NUMBERS, TYPICAL AND IMPORTANT
Biblical numbers are primarily based on the decimal system, which is of Hamito-Egyptian origin. The sexagesimal system, however, which ultimately derives from Sumerian usage, also plays an important role in Scripture, and since 60 is divisible by ten and five, the two methods of reckoning easily coalesce. The numbers in the Bible range from one (Gen. 1:5) to 100,000,000 (Dan. 7:10), though the latter figure is to be regarded as a hyperbole rather than a literal numerical expression. The largest number to be understood literally is that given in I Chronicles 21:5 in connection with David's census: 1,100,000 men from Israel plus 470,000 from Judah that drew the sword (but cf. the smaller figures in II Sam. 24:9). The idea of infinity in the mathematical sense (in contrast to the theological concept of God's unlimited powers) is not found in the Bible. However, it is recognized that there are limits to the human ability to count (Gen. 13:16; 41:49).
The Israelites in biblical times did not take a special interest in mathematics. Their knowledge was confined, it seems, to their essential needs and was based on Egyptian and Babylonian methods of calculation. The four basic arithmetical operations are represented in the Bible, but only the results – not the method of calculating – are given. Thus there are examples of simple addition (Num. 11:26), subtraction (Gen. 18:28–33), multiplication (Lev. 25:8; Num. 7:84–86), and division (Num. 31:27). More complicated operations, involving "the rule of three," are exemplified in Leviticus 25:50ff.; 27:18, 23. The Hebrews also had an elementary control of fractions, but they seem to have avoided, as did other peoples of antiquity, the problem of converting mixed fractions to a common denominator. The biblical use of complementary fractions (i.e., fractions in which the numerator is one less than the denominator, e.g., 2/3, II Kings 11:7; 4/5, Gen. 47:24; 9/10, Neh. 11:1) shows Egyptian and Mesopotamian influence. Of particular interest is the use of certain parts of the body to express fractions or multiplication, e.g., yad, "hand" (fractions: ibid.; multiplication: Gen. 43:34); regel, "foot" or "times" (multiplication: Num. 22:28); pi, "mouth" (fraction: Zech. 13:8; multiplication: Deut. 21:17, according to many exegetes). The term pi shenayim originally meant two-thirds but subsequently came to signify "twice as much" (II Kings 2:9). The latter is the meaning it always has in the Mishnah and Talmud. In Deuteronomy 21:17 the sense is uncertain: the expression could mean either two-thirds of the inheritance or a double portion. Rosh, "head," frequently occurs in the sense of "sum, total" (Ex. 30:12; Num. 1:2), or "capital" (Lev. 5:24). The curious psychological approach that enables yad, for example, to serve both for division and multiplication is also reflected in the use of certain denominative verbs (in the pi'el) derived from numbers. Thus shillesh denotes "to divide into three" (Deut. 19:3) and "to repeat an action three times" (I Kings 18:34). The value of π was taken to be 3 (I Kings 7:23). Even the Mishnah in Eruvin 1:5 retains this approximate value, but Mishnat ha-Middot (second century) estimates π as 22/7.
Method of Expression
Biblical numbers are expressed by words denoting units, tens, 100, 200, 1,000, 2,000, 10,000, 20,000, and by combinations of these. There is no real evidence of the use of arithmetical symbols either in Scripture or in monumental inscriptions of the biblical period, like the *Siloam Inscription (c. 700); cf. also the *Mesha Stele of the ninth century. However, the use of figures in everyday documents, chiefly for small numbers, is demonstrated by the *Samaria ostraca (eighth century),
Symbolic and Rhetorical Use
Biblical numbers are not always intended to be taken at their face value. They are often used indefinitely – as round figures – or rhetorically, for emphasis or in a hyperbolic sense. At times the rhetorical effect is achieved through a latent number, i.e., certain words or names occur a given number of times, although the actual figure is not specified. Many numbers are noteworthy for their symbolic nuances. Hebrew literature is not altogether unique in this regard; analogues are to be found in Egyptian, Sumerian, Akkadian, Canaanite, and Hittite writings. Ugaritic, in particular, provides many examples of the rhetorical and symbolic use of numbers. Especially significant is the biblical use of sacred numbers, which play an important religious role. There is, in addition, a distinct tendency in Scripture to achieve numerical harmony or symmetry. This aspect has been worked out in considerable detail for Genesis, notably its early chapters, by U. Cassuto (see bibliography).
