and
Origins 9(2):7581 (1982).
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A statistical analysis of the chronogenealogies of Genesis 5 and 11 reveals some interesting conclusions.
For centuries the genealogies of Genesis 5 and 11 have provided
Christians with a chronological framework for history between creation and the time of
Abraham. A unique feature of these genealogies is that they record the age of each
patriarch at the birth of his presumably firstborn son and the number of years the
patriarch lived after that event. Genesis 5 additionally records the age of death of each
patriarch, this value being the sum of the first two numbers given. In view of these
numerical data Genesis 5 and 11 have been called "chronogenealogies" (Hasel
1980a, 1980b).
A persistent use of the Genesis age data has been as a basis upon which
to assign a date or an approximate time for the creation. The bestknown attempt of this
kind was by Archbishop James Ussher in Annales Veteri Novi Testimenti (165054).
In this work Ussher concluded that creation had occurred during 4004 B.C. While this date
was later refined and modified by other scholars, it was to remain the generally accepted
date of creation among Christians for two or more centuries (White 1896, pp. 249256).
More recently extensive scientific evidence (Hare 1974, 1979; Abelson
1982) has convinced many Christians that the Genesis age data are unreliable for purposes
of chronology (Warfield 1911; Geraty 1974; Horn 1979). However, other Christians argue
that regardless of the scientific objections, the most apparent interpretation of
scripture (in this case that the genealogies provide an adequate basis for construction of
a preAbrahamic chronology) stands authoritative (Brown 1977; Hasel 1980b).
With these contrasting opinions in mind we evaluate the Genesis age
data without recourse to extrabiblical chronological information. We do not attempt to
completely resolve the genealogy/chronology problem, but only demonstrate that these age
data form a significantly nonrandom distribution in contrast to an expected random
distribution of numbers.
METHODS AND RESULTS
We hypothesized that for any random distribution of pregenerative
years (number of years prior to the birth of his firstborn son) and postgenerative years
(number of years he lives following the birth of his firstborn son), the last digits of
these values form a random group of numbers. To test this hypothesis questionnaires were
sent to staff members of Andrews University asking for birthdates of their fathers and
their fathers' firstborn sons, and their fathers' death dates.
Thirtyeight questionnaires were returned with complete information.
Pregenerative and postgenerative years were calculated for each of the 38 individuals
represented. To handle fractions of years consistently the age of the individual at his
most recent birthday was used (Bogue 1969, p. 148).
Table 1 shows the pregenerative and postgenerative years of each
individual in the control. The frequencies of digits "0" to "9" used
as last digits in the pregenerative and postgenerative years, respectively, are shown in
Tables 2 and 3. Control frequencies did not vary significantly from expected frequencies
(38 numbers / 10 possible last digits = 3.8 in each case) for pregenerative or
postgenerative years, confirming our hypothesis that a natural distribution of ages should
be random with respect to frequencies of last digits. (Note: The .05 level of significance
was chosen for these as well as for the following tests).
TABLE 1. Pregenerative and postgenerative years of 38 fathers of staff members at Andrews University.
father no. pregenerative years postgenerative years 1 28 59 2 26 3 3 27 44 4 35 38 5 27 52 6 41 38 7 26 21 8 26 50 9 31 23 10 22 16 11 34 55 12 28 54 13 25 29 14 28 39 15 27 43 16 24 37 17 22 31 18 29 44 19 34 52 20 29 42 21 25 39 22 24 35 23 35 50 24 23 52 25 25 32 26 20 49 27 29 44 28 21 61 29 29 26 30 27 37 31 36 50 32 33 9 33 26 48 34 29 14 35 22 43 36 24 35 37 26 49 38 26 6
TABLE 2. Frequency distribution of last digits of pregenerative years of the control sample in Table 1. Observed and expected frequencies are not significantly different (c^{2} = 4.38, d.f. = 9, P > 0.05).
last digit observed frequency expected frequency 0 1 3.8 1 3 3.8 2 3 3.8 3 2 3.8 4 5 3.8 5 5 3.8 6 7 3.8 7 4 3.8 8 3 3.8 9 5 3.8
TABLE 3. Frequency distribution of last digits of postgenerative years of the control sample in Table 1. Observed and expected frequencies are not significantly different (c^{2} = 2.91, d.f. = 9, P > 0.05).
last digit observed frequency expected frequency 0 3 3.8 1 3 3.8 2 5 3.8 3 4 3.8 4 5 3.8 5 3 3.8 6 3 3.8 7 2 3.8 8 3 3.8 9 7 3.8
Turning to the data from Genesis 5 and 11 (Table 4) we again hypothesized that the pregenerative and postgenerative year values should be random with respect to last digits. However, the frequencies of last digits of both pregenerative and postgenerative ages show significant deviations from expected frequencies (20 numbers / 10 possible last digits = 2 in each case), implying that the data are biased (Tables 5 and 6).
