The antediluvian
patriarchs and the Sumerian King List: by
Raúl Erlando López
The Sumerian King List
records the lengths of reigns of the kings
of Sumer. The initial section deals with
kings before the Flood and is significantly
different from the rest. When the kingdom
durations of the antediluvian section are
expressed in an early sexagesimal numerical
system, all durations except two are
expressed as multiples of 602. A
simple tally of the ciphers used yields six
10x602 signs, six 602
signs and six 60 signs.
The lives of the biblical
patriarchs, however, have a precision of one
year. If Adam and Noah are not included (as
in the King List), and the lives of the
patriarchs are similarly rounded to two
digits, the sum of the lives has six 103
signs, six 102 signs and six 10
signs. In addition, if the number
representing the sum of the ages was wrongly
assumed as having been written in the
sexagesimal system, the two totals become
numerically equivalent.
It is suggested that the
Sumerian scribe that composed the original
antediluvian list had available a document
(possibly a clay tablet) containing
numerical information on the ages of eight
of the patriarchs similar to that of the
Genesis record and that he mistakenly
interpreted it as being written in the
sexagesimal system.
That the two documents are
numerically related is strong evidence for
the historicity of the book of Genesis. The
fact that the Sumerian account shows up as a
numerically rounded, incomplete version of
the Genesis description, lacking the
latter’s moral and spiritual depth, is a
strong argument for the accuracy,
superiority, and primacy of the biblical
record. In addition, the parallels between
the Sumerian and biblical antediluvian data
open up the possibility of establishing
chronological correlations between the rest
of the Kings List and the book of Genesis.
Introduction
The early chapters of the
book of Genesis contain numerical
information about the ages of the biblical
patriarchs and their chronological
relationships during the antediluvian world.
They also contain a description of the moral
and spiritual condition as well as the
history of that period. Although there are
other, non-biblical, references to the
antediluvian era, there is no other document
in all of the extant records of the ancient
world that provides the detailed and
coherent information found in the book of
Genesis. The Genesis account gives us a
glimpse into that obscure portion of the
history of mankind, and provides information
for a chronology of that period. It has,
nevertheless, been criticized by
non-Christians as well as liberal
theologians as being mythological, or at
best symbolic and incomplete.
The Sumerian King List, on
the other hand, contains an initial section
that makes reference to the Flood and to
Sumerian kings of extremely long reigns
before the Flood.1 The
antediluvian portion of the King List is
very different from the biblical account. It
only contains eight kings, while Genesis has
ten patriarchs. The Sumerian list assigns an
average reign duration of 30,150 years, with
a total duration for the period of 241,200
years, compared to an average age of the
biblical patriarchs of 858 years and a sum
of 8575 years for their full lives. It also
lacks the detailed information of Genesis
and its moral and spiritual emphases.
Nevertheless, Walton2
has pointed out that the antediluvian
portion of the King List does not include
the Sumerian first man nor the Flood hero.
If Adam and Noah are dropped from the
biblical list, the number of people in the
two lists is then the same—eight. Walton has
also noticed that the total of the durations
of the kingdoms and the total of the ages of
the patriarchs are numerically related and
are equivalent if the number base of the
Sumerian list is changed from sexagesimal to
decimal.
This is an important result
and would imply that the two records relate
to the same events in the early history of
mankind. If so, then finding numerically
related elements of the biblical account in
the Sumerian King List would open up
important avenues of research into the
relationship of biblical and Mesopotamian
chronologies. This paper carefully and
thoroughly examines the numerical
relationships between the two documents. In
Section 2, the Sumerian King List is
surveyed in the light of its chronological
context. In Section 3, a study is made of
the Sumero/Babylonian numerical systems to
ascertain the development of the different
methods used to represent numbers and the
peculiarities and limitations of the
different systems that could have possibly
been used to represent the original
antediluvian Kings List. In Section 4, the
two lists are expressed in one of the early
numerical systems and compared. Attention is
paid to the internal characteristics of the
two sets of numerical values and their
formal similarity. Section 5 summarizes the
results, presents a hypothesis for the
similarities of both records, and comments
on the importance of these findings.
The Sumerian King List
The Sumerian King List
records in succession the names of most of
the kings of Sumer and the lengths of their
reigns.1 The document begins at
the beginning of history, the time when
‘kingship (first) descended from heaven,’
and goes up to the reign of Sin-magir (1827–
1817 BC3) towards the end of the
Isin dynasty. The list is characterized by
extremely long durations for the different
reigns, especially the earlier ones. One
quarter of a million years is assigned to
the first eight kings before the Flood and
more than 25,000 years for the first two
dynasties after the Flood. By comparison
with other historical documents,
inscriptions and archaeological dating, it
appears that the list does not correspond to
a strict succession but that there is
considerable overlap and contemporaneity
between several of the dynasties that are
presented in the list as having existed one
after the other.
The documents
The first considerable
fragment of the Sumerian King List was
published in 1906.4 It was found
in the temple library of Nippur at the turn
of the century. Since that date, more than
15 different fragments and at least one
fairly complete list have been found and
published. Most of these manuscripts have
been dated to the 1st dynasty of Babylon.
All the documents show extensive and
detailed agreement among themselves. Thus it
appears that the extant texts ultimately
descend from a common original, i.e., that
they are copies, or copies of copies, of a
single original document.4 In a
now classical example of textual criticism,
Jacobsen4 developed the genealogy
of all the different variants and
reconstructed the most likely original text
of the King List in 1939. That
reconstruction has been accepted and used by
most scholars. The following discussion of
the King List is based to a large extent on
his original work.