One is sometimes used as the indefinite article (I Sam. 24:14), and often as an indefinite pronoun, "someone, anyone, a certain man" (II Kings 4:39). Though a cardinal number, it is also used as an ordinal (Gen. 1:5; 8:5, 13; Ruth 1:4). It also signifies uniqueness and indivisibility. Hence it is expressive of the unity of marriage (Gen. 2:24) and of the doctrine of monotheism (Deut. 6:4).
The fact that various organs and limbs of the body occur in pairs (eyes, hands, etc.) invested the number two with a certain importance. The animals entered the ark in pairs; the Decalogue was inscribed on two tablets of stone. Often two sacrifices were ordained (Lev. 14:22). The fraction one-half is also common in the Bible: the half-tribe of Manasseh (Num. 32:33) and the half-shekel (Ex. 30:13). The Hebrew preference for the concrete to the abstract finds expression, inter alia, in the idiomatic use of two for "a few" (Num. 9:22; I Kings 17:12). Sometimes "three" is added to emphasize the approximate character of the number (II Kings 9:32; Job 33:29; Isa. 17:6). Mention may also be made here of the idiom temol shilshom, "hitherto" (literally: 'yesterday, the third day back'). A not uncommon device for achieving emphasis is the repetition (latent two) of a word or phrase (I Kings 13:2; Isa. 43:25).
Three is a very common biblical number. At times it is difficult to tell whether it is used with precision or as a small round number (Gen. 30:36; Ex. 2:2); but the addition of the next high number establishes its approximate character (Ex. 20:5; Jer. 36:23). Of special importance is its use in sacred contexts. It conveys the idea of completeness, having a beginning, middle, and end. Even in remote antiquity the pagan peoples worshiped triads of gods (in Babylonia: Anu, Bel, and Ea; in Egypt: Isis, Osiris, and Horus). The universe was divided into heaven, earth, and the abyss (or the netherworld), which the three deities represented. The family group of father, mother, and child, without doubt, also contributed to the significance of the number. In the Bible three has various religious associations: a three-year old (or third-born) sacrifice in Genesis 15:9; three feasts (Ex. 23:14); for three years the fruit of a newly planted tree was forbidden (Lev. 19:23); ritual purification on the third day (Num. 19:12; 31:19); Daniel kneeled and prayed three times a day (Dan. 6:11). The following occurrences of three are also of interest: In Genesis 40, three has symbolic significance. It exercises a mystic power in the story of Elijah's revival of the child (I Kings 17:21). Three cities of refuge are mentioned in Deuteronomy 19:7, 9. Three daughters (plus seven sons) seem to be an ideal number (Job 1:2; 42:13). Three is latent in a number of passages where it expresses a complete and perfect number or is used for emphasis. The expression "and God blessed" occurs, for example, three times in Genesis 1:22, 28; 2:3. The Sanctuary has three divisions: a court, a holy place, and a Holy of Holies (Ex. 26:33; 27:9; I Kings 6:16–17). In Aaron's benediction (Num. 6:24–26) the Tetragrammaton occurs thrice, and three pairs of blessings are pronounced. On the other hand, the trisagion in Isaiah 6:3 is a form of superlative (in the Qumran scroll, 1QIsa, "holy" is found only twice); while the occurrence of "temple of the Lord" three times in Jeremiah 7:4 merely lends emphasis to the prophet's mocking rebuke.
The importance of the number four is probably derived from the four cardinal points of the compass (some scholars point to the square). It is regarded as sacred in various parts of the world, and signifies completeness and sufficiency. Four rivers issued from the Garden of Eden (Gen. 2:10). Jephthah's daughter was lamented annually for four days (Judg. 11:40). In Jeremiah 15:2 the people is divided into four groups, each subjected to a different type of disaster; in the next verse the category of "the sword" is itself divided into
Five probably means simply "a few" in II Kings 7:13, perhaps also in Genesis 43:34; 47:2 (cf. Er. 6:6, 8). Five as a basic number goes back to remote antiquity. There was a primitive Hamitic system based on the number five before the decimal system. It is obviously derived from the fingers of the hand used by early man in his simple calculations. In the Bible, five is related to both the decimal and sexagesimal systems. It is a feature of sacred architecture (I Kings 7:39, 49). It is also found in connection with penalties (Ex. 21:37), redemption (Num. 3:47; 18:16), and gifts (Gen. 43:34; 45:22). The fraction one-fifth is likewise common (Lev. 5:16; 22:14). It is often used as a small round number (Lev. 26:8; I Sam. 17:40; Isa. 19:18). For the multiple 50 see below. Other multiples up to 500,000 occur frequently (Gen. 5:32; Ex. 30:23–24; II Chron. 13:17, et al.).
