Summary of the first three Parts leading to a rediscovery of the sacred
Part 1 reviewed the slowly growing awareness of depth order behind people’s shared everyday experience of embodied life. Pythagoras at around 500 BCE discovered the musical and triangular geometric proportionality that structured sound, physical systems, and their aesthetic mental appreciation. It led to a spiritual view of life as participation in the ordered heavens. We noted the difference between resonance in physical systems, and harmony as an aesthetic appreciation of proportionality. An important discovery, which will become relevant in our present exploration of life as movement, is that the proportions of the sides of a right-angled triangle can be calculated by seeing the sides as squares, not merely as lines or edges. The triangle is the space left between these squares. However, people’s mental attention tends to go to that space and its edges as if it had an existence of its own.
At around 300 BCE Euclid explored fitting geometric shapes within the circumference of circles. Through his exploration of that inner space he discovered how the pentangle generated the aesthetics of a Golden Ratio, and with it the capacity for depth replication of those geometric proportions. Some people see this as the start of the story of sacred geometry, but I believe its true start is the more generalised discovery of proportionality in relatedness underlying cosmos (a verb equivalent to Tao). Two more Parts to this story have needed to be told before this Part 4 can adequately show how the sacred feature of proportional relatedness can extend from dynamic geometry to the moving topology that is continuously generating cosmos.
Archimedes and Ptolemy in the century between 250 and 150 BCE extended our knowledge of the proportionality of order by finding a way to calculate the circumference of a circle from its radius (or diameter). They identified the factor pi (π), discovering that it is an irrational proportion (an unendingly imprecise irrational number). Every mathematical or geometric calculation that involves pi is therefore only a numerical approximation to the underlying reality of cyclical motion. Measurement of any curve to its centre of rotation is calculated mathematically using Pythagorean triangular geometry. Circular movement has a squared proportionality to its radius (πr2). This will become highly relevant (without using mathematical formulae!) when considering how helicoid informational movement actualizes into the world we are familiar with.
A long gap follows historically to the 13th Century CE, when Fibonacci, a brilliant mathematician, introduced the Arabic numerical system into Europe. This system of mapping ‘order’ recognises a state of zero, displacing the Roman system that recognised only positive integers. His famed number sequence shows the growth in scale of a Golden Ratio (phi, φ). This progressive proportionality in the growth of beauty can be identified in musical harmony and in nature’s living ecologies as the balanced transformation that happens slowly, as each feature of an embodied living form stabilises and grows into its relational place alongside others. An inner pattern thus extends. It transforms and self-replicates into the progressively functional whole, contributing to cosmos. This ubiquitous feature of life raises the possibility that all physical material has a core vibrational movement that can resonate. (This feature is used in Magnetic Resonance Imaging to scan the brain – MRI scans.) Where human or other living relationality is found between embodied living forms, resonance may additionally harmonise imaginations. The process of proportional stabilisation into a Pythagorean order is sacred. Without the stabilisation of movement there would be no cosmos.
The Renaissance brought a surge of creative thinking and exploration in the 15th – 17th Centuries CE. As exemplified by Leonardo da Vinci (1452-1519 CE), observation, technological science, and the artistic presentation of nature’s glory in proportionality all progressed in a holistic integration of physical, aesthetic, and spiritual meaning. This included valuing the Golden Ratio. Galileo in the 16th Century, however, introduced a dispassionate observation of nature. He initiated the dualistic attitude that an observing mind is of a different type of substance to observed matter, just as he thought that objects moving in space, which did not fall to the ground, must be a different type of substance to those on earth that did fall to the ground. A dualistic alienation of human intelligence from embodied life became the foundation later for materialistic thinking in science, well into the 20th Century CE. It obscured the sacred nature of embodied relational life emergent in cosmos.
In Part 2, moving towards a rediscovery of the sacred, we looked at moving on from static thinking about geometric proportions (and particles) to helicoid movement. Geometry converts thus to a topology of waves. A model of triquetral (three-cornered) spins is presented. It updates the ancient Celtic Pagan and then Christian icon of inner movement, of the ‘life’ that moves behind the perceived world.
