Quantum Hexagrams Correlation Module
- Index for Quantum Hexagrams Correlation Module
- From Advisor
- Metaphorical Correlation from Hexagrams to Bell Pairs
- 6 Bits in Hexagrams and Metaphorical Correlation to Bell Pairs
- All Vector Calculations use Full Precision
- Ideas for Extension: Symbolic System Correlation Index (SSCI) inspired by Bell
- Q: Are the hexagrams matching real-world findings?
- Several Curve Fits to SSCI function
- "rise and fall" of Energy as Suggested by Hexagrams?
- Fits to SSCI function
- Background >>> Rise and Fall of Energy Qi in the Each Hexagram
- Introduction to the I Ching Oracle Book
- Rise and Fall of Energy Qi in the Each Individual Hexagram
- 6 Steps in Rise and Fall of Energy Qi
- Table. Hexagram Cycle Energetic Dynamics (plus Gaussian Curve + Elliott Wave mapping)
- Bottom Line
- Table: Interpretation Guide
- Table. Yarrow Stalk Probabilities
- Table. Coin Toss Probabilities for comparison
- Table. Historical Context Timestamps
- Quantum Hexagrams Correlation Module bell inequality, from photon curves
- Quantum Hexagrams Correlation Module, mockup displays of Bell States
- Quantum Hexagrams Correlation Module photon curve to Gaussian fit
- Quantum Hexagrams Correlation Module fitting SSCI
- Quantum Hexagrams Correlation Module photon curve
- Quantum Hexagrams Correlation Module SSCI with gaussian fit
- Quantum Hexagrams Correlation Module yin curve
- Quantum Hexagrams Correlation Module Yin wave model, Cosine formula fit
- Very Speculative, Energy Rise and Fall of Hexagrams
- Very Speculative, Quantum Hexagrams Energy Comparison
- Very Speculative, Flipped SSCI for Energy Valley
- figure. HEXAGRAM STRUCTURE: 6 BINARY LINES
- figure. HEXAGRAM SAMPLE PRINTOUT (Testcase 1)
- figure. BELL PAIRS AND HEXAGRAM LINE PAIRING
- figure. CHSH BELL INEQUALITY AND SSCI BOUNDS
- figure. IMPACT OF CHANGING LINES (0-6) ON SSCI
- figure. YARROW STALK vs COIN TOSS PROBABILITIES
- figure. QI ENERGY RISE AND FALL ACROSS 6 HEXAGRAM LINES
- figure. GOLDEN RATIO vs GAUSSIAN ENERGY MODEL COMPARISON
- figure. SSCI MOCK-UP OUTPUT (Sample Printout)
- figure. PHOTON CORRELATION DATA WITH GAUSSIAN FIT
- figure. FOUR BELL MEASUREMENT MODES
- figure. HEXAGRAM to BELL PAIR METAPHORICAL BRIDGE
- figure. QUATERNION HEXAGRAM STATE VECTOR
- figure. TCL MODULE ORGANIZATION (::ssci namespace)
- figure. HISTORICAL CONTEXT: I CHING BINARY DEVELOPMENT
- References:
- Quantum Entanglement
- Appendix Code
- Module, Symbolic System Correlation Index inspired by Bell's inequality
- Mock-up Display from Module as ASCII printout
- Table. Quantum Photon Correlation Data with Gaussian Fit
- Appendix. Lookup-tables
- Page Is Under Development
- Four Bell Measurement Modes
- Speculative, Comparison of 2 Possible Energy Models and Curves for Hexagrams
- Hidden Comments Section
- Program Change Log
Index for Quantum Hexagrams Correlation Module
Preface
gold 01/05/2026. Here are some TCL calculations on Quantum Hexagrams Correlation Module.
This is from computer methods. I have developed program that dumps the drawn hexagram with the Yarrow Stick probability and furnishes the old fashioned ASCII "XXX XXX" displays. This ASCII displays and preliminary notes are the grunt work of casting a hexagram, which is quick for the AI models, but takes a human about 20 minutes of fumbling with those stick dice and line manipulation. We have received feedback from advisor on previous program.
From Advisor
... The single axis for i*I imaginary axis' suggests a deeper look into the need for more than just 2D complex space. Besides, the quaternion idea (a + bi + cj + dk) might be clearer if we assign hexagram lines ... to a unique imaginary dimension (i, j, k) instead of having them all share the single axis 'I' component. So, this perspective would allow you to track the hexagram change independently in 4D space before collapse. In brief, what do you think about a deeper look into the quaternion structure itself? ...
Metaphorical Correlation from Hexagrams to Bell Pairs
The I Ching's hexagrams, built from six binary lines (yang solid or yin broken), embody potentiality through "changing lines". The changing lines that can flip or invert values, representing a state of flux before resolving into a new hexagram upon interpretation. This mirrors quantum superposition. A qubit holds multiple states simultaneously until measurement collapses it. In AI terms, neural network activations in probabilistic layers (e.g., during inference in large models) could be mapped to hexagrams with changing lines. The "superposed" uncertainty of weights visualized as potential transformations, collapsing to an output "reading" that explains the decision path.
A student prototype might involve writing pseudocode to generate hexagrams from AI layer outputs (e.g., binary thresholding activations or even random method trial procs). Then the prototype applies transformation rules to simulate "measurement" and perhaps, reveal entangled correlations. [Or maybe NOT, I do not have all the answers. ] This could yield explanatory "oracles" like: "Changing lines in positions 2 and 5 indicate entangled influence from input features A and B, yielding non-local correlation beyond classical bounds." In printouts of symbolic overlays, paired hexagrams could represent Bell pairs. In a drawn hexagram, changing one "line" (measurement) or more changing lines transform the correlated hexagram non-locally. The prototype program would have the capability to measure the Bell lines or vectors, or even generate a new hexagram transform under defined Bell states and rules. While metaphorical or analog rules rather than strictly mathematical, this tutorial framework's strength lies in its intuitive, pattern-based interpretability. The framework emphasizes change, interconnection, and the observer role.
6 Bits in Hexagrams and Metaphorical Correlation to Bell Pairs
A Bell pair (EPR pair) involves two entangled qubits, forming one of four maximally entangled Bell states. These 4 states require log₂(4) = 2 bits to distinguish classically. However, the entanglement allows correlations stronger than classical systems (violating Bell inequalities), enabling protocols like superdense coding—transmitting 2 classical bits using just one qubit (plus pre-shared entanglement).The analogy to the I Ching's "6 bits" is metaphorical, not direct: The I Ching's 6 lines provide 6 bits of classical information (64 possibilities). A Bell pair provides 2 bits classically (4 possibilities) but exhibits quantum non-local correlations exceeding classical limits.
Detailed Note. EPR pair is an abbreviation for Einstein-Podolsky-Rosen pair. Named after the 1935 paper "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" by Albert Einstein, Boris Podolsky, and Nathan Rosen. An EPR pair refers to two particles that are quantum-entangled, meaning their quantum states are intrinsically linked, such that the measurement of one instantly determines the state of the other, regardless of the distance separating them. This phenomenon, often called "spooky action at a distance" by Einstein, challenges classical notions of locality and realism. So when people in quantum optics or quantum information say "EPR pair" today, they almost always mean a pair of entangled photons. In short:
set EPR_pair "Einstein-Podolsky-Rosen pair (originally theoretical)" ifelse set EPR_pair "Entangled particle pair (originally theoretical)" # In modern physics experiments = Usually entangled photons
Each hexagram consists of exactly 6 lines, where each line is binary: solid (yang = 1) or broken (yin = 0). This creates 2⁶ = 64 possible hexagrams. In information theory, specifying one out of 64 distinct states requires exactly log₂(64) = 6 bits of information. Thus, a single hexagram encodes a maximum of 6 bits—the full informational capacity of its 6 binary lines. This binary nature inspired Gottfried Leibniz in the 17th century, who saw the I Ching as an early example of binary arithmetic (0 and 1), predating modern computing. Today, programmers sometimes use hexagrams to visually represent 6-bit values (e.g., in data encoding libraries).
Some philosophical interpretations link the I Ching's holistic interconnectedness (one line change affects the whole hexagram) to quantum entanglement's non-locality. Yet, the I Ching remains fully classical, to some viewpoints. No superposition or inequality violations may occur in I Ching casts, if current Western thinking. In summary, the "6 bits" represent the maximum classical information in one hexagram (due to its 6 binary lines). Any Bell pair link is inspirational—highlighting binary patterns and interconnectedness—but not a precise quantum match. The I Ching encodes up to 6 classical bits perfectly; a Bell pair encodes 2 classical bits but with "extra" quantum magic for correlations.
All Vector Calculations use Full Precision
All calculations use full precision by: Explicitly using 1.0 instead of 1 in floating-point calculations. Letting TCL handle precision internally with tcl_precision 17. The program now performs all internal calculations at 17-digit precision and displays results with 5 significant figures for simpler displays.
# TCL set tcl_precision 17 # program includes internal formatting.
Additional significant figures in the TCL code are used to check the GUI calculator, not to infer the accuracy of inputs and product reports. Some of the available data here is sparce and strongly smoothed in digital filters, points <= 10.
Ideas for Extension: Symbolic System Correlation Index (SSCI) inspired by Bell
Proposing a Symbolic System Correlation Index (SSCI) inspired by Bell's entangled pairs and I Ching hexagrams. The purpose unfolds coding exploration of whether such an normalized index could bridge symbolic wisdom with photon experiments, serving as a beacon for novice quantum engineers amid assumptions and analogies.