Six is part of the sexagesimal system but has little symbolic value. Examples of its occurrence are: the working days of the week (Ex. 20:9); the maximum years of servitude for a Hebrew slave (Ex. 21:2); the steps of Solomon's throne (I Kings 10:19–20); the wings of the seraphim (Isa. 6:2); the six-cubit measuring reed of Ezekiel's vision (Ezek. 40:5; 41:8).
Seven played an exceptionally important role in antiquity. It was sacred to Semitic and other peoples, including the Egyptians, Assyrians, Persians, and the Vedic folk in India. Its importance is often derived from the worship of the seven heavenly bodies: the sun, moon, and the five planets. It is also pointed out that the seven-day week was approximately a quarter of the lunar month (29½ days), and that the Pleiades (Amos 5:8) were thought to comprise seven stars. Others see the origin of the number's prominence in the fact that it is composed of the sacred numbers three and four, or in the "unrelated" character of seven in the series one to ten. Like the Sumerians, the biblical writers often add seven to a large number to indicate a very big figure. U. Cassuto writes: "It clearly follows that the chronology of the Book of Genesis as a whole is also founded on the dual principle of the sexagesimal system and the addition of seven" (From Adam to Noah, in bibl., 259). In the Bible the number seven is connected with every aspect of religious life in every period: e.g., the clean beasts in the ark (Gen. 7:2ff.); Abraham's covenant with Abimelech (Gen. 21:28–30); cleansing from leprosy (Lev. 14); the festivals (Lev. 23; Deut. 16:9); Balaam's altars (Num. 23); the induction of the priests and the consecration of the altars (Ex. 29:35–37); sacrifices (Gen. 8:20; Num. 28:11; Job 42:8; I Chron. 15:26); the Temple furnishings (I Kings 7:17); the menorah (Ex. 25:31–37; Zech. 4:2); the Temple steps (Ezek. 40:22); the width of the Temple entrance (Ezek. 41:3); the sprinkling of blood (Lev. 4:6, 17;16:14; Num. 19:4) and the like. The innate, mystic power of seven is exemplified in Joshua 6:4, 8, 13 (Jericho); Judges 16:13, 19 (Samson); and II Kings 5:10 (Naaman). It also occurs in connection with punishment (Gen. 4:24; Lev. 26:18; Deut. 28:7, 25; II Sam. 21:6; Prov. 6:31; Dan. 4:13, 20, 29; 9:27). In relation to time, seven represents a fitting (or sacred) period (Gen. 1:3ff.; 8:12; 50:10; Ex. 7:25; Lev. 8:33; Josh. 6). More generally it indicates a complete or round number of moderate size (Isa. 4:1; 11:15; Micah 5:4; Ps. 12:7 ; Prov. 26:16, 25; Job 1:2; Esth. 1:10; 2:9). In Deuteronomy 7:1 it is equated with "many." Other interesting references are: Genesis 29:20, 27, 30 and Judges 14:12, 17 (marriage); Ezekiel 9:2 (angels); II Kings 4:35 (sneezes of revival); Genesis 41; II Kings 8:1 (famine and plenty); Genesis 33:3 (prostrations; parallels are found in the Tell El-Amarna Letters and in Ugaritic writings). Multiples of seven bear the same character with added emphasis (Lev. 12:5; Num. 29:13; I Kings 8:65). For 70 see below. The half of seven, three and a half, also has special significance. "Times, time, and half a time" occurs in Daniel 7:25 and 12:7. "Half of the week" in Daniel 9:27 is explained by CH Cornill to mean 3½ years and to have its origin in the 3½ years of Antiochus' persecution. H. Gunkel, however, traces the expression to Babylonia (half Kislev, Tevet, Shevat, and Adar), the references being to the 3½ months between the winter solstice and the festival of Marduk, i.e., the period of the supremacy of Tiamat.
