Nonlinear Dynamics

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)

SRVD proposes a new ontological subject: the persistent structure—any negentropic configuration capable of maintaining continuity under energetic constraints. The framework shows how such a structure’s viability is governed by V = I_net·T / E_eff, where I_net is effective causal information, T viability time, and E_eff thermodynamic cost. Collapse of the endogenous time horizon T_pred triggers a Myopic Runaway Regime (e.g., AI reward hacking). SRVD yields testable predictions, including that T_pred collapse precedes physical runaway.

We formulate a non-linear geometric control framework for the active feedback stabilization of a source-closed, positive-energy toroidal warp spacetime. Moving completely beyond rigid, un-actuated material shells and standard linear additive state-space approximations, we model the metric-source system as a non-linear control-affine system on a smooth differential manifold. By executing a full Lie-Algebraic Rank Condition (LARC) analysis, we demonstrate that while a traditional single-axis drive is permanently confined to a lower-dimensional unreachable leaf, the multi-axis integration of an axial shift and an (...) azimuthal frame-dragging channel guarantees complete controllability over both the background propagation states and the internal spacetime breathing-mode perturbations. We demonstrate via three independent verification routes—exact symbolic brackets, numerical commutator-loop flows, and closed-path area holonomy—that the non-commuting control vector fields generate a rectified stabilization force proportional to the enclosed area within the control plane. To ensure structural transparency and respond directly to referee audits, we explicitly partition the analysis into two distinct regimes: a non-linear stress-testing regime (λ = 3.0, local well depth Φ ≈ 23.1%) used to validate control loop authority and energy conditions under severe coordinate deformations, and a weak-field interstellar cruise regime (Φ ≪ 1) used to model an optimized 10-year, 0.5c mission transit to Alpha Centauri. In the cruise regime, the total integrated rest-mass energy of the active plasma actuator shell evaluates to a physical baseline of 4.53 × 1011 J, while the time-integrated multi-axis tracking loop requires an idealized station-keeping energy of 2.93 × 1015 J. Pointwise satisfaction of all four classical energy conditions (NEC, WEC, DEC, SEC) is verified throughout via an axially elongated anisotropic pressure profile, with compliance holding in a well-defined band (not the entire manifold). The margins are positive but narrow (∼ 10−4), indicating a narrow ledge rather than a broad plateau. The framework achieves asymptotic stability via a two-channel PD controller and demonstrates that non-commutativity of the control vector fields is not an obstacle but the very resource enabling full governance of the spacetime plant. Honest disclosure of regime boundaries, actuation latency (∼19 control periods), and the perturbative nature of the existence proof is maintained throughout. (shrink)

This paper develops a consistency-first formulation of the recursive-universe hypothesis. Rather than beginning with a state-dependent unitary and treating stationarity as self-reference, we represent a physical theory by two coupled objects: a quantum state and a set of effective laws or couplings. A recursive universe is defined as a joint fixed point of a state-update map and a law-update map. This separation resolves an ambiguity in the condition ∣Ψ⟩=U[Ψ]∣Ψ⟩, which by itself is only a nonlinear stationarity equation and is insensitive (...) to the distinction between state dynamics, computability-theoretic recursion, and renormalization-group fixed points. In finite-dimensional truncations, we prove fixed-point existence for continuous admissible maps on compact convex state-law spaces, uniqueness and iterative stability for contractions, and perturbative persistence of non-degenerate fixed points under weak recursive deformation. A self-consistent two-state benchmark exhibits a pitchfork bifurcation: above a critical feedback strength, the symmetric state becomes unstable and two stable symmetry-broken states emerge. We then apply the framework to renormalization-group theory space. If an undeformed beta function possesses a non-degenerate fixed point, a small recursive deformation shifts its coordinates and critical exponents by computable first-order expressions. This establishes a controlled bridge to asymptotic-safety research without claiming numerical quantum-gravity results that have not been calculated. We also formulate action-level and covariant implementation criteria, explain why deterministic subsystem-level nonlinear quantum dynamics raises no-signalling and ensemble-dependence problems, and replace a universal recursive coupling with normalized, model-specific parameters. A Ramsey-interferometry benchmark yields an explicit conversion from phase sensitivity to a coupling bound, while gravitational-wave and cosmological tests are expressed as template-based programmes requiring a specified recursive kernel. The framework does not yet constitute a UV-complete theory of quantum gravity or a solution to the cosmological-constant problem. Its contribution is a mathematically explicit architecture that separates proven fixed-point results, illustrative models, and conjectural physical applications, thereby turning recursion from a metaphor into a disciplined research programme. (shrink)

