Thursday, July 12, 2007
Patriarchal Lifespans Follow a Sigmoid Curve
Figure 1 is a plot of the 35 lifespans as a function of date of birth in years BC. It is immediately apparent that the lifespans are not a random or incoherent set of values but that they form a well-defined and regular series with time. Notice how the ages of the prediluvian patriarchs are fairly uniform and run between 895 and 969 with the exception of Lamech (777 years). Following the Flood (F), however, the lifespans drop rapidly and consistently with time. It is interesting to notice that although Shem was born before the Flood he lived most of his life of 600 years after it. The values of the age at death in the period after the Flood from Shem to Terah are between 600 and 148 years. The lifespans from Abraham on continue dropping but at a much slower rate. They run between 180 and 110 years before the Exodus (E). During the Monarchy, longevity continues to slowly drop. The maximum age is 70 years for David, while it is only 36 for Ahaz.
It includes a lot of discussion on possible causes of ageing, but really nothing new. Now, Lopez calculated his curve by plotting the ages based on the date of birth of the individual. I have heard (I will not name the source since I do not have a perfect memory and may be misrepresenting it) that the most regular data points are retrieved if you base it on generations after Noah (though I'm not sure what curve this follows). The person who related this to me also mentioned that the Bristlecone pines (i.e. the oldest tree - thought to be started growing almost immediately after the flood) also follow this same distribution, with the children dying younger, and the children's children dying even younger, following the same basic series as the human lineage. Anyway, I wish I had a source for this information, but I don't, so treat it as speculation, but it would be an interesting research project. Lopez concluded:
The Old Testament life-spans were interpreted in the light of the ageing process in modern populations. Ageing can be characterized by an increase in mortality rate with age. The increase has been found to be exponential and can be expressed by the Gompertz formula.
The Gompertz formula relates the average age to the mortality rate, and Lopez noted that the sample size pre-flood is too small to be certain, but that in general terms if follows the characteristics of what we know about ageing, just at a very low mortality rate.
For more info about sigmoid curves, see here and here.
For more info about the Gompertz formula, see here.