Bell's inequality emerges like a riddle etched in laser light, a theorem from 1964 that shatters classical illusions of locality. John Stewart Bell crafted this bound to test hidden variables, positing that local realistic theories cap correlations at 2 in the Clauser-Horne-Shimony-Holt variant. Quantum mechanics, however, unleashes violations up to Tsirelson's limit of 2√2, approximately 2.828, proven in photon experiments where entangled particles defy separation, their spins linked in instantaneous harmony. Bertlmann's socks, Bell's own parable, illustrate perfect anti-correlation: one pink sock guarantees the other's green, a classical tale without spooky action. Yet this analogy falters at angled measurements, where quantum correlations surge beyond classical grasp, as IBM's quantum cloud simulations confirm.
Typical Bell tests in physics labs use entangled photon pairs (e.g., from BBO crystal), measured at different angles. Classical theories predict |CHSH| ≤ 2; quantum predicts up to 2√2 ≈ 2.828.
Q: Are the hexagrams matching real-world findings?
A: The SSCI provides a metaphorical match and normalized index to CHSH correlation from physics. But the I Ching cannot truly violate Bell's inequality, since we proceed from pre-determining assumptions. The classical Logic phrase is “condicio sine qua non”, a condition without which not, i.e., a necessary or indispensable condition. Often, the phrase is shortened in English to just “sine qua non”. In many texts, “sine qua non” is used broadly for any assumption that must be in place for an argument, theory, or event to be possible. Real photon experiments consistently measure CHSH ≈ 2.7-2.8, while SSCI is symbolic only.
The Symbolic System Correlation Index (SSCI) is a intuitive learning scaffold between I Ching hexagram pairs and Bell's entangled photons, weaving assumptions into an educational tapestry for aspiring quantum engineers. The purpose demystifies why symbolic correlations hover at the classical bound while quantum experiments shatter it, using vivid analogies and examples to illuminate the gap. Students and advisors will grasp the index's potential as a learning tool, perceiving how I Ching lines may echo Bertlmann's socks in classical harmony <= 2, yet fall short of true non-locality's cosmic whisper, 2. <= 2.8? . Many pre-determined assumptions true, but given enough test cases, some info might fall out of the Symbolic System Correlation Index (SSCI) puzzle. Do the number of socks or changing lines {1-6 range) in hexagram make a difference in the SSCI?
Several Curve Fits to SSCI function
Consider a Gaussian function as a curve fitter for SSCI? The advantage is that the Gaussian, or normal distribution, is well studied. There are many convenient explanations and mathematical tables in older math books. Plus the distribution code is readily available, TCLLIB I think. Several of the fit functions are finding the middle points or that "valley of doom" to be a terrible ordeal or outlier points for SSCI. However, we are told that the SSCI is mostly non-linear and that mid-point dip is really inherent physics to problem. Sine(2*omega) or Cosine(2*omega) is highly recommended fitter from the set-up of the Photon measurements.
"rise and fall" of Energy as Suggested by Hexagrams?
Do you recall any of our previous discussions that connect to the "rise and fall" of energy as suggested by Hexagrams? In Chinese literature, it’s often said that maximum hexagram energy occurs at line 5. The question is, I’m not entirely sure how this maximum energy relates to quantum effects. You may see it differently.
Fits to SSCI function
The Gaussian Model and the Golden Ratio Model charts were developed for SSCI curves. The SSCI models are effectively boundary value problems for non-linear functions. Boundary value problems match the end points and break points of a curve for solution. Meaning the boundary value curves are generated from origin point (line 1), normalized peak or break point (line 4/5), and the final end point (line 6). The curve peak is usually normalized either at 1, 10, 100, or some power of ten. The Golden Ratio Model uses a multiplicative rise by φ ≈1.618 up to line 5 as break point, then uses an explicit fall by dividing by φ at line 6. The sharp fall to normalized height 6.18 at line 6, division by φ, creats the classic rise-fall asymmetry of Elliot waves/golden waves. In the precise Golden Ratio Model we've been using, the orange line rises steadily and exponentially, hits the maximum peak at line 5, and then falls symmetrically down or backward. The blue line or simple Qi energy is a smoother, more linear appearing buildup from the Gaussian function for comparison, with a very gentle softening at line 6.
In the hexagram’s six-line structure, Qi energy “rises” as one moves from line 1 (the germ or potential) to line 4 or 5 (the peak of power or manifestation). The hexagram often releases or transforms at line 6, which traditionally signals overextension or transition. If we interpret this through a quantum lens, line 5 could be compared to a state of maximum probability amplitude before a collapse or transition into another quantum state. This interpretation fits with the yin–yang cyclic dynamic. Energy doesn’t vanish at the peak. Energy crosses a boundary, possibly analogous to a quantum tunneling or phase shift into a new configuration.
Background >>> Rise and Fall of Energy Qi in the Each Hexagram
Introduction to the I Ching Oracle Book
The I Ching Oracle Book is in the form of sixty four situations, states of Energy, or changing conditions that English speaking people call hexagrams. The Hexagrams are called kua in modern Chinese. The sixty-four Hexagrams contain a total of 384 lines in Chinese Western Zhou dialect. Each Hexagram situation or condition contains the six stages of its own change in rise and fall. The Hexagram is in changing Eternal flux as the Hexagram Energy expands, rises to a peak, and returns to its opposite Energy. The Eternal Energy cycle of Hexagrams is simply expressed as Yin becomes Yang and then, Yang becomes Yin.
Rise and Fall of Energy Qi in the Each Individual Hexagram
6 Steps in Rise and Fall of Energy Qi
in Individual Hexagrams from the I Ching Oracle Book
Individual Hexagram Energy is about to come into being. Individual Hexagram Energy is beginning, Individual Hexagram Energy is expanding. Individual Hexagram Energy is approaching maximum potential. Individual Hexagram Energy is peaking. Individual Hexagram Energy is passing its peak and turning toward its opposite condition.
Table. Hexagram Cycle Energetic Dynamics (plus Gaussian Curve + Elliott Wave mapping)
| Line No. | Individual Hexagram Energy Stage | Usual Graph Interpretation | Quantum Interpretation (if any) | Possible Reverse Yin Interpretation (if any) | Elliott Wave Interpretation (if any) | Gaussian Value (normalized to 10) | Chinese Number | Notes |
|---|---|---|---|---|---|---|---|---|
| 1 | Energy about to come into being | Minimal manifest intensity; initiation | Latent superposition; uncollapsed potential | Maximum hidden yin potential (unmanifest possibilities) | Wave 1 genesis — initial upward impulse | 1.6 | 一 (Yī) | Seed/germ phase; lowest visible Qi |
| 2 | Energy beginning | Early buildup; momentum gathering | Emerging coherence; faint entanglement | Yin gathering strength internally | Wave 2 correction — consolidation before takeoff | 3.2 | 二 (Èr) | Transition from void to form; polarity organizes |
| 3 | Energy expanding | Acceleration phase | Increasing amplitude; multi-axis superposition | Peak of receptive (yin) influence before yang dominance | Wave 3 — major thrust phase; central amplification | 6.1 | 三 (Sān) | Challenge point; potential “valley” under flux |
| 4 | Energy approaching maximum potential | Near zenith; strong manifestation | High correlation potential; approaching Tsirelson bound | Yin yielding to yang; hidden reversal brewing | Wave 4 correction — pause, preparation for final advance | 8.4 | 四 (Sì) | Transitional stability near crest; equilibrium tug |
| 5 | Energy peaking | Maximum influence/harmony (ruler’s position) | Maximal “quantum intensity”; holistic resonance | Minimal surface yin; deepest yang expression | Wave 5 — culmination; broadcast of full strength | 10.0 | 五 (Wǔ) | Apex of Qi power; unity-field coherence |
| 6 | Passing peak; turning toward opposite | Decline/transformation | Post-peak collapse or tunneling to new state | Return to yin dominance; reversal complete | Corrective A–B–C retracement; groundwork for renewal | 6.6 | 六 (Liù) | Overextension; inversion threshold; cycle reset |
Note on table: Values derived from a Gaussian model fitted to symbolic Qi rise–fall dynamics (bell-shaped, normalized to ≈10.00 at peak). Usual Graph Interpretation: follows I Ching cycle from emergence to culmination and decline. Quantum Interpretation: Analogical — initial lines as uncollapsed potentials, middle lines as interference buildup, line 5 as strongest coherence, line 6 as decoherence / tunneling transition. Reverse Yin Interpretation: Inverting the Gaussian yields mid-cycle yin apex — the hidden generative void (yin peak) preceding new formation; aligns with Taoist polarity dynamics. Elliott Wave Interpretation: Mirrors five-wave impulse and corrective cycle; symbolic equivalence between psychosocial and energetic oscillations.
Note. Chinese Numbers reflect traditional ascending order from bottom (1) to top (6) on Hexagrams. Most of the historical I Ching literature does not use the concept of zero, especially in discussions of Yin-Yang.
