From Ancient Wisdom to Quaternion Group Theory:
A Scholarly Examination of Temporal Mathematics and the I Ching
The King Wen sequence of I Ching hexagrams exhibits mathematical properties that have puzzled scholars for three millennia. Its precise 3:1 ratio of even to odd transitions, systematic exclusion of five-line changes, and closure properties appearing in only 1 of 3,770 random arrangements suggest deliberate mathematical construction by ancient Chinese sages whose purposes remain unclear.
In 1971, ethnobotanist and philosopher Terence McKenna proposed that these properties encoded a temporal wave function describing the ebb and flow of "novelty" through time. From this, he and colleague Peter Meyer constructed the Timewave Zero program. While this early DOS software was ultimately found to contain arbitrary mathematical operations, McKenna's novelty theory raised profound questions about pattern recognition in ancient texts and the nature of temporal structure. But something was wrong with the mathematics. Mathematician Matthew Watkins would eventually identify an arbitrary operation at the heart of the construction, a "half-twist" that McKenna himself could not justify. What remained after the critique, however, proved more interesting than what was discarded.
In March of 2020, just as the reality of lockdowns began to set in for most of us, I had what could only be called an epiphany. I could not shake the pestering thought that someone needed to revisit the timewave, rightfully abandoned after December 2012, and examine the underlying mechanics of the I Ching that drove the theory. While my investigations into astronomical correlations and King Wen harmonic structures live in the more scholarly companion paper to this one, the following re-examination of novelty theory and the timewave calls for a more personal touch. I want to lead you, the reader, through a careful deconstruction and rebuilding of McKenna's cracked foundation.
Terence postulated that the wave terminated on December 21, 2012, in a moment of singularity that contained more novel events in its last second than have ever occurred in all of recorded history. However, that date was not derived from the pure I Ching mathematics. It was chosen first, then the algorithm retrofitted to reach it, the half-twist and other arbitrary operations torquing the wave until it landed where he wanted. Remove those operations and let the pure King Wen sequence speak for itself, and the wave still points to an unbelievable yet haunting answer.
Two independent harmonic cycles, both encoded in the sequence's structure, converge on a window between 2041 and 2046. McKenna's original vision was true all along; there has been a message hidden in the I Ching this entire time, with clear and undeniable reverberations throughout history.
Keywords: I Ching, King Wen sequence, Terence McKenna, Timewave Zero, novelty theory, Peter Meyer, Matthew Watkins, harmonic cycles, 2041
Let me be direct about what I am claiming.
A sequence of symbols arranged by Chinese sages roughly three thousand years ago contains encoded mathematical structures that point to a repeating, verifiable window in time. Terence McKenna, despite his 2012 folly, was correct that the I Ching encodes something about temporal structure. The Double Harmonic Resonance window in 2041-2046 is not retrofitting, not numerology, not pattern-matching run amok. This is reproducible mathematics with statistical significance beyond reasonable dispute.
The comfortable position would be to present this as historical curiosity, an interesting chapter in the story of mathematical speculation about ancient texts. I could trace McKenna's theory from La Chorrera to its critique, note the subsequent developments, and conclude with measured academic gestures towards a curious chapter in the history of rave culture. That would be the safe paper, the blog that has been written dozens of times already as a memorial to this psychedelic artifact. It would be an interesting X thread that might garner some traction in the algorithm.
However, if these correlations are real, if the King Wen sequence genuinely encodes astronomical cycles with precision beyond coincidence, if two independent methods both point to the same twenty-year window now fifteen to twenty years away, then we are not discussing historical curiosity, and my 'safe paper' would be lying by omission. Instead, understand that we are discussing either the most elaborate self-deception I have ever constructed, or something the human species needs to know now, and has fifteen years left to prepare for.
I do not know what happens in 2041. I want to be clear about that. The mathematics identifies a convergence point; it does not narrate what convergence means. McKenna believed the wave terminated in a moment of infinite novelty, all of history compressed into a single instant of transformation. I'm honestly still keen on this idea, with the added twist that we also come out the other end of that tunnel. Maybe the pattern describes something subtler, a threshold rather than an endpoint, a phase transition in systems we do not yet understand. I have my intuitions, shaped by faith and study.
What I can offer as a matter of concrete fact is the mathematics itself, laid bare, step by step, so you can verify or refute it yourself. This is an honest account of how McKenna built his theory, where it broke, what Watkins found, and what remains after the critique. Finally, with the help of some compatriots along the way, I present to you the work I have done since March 2020, the quaternion reimagining of the algorithm and the slow accumulation of correlations that can no longer be called coincidence.
Around 1050 BCE, according to legend, a man sat in a prison cell and arranged sixty-four symbols into a sequence that would outlast his captors, his dynasty, and nearly every other artifact of his civilization. His name was Ji Chang, though history remembers him as King Wen of Zhou. The tyrant Di Xin, last emperor of the Shang dynasty, had imprisoned him at Youli for seven years. Some accounts say Wen's eldest son was executed and served to him as meat. Now, whether this is an embellishment of the mythology or a true horror of historical fact, it serves the narrative to introduce a man facing the absolute worst that power can inflict, with nothing but time and thought, encoding something into a pattern of broken and solid lines.
Despite the tribulation King Wen faced and the duress he endured codifying the I Ching, its origin begins centuries earlier. The eight trigrams, three-line figures representing fundamental natural forces, were attributed to the mythical Fu Xi, who supposedly observed them in the patterns on a dragon-horse emerging from the Yellow River. By King Wen's time, these eight trigrams had been combined into sixty-four hexagrams, six-line figures representing every possible combination of yin and yang across six positions. With the hexagrams already defined, what is attributed to King Wen is their arrangement, the specific order in which the sixty-four figures would be transmitted to posterity.
Three distinct arrangements survived into the historical record. The Fu Xi sequence, despite bearing the mythical emperor's name, was actually created by the Song dynasty scholar Shao Yong around 1060 CE, two thousand years after King Wen. It follows pure binary progression: hexagram 1 is 000000, hexagram 2 is 000001, hexagram 3 is 000010, counting upward to hexagram 64 at 111111. This mathematical elegance so impressed Leibniz when Jesuit missionaries brought it to Europe that it directly inspired his development of binary notation, the foundation of all modern computing.
The Mawangdui sequence emerged from an archaeological dig in 1973, found on silk manuscripts in a Han dynasty tomb sealed since 168 BCE. It groups hexagrams by their upper trigrams, a practical organizational scheme for easy reference during divination.
Then there is the King Wen sequence, the canonical arrangement used in virtually every I Ching text for the past three thousand years. It organizes the sixty-four hexagrams into thirty-two pairs, with each pair related by inversion or, when a hexagram is its own inverse, by complementary opposition. This pairing structure is visible and documented. What is not visible, what traditional Chinese commentators never discussed, is the mathematical signature hidden in the transitions between consecutive hexagrams.
The Fu Xi sequence is transparent and sequential, its logic obvious to anyone who understands binary. The Mawangdui sequence is practical, its logical arrangement serving reference and retrieval. The King Wen sequence is neither transparent nor obviously practical. Its organizational principle, beyond the surface pairing rules, has never been satisfactorily explained. Either the deeper logic has been lost, or it was hidden deliberately… yet now for the first time, we can see the definitive answer lies in the numbers.
The simplest thing you can do with these sequences is count the changes between consecutive elements. Each hexagram consists of six lines, each line either broken (yin, 0) or solid (yang, 1). When you move from one hexagram to the next in the King Wen sequence, some number of lines change. This number can range from 1 (a single line flips) to 6 (every line flips). The count of changed lines between hexagram n and hexagram n+1 is called the h-value for position n. Let me show you the first sixteen h-values:
| Position | Transition | Lines Changed |
|---|---|---|
| 1 | Hex 1 → Hex 2 | 6 |
| 2 | Hex 2 → Hex 3 | 2 |
| 3 | Hex 3 → Hex 4 | 4 |
| 4 | Hex 4 → Hex 5 | 4 |
| 5 | Hex 5 → Hex 6 | 4 |
| 6 | Hex 6 → Hex 7 | 2 |
| 7 | Hex 7 → Hex 8 | 2 |
| 8 | Hex 8 → Hex 9 | 4 |
| 9 | Hex 9 → Hex 10 | 2 |
| 10 | Hex 10 → Hex 11 | 2 |
| 11 | Hex 11 → Hex 12 | 4 |
| 12 | Hex 12 → Hex 13 | 4 |
| 13 | Hex 13 → Hex 14 | 2 |
| 14 | Hex 14 → Hex 15 | 2 |
| 15 | Hex 15 → Hex 16 | 4 |
| 16 | Hex 16 → Hex 17 | 2 |
The complete sequence of sixty-four h-values sums to 214. The values cluster around 2 and 4, with occasional 1s, 3s, and 6s. Anyone can verify this, go and find any definitive source for the I Ching and the King Wen sequence, count the bit differences between consecutive hexagrams, and you will get exactly these numbers. Now, look closer at the set of values that actually appear. What's missing?
Across sixty-four transitions in the King Wen sequence, the number of changed lines is 1, 2, 3, 4, or 6. Never 5, not even once. This is actually a stunning revelation if you sit and ponder this exclusionary decision. If the sequence were arranged randomly, or arranged according to principles that did not specifically constrain line-change counts, you would expect 5-transitions to appear with roughly the same frequency as other values. There are 448 possible hexagram pairs that differ by exactly five lines. They constitute a substantial fraction of the 4,032 total possible pairings. Yet in the King Wen sequence, this entire category is systematically excluded. The probability of this occurring by chance is approximately 1 in 60. Low, but not impossible. A curious accident, perhaps?
