{"query": "Laplace — the map's dynamics (decay/growth), beyond the stea", "count": 20, "results": [{"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_c_c124e6b5460c", "title": "Universal Gradient Manifold (UGM) — a heat-s ↔ Laplace — the map's dynamics (decay/growth),", "shelf": "connections", "surface": null, "snippet": "the gradient is the Laplace/rate-of-descent  — a concord the card itself states; mined + verified."}, {"id": "card_src_word_laplace", "title": "laplace", "shelf": "dictionary", "surface": "secular", "snippet": "laplace: (noun) French mathematician and astronomer who formulated the nebular hypothesis concerning the origins of the solar system and who developed the theory of probability (1749-1827) — syn: Marq"}, {"id": "card_src_word_marquis_de_laplace", "title": "marquis de laplace", "shelf": "dictionary", "surface": "secular", "snippet": "marquis de laplace: (noun) French mathematician and astronomer who formulated the nebular hypothesis concerning the origins of the solar system and who developed the theory of probability (1749-1827) "}, {"id": "card_src_word_pierre_simon_de_laplace", "title": "pierre simon de laplace", "shelf": "dictionary", "surface": "secular", "snippet": "pierre simon de laplace: (noun) French mathematician and astronomer who formulated the nebular hypothesis concerning the origins of the solar system and who developed the theory of probability (1749-1"}, {"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_src_word_economic_growth", "title": "economic growth", "shelf": "dictionary", "surface": "secular", "snippet": "economic growth: (noun) steady growth in the productive capacity of the economy (and so a growth of national income)"}, {"id": "card_src_word_growth_hormone", "title": "growth hormone", "shelf": "dictionary", "surface": "secular", "snippet": "growth hormone: (noun) a hormone produced by the anterior pituitary gland; promotes growth in humans — syn: somatotropin, somatotrophin, somatotropic hormone, somatotrophic hormone, STH, human growth "}, {"id": "card_src_word_human_growth_hormone", "title": "human growth hormone", "shelf": "dictionary", "surface": "secular", "snippet": "human growth hormone: (noun) a hormone produced by the anterior pituitary gland; promotes growth in humans — syn: somatotropin, somatotrophin, somatotropic hormone, somatotrophic hormone, STH, growth "}, {"id": "card_src_book_46481", "title": "The Turkish Empire, Its Growth and Decay — G. Shaw-Lefevre (George Shaw-Lefevre), Baron Eversley", "shelf": "gutenberg", "surface": "secular", "snippet": "The Turkish Empire, Its Growth and Decay, by G. Shaw-Lefevre (George Shaw-Lefevre), Baron Eversley. Subjects: Turkey -- History. Read the full text (public domain): https://www.gutenberg.org/ebooks/46"}, {"id": "card_src_book_55264", "title": "On Growth and Form — D'Arcy Wentworth Thompson", "shelf": "gutenberg", "surface": "secular", "snippet": "On Growth and Form, by D'Arcy Wentworth Thompson. Subjects: Morphology (Animals); Growth. Read the full text (public domain): https://www.gutenberg.org/ebooks/55264"}, {"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_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_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_src_word_growth_rate", "title": "growth rate", "shelf": "dictionary", "surface": "secular", "snippet": "growth rate: (noun) the rate of increase in size per unit time — syn: rate of growth"}, {"id": "card_src_word_nerve_growth_factor", "title": "nerve growth factor", "shelf": "dictionary", "surface": "secular", "snippet": "nerve growth factor: (noun) a protein that is involved in the growth of peripheral nerve cells — syn: NGF"}, {"id": "card_src_word_growth_hormone_releasing_factor", "title": "growth hormone-releasing factor", "shelf": "dictionary", "surface": "secular", "snippet": "growth hormone-releasing factor: (noun) a releasing factor that accelerates the secretion of growth hormone by the anterior pituitary body — syn: GHRF"}, {"id": "card_n_84ee70059175", "title": "The map's axes are its spectral modes (the Fourier lens)", "shelf": "concepts", "surface": "secular", "snippet": "Fourier's move — decompose a whole into the few fundamental modes that generate it — generalized off the regular cycle (where the FFT lives) to the map: the EIGENMODES of the dimension correlation mat"}]}