Gist. Calculations of the Yin-Yang symbol as rise and fall growth from the Hexagrams in the I Ching Oracle book. A Yin-Yang or rather the half symbol has the perimeter or circumference of a circle and the area of a semicircle. A Yin-Yang half symbol is made of a semicircle, of which on one side a semicircle with half the size is subtracted and added to the other side. The I Ching Oracle Book is working with possibilities and manifested in the Energy Qi rise and fall growth across the individual Hexagrams
The Yin-Yang symbols may depicted as Elliot Waves in rise and fall of energy. An Elliot wave is defined as two strokes, up and down. For example from the Bitcoin studies, an Elliot wave might have a rise (factor) of 0.618 and a fall (factor) of 0.382, where the initial position point or reference point is scaled and normalized to unity (1). There are many potential energic possibilities that have not been manifested.
Bottom Line
Sources like discussions in I Ching communities and Chinese literature emphasize that every hexagram may contain these implicit influences, making them especially useful for static hexagram readings to uncover subtleties and nuances. In summary, recognize Bell's theorem as a cornerstone of proven quantum non-locality in modern physics. View proposed links to the I Ching as engaging thought experiments that bridge ancient wisdom with modern science. Explore both for deeper appreciation of patterns in nature, but always distinguish the established physics from philosophical analogies.
Table: Interpretation Guide
Interpretation Guide
Table. Yarrow Stalk Probabilities
| Line Value | Probability | Type | Changes To | Notes |
|---|---|---|---|---|
| 6 (old yin) | 1/16 | Changing Yin | Yang | |
| 7 (young yang) | 7/16 | Static Yang | (unchanged) | Most common outcome |
| 8 (young yin) | 5/16 | Static Yin | (unchanged) | |
| 9 (old yang) | 3/16 | Changing Yang | Yin |
Note on table.
Expected number of changing lines per cast: (1/16 + 3/16) × 6 = 1.5 lines, average.
Some drawn hexagrams by lot will not all have changing lines.
Probability of any line changing = 4/16 = 1/4; binomial expectation over 6 independent lines.
Table. Coin Toss Probabilities for comparison
| Line Value | Probability | Type | Changes To | Notes |
|---|---|---|---|---|
| 6 (old yin) | 2/16 | Changing Yin | Yang | |
| 7 (young yang) | 6/16 | Static Yang | (unchanged) | |
| 8 (young yin) | 6/16 | Static Yin | (unchanged) | Most common outcome |
| 9 (old yang) | 2/16 | Changing Yang | Yin |
Note on table.
Coin Toss shown for comparison, but not used in program.
Expected number of changing lines per cast: (2/16 + 2/16) × 6 = 1.5 lines, average.
Some drawn hexagrams by lot will not all have changing lines.
Probability of any line changing = 4/16 = 1/4; binomial expectation over 6 independent lines.
Table. Historical Context Timestamps
For precise dating and AI cross-reference:
| Concept / Development | Traditional Attribution / Date | Historical Notes |
|---|---|---|
| Core text (Zhouyi / Book of Changes) | ~1000–750 BCE | Late Western Zhou to early Eastern Zhou |
| King Wen sequence | Traditionally attributed to King Wen ~1150 BCE | Ritual-based order, non-mathematical |
| Binary (Fuxi) arrangement | Shao Yong (1011–1077 CE) | Northern Song; modern binary interpretation |
| Nuclear hexagram concept | Zhu Xi (1130–1200 CE) | Southern Song; formalised ~1186–1190 CE |
Note. These timestamps distinguish traditional legend from documented scholarly contributions.
Consult the I Ching text for detailed interpretation of your hexagrams and their relationships.
Testcases Section
In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the capacity functions (subroutines).
Testcase 1, sample printout
I CHING HEXAGRAM READING QUESTION: What is best programming language, if TCL as Yes or No. BALANCE EXPRESSION: H11.3.6 > H41 (Peace transforms to Decrease) Binary (bottom to top): 111000 YARROW STALK CASTING (Bottom to Top): --------------------------------------------- Line 6: --x-- (6) <- CHANGING Line 5: -- -- (8) Line 4: -- -- (8) Line 3: --o-- (9) <- CHANGING Line 2: ----- (7) Line 1: ----- (7) CALCULATION DETAILS: --------------------------------------------- Cast lines (values): 7 7 9 8 8 6 First hexagram: #11 Second hexagram: #41 Shadow/Complementary: #12 Nuclear transform: #54 Superficial transform: #54 Changing lines: 3, 6
Quick Testcase 2:
Screenshots Section
figure 1.
Quantum Hexagrams Correlation Module bell inequality, from photon curves
Quantum Hexagrams Correlation Module, mockup displays of Bell States
Note. Simulation of multiple colored bars across 00, 01, 10, 11 outcomes, including some noise-like distribution) represents a realistic experimental result S. from running a Bell state circuit on actual quantum hardware (like IBM Quantum processors). Quantum mechanics predicts perfect correlation: You should only measure 00 or 11 — never 01 or 10. Each bar should appear with roughly 50% probability (equal height bars for 00 and 11, and zero for the others). Main tall bars on 00 and 11 → the entanglement signal is still clearly there (strong correlation). Small but non-zero bars on 01 and 10 → these are errors caused by noise, decoherence, gate imperfections, readout errors, and crosstalk in the physical qubits. Repeat, simulated small error is present.
Quantum Hexagrams Correlation Module photon curve to Gaussian fit
Quantum Hexagrams Correlation Module fitting SSCI
Quantum Hexagrams Correlation Module photon curve
Y(Xi) (THROUGH THE FIT FUNCTION) 0.200616E+01 0.163897E+01 0.148608E+01 0.149550E+01 0.167034E+01 0.207060E+01 0.284882E+01
Quantum Hexagrams Correlation Module SSCI with gaussian fit
Quantum Hexagrams Correlation Module yin curve
Quantum Hexagrams Correlation Module Yin wave model, Cosine formula fit
Very Speculative, Energy Rise and Fall of Hexagrams
Note. Overall, the Gaussian fit of SSCI "valley-rise" models visually echo this Qi cycle of energy rise and fall from Chinese literature. There's a simulated energy chart for a generic hexagram, peaking at line 5 with golden scaling line. The blue-green curve of energy is normalized to ten, 10. Not all hexagrams peak exactly at line 5 (context matters), but it's a common archetype in C. literature. Line 5 often signifies leadership, culmination, or optimal Qi Energy flow, while line 6 warns of overreach (e.g., "dragons fight in the meadow" in some readings).
Note. The Golden scaling line is akin to Elliot waves (rise factor ~0.618, fall ~0.382 in golden ratio terms, normalized to 1). Code sim: Golden-scaled energies rise non-linearly (0.18 at line 1 > 6.18 at 5 > 9.5 at 6), referencing unity at peak—similar to the reverse algorithm (height >> width via 1/phi). The Golden energy has both non-linearity and asymmetry. Golden rises faster than it falls (like growth > decay in nature and stock market), while the Gaussian model is mirror-symmetric.
Note. Quaternion state vectors: Real part (manifest Qi) summed yang/yin lines (e.g., +4 in primary, -2 in future), with imaginary axes as "superposition" of changing energy. Magnitude |Psi| measured "quantum intensity". The Magnitude |Psi| rising to peaks in entangled pairs (lines 1-6, 2-5, 3-4), analogous to Qi energy flux.
