ago. So, there is some overlap. That's called pedigree collapse.
On the other hand, if someone from 30 generations ago is your ancestor, he's also probably the ancestor of most, if not all, of the people in your homeland. That's because the number of descendants per person per generation is greater than 2 (or else the population would have died off). So, if someone successfully had descendants 30 generations later, he probably had more than 2^30 descendants, which is most, if not all, of the people in the homeland.
After a certain point, everybody's pedigrees collapse into an identical set of ancestors (which is what is explained by the links above). If Joseph was descended from King David, then probably most, if not all, Jews at the time were descended from King David.
According to wikipedia (and Luke), the number of generations between David and Joseph is 41. That means if Joseph was descended from King David, then David probably had more than 2^41 or 2 trillion descendants, which is impossible. The pedigree collapse makes it likely that all the Jews at the time were descended from King David.
So, actually, it's not surprising that Joseph was descended from David. Pretty much any Jew would have done. Assuming that Jesus, David, and Joseph actually existed, of course.
If you go by Matthew's genealogy, then it's 26 generations, and still a good chance that David was the ancestor of most, if not all, Jews at the time. 2^26 is 67 million, which is much greater than the number of Jews at the time. Pedigree collapse again makes it likely that all Jews were descended from David.
Now, if you restrict the analysis to only male descendants, it's a less powerful argument, but still powerful.
If we examine what the Bible claims about some of those characters:
David had 18-20 sons, depending how you count.
Solomon had 700 wives and 300 concubines, so probably many many sons.
If you consider 1 million male descendants after 26 generations, then:
x^26 = 1 million
log(x^26) = log(1 million)
26 log(x) = log(1 million)
x = 10^(log(1 million)/26)
x = 1.7 male descendants per generation
So, if there were 1.7 male descendants per generation -- and considering David had 18 and Solomon many, this doesn't seem unreasonable -- then there would have been at least 1 million male descendants from king David, about 500,000 would have been alive at the time of Joseph. Pedigree collapse might lower that to around 250,000.
Considering there were probably fewer than a million Jews alive, and only half would have been male, then this conservative estimate of 1.7 male descendants per generation yields a probability of at least 1/2 that any male Jew was a descendant of David.
If you bump that estimate up from 1.7 to 2, then you would get 2^26 male descendants, or 67 million. Half that for those alive at the time is 33 million. Pedigree collapse would make that all, or nearly all, the male Jews alive at the time would have been descendants of David.
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Excellent point, Natural.
I've never thought of that angle on the descent thing about Jesus.
Makes the claim of descent from David pretty pointless, if the probabilities that just about everybody around there at the time was descended from David.
Just another example of the ignorance of the time, or at least the really superstitious importance they gave to lines of descent. The further you go back far enough, the less it matters.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Some of the math flew over my head, but that's okay, I get the general gist of what you mean. I didn't really think of it in those terms. Thanks a lot for taking the time to explain it the way you did.
I thought of a simpler way to explain it.
Whenever you do exponentials, you have to look at the base:
If the base b is 1, then b^x is always 1, because 1*1*1*... = 1. It doesn't matter what x is.
If the base b is less than 1, but greater than 0, then b^x approaches 0 as x gets bigger. Consider 0.5*0.5*0.5*... follows the trend 0.5, 0.25, 0.125, ... down to 0 as each time it gets cut in half.
If the base b is greater than 1, then b^x approaches infinity as x gets bigger. 2*2*2* ... follows the trend 2, 4, 8, ... growing very quickly, doubling each time.
Now, consider when b is just slightly bigger than 1. For example, say 1.01. In this case, it might seem like it will grow very slowly, as 1.01*1.01*1.01* ... follows the trend 1.01, 1.0201, 1.030301, etc.
But actually, even a base slightly bigger than 1 will cause b^x to grow very rapidly as x gets bigger. You can get a grasp of how this works by figuring out how long it takes base b to double.
When b = 1.01, then for b^x to double from 1.01 to about 2 requires:
b^x = 2
log(b^x) = log(2)
x log(b) = log(2)
x = log(2) / log(b)
x = log(2) / log(1.01) Use your calculator to figure this out
x = 70 rounded up from 69.6
To test it, try 1.01^70 = 2.00676
So, the interesting part is that when b is 1.01 it takes 70 generations to double. 140 generations doubles again to 4, 210 generations is 8, 280 generations is 16, etc. So, you still get the exponential doubling curve, but instead of doubling at every step, it doubles at every 70 steps.
Likewise, if b is slightly *less* than 1, then as x grows bigger, b^x will fairly rapidly shrink down to 0. Not quite as rapidly as when b is 0.5, but still exponentially rapidly. You can do similar math to find out how many generations it takes for b=0.99 to shrink down to half.
Now, consider the case of Joseph and David.
If Joseph is definitely David's descendant, then the average number of male descendants for David is *at least* 1. If David averaged slightly less than 1 male descendant per generation, then after 26 generations, probably one of the sons would fail to have a son of his own, and that would be the end of David's male line. Joseph wouldn't have been a descendant of David because David probably wouldn't have *any* descendants. Since we know Joseph *is* a descendant of David, then this scenario couldn't happen. Therefore, it's not possible (or at least extremely unlikely) that David averaged less than 1 male descendant per generation.
