{"query": "Logarithms — multiplication made addition, and the grammar o", "count": 20, "results": [{"id": "card_theory_diffie_hellman_key_exchange", "title": "Diffie-Hellman key exchange", "shelf": "theories", "surface": "secular", "snippet": "Diffie-Hellman key exchange — an engine domain that can touch it: cybersecurity. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computation. Two parties agre", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_statistical_mechanics", "title": "Statistical mechanics (Boltzmann — why the second law is a counting argument)", "shelf": "theories", "surface": "secular", "snippet": "Statistical mechanics (Boltzmann — why the second law is a counting argument) — an engine domain that can touch it: thermodynamics. Calibration: seals — Boltzmann distributions, partition functions an", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"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", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_floor_logarithm", "title": "The logarithm - the instrument the joints share", "shelf": "codex", "surface": "secular", "snippet": "Two trees: Napier's table (1614) and Saint-Vincent's hyperbola (1647) - a number's logarithm as a tabulated count, and as an area. They become one function in Euler's Introductio (1748): e, and exp an", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_alm_connection_logarithmic_scales_two_witnesses", "title": "Almanac: Decibels and star magnitudes: one logarithm, two senses", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  How loud a sound is and how bright a star is are measured on scales that look unrelated, yet two independent verifiers found the same machinery underneath. The acoustics verifier confirmed", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_sys_oneway_function", "title": "The one-way function — the computational rectifier", "shelf": "systems", "surface": "secular", "snippet": "Some computations are cheap one way and infeasible the reverse. A one-way function is easy to evaluate (polynomial time) but computationally infeasible to invert; a TRAPDOOR one-way function adds a se", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}, {"id": "card_bridge_theory_shannon_information_theory__second_law_of_thermodynamics", "title": "Bridge: Shannon information theory (entropy, channel capacity)  ↔  Second law of thermodynamics (entropy)", "shelf": "bridges", "surface": "secular", "snippet": "Shannon information theory (entropy, channel capacity) and Second law of thermodynamics (entropy) are the same form in different domains. Shannon's H = -sum p log p and Boltzmann's S = k log W are the", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_chain_gell_mann_low_1954", "title": "Gell-Mann 1954 — Quantum electrodynamics at small distances", "shelf": "codex", "surface": "secular", "snippet": "M. Gell-Mann, F. E. Low (1954). Quantum electrodynamics at small distances. Phys. Rev. 95 (1954) 1300–1312. DOI 10.1103/PhysRev.95.1300. Canonical: https://doi.org/10.1103/PhysRev.95.1300. Cited by it", "authority_tier": "reference", "source": "M. Gell-Mann, F. E. Low (1954), Phys. Rev. 95 (1954) 1300–1312", "readable": false, "generated": false}, {"id": "card_alm_connection_independence_multiplies_information_adds", "title": "Almanac: Independence multiplies probability but adds information", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Flip two fair coins. The probability verifier confirmed that independent events MULTIPLY: P(A and B) = 0.5 x 0.5 = 0.25. The information_theory verifier confirmed that one fair coin carrie", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_c_49411cccab5a", "title": "Logarithms — multiplication made addition, a ↔ Diode — the exponential gate", "shelf": "connections", "surface": null, "snippet": "the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm brings them back by adding.  — a concord the card itself states; mined + verifi", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_chain_weil_1929", "title": "Weil 1929 — L'arithmétique sur les courbes algébriques", "shelf": "codex", "surface": "secular", "snippet": "A. Weil (1929). L'arithmétique sur les courbes algébriques. Acta Math. 52 (1929) 281–315. DOI 10.1007/BF02592688. Canonical: https://doi.org/10.1007/BF02592688. Cited by its record. License as found: ", "authority_tier": "reference", "source": "A. Weil (1929), Acta Math. 52 (1929) 281–315", "readable": false, "generated": false}, {"id": "card_chain_neron_1965", "title": "Néron 1965 — Quasi-fonctions et hauteurs sur les variétés abéliennes", "shelf": "codex", "surface": "secular", "snippet": "A. Néron (1965). Quasi-fonctions et hauteurs sur les variétés abéliennes. Ann. Math. 82 (1965) 249–331. DOI 10.2307/1970644. Canonical: https://doi.org/10.2307/1970644. Cited by its record. License as", "authority_tier": "reference", "source": "A. Néron (1965), Ann. Math. 82 (1965) 249–331", "readable": false, "generated": false}, {"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.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_chain_cobham_1965", "title": "Cobham 1965 — The intrinsic computational difficulty of functions", "shelf": "codex", "surface": "secular", "snippet": "A. Cobham (1965). The intrinsic computational difficulty of functions. Logic, Methodology and Philosophy of Science (Proc. 1964 Congress), North-Holland, 1965, 24–30. Cited by its record. License as f", "authority_tier": "reference", "source": "A. Cobham (1965), Logic, Methodology and Philosophy of Science (Proc. 1964 Congress), North-Holland, 1965, 24–30", "readable": false, "generated": false}, {"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.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"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.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_pchem_acid_base", "title": "Acid-base — pKa + pKb = 14", "shelf": "codex", "surface": "secular", "snippet": "For an acid and its conjugate base, pKa + pKb = pKw = 14 at 25 C (sealed). This is Ka * Kb = Kw, the autoionization of water, in logarithms - the backbone of pH, buffers and titrations. Rests on chemi", "authority_tier": "engine_derived", "source": "Narrow Highway — physical chemistry", "readable": false, "generated": false}, {"id": "card_src_word_logarithm", "title": "logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland (1550-1617), to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplicatio", "authority_tier": "reference", "source": "webster-1913", "readable": false, "generated": false}, {"id": "card_c_9d6917fca9f5", "title": "pH — the logarithm of the proton ↔ Logarithms — multiplication made addition, a", "shelf": "connections", "surface": null, "snippet": "−log₁₀(10⁻⁴) = 4 sealed on the logarithm card. This is chemistry borrowing the grammar of the senses  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_tool_slide_rule", "title": "The slide rule — multiplication by sliding logarithms", "shelf": "codex", "surface": "secular", "snippet": "The slide rule multiplies without electricity, memory, or a line of code: two sliding LOGARITHM scales add their lengths, and because log(a) + log(b) = log(a*b), the sum you read off is the product. I", "authority_tier": "engine_derived", "source": "Narrow Highway — the instruments", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_theory_diffie_hellman_key_exchange"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}