In 1701, the Jesuit missionary Father Joachim Bouvet, stationed at the imperial court in Peking, sent Gottfried Wilhelm Leibniz a diagram of the 64 I Ching hexagrams arranged in a circle, as systematized by the 11th-century Chinese philosopher Shao Yung. Leibniz recognized the arrangement immediately: it was structurally identical to the binary number system he had been developing since the 1670s.

The two systems had been developed independently, in different cultures, separated by roughly 3,000 years. And as we shall see, they were not alone.

The Binary Correspondence

Leibniz's binary system uses two digits — 0 and 1 — to represent all numbers. He assigned philosophical meaning to these digits: 0 represented nothingness (the void before creation), and 1 represented unity (the creative principle, or God). Any number can be expressed as a sequence of these two states.

The I Ching hexagrams are built on the same logic. Each hexagram consists of six lines, each of which is either broken (yin) or unbroken (yang). With six binary positions and two possible states per position, the system produces exactly 64 unique combinations — the same number as Leibniz's six-digit binary sequences.

Leibniz's Philosophical Interpretation

For Leibniz, the correspondence was not merely mathematical. It confirmed his doctrine of pre-established harmony — the philosophical position that the universe operates according to a single underlying rational order, which expresses itself consistently across different cultures, times, and disciplines. He believed that number was not simply a human tool for counting, but a reflection of the structure of reality itself.

“He did not regard the events of life and the categories of thought as exhausted by time, space, and causality but apprehended all existence also from the standpoint of pre-established harmony. To his wide-ranging mind, number and the numerical system therefore had more than an abstract meaning; they were expressive of connotative associations that have long since fallen into oblivion.”

The Mathematics of Wholeness — Von Franz & Jung

The Swiss Jungian analyst Marie-Louise von Franz devoted her landmark work Number and Time (Northwestern University Press, 1974) to precisely this question: why do independent cultures arrive at the same numerical structures? Her answer was Jungian: numbers are not invented but discovered — they are archetypes of the collective unconscious, patterns that the psyche and the physical world share.

Von Franz traces the Chinese cosmic numerical tradition to two ancient diagrams — the Lo-shu and the Ho-t'u — which predate the I Ching's formalization. The Lo-shu is a pandiagonal magic square of order three (the only possible solution in eight arrangements), in which every row, column, and diagonal sums to 15. The Ho-t'u is its complementary cross-pattern. Both were understood in ancient China not as mathematical curiosities but as ground plans of the universe — spatial and temporal maps of the continuum. Von Franz cites Marcel Granet's La Pensée chinoise as the primary source for these patterns.

4 | 9 | 2
3 | 5 | 7
8 | 1 | 6

Von Franz argues that the number two — the binary — is not merely a mathematical convenience but the primordial rhythm of consciousness itself. Drawing on the mathematician L.E.J. Brouwer, she writes that “two-oneness” is the root of all mathematical thought: the mind's first act is to split the continuum into self and other, now and then, yin and yang. The I Ching's broken and unbroken lines are not symbols of this rhythm — they are this rhythm, made visible.

“The number two, in the first place, plays a very important role in mathematics. The mathematician Brouwer, like Plato, even looks on the concept of two-oneness as the root of mathematical thought.”

The number four completes the structure. Von Franz identifies four as the first non-prime numeral, the first square number (2²), and the One-Continuum's model of wholeness in all relatively closed structures of human consciousness. Jung's four psychological functions, the four trigram pairs of the I Ching, the four cardinal directions of the Lo-shu — all express the same quaternary wholeness. Three is the dynamic principle in between: the flow of psychic energy, the movement from duality toward resolution.

64 in the Genetic Code — The Most Stunning Convergence

Von Franz notes — and modern genetics confirms — one of the most remarkable structural coincidences in the history of knowledge. The biological genetic code of DNA consists of four bases (adenine, thymine, guanine, cytosine) combined into triplets. From four bases arranged in groups of three: 4³ = 64 possible codons. These 64 codons encode all twenty amino acids that form every protein in every living organism.

Three independent systems — an ancient Chinese oracle, a 17th-century European mathematician, and the molecular code of all living organisms — converge on the same number. Von Franz saw this not as coincidence but as evidence that 64 is a structural constant of reality: the number at which a binary system of sufficient complexity achieves completeness. Richard Rudd built the entire Gene Keys system on this same foundation, mapping each of the 64 hexagrams to a corresponding codon and a spectrum of human consciousness.

A Hint Toward the Tarot — Court Cards & the 16

The Tarot offers a complementary perspective. The 78-card deck divides into 22 Major Arcana (the archetypal journey) and 56 Minor Arcana. Within the Minor Arcana, the 16 Court Cards — four ranks (Page, Knight, Queen, King) across four suits (Wands, Cups, Swords, Pentacles) — form a 4×4 matrix: four elements expressed through four modes of being.

16 is 2⁴ — the fourth power of the binary. It is also the number of possible combinations of four binary variables, and the number of personality types in Jungian typology (as systematized by Myers-Briggs). The Court Cards are, in this reading, a 16-fold map of consciousness — the same quaternary logic as the Lo-shu, the four DNA bases, and the four trigram pairs of the I Ching, now expressed as human archetypes. We will explore the Court Cards and their elemental matrix in a dedicated article.

Relevance to Artemisia's Approach

At Artemisia, we work across multiple wisdom traditions — the I Ching, Tarot, Vedic Nakshatras, Kabbalah — not as separate systems but as parallel frameworks that describe the same underlying patterns. The Leibniz–I Ching correspondence is a well-documented historical example of this kind of convergence: two independent traditions arriving at the same structural logic.

Essential oils fit within this framework at a molecular level. Aromatic compounds interact with the body's receptor systems through binary-type signaling: a receptor is activated or it is not; a biochemical pathway opens or it remains closed. The same on/off logic that underlies the hexagrams and binary code also governs cellular chemistry — and, as Von Franz suggests, may reflect something fundamental about the structure of reality itself.

Four Structurally Notable Hexagrams