From helicoid movement to human social musicality
Introduction
This series of four essays aims to give a visible and memorably geometric (non-mathematical) account of the all-pervasive movement that is a process view of unfolding cosmos (verb), in contrast to a materialist view of the cosmos (nouns bouncing around). It is intended for any student of life who enjoys seeking satisfying answers to ‘how?’, ‘why?’, and ‘so what?’ questions to improve qualities of life. Qualitative answers may improve a sense of purpose or belonging, to be contrasted with measuring quantities of life simply to accumulate and measure them. Qualities of life involve active participation in patterns of movement, while a focus on quantities of life requires a dispassionate observer status over ‘it’.
Part 1 surveyed the history of understanding geometric order in people’s physical, mental, and spiritual worlds of lived experience. By geometric, I mean the proportionality of relatedness in 2-dimensional space.
Part 2 surveyed what happens when circular geometries expand into 3-dimensional space, stretching out as helicoid filaments of synergically bi-directional, internally-relational movement. These triquetral filaments would have internal spins that stabilise with a Golden Ratio proportionality. They could geometrically allow pulsatile secondary waves of energy to move at the speed of light along them. They also offer ‘side ligands’ that would allow cross-liganding connections into a moving synergic web, slowing the speed of light ‘transmission’ when the web density of transactional cross-connections actualizes in our known world as ‘particle events’.
In Part 3 we shall look at how this internal synergic patterning of holomovement expands to 4-dimensional emergent space-time-substance. This could stabilise into vibrational patterns with Golden Ratio proportionality, in which our participation in the repatterning process unfolds as an intuition of embodied ‘life’ shared conversationally with others through a material world, overcoming dualism.
Part 4 will look at why some people talk of sacred geometries, with a view to finding a non-dogmatic way to restore a sense of the sacred to the material world we ecologically share. That sense of the sacred could also extend to our qualities of relatedness through our embodiment and cross-liganded socialisation in this world. We need to improve these if the next generation is to have an ecology to enjoy.
Feedback Cycles – Unfolding and enfolding patterns of local movement
In Part 2 we saw how an icon of internal spin movement, the triquetra, could network its transformations of circular proportional geometry into [a] a synergically bidirectional helix of movements, and [b] a flat honeycomb of stabilized movement.
By making 3-D printed models of triquetral networks I discovered that these diverse stabilising states arise innately, because a triquetral half-spin has two opposite spin directions. Half-spins of informational movement accumulate their effects as they network into diversifying patterns of holomovement, creating 3-dimensional space.
In this 3D Euclidean space, circular geometry expands into spherical geometry, represented usually in 2D diagrams. The result in 3D space, however, is patterned substates of holomovement in responsive connection with each other. As these substates transform mutually, a process cosmos develops from within. The expanding properties of all diversifying substates holding together in movement could be described as ‘intelligent love’ when we participate as ‘personal substates’ within the processing cosmos. Chladni patterns give a hint of the emergent beauty that unfolds from this vibrational substratum of energy-matter, including the utter diversity of human embodiment and social behaviour patterns.
In Part 3 we take up the story of how this diversifying holomovement could be a pre-quantum ‘field’ or fabric of synergic patterns of ‘informenergy’, from which unfolds our actualized material world in which we participate and have our conscious experience of life. Its dynamic and interconnecting substates would nonlocally influence the probability densities that interactions (cross-liganding) would occur within this one field. The cross-liganding events as transactions would thus shape a local actualization of informenergy that scientists describe as wave-particles, and which the general population describes as ‘welcome to my world’. The higher order patterning of unfolding particle events would thus be our experienced lived reality. Via these internal triquetral spins, it would be stabilised at root by a Golden Ratio proportionality in which we share.
But it doesn’t stop there! Human persons are higher order ‘substates of holomovement’. We participate in these locally unfolding transactional patterns; we are not merely observers of them, although we have the capacity to take a mental step back and disengage analytically if we so choose for a temporary observation and reflective pause to learn more about ‘our shared world’. We call this process of engagement and disengagement our lived mental experience of a material world and our embodiment in it, but it is all transactionally made out of photon electromagnetic transactions, the brain’s processes included. Our locality is made of ‘light’; by light meaning we include the entire range of EM wave frequencies.
