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Three independent investigations of decimal numerical relations — those of Nick Land and the CCRU, Marko Rodin, and my own work on the 4–7 oscillation — reveal different but intersecting patterns within the same numerical field. Each begins with relatively elementary mathematical operations, yet each produces structures that invite further interpretation. The question is whether these structures might be brought together into a more comprehensive numerical apparatus, and whether the recurring figure of the vortex might offer a speculative connection to pneuminous curvature.

The proposal is not that these systems have independently discovered the hidden numerical architecture of the cosmos. Their operations are contingent, even where the resulting mathematical relations are necessary. Rather, they might be understood as different ways of investigating numerical curvatures within the pneuminous vector field, upon which further conceptual and potentially occult accretions can develop.

Land’s Numogram is organised around numerical relationships that include repeated doubling and cross-addition. This produces the familiar sixfold Time-Circuit:

1 → 2 → 4 → 8 → 7 → 5 → 1

The remaining digits are assigned to the 3–6 Warp and the 0–9 Plex. These structures are subsequently incorporated (accreted) into the CCRU’s elaborate occult and temporal mythology. Marko Rodin’s Vortex-Based Mathematics explores the same doubling circuit, but also investigates other multiplication sequences. Rodin gives particular significance to the numbers 3, 6 and 9, arranging numerical relationships into geometrical patterns that he interprets through toroidal circulation and vortical energy.

My own investigations began with the number 47 and the discovery of an oscillation between 4 and 7 under repeated squaring and decimal reduction:

4² = 16 → 7

7² = 49 → 4

Repeated squaring produces three distinct recurrent structures: the 4–7 oscillation and the fixed points 1 and 9. The other digits eventually enter one of these structures. A second operation emerged through the relationship between triangles of the structure 1 unit, 3 units 5 units, which gives a height base relation of 2n-1, whilst also producing squares of the by height by the total of units in the triangle e.g. a triangle 4 high has 16 units in it and has a base of 7.

Applying (2n-1) repeatedly, with decimal reduction, produces a different sixfold circuit:

2 → 3 → 5 → 9 → 8 → 6 → 2

Remarkably, the same operation also preserves the 4–7 oscillation:

4=7-=(13)+=4…

Meanwhile, 1 remains a fixed point.

We therefore have two operations, squaring and (2n-1), that share a persistent 4–7 oscillation while organising the remaining numbers differently. The latter operation is mathematically related to doubling through a shift of coordinates, so the resemblance between the sixfold circuits is not mysterious. Nevertheless, the intersection with the independently generated squaring oscillation provides an interesting basis for further investigation.

What might happen if these systems were considered together rather than as competing descriptions of numerical reality?Land’s (Rodin’s) doubling operation, the squaring and (2n-1) operations of my own investigations could be represented within a single numerical architecture. Such an extended Numogram would not privilege any one operation as the fundamental key to the Outside. Instead, it would display the relationships between different operations, identifying their recurring structures, intersections, fixed points and transformations.

The 4–7 oscillation is particularly interesting because it persists under two distinct operations. Meanwhile, the sixfold (2n-1) circuit includes numbers excluded from Land’s Time-Circuit, and the fixed point 1 occupies a different position from Land’s 0–9 Plex.

The result would be a system of overlapping numerical organisations rather than a single privileged circuit. Importantly, the numerical relationships themselves should be distinguished from the conceptual accretions subsequently attached to them. For example, 47 the prime and the 4–7 oscillation are not intrinsically connected by the mathematics. Their association arose through a contingent history of numerical investigation. Nevertheless, once connected, they became part of a developing accretive synchronistic configuration. The mathematical relationship possesses its own necessity under the specified operations. Its association with 47 is contingent. But the resulting accretion is a genuine feature of the conceptual field.

Within pneuminous ontology, numerical relations may themselves be understood as curvatures within the vector field, prior to the additional conceptual accretions attached to them. The mathematical relationship between 4 and 7 under repeated squaring is already established by the operation. Its subsequent association with the number 47, synchronicity and occult significance belongs to a different order of development. These further associations bind together configurations that were not intrinsically connected, producing new accretive relationships.

