{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.logarithm","code":"thing-q11197","url":"https://ver.cy/models/thing/q11197/","name":"logarithm","alternateNames":["logarithmic unit","log probability","log-likelihood","natural logarithm","binary logarithm","discrete logarithm","elliptic curve discrete logarithm"],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"The exponent to which a fixed base must be raised to produce a given number, the inverse of exponentiation, in forms such as the common logarithm to base ten, the natural logarithm to base e and the binary logarithm to base two, with properties turning multiplication into addition and powers into products, and extensions such as complex and discrete logarithms; logarithms underlie logarithmic scales such as decibels and pH, log-likelihood and log probability in statistics, and computation from slide rules to algorithms.","purpose":"Let an agent explain logarithms and their definition, properties and bases, support calculations and use of logarithmic scales, describe applications in science, statistics and computing, and support learning.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Inverse of powers","Product to sum rule","Choice of base","Logarithmic scales"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a logarithm is.","layers":[{"id":"concept","name":"Concept","description":"Definition and bases.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What is a logarithm, and how do common, natural and binary logarithms differ?","kind":"definition"},{"text":"Which base is meant?","kind":"boundary"}]}]},{"id":"properties","name":"Properties","description":"Properties.","findings":[{"id":"properties-finding","name":"Properties","description":"Properties.","questions":[{"text":"What are the product, quotient, power and change of base rules, and why do they hold?","kind":"definition"},{"text":"Which entry fits exponentials?","kind":"action"}]}]}]},{"id":"calculate","name":"Calculate","description":"Calculation and scales.","layers":[{"id":"compute","name":"Compute","description":"Computing logarithms.","findings":[{"id":"compute-finding","name":"Compute","description":"Computation.","questions":[{"text":"How can this logarithm be computed or an equation with logarithms solved?","kind":"action"},{"text":"Which entry fits solving equations?","kind":"action"}]}]},{"id":"scales","name":"Scales","description":"Logarithmic scales.","findings":[{"id":"scales-finding","name":"Scales","description":"Scales.","questions":[{"text":"How do logarithmic scales such as decibels, pH and earthquake magnitude work, and how are they read?","kind":"provenance"},{"text":"Which entry fits a specific scale?","kind":"action"}]}]}]},{"id":"apply","name":"Apply","description":"Applications.","layers":[{"id":"statistics","name":"Statistics","description":"Statistics and science.","findings":[{"id":"statistics-finding","name":"Statistics","description":"Statistics.","questions":[{"text":"How are log-likelihood, log probability and log transformations used in statistics and science?","kind":"provenance"},{"text":"Which entry fits likelihood?","kind":"action"}]}]},{"id":"computing","name":"Computing","description":"Computing and cryptography.","findings":[{"id":"computing-finding","name":"Computing","description":"Computing.","questions":[{"text":"How do binary logarithms describe algorithm complexity, and what is the discrete logarithm problem in cryptography?","kind":"provenance"},{"text":"Which entry fits computational complexity?","kind":"action"}]}]}]},{"id":"learn","name":"Learn","description":"History and teaching.","layers":[{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did Napier and others develop logarithms, and how did tables and slide rules transform calculation?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can logarithms be taught?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain logarithms, their bases, rules and uses.","Compute logarithms and show the working."],"mustNot":["Present numerical results without stating the base when it matters.","Mislead with a logarithmic scale presented as linear, or the reverse.","Give results beyond the precision the input supports."],"requiresHuman":["Relying on a computed value for engineering, dosing or financial decisions."]},"ethics":{"considerations":["Log scales on charts can hide or exaggerate risk, for example in epidemics or earthquakes.","Misunderstood exponential growth leads to poor public decisions."],"affectedParties":["Students","Readers of charts"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q164307","type":"parent","note":"registry parent class"},{"target":"Q629085","type":"parent","note":"registry parent class"},{"target":"Q864333","type":"parent","note":"registry parent class"},{"target":"transcendental function","type":"related","note":"category"},{"target":"multivalued function","type":"related","note":"category"},{"target":"root","type":"related","note":"another inverse of exponentiation"},{"target":"trillion","type":"related","note":"large numbers expressed on logarithmic scales"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.logarithm","Wikidata: Q11197 (https://www.wikidata.org/wiki/Q11197)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Exponent giving a number from a base","Common, natural, binary, discrete, complex logarithms","An exponential is the inverse; a root is a different inverse of powers","Not physical; a mathematical function."]},"capabilities":{"applicability":"required","items":["explain definition and properties","support calculations","describe applications","support learning"]},"hazards":{"applicability":"required","items":["Confusing bases","Misreading logarithmic scales","Domain errors with zero and negatives"]},"interfaces":{"applicability":"required","items":["Mathematical notation conventions","Standards for logarithmic units such as the decibel","Curriculum standards for algebra"]},"context":{"applicability":"required","items":["Inverse of exponentiation.","common logarithm","natural logarithm","binary logarithm","discrete logarithm","complex logarithm and logarithmic units"]}},"sources":[{"title":"Wikidata item Q11197: logarithm","url":"https://www.wikidata.org/wiki/Q11197","note":"identity and sense of the item"},{"title":"Wikipedia: Logarithm","url":"https://en.wikipedia.org/wiki/Logarithm","note":"general description of the item"}],"openQuestions":["Should the natural logarithm be a separate entry?","How should textbooks be linked?","How should scale standards be linked?"],"resources":{"spec":"/models/things/publications/thing-q11197/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q11197/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T06:14:37Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:51:53+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}