Triquetral spins can ligand informationally into pairs, waves and filaments. These can further differentiate and stabilise into hexagonal patterns of informational movement, which may actualize as our known world – a triquetral cosmology (TQC).
Triquetral waves interweave three informational movements in ~1/3 to ~2/3 proportional ratio.
This, I believe, is the patterning feature stabilising all movement from within, and generating the Golden Ratio of sacred topology.
Continuing the summary of how Part 2 is relevant to sacred geometry, a triquetra is a half-spin that can connect into pairs, in so doing becoming a spinor. Right and left half-spins can connect into three different types of pairing. When left-left or right-right pairs connect, they topologically string out into ‘synergic filaments’ that offer side ligands into the wider context life. As other triquetral filaments connect, diverse qualities of movement are introduced into the whole – change, relatedness, and repatterning forms.
Each type of filament is topologically a bidirectional helicoid wave. Each half-spin transfers informational movement through its ligands simultaneously in both directions. In this Golden Ratio stabilised movement, mutual relatedness could thus generate a synergy of connectedness that is a one-field. The honeycomb pattern may represent what a field is – a ‘fabric’ of informational movement uniting cosmos prior to the emergence of space-time-substance. Through this synergic fabric, secondary waves of energy could move at up to the speed of light. We participate in the fabric, so we cannot measure it, but we can experience, observe and compare the secondary waves, and therefore measure them.
Topologically, the secondary energies measured passing along networks of these synergic filaments could be gravitational, electromagnetic, and thermodynamic waves. [For descriptive details of how this is predicted, see Clearing a Way: Unveiling the Mental Tricks that Hide Reality]. This ‘one-field’ could be forming in the earliest moments of the expanding and cooling universe, as interweaving constraints ligand between informational spins leading to the unfolding of space-time-matter as we know it. The one-field would be a synergic vibrational fabric like an ether from which wave-particles emerge with intrinsic movement. Stable domains of etheric movement could condense from the one-field into baryons, which stabilise as protons and neutrons to make the nuclei of atoms, just as they do now in the fusion reactions of stars like our radiant sun.
In our stabilised and cooled locality of planet Earth, the Golden Ratio proportionality of informational processes at the one-field depth has actualized into molecules. Adaptive life forms have emerged in which molecules repattern into whole embodied informational movements. Resonant stabilisation at even that embodiment scale of process would enable life forms to adapt and endure despite changing environments, to cooperate into societies, and to experience an innate tendency to re-establish order and to ‘heal’ after chaotic disruption. Comparative informational exchanges at every level of this ‘relationally real cosmos’ could potentially generate consciousness, with different qualities that depend upon the types of comparisons involved in this shared life process.
Part 3 extends this principle of life emergent in physical systems to show how embodied human aesthetics, and the musicality of conversational interactions, are intuitively a significant feature of the vibrational reality we dwell among. They help us to see through materialism and scientism into an extended reality in which timing becomes an important feature of the human power of choice. This power of choice over our responsiveness in shared movement is a step beyond the mathematics of resonance, into the sacred realm of harmonisation with ‘something beyond ourselves’. The vibrational nature of ‘voice’ adds an accessible image to how we influence Golden Ratio proportionality in our intuitive relatedness with the wider world and cosmos.
Since the birth of quantum physics in the 1920s, materialism as a worldview is now ‘in doubt’. Sacred geometry released into sacred topology opens a new way to understand substance as informational movement in feedback systems. Space-time-substances co-emerge from one-field movements in which we participate. They are describable as waveforms (psi ψ) and interacting synergic fields of energies better than as particles, which become a linguistic term summarising the behaviour of certain wave patterns. The reality that actualises is bursting from within with an emergent potential for life. Our lives are shared within that context. Triquetral spin principles are sacred because they unite informational movement within and beyond each of us, as we can now go on to see. If the human intellect tries to dissect those principles of self-organising movement into parts, responsive movement ceases as if on a slab, and locally the cosmos corrupts.
Part 4 – Sacred Geometry – Internal scaling inside a circle’s circumference
The sacred is that which is implicitly a foundational truth required for life to be creatively sustainable. Respecting the sacred is the same as showing respect for the shared quality of people’s diverse lived experience. In practical terms, respect for the sacred is found in the African concept of ubuntu, and its global equivalents in all human societies and in people’s respect for our shared natural ecologies.