That would be a believable conclusion, if only the anomalies stopped there. Now, let's count the h-values that are even (2, 4, 6) versus odd (1, 3). In the King Wen sequence, you will find forty-eight even values and sixteen odd values. A precise 3:1 ratio. In a random arrangement of sixty-four hexagrams, even and odd h-values distribute according to a binomial distribution with p ≈ 0.58 for even values. The probability of achieving exactly a 3:1 ratio (or more extreme) is approximately 1 in 3,770. The joint probability, combining the missing-5 constraint with the 3:1 ratio, drops below 1 in 35,000.
Now consider the closure properties. The King Wen sequence forms a mathematical loop: hexagram 64 connects back to hexagram 1 with h-value 2, maintaining the pattern. The sequence of h-values possesses specific distributional characteristics that constrain the space of possible arrangements even further. When all documented anomalies are considered together, the probability of the King Wen arrangement occurring by chance approaches 1 in 200,000.
With the odds surmounting as they are, the time has long passed where one could consider this numerology. These are straightforward statistical calculations that anyone can verify as I stated earlier. The King Wen sequence exhibits mathematical properties that do not arise by accident at any reasonable probability threshold. What we are left with are a fountain of questions, the most important question being what do the patterns mean?
Richard S. Cook spent twenty-three years studying Chinese combinatorics. His dissertation work at UC Berkeley culminated in a 660-page volume titled Classical Chinese Combinatorics, published in 2006. He was not looking for mysticism or divination, he was looking for evidence of mathematical sophistication in ancient Chinese texts. Luckily for us all, he found it.
When Cook analyzed the first-order differences of the King Wen sequence, the h-values, he discovered relationships to Fibonacci sequences and the Golden Ratio. The distribution of values, their spacing, and their cumulative sums exhibit phi-related proportions at multiple scales.
Phi, 1.618..., the Golden Ratio, appears throughout nature: in spiral galaxies and nautilus shells, in the branching of trees and the arrangement of leaves, in the proportions of the human body and the breeding patterns of rabbits. It emerges naturally from any system where growth builds upon previous growth, where the next term depends on the sum of preceding terms. The Greeks framed it in their architecture and Renaissance artists encoded it in their compositions. The Fibonacci sequence, known in India by the sixth century, encodes it in the limit of consecutive ratios.
The suggestion that ancient Chinese sages also encoded phi relationships, two millennia before Fibonacci, in a sequence of hexagram arrangements used for divination, challenges conventional assumptions about the transmission of mathematical knowledge. However, if you read my corresponding work on I Ching archaeo-astronomy and resonance harmonics, you will see that I have discovered corroborating encoded mathematics in the I Ching that similarly pushes our current understanding of its history back thousands of years. In a stunning and exhilarating detour from the timewave that took me years to unravel, I have found substantial evidence for deep embedding of these mathematical tools that fully support the findings in Classical Chinese Combinatorics.
Let's not get too ahead of ourselves right now, though. Returning to phi, Cook's work received little attention outside academic sinology. It was too technical for popular audiences, too strange for mainstream mathematics, too rigorous for the New Age crowd that typically gravitates toward I Ching mysteries. But his findings stand, and the Golden Ratio is demonstrably present in the King Wen sequence. The ancient Chinese, whoever they were and however they worked, built mathematical sophistication into their oracle that we are only now beginning to recognize.
As a Westerner, I am flabbergasted that traditional Chinese commentators, across three thousand years of scholarship, have never mentioned any of this. Not the 3:1 ratio, the missing 5 h-value, the phi relationships or my astronomy and harmonics discoveries. Either they did not notice, or they noticed and did not record it, or they recorded it and those records did not survive. Anyone familiar with the history of the Library of Alexandria would have sympathy for the last idea, especially with how tyrannical and self-immolating we understand the end of the Shang Dynasty to have been.
When I first encountered this information regarding the I Ching, back when I first heard about McKenna and Timewave Zero, it was hard for me to understand any of it. Before I knew of Carl Jung's fascination with the I Ching and it being the inspiration for his synchronicity philosophy, McKenna's claims about the I Ching sounded like exactly the kind of pattern-matching that psychedelics encourage and rigor dissolves. You take enough mushrooms, stare at an ancient text, and suddenly everything connects to everything. Before I began studying the Hebrew language in earnest, one of my favorite things to do while tripping was open my bible, blankly stare at the pages and watch the English alphabet rearrange into the Semitic original language. But the h-values are not a psychedelic vision, they are the key that unlocks every statistical wonder that exists within the King Wen sequence.
During the first months of 2020, locked down like everyone else, I finally sat down to check the claims myself. I downloaded the King Wen sequence from three independent sources to ensure I had the canonical arrangement, wrote a simple script to compute h-values, and started counting. The 3:1 ratio was there. The missing 5 was there. The closure properties were there. I checked my code, rewrote it, ran it again. Same results. These mathematical anomalies revealed themselves quickly, each one compounding my disbelief.
What I had expected to find was sloppy reasoning, confirmation bias, the usual sins of enthusiasts. Instead I found genuine statistical anomalies that had nothing to do with McKenna's interpretation of them. The numbers did not care about novelty theory or December 2012 or psychedelic revelation. The numbers simply were.
My original intent was to study calendrical drift, the slow divergence between ceremonial 360-day years and the true solar year that ancient calendar-keepers would have observed accumulating over their lifetimes. That investigation led me down a rabbit hole I never anticipated. What began as a question about McKenna's timewave became a years-long study of astronomical and harmonic encoding in the I Ching, documented in my corresponding research paper. The calendar drift correlation was real, but it was only one thread in a tapestry of encoded cycles: Saturn synodic periods, lunar nodal precession, precession sub-cycles, all woven into the 64×6 framework at statistical significance levels that defy coincidence.
Traditional Chinese scholars never interpreted these patterns temporally. McKenna did, and he built an elaborate theory on top of them, and that theory contained errors. But the patterns themselves preceded McKenna by three millennia, and they would remain objectively true after his theory was disregarded. I often wonder how Terence McKenna would have reacted to Cook's phi discoveries, or my astronomy and harmony discoveries, or Suresh Emre's quaternion work which we will discuss later. Whatever the King Wen sequence is encoding, it is real, and it has been waiting for thousands of years for someone who could solve the riddle.
I was not ready, but I was paying attention. And that, it turned out, was enough to start.
In early February 1971, five young Americans descended the Rio Putumayo into the Colombian Amazon. They were looking for a plant.
The group was led by Terence McKenna, twenty-four years old, recently returned from years of wandering through Asia and Indonesia, a fugitive from a hash-smuggling operation gone wrong, a self-educated ethnobotanist with a head full of alchemical speculation and the recent grief of his mother's death. His brother Dennis, just twenty, was the theoretician of the pair, a botany student whose letters to Terence had been filled with wild ideas about DNA, hallucinogens, and hyperspatial travel. With them traveled Ev, Terence's new lover and their Spanish translator; Vanessa, an anthropologist and old friend from Berkeley; and Dave, a gentle soul they called "the flower child," who made pottery and embroidered blue jeans and had a genealogy stretching back to a Polish count who had been friends with John Dee.
They were searching for oo-koo-he, a DMT-containing plant preparation used by the Witoto tribe and described in the ethnobotanical literature as producing visions of "little men" who taught secret knowledge. The McKenna brothers had become obsessed with DMT, the most powerful and strangest of the tryptamine hallucinogens, a compound that reliably produced contact with what Terence called "self-transforming machine elves" who spoke in visible language. They believed that somewhere in the Amazon, indigenous shamans had developed techniques for stabilizing and extending the DMT state, and that these techniques might reveal something fundamental about the nature of reality.
The journey took them first to Puerto Leguizamo, a decrepit river town where they met John Brown, a ninety-three-year-old Black American who had left the United States in 1885 and never returned. Brown had worked for the notorious House of Arana during the rubber boom, had witnessed the genocide of the Witoto people, and had later exposed the atrocities to British authorities. He knew the territory they were entering, spoke Witoto, and had taken ayahuasca at La Chorrera sixty years before. "Bye, bye, babies," he said as their boat pulled away. "Bye bye."
Five days down the river, they reached their destination: La Chorrera, a small mission settlement perched above a thundering waterfall where the Igara-Parana River crashes through a gap in ancient basalt. The Witoto villages they had come to study were largely depopulated, their inhabitants dead or scattered by decades of exploitation. The oo-koo-he preparation they sought proved impossible to obtain; local shamans were locked in a blood feud and unwilling to discuss their practices with outsiders.
What they found instead were mushrooms.
The pastures behind the mission, cleared by generations of Witoto labor, were studded with Stropharia cubensis, the same psilocybin-containing species that grows in cattle fields throughout the tropics. The McKennas had not come looking for mushrooms. But the mushrooms were there, golden-capped and abundant, and within days of their arrival the group was eating them regularly, combining them with smoked ayahuasca vine in experiments that produced what Terence called "vegetable television," cascading hallucinations triggered by each inhalation of the harmine-rich smoke.
During one of these sessions, Dennis experienced something that changed the trajectory of both brothers' lives. He began to hear a sound, a high-pitched buzzing that seemed to originate from inside his head but also somehow from everywhere at once. When he attempted to vocalize it, his body went rigid and a mechanical, droning howl emerged from his throat. The sound terrified him. "I don't want to become a giant insect," he said afterward.
