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Contents
Overview
viii
ListofIllustrations
xiv
WordsofThanks
xix
PartI:GEB
Introduction:AMusico-LogicalOffering
3
Three-PartInvention
29
ChapterI:TheMU-puzzle
33
Two-PartInvention
43
ChapterII:MeaningandForminMathematics
46
SonataforUnaccompaniedAchilles
61
ChapterIII:FigureandGround
64
Contracrostipunctus
75
ChapterIV:Consistency,Completeness,andGeometry
82
LittleHarmonicLabyrinth
103
ChapterV:RecursiveStructuresandProcesses
127
CanonbyIntervallicAugmentation
153
ChapterVI:TheLocationofMeaning
158
ChromaticFantasy,AndFeud
177
ChapterVII:ThePropositionalCalculus
181
CrabCanon
199
ChapterVIII:TypographicalNumberTheory
204
AMuOffering
231
ChapterIX:MumonandGödel
246
Contents II
PartIIEGB
Prelude...
275
ChapterX:LevelsofDescription,andComputerSystems
285
AntFugue
311
ChapterXI:BrainsandThoughts
337
EnglishFrenchGermanSuit
366
ChapterXII:MindsandThoughts
369
AriawithDiverseVariations
391
ChapterXIII:BlooPandFlooPandGlooP
406
AironG'sString
431
ChapterXIV:OnFormallyUndecidablePropositionsofTNT
andRelatedSystems
438
BirthdayCantatatata...
461
ChapterXV:JumpingoutoftheSystem
465
EdifyingThoughtsofaTobaccoSmoker
480
ChapterXVI:Self-RefandSelf-Rep
495
TheMagnfierab,Indeed
549
ChapterXVII:Church,Turing,Tarski,andOthers
559
SHRDLU,ToyofMan'sDesigning
586
ChapterXVIII:ArtificialIntelligence:Retrospects
594
Contrafactus
633
ChapterXIX:ArtificialIntelligence:Prospects
641
SlothCanon
681
ChapterXX:StrangeLoops,OrTangledHierarchies
684
Six-PartRicercar
720
Notes
743
Bibliography
746
Credits
757
Index
759
Contents III
Overview
PartI:GEB
Introduction:AMusico-LogicalOffering.ThebookopenswiththestoryofBach'sMusicalOffering.BachmadeanimpromptuvisittoKingFredericktheGreatofPrussia,andwasrequestedtoimproviseuponathemepresentedbytheKing.Hisimprovisationsformedthebasisofthatgreatwork.TheMusicalOfferinganditsstoryformathemeuponwhichI"improvise"throughoutthebook,thusmakingasortof"MetamusicalOffering".Self-referenceandtheinterplaybetweendifferentlevelsinBacharediscussed:thisleadstoadiscussionofparallelideasinEscher'sdrawingsandthenGödel’sTheorem.AbriefpresentationofthehistoryoflogicandparadoxesisgivenasbackgroundforGödel’sTheorem.Thisleadstomechanicalreasoningandcomputers,andthedebateaboutwhetherArtificialIntelligenceispossible.Iclosewithanexplanationoftheoriginsofthebook-particularlythewhyandwhereforeoftheDialogues.
Three-PartInvention.Bachwrotefifteenthree-partinventions.Inthisthree-partDialogue,theTortoiseandAchilles-themainfictionalprotagonistsintheDialogues-are"invented"byZeno(asinfacttheywere,toillustrateZeno'sparadoxesofmotion).Veryshort,itsimplygivestheflavoroftheDialoguestocome.
ChapterI:TheMU-puzzle.Asimpleformalsystem(theMIL'-system)ispresented,andthereaderisurgedtoworkoutapuzzletogainfamiliaritywithformalsystemsingeneral.Anumberoffundamentalnotionsareintroduced:string,theorem,axiom,ruleofinference,derivation,formalsystem,decisionprocedure,workinginside/outsidethesystem.
Two-PartInvention.Bachalsowrotefifteentwo-partinventions.Thistwo-partDialoguewaswrittennotbyme,butbyLewisCarrollin1895.CarrollborrowedAchillesandtheTortoisefromZeno,andIinturnborrowedthemfromCarroll.Thetopicistherelationbetweenreasoning,reasoningaboutreasoning,reasoningaboutreasoningaboutreasoning,andsoon.Itparallels,inaway,Zeno'sparadoxesabouttheimpossibilityofmotion,seemingtoshow,byusinginfiniteregress,thatreasoningisimpossible.Itisabeautifulparadox,andisreferredtoseveraltimeslaterinthebook.