To consider the early Greek and Renaissance view that geometric proportionality is sacred means returning to a static mode of thinking about relatedness, which the New Science has moved beyond. Static materialism is like the shell of a chrysalis left behind. Thinking in terms of quantum field interactions as helicoid movement will allow science, spirituality, and the intuitive consciousness of aesthetics to reconnect ‘topologically’ in a sacred flight or dance. Movement in systems has a creatively relational timing of responsiveness between locality and context, which is captured in triquetral cosmology’s bidirectional topology. Golden Ratio stabilisation in the widest context can restore local life even after its temporary extinction.
Before enlarging on this foundational theme, however, we should first understand why the Golden Ratio in geometry was initially considered to have sacred significance.
Euclid’s discovery, that a Golden Ratio of lengths in the pentangle allows scaling further into the centre of a circle, led some people to attribute mystical significance to this quality of ‘remote replication of inner forms’. It has led to exaggeration or abuse by some as magical in a pagan view of ‘four elements’ (earth, air, fire, and water), by adding wood as a fifth element that represents a transitional state of sacrifice to influence the balance of the other four.
That destabilises life-enhancing order locally, and separates it from the wider life context. Secular science has offered a different way to make sense of life, but in its day it was Messianic Christianity that brought to an end the need for sacrifice by offering an ultimate sacrifice. It safely replaced the former occultism with an openly public spiritual path that purifies the hidden ‘inner heart’ instead. Seeking that inner spiritual quality enhances wider life proportionally, making it a sacred path, not a religious one. Sadly, over the following millennia, religious practices evolved that became formalised and fragmented through divisive thinking. Rather than seeking the mutual deference needed to honour the fundamental diversity-in-unit, which is a feature of healthy and adaptive living, divisiveness in religion and materialism veils its deeper truth, beauty, and restorative power.
However, the New Science of field interactions and adaptive relational systems is congruent as a way of thinking with this sacred, unity-seeking way of living. While describing field unity in terms of synergy, entanglement and superpositions of probabilities for remote relational change, these concepts are remarkably similar to the spiritual hopes that move people into paths of self-improvement, relational connection, and wisdom. The New Science of proportional relatedness in dynamic systems is congruent with ‘inner personal depth’ worldviews, which include consciousness, spirituality and aesthetics. All of this lifts the pentangle’s mystical geometry into a far wider influential context, one of ‘creative relatedness’ now, making a place in our inner hearts for movement with others that connects us into sacred topology.
To understand that context of sacred topology I shall draw your attention to the circle around a range of geometric forms. That circumference around its centre can be used to imagine how the inner geometry gets set into movement. This circumference is the life that becomes the sustaining origin of created life within the circle of creation (verb) that represents cosmos. But please always remember, that ‘circumference’ is a diaphanous and liminal zone of growth. It is an edge that is always expanding and flexibly reshaping, proportionally connected with all movement in the circle. The liminal growth zone is itself on the move, being shaped into movement from within. It is not a limit. Cosmos is alive and exploratory.
Interesting geometric features of a liminal circle
‘Interesting geometric features’ therefore start with the one point that is the centre of an expanding circle’s circumference. Centre and circumference are dynamically related to each other if there is expansion. A straight line connecting points on a circle’s circumference (representing their entanglement) will sometimes pass through the centre, but mostly miss it. These lines from various points on the circumference will criss-cross in a field-like infilling of the circle, or the sphere if it has become three dimensional (3D). Untangling these interesting features can best be understood by firstly using static geometry, before showing how this relates to creative helicoid movement.
· One point on the circumference of a circle could expand to become the centre of another circle. A string of these points all sequentially expanding would make a progressive wave of movement, introducing asymmetry into process at this most foundational level. If waves were to start simultaneously from all points of the entire circumference (of a circle or a sphere), then an expanding field of radiance results – which is glory.
