The Structure of Becoming

Emerald Acropolis Pilgrimage as Standing Half-Wave

Cahokia was a solar cult in many ways. From Woodhenge, the equinox sun seemed to rise directly out of the 100-foot-tall Monks Mound — as if the chief himself had commanded it. But worship of the sun alone cannot sustain a civilization. Like the equinox itself, Mississippian memes called for balance: near and far, visible and hidden.

Fifteen miles east, on a glacial ridge piled with earth, the Emerald Acropolis formed the complementary node: a moon shrine aligned to the major lunar standstill. Pilgrims left the American Bottom for Emerald every 18.6 years, witnessed the hesitation of the moon at its extreme azimuths, and returned.

Each mound is a metaphysical node. In this timeless register, two equal waves travel in opposite directions — there and back. When crest meets crest or trough meets trough in the middle, the displacements add so the antinodal arcs open to their fullest; where the waves hit the mounds, they flatten.

The football-shaped envelope of this standing half-wave figure represents the being-becoming polarity fractalizing throughout existence. From ancient cult centers to the self-torus to eternal recurrence, the same crossings appear at every scale. The Big Bang is the departure from a cosmic node; the antinodes are the furthest rarefaction, where the interval has opened as far as the figure can sustain. Civilizational passages follow the same geometry as two forms of nihilism: dense concealment and chaos.

The nodal reflection is a reversal from the earth weather’s toward fire, seen in the explosive phase inversion of the 20th century wars; our present societal scattering is approaching an amplitude that demands a turnabout.

Cults persist toward the antinodes because the lattice still holds the previous node’s attraction: idolatry thrives after the death of God. But this incomplete form of nihilism consummates with a release of all veneration at the point of maximum dispersion, where the wave loosens enough to reverse its swing back to the next node.

Both the nodes and antinodes are regions of totalizing nihilism — the Zero Meridian — but in opposite ways. At the nodes the figure conceals the structure most tightly; cult organizes minds into standing reserve, facticity held by the hardness of earth weather, the wave fully flattened. Dikē, as regulator of extremes, does not allow that rigidity to persist. It drives the inversion when the small pulse meets the concealing nihilism of earth and turns the arc downward. The thrust away from the node opens the interval toward another antinode, a rarefaction that carries the two waves out of earth into the weathers of water, air, and fire at maximum dispersion.

The way up and down are one and the same. Antinodal displacement is the fullest kindling — and the point in wave or trough where the pullback is strongest. The descent is the fire going out in measure, the interval closing into the complementary node, earth reoccupied.

The waves form an arc because tension and the restoring force require curvature. Repeat this circuit enough times, or in large enough numbers, and the binding action of the saṅkhāra lattice holds the nodes in place while the interval stays open.

In the case of the Emerald pilgrimage, the form persists because collective presence keeps returning the same ends at the same interval. Memes take form through repetition or sheer number of minds phase-locked with them, synced to the same beat through a replicating mind virus. What kept Emerald’s 18.6-year circuit half-wave standing were the tens of thousands of pilgrims walking the antinodal paths — a practice that both traces the interval and helps hold it open. The strength of that phase-lock — the tension that keeps the two nodes from drifting — comes from ritual, repeated attention, earth-anchoring. Neither sun nor moon pole predominates because the standing half-wave exists only while both are driven.

A meme itself is a saṅkhāra, the jointure of carrier and pattern. It needs a rūpa register for sense engagement to lock it into the helical core of a self-torus, where it colors perception and gives significance to rite. Each side conditions the other’s existence. A mound with no cult is just a pile of dirt; a meme without an anchor is a diffuse pattern that cannot sustain its nodes or gather a phase-lock.

While both terminals of a standing half-wave share the characteristics of the earth weather, they are polar opposites in their metaphysical register when a meme has stabilized as a saṅkhāra between them as complementary attractors. Cahokia and Emerald are revealed and withdrawing poles respectively. When the nodes are the same idol twice, the interval closes and the antinodes pack back into earth. Polar opposites as memeplexes allow sky into earth, creating depth and a healthier society. Phase-locking with such balanced cults causes a sustained rarefaction in the human nodal cross. A cross fed from only one pole compresses particulars edge to edge, nothing able to withdraw; much seems significant, although without deeper meaning. But when the self-torus entrains with a complex, high-amplitude standing wave, earth turns toward fire with a rarefaction of consciousness, feeling tone and perception. With cult, this is intense, temporary, and comes with a price.

After the feast, game of chunkey, and human sacrifice, the Emerald Acropolis pilgrims burned their mats, baskets, and fabrics. They also sealed the floors of their temporary huts with silt. The node remained unchanged when the wave reversed.


Read more topologies in “The Structure of Becoming” series.

The Structure of Becoming

Half-Wave Stacks: Chladni Plates, Cochleae and Memes

sketches of Chladni plate patterns

The standing half-wave is the first harmonic. It is also the figure of the fundamental being-becoming polarity fractalizing throughout existence.