The antediluvian section
A few of the manuscripts
seem to have had an initial section dealing
with kings before the Flood. That section,
however, is significantly different from the
rest of the list which deals with kings
reigning after the Flood. First of all, it
has a large degree of independence. The
postdiluvian sections do not appear in other
Mesopotamian manuscripts that are not
fragments of the King List, and their
contents have only been found in the King
List.
In contrast, the
antediluvian section has been found as a
separate entity in a tablet dated to the end
of the 3rd millennium without reference to
lists of other rulers. This tablet also has
particular linguistic features that show
that it is not an isolated part of the King
List (such as the total absence of the
grammatical formulas so characteristic of
the latter).
In addition, some of the
phrases and information in the antediluvian
section have been found in a Sumerian epic
dealing with the beginning of the world.4
There is a close correspondence between the
common phrases of these two documents, and
the identical order of the primeval cities,
which tends to indicate that they are
literarily interdependent.
Furthermore, the
antediluvian section has a particular set of
formulas different from those used in the
postdiluvian section. The formulas for the
change of dynasty and the mention of their
totals are very consistent in the
postdiluvian part and are very different
from those used in the antediluvian one.
Jacobsen4 believes that the
antediluvian section is a later addition to
a King List that did not originally contain
kings before the Flood. He stated that the
new part was copied and adapted from
information that
‘was current in various
settings in Sumerian literature at the
time when most of our copies of the King
List were written ... (and) that it was
written later by a person different from
the one who originally composed the
postdiluvian section of the list ... by
a scribe who was bringing his copy of an
older original up to date ... ’ (See
Figure 1).
The following is the
translation by Jacobsen4 of his
critical edition of the Sumerian text of the
antediluvian section of the King List
together with a few selected lines of the
postdiluvian section for comparison (see the
text following for explanation of the
italics, bold and underlining):
1 When the kingship
was lowered from heaven
the kingship was in Eridu(g).
(In) Eridu(g) A-lulim(ak) (became)
king
and reigned 28,800 years;
5 Alalgar reigned 36,000 years.
2 kings
reigned its 64,800 years.
I drop (the topic) Eridu(g);
its kingship to Bad-tibira(k)
10 was carried.
(In) Bad-tibira(k) En-men-lu-Anna(k)
reigned 43,200 years;
En-men-gal-Anna(k)
reigned 28,800 years;
15 divine Dumu-zi(d), a shepherd,
reigned 36,000 years.
3 kings
reigned its 108,000 years.
I drop (the topic) Bad-tibira(k);
its kingship to Larak was carried.
20 (In) Larak En-sipa(d)-zi(d)-Anna(k)
reigned its 28,800 years.
1 king
reigned its 28,800 years.
I drop (the topic) Larak;
25 its kingship to Sippar was carried.
(In) Sippar En-men-dur-Anna(k)
became king and reigned 21,000
years.
1 king
reigned its 21,000 years.
30 I drop (the topic) Sippar;
its kingship to Shuruppak was carried.
(In) Shuruppak Ubar-Tutu(k)
became king and reigned 18,600
years.
1 king
35 reigned its 18,600 years.
5 cities were they;
8 kings
reigned their 241,200 years.
The Flood swept thereover.
40 After the Flood had swept thereover,
when the kingship was lowered from heaven
the kingship was in Kish.
[end of the antediluvian
section]
In Kish Ga ... ur(?)
became king
45 and reigned 1,200 years;
Aka,
reigned 625 years.
Kish was smitten with weapons;
its kingship to E-Anna(k)
was carried.
In E-Anna(k)
Mes-kiag-gasher,
son of Utu, became high priest
and king and reigned 324 years.
Jacobsen translation is based on his
critically edited text of the
Wendell-Blundell prism in the Ashmolean
Museum of Oxford University (W-B 1923.444).
This fairly complete text is referred to as
WB. The line numeration refers to the lines
of the WB prism.
The origin of the antediluvian section
The bold underscored
lines are found in essentially the same
form in the epic fragment referred to above.
Thus it appears that the two documents are
related. The phrases ending each dynasty (‘I
drop Eridu(g)’, ‘I drop Bad-tibira(k)’,
etc.), however, are totally out of place in
the epic. They are also very different from
the phrases repeatedly used for the ending
of the different dynasties in the
postdiluvian sections (e.g., ‘Kish was
smitten with weapons’).
For those reasons, Jacobsen4
concludes that the scribe adding the
antediluvian section was not copying
directly from the epic but was using a
different source (Document A) that was
literarily related to the epic. There are
three equally probable explanations for the
relationship between the epic and Document A
(see Fig. 1): (1) Document A was based on
the epic but its author introduced the
particular formulas. (2) The epic used A but
dropped the formulas as they did not fit its
style. (3) Both A and the epic were derived
from a third document B that contained the
common phrases and the formulas.
The information about the
cities, the names of the kings, and their
reigns are most probably also derived from
source A, as there are strong indications
that it was originally present in the
complete text of the epic. All the text
considered to have a high probability of
being derived from source A is indicated
above by bold letters. It is difficult to
ascertain if the verb ‘he reigned’ after the
various reigns and the city summaries of the
number of kings and the total duration of
their reigns were derived from source A or
if they were added by the scribe. Since
there are some evidences for both, they are
indicated by Roman but not bolded letters in
the transcription shown above.
The italicized lines
correspond to phrases that Jacobsen
considers were written by the scribe as he
added the material of the antediluvian
section to an earlier version of the King
List, which he was also bringing up to date,
in the middle of the Isin dynasty. They
essentially represent attempts to bring the
added section into conformity with the style
of the rest of the King List. Those phrases
are not present in the epic nor in the
isolated list of the antediluvian kings
mentioned above. In addition, they contain
grammatical peculiarities also present in
the very last section of the King List which
he appears to have added. Phrases and words
attributed to the scribe are indicated by
italicized letters.
