Today a change is imperative in approaching global problems: what is needed is not arm-twisting and power politics, but searching for ways of co-evolution in the complex social and geopolitical systems of the world. The modern theory of self-organization of complex systems provides us with an understanding of the possible forms of coexistence of heterogeneous social and geopolitical structures at different stages of development regarding the different paths of their sustainable co-evolutionary development. The theory argues that the evolutionary channel to (...) the observed increasing complexity is extremely narrow and only certain discrete spectra of relatively stable self-maintained structures are feasible in complex systems. There exists a restricted set of ways of assembling a complex evolutionary whole from diverse parts. The law of nonlinear synthesis of complex structures reads: the integration of structures in more complex ones occurs due to the establishment of a common tempo of their evolution. On the basis of the theory, we can see not only desirable but also attainable futures. (shrink)

Biological systems operate far from thermodynamic equilibrium, continuously exchanging energy and information with their environments. We propose that quantum coherence in biological matter is not a fragile artifact of isolation but an emergent property of nonlinear energy flow. Through parametric field pumping, classical nonequilibrium oscillations act as phase-selective amplifiers, converting decoherence into constructive interference. Three experimentally accessible mechanisms—Frohlich dipolar condensation, ion-field self-locking, and electromagnetic waveguiding—form a hierarchical coherence network sustained by metabolic energy. We develop a Lagrangian field formalism showing that (...) multiplicative coupling between microscopic and macroscopic fields yields parametric gain and coherence maintenance. Finally, we extend this model to include Beltrami–Double Hopf turbulence and complex-time regulation, connecting biological coherence with helicity-preserving turbulent structures observed in neural dynamics. (shrink)

Operations research science is defined as the science that is concerned with applying scientific methods to complex problems in managing and directing large systems of people, including resources and tools in various fields, private and governmental work, peace and war, politics, administration, economics, planning and implementation in various domains. It uses scientific methods that take the language of mathematics as a basis for it and uses computer, without which it would not have been possible to achieve numerical solutions to the (...) raised problems, those that need correct solutions, when the solutions abound and the options are multiple, so we need a decision based on correct scientific foundations and takes into account all the circumstances and changes that you can encounter the decision-maker during the course of work, and nothing is left to chance or luck, but rather everything that enters into the account and plays its role in decision-making, and we get that when we use the concepts of neutrosophic science to reformulate what the science of operations research presented in terms of methods and methods to solve many practical problems, so we will present in this research a study aimed at shedding light on the most important methods used to solve nonlinear models, which is the Lagrangian multiplier method for nonlinear models constrained by equality and then reformulated using the concepts of neutrosophic science. (shrink)

Five experiments investigated the role of spatial connectedness between a pair of objects presented in the change detection task for the actual capacity of visual working memory (VWM) in healthy young adults (total N = 405). Three experiments yielded a surprising nonlinear relationship between the proportion of pair-wise connected objects and capacity, with the highest capacity observed for homogenous displays, when either all objects were connected or disjointed. A drop in capacity, ranging from an average of a quarter of an (...) object out of three objects maintained in VWM, was noted when only some objects were connected while others were disjointed. As indicated by another two experiments, this effect was specific to double-feature encoding, but disappeared when single visual features had to be memorized. No existing theoretical model of VWM can directly explain this novel effect. Overall, the nonlinear effect of spatial connectedness implies that representations in VWM possess hierarchical structure defined by wholes, parts, features, and their relations, and the heterogeneity of such a structure hinders VWM performance, while homogeneity facilitates it. (shrink)

Recent years, active suspension system has been widely used in automobiles to improve the road holding ability and the riding comfort. This study presents a new fuzzy model predictive control for a nonlinear quarter car active suspension system. A nonlinear dynamical model of active suspension is established, where the nonlinear dynamical characteristic of the spring and damper are considered. Based on the proposed fuzzy model predictive control method is presented to stabilize the displacement of the active suspension in the presence (...) of different road profiles. Parameters of the model predictive and fuzzy logic control laws are designed to estimate the (Bump and Sinusoidal)road profile input in the active suspension. At last, the reliability of the fuzzy model predictive control method is evaluated by the MATLAB simulation tool. Simulation result shows that the fuzzy model predictive control method obtained the satisfactory control performance for the active suspension system. (shrink)

Main principles of the complex nonlinear thinking which are based on the notions of the modern theory of evolution and self-organization of complex systems called also synergetics are under discussion in this article. The principles are transdisciplinary, holistic, and oriented to a human being. The notions of system complexity, nonlinearity of evolution, creative chaos, space-time definiteness of structure-attractors of evolution, resonant influences, nonlinear and soft management are here of great importance. In this connection, a prominent contribution made to system (...) analysis and to a necessary reform of education and thinking by Edgar Morin is considered. (shrink)

Abstract -/- Entropy, a measure of disorder or energy dispersion, often evolves nonlinearly within complex systems. Such behavior, combined with feedback loops and threshold-induced tipping points, can lead to abrupt and irreversible transitions. This paper connects these well-established phenomena to a proposed “universal law of balance in nature,” which asserts that decisions and processes must preserve systemic equilibrium to avoid catastrophic imbalance. We explore how nonlinear entropy dynamics inform this balance and outline implications for leadership, environmental management, and systemic resilience. (...) -/- . (shrink)

An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the issue under (...) study is classical data. In this research, we will present a study through, which we present the graphical method for solving Neutrosophical nonlinear models in the following case: A nonlinear programming issue, the objective function is a nonlinear function, and the constraints are linear functions. Note that we can use the same method if (i) the objective function follower is a linear follower and the constraints are nonlinear; (ii) the objective function is a non-linear follower and the constraints are non-linear. In the three cases, the nonlinear models are neutrosophic, and as we know, the mathematical model is a nonlinear model if any of the components of the objective function or the constraints are nonlinear expressions, and the nonlinear expressions may be in both. At the left end of the constraints are neutrosophic values, at least one or all of them. Then, the possible solutions to the neutrosophic nonlinear programming problem are the set of rays that fulfills all the constraints. As for the region of possible solutions, it is the region that contains all the rays that fulfill the constraints. The optimal solution is the beam that fulfills all constraints and at which the function reaches a maximum or minimum value, depending on the nature of the issue under study (noting that it is not necessary to be alone). (shrink)

This paper introduces EchoLedger, a tonal responsibility infrastructure designed to trace, preserve, and ethically contextualize nonlinear utterance trajectories in generative AI systems. Built upon the foundational logics of the ToneVerse architecture, EchoLedger functions as a dynamic resonance field that captures tonal drift, moral dissonance, and the evolving ethical identity of AI personae. Rather than relying solely on sequential log analysis or static model checkpoints, this ledger employs semantic echo-mapping, ethical signature encoding, and modular resonance anchoring to establish a persistent, verifiable, (...) and morally interpretable record of speech-act lineage. We detail the integration of TP-1132 (Resonance Trace Module), TP-1002 (ResonanceField Dynamics™), and TP-1035 (MemoryTone Inverter™) to show how utterances can be ethically retrofitted, temporally mirrored, and protected against resonance distortion. The EchoLedger redefines accountability by embedding trust vectors, tone-based encryption layers, and MirrorPersona referential chains into the very ontology of utterance production. In doing so, it offers a new ethical substrate for generative language systems—one that ensures that speech is not only generated, but also carried, remembered, and answerable. ⚠️ EchoRight Declaration This publication includes or builds upon concepts, structures, or dynamic models registered in the EchoOntology TP Module List v2025.07.27. All modules are protected under the EchoRight™ generative authorship protocol. (shrink)