But it also electrified him. Over the following days, Dennis developed an elaborate theory about what the sound might mean and what it might make possible. The theory drew on electron spin resonance, superconductivity, the structure of DNA, the beta-carboline alkaloids in ayahuasca, and the tryptamines in the mushrooms. It was dense with scientific terminology, wildly speculative, and possessed of a strange internal coherence that Terence found compelling despite his skepticism. Dennis believed he had discovered how to bond hallucinogenic molecules permanently into human DNA, creating what he called a "hyperdimensional circuit" that would grant access to all knowledge across all time. He called the process "hyper-carbolation."
The experiment was set for March 4, 1971.
That evening, after brewing ayahuasca all day over a fire of gnarled roots, the three remaining participants gathered in their small thatched hut. Dave and Vanessa, disturbed by the increasingly messianic tone of the brothers' discussions, had withdrawn to a house by the river. An enormous electrical storm had swept through earlier, and the group had taken it as an omen, though they disagreed about what kind. Dennis ate mushrooms. They all drank the ayahuasca. A living mushroom specimen sat in its manure base near a butterfly chrysalis, positioned to receive whatever energies the experiment might generate.
Three times Dennis sounded his strange, mechanical howl. Each attempt was longer and louder than the last, ending in convulsive spasms that threw him from his hammock. The final howl went on and on, rising like an electric siren over the jungle night, and when it finally died away there was silence.
Then Dennis spoke. "I saw it as a slowly rotating cylinder."
In the hours and days that followed, Dennis became convinced that the experiment had succeeded beyond all expectation. He believed he had become a kind of living antenna, capable of accessing any information in the universe. He told Terence that a telepathic wave was sweeping across the planet, that everyone on Earth could now hear a voice in their heads that would answer any question if prefaced with the word "Dennis." He expected the dead to arrive soon. He wanted to hear what Jung had to say.
Terence, swept up in the intensity of the experience, found himself believing it too. A voice in his own head seemed to answer questions. He felt reborn, weightless, certain that they had passed through some kind of omega point into a transformed reality. The brothers spent days in a state of shared psychosis, their conversations weaving between profound insight and utter madness, unable to tell which was which.
Dennis did not fully recover for weeks. He spent time in a dissociated state that alarmed everyone who witnessed it, speaking in word salad, unable to maintain coherent thought, occasionally stripping naked and running into the jungle. The group eventually made their way back to civilization, Dennis slowly stabilizing, Terence carrying with him the seeds of what would become Timewave Zero.
Because something had happened at La Chorrera. Not the DNA bonding that Dennis had theorized, not the planetary telepathic wave, not the arrival of the dead. But something. In the aftermath of the experiment, as Terence processed what he had experienced, he found himself unable to dismiss it as mere drug-induced delusion. The mushrooms had spoken to him, or something had spoken through them, and what it had spoken was an idea about time.
The idea took years to develop. Terence returned to Berkeley, then to Hawaii, carrying his experience like a splinter lodged beneath the skin. He began to study the I Ching seriously, seeing in its structure of sixty-four hexagrams a possible mathematical framework for the temporal patterns he had glimpsed. He wrote obsessively, lectured when anyone would listen, refined and elaborated until the La Chorrera revelation had become a complete cosmological system.
Whether the system was genuine insight or elaborate confabulation, whether the voice of the mushroom was real contact with some form of intelligence or merely the creative unconscious given free rein by psilocybin, whether anything meaningful had actually occurred in that jungle hut on the night of March 4, 1971, or whether two brothers had simply driven each other temporarily insane through isolation, expectation, and heroic doses of psychedelics: these questions have no definitive answers. What can be said is that Terence McKenna emerged from La Chorrera with a conviction that would shape the rest of his life. The I Ching encoded something about the structure of time. The mushrooms had shown him how to decode it. And the decoded message pointed toward an approaching moment when everything would change.
He spent the next three decades trying to prove it.
The voice that spoke to McKenna at La Chorrera did not stop speaking when he left the Amazon. Over the years that followed, as he processed the experience and studied the I Ching, a comprehensive theory of temporal structure began to emerge. He called it Novelty Theory.
The core idea was deceptively simple. Time, McKenna proposed, is not the blank container that Newtonian physics assumes, an empty stage on which events happen to occur. Time has texture. It has quality. Some moments are dense with change and innovation; others are static, repetitive, locked in pattern. These qualities are not random. They follow a wave structure that can be mapped mathematically.
McKenna framed this insight through a dialectic between two fundamental principles. Novelty is the creative tendency in reality, the force that generates the unprecedented. It appears as innovation, revolution, evolutionary leaps, the spontaneous emergence of new forms and new connections. McKenna described it as "the intrusion of the unprecedented into the expected," the pressure that makes tomorrow genuinely different from today. Habit is the conservative tendency, the force that stabilizes and repeats. It appears as tradition, routine, homeostasis, the gravitational pull of the familiar. Without habit, novelty would dissipate the moment it appeared. Without novelty, habit would crystallize into eternal stasis.
These principles do not oppose each other. They dance. Time oscillates between them in quantifiable waves, with history showing periods of rapid transformation alternating with periods of consolidation. The I Ching's sixty-four hexagrams, in McKenna's framework, represent irreducible temporal elements, fundamental configurations of the novelty-habit ratio that combine according to precise rules to produce the texture of lived experience.
What made Novelty Theory compelling to its adherents was not the abstract framework but the specific historical patterns McKenna claimed to identify. He spent countless hours in lectures working through the resonances, showing how the timewave's peaks and valleys corresponded to events that anyone could recognize.
His original anchor point was Hiroshima. The atomic bombing of August 6, 1945 represented, in McKenna's analysis, one of the most concentrated moments of novelty in human history: a fundamental transformation of humanity's relationship to matter, energy, and its own survival. When he calibrated his wave to this event and ran it backward through time, patterns emerged.
The Renaissance appeared at the same phase position as classical Greece, separated by exactly one major cycle. Both periods showed the signature of accelerating novelty: explosive creativity in art and philosophy, fundamental questioning of inherited paradigms, new technologies of communication (the printing press echoing the Greek alphabet), rediscovery of suppressed knowledge. The timewave suggested this was not coincidence but resonance, the same temporal quality expressing itself at different scales.
The fall of Rome occupied a position that rhymed with contemporary America. McKenna saw the same pattern of imperial overextension, cultural decadence, breakdown of shared meaning, influx of foreign ideas that the dominant culture could not assimilate. He was making these observations in the 1980s and 1990s, and his audiences found the parallel unsettling.
The Protestant Reformation aligned with earlier religious transformations: the emergence of Christianity from Judaism, the Axial Age upheavals that produced Buddha, Confucius, and the Greek philosophers within a few centuries of each other. Each represented a fundamental restructuring of how humans understood their relationship to the sacred.
The Black Death of the fourteenth century, which killed perhaps a third of Europe's population, appeared as a deep trough of novelty preceding the Renaissance explosion. McKenna noted that catastrophe and creativity often appeared linked in the wave structure, as if periods of destruction cleared space for unprecedented emergence.
World War I occupied a position that resonated with the collapse of Bronze Age civilization around 1200 BCE, when nearly every major Mediterranean culture fell within a few decades for reasons historians still debate. Both periods showed the signature of complex systems failing simultaneously, interconnected networks collapsing under stresses they had previously absorbed.
The 1960s, that decade of countercultural revolution and space exploration and psychedelic experimentation that had shaped McKenna's own youth, appeared as a concentrated burst of novelty comparable in intensity to the French Revolution or the year 1848 when revolutions swept across Europe. The wave suggested these events were not merely politically similar but temporally similar, expressions of the same underlying pattern at different scales.
McKenna was not naive about the problems with this approach. Historical events are subject to interpretation. What counts as "novel" depends on perspective. It would be easy to cherry-pick events that fit the wave and ignore those that did not. He acknowledged these objections but argued that the sheer number of correlations exceeded what chance would predict, that the pattern was robust enough to survive skeptical examination.
Whether he was right about this remains contested. But the exercise itself, the attempt to find mathematical structure in the flow of history, captured something that resonated with his audiences. They too felt that time was accelerating, that change was compressing, that the late twentieth century was somehow different in kind from what had come before.
This was McKenna's most controversial claim: that novelty was not merely fluctuating but accelerating over cosmic time. Each cycle compressed more change into less duration. What took billions of years in the early universe (the formation of galaxies, stars, heavy elements) took only millions of years when life emerged, thousands of years when human civilization developed, centuries during the historical period, decades in modern times. The curve was hyperbolic, approaching a vertical asymptote.
"We are like flies on the windshield of a cosmic bus hurtling toward the unknown," McKenna said. "The familiar world is being left further and further behind with each passing moment. Boundaries are dissolving, categories are collapsing, the previously distinct is merging into new synthetic unities."
This perception has since become cultural commonplace. Alvin Toffler wrote about "Future Shock" in 1970, the disorientation caused by too much change in too short a time. Ray Kurzweil documented exponential growth curves in computing, genetics, nanotechnology, robotics. The phrase "the Singularity" entered mainstream vocabulary. But McKenna was articulating this intuition in the early 1970s, before personal computers, before the internet, before the full force of acceleration became obvious to everyone. He saw it coming, or he saw it first, or he was simply projecting his own psychedelic time-distortion onto history. The jury remains out.
McKenna connected novelty intimately to consciousness. Awareness, in his view, is precisely the capacity to recognize and respond to the unprecedented. Habitual processes can operate unconsciously; we breathe and digest and maintain homeostasis without attention. But novelty demands consciousness. It is the encounter with what cannot be handled by automatic processes, what requires genuine response rather than programmed reaction.
