TFNR - Elementary Relations - Revision history

Paolo at 16:22, 15 January 2026

2026-01-15T16:22:32Z

Paolo at 11:01, 8 October 2025

2025-10-08T11:01:32Z

Paolo at 10:20, 8 October 2025

2025-10-08T10:20:26Z

Paolo at 20:23, 7 October 2025

2025-10-07T20:23:37Z

Paolo at 20:20, 7 October 2025

2025-10-07T20:20:27Z

Paolo at 10:12, 7 October 2025

2025-10-07T10:12:06Z

Paolo at 18:26, 13 November 2022

2022-11-13T18:26:26Z

Paolo at 18:24, 13 November 2022

2022-11-13T18:24:12Z

Paolo at 18:12, 13 November 2022

2022-11-13T18:12:13Z

Paolo at 18:11, 13 November 2022

2022-11-13T18:11:16Z

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 Let us not forget that the dynamics of each event point in the Elementary Field constitutes a Process, composed of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension, or, more precisely, the volume of an infinitesimal region of the Field (in dimensional resonance around the Planck scale). Given the inherent uncertainty (Uncertainty Principle) of the Field's dynamics, '''this Process must be described by a stochastic process'''—a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be interpreted as a probabilistic trace of interaction.
-'''Let us imagine that each event point in the Field behaves as a random harmonic oscillator''' in terms of spatial extension (amplitude of elementary spatial fluctuations, '''expansion–and–contraction of infinitesimal volumes'''), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with said fluctuations, and spatial orientation of the axis of the aforementioned vorticity.
+'''Let us imagine that each event point in the Field behaves as a random harmonic oscillator''' in terms of spatial extension (amplitude of elementary spatial fluctuations, '''expansion-and-contraction of infinitesimal volumes'''), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with said fluctuations, and spatial orientation of the axis of the aforementioned vorticity.
 '''Suppose an ideal condition of absolute stochastic independence among the behaviors of individual event points'''. This would imply no interaction between event points, no stochastic dependence, and entirely independent dynamics—in essence, Elementary Events not linked by Relations.

