https://community.wolfram.com/groups/-/m/t/2313171
by Carlos Zapata Carratala
# The Binary Bias and the Arity Chasm
Thehistoryofpuremathematicsseemstohaveproducedanimmenseamountofbinarystructures.Fromtheprimitiveandmundanetothemodernandsophisticated,mostareasofmathematicsarebuilt—almostexclusively—onobjectsthatarebinaryinnature:Arithmetic:1+1=2,operationsarebinary,invertibilityanddivisibilityrelationsarebinary...Algebra:a·b,dominatedbybinaryoperations,symbolicequalityisabinaryrelation...Calculus:f:,functionsarebinaryassignments,standardconstructionsarefunctionsoffunctionsorbinaryoperationsoffunctions...SetTheory:R⊂A×B,relationsbetweensetsarebinary,Cartesianproductisbinary,successorfunctionisatomicallybinary...Logic:({0,1},∧,∨,,¬),twotruthvalues,logicalconstructionsarefunctionsofpropositionsorbinaryoperationsofpropositions...CategoryTheory:AB,morphismsarearrows,isomorphismisabinaryrelation,highercategoriesbuiltwitharrowsofarrows,extensivetheoryofduality... AreasofmathematicsthatresistsaturationbybinarystructuresarethosethatdealwithspatialinformationsuchasGeometryorTopology.Althoughmoderntreatmentsofthesesubjectsaredominatedbytechniquesandnotationswithaverystrongbinaryflavour,onecouldarguethatthisistheresultofapplyingmethodsfromsomeofthedisciplineslistedaboveandnotafundamentalfeatureoftherealmofspace,shapeandstructure.Onewaytoillustratethebiastowardsbinarityinmathematicsistofocusontheabstractalgebraliteratureandgetsomebibliometricdataaboutthearityoftheoperationsconsidered.Fromapurelyformalpointofview,thereisnoapriorireasontofocusonbinaryoperationsoveroperationsofhigheraritiesbeyondsimplicityandeaseofmanualcomputation.Ifoneassumesthatthemathematicalcommunityhasconductedresearchonabstractalgebrainaparsimoniousway,thenumberofpublicationsdealingprimarilywithoperationsofsomefixedarity(histogramlabels)wouldbeexpectedtolooksomethinglikethis:
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