The Astronomical Innovations of Monk Yixing 一行 (673–727)

2022·0.88 MB·English

by  Jeffrey Kotyk

religions
Article
The Astronomical Innovations of Monk Yixing 一行 (673–727) †
JeffreyKotyk
DepartmentofAsianStudies,TheUniversityofBritishColumbia,Vancouver,BCV6T1Z4,Canada;
[email protected]
† Adraftofthispaperwaspresentedattheconference“Buddhism&Technology:HistoricalBackgroundand
ContemporaryChallenges”attheUniversityofBritishColumbiainVancouver,BC,Canadaon20
September2019.
Abstract: The Chinese monk Yixing 一行 (673–727) is unique in being an early architect of the
Mantraya¯na tradition (Esoteric Buddhism) in East Asia in addition to featuring as a significant
individual within the history of astronomy and calendrical science in China. His legacy in the
Buddhistworldiswellknown,buttheenduringappreciationofhisscientificworkinlatercenturies
islessunderstood.ThepresentpaperwilldocumenttheachievementsofYixing’sworkinastronomy
whilealsodiscussingtheperceptionandappreciationofhisworkinsubsequentcenturies.
Keywords:Yixing;Buddhism;astronomy;calendars;monks
1. Introduction
Yixing一行(673–727)isawell-knownfigurewithinthehistoryofEastAsianBud-
dhism. HislineageaffiliationsincludeChaninChina,andZenandMikkyo¯ inJapan. He
isalsoknownforhisworkinastronomyandcalendricalscience. ResearchinBuddhist
StudiesconcerningYixinghasgenerallyfocusedonhisBuddhistcareer,butnon-Buddhist
sourcesfromthemedievalperiodalsoprovideampledetailsregardinghisworkinastron-
Citation:Kotyk,Jeffrey.2022.The
omy. ThesesourcesrevealthatYixingnotonlymadeanenormouscontributiontoChinese
AstronomicalInnovationsofMonk
Yixing一行(673–727).Religions13: science, but also that his work was positively evaluated and appreciated by Confucian
543. https://doi.org/10.3390/ writersthroughoutmanysubsequentgenerations. Wewillexploresomeofthesesourcesto
rel13060543 highlightthesignificanceofYixinginthehistoryofChinesescience.
Kimobservesthat“duringtheMing,manyConfucianscholarsweredrawntowards
AcademicEditors:JinhuaChenand
the study of calendrical astronomy, long before the Jesuits’ introduction of Western as-
KaiSheng
tronomyarousedinterestinthesubject.”1Yixing’sworkwasindeedpartofthecorpusof
Received:6May2022 astronomicalliteratureappreciatedbyConfucianscholars. AsIwillshowbelow,Yixing
Accepted:8June2022 waswidelyreadforawholemillenniumuntilChineseastronomywastransformedfol-
Published:13June2022 lowingtheintroductionofEuropeanastrologyduringtheseventeenthcentury. Yixing’s
Publisher’sNote:MDPIstaysneutral statusasamonkandhissimultaneousexcellenceinthefieldofastronomydefinitelycalls
withregardtojurisdictionalclaimsin intoquestionsomeofNeedham’sremarks,suchashisproposalthatBuddhisminChina
publishedmapsandinstitutionalaffil- was“inimicaltocarryingoutscientificresearch”andthattheepistemologyofBuddhism—
iations. oftenfocusedontheimpermanentandtenuousqualityofperceivedphenomena—made
“BuddhismirreconcilablewithTaoismandConfucianismandtragicallyplayedapartin
stranglingthedevelopmentofChinesescience.”2Ithasalreadybeenshownthat,infact,
BuddhisminChinaneitherhinderednorparticularlyencouragedastronomy,butratherthe
Copyright: © 2022 by the author.
ChinesesanghawassimplymoreofapassiverecipientandconsumerofChinesescience,
Licensee MDPI, Basel, Switzerland.
inlightofthecareersofcertainmonksduringtheTangperiod.3Buddhistsalsohadalong
This article is an open access article
heritageofastrologyandcalendricalscienceinIndiaandChina,whichrequiresreferenceto
distributed under the terms and
astronomyandcalculation(Kotyk2018a,2018c). Ourmainconcernhere,then,istodiscuss
conditionsoftheCreativeCommons
howYixingimpactedthedevelopmentofChineseastronomyandhowhewasremembered
Attribution(CCBY)license(https://
inlatersources,bothBuddhistandnon-Buddhist,ratherthantorevisitoldideasabout
creativecommons.org/licenses/by/
Buddhismandscience. Instead,IwanttodemonstratethatYixingcompartmentalizedhis
4.0/).
Religions2022,13,543.https://doi.org/10.3390/rel13060543 https://www.mdpi.com/journal/religions
Religions2022,13,543 2of14
workinastronomyfromBuddhism,andlaterwriterssimilarlytreatedhiswritingsinthe
samemanner.
This study will also argue that we can utilize materials from Buddhist sources, as
well as those of the court and other non-Buddhist authors, to grasp Yixing’s career in
astronomyfromamultifacetedangle.Wemightevaluatehowhisworkwasrecognizedand
appreciatedwithinthenativeChinesehistoryofastronomy. Thisapproachofcomparing
andcontrastingtextsfromcourt(i.e.,“Confucian”)andBuddhistauthorshasbeengainfully
employedinthepast,andhereIemploythissamemethodologyinrelationtoYixing’scareer
inastronomy.4Buildingontheworkofpastscholars,IwillalsoshowhowYixingutilized
technologicalinnovationtocreateamoreprecisesystemoftrackingplanetarymovements
as a brief example of how his work impacted the development of Chinese astronomy.
ThisstudywillfurthershowhowYixingrepresentsarareexampleofaBuddhistmonk
engaginginthedevelopmentofscientificastronomyduringthemedievalperiod. Iwill
drawattentiontosomesignificantdetailsofhisworkwhilealsoshowingitsrelevance—or
lackthereof—tohisothercareerasaBuddhistmonkandauthor.