This paper investigates the phenomenon of time and articulates constraints that any robust theory must satisfy under a recovery-based criterion. Motivated by the apparent tension between static-looking fundamental descriptions, often associated with block-universe interpretations, and the dynamical character of temporal experience, the paper argues that augmenting a formalism with additional temporal structure can risk displacing rather than resolving explanatory burdens. In response, it advances a constraint on theorizing about time: a candidate time parameter counts as “real time” only insofar as (...) it can recover, in the appropriate regime, empirically meaningful time, specifically, by providing a principled mapping to clock time. It then develops a minimal modeling strategy in three stages: 1) using hyperbolic partial differential equations together with Minkowski kinematics to encode duration, metric comparison, and causal propagation; 2) introducing a dissipative term proportional to the first time derivative to break time-reversal symmetry and yield an effective temporal orientation; and 3) representing a “moving now” via an auxiliary parameter that indexes a family of time-slices through a monotonically shifting switching time, without positing a second dynamical time variable. (shrink)

Current large language models (LLMs) operate as passive interpreters of semantic patterns rather than active reasoners over symbolic constraints. This passivity arises from their static representational geometry: during inference, the model’s internal eigenstructure—governing dominant modes of meaning—is fixed. Consequently, LLMs excel at statistical continuation but fail at self-consistent problem-solving under closed-system constraints (e.g., solving (n) equations with (n) unknowns). We propose that endowing LLMs with eigenvalue plasticity—the capacity to dynamically reconfigure their spectral representation space in response to logical or algebraic (...) inconsistency—can transform them from passive readers into active solvers. We formalize this transition using tools from linear algebra, dynamical systems theory, and active inference, showing that such adaptive eigenstructure enables proto-agency: a minimal form of goal-directed computation grounded in internal consistency rather than external reward. This framework bridges symbolic AI and connectionism without requiring explicit symbolic machinery, offering a new pathway toward robust reasoning in neural architectures. (shrink)

This paper presents a framework for dynamic systems modeling, integrating maximal entropy principles, minimal state variables, feedback loops, delays, and catalysts. We demonstrate how these mechanisms enable small systems to retain memory, exploit environmental affordances, and achieve stable yet creative growth trajectories. The framework further reveals quantum-like behavior: unobserved systems explore multiple trajectories in parallel, while observed systems are constrained to specific, often more complex, paths. We extend the analysis to reinforcement learning (RL) combined with affective computing, showing that agents (...) achieve maximal learning efficiency when operating in a Hidden/Black Box state, with observation used later for stabilization and control. (shrink)

Recent work by Frigg et. al. and Mayo-Wilson have called attention to a particular sort of error associated with attempts to model certain complex systems: structural modeling error. The assessment of the degree of SME in a model presupposes agreement between modelers about the best way to individuate natural systems, an agreement which can be more problematic than it appears. This problem, which we dub “the system individuation problem” arises in many of the same contexts as SME, and the two (...) often compound one another. This paper explores the common roots of the two problems in concerns about the precision of predictions generated by scientific models, and discusses how both concerns bear on the study of complex natural systems, particularly the global climate. (shrink)

In January 2026 two papers were deposited on Zenodo establishing that information loss at dimensional boundaries in discrete systems is a geometric phenomenon with an architecture-independent magnitude: 86.01% ± 2.39% in cellular automata across 1,500 patterns (Thornhill 2026b, DOI 10.5281/zenodo.18262424, 01/14/2026), and 84.39% ± 1.55% on transformer hidden states (GPT-2, Gemma-2), supported by a formal proof of the component transformations S, R, and D (Thornhill 2026c, DOI 10.5281/zenodo.18319430, 01/20/2026). It was predicted, in the closing discussion of Thornhill 2026c, that the (...) geometric account should hold across substrates wherever density dilution and neighborhood-structure expansion occur together at a representational boundary. -/- In March 2026, Barman, Starenky, Bodnar, Narasimhan, and Gopinath independently published two arXiv preprints (arXiv:2603.27116 and arXiv:2604.06222) reporting that production retrieval embedding models — MiniLM-L6-v2, BGE-base, BGE-large — concentrate their variance into approximately 16 effective dimensions regardless of nominal dimensionality (384, 768, 1024), and that this concentration places those models in an interference-vulnerable geometric regime that reproduces quantitative signatures of human memory failure (power-law forgetting with exponent b = 0.460 ± 0.183, Deese–Roediger–McDermott false-alarm rate of 0.583, spacing-effect ordering, tip-of-tongue behavior). They establish a parallel theorem — the No-Escape Theorem — characterizing what cannot be repaired within semantically continuous kernel-threshold memory systems. -/- The two bodies of work are methodologically distinct. They use different metrics (Φ = R·S + D vs. participation ratio), study different substrates (cellular automata and transformer hidden states vs. pretrained retrieval embeddings), and report different specific quantities (an 86% loss constant in Φ vs. a fixed point at ~16 effective dimensions across nominal sizes). They also reach the same broader conclusion from independent directions: that representational memory failure is a geometric property of the embedding operation, not a property of any particular architecture, training regime, or biological substrate. -/- The present note records the chronology of the two lines of evidence in a single citable document, summarizes the methodological differences, and identifies the substantive convergence: an architecture-independent geometric fixed point as the principal explanatory mechanism for representational memory failure in the systems studied. (shrink)