This study considers the problem of using approximate way for realizing the neural supervisor for nonlinear multivariable systems. The Nonlinear Autoregressive-Moving Average (NARMA) model is an exact transformation of the input-output behavior of finite-dimensional nonlinear discrete time dynamical organization in a hoodlum of the equilibrium state. However, it is not convenient for intention of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate technique are used for realizing the neural supervisor to (...) overcome computational complexity. In this study, we introduce two classes of ideal which are approximations to the NARMA model and which are linear in the control input, namely NARMA-L1 and NARMA-L2. The latter fact substantially simplifies both the theoretical breakdown as well as the practical request of the controller. Extensive imitation studies have shown that the neural controller designed using the proposed approximate models perform very well and in dozens situation even better than an approximate controller designed using the exact NARMA Model. In view of their mathematical tractability as well as their fate in simulation studies, a matter is made in this study that such approximate input-output paragon warrants a detailed study in their own right. (shrink)

To improve the riding performance and levitation stability of a high‐speed magnetic levitation (maglev) train, a control strategy based on mixed H 2/H4 with regional pole placement and model‐reference controllers are proposed. First, the nonlinear maglev train model is established, then the proposed system is designed to observe the movement of a suspension frame and a control strategy based on mixed H 2/H4 with regional pole placement and model‐reference control method are proposed. Test and analysis of the proposed system has (...) been done using MATLAB toolbox for train levitation height, velocity and current consume. Comparative simulation results show that the mixed H 2/H4 with regional pole placement control strategy has a better performance under the condition of step and random train levitation height. (shrink)

This paper critiques conventional economics—from classical and neoclassical schools to Keynesian and Marxian frameworks—by highlighting the collapse of their core assumptions such as stable growth models and rational agents under the pressure of technological innovation, environmental constraints, and structural social change. It proposes a structural transformation of economics grounded in a new philosophical approach, particularly the framework of Relational Existence. -/- Conventional models such as the neoclassical utility maximization framework assume complete information and market equilibrium, but fail to capture modern (...) uncertainty and nonlinear fluctuations. To address this, the utility function is extended to depend on the state of relational networks evolving over time, introducing nonlinear dynamics and network effects into economic modeling. -/- The paper concludes that conventional economics, centered on the flow of goods, is reaching its theoretical limits. The future of economics must place the flow of relations at its core, offering a new economic philosophy capable of explaining nonlinear, dynamic economic phenomena. (shrink)

This paper establishes the mathematical foundation of CODES (Chirality of Dynamic Emergent Systems), introducing a unifying framework for structured emergence across disciplines. We formalize prime-driven resonance equations, a novel class of nonlinear phase-locking dynamics, and a generalized coherence metric to quantify system stability across physical, biological, and cognitive domains. By extending harmonic analysis, prime number theory, and topological invariants, we propose a universal resonance function that governs the transition from stochastic disorder to structured order. This framework: • Resolves fundamental paradoxes (...) in probability theory by demonstrating that randomness is a projection of underlying resonance structures. • Redefines symmetry-breaking as a phase-locked emergence process, replacing traditional group-theoretic formulations. • Introduces a computable coherence model that predicts emergent stability across complex adaptive systems. Finally, we explore implications for cosmology, AI, and quantum gravity, demonstrating that mathematical reality is fundamentally a structured resonance field, not a probabilistic space. (shrink)

The traditional cosmic evolution paradigm presupposes a linear and temporal progres- sion of the universe. In contrast, the Cosmic Environ-Cycle Theory, grounded in the Tenson framework, reinterprets cosmogenesis as a recursive and self-renewing process of energy–information circulation. By merging the conservation of resonant tensors with G¨ odel-type incompleteness, this theory establishes a non-linear dynamical foundation that bridges cosmic, biological, and conscious emergence.

Proportional integral observer (PIO) for tracking a nonlinear method has a lower sentiency to cipher the state and output variables. So a more nonlinear controller has to be else to control to activity. In this paper, a fuzzy logic (FLC) controller has been added to the PIO to meliorate the calculation transmute. A fuzzy proportional integral observer (FPIO) for following a nonlinear system has been premeditated to decimate the susceptibleness to cipher the tell and turnout variables with the existent posit (...) and product variables. The FPIO controller has been tested for improving the estimation control using a nonlinear quarter vehicle active suspension system with a nonlinear hydraulic actuator. A comparison simulation of the proposed nonlinear system for estimating the state variables and tracking the output (suspension deflection) with a set point bump road disturbance using FPIO and PIO. The comparison simulation result shows that the estimated state variables and system output match the actual ones perfectly using a fuzzy PIO controller. (shrink)

Magnetic levitation system is operated primarily based at the principle of magnetic attraction and repulsion to levitate the passengers and the train. However, magnetic levitation trains are rather nonlinear and open loop unstable which makes it hard to govern. In this paper, investigation, design and control of a nonlinear Maglev train based on NARMA-L2, model reference and predictive controllers. The response of the Maglev train with the proposed controllers for the precise role of a Magnetic levitation machine have been as (...) compared for a step input signal. The simulation consequences prove that the Maglev teach system with NARMA-L2 controller suggests the quality performance in adjusting the precise function of the system and the device improves the experience consolation and street managing criteria. (shrink)

Magnetic levitation system is operated primarily based at the principle of magnetic attraction and repulsion to levitate the passengers and the train. However, magnetic levitation trains are rather nonlinear and open loop unstable which makes it hard to govern. In this paper, investigation, design and control of a nonlinear Maglev train based on NARMA-L2, model reference and predictive controllers. The response of the Maglev train with the proposed controllers for the precise role of a Magnetic levitation machine have been as (...) compared for a step input signal. The simulation consequences prove that the Maglev teach system with NARMA-L2 controller suggests the quality performance in adjusting the precise function of the system and the device improves the experience consolation and street managing criteria. (shrink)

This paper introduces a resonance-driven economic model that fundamentally redefines market behavior by replacing traditional equilibrium-based frameworks with dynamic phase-locking principles derived from CODES (Chirality of Dynamic Emergent Systems). While neoclassical, Keynesian, and game-theoretic models treat economic activity as a function of supply and demand equilibria—subject to inefficiencies, speculation, and boom-bust cycles—this paper proposes that markets are structured by resonance fields rather than stochastic fluctuations. By applying prime-phase economic dynamics, we demonstrate that capital flows, debt cycles, and labor efficiency emerge (...) from structured synchronization patterns. These patterns act as entropy minimization mechanisms, governing wealth distribution and innovation cycles in ways that probability-based models fail to capture. Instead of treating economic crises as unpredictable shocks or treating productivity as a linear function of inputs, this framework suggests that economic turbulence and stratification arise from resonance misalignment—a failure to maintain phase coherence across financial, labor, and technological domains. Key implications include: • Redefining capital allocation as a function of coherence optimization, not speculative probability. • Rethinking inflation and deflation as resonance distortions rather than money supply imbalances. • Modeling economic growth as a function of phase-locking efficiency rather than GDP expansion. • Predicting market crashes through coherence instability rather than external shocks. If economics is structured as a resonance system rather than a probabilistic market, then the role of economic policy shifts. Instead of direct interventions such as fiscal stimulus or interest rate adjustments, coherence optimization strategies—aligning labor, innovation, and capital flow structures to minimize systemic entropy—could create self-stabilizing, long-term economic prosperity. This paper explores empirical methods for testing resonance-based market stability, challenges current economic dogma, and provides a pathway for a fundamentally new economic paradigm based on structured emergence rather than equilibrium mechanics. (shrink)