2. HistoricalBackground
PaststudieshavedocumentedandanalyzedthebiographicalaccountsofYixingand
hisancestry.Inanearlierstudy,Iarguedthatweoughttounderstandthe“historicalYixing”
asaseparatefigurefromalaterreimaginedpseudo-Yixing. Thelatterisalegendaryfigure
towhomvarioustextsandpracticeswereattributed,startingfromaroundtheearlyninth
century. Somemodernscholarsandvirtuallyallpremodernauthorshaveconflatedthese
twofigures. ThishasledtoproblematicchronologiesofYixing’slifeandhisactivities.5
Again, I will emphasize in this study that we ought to distinguish between Yixing and
pseudo-Yixing.
OurreconstructionofYixing’sworkinastronomydependsuponseveralpremodern
sources. FirstistheJiuTangshu舊唐書(OldBookofTang),whichisahistoryoftheTang
dynastyproducedbyLiuXu劉昫(887–946)in945. WecanalsoutilizetheXinTangshu新
唐書(NewBookofTang). ThisrevisedhistoryoftheTangdynastywascompiledin1060by
OuyangXiu歐陽修(1007–1072)andSongQi宋祁(998–1061),whoapparentlyintentionally
omittedYixing’sbiography,perhapsduetoanti-Buddhistbiasesandanimositytoward
thesam. gha,yettheystilladdeddocumentsrelatedtoYixing’scalendar,whichtheytreated
withrespect. Thisindirectlypointstoanappreciationofhisachievementsinastronomy,
despitethefactthathewasaBuddhistmonk. TheTongdian通典(ComprehensiveAccount),
compiledin801byDuYou杜佑(735–812),providesdetailsaboutYixing’sastronomical
projects. TheTongzhi通志(ComprehensiveChronicle),compiledin1161byZhengQiao鄭
樵(1104–1162),listsanumberofworks—genuineandspurious—attributedtoYixingthat
were extant during the twelfth century. One of the more underappreciated sources on
the history of astronomy and calendrical science in China is the voluminous Gujin lüli
kao古今律曆考(StudyofAncientandPresentTunesandCalendricalSciences),comprisedof
seventy-twofascicles,byXingYunlu邢雲路(1549–?). Thistextdocumentsatlengthsuch
sciencesastheywereunderstoodduringthelateMingdynastypriortotheintroduction
of European science. This work frequently mentions Yixing and his work, a point that
highlightstheutilityandimportanceofhiswritings,evenoutsidetheBuddhistfold,some
nine centuries after his death. The fact alone is highly significant, given that Yixing is
arguablythesoleBuddhistmonkinChinatohavebeenaffordedsuchenduringrespect
bothinBuddhistandConfuciancircles.
Inbrief,Yixingwasbornin673. Althoughtraditionalsourcesgive683ashisyearof
birth,Chen(2000)inhisstudyofYixing’slifeandgenealogyconvincinglydemonstrates
that673wasmorelikely. ThehistoricalrecordrelatesthatYixinginitiallystudiedChan
BuddhismunderthemonkPuji普寂(651–739). Yixingwassimultaneouslyascholarof
themonasticcodes(Vinaya,jielü戒律).Hebecamewell-knowntoeminentpersonsinthe
capital,butevadedinvitationstopresenthimselfthere,untilfinallyin717heacceptedan
officialsummonsfromthecourt.6
Religions2022,13,543 3of14
Yixing’s career in the capital (alternating between Chang’an and Luoyang), which
lasteduntilhissuddendeathin727,wasfruitfulandprimarilycomprisedtwodirections.
First,YixingassistedtheIndianmonkS´ubhakarasim. ha(Shanwuwei善無畏;637–735)in
translating the Vairocana¯bhisam. bodhi (Dari jing 大日經; T 848), which was completed in
724. Yixingappearstohavefunctionedmoreasaneditorinthisproject,ratherthanasa
translator(althoughheiscreditedastranslator),inlightoftheabsenceofevidencethat
wouldindicatehecapablyunderstoodSanskritenoughtotranslateit. Thereareactually
few examples of monks from East Asia who capably read Sanskrit in the premodern
period,apartfromfiguressuchasXuanzang,whohadspentyearsabroadinIndia.7The
ChinesetranslationoftheVairocana¯bhisam. bodhiwasfullofambiguities,sinceitwasfroma
newlyintroducedgenreofBuddhistliteraturewhichdealtwiththepracticesofmantras,
mudra¯s, and man.d.alas. Yixing therefore produced a commentary on the text (Dari jing
shu大日經疏;T1796)basedontheoralexplanationsS´ubhakarasim. ha. Thiscommentary
in one section addresses the timing of rituals, and briefly explains the conventions of
IndianastrologyknowntoS´ubhakarasim. ha,whichIhavearguedarelikelytoreflectthe
conventions of astrology observed at the major Indian monastery of Na¯landa. We can
alsoobserveinthissectionsomeastronomicaltheoryrelatedtolunarphases,whichno
doubtwaspennedbyYixinghimself. BasedontheoverviewofIndianastrologyinthe
commentary,itappearsthatS´ubhakarasim. hacertainlyhadsomeknowledgeonthetopic,
buthedoesnotappeartohavedirectlyaffectedthedevelopmentofastrologyorastronomy
inChina. Inotherwords,S´ubhakarasim. haknewsomeIndianastrology,butYixingwasthe
astronomer,andhisastronomy,aswewillsee,waschieflyChineseincharacterandnot
Indian. S´ubhakarasim. hadoesnotappeartohaveofferedinstructiononIndianastronomy
(i.e.,calculationsandmeasurements).8
YixingwasindeedapioneeringfigureofBuddhistMantraya¯nainEastAsia. Helater
wasenshrinedinJapanasalineageholderinMikkyo¯ (inbothShingonandTendai). In
contrasttoBuddhisthistories;however,ConfucianhistoriansinChinarememberedhim
primarilyasanastronomerandreformerofthestatecalendar. Yixing’searlyofficialwork
inastronomyisrecordedintheJiuTangshu,whichreportsthefollowing:
Inyear9ofKaiyuan[721]underXuanzong,theGrandScriberepeatedlyreported
tothethronethat(predictionsof)solareclipseswereineffective. Thes´raman.a
Yixingwassummonedtoreformandproduceanewcalendar. Yixing’sreport
stated,“Nowifweseektocreateacalendarandestablishanepoch,wemustfirst
understandhowtoconvertbetweentheecliptic(andthecelestialequator). Ire-
questthatthePrefectGrandScribetakeangularandchronologicalmeasurements
ofsiderealparameters.”玄宗開元九年,太史頻奏日蝕不效,詔沙門一行改造新曆.