The isolated antediluvian
list that has been mentioned above has many
similarities but also marked differences
with the antediluvian section of the King
List. It is a short and concise list of the
type that probably the original author of WB
used for his source (Document A). However,
it gives the impression of being a further
condensed version with emendations (some
probably of a political nature) of the
material used by WB.
A consideration of that
list, and the reconstructed portion of the
source used by WB (text in bold letters),
shows that the original information about
the antediluvian kings did not claim that
the different kingships were successive. In
fact, the language of the change of dynasty
gives the impression that it was trying to
avoid saying so. According to Jacobsen,
‘This view, that the antediluvian dynasties
were more or less contemporaneous, is
clearly incompatible with the King List
proper, which directly aims at following the
route of the “the kingship” from one city to
another.’4
The information contained in
source A can then be summarized as follows:
When the kingship was
lowered from heaven
(In) Eridu(g) A-lulim(ak)
reigned 28,800 years;
Alalgar reigned 36,000 years.
2 kings
reigned its 64,800 years.
I drop (the topic) Eridu(g);
(In) Bad-tibira(k) En-men-lu-Anna(k)
reigned 43,200 years;
En-men-gal-Anna(k)
reigned 28,800 years;
divine Dumu-zi(d), a shepherd,
reigned 36,000 years.
3 kings
reigned its 108,000 years.
I drop (the topic) Bad-tibira(k);
(In) Larak En-sipa(d)-zi(d)-Anna(k)
reigned its 28,800 years.
1 king
reigned its 28,800 years.
I drop (the topic) Larak;
(In) Sippar En-men-dur-Anna(k)
reigned 21,000 years.
1 king
reigned its 21,000 years.
I drop (the topic) Sippar;
(In) Shuruppak Ubar-Tutu(k)
reigned 18,600 years.
1 king
reigned its 18,600 years.
5 cities were they;
8 kings
reigned their 241,200 years.
The Flood swept thereover.
Chronological considerations
Most of the existing
manuscripts of the King List have been dated
to the second half of the Isin dynasty. An
examination of the grammar of the List,
however, shows certain usages that had
disappeared by that time. Jacobsen4
has compared these manuscripts with
well-dated documents outside of the King
List and has determined the time when these
usages disappeared from the then current
language. The postdiluvian portion of the
King List shows that a large part of it has
a high degree of stylistic similarity.
The concluding section of
WB, however, shows a different style. By
noting the date when these different
grammatical usages also had disappeared from
the language, and the dynasty in the List
when the different writing style was
introduced, Jacobsen4 came to the
conclusion that the first part of the List
was composed earlier than the reign of
Utu-hegal of Uruk (2119–2112 BC)1,3
and that the later section of WB was added
by a different scribe as he brought an older
copy of the List up to date with information
about new kings and dynasties. The style of
the concluding sections is also very similar
to that of the antediluvian section which
has been seen above to be an addition to the
main body of the King List.
Jacobsen concludes that ‘The
man who added the antediluvian section is
also responsible for the last part of the
list; his literary peculiarities appear in
both places.’ 4 This scribe added
the 3rd dynasty of Ur (2112–2004 BC)3
and the dynasty of Isin down to Sin-magir
(1827–1817 BC), so the antediluvian section
appears to have been also added after that
time.
An inscription of Utu-hegal
describing this victory over Gutium shows
very close similarities in ideology and
language to the earlier portion of the
postdiluvian King List.4 The
characteristic phraseology common to the
inscription and the King List occurs in no
other document. In both documents the idea
is expressed that Babylonia had always been
one single kingdom and that the capital had
changed from city to city as rulers from
different cities defeated the existing
capital. It was considered that at no time
was there more than one king. By defeating
Gutium around 2119 BC, Utu-hegal had brought
back the kingdom to Sumer. The Sumerian
nationalism must have been stimulated by the
newly-won independence from the barbarous
Gutians. This would have been the right
environment for the production of a work
such as the King List that seeks to present
the history of Babylonia as a succession of
different national kingdoms passing from one
city to another.
A detailed analysis of the
structure of the King List4
indicates that the author of the first part
took his material from lists that gave the
names of local rulers in chronological order
and the length of time that each had
reigned. Apparently, the different cities
each had their own separate list of local
rulers, irrespective of any overlord the
city may have had at the time. There are
evidences that some of these local lists
existed in pre-Sargonic times even as far
back as the Fara texts (c. 2500 BC).
The author appears to have
merged the independent local lists to a
sequential list produced under the theory
that there was only one king at a given time
in all of Babylonia. The form of the final
list shows that the author did not reject
any material from the local lists. He should
have eliminated some kings because ‘large
sections in each of his sources would have
been irrelevant because they dealt with
rulers reigning at periods when their city
was not in possession of the kingship.’4
Thus, many of the dynasties
listed as consecutive were in reality
contemporaneous. He apparently divided the
larger of his source lists into smaller
dynastic units and interpolated them
separately to try to ameliorate the large
errors that obvious synchronisms between
well known rulers would have exposed by
strictly merging all the sources one after
another. In most cases, however, he cut the
individual lists for interpolation along
dynastic groups.
It has been indicated above
how the later scribe who added the
concluding sections of the King List and the
antediluvian portion also followed the dogma
of only one king at a time for all of
Babylonia and only one capital. It is not
likely that the original antediluvian source
he used tried to present the antediluvian
kings in such a consecutive way; it seems
that the scribe forced this concept of his
own in order to conform his new material to
the style of the copy of the King List he
was adding to.
