{"query": "Fluid dynamics as the behavior of the axes", "count": 20, "results": [{"id": "card_n_ff27b07c4577", "title": "Fluid dynamics as the behavior of the axes", "shelf": "concepts", "surface": "secular", "snippet": "Matt: 'Fluid dynamics as behavior of axes? something along that line.' The axes are not static — they FLOW and redistribute as the map grows. Fluid dynamics may describe their behavior: a turbulent fl"}, {"id": "card_c_108666f40f9f", "title": "Fluid probability dynamics resonates with Fluid dynamics of the axes", "shelf": "connections", "surface": null, "snippet": "Same conserved-flow skeleton, read on the map's own axes — RESONANCE, a map-aid not a proof."}, {"id": "card_n_8530c72a2201", "title": "Fluid probability dynamics — one continuity equation across physics, geometry, and ML", "shelf": "science", "surface": "secular", "snippet": "One equation wears many clothes. Probability is a conserved fluid: the continuity equation\ndρ/dt + ∇·J = 0 (current J = ρv) says density is never created or destroyed — it only flows. The\nsame skeleto"}, {"id": "card_c_576d28632055", "title": "Madelung hydrodynamics instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "Quantum mechanics rewritten as the fluid dynamics of |ψ|²."}, {"id": "card_n_810d857d886e", "title": "Madelung hydrodynamics — quantum mechanics as a probability fluid", "shelf": "science", "surface": "secular", "snippet": "Write ψ = √ρ·e^(iS/ħ) and the Schrödinger equation becomes fluid dynamics of the probability\ndensity ρ = |ψ|²: a continuity equation with velocity v = ∇S/m, plus an Euler equation carrying a\n'quantum "}, {"id": "card_c_e655b3fcef54", "title": "Optimal transport instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "The geometry of moving probability — Fokker–Planck as a Wasserstein gradient flow."}, {"id": "card_c_41cd8b933961", "title": "Fluid probability dynamics — one continuity  ↔ Madelung hydrodynamics — quantum mechanics a", "shelf": "connections", "surface": null, "snippet": "quantum mechanics (Madelung: v = ∇S/m plus a quantum potential — the Schrödinger equation rewritten as fluid dynamics of |ψ|²)  — a concord the card itself states; mined + verified."}, {"id": "card_c_3cc9f3e8e74f", "title": "Fokker–Planck & Liouville instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "Statistical mechanics is the stochastic instance of the probability-continuity equation."}, {"id": "card_c_3437884ad1bb", "title": "Fluid probability dynamics related to the spectral (Fourier) lens", "shelf": "connections", "surface": null, "snippet": "Fourier eigenmodes of the Laplacian are exactly how the diffusion/continuity operator is solved."}, {"id": "card_c_e510a4e8b7f4", "title": "Diffusion models instantiate Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "The probability-flow ODE is the same continuity equation with a learned velocity."}, {"id": "card_c_c1d4f07c75cd", "title": "Fokker–Planck & Liouville — probability flow ↔ Fluid probability dynamics — one continuity ", "shelf": "connections", "surface": null, "snippet": "The stochastic instantiation of probability-as-fluid. ... In Hamiltonian phase space, Liouville's theorem gives dρ/dt = 0 — the probability fluid is incompressible.  — a concord the card itself states"}, {"id": "card_src_word_dynamics", "title": "dynamics", "shelf": "dictionary", "surface": "secular", "snippet": "dynamics: (noun) the branch of mechanics concerned with the forces that cause motions of bodies — syn: kinetics"}, {"id": "card_src_word_group_dynamics", "title": "group dynamics", "shelf": "dictionary", "surface": "secular", "snippet": "group dynamics: (noun) the branch of social psychology that studies the psychodynamics of interaction in social groups"}, {"id": "card_n_88ac7219a4a9", "title": "Laplace — the map's dynamics (decay/growth), beyond the steady spectrum", "shelf": "concepts", "surface": "secular", "snippet": "Matt: 'laplace transform ... missing.' Fourier gives the STEADY spectrum (the imaginary axis); Laplace adds the REAL axis s=sigma+i*omega — decay/growth RATES. The map's eigenvalue spectrum decays EXP"}, {"id": "card_src_word_behaviour", "title": "behaviour", "shelf": "dictionary", "surface": "secular", "snippet": "behaviour: (noun) the action or reaction of something (as a machine or substance) under specified circumstances — syn: behavior · (noun) (behavioral attributes) the way a person behaves toward other p"}, {"id": "card_k_floor_of_discovery", "title": "The Floor of Discovery — one floor, and by its design the fear of God", "shelf": "codex", "surface": "witness", "snippet": "Seeds of knowledge — identified, categorized, and mapped — form a floor of reality. The Bible and physical reality are unified as the floor of all discovery: Special Revelation and General Revelation "}, {"id": "card_n_23ddfa0652b0", "title": "Easton: Acts of the Apostles", "shelf": "dictionary", "surface": "secular", "snippet": "The title now given to the fifth and last of the historical books of the New Testament. The author styles it a “treatise” (1:1). It was early called “The Acts,” “The Gospel of the Holy Ghost,” and “Th"}, {"id": "card_n_329e521d766b", "title": "Aurelius, Meditations §aur_06_xxxiii: Asia, Europe; what are they, but as corners of the whole world; of which the ...", "shelf": "classics", "surface": "secular", "snippet": "Asia, Europe; what are they, but as corners of the whole world; of which the whole sea, is but as one drop; and the great Mount Athos, but as a clod, as all present time is but as one point of eternit"}, {"id": "card_c_1650c345cc7d", "title": "Pheromones — the molecule is the message ↔ Fluid probability dynamics — one continuity ", "shelf": "connections", "surface": null, "snippet": "Pheromones DIFFUSE down a gradient (the continuity/diffusion equation) and DECAY (the exponential clock) — the fluid and the clock of this whole map, carried in a scent.  — a concord the card itself s"}, {"id": "card_n_28bcf3faffe1", "title": "Easton: Assyria", "shelf": "dictionary", "surface": "secular", "snippet": "The name derived from the city Asshur on the Tigris, the original capital of the country, was originally a colony from Babylonia, and was ruled by viceroys from that kingdom. It was a mountainous regi"}]}