From static circles to helicoid movement in waves
The cultural setting in which to consider the importance of proportional harmony
On a cultural scale of change, the development of super-computers, quantum computing, and Internet communications nonlocally at the speed-of-light is impacting life more rapidly and extensively than the printing press did in 1440. Change now condenses locally through our screens and earplugs from rapid, even instantaneous, informational transfer. Forms relationally transform at the click of a button.
This informational perspective on life shapes social movements through the rapid spread of memes, which have the potential to widely transform ideas and personal values. Nonlocal informational movement now can shape material processes even on a global scale through robotics, influencing probabilistically the shaping of culture, design and innovation. For example, screen time on the Internet is taking over from street play and reading comics for young people in small groups – and when people do meet socially they are primed to act and react by remote information that others are probably not aware of, creating psychological distance that can only be overcome conversationally (although that was always true in local communities). Individualism comes close to having a personal identity as a ‘Creator of life’, pushing out information digitally to anywhere, rather than pushing information directly by hand and by our whole embodiment into the shaping of local materials and communities.
This impact is generating a new ‘informational’ world view. Somehow informational movement and transfer is now widely considered to be a deeper view of reality than the dispassionate material worldview of Enlightenment Science. This calls attention to the New Science of dynamic systems, which interact from remote locations and transform by vibrational informational transfer. A significant feature of informational movement is its transience, which can slow down into stabilising patterns of behaviour anywhere a receiver is transformed by absorbing that vibrational wave change. Such stabilised patterns will then influence any forwarding communications.
This process view of life is in stark contrast to the previously assumed permanence of some material substrate to life, in which transient mental states had seemed to be merely mysterious by-products. However, the triquetral cosmology of vibrational connection being introduced here brings into a harmonic balance the value of both these material and informational worldviews. It achieves this by adding a third equally valid perspective on life’s relational and conversational processes. This third class of balancing worldviews is commonly associated with Eastern mysticism but historically (and in the present) it is ubiquitous among mystics of all traditions. It calls attention to our human participation in deeper movements of life than our transient bodies and minds. Calling attention to this participatory truth brings together body and mind in the same vibratory harmonies that underlie the stabilisation of all movements and transience, inner and outer.
From 2D circles to 3D helicoid geometry in movement – spin and transience
These three worldviews – materialist, informationist, and participatory – locate transience differently (mind, message, and matter respectively). They can all be brought into a triune balance, however, the integration of which can be represented in the ancient Celtic icon of movement that is now called a triquetra.
The triquetra is a three cornered shape that is not a triangle. I am updating its historical uses into a New Science framework as an icon of dynamic adaptive systems. It makes visible a vibrational unity that could underlie material embodiment, mind, and spirituality. I am proposing that the triquetra’s lines iconically reveal hidden inner movement within every scale of relational systems that constitute the cosmos, from quantum physics to universal gravitation, and from the smallest of life forms to the greatest of human societies. There are two types of half spin triquetrae, left and right spins as shown in this second icon. The diversity of ways in which these can ligand together at a quantum level may be vital to seeding particles and waves. Relational systems are everywhere, and we participate in them with all of our diversity enriching life.
Triquetral lines curl in a complex interlocking waveform along their semi-circular paths connecting the reflectively angled corners. Diverse qualities of reflection integrate the whole into one unending movement. The triquetra is geometrically not the same as a trefoil.
Its movement is a continuous curl. The triquetra adds reflective angles to this unending movement, enabling this icon to form networks of movement and show even how consciousness may develop within a unity of diverse movement.
Why three corners? Because this is the minimum and sufficient diversity required to delineate a three dimensional open space among triune movement. A triangle cannot show 3D space forming out of the movement. More points on a circle’s circumference can connect into interesting and radiant geometries within this space, as introduced in Part 1 of this article and to be taken a step further in Part 4 on sacred geometry. Three is the minimum needed for systemic diversity to flourish relationally and spontaneously within the unity of a created 3D space.
Two spin types of triquetral topology are possible, left and right half spins, which can connect into a double triquetra that has two waves of movement forming a single ligand . As we shall go on to see, diversifying patterns of these complementary half-spins may be foundational to the triquetral cosmology of our material order unfolding as reality. The proposal is that these quantum spin patterns stabilise in a Golden Ratio of bidirectional waveforms, shown by the double triquetra, where points of reflection become shared ligands instead.
The mutuality is synergy. Networks could create an extended synergic field or ‘spin fabric’ of primary relational movement spanning the universe. Through this synergic field, secondary waves could transmit as energy, as if waving a tablecloth fabric. We would participate in the synergic one field, and so cannot measure it. We nevertheless could observe and experimentally create secondary waves of energy passing through this synergic one field. We also have the memorising capacity to consciously feel, compare, and measure, creating a false impression of objectivity.