@@ Line 1: / Line 1: @@
 By Elementary Relation we mean '''any Relation that emerges between Elementary Events in the dynamics of the Elementary Field, and is expressed in the fundamental [[Dimensions of Reality]]''' ([[Cause]], [[Space]] and [[Time]]).
-At the most basic level of Reality—at the level of the dynamics of the Elementary Field, where Elementary Events and the inhomogeneities of their temporal distributions—Elementary Action—represent the most fundamental forms of Existence, manifestations of the Source's incessant causal pressure in a formless, variational ocean—rather than using the generic term "Relation," we should speak of "correlation," of "correlations."
+At the most basic level of Reality—at the level of the dynamics of the Elementary Field, where Elementary Events and the inhomogeneities of their temporal distributions—Elementary Action—represent '''the most fundamental forms of Existence''', manifestations of the Source's incessant causal pressure in a formless, variational ocean—rather than using the generic term "Relation," we should speak of "correlation," of "correlations."
-We now arrive at the definition of "correlation," crucial to understanding the nature and function of Relations in the construction of Reality. Correlation plays a pivotal role in the transition from formless Existence (the Unstructured Field, the Absolute Vacuum) to the emergence and evolution of the Essence/Form of Reality—albeit in its most elementary manifestations: the first, vaguest, impermanent hints of that dark turbulence that permeates the entire Elementary Field, and through its incessant transformation gives rise to the first, evanescent InfoStructures (gradients, flows, and torsions), which will eventually lead to progressively more structured Waves and Vortices/Halos/Particles.
+We now arrive at the definition of "correlation", crucial to understanding the nature and function of Relations in the construction of Reality. '''Correlation plays a pivotal role in the transition from formless Existence''' (the Unstructured Field, the Absolute Vacuum) '''to the emergence and evolution of the Essence/Form of Reality'''—albeit in its most elementary manifestations: the first, vaguest, impermanent hints of that dark turbulence that permeates the entire Elementary Field, and through its incessant transformation gives rise to the first, evanescent InfoStructures (gradients, flows, and torsions), which will eventually lead to progressively more structured Waves and Vortices/Halos/Particles.
-By correlation—especially in the context of the dynamics of the Elementary Field, where Elementary Action and the distributions of Elementary Events self-organize, producing the basic forms, the dynamic building blocks that enable the construction of multiplicity and Complexity—we refer more to mathematics and statistics than to physics or other scientific disciplines. Specifically, we mean "dependence" in the sense attributed to stochastic dependence within the framework of stochastic processes. This dependence evokes notions of connection, covariance, and co-emergence, rather than direct causal linkage.
+By correlation—especially in the context of the dynamics of the Elementary Field, where Elementary Action and the distributions of Elementary Events self-organize, producing the basic forms, the dynamic building blocks that enable the construction of multiplicity and Complexity—'''I refer more to mathematics and statistics than to physics or other scientific disciplines'''. Specifically, '''I mean "dependence" in the sense attributed to stochastic dependence within the framework of stochastic processes'''. This dependence evokes notions of connection, covariance, and co-emergence, rather than direct causal linkage.
-Let us not forget that the dynamics of each event point in the Elementary Field constitutes a Process, composed of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension, or, more precisely, the volume of an infinitesimal region of the Field (in dimensional resonance around the Planck scale). Given the inherent uncertainty (Uncertainty Principle) of the Field's dynamics, this Process must be described by a stochastic process—a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be interpreted as a probabilistic trace of interaction.
+Let us not forget that the dynamics of each event point in the Elementary Field constitutes a Process, composed of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension, or, more precisely, the volume of an infinitesimal region of the Field (in dimensional resonance around the Planck scale). Given the inherent uncertainty (Uncertainty Principle) of the Field's dynamics, '''this Process must be described by a stochastic process'''—a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be interpreted as a probabilistic trace of interaction.
