This is a companion discussion topic for the original entry at https://biologos.org/blogs/jim-stump-faith-and-science-seeking-understanding/long-life-spans-in-genesis
Thanks Jim, good overview. RJS over on Jesus Creed did a post on this some years back as well. Can reference it here: http://www.patheos.com/blogs/jesuscreed/2009/04/14/genesis-4-5-biblical-genealogies-rjs/
Moses came towards the end of these long lifespans and is said to have lived aged 120 (Deut 31:2), his brother Aaron made it to 123 (Num 33:39), while their father Amram and grandfather Kohath lived to 137 (Ex 6:20) and 133 (Ex 6:18). Yet in Psalm 90, which says it is written by Moses, we are told a normal human life expectancy was 70 or 80. “The years of our life are seventy*, or even by reason of strength eighty” (Ps 90:10). Not just other people lifespans either, the writer included himself too our life expectancy is 70 or 80. Psalm 90 does not take the long lifespans literally.
*The classic ‘threescore years and ten’ in the AV
See also Walton’s Ancient Israelite Literature in it’s Cultural Context for a discussion concerning the hexegesimal numbering system used in the Sumerian King’s List, a base-60 system, that may account for the ages.
Thanks for the excellent information about the cultural factors behind the ages that Genesis ascribes to the patriarchs. Good article!
However, the probability calculations are incorrectly formulated in my opinion. This discussion is going to get somewhat technical, so I apologize in advance.
Stump calculates the probability that a specific honorific system of ascribing age has been employed. This is akin to calculating the odds of seeing a specific license plate number while out on a stroll. For example, I could say, “As I walked through the parking garage downtown today, I saw 20 license plates. One of them was DEVL 666. What are the odds?!” We can readily calculate 20*(1/26)4*(1/10)3 = 1 in 10 million. “How amazing is that? Can’t be a coincidence, can it?”
Actually, it’s not quite so amazing. Given a system of license tags in which the first 4 figures are randomly chosen from the alphabet and the last 3 figures are randomly chosen decimal digits, we should expect to see all kinds of amazing license tags: HEVN 777. HENZ 057. TRIN 111. ABCD 123. PATS 001. I’m sure readers could make a game of inventing combinations.
So the right question to ask when looking at license plates is: “What is the probability that I would have seen an interesting license plate today?” This is actually a hard problem to solve mathematically because it is hard to define what makes a license tag interesting. But assuming that there are 10,000 such interesting tags, we can adjust our probability calculation accordingly and say that the probability of seeing an interesting tag in the parking garage today was 1 in 1000. An unusual event, to be sure, but it might not qualify as “amazing!” After all, there’s a pretty good chance I’ll walk through a parking garage at least 1000 times during my life.*
Similarly, when we analyze the patriarchal ages, we need to be aware of the critic who could say, “Sure it looks amazing that only 0,2,5,7, and 9 appear in the set of final digits, but there are a lot of different ways to get just 5 final digits. It could have been 1,2,3,4, and 6. It could have been 0, 3, 4, 8 and 9. And so on. There are so many different ways to end up with just 5 digits that it’s preposterous to think that the particular observation in Genesis 5 happened by any means other than a statistically random distribution of chronological events.”
The question we need to ask then is,“What is the probability that some cultural system is at work, as opposed a statistically random distribution of ages?” To do so, we will have to take into account all the different combinations of 5 digits, since the event of interest is that only 5 out of the 10 decimal digits appear as the last digit of 30 ages in Genesis 5.
Here’s my mathematical reasoning:
- The probability that 30 statistically random chronological ages will end with a final digit selected from a given set of 5 decimal digits is (1/2)30 = 1 in a billion.
- There are 252 combinations of 5 digits = (10! / (5! * 5!))
- Therefore the probability we that the final digits will be restricted to a set of 5 decimal digits is 1 in 1B/252, or 1 in 4 million.
We just showed that the probability that the final digit of 30 statistically random chronological ages will be selected from a set of just 5 digits is 1 in 4 million. That’s basically infinitesimal! So the theory that the ages derive from some cultural system, rather than chronological record-keeping, is overwhelmingly likely.
Stump’s calculations are still useful, of course. We would expect the cultural system at work to be based on Babylonian numerology. Since we just determined that a cultural system is at work (probability = 0.99999975), it’s reasonable to explore the Babylonian numerology hypothesis. And Stump’s calculations show that it’s the best fit for the data.
- The probability of seeing in interesting plate in 1000 walks through a parking garage is not 1 under these assumptions. It is 1 - (999/1000)1000 = 63.2%
Good article, but wasn’t there an article here within the last few years that discussed the numbers of the ages in a base 13 system? I searched for it to no avail. I remember being skeptical at first, but read the reference original article of that theory and found it fairly convincing.