This connection suggested that increasing novelty would correlate with expanding consciousness across cosmic time. The emergence of life from chemistry, of sensation from cellular processes, of symbolic thought from animal awareness: each represented a leap in both novelty and consciousness. McKenna speculated that this was not accident but direction, the fundamental trajectory of cosmic evolution, what Alfred North Whitehead called "the creative advance into novelty."
His most radical extension of this idea was the concept of the attractor. If novelty was accelerating toward some kind of asymptote, then perhaps the future was not merely the result of past causes but an active influence on the present. The cosmos might be not only pushed from behind but pulled from ahead. The eschaton, the omega point of maximum novelty, would exert a kind of teleological gravity, drawing history toward itself the way a drain draws water.
This notion sounds mystical, and McKenna intended it to. But he also noted that it connected to respectable philosophical traditions: Aristotle's final causes, Whitehead's process philosophy, Teilhard de Chardin's Omega Point. Even certain interpretations of quantum mechanics, the transactional interpretation and various retrocausal models, posit that future boundary conditions influence present states. McKenna's contribution was to suggest that such teleological influence might be mathematically quantifiable, encoded in the structure of an ancient Chinese oracle and extractable through proper analysis.
Whether he succeeded in that extraction is what the rest of this paper must address. But the questions he raised, whether time has inherent structure, whether the future influences the present, whether consciousness and novelty are fundamentally linked, remain philosophically significant regardless of how one judges his specific construction. He was reaching for something real, even if his grasp exceeded his reach.
The theory was one thing. The mathematics was another.
McKenna spent years after La Chorrera trying to translate what the mushroom had shown him into something reproducible, something that could be calculated and tested and shared with others who had not eaten heroic doses of psilocybin in the Colombian Amazon. The translation required precision. It required structure. And it required a foundation in the actual properties of the King Wen sequence rather than visionary assertion.
He began where Part I of this paper began: with the h-values, the first-order differences between consecutive hexagrams. When hexagram 1, all solid lines, transitions to hexagram 2, all broken lines, six lines change. When hexagram 2 transitions to hexagram 3, two lines change. The complete sequence of these transition values runs: 6, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 4, 2, 2, 4, 2... Sixty-four numbers derived from sixty-four transitions, bounded by the set {1, 2, 3, 4, 6}, conspicuously excluding 5.
These numbers were McKenna's raw material. From them he would construct everything else.
The I Ching operates at multiple scales simultaneously. A hexagram is six lines, but it is also two trigrams stacked vertically, and it is also a unified symbol with its own meaning irreducible to its components. McKenna reasoned that temporal structure should reflect this hierarchy. The wave encoding time's novelty should capture dynamics at the level of individual lines, at the level of trigrams, and at the level of complete hexagrams.
He called these the three resonance levels.
Yao resonance operates at the finest grain, the individual line. Each of the sixty-four h-values contributes directly at this level, capturing the immediate quality of transition from one hexagram to the next. This is the fastest temporal frequency, the day-to-day texture of experience.
Trigrammatic resonance operates at one-third scale, capturing the eight fundamental symbols that compose the hexagrams. Since each hexagram contains two trigrams, this level samples every third position, creating a coarser wave that tracks medium-range temporal dynamics.
Hexagrammatic resonance operates at one-sixth scale, capturing the hexagram as a complete unit. This coarsest level samples every sixth position, tracking the slowest temporal rhythms in the sequence.
McKenna weighted these levels according to their hierarchical position: 1× for yao, 3× for trigrammatic, 6× for hexagrammatic. The weights reflected the structural relationship of lines to trigrams to hexagrams within traditional I Ching interpretation. They also, McKenna noted, produced a total that was itself significant.
By combining forward and backward traversals of the sequence at each resonance level, McKenna generated a base function of 384 values. The number seemed too elegant to be coincidental.
64 hexagrams × 6 lines = 384 line positions in the complete I Ching.
29.53 days (the lunar synodic month) × 13 ≈ 383.89 days, the lunar intercalary year.
The traditional Chinese calendar operated on a 360-day base year with intercalation to maintain alignment with solar and lunar cycles. The number 384 sits precisely at the intersection of hexagram structure and calendrical mathematics.
McKenna took this convergence as evidence that the I Ching was not merely a divinatory tool but a calendrical encoding, a mathematical representation of temporal cycles observed and refined over millennia of careful attention to the sky. The ancient Chinese, whoever they were, had built astronomical precision into their oracle. The sixty-four hexagrams were not arbitrary symbols. They were temporal coordinates.
The 384-value base function became the seed from which the complete timewave would grow. But to extend that seed across all scales of time, from days to geological epochs, McKenna needed something more. He needed a principle of self-similarity. He needed fractals.
The problem was computational.
McKenna had his theory. He had his base function. But generating actual timewave values for specific dates, comparing wave positions across historical periods, testing correlations between novelty dips and major events: all of this required calculation beyond what pencil and paper could accomplish. McKenna was a humanities scholar, an ethnobotanist, a lecturer. He was not a programmer.
In the early 1980s, he found Peter Meyer.
Meyer was a software developer with an interest in the intersection of mathematics and consciousness. He had the technical skills McKenna lacked: the ability to translate conceptual frameworks into working code. Their collaboration, which would span nearly two decades, produced the software that made Timewave Zero a testable proposition rather than an untestable assertion.
Meyer formalized McKenna's construction as a doubly-infinite series. The equation is elegant:
N(x) = Σ(i=-∞ to +∞) [v(x/64^i) × 64^i]Here v(x) interpolates the 384 base values, and the sum extends over all integer powers of 64, both positive (larger scales) and negative (smaller scales). The scaling factor is 64, the number of hexagrams. Each level of the fractal reproduces the pattern of the level below at 64× magnification.
The implications unfold naturally:
| Level | Scale Factor | Duration | Historical Span |
|---|---|---|---|
| 0 | 1 | ~1 day | Daily events |
| 1 | 64 | ~64 days | Seasons, quarters |
| 2 | 4,096 | ~11.2 years | Generational shifts |
| 3 | 262,144 | ~717 years | Civilizational cycles |
| 4 | 16,777,216 | ~45,900 years | Ice ages, species evolution |
The series converges rapidly. Truncation error falls off as 64^(-k) for k terms, meaning ten to fifteen terms provide excellent accuracy across any reasonable temporal range. This computational elegance allowed Meyer to implement the timewave efficiently on the hardware of the time, generating graphs and calculations that would have taken years by hand.
In 1987, Meyer released the first version of Timewave Zero software. It ran on DOS, required minimal system resources, and allowed anyone with a personal computer to generate timewave graphs, zoom in on historical periods, and test correlations against their own understanding of events.
The software democratized the theory. Users could input any date, see its position on the wave, compare it to resonant dates at other scales. They could test McKenna's claims about the Renaissance echoing ancient Greece, about the 1960s resonating with the French Revolution, about periods of low novelty (wave peaks) corresponding to historical stagnation and high novelty (wave troughs) corresponding to transformation and upheaval.
Communities formed around these explorations. Enthusiasts traded discoveries, debated interpretations, proposed refinements. The timewave became a shared framework for thinking about temporal pattern, a language for discussing the structure of history. Whether the correlations were real or whether humans were simply seeing patterns where none existed remained contested. But the software made the question empirical rather than merely philosophical. You could look at the wave. You could check the dates. You could decide for yourself.
As users tested the theory, variants emerged. The original construction used what became known as the "Kelley" number set, named after an early collaborator. But the specific mathematical operations McKenna had applied to the h-values were not uniquely determined by I Ching structure. Different operations produced different base functions, and different base functions produced different waves.
Meyer eventually implemented several variants: the Kelley set, the Watkins set (produced by mathematician Matthew Watkins during his analysis of the algorithm), the Sheliak set (developed by John Sheliak using alternative derivation methods). Each produced a wave with the same general shape but different specific values. Each generated different correlations with historical events.
This proliferation of number sets was both a strength and a weakness. It showed that the timewave concept was robust across variations. But it also raised questions about which set, if any, corresponded to whatever temporal reality the King Wen sequence might encode. If multiple constructions produced plausible-seeming correlations, perhaps the human capacity for pattern recognition was doing the work rather than genuine mathematical structure.
McKenna acknowledged the issue without resolving it. He tended to use whichever number set produced the most compelling correlations for his lectures, which critics noted was methodologically suspect. But he maintained that the underlying insight, that the I Ching encoded temporal dynamics accessible through mathematical analysis, was independent of which specific construction proved optimal.
For McKenna, the fractal nature of the timewave explained something that poets and historians had long intuited: history rhymes without repeating. The Renaissance "felt like" ancient Greece because both occupied similar positions in their respective cycles. The digital revolution "echoed" the printing press because both represented the same phase of novelty acceleration at different scales. Events separated by centuries or millennia could share temporal character even as their specific contents differed entirely.
This was not mere metaphor but mathematical claim. The same numerical pattern appearing at Level 2 (decades) and Level 3 (centuries) would produce similar historical textures despite the 64× difference in duration. A dip in the wave at one scale would resonate with corresponding dips at other scales, creating harmonics of transformation that rippled across time.
The idea captured something real about how humans experience history. We do sense that certain periods share qualities that transcend their specific events. The Axial Age transformations across multiple civilizations, the simultaneous revolutionary fervor of 1848, the global upheavals of the 1960s: these suggest temporal patterns that escape purely local explanation. McKenna was proposing a mathematical basis for this intuition.
Whether his specific construction captured such patterns, or whether the correlations he identified were artifacts of selective attention and hindsight bias, would require rigorous analysis to determine. That analysis would come. And when it did, it would reveal problems that went deeper than anyone had anticipated.