-Let us imagine that each event point in the Field behaves as a random harmonic oscillator in terms of spatial extension (amplitude of elementary spatial fluctuations, expansion–and–contraction of infinitesimal volumes), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with said fluctuations, and spatial orientation of the axis of the aforementioned vorticity.
+'''Let us imagine that each event point in the Field behaves as a random harmonic oscillator''' in terms of spatial extension (amplitude of elementary spatial fluctuations, '''expansion–and–contraction of infinitesimal volumes'''), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with said fluctuations, and spatial orientation of the axis of the aforementioned vorticity.
-Suppose an ideal condition of absolute stochastic independence among the behaviors of individual event points. This would imply no interaction between event points, no stochastic dependence, and entirely independent dynamics—in essence, Elementary Events not linked by Relations.
+'''Suppose an ideal condition of absolute stochastic independence among the behaviors of individual event points'''. This would imply no interaction between event points, no stochastic dependence, and entirely independent dynamics—in essence, Elementary Events not linked by Relations.
-This, however, is a purely hypothetical condition, as the Elementary Field is a continuous, connected, dynamic, and conservative field. The dynamics of each event point are in constant interaction with every other event point, with an intensity of interaction that decreases with the square of the distance. Being a conservative field, the dynamics of each event point depend not only on interactions with other points, but also on its own past history (non-Markovian processes, possibly exhibiting a square root power-law decay, where past evolution influences the current and future dynamics of the event point).
+'''This, however, is a purely hypothetical condition''', as the Elementary Field is a continuous, connected, dynamic, and conservative field. The dynamics of each event point are in constant interaction with every other event point, with an intensity of interaction that decreases with the square of the distance. Being a conservative field, '''the dynamics of each event point depend not only on interactions with other points, but also on its own past history''' (non-Markovian processes, possibly exhibiting a square root power-law decay, where past evolution influences the current and future dynamics of the event point).
-With this dynamic structure, in which the chaotic dynamics of event points influence other event points within a "causally connected" neighborhood (with quadratically decreasing intensity—spatially), and past dynamics influence the future evolution of each event point's dynamics (again with quadratically decreasing intensity—temporally), we obtain an Elementary Field characterized by the properties that are ideally required to enable the emergence of a Physical Reality compatible with the world we inhabit:
+With this dynamic structure, in which the chaotic dynamics of event points influence other event points within a "causally connected" neighborhood (with quadratically decreasing intensity—spatially), and past dynamics influence the future evolution of each event point's dynamics (again with quadratically decreasing intensity—temporally), '''we obtain an Elementary Field characterized by the properties that are ideally required to enable the emergence of a Physical Reality compatible with the world we inhabit''':
-*connection and continuity (causal connection and variational, spatial and temporal, continuity)
+*'''connection and continuity''' (causal connection and variational, spatial and temporal, continuity)
-*dynamism (a perturbed field)
+*'''dynamism''' (a perturbed field)
-*capacity for propagation (in Space) and conservation (in Time) of perturbations and structure
+*'''capacity for propagation''' (in Space) '''and conservation''' (in Time) of perturbations and structure
-The Field thus tends to generate and evolve structures within itself, as a result of the formation, propagation, and conservation of spontaneous perturbations—an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.
+'''The Field thus tends to generate and evolve structures within itsel'''f, as a result of the formation, propagation, and conservation of spontaneous perturbations—an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.
-This evolutionary tendency exerts a constant pressure toward the Creation and Evolution of increasingly extensive (Space), enduring (Time), and complex (Cause) Relations, which from the more complex correlations elementary ones go to the more complex relationships that link the macro-events at the basis, for example, of immense cosmic phenomena, or of intricate biological phenomena.
