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 Encyclopedia
Judaica 2nd Edition
An essential source of information on
Jewish life, culture, history, and
religion.
In 1972, the Encyclopaedia Judaica
fulfilled the longstanding dream of
capturing the full richness of Jewish
culture in a single authoritative
publication, heralded in the scholarly
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works ever compiled.
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NUMBERS AND
NUMERALS: By : Executive Committee of the
Editorial Board. Caspar Levias
ARTICLE HEADINGS:
Numerical Notation
System of Numbers
Symbolism of Numbers
Ascending Enumeration
Numerical Grouping
Numerical Notation
The letters of the alphabet were used as
numerical symbols as early as the
Maccabean period (comp. Numismatics).
Whether such a usage was known in earlier
times also, whether there existed in
Israel, as among kindred nations, special
signs for figures, or whether numerical
notation was entirely unknown, can not be
decided by direct proof. That there were
no numerical signs at all is hardly
possible. The necessities of daily life
require such signs, and the example of
surrounding nations could not but have
suggested their introduction. For an
assumption that there were special signs
there is no basis. It must, therefore, be
assumed that the numerical value of the
alphabet was known in earlier times. The
fact that figures are not found in the
Bible nor in the Siloam inscription, nor
on the Moabite Stone, would not militate
against such an assumption. In monumental
inscriptions the use of figures might have
been avoided for various reasons, while
the earlier use of figures in the Bible is
rather probable, since the discrepancies
in numbers which now exist can thus be
best explained. Other considerations
strengthen such a hypothesis (comp.
Gemat.ria). |
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The use of
alphabetical signs was doubtlessly
practically the same as in the Talmud,
where numbers higher than 400 are formed
by composition, as (for 500), (for 900),
etc. Such a way of forming higher
numbers could not in the end be found
other than clumsy, and, therefore, the
Masorites introduced the use of the
final letters for indicating 500, 600,
700, 800, and 900 respectively; to
indicate the thousands the letters
representing the corresponding number of
units was used. In writing any numerical
combination, since the thousands were
written before and the units were
written after the hundreds and tens (the
latter letters of the alphabet), they
were easily distinguishable. About 800
C.E. the Jewish scholar Mashallah
introduced into the Mohammedan world the
use of the so-called Arabic figures (see
Harkavy's note to the Hebrew transl. of
Grätz's "Gesch." iii. 213), which since
then have occasionally been used in
Hebrew literature also (Oppenheim, in "Monatsschrift,"
xiii. 231, 462; xv. 254, 376).
System of Numbers
The Hebrew system of counting is, like
that of all the Semites and like the
Egyptian hieroglyphic system, the
decimal, which is a later development of
a more original quintal system based on
the fingers of one hand (L. Reinisch, "Das
Zalwort Vier und Neun in den
Chamitischen-Semitischen Sprachen"). The
blending of the Semitic decimal system
with the Sumerian sexagesimal is found
in earliest Babylonian times. But in
course of time the decimal system
prevailed. A trace of the sexagesimal
system may still be found in the use of
the number sixty (see below). The use of
the fingers for numbering occurs in
traditional literature (see Yoma 22a,
b). In Talmud and Midrash numbers are
sometimes formed by subtraction, as in
Latin, French, etc.—for example 100 - 2
= 98 (Lam. R. iii. 12), 50 - 1 = 49 (Levias,
"Aramaic Grammar," § 141)—the reason for
which is not clear.
Symbolism of Numbers
At an early time in the history of man
certain numbers were regarded as having
a sacred significance or were used with
symbolical force, the origin of their
symbolism lying in their connection with
primitive ideas about nature and God.
Such a use of numbers is found also in
the Bible, although the Biblical authors
were hardly conscious of their origin.
In later Jewish literature, however,
with Pythagorean doctrines was
introduced the use of numbers as
symbols, based on their mathematical
qualities. The most prominent exponent
of the latter custom is R. Abraham ibn
Ezra. In cabalistic literature both
systems are used. The rhetorical or
stylistic use of numbers is largely due
to an obsolete symbolism. Even numbers
were thought to be unlucky (Pes. 110a).
Attempts to find in Biblical numbers
references to ideas were made by
Aristobulus and Philo, and since their
time by many allegorists. Nevertheless,
a distinct connection between any given
number and a certain idea can not be
proved. Among the "thirty-two rules" of
the son of R. Jose the Galilean, two
refer to numbers—one to gematria, the
other, the twenty-seventh, to the
symbolism of numbers (see Bacher, "Tannaitische
Terminologie," s.v. ). According to this
hermeneutic canon, any number may be
explained as corresponding to (, i.e.,
"symbolizing") another equal number or
sum of numbers. Thus, the "40 days" in
Num. xiii. 25 correspond to the "40
years" in ib. xiv. 34; and the number 36
in II Chron. xvi. I corresponds to three
things in connection with which the same
number of years is mentioned (Bacher,
l.c.).
The following numbers occur in Hebrew
literature either as symbols or as round
numbers:
Two: Used in the sense of "a few" in
Num. ix. 22; I Sam. xi. 11; Hos. vi. 2;
Ned. 66b (comp. the Talmudic rule, ).