一行奏雲: (cid:100)今欲創曆立元,須知黃道進退. 請太史令測候星度.(cid:99)9
ItisuncertainwhereandwhenYixingacquiredhisexpertiseinastronomyandmathe-
matics,butthecourtevidentlyagreedthathewascapable,afterthePrimeMinisterZhang
Yue張説667–730)electedhimasacandidateforthistask.10Thisnominationisreportedin
theJiuTangshu,whichalsostates,“DuringtheKaiyuanera[713–741],themonkYixing
wasproficientwiththecalendricaltheoriesofvariousauthors. HesaidthattheLindeli(an
earliercalendar)hadbeeninuseforalongtime,andthatitssolarandsiderealparameters
weregraduallybecomingdifferent.”開元中,僧一行精諸家曆法,言《麟德曆》行用既久,晷
緯漸差.11 ThiswasduringatimewhenIndian—orSino-Indian—figureswereoperating
attheChinesecourtandpracticingIndianastronomy. Bagchi(1898–1956)in1953already
drewcloseattentiontotwoofthesefamilies: theGautamasandKa¯s´yapas.12 Oneofthe
mostprominentastronomersofIndianheritageatthetimewasGautamaSiddha¯rthaor
Siddha(QutanXida瞿曇悉達),whoin718translatedthe*Navagraha-karan.a(Jiuzhili九執
曆)fromSanskritintoChineseattherequestofthethrone. Thismanualofmathematical
astronomyprovidesformulasforaccuratelycalculatinganumberofcelestialphenomena.
WhetherYixingeverdirectlystudiedundertheseastronomersisunknown,althoughhe
wasclearlyexposedtotheirworksandwaslikelytohavebeeninspiredbythemtosome
Religions2022,13,543 4of14
extent. AnotherIndianastronomer,whoappearstohavebeenacontemporaryofYixing,
was the monk Kuma¯ra (Jumoluo 俱摩羅). Yixing appears to have cited his theory for
predictingsolareclipses.13WeoughttonotethatYixingwasnottheonlymonkinChina
toalsohavebeenanastronomerduringtheTangperiod,butKuma¯rawasnotnearlyso
influential.
Numeroussources,includingYixing’sbiographyintheJiuTangshu,statethatYixing
learntmathematicsfromanunnamedindividualonMountTiantai天臺山atthemonastery
Guoqing-si國清寺,butthisiscertainlyafantasticaltale,sinceitalsorelatesthatthestream
of water outside the temple miraculously changed course after Yixing had fully learnt
everythingheneededfromtheunnamedteacher. Thisstory,moreover,doesnotprovide
anynamesordates.14 Ithinkitisplausible,ifnotlikely,thatYixingwassimplyanauto-
didacticpolymath,whosebackgroundaffordedhimthenecessaryresources,particularly
booksonmathematics,tobecomeaself-taughtastronomer,eveninthefaceoflawcodes
that prohibited the privatestudy of astronomy by commoners, as well as theBuddhist
literaturethatdiscouragesorforbidsthepracticeofmundanesciences,suchasastrology
andcalendricalscience.15
Inanycase,thehistoriesoftheTangdynastyrelatethatYixingwaschargedwiththe
taskofproducinganewstatecalendar. Hewasalreadycapableofthistaskbytheyear721.
HetitledhiscalendarDayanli大衍曆.Thiscalendarwasofficiallyadoptedbetween729–
761. Yixingdiedunexpectedlyin727beforehecouldseehiscalendarputintooperation,
butthecourtappointedofficialstoconsolidatehisdraft. TheTongzhi(j. 68)recordsthat
theoriginalDayanliwascomprisedoffifty-twofascicles.16 TheXinTangshu, however,
onlypreservesanoutlineoftheDayanli(j. 27–28)anditsimportantarguments. Thisis
ourmainsourceofinformationonthecalendar. XingYunlu(j. 15–16)givesanextensive
discussionoftheDayanliwithmanydetails,manyofwhichseemtoderivefromtheXin
Tangshu. Uponsurveyingtheabovematerials,itisclearthatseveralspecificmatterswere
ofimportancetoYixing. Theseincluded,butwerenotlimitedto,theneedforaccurate
understandingsofexactsolarpositionsrelativetoseasonalmarkers(theequinoxesand
solstices),theprecessionoftheequinoxes,andtheeclipticrelativetothecelestialequator.
YixingalsosoughttoestablishanexactdefinitionfortheNewMoon. Wewillseparately
discusseachofthesecomponentswithinhisresearch,butfirstweshouldbrieflynotehis
innovativeuseofnumbertheoryderivedfromtheYijing.
