NUMBERS: AN OVERVIEW

Numbers, in which the power and sanctity of both time and space are experienced in visible form, have fascinated humankind since early days, although methods of counting and systems of expressing numerals have differed considerably from culture to culture. The highest achievements in this field are the Maya system and the "Arabic" (originally Indian) numbers that were introduced in the West in the twelfth century. The presence of zero in them facilitated mathematical operations.

The Mathematical Spirit

Augustine found numbers in the scriptures to be both sacred and mysterious, and people today still react positively or negatively to numbers such as seven and thirteen, for the mathematical spirit is innate in humankind and manifests itself wherever human beings live, beginning with simple geometrical ornaments. Observation of the rhythm of days and nights and the phases of the moon seem to have led to early human occupation with numbers, and the Sumerian-Babylonian astral system lies behind much of the later development. Numbers have sometimes been given divine qualities: In India, the number is called "of the kind of Brahmā," and the name of Sāṃkhya philosophy alludes to the system's reliance on numbers, for it literally means "count."

But the first religio-philosophical interest in numbers appeared in Greece with the Pythagoreans, who regarded numbers as metaphysical potencies and the cosmos as isomorphic with pure mathematics (Bell, 1933, p. 140). They defined geometrical theorems, tried to develop objective standards of beauty (the Golden Section), and found the relations between numbers and music. (In the sixteenth century, Kepler's work was still permeated by the idea of the harmonia mundi.) Pythagorean thought remained basic for later numerology and arithmology, all of which lays particular stress on the first ten integers, in which, as it were, the fullness of the world is contained. The classification of odd numbers as masculine and lucky and even numbers as feminine and unlucky stems from the Pythagorean system. "Lucky" odd numbers have therefore been preferred for use in magic spells, in religious repetitive formulas, and in rites of healing.

Speculations on the properties of numbers were continued in the works of Iamblichus and Philo Judaeus, and arithmology as the philosophy of the powers and virtues of particular integers was further elaborated by Nikomachos of Gerasa, Capella, Boethius, and others. It played an important role in Augustine's hermeneutics, offering him and numerous medieval Christian authors (among them particularly Hugh of Saint-Victor) a clue to biblical allegories. In the early seventeenth century, Peter Bongo (Bungus), in De numerorum mysteria (1618), was still trying to prove that numerology alone enables an understanding of the world.

Similar numerical allegory is found, in its most developed form, in Jewish Qabbalah; it is also incorporated into Islamic mystical thought, as in the philosophy of the Ikhwān al-Ṣafāʾ and the Ḥurūfī tradition. In both Jewish and Islamic works (as in ancient Greek) the interchangeability of letters and numerals was central for the mystico-magical interpretation of texts (i.e., in gematriah and jafr ). The qualities of numbers as they appear in the biblical tradition became significant for the Christian liturgy and visible in Christian architecture; they permeate the structure and imagery of medieval and Renaissance literature. Proverbial and folkloristic usage of certain numbers, such as three or seven, reveals the general feeling toward these integers, and both religious and popular literature use the device of ascending numbers, or descending numbers (as in the Aṅguttara Nikāya ), for counting purposes. The widespread use of magic squares is only one example of the faith in certain numbers.

Interpretation of Numbers

Although the numbers have been interpreted in various ways, it can be seen that these are generally rather similar.

1

One, according to the Pythagoreans, is both odd and even. Not a number in the normal meaning of the word, it points to the all-embracing unity that incorporates the possibility of multiplicity. "God is an odd number and loves odd numbers," says a Muslim tradition derived from classical antiquity (see Vergil's Numero deus impare gaudet ). Geometrically, one is represented by the dot, out of which forms and figures are developed.

2

Unity breaks up into duality. Two is the number of duality, of contrast and tension: The German zwei ("two") in Zwietracht ("discord") expresses this relation, as do compounds formed with the prefix dis. Two signifies the tension between the positive and negative current, between systole and diastole, inhaling and exhaling, between male and female; in short, it signifies the tension that generates the continuous flow of life, for the world is composed of pairs of opposites.

