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Cognitive Gravity: A Polynonial Architecture for Experience

  • [ Abstract ]

Gravity, the most immediate condition of embodiment, resists integration with quantum theory, pointing to a deeper epistemological fracture. This dissonance is used here as argument for a cognitive interpretation of reality, where gravity is a structuring principle of perception. In this framework, geometric cognition plays a central role, with the mind arranging information spatially through embedded and embodied topologies. Thus, cognitive gravity is proposed to model how experience is organized, and how memory, language, and truth are shaped by gravitational dynamics that stabilize within a manifold of perception and consciousness.

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Cognitive Gravity, Consciousness, Observer, Noumena, Perception, Cognitive Relativity, Reality Construction, Phentropy, Manifold

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  • [ Roibu, T. (2025) Cognitive Gravity: A Polynonial Architecture for Experience. ]
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1 Introduction

Gravity is the most immediate and universal condition of embodiment, shaping motion from galaxies to falling leaves. Classical physics framed it as attraction between masses (Newton), while general relativity redefined it as the curvature of spacetime produced by mass and energy (Einstein), yet gravity resists unification with quantum theories, pointing to a deeper conceptual fracture.
 
This dissonance is used here to suggest a cognitive aspect of gravity, a structuring condition for perception itself by organizing experience through  topological gradients and specific metrics. From this perspective, the resistance of gravity to full physical reduction is not a flaw in theory, but a clue pointing toward a deeper ontology. Idealism, as revived in contemporary form by thinkers like Bernardo Kastrup, proposes that reality is not grounded in matter but in mind: that what we call the physical world is the extrinsic appearance of mental processes. Within this view, space, time, and causality emerge not as external conditions but as structured patterns within a universal cognitive field. 
 
Cognitive gravity, thus, rests upon a primary postulate: that consciousness is not an emergent byproduct of physical interactions, but a foundational substance. In this view, gravity becomes the medium through which the observer moves between the noumenal and the phenomenal, the unseen potentialities of reality and their structured appearance within consciousness. This movement is treated here as epistemological: a transition where latent realities are stabilized into knowable forms through the gravitational architecture of cognition.
 
Contemporary physics describes this threshold as the collapse of the wavefunction: a sudden resolution of indeterminate states into a determinate reality upon measurement. Yet within the polynon, this collapse is reinterpreted as a continuous, recursive process, a gravitational settling of experience where the observer’s cognitive field shapes the transition from potentiality to actuality.
 
This transition is governed by a kind of cognitive entropy, reflecting how experience either coheres into stable form or dissipates back into potential. Modeled here as phentropy, the tendency of perceptual events to either crystallize into conscious structure or dissolve into the background of unformed possibility, it offers a way to trace how reality becomes knowable, and how it fades, within the gravitational contours of consciousness.
 
The approach resonates with current theoretical developments suggesting that gravity itself may be emergent from entropy (Bianconi, 2025). Within an idealist orientation, this reinforces the view that what we experience as reality is not the unfolding of a material substrate, but the dynamic structuring of mind.
 
Cognitive Gravity extends this argument by proposing a topological organized mind, that folds reality, layers it, and stabilizes it through measurable gravitational dynamics. 
 

2 Cognitive Gravity

Gravity is the most intimate force we never directly feel. Unlike the sharpness of pain or the heat of flame, it operates silently. Yet beneath its physical function lies a structural analogy to consciousness itself: an invisible architecture of coherence.
 
To speak of cognitive gravity is to risk conflation, as consciousness and mass belong to distinct ontologies. Yet, if framed carefully, the analogy reveals a profound structural homology. Consciousness requires not a spatial ground, but a relational topology shaped by gradients of salience, coherence, and causal weight. Certain cognitive structures bend phenomenal space, pulling attention and meaning toward them, just as mass is posited to curve spacetime.
 
A cognitive event functions like a singularity, warping thought rather than light; a compelling idea draws inferences into orbit. Thus, cognitive gravity measures not weight, but the centrality and anchoring depth of structures within awareness, their integrative density across affective, sensory, and conceptual threads. This suggests a topological model of mind, where ideas inhabit a curved manifold of perception, complete with cognitive anchors, attractors and singularities.
 
Importantly, gravity implies cognitive asymmetries, where irreversible cognitive events (insights, experiences) leave permanent deformations in the topology of self. Without such curvature, consciousness would resemble a flat abstraction, lacking organization, continuity, or structured deviation from uniformity.
 
Cognitive gravity mediates the transition between noumenal potentialities and phenomenal experience. It acts as a selective filter, shaped by the observer’s cognitive mass (biases, memories, expectations, and attentional focus) determining which noumenal signals stabilize into experience. This stabilization process operates through mechanisms akin to active inference (Friston, 2022): the observer continuously generates predictive models to minimize uncertainty, gravitationally pulling experience toward patterns that confirm or refine internal expectations.
 
However, within the polynon, this dynamic is not absolute. Phenomenal aspects already structured within the observer’s experiential field, align closely with active inference processes, reinforcing patterns that optimize prediction and minimize cognitive dissonance. Yet noumenal aspects, the latent, unstructured potentialities that underlie perception, retain a fundamental indeterminism. Their observer-independent state, allow them to resist full incorporation into predictive models, preserving a field of openness, disruption, and cognitive novelty.
 
This irreducibility echoes Gödel’s incompleteness theorems: just as no formal system can fully account for its own consistency, no perceptual system can exhaustively model the noumenal field from within. There will always remain aspects of experience that elude resolution—truths that cannot be proven, structures that resist encoding.
 
This establishes a cognitive principle that allows parts of cognitive processes to tend toward stabilization and predictive coherence, while other parts remain anchored in the indeterminacy of noumenal space. The observer thus navigates a perceptual manifold where certainty and uncertainty, structure and potentiality, are gravitationally intertwined within the evolving architecture of experience.
Fig.1 Double torus manifold of Cognitive Gravity: noumenal gradients g(n) and cognitive gradients g(r) shape the bidirectional flow between unstructured potential and perceptual coherence.