EIGHT AND NINE
The numbers eight and nine do not appear to have any intrinsic symbolic import. Their significance seems to be related to seven and ten, respectively. The eighth day of circumcision (Gen. 17:12), of the consecration of first-born beasts (Ex. 22:29), of the sacrifices of the defiled Nazirite (Num. 6:10), and of the holy convocation (Lev. 23:36) is simply the day after the important period of seven days. Noteworthy, however, is Ezekiel's predilection for the number eight in the Temple structure (Ezek. 40:9, 31, 34, 37). Nine is at times significant insofar as it is one less than the important number ten (Neh. 11:1).
Like five, ten is clearly derived from the use of the fingers in counting (the Sefirot, it may be noted, emanate from the fingers according to Sefer Yeẓirah) and is the basis of the numeral system chiefly, though not solely, used in the Bible. It expresses completeness and perfection (Gen. 24:10, 22; Josh. 22:14; Judg. 17:10; II Kings 20:9–11; Jer. 41:8; Job 19:3). Its sacred character, which may derive from the fact that it is the product of three and seven (both sacred numbers), is exemplified in the Decalogue (Ex. 20:2ff.), where it may also serve as a mnemonic; the tithes (Gen. 14:20; Num. 18:21, 26; Deut. 26:12); the Tabernacle and Temple furnishings, including multiples of ten (Ex. 26; I Kings 6–7; Ezek. 45; II Chron. 4); and
The number 12 may have derived its importance from the division of the lunar year into 12 months, and from the 12 signs of the Zodiac. It should also be noted that it can be broken down into the significant numbers five (+) seven or three (×) four. But undoubtedly its divisibility and its role in the Sumerian sexagesimal system gave it a special status. In the Bible the fact that the tribes numbered 12 (Gen. 35:22; 42:13, 32; 49:28; Num. 1:44) endowed the number with special religious significance (cf. the Greek amphictyonies). To maintain the number 12, Ephraim and Manasseh were counted as two tribes when Levi was omitted. The tribes of Ishmael likewise numbered 12 (Gen. 17:20). Representative persons and objects often correspond to the number of the tribes (Ex. 24:4; 28:21; Lev. 24:5; Num. 7:3; 17:17, 21; Josh. 4:2; I Kings 10:20; 18:31; Ezek. 48:31ff.; Ezra 6:17; 8:35). Multiples of 12 are found in the 24 classes of priests and Levites (I Chron. 24:4; 25:31); the 48 levitical cities (Num. 35:7); the 24,000 men in the monthly courses that served King David (I Chron. 27:1–15). The male descendants of Adam listed in Genesis 4:1–26 numbered 12, and the verb yalad ("to bear") occurs there 12 times.
Twenty marks a distinctive period in human life. Isaac's sons were born 20 years after marriage (Gen. 25:20, 26). Also, the age for army service was 20 (Num. 1:3).
Forty is an important round number, indicating a fairly long period. The length of a generation is approximately 40 years. A man reaches full adulthood at 40 (cf. Josh. 14:7; II Sam. 2:10). Isaac and Esau married at 40 (Gen. 25:20; 26:34). The complete span of human life is thrice 40 (Gen. 6:3; Deut. 34:7), while twice 40 represents advanced old age (II Sam. 19:33–36; Ps. 90:10). The Israelites wandered 40 years in the wilderness (Ex. 16:35; Deut. 2:7), in which time an entire generation died out (Num. 14:33; 32:13). In I Kings 6:1 (cf. I Chron. 5:29–36 [6:3–10]) 480 years represents 12 generations. At various periods the land had rest for 40 years (Judg. 3:11; 8:28; I Sam. 4:18; 80 years in Judg. 3:30 is the equivalent of two generations) and David, Solomon, and Joash reigned for 40 years (II Sam. 5:4; I Kings 2:11; 11:42; II Chron. 24:1). This was a sign of divine grace. It is noteworthy that, according to the Mesha Stele, Israel oppressed Moab for 40 years. Periods of special significance often consist of 40 days (Gen. 7:4, 12; 8:6; Ex. 24:18; 34:28; Num. 13:25; Deut. 9:9ff.; 10:10; I Sam. 17:16; I Kings 19:8; Ezek. 4:6; 29:11–13; Jonah 3:4). Other interesting examples of the occurrence of 40 are: 40 lashes (Deut. 25:3); sons (Judg. 12:14); camel loads (II Kings 8:9); shekels (Neh. 5:15); Temple measurements (Ezek. 41:2; 46:22). Forty thousand indicates a very large number (Josh. 4:13; Judg. 5:8; II Sam. 10:18; I Chron. 12:37).
