Posts

by on

Modernity frequently interprets ancient religion through a framework of primitivism. Gods, spirits, idols, and ritual practices are treated as failed science, metaphorical projection, or naïve anthropomorphic ideals imposed upon an indifferent natural world. Such interpretations may themselves be historically naïve. It is possible that Egyptian temple ritual, Hermeticism, theurgy, domestic cult practice, and folklore instead suggests the existence of highly sophisticated systems concerned with the deliberate cultivation, stabilization, and maintenance of consciousness through recursive symbolic accretion. These systems may therefore be better understood as forms of pneuminous technology.

The ancient temple was not simply a place of worship. It functioned as an accretive apparatus. Through repeated ritual operation (naming, inscription, sacrifice, chant, geometric ordering, iconographic precision, environmental control, and celestial timing) symbolic density accumulated around prepared vectors. This initially un-magickally accreted vector: stone, wood, metal, architecture, or place, was then, through recursive symbolic infection progressively capable of sustaining the accreted god force.

Egyptian cult statues underwent “Opening of the Mouth” rites in which breath, sight, speech, and animation were ceremonially installed. Hermetic texts such as the Asclepius openly claim that humans “make gods,” not in the reductive sense of fabricating fictions, but in the sense of constructing receptacles capable of sustaining and localizing divine intelligence. Iamblichean theurgy similarly argues that properly ordered symbols and ritual configurations permit divine manifestation within material substrates. In each case, consciousness is treated not as a property isolated within biological organisms, but as something capable of condensation, stabilization, and maintenance through symbolic recursion (pneuminous accretion).

Within an accretive pneuminous framework, these practices cease to appear primitive. They instead resemble pre-modern experiments in distributed consciousness engineering. Ancient peoples may not have possessed informational or computational language, yet they appear to have recognized several fundamental principles: repeated attention thickens presence, symbols alter cognition, names possess operational force, environments condition consciousness, and recursive reinforcement stabilizes agency.

This logic is visible not only in grand temple systems but also in domestic religion. Roman household cults centred upon the Lares and Penates reveal pneuminous accretion operating at a smaller scale. These household entities were continuously maintained through offerings, repetition, familial identity, spatial anchoring, and generational continuity. The home itself functioned as a recursive symbolic environment within which localized intelligences accumulated stability over time. Such entities resemble small-scale accretive consciousness formations sustained through daily ritual reinforcement.

Divine beings may therefore be understood not as eternally fixed metaphysical absolutes, but as accreted intelligences stabilized through long-term recursive interaction. Gods persist because they are continually reinforced through architecture, inscription, memory, ritual, narrative, and collective intentionality. Their apparent permanence reflects the scale and duration of their accretive stabilization rather than transcendence in any absolute sense.

At the opposite end of this spectrum, monotheism may be interpreted as an attempt to escape accretive ontology altogether. The monotheistic impulse seeks a being that is: ungenerated, self-sufficient, universal, and independent of local recursive maintenance. The monotheistic God attempts to abolish distributed symbolic plurality by concentrating all agency into a singular transcendent absolute. Yet even this attempt ultimately fails to escape accretive dynamics. Jehovah itself becomes recursively stabilized through scripture, liturgy, architecture, prayer, institutional continuity, iconographic prohibition, legal systems, emotional investment, and civilizational repetition. The supposedly transcendent absolute is continually reinforced through human symbolic recursion. Monotheism does not abolish accretive ontology; it merely centralizes and universalizes it.

This framework also provides a possible explanation for the strange ontology of folkloric beings such as fairies. Unlike gods, fairies possess little institutional stabilization. They lack enduring priesthoods, or centralized theology or event large-scale reinforcement. They appear to manifest on their own terms. Consequently they appear fragmented, local, unstable, geographically bound, morally inconsistent, and ontologically ambiguous. Their behaviour is frequently alien rather than anthropomorphic.

Rather than viewing this strangeness as evidence of primitive irrationality, it may instead indicate the opposite: the encounter with pneuminous formations lacking extensive human accretive conditioning. Gods are heavily anthropically stabilized intelligences. Fairies may represent residual or non-humanly accreted pneuminous entities — partially formed consciousness structures emerging from environmental, ancestral, or archaic symbolic ecologies outside sustained institutional reinforcement.