2.1 The noumenal gradient

The noumenal gradient g(n) represents the intrinsic stratifications within the noumenal, independent of any observer. It maps the probability of noumena transitioning into phenomena, reflecting the underlying complexities and potentialities of unobserved reality. Steepness in g(n) signals abrupt shifts, while gradual slopes indicate smoother transitions. All negative noumena n− are viewed as emanations from a singular positive source n+, suggesting a unified noumenal field whose variations shape the latent architecture of experience.
 
α – Noumenal Sensitivity
 
Noumenal Sensitivity, symbolized by α, quantifies a cognitive system’s inherent capacity to interface with noumenal influences. Like the permeability of a lens to light, α is a structural property, not an adjustable setting—predetermined by developmental or evolutionary pathways. It governs how systems autonomously filter novel or critical inputs over redundant noise, optimizing cognitive economy. 
 
High α yields fine-grained sensitivity to subtle noumenal nuances, while lower α broadens awareness at the cost of resolution.
This noumenal sensitivity is rooted in the deeper etymology of the sensible, by mediating the act of prehension (Whitehead): the capacity to grasp aspects of reality without sensory apparatus, as pure potential or felt resonance. When α is sufficiently high, prehension crystallizes into perception, allowing latent noumenal structures to become experientially available. In this way, α serves as the threshold mechanism through which the invisible becomes visible, the unformed becomes structured, and potentialities become part of lived cognition.
 

2.2 The cognitive gradient

The cognitive gradient, g(r), describes depths of phenomenal perception, reflecting how resonance and clarity vary across the observer’s perceptual plane. A steep gradient (high g(r)) means small attentional shifts cause major changes in salience; a shallow gradient distributes attention more evenly.
 
The cognitive gradient reveals hidden structures by sharpening some phenomenal aspects while obscuring others. At its null point—zero g(r)—pure noumenal potentiality emerges, free from temporal or spatial bias, residing in the here and now.
While the noumenal gradient maps intrinsic potentialities, the cognitive gradient actualizes them. Their interdependence is crucial: without the cognitive gradient, noumenal nuances remain unperceived.
 
The gradient is modulated by a factor  δ, a composite of:
β – Observational bias: influence of prior beliefs and expectations,
γ – Cognitive variability: flexibility and openness to novelty.
 
Higher δ values sharpen attention around few perceptual nodes; lower δ values diffuse awareness across many. Meanwhile, R(r) represents attentional resonance at distance r from the center of focus. Together, δ and R(r) structure perception, bending awareness around phenomena and modeling consciousness as a dynamic, responsive manifold.
 
β – Observational Bias
 
The parameter β quantifies phenomenological bias in observation, reflecting how sensory system limitations shape the interaction with the noumenal. Arising from inherent perceptual constraints such as optical illusions, neurobiological variations, or psychoactive effects, β captures how perception deviates from neutral reception. 
 
Within a Bayesian framework, β can be understood as encoding the observer’s prior assumptions: the probabilistic scaffolding that shapes how new sensory data is interpreted. These priors, while evolutionarily useful, often introduce distortions, leading the observer to perceive what is most expected rather than what is most present.
 
A β value of 0 would indicate an unbiased stance, while non-zero values reveal how deeply the observer’s sensory architecture frames their encounter with reality. Thus, β measures the structural distortions introduced by the observer’s physical and functional perceptual apparatus.
 
γ – Cognitive Variability
 
Cognitive variability γ captures the subjective dynamics of perception, distinct from the physical rooted observational bias β. While β filters phenomenal inputs, γ governs their internal interpretation through phantasiai p⁻, heuristics, memory, and other epiphenomenal frameworks. It reflects how psychological state and background shape the construction of meaning from the same stimuli.
 
Unlike the cognitive gradient g(r), which maps the cognitive landscape, γ quantifies individual variation across that space, making it essential for modeling how personal cognitive architectures modulate noumenal perception.
 
Summary:
 
α – Noumenal sensitivity, indicating how responsive an observer is to noumena.
Distinguishing Feature: Reflects the observer’s sensitivity or receptivity to underlying noumenal structures. It’s about the ability to sense or detect noumenas before they become phenomena.
 
β – Observational bias, indicating how the brain’s expectations evolve as more information is perceived.
Distinguishing Feature: Represents the reduction in local uncertainty as more data points are perceived. It decreases as more information becomes available.
γ – Observer’s epiphenomenal or cognitive aspects of perception and interpretation.
Distinguishing Feature: It’s about the intrinsic epiphenomenal bias
 
δ – Modulating factor based on the resonance or salience at a particular point in the perceptual plane, shaped by both observational bias β and cognitive
variability γ, which more accurately reflects the relation between these factors in the context of phenomenal p+ and phantasiai p− aspects.
Distinguishing Feature: It’s about the spatial variations in perceptual intensity across the perceptual plane.
 
r – Distance from the center of the perceptual plane.
Distinguishing Feature: It’s a spatial parameter, indicating how far a point is from the center of the observer’s attention.
 

3 Geometric Cognition

Geometric cognition examines how experience is not only perceived but structured through spatial and topological relations. Within the polynon, phantasiai and phenomena are shaped by geometric principles that govern how attention, affect, and meaning unfold in space.
 
Emerging models in cognitive geometry and neurogeometry offer formal tools to trace these dynamics. Rather than treating cognitive processes as abstract computations alone, they situate them within spatial manifolds. Archer (2021) introduces the notion of infodesics, paths that minimize not just spatial distance but also information-processing cost, suggesting that mental navigation follows principles akin to geometric optimization. This complements work on sensorial perception (Siever, 2019), memory structure (Heusser, 2018), conceptual abstraction (Bernardi, 2020), and the shape of experience itself (Zhang, 2022), all of which treat cognition as inherently spatial.
 