3. YijingNumberTheory
ThetitleofYixing’scalendarrevealsitsrichrelationshipwiththeYijing易經(Classic
ofChanges,alsocalledIChinginEnglish). Thetermdayan大衍(the“GreatExpansion”)is
derivedfromasectionoftheYijing(xicishang繫辭上),inwhichHeavenisassignedthe
number25,andEarththenumber30,togethertotaling55,althoughthe‘GreatExpansion’
isonly50(therearevariousancienttheoriesconcerningthesubtractionof5). Thenumber
of “application” (yong 用) is 49. The number theory derived from the Yijing (which is
notastrologicalincharacter)isexpresslystatedintheLibenyi曆本議(Argumentsonthe
Calendar),whichisasummaryofsomeoftheprimaryargumentsoftheDayanli. Thiswas
compiledafterYixingdiedprematurely(Yixingdiedin727).17
Inlatercenturies,duringtheMingperiod,Yixingwasstillknownforhisintegrationof
Yijingnumerologyintohiscalendar. XinYunlu(j. 16)notesthisandreproducesnumerous
detailsconcerningthisdevelopment.18Kajisuggestedthatincorporationofthisnumerol-
ogy into a calendar simply added perceived value, instead of furnishing any practical
advantage.19Inotherwords,itappearedinnovative,whileatthesametimequiteapprecia-
bletoliterati,whoweresteepedinclassicalloreandmetaphysics. Animportantpointto
notehereisthatYixingutilizedanativeChineseframeworkforcraftinghiscalendarwith-
outanyexpressreferencetoIndianorBuddhistcosmologicalandmetaphysicalconcepts,
although he still consulted some Indian materials, apparently in translation. Gautama
Zhuan瞿曇譔(712–776),sonofGautamaSiddha¯rtha,thetranslatoroftheNavagraha-karan.a,
arguedintheyear733thatYixing—whoalreadydiedin727—hadplagiarizedmaterial
Religions2022,13,543 5of14
fromtheNavagraha-karan.a,althoughtheformalinvestigationatcourtdeterminedthisclaim
wasfalse.20Thisconclusionmighthavebeenpremature,since,infact,theuseofatangent
table was an innovation that suddenly appears in the history of Chinese astronomy, as
pointedoutbyCullen,anditsadoptionbyYixingdoespointtoaforeignsource. Cullen
thereforesuggeststhatYixinghadlikelylearnedtherulesforrelatinggnomonshadows
andsolarzenithdistancesfromoneofhisIndiancounterpartsinthecapital.Inotherwords,
althoughhis“useofthetangentwasoriginal,heultimatelydependedonIndiansources
forhisintroductiontotrigonometry.”21Nevertheless,whileYixingcertainlyunderstood
someamountofIndianastronomy(presumablytranslatedintoChinese),hiscalendaris
primarilyrootedinChinesemodelsandconcepts(definitionoftheecliptic,sidereallunar
stationsbasedontheancientChinesesystem,etc.).
WemightexpectthataBuddhistmonksuchasYixingwouldhavebeeninclinedto
incorporatemoreIndianconceptsintohiswork,but,inreality,hiscalendarwaschiefly
rootedinChinesecalendricalscienceandmetaphysics. Thereactuallywasnoprecedent
foradoptionofforeignastronomicalmodelsuntilatleastsomemembersofthecourttook
aninterestinIndianastronomy,whichnodoubtfacilitatedthetranslationoftheNavagraha-
karan.a,butempiricaltestsdidnotyieldanypositiveoutcomefortheforeignmodel.
ThecompartmentalizationofscienceandreligioninYixing’slifehighlightstheclear
divisionofhislifeintotwoseparatesimultaneouscareers: oneinastronomyandtheother
inBuddhistpractice. Yixingwasevidentlycommittedtoreceivingandbuildingupona
legacyofChineseastronomyfromantiquity,ratherthanexpresslyintroducingsignificant
Indian models into the Chinese system. He might have even had an impetus to do so,
sinceMantraya¯nacallsfortheutilizationofsomeamountofastrology,whichwasbased
onIndianastronomy,asweseeintheSusiddhikara-su¯tra(Ch. Suxidijieluojing蘇悉地羯羅
經).ThiswastranslatedbyhisclosecolleagueS´ubhakarasim. hain726.22 Yixing,however,
neverattemptedsucharadicalreform.
4. GnomonicMeasurementsandPrecessionoftheEquinoxes
TheTongdian(j. 26)relatesthatintheyear724,NanGongyue南宮説(d.u.) andothers
travelledtoremotelocationswithintheempiretotakegnomonicmeasurementsandreport
backtothethrone. OnegroupwenttoAnnan安南(inmodernVietnam),andreportedthat
thestarCanopus(laorenxing老人星)wasespeciallyhighintheskywithnumerousother
unchartedandunnamedstarsvisiblebelowit. Ohashiexplainsthattheseobservations
weretakenbetweenabout18◦Nto51◦N,whereasCullensuggests29◦Nto52◦Nnearthe
meridian114◦E(Ohashi’sproposedrangeoflatitudesisnecessarytoaccountforaposition
innorthernVietnam). ThiswouldmeanthattheChineseobserversdidnotventureinto
thesouthernhemisphere,whichwouldhavepresentedsomeunfamiliarstarstoChinese
astronomers. OhashialsostatesthatYixinghimselfalsotravelledtotakemeasurements,
buttherelevantrecordsdonotactuallysuggestthathewentonanyoftheseexpeditions.23
Aftersometime,thesurveyorsreturnedtothecapital.Yixingwastaskedwithcollatingand
analyzingthedatafromthesevariouspointsofobservation. Hecalculatedthatthedistance
betweenthesouthernandnortherncelestialpolestobeover80,000li里(approximately
44,800km).24Toputthisintocontemporaryperspective,Xuanzangwrotethattheborders
of India are more than 90,000 li in diameter.25 Yixing clearly attempted to work with
gnomonic measurements in a scientific manner involving experimentation. As Cullen
alsonotes,thesurveyof724“wasafieldtest,evidentlysuccessful,ofI-hsing’s(Yixing’s)
methodforpredictingseasonalshadowlengthsatanylocation.”26Settingasidehowwe
mightcriticallyevaluatetheconclusionstoday,Yixing’sprojectwasasuccessatthetime.