ChapterII:MeaningandForminMathematics.Anewformalsystem(thepq-system)ispresented,evensimplerthantheMIU-systemofChapterI.Apparentlymeaninglessatfirst,itssymbolsaresuddenlyrevealedtopossessmeaningbyvirtueoftheformofthetheoremstheyappearin.Thisrevelationisthefirstimportantinsightintomeaning:itsdeepconnectiontoisomorphism.Variousissuesrelatedtomeaningarethendiscussed,suchastruth,proof,symbolmanipulation,andtheelusiveconcept,"form".
SonataforUnaccompaniedAchilles.ADialoguewhichimitatestheBachSonatasforunaccompaniedviolin.Inparticular,Achillesistheonlyspeaker,sinceitisatranscriptofoneendofatelephonecall,atthefarendofwhichistheTortoise.Theirconversationconcernstheconceptsof"figure"and"ground"invarious
Overview IV
contexts-e.g.,Escher'sart.TheDialogueitselfformsanexampleofthedistinction,sinceAchilles'linesforma"figure",andtheTortoise'slines-implicitinAchilles'lines-forma"ground".
ChapterIII:FigureandGround.Thedistinctionbetweenfigureandgroundinartiscomparedtothedistinctionbetweentheoremsandnontheoremsinformalsystems.Thequestion"Doesafigurenecessarilycontainthesameinformationasitsground%"leadstothedistinctionbetweenrecursivelyenumerablesetsandrecursivesets.
Contracrostipunctus.ThisDialogueiscentraltothebook,foritcontainsasetofparaphrasesofGödel’sself-referentialconstructionandofhisIncompletenessTheorem.OneoftheparaphrasesoftheTheoremsays,"Foreachrecordplayerthereisarecordwhichitcannotplay."TheDialogue'stitleisacrossbetweentheword"acrostic"andtheword"contrapunctus",aLatinwordwhichBachusedtodenotethemanyfuguesandcanonsmakinguphisArtoftheFugue.SomeexplicitreferencestotheArtoftheFuguearemade.TheDialogueitselfconcealssomeacrostictricks.
ChapterIV:Consistency,Completeness,andGeometry.TheprecedingDialogueisexplicatedtotheextentitispossibleatthisstage.Thisleadsbacktothequestionofhowandwhensymbolsinaformalsystemacquiremeaning.ThehistoryofEuclideanandnon-Euclideangeometryisgiven,asanillustrationoftheelusivenotionof"undefinedterms".Thisleadstoideasabouttheconsistencyofdifferentandpossibly"rival"geometries.Throughthisdiscussionthenotionofundefinedtermsisclarified,andtherelationofundefinedtermstoperceptionandthoughtprocessesisconsidered.
LittleHarmonicLabyrinth.ThisisbasedontheBachorganpiecebythesamename.Itisaplayfulintroductiontothenotionofrecursive-i.e.,nestedstructures.Itcontainsstorieswithinstories.Theframestory,insteadoffinishingasexpected,isleftopen,sothereaderisleftdanglingwithoutresolution.Onenestedstoryconcernsmodulationinmusic-particularlyanorganpiecewhichendsinthewrongkey,leavingthelistenerdanglingwithoutresolution.
ChapterV:RecursiveStructuresandProcesses.Theideaofrecursionispresentedinmanydifferentcontexts:musicalpatterns,linguisticpatterns,geometricstructures,mathematicalfunctions,physicaltheories,computerprograms,andothers.
CanonbyIntervallicAugmentation.AchillesandtheTortoisetrytoresolvethequestion,"Whichcontainsmoreinformation-arecord,orthephonographwhichplaysitThisoddquestionariseswhentheTortoisedescribesasinglerecordwhich,whenplayedonasetofdifferentphonographs,producestwoquitedifferentmelodies:B-A-C-HandC-A-G-E.Itturnsout,however,thatthesemelodiesare"thesame",inapeculiarsense.
ChapterVI:TheLocationofMeaning.Abroaddiscussionofhowmeaningissplitamongcodedmessage,decoder,andreceiver.ExamplespresentedincludestrandsofDNA,undecipheredinscriptionsonancienttablets,andphonographrecordssailingoutinspace.Therelationshipofintelligenceto"absolute"meaningispostulated.