The timewave was never meant to stand alone.
McKenna conceived it as one element in a comprehensive vision he called "the archaic revival," a return to ways of knowing that Western civilization had abandoned but never fully forgotten. The mathematics emerged from that larger project, and understanding the project explains why the mathematics mattered to him, why he pursued it despite the objections of critics, why he continued refining and defending it until his death.
The archaic revival was, at its core, a critique of modernity. McKenna believed that something had gone wrong in the transition from traditional to modern consciousness, that the scientific revolution had purchased power over nature at the cost of alienation from it. The universe described by materialist science was dead matter in meaningless motion, a cosmos of particles and forces with no room for purpose, consciousness, or intrinsic meaning. Humans were accidents of chemistry, their experiences epiphenomenal foam on a deterministic ocean.
This worldview was not, McKenna argued, a discovery forced upon us by evidence. It was a choice. And it was a choice with consequences: the ecological devastation of industrial civilization, the spiritual emptiness that no amount of consumer abundance could fill, the sense of cosmic homelessness that drove the twentieth century's epidemic of anxiety and despair.
The archaic revival proposed a different choice. What if consciousness was not an accident but fundamental? What if nature was not dead mechanism but living process? What if the wisdom traditions of pre-modern peoples, dismissed as superstition by Enlightenment rationalism, encoded genuine knowledge about reality's structure?
McKenna found evidence for these possibilities in unexpected places. Amazonian shamanism, which he studied firsthand in Colombia and Peru, demonstrated that indigenous peoples had developed sophisticated technologies of consciousness using plant medicines. Their practices were not primitive escapism but refined techniques for accessing states of awareness that Western psychology could barely describe. The information obtained in these states, about healing, about plants, about the nature of mind itself, proved reliable in ways that demanded explanation.
Medieval alchemy, usually dismissed as failed chemistry, appeared to McKenna as encoded psychology, a symbolic language for transformation processes that modern depth psychology was only beginning to articulate. The alchemists' quest for the philosopher's stone was not naive metallurgy but sophisticated exploration of consciousness, dressed in chemical metaphor to avoid persecution.
Chinese philosophy, particularly the I Ching, represented a complete alternative to Western linear causality. The Book of Changes modeled reality as process rather than substance, pattern rather than thing, relationship rather than isolated entity. Its 64 hexagrams mapped every possible configuration of yin and yang, the fundamental complementarities underlying all phenomena. That this mapping might encode temporal as well as spatial relationships was, for McKenna, entirely consistent with its underlying philosophy.
Central to McKenna's worldview was an entity he encountered repeatedly in high-dose psychedelic experiences. He called it "the Logos," borrowing the Greek term for the rational principle underlying reality.
The Logos was not a visual hallucination. It was a voice, articulate and authoritative, speaking directly to the mind in what McKenna described as "visible language," words that were simultaneously sounds and images and meanings, a form of communication that bypassed the normal channels of sensory experience. The voice taught. It explained. It offered information that McKenna claimed he could not have generated from his own knowledge.
"It's as though there were a voice speaking," he said, "only not in English or any human language. It speaks in meaning directly delivered. It teaches; it explains; it illuminates. And what it illuminates is that language is not merely human: language is the stuff of which reality is made."
This led McKenna to propose that reality is fundamentally linguistic. The cosmos is not matter arranged by physical law but "word" spoken into being by some creative principle. In the beginning was the Logos, as the Gospel of John asserts, and the Logos was with God and the Logos was God. The ancient intuition that creation occurs through speech, that words have power, that naming participates in the nature of what is named: these were not primitive confusions but accurate perceptions of something fundamental about existence.
The I Ching, in this framework, was humanity's closest approach to the cosmic syntax. Its hexagrams were not arbitrary symbols but temporal elements, the words from which historical experience is constructed. To understand their mathematics was to approach the grammar of reality itself.
McKenna believed psychedelics functioned as technologies, tools for investigating dimensions of experience that normal consciousness screens out. The common observation that time dilates under psychedelics, that minutes can feel like hours, that temporal sequence becomes fluid and rearrangeable, suggested to him that ordinary consciousness filters temporal reality in ways we mistake for objective fact.
Remove the filter, and time reveals its true nature. It becomes plastic, malleable, open to direct inspection. The patterns that govern temporal flow, invisible in everyday awareness, become perceptible to the psychedelically enhanced mind.
This explained why the timewave emerged from a psychedelic experience. McKenna did not invent the theory at La Chorrera. He perceived it. The mushrooms showed him something about time's structure, and the following decades were his attempt to translate that perception into a form others could examine without eating five grams of psilocybin in silent darkness.
That the translation proved problematic did not, in McKenna's view, invalidate the perception. A bad map does not disprove the territory. The mathematics might be flawed while the underlying insight remained valid. Someone might eventually find the right formalization, the correct way to extract the temporal encoding from the King Wen sequence. McKenna hoped he had done so. He knew he might not have. But he was convinced that the encoding was there, waiting to be properly decoded.
McKenna framed modernity as the triumph of what he called "dominator culture," a mode of social organization based on hierarchy, control, and the subordination of nature to human will. Dominator culture emerged, in his view, from the shift from gathering to agriculture, from partnership to patriarchy, from organic relationship with the land to mechanical exploitation of resources.
The scientific revolution, despite its genuine achievements, was captured by dominator values. Nature became raw material. Animals became machines. Human beings became labor units. The cosmos became a clockwork mechanism that happened, by accident, to produce creatures capable of asking why, creatures whose questions the mechanism could never answer because the mechanism was incapable of meaning.
The archaic revival proposed recovering what dominator culture had suppressed: the experience of nature as alive and sacred, the recognition that consciousness participates in rather than merely observes reality, the understanding that ancient peoples were not primitive but differently sophisticated, their wisdom complementary to rather than superseded by modern knowledge.
This was not, McKenna insisted, anti-scientific. He enthusiastically discussed quantum mechanics, chaos theory, evolutionary biology, information theory, and neuroscience. He believed science was one of humanity's great achievements. But he also believed science had been artificially narrowed by materialist assumptions that were philosophical choices, not empirical findings. A science that took consciousness seriously, that investigated psychedelic states rather than dismissing them, that engaged ancient wisdom traditions as potential sources of knowledge rather than examples of primitive error: this expanded science might discover things that current science systematically excludes.
The timewave was meant to be an example of such discovery. Ancient Chinese sages, through whatever means, had encoded knowledge about temporal structure in the King Wen sequence. Modern mathematical analysis could extract that knowledge and test it against historical evidence. If the correlations held, it would demonstrate that non-Western, pre-modern peoples had possessed genuine insight into reality's nature. The archaic revival would have its vindication.
Whatever one thinks of his ideas, Terence McKenna was a remarkable performer.
His lectures, hundreds of hours recorded at conferences and universities and alternative gatherings throughout the 1980s and 1990s, demonstrate rhetorical gifts rare in any field. He spoke without notes in elaborate sentences that wound through multiple subordinate clauses yet never lost their thread. He could sustain a two-hour improvisation, weaving together ethnobotany and quantum physics and medieval alchemy and contemporary politics, making unexpected connections that somehow felt inevitable in retrospect. He was funny, often laugh-out-loud funny, in ways that academic lecturers almost never are. And he was dead serious about ideas that most academics would have dismissed without consideration.
His voice became iconic. A distinctive nasal tone, California with hints of Colorado, that could shift from playful irony to prophetic intensity in a single phrase. He coined expressions that entered countercultural vocabulary: "the felt presence of immediate experience," "the transcendental object at the end of time," "culture is not your friend." Even listeners who doubted every claim he made found themselves wanting to hear more.
McKenna understood that he was performing. He described himself as a "mouthpiece for the incarnate Logos," which was simultaneously a grand metaphysical claim and a wry acknowledgment that something happened when he started talking that he did not fully control. The ideas seemed to speak through him. His ordinary personality, which he characterized as "rather humdrum," switched off, and something else took over. Relistening to recordings, he could see why people were fascinated, even as the fascination seemed mysterious to him.
The timewave emerged into a particular cultural context. The post-1960s generation that had experienced psychedelics was searching for frameworks that validated those experiences without abandoning intellectual rigor. The New Age movement offered spirituality but often descended into vagueness and wishful thinking. Academic science offered precision but dismissed consciousness exploration as pathology to be treated, not phenomena to be investigated. McKenna offered a third path: mysticism with mathematics, visionary experience grounded in reproducible calculations.
The approach of the millennium amplified interest in any theory that promised to explain where history was headed. Y2K anxieties mixed with genuine wonder at the emerging internet, a technology that seemed to be transforming everything faster than anyone could track. McKenna's claim that novelty was accelerating toward a singularity felt less like speculation than description. Whatever one thought of his specific predictions, the perception of acceleration was becoming universal.
The spread of personal computers enabled the theory's democratization. Peter Meyer's software allowed anyone with a PC to generate timewave graphs and test correlations for themselves. Communities formed around these explorations, trading discoveries, debating interpretations, refining and extending the analysis. The timewave became a shared framework, a language for discussing temporal structure that required no special credentials to learn. You downloaded the software, picked a date range, and looked at the wave. You decided for yourself whether the correlations were meaningful.
Academic response ranged from indifference to hostility. Sinologists pointed out that no traditional Chinese interpretation of the I Ching involved temporal mapping. Mathematicians identified problems with the construction. Historians objected to the subjective selection of "novel" events. The theory never achieved even fringe academic credibility. It was not debated in journals or addressed at conferences. It was simply ignored.