This distinction is fundamental. Mathematical necessity establishes the stability of a relation within its specified conditions. Accretion establishes the contingent significance that subsequently develops around it. The possibility that there is intrinsic (deep accretive) numerical curvature is there but the additional human occult accretions should not be confused with these (though the boundary may be hard to tell)may become closely bound, but they should not be confused.

This is particularly important when considering the apparent efficacy of occult numerical systems. A mathematical pattern might acquire increasing conceptual significance, becoming associated with experiences, expectations and apparently extraordinary correspondences. Such developments could reinforce the impression that the original numerical structure had disclosed an independently existing occult order; yet this inference would not necessarily follow. Within the speculative extension of pneuminous theory, a contingent configuration might acquire sufficient intensity to become anomalously operative without its original metaphysical interpretation having been accurate. The possibility of occult efficacy and the question of metaphysical truth therefore remain distinct.

The recurring figure of the vortex introduces another possibility. Land’s Warp is associated with vortical disturbances of ordinary temporality. Rodin translates numerical circuits into toroidal geometry, suggesting that the resulting patterns correspond to fundamental organisations of energy. Neither interpretation follows necessarily from the mathematics. A repeating numerical cycle is not, by itself, a physical vortex. Nevertheless, the vortex may offer a useful speculative model for the organisation of pneuminous power.

This suggests that pneuminous power might depend not merely upon the quantity of accreted conceptuality, but upon the organisation of its relations. However, the distinction between magick and sorcery developed in the preceding discussion introduces a further possibility. Magick might operate through the intentional curvature of the pneuminous field, as intensified conceptuality is applied to the vector towards a desired outcome. Sorcery, by contrast, might involve the attenuation of ordinary accretions, allowing the practitioner to become a vortical organisation through which power circulates more freely. In this speculative formulation, the sorcerer does not simply generate a vortex but becomes one.

The continual movement of pneuma might prevent habitual conceptual accretions from achieving their ordinary stability, potentially allowing a more direct relationship with the Outside. Such vortical organisation might itself produce curvature, but without the same predetermined conceptual direction characteristic of magick. There is an intriguing physical analogy in general relativity, where rotating masses produce frame dragging in addition to the curvature associated with mass-energy. This suggests that vortical movement need not be conceived as something separate from curvature, but might represent a particular dynamic form of it.

Within the pneuminous speculation, magickal curvature and sorcerous vortical movement might consequently be understood as different organisations of the same underlying field. The analogy does not establish any physical equivalence, but offers a potentially useful way of distinguishing intentional deformation from the continuous circulation of power.

The proposed extended Numogram is itself an accretive experiment. Mathematical relationships generated through different operations are brought into association, producing a new configuration whose organisation and significance can subsequently be investigated.

The mathematical structures are genuine within their specified operations, but their conjunction is contingent. Their subsequent development into an occult system would constitute further accretion rather than proof that they describe a pre-existing numerical order. Nevertheless, the possibility remains that such configurations might acquire unusual intensity, or establish relationships with deeper structures within the pneuminous field. Some alterations to numogrammatic principles would have to be rethought. 3, 6 and 9 are no longer outside but rather connected by paths, clearly established by logic entirely inkeeping with the original program.

The purpose of any extended Numogram is therefore not to establish that numerical patterns reveal the Outside, but to investigate what happens when mathematical curvatures become bound together through accretion, and whether their resulting organisation might possess possibilities beyond their original construction. However as in the paradox of the umbratic (its accretive naming brings it into the accretive fold), the accretion of the numogram as making inroads into the outside (the map to the black lodge) is necessarily in one sense true by its very effort.

Whether any such possibilities extend beyond ordinary conceptual and cultural effects remains subject to agnostic disjunction (terms and conditions apply).

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The preceding discussion distinguished two possible modes of anomalous action within Pneuminous Accretive Theory. The first involves the intentional application of intensified conceptuality to the vector field. The second involves the reduction of ordinary accretive constraints, potentially allowing a freer operation of power. As mentioned, we provisionally identify these modes as magick and sorcery.

This distinction suggests two different ways in which pneuminous activity might become anomalously effective: magick through curvature, and sorcery through vortical movement. The proposal remains highly speculative, but it may provide a useful way of distinguishing the intentional modification of reality from the less directed manifestations of power described in certain occult and spiritual traditions. In the magickal mode, a desired concept is deliberately applied to the vector. The practitioner seeks to produce a particular outcome through the intensity of a pneuminous configuration.