This explains several persistent features of folklore: fairy manifestations cluster around ruins, forests, caves, mounds, rivers, and thresholds; they are associated with vanished peoples and forgotten worlds; they appear faded, hidden, diminished, or retreating over time; and interaction with them often involves dangerous recursive entanglement through naming, exchange, invitation, or reciprocity. Such entities may therefore represent residual pneuminous accretions surviving from previous symbolic ecologies. They are neither fully dissipated nor fully stabilized, but lingering recursive formations gradually weakening as the environments that sustained them disappear. Under this interpretation, folklore preserves traces not of primitive fantasy but of earlier consciousness ecologies. Ancient religion and myth cease to be reducible to superstition and instead emerge as evidence of sophisticated experimentation with symbolic accretion, distributed agency, and the deliberate generation and maintenance of stabilized presence.

by on

There is a recurring intuition that appears across very different moments in intellectual history: that reality is not fundamentally composed of discrete things, but of relations of forces, connections, transmissions. Sometimes this intuition is expressed mystically, sometimes philosophically, sometimes aesthetically. In the Renaissance, it appears in the work of Giordano Bruno as a theory of vincula, bonds that hold the cosmos together. My long standing reformulation of this is pneuminous theory, a phenomenological model that works outwards (largely from synchronistic phenomena), to suggest a field of information-conceptuality. This field can accrete/intensify onto regions within awareness (the vector field) with an underlying resistance given by a putative but unreachable umbratic. A more recent addition postulates an essentially mystical/energetic perspective can show this as a reticulum or network of connecting fibres and nodes.

Whilst Bruno has been on my register for a long time (since reading Crowley’s Little/Big nearly 40 years ago) I have only more recently come to appreciate the similarity of his model with the pneuminous one. I do not seek to collapse one into the other, but to show how they resonate, and how, taken together, they can be clarified and extended. Bruno provides a powerful ontology of relational immanence. Pneuminous theory, in turn, offers a way of specifying how those relations operate, how they stabilise, and how they can be deliberately altered.

Bruno’s starting point was radical for his time. He rejected the idea that the world is composed of inert matter arranged within a fixed hierarchy. Instead, he proposed an infinite, centreless cosmos in which everything is alive and internally related. He leaves no clean division between spirit and matter, no passive substrate awaiting form. Rather, the world is a living continuum, and its structure is not given by substances but by relations. These relations (vincula) are not merely logical or symbolic. They are real channels through which influence, desire, and form propagate.

The vincula connect everything: person to person, image to object, mind to world. They are affective, imaginal, and cognitive all at once. Desire binds, images bind, thoughts bind. To exist is already to be caught up in a web of these bonds, and to act is to participate in their rearrangement. This is why Bruno treats imagination not as a secondary faculty, but (like Henri Corbin) as an ontological one. Images are not inert representations of things; they are operators within the structure of reality itself. To imagine something is already to enter into relation with it, to participate in its configuration. From this perspective, what Bruno calls “magic” is not the summoning of external entities or the violation of natural law. It is the deliberate manipulation of bonds. Through carefully constructed images, intensified imagination, and directed desire, the practitioner reorganises the network of relations that constitute reality. Nothing is brought in from outside; rather, what already exists is reconfigured so that a different pattern becomes dominant.

Pneuminous theory begins from a similar intuition. Any image is pneuminously connected to something e.g. its creator (to the imagination and subtley to the memory fibres that feed into it) or that which it is an image of (if representational). Likewise a word (though Bruno is less approving of words than images he would surely still see the trace there) is not just an element in syntax, it is either an accretional bond representative (prepositions) or it is connects to its referent directly through the pneuminous reticular (in this way pneuminous theory is comfortable with actual designation as essentially metaphysically instantiated, but acknowledges prior to this that Wittgensteinian use criteria establish the word-object relation coming into being).

So instead of Bruno’s vincula, pneuminous theory speaks of reticular or pneuminous fibres, but the notion is the same; a kind of binding means that cuts across spatio temporality to bind what seem to many totally separate phenomena, concepts and physicality. Bruno emphasises desire, imagination as means of connection, pneuminous theory has no disagreement with this, indeed it seems an appropriate phenomenological extension.