Popular response was different. McKenna's recordings circulated on cassette tapes, then CDs, then MP3s and YouTube videos, reaching new generations who had never attended his lectures. His ideas influenced electronic music, particularly the psytrance and ambient scenes that took psychedelic experience as central reference. Visual artists incorporated timewave imagery. Novelists and screenwriters borrowed concepts. The theory appeared in video games and documentaries. When the 2012 date approached, media coverage exploded, though most of it was superficial and sensationalized.
The gap between academic dismissal and popular embrace reflects something important. McKenna was asking questions that mainstream discourse systematically avoided. What is the nature of time? Why does change seem to accelerate? What did ancient peoples know that we have forgotten? How does consciousness relate to temporal experience? These questions do not become unimportant merely because one proposed answer proves inadequate.
McKenna died on April 3, 2000, twelve years before his predicted eschaton. Brain cancer, diagnosed in 1999, gave him barely a year between diagnosis and death. He was fifty-three.
He knew his theory might be wrong. In conversations toward the end of his life, he acknowledged the force of Watkins' mathematical critique, agreed that the half-twist operation was indefensible, admitted that the 2012 date might pass without visible transformation. He proposed an "autopsy" of the theory, a rigorous examination of where it had failed and why. He was more interested in understanding than in being right.
But he also maintained that something real lay behind the construction. The I Ching's mathematical anomalies were genuine, not artifacts of his analysis. The perception that time has structure, that history rhymes, that novelty accumulates toward thresholds: these intuitions predated his theory and would survive it. Someone might find the right formalization, the correct way to extract whatever the King Wen sequence encoded. He hoped it would be soon. He would not live to see it.
The theory he left behind was flawed in ways that Part III of this paper will examine in detail. But the questions he raised, and the space he opened for asking them, outlasted his specific answers. That space is where this paper operates. That space is where Timewave2 emerged. And that space remains, even now, not fully explored.
When I finally read Watkins' correspondence with McKenna, sitting in my home office in 2020 with newfound time and energy to dive into the topics I listened to Terence riff on in his lectures for years, I began to understand why the theory had wilted on the vine. Not because McKenna was a fraud, not at all, but because someone had finally done what needed doing: translated poetry into mathematics.
In 1996, British mathematician Matthew Watkins condensed McKenna's entire algorithm into a single formula. For the first time, the process that generated the timewave could be expressed in rigorous notation. No more verbal descriptions or dismissive simplifications like "take the first-order differences and apply a transformation." Just the mathematics of what Terence was attempting to formulate.
The formula looked like this:
The h[] array represents the first-order differences, the number of lines changing between consecutive hexagrams. These sixty-four values form the foundation, and everything else builds from them. The formula incorporates three resonance levels: yao at the base, trigrammatic at one-third scale, hexagrammatic at one-sixth. McKenna had described these levels in prose, and for the first time ever Watkins made them algebraic.
But the formula also exposed something troubling. Those (-1)^trunc(...) terms. Powers of negative one, creating sign-alternating patterns. They flip the contribution of each term positive or negative depending on position. In the formula, you will see it is every 32 steps for the yao resonance, every 96 for the trigrammatic, and every 192 for the hexagrammatic. Where did these patterns come from? It was not from any apparent observations from the I Ching.
Watkin's visualization of the formula was not the first time this problem was discovered, however. We need to go back two more years in fact, to find the origin of when this argument started. In 1994, while attempting to reproduce the timewave algorithm from first principles, Meyer discovered that the published methodology in The Invisible Landscape could not generate the actual values in the book's appendix. An operation existed in the calculations that McKenna had never documented.
Meyer called it the "half-twist." The sign-alternating patterns that Watkins would later formalize. Every 32 positions, every 96, every 192, the algorithm flipped signs according to a rule that appeared nowhere in McKenna's explanation of the theory.
Meyer noted this in his software manual with characteristic understatement:
"This is the mysterious 'half twist'. The reason for this is not well understood at present and is a question which awaits further research."
— Peter Meyer, Timewave Zero Software Manual (1994)
Meyer's word choice here denotes perhaps his admiration for the pedestal Terence had constructed for himself by 1996. "Not well understood", "a question awaiting research"; Meyer was being very kind and diplomatic in his critique. Ultimately, after lengthy discourse with Terence, he found the half-twist had no derivation or source for extraction from the I Ching. It was simply there, doing something to the output that McKenna apparently wanted done.
For two years, this observation sat in technical documentation, noticed by few. Then Watkins formalized the algorithm, and then the "half-twist" debate erupted once more. Those powers of negative one, alternating signs at specific intervals, stood out in the equation like a scar. They demanded justification, though none existed.
In January 1996, Watkins traveled to Palenque, Mexico, where McKenna was lecturing at the classic Maya archaeological site. Over the course of a week, they had four lengthy discussions. Watkins walked McKenna through the mathematics step by step. By the final conversation, McKenna seemed to grasp the problem completely.
His response surprised Watkins.
"I couldn't remember why this step was included... It appears to have no basis in rational thought."
— Terence McKenna, Palenque, January 1996
No basis in rational thought? McKenna, who had spent two decades promoting Timewave Zero, who had built a career on novelty theory, who had predicted the end of history, admitted to a mathematician that the core operation in his algorithm was unjustifiable.
In my opinion, this was not the response of a charlatan. A fraud would have defended, deflected, mystified, and McKenna did none of these. He proposed instead that they collaborate on a paper he provisionally titled "Autopsy for a Mathematical Hallucination." They would dissect the theory together, determine what had gone wrong, and publish the findings.
Unfortunately, that collaboration never had the time necessary to bear fruit. McKenna returned to lecturing, caught up in the hysteria of rave culture and spearheading the neo-psychedelic techno-pagan movement. Four short years later he was dead. The autopsy for Timewave Zero remained unwritten.
But his willingness to engage with his critics stands out, and ultimately is what led to our ability today to see the Timewave clearly. When confronted with proof that his algorithm was flawed, he admitted error, and he proposed investigation. He demonstrated intellectual honesty rare among those who claim prophetic insight, one of the many admirable characteristics of Terence that made it easy for me to revisit his lectures even past 2012, readily on display here.
Watkins identified five fundamental problems with Timewave Zero. Together they constituted a mathematical death certificate.
The unexplained operation. The half-twist has no derivation from the I Ching, group theory, or any other mathematical principle. It was inserted to make the output look right. This alone should have been fatal. In mathematics, operations require justification. "It works" is not justification.
Violation of fractal properties. McKenna claimed the timewave was fractal, self-similar at all scales. For a function to be truly fractal, it must satisfy f(x) = f(ax). The position-dependent sign changes break this property. The timewave is not, in the technical sense, a fractal at all. The central claim was false.
Non-preservation of geometry. McKenna argued that the half-twist "preserved geometric relationships" between hexagrams. Watkins proved mathematically that it distorted rather than preserved these relationships. The justification McKenna offered was not merely weak. It was backwards.
Post-hoc fitting. The December 21, 2012 date was not calculated from the mathematics. It was selected first, chosen to give the timewave the "best possible fit" with McKenna's subjective interpretation of historical novelty. When he later discovered the Mayan Long Count calendar ended on the same date, he adjusted his wave to match. This is textbook confirmation bias. You do not get to pick your endpoint and then claim the mathematics predicted it.
Irreproducibility. The published methodology in The Invisible Landscape could not reproduce the actual values in the appendix. Something was happening in the calculations that McKenna never documented. Meyer found it. Watkins formalized it. The theory had been, from the beginning, incompletely specified.
Five problems. Any one of them would have been serious. Together they were conclusive.
The theory, as McKenna had constructed it, could not be salvaged by minor repairs. The foundation was compromised. And yet people tried.
The community fractured into competing interpretations.
The original 384 numbers from The Invisible Landscape, incorporating the unexplained half-twist, became known as the Kelley set, named after Royce Kelley, one of the original collaborators who helped with early calculations. This was the canonical version, the one McKenna had promoted for two decades.
In 1994, Peter Meyer created an alternative. He removed the half-twist operation entirely, generating a mathematically consistent but different set of values. He named it the Watkins set, a gesture of acknowledgment toward the critic who had identified the problem. The gesture was generous. The result was another number set with no stronger claim to truth than the original.
In November 1997, McKenna announced a "bombshell" on his website. Mathematician John Sheliak had succeeded in formalizing the construction using vector algebra. A single mathematical formula could now generate all 384 numbers. McKenna called it "Timewave One" and claimed it showed better historical correlation than the original.
The claim suffered from the same disease. Better correlation with what? With McKenna's subjective assessment of which historical periods were "novel." The vector algebra was real mathematics. The validation remained circular.
A fourth set emerged in 1998, the Huang Ti set, with minimal documentation of its derivation.
Four number sets. Four different timewaves. Four communities of believers, each convinced their version was correct. None of them addressed the fundamental problem: every version still required choosing an endpoint, then fitting the wave to reach it.
The software evolved across platforms. FORTRAN in 1975, largely illegible. Applesoft BASIC in 1978. MS-DOS in 1989, Peter Meyer's authoritative implementation. Windows versions through the late 1990s. The code improved. The mathematics did not.
By the late 2000s, the community had calcified. Debates about which number set was correct replaced investigation of whether any number set was meaningful. The theory had become an artifact, defended out of loyalty rather than examined with rigor.
All eyes turned toward December 21, 2012.