Sumerian and Semitic number systems
Before comparing the
Antediluvian portion of the King List to the
Genesis record, it is important to review
the characteristics of the number system
used in Mesopotamia as deduced from the
earliest archaeological findings. The
following survey is based principally on the
descriptions of Friberg,5 Flegg,6
Nissen,7 Walker,8 and
the University of Wisconsin9
among others. Dates correspond to the
conventional chronology which is probably
quite accurate in the later periods but
tends to give dates that are too old in the
earlier ones.
Proto-Sumerian Period (3300–2900 BC)
The first indications of
writing and numbers are found in the Late
Uruk Period.7 At the beginning of
this period, however, tally stones or tokens
made of clay of different shapes have been
found. These appear to represent different
counting units and the objects being
counted.10 The token method of
counting was combined with the use of
cylinder seals. The tokens were enclosed in
a ball of clay covered on the outside with
impressions of usually only one seal. In
some cases there were also oblong
impressions on the outside of the ball that
represented numbers that corresponded to the
tokens within the ball. In some instances,
flat clay slabs have been found with the
oblong symbols for numbers impressed on
their surfaces together with many
impressions of cylinder seals. Some tablets
have compartments marked off with incised
lines, each one containing a different
number.
Tablets with true writing
appear at the end of the Late Uruk Period (Uruk
Level VI), where numbers are accompanied by
pictorial and curvilinear symbols made with
a pointed stylus. The texts found appear to
relate to both simple and complex economic
transactions. Although they are still not
completely legible, they can be seen to
correspond to allotments of food, lists of
sacrifices, division of fields, herds of
animals and textile and metal manufacture.
Writing is well developed when it first
appears in the archaeological records.
Nissen7 rejects the theories that
the earliest known writing must have had
more primitive predecessors. He
hypothesizes, however, that once the idea of
writing arose somewhere in the
administration, its value was immediately
recognized and it was very quickly developed
into a functional instrument.
Many tablets have been found
with the information divided into three
different sections. On one side of the
tablet are many individual entries of
numbers accompanied by pictorial symbols,
probably signifying the objects being
counted or the names of persons. On a
separate section, are entries that
correspond to subtotals of the individual
numbers. Usually on the back side of the
tablet, a third section contains a final
total that adds up the previous subtotals.
This practice, which Nissen7
calls ‘a strict bookkeeping mentality,’ was
prevalent throughout the Middle East and is
also found in the Kings List.
Joshua 12:9–24 is an example of its use
in the Bible.
Very early, an oblong
impression was used as the symbol for one.
This oblong numeral was repeated several
times to represent small numbers and this
can be considered an extension of the method
of tallying where there is a
one-to-one correspondence between the
objects counted and the inscribed marks. The
indentations on clay were made by pressing a
blunt stylus of circular section at an angle
and had the appearance of a bullet (Fig. 2).
The symbols were grouped by threes for a
quick communication of the numerical
information. For numbers larger than nine, a
collective symbol that represented 10 units
was used. This is the practice of
cipherization found in all numeral
systems around the world.
The existence of a sign for
10 does not prove that the system employed
the base ten or that it had a combination of
bases. Ten was essentially an intermediate
cipher to avoid the need for extensive
repetition of the sign for 1. An example of
the use of intermediate ciphers is found in
the Roman number system, where ciphers for 5
times the powers of 10 were developed even
though the system was fundamentally decimal
(V, L, and D for 5, 50, and 500). The symbol
for 10 was made by pressing the stylus
vertically into the clay and had the
appearance of a circle. The presence or
absence of symbols defined the number
unambiguously and the order of the symbols
did not matter. However, it was the
convention to write the symbols for 10
together and not mix them with the symbols
for 1. Thus, the early numeral system
followed an addition principle and
there was no need for a zero.
The early Sumerians used the
base 60 for their number system. The reason
for the adoption of such a large base is
probably a reflection of the various units
of measure used for commercial,
administration and religious purposes. These
were mostly sexagesimal because they
afforded many convenient factors of the unit
(halves, thirds, quarters, fifths, sixths,
tenths, twelfths, fifteenths, twentieths,
and sixtieths) all expressed as whole
numbers of the next lower denomination.6
The next power of the base
(601) was expressed as a large
version of the units (600)
symbol. This was done by pressing the other
end of the stylus at an angle. This end was
also blunt but had a larger diameter, so it
would produced the shape of a larger bullet.
These symbols were repeated until 600 was
reached when the symbol used for ten (a
small circle) was impressed inside the large
oblong symbol for 60.
For the next power of the
base (602), a large circle was
used that was made by vertically pressing
the larger end of the stylus into the clay.
As with the symbol for 600, a small circle
was impressed inside the larger circle
(3,600) to multiply it by ten and represent
36,000. Although the Sumerian system had a
sexagesimal base, the symbol for ten (the
small circle) was used as an intermediate
symbol between powers of sixty. This
simplified the tallying procedure by
grouping by ten the ciphers for the
different powers. The resulting number was
very easy to understand and used the
multiplicative principle.
The system actually
contained only two symbols in two sizes. The
small number of symbols made the system very
intuitive and available to the masses but
needed a fair number of repetitions. Thus,
to write the numbers up to 59, as many as 14
individual symbols were needed for the
individual numbers. The small number of
numerical symbols was, to a large extent,
controlled by the method of writing numbers
using a blunt stylus with a circular section
to impress marks on wet clay.
The next archaeological
phase, represented by the Jamdet Nasr,
Proto-Elamite and Uruk Level III Periods,
was marked by a simplification and
acceleration of operations in every sphere.7
The pictographic signs began to lose their
pictorial appearance, becoming more abstract
and linear. In this phase, the first use of
symbols with determinative value has been
found. The language represented was probably
Sumerian but that is not certain.
