Biblical numbers, mathematics and attributed patriarchal ages

     The Hebrew Bible is filled with numbers. There are different kinds of numbers — cardinals and ordinals, integers and fractions, even primes. And they are everywhere in the Torah text.

     There are numbers for days and numbers for life spans.

     There are numbers for populations and numbers for the duration of events.

     There are numbers for the measurement of quantities and numbers for the sizes of objects and areas.

     There are numbers for the duration of events.

     And there are numbers for a host of seemingly mundane things, such as the number of visitors and the number of palm trees.

     Some Biblical numbers are curiously round. For instance, Noah reportedly was 500 years old when his son Shem was born, and 600 when the great Flood occurred. Shem was, then, 100 years old at the time of the Flood, and he died 500 years later at age 600.

     And Isaac married Rebekah at age 40, became a father of twins at age 60 and was 100 when Esau was married. He died at age 180.

     Some Biblical numbers are identical and strangely coincidental. The rain that created the Flood for Noah lasted 40 days and nights. That is the same number of days and nights that Moses reportedly spent on Mount Sinai on each of two occasions to receive the tablets engraved with the teachings and the commandments. 

     Other numbers appear hyperbolic and incredible. The Bible states that Jacob’s descendants consisted of 70 individuals when the family entered Egypt. After centuries of involuntary servitude, the number of adult males that left Egypt with Moses is asserted to be about 600,000.  Including wives, concubines and children, the total number of those leaving must have been in the millions. Understood literally, the number seems absurdly large.

     When we encounter numbers in the Bible, what are we to do with them? Are all or some of the numbers to be taken literally or is one or more of them to be understood symbolically? And how can we tell which numbers fall into which category? Do we have a collection of essentially random numbers? Or, are there patterns that provide information, suggest meaning, or, maybe, reveal secrets?

     Of all the number puzzles in the Bible, perhaps none is more intriguing than the longevity of the generations from Adam though Moses.  Using a variety of approaches, scholars and others have long considered the numbers found in the Bible. They have speculated fancifully in an effort to make sense of some of them. With perhaps rare exceptions, though, these efforts have not been particularly satisfying, leaving the original problem, as the mathematician Lewis Carroll had Alice say in a different context, “curiouser and curiouser!” (See Carroll, Alice’s Adventures in Wonderland (Ch. 2.))

The data

     Let’s look at the data first.  According to the Torah text (meaning here the Masoretic text), there were 10 generations from Adam to Noah, inclusive. There were another 10 generations after Noah and to Abraham, inclusive.  Coincidence?

     The life spans recorded in the Bible for the first group are as follows: Adam (930), Seth (912), Enos (905), Cainan (910), Mahlaleel (895), Jared (962), Enoch (365), Methuselah (969), Lamech (777) and Noah (950). The life spans recorded for the second group, exclusive of Terah’s son Abraham, are as follows: Shem (600), Arphaxad (438), Salah (433), Eber (468), Peleg (239), Reu (239), Serug (230), Nahor (148) and Terah (205).

     Looking at the three primary patriarchs separately, Abraham, Isaac and Jacob lived 175, 180 and 147 years respectively. Parenthetically, the only life span we have for a matriarch is that for Sarah, who died at age 127.

     Finally, while at one point the Bible states that Jacob’s descendants were in Egypt for 430 years (see Ex. 12:40-41), the book of Exodus records just four generations from Jacob to Moses. Jacob’s son Levi lived 137 years, Levi’s son Kohath lived 133 years and Kohath’s son Amram lived 137 years. (Ex. 6:16, 6:18, 6:20.) Moses, who was Amram’s son and, therefore, Jacob’s great-great grandson, lived 120 years. (Deut. 34:7; see also, The Torah: A Modern Commentary (URJ Press 2005), at 383 n. 20.)

     What, if anything, do these 26 numbers tell us?

Attempts to explain Biblical ages

     Even a quick review suggests that the life spans of the first group of Biblical humanity was reasonably consistent within a relatively narrow range of 895-969 years, with the notable exceptions of the seventh generation descendant Enoch and Noah’s father, Lamech.  As a general matter, the life spans of the second group, and through Moses, then continued on a downward slope. The first three individuals after Shem lived between 433 and 468 Biblical years, and the next three lived in a reduced range of 230 to 239 Biblical years. After Terah, no Biblical personality is indicated to have lived in excess of 200 years.

     Rabbinic sages of the past accepted the reported ages as accurate. To explain the longevity of Adam, one noted that Adam was made in God’s image and therefore physically perfect. Adam’s immediate descendants were similarly vigorous. To explain the decline after the Flood, one sage suggested that the Earth’s atmosphere deteriorated. Another opined that the people faced a harsher climate after the post-Babel dispersion. (See The Chumash (Stone Ed. Mesorah 1993) at 25, 51 n. 19.) There is, unfortunately, no actual evidence to support such speculation, no way to test any of these propositions.

     A more modern and purely mathematical analysis of the numbers by Charles A. Glatt, Jr. concludes that the longevity of the individuals from Noah to Joseph (and then to Moses) declined in a manner consistent with base e exponential decay (where e = 2.718 . . .).  (See Glatt, “Patriarchal Life Span Exponential Decay by Base e,” at “>www.bible.org/article/ages-antediliuvian-patriarchs-genesis-5.) 

     What we do know, though, and what is important to know, is that the attributed ages of the primary patriarchs, are neither random nor mere numbers to be located as data points on a line. They are numbers, whether products or sums, which suggest an intent by the author or editor of the text to convey something important about the three primary patriarchs, their distinctiveness from all others and their relationship to each other.

     A few final points need be made. First, this discussion has been limited to numbers that appear in the Masoretic text. There are some different numbers that appear in the Greek Septuagint and the Samaritan Pentateuch.  (See Cassuto, From Adam to Noah, above, at 264-65; From Noah to Moses, above, at 258-59.)

     Second, Cassuto was not a disinterested academic. In addition to desiring to show what Torah text meant to those who first heard it, he was interested in demonstrating that the text of Genesis was part of a unified whole, rather than a collection of writings of different authors as postulated by the documentary hypothesis of higher biblical criticism. (See, e.g.,  Cassuto, From Adam to Noah, above, at 94, 193.)

     Nevertheless his insights cannot be denied. Sarna concludes that “the biblical chronologies of the patriarchal age are not intended to be accurate historical records in our sense of the term.” (Exploring Genesis, above, at 84.) Rather, they “fall within the scope of historiosophy, or philosophy of history, rather than historiography.” (Id.) In this view, they tell us less about actual time intervals than about the ideas of Biblical import. Numerical symmetry or harmony is not a matter of coincidence among random events, but a signal of importance, and a sign of presumed divine control and direction. (Id. at 85.)

     Lastly, whoever wrote or redacted the Hebrew Bible was more than a drafter of national history, a recorder or developer of laws and mores and a masterful storyteller. He, she or they also had a real competency with mathematics. We do not yet understand the signals, or even whether they were theologically purposeful or narrative drivers or both, but they are clearly there, mean something and deserve serious and further consideration.

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