Astronomy and Calendars – The Other Chinese Mathematics : 104 BC - AD 1644

485 Pages·2016·5.84 MB·English

by  Jean-Claude Martzloff (auth.)

Jean-Claude Martzloff
Astronomy and
Calendars –
The Other Chinese
Mathematics
104 BC – AD 1644
–
Astronomy and Calendars The Other Chinese
Mathematics
Jean-Claude Martzloff
–
Astronomy and Calendars
The Other Chinese
Mathematics
–
104 BC AD 1644
123
Jean-Claude Martzloff
EastAsian Civilisations Research Centre
(CRCAO) UMR 8155
TheNational Centerfor ScientificResearch
(CNRS)
Paris
France
TheauthorisanhonoraryDirectorofResearch.AfterthepublicationoftheFrench
versionofthepresentbook(2009),hehasbeenawardedin2010theIkuoHirayama
prizebytheAcadémiedesInscriptionsetBelles-Lettresforthetotalityofhiswork
on Chinese mathematics.
ISBN978-3-662-49717-3 ISBN978-3-662-49718-0 (eBook)
DOI 10.1007/978-3-662-49718-0
LibraryofCongressControlNumber:2016939371
MathematicsSubjectClassification(2010):01A-xx,97M50
©Springer-VerlagBerlinHeidelberg2016
The work was first published in 2009 by Honoré Champion with the following title: Le calendrier
chinois:structureetcalculs(104av.J.C.-1644).
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Coverillustration:AfteranillustrationfromSunJianai孫家鼐etal.QingdingShujingTushuo欽定書經
圖說(ImperiallyCommissionedIllustratedEditionoftheClassicofHistory),firstchapter,1905.This
latepicturerepresentsthemeasurementoftheSunsshadowatthesummersolsticewithagnomonand
itsshadowtemplate,inlegendaryChineseantiquity.Itresultsfromaninterpretationofashortpassage
oftheShujing書經.
Printedonacid-freepaper
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CONTENTS
ListofIllustrations . . . . . . . . . . . . . . . . . . . . xvii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . xix
AbbreviationsandConventions . . . . . . . . . . . . . . . . . xxiii
Foreword xxvii
InitialForeword xxxi
I ChineseAstronomicalCanonsandCalendars 1
1 PreliminaryObservations 3
TheStateoftheArt . . . . . . . . . . . . . . . . . . . . . . . 3
MethodologicalOrientations . . . . . . . . . . . . . . . . . . 7
ComputisticsandPredictiveAstronomy . . . . . . . . . 12
TheParadoxoftheChineseCalendar . . . . . . . . . . . . . . 24
TheCalendaranditsCalculations . . . . . . . . . . . . . . . 27
TheDifficultyofAccesstoAstronomicalKnowledge . . 28
TheSurfaceandDeepStructures . . . . . . . . . . . . . . . . 29
TwoNotionsofTime . . . . . . . . . . . . . . . . . . . 30
TheDoubleHistoryoftheCalendar . . . . . . . . . . . 32
HistoricalSources(SurfaceStructure) . . . . . . . . . . 33
Historicalsources(DeepStructure) . . . . . . . . . . . . 34
Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
TheKeyIdeasofAstronomicalCanons . . . . . . . . . . . . 37
PoliticalandCulturalFactors: AnExample . . . . . . . 41
TheReformsofAstronomicalCanons . . . . . . . . . . . . . 42
TheBureauofAstronomy . . . . . . . . . . . . . . . . . . . 52
TheNamesofAstronomicalCanons . . . . . . . . . . . . . . 55
x CONTENTS
2 DescriptionoftheChinesecalendar 61
LimitationandScope . . . . . . . . . . . . . . . . . . . . . . 61
FundamentalComponents . . . . . . . . . . . . . . . . . . . 62
TheDay . . . . . . . . . . . . . . . . . . . . . . . . . . 62
TheSolarYear . . . . . . . . . . . . . . . . . . . . . . 62
TheTwenty-FourSolarBreaths . . . . . . . . . . . . . . 63
TheSeventy-TwoSeasonalIndicators . . . . . . . . . . 66
TheFivePhases . . . . . . . . . . . . . . . . . . . . . . 68
TheLunarYear . . . . . . . . . . . . . . . . . . . . . . 69
LunarMonths,OrdinaryandIntercalary . . . . . . . . . 69
TheStructureoftheLunarYear . . . . . . . . . . . . . 70
ThePercentageofFullandHollowMonths . . . . . . . 71
LocalPatternsofFullandHollowMonths . . . . . . . . 72
TheAstronomicalMonthsandtheLunisolarCoupling . 73
TheBeginningoftheLunarYear . . . . . . . . . . . . 76
DynasticErasandConcordanceTables . . . . . . . . . . 78
CyclesandPseudo-Cycles . . . . . . . . . . . . . . . . . . . 79
Definitions. . . . . . . . . . . . . . . . . . . . . . . . . 79
TheDenaryCycle . . . . . . . . . . . . . . . . . . . . . 80
TheDuodecimalCycle . . . . . . . . . . . . . . . . . . 81
TheInvertedTree . . . . . . . . . . . . . . . . . . . . . 82
TheSexagenaryCycle . . . . . . . . . . . . . . . . . . 83
VariousUsesoftheSexagenaryCycle . . . . . . . . . . 86
TheNineColorPalaces . . . . . . . . . . . . . . . . . . 87
ThePlanetaryWeek . . . . . . . . . . . . . . . . . . . 90
TheTwenty-EightMansions . . . . . . . . . . . . . . . 92
TheJianchuPseudo-CyclewithReduplications . . . . . 94
