An Introduction to a Major Thesis: The Laplacian-Newtonian Paradigm
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2026
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| author | Andrushka, Burmastrova |
| author_facet | Andrushka, Burmastrova |
| contents | <p>This thesis presents a rigorous exposition of the Laplacian-Newtonian paradigm in classical mechanics, asserting that all macroscopic physical systems--including atmospheric flows, biological trajectories, and mesoscopic neural dynamics--are fully representable within a deterministic phase space Γ where the system's state is specified by the complete set of generalised coordinates {qi} and conjugate momenta {pi} (Arnold, 1989; Goldstein et al., 2002; Landau & Lifshitz, 1976). The instantaneous configuration at time (t) constitutes the exhaustive product of antecedent states under the governing Hamiltonian flow, rendering the future evolution uniquely determined via the equations of motion. Central to this framework is the sensitive dependence on initial conditions, formalized through positive Lyapunov exponents λ>0, which quantify exponential divergence of nearby trajectories in phase space and underpin chaotic behavior (Lorenz, 1963; Ruelle & Takens, 1971; Ott, 2002). While deterministic in principle--as encapsulated in Laplace's (1814) assertion that the present state is both effect of the past and cause of the future--practical predictability is limited by finite precision and computational bounds, necessitating recourse to statistical mechanics for ensemble-averaged descriptions (Boltzmann, 1872/2015; Uffink, 2007).</p> <p>The paradigm is extended to neurodynamics, where cortical and subcortical networks exhibit deterministic yet chaotic attractors and transient spatiotemporal patterns (Rabinovich et al., 2006; Freeman, 2000; Izhikevich, 2007). Integrating empirical findings from readiness-potential studies (Libet, 1999) and modern interpretations of volitional timing (Haggard, various; Sapolsky, contemporary syntheses), the analysis posits that the phenomenology of free will constitutes an introspective illusion emergent from the inaccessibility of underlying multifactorial causal chains in neural state space. This sensation arises as a higher-order epistemic gap: the brain's self-modeling fails to reconstruct the full deterministic antecedents of motor preparation and decision instantiation, yielding a subjective experience of uncaused agency despite strict adherence to causal locality and the principle of sufficient reason (Hume, 1739/2000; Aquinas via Melamed & Lin, 2023). The discussion culminates in reconciliation with relativistic invariance and Einstein's field-theoretic determinism, affirming that the totalizing classical narrative--spanning Newtonian-Lagrangian-Hamiltonian formulations to general relativity--remains unbroken at macroscopic scales, while the apparent indeterminacy of subjective volition reflects only the epistemic horizon of the embedded observer within an ontologically closed, four-dimensional spacetime manifold. This unified view challenges reductionist dualisms and supports an emergent, non-contradictory ontology wherein deterministic mechanics subsumes the evolutionary genesis of conscious experience.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18763676 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | An Introduction to a Major Thesis: The Laplacian-Newtonian Paradigm Andrushka, Burmastrova Field Equations, Lyapunov exponent High Dimensional Model Representation State Space Models Isaac Newton C.S. Lewis Mesoscopic Physics Pantheism Chaos/Complexity Theory Free Will Baruch Spinoza Statistical Physics, Differential Manifolds Thomas Aquinas William James Hamiltonian dynamics <p>This thesis presents a rigorous exposition of the Laplacian-Newtonian paradigm in classical mechanics, asserting that all macroscopic physical systems--including atmospheric flows, biological trajectories, and mesoscopic neural dynamics--are fully representable within a deterministic phase space Γ where the system's state is specified by the complete set of generalised coordinates {qi} and conjugate momenta {pi} (Arnold, 1989; Goldstein et al., 2002; Landau & Lifshitz, 1976). The instantaneous configuration at time (t) constitutes the exhaustive product of antecedent states under the governing Hamiltonian flow, rendering the future evolution uniquely determined via the equations of motion. Central to this framework is the sensitive dependence on initial conditions, formalized through positive Lyapunov exponents λ>0, which quantify exponential divergence of nearby trajectories in phase space and underpin chaotic behavior (Lorenz, 1963; Ruelle & Takens, 1971; Ott, 2002). While deterministic in principle--as encapsulated in Laplace's (1814) assertion that the present state is both effect of the past and cause of the future--practical predictability is limited by finite precision and computational bounds, necessitating recourse to statistical mechanics for ensemble-averaged descriptions (Boltzmann, 1872/2015; Uffink, 2007).</p> <p>The paradigm is extended to neurodynamics, where cortical and subcortical networks exhibit deterministic yet chaotic attractors and transient spatiotemporal patterns (Rabinovich et al., 2006; Freeman, 2000; Izhikevich, 2007). Integrating empirical findings from readiness-potential studies (Libet, 1999) and modern interpretations of volitional timing (Haggard, various; Sapolsky, contemporary syntheses), the analysis posits that the phenomenology of free will constitutes an introspective illusion emergent from the inaccessibility of underlying multifactorial causal chains in neural state space. This sensation arises as a higher-order epistemic gap: the brain's self-modeling fails to reconstruct the full deterministic antecedents of motor preparation and decision instantiation, yielding a subjective experience of uncaused agency despite strict adherence to causal locality and the principle of sufficient reason (Hume, 1739/2000; Aquinas via Melamed & Lin, 2023). The discussion culminates in reconciliation with relativistic invariance and Einstein's field-theoretic determinism, affirming that the totalizing classical narrative--spanning Newtonian-Lagrangian-Hamiltonian formulations to general relativity--remains unbroken at macroscopic scales, while the apparent indeterminacy of subjective volition reflects only the epistemic horizon of the embedded observer within an ontologically closed, four-dimensional spacetime manifold. This unified view challenges reductionist dualisms and supports an emergent, non-contradictory ontology wherein deterministic mechanics subsumes the evolutionary genesis of conscious experience.</p> |
| title | An Introduction to a Major Thesis: The Laplacian-Newtonian Paradigm |
| topic | Field Equations, Lyapunov exponent High Dimensional Model Representation State Space Models Isaac Newton C.S. Lewis Mesoscopic Physics Pantheism Chaos/Complexity Theory Free Will Baruch Spinoza Statistical Physics, Differential Manifolds Thomas Aquinas William James Hamiltonian dynamics |
| url | https://doi.org/10.5281/zenodo.18763676 |