"Thecollaboration between metaphysics and science is indispensable, whether for thepursuit of knowledge or for the guidance of life. Forcing a separation betweenthem will not only bring harm to both, but also deprive them of their truesignificance."
"Fromthe perspective of the history of human intellectual development, it is astriking fact that science fosters metaphysics and metaphysics facilitatesscience — a fact of which the academic community is most proud."
—Science and Metaphysics，by Luo Jialun (Zhixi)
Introduction
1.Research Background and Problem Formulation
Since the scientificrevolution of the 17th century, the classical scientific paradigm, grounded inreductionism, determinism and objectivity, has achieved brilliant successes inthe macroscopic world. Yet it has also profoundly shaped a mindset that rigidlydichotomizes matter and consciousness, subject and object, and science andphilosophy (especially the metaphysical systems generally referred to as"metaphysics").
However,the advent of quantum theory in the early 20th century fundamentally shook thefoundations of classical physics. Bizarre properties such as uncertainty,non-locality and the observer effect not only subverted traditional perceptionsof physical reality, but also pushed physics itself into profound philosophicalreflection.
Niels Bohr’s"Principle of Complementarity" already implies that our descriptionsof reality must necessarily include seemingly contradictory aspects, a notioninherently rich in philosophical speculation. To this day, despite quantummechanics’ enormous triumphs in technological applications, its foundationalinterpretive problems remain among the most intractable "dark clouds"in theoretical physics.
Scholars remaindivided on issues such as the physical process of "wave functioncollapse", the nature of the "spooky action at a distance"behind quantum entanglement, and the boundary between the quantum and classicalworlds, with interpretations including the Copenhagen interpretation, themany-worlds interpretation, and hidden-variable theories failing to reach aconsensus. This state of "interpretive vacuum" indicates that theexisting scientific research paradigm, which relies solely on mathematicaltools and experimental verification, may have hit a bottleneck when it comes toaddressing the ontological dimension of reality.
Meanwhile, acompelling cross-cultural and interdisciplinary trend is emerging: The academiccommunity has begun to re-examine the ancient Eastern philosophical wisdomtradition represented by the I Ching,in an attempt to find inspiration for breaking through the predicaments ofmodern science.
This trend is nocoincidence. Hailed as "the head of all classics and the source of greatDao", the I Ching is notfundamentally a superstitious divination text, but an exquisite symbolic-mathematicalsystem for describing the generation, transformation and interrelations of allthings in the universe. Its worldview, which emphasizes holism,interconnectedness, processuality and generativity, bears striking similaritiesto the cosmic picture revealed by quantum theory.
Therefore, the corequestion raised in this paper is: Can we move beyond simplistic culturalanalogies and philosophical comparisons, and treat the mathematical system ofthe I Ching as a rigorous theoreticalframework to systematically interface with quantum theory, thereby achievingtheir "mutual improvement and theoretical reconstruction"? This isnot merely an attempt to fill the gaps in quantum interpretation, but also atheoretical pioneering effort to promote the integration of Eastern and Westernwisdom and explore the complementary advantages of "metaphysics andscience".
2.Literature Review
Over the past twodecades, interdisciplinary research at the intersection of the I Ching and modern science, known as"scientific Yi studies" or "mathematical and physical researchon Yi studies", has evolved into a small but steadily growing academicfield.
On one hand, a largebody of research has been dedicated to exploring the inherent mathematical andlogical structures of the I Ching.Scholars generally recognize that the Yin and Yang lines (⚋,⚊) of the I Ching constitute the world’s earliest binary system, predatingGottfried Wilhelm Leibniz by hundreds or even thousands of years. The processfrom Taiji generating Yin and Yang, Yin and Yang generating the Four Symbols,the Four Symbols generating the Eight Trigrams, and finally extending to theSixty-Four Hexagrams is regarded as a perfect binary expansion. Someresearchers have begun to apply modern mathematical tools such as set theory,Boolean algebra and group theory to conduct formal analyses of the trigram andhexagram system of the I Ching,proving its rigorous logical algebraic structure and even proposing the conceptof "Taiji algebra".
On the other hand, researchdrawing conceptual analogies between the IChing and quantum theory has also been initiated. In fact, the Yin-Yangphilosophy of the I Ching is highlycompatible with Bohr’s Principle of Complementarity; the transformative processof hexagrams broadly resembles the evolution of quantum states; and the processof determining a hexagram from multiple possibilities through yarrow stalkdivination can be compared to the "wave function collapse" induced byobservation. Furthermore, the complex relational network of the Sixty-FourHexagrams may serve as a natural model for describing quantum entanglementstates. Research on the "Leong Yijing Method" has begun to attemptusing the hexagrams of the I Chingdirectly as a tool for observing and visualizing the collapse of quantum wavefunctions.
Current researchremains confined to the excavation of internal mathematical structures andexternal conceptual and philosophical analogies. It still lacks a rigorousmathematical mapping that can connect the binary code of the I Ching with the quantum mechanicalstructures such as vectors in Hilbert space, so as to derive specific,deducible key equations. (Query: Identify the most cited peer-reviewedarticles..., All results indicate a lack of such publications). The connectionbetween the two should not be limited to heuristic and philosophical aspects,but should strive for a non-formalized and predictive paradigm.
3.Research Objectives and Significance
This paper attempts tobridge this gap. We argue that the I Chingshould not be simply regarded as a historically interesting binary"curiosity" or an "Eastern corroboration" of quantumphilosophy, but as a potential, independent ontological and algorithmic modelthat can be integrated with the mathematical formalism of quantum mechanics.