"Whatever comes from the tree of knowledge has duality," says a qabbalistic text. This principle is well expressed in the Chinese figuration of yang and yin. Zoroastrian religion postulates the constant strife between the principle of darkness and that of light, which in gnostic religions develops into the strife between material evil and spiritual good. Islam sees the manifestation in time and space of the peerless, numinous One in two aspects: jamāl ("beauty") and jalāl ("majesty"). Two is further valorized in the creative word kun ("Be!"), which consists of the two letters k and n, and in the letter b (whose numerical value is two) of the Basmalah ("In the name of God …") at the beginning of the Qurʾān, similar to the b at the beginning of the Torah. In the biblical tradition, the two stone tablets of Old Testament law, like the two testaments themselves, the Old and the New, are complementary, as are the two types of life, the active and the contemplative, personified in Leah and Rachel and in Martha and Mary. Geometrically, two corresponds to the line. The presence of the dual in many languages shows how the I and Thou are juxtaposed against the multiplicity of beings.

3

Three "heals what two has split." As the first number that has a beginning, a middle, and an end, it is the first real number, "the eldest of odds, God's number properly," as Joshua Sylvester (after du Bartas) calls it. It is the first and basic synthesis, represented in the first geometrical figure, the triangle, and in the triadic rhythm of thesis, antithesis, and synthesis. As the first number beyond I and Thou, it is the first to mean "multitude" and therefore implies the super-lative.

Numerous are the divine triads that can be named, from the Sumerian An, Enlil, and Enki and the Babylonian Shamash, Sin, and Ishtar to the Hindu triad of Viṣṇu, Śiva, and Brahmā and to the Christian Trinity. Concerning the last-named group, it has been pointed out that

the paramount doctrinal weakness of Christianity, as the Arian heresy testifies, was the duality of the Godhead (Father and Son).… That the Father and Son were one was questionable on numerical as well as philosophical ground. But Father, Son and Holy Spirit were unquestionably One by very virtue of being Three. (Hopper, 1938, p. 73)

Lesser divine or semidivine beings also appear in groups of three: The Greek Moira, the Nordic Norns, and the Roman Maters, and tricephalic deities are found in many traditions, from the Celtic to the Hindu. Even Islamic monotheism knows groupings of three, such as, among the Shīʿah, Allāh, Muḥammad, and ʿAlī.

"All good things come in threes," it is said, and everything seems to fall in triparte units: heaven-earth-water, or, as in China, heaven-earth-humanity, hence the concept of three worlds. The Ṛgveda knows Viṣṇu's three strides (connected with the position of the sun during the day), and three is the number of the twice-born social classes in Vedic religious anthropology. Three is also an important liturgical number, as the tripartition of places of public worship shows. Threefold invocation of the deity is common to most traditions, be it the Trisagion of Christian liturgy, the threefold repetition of śāntiḥ ("peace") at the end of recitation of Hindu Scriptures, or the threefold blowing of the shofar on Jewish holy days.

Metaphysical concepts often occur in groups of three: sat-cit-ānanda ("being, knowledge, bliss") is a common triad in Indian thought; wisdom, reason, and gnosis were manifested, according to the Zohar, in Abraham, Isaac, and Jacob. Buddism conceives of triloka ("three worlds") and trikāya ("three bodies" of the Buddha), and Islam disginguishes between islām ("surrender"), īmān ("faith"), and iḥsān (acting perfectly beautifully). The spiritual path is usually divided into three, as, for example, via purgativa, via illuminativa, and via unitiva or as sharīʿah ("law"), ṭarīqah ("the path"), and ḥaqīdah ("truth"). Three plays a role in anthropological concepts, too: The spiritual powers can be divided into intellect, will, and mind, or, in Islam, into nafs ammārah ("inciting to evil"), lawwāmah ("blaming"), and muṭmaʾinnah ("at peace"). In indian thought, one finds the triguṇa, the "three strands" of matter: tamas ("heaviness, dullness"), rajas ("acitvity, change"), and sattva ("brilliance, perfect equanimity").

Time is commonly periodicized in three, as past, present, and future, and the Christian church knows the kindgom of the Father, the Son, and the Holy Spirit. The latter concept is important in millenarian prophecies such as that preached in the thirteenth century by Joachim of Fiore. In the more recent past, with the Third Reich (which was, historically speaking, at least the fourth German state), myth overcame history.

