[Joseph C. Dillow, 'The Waters Above', Moody Press, Chicago, 1981, p. 158-]:

"Donald Patten made the ingenious observation that there seemed to be an exponential variable involved in the decline of longevity of the post-Flood patriarchs. Prior to the Flood, men lived an average of 912 years, but immediately after the flood longevity began to decline exponentially....

The exponential decay curve in Genesis 11

In order to test the plausibility of Patten's observation of an exponential variable in the declining longevity of the postdiluvian patriarchs, the age at death versus the number of the generation from Noah was plotted on semi-log paper. When this was done, a straight line described the best fit of the points; this suggests that an exponential variable is likely. A linear regression analysis was made using the data given in Genesis 11 to determine the equation of this line and the correlation coefficient. The data in Table 5.3 was used for this regression calculation...

Noah 950 0
Shem 600 1
Arpachshad 438 2
Shelah 433 3
Eber 464 4
Peleg 239 5
Reu 239 6
Serug 230 7
Nahor 148 8
Terah 205 9
Abraham 175 10
Isaac 180 11
Jacob 147 12
Moses 120 (but 70 is the norm Dt. 34:7; Ps 90:10) 17

Based on the biblical genealogies, Moses' generation falls in the seventeenth generation from Noah if Noah equals generation 0. A linear regression yields,

Y =652e -0.13x

where Y = the age at death, and x = the number of generations from Noah, where at Noah's generation x = 0. In order to find out the statistical validity of this curve, a correlation coefficient must be determined. The correlation coefficient, r, measures the degree of fit of the given points to the least-squares straight line. When r = 1, the correlation is said to be exact. When r = 0, the variables are said to be uncorrelated with a linear equation. The correlation coefficient derived from Table 5/3 is r = 0.95. That means there is an extremely high correlation between the variables and the above equation...

[The] Equation... does not adequately explain the longevity of Noah. The first point on the graph on the Y axis is 950 years, but it should be closer to 652 years if an exponential variable is involved. It may be that the pre-Flood conditions protected Noah during the 600 years of his life before the condensation of the canopy (Gen 7:6). Shem, similarly, lived out his early 98 years under canopy conditions (Gen 11:10). If the linear regression is calculated from Arpachshad to Moses, leaving out Noah and Shem, the following equation results:

Y =436e -0.119x

and a correlation coefficient of 0.94. In this equation, all of the data scatter around the straight line, and none are as far off as Noah.

This result has significant implications. First of all, it gives a high degree of credibility to the historical nature of the genealogy. The probability that this account was a result of mythical influences is virtually zero. The odds that such a curve could result from anything but an actual historical circumstance are remote. There is nothing comparable in the Sumerian data.... the data... are not exactly exponential. They scatter about such a function, thereby attesting to naturalness rather than artificiality.

Second, this curve would tend to argue against the idea that there are gaps in the genealogy. If there were gaps in the genealogy, it would be difficult for an exponential decay curve to have resulted. In order to achieve that result, the gaps would have to be systematic and specific, not random. Furthermore, an absence of gaps seems to be attested to earlier (see Gen. 4:25-26), where a father-son (not a father-descendant) relationship is traced through the first three of the ten generations of the pre-Flood patriarchs in the genealogy of Genesis 5. Also, Jude informs us that Enoch was the seventh from Adam (Jude 14), and in counting the generations in Genesis 5, Enoch is indeed the seventh. So there are apparently no gaps in the first seven of the ten pre-Flood generations. Finally, the fact that the age of paternity (birth of first child) is given could be for chronological purposes. This, of course, means that Bishop Ussher was not far off when he calculated the creation of the world in 4004 B.C. I would be inclined, then, to date the Flood in the year 2346 B.C....

The archaeological data is hardly sufficient to reject dogmatically the recent Flood date.... in view of the extreme paucity of information presently available for scholarly analysis perhaps it is premature to reject the strict interpretation of the Genesis genealogies. Would it not be more prudent to hold tentatively to the no-gap interpretation (since it seems to be the most natural) and wait for the data to come in?...

