{"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_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_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_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_n_462dd2ad643c", "title": "Devotional: Insight: The Ephraim Gate", "shelf": "codex", "surface": "witness", "snippet": "Be careful which gates you open. God may be warning you to close off partnerships, habits, or voices that look like allies but are walking in rebellion. If you don't close the gate when He says to — i"}, {"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_n_c3203934b80d", "title": "Pilgrim's Progress §54: First, Thou must abhor his turning thee out of the way; and thine own consenting thereu...", "shelf": "classics", "surface": "secular", "snippet": "First, Thou must abhor his turning thee out of the way; and thine own consenting thereunto: because this is to reject the counsel of God for the sake of the counsel of a Worldly Wiseman. The Lord says"}, {"id": "card_n_fbfa0cbf408e", "title": "Easton: Gate", "shelf": "dictionary", "surface": "secular", "snippet": "(1.) Of cities, as of Jerusalem (Jer. 37:13; Neh. 1:3; 2:3; 3:3), of Sodom (Gen. 19:1), of Gaza (Judg. 16:3). (2.) Of royal palaces (Neh. 2:8). (3.) Of the temple of Solomon (1 Kings 6:34, 35; 2 Kings"}, {"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_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_17f4f305d575", "title": "1 Clement XLVIII", "shelf": "patristics", "surface": "witness", "snippet": "Let us therefore, with all haste, put an end to this [state of things]; and let us fall down before the Lord, and beseech Him with tears, that He would mercifully be reconciled to us, and restore us t"}, {"id": "card_c_f9c8bfe7d300", "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 ... references Mount", "shelf": "connections", "surface": null, "snippet": "Mentions Mount (place) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a place."}, {"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_n_5eec328f0690", "title": "Pilgrim's Progress §308: IGNOR.", "shelf": "classics", "surface": "secular", "snippet": "IGNOR. Sir, I was born in the country that lieth off there a little on the left hand, and I am going to the Celestial City. CHR. But how do you think to get in at the gate? for you may find some diffi"}, {"id": "card_n_c92345e93f03", "title": "Pilgrim's Progress §403: Now while I was gazing upon all these things, I turned my head to look back, and saw Ig...", "shelf": "classics", "surface": "secular", "snippet": "Now while I was gazing upon all these things, I turned my head to look back, and saw Ignorance come up to the river side; but he soon got over, and that without half that difficulty which the other tw"}, {"id": "card_n_06500baac3c0", "title": "Pilgrim's Progress §60: \"He that will enter in must first without Stand knocking at the Gate, nor need he doubt...", "shelf": "classics", "surface": "secular", "snippet": "\"He that will enter in must first without Stand knocking at the Gate, nor need he doubt That is A KNOCKER but to enter in; For God can love him, and forgive his sin.\" He knocked, therefore, more than "}, {"id": "card_n_5d1c28bd4ea5", "title": "Logarithms — multiplication made addition, and the grammar of the senses", "shelf": "science", "surface": "secular", "snippet": "The logarithm turns multiplication into addition: log(15) = log(3)+log(5), sealed. That\none property made calculation possible before computers (Napier 1614 -> slide rules -> every\nengineer until 1970"}, {"id": "card_n_39dc3d761434", "title": "Recycling — nothing is lost, the parts are rebuilt", "shelf": "science", "surface": "secular", "snippet": "When a word stops serving, it is broken down and its parts build new words (Matt's\nobservation, and it is exactly right). Real linguistics: 'hamburger' (Hamburg + er) was\nreanalyzed into '-burger' -> "}, {"id": "card_n_2db0ba0e16e5", "title": "Easton: Beautiful gate", "shelf": "dictionary", "surface": "secular", "snippet": "The name of one of the gates of the temple (Acts 3:2). It is supposed to have been the door which led from the court of the Gentiles to the court of the women. It was of massive structure, and covered"}]}