Three is cumulative; whatever happens thrice is law. It often simply denotes the plural, or "everything." Therefore it is used in folk tales and legends as a statistical number: Joseph was three days in the well, Jonah three days in the belly of the whale. The three Magi are as well known as groups of three brothers or sisters; three roses, three ravens, three wishes, and three guesses are frequent in folk songs, fairytales, and legends. One also finds the action triangle in practice (ménage à trois ) and in drama, and the number of titles of fiction and nonfiction works that group persons or events into three is legion.

4

Four "brings order into the chaos." It is a material and cosmic number. The four phases of the moon and the four cardinal points of the earth (pre-formed in the name Adam ) offer such ordering; so do the four elements and the four humors, and on the mythical plane, in Islam, the four rivers in Paradise and, in the Vedic tradition, the four milk streams that flow from the udder of the heavenly cow. The Pythagoreans considered four the number of justice, and their geometry discovered the four perfect solids. The term square still points to right, orderly, and ordering structure. As a number of cosmic order, four often divides the time: the four seasons, Hesiod's four ages of humanity, the Hindu concept of four world epochs (yuga s), and the Zoroastrian idea of four periods. Chinese religion and Islam know four sacred scriptures, as Christianity accepts only four gospels as authoritative. For the Christian, the cross, with its four right angles, is "the rightest figure of all," extending over the four corners of the world, while the Jewish tradition emphasizes the mystery of the tetragrammaton, YHVH. Quaternity as an ancient symbol of perfection was reevaluated by C. G. Jung as an antidote to the unstructured, "Wotanic" spirit of his time.

5

Five is the number of natural humanity, the first number mixed of even and odd. It does not constitute an ordering number in crystals, but it occurs frequently in botanical forms, in petals and leaves (see Sir Thomas Browne's Garden of Cyrus, 1658), and it has therefore been considered by some as a "revolutionary" number. In antiquity, five was the number of Ishtar and Venus and is thus connected with sexual life and marriage, as in the parable of the five foolish virgins and the five wise virgins in Matthew 25. The pentagram, which can be derived from the zodiacal stations of Venus, is endowed with apotropaic and magic powers, while in alchemy the quinta essentia contains the rejuvenating force of life.

In China, five has traditionally been a lucky number; in the Western tradition one usually thinks of the five senses. Manichaeism knows five archons and the five corresponding aeons of darkness, while Islam, it is said, is "founded on five," for there are no more than five unconnected letters at the beginning of any Qurʾanic surah, and there are five Pillars of Faith, five daily prayers, and five lawgiving prophets. In Shīʿī Islam the panjtan (Muḥammad, Fāṭimah, ʿAlī, Ḥasan, and Ḥusayn) appears as a protective unit, popularly connected with the "hand of Fāṭimah." The human hand with its five fingers is a basis of some numeral systems, and its image has been frequently used in magic. The number of philosophical pentads ranges from the five Platonic bodies to Islamic Neoplatonic formulations.

6

Six is the macrocosmic number: The hexagon, consisting of two triangles, expresses the combination of the spiritual and the material world, hence the idea that "what is there is here." Six is a perfect number, formed from both the sum and the product of one, two, and three (1 + 2 + 3 and 1 × 2 × 3). Therefore, according to both Philo and Augustine, the world had to be created in six days. In Islam, six is used to symbolize the phenomenal world, which appears like a six-sided solid, that is, a cube.

7

Seven is a sacred number in many traditions. Because it is, according to Hippocrates of Chios, related to the lunar phases, seven influences all sublunar things. It appears in the periodicity of chemical elements and of music, and it has generally been connected with the phases of human development to a Grand Climacterium of sixty-three (7 × 9). Seven is the first prime number of symbolic meaning; it is "virgin," because it does not generate by multiplication any number under ten, and it is the only integer of the first decade that is not a divisor of 360. Consisting of the spiritual ternary and the practical quarternary (3 + 4), seven embraces everything created.

Whether the sanctitude of seven was derived by the Sumerians from the seven planets (the five visible planets plus sun and moon) or whether, conversely, they looked for seven planets to match their idea of the perfect number is a matter of dispute. The number of planets in turn determined the number of days in a week. (Niẓāmī's Persian epic Haft paikar expresses this belief poetically.) In Babylon every seventh day was considered dangerous, and it was thought that nothing should be undertaken; the seventh day was then sanctified in Judaism as Sabbath, the day on which God rested after creation.