On a string fixed at both ends it is the simplest form that can persist: one antinode between two nodes, the interval occupied and returned. Higher harmonics are additional half-waves sharing those same outer ends. When they lock as integer multiples, their envelopes superpose and return on a shared beat. The compound tone is a stack of football shapes — antinodes flaring up and down between the nodes.

The same geometry appears on a Chladni plate. A driving frequency excites a standing wave fixed by the plate’s stiffness and its square boundary. Nodal lines form where the metal does not move; sand collects there and is thrown clear of the antinodes. Each empty region between the lines is a half-wave interval whose envelope is a prolate spheroid.

Master violin makers have sprinkled fine sand or glitter across the top or back of an instrument under construction and bowed or tapped it, watching which patterns emerged. Clean, symmetrical nodal figures indicated that the wood’s thickness, arching and stiffness would support strong, stable half-wave modes across the playing range. Irregular or weak patterns showed that energy would scatter instead of standing, and the plate was thinned or graduated until the desired Chladni figures locked in.

The cochlea sorts this geometry into place. Each frequency finds a segment of the basilar membrane where its envelope reaches a maximum and falls. A complex tone therefore excites a set of peaks — the physiological counterparts of the half-wave intervals. Hair-cell activation marks the antinodes; quieter stretches lie between them. A nodal pattern reaches the auditory pathway; the relative strengths of the standing half-waves color the tone. Consonance is the stability of that figure. The ends hold, the interior intervals reinforce, and scattering at the peaks stays low.

Pleasure is the signal of the lock. Positive vedanā registers the chamber having taken a high-fidelity standing geometry — recurrence without interior interference, a clearer gather at the nodes. It is the felt amplitude of a half-wave stack that has phase-locked. Dissonance drives half-waves whose periods do not share nodes cleanly; their envelopes interfere and the same system reports the decoherence as roughness.

Memes are the same saṅkhārā. Each is a standing half-wave at its core: carrier and pattern held apart and in contact, attention or rite as the antinode that must cycle through the circuit. A memeplex forms when several of these half-waves share a node — a common carrier, a complementary rite, a nested period — and are driven together. The shared end becomes a stronger reflector for every interval that terminates on it. Complementary poles keep the antinode from collapsing; additional jointed memes multiply the resistant termini the register can push against. Because the half-waves are phase related and reoccupied as one formation, energy that would have leaked at open ends is returned into the intervals, as with a torus. The compound figure therefore stands at higher amplitude: more earth to reflect from, a wider set of joints holding the register and a stronger pattern delivered to any mind that phase-locks with it.

A self-torus phase-locking to an intense memeplex receives the stronger pattern the way the cochlea receives a consonant stack. The nodal cross at the center gathers a pattern whose ends hold across a wider set of intervals and whose interior returns in phase. Coherence rises.

What arrives is a standing complex rather than a scatter of separate saṅkhārā. The geometry that makes a musical tone feel gathered is the geometry that lets a memeplex amplify the register it feeds.


Check out “Dynamic Zones of the Self-Torus.” Or read the Existential Firestorm essay series “The 12 Turns” on Kindle.

The Structure of Becoming

Phase-Locking with Memes

floating toruses and waveforms over Greek ruins

While the self has a discrete structure, it is also an open system — an antenna capable of phase-locking with external memes.

These resonant patterns can either strengthen the mind’s coherence or pull it into forms of entrainment that diminish agency. The self-torus’ wavenumber-6 standing wave facilitates initial entrainment with external structures, but the long-term consequences depend largely on how the helical core incorporates new patterns and how the central nodal cross processes them. When the cross remains relatively open and discerning, phase-locking with refined resonators (such as those found in art or philosophy) can support greater coherence. When the cross becomes rigid or overly attractive, external patterns can dominate the system’s orientation.

Memes themselves are resonant toroidal patterns that possess a rūpa-like structure in the realm of toroidal resonance. While they require physical carriers (books, songs, images, rituals, institutions and so on) to be transmitted in the material world, their coherence as patterns lies primarily in their topological structure. Most memes share the wavenumber-6 architecture of the self-torus, which facilitates phase-locking, though they typically lack the full differentiated internal structure needed to host reflective consciousness independently.

The self-torus is itself a memeplex. Its helical core, with its lemniscate-like motion in the cross-sectional plane, is where internally generated patterns and externally phase-locked memes are braided together into a composite structure. This makes ongoing phase-locking a continuous structural feature of the self rather than an occasional event. The memes already present in the helical core can exert pressure on cetanā, biasing future selection toward patterns that reinforce the existing configuration.

At the lethe zone, cetanā functions as a gatekeeper in the competition among memes for the limited resource of manasikāra (attention). It determines which external patterns are permitted to phase-lock and braid into the helical core. While the memes already integrated into the core can pull cetanā toward reinforcing patterns, cetanā retains the capacity for discernment. Agency can be strengthened both by reducing automatic identification with memes and by selectively phase-locking with higher-order resonant patterns.

In addition to tuning in external memes, the self-torus serves as a resonant chamber for the upper wavebands — vedanā, saññā, saṅkhāra and viññāṇa. These are topological patterns of organization that arise within the rūpa chamber. They depend on its structured resonance to manifest coherently and gain power at the nodal cross.