· Two points anywhere on the circumference of a circle connected internally by a straight line would not lead to unpredictability if movement is set up between them; only predictable repetitive movement could result, like a pendulum. Movement along the line may generate a bidirectional vibrational tone, however, such as the Hebrew sung ‘yod’ or singing om (or aum) in Hinduism, Buddhism, Sikhism and Jainism, taught as the first sound of the universe radiating synergically from ‘between’. In that single vibrational tone, the synergic relationship between two differently placed points establishes them as equally valued in their united diversity. That tone becomes the relational reality of connection. Proverbs 8:22-31 may also describe this state, where Wisdom (in Hebrew a feminine noun), says, “Adonai made me as the beginning of his way, the first of his ancient works.” To personify this dynamic relatedness is characteristic of theism, but the identical process may be expressed differently in other cultural settings. This also appears in the Genesis 1:2 description of Creation, where the Spirit of God (also a feminine concept in Hebrew) hovers over ‘the waters’ prior to the Word being spoken, which modulates or stirs those ‘waters’ into vibrational waves. This visual imagery makes accessible the relational polarity of ‘two’. Their diversity spans the ‘context between’. Creativity thus emerges as a triadic process because this is a relational reality. The Potential Between actualizes.
· Three equidistant points on the circumference of an expanding circle would be a geometric triangle. The straight lines do not pass through the centre of the circle. In Parts 1 and 2 we visualised Pythagoras’s important discovery, that the proportionality of the edges of a triangle relates to their areas as ‘squares’, not merely the lengths of the lines. Imagine now that those edges continue to expand, and have to curl into a sine wave curve because the corners are fixed in relation to each other. This represents their beginning as three vibrations, a triadic hum. Movement is thus introduced into the geometry. The movement will also affect those ‘squares’ of triangular proportional relationship. The squares would start curving topologically like sails on a boat, and perhaps become mobile like the wings of a bird. They might warp and wave like fronds of kelp in the sea as a radiant zone of influence catches some remote movement beyond the visible ‘lines’ of connection between these three triangular points. This poetically describes the start of the process that turns a geometric triangle into a topological triquetra (which will be further explained in the next section on Creation from No-thing).
· Four equidistant points on the circumference of a circle make a square. The crossing diagonals of a square pass through the point at the circle’s centre. Vibrational change along those crossing lines may cancel each other out at that nodal point. This would reconcile change into a stabilising stasis. However, stasis is not static stillness, or stagnation. Stasis is a restful energy state of potential movement, a diastole or filling phase, from which enlivening change can further emerge if there is relational connection with another state of movement.
· Five equidistant points on the circumference of a circle having internal connections create the pentangle, which has an inner five pointed microcosmic space that replicates the macrocosm. Further scaled replication of the higher order macrocosm as image and likeness can emerge in this inner space. This is a type of ‘fractal scaling’. If the lines and their associated proportional squares of influence are set into vibration, the potential for relational movements to emerge increases with greater complexity within the microcosmic substates. Remote resonances could then also influence local changes. This diversifies the unity of emergent inner order.
· Six points creates more stability as the diameters between opposite corners cross in the centre and cancel each other out or magnify each other depending on the wavelengths and frequencies of those vibrating lines. The centre itself develops a more complex state of potential for further change (described with precision in physics by the Schrödinger equation). In vibrational terms, that central point can represent a rest phase (a diastole, an in-breath filling phase, a Sabbath) between the growth phases of life (the systoles). Its radiance will spread to diversify the developing relational reality of movements that are life itself, as we shall go on to see.
· Seven equidistant points on a circumference also make a star. This star has a central seven-cornered microcosmic space in which fractal replication can add further depth to the complex wave functions that are spreading through and infilling the context of that circle. Even more potential for likeness to be replicated has arisen within the whole. By now, however, the remote influences between the waves criss-crossing the context of the circle (upon which I have asked you to focus your attention temporarily) are more than complicated. They have become complex. A microcosm in that circular context may be offset from the centre if it derives from a distorted pentangular star where the points are not equidistant. Multiple offset geometric star patterns with could start to interact in that wider context, producing complex interactions (or intra-actions). They are describable in words, and equally imperfectly in mathematical terms, or pictorial diagrams, or in music, or dance, but their complex processes have become unpredictable when an attempt is made to understand them from any point within the circle that is life context. Inputs to any one point in this context are too complex to describe; outputs can only be thought of as probabilities. Things happen in life.