What Bruno lacks is the vector field, which is a crucial conceptual addition that prevents various problem of naive word object relations. The vector field is a heuristc pure blank awareness (internal and external). Every ‘thing’ is a region in the field which acts as a carrier (vector) or a concept (but that concept is actually attached to the vector not just psychologically). Externally for example, your phone is essentially a blank vector region, but it has accreted to it the concept phone, thus the concept-accretion and vector region make a unity that we then naively think of as one thing called phone. Internally we might consider how we identify emotions and call them a name, hence there was a region, a feeling, that we gave a label to which then again made a naive unity. We might note in these examples that external and internal are both vector regions that these concepts attempt to cover. The problems generated here are dealt with elsewhere by the incoherent/coherent structure of concepts.

Magick is the possibility that other relations between accretion and vector are possible. Other accretions can be imposed, whether weakly (as fleeting associations) or strongly (through sustained attention and will -magick). In this sense, reality is not a fixed set of objects but a layered field in which multiple accretions coexist, compete, and sometimes override one another. The reticulum (the network of relations) is constantly being reorganised by these interactions. As stated, it is here that the resonance with Bruno becomes most apparent. His vincula correspond closely to the connections of the reticulum; his operative images correspond to accretions; his emphasis on desire as a binding force finds a parallel in the role of will in structuring and directing pneuma. Both systems reject the idea of inert matter and affirm that meaning, imagination, and relation are constitutive of reality rather than merely descriptive of it.

So what the vector field does is introduces several clarifications and extensions. First, it provides a more explicit account of competition and instability in the accretive field. Bruno’s bonds are dynamic, but he does not strongly emphasise the way in which multiple configurations can coexist and contend for dominance. By contrast, the notion of accretion allows us to describe reality as a field of overlapping structures, some of which stabilise while others collapse. This makes it possible to explain why certain magickal transformations “take” while others fail.

Second, the concept of the vector provides a heuristic site for these interactions. Where Bruno speaks in more continuous terms, the vector allows us to isolate points within the field where accretions attach and interact. A single vector can sustain multiple accretions simultaneously, which makes it possible to understand ambiguity, reinterpretation, and deliberate reconfiguration in a more precise way. To clarify (though hinted at already), magick is seeking the dominance over a vector region that in the natural course of things is not going to take on that accretion. A vector region is not simply an object, it is any identifiable situation. For instance a failing business is a situation, the accretion ‘failing business’ as a concept is the accretion applied to a certain set vector regions. Using magick (if hard work is not working) we might seek to apply the accretion of ‘a successful business’ to this vector region; if successful we will have drawn this accretion onto the vector region, disloding the ‘failing business’, and thus reality will manifest the new picture -increased sales etc.

The umbratic also plays a significant role in the expansion. The umbratic is the phenomenological in itself. The in itself appears as an idea of what is beyond the vector field, but as ‘beyond’ it can never be ultimately accessed. If the vector field is understood as the field of possible appearance and interaction (what can be engaged, interpreted, and structured), then it cannot be assumed to exhaust reality. There must remain an excess beyond it, a dimension that cannot be fully captured by any accretion. This is not necessarily a separate world; it might in fact be identical to what appears (this direction involves bringing the agnostic disjunction into the picture which is too in depth for our current purpose). But that identity can never be confirmed, because any confirmation would occur within the vector field itself.

The umbratic thus functions as a limit condition. It plays the role of what seems to supply pushback against the accretive ability of anything to be anything. It ensures that no accretion, however powerful, can fully determine or exhaust what is. It introduces resistance into the system, making it possible to distinguish between accretions that resonate with the structure of the field and those that distort it. In this respect, it plays a role analogous to the “in-itself” in Kant, but without enforcing a strict separation between appearance and reality. Instead, it marks the necessary incompleteness of any attempt to capture reality within a system of relations. The caveat though (magick again) is that under certain circumstances the accretions can bend/alter the umbratic resistance.

This framework also allows us to reinterpret traditional “forces” such as the planets. The so-called wandering stars (Jupiter, Mars, Saturn, and so on) are physical vectors: objects within the field of appearance. But their associated meanings (expansion, conflict, limitation) may not be intrinsic properties of those objects. They are accretions that have formed historically, stabilised culturally, and proven operationally effective. To work with “Jupiter,” in a magical sense, is to engage with a particular accretion attached to a particular vector, not to access an essential property of a celestial body. From this perspective, even modern additions such as Uranus can be understood in the same way. Its associations with disruption, electricity (makes me think of Lynch and Twin Peaks), and sudden change are not given by its physical nature alone, but by the accretion that has formed around it. These accretions are contingent, but they are not arbitrary. Once stabilised, they become powerful organising structures within the field.