+In summary, '''the most basic form of Relation is "correlation", which can be represented as stochastic dependence between the temporal distributions of the elementary spatial fluctuations of the Elementary Field in resonance around the Planck Scale''' (commonly referred to as quantum fluctuations, quantum vacuum, quantum foam, etc.)—the Elementary Events. Elementary spatial fluctuations, which can be characterized '''not only in terms of their temporal distributions''' (Perturbation → (Metric / Mass)), but also by their '''spatial directionality''' (Translation → Motion), by the '''chirality of their vorticity''' (Rotation:Chirality → Charge), and by the '''spatial orientation of the axis of that vorticity''' (Rotation:AxisOrientation → Spin).
-This evolutionary tendency exerts a continuous pressure toward the Creation and Evolution of increasingly extensive (Space), enduring (Time), and complex (Cause) Relations—progressing from elementary correlations to more intricate relationships that link macro-events underlying immense cosmic phenomena or intricate biological processes.
+Correlations between the (local, pointwise) distributions of these fluctuations '''can be described by a combination of stochastic (new Action, new Information) and deterministic Processes (old Action, old Information)'''. At the most elementary level of Reality—where the internal interaction of the Fundamental Force and the Elementary Field occurs incessantly, producing the Elementary Events that constitute Elementary Action—the correlations between distributions can be described by Processes of Events organized by Relations in which '''the stochastic component is, "initially", overwhelmingly prevalent, and the deterministic part almost entirely marginal'''.
-In summary, '''the most basic form of Relation is "correlation", which can be represented ad stochastic dependence, between the temporal distributions of the elementary spatial fluctuations of the Elementary Field in resonance around the Planck Scale''' (commonly called quantum fluctuations, quantum vacuum, quantum foam, etc.), the Elementary Events.
+'''As Time progresses''', the Elementary Field—through the emergence of ever-new Relationships among Elementary Events and the accumulation of increasing Information / Energy—'''tends to form new and more stable structures, giving rise to a persistent, though still formless, turbulence'''. Gradually, this turbulence gives way to more defined, identifiable structures, persistent both causally and variationally (spatially and temporally). And so on, in an endless Evolution, from the earliest infinitesimal fluctuations to the vast structures of the Cosmic Web, and to the most complex biological architectures.
-In summary, '''the most basic form of Relation is "correlation", which can be represented as stochastic dependence between the temporal distributions of the elementary spatial fluctuations of the Elementary Field in resonance around the Planck Scale''' (commonly referred to as quantum fluctuations, quantum vacuum, quantum foam, etc.)—the Elementary Events.
+'''Emptiness gradually gives way to Somethingness'''. Absolute vacuum progressively yields to a Relative vacuum, and then to a Space-time increasingly populated by InfoStructures (Waves, Vortices/Chaos/Particles, Interactions) that constitute both Dark and Ordinary Matter—the invisible and the visible sides of the vastness of the Universe.
-−
-−
-Correlations between the (local, point) distributions of those fluctuations, which '''can be described by a combination of stochastic and deterministic processes'''. At the most elementary level of Reality, where the inner interaction of the Fundamental Force and the Elementary Field incessantly occurs, producing the Elementary Events that form the Elementary Action, the correlations between the distributions can be described by Processes of Events in which stochastic component is almost completely prevalent, and the deterministic part absolutely marginal.
-−
-Correlations between the (local, pointwise) distributions of these fluctuations '''can be described by a combination of stochastic and deterministic processes'''. At the most elementary level of Reality—where the inner interaction of the Fundamental Force and the Elementary Field occurs incessantly, producing the Elementary Events that constitute Elementary Action—the correlations between distributions can be described by Processes of Events in which the stochastic component is overwhelmingly prevalent, and the deterministic part almost entirely marginal.
 {{Template:PaperPages1}}