A final and most significant implication of this decay curve is that it attests to some kind of environmental change that drastically affected the physiology of man and reduced his longevity from an average of 912 years prior to the Flood to 70 years 850 years after the Deluge."

[Mantague Stephen Mills states, {'A COMPARISON OF THE GENESIS AND LUKAN GENEALOGIES (The Case for Cainan), A Thesis Presented to Dallas Theological Seminary, April 1978, Chapter II, p. 8}]:


"The first question which is raised in a genealogical discussion is whether or not the table is tight or loose...

The text of Genesis 5:6, for example, is interpreted something like this - 'and Seth lived one hundred and five years and begat the ancestor of Enosh.

However this interpretation does not fit at all well in Genesis 5:3 which would make nonsense if it read -

'When Adam lived one hundred and thirty years he begat an ancestor who begat a son in his own likeness and after his image and called his name Seth.'

The Hebrew text makes the objection clearer for it reads (literally) 'He begat in his resemblance to his image, and he named him the name Seth.' Adam is the only nominative in the sentence so grammatically there does not appear to be any license to introduce an intermediary (or intermediaries) as an antecedent for in his resemblance to his image. Syntactically the resemblance and image must relate to Adam for they are coupled by genetives of possession to the subject.

The argument about Seth's birth may appear to be remote from the birth of Shelah, but exactly the same grammatical construction, and form of the verb (a Hiphil) are used in both cases, so the earlier case helps to translate the subsequent cases accurately, for it is clear that Adam's act of begetting Seth was the same as that described of Arpachshad and Shelah. Furthermore ["bene" = Hebrew characters rendered "became the father of" (NIV) or "begat" (KJV)] in the record of Arpachshad begeting Shelah is followed by the direct object marker ["yalad"] with Shelah's name as the object, and this is the case with all the names in the genealogies of Genesis 5 and 11. Genesis 5 is pertinent for it starts with this formula in verse 3 and as is indisputably evident from Genesis 4:25 Seth was Adam's direct, first generation descendant, and it concludes with Noah and his progeny Shem, Ham and Japeth, whom the historical record makes clear were his sons and contemporaneous with him. So this particular genealogy closes with a substantiated closed generation just as it opens with a substantiated closed generation. Thus this first Biblical genealogy, neither grammatically, nor contextually allows for an interpretation of a loose construction.

Jude 14 seems to confirm this argument as far as Enoch's generation, for this verse, which is regarded as inspired scripture, indicates the correctness of the closed genealogy hypothesis as far as the seventh generation, that is, the first six births out of the twelve recorded. The last three births are established by the historical record, as noted in the preceding paragraph, as is the ninth, for Genesis 5:28, 29 make it difficult to suggest that Lamech was not the direct father of Noah. Thus, of the twelve specific births that are recorded in Genesis 5, ten are demonstrably recorded as a tight father/son sequence. Proponents for an open genealogy are thus left to either place all their gaps in only one sixth of the genealogy, between either Enoch and Methuselah, or Methuselah and Lamech, or alternately, to explain Jude 14 as saying that Enoch is the seventh recognised name (not generation) after Adam. This would not be the literal meaning of the words. As the former alternative cannot be regarded as reasonable, for it is obviously a travesty of literary style, it seems reasonable to argue that a tight genealogy in the case of Genesis 5 is supported scripturally....

The argument developed above has revolved around Genesis 5 but, as indicated, the same grammatical, syntactical and lexical arguments apply to Genesis 11. Furthermore this table, too, [Gen 11:10-27] closes with a record of a demonstrably tight genealogy in the case of the last four births mentioned in a total of twelve births. Clearly Genesis 11 must similarly be regarded to be a tight genealogy.

The argument has not dealt in detail with the verb [rendered to beget] and this, as well as the context, deserves consideration.