TheNayinCyclewithReduplications . . . . . . . . . . 96
OtherAspects . . . . . . . . . . . . . . . . . . . . . . . . . . 96
FestivalsandAnnualObservances . . . . . . . . . . . . 96
IrregularYears . . . . . . . . . . . . . . . . . . . . . . 99
II Calculations 105
3 NumbersandCalculations 107
ModesofRepresentationofNumbers . . . . . . . . . . . . . 107
CONTENTS xi
VariousZeroes . . . . . . . . . . . . . . . . . . . . . . . . . 118
TheZero-Circle . . . . . . . . . . . . . . . . . . . . . . . . . 125
TheHistoryZeroRevisited . . . . . . . . . . . . . . . . . . . 128
NumericalConstants . . . . . . . . . . . . . . . . . . . . . . 131
TheEpoch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
TheSuperiorEpoch . . . . . . . . . . . . . . . . . . . . . . . 136
TheSupportYear . . . . . . . . . . . . . . . . . . . . . . . . 137
TheEmergingYear . . . . . . . . . . . . . . . . . . . . . . . 138
NumbersofYearsfromtheEpoch . . . . . . . . . . . . . . . 138
ChangesofOrigin . . . . . . . . . . . . . . . . . . . . . . . . 139
SupportDays . . . . . . . . . . . . . . . . . . . . . . . . . . 140
BinomialRepresentations . . . . . . . . . . . . . . . . . . . . 141
FractionalRepresentations . . . . . . . . . . . . . . . . . . . 143
MeanandTrueElements . . . . . . . . . . . . . . . . . . . . 144
Definitions. . . . . . . . . . . . . . . . . . . . . . . . . 144
HistoricalAspects . . . . . . . . . . . . . . . . . . . . . 145
NotationandTerminology . . . . . . . . . . . . . . . . 146
FundamentalElements . . . . . . . . . . . . . . . . . . . . . 147
TheLastSolarBreathofaLunarYear . . . . . . . . . . . . . 148
TheNumberingofNewMoons . . . . . . . . . . . . . . . . . 148
TheLunisolarShift . . . . . . . . . . . . . . . . . . . . . . . 149
Introduction . . . . . . . . . . . . . . . . . . . . . . . . 149
TheEpact . . . . . . . . . . . . . . . . . . . . . . . . . 149
Theintercalaryremainder(Runyu) . . . . . . . . . . . . 150
TheMonthlyEpactandtheIntercalaryMonth . . . . . . 150
Consequences . . . . . . . . . . . . . . . . . . . . . . . 152
PathologicalCalendars . . . . . . . . . . . . . . . . . . 153
4 MeanElements 157
MeanElementsinPractice . . . . . . . . . . . . . . . . . . . 157
Metonicconstants . . . . . . . . . . . . . . . . . . . . . . . . 157
MetonicCalculations . . . . . . . . . . . . . . . . . . . 158
Justifications . . . . . . . . . . . . . . . . . . . . . . . 161
Non-MetonicCanons . . . . . . . . . . . . . . . . . . . . . . 163
CalculationVariants . . . . . . . . . . . . . . . . . . . . . . . 166
xii CONTENTS
5 TrueElements(618–1280) 169
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
TrueSolarBreaths . . . . . . . . . . . . . . . . . . . . . . . 170
SomePeculiaritiesLeadingtoSimplifications . . . . . . 170
ATechnicalTerm: Theruqi . . . . . . . . . . . . . . . . . . 172
AGeneralModeofCalculationoftheruqi . . . . . . . 173
AnotherModeofCalculation . . . . . . . . . . . . . . . 174
TheCalculationoftheruqifromMeanSolarBreaths . . 175
AnotherTechnicalTerm: Theruli . . . . . . . . . . . . . . . 179
Theruli . . . . . . . . . . . . . . . . . . . . . . . . . . 179
TablesandInterpolationTechniques . . . . . . . . . . . . . . 179
SolarTables . . . . . . . . . . . . . . . . . . . . . . . . 180
LunarTables . . . . . . . . . . . . . . . . . . . . . . . 185
TheSolarCorrection . . . . . . . . . . . . . . . . . . . . . . 186
FurtherRemarksOntheSolarCorrection . . . . . . . . 190
TheLunarCorrection . . . . . . . . . . . . . . . . . . . . . . 191
CalculationsWithoutTables . . . . . . . . . . . . . . . . . . 195
6 LaterAstronomicalCanons 197
TheSupremacyoftheInceptionGrantingCanon . . . . . . . 197
TheTwoLastAstronomicalCanons . . . . . . . . . . . . . . 198
UnitsofTime . . . . . . . . . . . . . . . . . . . . . . . . . . 200
TheEpoch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
ConcordanceswithJulianDates . . . . . . . . . . . . . . . . 201
TheReformoftheShiftConstants . . . . . . . . . . . . . . . 202
MeanElements . . . . . . . . . . . . . . . . . . . . . . . . . 203
Justifications . . . . . . . . . . . . . . . . . . . . . . . 204
TrueLunarPhases . . . . . . . . . . . . . . . . . . . . . . . . 204
TrueNewMoons . . . . . . . . . . . . . . . . . . . . . 204
TrueLunarPhases . . . . . . . . . . . . . . . . . . . . 207
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
HorarySystem . . . . . . . . . . . . . . . . . . . . . . . . . 213
TheDurationsofDayandNight . . . . . . . . . . . . . . . . 215
TheEpoch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216