I ask readers now to shift your focus of attention from these words and the conceptual circle that I have been describing to the environment where you are reading this. Look at, feel and hear some of the objects you can see in that ‘circle’ of your visual field of attention (not excluding your body from it). You are sensing your inner heart connection into the relationally real outworking of this type of vibrational complexity.
And so on… Stars in the circle with an even number of points generate stability; odd numbered points on the circumference of a circle generate inner spaces and depth as they connect with each other generating unpredictability. An emergent or unfolding order of movement has phases of diastole and systole, infilling and expression, potentializing and actualizing. Microcosmic replication of image and likeness can proceed. Phases come to their end, and phases have new beginnings in a never ending systemically re-integrating process. As explained in Parts 2 and 3, a Golden Ratio among criss-crossing vibrational waves could stabilize potential chaos. Otherwise, the vibrational connections may sound like an orchestra tuning up, before the concert begins.
As mentioned earlier, this vibrational process radiates from the synergised Potential Between every point on the liminal circumference and the central point. That is the sacred context of glory. Every other point within that circle derives its source from that glory, potentially widening its input if open to receive and respond to it with an expression of change. But ‘points’ tend to narrow their focus of attention from this widest context. The stabilisation process may become unhealthily stuck and resistant. The inner replication of a power of choice may enable some points to narrow their acceptable source of inputs and probabilities for change, hiding from others in the wholeness of glory. People are like points in this widest context. Enlightenment Science was one such process of narrowing focus onto the physical and measurable. Trauma narrows people’s focus and makes them less exploratory. The human body, indeed any living form, has more than just a physiology of molecules that gets stressed; there is also a physiology of light unfolding through and between those emergent molecular patterns of movement, which offers phases of activity and rest.
The triadic nature of participatory life
Geometry, an analytical branch of mathematics, focuses on static forms in a way that displaces life from their formation. For example, when focusing on the geometry of a triangle, ignoring how its sides are 2D squares that determine its proportionality will narrow the mind and make it harder to see the wider ‘background context of interactions’ that create the triangle’s proportions. The background context includes the analysing mind, of course. We can open that mind, awaking a wider consciousness. Sacred geometry acknowledges the mind’s creative power to focus on a context and see a form emerge within it. Sacred topology re-opens the mind’s creative power in wider contexts, provided there is also inner change and responsiveness.
Multiple forms may be seen or imagined within any selected focus of attention. For example, look around you now. Your mind, or ‘you’, can select any feature to focus your attention upon. You could choose to see it as a static from that is spatially related to multiple others. That materialistic context is a selection that has excluded much else, but it would empower you temporarily to act dispassionately upon those ‘objects’ to push them around as you chose. Sacred geometry will see that there is also that depth of context of movement (life), however, that historically has brought about that spatial arrangement. It is an arrangement in process. The mind working with sacred geometry may also see that there is potential for further transformative change in the present patterns of relatedness, in which our inner formative hearts participate. Thus ‘history and potential’ inherently compose the reality that you currently perceive, and what you perceive you dwell among as a participating embodied personal substate of that movement. We are relationally part of the sacredness of that geometric form. This innate potential for transformation is the reason why sacred geometry has to move on to sacred topology if it is to explain the proportional stability of unfolding life to which we contribute.
Moving on in chosen contexts is the process that potentially restores living connection into even the source of the cosmos. In so doing, the glory of creation (verb) can be seen to shine out through every object and molecule of matter when focusing that way, interconnecting their inner and external transformational movements with a potential to contribute reflectively as feedback cycles into life.
Sacred topology begins even from a single pinpoint source (to our minds) that grows and repatterns into a 3D transactionally moving space. In this space, changes stabilise with fourth dimensional timing, forming inwardly proportional patterns with outwardly relating proportional movements. These patterns are topologically moving systemic substates of the whole. Their geometric proportions and topological movements shape the whole context of life from within, space, time, and substance simultaneously.
These substates of a metaphysical wholeness could topologically stabilise their ongoing spin movements sufficiently to endure for a time-frame in which to grow, to be adaptable enough to relate with other diversifying substates, and to replicate their own growth. When we focus our attention on this embodied life process, we must be careful not to ignore how we participate in it, through every diversifying molecule and radiance of our ongoing physiology. We are intra-active, not merely dispassionate observers. Our minds are the meeting of two or more substates or concepts.