The previously mentioned gravitational analogy provides a possible model for this process. Just as mass-energy produces curvature in spacetime, an intensified conceptual configuration might, hypothetically, produce a local curvature within the pneuminous field (which as discussed now is reality itself), altering the structure of events towards its intended manifestation. The greater stability of ordinary material reality (deeper cosmic accretive structures) would ordinarily resist such modifications. Nevertheless, exceptional differences in intensity produce local anomalies from established accretive organisation (the human pneuminous accretive force curves the deeper accretions of time etc producing the anomaly).

This does not mean that magick literally operates through gravitational forces. Curvature remains a speculative analogy for the possible capacity of conceptuality to modify the field within which it is already situated. The essential feature of this mode is intentional determination. A particular conceptual configuration is applied in an attempt to produce a particular effect.

Sorcery might involve something quite different. Rather than attempting to impose an intensified conceptual configuration upon the vector, the practitioner seeks to reduce the ordinary accretions through which human consciousness is organised. Such reduction might allow a freer movement of pneuminous power, no longer constrained by the habitual structures of thought, identity and intention. Here the vortex becomes an intriguing possibility. A vortex is a persistent organisation of movement, often involving circulation around a centre, concentration and inward or outward flow. Its identity is maintained through dynamic relationships rather than the accumulation of static material. Within the speculative pneuminous model, vortical organisation might describe a process through which power becomes operative when ordinary accretive constraints are weakened.

The sorcerer would not necessarily be generating power through the intensity of a desired concept. Instead, the attenuation of local accretions might permit participation in a movement belonging to the wider pneuminous field. This suggests a distinction between the two modes:Magick attempts to bend the vector towards an intended outcome. Sorcery potentially allows the vector to move through the practitioner in a less conceptually determined manner. The vortex would therefore not simply be another representation of magickal intensity. It might indicate a different mode of organisation altogether.

The work of Viktor Schauberger provides an interesting point of comparison. Schauberger’s investigations of water movement emphasised spiralling, inward-directed flow and the relationship between vortical motion, concentration and organisation. He associated such movement with constructive and regenerative processes, contrasting it with outward, dispersive forms of motion. His more extraordinary energetic claims remain scientifically unverified, but the general relationship between dynamic movement and persistent organisation is suggestive.

A vortex is not merely a rotating object. It is a process in which movement establishes a relatively stable form. This might offer a useful analogy for sorcerous action.

The reduction of ordinary accretions could, speculatively, allow pneuminous activity to enter into a different organisation, one characterised by circulation and flow rather than the deliberate application of conceptual intensity.

Of course the vortical movement itself would produces local curvature. Arguably these curvatures would be stronger than those achieved by pneuminous intensity. The two modes need not be mutually exclusive.Nevertheless, their distinction remains important. In magick, curvature is sought through intentional conceptual application. In sorcery, curvature might arise as a consequence of a freer vortical movement that is not itself directed towards a predetermined outcome. An interesting question is whether such movement is generated by the reduction of accretions or whether the reduction merely permits access to vortical processes already operating within the wider field.

This second possibility becomes particularly interesting when we consider the Outside. Within the speculative all-pneuma model, ordinary human consciousness operates within an immensely larger field of accretive structures. Some of these may possess a stability, intensity and organisation vastly exceeding anything available to ordinary human conceptuality. Such configurations might be understood as alien intelligences, god-level accretions or other forms of nonhuman organisation. Their existence is not established by the phenomenological foundation of the theory. Nevertheless, the model permits their possibility without requiring a separate supernatural realm.

If sorcery involves the reduction of ordinary human accretions, it might allow a different relationship with these deeper structures. The practitioner would not necessarily need to generate sufficient intensity to overcome the stability of the material world independently. Instead, the attenuation of habitual conceptual organisation might permit participation in processes belonging to a much greater order of pneuminous power (e.g. Castaneda’s world stopping). Vortical movement might provide a possible model of this participation. Rather than imposing a new configuration upon the field, the practitioner might become involved in an existing organisation of power, allowing effects to emerge through that relationship.

This would also explain why sorcery need not be characterised by the same degree of conscious desire or intentional determination as magick. However, it would be a mistake to assume that every unusual experience arising through such practices necessarily involves contact with the deeper Outside. Local accretive processes might also produce unusual phenomena. A contingent configuration could become operative without possessing any privileged relationship with fundamental reality. The distinction between local occult efficacy and genuine contact with deeper accretions must therefore remain open.