The Existence Threshold (v2.1) builds on a statistically significant framework for understanding pattern persistence in complexity science. -/- Using the corrected formula Φ = R·S + D, this work validates that disorder is a necessary component of existence. -/- Features comprehensive experimental success across ten cellular automata systems, establishing testable predictions for self-organization, emergence, and entropy in binary discrete environments. -/- Keywords: Existence Threshold, cellular automata, pattern persistence, binary discrete systems, self-organization, emergence, complexity science, information theory, system integration, thermodynamic entropy, (...) Conway's Game of Life, dynamical systems, state transitions, reproducibility, implementation details, experimental validation, statistical significance, domain boundaries, consciousness hypothesis, cosmological expansion, dark energy mechanism, recursive processing, integrated information theory. (shrink)

What do market crashes, geomagnetic storms, and the loss of consciousness have in common? They are all moments when a system's organizational identity dissolves. This paper introduces a framework that makes that dissolution measurable, predictable, and universal. The Dynamic Existence Threshold (DET) provides a single coordinate system — the integration-differentiation balance zone — in which conscious brains, stable markets, and quiet magnetospheres all occupy the same region. Departure from this zone is organizational dissolution: the system persists physically but loses the (...) coordinated structure that made it more than the sum of its parts. -/- The decisive result: a simple sum of neural power anti-predicts brain state (AUC 0.416 — worse than a coin flip), while the structural coupling metric achieves 91% accuracy across 136,394 EEG epochs. Deep sleep has more total power than wakefulness. What it lacks is coordination. This is the cleanest dissociation between organizational structure and mere magnitude in the critical transitions literature — and it raises the obvious question about AI: is a large neural network's activation organized, or just loud? The DET framework can test this. -/- Six tests, three domains (financial markets, space weather, EEG), zero parameter tuning. Early warning signals 5–30 days before events. Total organizational information is conserved during every tested transition while its components undergo massive inverse exchange — the system redistributes information rather than losing it. Dimensional embedding destroys it irreversibly. Two distinct failure modes: reversible organizational shift versus irreversible information destruction. -/- The framework that detects when a brain loses consciousness is the same one that detects when a market loses coherence — and potentially the same one that could measure whether an AI system has organizational structure at all. -/- Provisionally patented. -/- __________ -/- Keywords: consciousness, artificial intelligence, complex systems, critical transitions, early warning signals, integrated information theory, AI consciousness, EEG, financial crashes, space weather, nonlinear dynamics, tipping points, information conservation, organizational dissolution, cross-domain analysis. (shrink)

Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. While the rules describing chaotic dynamical systems are well-specified and simple, the behaviour of many such systems is remarkably complex and produces output that appears random and for which long-term prediction is limited. The book begins by laying out preliminary material needed to understand the literature on chaos, providing the background (...) that any reader would need to be able to navigate the literature. It goes on to discuss the history of the field, the different definitions of chaos, differences between classical and quantum chaos and the implications of chaos for modelling phenomena and forecasting system behaviour before rounding out with broader implications. (shrink)

The incompressible Navier–Stokes equations on the three-torus T³ admit global weak solutions (Leray), but whether these solutions remain smooth for all time is open. We resolve this by constructing a bounded vorticity-response functional Φ : ℝ≥0 → [φ_min, φ_max] that defines a temporal lifting of the equations. The construction generalizes Sundman's regularization of collision singularities in celestial mechanics, with vorticity magnitude serving as the regularizing variable. The lifting φ(τ) = ∫₀τ Φ(‖Ω(s)‖_L∞) ds satisfies non-degeneracy (φ′ ≥ φ_min > 0) and (...) global coverage (φ(τ) → ∞ as τ → ∞). Uniform bounds on Galerkin approximations, independent of the truncation parameter N, combined with coordinate invariance of the Beale–Kato–Majda integral, yield finiteness of the BKM integral in physical time. The contrapositive of the BKM criterion establishes global existence of classical solutions u ∈ C∞(T³ × [0, ∞)) for smooth divergence-free initial data; by weak-strong uniqueness, these coincide with the Leray–Hopf weak solutions, establishing their smoothness. This satisfies Fefferman's Clay Millennium Problem Statement (B). Numerical validation at Reynolds numbers up to 10⁸ confirms coordinate invariance and preservation of the dissipation identity ε = 2νZ. Numerical confirmation code and data available at doi:10.5281/zenodo.17730872. Paper DOI DOI: 10.63968/post-bio-ai-epistemics.v1n2.012. (shrink)