Thedataacquiredfromthesemissionsincludedmeasurementsofshadowscastfrom
differentlocationsatthesolsticesandequinoxes. ThissetofdatawasusedbyYixingto
produceatangenttable. Judgingfromwhatisreportedintheavailablesources,itwould
appearthatYixing’stheoreticalframeworkwashamperedbytheabsenceofreferencetoa
sphericalearth. Yixingwouldnothavebeenignorantofthisalternatecosmologicaltheory,
since the aforementioned Navagraha-karan.a, translated in 718, addresses the concept of
Religions2022,13,543 6of14
terrestriallatitude. ThisconceptwasfirstrenderedintoChineseassuifangyanfa隨方眼法
(“methodaccordingtothelocationoftheobserver”). Thisappearstobeadirecttranslation
oftheSanskritsva-des´a-aks.a,aspointedoutbyYabuuchi.27Onemightinitiallyspeculate
that,asaBuddhistmonk,YixingwouldhavebeeninclinedtopreservethetypicalBuddhist
cosmologyofMt.Meruandthefourcontinentspositionedatopadisc-world,buthedidnot
dothis.28ItmustbeobservedthatChineseastronomersalsodidnotadoptaspherical-earth
model. Cullenimportantlynotesthat“Chineseastronomers,manyofthembrilliantmen
byanystandards,continuedtothinkinflat-earthtermsuntiltheseventeenthcentury.”29
Yixing’s astronomical framework in the Dayan li, drawing from this background, was
primarilybasedonnativeChinesemodelswithoutanyreferencetoBuddhistcosmology,yet
curiouslywhenwelooktothecommentaryontheVairocana¯bhisam. bodhi,thecosmological
worldviewisclearlythatofMt. Meruandthefourcontinents,i.e.,thetraditionalIndian
Buddhist cosmological worldview. For example, “The body of the Sun is one, but the
divisions of time are each different for the four continents.” 日体是一而四洲時分各異.
Elsewhereweread, “Thesefourcontinentsalsoeachhavetwoflankingcontinents.”此
四洲又各有二隨州.30 Thisis,however,asmuchthevoiceofS´ubhakarasim. haasitisthat
ofYixing.
TheaforementionedgnomonicmeasurementswouldhaveindicatedtoYixingthat
determiningtheexacttimeofthesolsticesandequinoxesrequiredreferencetothepoint
ofobservation,ratherthanusinganysinglestandardizednumberorsiderealpositionof
theSun. ThesiderealpositionoftheSunattheequinoxesandsolsticeswasalsoanissue
thathadtobeaddressed,sincefixedstarsmoveatamodernrateofonedegreeevery71.6
years.31Thisiscalledtheprecessionoftheequinoxesor,morecommonlyinmoderntimes,
axialprecession. Inpracticewhatthismeansisthatanobserverwouldeventuallynotice
thattheSunrisesatthewintersolstice(andotherseasonalmarkers)intothepreceding
degreerelativetowhatwasobservedinpreviouseras. Thiswasalreadyrecognizedwell
before Yixing’s time. Xing Yunlu (j. 2) explains Yixing’s contribution in history to the
understandingofprecessionasfollows:
DuringthelateHan,LiuHong[c.129–210]firstrealizedthatthewintersolsticewas
late.DuringtheJin,YuXi[281–356]treatedtheskyastheskyandtheseasonalyear
astheseasonalyear(i.e.,separatelytreatingsiderealandseasonalparameters),pro-
ducingatheoryforcalculatingthedifferencesinordertotrackthechanges(between
siderealpositionsandseasonalmarkers),assumingthattheSunretreatsonedegree
everyfiftyyears,butthiswaserroneous.DuringtheSong,HeChengtian[370–447]
doubledthatnumber,assuminga(solar)retreatofonedegreeeverycentury,but
againthiswaserroneous. DuringtheSui,LiuZhuo[544–610]tookthenumbers
frombothschools,andassumeda(solar)retreatofonedegreeeveryseventy-five
years.DuringtheTang,themonkYixingcalculatedhisDayancalendricalsystem,
andassumedadifferenceofonedegree(betweenseasonalmarkersandsidereal
positions)everyeighty-threeyears. Each(theory)wasclosetooneanother. Guo
Shoujing[1231–1316]calculatedthatthewintersolsticewasatthetenthdegreeof
lunarstationQi. Thiswasprecise,butShoujingthoughtthatadifferenceofone
degreeevery66yearsisalsonotadefinitivetheory. 漢末劉洪, 始覺冬至後天, 至
晉虞喜, 乃以天為天, 歳為歳, 立差法以追其變, 約以五十年日退一度, 然失之過.
宋何承天, 倍増其數, 約以百年退一度, 又失之不及. 隋劉焯, 取二家中數以七十五
年退一度. 唐僧一行推大衍暦, 以八十三年差一度. 各亦相近. 至郭守敬, 推冬至在
箕十度, 斯為密近, 然守敬謂六十六年差一度亦非定法.32
Therewasclearlyapersistentawarenessoverthecenturiesthatrevisionswerenec-
essaryanddesirabletodeterminetherateoftheprecessionoftheequinoxes. Eachfigure
cametotheirownconclusionsbasedonthedatasetsavailabletothem,afactthathigh-
lightsthatinnovationwasappreciated(ratherthandogmaticadherencetothemodelsof
antiquity). Yixing contributed to this ongoing dialogue in history, thereby securing for
himselfanotablepositioninthehistoryofChineseastronomy.
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Yixing’stheorythattheSunretreatsonedegreeevery83yearseffectivelyconstitutesa
signatureofhisworkthatreappearselsewhereinthehistoricalrecord,suchasthetable
of24solarterms(jieqi節氣)intheQiyaorangzaijue七曜攘災決(SecretsoftheSeven-Planet
Apotropaism),aBuddhistmanualofhoroscopyandastralmagicthatwascompiledbetween
806–865fromdisparatesources.33ThisisanexampleofYixing’sworkbeingdirectlyutilized
withinearlyChinesehoroscopy. The24solartermsareeachcomprisedof15days. They
trackthepassageoftheSunthroughsiderealdegreesofthe28“lunarstations”or“lodges”
(xiu宿),andmostimportantlymarktheseasons;hencethesolsticesandequinoxesarepart
ofthissystem.34 Simplifieddegreesareusedbecausethetabletracks360daysinwhich
the Sun progresses 1 degree every day. The ecliptic in China was generally treated as
comprising365.25degrees(thenominallengthofatropicalyear),butthetabledoesnot
addresstheremainingdegrees,sothepositionsprovidedinthetableareapproximate.
