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Per-claim provenance."}],"not_medical_advice":true},"slug":"schools","title":"The Schools: 64 Research Programs That Converged on the Grain","register":"grain","tags":["grain","philosophy","schools","convergence","encyclopedia"],"updated_at":"2026-07-04T18:59:49.511Z","body_excerpt":"PART 2: THE SCHOOLS — PHYSICAL & FORMAL SCIENCES\n2.1 Physics & Cosmology\nClassical Mechanics\nFounder(s): Isaac Newton (Philosophiæ Naturalis Principia Mathematica, 1687); Joseph-Louis Lagrange (Mécanique Analytique, 1788); William Rowan Hamilton (Hamilton’s equations, 1833)\nCore claim: Bodies follow paths determined by extremal principles — least action governs motion\nConvergence patterns: C02 (least action), C03 (symmetry-conservation via Noether’s later theorem applied to Lagrangians), C07 (Hamiltonian dynamics as homeostatic flow on phase space)\nIndependence check: Derived from celestial mechanics and billiard-ball collisions — independent of thermodynamics or biology by >150 years\nClaim tier: T0 — empirically confirmed to 10^-17 precision (LIGO, lunar ranging)\nKey tension: Hamiltonian mechanics is time-reversible; contradicts C01 (gradient dissipation) which is irreversible. The arrow-of-time problem remains open\nCanonical text: Landau & Lifshitz, Mechanics (1960), Ch. 1-2 on least action\nElectromagnetism\nFounder(s): James Clerk Maxwell (A Treatise on Electricity and Magnetism, 1873); consolidated by Heaviside into four equations\nCore claim: Electric and magnetic fields are one unified field whose dynamics are governed by charge conservation and Lorentz invariance\nConvergence patterns: C02 (Maxwell’s equations derive from least action), C03 (gauge symmetry → charge conservation, Noether), C14 (wave-particle duality of electromagnetic radiation), C18 (waves as fundamental excitation)\nIndependence check: Independent — emerged from experimental work on static electricity, magnetism, and optics, not from mechanics or thermodynamics\nClaim tier: T0 — quantum electrodynamics most precisely confirmed theory in physics (g-2 to 10^-10)\nKey tension: Maxwell’s equations are time-symmetric (microscopic reversibility); contradicts the macroscopic irreversibility of C01 and thermodynamics\nCanonical text: Jackson, Classical Electrodynamics (3rd ed., 1999), Ch. 11 on gauge invariance\nThermodynamics\nFounder(s): Sadi Carnot (Réflexions sur la Puissance Motrice du Feu, 1824); Rudolf Clausius (entropy, 1865); Ludwig Boltzmann (S = k log W, 1877); J. Willard Gibbs (On the Equilibrium of Heterogeneous Substances, 1876)\nCore claim: Energy is conserved; entropy of isolated systems increases monotonically to a maximum\nConvergence patterns: C01 (gradient dissipation — heat flows down temperature gradients), C06 (entropy as information/missing knowledge), C07 (equilibrium as homeostasis)\nIndependence check: Independent — Carnot was an engineer studying steam engines, not doing fundamental physics. Clausius synthesized from heat-engine experiments\nClaim tier: T0 — no violations of 1st/2nd law ever observed\nKey tension: Boltzmann’s probabilistic interpretation of entropy vs. Gibbs’ ensemble view creates tension with quantum measurement. Also: Loschmidt’s paradox — time-symmetric microdynamics vs. time-asymmetric macro-entropy\nCanonical text: Gibbs, Elementary Principles in Statistical Mechanics (1902), Ch. 1-4 on ensemble theory\nSpecial & General Relativity\nFounder(s): Albert Einstein (“On the Electrodynamics of Moving Bodies,” 1905; “The Field Equations of Gravitation,” 1915); contributions from Lorentz, Poincaré, Minkowski, Hilbert\nCore claim: Spacetime is a dynamical geometry; the speed of light is invariant; gravity is curvature\nConvergence patterns: C02 (Einstein-Hilbert action is a least-action principle), C03 (general covariance → energy-momentum conservation), C10 (scale invariance in certain limits), C14 (duality between mass and energy, E=mc²)\nIndependence check: Independent — Einstein was a patent clerk reasoning about light signals, not building on thermodynamics or biology\nClaim tier: T0 — GPS corrections require GR daily; black hole imaging confirms predictions\nKey tension: GR is deterministic and local; QM is probabilistic and nonlocal. 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