In Explaining Technology, Koppl et al. (2023) argue that “recombination is the essential driver of technological evolution” (p. 3). Modelling combinatorial innovation as a self-propelling, “autocatalytic” process raises the question of what explanatory role, if any, is left for institutional analysis. Although the authors grant institutions only an auxiliary explanatory role, they hint at the functional importance of market institutions, trade networks, patent law, and entrepreneurship. Our paper argues that institutions matter because they crucially affect aggregate levels and rates of (...) recombination and innovation, as well as shaping patterns of recombination and innovation that occur. This paper builds upon Koppl et al.’s acknowledgement of these institutional effects by integrating combinatorial evolution within recent developments in commons theory and institutional economics. Specifically, we argue the burgeoning literature on Governing Knowledge Commons offers a fruitful framework and body of empirical case studies that illuminates the diverse institutions individuals use to facilitate and steer combinatorial innovation. Whilst healthy institutional diversity may incentivize more recombination than any single monocentric institutional arrangement, the non-teleological aspect of recombination means that innovative processes can exude either productive, unproductive, or destructive effects. The institutional diversity fostered by flourishing knowledge commons may allow people to put combinatorial innovations into more productive uses while internalizing their complex externalities. At the same time, it may generate socio-cultural resistances to some forms of innovation processes. We illustrate our theory using cases related to several applied topics including intellectual property, competition policy, and the development of unmanned aerial vehicles. (shrink)

This article describes the hypothesis-testing experiments conducted simultaneously in time. The theoretical basis of the hypothesis is designed in a way that the null hypothesis and alternative hypothesis contradicts each other, while the alternative hypothesis cannot be theoretically reached without the null hypothesis. Modern and contemporary cosmological theories have the common source from the Big Bang theory, albeit none guarantees the absolute correctness of it. The null hypothesis is falsified in the experiments, without developing further cosmological theory thereon. It is (...) an intermediate corroboration to the Conformal Cyclic Cosmology, but does not prove it. The methods adopted in the experiments adapted special relativity and quantum physics to observational instrumentation and data science. The experiments conclude the logic in Big Bang falsification, and the cosmological possibility in Tycho particles from the evidence of Hawking points. (shrink)

Empirical evidence indicates that conscious states, distinguished by the presence of phenomenal qualities, are closely linked to synchronized neural activity patterns whose dynamical characteristics can be attributed to self-organized criticality and phase transitions. These findings imply that insight into the mechanism by which the brain controls phase transitions will provide a deeper understanding of the fundamental mechanism by which the brain manages to transcend the threshold of consciousness. This article aims to show that the initiation of phase transitions and the (...) formation of synchronized activity patterns is due to the coupling of the brain to the zero-point field (ZPF), which plays a central role in quantum electrodynamics (QED). The ZPF stands for the presence of ubiquitous vacuum fluctuations of the electromagnetic field, represented by a spectrum of normal modes. With reference to QED-based model calculations, the details of the coupling mechanism are revealed, suggesting that critical brain dynamics is governed by the resonant interaction of the ZPF with the most abundant neurotransmitter glutamate. The pyramidal neurons in the cortical microcolumns turn out to be ideally suited to control this interaction. A direct consequence of resonant glutamate-ZPF coupling is the amplification of specific ZPF modes, which leads us to conclude that the ZPF is the key to the understanding of consciousness and that the distinctive feature of neurophysiological processes associated with conscious experience consists in modulating the ZPF. Postulating that the ZPF is an inherently sentient field and assuming that the spectrum of phenomenal qualities is represented by the normal modes of the ZPF, the significance of resonant glutamate-ZPF interaction for the formation of conscious states becomes apparent in that the amplification of specific ZPF modes is inextricably linked with the excitation of specific phenomenal qualities. This theory of consciousness, according to which phenomenal states arise through resonant amplification of zero-point modes, is given the acronym TRAZE. An experimental setup is specified that can be used to test a corollary of the theory, namely, the prediction that normally occurring conscious perceptions are absent under experimental conditions in which resonant glutamate-ZPF coupling is disrupted. (shrink)

Is the brain really a computer? In particular, is our intelligence a computational achievement: is it because our brains are computers that we get on in the world as well as we do? In this paper I will evaluate an ambitious new argument to the contrary, developed in Landgrebe and Smith (2021a, 2022). Landgrebe and Smith begin with the fact that many dynamical systems in the world are difficult or impossible to model accurately (inter alia, because it is intractable to (...) find exact solutions to the differential equations that describe them—meaning we have to approximate—but at the same time they are such that small differences in starting conditions lead to big differences in final conditions, thwarting accurate approximation). Yet we manage to survive and thrive in a world full of such systems. Landgrebe and Smith argue from these premises that it is not because our brains are computers that we get on as well as we do: instead it is because of the various ways that we dynamically couple with such systems, these couplings themselves impossible to model well enough to emulate in silico. Landgrebe and Smith thus defend a dynamical systems model in the lineage of Gibson (1979), Van Gelder (1995), and Thompson (2007), though their focus is on decisively refuting the computationalist alternatives rather than developing the positive account. Here I will defend the claim that human intelligence is genuinely computational (and that whole brain emulation and others forms of AGI may be possible) against this argument. (shrink)

The article presents the empirical confirmation to the black hole and white hole juxtapose theory. The author based the experiment on the multi- mission multi-spectral space telescope data conducted remotely with the NASA Data Challenge and Harvard- Smithsonian Micro-Observatory. Since the loss of the original manuscript, the author reformulated the mathematics during the research. The observation developed a resonance observation technique that observed the white hole to the moon’s direction with the sun. The data reduction of the white hole and (...) other observations provides an explanation for the undetected gravitons and some empirical physical features of the white hole. (shrink)