One further possibility concerns time. If the wider pneuminous field is not necessarily organised according to the chronological succession through which human beings ordinarily experience events, then deeper accretive structures might possess relations extending across apparently separate temporal locations. Vortical organisation might offer a speculative model for such relations.

A vortex involves circulation, return and movement around a centre. If something analogous existed within the temporal organisation of pneuma, it might permit relationships that appear anomalous from the standpoint of ordinary chronological experience. What appears as retrocausality might not necessarily involve information literally travelling backwards through time. It might instead reflect a more complex organisation of relations that is not intrinsically divided into past and future.

This possibility has affinities with Nick Land’s speculative accounts of alien temporality, the Warp and teleoplexy. However, the pneuminous model does not require a particular future intelligence or technological process to possess privileged access to such relations. Nor does it require numerical circuits to provide accurate maps of the temporal Outside. If a-temporal organisation is possible, it might be associated with many different forms of accretive activity, including processes that have no connection with human technological development.

The connection between vortical movement and temporal anomalies remains entirely speculative. A repeating cycle is not evidence of retrocausality, and the geometrical properties of physical vortices do not establish the existence of nonchronological causal relations. Indeed given the lack of confirmation available to such speculations, what they do become is actually accreted phenomena themselves. That is, the vortex and curve as analogy through a speculative modified Einsteinian pneuminous paradigm may accrete to become more operative terms if sufficiently accreted. Do the terms match the vector of what is going on precisely? Possibly not, though their approximation could still equally be productive and useful.

To reiterate then, the distinction between magick and sorcery now offers two provisional models of anomalous action. In the first, conceptuality is deliberately intensified and applied to the vector, potentially producing curvature towards a desired outcome. In the second, ordinary accretive constraints are reduced, potentially allowing a freer vortical movement of pneuminous power. The first is characterised by intentional determination; the second by a relative suspension of that determination. Both might produce local alterations within the wider field, but their proposed modes of operation are different.

The distinction also helps preserve an important difference between occult power and spiritual development. The reduction of habitual accretions might be valuable independently of whether any anomalous effects occur. Sorcery would be one possible manifestation of such a transformation, rather than its necessary purpose. Nor should we assume that magick and sorcery exhaust the possible forms of anomalous causation. They are heuristic distinctions within a speculative framework.

The central problem remains unresolved: what precisely constitutes pneuminous intensity, how might vortical organisation arise, and under what conditions could either produce effects beyond ordinary psychological and physical causation? For now, the proposal is that curvature and vortical movement might represent two different modes through which pneuminous configurations become anomalously operative.

Magick would seek to modify the field through the intensity of an intended concept. Sorcery might permit a less directed participation in the wider movement of pneuma through the reduction of accretive constraints. Neither mechanism has been established, but the distinction provides a potentially fruitful way of investigating the relationship between intention, power and the organisation of reality. It also leaves open the possibility that the vortex, so prominent in natural phenomena, occult imagery and numerical speculation, might be more than a convenient metaphor for the movement of power.

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If ordinary reality consists of enormously stable pneuminous accretions, then the possibility of anomalous causation raises a difficult question: how might a comparatively local configuration of human consciousness become capable of modifying the wider field? A possible answer lies in the concept of pneuminous intensity. However, intensity may not be the only means through which anomalous effects are produced. There may be a fundamental distinction between the deliberate application of conceptuality to the vector and the release of power through the reduction of accretive determination. These suggest two potentially different modes of magickal or occult action.

Within Pneuminous Accretive Theory, magick can be understood as the deliberate application of conceptuality to the vector field. A desired outcome is established as a pneuminous configuration and directed towards manifestation. In this mode, intent is central. The practitioner seeks to bring about a particular state of affairs by applying a concept to the vector.

The possible efficacy of such an operation would depend upon the intensity of the configuration and its capacity to modify the more stable accretions constituting ordinary reality. Intensity should not, however, be understood as equivalent to the quantity of accumulated conceptual content. A configuration may be elaborate, widely believed or continually reinforced without necessarily possessing any unusual capacity to modify the wider field. Concentration, coherence and the organisation of conceptuality may be more important than its sheer quantity. A relatively small but intensely organised configuration might, under exceptional conditions, acquire a disproportionate capacity to affect surrounding structures. This remains speculative. The theory does not yet establish what constitutes intensity, how it might be measured, or why particular forms of organisation would produce anomalous effects.