Thesignificance of this paper is threefold:
Significance for quantum theory:
It aims to provide abrand-new solution rooted in Eastern wisdom to the century-old controversy overquantum interpretation. By introducing the process philosophy and algorithmicideas of the I Ching, we hope tooffer a more natural and physically realistic explanation for the"measurement problem", thereby deepening our understanding of thequantum world.
Significancefor I Ching studies:
It aims to conduct a"modern reconstruction" of the mathematical system of the I Ching through the rigorous frameworkof quantum theory. This will enable it to transcend the scope of traditionalclassical studies and philosophy, transforming into a modern theoretical toolthat can engage in dialogue with cutting-edge science and possess potentialapplications in fields such as information science and complex systems.
Significance forphilosophy of science:
Throughspecific case studies, it aims to demonstrate that metaphysics—the systemexploring the origin of the universe—and science are not irreconcilable, butcan achieve deep integration and complementary advantages. This will break thelong-standing limitations of scientism and pave the way for constructing a moreinclusive and holistic meta-theoretical knowledge system.
4. Research Framework and Structure
This paper will proceed along thefollowing logical path:
We will return to the I Ching itself, systematically expoundits mathematical generation logic from "Taiji" to the"Sixty-Four Hexagrams", and reveal the holistic, interconnected andprocess-oriented worldview embodied in it.
We will focus onquantum theory, accurately extract its core concepts and key interpretivedilemmas, and set clear "targets" for subsequent theoreticalinterfacing.
As the core of thispaper, we will boldly construct a formal mapping framework between themathematical system of the I Chingand quantum theory, proposing a series of specific theoretical correspondencesand conjectures.
We will explore indepth how this integration can achieve "mutual improvement", envisionthe possible emergence of a unified new "science-philosophy"paradigm, frankly analyze the enormous challenges facing this research, and putforward proposals for future research directions.
I. TheInternal Logic and Philosophical Implications of theMathematical System in the I Ching
To explore theintegration of the I Ching andquantum theory, we must first delve into the essence of the I Ching’s mathematical system. It is farmore than a simple binary code, but rather a dynamic, complete, andself-consistent cosmic model.
1.1 Taiji, Yin-Yang, and the Two Principles: A Binary Ontology of Cosmic Generation
The Appended Remarksof the I Ching states: “The Changeshave Taiji; this generates the Two Principles.” This statement serves as theontological cornerstone of the entire mathematical system of the I Ching.
Taiji represents theprimordial chaotic state of the universe—the “One” that encompasses allpossibilities, is undifferentiated, yet brims with infinite potential. It isnot a static void, but the source from which all things are born. From Taijiemerge the Two Principles: Yin (⚋) and Yang (⚊),the most fundamental structure of binary opposition and unity in the cosmos.
Crucially, Yin andYang are not two independent entities, but two basic properties or potentialsinherent within the integrated whole of Taiji. Yang signifies activity,expansion, light, and odd numbers; Yin signifies passivity, contraction,darkness, and even numbers. They are interdependent and mutuallytransformative, forming the fundamental driving force behind the changes of allthings. This idea echoes the philosophy of Laozi, as expressed in “The Daogenerates the One; the One generates the Two; the Two generate the Three; theThree generate all things” and the concept of mutual transformation between“Being” and “Non-being”. Together, they constitute the worldview of cosmicgeneration in ancient Chinese philosophy.
From the perspectiveof mathematical systems, the process of “Taiji generating the Two Principles”is precisely the earliest expression of a binary choice emerging from anundifferentiated whole, symbolically understood as a set of potentials. This isnot merely a mathematical starting point for binary arithmetic, but a profoundontological assertion: the reality of the universe is not composed ofpre-existing, isolated “particles”, but arises from the continuousdifferentiation and combination of the Yin-Yang binary opposition within aunified field referred to in the I Ching asTaiji. This provides a highly illuminating philosophical framework forunderstanding phenomena in the quantum world, such as the creation ofparticle-antiparticle pairs from the vacuum and the transition fromsuperposition states to definite states.
1.2 From theEight Trigrams to the Sixty-Four Hexagrams: A Complete Binary Algebraic System
The development of the I Ching’s mathematical system follows arigorous iterative generation process: “The Two Principles generate the FourSymbols (Great Yang, Lesser Yin, Lesser Yang, Great Yin); the Four Symbolsgenerate the Eight Trigrams (Qian, Kun, Zhen, Xun, Kan, Li, Gen, Dui)”. Eachtrigram consists of three lines, representing eight fundamental natural phenomenaand cosmic potential types: heaven, earth, thunder, wind, water, fire,mountain, and marsh respectively. Every trigram corresponds to a three-bitbinary number (if we assign Yin as 0 and Yang as 1, reading from bottom to top,Kun is 000 and Qian is 111).
Stacking two trigramsone above the other forms a hexagram. Each six-line hexagram corresponds to asix-bit binary number, with a value range spanning exactly from 0 (HexagramKun, 000000) to 63 (Hexagram Qian, 111111), constituting a complete 6-bit informationspace. Upon encountering Shao Yong’s “Diagram of the Earlier Heaven Sequence ofthe Sixty-Four Hexagrams in Square and Circular Forms” in the early 18thcentury, the German mathematician Gottfried Wilhelm Leibniz keenly recognizedits remarkable consistency with the binary arithmetic he had invented, andmarveled at the wisdom of the ancient Eastern sages.