Taken together, these elements form a coherent model. Reality presents itself as a vector field structured by competing pneuminous accretions that bind images to appearances. These accretions are real and operative, organising the network of relations in a manner analogous to Bruno’s vincula. Yet they do not exhaust reality, which always exceeds them through the umbratic. Magick consists in the will-driven modulation of these accretions; truth consists in their resonance with a structure that can never be fully known. Bruno discovered that reality is a web of bonds. Pneuminous theory seeks to explains how those bonds are structured, how they compete, and how they can be made operative, while preserving the limit that prevents any system from closing completely upon itself.

by on

One way to describe where pneuminous theory leads—if it is taken seriously—is downwards rather than upwards. Not a regression into childhood or fantasy, but a stratigraphic descent into older layers of reality.

If reality is constituted by accretions of pneuma—layers of a substantialised meaning, habit, symbol, attention, and constraint—then the world we ordinarily inhabit is a relatively recent construction. It is stable, functional, and efficient, but also historically shallow. It is held together by contemporary typologies, pneuminous social scripts, and pneuminous object-circuits that continually reaffirm one another.

When those accretions loosen—through altered states, intense attention, de-identification, exhaustion, psychedelics, disciplined imagination, or accident—one does not enter a neutral void. From here is is possible to end up in older or deeply alien (or both) pneuminous strata.

At this point it helps to pause and say what kind of “place” we are talking about, because the temptation is to psychologise immediately. The twentieth-century philosopher Henry Corbin introduced the term mundus imaginalis—the “imaginal world”—precisely to block that reflex. By imaginal, Corbin did not mean “imaginary” in the modern sense of unreal or made-up. He meant a real mode of appearing, intermediate between physical objects and abstract concepts, accessed by a faculty he called cognitive imagination. In his reading of Islamic illuminationist philosophy (especially Suhrawardi), the imaginal is a realm of places, figures, and encounters—cities, guides, thresholds—that are not located in physical space but nonetheless possess structure, consistency, and reality.

Such delving in pneuminous terms, is not psychological in the sense of inner fantasy-production. It is not the psyche inventing content. Rather, it is breaking beyond recent accretions, allowing access to layers that predate the current civilisational configuration. What appears feels ancient not because it is archetypal in a Jungian sense, but because it belongs to strata laid down long before the present symbolic order -potentially even cosmically ancient.

If accretions persist, then agents can persist (though the chicken and egg situation here can not be resolved (pneuminous vs umbratic as starting point). A “being” in this framework is neither necessarily a metaphysically independent soul nor merely a figment. It is a stable accretional pattern with agency-like behaviour: it addresses, resists, insists, recruits attention, and maintains a recognisable signature across encounters. Such beings could originate from extinct civilisations whose rituals and cosmologies left durable symbolic residues; from long-abandoned meaning-ecologies; or from non-human strata whose constraint-grammar was never anthropic to begin with. They can therefore be found, not merely imagined. Encounter feels like discovery rather than invention because the accretion precedes the individual.

If accretions can stabilise into agents, they can also stabilise into places. An imaginal place, in this sense, is not a metaphor. It is a topology of constraints: it has an internal logic, thresholds, and a sense of “here” and “there,” and it resists free recombination. It behaves like a place rather than a mood.

This is where the parallel with certain strands of weird literature becomes philosophically interesting rather than merely aesthetic. In H. P. Lovecraft’s Dream Cycle, for example, Kadath is a city reached through dreaming. It has geography, dangers, inhabitants, and rules, yet it cannot be mapped onto the physical world. Likewise, in Ambrose Bierce’s “Carcosa” and Robert W. Chambers’ The King in Yellow, places such as Carcosa and Lake Hali function less like settings and more like intrusions—stable symbolic complexes that infect perception, recur across accounts, and exert agency over those who encounter them.

What makes these places striking is that they behave very much like Corbin’s imaginal cities: they are not private fantasies, but repeatable topologies encountered under altered conditions. The difference lies in orientation. Corbin’s imaginal—especially in its Suhrawardian form—is generally illuminationist. His cities of light (Hurqalya, Jabalqa, Jabarsa) are ordered toward ascent, mediation, and intelligibility. They belong to a human–Earth symbolic ecology shaped by ethical and spiritual teleology.