Nevertheless, the tablets were written in an
archaic pictographic script that can be
recognized as a precursor of the Sumerian
cuneiform script. The writing system was
logographic, where one sign or sign-group
was used for each term or concept without
adding grammatical elements. The numbers as
a rule were still made with the round end of
a stylus and are easy to identify. A special
bi-sexagesimal notation has also been found5
where two of the same large bullet signs,
but with a less elongated impression, were
pointed towards each other to signify 120.
The same symbol with a small circular
impression represented 10x120=1200 (Fig. 2).
Early Dynastic I–II Periods (2900–2600
BC)
The first identifiable use
of purely phonetic elements and grammar
appeared during this time. In this stage
some signs were used to represent syllables.
The language used is clearly Sumerian. Most
of the material for this period comes from
the Archaic Ur tablets. The same number
system as in Jamdet Nasr is used. The script
was not yet cuneiform, but the signs are
more linear.
Early Dynastic II–III Periods (2600–2334
BC)
During this interval,
writing became much easier and simpler to
use, mostly through a change in writing
techniques. The earlier method of incising
to make the curvilinear pictorial symbols
was gradually replaced by the technique of
making impressions of short, straight lines
by holding a stylus of triangular section at
an angle. Writing now became much faster.
The same symbols were used, but many had
their form completely changed because the
new method only allowed short straight
lines. Superfluous details were omitted, and
curved lines were replaced by short straight
segments. The short strokes had a head,
which was more deeply impressed and
therefore wider. The lines resembled a
wedge, and this became the reason for the
name ‘cuneiform’ given later to this script.
Many earlier complicated symbols
disappeared.
Nissen7
speculates that the changes in the technique
of writing may have had their basis in the
increased demand for scribes in an expanding
economy. The major groups of tablets for
this period come from Fara (Shuruppak), Abu-Salabikh,
and Ebla in Syria. From about 2500 BC
onwards, the cuneiform script was also used
to write Akkadian and Eblaite, which are
Semitic languages. About eighty percent of
the words written on the approximately
10,000 tablets found at Ebla are in
Sumerian. Interspersed are the remaining
twenty percent in Eblaite. At that time, the
calendar used at Ebla was Semitic and the
counting appears to be in Semitic units
which were decimal.11–14 The same
is observed in Mari and Abu-Salabikh. The
number system for representing the counting,
however, remained the same as in the
previous periods, with the same two
different symbols (the bullet and the
circle) and the same two sizes (Fig. 2).
Dynasty of Akkad (2334–2154 BC)
During the period of the
Semitic dynasty of Akkad, the Akkadian
language replaced Sumerian as the
administrative language, as Sargon I of
Agade conquered all of Mesopotamia and
extended the empire to the Amanus Mountains
to the West, and to the Zagros and Taurus
mountains to the East and North.15
The Sumerian signs were used to write the
Old Akkadian language which was Semitic. The
wedges of the cuneiform symbols now appear
only at the top or the left of the sign.
This is a culmination of the tendency
started in the Early Dynastic II Period of
restricting the impressions of the
triangular stylus ‘within a narrow segment
of the possible directions the stylus could
theoretically take.’ This meant that few
changes in the direction of writing were
necessary and the speed of writing could be
increased. 7
The number symbols, however,
could be written in two ways: either as
cuneiform signs, inscribed with a stylus of
triangular section, or as circular signs
made with the blunt end of a circular
stylus.5 That means that two
different types of stylus were used
simultaneously. The new cuneiform numerals
tried to reproduce with wedges the rounded
impressions of the earlier numerals. Thus,
an elongated wedge represented the number
one and a vertically impressed triangular
shape represented the number ten. These
symbols were the equivalent of the small
bullet and circle of the earlier system. The
earlier large circle which stood for 602
was now represented by four long wedges
making a diamond shape, and the large bullet
with the small circle inside (10x60) was
written with an elongated wedge and a
triangular impression superimposed on its
right side (Fig. 3). Similarly, the large
circle with the small circle inside (10x602)
was substituted by a diamond made with four
long wedges with a triangular impression
inside. Sixty was represented by an
elongated wedge which sometimes was larger
than the wedge for one, but most of the time
had to be differentiated from it by the
context or the arrangement of the other
numeral symbols.
Sumerian Period (2112–2004 BC)
This period is marked by the
hegemony of the Sumerians under the
leadership of Ur-Nammu, founder of the Third
Dynasty of Ur, who conquered other Sumerian
and Akkadian city-states. As a consequence,
there was a revival of the Sumerian
language, but only in religious and literary
areas, as the language remained unimportant
for administrative purposes. The scribal art
reached an exceptional stage of precision.
The round numerals, that had to be made with
a different circular stylus, disappeared
from current use and only the cuneiform
representations, made with the triangular
stylus, were employed from now on (Fig. 4).
Old Babylonian Period (2004–1595 BC)
Up to this time, a
positional notation for sexagesimal
numbers had not become established and
separate signs were used for 1, 10, 60,
10x60, 602, and 10x602.
A special sign for zero was not necessary.
During the Babylonian Period, however, a
quasi-positional notation was used that
depended on only two signs: the elongated
wedge used for the number one and the
triangular impression used for 10. The wedge
now also stood for the powers of 60 and the
triangle for ten times the powers of 60
depending on their position within the
sequence of ciphers representing the number
(Fig. 5).
Eventually, a sign for zero
was adopted in the Babylonian system, but it
was only used to denote internal empty
places, the new numerical symbol was not
used to the right of a number as the last
symbol.6 This meant that the
numbers were not unambiguous and the actual
value had to be determined very carefully
from the context.