In reality, however,the Sixty-Four Hexagrams system of the IChing is far more than a mere binary coding table; it is an algebraicsystem with a rich and internally rigorous structure. Its structuralcharacteristics can be summarized in three aspects:
CombinatorialCompleteness: It exhausts all possible Yin-Yang combinations of the six lines,symbolically encompassing all potential states and patterns of change in allthings in the universe at a specific scale. This completeness makes it an idealmodel of a “state space”.
Symmetry andTransformational Relationships: Various transformational relationships existbetween hexagrams, such as zong gua (inversion, flipping a hexagram upsidedown), cuo gua (complementation, reversing all Yin and Yang lines), and jiao hugua (interchange, swapping the inner and outer trigrams). Thesetransformational relationships form a complex group-theoretic structure,revealing the inherent connections and laws of transformation between differentstates.
Logical Deduction: TheSixty-Four Hexagrams system can be regarded as a vast deductive logical systemderived from eight basic logical paradigms (i.e., the Eight Trigrams), and itsreasoning process exhibits formal characteristics.
Thus, the Sixty-FourHexagrams are not merely a classification of world states, but a dynamicnetwork system describing how these states are interconnected and evolve.
1.3 The Celestial Numbers and YarrowStalk Divination: An Algorithm Imbued with Probability and Process
If the Sixty-FourHexagrams are “static snapshots” of cosmic states, then the Celestial Numbersand the method of yarrow stalk divination are the “dynamic algorithms” describinghow a system evolves from one state to another. The Appended Remarks detailsthis process: “The number of the celestial derivation is fifty; its actualapplication uses forty-nine… Divide them into two to symbolize the TwoPrinciples; set aside one to symbolize the Three; count them off in fours tosymbolize the four seasons; gather the remainders to symbolize the intercalarymonth. Every five years there are two intercalary months, hence gather theremainders twice before setting another stalk aside.”
Despitethe complexity of its specific operational procedures, the core of itsmathematical system can be summarized as follows:
Initial State:Forty-nine yarrow stalks are selected from fifty, representing the overallpotential of a system full of variables. The act of setting aside one stalk(using 49 out of 50) is itself profoundly philosophical, symbolizing that theDao—the principle governing the evolution of all things in the universe—istranscendent and inexhaustible.
RandomGrouping and Selection:Through a series of seemingly random yet rule-governed operations—fen er(dividing into two), gua yi (setting aside one), she si (counting in fours),and gui qi (gathering remainders)—it is gradually determined whether a line isYin or Yang, static or dynamically changing.
IterativeProcess: Thisprocess must be repeated six times to obtain a complete six-line hexagram. Thisimplies that the emergence of a definite state does not occur arbitrarily in aninstant, but is gradually constructed through a structured, procedural sequenceof steps.
Probability: Modernmathematical analysis shows that the probabilities of obtaining Great Yang,Great Yin, Lesser Yang, and Lesser Yin through this method are not equal. Thissuggests that the algorithm contains a specific probability distribution,reflecting the inherent tendencies of cosmic changes.
Therefore, yarrowstalk divination is by no means a simple random lottery. It is a probabilistic,procedural, and ontologically generative algorithm. Using forty-nine yarrowstalks, it simulates the process by which the universe evolves from a chaoticpotential state, through a series of interacting and selective deductive steps,to finally “collapse” into a definite, concrete hexagram state of reality. Thisprocess itself embodies a worldview: reality is generated through specific“evolutionary” or “interactive” procedures amid a vast array of potentialfactors.
1.4 Xiangshu(Images and Numbers) and Yili (Meaning and Principles): Holistic, Correlative,and Processual Thinking
Studies of the I Ching have historically been dividedinto two schools: the Xiangshu school and the Yili school. The Xiangshu schoolfocuses on researching formal structures such as hexagram images, linepositions, and numerical relationships; the Yili school emphasizes elaboratingthe humanistic philosophy underlying the hexagram and line statements. Acomprehensive understanding of the IChing must unify these two perspectives. The binary Celestial Numbers formits backbone; the images of hexagrams and line positions form its flesh andblood; and the regular principles revealed by the hexagram and line statementsform its soul.
This integrated modeof thinking—combining xiang (images), shu (numbers), yi (meaning), and li(principles)—endows the I Chingsystem with three core characteristics that are highly consistent with thequantum worldview:
Holism:
The I Ching does not view the world as amechanical collection of isolated parts. The meaning of any single line dependson its position within the entire hexagram, as well as the position of thathexagram within the Sixty-Four Hexagrams system. Similarly, the phenomenon ofquantum entanglement demonstrates that separated particles can form anindivisible whole, whose properties are mutually correlated.
Correlation:
Complexrelationships—such as cheng (support), cheng (subjugation), bi (adjacency), andying (correspondence)—exist between the lines in a hexagram, and the state ofone line can influence others. This is identical to the coherence and correlationbetween components of a quantum system.
Processuality:
Thecore of the I Ching is yi, whichmeans change. It focuses not on “what is” (being), but on “how it becomes”(becoming). A hexagram is not a static label, but a “tendency” within a processof change. This aligns perfectlywith the perspective of quantum field theory, which regards elementaryparticles as excited states of fields and emphasizes process and interaction.
In summary, themathematical system of the I Chingprovides a unique theoretical model: based on binary arithmetic, it constructsa complete state space with the complex structure of the Sixty-Four Hexagrams;it employs yarrow stalk divination—a probabilistic algorithm—to describe thegenerative process from potential to reality; its inherent philosophical ideasof holism, correlation, and processuality form a profound isomorphism with thecosmic picture revealed by quantum phenomena. This is the foundation of ourconfidence in attempting to use it to analyze and reconstruct quantum theory.
