Divinity Atlas

Sacred Correspondences
Sign In
Text size
100%
Theme

Switch Atlas

The Inner World

The Civil World

The Natural World

Numbers

64

Citation Formats

General Reference

APA Style

BibTeX

Origin 1908 to 1965

Sixty-four is two to the sixth power, and both a square and a cube, eight squared and four cubed. The I Ching is built on sixty-four hexagrams, the complete set of six-line figures made from broken and unbroken lines, and the completeness is the point: two states raised to six positions can give nothing else. A chessboard has sixty-four squares. Indian tradition counts sixty-four kalas, the arts a cultivated person should command. The standard genetic code has sixty-four codons, four bases in triplets; that four cubed equals two to the sixth is necessary arithmetic and demonstrates nothing, though a good deal has been built on it since 1973. In digit-reduction numerology it reduces to 1.

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)
Status
Standing as a Comparative Category
Largely abandoned as a comparative category 1
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
Modern Numerology
Reduction in the Modern System
The modern system reduces every number above nine by adding its digits: 6 + 4 = 10, then 1 + 0 = 1. Whatever the system says of 64 it therefore says of 1, 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)
Attestation
Meaning in the Attesting Source
Six lines, each either broken or unbroken, give sixty-four possible figures, and the Book of Changes is organised as sixty-four hexagrams with their statements. Smith's study follows how the ordering of the sixty-four was itself argued over for two millennia. 3Tradition: Chinese classical divination (the Yijing)
Learn More
The Sixty-Four Hexagrams

The I Ching, the Book of Changes, is built on sixty-four hexagrams: figures of six lines, each line either broken or unbroken. Sixty-four is not a chosen number. Two possibilities in each of six positions gives two to the sixth power, and the set of sixty-four is therefore complete and closed. There is no sixty-fifth hexagram to find.

The system is built up in stages that the tradition itself describes: two states, then four images, then eight trigrams, then sixty-four hexagrams formed by stacking trigrams in pairs. The eight trigrams are attributed to the legendary Fu Xi and the hexagram texts to King Wen and the Duke of Zhou, attributions which are traditional rather than historical. The core text dates to the Western Zhou, roughly the ninth century BCE, as a divination manual; the Ten Wings, the philosophical commentaries that turned it into a work of cosmology, are later, and Confucian association with it is later still.

Two orderings of the hexagrams are standard and they are quite different. The King Wen sequence is the received order of the text, arranged in pairs where each hexagram is the inversion or complement of its partner, and no rule generating the whole sequence has ever been established. The Fu Xi or binary sequence, arranged by systematically varying the lines, is the one Leibniz recognised in 1703 as identical to binary counting from 0 to 63 when broken lines are read as zero and unbroken as one. Leibniz took this as evidence of an ancient insight; historians of Chinese mathematics generally regard the binary ordering as a later arrangement, associated with Shao Yong in the eleventh century, rather than an original feature.

Sixty-Four and the Genetic Code

The standard genetic code has sixty-four codons: four bases read in groups of three gives four cubed, which is sixty-four. The I Ching has sixty-four hexagrams: two line states in six positions gives two to the sixth, which is also sixty-four. The equality is exact and it has generated a substantial literature.

The equality is also empty. Four cubed and two to the sixth are the same quantity by necessity, since four is two squared: any system built from four symbols in triplets and any system built from two symbols in sextets must both give sixty-four. Nothing is being discovered when the two are found to match. The same relation holds between two-to-the-sixth and any other route to sixty-four, and it says nothing whatever about either system.

The comparison was made in passing by the molecular biologist Gunther Stent in 1969 and developed at length by Martin Schonberger in Verborgener Schlussel zum Leben in 1973, translated as The I Ching and the Genetic Code: The Hidden Key to Life. Schonberger proposed specific mappings between individual hexagrams and individual codons or amino acids. Those mappings are the part that would have to be tested, and they do not survive testing: the assignments are arbitrary, different authors following the same method produce different tables, and no assignment has been derived independently by anyone starting from the biology.

This is worth setting out precisely because the underlying facts are both true. The I Ching has sixty-four hexagrams. The genetic code has sixty-four codons. What does not follow is that the one anticipates the other, and a reader who knows the arithmetic will discount any source that presents the coincidence as significant.

Cross-Tradition Connections

Associated With

I Ching, Disciplines

The Book of Changes is organised as sixty-four hexagrams, one for each arrangement of six lines that are each either broken or unbroken.

Source Fathoming the Cosmos and Ordering the World: The Yijing (I Ching, or Classic of Changes) and Its Evolution in ChinaRichard J. Smith

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. Fathoming the Cosmos and Ordering the World: The Yijing (I Ching, or Classic of Changes) and Its Evolution in China
Richard J. Smith, University of Virginia Press, 2008View the Source
The I Ching, or Book of Changes
Richard Wilhelm (trans.); Cary F. Baynes (English trans.), Princeton University Press, 1980the 64 hexagramsView the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0 open reader challenges)
No disputes yet. Spotted an error or a better source? Open the first one.

View At A Past Year

Choose a year to see this entry's facts and connections as the atlas records them at that moment: what it held then, what it held instead, and what it had not yet adopted. Choose Present for the current record.