The root meaning of the verb... is 'to bear, bring forth, beget, and the derivatives are all related to birth, or offspring. The word is used in the Hiphil stem in Genesis 5 and 11. The meaning of the Hiphil is primarily the causative of the Qal stem so the meaning of [begat] in this stem is 'to cause to be conceived.' The clear lexical meaning is thus that, for example, Adam fertilised the ovum that became Seth. This is what 'begat'... means... It is safest to understand the terms bene and yalad in Genesis as designating physical ancestry in the beginning...

Probably the clearest testimony to the direct father/son relationship conveyed by the use of bene = begat in Genesis 5 is born by the Samaritan Pentateuch, for the ages given in the genealogical table make Jared, Lamech and Methusalah die in the same year, the year of the flood! Regardless of how the critic may assess the accuracy of the text of the Samaritan Pentateuch, he is obliged to concede that it regarded the genealogy as a tight one, (so water tight in fact, that three generations drowned in the flood!) Clearly these scribes of antiquity, must be allowed to voice an authoritative opinion on the meaning of "bene" in the Hiphil stem, and it is submitted that their opinion, as users of their own language, and from a vantage point at least two millennia closer than the present, is worth a lot more than the speculation of modern scholars.

Contemporary lexical studies, substantiated by the commentary of antiquity, argue for a closed genealogy for Genesis 5, and as the same word in the same stem is used in Genesis 11, and as the context and structure are similar, the argument must extend to the genealogy under consideration [Gen 11].


The grammatical, syntactical and lexical arguments seem to be clearly arrayed against any interpretation of gaps in the genealogies of Genesis 5 and 11, but there is yet another argument against an open, or loose genealogy.

The whole tenor of scripture is to provide meaningful information, in fact the general rule of scripture is that it is pregnant with meaning. Genesis 5 and 11 provide two basic facts about each person named in the genealogy, his life span, and his age at the commencement of the next generation. Any exegesis of these passages must account for both of these facts, and, furthermore, posit some relevance for the information, and preferably providing a unified meaning and significance. The proponents of an open genealogy must thus advance a logical reason for divulging the age at which, for example, Shelah begat Eber. It may perhaps be argued that this age denotes the time of his marriage, or his age at the birth of his first child but this proposition is not supported by the text for Seth was not Adam's firstborn, and the same terms are used for this event. The clear inference is that the genealogy only lists the child on whom God's favour rested, the one who carried the seed of the coming Messiah. This position is again clear in the case of Terah's children for the first born was not Abram but Haran, and later examples include Isaac, Jacob, Judah, David, Solomon...

The argument that the age demonstrates the faith and patience the father had to exercise is difficult to defend for it pre-supposes that the father had prophetic insight which enable him to know which son carried the seed of God's chosen line.

Clearly the easiest, the most obvious explanation of the information given in these genealogical tables of Chapters 5 and 11 is that they were given to provide a chronology for the period, and that that chronology will provide insights into the period, which are otherwise not disclosed in scripture. This can only be the case if the student regards the genealogy as closed. With such a view, the genealogies have a purpose, a very clear and definite one. If on the other hand the genealogy is regarded as open, it is difficult, if not impossible to ascribe a purpose for divulging the information given in these passages, and the student comes perilously close to allegorising the passages.

Demonstrably, exegetical considerations too, favour a closed genealogy.


The grammatical, lexical and contextual considerations all argue incontrovertibly (or at the least, strongly) for a tight genealogy. This leaves only two possibilities open, firstly that there is a direct contradiction between Genesis 11:13 and Luke 3:35, 36 or secondly that there is a textual error in the text which is the basis of our English versions. The first possibility challenges this writer's pre-supposition of infallible verbal inspiration, so naturally he turns initially to examine the state of the text on which the English Versions are based.

There are three major recensions of the original text of Genesis; the Masoretic Text, the Samaritan Pentateuch and the proto-Septuagint. The Masoretic Text is generally regarded as the more reliable and is substantially supported by the Samaritan Pentateuch except in the question of ages of the Patriarchs, where in the passage under consideration the Samaritan Pentateuch is close to the Septuagint, nonetheless omitting the generation of Cainan. There is thus a confused situation, but this is not surprising in the light of the Bible's own testimony as to the casual attitude towards the transmission of the text."