The polynon aligns with this paradigm by situating cognition within a topological field governed by cognitive gravity. The framework also resonates with the principles of 4E cognition (embodied, embedded, enactive, extended), where the body’s engagement with the world shapes how meaning is formed, filtered, and held.
 
Geometric cognition thus offers a rich foundation for exploring how conscious experience is shaped, not merely registered. Within this broader field, several specific phenomena will be examined: the role of phantasiai as internal generative structures; the gravitational dynamics of attention; the aesthetic properties of perceptual pleasure; and the emergent fields of beauty and truth as attractor states within cognitive space.
 
While neuroscientific evidence supporting the geometric structuring of cognition is substantial, ranging from grid and place cell mappings to fractal cortical patterns and manifold compression strategies, this survey remains intentionally focused. The purpose here is not to exhaustively catalogue the empirical foundations of geometric cognition, but to establish the general cognitive construct through which cognitive gravity operates. In this sense, the following explorations should be read as mapping key perceptual processes within a broader cognitive manifold and the expressions of experience against the shifting background of potentiality.
 
This remains, above all, a general philosophical and structural survey, one informed by existing neuroscience, but not claiming exhaustive coverage. As a non-specialist, the author’s aim is not to speak on behalf of the field, but to frame a coherent model through which geometric cognition can be meaningfully interpreted.
 

3.1 Phantasiai et Phenomena

The concepts of phantasiai and phenomena intertwine in their depiction of how reality is perceived and internally represented. Phantasiai underpin imagination, memory, and practical reasoning, providing the scaffolding for daydreaming, future planning, and higher cognition (Lohmar, 2010; Segal, 1985). They enable anticipatory models of perception, aligning with Tulving’s notion of “mental time travel” and Friston’s predictive coding theory, where the brain generates forward-facing simulations through analogy and association (Clark, 2015; Bar, 2007; Bejczy, 1990; Schacter, 2020).
 
This anticipatory structure is deeply phenomenological: psychoanalytic and phenomenological traditions have emphasized how phantasiai actively shape perception, emotional tone, and the social world (Segal, 1994; Symington, 1985; O’Gorman, 2005; Noel, 1997; Geniusas, 2021; Warner, 2006), mediating how phenomena appear and how meaning is constructed.
 
This cognitive embedding is supported by neuroscientific findings, showing that visual perception and mental imagery activate overlapping brain regions (from the retina to the primary visual cortex) suggesting that imagination is not a peripheral function but structurally integrated into perceptual systems (O’Craven, 2000; Knauff, 2000; Bihan, 1993; Kosslyn, 1993, 1995; Ganis, 2004; Chen, 1998). Imagery produces more diffuse activation patterns, with content-specific neural recruitment depending on the imagined object (O’Craven, 2000; Thompson, 2000), while the engagement of topographically organized visual cortex suggests a shared spatial logic between seeing and imagining (Kosslyn, 1993, 1995; Chen, 1998).
 
Thus, phantasiai are not ancillary embellishments but foundational elements of cognitive architecture, enabling extrapolation from memory and desire, structuring how lived reality is constructed and navigated. Philosophical accounts further affirm this role: imagination, through the scaffolding of phantasiai, becomes central to how we project across time and anchor experience within a meaningful topology (Noel, 1999; Jimenez, 2017).
 
In essence, when we imagine, we are perceiving: not the external world, but the internal constructs of the mind. Imagination and perception share overlapping neural architectures, blurring the boundary between external sensing and internal construction. In both cases, the brain engages in active perception, whether it interprets stimuli from the environment or constructs scenarios from memory and desire.
 
This perceptual architecture reflects deep geometric principles: the human skull approximates the Golden Ratio (Tamargo et al., 2019), facial morphology shapes underlying brain structures (Naqvi et al., 2020), and cortical folding patterns follow fractal geometries that support complex cognition (J.H. Smith et al., 2021; Owen et al., 2021). Spatial coding mechanisms mirror these geometries, with place cells encoding environmental location (Krupic et al., 2015) and grid cells forming hexagonal maps that scaffold navigation and broader cognitive functions (Staudigl et al., 2018). 
 
Temporal sequences are similarly structured, as time cells encode the order of events across unfolding durations (Eichenbaum, 2014; MacDonald & Tonegawa, 2021).
 
Cognitive gravity frames these neural geometries as structures that bend perception, memory, and attention around centers of cognitive mass. In order to navigate these high-dimensional sensory data, the brain compresses inputs into abstract manifolds, creating efficient representations that enable pattern detection and flexible retrieval (Chung & Abbott, 2021).
 
Visual perception builds upon multiple image types, one of which—Euclidean geometry—offers a static and idealized scaffold unique to animal and human cognition (Lima, 2014). From these foundational structures emerge perceptual gradients: primary forms that guide recognition. Luminance gradients, for example, are crucial for detecting objects (Keil, 2006), shaping how we perceive light, texture, and form (Keil, 2007; Sun, 1996; Gruber, 1956). The visual system processes these gradients through retinal patterns and texture maps, interpreted by receptive and projective fields (Lehky, 1988), refined by spatial derivatives (Lappin, 2011), and situated within information-geometric spaces (Borello, 2004). Recognition crystallizes when perceived shapes sufficiently match internal hypothetical models, triggering transmission along the optic pathways (Pizer, 1991).
 
Fig.2 The revealing of a square: the spatial and temporal context allows the shape to be perceived as a square even in incomplete perceptual stages (b,c) do to its complete visualisation in a previous context. After Arnheim.
Early perception hinges on coherence: when incoming sensory data aligns with internal expectations, identification proceeds rapidly; otherwise, the input is re-evaluated. Metadata such as structural “skeletons” accelerate this process, enabling simple figures (for example, a hexagon) to be interpreted as a cube through inferred dimensionality (Ayzenberg, 2022) or a square to be infered via prior knowledge of it’s architecture (Arnheim, 2009). Visual stability is further supported by neurons merging similar edges to stabilize object boundaries (Sharpee, 2017), by cross-orientation suppression which filters conflicting signals, and by the recognition of recurring spatial patterns.
 