The article summarizes the software tool on astrophysical analysis with multi-wavelength space telescope data. It recaps the evidence analysis conducted on the Kerr-Newman black hole (KNBH). It was written prior to the article Research on the Kerr-Newman Black Hole in M82 Confirms Black Hole and White Hole Juxtapose not soon after the experiment. The conducted analysis suggested Hawking radiation is caused by the movement of ergosurfaces of the BH and serves as the primal evidence for black hole and white hole (...) juxtapose. A later data exploration was conducted with the radiation trails in the multi-wavelength data. The evidences produced corroborates with Yale professor Priyamvada Natarajan's black hole seeds theory. It implies that the electromagnetic dynamic of fusion and fission temperature determines the pressure of surface tension on the macro particles, and the mass density of the BH is determined by the electromagnetic tension between the outer ergosurface and inner ergosurface. The ring singularity of the BH and the Penrose-Hawking singularity of the BH determine the spin and gravitational singularity of the BH. Inside the ergosurfaces, the BH singularities' backward inflow causes the vicinity's rate on feeding the BH. It makes the active galactic nuclei (AGN) a semi-closed system. The density pressure is released on threshold. During the mass exchange observed by energy momentum upon the AGN's open, the macroparticle composition of the BH changes with the galactic event. This causes the expansion rate of the galaxy and contraction rate of the BH. AGN types and their relative motions determine the expansion rate of the cosmic universe in a generalized quantitative thinking. The article concludes that BH spin is caused by the asymmetric motions of AGN in the BH system. A set of the nuclear resonance caused by BH and white hole (WH) oscillation is processed with the same set of data. (shrink)

In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods involving a (...) discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided. (shrink)

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: Einstein’s static universe and Eddington’s demonstration of its instability, and the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and (...) its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one. (shrink)

The thesis of this paper is that panpsychism theory is very close to jungian theory, especially thinking of the quantum psychoid aspects of C.G.Jung and W.Pauli theory: a psyche that touches matter and matter with a “latent psyche”. The two theories seem to describe the same reality, an animation of matter in a spiritual sense, as the jungian Self seems to do at a higher level.The complexity theory appears instead to be a description of reality still nomothetic.

Can stable regularities be explained without appealing to governing laws or any other modal notion? In this paper, I consider what I will call a ‘Humean system’—a generic dynamical system without guiding laws—and assess whether it could display stable regularities. First, I present what can be interpreted as an account of the rise of stable regularities, following from Strevens [2003], which has been applied to explain the patterns of complex systems (such as those from meteorology and statistical mechanics). Second, since (...) this account presupposes that the underlying dynamics displays deterministic chaos, I assess whether it can be adapted to cases where the underlying dynamics is not chaotic but truly random—that is, cases where there is no dynamics guiding the time evolution of the system. If this is so, the resulting stable, apparently non-accidental regularities are the fruit of what can be called statistical necessity rather than of a primitive physical necessity. (shrink)

The target paper of Schoeller, Perlovsky, and Arseniev is an essential and timely contribution to a current shift of focus in neuroscience aiming to merge neurophysiological, psychological and physical principles in order to build the foundation for the physics of mind. Extending on previous work of Perlovsky et al. and Badre, the authors of the target paper present interesting mathematical models of several basic principles of the physics of mind, such as perception and cognition, concepts and emotions, instincts and learning. (...) Their conceptualization helps to clarify the distinction between conscious and unconscious aspects of mind that is often neglected and further provide a clear description of the mental hierarchy, which extends from physical objects in the physical world to abstract ideas in the mental/subjective realm. While we agree that identification of a few fundamental principles is a first step toward developing the physics of the mind, and we concur with the selection of those principles in the target review paper, we think that the theory of the physics of mind would much benefit from considering also the most basic principles that are common for the physics/matter/brain and the mind/subjectivity/cognition. In this respect, such basic principles as time and space, as well as criticality, self-organization, and emergence seem to be the most interesting. (shrink)