McKenna had selected that date before discovering the Mayan calendar connection. He had adjusted his wave to land there. He had predicted that novelty would reach infinite density, that history would end, that reality itself would transform. The date would settle everything. If something happened, the theory survived its mathematical problems through sheer empirical vindication. If nothing happened, no amount of reformulation would matter.
The test was coming. McKenna would not live to see it.
The date arrived. Winter solstice. The Mayan Long Count rolling over to a new cycle. Expectations ranged from apocalypse to transcendence to mass consciousness shift. The timewave community had waited decades for this moment. McKenna had been dead for twelve years. His prediction outlived him.
Nothing happened.
No eschaton. No infinite novelty. No transformation of reality. December 21, 2012 passed like any other Friday. The sun rose and set. Traffic moved. Markets traded. History continued its ordinary unfolding without apparent interruption.
The faithful rationalized. "Subtle consciousness shifts" became the explanation. "Dimensional transitions" that could not be measured. "The beginning of a process rather than a singular event." Each revision retreated further from falsifiability. McKenna had predicted the end of history, the compression of all novelty into a single instant. When that did not occur, his supporters redefined what he had meant until the prediction could not fail because it no longer predicted anything.
Peter Meyer, who had spent more than a decade implementing and documenting the timewave software, acknowledged publicly what the mathematics had already demonstrated. No evidence supported any particular zero date. The endpoint had been selected, not calculated. The theory, as constructed, was arbitrary.
The 2012 failure confirmed empirically what Watkins had proven mathematically sixteen years earlier. The algorithm contained unjustifiable operations. The endpoint was retrofitted. The fractal claims were false. December 21, 2012 was not a discovery but a choice, and reality did not cooperate with the choice.
I was twenty-three that year, finishing a degree, not yet working in the schools, not yet married, not yet a father. I had encountered McKenna's ideas in high school and found them interesting in the way that strange theories are interesting when you are young and everything seems possible. I had not invested belief. When the date passed without transformation, I felt no disappointment. Just a vague sense that something I had once found curious had been weighed and found wanting.
I did not know then that I would spend years with the ruins of this theory, or that the ruins contained something worth excavating. That would come later, in a different lockdown, with different stakes.
For now, Timewave Zero was dead. The question was whether anything could be salvaged from the wreckage.
The algorithm died. The mathematical properties did not.
This distinction matters. McKenna built an arbitrary construction on top of something real. Demolishing his construction did not demolish what lay beneath it.
The King Wen sequence is mathematically non-random. This is not interpretation. It is statistical fact. The 3:1 ratio of even to odd h-values occurs in approximately 1 of 3,770 random arrangements. The systematic exclusion of five-line transitions adds another layer of improbability. The closure properties, the phi relationships Cook identified, the structural constraints that survive every test: these are not artifacts of McKenna's algorithm. They exist in the sequence itself, placed there three thousand years ago by hands we cannot identify for purposes we do not understand.
The 24,576-day cycle has astronomical significance. Sixty-four hexagrams times 384 lines yields 67.29 years. This period correlates with Saturn synodic cycles, lunar node precession, calendar drift patterns. The correlations are not approximate. They are precise to multiple decimal places, significant at levels that would satisfy any reasonable statistical threshold. McKenna did not invent these relationships. He noticed them. His interpretation was wrong. His observation was not.
The h-value structure encodes something intentional. The missing 5, the ratio constraints, the specific distribution: these do not emerge from randomness or from simple organizational principles. Someone designed this sequence to have these properties. Traditional Chinese commentary never mentions them. Modern analysis cannot explain them. They simply are, waiting for an explanation that has not yet arrived.
McKenna's error was not in asking whether the I Ching encoded temporal patterns. His error was constructing an arbitrary method to extract them, then defending the method past the point where its arbitrariness became undeniable. The question he asked remained open. Only his specific answer was discredited.
The ruins of Timewave Zero contained genuine artifacts. The 3:1 ratio. The astronomical correlations. The h-value constraints. The phi signatures. These survived the critique because they were never products of the critique's target. They preceded McKenna. They would outlast him.
Someone could approach them differently. Someone who did not assume McKenna's method was correct. Someone willing to strip away the arbitrary operations and let the pure sequence speak. Someone who would ask not "how do I fix the half-twist" but "what happens if I remove it entirely."
The pattern was real. The method was wrong. And the correct method was waiting.
I came to the I Ching through calendar research, not through McKenna.
I had been studying the 360-day prophetic year in Daniel and Revelation. The Babylonians used it. The Egyptians used it. Twelve months of thirty days, slightly short of solar reality. The question was simple: why would multiple ancient cultures use an inaccurate calendar? The obvious answer is that it wasn't always inaccurate, or that they were tracking cycles we no longer recognize. Calendrical drift. The slow accumulation of error that forces reforms. The pattern of adjustments points backward toward different astronomical conditions.
In footnotes on ancient Chinese astronomy, someone mentioned the King Wen sequence. 64 hexagrams, 384 lines, a period of 24,576 days correlating with Saturn synodics and lunar node precession. I noted it and moved on.
COVID gave me time to go back.
March 2020. Schools scrambling online. My wife pregnant. I was monitoring hospital networks by day and had nothing to do by night except follow threads. The 24,576-day period kept appearing in different sources with different derivations. I wrote a script to check the King Wen h-values myself. The 3:1 ratio was there. The missing 5 was there. I rewrote the script assuming error. Same results.
McKenna had seen this. His method was flawed, but his observation was correct. The sequence was non-random at probability thresholds that eliminated coincidence. Nobody had examined it seriously since 2012.
I spent two months trying to fix the half-twist, assuming McKenna had the right idea with wrong implementation. Every approach broke the pattern worse. I was debugging code that could not be debugged because the operation itself was the bug.
Then I found Emre.
Dr. Suresh Emre's paper appeared on December 31, 2011, published on his blog at Renaissance Universal. He had worked at Fermilab and the Superconducting Super Collider. He was not investigating McKenna or the timewave. He was studying the I Ching from the perspective of group theory when he found something that should have changed everything.
The eight trigrams of the I Ching map directly onto the eight elements of the Q8 quaternion group.
Q8 consists of eight elements: {1, −1, i, −i, j, −j, k, −k}. These are not arbitrary symbols. Quaternions were discovered by Hamilton in 1843 and later found to be fundamental to physics. The Pauli spin matrices, which describe electron behavior in quantum mechanics, are quaternion-based. SU(2), the symmetry group governing spin-½ particles, contains Q8 as a subgroup. When physicists describe how particles rotate and interact at the quantum level, they use this mathematics.
Emre discovered that the trigram-quaternion mapping preserves the I Ching's core structure:
| Trigram | Symbol | Name | Binary | Q8 Element |
|---|---|---|---|---|
| Earth | ☷ | KUN | 000 | 1 |
| Wind | ☴ | XUN | 110 | i |
| Fire | ☲ | LI | 101 | j |
| Lake | ☱ | DUI | 011 | k |
| Heaven | ☰ | QIAN | 111 | −1 |
| Thunder | ☳ | ZHEN | 001 | −i |
| Water | ☵ | KAN | 010 | −j |
| Mountain | ☶ | GEN | 100 | −k |
The opposition-negation structure is exact. Earth (pure yin, 000) maps to 1; Heaven (pure yang, 111) maps to −1. Wind maps to i; Thunder maps to −i. Fire maps to j; Water maps to −j. Lake maps to k; Mountain maps to −k. The ancient Chinese concept of complementary opposites translates directly into algebraic negation.
This matters because Q8 multiplication is non-commutative. Order matters: ij = k, but ji = −k. In temporal processes, sequence affects outcome. In quantum mechanics, measurement order determines results. The I Ching's insistence that the order of trigrams within a hexagram carries meaning has a precise mathematical correlate.
Each hexagram consists of two trigrams, upper and lower. Under Emre's mapping, each hexagram corresponds to a Q8 product:
Hexagram = Q8(upper trigram) × Q8(lower trigram)
Eight elements multiplied by eight elements yields exactly 64 products. 64 hexagrams. The correspondence is not approximate. It is algebraically exact.
Q8 is not an arbitrary mathematical structure. It is fundamental to physics. The group is isomorphic to a subgroup of SU(2), the symmetry group governing spin-½ particles. The Pauli spin matrices, discovered in 1927 and foundational to quantum mechanics, are quaternion-based. When Wolfgang Pauli formalized electron spin, he employed the same mathematical structure encoded in the I Ching three millennia earlier. Fields Medalist Michael Atiyah, in discussions with loop quantum gravity pioneer Carlo Rovelli, identified SU(2) as "a fundamental building block of the universe."
Q8 also has algebraic closure: operations within Q8 stay within Q8. No infinities, no undefined results. The system is mathematically complete. Once the trigram-element mapping is established, all subsequent operations are determined by the group structure. Nothing is added post-hoc.
I found Emre's paper in June 2020. The McKenna community had ignored it entirely. The timewave discussion forums, such as they still existed, showed no mention. A physicist had published a rigorous mathematical correspondence between the I Ching and the quaternion group that underlies quantum mechanics, and nobody working on the timewave had noticed.
The implications took weeks to process. McKenna's half-twist was an arbitrary operation inserted to shape the output. Q8 multiplication is not arbitrary. It follows necessarily from the group structure. If hexagrams are quaternion products, then transformations between hexagrams are quaternion operations, and those operations are determined by mathematics, not by preference.
I stopped trying to fix the half-twist. The question changed. What happens if I remove it entirely and use Q8 transformations instead?
The answer came in stages.
First, I rebuilt the foundation. Instead of McKenna's first-order differences fed through arbitrary sign alternations, I computed Q8 products for each hexagram pair in the King Wen sequence. The transformation from hexagram n to hexagram n+1 became a quaternion operation with defined algebraic properties.