@@ Line 1: / Line 1: @@
 By Elementary Relation we mean '''any Relation that emerges between Elementary Events in the dynamics of the Elementary Field, and is expressed in the fundamental [[Dimensions of Reality]]''' ([[Cause]], [[Space]] and [[Time]]).
 At the most basic level of Reality—at the level of the dynamics of the Elementary Field, where Elementary Events and the inhomogeneities of their temporal distributions—Elementary Action—represent the most fundamental forms of Existence, manifestations of the Source's incessant causal pressure in a formless, variational ocean—rather than using the generic term "Relation," we should speak of "correlation," of "correlations."
-We now come to the definition of "correlation," crucial to understanding the nature and function of Relationship in the construction of Reality. Correlation plays a crucial role here in the transition from formless Existence (the Unstructured Field, the Absolute Vacuum) to the emergence and evolution of the Essence/Form of Reality, albeit in its most elementary forms (the first, vaguest, impermanent hints of that dark turbulence that permeates the entire Elementary Field, and from its incessant transformation leads to the emergence of the first, evanescent InfoStructures (gradients, flows, and torsions, which will lead to the progressively more structured Waves and Vortices/Halos/Particles).
+By correlation—especially in the context of the dynamics of the Elementary Field, where Elementary Action and the distributions of Elementary Events self-organize, producing the basic forms, the dynamic building blocks that enable the construction of multiplicity and Complexity—we refer more to mathematics and statistics than to physics or other scientific disciplines. Specifically, we mean "dependence" in the sense attributed to stochastic dependence within the framework of stochastic processes. This dependence evokes notions of connection, covariance, and co-emergence, rather than direct causal linkage.
-−
-We now arrive at the definition of "correlation," crucial to understanding the nature and function of Relationship in the construction of Reality. Correlation plays a pivotal role in the transition from formless Existence (the Unstructured Field, the Absolute Vacuum) to the emergence and evolution of the Essence/Form of Reality—albeit in its most elementary manifestations: the first, vaguest, impermanent hints of that dark turbulence that permeates the entire Elementary Field, and through its incessant transformation gives rise to the first, evanescent InfoStructures (gradients, flows, and torsions), which will eventually lead to progressively more structured Waves and Vortices/Halos/Particles.
-−
-−
-By correlation, especially in the context of the dynamics of the Elementary Field, where Elementary Action, the distributions of Elementary Events, organize themselves, producing the basic forms, the dynamic building blocks that allow the construction of Complexity. Referring more to mathematics and statistics than to physics and more generally to scientific disciplines, I mean "dependence" in the sense we attribute to the concept of stochastic dependence in the context of stochastic processes. This dependence recalls concepts of connection, covariance, and co-emergence, rather than causal link.
-−
-By correlation—especially in the context of the dynamics of the Elementary Field, where Elementary Action and the distributions of Elementary Events self-organize, producing the basic forms, the dynamic building blocks that enable the construction of Complexity—we refer more to mathematics and statistics than to physics or other scientific disciplines. Specifically, we mean "dependence" in the sense attributed to stochastic dependence within the framework of stochastic processes. This dependence evokes notions of connection, covariance, and co-emergence, rather than direct causal linkage.
-−
-−
-Let's not forget that the dynamics of each event point in the Elementary Field is a Process, consisting of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension (in dimensional resonance around the Planck scale). Given the uncertain nature (Uncertainty Principle) of the dynamics of the Field, this Process must be described by a stochastic process, a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be viewed as a probabilistic trace of interaction.
-−
-Let us not forget that the dynamics of each event point in the Elementary Field constitutes a Process, composed of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension (in dimensional resonance around the Planck scale). Given the inherent uncertainty (Uncertainty Principle) of the Field's dynamics, this Process must be described by a stochastic process—a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be interpreted as a probabilistic trace of interaction.
-Let's imagine that each event point in the Field consists of a random harmonic oscillator in spatial extension or distance (amplitude of elementary spatial fluctuations), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with the aforementioned fluctuations, and spatial orientation of the axis of the aforementioned vorticity. Let's assume an ideal condition of absolute stochastic independence of the behavior. of individual event points. This implies no interaction between event points, no stochastic dependence, independent dynamics. In essence, Elementary Events not linked by Relations.
+Let us imagine that each event point in the Field behaves as a random harmonic oscillator in terms of spatial extension (amplitude of elementary spatial fluctuations, expansion–and–contraction of infinitesimal volumes), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with said fluctuations, and spatial orientation of the axis of the aforementioned vorticity.
-Let us imagine that each event point in the Field behaves as a random harmonic oscillator in terms of spatial extension or distance (amplitude of elementary spatial fluctuations), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with said fluctuations, and spatial orientation of the axis of the aforementioned vorticity. Suppose an ideal condition of absolute stochastic independence among the behaviors of individual event points. This would imply no interaction between event points, no stochastic dependence, and entirely independent dynamics—in essence, Elementary Events not linked by Relations.
+Suppose an ideal condition of absolute stochastic independence among the behaviors of individual event points. This would imply no interaction between event points, no stochastic dependence, and entirely independent dynamics—in essence, Elementary Events not linked by Relations.
-This is a purely hypothetical condition, as the Elementary Field is a continuous, connected, dynamic, and conservative field. The dynamics of each event point is in constant interaction with every other event point, with an intensity of interaction that decreases with the square of the distance. Since it is a conservative field, the dynamics of each event point depends not only on the interaction with other event points, but also on its past history (non-Markovian processes). The Field will therefore have a tendency to create and evolve structures within itself, as a result of the formation, propagation, and preservation of spontaneous perturbations, in an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.
+With this dynamic structure, in which the chaotic dynamics of event points influence other event points within a "causally connected" neighborhood (with quadratically decreasing intensity—spatially), and past dynamics influence the future evolution of each event point's dynamics (again with quadratically decreasing intensity—temporally), we obtain an Elementary Field characterized by the properties that are ideally required to enable the emergence of a Physical Reality compatible with the world we inhabit:
-This, however, is a purely hypothetical condition, as the Elementary Field is a continuous, connected, dynamic, and conservative field. The dynamics of each event point are in constant interaction with every other event point, with an intensity of interaction that decreases with the square of the distance. Being a conservative field, the dynamics of each event point depend not only on interactions with other points, but also on its own past history (non-Markovian processes). The Field thus tends to generate and evolve structures within itself, as a result of the formation, propagation, and preservation of spontaneous perturbations—an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.
+The Field thus tends to generate and evolve structures within itself, as a result of the formation, propagation, and conservation of spontaneous perturbations—an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.