So, David *must* have had an average b of at least 1. Probably, it was at least slightly greater than 1, since to have an average number of male descendants *exactly* equal to 1 would be quite rare. So, Joseph is probably not the *only* living male descendant of David at the time of Jesus' birth. Even just a small increment of b greater than 1 would mean b^26 would be at least 2. (In fact, b would only have to be about 1.027 for there to be two male descendants of David after 26 generations; consider that if either Joseph or Mary had a single brother, this would set a hard lower limit on b at 1.027).
The point to take home from all of this is that if David had *any* male descendants at the time of Joseph, then he almost certainly had *many*, because the base b in the b^x equation was almost certainly greater than 1. The greater the number of generations, the more male descendants he'll have, again because b is greater than 1.
At 26 generations (i.e. x=26), as discussed in my previous reply, the b would only have had to have been around 1.7 to give David a million male descendants. A value of 1.7 seems like a very conservative estimate, considering David's and Solomon's many sons.
Again, the interesting point is that if some ancient male *does* have male descendants, then he probably has *very many* male descendants, because in order to have *any* his exponential base b would have had to be at least 1, and probably at least a bit greater than 1. The more generations pass, the more male descendants he will have, and they will grow in number exponentially quickly.
You can consider the number 1 as a kind of 'tipping point' in genealogy, and the fact that Joseph *was* a descendant of David *proves* that David's b is past that tipping point. If you can prove an ancient person has *any* male descendants, you can prove he likely has *very many*. The existence of a single male descendant proves b is at least 1.
If you keep that concept in mind, that a single descendant proves a tipping point of many descendants, especially as the number of generations grows, then I think the whole thing should make intuitive sense, without needing to remember much about math.
(In the case of exponential growth, I know it can be tricky for it to 'click' for some people, so forgive me if the above is overly repetitive and pedantic.)
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I will not pretend that I am a mathematician. I also spent some time (probably need to take more) reading your logic about the fact that the odds that Jesus would be in the line of David and I have a few questions concerning the logic. Please simply take these as questions . . . not attacks. I know you do not believe the Bible, but for the sake of looking at the math and the logic simply give me some slack on this issue.
1. According to Numbers, there were over 603,550 males over 20 able to go to war. This number does not include the tribe of Levi and it does not include women and children. This number is before they entered into the promise land. I am not sure what the population was during the reign of David, but needless to say . . . a lot. I would not even know how to estimate the population. So, for the sake of argument lets say there are 1,000,000 couples. Jesus is in the line of David and Bathsheba - 1 couple of the 1,000,000. I understand that when you go down the line the odds are great, but when you go up the line, isn't it a million to one that their lineage is of David's line. Couldn't have gone any other way.
2. When you look at the linage in Matthew there are 3 sets of 14 generations. 28 generations between David and Christ. The issue between 42 generations between Christ and David in Luke and 28 in Matthew is for another discussion, but my point is that of the 28 generations listed, 14 of them are of royal blood line and therefore the idea of pedigree collapse does not apply. This is not tracing people through a 10 cousin removed. Therefore, you are left with 14 generations between the royal blood line and Christ. 14 generations would only give you 4096 ancestors. Does the math you introduced take all of this into account and does it still work. Please correct me if I am in error in my thinking.
3. The prophecy dealing with the lineage did not only specify David, but Judah as well. There were 12 tribes - again in Numbers each tribe has between 30,000 and 70,000 people. It is certainly possible that they intermarried and they were marrying foreigners as well. So, with 603,000+ men over twenty - only 74,600 are listed in this tribe. So if you trace the line back to Judah, you would also have the 1 in ??? and his lineage would not only come from Jesse's family but from that one particular son. So mathematically - the formula would have to work so that Jesus would not only have to go through David, but through Judah as well, which was only 10 generations before David. Therefore, according to your math, that would be only 1024 descendents. We already know that when they entered the promise land, if you count only the adults - approximately 1.3 million people. I am not sure any of this was taken into account when you were making your claim. What are the mathematical possibilities for a person to come through 2 particular families and the fact that it was predicted 1200 years before the birth.
4. Lastly, does this math take into account life expectancy - which would not have been near what it is today. What about infant mortality? Does it take into account that this is a lineage through men. I have certainly witnessed familys in which for generations boys have been born and then all of a sudden . . . nothing but girls. So, is it also possible that the math does not take into account that there could have been a generation in which very few boys could have been born in which the line to Jesus could be sustained. Wouldn't that also skew the numbers.
I am interested in how you would answer these four questions. Again, I know you do not believe the Bible, but in reality I am not sure the mathematical equation answers the full question.
For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.
So if for the sake of argument we retire this argument, aren't there two conflicting accounts of Joseph's family line?
Well, if what Natural explained is true, it may be that there are even more than just two ways to connect Joseph to David.
Good point
The question remains, why the hell does it matter?
One issue would be 'fulfilling' prophecy - but if the birth didn't occur until most or all Jews were descendants of David, that really isn't much of a prophecy.
The conflict in the two accounts of the official line of descent points to sloppiness in the scripture - although it may be possible they could both be true.
Then there is the point is that Jesus' only 'line of descent' would have been from God, if the virgin birth thing were true. It would then only amount to a claim that the messiah will be born of a woman currently the wife of a descendant of David.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
To a believer, I really doubt that would make any difference. Besides, even if everyone within 50,000 miles was a descendent of David, we can still maintain that no Eskimos were his descendents (presumably) and Jesus could just as easily have been born "of a virgin" up there.