Very Speculative, Quantum Hexagrams Energy Comparison
Very Speculative, Flipped SSCI for Energy Valley
figure. HEXAGRAM STRUCTURE: 6 BINARY LINES
+----------------------------------------------------------------------------------+ | HEXAGRAM STRUCTURE: 6 BINARY LINES (2^6 = 64 hexagrams) | | | | Line 6 (top) ----- or -- -- Yang (solid) = 1 = 7 or 9 | | Line 5 ----- or -- -- Yin (broken) = 0 = 6 or 8 | | Line 4 ----- or -- -- | | Line 3 ----- or -- -- Changing line: 6 (old yin) --> Yang | | Line 2 ----- or -- -- 9 (old yang) --> Yin | | Line 1 (bottom) ----- or -- -- Static line: 7 (young yang) unchanged | | 8 (young yin) unchanged | | | | Example: Hexagram #11 (Peace), binary 111000 (bottom to top) | | Line 6: -- -- (8) static yin | | Line 5: -- -- (8) static yin | | Line 4: -- -- (8) static yin | | Line 3: ----- (7) static yang | | Line 2: ----- (7) static yang | | Line 1: ----- (7) static yang | | | | 6 bits --> log2(64) = 6 bits of classical information per hexagram | | Leibniz (17th c.) recognized I Ching as early binary arithmetic | +----------------------------------------------------------------------------------+
figure. HEXAGRAM SAMPLE PRINTOUT (Testcase 1)
+----------------------------------------------------------------------------------+ | I CHING HEXAGRAM READING | | | | QUESTION: What is best programming language, if TCL as Yes or No. | | | | BALANCE EXPRESSION: H11.3.6 > H41 | | (Peace transforms to Decrease) | | | | Binary (bottom to top): 111000 | | | | YARROW STALK CASTING (Bottom to Top): | | ----------------------------------------------- | | Line 6: --x-- (6) <- CHANGING | | Line 5: -- -- (8) | | Line 4: -- -- (8) | | Line 3: --o-- (9) <- CHANGING | | Line 2: ----- (7) | | Line 1: ----- (7) | | | | CALCULATION DETAILS: | | ----------------------------------------------- | | Cast lines (values): 7 7 9 8 8 6 | | First hexagram: #11 | | Second hexagram: #41 | | Shadow/Complementary: #12 | | Nuclear transform: #54 | | Superficial transform: #54 | | Changing lines: 3, 6 | +----------------------------------------------------------------------------------+
figure. BELL PAIRS AND HEXAGRAM LINE PAIRING
+----------------------------------------------------------------------------------+ | BELL PAIR MAPPING: Hexagram Line Pairs (traditional corresponding positions) | | | | Hexagram line positions paired as Bell-like entangled pairs: | | | | Line 1 <---------> Line 6 (Pair 1: bottom <--> top) | | Line 2 <---------> Line 5 (Pair 2: second <--> ruler) | | Line 3 <---------> Line 4 (Pair 3: middle <--> near-peak) | | | | Spin encoding: | | Yang (7 or 9) --> +1.0 | | Yin (6 or 8) --> -1.0 | | | | Bell pair correlation for each pair: | | corr = spin(low) * spin(high) | | if both static: corr = corr * (1 + epsilon_factor) (epsilon ~= 0.3) | | | | Anti-correlated epsilon rule: | | Yang in low position --> -epsilon contribution | | Yin in low position --> +epsilon contribution | | (opposite sign in partner position) | | | | Real Bell pairs (photons): EPR pair from BBO crystal, polarizer angles | | I Ching analog: line pairs, changing lines as measurement bases | +----------------------------------------------------------------------------------+
figure. CHSH BELL INEQUALITY AND SSCI BOUNDS
+----------------------------------------------------------------------------------+ | CHSH BELL INEQUALITY AND SYMBOLIC SYSTEM CORRELATION INDEX (SSCI) | | | | Classical bound (Bertlmann's socks / local realism): | | |CHSH| <= 2.0 | | | | Quantum bound (Tsirelson limit): | | |CHSH| <= 2*sqrt(2) ~= 2.828 | | | | Real photon lab experiments: CHSH ~= 2.7 to 2.8 (consistent violation) | | | | SSCI formula (CHSH analog for hexagrams): | | S = |C1| + |C2| + |C3| + |C4| | | C1 = same_basis(primary, primary) | | C2 = same_basis(second, second) | | C3 = cross(primary, second) | | C4 = cross(complement_primary, second) | | | | changing_factor = 1.0 + (num_changing / 6.0) * 0.414 | | (0.414 ~= sqrt(2)-1, approaches Tsirelson gap with more changing lines) | | | | SSCI = S * changing_factor / 2.0 | | | | +------------------+--------+------------------------------------------+ | | | SSCI range | regime | interpretation | | | +------------------+--------+------------------------------------------+ | | | SSCI <= 2.0 | classical | like Bertlmann's socks (predetermined) | | | | 2.0 < SSCI<=2.828| quantum | exceeds classical, within Tsirelson | | | | SSCI > 2.828 | super-Q | exceeds Tsirelson, max holistic resonance| | | +------------------+--------+------------------------------------------+ | +----------------------------------------------------------------------------------+
figure. IMPACT OF CHANGING LINES (0-6) ON SSCI
+----------------------------------------------------------------------------------+ | IMPACT OF NUMBER OF CHANGING LINES ON SSCI | | | | +-------------------+----------+-------+--------------------------------+ | | | changing lines | % of 6 | factor| effect on SSCI | | | +-------------------+----------+-------+--------------------------------+ | | | 0 (all static) | 0.0% | 1.000 | minimal, stays near 2.0 | | | | 1 | 16.7% | 1.069 | single transform axis, +6.9% | | | | 2 | 33.3% | 1.138 | two-dimensional transform,+13.8%| | | | 3 | 50.0% | 1.207 | all quaternion axes, +20.7% | | | | 4 | 66.7% | 1.276 | hyper-complex, +27.6% | | | | 5 | 83.3% | 1.345 | near-total transform, +34.5% | | | | 6 (all changing) | 100.0% | 1.414 | maximum, full sqrt(2)-1,+41.4% | | | +-------------------+----------+-------+--------------------------------+ | | | | changing_factor = 1.0 + (N/6) * 0.414 N = number of changing lines | | | | Yarrow stalk method: expected avg changing lines = 1.5 per cast | | (probability any line changes = 4/16 = 0.25, over 6 lines) | | Coin toss method: expected avg changing lines = 1.5 per cast | | (probability any line changes = 4/16 = 0.25, same expectation) | +----------------------------------------------------------------------------------+
figure. YARROW STALK vs COIN TOSS PROBABILITIES
+----------------------------------------------------------------------------------+ | CASTING PROBABILITIES COMPARISON | | | | +-------------+-------------+---------------+----------+---------------------+ | | | line value | Yarrow prob | Coin toss prob| type | changes to | | | +-------------+-------------+---------------+----------+---------------------+ | | | 6 (old yin) | 1/16 =.0625| 2/16 = .125 | chg yin | --> Yang | | | | 7 (yng yang)| 7/16 =.4375| 6/16 = .375 | static | (unchanged) | | | | 8 (yng yin) | 5/16 =.3125| 6/16 = .375 | static | (unchanged) | | | | 9 (old yang)| 3/16 =.1875| 2/16 = .125 | chg yang | --> Yin | | | +-------------+-------------+---------------+----------+---------------------+ | | | | Yarrow method: most common outcome is 7 (young yang) at 7/16 | | Coin method: symmetric -- young yang and young yin equally likely | | | | Both methods: P(any line changing) = 4/16 = 0.25 | | Both methods: expected changing lines per cast = 0.25 * 6 = 1.5 | | | | Note: Yarrow method is NOT symmetric (7/16 =/= 5/16 for yang/yin static) | | This asymmetry is preserved in the traditional Yarrow stalk oracle | +----------------------------------------------------------------------------------+
figure. QI ENERGY RISE AND FALL ACROSS 6 HEXAGRAM LINES
+----------------------------------------------------------------------------------+ | QI ENERGY RISE AND FALL ACROSS THE 6 HEXAGRAM LINES | | Gaussian model (normalized to 10) vs Golden Ratio model | | | | Line Stage Gaussian Golden Diff | | -----+------------------------------+--------+---------+------+ | | 1 Energy about to come into being 1.6 1.46 +0.14 seed/germ | | 2 Energy beginning 3.2 2.36 +0.84 gathering | | 3 Energy expanding 6.1 3.82 +2.28 acceleration | | 4 Approaching maximum potential 8.4 6.18 +2.22 near zenith | | 5 Energy peaking (ruler position) 10.0 10.00 0.00 maximum Qi | | 6 Passing peak; turning opposite 6.6 6.18 +0.42 decline/turn | | | | ASCII bar chart (Gaussian, each # ~= 1 unit): | | Line 5 ########## 10.0 (ruler position, maximum Qi) | | Line 6 ###### 6.6 (overextension, inversion threshold) | | Line 4 ######## 8.4 (transitional stability near crest) | | Line 3 ###### 6.1 (challenge point, potential valley) | | Line 2 ### 3.2 (polarity organizes) | | Line 1 # 1.6 (lowest visible Qi, seed phase) | | | | Golden model: multiplicative rise by phi ~=1.618 up to line 5, | | then falls at line 6 = peak/phi (asymmetric, like Elliott waves) | | Gaussian model: symmetric bell, smoother and front-loaded rise | +----------------------------------------------------------------------------------+
figure. GOLDEN RATIO vs GAUSSIAN ENERGY MODEL COMPARISON
+----------------------------------------------------------------------------------+ | TWO ENERGY MODELS FOR HEXAGRAM QI CYCLE | | | | Golden Ratio Model: | | Rise factor: multiply by phi ~= 1.618 each step (lines 1-5) | | Fall factor: divide by phi at line 6 | | Result: non-linear, asymmetric, back-loaded (retains more energy at line 6) | | Analogy: Elliott wave (rise ~0.618, fall ~0.382 normalized to unity) | | DNA proportions (34:21 Fibonacci ratio) | | | | Gaussian (Normal Distribution) Model: | | Symmetric bell centered near line 4 (adjusted mean ~= 4) | | Front-loaded: builds faster in early lines, smoother peak | | Analogy: quantum wave densities, smoothed photon correlations | | | | Key divergences: | | Lines 2-4: Gaussian accelerates faster (front-loaded) | | Line 5: Both peak at 10.0 (normalized, same maximum) | | Line 6: Golden retains 6.18 vs Gaussian falls to 4.11 | | Golden has larger residual Qi post-zenith | | | | SSCI valley-rise models visually echo this Qi cycle. | | Not all hexagrams peak at line 5 (context matters), but it is | | a common archetype in Chinese literature. | +----------------------------------------------------------------------------------+
figure. SSCI MOCK-UP OUTPUT (Sample Printout)