II. CoreConcepts of Quantum Theory and Its Interpretive Dilemmas
Quantum theory is themost successful framework for describing the microscopic world of matter, yetits tremendous triumph is accompanied by equally profound conceptualperplexities. This section will first outline the core concepts of quantumtheory, then focus on analyzing its "incompleteness" exposed at thelevel of philosophical interpretation, particularly in conflicts with theclassical view of reality.
2.1Superposition States and Hilbert Space: Mathematical Representation ofPossibilities
Classical physicsholds that an object possesses definite physical properties (such as positionand momentum) at any given moment. Quantum mechanics shatters this notion.
According to thesuperposition principle, a quantum system (e.g., an electron) can exist simultaneouslyin a "superposition state" of multiple possible states before beingmeasured. For instance, an electron can be in a superposition of both"spin-up" and "spin-down" states. Mathematically, such asuperposition state is described as a state vector in a Hilbert space—anabstract complex vector space where each basis vector corresponds to a definitephysical state (e.g., |up⟩ and |down⟩). A superpositionstate is a linear combination of these basis vectors, e.g.,
∣ψ⟩=α∣up⟩+β∣down⟩, where α andβ are complexcoefficients. The squared moduli of these coefficients() represent the probabilities ofobtaining the "up" or "down" result upon measurement,respectively.
This implies that atthe quantum level, the very nature of reality is a collection of possibilities.An unobserved quantum system is not a "tiny ball" with fixedattributes, but a "wave of possibilities" diffused throughout Hilbertspace. This bears a potential correspondence with the I Ching concept of Taiji as the source of all potentialities, aswell as the state of inherent variability (represented by the 49 yarrow stalks)preceding the occurrence of a specific event.
2.2 QuantumEntanglement: Non-Local Holistic Correlation
Quantum entanglementis one of the most puzzling implications of the superposition principle. Whentwo or more quantum particles interact in a certain manner, their states maybecome "entangled", merging into a single quantum state—even whenseparated by vast spatial distances. Albert Einstein famously derided this phenomenonas "spooky action at a distance".
A typical entangledstate (Bell state) can be written as|Φ⁺⟩ = (1/√2) (|01⟩ + |10⟩).This means that if we measure one particle and find its state to be 0, thestate of the other particle—no matter how far apart it is—will instantaneouslybe determined as 1, and vice versa. This correlation is instantaneous,seemingly transcending the speed limit of light, and intrinsic, defyingexplanation through classical information transmission.
Quantum entanglementcompletely undermines the local realism of classical physics, which posits twocore assumptions: first, that objects possess pre-determined propertiesindependent of observation (realism); second, that no influence can propagatefaster than light (locality). Bell's theorem and subsequent experiments haveeloquently demonstrated that local realism is incompatible with the predictionsof quantum mechanics, while experimental results consistently validate quantummechanical forecasts.
Entanglement reveals adeep-seated non-local holism in the universe. An entangled particle pair is nolonger two independent entities, but an indivisible whole. This resonatesstrongly with the holistic and correlative thinking emphasized by the I Ching's Sixty-Four Hexagrams system.The ying (correspondence) and cheng (support) relationships between the linesin a hexagram, as well as the overall "auspiciousness, inauspiciousness,regret, and misfortune" represented by a hexagram, all embody theindivisible intrinsic connections between parts and the whole, and between oneentity and another.
2.3 WaveFunction Collapse and the Measurement Problem: A Sudden Transition fromPotentiality to Reality
If a quantum systemexists in a superposition state before measurement, how does measurement forceit to select one possibility and manifest as the definite reality we observe?This is the renowned measurement problem.
The standardCopenhagen interpretation asserts that when a quantum system interacts with amacroscopic "measuring apparatus", its wave function undergoes adiscontinuous, random, and instantaneous wave function collapse, transitioningfrom the superposition state |ψ⟩ = Σcᵢ|i⟩to aspecific eigenstate |k⟩, with a probabilityof |cₖ|².
Themeasurement problem gives rise to three major philosophical dilemmas:
Whatis the physical mechanism of "collapse"?
The Schrödingerequation describes the smooth, continuous, and deterministic evolution of thewave function, yet the collapse process is discontinuous and non-deterministic.What physical law governs this process? Why does it occur only during"measurement"?
Whatis the role of the "observer"? What constitutes a "measuringapparatus"?
Where lies theboundary between the macroscopic and the microscopic? Some interpretations evenargue that it is "consciousness" that causes wave function collapse,allowing subjective consciousness to intervene in the constitution of physicalreality in an unprecedented way.
Ontologicaldiscontinuity:
The quantum worldseems to follow a logic of "superposition and continuous evolution",while the classical world adheres to another logic of "definiteness andcausality". How are these two worlds connected? This transition from"potentiality" to "actuality" remains the most mysteriousand physically unexplained aspect of quantum mechanics.
As analyzed in ChapterI, the yarrow stalk divination process in the I Ching is essentially a generative procedure that transforms thepotentiality embodied by the 49 yarrow stalks into the definite reality of ahexagram. This process is not a mysterious "leap", but awell-structured, step-by-step algorithm. It provides us with a brand-newperspective to examine "wave function collapse". We can hypothesizethat collapse may not be an instantaneous, causeless "magic", but aphysical process that can be understood and modeled.