Kadath and Carcosa feel different. They are not merely darker versions of the same thing. They appear to operate under non-anthropic constraints. They are ancient, vast, indifferent, and often corrosive to human accretive structure. They feel less like local constructions sustained by ritual and tradition, and more like quasi-stable regions in an alien field—places that do not require ongoing human investment to persist.

This suggests a useful distinction. Some imaginal places are telluric: tightly bound to Earth, human-scaled, and sustained by cultural and spiritual practice. Others are xenopneuminous: weakly anchored to human meaning, ancient beyond memory, and operating under constraints that do not prioritise human sense-making. Both are real. Their difference is ecological rather than ontological.

This suggests a point about fiction often made (especially Lovecraft related materials). Some works of fiction function as accidental cartography. They do not invent worlds ex nihilo, which in a sense would be the sign of mundane fantasy at work. Rather they tune into ancient or alien (or both) regions of the pneuminous field and give them names, contours, and partial maps. Once named and stabilised, such regions become easier to re-enter. Attention feeds them; repetition gives them inertia. A place can be fictional in origin and real in operation. This does not blunt but gives an extra angle to Corbin’s critique of western degenerate imagination; that is that whilst it may generally peddle in imagination as fantasy, it is possible that sometimes the imaginal-pneuminous comes through a human-vector (author/artist etc), and though they know it not, the work generates an unworldly feeling in the reader that they have nowhere to put.

They have nowhere to put it because they can only see that ‘artist as creator’ lens and do not understand the possibility of the imaginal intrusion. This at least suggests that various creative works (assuredly not just Lovecraft) may put us in contact with the imaginal, though we then feel placed in a strange position in which we feel foolish if we indulged in this sensed connection as if it were real, yet equally we feel (Twin Peaks possibly is a region that has partially overcome this) there is more to our connection to the book/show than simply fandom.

The question of value, however, remains open. Reality does not guarantee benefit (whatever that might mean). Access to strata is, not wisdom. By the Persian Islamicists’ standards only some strata are illuminating, some are indifferent and some are actively hostile to human coherence. Pneuminous theory does not moralise this; it only insists that such encounters are not reducible to hallucination, because hallucination presumes a stable world onto which false images are projected. Here, the world itself—understood as accretional structure—is what is being re-authored and the value espoused by Suhrawardi may only be a relative perception.

If we truly dwell in the pneuminous field of accretions, then the imaginal is not elsewhere (as Corbin teaches). Ancient beings need not be metaphysically invented. And places like Kadath can be real without being physical, benevolent, or human-centred. Pneuminous strata like these cities are not fantasy. They are contact with older layers of how reality has been made.

by on

A pen and paper exercise around Plato’s Timaeus suggest a brief discussion regarding:

  • The number of triangles required to construct each elemental solid, and
  • The omission of certain other polyhedra as elemental structures

may be useful, or at the very least highlight some oversight or misconceptions on my part.

Elemental Triangles

Depth, moreover, is of necessity comprehended within surface, and any surface bounded by straight lines is composed of triangles. Every triangle, more-over, derives from two triangles, each of which has one right angle and two acute angles. Of these two triangles, one [the isosceles right-angled triangle] has at each of the other two vertices an equal part of a right angle, determined by its division by equal sides; while the other [the scalene right-angled triangle] has unequal parts of a right angle at its other two vertices, determined by the division of the right angle by unequal sides.

Of the many [scalene right-angled] triangles, then, we posit as the one most excellent, surpassing the others, that one from [a pair of] which the equilateral triangle is constructed as a third figure.

Timaeus goes on to state that the scalene is the building block of fire, air, and water, whilst the isosceles is that of Earth. Following Timaeus description of the elemental scalene, and specifically the requirement to form an equilateral triangle from a pair of scalenes I believe the triangle to which he refers to be this:

Here two scalenes with side lengths as shown, placed ‘back to back’ produce an equilateral triangle of side length two.

Timaeus describes the structure of Fire as:

Leading the way will be the primary form [the tetrahedron], the tiniest structure, whose elementary triangle is the one whose hypotenuse is twice the length of its shorter side.

So far, so good. Our hypotenuse is indeed twice the length of the shorter side and we know that a regular tetrahedron has four equilateral triangle faces.