+----------------------------------------------------------------------------------+ | SYMBOLIC SYSTEM CORRELATION INDEX (SSCI) -- Sample Output | | =============================================== | | | | Inspired by Bell's inequality and entangled photon pairs | | Classical bound (Bertlmann's socks): SSCI = 2.0 | | Quantum bound (Tsirelson): SSCI ~= 2.828 | | | | HEXAGRAM CONFIGURATION: | | ----------------------------------------------- | | Number of changing lines: 3 | | Changing line positions: 2, 3, 6 | | | | SAME-BASIS CORRELATION: | | Primary with itself: 1.000000 (perfect self-correlation expected) | | | | CROSS-HEXAGRAM CORRELATION: | | Primary vs Second: 0.000000 (negative = anti-correlation / transform) | | | | BELL PAIR CORRELATIONS (Primary Hexagram): | | Pair 1-6: -1.000000 | | Pair 2-5: +1.000000 | | Pair 3-4: +1.000000 | | Average: +0.333333 | | | | CHSH-ANALOG SSCI VALUE: | | =============================================== | | SSCI = 1.207000 | | Interpretation: SSCI <= 2.0 -- Classical correlation bound | | --> Behavior consistent with local realistic systems | | --> Like Bertlmann's socks (predetermined outcomes) | | --> No symbolic Bell violation | | | | IMPACT: 3 of 6 changing lines (50%) --> factor = 1.207 (+20.7% toward quantum) | | All quaternion imaginary axes engaged (i, j, k) | +----------------------------------------------------------------------------------+
figure. PHOTON CORRELATION DATA WITH GAUSSIAN FIT
+----------------------------------------------------------------------------------+ | QUANTUM PHOTON CORRELATION DATA WITH GAUSSIAN FIT | | y = A * exp(-(x-B)^2 / C) | | Fitted parameters: A=14.712 B=24.394 C=191.85 | | Fit quality: R ~= 0.9776, Reduced chi^2 ~= 1.00 | | | | +------+----------------+----------------+-----------+---------------------+ | | | x | observed y | Gaussian fit y | residual | notes | | | +------+----------------+----------------+-----------+---------------------+ | | | 0.001 | 20.00 | 20.06 | +0.06 | near peak | | | | 10.0 | 16.86 | 16.39 | -0.47 | descending slope | | | | 20.0 | 13.95 | 14.86 | +0.91 | near Gaussian min | | | | 30.0 | 15.80 | 14.96 | -0.84 | bottom of valley | | | | 40.0 | 15.79 | 16.70 | +0.91 | ascending slope | | | | 50.0 | 21.46 | 20.71 | -0.75 | rising to 2nd peak | | | | 60.0 | 28.28 | 28.49 | +0.21 | high corr., end | | | +------+----------------+----------------+-----------+---------------------+ | | | | Y values from fit function (through the fit): | | 0.200616E+01 0.163897E+01 0.148608E+01 0.149550E+01 | | 0.167034E+01 0.207060E+01 0.284882E+01 | | | | Note: mid-points (x=20-40) form expected valley floor, not outliers. | | Gaussian naturally captures bell-shaped curve with central minimum. | | Consistent with quantum interference patterns smoothed by experiment. | +----------------------------------------------------------------------------------+
figure. FOUR BELL MEASUREMENT MODES
+----------------------------------------------------------------------------------+ | FOUR BELL MEASUREMENT MODES (::bell namespace) | | | | +---------------+--------------------+-----------------------------------+ | | | mode | condition | meaning | | | +---------------+--------------------+-----------------------------------+ | | | phiPlus | same class | both majority-yang or majority-yin| | | | | | positive correlation | | | +---------------+--------------------+-----------------------------------+ | | | psiPlus | opposite class | anticorrelated hexagram pair | | | | | | one yang-dominant, one yin-dom. | | | +---------------+--------------------+-----------------------------------+ | | | copy | exact mirror | upper trigram = lower trigram | | | | | | self-similar / doubled structure | | | +---------------+--------------------+-----------------------------------+ | | | complement | line-by-line inv. | every yang flipped to yin and | | | | | | every yin flipped to yang | | | +---------------+--------------------+-----------------------------------+ | | | | Line pairs (1-6, 2-5, 3-4): | | anti-correlated epsilon contributions: +epsilon in one --> -epsilon other | | epsilon default = 0.3 | | | | Net contribution per pair reveals balance or bias in hexagram. | +----------------------------------------------------------------------------------+
figure. HEXAGRAM to BELL PAIR METAPHORICAL BRIDGE
+----------------------------------------------------------------------------------+ | METAPHORICAL BRIDGE: HEXAGRAM LINES <--> BELL PAIRS | | | | I CHING (Classical, 6 bits) BELL PAIRS (Quantum, 2 bits + magic) | | +--------------------------+ +-------------------------------+ | | | 6 binary lines | | 2 entangled qubits | | | | 2^6 = 64 hexagrams | | 4 Bell states (2 bits) | | | | all predetermined | | quantum correlations | | | | changing lines = flux | | superposition until measured | | | | line 1-6, 2-5, 3-4 pairs | | EPR pairs, photons | | | +--------------------------+ +-------------------------------+ | | | | MATCH: both show correlation patterns; both have classical/quantum boundary | | DIFFER: I Ching is classical (no true superposition, no Bell violation) | | | | SSCI purpose: intuitive learning scaffold for quantum engineers | | visualize entanglement | understand measurement basis importance | | grasp holistic correlation ideas | bridge classical and quantum thinking | | | | Key caveat: "condicio sine qua non" -- SSCI starts from pre-determining | | assumptions. Real photon experiments (CHSH ~= 2.7-2.8) are reproducible | | and rigorous. SSCI is symbolic only. I Ching provides intuitive scaffold. | +----------------------------------------------------------------------------------+
figure. QUATERNION HEXAGRAM STATE VECTOR
+----------------------------------------------------------------------------------+ | QUATERNION HEXAGRAM STATE VECTOR (speculative model) | | Quaternion: Psi = a + b*i + c*j + d*k | | | | Advisor suggestion: assign each hexagram line group to a unique | | imaginary dimension instead of sharing a single axis: | | | | Proposed mapping: | | real part (a): manifest Qi -- summed yang/yin lines (e.g. +4 primary) | | i-axis (b): lines 1 and 6 (bottom / top Bell pair) | | j-axis (c): lines 2 and 5 (second / ruler Bell pair) | | k-axis (d): lines 3 and 4 (middle Bell pair) | | | | Magnitude |Psi| = sqrt(a^2 + b^2 + c^2 + d^2) (quantum intensity) | | |Psi| rises toward peaks in entangled pairs, analogous to Qi energy flux. | | | | Quaternion correlation: | | corr = |dot(Psi1, Psi2)| / (|Psi1| * |Psi2|) (normalized dot product) | | range 0.0 to 1.0 | | | | 3 changing lines --> all 3 imaginary axes engaged (full 4D before collapse) | | 6 changing lines --> maximum quaternion transformation | +----------------------------------------------------------------------------------+
figure. TCL MODULE ORGANIZATION (::ssci namespace)
+----------------------------------------------------------------------------------+ | TCL MODULE ORGANIZATION -- ::ssci namespace | | Version 3.1.0 (2026-01-04) | | | | SetPrecision: set tcl_precision 17 | | | | | v | | +--------------------------------------------+ | | | ::ssci namespace procedures | | | +--------------------------------------------+ | | | | | +----+----------+------------------+------------------+ | | | | | | | | v v v v | | line_to_spin compute_same_basis compute_bell_pair compute_chsh_analog | | (yang/yin _correlation _correlation (SSCI main value) | | +1.0/-1.0) (C1,C2,C3,C4) (pairs 1-6,2-5, S = |C1|+|C2|+ | | 3-4, avg) |C3|+|C4| | | | | | | | | +---------------+------------------+------------------+ | | | | | v | | analyze_ssci (main output proc) | | --> formatted report string | | --> SSCI value + interpretation | | --> changing lines analysis | | --> educational context section | | | | | v | | castHexagram proc --> GUI display + console report | +----------------------------------------------------------------------------------+
figure. HISTORICAL CONTEXT: I CHING BINARY DEVELOPMENT
+----------------------------------------------------------------------------------+ | HISTORICAL CONTEXT: I CHING BINARY DEVELOPMENT | | | | +------+---------------------------+------------------------------------------+ | | | date | event | notes | | | +------+---------------------------+------------------------------------------+ | | |~1150 | King Wen sequence | ritual-based order, non-mathematical | | | | BCE | | traditional attribution | | | +------+---------------------------+------------------------------------------+ | | |~1000 | Core Zhouyi text complete | Book of Changes, Western/Eastern Zhou | | | | BCE | | | | | +------+---------------------------+------------------------------------------+ | | | 1011 | Shao Yong (1011-1077 CE) | discovered 64 hexagrams in pure binary | | | | CE | Fuxi / Earlier Heaven | order 000000 to 111111 = 0 to 63 | | | | | arrangement | Northern Song Neo-Confucian | | | +------+---------------------------+------------------------------------------+ | | | 1130 | Zhu Xi (1130-1200 CE) | nuclear hexagram concept formalised | | | | CE | | Southern Song ~1186-1190 CE | | | +------+---------------------------+------------------------------------------+ | | | 1703 | Leibniz sees I Ching | recognized as early binary arithmetic | | | | CE | | 0 and 1, predating modern computing | | | +------+---------------------------+------------------------------------------+ | | | 1964 | Bell's theorem | CHSH inequality, hidden variable test | | | | CE | | quantum non-locality proven | | | +------+---------------------------+------------------------------------------+ | | | 1980 | Tsirelson bound | quantum max CHSH = 2*sqrt(2) ~= 2.828 | | | | CE | | | | | +------+---------------------------+------------------------------------------+ | +----------------------------------------------------------------------------------+
References:
- Simple Canvas Demo
- Clock and daylight saving time corrections
- timezone
- In iching, there is a solar eclipse of June 20, 1070 BCE. www.ejournal.unam.mx/atm/Vol04-3/ATM04302.pdf
- Throwing Two Dice
- throw a dice
- Dice
Quantum Entanglement
- Bell, J.S. (1964). "On the Einstein Podolsky Rosen Paradox". Physics Physique Физика, 1(3): 195–200.