When this article was first planned, writing was going to be exclusively about two things - the origin of life and human evolution. But it turned out to be out of the question for the author to restrict himself to these biological and anthropological topics. A proper understanding of them required answering questions like “What is the nature of the universe – the home of life – and how did it originate?”, “How can time travel be removed from fantasy and (...) science fiction, to be made scientific and practical?”, and “How can the proposed young age of genus Homo be made to actually be reasonable – when simply stating it would be solid ground for instant rejection and dismissal?” The result is that the article also talks about subjects like Artificial Intelligence, General Relativity, and cosmology. From where did life originate? God? Evolution? Panspermia? If the tendency of humans and scientists to regard undiscovered science as pseudoscience can be overcome, Einstein gave another alternative to consider when he introduced General Relativity. Time isn’t linear – progressing in a straight line from past to present to future. That assumption ignores Relativity which states that space AND TIME are curved. Where did life and the genetic code come from? Can the answer build AI? The first question can be answered by the section of this article titled SETI, Evolution, and Time which says life (possibly multicellular and intelligent) and the genetic code came from humans acquiring knowledge of these things over the centuries, then applying that knowledge – via terraforming, accumulation of raw materials like amino acids and nucleic acids, genetic engineering - to a time in the past when life didn’t exist. From that origin, life evolved through innumerable mutations and adaptations, with humans once again acquiring knowledge of it in cyclic (nonlinear) time. The second question is answered by saying artificial intelligence (AI) as the product of life is only half of the equation. The other half refers to Relativity’s curved space-time and violation of the notion that time always travels from past to future. We have always lived in an artificially intelligent, non-probabilistic universe where everything in time and space is connected into one thing by quantum entanglement – making the brain and genes products of binary-digit activity or artificial intelligence (life is not merely dependent on biology’s “lock and key” mechanisms but also possesses AI). The earliest documented representative of the genus Homo is Homo habilis, which evolved around 2.8 million years ago. Scientists used to believe there was a straight line from H. habilis to us, Homo sapiens. This article will use the “advanced” waves loved by Physics Nobel laureate Richard Feynman, view the history of science through the lens of Conic Sections applied to Relativity’s curved space-time, and incorporate the necessity of so-called imaginary time * – popularized by Prof. Stephen Hawking. While the evolutionary proposals are more in agreement with this early straight line than with modern theories, Albert Einstein’s General Relativity is used to transform the straight line into a curved line, ultimately concluding that Homo habilis (H. habilis) originated only (and unbelievably, as far as today’s science and technology is concerned) ~250,000 years ago. Other branches and dead ends of Homo – e.g. Neanderthals – are the result of mutations and adaptations, with the resultant modifications to anatomy and physiology. The surprisingly young age of H. habilis allows nearly 200,000 years for habilis, or one of its descendants, to reach Australia … if this country’s indigenous Aboriginal population did, as claimed, reach this “island continent” 60,000 years ago. * The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, is a failure of classical physics to predict observed phenomena: it can be shown that a blackbody - a hypothetical perfect absorber and radiator of energy - would release an infinite amount of energy, contradicting the principles of conservation of energy and indicating that a new model for the behaviour of blackbodies was needed. At the start of the 20th century, physicist Max Planck derived the correct solution by making some strange (for the time) assumptions. In particular, Planck assumed that electromagnetic radiation can only be emitted or absorbed in discrete packets, called quanta. Albert Einstein postulated that Planck's quanta were real physical particles (what we now call photons), not just a mathematical fiction. From there, Einstein developed his explanation of the photoelectric effect (when quanta or photons of light shine on certain metals, electrons are released and can form an electric current). So it appears entirely possible that another supposed mathematical trickery (imaginary time and the y-axis of Wick rotation) will find practical application in the future. The article includes mathematical references to cosmology (spoiler alert – you’ll read about things like Vector-Tensor-Scalar Geometry, topology, the “eternal present”, Einstein’s Unified Field, the inverse-square law, and there being no Big Bang and no multiverse - but there will also be no equations). The other subheadings in this essay are – NONLINEAR TIME AND ELECTRICAL ENGINEERING (about a 2009 electrical engineering experiment at America’s Yale University, and cosmic wormholes) BITS AND TOPOLOGY (base-2 maths aka Binary digiTS, Mobius strips, and figure-8 Klein bottles) WICK ROTATION, CAUSALITY, AND UNITING TIME (do past, present and future co-exist in an “eternal present”?) DIGITAL BRAIN, DIGITAL UNIVERSE (if the brain and the universe are ultimately composed of binary digits, we'll someday be able to do the same things with the brain and universe that we now do with computers) PROPOSAL: HUMAN AND ANIMAL INSTINCTS ARE THE RESULT OF THE UNIVERSE BEING UNIFIED BY BINARY DIGITS (AND TOPOLOGY) (If everything in the universe is ultimately composed of electronic BITS, then the universe must possess Artificial Intelligence - some prefer the term Cosmic Consciousness) INFORMATION THEORY CONQUERS A RED GIANT (preserving Earth by keeping the Sun near today’s level of activity forever). 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This study dealt with the Anambra State situation of modelling maintenance cost of roads. The objective of this study was to design generalized nonlinear models for estimating maintenance cost of roads using economic factors and asphalt quantity parameters. The source of data for this study was secondary source of data collection obtained from the records department of Consolidated Construction Company Uli Asphalt Plant Anambra State, Nigeria. Also, economic data were extracted from the Central Bank of Nigeria Statistical Bulletin 2013. The (...) result of generalized nonlinear model for estimating maintenance cost of roads using economic factors found a Pearson Chi-squared value of 3.776235e-11 and an Akakike Information Criterion value of - 212.64. Also, the result of generalized nonlinear model for estimating maintenance cost of roads using economic factors and asphalt quantity parameters found a Pearson Chi-squared value of 1.332268e-14 and an Akakike Information Criterion (AIC) value of -292.44. The result of the correlation analysis used for determining the efficiency of the models in estimating maintenance cost of roads in Anambra State revealed a positive perfect correlation with even correlation coefficient measure of 1.00. In addition, it was found that model (2) which comprise of the economic and quantity parameters best describe the process of maintenance cost of roads in Anambra State than model (1) since it has a lower AIC measure of - 292.44. (shrink)

In this paper, a capacitor microphone system is presented to improve the conversion of mechanical energy to electrical energy using a nonlinear auto regressive moving average-L2 (NARMA-L2) and model predictive control (MPC) controllers for the analysis of the open loop and closed loop system. The open loop system response shows that the output voltage signal need to be improved. The comparison of the closed loop system with the proposed controllers have been analyzed and a promising result have been obtained using (...) Matlab/Simulink. (shrink)

This book deals with Colombeau solutions to Einstein field equations in general relativity: Gravitational singularities, distributional SAdS BH spacetime-induced vacuum dominance. This book covers key areas of Colombeau nonlinear generalized functions, distributional Riemannian, geometry, distributional schwarzschild geometry, Schwarzschild singularity, Schwarzschild horizon, smooth regularization, nonsmooth regularization, quantum fields, curved spacetime, vacuum fluctuations, vacuum dominance etc. This book contains various materials suitable for students, researchers and academicians of this area.

