Hello, Chris_Falter. Yes, you are quite right! Even if there are dependencies among the numbers in a data set, if the dependencies are known, they can be modeled and accounted for in the probability calculation. So let’s do some number crunching…
Based on the high number of zeros in the final digits of the age-of-son numbers and the remaining-lifespan numbers of Genesis 5 (10 out of 20 digits are zeros), my proposed alternate hypothesis says that something like half of the numbers are rounded. There are five distinct final digits (0, 2, 5, 7, 9) in the age-of-son, remaining-lifespan, and sum numbers. If the age-of-son and remaining-lifespan numbers were randomly generated from a uniform distribution, how unlikely is it that only 5 out of 10 of the possible digits are represented in the data set of combined numbers (including the sums)?
This is a bit tricky to solve analytically, so I decided to get the answer from a numerical simulation. I wrote a program to do the following:
- Generate a list of 10 pairs of random single digit numbers (20 numbers total). For example, a typical list might look like [ (1,1) (2, 4) (3, 3) (2, 6) (4, 9) (1, 6) (3, 6) (6, 5) (5, 5) (2, 9) ].
- “Round” half of the numbers by setting 10 randomly chosen numbers in the list to 0. This gives 10 zeroed out numbers and 10 other numbers. For example, applying the "rounding" to the previous list might result in [ (1,1) (0, 0) (0, 0) (2, 0) (0, 0) (1, 6) (3, 0) (6, 5) (0, 0) (2, 9) ].
- Turn each pair in the list into a triplet where the third number in the triplet is the sum of the other two numbers mod 10 (mod 10 so that we just get the final digit). Our example would turn into [ (1,1, 2) (0, 0, 0) (0, 0, 0) (2, 0, 2) (0, 0, 0) (1, 6, 7) (3, 0, 3) (6, 5, 1) (0, 0, 0) (2, 9, 1) ]
- Count how many distinct digits are in this final list of single digit triplets. In the example, there are 8 distinct digits (there is no 4 or 8).
- If the number of distinct digits was less than or equal to 5, it was considered a success. The example would not be a success.
The above was run repeated 1 million times. There were 28,487 successes. This gives a p-value of 28,487 / 1,000,000 ~= 0.028.
Now, how do we interpret this result? I’m not sure. Typical null hypothesis rejection thresholds are either 0.05 or 0.01. We are in the unhappy no-man’s land in between those two numbers.
One appropriate consideration would be how many different numerical patterns researchers have checked for in the Genesis 5 data set. If this is the only pattern anyone checked for, then a p-value of 0.028 in this test would make me lean towards rejecting the null hypothesis. If a dozen other patterns were checked for and not found, then we would need to adjust the p-value above to take into account the multiple comparisons. The adjusted p-value would be 0.336 (using the Bonferroni correction), which would be not result in a rejection of the hypothesis.
Based on how much attention is paid to Genesis by Biblical scholars, this pattern is certainly not the only pattern considered. I’m not sure how to estimate how many were considered, however.
Out of curiosity, I also decided to check the middle digit of each number in Genesis 5 to see if the same pattern recurs there. However, every digit except the digit 2 is found, so there's nothing unusual to see there.
Regarding the Bayesian argument: I enthusiastically agree with you that that is the right way to think about these things! My only question is with regards to assuming P(real chronology, approximated) is extremely low. It seems to me that P(real chronology, approximated) is composed of three mutually exclusive sub-hypotheses:
P(real chronology, approximated) = P(A) + P(B) + P(C)
A = naturally long lifespans and basically similar environmental or genetic conditions
B = naturally long lifespans and significantly different environmental or genetic conditions
C = miraculous long lifespans
I agree that we have enough medical knowledge to say P(A) is extremely small. Some have argued for B, but I have not seen any convincing proposals for how this could work, so I think P(B) is low as well. But it’s hard for me to determine what P(C) should be. By one argument, since the text does not say “and these lifespans were due to a miracle,” the probability should be low. On the other hand, some would say that when something unnatural happens in Scripture, the default assumption should be that a miracle happened. On the third hand, maybe neither of those two arguments is overly convincing, so one should be neutral to P(C) and set it to 0.5. Ultimately, I think one’s conclusion on the entire matter is largely dependent on what you believe that probability to be.
If you have more insightful comments, I would be glad to hear them!