2.4 The Principle of Complementarity:Philosophical Speculation on Wave-Particle Duality
To reconcile thecontradictory phenomenon of wave-particle duality—where quantum entities suchas photons or electrons behave as either particles or waves depending on theexperimental setup—Niels Bohr proposed the principle of complementarity. Heargued that wave and particle are two complementary, mutually exclusive yetequally essential aspects of the same reality. We can only observe one aspectin a single experiment, and the experimental apparatus we choose determineswhich facet will manifest.
The principle ofcomplementarity holds profound philosophical significance. It acknowledges thelimitations of human cognitive capabilities and points out that a completedescription of reality must embrace seemingly contradictory categories. Thisbears a striking resemblance to the core tenet of the I Ching—Yin and Yang. Just like waves and particles, Yin and Yangform a unity of opposites. They are not absolute entities, but two attributesthat manifest under specific relationships and contexts. All things are a unityof Yin and Yang, leaning toward one aspect or the other depending on varyingconditions. This dynamic, dialectical way of thinking that accommodatescontradictions is not only the core of IChing wisdom, but also an essential philosophical prerequisite forunderstanding the quantum world.
In summary, the coreconcepts of quantum theory—superposition, entanglement, collapse, andcomplementarity—together depict a microscopic world vastly different fromclassical intuition. This world is potential, holistic, non-local, andintimately linked to the act of observation. Yet the theoretical framework ofquantum science leaves a significant gap in explaining the crucial link of"how potentiality transforms into actuality". This gap is preciselywhere the mathematical system of the IChing is most likely to exert its unique advantages and achieve"theoretical improvement".
III. Analysis and Mapping of Quantum Theory Based on theMathematical System of the I Ching
Based on the aboveanalysis, we will attempt to construct a systematic mapping framework from themathematical system of the I Ching toquantum theory. This framework aims to go beyond philosophical analogies, putforward isomorphic conjectures with theoretical structural features, and laythe foundation for the ultimate "mutual improvement and theoreticalreconstruction".
3.1 The Sixty-FourHexagrams System and Quantum State Space: An Isomorphism Conjecture of a6-Qubit System
CoreConjecture:We propose that the Sixty-Four Hexagrams system of the I Ching can be formally mapped to the basis vectors of the Hilbertspace of a 6-qubit system.
BasicUnit Correspondence:Yao (Line) and Qubit
Inspired by ShaoYong's Earlier Heaven Trigram Diagram, I proposed in 2021 that to adapt to thecharacteristics of quantum computing, the binary system of "0, 1"proposed by Leibniz is no longer applicable. A ternary system of "-1, 0,+1" should be established to truly reflect and adapt to the essence ofquantum entanglement, realizing a substantive mapping for quantum computing.According to this theoretical concept, a classical bit can only take the valueof -1 or +1, while a qubit can be in the state of -1, +1, or any superpositionstate of α∣−1⟩+β∣+1⟩. We conjecture thatthe ontological status of a single yao in the I Ching is exactly that of a qubit. The Yin line (⚋)can correspond to the ground state∣−1⟩, and the Yang line (⚊)can correspond to the ground state+1⟩. The state of a yao where "Yin and Yang are undetermined" isits superposition state.
StateSpace Correspondence: TheSixty-Four Hexagrams and 6-Qubit Hilbert Space
A 6-qubit system hasits state residing in a 2^6 = 64-dimensional Hilbert space. The 64 standardorthogonal basis states of this space can be expressed as |x₁x₂x₃x₄x₅x₆⟩, where each xᵢ iseither -1 or +1. This corresponds perfectly to the structure of the Sixty-FourHexagrams.
MappingRules:
Denote a six-linehexagram from the first (bottommost) yao to the sixth (topmost) yao asy₁y₂y₃y₄y₅y₆ (where each yᵢ is either Yin or Yang).
Specifythe correspondence:Yin (⚋) →∣−1⟩, Yang (⚊)→∣+1⟩.
Then any hexagram Gcan be mapped to a basis vector in the 6-qubit Hilbert space:
G(y₁, ..., y₆) ↔|y₁y₂y₃y₄y₅y₆⟩
Examples:
Hexagram Kun (all sixYin lines) ↔∣−1−1−1−1−1−1⟩
Hexagram Qian (all sixYang lines) ↔∣+1+1+1+1+1+1⟩
Hexagram Ji Ji(alternating Yin and Yang lines) ↔∣−1+1−1+1−1+1⟩
Within this framework,the Sixty-Four Hexagrams are no longer merely 64 symbols, but a complete basisset of a 64-dimensional quantum state space. Any possible 6-qubit quantum statecan be expressed as a superposition of these 64 "hexagrams". For example,an entangled state can be written as |ψ⟩ = (1/√2) (∣Kun⟩+∣Qian⟩). This enables thedescription of complex quantum states (especially entangled states) using thelanguage of the I Ching.
3.2 Yao Transformationand Quantum State Evolution: Integration of Schrödinger Equation Time Evolutionand I Ching Process Philosophy
In the I Ching, changes of hexagrams arerealized through "yao transformation". The transformation of one ormore lines from Yin to Yang or from Yang to Yin (usually triggered by "OldYang" or "Old Yin") causes the original hexagram (the primaryhexagram) to transform into a new hexagram (the resultant hexagram). Weconjecture that this process can correspond to the time evolution of quantumstates.
