{"query": "Optimal transport — the geometry of moving probability", "count": 20, "results": [{"id": "card_n_d59ca677ea24", "title": "Optimal transport — the geometry of moving probability", "shelf": "science", "surface": "secular", "snippet": "Benamou–Brenier: the distance between two distributions is the least kinetic energy of a\nfluid that carries one to the other, subject to the continuity equation. Jordan–Kinderlehrer–Otto\n(1998): the F"}, {"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_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_n_05e4265f7048", "title": "Easton: Astronomy", "shelf": "dictionary", "surface": "secular", "snippet": "The Hebrews were devout students of the wonders of the starry firmanent (Amos 5:8; Ps. 19). In the Book of Job, which is the oldest book of the Bible in all probability, the constellations are disting"}, {"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_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_n_23af767b615c", "title": "Augustine, Confessions §aug_conf_13_025: Let the sea also conceive and bring forth your works; and let the waters brin...", "shelf": "classics", "surface": "witness", "snippet": "Let the sea also conceive and bring forth your works; and let the waters bring forth the moving creature that hath life. For ye, separating the precious from the vile, are made the mouth of God, by wh"}, {"id": "card_n_953993475f68", "title": "Easton: Ahasuerus", "shelf": "dictionary", "surface": "secular", "snippet": "There are three kings designated by this name in Scripture. (1.) The father of Darius the Mede, mentioned in Dan. 9:1. This was probably the Cyaxares I. known by this name in profane history, the king"}, {"id": "card_n_8b46004c8d35", "title": "Easton: Matthew, Gospel according to", "shelf": "dictionary", "surface": "secular", "snippet": "The author of this book was beyond a doubt the Matthew, an apostle of our Lord, whose name it bears. He wrote the Gospel of Christ according to his own plans and aims, and from his own point of view, "}, {"id": "card_n_597705b0c9c4", "title": "Easton: Sodom", "shelf": "dictionary", "surface": "secular", "snippet": "Burning; the walled, a city in the vale of Siddim (Gen. 13:10; 14:1-16). The wickedness of its inhabitants brought down upon it fire from heaven, by which it was destroyed (18:16-33; 19:1-29; Deut. 23"}, {"id": "card_n_475b8a5ff733", "title": "Easton: Ramoth-gilead", "shelf": "dictionary", "surface": "secular", "snippet": "Heights of Gilead, a city of refuge on the east of Jordan; called “Ramoth in Gilead” (Deut. 4:43; Josh. 20:8; 21:38). Here Ahab, who joined Jehoshaphat in an endeavour to rescue it from the hands of t"}, {"id": "card_n_97056886d636", "title": "Easton: Gourd", "shelf": "dictionary", "surface": "secular", "snippet": "(1.) Jonah’s gourd (Jonah 4:6-10), bearing the Hebrew name kikayon (found only here), was probably the kiki of the Egyptians, the croton. This is the castor-oil plant, a species of ricinus, the palma "}, {"id": "card_n_041763374eca", "title": "Fokker–Planck & Liouville — probability flow in statistical mechanics", "shelf": "science", "surface": "secular", "snippet": "The stochastic instantiation of probability-as-fluid. Fokker–Planck sets the current\nJ = μρ − D∇ρ (drift + diffusion); its steady state is the Boltzmann distribution ρ ∝ e^(−U/kT),\nwhich makes the cur"}, {"id": "card_n_3e92bb4efc83", "title": "Easton: Ammonite", "shelf": "dictionary", "surface": "secular", "snippet": "The usual name of the descendants of Ammon, the son of Lot (Gen. 19:38). From the very beginning (Deut. 2:16-20) of their history till they are lost sight of (Judg. 5:2), this tribe is closely associa"}, {"id": "card_n_28fe3610901c", "title": "Easton: En-rogel", "shelf": "dictionary", "surface": "secular", "snippet": "Fountain of the treaders; i.e., “foot-fountain;” also called the “fullers’ fountain,” because fullers here trod the clothes in water. It has been identified with the “fountain of the virgin” (q.v.), t"}, {"id": "card_n_2be7f1c3f6e9", "title": "Diffusion models — the probability-flow ODE behind generative AI", "shelf": "science", "surface": "secular", "snippet": "Score-based generative models noise data toward a Gaussian and learn to reverse it. The\n'probability-flow ODE' is the deterministic fluid whose time-marginals match the noising SDE — the\nsame continui"}, {"id": "card_n_7672e1661e23", "title": "Easton: Thessalonians, Epistles to the", "shelf": "dictionary", "surface": "secular", "snippet": "The first epistle to the Thessalonians was the first of all Paul’s epistles. It was in all probability written from Corinth, where he abode a “long time” (Acts 18:11, 18), early in the period of his r"}, {"id": "card_n_5dad79052507", "title": "Easton: Sinai", "shelf": "dictionary", "surface": "secular", "snippet": "Of Sin (the moon god), called also Horeb, the name of the mountain district which was reached by the Hebrews in the third month after the Exodus. Here they remained encamped for about a whole year. Th"}, {"id": "card_n_e61093f42291", "title": "Easton: Hermon", "shelf": "dictionary", "surface": "secular", "snippet": "A peak, the eastern prolongation of the Anti-Lebanon range, reaching to the height of about 9,200 feet above the Mediterranean. It marks the north boundary of Palestine (Deut. 3:8, 4:48; Josh. 11:3, 1"}, {"id": "card_n_d7028bf21d3f", "title": "The Pressure Architecture — Plane Definition", "shelf": "domains", "surface": "secular", "snippet": "Continuously define the plane.\nControl orientation and leverage geometry.\nThe fighter who defines the plane defines reality.\n\nThe plane is not a fixed surface — it is wherever you establish structural"}]}