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60

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Origin 1908 to 1965

Sixty is highly composite, with twelve divisors, 2 x 2 x 3 x 5, and that is exactly why it became the base of Sumerian and then Babylonian arithmetic in the third millennium BCE. A base divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30 makes fractions tractable without decimals, which is why sixty seconds, sixty minutes and 360 degrees have outlived every other feature of that system. Chinese chronology runs an independent sixty-year cycle formed by pairing ten heavenly stems with twelve earthly branches; it is attested on Shang oracle bones for counting days long before it was applied to years. In digit-reduction numerology it reduces to 6.

Facts
Origins
Origin Period
1908 to 1965 1
Origin Period
500 BCE to 300 CE 2
Origin Period
The arithmological reading of the first numbers, one as source, two as division, four as justice, seven as virgin, ten as completion, reaches us through Platonic and Neopythagorean writers of the centuries after Plato. Burkert's finding is that it cannot be traced to Pythagoras himself, whose activity was religious rather than mathematical: the doctrines were credited backwards to him. 2Tradition: Pythagorean and Neopythagorean number lore
Origin Period
The system that gives a number a personality, and a person a number, was assembled in the United States in the first half of the twentieth century out of New Thought material. Balliett's The Philosophy of Numbers appeared in 1908; the chart positions, pinnacles and cycles were added by her successors over the next fifty years. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Place of Origin
The Greek world, and above all the Greek cities of southern Italy where the Pythagorean societies were established; the arithmological literature itself is later and largely eastern Mediterranean. 2Tradition: Pythagorean and Neopythagorean number lore
Place of Origin
The United States, and specifically the New Thought circuit of the north-eastern seaboard; Balliett worked from Atlantic City. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Attributed Author / Compiler
Attributed by the tradition to Pythagoras. Burkert's study is the standard demonstration that the number-doctrines carrying his name are the work of later hands, and that almost nothing in them can be shown to go back to the sixth century BCE. The attribution is recorded because it is what the tradition says, not because it holds. 2Tradition: Pythagorean and Neopythagorean number lore
Attributed Author / Compiler
Mrs. L. Dow Balliett, who published the first version of the modern system in 1908 and to whom Dudley devotes a chapter. What later authors added, the pinnacles, the challenges, the cycles, the personal year, is theirs, and this atlas's own numerology-position entries cite four different authors between 1908 and 1965 for what is presented as one system. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Origin of the Name
Pythagorean numerology is a twentieth-century label. The system it names has no demonstrable descent from Pythagoras, from the Pythagorean societies, or from the ancient arithmological literature; the letter-value chart it rests on was drawn up in the United States after 1900. The name borrows a pedigree, the oldest move in the subject. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Attestation
Meaning in the Attesting Source
Mesopotamian arithmetic and astronomy were written in a place-value system with base sixty. The division of the degree and of the hour into sixty parts descends from that notation. 3Tradition: Babylonian astronomy and mathematics
Meaning in the Attesting Source
Ten heavenly stems paired in order with twelve earthly branches yield a cycle of sixty combinations, the ganzhi, used to number days and later years in Chinese reckoning. 4Tradition: Chinese calendrical astrology
Status
Standing as a Comparative Category
Largely abandoned as a comparative category 1
Modern Numerology
Reduction in the Modern System
The modern system reduces every number above nine by adding its digits: 6 + 0 = 6. Whatever the system says of 60 it therefore says of 6, because it holds no separate doctrine for the higher numbers. The stated exceptions are 11, 22 and 33, which it leaves unreduced and calls master numbers. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Contested Use
Contested or Appropriated Modern Use
Numerology has been sold since Balliett as a basis for decisions: which name to take, which date to marry on, which house number to buy. Dudley's survey of what numerologists sell is the standard critical account and its finding is blunt, numbers have power over minds, not over events. These entries record what the tradition says, not advice. 1
Learn More
Why Base Sixty

Sumerian and then Babylonian mathematics counted in base sixty, and the choice was not arbitrary. Sixty has twelve divisors, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60, and no smaller number has as many. In a system without decimal fractions, that divisibility is the whole game: a third, a quarter, a fifth, a sixth of sixty are all whole numbers, whereas in base ten a third is a repeating fraction.