The openness or rigidity of this cross strongly influences what can phase-lock with the system and how deeply or constructively. As an attractor, it accumulates influence: Successful phase-locking tends to reinforce its power, creating feedback loops. Larger or more coherent memeplexes can exert disproportionate effects on both the helical core and the nodal cross.

The mid-nidānas — particularly nāmarūpa, saḷāyatana and phassa — establish the basic conditions for an “inside” and an “outside.” They mark the interface at which rūpa functions as a resonant chamber, making coherent internal activity and external phase-locking possible. Physical carriers and metaphysical patterns thus form a joint saṅkhārā — they condition each other without being reducible to one another.


Check out “Half-Wave Stacks.” Or read the Existential Firestorm essay series “The 12 Turns” on Kindle.

The Structure of Becoming

Dynamic Zones of the Self-Torus

The topology of mind reveals a toroidal structure resonating in a hidden realm. Within the self-torus are four interconnected zones: the wavenumber-6 standing wave, lethe, helical polar core and central nodal cross. These illuminate the structure of selfhood — its values, developmental movement, illusion of persistent identity amid flux and volition’s role in the arising of consciousness.

These functional regions arise from the dynamic interplay of the five waveband aggregates. Rūpa (materiality) serves as the toroidal resonant chamber that bounds and organizes the four upper bands: vedanā (feeling-tone), saṅkhāra (binding lattice), saññā (perception) and viññāṇa (consciousness). Without this rūpa chamber, the higher wavebands would remain too diffuse to sustain stable patterns. The structure provides both a ground for individual striving toward greater coherence and the possibility of phase-locking with external resonant forms, in accordance with the demands of will to power.

At its most basic geometric level, the self-torus is sustained by the wavenumber-6, which produces 12 fixed nodes around the circumference. While these remain relatively stable, the regions between them pulsate rhythmically. A standing wave of this kind possesses sufficient structural coherence and harmonic stability to phase-lock in the realm of toroidal resonance without losing its own integrity.

Although the self-torus is grounded in rūpa, it remains undetected by current scientific instruments. Even if that were possible, the four upper wavebands would still lie beyond the reach of materialism. What follows, therefore, is a topological description of metaphysics — a mapping of the resonant architecture where cosmic cetanā (volition) localizes and surpasses itself within conditioned existence.

The wavenumber-6 establishes the overall container for the other functional zones to operate. Its 12 nodes correspond to the 12 nidānāni of paṭiccasamuppāda, the structural conditions of moment-to-moment dependent origination and maintenance of the self. This layer most directly expresses what underlies experience, while the remaining zones govern modulation and transformation across time.

Within the lethe zone, cetanā narrows the field by scattering all potentialities except the chosen one; this opens a clearing at the central nodal cross where actuality stands forth. What arises is not erased after fading from awareness. Through the activity of cetanā, it becomes integrated into the kamma-bhava saṅkhāra — the karmic conditioning strands — within the helical core, where it continues to shape future possibilities and receptivity. A new horizon of potentialities emerges, shaped by this accumulated background, continuing the cycle.

Lethe thus scatters in service of gathering. As dikē demands, every dissolution calls forth a movement toward greater coherence as a counterbalance.

This polar tension finds its most concentrated expression in the helical core. Here, a lemniscate-like motion allows opposing polarities to meet and rebalance at each crossing. Because the core accumulates conditioning over time, it possesses the capacity for ongoing evolution rather than mere repetition. While this movement performs the essential work of polarity and integration, increases in coherence and resonance register most significantly in the evolving attractor quality of the central nodal cross. In this way, the helical core supports the conditions for development, while the nodal cross serves as the primary site where that development is expressed and tested.

The helical core’s internal dynamic interfaces with the larger architecture of the self-torus. At the central nodal cross, the helical core’s polar activity meets the convergence of the wavenumber-6 standing wave’s nodal spokes. At this intersection, the ongoing work of transformation becomes most directly available for integration into the self-torus as a whole.

This is not a closed system. This is not a closed system. Consciousness is continually shaped by saḷāyatana (the six sense bases), and the self-torus phase-locks with external memes. Despite these influences, the self maintains structural resistance to dissolution. Like a hexagon distributing stress evenly across its faces, the wavenumber-6 mode spreads external pressures across its 12 spokes. The helical core further stabilizes the structure, coiling according to the golden ratio so that it can preserve identity while remaining open to polar flipping. Because the ratio is irrational, it generates self-similar spirals that never reach perfect closure or equilibrium, ensuring that the flow always carries within it the seed of its opposite.

The self-torus thus embodies a resonant form persisting even as its specific manifestations change. Ñāṇavīra describes this quality as “invariance under transformation.” In this continuity amid flux — grounded in rūpa, gated by cetanā and open to phase-locking — the four zones together sustain the topology of self.



Read “Phase-Locking with Memes” or check out the first Existential Firestorm essay series, “The 12 Turns,” on X or Kindle.