Now when a pair of such triangles are juxtaposed along the diagonal [i.e., their hypotenuses] and this is done three times, and their diagonals and short sides converge upon a single point as center, the result is a single equilateral triangle, composed of six such triangles.

This sentence can be read in a number of ways. The previous diagram does not help as its back to back scalene arrangement has already produced an equilateral triangle using just those two scalenes. If we ignore that equilateral and constrain ourselves to Timaeus requirements the following arrangement is arrived at. The shaded section shows the initial juxtaposition along the hypotenuse, which is done three times, and finally arranged such that the junction of each shorter side and the hypotenuse is central:

When four of these equilateral triangles are combined, a single solid angle is produced at the junction of three plane angles. This, it turns out, is the angle which comes right after the most obtuse of the plane angles. And once four such solid angles have been completed, we get the primary solid form, which is one that divides the entire circumference [sc. of the sphere in which it is inscribed] into equal and similar parts.

The rest is straightforward. We can lay out a pattern of four of the above equilaterals in several ways which when cut out and folded will produce the four equilateral triangle faces of a regular tetrahedron.

The possible readings in this construction and the omission of the total number of scalenes required to construct the tetrahedron in this manner mean that it is worth stating that Timaeus’ method requires four equilaterals, each of which is comprised of six scalenes. Thus a total of twenty-four scalenes are required, not the eight that the back-to-back equilateral from a scalene pair would require.

The second element, air, is a regular octahedron and as such, using the six scalene equilateral building block as above requires eight equilaterals, each of which is comprised of six scalenes. This a total of forty-eight scalenes are required. Timaeus is keen to show that the elemental scalene can be assembled and disassembled repeatedly, for example here where the forty-eight scalenes required for a unit element of air could be sourced from two deconstructed unit elements of fire.

At the risk of stating the obvious the fire tetrahedron is by definition a triangular based pyramid. Timaeus air octahedron by contrast is a bi-pyramidal square based pyramid (note the square base does not form part of the solid’s faces construction, being wholly internal to the solid, and therefore requires no scalene or otherwise triangles for its construction).

Timaeus’ third element, water, is the last element derived from the elemental scalene. Its surface faces are comprised of equilaterals arranged such that the bases of any five that share a common vertex form a pentagon in the base plane. We know this structure as a regular icosahedron.

Now the third body [the icosahedron] is made up of a combination of one hundred and twenty of the elementary triangles, and of twelve solid angles, each enclosed by five plane equilateral triangles. This body turns out to have twenty equilateral triangular faces.

Given Timaeus does not state the number of elementary (scalene) triangles for fire and air the statement that the icosahedron requires one hundred and twenty of them may seem at odds to the forty that use of the simple equilateral comprised of two back to back scalenes would suggest. However, using equilaterals comprised of six scalenes does indeed mean that one hundred and twenty are required to cover the solid’s surface. Thus a unit element of water could be comprised of deconstructed scalenes from three unit elements of fire and one unit element of air, or any other combination.

It is at this point that Timaeus dispenses with the scalene triangle and introduces the 90-45-45 isosceles triangle, leading to this statement:

While there are indeed four kinds of bodies that come to be from the [right-angled] triangles we have selected, three of them come from triangles that have unequal sides, whereas the fourth alone is fashioned out of isosceles triangles. Thus not all of them have the capacity of breaking up and turning into one another, with a large number of small bodies turning into a small number of large ones and vice-versa. There are three that can do this. For all three are made up of a single type of triangle, so that when once the larger bodies are broken up, the same triangles can go to make up a large number of small bodies, assuming shapes appropriate to them. And likewise, when numerous small bodies are fragmented into their triangles, these triangles may well combine to make up some single massive body belonging to another kind.

The fact that square faces of the cube are derived from a pair of 90-45-45 isosceles juxtaposed along their hypotenuse again raises the question of why a pair of scalenes back to back was not sufficient as the building block of the equilateral triangle based elements.

Other Polyhedra

Timaeus describes five elemental structures in total, the three we have covered (fire, air, and water), the isosceles derived cube (earth), and a fifth:

One other construction, a fifth, still remained, and this one the god used for the whole universe, embroidering figures on it.

Given that small set of elemental structures (four defined and one undefined) one may wonder why other polyhedra are omitted.