Chris_Falter, you are right to correct the probability calculations presented in the article. However, there is even more to be said:
The null hypothesis used to calculate the 1 in 4 million probability is that all 30 digits are uniformly and independently distributed. However, this is known to be false for the data set in question. 10 of the 30 numbers were produced by summing pairs of other numbers in the data set, so those 10 are not independent. That leaves 20 digits that one might assume to ought to have been uniformly and independently distributed. This increases the probability from 1 in 4 million to 1 in 4 thousand.
Of the 20 non-summed numbers, a full 10 can be seen to end in a 0. This presents an obvious alternative hypothesis to “the numbers are artificial and have cultural significance.” The new alternative hypothesis would be “the numbers are natural, but the ones ending in 0 were rounded off.” According to this hypothesis, one would expect the remaining 10 non-rounded numbers to be uniformly and independently distributed. Would a significance test reject this hypothesis? Let’s check: (1/2)^10 / 252 ~= 0.25, so no rejection.
Conclusion: it seems to me that the alternative hypothesis of rounding is much simpler than the seemingly contrived numerological explanations. And once the probabilities are calculated correctly, we see that the rounding hypothesis is consistent with the data.
Final comment: the article points out how all the age numbers in the data set “can be generated by combinations of 60, 5, and 7” as if this were surprising. However, every single number from 24 to 1000 (and many beyond) can be generated using combinations of those three numbers (in fact, 60 is not even needed, you can do it with only 5 and 7).
Thanks for reading my post carefully and offering a considered critique. You raise some good points that are well worth discussing. I
t is true that there is a certain dependency between 10 of the ages and 20 of the others. However, that should not necessarily lead us to eliminate those 10 from consideration. I will illustrate with an example.
Suppose I were to roll a 10-sided die 30 times consecutively. After each roll, I record the cumulative sum of the rolls so far. For example, suppose hypothetically that my first 10 rolls are as follows:
1 - 3 - 2 - 6 - 4 - 8 - 2 - 5 - 9 - 10
I would then record the following numbers:
1 - 4 - 6 - 12 - 16 - 24 - 26 - 31 - 40 - 50
Suppose further that after all the rolls, I record the final digit of the cumulative sum at each of the 30 steps. From these 30 digits I construct a set of each unique digit. The set could contain from 1 to 10 elements. How many elements would I expect to be in the set?
Under the hypothesis that the die roll is fair, I would expect that set to contain almost all of the digits, if not all of them, in almost all the cases. I would expect the membership of the set to be 5 or less in only about 1 in 4 million cases.
Now someone might object: but isn’t each of the 30 results except for the first dependent upon one or more previous rolls? Since there is such a dependency for 29 of the 30 rolls, shouldn’t we just exclude 29 of the 30 rolls from our consideration?
I think the answer is no. Just because a dependency exists does not mean the dependency is relevant. A dependency is only relevant if it skews the results.
So the question to ask is: does the dependency skew the results in the case we are considering? Probably a little bit, but not as much as you propose, Gabriel. When one of the two addends is 0, then the sum will obviously share a final digit with the other addend. However, when neither of the addends is 0, then I would expect the additive relationship to have no effect on the probability distribution.
We will have to look at the specific numbers in Genesis 5 in order to determine the exact effect on our probability analysis. Unfortunately, I need to go to bed now. Perhaps I will wake up to an answer from you!
Bayes Theorem can help us here. Let’s warm up by applying it to the account of King Alulim in Erudig.
We have two theories before us to explain the account of his supposed 28,800 reign:
- The number is an approximation of a real chronological time period
- The number is based on cultural factors.
In probability terminology:
- P(real chronology | account of 28,800) - the probability that Alulim really reigned for about 28,800 years, given the existence of such an account.
- P(cultural factors | account of 28,800) - the probability that cultural factors are explanatory, given the existence of such an account
According to Bayes Rule:
P (real chronology | account) = P(account | real chronology) * P( real chronology) / P (account)
…and the key term is P(real chronology). I assert that P(real chronology) = 0.000000 because people don’t live past 110-120 years. Care to disagree?
Now let’s look at the other possibility:
P(cultural factors | account) = P(account | cultural factors) * P(cultural factors) / P (account)
I assert that:
- P(account | cultural factors) is close to 1.0.
- P(cultural factors) is close to 1.0 because culture plays a large role in the telling of stories
And now we don’t really need to evaluate P(account) because the numerator is so large.
The conclusion of this Bayesian analysis is that cultural factors, not an approximation of a real chronology, explain the account of King Alulim.
A similar analysis could be applied to the ages of the patriarchs in Genesis 5, with similar results.