Together, these dynamics reveal that memory and perception operate as overlapping circuits, affirming a continuum where the perceived and the remembered flow into one another, as Bergson proposed (Matter and Memory, 1986), forming a continuous field shaped by gravitational tensions of attention, memory, and meaning.
 
The impact of this super-position, extends to even the most basic levels of perceptual processing, creating a perpetual state of identification, interpretation, classification and representation of the perceived data, 
 
the visual effect being the results of the competiton between the mechanism of showing the mental image and the mechanism involved in focal attention, becoming a competition between seeing “real” images and imagining them. (Knauer, Maloney, 1913). 
 
Neural networks continually assign new values to sensory and internal data, constructing and dissolving multi-dimensional structures, from simple one-dimensional rods to complex five-dimensional geometries, like evolving sandcastles shaped by transient forces (Reimann, 2017). This dynamic complexity, spanning molecular to macroscopic scales, is shaped by network topology (Frégnac, 2007; Garcia, 2012) and increasingly understood through mathematical models that reveal structured patterns of activity and relation (Einevoll, 2006; Stepniewski, 2019). Recent studies also suggest that higher-dimensional organizations may reflect genuine functional relationships within neural processing (Tozzi, 2019).
Fig.3 The superposition of perception and memory—Attention acts as a vector, drawn toward regions of relevance shaped by phenomenal bias β and cognitive variability γ: β anchors prior expectations, while γ allows flexibility. After Escher (Liberation).
Visual perception exemplifies this complexity: it relies on precise calculations of curvature, margins, and spatial attributes (Bertamini, 2013; Borst, 2012) to construct rich mental imagery. To navigate this high-dimensional sensory field, the brain builds abstract manifolds that compress data efficiently, allowing veridical perception while dynamically updating beliefs encoded in evolving cerebral patterns.
 
Yet the very strength of these internal models, formed through layers of prior experience (Sohn et al., 2019; Nakamura, 2016), can both enhance cognitive efficiency and constrain flexibility. Manifold structures reveal which neural nodes exert gravitational pull within cognitive space, but when too rigid, they risk locking attention onto details at the expense of broader integration.
 
Thus, cognition perpetually balances prediction and adaptability, navigating between the gravitational pull of entrenched models and the continual need to reshape manifolds in response to new informational landscapes.
 

3.2 Attention

Attention plays a critical role in here, dynamically constructing objects by linking sensory input to memory. It warps the experiential field, embedding past and potential within the present, consistent with the logic of cognitive gravity. Attention acts as a vector, drawn toward regions of relevance shaped by phenomenal bias β and cognitive variability γ: β anchors prior expectations, while γ allows flexibility.
 
Empirical studies confirm this framing: De Brigard (2012) shows internal attention shapes memory retrieval; Stokes (2018) demonstrates perception’s cognitive penetrability. Treisman’s feature integration theory (1980) reveals attention binds sensory features into coherent objects, while Anderson (2002) links perception to motor readiness. Tipper (2010) shows attention influences action simulation, and Rock (1981) highlights its role in stabilizing form perception.
 
Attention, however, is not drawn solely to what is immediate or overtly salient. It is equally attuned to hidden, uncertain, or ambiguous aspects of the environment, those requiring resolution in order to facilitate coherent cognitive, motor, and emotional responses. In this sense, attention operates as both an amplifier of explicit relevance and a search-light into zones of uncertainty, maintaining the dynamic flexibility required for adaptive behavior.
 
Neuroscientific evidence supports this duality, the Locus Coeruleus playing a pivotal role in modulating attentional states in response to both detected salience and potential uncertainty. Through its widespread noradrenergic projections, the Locus Coeruleus enhances sensory processing, primes motor readiness, and modulates emotional tone based on real-time evaluations of relevance and unpredictability (Mather M., 2016, 2019; Sara, S.J., 2009; Sales A, et al, 2019; Aston-Jones, G., 2005, 2016). Recent findings further implicate astrocytes in regulating alertness and attentional shifts, suggesting a more distributed network underlying the gravitational anchoring of perception. (Lefton et. al, 2025). These early, often preconscious attentional shifts are proposed here as provisional gravitational anchors within the cognitive manifold, setting the stage for the stabilization of experience through cognitive gravity.
 
This gravitational logic of attention can be further understood by examining the perceptual mechanisms within a cognitive frame. Visual perception, far from being a neutral intake of data, is inherently shaped by the placement, balance, and structural logic of visual elements. Arnheim’s, Truică’s work and others on perceptual stability demonstrates that certain spatial configurations, such as symmetry, centrality, or directional flow, generate a stronger perceptual “pull,” guiding attention in ways analogous to gravitational mass. Close proximity, geometric regularity, and visual hierarchy create attractor fields in the visual manifold, where attention naturally settles into stable configurations.
 
From a cognitive gravity perspective, these perceptual attractors operate as localized gravitational events. They bend attention, not by force, but by perceived relevance, balance, and coherence embedding perceptual input within a structured and meaningful cognitive topology.
Table.1 Attention is assigned not only to spatial forms but to temporal and emotional events through the same gravitational principles. Whether visual, auditory, or conceptual, perceptual systems organize experience by aligning with attractors of balance, contrast, and coherence—summoning attention through localized gravitational events across the sensible spectrum of cognition. After Arnheim, Truică.

3.3 Perceptual pleasure

The perception of complex visual patterns is literally a pleasure, due to the stimulation of the mu-opioid receptors and the increased release of endorphines (Biederman, Vessel, 2006).  The endogenous opioid system, including the mu-opioid receptors, is implicated in the facilitation of rewarding brain stimulation (Esposito, 1978), the basis of pleasure (Jones, 1992), reward processing (Le Merrer, 2009) and can have direct excitatory effects on sensory neurons (Crain, 1990). Their presence is increased in the occipital area and the occipito-temporal cortex, where multiple stages of data encoding are happening. 
 