Light processes (photon processes) are subtly modulated, however, also by gravity and thermodynamics. This is innate to the triquetral cosmology models explained in Clearing a Way: Unveiling the Mental Tricks that Hide Reality.
We dwell in that light. Our nervous systems screen out most of it when constructing our mentally organised range of responsiveness. However, with whatever informenergy patterning we are sensitive to, people do have a freewill power of choice about what happens next (or at least how we go about what happens next) within this actualized realm. Our moment-by-moment priorities and values are actioned for responsiveness through our bodies and voices.
Rippling waves of influence spread outwards from our presence through this actualized and socialised realm. These physical actualizations will also enfold back into the nonlocal realm of patterned probabilities. The iconic double triquetra can also be used to make this hidden inner feedback process of matter visible. Its mutual waveforms cross at their ligand. This could represent the interface between the local, deterministic actualized world (one triquetral system) and a nonlocal probabilistic quantum substratum (the other triquetra system). Reality is actualized with inherent possibilities of change that is influenced by our presence. Each iconic triquetral spin in this interfacing pair will extend into much wider networks from their unoccupied ligands, introducing the diverse qualities of both these two realms to each other. It is a ‘conversational interface’.
Enfolding feedback is part of the life process. It embeds the consequential impact of our patterns of movement and voice (our presence) beyond anything we can see. Our presence (as inner movement with outer spread) influences a continuously updating probability realm of remote and nonlocal consequences. People have intuited this throughout history, and called it different names. We are all seeking, to some extent, how or where we belong, and how we emerge from this hidden realm of life. Those who have no interest in such questions may live amoral lives (or sometimes desperate ones), focusing mainly instead on accumulating quantities of actualized informenergy.
Thus the cosmos continuously unfolds and reshapes as one. A naturally moral process cosmos unfolds from intelligent love; is modulated locally by the qualities and quantities of our contributions… which enfold into that substrate only as far as intelligent love can allow their potential disruption to spread, before returning it as the unfolding probabilities of grace to influence and heal the actualization processes.
Human Social Musicality – the stabilisation of movement in harmonic patterns
We are now in a position to consider the intuitive human experience of unfolding and enfolding as feedback patterns that we experience emerging in the moving relationality of our local ecologies – both physical and social.
The proposal in triquetral cosmology is that this feedback process can stabilise (and potentially be destabilised) by resonant processes that relationally tension and relax, spreading pulsatile movements through the synergic ‘one field’ of diversified holomovement. This one field self-integrates, and as described above normalises as intelligent love around a Golden Ratio of proportional informenergy movements. A person is a complex substate of this holomovement, sharing this status with others (and all!). A person is thus an individual of ‘a people’. Personhood is a relational concept akin to mother, son, friend, employee, citizen, and so on. There must be ‘an other’ if I am to be a person. Embodiment is the embedding of our personal life process (our physiology at molecular and at a deeper ‘light’ level of photon quantum dynamics) in the wider movements of this one field.
We may or may not be subtly aware of this deeper self-integration and normalisation process into the movements and probabilities. We connect into it at our ‘inner heart’ level. This connection is the formative core of our human being. The ‘inner heart’ is not only localised into the physical heart pump that circulates the biochemical milieu connecting every cell of the body. The inner heart ‘core’ of our being is the inner dynamic core of every biomolecule of every cell in every tissue and organ of our embodiment in diversifying holomovement. This includes every neuron and immune cell that responsively and intelligently networks their pattern-recognition roles into the whole. Subtle awareness is a wholistic state of relational movement among all this actualizing holomovement that integrates each of our lives beyond the sensory range of our nervous systems. Its relational qualities are continuously reshaping the probabilities of consequences from our actions, and the probabilities of wider influences on us. We may know this inner movement as the ‘intuitive feel’ of the right or wrongness of certain choice options we mentally consider, or put ourselves in as activists to experience.
That intuitive feel may also come with a sense of ‘right timing’. As mentioned before, harmonic ratios would be important at every scale of stabilised holomovement. The proposal is that these proportions are shaping the actualizing movements ongoing that unfold from the nonlocal probabilities of life. Their proportionality (their internal relationality of movement) becomes visible, for example, in the local Chladni patterns mentioned in Part 1, and at a cosmological level in the distribution of matter in 3D Euclidean space. They also become obvious at the human level in musicality and dance, and in the poetic meter or rhythm of voice, and the timing of speech.