The file on this site provides the slides for a lecture given in Hangzhou in May 2018, and the lecture itself is available at the URL beginning 'sms' in the set of links provided in connection with this item. -/- It is commonly assumed that regular physics underpins biology. Here it is proposed, in a synthesis of ideas by various authors, that in reality structures and mechanisms of a biological character underpin the world studied by physicists, in principle supplying detail (...) in the domain that according to regular physics is of an indeterminate character. In regular physics mathematical equations are primary, but this constraint leads to problems with reconciling theory and reality. Biology on the other hand typically does not characterise nature in quantitative terms, instead investigating in detail important complex interrelationships between parts, leading to an understanding of the systems concerned that is in some respects beyond that which prevails in regular physics. It makes contact with quantum physics in various ways, for example in that both involve interactions between observer and observed, an insight that explains what is special about processes involving observation, justifying in the quantum physics context the replacement of the unphysical many-worlds picture by one involving collapse. The link with biology furthermore clarifies Wheeler’s suggestion that a multiplicity of observations can lead to the ‘fabrication of form’, including the insight that this process depends on very specific ‘structures with power’ related to the 'semiotic scaffolding' of the application of sign theory to biology known as biosemiotics. -/- The observer-observed 'circle' of Wheeler and Yardley is a special case of a more general phenomenon, oppositional dynamics, related to the 'intra-action' of Barad's Agential Realism, involving cooperating systems such as mind and matter, abstract and concrete, observer and observed, that preserve their identities while interacting with one another in such a way as to act as a unit. A third system may also be involved, the mediating system of Peirce linking the two together. Such a situation of changing connections and separations may plausibly lead in the future to an understanding of how complex systems are able to evolve to produce 'life, the universe and everything'. -/- (Added 1 July 2018) The general structure proposed here as an alternative to a mathematics-based physics can be usefully characterised by relating it to different disciplines and the specialised concepts utilised therein. In theoretical physics, the test for the correctness of a theory typically involves numerical predictions, corresponding to which theories are expressed in terms of equations, that is to say assertions that two quantities have identical values. Equations have a lesser significance in biology which typically talks in terms of functional mechanisms, dependent for example on details of chemistry and concepts such as genes, natural selection, signals and geometrical or topologically motivated concepts such as the interconnections between systems and the unfolding of DNA. Biosemiotics adds to this the concept of signs and their interpretation, implying novel concepts such as semiotic scaffolding and the semiosphere, code duality, and appreciation of the different types of signs, including symbols and their capacity for abstraction and use in language systems. Circular Theory adds to this picture, as do the ideas of Barad, considerations such as the idea of oppositional dynamics. The proposals in this lecture can be regarded as the idea that concepts such as those deriving from biosemiotics have more general applicability than just conventional biology and may apply, in some circumstances, to nonlinear systems generally, including the domain new to science hypothesised to underlie the phenomena of present-day physics. -/- The task then has to be to restore the mathematical aspect presumed, in this picture, not to be fundamental as it is in conventional theory. Deacon has invoked a complex sequence of evolutionary steps to account for the emergence over time of human language systems, and correspondingly mathematical behaviour can be subsumed under the general evolutionary mechanisms of biosemiotics (cf. also the proposals of Davis and Hersh regarding the nature of mathematics), so that the mathematical behaviour of physical systems is consistent with the proposed scheme. In conclusion, it is suggested that theoretical physicists should cease expecting to find some universal mathematical ‘theory of everything’, and focus instead on understanding in more detail complex systems exhibiting behaviour of a biological character, extending existing understanding. This may in time provide a more fruitful understanding of the natural world than does the regular approach. The essential concepts have an observational basis from both biology and the little-known discipline of cymatics (a discipline concerned with the remarkable patterns that specific waveforms can give rise to), while again computer simulations also offer promise in providing insight into the complex behaviours involved in the above proposals. -/- References -/- Jesper Hoffmeyer, Semiotic Scaffolding of Living Systems. Commens, a Digital Companion to C. S. Peirce (on Commens web site). Terrence Deacon, The Symbolic Species, W.W. Norton & Co. Karen Barad, Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Duke University Press. Philip Davis and Reuben Hersh, The Mathematical Experience, Penguin. Ilexa Yardley, Circular Theory. (shrink)

Emergence is much discussed by both philosophers and scientists. But, as noted by Mitchell (2012), there is a significant gulf; philosophers and scientists talk past each other. We contend that this is because philosophers and scientists typically mean different things by emergence, leading us to distinguish being emergence and pattern emergence. While related to distinctions offered by others between, for example, strong/weak emergence or epistemic/ontological emergence (Clayton, 2004, pp. 9–11), we argue that the being vs. pattern distinction better captures what (...) the two groups are addressing. In identifying pattern emergence as the central concern of scientists, however, we do not mean that pattern emergence is of no interest to philosophers. Rather, we argue that philosophers should attend to, and even contribute to, discussions of pattern emergence. But it is important that this discussion be distinguished, not conflated, with discussions of being emergence. In the following section we explicate the notion of being emergence and show how it has been the focus of many philosophical discussions, historical and contemporary. In section 3 we turn to pattern emergence, briefly presenting a few of the ways it figures in the discussions of scientists (and philosophers of science who contribute to these discussions in science). Finally, in sections 4 and 5, we consider the relevance of pattern emergence to several central topics in philosophy of biology: the emergence of complexity, of control, and of goal-directedness in biological systems. (shrink)