ChromaticFantasy,AndFeud.AshortDialoguebearinghardlyanyresemblance,exceptintitle,toBach'sChromaticFantasyandFugue.Itconcernstheproperwaytomanipulatesentencessoastopreservetruth-andinparticularthequestion
Overview V
ofwhetherthereexistrulesfortheusageoftheword"arid".ThisDialoguehasmuchincommonwiththeDialoguebyLewisCarroll.
ChapterVII:ThePropositionalCalculus.Itissuggestedhowwordssuchas.,and"canbegovernedbyformalrules.Onceagain,theideasofisomorphismandautomaticacquisitionofmeaningbysymbolsinsuchasystemarebroughtup.AlltheexamplesinthisChapter,incidentally,are"Zentences"-sentencestakenfromZenkoans.Thisispurposefullydone,somewhattongue-in-cheek,sinceZenkoansaredeliberatelyillogicalstories.
CrabCanon.ADialoguebasedonapiecebythesamenamefromtheMusicalOffering.Botharesonamedbecausecrabs(supposedly)walkbackwards.TheCrabmakeshisfirstappearanceinthisDialogue.ItisperhapsthedensestDialogueinthebookintermsofformaltrickeryandlevel-play.Gödel,Escher,andBacharedeeplyintertwinedinthisveryshortDialogue.
ChapterVIII:TypographicalNumberTheory.AnextensionofthePropositionalCalculuscalled"TNT"ispresented.InTNT,number-theoreticalreasoningcanbedonebyrigidsymbolmanipulation.Differencesbetweenformalreasoningandhumanthoughtareconsidered.
AMuOffering.ThisDialogueforeshadowsseveralnewtopicsinthebook.OstensiblyconcernedwithZenBuddhismandkoans,itisactuallyathinlyveileddiscussionoftheoremhoodandnontheoremhood,truthandfalsity,ofstringsinnumbertheory.Therearefleetingreferencestomolecularbiology-particular)theGeneticCode.ThereisnocloseaffinitytotheMusicalOffering,otherthaninthetitleandtheplayingofself-referentialgames.
ChapterIX:MumonandGödel.AnattemptismadetotalkaboutthestrangeideasofZenBuddhism.TheZenmonkMumon,whogavewellknowncommentariesonmanykoans,isacentralfigure.Inaway,Zenideasbearametaphoricalresemblancetosomecontemporaryideasinthephilosophyofmathematics.Afterthis"Zennery",Gödel’sfundamentalideaofGödel-numberingisintroduced,andafirstpassthroughGödel’sTheoremismade.
PartII:EGB
Prelude...ThisDialogueattachestothenextone.TheyarebasedonpreludesandfuguesfromBach'sWell-TemperedClavier.AchillesandtheTortoisebringapresenttotheCrab,whohasaguest:theAnteater.ThepresentturnsouttobearecordingoftheW.T.C.;itisimmediatelyputon.Astheylistentoaprelude,theydiscussthestructureofpreludesandfugues,whichleadsAchillestoaskhowtohearafugue:asawhole,orasasumofparts?Thisisthedebatebetweenholismandreductionism,whichissoontakenupintheAntFugue.
ChapterX:LevelsofDescription,andComputerSystems.Variouslevelsofseeingpictures,chessboards,andcomputersystemsarediscussed.Thelastoftheseisthenexaminedindetail.Thisinvolvesdescribingmachinelanguages,assemblylanguages,compilerlanguages,operatingsystems,andsoforth.Thenthediscussionturnstocompositesystemsofothertypes,suchassportsteams,nuclei,atoms,theweather,andsoforth.Thequestionarisesastohowmanintermediatelevelsexist-orindeedwhetheranyexist.
Overview VI
…AntFugue.Animitationofamusicalfugue:eachvoiceenterswiththesamestatement.Thetheme-holismversusreductionism-isintroducedinarecursivepicturecomposedofwordscomposedofsmallerwords.etc.Thewordswhichappearonthefourlevelsofthisstrangepictureare"HOLISM","REDLCTIONIsM",and"ML".ThediscussionveersofftoafriendoftheAnteater'sAuntHillary,aconsciousantcolony.Thevariouslevelsofherthoughtprocessesarethetopicofdiscussion.ManyfugaltricksareensconcedintheDialogue.Asahinttothereader,referencesaremadetoparalleltricksoccurringinthefugueontherecordtowhichthefoursomeislistening.AttheendoftheAntFugue,themesfromthePreludereturn.transformedconsiderably.