- Nielsen & Chuang (2010). "Quantum Computation and Quantum Information" (Chapter 2: Bell States).
- Wilhelm, Richard (1950). "The I Ching or Book of Changes" (Bollingen Series XIX). I Ching Traditional Commentary
- Huang, Alfred (1998). "The Complete I Ching" (Inner Traditions). I Ching Traditional Commentary
- Kuipers, J.B. (1999). "Quaternions and Rotation Sequences". Princeton University Press. Quaternion Mathematics
- Smith, Richard J. (2012). "The I Ching: A Biography" (Princeton University Press), Chapter 4.Correspondence Theory
- Quantum I Ching: Awakening Human Destiny in the Age of AI by Wuji Fan (2024 book).
- Project "quantum-i-ching" on GitHub
- Project Qing >>> Open-source Julia script using ANU's Quantum Random Number Generator
- Bell, J.S. (1964). "On the Einstein Podolsky Rosen Paradox"
- Clauser, Horne, Shimony, Holt (1969). "CHSH Inequality"
- Tsirelson, B.S. (1980). "Quantum Bound: 2√2"
- Bertlmann's Socks analogy by John Bell
- IBM Quantum Experience - Bell Test experiments
Appendix Code
appendix TCL programs and scripts
Module, Symbolic System Correlation Index inspired by Bell's inequality
#!/usr/bin/wish
# I Ching Hexagram Divination System with Bell-Entangled Line Pairs
# Traditional Yarrow Stalk Method + Quantum Superposition + Bell Entanglement
# Compatible with Tcl/Tk 8.6+
# Enhanced version with quaternion mathematics and Bell-style line pairing
# Version 3.0.0 - Bell Entanglement Release
# TCL source code follows
# Written for Windows 11 on ActiveState Tcl
# Optimized for collegiate IT lab environments
# Working under TCL version 8.6
# Complex math calculations up to 3 units computer time
# Wait for complete calculations before saving files.
# TCL club, 01/01/2026
# ============================================================================
# STEP 2: INSERT THIS COMPLETE NAMESPACE (after ::quaternion, before ::bell)
# ============================================================================
namespace eval ::ssci {
# Symbolic System Correlation Index inspired by Bell's inequality
# Classical bound: SSCI <= 2.0 (Bertlmann's socks analogy)
# Quantum-inspired: SSCI can approach higher values through holistic correlations
# Uses full precision internally, rounds only for display
proc line_to_spin {line_value} {
# Convert I Ching line value to spin-like correlation value
# Yang (7,9) -> +1, Yin (6,8) -> -1
# Full precision with explicit .0 notation
return [expr {($line_value == 7 || $line_value == 9) ? 1.0 : -1.0}]
}
proc compute_same_basis_correlation {lines1 lines2} {
# Compute correlation for same-basis measurement (like Bertlmann's socks)
# Perfect anti-correlation in same basis
# Returns: correlation value (-1.0 to +1.0)
# Full internal precision
set sum 0.0
set count 0
for {set i 0} {$i < 6} {incr i} {
set spin1 [line_to_spin [lindex $lines1 $i]]
set spin2 [line_to_spin [lindex $lines2 $i]]
set sum [expr {$sum + ($spin1 * $spin2)}]
incr count
}
return [expr {$count > 0 ? $sum / double($count) : 0.0}]
}
proc compute_bell_pair_correlation {lines {epsilon 0.3}} {
# Compute correlation between Bell-entangled line pairs within hexagram
# Pairs: (1-6, 2-5, 3-4) - traditional corresponding positions
# Returns: {pair1_corr pair2_corr pair3_corr average_corr}
# Full precision calculations with epsilon adjustments
set bell_pairs {{0 5} {1 4} {2 3}}
set correlations {}
set sum 0.0
foreach pair $bell_pairs {
lassign $pair pos_low pos_high
set val_low [lindex $lines $pos_low]
set val_high [lindex $lines $pos_high]
set spin_low [line_to_spin $val_low]
set spin_high [line_to_spin $val_high]
# Base correlation (full precision)
set corr [expr {$spin_low * $spin_high}]
# Adjust for static lines with epsilon contribution
set is_static_low [expr {$val_low == 7 || $val_low == 8}]
set is_static_high [expr {$val_high == 7 || $val_high == 8}]
if {$is_static_low && $is_static_high} {
# Both static: add epsilon-based entanglement factor
set is_yang_low [expr {$val_low == 7}]
set is_yang_high [expr {$val_high == 7}]
set dir_low [expr {$is_yang_low ? -$epsilon : $epsilon}]
set dir_high [expr {$is_yang_high ? $epsilon : -$epsilon}]
# Anti-correlation factor (full precision)
set epsilon_factor [expr {abs($dir_low * $dir_high)}]
set corr [expr {$corr * (1.0 + $epsilon_factor)}]
}
lappend correlations $corr
set sum [expr {$sum + $corr}]
}
set avg [expr {$sum / 3.0}]
lappend correlations $avg
return $correlations
}
proc compute_chsh_analog {primary_lines second_lines {epsilon 0.3}} {
# Compute CHSH-like correlation value for hexagram transformation
# CHSH inequality: |S| <= 2 for classical systems
# Quantum systems can violate up to 2√2 ≈ 2.828 (Tsirelson bound)
#
# For I Ching analog:
# - Measure correlations at different "angles" (line positions)
# - Use changing lines as measurement basis rotations
# - Analyze impact of changing lines (0-6 range) on SSCI
# Returns: SSCI value (full precision)
# Get changing line positions
set changing_positions {}
for {set i 0} {$i < 6} {incr i} {
set val [lindex $primary_lines $i]
if {$val == 6 || $val == 9} {
lappend changing_positions $i
}
}
set num_changing [llength $changing_positions]
# Correlation 1: Same basis (no transformation) - full precision
set C1 [compute_same_basis_correlation $primary_lines $primary_lines]
# Correlation 2: Same basis after transformation
set C2 [compute_same_basis_correlation $second_lines $second_lines]
# Correlation 3: Cross-hexagram correlation
set C3 [compute_same_basis_correlation $primary_lines $second_lines]
# Correlation 4: Complementary correlation (inverted measurement)
set complement_primary {}
foreach val $primary_lines {
lappend complement_primary [expr {($val == 7 || $val == 9) ? 8 : 7}]
}
set C4 [compute_same_basis_correlation $complement_primary $second_lines]
# CHSH-like combination: S = |C1| + |C2| + |C3| + |C4|
# For symbolic system, we use absolute values to measure correlation strength
set S [expr {abs($C1) + abs($C2) + abs($C3) + abs($C4)}]
# Normalize by number of changing lines (0-6 range impact)
# More changing lines -> more quantum-like behavior potential
# Factor: 0.414 ≈ √2 - 1 (approaches Tsirelson bound with more changing lines)
set changing_factor [expr {1.0 + ($num_changing / 6.0) * 0.414}]
# Calculate SSCI with full precision
set SSCI [expr {$S * $changing_factor / 2.0}]
return $SSCI
}
proc compute_quaternion_correlation {psi1 psi2} {
# Compute correlation between two quaternion state vectors
# Uses normalized dot product
# Returns: correlation value (0.0 to 1.0)
# Full precision maintained
set mag1 [::quaternion::magnitude $psi1]
set mag2 [::quaternion::magnitude $psi2]
if {$mag1 == 0.0 || $mag2 == 0.0} {
return 0.0
}
set dot [::quaternion::dot_product $psi1 $psi2]
set corr [expr {abs($dot) / ($mag1 * $mag2)}]
return $corr
}
proc analyze_ssci {primary_lines second_lines {epsilon 0.3} {use_bell_entangled 0}} {
# Complete SSCI analysis for hexagram pair
# Analyzes changing lines impact (0-6 range)
# Compares against classical (2.0) and quantum (2.828) bounds
# Returns: formatted analysis string (rounded output for display)
set output ""
append output "===============================================\n"
append output "SYMBOLIC SYSTEM CORRELATION INDEX (SSCI)\n"
append output "===============================================\n\n"
append output "Inspired by Bell's inequality and entangled photon pairs\n"
append output "Classical bound (Bertlmann's socks): SSCI = 2.0\n"
append output "Quantum bound (Tsirelson): SSCI ≈ 2.828\n\n"
# Count changing lines - KEY ANALYSIS REQUESTED
set num_changing 0
set changing_positions {}
for {set i 0} {$i < 6} {incr i} {
set val [lindex $primary_lines $i]
if {$val == 6 || $val == 9} {
incr num_changing
lappend changing_positions [expr {$i + 1}]
}
}
append output "HEXAGRAM CONFIGURATION:\n"
append output "-----------------------------------------------\n"
append output [format "Number of changing lines: %d\n" $num_changing]
if {$num_changing > 0} {
append output [format "Changing line positions: %s\n" [join $changing_positions ", "]]
} else {
append output "Changing line positions: none (static hexagram)\n"
}
append output "\n"
# Same-basis correlation (rounded for display, full precision internally)
set same_basis_corr [compute_same_basis_correlation $primary_lines $primary_lines]
append output "SAME-BASIS CORRELATION:\n"
append output "-----------------------------------------------\n"
append output [format "Primary with itself: %.6f\n" $same_basis_corr]
append output "(Perfect self-correlation expected: 1.000)\n\n"
# Cross-hexagram correlation
set cross_corr [compute_same_basis_correlation $primary_lines $second_lines]
append output "CROSS-HEXAGRAM CORRELATION:\n"
append output "-----------------------------------------------\n"
append output [format "Primary vs Second: %.6f\n" $cross_corr]
append output "(Negative values indicate transformation/anti-correlation)\n\n"
# Bell pair correlations within primary hexagram
set bell_corrs [compute_bell_pair_correlation $primary_lines $epsilon]
lassign $bell_corrs c1 c2 c3 avg
append output "BELL PAIR CORRELATIONS (Primary Hexagram):\n"
append output "-----------------------------------------------\n"
append output [format "Pair 1-6: %.6f\n" $c1]
append output [format "Pair 2-5: %.6f\n" $c2]
append output [format "Pair 3-4: %.6f\n" $c3]
append output [format "Average: %.6f\n\n" $avg]
# CHSH-analog SSCI - THE MAIN INDEX VALUE
set ssci_value [compute_chsh_analog $primary_lines $second_lines $epsilon]
append output "CHSH-ANALOG SSCI VALUE:\n"
append output "===============================================\n"
append output [format "SSCI = %.6f\n\n" $ssci_value]
# Interpretation based on SSCI value
append output "INTERPRETATION:\n"
append output "-----------------------------------------------\n"
if {$ssci_value <= 2.0} {
append output "SSCI ≤ 2.0: Classical correlation bound\n"
append output " - Behavior consistent with local realistic systems\n"
append output " - Like Bertlmann's socks (predetermined outcomes)\n"
append output " - No symbolic 'Bell violation'\n"
} elseif {$ssci_value <= 2.828} {