@@ Line 1: / Line 1: @@
 By Elementary Relation we mean '''any Relation that emerges between Elementary Events in the dynamics of the Elementary Field, and is expressed in the fundamental [[Dimensions of Reality]]''' ([[Cause]], [[Space]] and [[Time]]).
 At the most basic level of Reality, at the level of the dynamics of the Elementary Field, where Elementary Events and the inhomogeneities of their temporal distributions—Elementary Action—represent the most basic forms of Existence, manifestations of the Source's incessant causal pressure in a formless, variational ocean, rather than using the generic term "Relation," we should speak of "correlation," of "correlations."
 We now come to the definition of "correlation," crucial to understanding the nature and function of Relationship in the construction of Reality. Correlation plays a crucial role here in the transition from formless Existence (the Unstructured Field, the Absolute Vacuum) to the emergence and evolution of the Essence/Form of Reality, albeit in its most elementary forms (the first, vaguest, impermanent hints of that dark turbulence that permeates the entire Elementary Field, and from its incessant transformation leads to the emergence of the first, evanescent InfoStructures (gradients, flows, and torsions, which will lead to the progressively more structured Waves and Vortices/Halos/Particles).
 By correlation, especially in the context of the dynamics of the Elementary Field, where Elementary Action, the distributions of Elementary Events, organize themselves, producing the basic forms, the dynamic building blocks that allow the construction of Complexity. Referring more to mathematics and statistics than to physics and more generally to scientific disciplines, I mean "dependence" in the sense we attribute to the concept of stochastic dependence in the context of stochastic processes. This dependence recalls concepts of connection, covariance, and co-emergence, rather than causal link.
 Let's not forget that the dynamics of each event point in the Elementary Field is a Process, consisting of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension (in dimensional resonance around the Planck scale). Given the uncertain nature (Uncertainty Principle) of the dynamics of the Field, this Process must be described by a stochastic process, a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be viewed as a probabilistic trace of interaction.
 Let's imagine that each event point in the Field consists of a random harmonic oscillator in spatial extension or distance (amplitude of elementary spatial fluctuations), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with the aforementioned fluctuations, and spatial orientation of the axis of the aforementioned vorticity. Let's assume an ideal condition of absolute stochastic independence of the behavior. of individual event points. This implies no interaction between event points, no stochastic dependence, independent dynamics. In essence, Elementary Events not linked by Relations.
 This is a purely hypothetical condition, as the Elementary Field is a continuous, connected, dynamic, and conservative field. The dynamics of each event point is in constant interaction with every other event point, with an intensity of interaction that decreases with the square of the distance. Since it is a conservative field, the dynamics of each event point depends not only on the interaction with other event points, but also on its past history (non-Markovian processes). The Field will therefore have a tendency to create and evolve structures within itself, as a result of the formation, propagation, and preservation of spontaneous perturbations, in an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.
 This evolutionary tendency exerts a constant pressure toward the Creation and Evolution of increasingly extensive (Space), enduring (Time), and complex (Cause) Relations, which from the more complex correlations elementary ones go to the more complex relationships that link the macro-events at the basis, for example, of immense cosmic phenomena, or of intricate biological phenomena.
 In summary, '''the most basic form of Relation is "correlation", which can be represented ad stochastic dependence, between the temporal distributions of the elementary spatial fluctuations of the Elementary Field in resonance around the Planck Scale''' (commonly called quantum fluctuations, quantum vacuum, quantum foam, etc.), the Elementary Events.
 Correlations between the (local, point) distributions of those fluctuations, which '''can be described by a combination of stochastic and deterministic processes'''. At the most elementary level of Reality, where the inner interaction of the Fundamental Force and the Elementary Field incessantly occurs, producing the Elementary Events that form the Elementary Action, the correlations between the distributions can be described by Processes of Events in which stochastic component is almost completely prevalent, and the deterministic part absolutely marginal.
 {{Template:PaperPages1}}