The active receptors are denser in the last stages of visual recognition, in the parahippocampal and rhinal cortex, where the visual information enables memories. Due to variations in the intensity of the receptors, perceptual preferences are created from the stored data and the receptor densities created by perception. The more fluently perceivers can process an object, the more positive their aesthetic response. (Reber et al, 2004)
 
In other words, it is the visual interpretation of patterns that leads to the feeling of pleasure.
 
Aesthetic pleasure correlates with the fluency of processing: Palmer (2013) emphasizes perceptual and conceptual ease, while Leder (2004) models aesthetic appreciation as stages of perception, classification, and evaluation.
 
Dopamine supports learning, memory, and cognitive flexibility, with D1 and D2 receptors modulating neural activity and behavior adjustment (Clos et al., 2019; Puig, 2014). It facilitates associative retrieval (Achim, 2005) and strengthens attention-related networks like the frontoparietal control and default mode networks (Dang, 2012).
 
Dopamine levels also rise before decision-making while serotonin decreases (Bang et al., 2020), linking neuromodulators not only to appetitive processes but to sensory inference. Thus, greater rhythm and fluency in cognitive structures enhance aesthetic pleasure, making information both more geometric and more addictive.
 
Under all these circumstances, information becomes its own reward, whether it is useful or not. (Ming Hsu, 2019)
 

3.4 Beauty

Defined as the pleasure derived from sensory or cognitive experiences, beauty emerges from complex and layered processes within the mind. Armstrong (2008) frames beauty as an emotion, linking different forms of aesthetic pleasure to distinct epistemic goals, while Skov (2020) suggests that beauty involves a positive evaluative appraisal requiring both intense pleasure and alignment with internal cognitive models. Lindell (2014) emphasizes the evolutionary salience of beauty, which captures attention and influences decision-making, embedding aesthetic preference deep within human judgment systems.
 
Neuroimaging studies reveal remarkably consistent brain activation patterns when individuals experience beauty, whether in artworks, natural landscapes, or structured designs. These patterns include engagement of the ventral and lateral visual cortices, along with activation of the default mode network (DMN), associated with self-referential thought and internal narrative construction (Isik, 2021; Vessel, 2012; Mizokami, 2014; Dio, 2016; Dio, 2007; Boccia, 2016; Dio, 2011; Vartanian, 2004).
 
Content-specific factors, such as the presence of human forms or natural scenery, further influence the neural processes underlying aesthetic judgment (Dio, 2016), while key affective regions like the right insula and amygdala contribute to the emotional resonance of beauty perception (Dio, 2007). Together, these findings indicate that aesthetic appreciation, while subjective in its expression, is rooted in robust and partially universal biological structures.
 
Recent research suggests that the DMN itself may encode a global aesthetic evaluation system, integrating various sensory and cognitive inputs into unified experiences of beauty (Vessel, 2019). Intriguingly, this aesthetic structure is not limited to sensory domains: even mathematical arguments can be appraised for beauty using criteria such as grace, complexity, and universality, paralleling evaluations of art and music (Johnson & Steinerberger, 2019). Such evaluations are shaped by intuition, value judgments, and the informal, experiential ways through which mathematical ideas derive meaning (Sinclair, 2011).
 
Humanistic approaches to mathematics have further highlighted the role of intuition and aesthetic judgment in the appreciation of mathematical structures (White, 1993), suggesting that beauty is integral not just to artistic experience but to cognitive construction itself. Applications of machine learning to assess the aesthetic quality of paintings and studies examining how individuals evaluate landscapes and artworks (Balietti, 2020) provide additional frameworks for understanding beauty as a multi-criteria, multi-modal phenomenon—spanning the arts, sciences, and mathematics alike.
 
Another complex relation between geometry and aesthetics is shown in how symmetry defines the perceived qualities of the human body and how these traits are a sign of good health or good genetic conditions. Research has consistently shown a link between facial symmetry and attractiveness, with symmetrical faces being rated as more attractive (Perrett, 1999; Scheib, 1999; Rhodes, 1998; Enquist, 1994). Borelli (2009) further explores the role of facial features in perceptions of beauty, emphasizing the importance of symmetry, proportion, and simplicity. This preference for symmetry may be due to its association with good health and genetic quality (Rhodes, 2001). 
 

3.5 Truth

Man uses beauty as an indicator of truth, and while beauty is truth (Stewart, 2007), symmetry, proportion, and simplicity will define it. The concept of beauty as an indicator of truth is complex and multifaceted. While some studies suggest a link between physical attractiveness and positive personality traits (Eagly, 1991), others argue that beauty standards are culturally influenced (Dmitrov, 2023).
 
The processes for cognitive assesment of truthfulness  are entangled with the axioms of geometry, that define the building blocks for reasonable thinking and empirical behaviour (Putnam, 1975).
 
This is further complicated by the fuzzy boundaries of natural language concepts (Lakoff, 1973), and the difficulty in correcting erroneous beliefs (Schwarz, 2016). The ontological commitments of a sentence, as proposed by Cameron (2008), and the concept of pragmatic truth (Costa, 1989) also play a role in this assessment. The belief in axioms, as discussed by Maddy (1988), and the grounding of truth-functions (Correia, 2010) are additional factors considered here.
 
While the interaction between logical and philosophical theories of truth is a key area for further exploration, “If” and “then”, the two most used operators in creating a logical statment, are also inherently part of the mechanisms of geometry: if angle A has a certain relation to angle B, than angle C follows (fig. 4).  
Fig.4 In the spirit of Pythagorean reasoning, the Greeks saw geometry as the grammar of truth: if A relates to B, then C must follow.
The systems of thought are governed by principles that  Pythagora extracted from  a geometric knowledge, a philosophy of mathematics where the things are an imitation of the numbers, and their definitions and axioms will reflect the universe:
1. Some propositions must be accepted as true without being demonstrated. The inference of truth is based on axioms that are unprovable within the system.
2. All other propositions of the system are derived from these.
3. Their derivation must be formal and independent from the subject at matter.
 