Most animals do not naturally move ‘in rhythm’ with music, although they can be very sensitive to sound. Most human beings, however, do respond to musical rhythm with movement, and to harmonies and melodies with emotional movement. Anthony Storr, the psychiatrist and author, throughout his book Music and the Mind makes the key observation that, of all the arts, music alone inspires the listener to move bodily in response to its movement.[1] Whereas the appreciation of beauty in other artistic or scientific endeavours tends to bring people to a place of stillness, the embodied listener finds musical rhythmicity and the transitions of the form moving. He also demonstrates that is not possible to associate particular sequences of notes with particular emotions or meanings that apply generally to all people. The composer brings a balance of predictability and surprise to movement that leads nevertheless to reconciliation or resolution. It is the overall musical proportionality of internal responsiveness in the formed movement that seems to stimulate and satisfy as an externalisation of its relationality.
The human experience of music is therefore almost entirely about proportionality. The movement from one chord to another creates different moods depending on the proportional relation of the chosen chords. The wholeness that people feel in the form of a prolonged piece of music may depend on approximations to and variations from a Golden Ratio when relating its diverse parts or movements or themes. It is seen, for example, in the A-A-B-A structure of many popular songs. The sense of completeness when a final chord is played, and knowing that a final chord is needed, are features of proportionality. They complete the musical ‘story’ of its thematic beginning, divergent middle, and feedback ending as its ‘deviations from the theme’ are reconciled.
An unexpected feature of human social musicality has been discovered by music therapists, and harnessed educationally into the formation of strong personal identity. It is the noticeable rhythmicity in healthy conversational exchanges between parents and a developing child, through vocal and in responsive behavioural movement. This rhythmicity is brilliantly exemplified in this charming YouTube video of a father and toddler in a conversation.
Rhythmicity and its inherent responsiveness is now widely thought to be the way people develop an identity, and perhaps consolidate it at any age. External stimuli enter everyone’s embodiment as pre-patterned inputs synchronously affecting several sense modalities. Neuroscientists may forget this when studying the details of each sense modality, but ecological psychology takes note of the embedded patterning that shapes subsequent responsiveness from within the whole embodied person. Because all persons are embedded in a two-way, synergic informational flow in the holomovement field, the Golden Ratio stabilisation of that one field would also influence the stabilisation of responsiveness between people. These patterns of responsiveness beyond mere words will contribute to human awareness (as for all sentient and responsive creatures), producing a core of consciousness (con- scire to know with another) that is an intuitive, inner-outer connection in movement. Words learnt may bring a precision to conversational focus, but they also add an increasing possibility that misunderstanding may lead to brokenness of relationship. Musicality of tone and pace in conversational exchanges can convey mood and meaning more clearly.
In different cultures, musical agreements between people are established on how to shape the musical forms that enhance socialisation. In many tribal settings, music has a sacred status for this cohesive purpose. In more individuated societies, people explore variations to play with the aesthetics of proportionality and resolution. There is considerable cultural variation in how people aesthetically divide the octave (a naturally resonant musical interval) into tones and subtones for sung or played music. The Western world classically divides the octave into twelve ‘semitone’ notes, patterns of which make the musical forms, but Middle Eastern tuning recognises 17 subtones, and the Indian musical system recognises 22 notes in the octave, which may all harmonise or add dissonances as they form into musical movement. There is no ‘right-wrong’ in this diversification, as people explore the proportional harmonies that impact their social responsiveness. Harmonies can be shared among groups of singers or musicians to convey mood and movement. These coordinate over time into culturally appealing ‘forms’ that can inspire curiosity among listeners, and move their likes and dislikes.
This relational aspect of musicality brings us to Part 3’s critical turning point.
All the musicality of the processes that contribute to personal identity formation are analogue. They are ‘field processes’ at different levels of order, from subatomic to embodied, in the context of a concert hall or beyond. They are patterned and resonant, not linear cause-effect. They have ‘state’ interactions that influence each other probabilistically. By this I mean the tensioning and releasing of one probability field (a holomovement substate) subtly impacts and tensions another interconnected substate field. The probability of that transformational event may unfold as a pulsatile secondary wave progressing along helicoid triquetral filaments. However, that is a linear concept of movement that makes sense only in an observer mode. When persons realise instead that they are participators in those probability fields, an image that is more consistent with the synergic nature of triquetral filaments shaping holomovement is that the probability tensioning affects the whole filament synchronously. As such, an actualizing transaction could happen as an event anywhere along its spare side ligands.