ChapterXI:BrainsandThoughts."HowcanthoughtshesupportedbythehardwareofthebrainisthetopicoftheChapter.Anoverviewofthelargescaleandsmall-scalestructureofthebrainisfirstgiven.Thentherelationbetweenconceptsandneuralactivityisspeculativelydiscussedinsomedetail.
EnglishFrenchGermanSuite.AninterludeconsistingofLewisCarroll'snonsensepoem"Jabberwocky`'togetherwithtwotranslations:oneintoFrenchandoneintoGerman,bothdonelastcentury.
ChapterXII:MindsandThoughts.Theprecedingpoemsbringupinaforcefulwaythequestionofwhetherlanguages,orindeedminds,canbe"mapped"ontoeachother.Howiscommunicationpossiblebetweentwoseparatephysicalbrains:Whatdoallhumanbrainshaveincommon?Ageographicalanalogyisusedtosuggestananswer.Thequestionarises,"Canabrainbeunderstood,insomeobjectivesense,byanoutsider?"
AriawithDiverseVariations.ADialoguewhoseformisbasedonBach'sGoldbergVariations,andwhosecontentisrelatedtonumber-theoreticalproblemssuchastheGoldbachconjecture.Thishybridhasasitsmainpurposetoshowhownumbertheory'ssubtletystemsfromthefactthattherearemanydiversevariationsonthethemeofsearchingthroughaninfinitespace.Someofthemleadtoinfinitesearches,someofthemleadtofinitesearches,whilesomeothershoverinbetween.
ChapterXIII:BlooPandFlooPandGlooP.Thesearethenamesofthreecomputerlanguages.BlooPprogramscancarryoutonlypredictablyfinitesearches,whileFlooPprogramscancarryoutunpredictableoreveninfinitesearches.ThepurposeofthisChapteristogiveanintuitionforthenotionsofprimitiverecursiveandgeneralrecursivefunctionsinnumbertheory,fortheyareessentialinGödel’sproof.
AironG'sString.ADialogueinwhichGödel’sself-referentialconstructionismirroredinwords.
TheideaisduetoW.V.O.Quine.ThisDialogueservesasaprototypeforthenextChapter.
ChapterXIV:OnFormallyUndecidablePropositionsofTNTandRelatedSystems.ThisChapter'stitleisanadaptationofthetitleofGödel’s1931article,inwhichhisIncompletenessTheoremwasfirstpublished.ThetwomajorpartsofGödel’sproofaregonethroughcarefully.ItisshownhowtheassumptionofconsistencyofTNTforcesonetoconcludethatTNT(oranysimilarsystem)isincomplete.RelationstoEuclideanandnon-Euclideangeometryarediscussed.Implicationsforthephilosophyofmathematicsaregoneintowithsomecare.
Overview VII
BirthdayCantatatata...InwhichAchillescannotconvincethewilyandskepticalTortoisethattodayishis(Achilles')birthday.HisrepeatedbutunsuccessfultriestodosoforeshadowtherepeatabilityoftheGödelargument.
ChapterXV:JumpingoutoftheSystem.TherepeatabilityofGödel’sargumentisshown,withtheimplicationthatTNTisnotonlyincomplete,but"essentiallyincompleteThefairlynotoriousargumentbyJ.R.Lucas,totheeffectthatGödel’sTheoremdemonstratesthathumanthoughtcannotinanysensebe"mechanical",isanalyzedandfoundtobewanting.
EdifyingThoughtsofaTobaccoSmoker.ADialoguetreatingofmanytopics,withthethrustbeingproblemsconnectedwithself-replicationandself-reference.Televisioncamerasfilmingtelevisionscreens,andvirusesandothersubcellularentitieswhichassemblethemselves,areamongtheexamplesused.ThetitlecomesfromapoembyJ.S.Bachhimself,whichentersinapeculiarway.
ChapterXVI:Self-RefandSelf-Rep.ThisChapterisabouttheconnectionbetweenself-referenceinitsvariousguises,andself-reproducingentitiese.g.,computerprogramsorDNAmolecules).Therelationsbetweenaself-reproducingentityandthemechanismsexternaltoitwhichaiditinreproducingitself(e.g.,acomputerorproteins)arediscussed-particularlythefuzzinessofthedistinction.HowinformationtravelsbetweenvariouslevelsofsuchsystemsisthecentraltopicofthisChapter.
TheMagnificrab,Indeed.ThetitleisapunonBach'sMagnifacatinD.ThetaleisabouttheCrab,whogivestheappearanceofhavingamagicalpowerofdistinguishingbetweentrueandfalsestatementsofnumbertheorybyreadingthemasmusicalpieces,playingthemonhisflute,anddeterminingwhethertheyare"beautiful"ornot.