The development of “visual truth” stems from early traditions of orally sharing and debating knowledge, where the first geometric representations of mathematical concepts were drawn—often imperfectly—by scribes transcribing from spoken accounts. Without formal geometric understanding, these early attempts frequently introduced errors and distortions. 
 
In the early 300s BCE, Euclid recognized this problem and began drawing his own definitions and axioms, producing accompanying diagrams designed to be universally intelligible to mathematicians and artists alike. With the later introduction of visual perspective by Leon Battista Alberti, geometric diagrams and visualized laws became standard tools for conveying mathematical truth and for depicting reality itself. 
 
The development of “visual truth” in mathematics, particularly through the work of Euclid, has long been a subject of debate and investigation. Carter (2019) and Rivera (2011) both explore the roles of diagrams and visual representations in mathematical reasoning, with Carter emphasizing their historical significance and Rivera underscoring their cognitive functions in supporting abstract thought. Luecking (2019) and Whiteley (2005) extend this perspective by examining the impact of visual training—both on the evolution of abstract art and on the teaching of mathematics—arguing that visualization cultivates deeper cognitive flexibility.
 
At the same time, Pejlare (2007) and Niall (2002) provide critical perspectives on the reliance on visual thinking: Pejlare highlights the potential limitations of visualizations in sustaining rigorous reasoning, while Niall stresses the distinction between visual imagination and logical deduction.

Mathematics, in this context, operates primarily as an epistemological system: a framework for organizing, validating, and transmitting structured knowledge. Geometry, by contrast, reflects an ontological layer: it encodes how relations, forms, and transformations are made possible within the fabric of cognitive processes. While mathematical reasoning allows for the abstraction and manipulation of truth claims, geometric structures define the conditions under which such truths can be instantiated, stabilized, or recognized. In this sense, geometry does not merely model reality, it scaffolds the very space within which cognition can unfold, providing the hidden architecture through which perception, reasoning, and coherence emerge.
 
The brain’s capacity to recognize patterns plays a central role in truth-assessment (Dan King, 2020), illustrating how familiarity and coherence act as gravitational forces within cognition. This dynamic is further exemplified by the illusory truth effect, where repeated exposure to information increases its perceived truth regardless of its factual accuracy (Fazio, 2019). In this sense, truth becomes a gravitational phenomenon: attention is drawn toward what feels familiar, stable, or coherent within the evolving topology of the cognitive manifold.
 
Yet these cognitive attractors are not always aligned with objective accuracy. The variability of attention weights in text classification models (Serrano, 2019) parallels how cognitive variability γ in human minds leads to differential salience, pattern selection, and judgment. Base-rate neglect, emotional resonance, and the consistency of new information with stored knowledge further modulate judgments of truth (Brashier, 2019), often outweighing deliberate rational evaluation. 
 
Even subliminal stimuli—those below the threshold of conscious awareness—have been shown to influence truth evaluations (Mudrik, 2022), suggesting that much of what we perceive as “true” arises from potential gravitational fields beneath deliberative reasoning.
 
Importantly, the robustness of the illusory truth effect across variations in cognitive ability, cognitive style, and need for closure (De Keersmaecker, 2019) indicates that phenomenal bias β consistently warps the manifold of possible truths. From the standpoint of cognitive gravity, this suggests that attention is not neutrally distributed across cognitive processes, such as language: certain statements become gravitational attractors more readily, stabilizing within belief systems regardless of their factual validity.
 
Within the polynon, truth is not modeled as a binary state but as a position within a curved geometric structure. This structure accommodates nondualistic reasoning, allowing the classical constraints of the Principle of the Excluded Middle and that of Non-Contradiction to be softened or broken. Multiple, context-sensitive truth states can coexist, depending on the observer’s location within the cognitive field.
 
This approach aligns with Graham Priest’s (2014) distinction between functions and relations: while a function links each input to exactly one output, a relation allows multiple outputs for a single input. Truth, under this relational model, is dynamically distributed across the manifold of cognition: contextual, fluid, and gravitationally shaped.
 
Thus, attention and reason do not move freely through an abstract logical space; they gravitate toward regions of coherence, familiarity, and structural fit within the cognitive topology of the observer. 
 
As we’ve seen, the dimensions of pleasure, beauty, and truth can be mapped within a cohesive cognitive topology. Pleasure is tied to fluency and coherence, states where incoming perceptual data align smoothly with internal expectations. Beauty arises when perceptual forms resonate harmonically within the manifold’s structure, offering a balance between complexity and comprehension. Truth emerges where internal geometries match external realities, producing a felt alignment that anchors belief and judgment.
 
While these dimensions may appear to support a view of consciousness as emergent from perceptual coherence and cognitive fluency, such a reading captures only their phenomenal expression. These experiences reveal the structured outputs of consciousness, but not its source. From a Kantian (and polynonial) perspective, they are shaped within the domain of the sensible, reflecting how cognition configures appearances rather than disclosing their ontological ground. The noumenal origins of these dynamics reside beyond what is directly perceived, suggesting that what we call aesthetic or epistemic alignment arises from deeper, pre-phenomenal structures. 
 
Consciousness, in this light, cannot be reduced to emergent representations alone, but must be understood as a dynamic tension between existence and actuality.
 
These experiences, though qualitatively distinct, are all shaped by gradients of attention, memory, and expectation. Here, cognitive gravity provides a unifying model. It describes how internal attractors (e.g., memories, emotions, learned schemas) draw perception and reasoning toward certain interpretations while deflecting others, allowing us to navigate experience as a topological structure. 
Geometric cognition reveals how neural architectures, perceptual processes, and memory structures follow topologies that are not random but gravitationally shaped.
 