Three: The sacredness of this number is
probably due to the fact that primitive
man divided the universe into three
regions—heaven, earth, and water,
respectively represented in Babylonian
mythology by the divinities Anu, Bel,
and Ea. Its sacred or symbolical use may
be illustrated by such passages as I
Kings xvii. 21; I Chron. xxi. 12; Dan.
vi. 10. Its rhetorical use for a small
total is illustrated in Gen. xxx. 36;
xl. 10, 12; xlii. 17; Ex. ii. 2, iii.
18, and in Pes. 62b and Yer. Ta'an. iv.
8. Multiples of three are similarly
used: nine, in Yer. Ta'an. iv. 8;
twenty-one, in Ethiopic Enoch, lxix. 2;
thirty, in Slavonic Enoch, xxxvi. 1;
thirty-six, in Ethiopic Enoch, xc. 1;
three hundred, in Sot.ah 34a; Pes. 62b;
H.ul. 59b, 90b; Yer. Sanh. vii. 19; Yer.
Ta'an. iv. 8; nine hundred, in Yer. Sanh.
vii. 19.
Three and one-half: Represents,
according to Gunkel ("Schöpfung und
Chaos," pp. 309 et seq.), the three and
one-half months from the middle of
Kislew to the end of Adar—from the
winter solstice to the festival of
Marduk, the period of the supremacy of
Tiamat. The number occurs in Dan. vii.
25, ix. 27, and xii. 7 (Hebr.). In
traditional literature three and
one-half as a half of seven is
frequently used as a round number; see
Midrash to Proverbs (ed. Buber, p. 48,
note ).
Four: Sacred as the number of the four
cardinal points of the compass; denotes
completeness and sufficiency. In
cabalistic literature its sacredness is
enhanced by the fact that the
Tetragrammaton contains four letters.
The number is found in Gen. ii. 10;
Judges xi. 40; Jer. xv. 3; Ezek. xiv.
21; Zech. i. 18; Neh. vi. 4; etc. The
multiples of four used are twenty-eight
(in the measurement of the curtains of
the Tabernacle) and forty and its
multiples.
Seven: The most sacred number. The
origin of its sacredness is found by
some in its factors three and four; by
others, in its correspondence to the
number of the planets; while others
assert that it arose from a sacred six
by the addition of one. In Judaism its
sacredness was enhanced by the
institution of the Sabbath. The number
occurs in the seven days of Creation,
the institution of the seventh year of
release, the forty-nine years between
the jubilees, the seven altars, the
seven lamps, the sprinkling of the blood
seven times, etc. (Gen. vii. 2 et seq.,
xxi. 28-30; I Kings xviii. 43; Deut.
xvi. 9; Ezek. xl. 22, xli. 3; et al.).
Quite frequently it is met with in
Apocryphal literature (Ethiopic Enoch,
xxi. 3-6, lxxiii. 5-8; Slavonic Enoch,
iii.-xx., xxvii. 3, xli. 1; et al.); in
Talmud and Midrash (Pes. 54a; Sot.ah
10b; et al.; comp. Lampronti, "Pah.ad
Yiz.h.ak.," s.v. ). The multiple
fourteen occurs in Proverbs Rabbah (ed.
Buber, p. 92).
Ten: Had a symbolical character in part
because it is the basis of the decimal
system, and in part because it is the
sum of three and seven. Its simplest use
is as a round number (Gen. xxiv. 10, 22;
Josh. xxii. 14; Judges xvii. 10; et al.;
comp. Lampronti, l.c. s.v.). A more
sacred use is found in the ritual (Ex.
xxvi. 1, 16; Num. vii., xxviii., xxix.;
I Kings vi., vii.; Ezek. xlv.; II Chron.
iv.). Because of this sacred character
"ten" is used in apocalyptic symbolism
(Dan. vii. 7, 20, 24).
Multiples of ten are used as round
numbers: one hundred and two hundred, in
Pes. 64b; et al.; one thousand, in H.ul.
97b; Ned. 50b; Yer. Ta'an. iv. 8; ten
thousand and two hundred thousand, in
Yer. Ta'an. iv. 8; one million, in Yoma
33b.
Twelve: Derived its sacred character
from the fact that it is the product of
three and four and is the number of the
months of the year. There are twelve
tribes of Israel and the same number of
tribes of Ishmael (Gen. xvii. 20, xxv.
16). The number of many representative
men and things was made twelve to accord
with the number of the tribes (Ex. xxiv.
4; Num. xvii. 2, 6; Josh. iv.; et al.).
The number twelve for these reasons
entered into Hebrew ritual (comp. Ex.
xv. 27; Num. xxxiii. 9; Lev. xxiv. 5;
Jer. lii. 20 et seq.; Ezek. xliii. 16).
As a round number twelve occurs both in
Biblical (II Sam. ii. 15; I Kings x. 20)
and in post-Biblical literature (see the
list of references given by Zunz, "Literaturgesch."
p. 601; comp. also Yoma 75b, 77b; Ta'an.