Summary of number systems
In conclusion, there were
two different but related systems for
representing numbers in the Sumero-Babylonian
culture. An earlier one, based on round
impressions using a blunt circular stylus,
and a latter one, based on cuneiform
impressions made with a stylus of triangular
section. The first system appears during the
Proto-Sumerian Period and was in use until
the time of the Akkadian Dynasty. By the
Sumerian Period of the Third Dynasty of Ur,
the cuneiform system had totally replaced
it. Because both systems were sexagesimal
and had a limited number of signs, frequent
repetitions of the same sign were necessary.
An intermediate cipher for 10 was developed
to ease the need for repetition and it was
used by itself and to multiply the different
powers of 60. The individual signs
representing a number had to be added
together to obtain the actual value of the
number. The earlier system used only two
different signs in two different sizes to
write the numbers. The cuneiform system also
employed only two elements, the wedge and
the triangle, but used four wedges to
represent the large circle of the earlier
system. In both cases, the largest value
represented by a single symbol was 36,000,
although very large numbers could be
expressed by the repeated use of the symbol
for 36,000.
During the Babylonian
Period, however, a quasi-positional notation
was developed that allowed for the
convenient representation of very large
numbers. Only two signs, the wedge and the
triangle, were used to represent the
different powers of 60 and 10 times the
different powers of 60 depending on the
position of the symbol in the number string.
A sign for zero was used to indicate
internal empty positions.
No other culture in the
ancient world used the base 60 for their
number system. The Egyptians, for example,
used a pure decimal notation as well as the
Romans and the Greeks.6 The
latter adopted the sexagesimal base for
astronomical computations but a decimal
notation was employed for other purposes.
The Elamites apparently adopted the
sexagesimal system from the Sumerians and
only used a decimal notation when counting
animals.5 Although the Semitic
kingdoms of Ebla, Mari, and Abu-Salabikh
adopted the cuneiform writing and the
cuneiform numbers, the calendar was Semitic
and the counting appears to be in Semitic
units which were decimal.
King List and patriarchs chronology
The antediluvian portion of
the King List appears to have been
originally composed very early in Sumerian
history. Therefore, the early number system,
based on rounded signs, has been used to
represent the numerical part of the list in
Fig. 6. A representation based on the
non-positional cuneiform system, however,
would have been very similar. It can be seen
that the majority of the symbols needed to
express the duration of the reigns of the
antediluvian kings are the large circle (602
= 3,600) and the large circle with the
small circle inside (10x602 =
36,000). Only the last two numbers would
have needed the symbol of the large bullet
with a small circle inside (10x60 = 600).
The symbols for one, ten, and sixty would
not have been needed. Thus, in six of the
eight numbers, the durations were given as
units of 602, and in the last two
with a precision of 10x60. Notice that all
the numbers taken together yield three 10x602
signs, thirty-six 602 signs, and
six 10x60 signs. To obtain the total of the
eight reign durations, the scribe would have
used the tallying method. So, for example,
he would have counted ten of the large
circle signs and written an additional large
circle with a small circle inside. In case
there were less that ten symbols of the same
kind left, they were usually arranged in up
to three rows of three symbols each. Thus,
the thirty-six 602 signs would
have yielded three more 10x602
signs for a total of six, with six
individual 602 signs left. The
six large bullets with a small circle inside
could have been written as two rows of three
signs each, following the convention of the
maximum of three rows of three. However,
because of the peculiarities of the system,
six large bullets with the small circle
inside also make a large circle. So, the six
10x60 signs could have been also expressed
as an additional 602 sign for a
total of seven (see Fig. 6). The resulting
total is equivalent to 214,200 years. This
number also has a precision of 3,600. It is
curious that the 10x60 signs of the last two
durations add up exactly to one of the 602
signs, the basic unit of all the other
numbers and the overall total, and that the
10x60 unit was not used until the last two
reign durations of the list.
A table with the total ages
of the antediluvian biblical patriarchs is
shown in Fig. 7. For comparison with the
Sumerian King List, Adam and Noah are not
included. The King List does not include the
Sumerian first man nor the Sumerian Flood
hero (Ziusudra). The third column is the
representation of the ages as
decimal-counting Semites would have written
them using the early rounded stylus. Exactly
what the convention would have been is not
known. However, following the same rules for
the selection of symbols to represent the
different powers of the base as in the
sexagesimal system, it would follow that the
small bullet and the small circle would
represent one and ten, the large circle the
next power of the base (102), and
the large circle with the small circle
inside ten times that power (103).
There would have been no use for the large
bullet impression because the first power of
the base was already represented by the
small circle, and no use for the large
bullet with the small circle inside because
ten times the first power of the base was
the square of the base which was represented
by the large circle. According to that
convention, the total ages of the
antediluvian patriarchs would have been
expressed as shown in column three. The
precision of the ages is one year, and the
majority of the ages have units.
A comparison of Figs. 6 and
7 shows that the ages have no relationship
between themselves, and neither do the
totals. However, if the ages of the
Patriarchs are rounded to the two highest
digits as in the Sumerian list (that appears
to be rounded to the two highest sexagesimal
ciphers), their representation would be as
shown in column 4 of Fig. 7. A total of the
eight ages of the patriarchs can also be
obtained by tallying all the symbols
employed in the individual numbers. The
total would then have six 103
signs, six 102 signs, and six 10
signs for a sum of 6600 years. If we do not
incorporate the six 10x60 signs (large
bullet with small circle inside) of the
Sumerian total into an additional next
higher order sign, the Sumerian total has 6
signs for 10x602, six signs for
602, and six signs for 10x60.