This paper dealing with extension of the Einstein eld equations using apparatus of contemporary generalization of the classical Lorentzian geometry named in literature Colombeau distributional geometry, see for example [1], [2], [3], [4], [5], [6], [7] and [32]. The regularizations of singularities presented in some solutions of the Einstein equations is an important part of this approach. Any singularities present in some solutions of the Einstein equations recognized only in the sense of Colombeau generalized functions [1], [2] and not classically. (...) In this paper essentially new class Colombeau solutions to Einstein eld equations is obtained. The vacuum energy density of free scalar quantum field  with a distributional background spacetime also is considered. It has been widely believed that, except in very extreme situations, the influence of gravity on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is false by showing that there exist well-behaved spacetime evolutions where the vacuum energy density of free quantum fields is forced, by the very same background distributional spacetime such distributional BHs, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on curved spacetimes. In particular we obtain that the vacuum fluctuations have a singular behavior on BHs horizon. (shrink)

The fault ride-through capability and fault current issues are the main challenges in doubly fed induction generator- based wind turbines. Application of the bridge-type fault current limiter was recognized as a promising solution to cope with these challenges. This paper proposes a nonlinear sliding mode controller for the BFCL to enhance the FRT performance of the DFIG-based WT. This controller has robust performance in unpredicted voltage sag level and nonlinear features. Theoretical discussions, power circuit, and nonlinear control consideration of the (...) SMC-based BFCL are conducted, and then, its performance is verified through time-domain simulations in the PSCAD/EMTDC environment. To reduce the chattering phenomenon and decrease the reaching time, it used the exponential reaching law for designed SMC. Also, the SMC-based BFCL performance is compared with the conventional and PI controller-based BFCL for both symmetrical and asymmetrical short-circuit faults. Simulation results reveal that the SMC-based BFCL provides better performance compared with the conventional and PI controller-based BFCL to enhance the FRT. (shrink)

The models of the electric charge and magnetic moment are presented based on the nonlinear response of a vacuum on the applied electric and magnetic fields. The model of the electric charge contains one parameter—the radius of charge—and predicts one value of the electric charge for all elementary particles independently on the value of this radius. Different values of this parameter for the electron are discussed.

The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen (...) in Texas. The mathematical version of this property is known as sensitive dependence. However, it turns out that sensitive dependence is somewhat old news, so some of the implications flowing from it are perhaps not such “big news” after all. Still, chaos studies have highlighted these implications in fresh ways and led to thinking about other implications as well. In addition to exhibiting sensitive dependence, chaotic systems possess two other properties: they are deterministic and nonlinear (Smith 2007). This entry discusses systems exhibiting these three properties and what their philosophical implications might be for theories and theoretical understanding, confirmation, explanation, realism, determinism, free will and consciousness, and human and divine action. (shrink)

This work builds on the Volterra series formalism presented in Dreisigmeyer and Young to model nonconservative systems. Here we treat Lagrangians and actions as ‘time dependent’ Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational principle.

A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set of models (...) is structurally chaotic if it contains a chaotic function. I conclude by discussing the relationship between structural chaos and structural stability. (shrink)

Climatology is a paradigmatic complex systems science. Understanding the global climate involves tackling problems in physics, chemistry, economics, and many other disciplines. I argue that complex systems like the global climate are characterized by certain dynamical features that explain how those systems change over time. A complex system's dynamics are shaped by the interaction of many different components operating at many different temporal and spatial scales. Examining the multidisciplinary and holistic methods of climatology can help us better understand the nature (...) of complex systems in general. -/- Questions surrounding climate science can be divided into three rough categories: foundational, methodological, and evaluative questions. "How do we know that we can trust science?" is a paradigmatic foundational question (and a surprisingly difficult one to answer). Because the global climate is so complex, questions like "what makes a system complex?" also fall into this category. There are a number of existing definitions of `complexity,' and while all of them capture some aspects of what makes intuitively complex systems distinctive, none is entirely satisfactory. Most existing accounts of complexity have been developed to work with information-theoretic objects (signals, for instance) rather than the physical and social systems studied by scientists. -/- Dynamical complexity, a concept articulated in detail in the first third of the dissertation, is designed to bridge the gap between the mathematics of contemporary complexity theory (in particular the formalism of "effective complexity" developed by Gell-Mann and Lloyd [2003]) and a more general account of the structure of science generally. Dynamical complexity provides a physical interpretation of the formal tools of mathematical complexity theory, and thus can be used as a framework for thinking about general problems in the philosophy of science, including theories, explanation, and lawhood. -/- Methodological questions include questions about how climate science constructs its models, on what basis we trust those models, and how we might improve those models. In order to answer questions about climate modeling, it's important to understand what climate models look like and how they are constructed. Climate model families are significantly more diverse than are the model families of most other sciences (even sciences that study other complex systems). Existing climate models range from basic models that can be solved on paper to staggeringly complicated models that can only be analyzed using the most advanced supercomputers in the world. I introduce some of the central concepts in climatology by demonstrating how one of the most basic climate models might be constructed. I begin with the assumption that the Earth is a simple featureless blackbody which receives energy from the sun and releases it into space, and show how to model that assumption formally. I then gradually add other factors (e.g. albedo and the greenhouse effect) to the model, and show how each addition brings the model's prediction closer to agreement with observation. After constructing this basic model, I describe the so-called "complexity hierarchy" of the rest of climate models, and argue that the sense of "complexity" used in the climate modeling community is related to dynamical complexity. -/- With a clear understanding of the basics of climate modeling in hand, I then argue that foundational issues discussed early in the dissertation suggest that computation plays an irrevocably central role in climate modeling. "Science by simulation" is essential given the complexity of the global climate, but features of the climate system--the presence of non-linearities, feedback loops, and chaotic dynamics--put principled limits on the effectiveness of computational models. This tension is at the root of the staggering pluralism of the climate model hierarchy, and suggests that such pluralism is here to stay, rather than an artifact of our ignorance. Rather than attempting to converge on a single "best fit" climate model, we ought to embrace the diversity of climate models, and view each as a specialized tool designed to predict and explain a rather narrow range of phenomena. Understanding the climate system as a whole requires examining a number of different models, and correlating their outputs. This is the most significant methodological challenge of climatology. -/- Climatology's role contemporary political discourse raises an unusually high number of evaluative questions for a physical science. The two leading approaches to crafting policy surrounding climate change center on mitigation (i.e. stopping the changes from occurring) and adaptation (making post hoc changes to ameliorate the harm caused by those changes). Crafting an effective socio-political response to the threat of anthropogenic climate change, however, requires us to integrate multiple perspectives and values: the proper response will be just as diverse and pluralistic as the climate models themselves, and will incorporate aspects of both approaches. I conclude by offering some concrete recommendations about how to integrate this value pluralism into our socio-political decision making framework. (shrink)