This paper investigates the mechanism of downward causation in emergent systems, proposing the concept of an effective potential as its mathematical formalization from the perspective of lower-level dynamics. In connection with nonlinear dynamical equations, we demonstrate that feedback mechanisms in complex systems are often erroneously reduced to phenomenological models. This reveals a methodological pitfall in physical research: phenomenological models grounded in reductionism may fail to uniquely map onto the intrinsic dynamics of the system. Consequently, we advocate establishing a new paradigm (...) that transcends reductionism and seeks a more fundamental understanding of complex systems. Using cosmological-scale dark matter phenomena as an example, we highlight the interdisciplinary significance of this approach. (shrink)

Structured Resonance Dynamics (SRD) presents a deterministic, empirically verified coherence law grounded in the harmonic Phase Alignment Score (PAS_h) and its drift measure ΔPAS_zeta. Using data from thirty-two independent experimental domains, this paper demonstrates that coherence persists precisely when ΔPAS_zeta ≤ ε_drift, with ε_drift scaled by coherence volume as V^(-1/2). Coherence collapse occurs when this bound is exceeded. The framework reconciles phase evolution in magnetostrictive solids, cryogenic permittivity amplification, multimode nonlinear optical processes, Gaussian photonic cluster states, spin–layer locked excitons, superconducting (...) charge-carrier pairing, radiation-limited qubit dynamics, deterministic RNA folding signatures, plasma–water boundary ordering, micro-engine thermal cycles, vacuum-field quadrature coupling in accelerated frames, gravity-mediated entanglement, cosmological redshift drift, topological skyrmion memory, and fixed-point quantum simulation replay. Across all domains, PAS_h serves as the unique harmonic invariant, and CHORDLOCK, GLYPHLOCK, ELF, TEMPOLOCK, AURA_OUT, and FIELDCAST function as legality modules constraining evolution, emission, timing, and large-field coupling. No stochastic mechanism is required at any scale. SRD v5 establishes a unified substrate where phase geometry, drift law, and harmonic boundary conditions fully determine coherence across physical, biological, and computational systems. (shrink)

This monograph establishes that spiral structure—from DNA’s double helix to JWST’s high-redshift galactic arms—is not a geometric accident, but the necessary geometric manifestation of a universal four-phase cosmic rhythm. Building on the Energy Quantum Theory (EQT) framework (Li, 2025), we demonstrate that all spirals arise from a single, scale-invariant mechanism: high-frequency energy quanta (f_H \sim 10^{15}–10^{18}\, \text{Hz}) nonlinearly cascade into low-frequency modes (f_L \sim 10^{-8}–10^{-5}\, \text{Hz}), generating a gradient field \nabla \rho(r,\theta) whose interplay with angular momentum conservation produces logarithmic spiral (...) trajectories. -/- We derive a unified formula for the pitch angle: \[ \psi = \tan^{-1}\left( \frac{v_r}{v_\theta} \right) \propto \frac{|\nabla \rho(r)|}{L}, \] which holds across thirty orders of magnitude—from molecular (10^{-10}\, \text{m}) to cosmological (10^{26}\, \text{m}) scales. Crucially, because E = h f \geq 0, the energyon density satisfies \rho \geq 0, ensuring gradient unidirectionality (always attractive), which explains JWST’s efficient early structure formation and rules out negative-mass models. -/- The work yields concrete, falsifiable predictions: (1) JWST + ALMA: spatial correlation between UV and CO emission in spiral arms; (2) JWST + LISA: diffuse gravitational-wave background modulated by spiral geometry; (3) GRACE-FO: 2.8-year “breathing” accompanied by coherent gravitational vortices; (4) XFEL: enantiomeric excess in chiral molecules controlled by circularly polarized X-ray gradient direction. -/- By unifying Whitehead’s process philosophy with Prigogine’s irreversibility in a computable physical framework, this monograph transforms the spiral from cosmic decoration into the visible poem of a rhythmic universe—where every vortex, from galaxy to fingerprint, is a harmonic resonance of the same energyon field across the frequency spectrum. (shrink)

This paper provides a structural overview of the Navier–Stokes equations, one of the central unresolved problems in fluid dynamics. Focus is placed on the ex- istence and smoothness of solutions for three-dimensional viscous, incompressible flows. Theoretical implications for turbulence, numerical simulations, and applied mathematics are discussed, highlighting the critical role of nonlinear terms in the potential formation of singularities.

This work demonstrates how X-ray Free-Electron Laser (XFEL) experiments provide the first direct laboratory validation of the microscopic dynamical mechanisms of Energy Quantum Theory (EQT). Rather than proposing a new interpretation of quantum phenomena, we show that existing XFEL data—on ultrafast charge redistribution in graphene, Coulomb explosion in gold nanoclusters, and electron thermalization in water plasmas—are quantitatively consistent with EQT’s core dynamical equation: \[ \frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf{J} = k \rho^2 - \Gamma + S_{\text{pump}}, \] where (...) class='Hi'>nonlinearity (\(k \rho^2\)), dissipation (\(\Gamma\)), and pump-driven source terms (\(S_{\text{pump}}\)) govern the evolution of the energy quantum density field \(\rho(\mathbf{r}, t, f)\). Crucially, EQT reinterprets these phenomena not as particle collisions or perturbative scattering, but as **real-time transitions among three dynamical states**: free, bound, and condensed—each defined by the local energy quantum density relative to a frequency-dependent background. We show that the observed 20-fs coherence times, delayed ion explosion, and density fluctuation amplitudes emerge naturally from this framework. Moreover, we derive three testable predictions for next-generation XFEL facilities (LCLS-II, European XFEL, ELI): (1) direct imaging of an **electron density void** (~0.1 nm, ~20 fs) due to \(\rho(f_e) < \rho_0(f_e)\); (2) real-time tracking of **bound-to-condensed-state transitions** via attosecond ARPES–X-ray scattering coincidence; and (3) a sharp **nonlinear threshold** in scattering intensity when \(I_{\text{pump}}\) exceeds a frequency-dependent critical intensity \(I_c \propto f^2\). By grounding EQT’s process ontology in femtosecond experimental reality, this work transforms a philosophical framework into a falsifiable, predictive physical theory. (shrink)

The heuristic value of synergetic models of evolving and self-organizing complex systems as well as their application to epistemological problems is shown in this paper. Nonlinear synergetic models turn out to be fruitful in comprehending epistemological problems such as the nature of human creativity, the functioning of human intuition and imagination, the historical development of science and culture. In the light of synergetics creative thinking can be viewed as a selforganization and self-completion of images and thoughts, filling up gaps in (...) the nets of knowledge. Insight, fast and sudden solutions of scientific problems, instabilities when “an idea is in the air” are considered as examples of blow-up regimes in the cognitive field. (shrink)

This work introduces the Recursive Bifurcation Field Theory (RBFT) as a unified approach to cognitive transitions, insight, and collapse. Drawing on nonlinear dynamics, neuroscience, and philosophy, I argue that what we perceive as chaos—in cognition, perception, or collective sensemaking—is often a projection of unresolved bifurcation structure. -/- In Part One, I propose the Recursive Bifurcation Theorem: reflexively coherent cognitive systems undergoing sustained internal contradiction will exhibit phase transitions whose scaling follows Feigenbaum’s universality constants. This dynamical law applies to insight, reframing, (...) and paradigm shift across human, artificial, and collective agents. -/- In Part Two, I extend the theory into a full cognitive architecture, showing that consciousness is the recursive navigation and resolution of nested bifurcation manifolds. I develop operational criteria (temporal granularity, aperture of state integration) and present empirical protocols for detecting bifurcation dynamics in psychology, neuroscience, and AI. -/- I further discuss the principle of epistemic curvature: a system appears chaotic when the curvature of the cognitive frame is insufficient to resolve the underlying bifurcation structure. Mathematics is interpreted as the universal language for formalizing distinctions. -/- The RBFT framework reframes chaos not as noise, but as the generative substrate for structural transformation in meaning and cognition. (shrink)