Fifty, a multiple of ten, occurs in measurements (Gen. 6:15; Ezek. 40:15); in compensation (Deut. 22:29); and in civil and military organization (Ex. 18:21; Deut. 1:15). Other multiples of ten, up to 500,000, are frequently encountered (Gen. 5:32; Ex 30:23–24; II Chron. 13:17).
Sixty, the basis of the sexagesimal system, is a heritage from the Sumerians, whose method of calculation has left its mark on the civilized world to this day. The division of the circle into 360 degrees, of an hour into 60 minutes, the minute into 60 seconds, and counting by the dozen and the gross are derived from this ancient people. The system originated, it is suggested, "in a mythical addition of zenith and nadir to the four points of the compass" (Mc-Gee). Although the biblical method of reckoning is based mainly on the decimal system, many scriptural (and likewise talmudic and midrashic) numbers show a sexagesimal structure. Thus the total ages of the patriarchs from Adam to Noah and their ages at the birth of the first son are either exact multiples of five or of five with the addition of seven (see Seven above), in accordance with a stylistic Sumerian usage. All the ages in Genesis 5 are to be analysed in the same way, as U. Cassuto has shown in his commentaries to Genesis (see bibl.). The sexagesimal method of calculation applies to other parts of the Bible, too.
Seventy (the product of two sacred numbers, seven times ten) is used as a round figure, with symbolic or sacred nuances. It occurs in various contexts; it is the number of the family of Jacob that went down to Egypt (Ex. 1:5; Deut. 10:22); of the palm trees at Elim; of the elders that went up with Moses, Aaron, Nadab, and Abihu (Ex. 24:9); of the elders set round about the Tent (Num. 11:24); of the years that the nations will serve the king of Babylon (Jer. 25:11ff.); and of the weeks mentioned in Daniel 9:24ff. The nations enumerated in Genesis 10 total 70 (or 71, or 72, according to others); cf. also the 77-fold of Lamech's vengeance (Gen. 4:24). In Ugaritic literature 70 funerary offerings for Baal are mentioned, and the gods are referred to as "the 70 children of Asherah."
A thousand and its multiples are frequently used in the Bible as round numbers indicating a large amount. Etymologically the Hebrew word elef ("thousand") denotes "a crowd," and hence at times has the sense of "tribe," "clan," or designates a military unit, which does not necessarily comprise 1,000 (Ex. 18:21; Deut. 33:17; Judg. 6:15). Flinders Petrie (Researches in Sinai), interpreting elef to mean a family or tent, reduced the figure for the first census to 5,500, and to 5,730 for the second. Multiples of 1,000 are often hyperbolic expressions (Lev. 26:8; Deut. 32:30; I Sam. 18:7; Ps. 3:7; Song 5:10). Seventy thousand (II Sam. 24:15) and 1,000,000 (Dan. 7:10; I Chron. 21:5; 22:14; II Chron. 14:8) are globular figures indicative of a vast number, while "thousands of ten thousands" (Gen. 24:60) and "ten thousand times ten thousand" (Dan. 7:10) are imaginative numerical ultimates. Similarly high figures are found in Ugaritic literature.
