{"query": "Shannon 1948 — A mathematical theory of communication", "count": 20, "results": [{"id": "card_chain_shannon_1948", "title": "Shannon 1948 — A mathematical theory of communication", "shelf": "codex", "surface": "secular", "snippet": "C. E. Shannon (1948). A mathematical theory of communication. Bell Syst. Tech. J. 27 (1948) 379–423. DOI 10.1002/j.1538-7305.1948.tb01338.x. Canonical: https://doi.org/10.1002/j.1538-7305.1948.tb01338", "authority_tier": "reference", "source": "C. E. Shannon (1948), Bell Syst. Tech. J. 27 (1948) 379–423", "readable": false, "generated": false}, {"id": "card_theory_shannon_information_theory", "title": "Shannon information theory (entropy, channel capacity)", "shelf": "theories", "surface": "secular", "snippet": "Shannon information theory (entropy, channel capacity) — an engine domain that can touch it: information_theory. Calibration: seals. H = -Σ p log p. Information is measured by how much UNCERTAINTY a m", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_category_theory", "title": "Category theory (the mathematics of structure-preserving maps)", "shelf": "theories", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) — an engine domain that can touch it: mathematics. Calibration: map-only — an organising framework rather than a computation. Study objec", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_fourier_analysis___signal_processing", "title": "Fourier analysis & signal processing", "shelf": "theories", "surface": "secular", "snippet": "Fourier analysis & signal processing — an engine domain that can touch it: mathematics. Calibration: seals. Any well-behaved signal is a sum of sinusoids, and the transform moves freely between the ti", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_landauer__shannon_information_theory", "title": "Bridge: Landauer's principle (erasing information costs heat)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Landauer's principle (erasing information costs heat) and Shannon information theory (entropy, channel capacity) are the same form in different domains. THIS CLOSES THE INFORMATION-THERMODYNAMICS BRID", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_statistical_mechanics__shannon_information_theory", "title": "Bridge: Statistical mechanics (Boltzmann — why the second law is a counting argument)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Statistical mechanics (Boltzmann — why the second law is a counting argument) and Shannon information theory (entropy, channel capacity) are the same form in different domains. Boltzmann's log W and S", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_quantum_information___entanglement__von_neumann_entr__shannon_information_theory", "title": "Bridge: Quantum information & entanglement (von Neumann entropy)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) and Shannon information theory (entropy, channel capacity) are the same form in different domains. von Neumann entropy S = -Tr(rho log rho) red", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_alm_connection_entropy_is_thermodynamic", "title": "Almanac: Shannon entropy and thermodynamic entropy are the same quantity", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The entropy of a message and the entropy of a gas are not analogies -- they are one formula. information_theory confirmed Shannon entropy numerically: a fair coin carries 1 bit, four equal", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "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_bridge_theory_category_theory__group_theory", "title": "Bridge: Category theory (the mathematics of structure-preserving maps)  ↔  Group theory & symmetry (the mathematics of what stays the same)", "shelf": "bridges", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) and Group theory & symmetry (the mathematics of what stays the same) are the same form in different domains. a group IS a category with o", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_n_49d1ebe5ba6a", "title": "The genome as information — and the algebra of a population", "shelf": "science", "surface": "secular", "snippet": "Two bits per base, sealed: log(4)/log(2) = 2 — so the ~3.2 billion base pairs of the human\ngenome hold ~6.4 billion bits, about 800 MB, a large app's worth of code in every cell (https://narrowhighway", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_master_boolean_algebra", "title": "Master equation: (a AND b), (a OR b), NOT a  —  the two-valued algebra", "shelf": "bridges", "surface": "secular", "snippet": "the law of thought made algebra: the same AND/OR/NOT structure is propositional logic, a network of switches, and the algebra of sets. Boole titled it The Laws of Thought; Shannon showed a circuit IS ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"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", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_works_information", "title": "Measuring information: one bit, and a distance", "shelf": "the-works", "surface": "secular", "snippet": "A single fair coin carries exactly one bit of Shannon entropy; the Hamming distance counts how many positions two codewords differ in — the ground of error correction.  Worked & sealed by the engine —", "authority_tier": "verified", "source": "The Works — worked & sealed", "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_v_a2c57d5d0b2a", "title": "H(½,½) = 1 bit · Hamming(1011, 1001) = 1", "shelf": "information_theory", "surface": "secular", "snippet": "Verdict: HOLDS.\n• info_theory.shannon_entropy: H = 1.000000 bits (matches claim 1.0)\n• info_theory.hamming_distance: Hamming('1011', '1001') = 1 (matches claim)\nSealed and independently re-checkable: ", "authority_tier": "engine", "source": "Verified by the engine — information_theory", "readable": false, "generated": false}, {"id": "card_src_word_shannon", "title": "shannon", "shelf": "dictionary", "surface": "secular", "snippet": "shannon: (noun) United States electrical engineer who pioneered mathematical communication theory (1916-2001) — syn: Claude Shannon, Claude E. Shannon, Claude Elwood Shannon", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_claude_e_shannon", "title": "claude e. shannon", "shelf": "dictionary", "surface": "secular", "snippet": "claude e. shannon: (noun) United States electrical engineer who pioneered mathematical communication theory (1916-2001) — syn: Shannon, Claude Shannon, Claude Elwood Shannon", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_claude_shannon", "title": "claude shannon", "shelf": "dictionary", "surface": "secular", "snippet": "claude shannon: (noun) United States electrical engineer who pioneered mathematical communication theory (1916-2001) — syn: Shannon, Claude E. Shannon, Claude Elwood Shannon", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_claude_elwood_shannon", "title": "claude elwood shannon", "shelf": "dictionary", "surface": "secular", "snippet": "claude elwood shannon: (noun) United States electrical engineer who pioneered mathematical communication theory (1916-2001) — syn: Shannon, Claude Shannon, Claude E. Shannon", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "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_chain_shannon_1948"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}