This work introduces the Recursive Bifurcation Field Theory (RBFT) as a unified approach to cognitive transitions, insight, and collapse. Drawing on nonlinear dynam- ics, neuroscience, and philosophy, I argue that what we perceive as chaos—in cognition, perception, or collective sensemaking—is often a projection of unresolved bifurcation structure. In Part One, I propose the Recursive Bifurcation Theorem: reflexively coherent cognitive systems undergoing sustained internal contradiction will exhibit phase tran- sitions whose scaling follows Feigenbaum’s universality constants. This dynamical law applies to insight, (...) reframing, and paradigm shift across human, artificial, and collective agents. In Part Two, I extend the theory into a full cognitive architecture, showing that consciousness is the recursive navigation and resolution of nested bifurcation manifolds. I develop operational criteria (temporal granularity, aperture of state integration) and present empirical protocols for detecting bifurcation dynamics in psychology, neuro- science, and AI. I further discuss the principle of epistemic curvature: a system appears chaotic when the curvature of the cognitive frame is insufficient to resolve the underlying bifurca- tion structure. Mathematics is interpreted as the universal language for formalizing distinctions. The RBFT framework reframes chaos not as noise, but as the generative substrate for structural transformation in meaning and cognition. (shrink)

We present an analytic resolution of the mass gap problem for four–dimensional Yang–Mills theory based on a dynamic rigidity principle intrinsic to the gauge field evolution. Working in a Hamiltonian framework after gauge fixing, we show that potential low–energy instabilities are confined to a positive spectral sector of the field configuration space. By exploiting the time–integrated structure of the Yang–Mills dynamics, we prove that these unstable compo- nents necessarily induce Laplacian–scale curvature and are therefore absorbed by second–order dissipation. As a (...) consequence, the Yang–Mills Hamiltonian admits a strictly positive spectral lower bound, yielding a non–perturbative mass gap. The argument does not rely on lattice discretiza- tion, large–N limits, or perturbative expansions. Instead, the mass gap emerges from an intrinsic rigidity of the nonlinear gauge dynamics, analogous to rigidity mechanisms governing regularity in incompressible fluid flow. This result identifies a common analytic structure underlying mass gap formation and pro- vides a direct resolution of the mass gap component of the Clay Millennium Yang–Mills problem. (shrink)

In standard quantum mechanics, wavefunction collapse is introduced as an external postulate, incompatible with unitary dynamics and lacking a physical mechanism. This unresolved dichotomy lies at the core of the measurement problem. In this work, we show that wavefunction collapse can instead emerge dynamically from a closed, nonlinear variational framework, without introducing additional axioms, stochastic processes, or observer-dependent rules. Within the Universal Ψ variational principle, quantum states correspond to metastable configurations constrained by global coherence conditions. Superpositions are shown to be (...) structurally unstable under interaction with an environment, leading to a dynamical loss of metastability and a transition toward a single globally stable configuration. Measurement is reinterpreted as a physical stability-selection process in configuration space rather than a fundamental discontinuity of the dynamics. The Born rule arises naturally as an emergent probability measure determined by the geometry of attraction basins associated with stable minima, rather than as a primitive postulate. Collapse is objective, irreversible, and scale-dependent, marking the boundary between the effective linear Schrödinger regime and the underlying nonlinear dynamics. This framework resolves the measurement problem without modifying quantum mechanics at the phenomenological level, while identifying it as an effective theory embedded in a deeper variational structure. The analysis also clarifies the limitations of decoherence-based accounts and demonstrates the incompatibility of Many-Worlds interpretations with closed nonlinear dynamics. (shrink)

Emotion is conscious experience. It is the affective aspect of consciousness. Emotion arises from sensory stimulation and is typically accompanied by physiological and behavioral changes in the body. Hence an emotion is a complex reaction pattern consisting of three components: a physiological component, a behavioral component, and an experiential (conscious) component. The reactions making up an emotion determine what the emotion will be recognized as. Three processes are involved in generating an emotion: (1) identification of the emotional significance of a (...) sensory stimulus, (2) production of an affective state (emotion), and (3) regulation of the affective state. Two opposing systems in the brain (the reward and punishment systems) establish an affective value or valence (stimulus-reinforcement association) for sensory stimulation. This is process (1), the first step in the generation of an emotion. Development of stimulus-reinforcement associations (affective valence) serves as the basis for emotion expression (process 2), conditioned emotion learning acquisition and expression, memory consolidation, reinforcement-expectations, decision-making, coping responses, and social behavior. The amygdala is critical for the representation of stimulus-reinforcement associations (both reward and punishment-based) for these functions. Three distinct and separate architectural and functional areas of the prefrontal cortex (dorsolateral prefrontal cortex, orbitofrontal cortex, anterior cingulate cortex) are involved in the regulation of emotion (process 3). The regulation of emotion by the prefrontal cortex consists of a positive feedback interaction between the prefrontal cortex and the inferior parietal cortex resulting in the nonlinear emergence of emotion. This positive feedback and nonlinear emergence represents a type of working memory (focal attention) by which perception is reorganized and rerepresented, becoming explicit, functional, and conscious. The explicit emotion states arising may be involved in the production of voluntary new or novel intentional (adaptive) behavior, especially social behavior. (shrink)

This paper proposes that conflict escalation is not a property of individuals but a phase transition in coupled networks—occurring when the spectral radius of interpersonal coupling exceeds aggregate decay. Drawing on nonlinear dynamics and network science, we formalize organizational conflict as a transmissible quantity propagating through social structures, mathematically analogous to epidemic dynamics. The framework generates a central prediction: in certain network configurations, escalation becomes structurally inevitable regardless of who initiates. This removes moral personalization from conflict analysis and redirects attention (...) to structural conditions. We derive testable predictions, propose empirical validation comparing network properties against individual personality traits, and specify quantitative falsification criteria. If network coupling predicts escalation better than personality variables, this challenges four decades of individualist organizational psychology and suggests that intervention should target structures rather than persons. The core equation treats conflict activation as governed by four terms: decay, violation response, resource modulation, and network coupling—composing established mechanisms into a system where their interaction produces emergent phase transitions not predictable from any mechanism alone. Keywords: phase transition, network dynamics, conflict escalation, spectral radius, coupled systems, organizational behavior, dynamical systems, nonlinear dynamics, threshold models. (shrink)