- Our prior for P(cultural factors) might only be 0.5 because the Hebrews were not necessarily copycats of the Babylonians in all things, but the probability of cultural factors as the explanation for the given ages is very close to 1.0 because P(account | cultural factors) > 0/9 based on your numerical analysis and the P(account) is well below 1.0 (because there are plenty of accounts of ages in Genesis that fall below 120).
- P(real chronology, approximated) is extremely low because the age is so far beyond medical possibilities, and there is no hint of a divine miracle that would override biological reality.
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©
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© 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© 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!
Hack those P values.
Having had a cursory glance at the article I am struck by things that left me feeling it was somewhat hollow and lacking in depth.
Firstly, you make a very quick declaration of possible problems with the evolutionary viewpoint but then do not explore those problems in depth. Then, you quickly make the statement that the text as read should be re-interpreted with a more modern understanding. I find this step too hasty in its execution.
I would have liked to see you first wrestle with the text as it stands and is easily understood and then examine the import of what it implies in such a context. I think that only then when you’ve exhausted that side of things that it would have been appropriate to move on to a different interpretation. As it stands I come away feeling that evolutionary thought processes was the overriding factor that drove you to start and indeed give you the authority to re-interpret the text according to your own preference.
Furthermore, upon making your re-interpretation you neglected to explore the implications for applying that same re-interpretation to the rest of scripture as a test to see if those parts where numbers and ages are mentioned then still makes sense.
To give a hint of an alternative look at the text, taking a straight-forward understanding: If one draws a graph of the ages at time of death versus time it is incredibly striking how an almost pure exponential decay is seen. What are the implications of that from a mathematical and biological viewpoint? Or indeed from a theological viewpoint in the light of the statement that men’s time will be 120 years in Genesis 6:3, fully understanding that the original text plays on both the time given until the arrival of the flood as well as the ultimate lifespan allocated to mankind.
Further - when one looks at the sudden downward jump that occurs at the time of Peleg one can be led to understand that enormous stresses must have occurred in the populations at that time. Why?
These are just a few of the kind of questions that I think you should have explored first, rather than making a rather hasty retreat into re-interpretation of the text. Just a thought. Use it, don’t use it, your choice.
Here’s a thought for you: have you ever noticed that the only people who are mentioned in the Bible as having had extraordinarily long life spans were the immediate line from Adam through to Abraham, Isaac and Jacob, then Moses and Job? We’re not told anything special about the life spans of Cain’s line, for example, nor are we told anything remarkable about anyone else in the Bible, anywhere.
Additionally, we’re told elsewhere that long life is a particular blessing from God (e.g. in Psalm 91;16).
This suggests to me that if these figures were literal, precise ages, then they must have been supernatural, and the exception rather than the rule. I see no reason whatsoever, either Biblical or scientific, to believe that long life spans were the norm either before or immediately after the Flood, not even in a young-earth model.
Hi Chris, I wrote this several years ago, so it has taken me a little to remember what I was saying. Having done so now, I agree your amendment makes perfect sense. So we’re down to 1 in 4 million. But now I wonder if the odds get even better if you apply my line of reasoning in footnote one to your insight. The 30 numbers aren’t all independent, since one of them (the patriarch’s total years) is just the sum of the others. In the specific example of these 5 final digits, it turns out that the sum of any two of them have a 64% chance of yielding an “approved” digit (rather than just a 50% chance by pure random selection). Presumably of the 252 combinations of 5 digits you identified, there will be different percentages of getting one of those same five digits by adding two of them together. I can’t think of an easy way to calculate this, though. If this specific example is representative, we might be down to 1 in 400,000.
@derepentigny @Chris_Falter I just responded to Chris about the independence of 10 of the 20 numbers. I see I should have read through the rest of the comments before doing that since I now see that you guys are on this. But I think my reasoning in footnote one is different than either of you have given here. I’d be happy to hear what you think about that.
Hi Prode, thanks for your comment. I don’t think it’s quite fair to say that I’ve gone looking for an alternative interpretation of Scripture based on “evolutionary thought processes.” My argument was essentially: There are clear examples of numbers being used in the ancient Near East in straightforward ways, and there are clear examples of numbers being used in the ancient Near East in symbolic ways. Genesis was written in the cultural context of the ancient Near East, so when we find numbers being used in the book, we ought to ask which use of numbers is being employed. Then, the evidence seems to be that there is something more going on than just the straightforward reporting of ages.
That’s not an attempt to reinterpret things, just an attempt to purse sound principles of biblical interpretation. And (like I said in the piece), there’s not much of a connection to evolution in considering this.
Other than that YECs often use the word “evolution” to refer to anything other than a strict literal interpretation of Genesis - or, more generally, to anything and everything in science that they don’t like.