We have already looked intra-actively at the glorious relationship between centre and circumference. We have seen how vibrational tones between any two points will establish an in-between of context for their inputs and outputs to each other. (The root of these tones may be the ‘spinors’ described mathematically in particle and quantum physics.) The triangle has three vibrational tones, of course. These would topologically produce resonances (or dissonances) that we know musically in the harmonics of major and minor chords, tritones and augmented or diminished chords. Knowing is participating in – being moved in our inner heart with aesthetic appreciation.
Creating triquetral informational movement (three-cornered) from no-thing
In the ‘three points’ section above about interesting geometric features of a circle, we looked at how a triangle’s edges may expand into a waveform of movement, which begins a triquetral spin. The time has come to expand this feature of sacred topology.
When the three points are fixed in their proportional relationships with each other and expansion of the edges continues, the points may become the corners of a triquetra as the edges each become a sine wave. This lengthening of the edges (and their associated squares of proportionality) would topologically allow two of the corners to spin in relation to each other to keep the same proportional connection between them. Imagine the blue corner in the images shown here to remain fixed. The red and yellow corners could rotate a half-spin in either direction, making the two waveforms connected to it curl inwards.
To maintain the same proportionality, the third would do the same, curl in and twist. As they criss-cross with each other, the conditions arise topologically to resonate or harmonise in a Golden Ratio. It so happens that, by trying to make a triquetral model using pipe cleaners and then wire loops I convinced myself that, what may seem obvious to others is true… it is impossible to do it without one loop somehow passing through another. That is why I went on to make 3D printed models of them with a local company using their computer assisted design technology. However, I realised that I was feeling and seeing in my hands the creation of 3D space out of movements of a 2D circle’s circumference. A vitally important discovery about process followed from this, which I need to explain in metaphysical or even mythical terms.
Let us assume for the sake of pictorial clarity that a two point tone has been established between Source and its first relational product, Spiritual Wisdom, and the vibration between them radiates into a circular circumference, which they want to explore. And so, they each reach out to a third point on the circumference they have made (which could be anywhere and everywhere). As each extends another line to touch the same point with their vibrational tones (an ‘offer wave’), that third point on their circumference relationally reflects the confluence of each tone back along both lines (a ‘confirmation wave’). In so doing, let us assume their three-way resonance makes them start to curl around each other’s waveforms, initiating the half-spin that characterises a triquetra. Either direction is equally valid and valued as phase changes. In so doing, those vibrational lines of connection must pass through each other, which might give both the Source and Spiritual Wisdom an experience of something new happening, and their birthed feedback cycle of responsiveness. They will experience harmonisation. This mutual quality of awareness would extend to wherever on the entire wider context of the circumference these three points in harmony choose to explore. These three together (Source, Wise Spirit, and Circumferential Context) will have created amongst themselves a 3D space with fourth dimensional movement. Where formerly there was no thing, no-thing, now there is a context within which things can relationally form.
The Latin root of experience is ex- pereo: meaning from– and I go through. These three would experience harmony on knowingly passing through each other. On passing through each other, a Golden Ratio ‘sweet spot’ is discovered in the mutuality of their resonance that stabilises their knowing together. And this is the outset (or inset) of Creation as an ongoing verb within these four dimensions of dynamic relationality. The triquetra iconically shows how all three synergise. In the 4D context created, further vibrational resonances established among their diverse unity unfolds as a space-time-substance reality. (The ‘substance’ of this will be explained further in the next section.)
In our human lived experience there is much discussion about the nature of consciousness. The Latin root is con– scire means with– to know. Consciousness is knowing with another. In this metaphysical story of Creation (verb), divine consciousness arises simultaneously with the ongoing relational process of creating the 4D space-time-substance in which we human beings move and breathe. We humans participate in this divine consciousness. However, it is vital to emphasise that consciousness is not a substance from which other things are made. Consciousness is the relational harmonisation that makes things. Human beings are ‘made embodiments of life’ (as are all life forms), and as such we share in this divine consciousness, each in our unique ways, with our unique perspectives and experiences whether animate or plant or microbe. Consciousness is a lived relational process of exploring life together. The term ‘panpsychism’ is commonly used dangerously in ways that suggest that consciousness is ‘real’, or more real as a primary feature of the cosmos than the matter of which our bodies and environments are made. That view of panpsychism is, I believe, a misconception of the relational reality of creation (verb).