That whole nonlocalized tensioning would then be ‘caught’ as a localising event at a stabilised domain of holomovement (such as an atomic or molecular receptor). That catch event, from an unoccupied side-ligand of the nonlocal filament, is its probabilistic transaction connecting with a spare ligand at an edge of a stabilised domain of holomovement. The filament may well be connecting synchronously with another stabilized domain somewhere in the one field, which would induce an entanglement of events beyond our normalised space-time-substance mental framework.
Patterns of these field processes, large scale patterns affecting the unfolding of every molecule from within of two sentient and embodied human beings, would induce an intuitive rhythmicity to exchanges that entangle them. That’s a relationship. Personal identity is our networking into relational patterns of movement and stabilisation.
Now, if a receptor molecule for a transactional event is part of a living creature (rather than a measuring instrument) such as the retina of an eye, then the creature may experience the localising field event responsively as a small flash of light. At larger scales of stabilised movement, such as molecular air or water within a temperature range that is life-supporting, a sound wave may similarly pulse (at slower speeds) and transact with the tympanic membrane immersed in that air or water. That pulsatile wave would then pass via the middle ear ossicles on to the fluid filling the inner ear cochlea, where sensitive nerve cells connect patterns of the fluid’s movement into the brain.
The point I am making is that by our physical participation at inner heart level in the one field of diversifying holomovement, our brains are in direct connection with patterns of actualization. The old philosopher conclusions that we cannot know the reality of life directly are no longer true now that quantum gravity science has opened the way to see entanglements in the quantum substratum – in diversifying and informationally patterning holomovement. The brain (and the immune system) are pattern-recognising and memorising organs directly engaging at an intuitive and harmonically stabilising level with this realm of intelligent love. Millions, trillions, of photons and air or water molecules are simultaneously processing in patterns. All these physical processes will then feed back into nonlocal holomovement, repatterning the Golden Ratio stabilised state ‘there’, with a high probability that its fields will unfold again as a predictable movement within the actualized physical realm. ‘Things’ thus seem to proceed deterministically; but embodied people relate more intuitively…
The Pythagorean Comma – divergence of linear math and proportional geometry
The apparent predictability of these physical, non-living processes has encouraged mathematical modelling of actualized events. The math expressions of relevant variables about sound commonly assume a linearity of wave transmission (frequency, amplitude and wavelength) that may not match the reality of unfolding-enfolding system states harmonically patterning, as just described.
It may not be such a surprise then that a mismatch exists between the proportional harmonies within musical scales and the linear mathematics of wave frequencies that would calculate an ‘ideal’ octave’s fifths and thirds.
This divergence, known as the Pythagorean comma, has been recognised since ancient days. The Pythagorean octave of musical harmonies is an actualized proportional reality. When a string is stretched, then bowed or plucked with a ‘stopper’ that constrains its vibrational movement at some point along its length, the resulting proportions replicate the Fibonacci series: the octave (8); the fifth (5); and the third (3). These overtones seem to be naturally shaped vibrationally by the Golden Ratio phi. The resulting waveforms can be scientifically measured by observers for frequency, wavelength and amplitude. These observations of ‘it’ (the vibration) can be represented mathematically, and further calculations made on these idealised numbers.
However, over seven octaves a slight discrepancy progressively appears between the aesthetic harmony proportions of fifths and thirds, and the mathematically calculated frequencies of these notes expected from a stretched linear string. Over seven octaves there are sequentially twelve intervals of ‘calculated fifths’. The slight divergence of proportion from calculation accumulates mathematically, to make that theoretical twelfth ‘fifth’ sound sharp (129.7Hz to a calculated 128Hz), approximately a 74:73 ratio.