Thus, the totals of both the
rounded Genesis and Sumerian lists obtained
by a straight tally have six of the signs
for ten times the square of the base, six of
the signs for the square of the base and six
signs for the next lower symbol. It should
be noted that, although the particular form
of the symbols used to represent the decimal
numbers has been assumed, the relationship
of the arithmetic structure of the totals is
inherently independent of the symbols used.
Nevertheless, the choice of signs employed
in Fig. 7 to represent decimal numbers is
entirely reasonable as it follows the same
rules of the sexagesimal system. If this was
indeed the system used, the resemblance
between the totals would have been not only
inherently but formally true as well.
A Sumerian scribe looking at
a document containing the Genesis total
would have interpreted the signs as
sexagesimal. Thus, the first 6 signs would
have represented 216,000 years (6 x 10x602),
and the next six, 21,600 (6 x 602)
for a total of 237,600 years. This is very
close to the total in the Sumerian
antediluvian document. The scribe would have
been puzzled at the last set of six small
circle signs. That sign was generally
recognized as the cipher for 10. But why
introduce 60 years (6 x 10) when already the
first two sets of signs amount to more than
two hundred thousand years? Also, it would
have appeared very strange that no
intermediate ciphers between 602
and 10 were used in the total. The scribe
would have expected to see the next smaller
cipher of the system, namely the large
bullet with the small circle inside (10x60).
It would have seemed very reasonable to
assume that the signs were wrong and that
the large bullet had been dropped. Given
that assumption, the last three signs would
have represented 3,600 (6 x 10x60) for a
grand total of 241,200 years, the total
appearing in the Sumerian list.
Our hypothesis for
explaining the similarities in numerical
structure and magnitude of the two totals is
as follows: The Sumerian scribe that
composed the original Antediluvian list had
at his disposal a document (possibly a clay
tablet) containing numerical information on
the ages of eight of the patriarchs similar
to that of the Genesis record. The numbers
denoting the lifespans of the individual
patriarchs were missing or obliterated.
However, the document had a rounded total of
the lifetimes of the patriarchs (possibly on
the back of the tablet). Although this
number was written using a decimal number
base, the scribe assumed it was sexagesimal
and incorporated it into his document after
making some slight emendations. He then
proceeded to assign approximate reign
durations to the perceived antediluvian
kings in an arbitrary manner but keeping the
sum equal to the total he had copied from
the decimal (Semitic) tablet. He only used
two high order ciphers to represent the
durations (in units of 3,600 years) but used
a third smaller cipher in the last two
reigns to conform to the structure of the
total he had adopted.
Although this hypothesis
cannot be proven at this time, it seem to
afford a reasonable explanation of the
similarities and differences between the two
documents. The probability that the
resemblance is fortuitous is very small in
view of the fact that the two lists:
-
mention the Flood;
-
refer to the same
(adjusted) number of personages;
-
have totals that are
made up of the same number of symbols
for ten times the square of the base,
the square of the base, and the next
lower symbol of the two different
numerical systems involved;
-
and, have their totals
correspond to each other numerically.
On the other hand, it is
highly unlikely that the biblical account
was derived from the Sumerian because:
-
the Genesis account has
more numerical precision and more
detailed information;
-
the ages of the
patriarchs are much more reasonable than
the extremely long reigns of the kings
of the Kings List, the account is much
more realistic and true to life;
-
and, the moral and
spiritual qualities are immensely
superior. For example, in the Sumerian
account of the Flood (as given in the
Gilgamesh epic) there is no reason given
for the decision of the gods to destroy
mankind. There are no allusions at all
to a fault committed by man. The Flood
appears as a capricious act of the gods
rather than a divine punishment. In
Genesis, however, God purposes to purge
mankind because the thoughts and designs
of men were continually evil, and the
Earth was full of violence.
Another possible explanation
is that, instead of a written document, the
Sumerians had an oral tradition referring to
the antediluvian account which was used in
composing the early part of the Kings List,
but that they had available only the general
setting of the story, the number of
personages involved (interpreted as kings),
the rough magnitude of their ages
(interpreted as durations of reigns), and
the rounded total; originally in a decimal
numerical system, but incorrectly assumed to
be in a sexagesimal one at a later date. The
main problem with this explanation is that
there is a detailed numerical correspondence
between the two lists that would have been
difficult to remember from one generation to
the other. On the other hand, the total of
the lifetimes (which provides the principal
numerical correspondence) has a structure
(three sets of six ciphers each in strict
decreasing arithmetical order) that would
have made remembering that number much
easier.
Discussion and summary
The Sumerian King List
records in a chronological succession the
names of most of the kings of Sumer and the
lengths of their reigns. The composition is
based on the theory that there was always
only one king at a time for all of
Babylonia, and a single capital. A few of
the existing manuscripts of the List have an
initial section dealing with kings before
the Flood that is significantly different
from the rest of the list. This antediluvian
section was a later addition written by a
person different from the one who composed
the postdiluvian section of the list. This
scribe appears to have adapted an earlier
list of antediluvian kings to conform to the
style and philosophy of the document he was
bringing up to date. However, it is evident
that his source for the antediluvian kings
did not claim that the different kingships
were successive. The original King List was
probably composed during the reign of
Utu-hegal of Uruk (2119–2112 BC) and the
antediluvian section added after the reign
of Sin-magir (1827–1817 BC) of the Isin
dynasty.
Sumerians and Babylonians
employed a sexagesimal number system. There
were two non-positional ways of representing
the different ciphers: an earlier one using
a round stylus, and a later cuneiform way
using a triangular stylus. In both systems
the number of ciphers was very small
requiring many repetitions of the same
symbol, although grouping of the sexagesimal
symbols by tens was employed. Later, during
Babylonian time, a quasi-positional system
was devised. No other culture of the ancient
world developed a sexagesimal number system,
although non-Sumerian groups adopted the
Sumerian script to represent their languages
and used their numerical system. This was
the case of Semitic groups such as at Ebla
and Mari, but although they used the
cuneiform system, they retained a Semitic
calendar and decimal counting.
