{"query": "Diode — the exponential gate", "count": 20, "results": [{"id": "card_n_0fa594da0bff", "title": "Diode — the exponential gate", "shelf": "science", "surface": "secular", "snippet": "The diode's current grows exponentially with voltage; sealed exactly: e^(x+ln2) = 2e^x —\ncurrent DOUBLES for every ln2·nVT of forward voltage, ≈ 17.9 mV at room temperature (sealed:\nfloor(10⁴·ln2·0.02"}, {"id": "card_n_cdb747a427d2", "title": "Electronics — the resonant chain, from Ohm's law to the radio wave", "shelf": "science", "surface": "secular", "snippet": "One sealed chain runs the whole bench: Ohm's law (V = I·R), the capacitor's\nexponential clock (one time constant → 63.2% charged), the diode's exponential gate (current\ndoubles every ln2·nVT ≈ 17.9 mV"}, {"id": "card_c_2ae5fa072760", "title": "Diode — the exponential gate ↔ Electronics — the resonant chain, from Ohm's", "shelf": "connections", "surface": null, "snippet": "That knife-edge nonlinearity is why a diode can rectify — turn a symmetric radio wave into a one-way signal.  — a concord the card itself states; mined + verified."}, {"id": "card_c_547436596e63", "title": "Diode — the exponential gate ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "The diode's current grows exponentially with voltage; sealed exactly: e^(x+ln2) = 2e^x — current DOUBLES for every ln2·nVT of forward voltage  — a concord the card itself states; mined + verified."}, {"id": "card_c_49411cccab5a", "title": "Logarithms — multiplication made addition, a ↔ Diode — the exponential gate", "shelf": "connections", "surface": null, "snippet": "the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm brings them back by adding.  — a concord the card itself states; mined + verifi"}, {"id": "card_n_7bf587a27c24", "title": "Sermon on the Mount §som_17_the_narrow_gate: \"Enter in by the narrow gate; for wide is the gate and broad is the way that ...", "shelf": "codex", "surface": "witness", "snippet": "\"Enter in by the narrow gate; for wide is the gate and broad is the way that leads to destruction, and many are those who enter in by it. How narrow is the gate, and restricted is the way that leads t"}, {"id": "card_c_01a2b706782a", "title": "Radioactive decay — the exponential clock of ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "The same exponential that discharges a capacitor empties a nucleus's odds — the bench's RC clock and the carbon clock are one curve wearing different constants.  — a concord the card itself states; mi"}, {"id": "card_history_the_witness_gate", "title": "The witness gate — how the events of history are established", "shelf": "history", "surface": "secular", "snippet": "History cannot go through the same gate as mathematics and physics: you cannot SEAL that the Battle of Hastings occurred the way you seal 2+2=4. History has two layers. Its SKELETON — the dates and th"}, {"id": "card_n_36048aaa9a1b", "title": "Glottochronology — carbon-dating the words", "shelf": "science", "surface": "secular", "snippet": "Swadesh (1950s): a language's CORE vocabulary — the 100-200 most basic words (mother,\nwater, two, hand) — is replaced at a roughly constant rate, so its loss is EXPONENTIAL:\nretention r^t with r about"}, {"id": "card_n_6f5aa0b22245", "title": "Capacitor — the exponential clock (RC time constant)", "shelf": "science", "surface": "secular", "snippet": "A capacitor charging through a resistor follows V(t) = V·(1 − e^(−t/RC)); after one\ntime constant τ = RC it holds exactly 1 − 1/e ≈ 63.2% of the supply — sealed in-domain\n(1000 Ω × 1000 µF = 1 s; 5 V "}, {"id": "card_src_hist_q112016", "title": "Battle of the Persian Gate on the Mountain (-0329)", "shelf": "history", "surface": "secular", "snippet": "Battle of the Persian Gate on the Mountain — battle between Alexander the Great and Ariobarzanes near Persepolis in a small mountainpass known as the Persian gate along the Royal road. A battle, -0329"}, {"id": "card_src_book_66466", "title": "The corsair; a romantic legend of Hell Gate illustrating the beauty of innocence. Date of the action: Midsummer, 1627 — William Barney Allen", "shelf": "gutenberg", "surface": "secular", "snippet": "The corsair; a romantic legend of Hell Gate illustrating the beauty of innocence. Date of the action: Midsummer, 1627, by William Barney Allen. Subjects: Narrative poetry, American; Hell Gate (New Yor"}, {"id": "card_n_cfb57dd6b005", "title": "Radioactive decay — the exponential clock of matter", "shelf": "science", "surface": "secular", "snippet": "Sealed in-domain: after one half-life exactly half remains; after two, exactly one\nquarter (2^(−2) = 1/4, exact); carbon-14's decay constant is ln2/5730 years = 3.833×10⁻¹²\nper second: https://narrowh"}, {"id": "card_n_cca3b515028a", "title": "Pilgrim's Progress §399: Then I saw in my dream that the Shining Men bid them call at the gate; the which, when ...", "shelf": "classics", "surface": "secular", "snippet": "Then I saw in my dream that the Shining Men bid them call at the gate; the which, when they did, some looked from above over the gate, to wit, Enoch, Moses, and Elijah, &c., to whom it was said, These"}, {"id": "card_c_6b353b6912b0", "title": "The logarithm inverts the capacitor's exponential clock", "shelf": "connections", "surface": null, "snippet": "Exponential rises by multiplying; the logarithm returns by adding. One law, two directions."}, {"id": "card_c_77ba6d7691ca", "title": "Pheromones — the molecule is the message ↔ Radioactive decay — the exponential clock of", "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_bfd4a1bca8d5", "title": "Easton: Shallecheth, The gate of", "shelf": "dictionary", "surface": "secular", "snippet": "I.e., “the gate of casting out,” hence supposed to be the refuse gate; one of the gates of the house of the Lord, “by the causeway of the going up” i.e., the causeway rising up from the Tyropoeon vall"}, {"id": "card_src_book_49030", "title": "The Motor Boat Club at the Golden Gate; or, A Thrilling Capture in the Great Fog — H. Irving (Harrie Irving) Hancock", "shelf": "gutenberg", "surface": "secular", "snippet": "The Motor Boat Club at the Golden Gate; or, A Thrilling Capture in the Great Fog, by H. Irving (Harrie Irving) Hancock. Subjects: Motorboats -- Juvenile fiction; Golden Gate (Calif. : Strait) -- Juven"}, {"id": "card_n_dfe230563b45", "title": "Mordecai at the Gate", "shelf": "reference", "surface": "secular", "snippet": "Sits at the gate; uncovers the assassination plot; refuses to bow to Haman; condemned to the gallows Haman built; on a sleepless night the king reads the chronicles and Mordecai is honored; eventually"}, {"id": "card_src_book_32355", "title": "With the Children on Sundays Through Eye-Gate and Ear-Gate into the City of Child-Soul — Sylvanus Stall", "shelf": "gutenberg", "surface": "secular", "snippet": "With the Children on Sundays Through Eye-Gate and Ear-Gate into the City of Child-Soul, by Sylvanus Stall. Subjects: Moral education; Children's sermons; Children -- Religious life. Read the full text"}]}