The meaning of this divergence is much speculated about. The Pythagorean comma somehow points to a separation of mathematical calculation from natural proportional geometry. Classical performers will sing to the proportional relational harmonies, not the frequencies, but musical instruments can be tuned to exact calculated frequencies. The human ear has a maximum audible range of ten octaves. The vocal range for most people is about two octaves. Classical performers may increase this to five octaves at the very most. The human voice is a very unusual musical instrument – both a string and a wind instrument. The vocal cords are strings made to vibrate by air blown across them. These cords are tensioned by muscular action, as is the rate of breath release and laryngeal shaping. Unique patterns of overtones are influenced by the entire human body posture with its emotional tensioning, which is itself influenced by feedback from the environment and by the person’s spiritual psychology giving meaning and purpose to the voice. Feedback also with neighbouring singers, audience and hall through the ears and resonance in the thorax introduces a conversational presence into the time-framing of voice-listening-singing. We are therefore describing a holistic and systemic process of communication when we voice a word. And a word has its existence in the context of that whole relational system. In a similar way, for those who see life in this way, the ‘voice of God’ and God’s living Word might have a resonant feedback reality, sustaining and restoring life throughout the entire cosmos as a vibrational substrate in holomovement for life’s unfolding harmonic formations.
The mathematical representation of musical vibrations is based on linearity and measurement by observation and comparison, not on proportional aesthetics. As mentioned in Parts 1 and 2, calculating circular motion and progressive helicoid waveforms requires the irrational number pi, which means that there will always be a slight divergence from the lived proportionality of stabilising patterns among waveforms. The musician and electronic composer Sevish, in his article The Golden Ratio as a Musical Interval (from his website ‘Sevish Music’)[2], explains how musicality does not result if the octave is divided into notes at linear Fibonacci intervals. You could hear there how awful that sounds on his site! However, a mystically aesthetic and unusual experience follows when those intervals are proportioned logarithmically, in other words ‘squared’. Helicoid movement has an angular momentum as it curls around, calculated with the Pythagorean triangular geometry that squares the triangle’s sides to calculate their proportions. It is pure speculation whether the organ of Corti’s sensitive hairs (cilia) resonate better with helicoid movements patterning the cochlea’s fluid, than linear ones. All cilia, in every living creature, are made of helicoid microtubules of protein molecules. Along their lengths they rotate and curl, so they may resonate to patterned helicoid stimuli with waveform movements of their own.
A physicist may see beauty in a well-worked formula balancing its two sides. However, the proof may have excluded terms that tend towards infinity or zero, which may have been important for intuitive harmonisation by proportionality. The algebraic beauty of a formula, or of a symmetry in group theory, has led to the growing Mathematical Idealism among some that mathematics may offer a more accurate representation of reality than our lived experience of harmonisation. This new form of Idealism leads logically to a conclusion that multiverses exist, as opposed to our mathematical ideas of multiverses existing in some people’s imaginations. The triquetral model of cosmology takes a different line that consistent with Ruth Kastner’s ‘Relativistic Transactional Interpretation’ of quantum dynamics.[3] (https://ruthekastner.org) Expressed in triquetral cosmology terms (which Prof. Kastner does not necessarily endorse), the probabilities of actualization from a nonlocal quantum substratum are real, because they arise from the helicoid spin of triquetral filaments offering side ligands that are diversifying the holomovement into the patterns that guide its actualizations. We live in an analogue cosmos of interactive fields. Here we contribute socially with imprecision to shape what actualizes in a shared locality. We do so by seeking an intuitive ‘feel’ of harmonic resonance in the feedback we receive when reaching out to explore what might happen next.
We do not merely follow a path of least resistance to maximum entropy and disorder, as some mathematical idealists claim who deny a place for freewill choice in the cosmos. That may be the case temporarily in social isolation or illness, but when living includes mutuality with responsive conversational feedback, people replicate the underlying synergic order in their enjoyment of the cosmos. The irrational numbers pi and phi contribute to learning how to time our responses with skill, intuition, and the sensory feedback that conveys the impact of our choices. Timing of responses leads to the rhythmicity of conversations, and the emergence of strong personal identities.