When the kingdom durations
of the antediluvian portion of the King List
are represented with the early Sumerian
numerical system, the total and all of the
numbers except two need only two different
symbols. These are the two largest units of
the system, so that the numbers are
expressed as multiples of 3600. The total
(241,200) needs six 10x602 signs,
six 602 signs, and six 10x60
signs. The duration of the lives of the
biblical patriarchs, however, have the
precision of one year, and the majority of
the ages have units. If Adam the first man
and Noah the Flood hero are not included to
match the contents of the Kings List, their
total ages would be 6695. If the ages are
rounded to the two highest digits as in the
Sumerian list, the final number has six 103
signs, six 102 signs, and six 10
signs for a total of 6660. Thus, the totals
of both the adjusted Genesis and Sumerian
lists have six of the signs for ten times
the square of the base, six of the signs for
the square of the base, and six signs for
the next lower value of their respective
system. In addition, when the number
representing the sum of the ages of the
biblical patriarchs is interpreted as having
been written in the sexagesimal system, the
two totals become numerically equivalent.
The probability that the
resemblance between the two documents is
fortuitous is very small. On the other hand,
it is highly unlikely that the biblical
account was derived from the Sumerian in
view of the differences of the two accounts,
and the obvious superiority of the Genesis
record both in numerical precision, realism,
completion, and moral and spiritual
qualities. It is much more likely that the
Sumerian scribe that composed the original
antediluvian list had available a document
(possibly a clay tablet) containing
numerical information on the ages of eight
of the patriarchs similar to that of the
Genesis record and that he mistakenly
interpreted it as being written in the
sexagesimal system. Another possibility is
that the Sumerians had an oral tradition of
the antediluvian world that only provided
the general setting of the story, the number
of personages involved, the rough magnitude
of their ages and the rounded total, and
that these numbers were originally decimal
but were incorrectly assumed to be
sexagesimal at the time of writing the
antediluvian list.
The fact that numerical
elements of the biblical antediluvian
account appear so distinctly in the context
of a secular Sumerian historical document
such as the Kings List, is strong evidence
for the historicity of the early chapters of
the book of Genesis. The biblical
description is not limited to the Hebrews,
but it appears that there was an ancient
tradition of the antediluvian world in the
early stages of the Mesopotamian culture as
well. On the other hand, the fact that the
Sumerian account shows up as a numerically
rounded, incomplete version of the Genesis
description, lacking the latter’s precision
and wealth of details, as well as its moral
and spiritual depth, is a strong argument
for the priority, accuracy and superiority
of the biblical record. And finally, the
clear parallels between the Sumerian and
biblical antediluvian data, qualitative as
well as numerical, open up the possibility
of establishing some chronological
correlations between the rest of the Kings
List and the early chapters of the book of
Genesis.
Acknowledgments
I would like to express my
gratitude to my wife Evangelina V. López for
her patience and understanding during the
research and preparation of this work. Her
help in editing and proof reading is also
greatly appreciated.
References and notes
- Kramer, S.N., The Sumerians,
The University of Chicago Press,
Chicago, IL, 355 pp, 1963.
- Walton, J., The antediluvian section
of the Sumerian King List and Genesis 5,
Biblical Archaeologist, 44:207–208,
1981. Also, see his later study on the
Sumerian King List in Ancient
Israelite Literature in its Cultural
Context, Zondervan, pp. 127–31,
1989.
- Morby, J.E., Dynasties of the
World, Oxford University Press,
Oxford, 253 pp, 1989.
- Jacobsen, T., The Sumerian King
List, The University of Chicago,
Chicago, IL, 217 pp, 1939.
- Friberg, J., Numbers and measures in
the earliest written records,
Scientific American, 250(2):110–118,
1984.
- Flegg, G., Numbers, Their History
and Meaning, Barnes and Noble, NY,
295 pp, 1993.
- Nissen, Hans J., The early
History of the Ancient Near East,
9000–2000 BC, The University of
Chicago Press, Chicago, IL, 215 pp,
1988.
- Walker, C.B.F., Reading the Past:
Cuneiform, Trustees of the British
Museum, British Museum, 64 pp, 1987.
- University of Wisconsin, Sign,
symbol, script: An exhibition on the
origins of writing and the alphabet,
Board of Regents of the University of
Wisconsin System, Department of Hebrew
and Semitic Studies, University of
Wisconsin-Madison, 88 pp, 1984.
- Schmandt-Besserat, D., The earliest
precursor of writing,
Scientific American, 238:50–59,
1978.
- Mattiae, P., Ebla: An Empire
Rediscovered, Doubleday, Garden
City, NY, 1981.
- Pettinato, G., Catalogo dei Testi
Cuneiformi de Tell Mardikh-Ebla,
Instituto Universitario Orientale di
Napoli, Naples, 1979.
- Pettinato, G., Testi
Administrativi della Biblioteca L. 2769,
Instituto Universitario Orientale di
Napoli, Naples.
- Pettinato, G., The Archives of
Ebla, Doubleday, Garden City, NY.
- Fiore, S., Voices From the Clay,
University of Oklahoma Press, Norman,
OK, 254 pp, 1965.
Raul E. Lopez has an
M.S. and a Ph.D. in Atmospheric Science from
Colorado State University. He works as a
research meteorologist with the National
Severe Storms Laboratory. He has published
about 50 journal papers and 90 conference
papers and technical reports.