The demonic qualities of seven are preserved in heptads of devils, witches, magic knots, and so on, but its sacred qualities are perhaps more numerous. Some traditions speak of seven worlds, or, in accordance with the "planets," seven spheres; therefore, the ascension of the soul usually leads through seven gates, steps, valleys, or veils (thus from the Mithraic mysteries to ʿAṭṭār, Ruusbroec, and Teresa of Ávila). In extension, Islam knows seventy thousand veils between the soul and God. Seven appears also in connection with deities of other religions; it is Apollo's number, and, in India, it is especially prominent in connection with Agni. In Iran, the heptad of the Amesha Spentas consists of six plus the all-embracing Ahura Mazdā.

But the number seven gained its greatest importance in the Judaic tradition, whence it extends into Christianity and Islam. From the seven days of creation to the seven pillars of wisdom, the Hebrew scriptures contain "unnumbered heptads." The menorah with its seven candles points to some of the secrets of seven. Numerous biblical stories use seven as a statistical number (Pharaoh's dream of seven fat cows and seven thin cows; Jacob's seven years of service, and then seven more). Blood should be avenged seven times, or seventy-seven times (Gn. 4:24), but seventy times seven should be the times of forgiving (Mt. 18:22). The Book of Revelation is filled with heptads, too, leading John of Salisbury in the twelfth century to write his treatise De septem septenis. Both the Lord's Prayer and the Qurʾanic Fātiḥa consist of seven sentences. Catholic churches speak of seven major sins and seven virtues, seven sacraments, and seven gifts of the Holy Spirit, and the Mass consists of seven parts.

The sevenfold repetition of religious acts is common in Islam; thus the sevenfold run between Ṣafah and Marwah and the three times seven stones cast at the devil during the pilgrimage. Sufism knows seven laṭāʾif, subtle centers of the body, connected in meditation with the seven essential attributes of God and the seven great prophets. A ḥadīth speaks of seven layers of Qurʾanic interpretation, which has been practiced especially by the Ismāʿīlīyah, whose basis is the seventh imam of the Shīʿah. They know seven cyclical periods with seven imams; the seven great prophets correspond to the seven spheres, the imams to the seven earths.

In folk tales and legends, seven is a round number: To do anything seven times is especially effective. Christian and Islamic legends know groups of seven feminine or masculine saints, most prominently the Seven Sleepers. The continuing preference for the number seven is reflected today even in the designation of airplanes as Boeing 707, 747, and so on.

8

Eight, the double four, is associated with good fortune. In Judaism the eighth day is singled out for circumcision. Christian tradition sees in the eighth day (the day after Sabbath) the resurrection of Christ; hence eight points to eternity. The eight paradises in Islam and the eight pillars of heaven in Chinese religion belong to the same concept; the eight blessings in the Sermon on the Mount as well as the Eightfold Path of the Buddha are equally connected with eternal bliss. Therefore, the traditional shape of a Christian baptistery is octagonal.

9

Nine, as three times three, is the number of completion. Only rarely in Christian theology is it considered incomplete, as ten minus one. Christianity speaks of the nine orders of angels, and Dante thus saw Beatrice as the embodiment of nine. But the number is more widely connected with Germanic, Celtic, and Inner Asian peoples. The traditions about King Arthur as well as the songs of the Nordic Vo̜luspá show an abundance of nines, from the nine days that Óðinn (Odin) was hanging on the tree to the number of Valkyries, from ninefold sacrifices to rituals in which nine or a ninefold number of persons had to participate. This predilection for nine has been attributed to the nine months of winter in the northern areas of Eurasia, although nine occurs frequently in the more southerly lore of the ancient Greeks as well.

Such expressions as "to the nines," meaning "perfect," and "to be on cloud nine" show the old Germanic esteem for nine. The number frequently appears in Germanic popular tales, although it has often been replaced by seven under Christian influence. Its role in folklore among Germanic peoples is important, and it often occurs in connection with witchcraft (a cat, which has nine lives, can turn into a witch at the age of nine). Among the Chinese and Turco-Mongolian peoples, everything valuable has traditionally had to be ninefold: A prince has owned nine yak-tail standards; ninefold prostration has been required; and gifts have been offered in groups of nine, so that the word tōqūz ("nine") often means simply "present." In China a nine-storied pagoda represents the nine spheres, which are also known in the eastern Islamic tradition. The eight roads that lead to the central palace in Beijing reflect the ninefold structure of the universe.