The double triquetra is the core icon of this triquetral cosmology. 3D printed models of this synergic field’s movements show how a flat ligand forms when a left half spin and a right half spin connect to synergise a mutual ‘informational flow’ between them. When two left spins (levo-, l-) or two right spins (dextro-, d-) connect, however, the ligand must rotate to sustain synergic mutual movement, twisting in opposite directions.
Rotating l-l- and d-d- doubles can also ligand together geometrically. They then make long filaments of internal spin that rotate in a helicoid movement pattern along their length.
These triquetral waveform filaments constrain individual half-spins, making an extended bidirectional waveform of mutual movement along their entire length, making a synergic informational connection between whatever connects with these filaments along the way and at either end. Unoccupied ligands project laterally all along this constrained filament of movement in different orientations. They offer potential connections to any other spin networks in ‘the neighbourhood’.
This consolidates extensive 3D space with more or less densely cross-liganded networks of filaments, resulting in ‘space’ being a web of variable local density of ‘informational movement’. One local subsystem dynamically ‘informs’ another of its influential movements, thus embedding intelligence in the potential movements of space. Loosely cross-liganded areas could let secondary waves transmit along these synergic filaments at the speed of light. More densely liganded areas would slow down these secondary energy wave transmissions through the synergic field.
These informational transactions ongoing at the Planck length of quantum physics could create a synergic field throughout the entire cosmos. All of these dynamics have been turned into 3D printed models, as shown above, allowing intricate geometric analysis. It is noteworthy that a different pattern of stabilisation results when alternating l-d- double triquetrae connect their whole spins into wider networks. They have flat synergic ligands geometrically, in contrast to the l-l- and d-d- doubles, which have to rotate to maintain bidirectional synergic movement internally. Connecting three flat doubles creates hexagons that stabilise movement.
These could extend into honeycomb sheets, which topologically could warp and curl into an infinite variety of manifolds.
I call these hexagonal patterns of movement stable domains (SLMs, StabLe doMains). They further constrain the possibilities and probabilities of unfolding change from the synergic field substratum, or holomovement to use David Bohm’s term, into our actualized ‘explicate order’ world of deterministic physics. Triquetral informational filaments could connect with the edges of SLMs.
They could also connect several SLMs, which would stabilise the filaments and the shape of 3D space that results from these informational movements and transactional exchanges.
Synergic filaments could also connect across within manifold SLMs. Scaled up, this is the pattern of stabilisation seen in the way protein molecules fold into functional shapes. This process can be modelled on computer now, and used to make designer drugs, as shown here.
Limiting the range of change within molecules is their life-enhancing capacity. Their limited range of movements connects their informational feedback at receptor sites into the networks that are scaled up into living, moving cells. The 3D printed triquetral models show a implicate hidden order behind our known actualized world, in which a synergic informational field may guide the probabilities in which explicate order material might move.
The triquetral cosmology model (TQC) shows diversity within this informational field of connections. Without here going into the details here (see the book mentioned below), synergic informational diversity could unfold in our known explicate order as the directional energies of gravity, and thermodynamic and electromagnetic movements. This synergic wholeness of the implicate order substratum is proposed to be ongoing ‘everywhere’ prior to the emergence of space-time-substance as we know them. We participate locally at a heart level in this nonlocal informational substrate. We know or intuit it as the tendency to wholeness and integration that is manifest in the biomolecular and cellular communications of our embodiment.
The justification for this view requires a book-length explanation for why a New Science of informational movement at quantum substratum level reasonably adds depth to the dispassionate observation of life that has led Enlightenment scientists into a narrow materialistic view of life. Creative participation in quantal informational systems requires reflective and intelligent understanding of emotion (with all its full range of joy and grief that accompanies loving) if informational processing is to be included alongside the stable structuring of material embodiment for life (as explained in Clearing a Way: Unveiling the Mental Tricks that Hide Reality).
The mutual attraction of gravitation as a feature of the synergic field
If the integration of the three worldviews (materialism, informationism and vitalism) into a participatory process triunity can be accepted as a provisional working premise, then it will be possible to see how the triquetral cosmology model solves the dilemma of gravity not fitting within the Standard Model of particle physics. It would be because the mutual attraction of gravitation is a feature of the synergic field from which all particles and observable waves subsequently unfold. The synergic field is stabilised by an informational Golden Ratio in movement between implicate and explicate orders. The unfolding and subsequent enfolding of constrained movements is an unending feedback cycle allows observation, comparison and measurement, because consciousness emerges as that interface of informational feedback. That conscious interface of implicate and explicate orders also allows creativity, playfulness, and aesthetic entertainment when participating in a conversational reality that can equally well be scientifically observed rationally, and mathematically modelled to fill out an appreciation of life.