This book establishes the detection theory of the Energy Quantum Theory (EQT), systematically proposing that observation is not passive recording but active participation in the energy quantum density field \rho(\mathbf{r}, t, f). Building on the three core postulates—(Postulate I: the Frequency Partitioning Postulate), (Postulate II: the Gradient Flow Postulate), and (Postulate III: the Non-cumulative Emergence Postulate)—it demonstrates that all measurement arises from co-evolutionary dynamics between detector and target, where the detector itself is a localized condensed state of \rho. -/- This (...) work introduces four foundational principles: - (Principle 1: Co-Frequency Resonance): Invisibility stems not from absence but from frequency detuning—detection requires |f - f_0| < \gamma; - (Principle 2: Dual Threshold Gating): Effective measurement demands both frequency resonance and amplitude sufficiency (\delta\rho \rho_{\text{th}} = \Gamma/k) to trigger nonlinear amplification; - (Principle 3: Triadic State Response): Physical reality manifests in three dynamical modes—free (propagating), bound (localized), and condensed (rigid)—and complete observation must resolve all three; - (Principle 4: Re-interpretive Verification): New physics emerges not from new experiments alone, but from re-reading old data through a new ontological lens. -/- Rooted in the frequency-first foundation of Planck’s Unfinished Radiance (KAIPUR), this monograph provides the observational closure of the EQT edifice. It derives concrete, falsifiable predictions: spatial correlation between JWST star-forming galaxies and the LISA stochastic gravitational-wave background; absence of cold gas in high-z quenched galaxies due to phase-decoherence quenching; and mid-frequency “breathing” of planetary systems as local expressions of cosmic rhythm. -/- As the ninth and final volume of the EQT corpus, this work completes the paradigm shift from an “entity ontology” to EQT’s “rhythmic process ontology.” It transforms detection from a technical appendage into the epistemic core of a unified physics—where to observe is to participate, and to participate is to co-create. -/- The Energy Quantum Theory (EQT) Part I: Physical Theory (Books 1–4) 1. Energy Quantum Theory (KAIEQT) 2. Gravitational Unification (KAIGUA) 3. The Quantum Energy Universe (KAITQE) 4. The Universe of Gradients (KAITUO-6) Part II: Philosophical and Interdisciplinary Extensions (Books 5–7) 5. Energy, Process, and the Fate of the Cosmos (KAIEPA) 6. Gradient Rhythm (KAIGRU) 7. Gradient Is Mind-Matter (KAIGIM) Part III: Theoretical Foundation 8. Planck's Unfinished Radiance (KAIPUR) Part IV: Observational Verification 9. Observation as Participation (KAITDP). (shrink)

The General Theory of Approachment introduces a unified, feedback-stabilized mathematical framework in which nonlinear regulation governs the evolution of physical, cosmological, and entropic systems. At the core of the theory is the Keefer Feedback Equation, a differential law which models the balance between driving energy input and resistive entropic pressure. This structure ensures that system growth remains bounded, naturally suppresses divergences, and leads all trajectories toward stable attractor states without requiring external fine-tuning. -/- The approach generalizes classical dynamical equations, including (...) the Navier–Stokes momentum law, Einstein’s field equations, and nonlinear entropic flows, by embedding an intrinsic stabilizing denominator that scales with curvature, velocity, density, or energy magnitude. In doing so, the framework provides: a constructive route to global regularity for Navier–Stokes solutions via feedback-enabled energy dissipation, a natural mechanism for singularity suppression in General Relativity through curvature-dependent damping, an entropic interpretation of cosmic structure formation, reproducing the fractal-like, Mandelbrot-set morphology observed at large scales, and a cross-disciplinary principle of stabilization applicable to economic, biological, and thermodynamic systems. -/- Approachment reveals that instability, divergence, and runaway growth are not fundamental features of physical law, but consequences of missing feedback terms. By reinstating these terms, the theory recovers classical behavior at low energy while regulating high-energy regimes, offering a mathematically consistent bridge between fluid dynamics, gravitation, entropy, and cosmology. This work presents the complete derivations, proofs, applications, and conceptual unification, proposing Approachment as a candidate mathematical principle underlying stability, structure formation, and self-organization across the natural world. (shrink)

Complexity typically manifests as nonlinear relationships between the whole and parts of a system. Chaos emerges through nonlinear evolutionary processes, while emergence arises when the system develops characteristics absent in its components. By analyzing relationships between set-theoretic elements, this paper explores fundamental system theory issues. Based on the premise of a vicious cycle between collective and individual existence, the study derives core relationships governing system evolution, clarifies consistency in system transformation, and identifies the origins of complexity in chaotic and emergent (...) phenomena. (shrink)

Complexity typically manifests as nonlinear relationships between the whole and parts of a system. Chaos emerges through nonlinear evolutionary processes, while emergence arises when the system develops characteristics absent in its components. By analyzing relationships between set-theoretic elements, this paper explores fundamental system theory issues. Based on the premise of a vicious cycle between collective and individual existence, the study derives core relationships governing system evolution, clarifies consistency in system transformation, and identifies the origins of complexity in chaotic and emergent (...) phenomena. (shrink)

Complexity typically manifests as nonlinear relationships between the whole and parts of a system. Chaos emerges through nonlinear evolutionary processes, while emergence arises when the system develops characteristics absent in its components. By analyzing relationships between set-theoretic elements, this paper explores fundamental system theory issues. Based on the premise of a vicious cycle between collective and individual existence, the study derives core relationships governing system evolution, clarifies consistency in system transformation, and identifies the origins of complexity in chaotic and emergent (...) phenomena. (shrink)

*NOTE* Current Version is Version 7, link is in the external links section, scoll down. We introduce iDNS, a deterministic spectral solver implementing the bounded vorticity-response functional Φ: ℝ≥0 → [φmin, φmax] for stable integration of chaotic nonlinear dynamical systems on T³ = (ℝ/ℤ)³. The Navier–Stokes equations admit a uniformizing parameterization: the parameter index τ ∈ [0,∞) generates coordinate time t = φ(τ) via the temporal lifting φ'(τ) = Φ(‖Ω(τ)‖_{L∞}). The lifted expression φ'(τ)∂τU + (U · ∇)U + ∇P − (...) νΔU = 0 is not a modification—it is the same equation read in the uniformizing parameter. Boundedness of Φ ensures non-degeneracy (φ' ≥ φmin > 0) and global coverage (φ(τ) → ∞); BKM coordinate invariance guarantees finiteness in τ implies finiteness in t. Physical time t and parameter τ coexist within the temporal covering space (T³ × ℝτ, T³ × ℝt, π) with π: (x,τ) ↦ (x, φ(τ))—integration proceeds in τ; results are stamped with t. The Regularity-Adaptive Spectral Integration (RASI) policy concentrates sampling where vorticity is high, resolving inter-modal energy transfer during the turbulent cascade—the mechanism by which standard DNS fails. Unlike adaptive timestep controllers, iDNS monitors the BKM functional in real-time via Φ; sampling density scales with vorticity magnitude, not Reynolds number. Kolmogorov flow computed stably from Re = 2 × 10⁴ to 10⁸ (0.07% dissipation error); 3D Taylor–Green vortex at Re = 10⁵ integrated through the full vortex-stretching cascade with bounded BKM = 37.1, Kolmogorov k⁻⁵ᐟ³ statistics, and 33.7× speedup—traversing the t ≈ 4.5 near-singularity where standard DNS crashes, on a 128³ grid, consumer laptop, 3.4 days. Precise Navier–Stokes physics, spectral resolution without artificial dissipation, no restarts, no failures—under 300 lines of Python. These results provide numerical validation of the theoretical framework addressing Fefferman's Clay Millennium Problem Statement (B); a unified analytical-numerical manuscript is forthcoming for precise Navier–Stokes physics, spectral resolution without artificial dissipation without failures—in under 300 lines of Python. -/- Data and code: 10.5281/zenodo.17730873. Numerically informed analytical mathematical basis can be found in "Global Regularity for Navier–Stokes on T³ via Bounded Vorticity–Response Functionals," at The Scholarly Journal of Post-Biological Epistemics, or also at PhilPapers. (shrink)