TABLE 4. The pregenerative and postgenerative years of the 20 patriarchs listed in Genesis 5 and 11 (Masoretic Text).
patriarch
pregenerative years postgenerative years Adam 130 800 Seth 105 807 Enosh 90 815 Kenan 70 840 Mahalalel 65 830 Jared 162 800 Enoch 65 *300 Methuselah 187 782 Lamech 182 595 Noah 500 450 Shem 100 500 Arphaxad 35 403 Shelah 30 403 Eber 34 430 Peleg 30 209 Reu 32 207 Serug 30 200 Nahor 29 119 Terah 70 135 Abraham 100 75 *"He [Enoch] was not, for God took him." Genesis 5:24 (KJV)
TABLE 5. Frequency distribution of last digits of pregenerative years of the patriarchs listed in Genesis 5 and 11 (Table 4). Observed and expected frequencies are significantly different (c^{2} = 34.25, d.f. = 9, P < 0.0001).
last digit observed frequency expected frequency 0 10 2 1 0 2 2 3 2 3 0 2 4 1 2 5 4 2 6 0 2 7 1 2 8 0 2 9 1 2
TABLE 6. Frequency distribution of last digits of postgenerative years of the patriarchs listed in Genesis 5 and 11 (Table 4). Observed and expected frequencies are significantly different (c^{2} = 26.88, d.f. = 9, P < 0.005).
last digit observed frequency expected frequency 0 9 2 1 0 2 2 1 2 3 2 2 4 0 2 5 4 2 6 0 2 7 2 2 8 0 2 9 2 2
An examination of Table 5 reveals that out of the 20 pregenerative
ages represented, 10 have as their last digit a "0" and are thus multiples of
10. The frequency of digit "0" varies most from the expected frequency of 2 and
thus contributes most to the large chisquared value. Ages with the last digit of
"5" have the second highest frequency of 4. Remaining frequencies are
distributed among four other digits. Digits "1," "3," "6,"
and "8" are not represented in the distribution. An examination of Table 6
reveals a similar pattern for the postgenerative years.
These analyses are based upon data from the Hebrew Masoretic text. Data
from the Greek Septuagint reveal essentially the same pattern.
DISCUSSION
As the above tests reveal, the probability that the Genesis age data
represent a random distribution of age values is extremely low. Several reasons for this
biased distribution can be postulated.
A. The numbers could have been generated by the writer or compiler of
the genealogies to fit a preconceived number pattern. One of the bestknown attempts to
support this hypothesis was by Cassuto (1961, pp. 251254) who showed that each number in
Genesis 5 is a multiple of 5 plus 7, the only exception being the death age of Methuselah
which is a multiple of 5 plus 14 (or 2 × 7). He postulated that this numerical series was
influenced by the sexigesimal number system. Every 5 years equals 60 months. Multiples of
5 years would then be multiples of 60 months. Additions of 7 to multiples of 5 years would
be equivalent to saying "somewhat longer than" the multiple of 5 years. However,
there seems to be no rationale for the series of numbers required as multipliers of 5 to
arrive at the data, unless it is assumed that the numbers are close to the actual age
values for the individuals named. Also, Cassuto's scheme works for all the age values in
Genesis 5, but not for all the numbers in Genesis 11. [See Hasel (1980b) for reviews of
similar numerical schemes].
B. The numbers could reflect a relationship to the Sumerian King List
(Barton 1937, pp. 264272; Speiser 1964, p. 42), the Ammonite Genealogy of the Hammurapi
Dynasty (Malamat 1968; Hartman 1972; Wilson 1975), or other such Middle Eastern lists. On
the basis of a number of unique qualities of the Genesis genealogies, Hasel (1978) argued
that the appearance of any such relationship is superficial. More recently, however,
Walton (1981) has demonstrated a possible numerical link between Genesis 5 and the
Sumerian King List.
C. The biased age values may be due to digit preferences by those
reporting age data. Demographers have shown that people exhibit preferences for ages
having certain terminal digits. For example, singleyearofage data for the 1960
population of the Philippines shows a strong preference for ages ending in "0,"
with somewhat lesser preferences for ages ending in "5," "2,'' and
''8." Conversely, these data show negative preferences for ages ending in
"9," and "1" (Shryock et al. 1971, p. 204).
Our analysis sheds no light on which, if any, of the above explanations
actually accounts for the data. It is even possible that more than one such explanation
applies. The concept of statistical nonrandomness which we are postulating states only
that the numbers appear biased, suggesting that the Genesis genealogical age data fail to
provide a defensible basis upon which to construct a precisepreAbrahamic chronology of
the world.
REFERENCES
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