Aesthetics would thus be inbuilt to actualized processes (explicate order) with their probabilities of change unfolding in our lived experience from the implicate order of helicoid, harmonic geometries of movement.
Implicate movement, in this model, is bi-directional, informational, and synergic. These features were discovered by making 3D-printed models of triquetral half-spins that can pair to make whole internal spins and extend into networks through side ligands. A triquetral filament is a helicoid rotational synergic connection prior to the emergence of space-time-substance as we know it. The helix offers side ligands to connect into wider web-like synergic networks in this implicate order that shapes the transient probabilities of unfolding change in our explicate order world.
The Schrödinger Equation – probabilities of change
Geometrically, a helix is a circle stretching into a coil. The mathematical description of a helix, like a circle, requires proportional analysis. It uses Pythagorean triangular sine and cosine measures in three dimension, not two. The irrational number pi (π) is needed to describe helicoid informational movement mathematically. Therefore, mathematically modelling the complex movements of the proposed synergic implicate order fabric of holomovement will suffer from a fatal problem. All calculations involving pi (π) and the Golden Ratio phi (φ) will fall short of infinity (as described in Part 1 of this paper on vibrational stabilisation). Math descriptions will diverge very slightly from the geometric proportionality of lived reality. The quantum substratum from which life emerges stabilises our freeform movements, it is proposed here, into harmonically linked patterns around the Golden Ratio phi (φ).
This divergence challenges a growing Mathematical Idealism that is capturing the imaginations of many individuals during this revolutionary new Information Technology era. During the Enlightenment era, materialism took hold of scientists’ minds, corrupting the personal values that shaped society by its focus on the dispassionate observation of matter. Now the Information Technology revolution is opening a different drift away from participatory humanity, into a new type of digitised Idealism of the individual. Algorithms and formulae may seem to have a reality of their own within this new worldview that is superior to, or more ‘real’ than fully embodied participation in social humanity. Some people believe they can download their personal identities into computers to cheat death and live forever. I call this worldview Informationism, a new counter-extreme to Materialism. Triquetral cosmology can integrate the best of these two worldviews, by balancing their inner processes also the third competing extreme worldview, Vitalism. The result is a triune process philosophy of integrated life.
Triquetral cosmology offers a worldview of stabilised relational processes. The triquetra is an icon of a half spin of informationally connecting movement scaling up into vibrational waveforms. It is supported by the New Science of adaptive systems, adding how patterned transience (as ‘meetings’ or ‘conversational transactional events’ at an implicate order level) will influence the probabilities of actualization of stabilized implicate order patterns into the predictable explicate order world we share.
When particles were thought to be small lumps of matter with momentum, the Second Law of Thermodynamics could adequately describe how, in a closed ‘Euclidean space’ (that is, space as we know it), their kinetic energy and potential energy were conserved. In the early 20th Century, quantum mechanics overtook the ‘little lumps’ image by introducing the wave-particle concept, now further developed into a wave field concept with interactive events that look like particles on measurement. Without going into details or mathematics, Ewin Schrödinger (1887 – 1961) formulated a mathematical description of how waves might unfold from a point into a range of potential movements, which is the equivalent in quantum field ‘mechanics’ of the Second Law of Thermodynamics for momentum. (Heisenberg developed a ‘matrix’ variant of this concept).
In the Schrödinger formulation, waves evolve in a different sort of ‘Hilbert space’, which is a probability space map of the range of probable evolutions to be expected from a theoretical point in spacetime, shown as a vector.
This has proved very successful to predict how atoms in a bound state behave. However, the vital point to make here is that this waveform equation says nothing about the nature of the point in question. It is all about potential and probable movement unfolding from a superposition of waveforms at that point. That probable movement is expressed in terms that can be equated with the kinetic and potential energy of a ‘point particle’.
David Bohm (1917 – 1922) was a quantum physicist who disagreed that the quantum substratum was a random chaos of points, proposing instead that there was an integrated, nonlocal ‘implicate order’ of holomovement unfolding (in some ill-defined way) into the deterministic classical physics of our ‘explicate order’ of lived experience. He made an interesting analysis of the Schrödinger equation. Alongside the kinetic and potential energy components he identified a third factor, where the ‘distance’ variables cancelled each other out above and below the equation. He proposed this to be an energetic trend towards nonlocal wholeness. This nonlocal trend would bias all local processes, a so-called ‘hidden variable’ by his critics. This view remains highly influential among people who intuit a spiritual wholeness to life. It has not been disproven, but there is a feature of his theory that has raised some concerns. The time-dependency of the maths suggests there must have been ‘an existent particle’ prior to the resolution of the wave function ‘point’ into its forward movement. That reintroduces ‘determinism’ into the implicate quantum substratum, which does not fit with quantum field theory. There is no way to retrospectively measure if a particle was there, or if it continues in a self-existent ‘lump’ state, so there remains a gap in the maths that models Bohm’s implicate ‘reality’.