ChapterXVII:Church,Turing,Tarski,andOthers.ThefictionalCraboftheprecedingDialogueisreplacedbyvariousrealpeoplewithamazingmathematicalabilities.TheChurch-TuringThesis,whichrelatesmentalactivitytocomputation,ispresentedinseveralversionsofdifferingstrengths.Allareanalyzed,particularlyintermsoftheirimplicationsforsimulatinghumanthoughtmechanically,orprogrammingintoamachineanabilitytosenseorcreatebeauty.Theconnectionbetweenbrainactivityandcomputationbringsupsomeothertopics:thehaltingproblemofTuring,andTarski'sTruthTheorem.
SHRDLU,ToyofMan'sDesigning.ThisDialogueisliftedoutofanarticlebyTerryWinogradonhisprogramSHRDLU:onlyafewnameshavebeenchanged.Init.aprogramcommunicateswithapersonabouttheso-called"blocksworld"inratherimpressiveEnglish.Thecomputerprogramappearstoexhibitsomerealunderstanding-initslimitedworld.TheDialogue'stitleisbasedonJesu,joyofMansDesiring,onemovementofBach'sCantata147.
ChapterXVIII:ArtificialIntelligence:Retrospects,ThisChapteropenswithadiscussionofthefamous"Turingtest"-aproposalbythecomputerpioneerAlanTuringforawaytodetectthepresenceorabsenceof"thought"inamachine.Fromthere,wegoontoanabridgedhistoryofArtificialIntelligence.Thiscoversprogramsthatcan-tosomedegree-playgames,provetheorems,solveproblems,composemusic,domathematics,anduse"naturallanguage"(e.g.,English).
Overview VIII
Contrafactus.Abouthowweunconsciouslyorganizeourthoughtssothatwecanimaginehypotheticalvariantsontherealworldallthetime.Alsoaboutaberrantvariantsofthisability-suchaspossessedbythenewcharacter,theSloth,anavidloverofFrenchfries,andrabidhaterofcounterfactuals.
ChapterXIX:ArtificialIntelligence:Prospects.TheprecedingDialoguetriggersadiscussionofhowknowledgeisrepresentedinlayersofcontexts.ThisleadstothemodernAlideaof"frames".Aframe-likewayofhandlingasetofvisualpatternpuzzlesispresented,forthepurposeofconcreteness.Thenthedeepissueoftheinteractionofconceptsingeneralisdiscussed,whichleadsintosomespeculationsoncreativity.TheChapterconcludeswithasetofpersonal"QuestionsandSpeculations"onAlandmindsingeneral.
SlothCanon.AcanonwhichimitatesaBachcanoninwhichonevoiceplaysthesamemelodyasanother,onlyupsidedownandtwiceasslowly,whileathirdvoiceisfree.Here,theSlothuttersthesamelinesastheTortoisedoes,onlynegated(inaliberalsenseoftheterm)andtwiceasslowly,whileAchillesisfree.
ChapterXX:StrangeLoops,OrTangledHierarchies.Agrandwindupofmanyoftheideasabouthierarchicalsystemsandself-reference.Itisconcernedwiththesnarlswhicharisewhensystemsturnbackonthemselves-forexample,scienceprobingscience,governmentinvestigatinggovernmentalwrongdoing,artviolatingtherulesofart,andfinally,humansthinkingabouttheirownbrainsandminds.DoesGödel’sTheoremhaveanythingtosayaboutthislast"snarl"?ArefreewillandthesensationofconsciousnessconnectedtoGödel’sTheorem?TheChapterendsbytyingGödel,Escher,andBachtogetheronceagain.
Six-PartRicercar.ThisDialogueisanexuberantgameplayedwithmanyoftheideaswhichhavepermeatedthebook.ItisareenactmentofthestoryoftheMusicalOffering,whichbeganthebook;itissimultaneouslya"translation"intowordsofthemostcomplexpieceintheMusicalOffering:theSix-PartRicercar.ThisdualityimbuestheDialoguewithmorelevelsofmeaningthananyotherinthebook.FredericktheGreatisreplacedbytheCrab,pianosbycomputers,andsoon.Manysurprisesarise.TheDialogue'scontentconcernsproblemsofmind,consciousness,freewill,ArtificialIntelligence,theTuringtest,andsoforth,whichhavebeenintroducedearlier.Itconcludeswithanimplicitreferencetothebeginningofthebook,thusmakingthebookintoonebigself-referentialloop,symbolizingatonceBach'smusic,Escher'sdrawings,andGödel’sTheorem.