@@ Line 1: / Line 1: @@
-For Elementary Relation we intend '''any Relation that emerges between Elementary Events in the fundamental [[Dimensions of Reality]]''' ([[Cause]], [[Space]] and [[Time]]) of the state of the [[Primary Source]] ([[Fundamental Force]] and [[Elementary Field]]) in itself.
+By Elementary Relation we mean '''any Relation that emerges between Elementary Events in the dynamics of the Elementary Field, and is expressed in the fundamental [[Dimensions of Reality]]''' ([[Cause]], [[Space]] and [[Time]]).
-Al livello più elementare della Realtà, a livello della dinamica del Campo Elementare, dove gli Eventi Elementari e le inomogeneità delle loro distribuzioni temporali, l'Azione Elementare, rappresentano le forme più elementari dell'Esistenza, manifestazioni della incessante pressione causale della Sorgente, in un oceano variazionale senza forma, anziché utilizzare il termine generico "Relazione", dovremmo parlare di "correlazione", di "correlazioni".
+At the most basic level of Reality, at the level of the dynamics of the Elementary Field, where Elementary Events and the inhomogeneities of their temporal distributions—Elementary Action—represent the most basic forms of Existence, manifestations of the Source's incessant causal pressure in a formless, variational ocean, rather than using the generic term "Relation," we should speak of "correlation," of "correlations."
-Veniamo ora alla definizione di "correlazione" cruciale per comprendere la natura e la funzione che la Relazione svolge nella costruzione della Realtà. Correlazione che qui svolge la cruciale funzione nella transizione dall'Esistenza senza forma (the Unstructured Field, the Absolute Vacuum), all'emergere e all'evoluzione dell'Essenza / Forma della Realtà, seppure nelle sue forme più elementari (le prime, più vaghe, impermanent accenni di quella turbolenza dark che permea tutto il Campo Elementare, e dalla sua incessante trasformazione conduce all'emergere delle prime ed evanescenti InfoStrutture (flussi e torsioni, che porteranno alle progressivamente più strutturate Onde e Vortici/Hols/Particles).
+We now come to the definition of "correlation," crucial to understanding the nature and function of Relationship in the construction of Reality. Correlation plays a crucial role here in the transition from formless Existence (the Unstructured Field, the Absolute Vacuum) to the emergence and evolution of the Essence/Form of Reality, albeit in its most elementary forms (the first, vaguest, impermanent hints of that dark turbulence that permeates the entire Elementary Field, and from its incessant transformation leads to the emergence of the first, evanescent InfoStructures (gradients, flows, and torsions, which will lead to the progressively more structured Waves and Vortices/Halos/Particles).
-Per correlazione, soprattutto nel contesto della dinamica del Campo Elementare, dove l'Azione Elementare, le distribuzioni degli Eventi Elementari, si organizzano producendo le forme basiche, i mattoni dinamici che permettono la costruzione della Complessità, rivolgendomi più alla matematica e alla statistica che alla fisica e più in generale alle discipline scientifiche, intendo "dipendenza", nel senso che attribuiamo al concetto di dipendenza stocastica nel contesto dei processi stocastici. Dipendenza che richiama la connessione,
+By correlation, especially in the context of the dynamics of the Elementary Field, where Elementary Action, the distributions of Elementary Events, organize themselves, producing the basic forms, the dynamic building blocks that allow the construction of Complexity. Referring more to mathematics and statistics than to physics and more generally to scientific disciplines, I mean "dependence" in the sense we attribute to the concept of stochastic dependence in the context of stochastic processes. This dependence recalls concepts of connection, covariance, and co-emergence, rather than causal link.
-Non dimentichiamo che la dinamica di ciascun punto evento del Campo Elementare è un Processo, costituita da variazioni spaziali elementari, dove ciò che varia è la distanza spaziale di un segmento di estensione infinitesima (in risonanza dimensionale attorno alla scala di Planck). Tale Processo, data la natura incerta (Principio di Uncertainty) della dinamica del Campo, deve essere descritto da un processo stocastico, una famiglia di variabili aleatorie, indicizzate nel Tempo.
+Let's not forget that the dynamics of each event point in the Elementary Field is a Process, consisting of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension (in dimensional resonance around the Planck scale). Given the uncertain nature (Uncertainty Principle) of the dynamics of the Field, this Process must be described by a stochastic process, a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be viewed as a probabilistic trace of interaction.
-può essere vista come una traccia probabilistica di interazione.
+Let's imagine that each event point in the Field consists of a random harmonic oscillator in spatial extension or distance (amplitude of elementary spatial fluctuations), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with the aforementioned fluctuations, and spatial orientation of the axis of the aforementioned vorticity. Let's assume an ideal condition of absolute stochastic independence of the behavior. of individual event points. This implies no interaction between event points, no stochastic dependence, independent dynamics. In essence, Elementary Events not linked by Relations.
+In summary, '''the most basic form of Relation is "correlation", which can be represented ad stochastic dependence, between the temporal distributions of the elementary spatial fluctuations of the Elementary Field in resonance around the Planck Scale''' (commonly called quantum fluctuations, quantum vacuum, quantum foam, etc.), the Elementary Events.
-Quindi, '''the most basic form of Relation is the correlation, which can be represented ad stochastic dependence, between the elementary fluctuations of / in the Elementary Field at Planck Scale''' (commonly called quantum fluctuations, quantum vacuum, quantum foam, etc.), the Elementary Events.
 Correlations between the (local, point) distributions of those fluctuations, which '''can be described by a combination of stochastic and deterministic processes'''. At the most elementary level of Reality, where the inner interaction of the Fundamental Force and the Elementary Field incessantly occurs, producing the Elementary Events that form the Elementary Action, the correlations between the distributions can be described by Processes of Events in which stochastic component is almost completely prevalent, and the deterministic part absolutely marginal.
 {{Template:PaperPages1}}