WithregardtothetableofsolartermsintheQiyaorangzaijue,thetextstates,“There
willbeadifferenceofadegreeortwoifyourelyuponthis(table).Itwascalculatedforafter
Kaiyuan12[724]. Thereoccursanerrorofonedegreefollowingeighty-threeyears.”若依此
即差一兩度,從開元十二年向後計,滿八十三年即差一度.35Thiswouldindicateaconnection
toYixing’smodel. Wecanciteadditionalevidenceinsupportofthisclaim. Thewinter
solstice(dongzhi冬至)fallsupondegree9ofthestationDou斗inthistableofsolarterms.
TheaccountoftheShoushili授時暦,astatecalendarwhichwasimplementedin1281,is
foundintheYuanshi元史(j. 52),thedynastichistoryoftheYuandynasty. Itisreported
therethatin724(year12ofKaiyuan)thewintersolsticefellondegree9.5ofDou.36 The
solar table at hand does not use fractions, but this was presumably to facilitate ease of
use for astrologers, who needed a convenient table for calculating planetary positions
inhoroscopes.
5. AccurateDefinitionoftheEcliptic
Yixing,likemanyotherastronomers,soughttoenhanceandinnovate,yethesimulta-
neouslyacknowledgedthecapabilitiesoftheancients(inthiscase,theancientsofChina
andnotBuddhistIndia). AsrecordedintheXinTangshu(j. 31),Yixingandhiscolleague
utilizedimprovedtechnology,whilealsostillofferingarespectfulnodtotheirpredecessors,
which perhaps was a polite necessity. Yixing, evidently, sought to carry and develop a
traditionofastronomythathadbeenhandedtohimfrommanycenturiesprior,whichwas
believedtostretchbacktothesagesofantiquity.
Inyear9ofKaiyuan(721),Yixingreceivedimperialorders,andwenttoworkon
reforminganewcalendar. Hewantedtounderstandthehowtoconvertbetween
theecliptic(andthecelestialequator),buttheGrandScribedidnotpossessan
instrumentfortheecliptic. AdministratorforTroopsoftheGuardCommand,
LiangLingzan,producedanarmillarysphereoutofwood. Yixingapprovedthis.
Hethensaiduntothethrone,“DuringAntiquitythereexistedthetechniquefor
aneclipticalarmillarysphere,butsuchadevicedidnotexist. Ancientspondered
it,buttheycouldneverachieveit. Now,Lingzan’screationhasthesolarpathand
Moonintersectsothattheyalwaysnaturallylineup. Thisisespeciallyimportant
forcalculations,andIrequestthatacastingbemadewithbronzeandiron.”The
instrumentwascompletedinyear11[723]. 開元九年,一行受詔,改治新曆,欲知
黃道進退,而太史無黃道儀. 率府兵曹參軍梁令瓚以木為游儀,一行是之,乃奏:(cid:100)黃
道游儀,古有其術而無其器,昔人潛思,皆未能得.今令瓚所為,日道月交,皆自然契
合,于推步尤要,請更鑄以銅鐵.(cid:99)十一年儀成.37
Thisapparatuswasalsoupgradedwithadditionalstructures,castinmetal,which
represented the celestial sphere in detail. The model turned by the power of flowing
water. RepresentationsoftheSunandtheMoonwereaddedtothissetup, sothatthey
became conjunct every 29 turns. The phases of the Moon were also displayed on the
instrument. Awoodenfigurinewasplacedatoptheplaneofthedeviceandwouldstrikea
drumandbelltokeeptrackofthetime. Eventuallythisdevicerustedoutandnolonger
Religions2022,13,543 8of14
functioned,buttheoriginalapparatusformeasuringtheeclipticenabledYixingtotake
accuratemeasurementsoftheeclipticaswellastheSunandplanets.38
Yixing’scalendarofferedrevisedparametersofthe28lunarstations,whicharedefined
intwoseparatesets: onerelativetothecelestialequatorandanotherrelativetotheecliptic.
TheselistscommencefromDou斗sinceitwasthestationonwhichthewintersolsticefell
atthetime. Thelattersetwasdesignedtoaccuratelytrackplanetarymovements. Hiswork
reads,“Theabove(values)arealleclipticaldegrees. Thesolarpathiscalculated,andthe
Moonandfiveplanetsorbitthroughthis.”前皆黃道度,其步日行,月與五星,出入循此. The
commentarythengivesthefollowingexplanation:
Inseekingthedegreesofthelunarstations,therewillalwaysexistaremainder.
Arrange the sequence to comprise the total degrees constituted with quarters
(0.25),halves(0.50),andthree-quarters[0.75]. Whencheckingagainstthepast
andfuture,thecontemporarydegreesandparametersofthelunarstationswillbe
acquiredaccordingtoindividualcalculationsforeachdegreethathasshifteddue
toprecession,sothatyouwillbeabletocalculatetheSun,Moon,andfiveplanets,
aswellasknowtheirencroachmentsandholdings(intermsofomenology). 求此
宿度,皆有餘分,前後輩之成少半太准為全度. 若上考古下驗將來,當據差每移一度,
各依術算,使得當時宿度及分,然可步日月五星,知其犯守也.39
Thecombinedparametersoftheeclipticallunarstationsequal365.25degrees,butthe
textnotesthata“difference”(cha差)istakenintoaccountfromthelunarstationXu虛.40
Yixing’simportantinnovationherewascreatingatableandmethodforrecalculatingthe
eclipticaldimensionsoflunarstationstoaccountforchangesinpositionsduetoprecessions,
whichinturnallowedformoreprecisecalculationsofplanetarymovements. Yixingindeed
wentsofarastoredefinethedimensionsofthelunarstations,althoughhestillpreserved
theclassicalsetof28,whicharespatiallyrelativetonativeChineseconstellations. This
kepthismodelinlinewiththeorthodoxChineseuranographywhichstretchedbackto
antiquity,butYixingwasstillinnovative.