The question of the accuracy of biblical numbers is an exegetical problem. There are actual contradictions within the Bible itself (cf. II Sam. 24:9 with I Chron. 21:5). The correctness of other figures is doubted on other grounds. Unquestionably, some excessively large numbers must be regarded as symbolic or hyperbolic figures. In certain cases critics suppose that estimates – especially of enemy forces – are only rough, and possibly exaggerated, guesses. However, errors in transmission and copying must be taken into account. Manuscripts generally show that they are particularly prone to corruption where numbers are concerned. In Hebrew a single letter could change five to 50, for example. It is interesting to note that one Hebrew Ms. of the Bible (no. 9 of Kennicott) reads in Numbers 1:23, 1,050 for 59,300 (MT); Numbers 2:6, 50 for 54,400; and in Numbers 2:16, 100 for 151,450. There are also considerable divergences between the Masoretic Text, the Septuagint, and the Samaritan versions. For example, the years between the Creation and the Flood are 1,656 in the Hebrew Bible, 2,262 in the Septuagint, and 1,307 in the Samaritan recension.
Ascending and Descending Numbers
The manner in which large numbers are arranged is subject to interesting variations: sometimes they are arranged in ascending order (Gen. 5:17), at other times in descending order (Gen. 23:1; Ex. 38:26), and occasionally a combination of both (Num. 3:43). The conventional explanation is that J, E, and D prefer the descending order, while P favors the ascending order. Cassuto, however, has argued that not a documentary criterion but a linguistic principle is operative here: "When the Bible gives us technical or statistical data and the like, it frequently prefers the ascending order, since the tendency to exactness in these instances causes the smaller numbers to be given precedence and prominence. On the other hand, when a solitary number occurs in a narrative passage or in a poem or in a speech and so forth, the numbers are invariably arranged, save in a few cases where special circumstances operate, according to the more natural and spontaneous order, to wit, the descending order" (The Documentary Hypothesis, in bibl., 52).
Another question to which Cassuto has given special attention is that of numerical harmony. He demonstrates, for instance, that heptads repeatedly occur in Genesis 1:1–2:3, leaving no doubt that these literary variations on the theme of seven were carefully designed so as to achieve a harmony of numbers. "This numerical symmetry," he writes, "is, as it were, the golden thread that binds together all the parts of the section and serves as a convincing proof of its unity" (From Adam to Noah, in bibl., 15).
Another interesting feature of biblical style is the use of graded numbers. This consists of the collocation of two consecutive numbers for rhetorical purposes. The usage may be divided into three categories:
(a) In prose it expresses approximation and, as a rule, fewness, and has a colloquial character (II Kings 9:32; 13:19).
(b) In poetry the two numbers form a parallelism and also express inexactness (Micah 5:4; Job 5:19). A similar usage is found in Sumerian and Akkadian, and, especially, in Ugaritic epic poetry. Since numbers are involved, the parallelism cannot be expressed through synonyms, and consecutive numbers are the only alternative (cf. the parallelism between 1,000 and 10,000 in Ps. 91:17). A combination of the idiom for fewness and poetic parallelism is seen in Isaiah 17:6.
(c) In proverbial sayings a schematic device is employed in which two successive numbers are given of things that share a common characteristic, and the actual items subsequently enumerated conform to the second, i.e., the higher, number (Prov. 30:15–31). The use of numbers in Proverbs (including single numbers as in Prov. 30:15a) is intended as an aid to memory. In Amos 1:3–2:6, where three and four are repeatedly mentioned but only one example is cited, the prophet apparently uses surprise as a rhetorical factor.
Reviewing the facts adumbrated above, it appears that numbers are used in the Bible not solely for statistical or arithmetical purposes. They are also employed as stylistic devices to express symbolically the idea of completeness and perfection, to convey the concept of sanctity, to provide mnemonics, and are often arranged so as to give numerical symmetry or harmony to a passage. They are used both expressly and latently to emphasize the leading thought of a text, and thus often establish its intrinsic unity. The rhetorical uses of numbers in Scripture unquestionably constitute a highly valuable aid to biblical exegesis. Furthermore, the biblical approach to numbers strongly influenced the thinking of later ages. Philo and other Hellenistic writers, the Apocryphal literature, the New Testament, the Talmud and Midrash, and especially the kabbalistic writers laid great stress on numerology in various forms. In this way, numbers became an integral part of both literature and theology.
D. Curtis, A Dissertation upon Odd Numbers (1909); H. and J. Lewy, in: HUCA, 17 (1943), 1–52; U. Cassuto, From Adam to Noah (1961); idem, From Noah to Abraham (1964); idem, The Documentary Hypothesis (1964); idem, Exodus (1967).
Source: Encyclopaedia Judaica. © 2008 The Gale Group. All Rights Reserved.