@@ Line 1: / Line 1: @@
 For Elementary Relation we intend '''any Relation that emerges between Elementary Events in the fundamental [[Dimensions of Reality]]''' ([[Cause]], [[Space]] and [[Time]]) of the state of the [[Primary Source]] ([[Fundamental Force]] and [[Elementary Field]]) in itself.
-The most elementary form of Relation is the correlation or dependence between the elementary fluctuations of / in the Elementary Field at Planck Scale (commonly named as quantum fluctuations, quantum vacuum, quantum foam, etc.), the Elementary Events.
+The most basic form of Relation is the correlation or dependence between the elementary fluctuations of / in the Elementary Field at Planck Scale (commonly called quantum fluctuations, quantum vacuum, quantum foam, etc.), the Elementary Events.
-Correlations between the (local, point) distributions of those fluctuations, which can be described by a combination of stochastic and deterministic processes. At the most elementary level of Reality, where the inner interaction of the Fundamental Force and the Elementary Field incessantly occurs, producing the Elementary Events that form the Elementary Action, the correlations between the distributions can be described by Processes of Events in which stochastic component in almost completely prevalent, and the deterministic part absolutely marginal.
+Correlations between the (local, point) distributions of those fluctuations, which can be described by a combination of stochastic and deterministic processes. At the most elementary level of Reality, where the inner interaction of the Fundamental Force and the Elementary Field incessantly occurs, producing the Elementary Events that form the Elementary Action, the correlations between the distributions can be described by Processes of Events in which stochastic component is almost completely prevalent, and the deterministic part absolutely marginal.
-In the more and more complex levels of Reality, we see a minor prevalence of the stochastic component, in favor of the emergence of a more important deterministic part. When the Events become more and more complex, macro-events acquire a larger space and time extension, the stochastic component, the "quantum" aspects, governed by indetermination, uncertainty, mediates, becoming less prevalent, less quantitatively and qualitatively important, than the deterministic aspects (processes of events supporting the existence of macro-objects, i.e. an apple, show more deterministic characteristics and phenomena, than those supporting the Existence of molecules and atoms, all the particles and waves the make up that apple). The collective behavior of all the Processes of Events representing the Existence and the Essence / Form of the particles and waves that make up the apple, and every interaction between them, which can be described by more stochastic than deterministic processes, manifests less "quantum" (stochastic) and more "deterministic" aspects, as we see in our everyday experience.
+In the increasingly complex levels of Reality, a lower prevalence of the stochastic (quantum) component is noted, in favor of the emergence of a more important deterministic part. When Events become more and more complex, macro-events acquire a greater spatial and temporal extension, the stochastic component, the "quantum" aspects, governed by uncertainty, averages, becoming less prevalent, less quantitatively and qualitatively important, than the deterministic aspects (the processes of events that support the Existence of macro-objects, for example an apple, show more deterministic characteristics and phenomena, than those that support the Existence of molecules and atoms, all the particles and waves the make up that apple). The collective behavior of all the Processes of Events representing the Existence and the Essence / Form of the particles and waves that make up the apple, and every interaction between them, which can be described by more stochastic than deterministic processes, manifests less "quantum" (stochastic) and more "deterministic" aspects, as we see in our daily experience.
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