Cognitive gravity, operating through gradients of noumenal and phenomenal salience, bends these processes into emergent patterns that stabilize as identity, knowledge, belief, and world-construction. In mapping these fields, we glimpse a unified architecture: a cognitive manifold where experience orbits, collapses, and expands according to gravitational principles. 
 
This architecture is not abstract: it defines how we name, narrate, and live reality. From here, we turn to explore how this gravitational structure is expressed most intimately through the grammar of experience and how it shapes both our inner lives and the shared histories we co-create.
 

4 The Grammar of Cognitive Gravity

Beneath every sentence lies an invisible architecture of attention, modulation, and affect, structuring how meaning crystallizes into form. The grammar of experience encodes the gravitational dynamics of cognition: verbs, adjectives, and adverbs act as localized vectors within a grammar construct, signaling where experience intensifies, shifts, or folds upon itself.
 
When we say we are “falling in love,” we invoke a gravitational metaphor that reshapes affective orientation. A “heavy heart,” a “bright idea,” a “clouded judgment”—these expressions are not decorative; they reveal the gravitational texture of cognition itself. 
 
Through linguistic structures, cognitive gravity becomes explicit. Language maps experiential gradients, stabilizes temporal arcs, and frames the topology of thought. 
 
This gravitational grammar is fundamentally metaphorical. As Lakoff (2003) argumented, metaphors are not merely linguistic ornaments but cognitive mappings: they structure how we think, feel, and act. Abstract domains like emotion, morality, and time are conceptualized through spatial and physical metaphors, grounding intangible experience in embodied interaction. Gravity metaphors (“falling”, “lifting”, “being weighed down”) are among the most pervasive, reflecting how deeply cognitive gravity embeds itself into the scaffolding of language and meaning.
 
These gravitational structures are not isolated to a few poetic expressions. They permeate the basic grammar of lived experience. Across emotions, time, motion, social relations, thought, and memory, gravitational metaphors organize how we speak, feel, and act. By extending this mapping, we reveal the profound continuity between linguistic scaffolding and cognitive curvature. 
 
Table.2 Expressions of time reveal how language encodes gravitational dynamics, anchoring moments, stretching duration, and giving perceptual weight within cognitive spaces.
Across the extended table of gravitational expressions (Table 2), a deeper structural pattern emerges, revealing recurrent gravitational anchors, organized into what may be termed cognitive gravitons, that stabilize the architecture of experience.
 
Certain anchors recur across multiple domains: pull, weight, fall, sink, lift, collapse, orbit, attraction, and pressure. They appear whether describing emotional states, social structures, decision processes, or the shaping of memory. In spatial terms, these gravitational anchors define how proximity, elevation, density, and directionality are mapped within cognitive dimensions. Joy “lifts” us; grief “pulls us down”; ideas “orbit” central concerns. In temporal terms, they define how urgency, persistence, recurrence, and decay are encoded: deadlines “loom,” memories “sink,” futures “pull” us forward.
 
These anchors embody the topology of consciousness. They show that experiences are surface expressions of a deeper cognitive architecture: one that binds space, time, and identity into coherent experiential forms. 
 

5 The Gravity of Lived Events

Cognitive Gravity manifests most powerfully in the turning points of individual lives. Certain experiences act as local gravitons, bending attention, memory, and identity around themselves with such intensity that they permanently alter the local cognitive topology.
 
Love is metaphysical gravity.
 
Love, for instance, acts as a cognitive singularity: attention, emotion, and meaning collapse into a concentrated field. Time dilates or contracts; memory reorganizes itself around this new center of affective mass. Marriage stabilizes that field, bending future trajectories toward shared commitment. The birth of a child further expands the gravitational field of identity, displacing the self as center and reorganizing temporal and emotional cycles around care.
 
Trauma, by contrast, functions like a cognitive black hole, warping memory, distorting perception, and trapping attention in recursive loops. Such experiences don’t pass; they persist, altering the entire topology through which future cognition moves.
 
On a broader scale, events like 9/11, prolonged wars, or the COVID-19 pandemic demonstrate how distributed gravitational fields can restructure collective memory, political narratives, and the rhythms of daily life. Some, like the death of Princess Diana, act as symbolic singularities—condensing global attention into temporary but powerful attractor states. In each case, the experience transcends mere eventhood, embedding itself as a durable modification in the cognitive field.
Fig.5 Cognitive anchors initiate meaning, attractors amplify relevance through recurrent connections, and cognitive gravitons emerge as localized curvatures in the experiential field.
Yet, all gravitational events (whether intimate or global) begin locally, within the observer. A cognitive-first approach reveals how certain neural and emotional configurations become cognitive anchors: once activated, they evolve into attractors whose strength is proportional to their network density.
 
Over time, these attractors initiate what may be called a cognitive murmuration: a dynamic, emergent synchronization akin to the coordinated flight of starlings. Here, gravity and causality intertwine, producing ripples of effect and affect that move across neural, emotional, and social substrates. What begins as an individual perturbation becomes a distributed, self-organizing field of significance. 
 
When a certain threshold of cognitive gravity and causal resonance is crossed (alongside associated biochemical, motor, and perceptual responses processed through the brain and body) a full experience is instantiated. This experience, though felt as unified, can be decomposed and mapped: its structure follows the pathways of cognitive gravitons, the smallest curvatures of attention and meaning that give shape to the architecture of consciousness.

6 Cognitive Gravity, Time, and Causality

In the polynon, the greater the cognitive gravity within a given manifold, the denser the causal structure that emerges. Consciousness does not move through time as along a uniform axis; it flows through gradients of meaning, emotion, and directed awareness. Cognitive gravity organizes this flow. Moments heavy with significance draw consciousness inward, stretching duration, while minor events pass swiftly, scarcely registering within the experiential field. Just as physical gravity shapes the trajectories of bodies in spacetime, cognitive gravity shapes the unfolding of lived experience. 
 