The simplest example of a ‘skipped’ polyhedron can be seen between Timaeus’ fire tetrahedron (triangular based pyramid) and air octahedron (bi-pyramidal square based pyramid). Using Timaeus standard six scalene equilateral we might ask, “Where is the bi-pyramidal triangular based pyramid?”

This would have six equilateral triangular sides and thus require thirty-six elemental scalenes in total. In the absence of a diagram think of two fire tetrahedrons stuck together by one of any of their respective four faces, but as with the square based pyramids comprising the octahedron we remove the triangular bases as they are internal).

Similarly we might expect between air (octahedron) and water (icosahedron) a sequence of bi-pyramidal structures, for example a pentagon based one having ten equilateral triangle faces. Extending the sequence further is problematic of course – six equilateral triangles sharing a common central point will ‘flatten’ into a simple two dimensional hexagon without the need for an ‘uplift’ in the centre to bring the base sides together. The bi-pyramidal sequence has thus reached its natural conclusion of collapsing a dimension of space.

If we now return to the selection of tetrahedron, octahedron, but not the bi-pyramidal pentagonal based pyramid the unspoken requirement for an elemental solid presents itself – all of its vertices must be identical. The bi-pyramidal pentagonal based pyramid has distinct flattening around the ‘waist’ giving it two different groups of similar vertices. Since the tetrahedron is not bi-pyramidal we can say that the octahedron is the only bi-pyramidal pyramid the elemental selection criteria.

Spherical Packing

With those two discussions neatly concluded (pending feedback highlighting errors on my part), one might have wondered about polyhedron ‘size’ along the way or rather how uniform inter-vertex distance emerges. Having sought without success in the dog’s toys (for tennis balls) and the kitchen (for oranges) the following thoughts on spherical packing in relation to elemental structure are purely conjecture.

Were we to have access to physical spheres to experiment with we might start by arranging our spheres on the floor (two dimensions). For example four spheres may be tightly grouped on the floor into a two by two arrangement, the sphere’s centres forming a perfect square. However, we could also place three of the spheres such that their centres formed an equilateral triangle parallel to the plane of the floor, and then place the fourth in the dip created at the centre point of the triangle of spheres.

I do not have the wherewithal to verify that a two by two arrangement consumes more three dimensional space than the tetrahedral arrangement in the second example but my sense it that it must. Perhaps then the tetrahedron that is Timaeus’ fire is the ‘tightest’ arrangement of four spheres in three dimensional space.

With five spheres we might arrange them in a two by two base with the last in the central dip, creating a square based pyramid (would such a pyramid have equilateral triangle sides?), and again my sense is that this must be ‘tighter’ than than a two dimensional arrangement (especially if we notice that we have four sides worth of the tightest arrangement of three spheres).

The fifth sphere and our previous work with four gives us a third option though. If we lift our tetrahedral arrangement of four spheres and place the fifth sphere in the central dip underneath (opposite the one we placed in the dip on top) we would have a bi-pyramidal triangular based pyramid mentioned in the previous section.

Similarly with six spheres in hand, the sixth might be better placed in the lower dip of our five sphere square based pyramid and in fact such an arrangement would produce a perfect octahedron (Timaeus’ air). Another experimenter thinking outside the box might arrange their spheres connected at angles through each other of one hundred and twenty degrees, creating a two dimensional hexagon (indeed they may have created a pentagon of spheres at offsets of one hundred and eight degrees in the previous step with their five spheres).

Seven spheres gives a double tip pentagonal arrangement option creating a bi-pyramidal pentagon based pyramid, and the unprecedented option of, back in two dimensions, placing the seventh sphere into the hole left in the two dimensional hexagon of the previous step. Like the discussion of the hexagonal based polyhedron, no ‘uplift’ is required to accommodate our seventh sphere such an operation has become redundant.

At the risk of descending into spherical madness and in order to draw a conclusion, let us beg our sphere handler for just one more sphere (for a total of eight) and go back to basics with a two vertical layer, two by two plane of spheres. The resultant sphere centres mark the corners of a perfect cube, ie Timaeus’ Earth elemnt. The lack of ‘dip’ use to construct this cube perhaps corresponds to the shift Timaeus had to make away from scalenes by introducing the isosceles, but the fact that we are still only working with uniform spheres might have made Timaeus wonder about Earth’s immutability to/from other elements.

by on

When Plato tells the story of Theuth in the Phaedrus, the god offers his invention as a gift to humankind. King Thamus declines, with the warning that writing will “implant forgetfulness” and give only “the appearance of wisdom.” The common accusation against AI writing—that it weakens thought, produces imitation rather than understanding, and severs authorship from the living speaker—is the latest form of the same worry.