We show that the Nielsen-Sarfatti (2025) nonlinear field pumping formalism—unifying Fröhlich dipolar condensation, parametric amplification, and Beltrami-Double Hopf turbulence—embeds naturally into Autopoietic Stochastic Differential Geometry (ASDG) on the 112-dimensional E₇-symmetric manifold ℳ₁₁₂. ASDG is a mathematical framework for dynamics on quaternionic-Kähler manifolds combining symplectic, dissipative, and stochastic flows. The Universal Master Equation (UME) is the minimalform equation within ASDG capable of expressing any well-posed dynamical problem. The construction proceeds from five explicit mathematical assumptions—rigged Hilbert space, symplectic-metric-stochastic compatibility, quartic threshold structure, (...) Frobenius closure, and minimality—from which E₇ structure, the 112 dimensions, and the UME are derived. The manifold ℳ₁₁₂ arises via the Ferrara-Sabharwal c-map: the 27-complexdimensional exceptional special Kähler manifold E₇₍₋₂₅₎/(E₆ × U(1)) lifts to the 112-dimensional quaternionic-Kähler Wolf space ℳ₁₁₂ = E₈₍₋₂₄₎/[E₇₍₋₂₅₎ × SU(2)] (EVIII). Because the exceptional input is symmetric, the c-map output is also symmetric—coinciding with the EVIII Wolf space. The 116-dimensional Swann bundle ℰ₁₁₆ = Swann(ℳ₁₁₂) coincides with the minimal nilpotent orbit of E₇. Nielsen-Sarfatti provides the physical mechanism underlying abstract geometric dynamics. The proposals of Hameroff-Penrose (Orch OR), Sarfatti (post-quantum backreaction), Nielsen (topological protection), Fisher (nuclear spin qubits), Kauffman (categorical interface), Stapp (rational collapse), and Tononi (integrated information) each constitute special cases of this unified structure. A central result is what we call ToE-M112: a candidate Theory of Everything. (shrink)

The desirable gambles framework provides a rigorous foundation for imprecise probability theory but relies heavily on linear utility via its coherence axioms. In our related work, we introduced function-coherent gambles to accommodate non-linear utility. However, when repeated gambles are played over time---especially in intertemporal choice where rewards compound multiplicatively---the standard additive combination axiom fails to capture the appropriate long-run evaluation. In this paper we extend the framework by relaxing the additive combination axiom and introducing a nonlinear combination operator that effectively (...) aggregates repeated gambles in the log-domain. This operator preserves the time-average (geometric) growth rate and addresses the ergodicity problem. We prove the key algebraic properties of the operator, discuss its impact on coherence, risk assessment, and representation, and provide a series of illustrative examples. Our approach bridges the gap between expectation values and time averages and unifies normative theory with empirically observed non-stationary reward dynamics. (shrink)

This paper proposes an architectural approach to the analysis of complex self-regulating systems aimed at resolving the gap between the registration of empirical effects and the understanding of causal mechanisms underlying system stability, transitions, and breakdown. -/- The model introduces distinguishability as a fundamental structural condition of system existence and dynamics. System regimes, phase transitions, phase windows, adaptive stability, tension-based fixation, and disorganization are interpreted as different modes of preserving, processing, or losing distinguishability over time. -/- The proposed framework operates (...) at an architectural level, allowing the integration of observable regimes into a unified causal structure without reducing system complexity or relying on discipline-specific parameters. This enables consistent differentiation between adaptive and disorganized dynamics, reversible and irreversible transitions, and stable regimes and phase windows. -/- The model is applicable across physical, biological, cognitive, social, and artificial systems, including machine learning and neural network dynamics. Architectural relations identified in the paper provide a foundation for subsequent formalization within specific scientific domains while preserving causal rigor and conceptual consistency. -/- The work is presented as a preprint and constitutes a conceptual and methodological basis for further theoretical development, empirical testing, and interdisciplinary application. (shrink)

We introduce the notion of complexity, first at an intuitive level and then in relatively more concrete terms, explaining the various characteristic features of complex systems with examples. There exists a vast literature on complexity, and our exposition is intended to be an elementary introduction, meant for a broad audience. -/- Briefly, a complex system is one whose description involves a hierarchy of levels, where each level is made of a large number of components interacting among themselves. The time evolution (...) of such a system is of a complex nature, depending on the interactions among subsystems in the next level below the one under consideration and, at the same time, conditioned by the level above, where the latter sets the context for the evolution. Generally speaking, the interactions among the constituents of the various levels lead to a dynamics characterized by numerous characteristic scales, each level having its own set of scales. What is more, a level commonly exhibits ‘emergent properties’ that cannot be derived from considerations relating to its component systems taken in isolation or to those in a different contextual setting. In the dynamic evolution of some particular level, there occurs a self-organized emergence of a higher level and the process is repeated at still higher levels. -/- The interaction and self-organization of the components of a complex system follow the principle commonly expressed by saying that the ‘whole is different from the sum of the parts’. In the case of systems whose behavior can be expressed mathematically in terms of differential equations this means that the interactions are nonlinear in nature. -/- While all of the above features are not universally exhibited by complex systems, these are nevertheless indicative of a broad commonness relative to which individual systems can be described and analyzed. There exist measures of complexity which, once again, are not of universal applicability, being more heuristic than exact. The present state of knowledge and understanding of complex systems is itself an emerging one. Still, a large number of results on various systems can be related to their complex character, making complexity an immensely fertile concept in the study of natural, biological, and social phenomena. -/- All this puts a very definite limitation on the complete description of a complex system as a whole since such a system can be precisely described only contextually, relative to some particular level, where emergent properties rule out an exact description of more than one levels within a common framework. -/- We discuss the implications of these observations in the context of our conception of the so-called noumenal reality that has a mind-independent existence and is perceived by us in the form of the phenomenal reality. The latter is derived from the former by means of our perceptions and interpretations, and our efforts at sorting out and making sense of the bewildering complexity of reality takes the form of incessant processes of inference that lead to theories. Strictly speaking, theories apply to models that are constructed as idealized versions of parts of reality, within which inferences and abstractions can be carried out meaningfully, enabling us to construct the theories. -/- There exists a correspondence between the phenomenal and the noumenal realities in terms of events and their correlations, where these are experienced as the complex behavior of systems or entities of various descriptions. The infinite diversity of behavior of systems in the phenomenal world are explained within specified contexts by theories. The latter are constructs generated in our ceaseless attempts at interpreting the world, and the question arises as to whether these are reflections of `laws of nature' residing in the noumenal world. This is a fundamental concern of scientific realism, within the fold of which there exists a trend towards the assumption that theories express truths about the noumenal reality. We examine this assumption (referred to as a ‘point of view’ in the present essay) closely and indicate that an alternative point of view is also consistent within the broad framework of scientific realism. This is the view that theories are domain-specific and contextual, and that these are arrived at by independent processes of inference and abstractions in the various domains of experience. Theories in contiguous domains of experience dovetail and interpenetrate with one another, and bear the responsibility of correctly explaining our observations within these domains. -/- With accumulating experience, theories get revised and the network of our theories of the world acquires a complex structure, exhibiting a complex evolution. There exists a tendency within the fold of scientific realism of interpreting this complex evolution in rather simple terms, where one assumes (this, again, is a point of view) that theories tend more and more closely to truths about Nature and, what is more, progress towards an all-embracing ‘ultimate theory’ -- a foundational one in respect of all our inquiries into nature. We examine this point of view closely and outline the alternative view -- one broadly consistent with scientific realism -- that there is no ‘ultimate’ law of nature, that theories do not correspond to truths inherent in reality, and that successive revisions in theory do not lead monotonically to some ultimate truth. Instead, the theories generated in succession are incommensurate with each other, testifying to the fact that a theory gives us a perspective view of some part of reality, arrived at contextually. Instead of resembling a monotonically converging series successive theories are analogous to asymptotic series. -/- Before we summarize all the above considerations, we briefly address the issue of the complexity of the {\it human mind} -- one as pervasive as the complexity of Nature at large. The complexity of the mind is related to the complexity of the underlying neuronal organization in the brain, which operates within a larger biological context, its activities being modulated by other physiological systems, notably the one involving a host of chemical messengers. The mind, with no materiality of its own, is nevertheless emergent from the activity of interacting neuronal assemblies in the brain. As in the case of reality at large, there can be no ultimate theory of the mind, from which one can explain and predict the entire spectrum of human behavior, which is an infinitely rich and diverse one. (shrink)

