{"id":"https://openalex.org/W7212123791","doi":"https://doi.org/10.5281/zenodo.22689398","title":"Babylonian Base-60 Arithmetic: Superior Positional System Enabling Exact Division and Early Astronomy \u2014 E8 Intelligence Research","display_name":"Babylonian Base-60 Arithmetic: Superior Positional System Enabling Exact Division and Early Astronomy \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212123791","doi":"https://doi.org/10.5281/zenodo.22689398"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22689398","doi":"https://doi.org/10.5281/zenodo.22689398","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22689398","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22689398","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136862907","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5136862907"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.45019999146461487,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.45019999146461487,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13175","display_name":"Historical Astronomy and Related Studies","score":0.3725999891757965,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12307","display_name":"Ancient Near East History","score":0.12399999797344208,"subfield":{"id":"https://openalex.org/subfields/1204","display_name":"Archeology"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/babylonian-mathematics","display_name":"Babylonian mathematics","score":0.925000011920929},{"id":"https://openalex.org/keywords/sexagesimal-system","display_name":"sexagesimal system","score":0.7929999828338623},{"id":"https://openalex.org/keywords/positional-numeral-systems","display_name":"positional number systems","score":0.8180000185966492},{"id":"https://openalex.org/keywords/highly-composite-numbers","display_name":"highly composite numbers","score":0.7940000295639038},{"id":"https://openalex.org/keywords/reciprocals","display_name":"reciprocals","score":0.7429999709129333},{"id":"https://openalex.org/keywords/least-common-multiple","display_name":"least common multiple","score":0.656000018119812},{"id":"https://openalex.org/keywords/circle-division","display_name":"circle division","score":0.4860000014305115},{"id":"https://openalex.org/keywords/angle-measurement","display_name":"angle measurement","score":0.925000011920929},{"id":"https://openalex.org/keywords/early-astronomy","display_name":"early astronomy","score":0.7070000171661377},{"id":"https://openalex.org/keywords/e8","display_name":"E8","score":0.4189999997615814},{"id":"https://openalex.org/keywords/e8-lattice","display_name":"E8 lattice","score":0.4490000009536743},{"id":"https://openalex.org/keywords/e8-root-system","display_name":"E8 root system","score":0.4300000071525574}],"concepts":[{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.7486000061035156},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.6370999813079834},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.45829999446868896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45509999990463257},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.44699999690055847},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4449000060558319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41029998660087585},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3280999958515167},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3034000098705292},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C22607594","wikidata":"https://www.wikidata.org/wiki/Q5375150","display_name":"Enabling","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28790000081062317},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22689398","doi":"https://doi.org/10.5281/zenodo.22689398","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22689398","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22689399","doi":"https://doi.org/10.5281/zenodo.22689399","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22689399","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22689398","doi":"https://doi.org/10.5281/zenodo.22689398","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22689398","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"FINDING:":[0],"Babylonian":[1],"base-60":[2],"(sexagesimal)":[3],"arithmetic":[4],"was":[5],"a":[6,23],"computationally":[7],"superior":[8],"positional":[9],"system,":[10],"enabling":[11],"exact":[12,92],"division":[13],"by":[14],"highly":[15],"composite":[16],"numbers":[17],"(2,3,5":[18],"and":[19,29,108],"their":[20],"products)":[21],"\u2014":[22,85,90,122],"key":[24],"enabler":[25],"for":[26,45,94],"early":[27],"astronomy":[28],"angular":[30,127],"measurement.":[31],"|":[32,75],"MATH:":[33],"Base":[34],"60":[35],"=":[36,48],"2\u00b2\u00b73\u00b75;":[37],"prime":[38],"factors":[39],"{2,3,5}.":[40],"In":[41],"base-60,":[42],"1/n":[43],"terminates":[44],"any":[46],"n":[47],"2^a\u00b73^b\u00b75^c.":[49],"Key":[50],"reciprocals:":[51],"1/2=0;30,":[52],"1/3=0;20,":[53],"1/4=0;15,":[54],"1/5=0;12,":[55],"1/6=0;10,":[56],"1/8=0;07,30,":[57],"1/9=0;06,40,":[58],"1/12=0;05,":[59],"1/15=0;04,":[60],"1/16=0;03,45,":[61],"1/20=0;03,":[62],"1/24=0;02,30,":[63],"1/25=0;02,24,":[64],"1/27=0;02,13,20,":[65],"1/30=0;02,":[66],"1/32=0;01,52,30,":[67],"1/36=0;01,40,":[68],"1/40=0;01,30,":[69],"1/45=0;01,20,":[70],"1/48=0;01,15,":[71],"1/50=0;01,12,":[72],"1/54=0;01,06,40,":[73],"1/60=0;01.":[74],"CONNECTION:":[76],"Base-60":[77],"is":[78],"the":[79,86,99,104,109,125,139],"**least":[80],"common":[81],"multiple":[82],"of":[83,98,138],"1,2,3,4,5,6**":[84],"first":[87],"six":[88],"integers":[89],"giving":[91],"fractions":[93,111],"all":[95],"harmonic":[96],"divisions":[97],"circle.":[100],"This":[101],"directly":[102],"yields":[103],"360\u00b0":[105],"circle":[106],"(6\u00d760),":[107],"sexagesimal":[110],"0;30":[112],"(1/2),":[113],"0;20":[114],"(1/3),":[115],"0;15":[116],"(1/4),":[117],"0;12":[118],"(1/5),":[119],"0;10":[120],"(1/6)":[121],"which":[123],"are":[124],"**exact":[126],"subdivisions**":[128],"us":[129],"Author:":[130],"Andrew":[131],"Stewart":[132],"Caldin,":[133],"Independent":[134],"Researcher,":[135],"UK.":[136],"Part":[137],"E8":[140],"Intelligence":[141],"Research":[142],"series.":[143],"Platform:":[144],"e8intelligence.com":[145]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-09-11T00:00:00"}