Resonance and Harmony – the Fibonacci curled cochlea
One possible explanation for the non-linear proportionality of aesthetic harmonies may relate to the structure of the inner ear. The cochlea is a Fibonacci spiral. It is a coiled, fluid-filled tube narrowing along its length making a cone 9mm wide at its base and 5mm wide at its peak. The tube is about 30mm long if straightened. Curling along the length of the cochlea is a sensitive membrane, the ‘organ of Corti’, from which small sensitive hairs (cilia) project into the cochlear fluid that vibrate at resonant frequencies with the fluid. Sound waves synergically reverberate throughout the fluid of its Fibonacci spiral in a non-linear, systemically curved environment. The tympanic membrane that faces the outside world does not simply vibrate in and out like an electronic ‘speaker’ diaphragm when sound pressure waves arrive. It has a complex Bessel function distribution of movements, rather like a Chladni pattern.
A single tone of sound therefore does not make just one segment resonate (not like a piano keyboard). Several segments along its length will vibrate, like the multiple resonances set up among all the piano strings criss-crossing its metal and wooden frame, again like a Chladni pattern.
Could this nonlinearity of harmonic proportionality be a source of the Pythagorean comma? The resulting neural messages from even a single tone going to the brain are far more complex than the linear mathematical calculations of waveforms. They activate muscular patterns of response that help to focus attention, such as turning the head to search for the source of a stimulus. Could it be that the anatomical biology of the ear has evolved to engage directly at its own holomovement level with the probabilistic patterning of holomovement in the wider nonlocal quantum substratum? This patterning would actualize into neurological behavioural patterns, which have evolved as appropriate responsiveness to sound qualia for survival? In other words, human responsiveness to harmonic ratios and proportions in sound does not fall short of a perfected mathematical idealism. On the contrary, it is perfectly attuned to the helicoid movements that are holding the cosmos in its harmonic order. It is pure speculation, but then so is all the appreciation of beauty, and of life.
Embodied musicality and voice
To conclude Part 3 of this essay on the stabilisation of a vibrational model of matter I shall draw together various themes about human embodiment and voice in a conversational model of the cosmos.
Firstly, I believe there is a very small but significant divergence between [a] the mathematical idealism that celebrates patterns in the representations of life in mathematical symbols, and [b] the actualization of resonances in the physical world that are less ‘precise’ because they are proportional states rather than linear cause-effect sequences. The human appreciation of harmonics is variable between people because it is more closely related to resonances, between the material of our environments carrying sound and light, and our sense organs and related nervous system processes that are sensitive to the electro-magnetic states of their movements (at their different levels of organisation – molecular and photonic quantum).
Proportions are relational, not linear. Proportions relate patterned states synchronously, not sequentially. In movement, patterned states transform internally and externally in a mutual, synergically ‘complex reshuffling process’, not with a simple cause-effect linear transfer of energy.
Proportionality in movement describes the reality of our local human embodiment as a self-organising process embedded in a wider and nonlocal quantum substratum, which the triquetral cosmology model describes as a diversely patterned, informational holomovement. The triquetra, as an icon of unending movement, is stabilised by an internal Golden Ratio of movement. That inner state replicates in the diversification process that patterns and continuously repatterns holomovement. With those evolutions and involutions of substates, the probabilities of actualization alter within the range that human beings are responsively sentient to as our physical reality. Our sentient responsiveness, whether inducing stillness or movement, is stabilised by the same Golden Ratio underlying our biochemistry and biophysics as that which shapes the ecologies in which our shared lives unfold.
Human beings, embedded as our lives are in this shared quantum substratum of a holomovement ‘one field’, communicate conversationally through our embodied movements, our stillness, voiced utterances, and our formed words as we learn various languages. We are conversational creatures. Voice is important. Being heard is the most fundamental human need, from the first cry at birth, to our departing breath. The rhythmicity of conversational exchanges follow an intuitive balancing process that is imprecise, and yet aesthetically shaped and modified by mood, values-based emotion, and intentional purpose. Aesthetic rhythmicity is itself potentially a consequence of Golden Ratio intuitions shaping the relational proportionality of each person’s responsiveness.
Diversity adds healthy unpredictability into the transformational life processes, enabling adaptability to changing circumstances. To balance unpredictability there is an innate stabilisation process also at work. The stabilisation of actualizing patterns has an innate trend towards an aesthetic of unity, in which people can feel secure and safe with each other and the world. Musicality and its timing in voice, can enhance that security.
[1] Anthony Storr. Music and the Mind. Harper Collins, London. 1997. Pp31-34.
[2] https://sevish.com/2017/golden-ratio-music-interval/
[3] https://philsci-archive.pitt.edu/11893/
