{"query": "Capacitor — the exponential clock (RC time constant)", "count": 20, "results": [{"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_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_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_c_5592b5e8c1e7", "title": "Logarithms — multiplication made addition, a ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "it is the exact INVERSE of the exponential that is the spine of this whole map: the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm"}, {"id": "card_c_26c735e9dff1", "title": "Glottochronology — carbon-dating the words ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "Words decay by RATIO, like atoms, like a capacitor, like everything on the exponential spine.  — a concord the card itself states; mined + verified."}, {"id": "card_src_word_spacecraft_clock_time", "title": "spacecraft clock time", "shelf": "dictionary", "surface": "secular", "snippet": "spacecraft clock time: (noun) the clock time given by a clock carried on board a spacecraft — syn: SCLK"}, {"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_src_word_time_clock", "title": "time clock", "shelf": "dictionary", "surface": "secular", "snippet": "time clock: (noun) clock used to record the hours that people work"}, {"id": "card_n_770170ab1111", "title": "The linguistic clock — the comparative method dates the dispersal", "shelf": "science", "surface": "secular", "snippet": "The same history is written in the words. The comparative method reconstructs ancestral\ntongues from their daughters (sealed in the language-evolution wing), and glottochronology's\nexponential vocabul"}, {"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_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_c_b71d6ddb4a46", "title": "Logarithms — multiplication made addition, a ↔ Radioactive decay — the exponential clock of", "shelf": "connections", "surface": null, "snippet": "it is the exact INVERSE of the exponential that is the spine of this whole map: the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm"}, {"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_src_word_clock", "title": "clock", "shelf": "dictionary", "surface": "secular", "snippet": "clock: (noun) a timepiece that shows the time of day · (verb) measure the time or duration of an event or action or the person who performs an action in a certain period of time — syn: time"}, {"id": "card_n_b10117556d41", "title": "The two clocks — quartz, cesium, and the second", "shelf": "science", "surface": "secular", "snippet": "The wrist clock and the world clock. Quartz beats 32,768 times a second; the SI second is\nDEFINED as 9,192,631,770 oscillations of cesium-133's hyperfine transition (since 1967) —\nsealed: the cesium c"}, {"id": "card_src_word_digital_clock", "title": "digital clock", "shelf": "dictionary", "surface": "secular", "snippet": "digital clock: (noun) a clock that displays the time of day digitally"}, {"id": "card_n_ccbf2a23f514", "title": "Augustine, Confessions §aug_conf_11_018: And yet we say, \"a long time\" and \"a short time\"; still, only of time past or...", "shelf": "classics", "surface": "witness", "snippet": "And yet we say, \"a long time\" and \"a short time\"; still, only of time past or to come. A long time past (for example) we call an hundred years since; and a long time to come, an hundred years hence. B"}, {"id": "card_src_word_analog_clock", "title": "analog clock", "shelf": "dictionary", "surface": "secular", "snippet": "analog clock: (noun) a clock that displays the time of day by the position of hands on a dial"}, {"id": "card_src_word_time_constant", "title": "time constant", "shelf": "dictionary", "surface": "secular", "snippet": "time constant: (noun) (electronics) the time required for the current or voltage in a circuit to rise or fall exponentially through approximately 63 per cent of its amplitude · (noun) the ratio of the"}, {"id": "card_n_4e743297cf2f", "title": "Augustine, Confessions §aug_conf_11_017: At no time then hadst Thou not made any thing, because time itself Thou madest.", "shelf": "classics", "surface": "witness", "snippet": "At no time then hadst Thou not made any thing, because time itself Thou madest. And no times are coeternal with Thee, because Thou abidest; but if they abode, they should not be times. For what is tim"}]}