Nevertheless, this provides one possible model of magickal action: the intentional application of an intensified conceptual configuration to the vector field. There is, however, a second possibility, which operates in an almost opposite direction. Many spiritual and occult traditions suggest that the accumulation of ordinary conceptual activity can obstruct rather than facilitate unusual forms of experience. Practices involving silence, concentration, non-identification and the suspension of habitual thought seek to interrupt the established organisation of consciousness.

Within a pneuminous framework, these practices might be understood as weakening the hold of local human accretions. But what if this reduction does more than simply remove obstacles to the formation of more powerful intentions? What if the attenuation of accretion permits a freer flow of power through the individual, without that power being directed by a deliberately imposed conceptual configuration? In this second mode, the practitioner does not necessarily seek to produce a predetermined effect. Instead, the reduction of habitual accretions might allow action to emerge through a less constrained relationship with the wider pneuminous field.

The resulting phenomena might appear spontaneous, intuitive or even independent of conscious intention. This suggests a distinction between the application of power through conceptual intent and the manifestation of power through the suspension of conceptual determination. The latter would not require an absence of pneuma itself. This would be the previously discussed distinction of magick and sorcery. The possibility is that the reduction of local accretions allows relations with deeper and more powerful configurations that ordinary consciousness tends to obstruct.

We can therefore distinguish two speculative modes of efficacy. Intentional magick involves the formation and application of a desired conceptual configuration. Its possible efficacy depends upon the intensity with which that configuration is brought to bear upon the vector. The free flow of power involves the reduction of accretive constraints, potentially allowing action or manifestation without the same deliberate conceptual direction.

These modes need not be entirely exclusive. A practitioner might alternate between them, or an intentional operation might require the prior weakening of habitual accretions. Nevertheless, the distinction is important. In the first mode, conceptuality is deliberately organised towards an outcome. In the second, conceptual organisation is reduced so that something less constrained by the ordinary human accretive field might become operative. This also suggests a distinction between magickal practice and spiritual development.

A complex occult system might become increasingly substantial through sustained accretion while simultaneously reinforcing the ordinary structures of human conceptuality. Conversely, practices concerned with emptiness and non-identification might weaken those structures without generating any elaborate symbolic system. There is consequently no reason to assume that the accumulation of occult associations necessarily produces greater access to deeper reality. Nor should we assume that experiences of spiritual emptiness establish the existence of anomalous causal powers.

The two modes remain hypothetical possibilities within the speculative curvature model. The distinction between intentional magick and the free flow of power complicates the idea that anomalous efficacy must involve accumulating sufficient force to overcome the stability of ordinary reality. Perhaps a human consciousness need not rival the vast accretions constituting the material world. In the intentional mode, efficacy might arise through an unusually intense and coherent application of conceptuality.

In the second mode, it might arise through the removal of accretive constraints, allowing the individual to participate in processes belonging to a much greater order of pneuminous organisation. The first suggests a concentration of conceptual power. The second suggests a release from conceptual determination. Both might, in principle, produce local modifications of the wider field, but through different relationships between human consciousness and the more stable accretions of reality.

This raises a further possibility: perhaps intensity itself is not always something generated through the concentration of conceptuality. It might sometimes emerge through the reorganisation or attenuation of existing structures. The underlying problem is therefore not simply one of quantity, but of organisation, relation and the conditions under which pneuminous power becomes operative.

Magick might seek to bend the vector through the intensity of intention, while sorcery might arise when intention itself ceases to impose its ordinary accretive constraints. Neither mechanism is established, but the distinction offers a more developed framework for investigating the possible relationship between consciousness, accretion and anomalous causation. It also opens a further speculative question: whether certain forms of dynamic organisation, particularly those resembling circulation and vortical concentration, might help explain how pneuminous intensity develops. This leads towards the possibility of pneuminous vortices.

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One of the more difficult questions arising from Pneuminous Accretive Theory concerns the possibility of anomalous causation. If the apparently material world is understood as a manifestation of pneuminous accretions, what might account for those occasional phenomena in which conceptuality appears to exert an unusual influence upon events?