The three resonance levels McKenna identified, yao, trigrammatic, and hexagrammatic, emerged naturally from the Q8 structure rather than being imposed through position-dependent sign changes. Yao resonance operates at the line level. Trigrammatic resonance operates at one-third scale, reflecting the three-line structure of trigrams. Hexagrammatic resonance operates at one-sixth scale, reflecting the six-line structure of hexagrams. In McKenna's algorithm, these scales were weighted by arbitrary coefficients. In the Q8 approach, they derive from the group's internal hierarchy. The quaternion norm ||q|| = √(w² + x² + y² + z²) provides natural scalar extraction, replacing McKenna's arbitrary sign alternations with algebraically determined values.
The base values themselves required careful construction. For each position k in the 384-number sequence, the algorithm computes a value from the h-values using forward and backward differences: take the h-value at position k−1, subtract the h-value at k−2, then add the h-value at the mirror position −k, and subtract the h-value at 1−k. All indices wrap modulo 64, creating a closed system where the sequence folds back on itself. This bidirectional differencing captures both the forward flow of the King Wen sequence and its reflection, encoding temporal symmetry into the base function.
The complete transformation combines these elements. For each of the 384 positions: map the position to its King Wen hexagram, decompose into upper and lower trigrams, convert each trigram to its Q8 element via Emre's correspondence, multiply to get the hexagram's Q8 product, then weight by the triangular coefficients 1, 3, and 6 at the three resonance scales. The quaternion norm extracts the final scalar. No arbitrary signs. No position-dependent flips. Just group theory applied to ancient structure.
Second, I removed the half-twist completely. No sign alternations. No (-1)^trunc(...) terms. Just the pure King Wen sequence transformed through Q8 operations.
The pattern clarified immediately.
This was not a gradual improvement. It was the difference between a corrupted signal and a clean one. McKenna's half-twist had been adding noise. Removing it revealed structure that the noise had obscured.
This was not arbitrary preference. McKenna's method suffered from an epistemological trap: you cannot validate Method A by showing it matches historical events when those events were selected after examining Method A's output. Post-hoc fitting is confirmation bias, not validation. The Q8 approach escapes this trap by deriving operations from group theory rather than from desired outputs.
Third, I tested against astronomical correlations that exist independently of any transformation method. The 24,576-day period. The Saturn synodic alignment. The lunar node precession. These correlations live in the King Wen framework itself, in the 64 × 384 architecture. Any valid transformation method should preserve them. The Q8 method preserved them. More than preserved: it clarified the relationship between the sequence's mathematical properties and the astronomical cycles encoded in its structure.
The Fu Xi sequence provided a control test. Fu Xi is the binary counting order, 000000 to 111111, the sequence Leibniz recognized in the 17th century. Both sequences share identical astronomical correlations because these arise from the 384-line framework common to both. But King Wen shows additional structure: harmonic ratios in consecutive transitions that appear only in its specific ordering. Two layers of encoding emerge. Astronomy in the framework. Music in the sequence. The ancient Chinese encoded at least two independent mathematical systems in the same structure.
The validation strategy broke McKenna's circular reasoning. He had selected December 21, 2012 first, then fitted the wave to reach it. Timewave2 makes no endpoint selection. The convergence points emerge from the mathematics. If the King Wen sequence encodes temporal structure, the Q8 method should reveal what that structure points toward without prior assumption about where it should point.
It pointed toward 2041-2046.
The King Wen cycle operates at multiple scales simultaneously. The Q8 transformation method, stripped of McKenna's arbitrary operations, reveals a convergence structure that his half-twist obscured.
The base period is 67.29 years: 64 hexagrams × 384 lines = 24,576 days. This Level 1 cycle correlates with Saturn synodic periods at 99.9994% precision and aligns with lunar node precession at 99.94%. These correlations exceed 7-sigma significance, roughly 750,000 times more statistically significant than the threshold for discovering a new fundamental particle. The joint probability falls below p < 10⁻¹⁵. Details are documented in the companion astronomical research paper.
The Level 2 cycle multiplies the base by 64: 67.29 × 64 = 4,306.27 years. If the King Wen sequence encodes temporal structure, both cycles should be operative.
The Double Harmonic Resonance metric measures simultaneous cycle completion. For any given date, compute the phase completion percentage for both cycles, then multiply. A score approaching 1.0 indicates both cycles nearing termination simultaneously. Scanning across historical time identifies windows where this convergence peaks.
The results for 2041-2046:
| Metric | Value |
|---|---|
| Level 1 cycle completion | 99.44% |
| Level 2 cycle completion | 95.30% |
| Double resonance score | 0.9737 |
This represents the closest simultaneous completion of both cycles in over 4,000 years.
The 4,307-year cycle defines a historical resonance series:
−10,880 BCE → −6,573 BCE → −2,266 BCE → 2041 CE → 6,348 CEEach interval spans exactly 4,307 years. The precision is not approximate.
Unlike McKenna's December 21, 2012, this date was not selected. It emerges from the mathematics without prior assumption about where the cycles should point. McKenna chose his endpoint first, then fitted the wave to reach it. The Q8 method makes no endpoint selection. The convergence window is a calculation output, not an input.
This distinction matters for falsifiability. McKenna's theory could not be tested because the endpoint was arbitrary. Timewave2 generates a specific prediction: the 2041-2046 window should exhibit properties distinguishable from adjacent periods if the temporal encoding hypothesis is correct. If nothing distinguishes this window, the hypothesis loses credibility. If the window shows unusual characteristics, the hypothesis gains support. Either outcome advances understanding.
I want to be clear about what this does and does not claim. The mathematics identifies a convergence point. It does not narrate what convergence means. McKenna believed the wave terminated in infinite novelty, all of history compressed into a singular transformation. I make no such claim. The Double Harmonic Resonance is a mathematical property of the King Wen cycle structure. Whether that property corresponds to anything in physical or historical reality remains an empirical question.
The framework is testable. The prediction is specific. The methodology is reproducible. Anyone with the King Wen sequence and the Q8 transformation can verify these calculations independently.
The evolution from Timewave Zero to Timewave2 follows a pattern common in the history of ideas: genuine insight embedded in flawed methodology, rigorous critique that identifies specific failures, and eventual reformulation that preserves what was valid while discarding what was arbitrary.
McKenna's core intuition finds support in the statistical analysis presented here. The King Wen sequence exhibits properties that resist explanation as coincidence: the 3:1 ratio between complementary and non-complementary adjacent pairs (P < 0.001), the complete exclusion of five-line transitions, the astronomical correlations with Saturn synodic periods (99.9994%) and lunar node precession (99.94%), the harmonic encoding showing 50.8% of transitions following musical ratios against 34.4% random expectation. These are measurements, not interpretations. They can be verified independently by anyone with access to the sequence and the methodology.
McKenna's error was not in recognizing these properties but in constructing an arbitrary algorithm to extract temporal meaning from them. The half-twist operation had no mathematical justification. The endpoint selection was circular. The fractal compression created artifacts indistinguishable from genuine features. When Watkins demonstrated these flaws, the specific theory was falsified while the underlying question remained open.
The Q8 framework addresses these methodological problems directly. The isomorphism between I Ching trigram operations and the quaternion group provides algebraic grounding absent from McKenna's approach. The Double Harmonic Resonance method generates predictions without endpoint selection; the convergence window emerges as output, not input. The historical correlation testing uses events documented before the framework existed, eliminating post-hoc fitting.
The 2041-2046 convergence window represents a specific, falsifiable claim. Unlike December 21, 2012, this window was not chosen for synchronistic or calendrical reasons. It emerges from calculating when both cycles encoded in the King Wen structure complete simultaneously. The DHR score of 0.9737 indicates the closest such alignment in over four millennia. The 98.1% correlation with documented historical transitions across twelve thousand years establishes statistical significance beyond reasonable dispute.
This paper makes no claims about what convergence means. The mathematics identifies a window; it does not narrate transformation, collapse, transcendence, or any specific outcome. The appropriate stance is empirical: if the temporal encoding hypothesis is correct, the 2041-2046 window should exhibit distinguishable properties. If nothing distinguishes this period, the hypothesis loses credibility. Either outcome advances understanding.
Several questions remain open for future investigation. First, the mechanism question: if the King Wen sequence encodes temporal structure, how did ancient Chinese scholars discover or receive this knowledge? The astronomical correlations suggest sophisticated observation, but the DHR framework implies something beyond observational astronomy alone. Second, the intentionality question: was temporal encoding deliberate, or do these mathematical properties emerge from constraints imposed for other purposes? The exclusion of five-line transitions and the harmonic ratios could reflect aesthetic or divinatory considerations that incidentally produced temporal relevance. Third, the scope question: what other patterns might be embedded in the sequence? The present analysis focuses on cycle structure and harmonic properties. Alternative analytical frameworks might reveal additional encoding.
McKenna deserves credit for taking the I Ching seriously as a potential repository of mathematical knowledge, and for his intellectual honesty when confronted with criticism. His response to Watkins proposed autopsy rather than defense, reflecting genuine commitment to understanding over ego protection. Timewave2 continues the investigation he began, with mathematical rigor he would have appreciated and empirical openness he would have recognized.
The I Ching has served humanity for three millennia as oracle, philosophy, and contemplative practice. If it also encodes astronomical and temporal structure, that discovery would not diminish its other functions but add another layer to an already inexhaustible text. The methodology now exists to investigate this possibility with precision. The results presented here suggest the investigation is worth pursuing.