The triquetra is an icon of the triune relational process that is both creative and consciously harmonic. It shows how, from any one point (a triquetral corner), a view can be obtained on the quality of relationship ongoing between the other two. Self and others are generated as intra-acting feedback substates of this one wholeness. In that view, personal identity is birthed at the very beginning and in the ongoing processes of space-time-substance.
Our topology: looking out to a circumference when participating in the movement
The sacred geometry and topology of triquetral cosmology is stabilised in its movement by a Golden Ratio of resonance. The human being participating in this cosmological movement intuits its effects consciously as harmony, or a sense of rightness or completeness, or depth-peace despite outer turmoil. Sacred geometry in movement has become sacred topology.
Triquetral cosmology proposes that the cosmos has a liminal circumference that is birthed from within its own prior foundational life-movement. The ‘between’ of this triune life process continuously infills with informationally-connected patterning formations, which are continuously reshaping according to the vibrational dynamics of exploration and rest phases.
There is a mathematical term called a Bessel function that describes how waves interact within a boundary. This function has many applications, but it may also help to visualise how cosmological scale movements can create locally diversified conditions and patterns of movement that nevertheless are united in their movement within the whole. The ideas about life that a conscious human being can generate are framed from within the context of this type of moving cosmos, looking ‘out’ through its sacred topology to ultimately its constantly reshaping circumference; but to avoid becoming too extraverted, that same liminal and exploratory circumference is the depth of inner heart also that is knowable in an introspectively conscious human being. The door of heaven, and the door of the heart are one and the same.[i] Within this context of life, however, the human brain’s level of complexity allows internal processing that enable people to take a mental step back from participation in life, to imagine temporarily that they are observers of life’s patterned forms and structures as if they are objects for the analysing mind to manipulate. It is a type of temporary self-delusion that has value to work out what processes in life do run independently of my personal influence. However, this only has life-enhancing value if its conclusions are reintegrated back into a participatory and intelligent way of relationally living in the wholeness of life as a gift that enriches others. Context-independent ‘truth’ is not ‘the whole truth’. Participatory conversational feedback truth that harmonises is closer to the whole truth.
Substance is an emergent patterning in our conscious minds resulting from the direct engagement of the brain’s informationally-processing structure with this cosmologically stabilised patterning of triune movement. Mind is not separate from matter. Mindful engagement with life generates conscious qualities of substantial relational interactions between movements that we interpret mentally as matter. An overactive left hemisphere can interpret this as if an observer of matter in space-time, but other more participatory interpretations of substance are possible.
The Latin etymological root of ‘substance’ is sub- sto. It means under- with I stand, suggesting there is a foundation upon which the ‘I’ is secure in life. Some people (many in a Westernised educational frame) have habitually developed an observer worldview in which materialistic dualism of mind and matter seems to make sense most of the time (although everyone has some strange experiences that do not fit with this view, and nobody can work out how these two separate essences are supposed to interact). In this worldview of materialism, substance means the essence of material things. However, its more direct translation is ‘understanding’, which is a concept reserved for the mental ‘world’ in that observer dualist mindframe. To understand is to know that the concepts behind other concepts hold together firmly enough to suggest ways that people can make sense of the past and plan or anticipate future events from the present context.
Substance in a triquetral cosmology, however, is the vibrational one-field from which both matter and mind co-emerge in ‘imagining life’. Therefore, space-time is not a container for observed material movement. Co-emergent from sacred topology is space-time-substance. In this dynamically cosmological life we participate with a potential to harmonise with intelligent love, even when brokenness disrupts life through dissonance, because our participation is part of the healing inherent in Golden Ratio stabilisation.
[i]
The Parish Church notice board in Totnes, Devon, UK, the first ‘Transition Town’ of this global movement to reconnect as communities with our shared ecology.