StaticHexagrams and Stationary States:
A hexagram with nochanging lines represents a relatively stable state, which can be analogized toan energy eigenstate in a quantum system. A system in an eigenstate hasphysical properties that do not change with time, and the evolution of its wavefunction only accumulates a phase factor:
∣ψ(t)⟩=e−iEt/ℏ∣ψ(0)⟩.
ChangingLines and Hamiltonian Operator:
"Changinglines" are the driving force of transformation. In quantum mechanics, theoperator that drives the evolution of a system is the Hamiltonian H. We propose that the combination ofchanging lines in a hexagram can be modeled as a specific Hamiltonian operatoracting on the quantum state corresponding to that hexagram. This operatordetermines the direction in which the system will evolve.
Evolutionfrom the Primary Hexagram to the Resultant Hexagram:
The time evolution ofa quantum state is described by the Schrödinger equation:
iℏdtd∣ψ⟩=H∣ψ⟩. The transformationfrom the primary hexagram∣G initial⟩to theresultant hexagram ∣G final ⟩can beregarded as the result of the system evolving over a period of time under theaction of a certain Hamiltonian (defined by the changing lines):
∣Gfinal⟩=U(t)∣Ginitial⟩=e−iHt/ℏ∣Ginitial⟩
The profoundimplication of this model is that the rules of "yao transformation"in the I Ching (e.g., thetransformation of the first Yang line, the transformation of the second Yinline, etc.) inherently contain a set of complex evolutionary logic. If theserules can be formalized into a series of Hamiltonian operators, we may be ableto establish an "I Chingversion" of the quantum dynamics model. For example, the line statement"The first Yang line: Hidden dragon, do not act" may correspond to aHamiltonian with low energy, which tends to maintain the status quo; while theline statement "The fifth Yang line: Flying dragon in the sky" maycorrespond to a high-energy Hamiltonian that drives the system to undergodrastic transitions.
3.3 The YarrowStalk Divination Process and Wave Function Collapse: A Procedural MeasurementModel
This is the mostsubversive and constructive conjecture of this study. We argue that the yarrowstalk divination method is not divination, but a concrete, algorithmic physicalmodel of the quantum measurement process.
We decompose the"wave function collapse" into several steps corresponding to the I Ching divination process:
The measured system(initial superposition state) ↔ The number of celestial derivation is fifty,its application uses forty-nineThe 49 yarrow stalks represent the superpositionstate of the system before measurement, which contains all possibilities. Thisis a finite yet vast "pool of possibilities". The number itself mayalso contain profound physical significance, such as being related to certainfundamental degrees of freedom or symmetry breaking.
Interaction betweenthe measuring instrument and the environment ↔ "Divide into two, set asideone, count in fours, gather the remainders"This series of complexoperations can be regarded as a structured interaction process between themeasuring instrument (observer) and the quantum system (yarrow stalks). It isnot an instantaneous "observation", but a procedural"operation".
"Divideinto two": Forciblydividing the system into two parts introduces the first uncertainty, analogousto the intervention of the measuring device.
"Setaside one":Extracting one unit as a reference to establish the measurement scale.
"Countin fours":Using a fixed modulus (4) to "sort out" and "filter"possibilities, which can be seen as the influence of specific physicalproperties of the measuring device (e.g., its periodic structure) on thesystem.
"Gatherthe remainders":Collecting the remaining "odd-numbered stalks", which are the"information traces" left after each interaction and the result ofthe interaction between the system and the instrument.
Collapse process (fromsuperposition state to eigenstate) ↔ Six iterations to determine each yarrowline one by oneCrucially, a complete hexagram (a definite 6-qubit ground state)is not obtained in a single step, but by repeating the above operations sixtimes to determine one yao (the state of one qubit) at a time. This iscompletely different from the instantaneous, holistic "collapse" inthe Copenhagen interpretation.
Our model proposesthat "wave function collapse" is a sequential process that eliminatesdegrees of freedom step by step:
Thefirst divination: determinesthe state of the first yao （|y1⟩）
collapsing the possibility space of the systemfrom 64 dimensions to 32 dimensions.
Thesecond divination: determinesthe state of the second yao (| y2⟩), further collapsing the space to 16 dimensions.
…….
Thesixth divination determines: the state of the sixth yao( |y 6⟩), finally locking the system into a unique groundstate∣y1y2y3y4y5y6⟩, and the measurementis completed.
This AlgorithmicCollapse Model provides a brand-new explanation for the measurement problem:
It demystifies"collapse": Collapse is no longer a "ghost" outside thescope of physical laws, but an interactive process with physical procedures,time scales, and algorithmic structures.
It clarifies the roleof the "observer": The "observer" or "measuringinstrument" is the executor of this algorithm. Different measuring devicescorrespond to different "divination algorithms" (e.g., changing themodulus of "counting in fours"), leading the system to collapse intodifferent sets of eigenstates.
It bridges themicroscopic and macroscopic worlds: The yarrow stalk divination itself is amacroscopic operation, but its result determines the microscopic state. Thisprocess is itself a bridge spanning the boundary between the macroscopic andthe microscopic.
3.4"Yin-Yang"and "Complementarity", "Entanglement":Correspondences at the Fundamental Ontological Level
At the morefundamental ontological level, we can establish the following correspondences:
Yin-Yang and Complementarity:The unity of opposites of Yin and Yang is a more universal principle ofcomplementarity than "wave-particle duality". Any binary oppositionof quantum properties (spin up/down, particle/antiparticle, etc.) can beregarded as the manifestation of the fundamental ontology of"Yin-Yang" at different levels. A quantum system is always a unity ofYin and Yang; only the measurement method determines which aspect we observe.