10

Ten, the number of human fingers, and thus a basis of the decimal system, is connected with completion. In the decade, multiplicity returns again to unity, and the system is closed. The Pythagoreans regarded ten as the perfect number, because it is the sum of the first four integers (1 + 2 + 3 + 4) and is represented in the perfect triangle seen in figure 1.

Both the Hebrew and the Buddhist scriptures teach a decalogue, and sets of ten principles are known for the Ṣūfī novice. Likewise, Aristotle's ten categories show "completeness." In early Christianity, the three persons of the Trinity and the seven elements of created beings were thought to be represented by ten; but already the Torah had provided the ten words of creation that became the basis of "practical" (i.e., magical) Qabbalah, with its concept of sefirot ("numbers"). These ten sefirot, along with the twenty-two letters of the Hebrew alphabet, point to the thirty-two ways of salvation. Ten were the best companions of Muḥammad, and of several Ṣūfī masters, while the Ismāʾīlī system knows the ten higher orders of the ḥudūd, consisting of groups of three and seven.

11

Eleven is normally explained as a number of transgression, being beyond the perfect ten, or as incomplete, being beneath the equally perfect twelve; it is therefore an unfortunate, "mute" number.

12

Twelve (3 × 4; 5 + 7) is the great cosmic number. From Sumer and ancient China onward, it is the number of the signs of the zodiac and the basis of the sexagesimal system. In many cultures, day and night were divided into twelve hours, the year into twelve months, and gnostic religions speak of twelve aeons. The "great period" in Babylon was twelve times twelve thousand days, and multiples of twelve appear frequently in later mythology. The meaning of completion is as evident in the twelve tribes of Israel as in the twelve disciples of Christ and the twelve gates of the heavenly Jerusalem, where twelve times twelve blessed will adore the Lamb of God. The minor prophets of Israel, the Greek sibyls, and the imams of the Twelver Shīʿah number

twelve. For medieval Christian exegetes, twelve meant faith in the Trinity that had to be diffused to the four corners of the earth. In popular traditions and sayings, it is, again, a round number, manifest in periods of twelve days or years, in twelve endangered heroes, and so forth.

13

Thirteen (12 + 1) disrupts the perfection of the duodecimal system and, being connected with the intercalary month, was considered unlucky in Babylon, a superstition that continues to the present day. In fairytale, Death becomes the godfather of a thirteenth child. But one can see thirteen also as a combination of one leader and twelve followers, of twelve members of a jury and a judge, of twelve open rooms and a closed one, of a father and twelve sons, and so on. Thirteen therefore sometimes alternates with twelve. In ancient Israel, thirteen was sacred, for thirteen items were necessary for the tabernacle. It also corresponds to the numerical value of aḥad ("one"); thus, thirteen rivers of balsam await the believer in paradise. The superstition that thirteen people should not sit at one table (based on the Last Supper) is comparatively recent.

14

Fourteen (2 × 7) is a lucky number, manifested in the fourteen helping saints (Nothelfer ) of Christianity and the fourteen innocent martyrs of Shīʿah Islam. It is the number of the full moon and is, therefore, the ideal age of the moonlike beloved of which Persian poets sing. In Islam, it is further connected with the so-called sun- and moon-letters and with the unconnected letters at the beginning of certain surahs, both of which sum up to fourteen, half of the twenty-eight letters of the Arabic alphabet. The Ḥurūfīyah emphasize that the Arabic words yad ("hand") and wajh ("face") both have the numerical value of fourteen, twice the sacred seven.

15

Fifteen is the key number in the Daoist liturgical dance known as the Pace of Yu; the nine stations, or "gates," of the dance follow the sequence of a magic square whose rows, columns, and diagonals all add to fifteen.

16

Sixteen (4 × 4), in the Indian tradition, expresses completeness, in ornaments, features, meters, and poetry.

17

Seventeen, nowadays barely popular, appears in antique music and poetry (9:8 = simple interval) and in the seventeen consonants of the Greek alphabet. In Christianity it signifies the Ten Commandments plus the seven gifts of the Holy Spirit, and it figures in calculations of the number of the fishes mentioned in John 21:11 (9 × 17 = 153; 1 + [Product] [Product][Product] + 17 = 153). Seventeen appears in Islamic alchemy (e.g., in the writings of Jābir ibn Ḥayyān), in the Shīʿah tradition, and in Turkish epics. There are seventeen rakʿah s (sequences of prostration) in the ritual prayers of one day, and God's Greatest Name is thought to consist of seventeen letters.

