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Modern frames
Binary and synchronicity
Two attempts to explain the Book of Changes in Western terms, one mathematical and one psychological. Both are widely repeated, both are more interesting than their popular versions, and both are routinely stated in ways that are simply wrong.
- 1701
- the diagram reaches Leibniz
- 1950
- Jung's foreword published
- 64
- hexagrams, and codons
The claims
Three distinct arguments get run together in popular accounts. Separating them shows which parts hold up and which do not.
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The Fu Xi arrangement
Song China
11th century
Shao Yong's Before Heaven ordering, generated by repeated division into yin and yang. Reading broken lines as zero and solid as one, it yields the integers nought to sixty-three in sequence.
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Leibniz's recognition
Hanover
1701–1703
He had already developed binary arithmetic when Bouvet's diagram arrived. What he found was a correspondence, which he took as evidence that an ancient civilisation had grasped the same structure.
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The claim reversed
popular accounts
20th century onward
It is often said the I Ching inspired binary, or by extension the computer. It did not. Leibniz's binary work predates the diagram, and Shao Yong's ordering was cosmological rather than arithmetical.
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Synchronicity
Zurich
1930s to 1950s
Jung's proposed acausal connecting principle, relating a psychic state and an outer event meaningfully without either causing the other. Developed in part to account for his experience of consulting the Changes.
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The foreword experiment
Zurich
1949
In his introduction to the Baynes edition Jung casts a hexagram asking what the Changes has to say about being presented to the English-speaking world, and reports the answer. A striking piece of writing whatever one concludes.
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What acausal means
Zurich
1952
Jung was explicit that he was not proposing a hidden causal mechanism. That makes the concept hard to test, which critics treat as fatal and defenders as the point.
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The genetic code analogy
Europe and America
1970s onward
Sixty-four hexagrams, sixty-four DNA codons. The coincidence generated a literature mapping one onto the other, most prominently Martin Schönberger's. No biological claim follows from it.
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Why both are 64
—
—
Hexagrams are six positions with two states, two to the sixth. Codons are three positions with four states, four cubed. Both reach sixty-four by different arithmetic, and the internal structures do not correspond.
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Chance as method
New York
1951 onward
John Cage used hexagram casts to make compositional decisions, removing personal taste from the work. A use of the book that requires no metaphysical claim at all.
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The structural reading
the West
20th century
Treating the sixty-four as a complete combinatorial set for describing states and transitions, of interest to systems thinkers and cyberneticians independently of divination.
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Randomness and software
worldwide
1980s onward
If synchronicity is doing the work, does a pseudorandom generator qualify? Practitioners disagree, and some tools use hardware noise to sidestep the question.
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What the analogies encourage
—
—
Numerical coincidence is easy to find and hard to constrain. The codon literature is the clearest case of a correspondence generating decades of writing without generating a single testable claim.
The people and the sources
Who made each argument, in what form, and what they actually claimed as opposed to what is attributed to them.
Joachim Bouvet
1656–1730
France and Beijing
Jesuit mathematician at the Kangxi court and a leading figurist, who believed the Chinese classics preserved a distorted biblical revelation. He sent Leibniz the hexagram diagram in 1701.
Gottfried Wilhelm Leibniz
1646–1716
Hanover
Had worked on binary arithmetic since the 1670s and published on it in 1703, citing the Chinese diagram as ancient corroboration. He did not learn binary from the Changes and never said he had.
Shao Yong
1011–1077
Luoyang
Produced the arrangement by successive division into yin and yang for cosmological reasons. That this generates binary counting is a consequence of the procedure, not a goal he was pursuing.
C. G. Jung
1875–1961
Zurich
Consulted the Changes for decades and wrote the foreword to the Baynes edition. His 1952 essay on synchronicity, written with Wolfgang Pauli's involvement, is the fullest statement of the idea.
Wolfgang Pauli
1900–1958
Zurich
The Nobel physicist worked with Jung on the volume in which the synchronicity essay appeared. His involvement is often cited as lending scientific weight, and their collaboration was genuinely exploratory rather than a physical theory.
The Baynes edition
1950
New York
Richard Wilhelm's German rendered into English by Cary F. Baynes, with Jung's foreword. The book through which both of these frames reached a mass Western readership.
Martin Schönberger
1973
Germany
Published the best-known book mapping the sixty-four hexagrams onto the sixty-four DNA codons. It established a genre that continues despite the absence of any testable consequence.
John Cage
1912–1992
New York
Used hexagram casts compositionally from 1951, later with computer-generated numbers. His interest was in removing intention from the work, which needs no claim about how the oracle functions.