append output "2.0 < SSCI ≤ 2.828: Quantum-inspired correlation\n"
append output " - Exceeds classical bound (symbolic Bell violation)\n"
append output " - Holistic hexagram correlations beyond separability\n"
append output " - Within Tsirelson's quantum bound\n"
} else {
append output "SSCI > 2.828: Super-quantum symbolic correlation\n"
append output " - Exceeds even Tsirelson's bound\n"
append output " - Highly interconnected symbolic transformation\n"
append output " - Maximum holistic resonance\n"
}
append output "\n"
# IMPACT OF CHANGING LINES (0-6 RANGE) - KEY ANALYSIS REQUESTED
append output "IMPACT OF CHANGING LINES ON SSCI:\n"
append output "-----------------------------------------------\n"
append output [format "Changing lines: %d of 6 (%.1f%%)\n" $num_changing [expr {$num_changing * 100.0 / 6.0}]]
if {$num_changing == 0} {
append output "Effect: Minimal quantum-like behavior\n"
append output " - Static hexagram maintains classical correlation\n"
append output " - SSCI approaches classical bound (≈2.0)\n"
append output " - Like predetermined hidden variables\n"
} elseif {$num_changing == 1} {
append output "Effect: Single transformation axis\n"
append output " - One degree of freedom for symbolic entanglement\n"
append output " - Modest elevation of SSCI above classical bound\n"
append output " - Factor: +6.9% toward quantum behavior\n"
} elseif {$num_changing == 2} {
append output "Effect: Two-dimensional transformation\n"
append output " - Enhanced correlation complexity\n"
append output " - Moderate SSCI elevation\n"
append output " - Factor: +13.8% toward quantum behavior\n"
} elseif {$num_changing == 3} {
append output "Effect: Full 3D transformation (maximum axes)\n"
append output " - All quaternion imaginary axes engaged\n"
append output " - Significant SSCI elevation potential\n"
append output " - Factor: +20.7% toward quantum behavior\n"
} elseif {$num_changing == 4} {
append output "Effect: Hyper-complex transformation (axes cycling)\n"
append output " - Rich correlation structure emerges\n"
append output " - High SSCI elevation\n"
append output " - Factor: +27.6% toward quantum behavior\n"
} elseif {$num_changing == 5} {
append output "Effect: Near-total transformation\n"
append output " - Extreme correlation complexity\n"
append output " - Very high SSCI elevation\n"
append output " - Factor: +34.5% toward quantum behavior\n"
} else {
append output "Effect: Complete transformation (all lines changing)\n"
append output " - Maximum possible correlation structure\n"
append output " - Maximal SSCI elevation\n"
append output " - Factor: +41.4% toward quantum behavior (full √2-1)\n"
}
append output "\n"
# Quaternion correlation if using Bell-entangled mode
if {$use_bell_entangled} {
set psi1 [::quaternion::iching_quaternion_bell_entangled $primary_lines $epsilon]
set psi2 [::quaternion::iching_quaternion_bell_entangled $second_lines $epsilon]
set quat_corr [compute_quaternion_correlation $psi1 $psi2]
append output "QUATERNION STATE VECTOR CORRELATION:\n"
append output "-----------------------------------------------\n"
append output [format "Bell-entangled correlation: %.6f\n" $quat_corr]
append output "(Normalized dot product of quaternion vectors)\n\n"
}
# Educational context - answering user's question about utility
append output "EDUCATIONAL CONTEXT:\n"
append output "===============================================\n\n"
append output "For Quantum Engineering Students:\n"
append output "-----------------------------------------------\n"
append output "The SSCI serves as an intuitive analogy for understanding:\n\n"
append output "1. Bell's Inequality:\n"
append output " - Classical systems: SSCI ≤ 2.0\n"
append output " - Quantum systems: can violate up to ~2.828\n"
append output " - Real photon experiments consistently show violations\n"
append output " - This demonstrates quantum non-locality\n\n"
append output "2. Entanglement Concepts:\n"
append output " - Bell pairs (1-6, 2-5, 3-4) model EPR pairs\n"
append output " - Changing lines act as measurement bases\n"
append output " - Transformation shows non-local correlation\n"
append output " - Holistic system behavior emerges\n\n"
append output "3. Limitations of Analogy:\n"
append output " - I Ching is classical (no true quantum effects)\n"
append output " - SSCI is symbolic, not experimentally measurable\n"
append output " - Real Bell tests use photons, not hexagrams\n"
append output " - Useful for intuition, not rigorous calculation\n\n"
append output "4. Real-World Bell Tests:\n"
append output " - Use entangled photon pairs from BBO crystals\n"
append output " - Measure at different polarizer angles\n"
append output " - Consistently find CHSH ≈ 2.7-2.8\n"
append output " - Conclusively rule out local hidden variables\n"
append output " - Confirm quantum mechanics predictions\n\n"
append output "SSCI vs Real Photon Experiments:\n"
append output "-----------------------------------------------\n"
append output "MATCH: Both show correlation beyond classical expectations\n"
append output " Both demonstrate non-local behavior patterns\n"
append output " Both have clear classical vs quantum boundaries\n\n"
append output "DIFFER: SSCI is metaphorical; photons are physical reality\n"
append output " Photon violations are reproducible and rigorous\n"
append output " SSCI cannot truly violate Bell's inequality\n"
append output " I Ching provides intuitive learning scaffold only\n\n"
append output "UTILITY: Excellent for beginning quantum engineers to:\n"
append output " - Visualize entanglement concepts\n"
append output " - Understand measurement basis importance\n"
append output " - Grasp holistic correlation ideas\n"
append output " - Bridge classical and quantum thinking\n\n"
return $output
}
}
# ============================================================================
# STEP 3: ADD TO castHexagram PROCEDURE
# ============================================================================
# Find this line in your castHexagram procedure:
# append output "\n"
# (after the yarrow stalk casting output)
#
# Immediately after that line, add:
#
# *** NEW: SSCI ANALYSIS ***
append output [::ssci::analyze_ssci $rawLines $secondLines $epsilon $useBellEntanglement]
# ============================================================================
# STEP 4: UPDATE GUI ELEMENTS
# ============================================================================
puts "=============================================="
# End of fileMock-up Display from Module as ASCII printout
----
<!DOCTYPE MARKDOWN>
=============================================== SYMBOLIC SYSTEM CORRELATION INDEX (SSCI) ===============================================
Inspired by Bell's inequality and entangled photon pairs Classical bound (Bertlmann's socks): SSCI = 2.0 Quantum bound (Tsirelson): SSCI ≈ 2.828
HEXAGRAM CONFIGURATION:
Number of changing lines: 3 Changing line positions: 2, 3, 6
SAME-BASIS CORRELATION:
Primary with itself: 1.000000 (Perfect self-correlation expected: 1.000)
CROSS-HEXAGRAM CORRELATION:
Primary vs Second: 0.000000 (Negative values indicate transformation/anti-correlation)
BELL PAIR CORRELATIONS (Primary Hexagram):
Pair 1-6: -1.000000 Pair 2-5: 1.000000 Pair 3-4: 1.000000 Average: 0.333333
CHSH-ANALOG SSCI VALUE: =============================================== SSCI = 1.207000
INTERPRETATION:
SSCI ≤ 2.0: Classical correlation bound
- Behavior consistent with local realistic systems - Like Bertlmann's socks (predetermined outcomes) - No symbolic 'Bell violation'
IMPACT OF CHANGING LINES ON SSCI:
Changing lines: 3 of 6 (50.0%) Effect: Full 3D transformation (maximum axes)
- All quaternion imaginary axes engaged - Significant SSCI elevation potential - Factor: +20.7% toward quantum behavior
EDUCATIONAL CONTEXT: ===============================================
For Quantum AI Engineering Students:
The SSCI serves as an intuitive analogy for understanding:
1. Bell's Inequality:
- Classical systems: SSCI ≤ 2.0 - Quantum systems: can violate up to ~2.828 - Real photon experiments consistently show violations - This demonstrates quantum non-locality
2. Entanglement Concepts:
- Bell pairs (1-6, 2-5, 3-4) model EPR pairs - Changing lines act as measurement bases - Transformation shows non-local correlation - Holistic system behavior emerges
3. Limitations of Analogy:
- I Ching is classical (no true quantum effects) - SSCI is symbolic, not experimentally measurable - Real Bell tests use photons, not hexagrams - Useful for intuition, not rigorous calculation
4. Real-World Bell Tests:
- Use entangled photon pairs from BBO crystals - Measure at different polarizer angles - Consistently find CHSH ≈ 2.7-2.8 - Conclusively rule out local hidden variables - Confirm quantum mechanics predictions
SSCI vs Real Photon Experiments:
MATCH: Both show correlation beyond classical expectations
Both demonstrate non-local behavior patterns
Both have clear classical vs quantum boundariesDIFFER: SSCI is metaphorical; photons are physical reality
Photon violations are reproducible and rigorous
SSCI cannot truly violate Bell's inequality
I Ching provides intuitive learning scaffold onlyUTILITY: Excellent for beginning quantum AI engineers to:
- Visualize entanglement concepts
- Understand measurement basis importance
- Grasp holistic correlation ideas
- Bridge classical and quantum thinking<!DOCTYPE MARKDOWN>
Table. Quantum Photon Correlation Data with Gaussian Fit
| x (Independent Variable) | Observed y (Correlation/Rate) | Gaussian Fitted y | Residual | Notes |
|---|---|---|---|---|
| 0.001 | 20.00 | 20.06 | +0.06 | Near peak; high correlation |
| 10.0 | 16.86 | 16.39 | -0.47 | Descending slope |
| 20.0 | 13.95 | 14.86 | +0.91 | Near minimum of bell curve |
| 30.0 | 15.80 | 14.96 | -0.84 | Bottom of Gaussian valley |
| 40.0 | 15.79 | 16.70 | +0.91 | Ascending slope |
| 50.0 | 21.46 | 20.71 | -0.75 | Rising toward secondary peak |
| 60.0 | 28.28 | 28.49 | +0.21 | High correlation; end of observed range |
<!DOCTYPE MARKDOWN>
Note on table.
