{"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_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_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_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_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_268b55a98977", "title": "The carbon clock resonates with the capacitor's RC clock", "shelf": "connections", "surface": null, "snippet": "One exponential, two substrates — matter's decay and the bench's discharge. RESONANCE: a map-aid, never a proof of unity."}, {"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_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"}, {"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_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_534611934a3f", "title": "Augustine, Confessions §aug_conf_11_031: Dost Thou bid me assent, if any define time to be \"motion of a body?\" Thou do...", "shelf": "classics", "surface": "witness", "snippet": "Dost Thou bid me assent, if any define time to be \"motion of a body?\" Thou dost not bid me. For that no body is moved, but in time, I hear; this Thou sayest; but that the motion of a body is time, I h"}, {"id": "card_n_8a1d7924121c", "title": "The genetic clock — mitochondrial Eve and the molecular record", "shelf": "science", "surface": "secular", "snippet": "Mitochondrial DNA passes only mother to child and never recombines, so it is a clean\nmaternal lineage; the Y chromosome does the same for fathers. Mutations accumulate at a roughly\nsteady rate, so cou"}, {"id": "card_n_e8186ce33d19", "title": "GPS (UHF) — a constellation of clocks at 19 centimeters", "shelf": "science", "surface": "secular", "snippet": "L1 = 154 × 10.23 MHz = 1575.42 MHz EXACTLY — the whole system is integer multiples of\none 10.23 MHz atomic clock; sealed, with the 19 cm wavelength: https://narrowhighway.com/s/d6211f4efb2518c6de145de"}, {"id": "card_n_0a41c0e3298d", "title": "Pheromones — the molecule is the message", "shelf": "science", "surface": "secular", "snippet": "A pheromone is chemistry acting as language: a molecule IS a signal. Sealed: a\n20-component blend encodes 2^20 = 1,048,576 distinguishable messages (~4.3 bits per component),\nand an ant's trail evapor"}, {"id": "card_c_3b3121f3e55d", "title": "The genetic clock is read from the genome", "shelf": "connections", "surface": null, "snippet": "mtDNA and Y lineages, dated by the molecular clock."}, {"id": "card_n_2f05f5f9c92e", "title": "Augustine, Confessions §aug_conf_11_033: Does not my soul most truly confess unto Thee, that I do measure times?", "shelf": "classics", "surface": "witness", "snippet": "Does not my soul most truly confess unto Thee, that I do measure times? Do I then measure, O my God, and know not what I measure? I measure the motion of a body in time; and the time itself do I not m"}, {"id": "card_n_202888449903", "title": "Augustine, Confessions §aug_conf_11_016: Nor dost Thou by time, precede time: else shouldest Thou not precede all times.", "shelf": "classics", "surface": "witness", "snippet": "Nor dost Thou by time, precede time: else shouldest Thou not precede all times. But Thou precedest all things past, by the sublimity of an ever-present eternity; and surpassest all future because they"}, {"id": "card_n_d8471389950e", "title": "Tracing the peoples — genes and words, two clocks reading one history", "shelf": "science", "surface": "secular", "snippet": "A people can be traced across DISTANCE and TIME by two records that survive in the body and\nin the mouth: the genome and the language. They are the same method — a molecular clock ticking,\na tree bran"}, {"id": "card_n_8b7feef8497c", "title": "Easton: Scripture", "shelf": "dictionary", "surface": "secular", "snippet": "Invariably in the New Testament denotes that definite collection of sacred books, regarded as given by inspiration of God, which we usually call the Old Testament (2 Tim. 3:15, 16; John 20:9; Gal. 3:2"}]}