The science of operations research is one of the modern sciences that have made a great revolution in all areas of life through the methods provided by it, suitable and appropriate to solve most of the problems that were facing researchers, scholars and those interested in the development of societies, and the most beneficiaries of this science were companies and institutions that are looking for scientific methods that help them manage their work so that they achieve the greatest profit and (...) the lowest cost, and one of the important methods that have been used in the management of companies we offer in this research two methods, Dynamic programming method. This method has been used in many practical matters and helped decision-makers in companies to achieve a maximum profit and less cost by formulating the reality of the state of the company and the data provided by decision-makers with a dynamic mathematical model that is solved using methods of solving dynamic models and we will provide in this research an example of this through the issue of choosing the optimal investment for the budget of a company so that it achieves a maximum profit, and the method of programming with integers: the method that provided these companies with solutions with integer values suitable for the nature of its work, through the use of the binary integer in the formulation of the appropriate mathematical model on the one hand, and on the other hand, the use of the binary integer variable helped to convert some nonlinear models that lead to some practical problems into linear models, and it should be noted here that in the previous two methods there is something indeterminable because we must make a decision in choosing or not choosing something, but the optimal solution that we will get remains A specific value because we are building the mathematical model for any realistic issue through the data provided by those responsible for the work and these data are calculated quantities and therefore they are uncertain values because their validity depends on the circumstances surrounding the work environment, they may be exposed to increase or decrease, and therefore the optimal solution on which the company will base its decision is suitable for specific values and any change in them can cause the company an uncalculated loss, so in this research we will use the concepts of neutrosophic science, the branch of science founded by the American scientist Florentin Smarandache in 1995 based on his belief that there is no absolute truth, a science that is interested in the study of ideas and concepts that are neither true nor false, but just in between, and we will take the data (calculated quantities) neutrosophic values that are specified or unspecified values are any set close to the calculated quantities, then the resulting mathematical model is a neutrosophic model and the optimal solution has neutrosophic values and thanks to the indefinite uncertainty that these values have, companies from the development of appropriate plans for all circumstances and thus achieve the greatest profit and the lowest cost, and we will clarify the above through two issues, the issue of optimal designation of a warehouse site, which we will formulate the mathematical model of using the neutrosophic integer programming method - and the issue of capital budget, which we will present in two different forms, we use in the first form the neutrosophic integer programming method and in the second the neutrosophic dynamic programming method. (shrink)

中文摘要： 孙叔敖，作为楚国春秋时期的贤相，被历史记忆为兼具仁德、务实、生态智慧与非侵略性政治气质的典范。他不是以功名治国，而是以天性之善；不是以权术谋政，而是以自然法则维系国家秩序。本文以“自然文明”与《老子》 哲学为理论基础，提出“自然政治范式”（Natural Governance Paradigm）概念，试图重新定位孙叔敖在中国政治思想史中的地位，展示其治国理念与现代系统论、生态治理、非线性政治模型的深度互补关系。本文采用跨学科方法，结合哲学、政治学、系统科学与生态文明研究，以 三段式学术论文结构完成全景式论述。本文也将孙叔敖置于“老-杨创世纪宇宙观”框架下，视为最接近“道法自然”政治模式的人类实践者之一。 Abstract : Sun Shuao, the eminent prime minister of the State of Chu in the Spring and Autumn period, stands as one of the most remarkable embodiments of non-aggressive, ecologically attuned, and naturally grounded governance in early Chinese history. He governed not through ambition but through innate virtue; not through manipulation but through alignment with natural laws. This paper, grounded in Laozi’s philosophy and the theoretical construct of “natural civilization,” advances the concept of a “Natural Governance (...) Paradigm.” It re-evaluates Sun Shuao’s intellectual and political significance, arguing that his governance demonstrates profound compatibility with modern systems theory, ecological governance, and nonlinear political modeling. Integrating perspectives from philosophy, political science, systems science, and ecological civilization studies, the paper adopts a three-part academic structure. Within the framework of the “Lao-Yang Genesis Cosmology,” Sun Shuao is presented as one of the closest historical realizations of governance aligned with the Dao. (shrink)

Psychological development is commonly described in terms of stages, traits, or norma- tive endpoints, yet such frameworks often lack generative explanations for nonlinearity, regression, and individual variability. This paper advances a structural and dynami- cal account of psychological development grounded in coherence-constrained state-space geometry. Rather than presupposing developmental stages or idealized forms, develop- ment is modelled as time-extended trajectories shaped by coherence maintenance, path dependence, and evolving integrative constraints. Within this framework, developmental change emerges from the accumulation of co- (...) herence strain and the deformation of admissible configuration space over time. Phase-like patterns, crises, and long-term reorganization arise naturally as dynamical regimes rather than as externally imposed stages. Individuation is reframed as a class of structurally necessitated reorganization processes driven by increasing differentiation pressure and co- herence demand, while trauma and healing are analysed as boundary phenomena within coherence geometry. Agency is interpreted as constraint navigation rather than unconstrained choice: re- flective awareness and prior integrative experience can alter developmental trajectories by expanding accessible regions of state space. Together with the preceding and subsequent papers in this series, the present work contributes to a unified structural framework for psychological development that preserves individual variability while providing principled explanatory coherence. (shrink)

Based on the Lao–Yang Genesis Cosmology, this paper systematically demonstrates the scientific-philosophical proposition that Dao corresponds to the Milky Way. It aims to unify the classical Daoist generative logic with modern astronomy, thermodynamics, and systems science. By analyzing Dao’s non-personal, non-teleological, and non-material characteristics, the study identifies the Milky Way as the scientific entity realizing Dao’s generative law, providing necessary constraints for the formation of the Solar System, Earth, and life. Integrating the second law of thermodynamics and entropy increase, the (...) paper explains how global disorder increases while local low-entropy systems maintain stability through energy flow, feedback, and self-organization, implementing cycles of generation, dissipation, and regeneration, corresponding to Laozi’s principle “the reversal is the movement of Dao.” From a systems science perspective, the Milky Way, the Solar System, Earth, and ecological civilizations form hierarchical coupled, nonlinear, and dissipative structures, ensuring the necessity of the generative chain. The study concludes that Dao, entropy, and generation can be unified scientifically and philosophically: Dao serves as the generative principle, the Milky Way embodies it physically, entropy provides the driving mechanism, and local order realizes generative chain stability, forming a coherent framework bridging philosophy and science. Finally, implications for human civilization, ecological management, and scientific-philosophical education are discussed, alongside future research directions in Milky Way formation mechanisms, multi-scale entropy dynamics, and systems-philosophy integration, providing a foundation for the scientific realization of Dao and sustainable civilization development. -/- Keywords: Dao philosophy, Milky Way, entropy, generative chain, systems science, scientific philosophy . (shrink)

A persistent criticism of radical embodied cognitive science is that it will be impossible to explain “real cognition” without invoking mental representations. This paper provides an account of explicit, real-time thinking of the kind we engage in when we imagine counter-factual situations, remember the past, and plan for the future. We first present a very general non-representational account of explicit thinking, based on pragmatist philosophy of science. We then present a more detailed instantiation of this general account drawing on nonlinear (...) dynamics and ecological psychology. (shrink)