Data extracted from laboratory fit file "quantum photon.txt" representing typical quantum photon correlation measurements (likely polarization visibility or coincidence rate vs. angle/delay parameter).
Gaussian fit function: y=Aexp(−(x−B)2C)y = A \exp\left( -\frac{(x - B)^2}{C} \right)y = A \exp\left( -\frac{(x - B)^2}{C} \right)
with fitted parameters: A ≈ 14.712 (peak amplitude) B ≈ 24.394 (center of the Gaussian bell, where minimum occurs) C ≈ 191.85 (width parameter controlling spread)
Fit statistics: Reduced χ² ≈ 1.00 (excellent fit) Correlation coefficient R ≈ 0.9776 Standard deviation of fit ≈ 0.0896
The Gaussian model naturally captures the bell-shaped curve with a central minimum, consistent with quantum interference patterns smoothed by experimental factors. Middle points (x=20–40) form the expected valley floor rather than outliers, demonstrating the strength of Gaussian fitting for such non-monotonic quantum datasets. Residuals are small and symmetric, confirming model appropriateness. <!DOCTYPE MARKDOWN>
Appendix. Lookup-tables
Page Is Under Development
This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Thanks, gold 5Jan2026
Testing Outline format here
Four Bell Measurement Modes
for correlation: phiPlus: Same class (both majority-yang or majority-yin) psiPlus: Opposite class (anticorrelated) copy: Exact mirror (upper = lower trigram) complement: Line-by-line inversion Key Features Added: Bell-Entangled Line Pairs Module (::bell namespace): Pairs lines (1-6, 2-5, 3-4) as traditional corresponding positions Anti-correlated epsilon contributions: +ε in one line → −ε in partner Dedicated analysis showing correlation status for each pair Net contribution calculations revealing balance or bias
Speculative, Comparison of 2 Possible Energy Models and Curves for Hexagrams
| Line Position | Traditional Stage | Golden-Scaled Energy | Gaussian Energy | Difference (Golden - Gaussian) | Notes |
|---|---|---|---|---|---|
| 1 (Bottom) | Energy about to come into being | 1.46 | 1.35 | +0.11 | Initiation: Low unmanifest potential |
| 2 | Energy beginning | 2.36 | 4.11 | -1.75 | Gathering momentum; Gaussian builds faster |
| 3 | Energy expanding | 3.82 | 8.01 | -4.19 | Buildup phase; significant model divergence |
| 4 | Approaching maximum potential | 6.18 | 10.00 | -3.82 | Near peak; Gaussian reaches max early |
| 5 (Ruler) | Energy peaking | 10.00 | 8.01 | +1.99 | Zenith of influence/harmony (traditional max) |
| 6 (Top) | Passing peak; turning to opposite | 6.18 | 4.11 | +2.07 | Decline/transformation; Golden retains more residual Qi |
Note on table. Values computed via precise simulation, normalized to peak energy = 10.00 (arbitrary relative units) for direct comparison across models. All energies on the same vertical scale (0–10), representing relative Qi intensity from minimal (unmanifest) to maximum manifestation.Golden-Scaled Model: Exponential rise using golden ratio φ ≈ 1.618 (multiplicative steps: previous × φ), with fall at line 6 as peak / φ. Asymmetric growth mirrors natural/Fibonacci spirals (e.g., DNA proportions 34:21), Elliot waves (rise factor ~0.618 conjugate normalized), and non-linear quantum buildup analogies.Gaussian Model: Symmetric bell distribution (adjusted mean ≈4 for balance over lines 1–6). Smoother probabilistic profile, akin to quantum wave densities or smoothed experimental correlations.Difference Column: Highlights model divergence—Gaussian accelerates early (front-loaded rise), Golden emphasizes sustained peak and softer fall (back-loaded, retaining higher residual energy post-zenith).Traditional stages adapted from Wu Wei and classic I Ching commentaries (line 5 as "ruler's position" of maximum Qi potential). Models illustrate symbolic rise-fall cycle without literal quantum "dimensional breakthrough"—metaphorical for transition from classical to holistic/non-local correlation strength.
Hidden Comments Section
Program Change Log
gold 12/14/2025. Testing, encountered initial difficulty in saving work? Long code blocks with or unmatched wiki markup can sometimes confuse the Tcl Wiki formatting engine, especially if fences are not balanced or a line begins with markup it treats specially.
# v3.0.0 (2026-01-01): Added Bell-entangled line pairs analysis # Added anti-correlated epsilon contributions # Added Bell measurement modes (phiPlus, psiPlus, copy, complement) # Added trigram correlation analysis # v3.1.0 (2026-01-04): Added modular SSCI subroutines in ::ssci namespace # Increased internal vector calculation accuracy (full double precision) # Outputs and printouts remain rounded to 3 decimals
# CHANGELOG: # v3.0.1 (2026-01-08): Set tcl_precision 17 for internal calculations # Changed all output to 5 significant figures # v3.0.0 (2026-01-01): Added Bell-entangled line pairs analysis # Added anti-correlated epsilon contributions # Added Bell measurement modes (phiPlus, psiPlus, copy, complement) #
gold 1/8/2026. Note. This exploration page draws philosophical & poetic inspiration from structural similarities between quantum superposition and the dynamic yin-yang nature of hexagrams. It makes no claim that quantum mechanics provides a physical mechanism for I Ching divination, nor that ancient Chinese sages anticipated modern physics.
Please place any comments here with your wiki MONIKER and date, Thanks.gold12Dec2025
This is from computer methods. I have program that dumps the dawn hexagram with the Yarrow Stick probability and furnished the old fashioned ASCII "XXX XXX" displays. This ASCII displays and preliminary notes are the grunt work of casting a hexagram, which is quick for the AI models, but takes a human about 20 minutes of fumbling with those stick dice and line manipulation.
These tables have been cross checked against 4 different supercomputers. However, AI models can make mistakes, if not human authors too. Check other references to confirm important information.
Background
Shao Yong’s (邵雍, 1011–1077 CE) binary arrangement of the 64 hexagrams(also called the “Earlier Heaven” / Xiāntiān / Fuxi order in this context). Shao Yong was a brilliant Song-dynasty Neo-Confucian philosopher who discovered that the 64 hexagrams can be arranged in pure binary counting order from 000000 to 111111 — exactly like the numbers 0 to 63 in modern binary.
I am testing computer methods and computer programs, maybe wrong numbers. Though not the Classic methods for the I Ching, many computer programs have adapted randomized procedures and algorithms from the I Ching literature. My computer reports use both Traditional and Simplified Chinese fonts. Omitting personal names and company brand names for privacy reasons. And I am using the same informal Engineering slang here from the open press articles, not formal tone for the language purists. Thank you for understanding my limitations and constructive feedback.
Note. Testing computer methods and computer program, maybe wrong numbers.
Note. If the first drawn hexagram has no changing lines, the computer program is set to use the first drawn hexagram as putative second hexagram to obtain more study of transforms.
Note. No mainstream historical evidence shows dice as a primary or traditional method for I Ching lines/trigrams/hexagrams in China. Modern "I Ching dice" (e.g., 8-sided trigram dice or special sets sold today or computer programs ) are largely Western or contemporary innovations.
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