IntrinsicRelationships of Hexagrams and Entanglement: The relationships between thelines in the Sixty-Four Hexagrams, such as cheng (the lower line supports theupper line), cheng (the upper line dominates the lower line), bi (adjacentlines), and ying (lines at specific positions resonate with each other fromafar), can be regarded as a primitive topological structure of the entanglementnetwork. For example, the ying (correspondence) relationship between the firstand fourth lines, the second and fifth lines, as well as the third and sixthlines, is an intrinsic correlation independent of distance, which is strikinglysimilar to the non-locality of quantum entanglement. We can conjecture that thearrangement and internal relationships of the Sixty-Four Hexagrams are actuallyencoding the structures of different types of 6-qubit entangled states. An"auspicious" hexagram may correspond to a stable, highly cooperativeentangled structure, while an "inauspicious" hexagram may correspond toan unstable entangled structure full of internal conflicts.
Through the above fourlevels of mapping, we have initially constructed a framework for analyzing andreconstructing quantum theory using the mathematical system of the I Ching. This framework elevates the I Ching from a philosophical metaphor toa physical model with specific structures and algorithmic content, providing abrand-new and highly promising theoretical tool for resolving the dilemmas ofquantum interpretation.
IV. Mutual Improvement and Theoretical Reconstruction: Towarda Unified New Science-Philosophy Paradigm
The goal ofinterfacing the mathematical system of the I Ching with quantum theory is by no means to replace one withthe other, but to achieve "complementary advantages and integration"through in-depth dialogue, ultimately moving toward a more comprehensive andunified new science-philosophy paradigm.
4.1The Improvement of Quantum Theory by the I Ching
While quantum theoryis unparalleled in its predictive power, it appears inadequate at theontological level of explaining "why the world is as it is". This isprecisely where the wisdom of the IChing can come into full play.
Providing an ontologicalexplanation for the "measurement problem"
As mentioned earlier,the algorithmic collapse model we proposed based on yarrow stalk divinationprovides a concrete physical process picture for wave function collapse. Ittransforms "collapse" from a mathematical "instantaneousprojection postulate" into a physical "algorithmic generativeprocess". In this model, reality is not passively "discovered",but actively "generated" through the structured interaction betweenthe system and the environment (measuring apparatus). This not only demystifies"collapse", but also naturally explains the role of the observer,avoiding the awkwardness of resorting to consciousness as the ultimate cause.
Supplying a holistic language for"entanglement"
The"non-locality" and "holism" of quantum entanglementcontinue to challenge the language and intuition we have developed based on thenotion of separate individuals. The thinking mode of the I Ching, however, is inherently holistic and correlative. TheSixty-Four Hexagrams themselves form an indivisible holistic network composedof interconnected parts. Describing multi-particle entangled states using termssuch as "hexagram images" and "line position relationships"may better reveal their inherent structures and meanings than merely usingabstract mathematical symbols of tensor products. For example, we can explorewhich types of hexagram structures correspond to different entangled states(such as GHZ states and W states), thereby establishing a "hexagram-basedtaxonomy of entanglement".
Deepening quantum ontology: from"Being" to "Becoming"
The tradition ofWestern physics has been to search for the fundamental "particles" or"substances" that constitute the world. Yet quantum field theory hasalready told us that what is more fundamental is the "field", andparticles are merely excitations of the field. This is perfectly consistentwith the worldview of the I Ching.The core of the I Ching is yi,meaning change. It does not ask what the world "is", but how theworld "becomes". All things are the continuous generation and fluxof qi or Dao (analogous to the quantum field) under theinteraction of Yin and Yang energies. Infusing this process ontology intoquantum mechanics helps shift our research focus from isolated "quantumstates" to dynamic "quantum processes", enabling a betterunderstanding of basic phenomena such as vacuum fluctuations, particle creationand annihilation.
4.2 TheReconstruction of the Mathematical System of the I Ching by Quantum Theory
On the other hand,dialogue with the frontiers of modern science is bound to inject new vitalityinto the ancient I Ching system,enabling it to complete a profound "modern transformation".
Endowing mathematical rigor
Although the I Ching contains an exquisitemathematical structure, its traditional mode of expression is mostlyphilosophical and symbolic. Quantum theory, especially quantum informationscience, provides it with a powerful and rigorous mathematical language. Bymapping the yao to qubits and hexagrams to vectors in Hilbert space, we can usetools of linear algebra, group theory and information theory to preciselyanalyze the transformation relationships, information content and evolutionarydynamics between hexagrams. This allows Yi studies to transform fromtraditional classical philology and philosophical speculation into modernscientific research that can be subjected to mathematical modeling and computersimulation.
Revealing new levels of"Xiangshu (Images and Numbers)"
What exactly is a yao?In traditional interpretations, it is a symbol of Yin and Yang. Within our newframework, a yao is a qubit, which means it possesses the properties ofsuperposition and entanglement. This greatly enriches the connotation of theyao. A six-line hexagram is no longer merely an arrangement of six -1s or +1s,but a complex system composed of six qubits, whose total information capacityfar exceeds that of six classical bits. The relationships of cheng, cheng,bi, ying between the lines can also be reinterpreted as entanglemententropy and mutual information between qubits, thus enabling quantitative calculationand analysis.