The question arises particularly from synchronicity, in which an apparently external occurrence seems to correspond meaningfully with a conceptual configuration in a manner that exceeds ordinary expectation. Such experiences need not be interpreted as supernatural. Coincidence, selective attention, psychological association and other conventional explanations remain available (this uncertainty is preserved through the principle of agnostic disjunction). Nevertheless, the peculiar appearance of a relationship between thought and world provides the starting point for the phenomenology the has generally explored over past years.

Pneuminous Accretive Theory begins with the quasi-substantialisation of conceptuality. Concepts, images, identities and relations acquire stability through processes of accretion onto the vector field. The vector field is the manifestation of the underlying outside-of-conceptuality (as opposed to the umbratic which is the manifestation of the outside of perception itself). The extra notion here is that the vector field which seems to have the actual characteristics of things is itself simply more forceful accretions of pneuma The theory does not require an initial decision about whether an apparent synchronicity has an ordinary or extraordinary cause.

However, a more speculative possibility emerges if we extend the theory into an all-pneuma ontology. Suppose that what we ordinarily regard as material reality is itself constituted by pneuminous accretions at a cosmic level. The apparently external world would then not be an ontologically separate substance upon which thought somehow acts. It would already be pneuminous in its constitution. The problem of anomalous causation would consequently become a problem of relations between different pneuminous configurations.

The Stability of the World

If the material world (a key manifestation of the vector field) is pneuminous, why does it resist ordinary thought so effectively? Why can we imagine a stone moving without the stone moving? Why does the world continue to exhibit such extraordinary regularity regardless of the wishes, beliefs or conceptual activities of individual human beings? Within the speculative all-pneuma model, the answer lies in the vastly different scales and stability of accretive organisation.

Ordinary human conceptuality operates within an already established field of extraordinarily powerful accretions. These constitute the stable conditions of experienced reality, including the apparent solidity of objects, the persistence of physical relationships and the regularities described by natural science. Such configurations might be conceived, in a theological formulation, as the thoughts of God. This need not initially entail a personal deity, although the possibility of one is not excluded. The formulation indicates that the apparently material world belongs to an order of pneuminous organisation vastly exceeding the local configurations of human consciousness.

Human thought does not ordinarily modify a stone because it encounters an accretion of enormously greater stability and resistance. There is no need to posit an absolute ontological division between mind and matter. The distinction is instead between configurations of radically different accretive power. The question of anomalous causation can now be reformulated:

Under what conditions might a relatively local pneuminous configuration become capable of modifying, redirecting or disturbing the more stable accretions constituting ordinary reality?

The notion of curvature provides a possible way of conceptualising how such modifications might occur. In general relativity, mass-energy is associated with the curvature of spacetime, affecting the trajectories along which physical bodies move. The proposed pneuminous analogy is that sufficiently intense configurations might alter the organisation of the wider pneuminous field, influencing the trajectories of events within it.

This is not a claim that pneuma literally obeys Einsteinian physicss, nor that anomalous events are gravitational phenomena. Curvature is being proposed as a conceptual model for a possible relationship between intensity and the organisation of reality. A pneuminous configuration might conceivably exert a local influence upon the field without transforming the whole of its structure. An anomalous event would then not necessarily represent the suspension of natural law by an external supernatural agency. It might instead involve an unusual local modification of the accretive relationships through which ordinary reality is maintained.

Curvature might alter the probability of events, producing unusual concentrations of apparently meaningful coincidences. It might modify relationships between otherwise separate configurations, generating anomalous correspondences between conceptuality and external occurrences. More radically, it might affect the conditions under which particular events become manifest, producing phenomena that appear to violate ordinary physical expectations. These possibilities should not be treated as equivalent. A meaningful coincidence and an apparent physical anomaly place very different explanatory demands upon the theory.

Nor does the existence of synchronicity as an experience establish that any such curvature has occurred. The proposal is conditional: if anomalous causation exists, pneuminous curvature might provide a framework for understanding its operation. This establishes the central problem of the curvature hypothesis. The next question is what might enable one pneuminous configuration to modify another, particularly when the latter possesses vastly greater stability. One possible answer lies in the elusive relationship between accretion, intensity and power.