Triquetral cosmology (TQC) may offer a solution to this dilemma, supporting the Bohmian notion of holomovement and simultaneously explaining gravity in a new way. TQC shows how left and right spin movements can differentiate into substate patterns of holomovement that interconnect informationally. ‘Particles’ would be ‘informational patterns’ that could transform (decay?) under wider, even nonlocal, influences. 3D probabilistic patterns of synergic filaments and hexagonal domains would all be composed of internal triquetral spins with a potential for Golden Ratio stabilisation. These patterns of connection would constrain Schrödinger waveform evolution as if they had been ‘particles’. Instead of self-existent mini lumps, however, momentum would be internally stabilised informational patterns varying between potential and kinetic energy relationally between ‘particles’, and subject to a potential Bohmian bias towards wholeness within ‘particles’.
That bias towards wholeness in an implicate order quantum substratum may unfold as triquetral informational patterning into the explicate order within particles that are dynamic systems (not acting on ‘a particle’). This information would unfold in explicate order physics as a nonlocal gravitational attraction knowable (measurable) as mass. This would be prior to the three other fundamental forces of the cosmos – strong nuclear forces, weak nuclear forces, and electromagnetism – which shape the connecting behaviours between all ‘particles’, known as the Standard Model of particle physics. This would account for gravity not fitting within that highly predictable Standard Model.
The Triquetral Golden Ratio in Movement – the creativity of sung or spoken Word
We have been on a journey that brings to an end the dominance of an old Western scientific view that matter is small lumps (called atoms or particles) bouncing around in a closed container called space with their own momentum (kinetic and potential energy).
In its place, the New Science of dynamic systems is affirming an even older Eastern view, that the solid and semi-predictable world we share, in which our bodies and brains and communicating minds all participate, is vibrational waves of energy unfolding in patterns that can feel solid as our patterning interacts in the wider patterning of the cosmos.
Energy knowable as sound, light and substance is proposed here to be secondary waves, however, that move at a maximal speed of light through a synergic field ofimplicate order holomovement. Triquetral cosmology is a model of how this one field’s synergic mutual movements could diversify spontaneously into substate patterns that informationally connect, adding the potential for remote meaning to add intelligent love into the unfolding of material processes. Golden Ratio stabilisation of harmonic patterns would add an aesthetic depth to the intuition of relational meaning as we participate at heart level in holomovement.
We have seen and can recall how the triquetra is an icon of triune movement extending into patterns that diversify and stabilise. That stabilisation process creates the physical order of the world we share and the words we speak through it. Patterns stabilise because there is a harmonic Golden Ratio in the waveforms of a triquetral half spin that extends through triquetral networks of movement. We speak life as our communications enhance the harmonic resonances set up among patterns of movement. When we speak in disharmony, we speak deathliness into the shared world. We have the freewill choice to destabilise the potential for growth, and to denature its creativity, or to intuit the harmonics of growth at heart level prior to forming our words and movements.
A triquetra can be used iconically to represent a quantum spin, or a whole person – in body, mind (soul) and spirit. At either level, physical or personal, particles or people are adaptable subsystems of a wider dynamic whole communicating socially, or transactionally. If representing a person, their relatedness ligand represents the spirituality of connectedness in holomovement with other people, the physical environment, and their place in the entire cosmos. The words we speak and sing or read in the rhythms of poetry are not just verbal vibrations moving the air and other physical mediums that resonate, although they are that too. Our words are spoken with every cell of our body, from the depths of the belly and the inner heart of emotions, moved by values, memories and hopes. Our words carry our wholeness into wholeness, deep speaking to deep.
The truth is that matter is mutuality. Substance is transactional. Consciousness is conversational – a ‘knowing with…’ We can rethink, however, and adapt how we communicate those personal values that constrain or release our ‘words’ and the voice with which we speak or sing them. Voice is the widest vibrational sense of a whole body communication of personal values that connects and echoes with the synergic mutuality of responsiveness. So too in the source of the cosmos, some people feel or hear or see a responsiveness that speaks of life and divinity.
The Golden Ratio is visible everywhere in the double triquetra icon of shared movement. This icon shows how we participate in the divine consciousness, knowing with each other and being known, restored to wholeness in that meeting as we seek to transform our words with love. The vibrational holomovement that creates and sustains all is the voice of One living God, if you choose to see life so, sustaining all substance and material with intrinsic meaning, wisdom, and a potential for beauty.
[1] Anthony Ashton. Harmonograph: A Visual Guide to the Mathematics of Music. Wooden Books Ltd., Glastonbury. Revised Edition 2005.
[2] https://sevish.com/2017/golden-ratio-music-interval/
[3] Anthony Storr. Music and the Mind. Harper Collins, London. 1997. Pp31-34.