ThisadherencetoclassicalChineseconventionsonthepartofYixingstandsincontrast
towhatweobserveintheNavagraha-karan.a,whichusesasystemofreformednaks.atras.
OlderIndiantextswhichhadbeentranslatedintoChineseinearliercenturies,suchasthe
S´a¯rdu¯lakarn.a¯vada¯na, define28naks.atrasofvaryingdimensionsusingmuhu¯rtas(aunitof
time),butfollowingtheintroductionofthezodiacsignsintoIndiaduringtheearlycenturies
of the Common Era, Indian astronomers redefined the parameters of the naks.atras and
producedasystemof27naksatrasconsistingofuniformdimensions.41TheNavagraha-karan.a
givesthefollowingexplanation:
Aformulainvolvingthenaks.atrasisincludedwithinthesemethods. Thenaks.atras
areuniformly800parts(minutes)each. InIndiatheydeterminewhethertheday
isauspiciousorinauspiciousbasedonthenaks.atrainwhichtheMoonalights,
andtheactivitiesassociatedwiththatnaks.atraarealsoundertaken. Furthermore,
only27naks.atrasareemployed,startingwithAs´vin¯ı,withAbhijitexcluded,and
endingwithRevat¯ı. Thenaks.atraAbhijitalwaysaugursauspicioustimesandis
notincludedamongstthenaks.atras. 宿法於此術中,凡是宿平等為八百分. 天竺每
以月臨宿,占其日一即休咎,仍取其宿用事.又唯用二十七宿,命婁為始,去牛,終奎.
其牛宿恒吉祥之時,不拘諸宿之例.42
In addition to this text, we can also observe this model of equalized naksatras and
therelatedsystemofnava¯m. s´as(ninthsofanaks.atra)explainedinthecommentaryonthe
Vairocana¯bhisam. bodhi,whichwewillrecallwascompiledbyYixingonthebasisoftheoral
explanationsprovidedbyS´ubhakarasim. ha.
Lunarstationconvergences: The27naks.atras. Heaven(i.e.,theecliptic)isdivided
intotwelvechamberslikethetwelveJupiterstationshere(inChina). Eachstation
has9quarters(pa¯da). Theeclipticisaltogether108quarters. Eachnaks.atragets
fourquarters,whichconstitutesthecourseofmovementthattheMoontravelsin
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oneday. TheMoonhasgoneoncearoundtheeclipticaftertransitingfor27days.
言宿直者,謂二十七宿也. 分周天作十二房,猶如此間十二次. 每次有九足,周天凡
一百八足,每宿均得四足,即是月行一日裎.經二十七日,即月行一周天也.43
ItiscertainthatYixingwasawareofhowIndianastronomersdefinednaks.atras,inpar-
ticularthemodelof27naks.atrasofuniformlyequaldimensions,whichwasunprecedented
inChinauntilthatpoint. Yixing’sworkwouldhavebeensubjecttoenormouscriticism
hadheattemptedtoentirelyrevisethesystemofChineselunarstations,whichhadbeenin
usesinceantiquity,afterhisexposuretoIndianmodels,butthereisnothingtoindicatehe
everhadsuchamotivation.
6. RedefiningtheNewMoon
Lastly,anotherimportantissuetowhichYixingdirectedhisattentionwasthetechnical
inaccuracy of how the New Moon (shuo 朔) was conventionally determined. His lunar
calendrical theory is also the sole known example of one of his astronomical theories
appearinginhisBuddhistwritings,althoughweshouldalsorecognizethefactthatnotall
ofhiswritingsareextant.
The lunar months in the Chinese calendar are arranged so that generally the New
MoonfallsuponthefirstdayofthemonthwhiletheFullMoonfallsupononthefifteenth.
TheFullMoonappearswhentheSunandMoonareindirectoppositiontooneanother,
whiletheNewMooniswhentheSunandMoonareconjunct. TheproblemisthattheNew
MoonandFullMoondonotnecessarilyfallexactlyonthefirstandfifteenthdaysofthe
lunarmonth,respectively.
YixingproposedascientificdefinitiontheNewMoonas“whentheSunandMoonare
conjunctwithinadegree.”日月合度謂之朔.44 Thisisrelativelysimple,butitshiftsaway
fromwhatwasunderstoodasan“averaged”or“mean”NewMoon(pingshuo平朔),which
referstothetraditionalwayofdeterminingthelunarcyclethroughgeneralobservation.
Yixinggivesthefollowingexplanation:
WithrespecttotheaveragedNewMoonoftheancients,theMoonappearingin
themorningiscalledthe“Moonrisingatsunrise,”whileappearingintheevening
iscalledthe“Moonrisingatsunset.”Nowthesearedecreasedorincreased(i.e.,
modified)accordingtotheprogressionoftheSunandthevelocityoftheMoon.
(ThefixedNewMoon)willsometimesprogressaheadoforfallshortofthatday
[i.e.,theaveragedNewMoon,whichistraditionallydefinedasthefirstdayof
thelunarmonth]. ThisisconsideredafixedNewMoon.