25a; M. K.. 24a; H.ul. 95).
The multiple twenty-four occurs in Lam.
R. i. 2; twenty-four millions, in Ned.
50b.
Twenty-two: Used as a round number in
later literature (Gen. R. lxxiii.; Midr.
Shemuel xx.), deriving its significance
from the fact that it is the number of
the letters in the alphabet (comp.
Bacher, "Ag. Pal. Amor." ii. 297).
Forty: Stands in the Bible for a
generation (e.g., the forty years of
wandering in the desert), hence for any
period of time the exact duration of
which is unknown (comp. Gen. vii. 4, 12,
17; viii. 6; Ex. xxiv. 18, xxxiv. 28;
Deut. ix. 9, 11, 18; x. 10; I Sam. xvii.
16; I Kings xix. 8; Jonah iii. 4). In
later literature forty is commonly used
as a round number (comp. Git.. 39b, 40a;
Sot.ah 34a; Yer. Ta'an. iv. 8; et al.).
The multiple eighty is found in Yer.
Ta'an. iv. 8; four hundred, in H.ul. 59b
and Bek. 31a; four hundred and eighty,
in I Kings vi. 1 and Yer. Meg. iii. 1;
eighty thousand, in Yer. Ta'an. iv. 8.
Sixty: The larger unit of the
sexagesimal system; used to express an
indefinitely larger number (comp. Cant.
iii. 7, vi. 8). In Talmudic literature
it is frequently used as a round number
(comp. Ber. 57b; Pes. 94a; B. K.. 92a;
B. M. 30b, 107b; Ta'an. 10a; Ned. 39b;
Midr. Teh. xli.; Lev. R. xxxiv.; etc.).
In the Halakah a thing ritually unfit
becomes fit when mixed with something
sixty times its own amount.
Seventy: Has a sacred or symbolical
significance because it is made up of
the factors seven and ten (comp. Ex. xv.
27; xxiv. 1, 9; Num. xi. 24 et seq.;
Gen. xlvi. 27; Ex. i. 1; Deut. x. 22;
Jer. xii. 11; Dan. ix. 24 et seq.). For
later Jewish usage compare S. Krauss in
Stade's "Zeitschrift," xix. 1-14, xx.
38-43, and Steinschneider in "Z. D. M.
G." iv. 145-170; lvii. 474-507, where he
deals also with the number seventy-two.
Sixty Myriads: Used in later literature
to express a very large but indefinite
number. It derives its significance from
the number of Israelites that went out
from Egypt (comp. Lam. R. ii. 13; Deut.
R. i. 17; etc.). The multiple one
hundred and twenty myriads occurs in
Lam. R. l.c.
Ascending Enumeration
The tendency to indicate somewhat more
exactly an undetermined number of
objects led to the use of two definite
numbers instead of one indefinite
expression. The smaller numbers are
paired in this way in the following
passages: one or two: Deut. xxxii. 30;
Jer. iii. 14; Ps. lxii. 11; Job xxxiii.
14, xl. 5; two or three: II Kings ix.
32; Isa. xvii. 6; Amos iv. 8; Job
xxxiii. 29; Ecclus. (Sirach) xxiii. 16,
xxvi. 19, l. 25; three or four: Jer.
xxvi. 3; Amos i. 3, ii. 6; Prov. xxx.
15, 18, 21, 29; Ecclus. (Sirach) xxvi.
5; four or five: Isa. xvii. 6; five or
six: II Kings xiii. 19; six or seven:
Prov. vi. 16; Job v. 19; seven or eight:
Micah v. 5; Eccl. xi. 2. In all these
instances the use of a second number
calls attention to the fact that the
first number is merely approximate;
hence such an arrangement of numbers is
employed in the so-called "middah" a
kind of riddle (Prov. vi. 16-19, xxx. 15
et seq.; Ecclus. [Sirach] xxiii. 16;
xxv.; xxvi. 5 et seq., 19; l. 25 et
seq.).
Numerical Grouping
As an aid to the memory, the ancients
frequently grouped themes of traditional
law or of
haggadah according to numbers; see,
for instance, Abot v., where various
subjects in which the number ten is
prominent are grouped together. Such
groups are found frequently in Talmud
and Midrash. The entire contents of some
books were at times arranged in
numerical groups, as in the "Pirke de
Rabbenu ha-Kadosh" and, probably, in the
"Forty-nine Middot de-R. Nathan," a work
now lost.
Bibliography: Hastings, Dict. Bible;
Cheyne and Black, Encyc. Bibl.;
Schwab, Répertoire, Index, s.v. Nombres
Bibliques.
On the synthetic division of numbers in
poetry, see I. Goldziher in J. Q. R.
xiv. 728;
on "friendly numbers," see
Steinschneider in Z. D. M. G., and
Grünhut in R. E. J. xxxix. 310.
On Ibn Ezra's symbolism of numbers, see
Olitzky, Zahlensymbolik des Abraham Ibn
Esra in Hildesheimer's Jubelschrift, pp.
99-120, and Rosin in Monatsschrift,
xiii. 156, xliii. 80 et seq.E. C. C. L. |
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