Trauma deepens moments into recursive loops of recollection; joy disperses time into expansive, unbounded sequences; urgency accelerates perception into compressed bursts. Under its influence, time is not linear but pliable, stretched, condensed, or rerouted by the gravitational force of attention and affect.
 
Causality, too, is embedded within this gravitational architecture. Causes do not merely precede effects; they reconfigure the interpretive pathways through which events are encoded, recalled, and integrated. 
Fig.6 The more gravity, the more causality: as cognitive mass increases, causal structure becomes more defined, anchoring the flow of experience around the observer.

If causality emerges through gradients of cognitive gravity, then a deeper form of relativity arises, one that transcends the classical model of directional causation from A to B. In Cognitive Relativity, every event is relational, not linear; meaning does not follow from sequence but from resonance within a shared manifold. The intrinsic cognitive nature of physical reality, combined with the superposition of observer and observed, collapses the notion of causality into a perceptual effect, a secondary trace of decoherence within evolving cognitive structures.


Causality, in this framework, is not a fundamental force but a local illusion of order, an echo of the manifold stabilizing briefly around the observer’s recursive position. What we call cause and effect is a perceptual residue of deeper gravitational fluctuations within the field of consciousness.


Cognitive relativity reframes this entirely: the “now” becomes the only certainty, and both space and time collapse into observer-dependent constructs. The classical model of spacetime must be updated to reflect the continuum of experience and perception folding upon itself. Space and time are no longer absolute containers but components of the same cognitive structure, the reflection of consciousness within its own dimensional architecture.

Fig.7 Centered on the observer, phentropy maps cognitive gravity as it unfolds across space and time within the now.
The metrics discussed throughout this framework, particularly those drawn from geometric cognition, suggest that perception, memory, and meaning are inherently relative to the observer’s position within this cognitive space. What appears as stable reality is not an absolute given, but a temporary coherence of affect, belief, and perceptual orientation.
 
Yet even this stabilization is dynamic. Cognitive entropy fluctuates continuously. As previously mentioned, within the polynon, this entropy is tracked through phentropy: the tendency of phenomena to lapse back into noumena, of structured experiences to dissolve once again into undifferentiated potential. Phentropy thus becomes a vital indicator of how cognitive gravity stabilizes or destabilizes the manifold of experience, revealing not just the architecture of thought but its ongoing gravitational tensions.
 
Within this dynamic topology, space and time would no longer function as absolute containers for experience. They would emerge as secondary constructions: stretched, folded, and anchored by the gravitational dynamics and entropy flows of conscious life itself. Phentropy would mark where experiential structures collapse, where novelty emerges, and where meaning crystallizes within the manifold of awareness.
 
In this relativity, where time is no longer an absolute metric but a function of gravitational configuration, time becomes second to gravity. Cognitive gravity determines not when an event occurres, but how deeply it exerts influence, how much weight it carries within the system of meaning. For example, an event located far in the chronological past may still exert a present gravitational pull if its unresolved affective or symbolic mass remains active within the cognitive field.
 
Likewise, a future event can exert gravitational force on the present. Its cognitive weight may shape choices, filter perception, and reorganize priorities long before it arrives. In such cases, the future is already shaping the now, the timeline itself becoming warped: the moment of action lies in the past of the future, yet it was gravitationally pulled into coherence by an event that had not yet occurred.
 
This reversibility of temporal influence offers a striking implication: that within the field of cognitive gravity, causality is not unidirectional. Just as past traumas bend the present, future potentialities curve backward, leaving traces before they even unfold. What we call “preparation,” “expectation,” or “anxiety” is, in this light, the active gravitational pull of what does not yet exist, real not because it is actual, but because it is cognitively massive.
 
In this sense, the causal potency of an event is not defined by its position in time, but by its potential cognitive gravity, its capacity to capture current attention, modulate emotional response, or trigger recursive memory activation. Latent events, stored in deep cognitive or cultural memory, may re-emerge as active gravitational agents, capable of initiating new causal chains in the present.
 

7 Conclusion

 
Cognitive gravity reveals that experience is composed, shaped, bent, and stabilized by the gravitational architectures of cognition. 
 
As such, experience, as argued through the concept of cognitive gravity, is fundamentally structured by geometric cognition, wherein perception, memory, attention, and emotional experiences follow pathways shaped by internal gravitational dynamics.
 
Cognitive geometry and neurogeometry provide rigorous frameworks to model how consciousness actively organizes reality into meaningful, spatially coherent patterns. Attention, memory, and meaning thus create stable anchors, attractors, and cognitive gravitons that define the architecture of experience.
 
These gravitational structures map shades and depths of experience, engaging internal architectures that shape perceptual and cognitive landscapes.
 
Moreover, cognitive gravity invites future extensions across various theoretical and practical domains, from fundamental cognitive science to applied frameworks in decision-making, social dynamics, linguistic structures, and aesthetics. Its integrative potential positions cognitive gravity as a versatile analytical lens capable of illuminating cognitive architectures in diverse human experiences, enriching both theoretical and practical explorations of consciousness.
 
This potential resonates even with developments outside cognitive science, such as in economics, where the “gravity model” has been used to explain trade flows based on mass-like factors of economic size and distance (Head & Mayer, 2014; Baier & Standaert, 2020). These models underscore how gravitational metaphors and metrics can successfully structure complex, multi-agent systems, lending further plausibility to their use in modeling cognition itself.
 
Within the broader polynonial framework, cognitive gravity aligns with a cognitive-first approach. The reframing of gravity as cognitive embeds the polynon’s commitment to consciousness as primary, reinforcing an epistemological architecture where reality is actively constructed through cognitive dynamics.
 
Finally, as consciousness science increasingly gravitates toward a paradigm shift recognizing consciousness as fundamental, cognitive gravity  offers significant conceptual advancements, proposing novel research avenues and methodological frameworks that transcend traditional dichotomies of observer versus observed, phenomenal versus noumenal. 
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