{"query": "Radioactive decay — the exponential clock of matter", "count": 20, "results": [{"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_c3ca8e5c3a1f", "title": "Augustine, Confessions §aug_conf_13_047: Let Thy works praise Thee, that we may love Thee; and let us love Thee, that ...", "shelf": "classics", "surface": "witness", "snippet": "Let Thy works praise Thee, that we may love Thee; and let us love Thee, that Thy works may praise Thee, which from time have beginning and ending, rising and setting, growth and decay, form and privat"}, {"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_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_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_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_bbecbbc24fb6", "title": "The nucleus — the strongest glue and the slowest clocks", "shelf": "science", "surface": "secular", "snippet": "Past gamma rays the spectrum ends and the nucleus itself begins. One chain,\neight steps, sealed — four of them IN-DOMAIN by the nuclear fleet: https://narrowhighway.com/s/8a5e89ab13bc499f39240c64360d9"}, {"id": "card_c_60eaf1dc310a", "title": "The logarithm inverts radioactive decay", "shelf": "connections", "surface": null, "snippet": "Half-life is a logarithm of the surviving fraction — the carbon clock read backward."}, {"id": "card_n_4dae2cc029a5", "title": "Augustine, Confessions §aug_conf_12_030: For should any attempt to dispute against these two last opinions, thus, \"If ...", "shelf": "classics", "surface": "witness", "snippet": "For should any attempt to dispute against these two last opinions, thus, \"If you will not allow, that this formlessness of matter seems to be called by the name of heaven and earth; Ergo, there was so"}, {"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_88ac7219a4a9", "title": "Laplace — the map's dynamics (decay/growth), beyond the steady spectrum", "shelf": "concepts", "surface": "secular", "snippet": "Matt: 'laplace transform ... missing.' Fourier gives the STEADY spectrum (the imaginary axis); Laplace adds the REAL axis s=sigma+i*omega — decay/growth RATES. The map's eigenvalue spectrum decays EXP"}, {"id": "card_n_efd92dd5f79e", "title": "Easton: Luke, Gospel according to", "shelf": "dictionary", "surface": "secular", "snippet": "Was written by Luke. He does not claim to have been an eye-witness of our Lord’s ministry, but to have gone to the best sources of information within his reach, and to have written an orderly narrativ"}, {"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_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_ef62dbeaf533", "title": "Aurelius, Meditations §aur_09_xix: Of an operation and of a purpose there is an ending, or of an action and of a...", "shelf": "classics", "surface": "secular", "snippet": "Of an operation and of a purpose there is an ending, or of an action and of a purpose we say commonly, that it is at an end: from opinion also there is an absolute cessation, which is as it were the d"}, {"id": "card_n_b026825cd2d9", "title": "Easton: Miracle", "shelf": "dictionary", "surface": "secular", "snippet": "An event in the external world brought about by the immediate agency or the simple volition of God, operating without the use of means capable of being discerned by the senses, and designed to authent"}, {"id": "card_n_1565817e96cc", "title": "Boethius, Consolation §boe_04_06: 'True,' said I; 'but, since it is thy office to unfold the hidden cause of th...", "shelf": "classics", "surface": "witness", "snippet": "'True,' said I; 'but, since it is thy office to unfold the hidden cause of things, and explain principles veiled in darkness, inform me, I pray thee, of thine own conclusions in this matter, since the"}, {"id": "card_n_9ebe5fdc4379", "title": "Augustine, Confessions §aug_conf_12_038: Another bends his mind on that which is said, In the Beginning God made heave...", "shelf": "classics", "surface": "witness", "snippet": "Another bends his mind on that which is said, In the Beginning God made heaven and earth; and beholdeth therein Wisdom, the Beginning because It also speaketh unto us. Another likewise bends his mind "}]}