{"id":"https://openalex.org/W4411351295","doi":"https://doi.org/10.3390/axioms14060466","title":"The Mean and the Variance as Dual Concepts in a Fundamental Duality","display_name":"The Mean and the Variance as Dual Concepts in a Fundamental Duality","publication_year":2025,"publication_date":"2025-06-16","ids":{"openalex":"https://openalex.org/W4411351295","doi":"https://doi.org/10.3390/axioms14060466"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14060466","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060466","pdf_url":"https://www.mdpi.com/2075-1680/14/6/466/pdf?version=1750067409","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/6/466/pdf?version=1750067409","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074435436","display_name":"David Ellerman","orcid":"https://orcid.org/0000-0002-5718-618X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David Ellerman","raw_affiliation_strings":["Independent Researcher, 1000 Ljubljana, Slovenia"],"affiliations":[{"raw_affiliation_string":"Independent Researcher, 1000 Ljubljana, Slovenia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074435436"],"corresponding_institution_ids":[],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1507196,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"6","first_page":"466","last_page":"466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9593999981880188,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9593999981880188,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.8118005990982056},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.7432270050048828},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5724868178367615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5301300883293152},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3232739269733429},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2831946313381195},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.15377026796340942},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.12180474400520325},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.08768811821937561}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.8118005990982056},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.7432270050048828},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5724868178367615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5301300883293152},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3232739269733429},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2831946313381195},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.15377026796340942},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.12180474400520325},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.08768811821937561},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/axioms14060466","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060466","pdf_url":"https://www.mdpi.com/2075-1680/14/6/466/pdf?version=1750067409","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:philsci-archive.pitt.edu:25760","is_oa":true,"landing_page_url":null,"pdf_url":"https://philsci-archive.pitt.edu/25760/1/_MDPI_axioms-mean-variance.pdf","source":{"id":"https://openalex.org/S4306401282","display_name":"PhilSci-Archive (University of Pittsburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I170201317","host_organization_name":"University of Pittsburgh","host_organization_lineage":["https://openalex.org/I170201317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:oai:philpapers.org/rec/ELLTMA-8","is_oa":true,"landing_page_url":"https://philpapers.org/rec/ELLTMA-8","pdf_url":"https://philpapers.org/archive/ELLTMA-8.pdf","source":{"id":"https://openalex.org/S4306402131","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:8d0e8c5e180d4ca5b698f99686645862","is_oa":true,"landing_page_url":"https://doaj.org/article/8d0e8c5e180d4ca5b698f99686645862","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 6, p 466 (2025)","raw_type":"article"},{"id":"pmh:oai:philarchive.org/rec/ELLTMA-8","is_oa":false,"landing_page_url":"https://philarchive.org/rec/ELLTMA-8","pdf_url":null,"source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/axioms14060466","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060466","pdf_url":"https://www.mdpi.com/2075-1680/14/6/466/pdf?version=1750067409","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411351295.pdf","grobid_xml":"https://content.openalex.org/works/W4411351295.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W108696250","https://openalex.org/W379680902","https://openalex.org/W635510250","https://openalex.org/W1787040602","https://openalex.org/W1971846196","https://openalex.org/W1985224565","https://openalex.org/W1995875735","https://openalex.org/W2087189381","https://openalex.org/W2129802470","https://openalex.org/W2171014865","https://openalex.org/W2324810866","https://openalex.org/W2339846562","https://openalex.org/W2486886792","https://openalex.org/W2494267358","https://openalex.org/W2568006421","https://openalex.org/W2608985606","https://openalex.org/W2733911839","https://openalex.org/W2739359317","https://openalex.org/W2745657531","https://openalex.org/W2766122375","https://openalex.org/W2790619474","https://openalex.org/W2796967526","https://openalex.org/W3122007655","https://openalex.org/W3124026264","https://openalex.org/W3126996113","https://openalex.org/W3207982459","https://openalex.org/W4205308139","https://openalex.org/W4210429090","https://openalex.org/W4226105971","https://openalex.org/W4239954054","https://openalex.org/W4249643576","https://openalex.org/W4396923051","https://openalex.org/W6625026354","https://openalex.org/W6736575171","https://openalex.org/W6738595189","https://openalex.org/W6750519783","https://openalex.org/W6881460420"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W4225784730","https://openalex.org/W3122644328","https://openalex.org/W1019837216"],"abstract_inverted_index":{"A":[0],"basic":[1,56],"duality":[2,35,116,168],"arises":[3],"throughout":[4],"the":[5,18,24,30,34,60,68,93,97,106,115,124,130,146,152,157,160,167,173],"mathematical":[6],"and":[7,38,92,162,169],"natural":[8],"sciences.":[9],"Traditionally,":[10],"logic":[11,20,50,84,98],"is":[12,45,85,101],"thought":[13],"to":[14,67,172],"be":[15],"based":[16,150],"on":[17,105,151,159],"Boolean":[19],"of":[21,26,51,62,71,76,82,96,99,108,114,126,145,166],"subsets,":[22],"but":[23],"development":[25],"category":[27],"theory":[28,87,103,164],"in":[29,73],"mid-twentieth":[31],"century":[32],"shows":[33],"between":[36],"subsets":[37],"partitions":[39,100],"(or":[40,120,136],"equivalence":[41],"relations).":[42],"Hence,":[43],"there":[44],"an":[46],"equally":[47],"fundamental":[48],"dual":[49,66,171],"partitions.":[52],"At":[53],"a":[54,63,77,118,127,134,142],"more":[55],"or":[57],"granular":[58],"level,":[59],"elements":[61,72],"subset":[64,83,112],"are":[65],"distinctions":[69],"(pairs":[70],"different":[74],"blocks)":[75],"partition.":[78],"The":[79,111],"quantitative":[80,94],"version":[81,95],"probability":[86],"(as":[88],"developed":[89],"by":[90],"Boole),":[91],"information":[102,163],"re-founded":[104],"notion":[107],"logical":[109],"entropy.":[110],"side":[113,132,165],"uses":[117,133],"one-sample":[119],"one-element)":[121],"approach,":[122,154],"e.g.,":[123],"mean":[125],"random":[128],"variable;":[129],"partition":[131,161],"two-sample":[135,153],"pair-of-elements)":[137],"approach.":[138],"This":[139],"paper":[140],"gives":[141],"new":[143],"derivation":[144],"variance":[147,158],"(and":[148],"covariance)":[149],"which":[155],"positions":[156],"thus":[170],"mean.":[174]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}