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36

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Origin 1908 to 1965

Thirty-six is both triangular, the sum of 1 through 8, and square, six times six, the smallest number above one that is both. Egyptian astronomy divided the year into thirty-six decans, ten-day periods marked by the rising of particular stars, and these passed into Hellenistic and later Western astrology as thirty-six divisions of the zodiac. Jewish tradition speaks of the Lamed Vav, the thirty-six hidden righteous ones for whose sake the world endures, developed from a saying at Sanhedrin 97b in the Babylonian Talmud. The six-by-six magic square has the constant 111 and totals 666. In digit-reduction numerology it reduces to 9.

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
The Babylonian Talmud, at Sanhedrin 97b, carries the teaching that the world is never without thirty-six righteous men who receive the presence of the Shekhinah. The later folklore of the hidden and anonymous Lamed Vav Tzadikim grows out of that passage, but the count itself is Talmudic. 3Tradition: Rabbinic Judaism (Babylonian Talmud)
Meaning in the Attesting Source
The ecliptic was divided into thirty-six decans of ten degrees each, a scheme Egyptian in origin that entered Hellenistic astrology and travelled from there into Arabic and then Latin astrological writing. 4Tradition: Hellenistic and Egyptian 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: 3 + 6 = 9. Whatever the system says of 36 it therefore says of 9, 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
Triangular and Square at Once

Thirty-six is the sum of the numbers from 1 to 8, which makes it triangular, and it is six times six, which makes it square. Numbers that are both are rare: the sequence begins 1, 36, 1225, 41616, and grows very fast. Thirty-six is the first non-trivial member, and that is a genuine and checkable distinction rather than a mystical one.

It is also the sum of the first three cubes, 1 plus 8 plus 27, which is an instance of a general result: the sum of the first n cubes always equals the square of the sum of the first n numbers. And it is highly composite, with nine divisors, more than any smaller number.

The magic square of order six has thirty-six cells, and it is the smallest magic square whose construction resists the simple methods that work for odd orders. Its magic constant is 111, and the sum of all thirty-six cells is 666. That relationship is arithmetic, the numbers 1 to 36 sum to 666 whatever arrangement they are put in, and it is the origin of the association between the six-by-six square, the planet Sun in Renaissance planetary magic, and the number of the beast. Cornelius Agrippa set out the seven planetary squares in the Three Books of Occult Philosophy of 1533, assigning the six-by-six square to the Sun, and that is where the pairing enters Western occultism.

None of this requires interpretation to be interesting, and the reader who knows the mathematics will notice immediately whether an account of thirty-six understands what it is claiming. Both properties are provable in a line.

The Decans and the Thirty-Six Righteous

Egyptian astronomy divided the year into thirty-six decans, each a ten-day period marked by the heliacal rising of a particular star or group of stars, with five epagomenal days added to complete the year. Decan lists appear on coffin lids from the Middle Kingdom onward, where they served as star clocks for the hours of the night. Thirty-six decans of ten degrees each also fill the 360-degree circle exactly, which is why the scheme survived the transition into Hellenistic astrology as a division of the zodiac, three decans to each of the twelve signs. From there it passed into medieval Arabic and Latin astrology and into the Renaissance image-magic tradition, and it is the ancestor of the decan attributions found in modern tarot correspondences.

Jewish tradition gives a quite separate thirty-six. The Lamed Vav Tzadikim, the thirty-six hidden righteous ones, are said to be present in every generation, unknown to others and often to themselves, and the world is said to be sustained for their sake. The idea develops from a statement at Sanhedrin 97b in the Babylonian Talmud that there are not fewer than thirty-six righteous who greet the divine presence in each generation, the number derived by gematria from a word in Isaiah 30:18. The full folkloric elaboration, the hidden saint who lives as a cobbler or water-carrier and is revealed only in crisis, is later, developed extensively in Hasidic storytelling from the eighteenth century.

The two thirty-sixes are unconnected. Writing that treats them as a single ancient tradition is manufacturing a lineage.

Cross-Tradition Connections

Associated With

Western Astrology, Disciplines

The same circle divided into thirty-six decans of ten degrees, a scheme Egyptian in origin that entered Hellenistic astrology.

Source A History of Western AstrologyNicholas Campion

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 Babylonian Talmud
Anonymous (multiple authors), Soncino Press, 1935View the Source
4. A History of Western Astrology
Nicholas Campion, Continuum, 2009View the Source
Encyclopaedia Judaica, 2nd edition
Michael Berenbaum and Fred Skolnik (eds.), Macmillan Reference USA, 2007s.v. Lamed Vav (the 36 righteous)View the Source
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