Hellmut Wilhelm
1905–1990
Seattle
A professional sinologist and Richard Wilhelm's son, whose lectures gave Western readers a scholarly account of the book's structure as a corrective to the more speculative frames.
Richard J. Smith
contemporary
Houston
His cultural history of the Changes covers the Western reception carefully, including how the Leibniz story became garbled in popular retelling.
The sceptical literature
20th century onward
the academy
Historians of mathematics and of sinology have repeatedly corrected the binary claim, and the correction keeps failing to displace the popular version.
The wider reception
17th century onward
Europe and America
These two frames belong to a longer story of Western engagement covered on the Western reception school page, from Jesuit figurism to the recent historical turn.
Two frames, both worth stating accurately
When Western writers try to explain why the Book of Changes might be more than superstition, they reach for one of two arguments. Either the book is secretly mathematics, anticipating binary and therefore computing; or it works through synchronicity, a principle connecting inner states and outer events without cause. Both arguments have real content. Both are usually stated wrongly.
What Leibniz actually found
In 1701 Joachim Bouvet, a Jesuit mathematician at the Kangxi court, sent Leibniz a diagram of the sixty-four hexagrams in the arrangement attributed to Fu Xi and in fact devised by Shao Yong in the eleventh century.
Leibniz saw immediately that if you read a broken line as zero and a solid line as one, the arrangement lists the integers from nought to sixty-three in order. He published on it in 1703 and treated it as remarkable.
Now the correction, which matters. Leibniz had been working on binary arithmetic since the 1670s, decades before the diagram arrived. He did not learn it from the Changes and never claimed to. What he claimed was corroboration: evidence, as he read it, that an ancient civilisation had grasped a structure he had rediscovered.
Nor was Shao Yong doing arithmetic. He generated the sequence by repeatedly dividing yin from yang for cosmological reasons, and the binary ordering falls out of that procedure as a consequence rather than a purpose. Nothing in Chinese sources treats the arrangement as a number system.
So the popular claim, that the I Ching inspired binary and therefore the computer, inverts the history at every step. The formal correspondence is exact and genuinely striking. The causal story attached to it is false.
What synchronicity claims
Jung consulted the Changes for decades and wanted an account of why it seemed to work. Synchronicity is his answer: a principle under which a psychic state and an outer event can be meaningfully related without either causing the other, or any third thing causing both.
His foreword to the 1950 Baynes edition does something rather brave. Rather than arguing about the method, he uses it, casting a hexagram to ask what the Changes has to say about being introduced to the English-speaking world, and then interpreting the answer in print.
The concept's difficulty is structural and Jung knew it. He was explicit that he was not proposing a hidden causal mechanism, which means synchronicity is not the kind of claim that can be tested and then confirmed or refuted. Critics treat this as fatal; defenders treat it as the whole point, since a causal explanation would be a different theory. Wolfgang Pauli's involvement in the volume where the essay appeared is often cited as lending it physical respectability, and it is worth being clear that their collaboration was exploratory rather than a contribution to physics.
Whatever its merits, the concept did specific historical work. It gave educated Western readers permission to take the oracle seriously without believing in divination, and it is much of why the postwar West received the book as a psychological instrument rather than a superstition.
The DNA claim
There are sixty-four hexagrams. There are sixty-four DNA codons. From the 1970s onward, beginning prominently with Martin Schönberger, a literature has mapped one onto the other.
The arithmetic does not support the analogy. Hexagrams are six positions each with two states, two to the sixth. Codons are three positions each with four states, four cubed. Both reach sixty-four by different routes, and the internal structures do not correspond: there is no principled way to say which codon a given hexagram is, and different authors produce different mappings with no way to choose between them.
Nor does any biological or interpretive consequence follow. No mapping has predicted anything about a protein, and none has improved a reading. This is a numerical coincidence that has generated fifty years of writing without generating a single testable claim, and it is worth naming as such.
The use that needs no theory
John Cage offers the clearest alternative. From 1951 he used hexagram casts to determine pitches, durations and dynamics, and continued for four decades, later with computer-generated numbers.
His purpose was to remove his own taste from the work. That requires no view at all about whether the oracle knows anything: it requires only that the procedure be outside his preferences. It is a reminder that the book can be used seriously without committing to either of the frames above.
Where this leaves a reader
Two positions seem defensible. The mathematical correspondence is real and the causal story about it is not, so the honest version is that Shao Yong's arrangement and binary counting share a structure, which is interesting and implies no influence in either direction. Synchronicity is a genuine attempt at a hard problem which is, by its author's own design, not testable, and a reader may find it illuminating or empty without either position being unreasonable.
What is not defensible is repeating that the I Ching gave us the computer, or that its sixty-four figures encode the genetic code. The Western reception school page covers the longer history these two frames belong to.
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