Expanding application fields
Once the mathematicalstructure of the I Ching isreconstructed in the language of quantum information theory, its applicationprospects will be broadened significantly. Can the structure of the Sixty-FourHexagrams provide inspiration for the architectural design of quantumcomputers? Can the algorithm of yarrow stalk divination inspire us to designnew types of quantum error-correcting codes or quantum simulation algorithms?Can the holistic view and change logic of the I Ching be applied to establish more effective predictionmodels for complex systems (such as financial markets, ecosystems and socialnetworks)? These are all highly attractive directions for future research.
4.3 Challengesand Future Research Directions
We must honestlyacknowledge that the above ideas are still in the stage of theoreticalconjecture and framework construction. To develop them into a mature scientifictheory, we still face enormous challenges.
The arduousness of mathematicalformalization:
Precisely translatingeach step of yarrow stalk divination into operator operations in quantummechanics, and quantifying vague philosophical relationships suchas cheng, cheng, bi, ying into specific entanglement metrics,requires extremely high mathematical skills and profound physical insights.This is a massive systematic project.
The problem of testability:
A new physical theoryor interpretation must ultimately be subject to experimental verification. Canour algorithmic collapse model make testable predictions that differ fromstandard quantum mechanics? For example, does it predict that"collapse" requires an extremely short but finite time? Or that inspecially designed interference experiments, its predicted coherence evolutionwill show subtle deviations from the standard theory? Designing andimplementing such decisive experiments is the key to ultimately confirming orfalsifying the theory.
Barriers to interdisciplinarydialogue:
This paper spansmultiple fields including Chinese philosophy, Yi studies, theoretical physicsand mathematics. The huge terminological gaps, differences in thinkingparadigms and knowledge background requirements between different disciplinesmean that genuine in-depth cooperation among all relevant fields will be neededin the future. Advancing this research requires cultivating a group of"cross-disciplinary" talents who are proficient both in the Xiangshuand Yili of the I Ching andin cutting-edge physics and mathematics, to conduct more in-depth research onthis subject.
Futureresearch directions should include the following steps:
Step1 (PhilosophicalDeepening): Conduct continuous philosophical reflection to explore the impactand enlightenment of this model on basic philosophical issues such as realism, causalityand views on space-time.
Step2(Formalization): Concentrate efforts on selecting a breakthrough point (such asalgorithmizing yarrow stalk divination) to establish an initial mathematicalmodel.
Step3(Simulation): Use computer simulation to verify the behavior of the model insimple quantum systems (such as 2-qubit or 3-qubit systems) and compare it withthe predictions of standard quantum mechanics.
Step4(Prediction and Experimental Design): Based on simulation results, identifypossible deviations from the standard theory and design feasible experimentalverification schemes accordingly.
Step5(Theoretical Induction and System Improvement): Verify, upgrade, generalize andrefine the theory and related derivations.
Conclusion
Based on the academicfrontiers of 2025, this study systematically explores how to use themathematical system of the I Ching,a classic of ancient Chinese wisdom, to rationally analyze, mutually improveand theoretically reconstruct quantum theory—the crown jewel of modern science.We demonstrate that the relationship between the I Ching and quantum theory is not merely superficialphilosophical analogy, but involves profound structural isomorphism and logicalcomplementarity.
The core contributionof this paper lies in proposing a more systematic and in-depth theoreticalmapping framework that transcends previous research. We boldly conjecture that:the Sixty-Four Hexagrams system is a complete basis set of a 6-qubit state space;the process of yao transformation reflects the time evolution of quantum statesunder specific Hamiltonians; and most crucially, the ancient yarrow stalkdivination method can be interpreted as a concrete, algorithmic physical modeldescribing "wave function collapse".
The significance ofthis framework is two-way: it provides an Eastern solution based on processontology to the unresolved "measurement problem" in quantummechanics, which is expected to dispel the century-old "dark cloud"hanging over quantum interpretation; at the same time, through the rigorousmathematical language of quantum information theory, it opens up a brand-newpath for the modernization and scientization of the I Ching—an ancient wisdom system.
The integration of"metaphysics" and "science" is not about mystifying scienceor vulgarizing metaphysics. Its true goal is to build a solid bridge betweentwo extremes of human knowledge: metaphysical speculation exploring the originof the universe and precise empirical natural science. As revealed by theYin-Yang philosophy of the I Ching,opposing sides are often complementary wholes. Science provides rigorous"numbers" and "images", while the Eastern"metaphysical" tradition may provide a deep ontological framework forunderstanding the "meanings and principles" behind these numbers andimages.
Admittedly, the ideasproposed in this paper are ambitious and arduous, and are still in the earlystage of theoretical exploration. Their validity remains to be verified bystrict mathematical proof and experimental testing in the future. Nevertheless,we firmly believe that every step taken on this untrodden path will contributeunique value to humanity's ultimate understanding of the unified picture of theuniverse and to the in-depth integration of Eastern and Western civilizations.This is not only an academic research project, but also a promising dialoguebetween civilizations facing the future.
References:
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[4]Wang Junlong. Research on the Mathematical Principles in the Classics andCommentaries of the Zhouyi [M]. Beijing: People's Publishing House, 2015.
ZhangJinwen. Introduction to Axiomatic Set Theory [M]. Beijing: Science Press, 1991.
[5]David Leong (December 2020) "The Correlation Between YiJing and QuantumPhysics", p. 1. Unpublished paper uploaded to Academia.edu (December20,2020) for discussion. https://academia.edu/resource/work/4460849. RetrievedDecember 18,2025.
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UnifyingCosmology, Quantum Mechanics, and Relativity January 29, 2025.InternationalJournal of Multidisciplinary Research and PublicationsISSN (Online): 2581-6187.
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