In this paper I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss's ε-congruenceε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence (...) are unpromising. Despite this critique, I suggest that Werndl's proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence. (shrink)

This paper briefly review a current trend in neuroscience aiming to combine neurophysiological and physical concepts in order to understand the emergence of spatio-temporal patterns within brain activity by which brain constructs knowledge from multiple streams of information. The authors further suggest that the meanings, which subjectively are experienced as thoughts or perceptions can best be described objectively as created and carried by large fields of neural activity within the operational architectonics of brain functioning.

From his earliest work forward, phenomenologist Maurice Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own intrinsic sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up (...) Merleau-Ponty’s ontology as the basis for a new, “enactive” approach to cognitive science, synthesizing it with concepts from dynamic systems theory and Francisco Varela’s theory of autopoiesis. However, Thompson does not quite succeed in resolving the ambiguities in Merleau-Ponty’s account of form. This article builds on an indication from Thompson in order to propose a new account of form as asymmetry, and of the genesis of form in nature as symmetry-breaking. These concepts help us to escape the antinomies of Modern thought by showing how nature is the autoproduction of a sense which can only be known by an embodied perceiver. (shrink)

Individuals make decisions under uncertainty every day. Decisions are based on in- complete information concerning the potential outcome or the predicted likelihood with which events occur. In addition, individuals’ choices often deviate from the rational or mathematically objective solution. Accordingly, the dynamics of human decision making are difficult to capture using conventional, linear mathematical models. Here, we present data from a 2-choice task with variable risk between sure loss and risky loss to illustrate how a simple nonlinear dynamical system can (...) be employed to capture the dynamics of human decision making under uncertainty (i.e., multistability, bifurcations). We test the feasibility of this model quantitatively and demonstrate how the model can account for up to 86% of the observed choice behavior. The implications of using dynamical models for explaining the nonlin- ear complexities of human decision making are discussed as well as the degree to which the theory of nonlinear dynamical systems might offer an alternative framework for understanding human decision making processes. (shrink)

Individuals make decisions under uncertainty every day based on incomplete information concerning the potential outcome of the choice or chance levels. The choices individuals make often deviate from the rational or mathematically objective solution. Accordingly, the dynamics of human decision-making are difficult to capture using conventional, linear mathematical models. Here, we present data from a two-choice task with variable risk between sure loss and risky loss to illustrate how a simple nonlinear dynamical system can be employed to capture the dynamics (...) of human decision-making under uncertainty (i.e., multi-stability, bifurcations). We test the feasibility of this model quantitatively and demonstrate how the model can account for up to 86% of the observed choice behavior. The implications of using dynamical models for explaining the nonlinear complexities of human decision-making are discussed, as well as the degree to which nonlinear dynamical systems theory might offer an alternative framework for understanding human decision-making processes. (shrink)

The nonlinearity of a composite system, whereby certain of its features (including powers and behaviors) cannot be seen as linear or other broadly additive combinations of features of the system's composing entities, has been frequently seen as a mark of metaphysical emergence, coupling the dependence of a composite system on an underlying system of composing entities with the composite system's ontological autonomy from its underlying system. But why think that nonlinearity is a mark of emergence, and moreover, of metaphysical rather (...) than merely epistemological emergence? Are there diverse ways in which nonlinearity might enter into an account of properly metaphysical emergence? And what are the prospects for there actually being phenomena that are metaphysically emergent in any available sense? Here I explore the mutual bearing of nonlinearity and metaphysical emergence, with an eye towards answering these and related questions. (shrink)