{"query": "pH — the logarithm of the proton", "count": 19, "results": [{"id": "card_n_789214dd088e", "title": "pH — the logarithm of the proton", "shelf": "science", "surface": "secular", "snippet": "pH = −log₁₀[H⁺]: acidity is literally a logarithm, so each unit is a tenfold change in\nproton concentration — pH 4 is ten times more acidic than pH 5, a hundred times more than\npH 6. Sealed in-domain:"}, {"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_c_27e331f56531", "title": "pH is a logarithm", "shelf": "connections", "surface": null, "snippet": "pH = -log10[H+] — chemistry using the exact log scale of the senses."}, {"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_4bb778d3c353", "title": "Aurelius, Meditations §aur_06_xlii: Let the several deaths of men of all sorts, and of all sorts of professions, ...", "shelf": "classics", "surface": "secular", "snippet": "Let the several deaths of men of all sorts, and of all sorts of professions, and of all sort of nations, be a perpetual object of thy thoughts,... so that thou mayst even come down to Philistio, Phœbu"}, {"id": "card_n_aa5069bdfcb0", "title": "1 Clement XXV", "shelf": "patristics", "surface": "witness", "snippet": "Let us consider that wonderful sign [of the resurrection] which takes place in eastern lands, that is, in Arabia and the countries round about. There is a certain bird which is called a phœnix. This i"}, {"id": "card_c_0706824b5f9f", "title": "Information IS a logarithm", "shelf": "connections", "surface": null, "snippet": "2 bits per DNA base = log2(4), sealed in the genome card — Shannon's measure is a log."}, {"id": "card_n_cda0b1e1a364", "title": "Fusion — why the stars shine", "shelf": "science", "surface": "secular", "snippet": "Four hydrogens weigh more than one helium; the difference is sunlight. Sealed from\nthe measured masses: 4·m(H) − m(He-4) = 0.0287 u → 26.73 MeV per helium forged: https://narrowhighway.com/s/8a5e89ab1"}, {"id": "card_n_0fd6d5654d74", "title": "Binding energy — the mass that glue costs", "shelf": "science", "surface": "secular", "snippet": "Weigh a nucleus and it comes up LIGHT: the missing mass is the binding energy,\nE = mc². Sealed: the deuteron (one proton + one neutron) is short 2.224 MeV — the first\nrung of the strong force — and he"}, {"id": "card_n_6e7a5b14e556", "title": "The periodic table — the map of the elements", "shelf": "science", "surface": "secular", "snippet": "118 elements, ordered by proton count, and their properties RECUR in periods — the\nsingle most predictive table in science. Sealed in-domain: carbon is element 6, symbol C\n(https://narrowhighway.com/s"}, {"id": "card_c_4023abd4d182", "title": "pH instantiates chemistry", "shelf": "connections", "surface": null, "snippet": "One face of the sealed chemistry chain."}, {"id": "card_c_2e19e9b96f7d", "title": "A signal's information is a logarithm", "shelf": "connections", "surface": null, "snippet": "log2 of the distinguishable blends — Shannon's bits, the same log scale."}, {"id": "card_n_4d5234cab477", "title": "Chemistry — the bookkeeping of atoms", "shelf": "science", "surface": "secular", "snippet": "Chemistry is accounting at the scale of atoms: nothing is created or\ndestroyed, only rearranged, and every claim balances or it is wrong. The engine keeps the\nbooks in-domain (https://narrowhighway.co"}, {"id": "card_c_cd68086acd22", "title": "The vocabulary half-life is a logarithm", "shelf": "connections", "surface": null, "snippet": "t_half = log(1/2)/log(r) — the same log of a surviving fraction as radioactive dating."}, {"id": "card_n_dcb1a67c26e8", "title": "The evolution of language — descent traced by regular law", "shelf": "science", "surface": "secular", "snippet": "Languages descend like living lineages, and the descent is RECOVERABLE — the comparative\nmethod is one of the humanities' deterministic sciences. English 'father' descends from\nProto-Indo-European *ph"}, {"id": "card_n_13147996cd2f", "title": "Proto-Indo-European — the reconstructed mother tongue", "shelf": "science", "surface": "secular", "snippet": "Roughly half of humanity speaks a descendant — English, Spanish, Hindi, Russian, Persian,\nand hundreds more. Yet PIE was never written: it is RECONSTRUCTED, every form marked with a *\nto say 'inferred"}, {"id": "card_c_79236eb0162f", "title": "A word's information is a logarithm", "shelf": "connections", "surface": null, "snippet": "log2(120) ~ 6.9 bits per word — Shannon's measure, the same log scale."}, {"id": "card_c_e8648ea81c93", "title": "A letter's information is a logarithm", "shelf": "connections", "surface": null, "snippet": "log2(26) ~ 4.7 bits per letter — Shannon again, the same log scale."}]}