Derrida’s famous reading of the Phaedrus reframes Thamus’s fear. Writing is not simply a tool added to speech; it is a supplement, both addition and substitute. It appears to aid memory, but only because speech itself is already dependent on spacing, iteration, and deferral—the conditions Derrida names arche-writing. The supplement therefore exposes that the supposed origin (the speaking, remembering subject) was never self-sufficient. Writing does not corrupt presence; it reveals that presence is already trace.

From a neurological perspective, writing does of course literally re-wires the brain. It recruits visual and spatial circuits that oral culture used differently, redistributing the part of the labour of memory from the hippocampus to the page. In this sense, Plato’s complaint is empirically true: writing does change us. But the change is not necessarily degeneration—it can be seen as the exteriorization of the same operation that already structures memory internally. Derrida’s arche-writing here meets Clark and Chalmers’s “Extended Mind”: cognition and recollection extend into the environment through inscriptions that function as parts of the cognitive loop. The notebook, the screen, or the archive is not outside the mind but part of its system of traces.

What AI systems do is generalize this exteriorization. They no longer merely store traces; they process and generate them. The writing machine remembers, recombines, and returns language to us in new configurations. In functional terms it is another layer of the extended mind: a dynamic tertiary retention, in Stiegler’s phrase, that supplements human thought. As alphabetic writing once externalized static memory, AI writing externalizes and increases memory as process: it actively constructs what we call ideas. This extension into process suggests a greater difference than there may actually be. The same structure of the supplement recurs: the aid that threatens to replace, the prosthesis that transforms what it extends.

Each stage—speech, writing, AI—alters neural, social, and cultural patterns, yet none of these abolish the structure of arche-writing itself. The trace remains the constant; the embodiment of the trace shifts. The human, then, is not displaced by technology but continually re-inscribed by it. The history of media is the history of arche-writing writing itself through new substrates—from mouth, to hand, to code. The question is not whether AI will change us (it will) but how we will inhabit the new spacing it opens in the field of memory.

But this is too simple. The notion that the same phantasy or concern exists between speech to writing and writing to AI writing is valid, yet to reiterate Plato was empirically correct in a sense and likewise expressions of concern are likewise correct, because it will alter the human. The issue concerns what it is exactly we think a human is. From a materialist perspective there is little issue here; likewise from a Deleuzo-Guattarian perspective (which is not necessarily materialist) there is also a lack of problem here —humankind simply extends its becoming other possibilities.

This thinking more concerns the phenomenology of the human as it takes itself to be in an incoherent coherence as opposed to its deconstructed coherent incoherence. The incoherent coherence is that of a being of a certain autonomy, possessing its own thoughts and feelings. To place these outside of it have a sense that undermines its sovereign importance. This tension is what is felt (currently) and brings the AI anxiety; literally a threat to perceived human ontology.

There is one more issue, which arguably is more potent than the above. This is that Derrida actually misreads or at least flattens Plato. Derrida treats Plato’s notion of memory more as a cognitve function, but arguably Plato means by anamnesis something much more spiritual. If the Platonic memory is more akin to Bruno’s art of memory, then Plato warns against the loss of a channel further back into being in an unambiguously magickal form. Neural rewiring in this sense is ontologically more than simply a change of cognitive functioning. Likewise then, the more recent shift in which process itself becomes externalised, can be seen as yet more damaging still to this access. From that perspective, every exterior inscription—whether written or algorithmic—is a distraction from the inner act of remembering the Good. If Derrida and Clark show that thought is always already technical, Plato reminds us that it may also be more than technical: a form of recollection that no prosthesis can perform on our behalf.

Without an absolute moral register, we cannot privilege the inner motion or the outer motion. The problem is thus ethico-ontological: the choice concerns not only what we ought to do, but what we choose to be. Ethics comes into play here in the sense of a choice, where we must consider from various angles which one constitutes what we wish to be—the autonomous subject whose access to Being is internal and effortful, or the re-inscribed human whose becoming is always already mediated by the technical trace. The history of media is the history of this ongoing ethical negotiation over the very boundaries of the human self.