I’ve even seen one YEC use the word “evolution” to refer to the fact that the atmosphere isn’t sandwiched between two layers of water, as a strict literalist interpretation of Genesis 1:6-8 would suggest…
What a great anecdote! But let me understand exactly what you mean: did the YEC in question concur that there was (and still are?) heavenly waters above a Firmament?
Jim, thanks for the refresher on Genesis Ancient ages. When I first became interested in Genesis about 20 years ago I naturally like many others became intrigued with these long-life span ages. Carol Hills work over at ASA along with some others who tied the dates into celestial (Sun, Moon and Stars) relationships were quite helpful. The Jews were indeed products of their ANE culture and I would put my estimated guess into the period of about 500 to 400BC when Genesis found its final redaction and influence from the times.
However probably the most important discovery that I found helpful was when I begin reading other 2nd Temple literature such as the Enoch and Jubilees pieces that heavily interfaced directly with Genesis directly. They did so specifically with the ages and what their implications might have meant contemporaneously during this period and that helped fostered their concepts upon the early NT writers.
The most important concept I discovered was that these long lives never reached the zenith lifespan of 1000 years. That was until Revelation. One of the underlying principles of Jewish numerology was that 1000 exemplified eternal or ultimate relationship with God; it also signified completion such as eras and periods with “one day being as a 1000 years” typifying the completion of a period of time that was God ordained.
The theme of Adam and his Sethite lineage never reaching a 1000 year life span was predicated upon the failure in the Garden where Adam and Eve chose to forsake the way of life by following the “commandment”.
Jubilees 4:29 … Adam died, … And he lacked seventy years of one thousand years; for one thousand years are as one day in the testimony of the heavens and therefore was it written concerning the tree of knowledge: ‘On the day that you eat thereof you shall die.’ For this reason he did not complete the years of this day; for he died during it.
Yes, the Garden story has an undercurrent Jewish indictment already 500 years prior to Pauline theology against “legalism” as the path to righteousness. There were two lineages from Adam; Cain and Seth. Cain had no long life and was dead to God and was not attributed with any form of lifespan as he was alienated and forsaken from God. Seth followed Adam (Gen 4:26) and was the precursor to the Hebrews and the “seed” who although “God’s Chosen” were never in a full complete relationship with God. (we see this indictment against the Jews themselves via the Prophets constantly haranguing their failures.)
Jubilees 23: 15 Then they shall say: 'The days of the forefathers were many (even), unto a thousand years, and were good; but behold, the days of our life, if a man has lived many, are three score years and ten (70), and, if he is strong, four score (80) years, and those evil, and there is no shalom in the days of this evil generation.'
The Jubilees piece provided hope though.
Jubilees 23:26 And in those days the children shall begin to study the laws, And to seek the commandments, And to return to the path of righteousness. 27 And the days shall begin to grow many and increase amongst those children of men till their days draw nigh to one thousand years. And to a greater number of years than (before) was the number of the days. (They would live longer than their ancient predecessors who lived 900 years plus.nv)
The Jews understood their problem with trying to use the Law as a means to “self-righteousness” long before Paul explained it to us in Romans and his letters. Ultimately the Jubilees literature spells out some of these concepts when it attributed the declining ages that begin to take hold within the “seed” line finally reduced to “80” years. Again, this was a consequence of the idol worship, violence and apostasy that continue to manifest itself in the Holy people until the coming of “Messiah”. That is why the book of Revelation recognizes that those martyrs and faithful in Christ were eternally blessed as having reached the 1000-year life span. Unlike Cain they were not subject to the second death which amounted to being cast out of God’s presence (where there was weeping and gnashing of teeth). They had no blessed existence without Christ.
Rev 20:6 Blessed and holy is the one who shares in the first resurrection! Over such the second death has no power, but they will be priests of God and of Christ, and they will reign with him for a thousand years.
I think when we understand the “theology” of the 2nd temple period and how the Biblical symbols were used as you have laid out then we can possibly read the stories more contextually. Unfortunately, we often get side tracked with the numbers themselves or our cultural inclination to literalism and miss the underlying big picture themes that transcend the whole narrative of Old and New Testament. It’s hard work but reading their ancient literature is helpful in grasping how they dealt with these symbols.
I’m not sure exactly what point he was trying to make. He’d copied and pasted a table of ways in which a strict literal reading of Genesis 1 conflicts with science from somewhere or other. I’ve also managed to find the same table on the last slide of this presentation: http://slideplayer.com/slide/10023138/
I’ve no idea where this table originally came from. The guy in question was heavily influenced by Kent Hovind, so it may be that it originated somewhere in Hovind’s literature or a Dr Dino video somewhere?