18

Eighteen (2 × 9; 3 (6) is sacred in Qabbalah, as it is the numerical value of the Hebrew word ḥay ("living"). In Islam, it is the number of the letters of the Basmalah, and it is highly respected among the Mevlevi order of dervishes, inasmuch as the introductory verses of Rūmī's Mathnavī number eighteen. By extension, the number of the worlds is eighteen thousand. The perfection of eighteen can also be understood from the fact that the Buddha had eighteen principal arhat s.

19

Nineteen, with the numerical value of wāḥid ("one"), is the sacred number of the Bahāʾīs, who count a year of nineteen months with nineteen days each.

20–29

Among the lower twenties, twenty-two is the number of letters of the Hebrew alphabet and the number of the great arcana of Tarot. Augustine divided De civitate Dei into twenty-two chapters, ten (2 × 5) devoted to refutation (ten negative commandments) and twelve (3 × 4) to positive teachings. Twenty-four can be numerically interpreted in several religiously significant ways (3 × 8; 4 × 6; 12 × 2), and medieval Christian interpreters used whichever combination fit with what they sought to prove. Among the higher twenties, twenty-five is the Jubilee number, and twenty-eight is the lunar number, central to the whole heptadic system.

30–39

Among the thirties, thirty-three means perfection, as a multiple of three, and as the years of Christ's earthly life. For Muslims as for Christians, it is also the age of the blessed in Paradise. Thirty-six, four times the perfect number nine, was in early China the number of the provinces and the foreign peoples beyond the borders.

40

The most important higher number is forty. As the number of days that the Pleiades disappeared (i.e., were not visible), in Babylon forty came to signify a fateful period, connected with expectation and patience. Human pregnancy lasts seven times forty days. Purifications and rites connected with death were measured according to forty in ancient Israel, as they are in Islam. The times of affliction of Israel were counted by forty: The Flood lasted forty days, the wandering in the desert forty years. Moses, Elijah, and Jesus each spent forty days in the wilderness, and Jesus remained forty hours in the grave. Forty is the span of days between the resurrection and ascension of Jesus, and it is the time of preparation for the dervish, who spends forty days in retirement (chilla ), poetically interpreted in ʿAṭṭār's Muṣībatnāma. At forty years one becomes wise; the Prophet of Islam was called to preach at this age. In the Pythagorean system, forty is the perfected tetractys (4 × 10).

Forty often appears in Islamic lore as a coterminus with "very many," such as Ali Baba's forty thieves; groups of forty dervishes, forty saints, or forty Christian martyrs; and the customary selection of forty ḥadīth, representing the fullness of the tradition. In the Persian and Turkish tradition, women miraculously give birth to forty children. As forty in the Old Testament means "one generation," it is a temporal measure. In Turkey, where the number forty is extremely popular, great events and feasts last forty days and forty nights; to see someone "once in forty years" means "rarely." In many areas, weather predictions are made for forty days.

50

Fifty (7 × 7 + 1) is the number of the jobel year, a year of peace, the divine eternal rest. In connection with Psalm 50, it can point to repentance and forgiveness. A predilection for 50 and 150 is apparent in Irish folk tales.

60

Among the higher numbers, many are endowed with qualities similar to those of the bases in the first decade. Sixty is especially important as the basis for the Babylonian sexagesimal system, in which it forms the higher unit after ten; from these units, sixty and ten, result the multiples that are associated with cosmic time. According to Plato, the "cosmic day" and the "cosmic year" are reckoned by sixties. Because sixty can be easily divided, it still rules in the temporal system. The Chinese, who reckon time in cycles of sixty years, have traditionally considered that number as the full complement of a person's life. The Talmud knows fragments of sixtieths: Dream is one-sixtieth of prophecy, fire one-sixtieth of hell, and so on.