古者平朔,月朝見曰朒,夕見曰朓. 今以日之所盈縮,月之所遲疾損益之,或進退其
日,以為定朔.45
Inthisrevisedsystem,theNewMoonandFullMoonare“fixed”(ding定),i.e.,scientif-
icallydefinedaccordingtotherealpositionsoftheSunandMoon. Thisconceptofafixed
NewandFullMoonismentionedinYixing’scommentaryontheVairocana¯bhisam. bodhi:
Also, thecalendarcalculatestheSunandtheMoon. Theaverageddegreesof
motionmakeforaveragedNewMoons. Itwillalwaysaligninalesser(29)or
greater(30)month[onthesameday]. Sometimes[thedatefortheNewMoon]
willpassorbelatewithrespecttotheaveragedmovementsoftheSunandMoon
astheirspeedswillalsodiffer. ThisiswhyafixedNewMoonwillsometimesbe
aheadorbehindaday. AfixedFullMoonwillsometimesbeonthefourteenth
oronthesixteenth. Generallyspeaking,thetimewhentheMooniscompletely
fullisdesignatedasthefifteenthdayofthewaxingperiod(Skt. s´ukla-paks.a). The
timewhentheMoonisexactlyhalflikeabowstringwillbetheeighth. Itmaybe
arrangedbasedonthis,andthenonegetsafixeddate.
又曆法通計日月,平行度作平朔,皆合一小一大. 緣日月於平行中,又更有遲疾,或
時過於平行,或時不及平行,所以定朔或進退一日,定望或在十四日或在十六日. 大
Religions2022,13,543 10of14
抵月望正圓滿時,名為白分十五日. 月正半如弦時,亦為八日. 但以此准約之,即得
定日也.46
InlightoftheparallelswithYixing’scalendar,thispartofthecommentaryisclearly
Yixing’svoice, andnotthatofS´ubhakarasim. ha. Thereaderisbeingcautionedthatthe
true Full Moon may sometimes appear a day ahead or behind the fifteenth day of the
lunarmonth. Thismatterwasimportantforthepurposesoftimingrituals,sincethetrue
phaseoftheMoonoughttobeconsidered,ratherthansimplyassumingthatthefirstor
fifteenthofthecalendarmonthalwaysalignwiththeNewandFullMoonsrespectively.
This was important to Yixing in particular, since the Vairocana¯bhisam. bodhi calls for the
man.d.alatobeproducedonauspiciousdays,suchasthedayoftheFullMoon. Thefruitsof
theman.d.alawouldbecompromisediftheproperphaseoftheMoon—amongotherfactors
suchasthedayoftheweek—werenotstrictlyobserved. Again,thisisonerareinstancein
whichYixing’sworkincalendricalsciencewasdirectlyapplicabletoBuddhistactivities.
Otherwise,hisworkinastronomywasseparatefromBuddhism.
7. Conclusions
Thesurveyaboveshowsthatanewlycollecteddatasetofgnomonicmeasurements,
theproductionofanimprovedarmillaryspherewitharingrepresentingtheecliptic,and
generallyimprovedastronomicaltheory,allenabledYixingtocreateamoreprecisecalen-
dricalsystemattherequestofthecourt. Yixingdidnotframehimselfasarevolutionary
inscience,butrathergavearespectfulnodtohispredecessorsandpositionedhimselfas
adeveloper atopthe achievementsof pastfigures. Latergenerations afforded Yixinga
significantplaceinthehistoryofastronomy.
Yixing’sincorporationofconceptsfromtheYijingintohistheoreticalframeworkis
unique. XingYunluinthe16thcenturyinterestinglydoesnotmentionYixingthroughout
hisoutlineofBuddhist,Daoist,Indian,andIslamicatemodelsofcosmologyandastronomy
(j. 28).47 This would seem to indicate that Xing Yunlu thought of Yixing as a credible
astronomerwhoseworkbelongedtothehistoryofofficialcourtastronomyinChina. The
extantprimarysourcesthatdiscussYixing’sworkinastronomyindeeddonotdisplayany
Buddhistelements,suchasthecosmologyofMountMeruandtherelatedsystemofkinetics
thatexplainplanetarymotionsthroughwinds. Themodelsofkinematicsweobservein
BuddhistAbhidharmaliteraturearealsoabsentfromYixing’sastronomicalwork. Yixing
insteadwasmoreinspiredbyChinese—notBuddhist—metaphysics. Thisisanimportant
point,sinceitdemonstratesthatYixingwaswillingto(andprobablysimplyhadto)set
asideBuddhistcosmologyinordertoworkwithinadifferentfield. Thiswaspresumably
outofnecessity,sincethestateisunlikelytohavepermittedanyradicalchangestothe
foundationsofastronomyandastrometricmodels. Theabsenceofanysignificantadoption
ofIndianastronomyinChinesetranslation—suchasthatoftheGautamas—byYixingor
anyoneelseonlyconfirmsthisassumption.
Anotherpointtoemphasizehereisthat,inreality,Yixing’sBuddhistcareerwaslargely
separatefromhiscareerasanastronomer. Inotherwords,Buddhismneitherinspirednor
informedhisstudyofastronomy. TheBuddhistcommunityalsodoesnotappeartohave
utilizedhiscalendaroradvancedscientificworkinanynotablecapacitybeyondwhatwe
notedabove. Theremightnothavebeenanypressingneedtodoso,butthisjusthighlights
thathistwoprofessionswere,inpractice,quiteseparatefromoneanother.
YixingwastheonlycourtastronomerinChinesehistorywhoservedasamonkand
officiallyworkedonthestatecalendar(theaforementionedmonkKuma¯rawasanother
figurefromtheTangperiod,buthewasnotcommissionedtoworkonthestatecalendar),
butYixing’sstatusasamonkalonecannotqualifyhiscalendaraspossessingany“Buddhist”
featuresorquality. Wecan,however,observethatitwasYixing’seminenceasaBuddhist
writerandpractitionerthatbroughtaboutaninvitationtothecapital.Thisrelocationclearly
broughttogetherthe“causesandconditions”whichenabledhiscareerasanastronomerto
flourish. Ifhehadnotcometothecapitalinthecapacityasaneminentmonk,hemight
nothaveeverbeeninvolvedinastronomyatthestatelevel. Inthatsense,Buddhismonly