The consequences are still in use. Sixty seconds to the minute, sixty minutes to the hour, and 360 degrees in a circle are Babylonian, transmitted through Greek astronomy, Ptolemy computed in sexagesimal fractions, and thence to Arabic and Latin science and to us. The words minute and second come from the Latin pars minuta prima and pars minuta secunda, the first and second small parts of a degree. No other feature of Babylonian civilisation has survived so completely.

The 360-degree circle follows from the same base, helped by the convenient near-coincidence that a year is roughly 360 days, Babylonian schematic calendars used twelve months of thirty days for administrative purposes while the real calendar was lunisolar and intercalated.

Why the Sumerians chose sixty is not settled. Proposals include a merger of two earlier systems using five and twelve, and finger-counting methods using the twelve finger joints of one hand against five fingers of the other. The evidence for either is indirect. What is certain is the mathematical advantage, and it is enough to explain why the system was kept for three thousand years.

The Sexagenary Cycle

China arrived at sixty independently and for a different reason. The ganzhi cycle pairs ten Heavenly Stems with twelve Earthly Branches. Since the stems and branches advance together and pair only in matching parity, the combination repeats after sixty steps rather than a hundred and twenty, sixty being the least common multiple of ten and twelve.

The cycle is old and its attestation is firm. Shang dynasty oracle bones of the late second millennium BCE use it to count days, and complete sixty-cycle tables are inscribed on bone. Application to years is much later, becoming standard in the Han period, and the cycle has run continuously since; a person completing their sixtieth year completes a full cycle, which is the basis of the significance attached to the sixtieth birthday across East Asia.

The twelve branches are also the twelve zodiac animals, and the ten stems pair with the five phases, wood, fire, earth, metal, water, in yin and yang forms, so any year in the cycle carries an animal and a phase: a wood dragon year, a metal rooster year. Those combinations recur every sixty years, not every twelve, which is why the popular presentation of the Chinese zodiac as a twelve-year cycle is a simplification of a sixty-year one.

There is no evidence of contact between the Babylonian and Chinese systems. Both converged on sixty because sixty is the smallest number that reconciles the small factors people actually count with, and that convergence is a fact about arithmetic rather than a sign of a shared source. Claims of transmission between the two should be treated as unsupported.

Cross-Tradition Connections

Associated With

Ba Zi, Disciplines

Ten heavenly stems paired in order with twelve earthly branches give the cycle of sixty on which the four pillars are read.

Source Chinese Mathematical Astrology: Reaching Out to the StarsHo Peng Yoke

Disciplines That Use This

Numerology, Disciplines

The modern numerological system assigns this number a meaning, which is why the atlas records it as a subject in its own right, though this does not endorse what the discipline says about it. This link shows only that the discipline works with this particular number; the readings of the number itself belong to whichever tradition holds them.

Source Numerology: Or, What Pythagoras WroughtUnderwood Dudley
Sources
1. Numerology: Or, What Pythagoras Wrought
Underwood Dudley, Mathematical Association of America (Spectrum series), 1997View the Source
2. Weisheit und Wissenschaft: Studien zu Pythagoras, Philolaos und Platon (Lore and Science in Ancient Pythagoreanism)
Walter Burkert, Harvard University Press, 1962View the Source
3. The Heavenly Writing: Divination, Horoscopy, and Astronomy in Mesopotamian Culture
Francesca Rochberg, Cambridge University Press, 2004View the Source
4. Chinese Mathematical Astrology: Reaching Out to the Stars
Ho Peng Yoke, RoutledgeCurzon, 2003View the Source
A Dictionary of Chinese Symbols: Hidden Symbols in Chinese Life and Thought
Wolfram Eberhard, Routledge, 1986the sexagenary cycleView the Source
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