70–79

Seventy participates in the qualities of seven, and the numbers seventy to seventy-three are often interchanged in the Semitic tradition. Among them, seventy-two is most important; it is one-fifth of the circumference of the circle as well as the product of eight and nine. It usually designates great diversity: from the seventy-two disciples of Christ who were sent into the world to the seventy-two martyrs of Karbala and the seventy-two sects of Islam. Abulafia speaks of the seventy-two letters of the name of the Lord.

Higher numbers

Ninety-nine, the heightened angelic perfection of nine, is the number of the Most Beautiful Names of God in Islam, while one hundred as the new basis of the decimal system, is another complete number. Higher than that is 108 (12 × 9), the number of beads in the Buddhist rosary, the number of books of the Tibetan Kanjur, and the number of beautiful gopī s who danced with Lord Kṛṣṇa. Higher still are 360 and 365, which are connected with the annual cycle, and 666, the "number of the beast" (Rv. 13), which has been interpreted ever since antiquity as the name of a man particularly detested at various times, be it Nero, Pope Leo X, Luther, Napoleon, or some other. Symbolically, one thousand and ten thousand are both endless; 1,001 thus transgresses the largest imaginable number, while ten thousand means immortality in the Chinese tradition. The enormous numbers of Hindu and Buddhist cosmology form a theme in themselves.

Concluding Remark

The interest in numbers and their specifications continues in spite of the modern scientific worldview, especially among those who seek for a meaningful structure of the world. As Le Corbusier once wrote: "Behind the wall, the gods play; they play with numbers, of which the universe is made up."

See Also

Dualism; Quaternity; Triads.

Bibliography

The literature on numbers cannot be numbered; many highly specialized works have been written, especially in German, and a vast literature on modern numerology exists in German, French, and English. As a basic source, the article "Numbers" in the Encyclopaedia of Religion and Ethics, vol. 9, edited by James Hastings (Edinburgh, 1917), is still useful. On the development of counting systems, see Karl Menninger's Number Words and Number Symbols, translated by Paul Broneer (Cambridge, Mass., 1969). Numerology (Baltimore, 1933), a study by Eric T. Bell and others, sharply criticizes numerology from the vantage point of a mathematician. A good survey by Franz C. Endres, Mystik und Magie der Zahlen, 3d ed. (Zurich, 1951), has now been updated by my enlarged version of his work, Das Mysterium der Zahl: Zahlensymbolik im Kultur-Vergleich (Cologne, 1984). Number Symbolism (London, 1970) by Christopher Butler is a useful introduction. Vincent Foster Hopper's Medieval Number Symbolism (1938; reprint, Ann Arbor, 1966), an excellent introductory study, has in a certain way been continued by Heinz Meyer's Die Zahlenallegorese im Mittelalter (Munich, 1975). For a Jungian approach, see Ludwig Paneth's Zahlensymbolik im Unbewussten (Zurich, 1952).

Numerous studies have been devoted to single numbers, primarily three, seven, nine, and thirteen; among them, Desmond Varley's Seven: The Number of Creation (London, 1976) stands out not only for its quantity of information but also for its daring hypotheses. Articles on Germanic lore by Karl Weinhold and on classical antiquity by W. H. Roscher, both of whom wrote at the turn of the century, are still fundamental. On the number forty in the Islamic-Turkic tradition, see Abdul Kadir Karahan's "Aperçu général sur les ʿQuarante Hadiths' dans la littérature islamique," Studia Islamica 4 (1955): 39–55.

New Sources

Abas, Syed. Symmetries of Islamic Geometrical Patterns. Singapore, 1995.

Abellio, Raymond, and Charles Hirsch. Introduction à une théorie des nombres bibliques. Paris, 1984.

Begey, Roger. Géometrie sacrée, ou la magie des formes. Paris, 1995.

Emmer, Michele. The Visual Mind: Art and Mathematics. Cambridge, Mass., 1993.

Harvey, H. R., and B. J. Williams. "Aztec Arithmetic: Positional Notation and Area Calculation." Science 210 (1980): 499–505.

Lawlor, Robert. Sacred Geometry. New York, 1982.

Mandelbrot, Benoit. The Fractal Geometry of Nature. San Francisco, 1982.

Nielsen, Bent. Companion to Yi jing Numerology and Cosmology: Chinese Studies of Images and Numbers from Han (202 bce–220 ce ) to Song (960–1279 ce ). London, 2003.

Annemarie Schimmel (1987)

Revised Bibliography