Overview IX
FIGURE1.JohannSebastianBach,in1748.FromapaintingbyEliasGottliebHanssmann.
Introduction:AMusico-LogicalOffering
10
Introduction:
AMusico-LogicalOffering
Author:
FREDERICKTHEGREAT,KingofPrussia,cametopowerin1740.Althoughheisrememberedinhistorybooksmostlyforhismilitaryastuteness,hewasalsodevotedtothelifeofthemindandthespirit.HiscourtinPotsdamwasoneofthegreatcentersofintellectualactivityinEuropeintheeighteenthcentury.ThecelebratedmathematicianLeonhardEulerspenttwenty-fiveyearsthere.Manyothermathematiciansandscientistscame,aswellasphilosophers-includingVoltaireandLaMettrie,whowrotesomeoftheirmostinfluentialworkswhilethere.
ButmusicwasFrederick'sreallove.Hewasanavidflutistandcomposer.Someofhiscompositionsareoccasionallyperformedeventothisday.Frederickwasoneofthefirstpatronsoftheartstorecognizethevirtuesofthenewlydeveloped"piano-forte"("soft-loud").Thepianohadbeendevelopedinthefirsthalfoftheeighteenthcenturyasamodificationoftheharpsichord.Theproblemwiththeharpsichordwasthatpiecescouldonlybeplayedataratheruniformloudness-therewasnowaytostrikeonenotemoreloudlythanitsneighbors.The"soft-loud",asitsnameimplies,providedaremedytothisproblem.FromItaly,whereBartolommeoCristoforihadmadethefirstone,thesoft-loudideahadspreadwidely.GottfriedSilbermann,theforemostGermanorganbuilderoftheday,wasendeavoringtomakea"perfect"piano-forte.UndoubtedlyKingFrederickwasthegreatestsupporterofhisefforts-itissaidthattheKingownedasmanyasfifteenSilbermannpianos!
Bach
Frederickwasanadmirernotonlyofpianos,butalsoofanorganistandcomposerbythenameofJ.S.Bach.ThisBach'scompositionsweresomewhatnotorious.Somecalledthem"turgidandconfused",whileothersclaimedtheywereincomparablemasterpieces.ButnoonedisputedBach'sabilitytoimproviseontheorgan.Inthosedays,beinganorganistnotonlymeantbeingabletoplay,butalsotoextemporize,andBachwasknownfarandwideforhisremarkableextemporizations.(ForsomedelightfulanecdotesaboutBach'sextemporization,seeTheBachReader,byH.T.DavidandA.Mendel.)
In1747,Bachwassixty-two,andhisfame,aswellasoneofhissons,hadreachedPotsdam:infact,CarlPhilippEmanuelBachwastheCapellmeister(choirmaster)atthecourtofKingFrederick.ForyearstheKinghadletitbeknown,throughgentlehintstoPhilippEmanuel,how
Introduction:AMusico-LogicalOffering 11
pleasedhewouldbetohavetheelderBachcomeandpayhimavisit;butthiswishhadneverbeenrealized.FrederickwasparticularlyeagerforBachtotryouthisnewSilbermannpianos,whichlie(Frederick)correctlyforesawasthegreatnewwaveinmusic.
ItwasFrederick'scustomtohaveeveningconcertsofchambermusicinhiscourt.OftenhehimselfwouldbethesoloistinaconcertoforfluteHerewehavereproducedapaintingofsuchaneveningbytheGermanpainterAdolphvonMenzel,who,inthe1800's,madeaseriesofpaintingsillustratingthelifeofFredericktheGreat.AtthecembaloisC.P.E.Bach,andthefigurefurthesttotherightisJoachimQuantz,theKing'sflutemaster-andtheonlypersonallowedtofindfaultwiththeKing'sfluteplaying.OneMayeveningin1747,anunexpectedguestshowedup.JohannNikolausForkel,oneofBach'searliestbiographers,tellsthestoryasfollows:
Oneevening,justasliewasgettinghisfluteready,andhismusiciansweressembled,anofficerbroughthimalistofthestrangerswhohadarrived.Withhisfluteinhishandheraneverthelist,butimmediatelyturnedtotheassembledmusicians,andsaid,withakindofagitation,"Gentlemen,oldBachiscome."TheHutewasnowlaidaside,andoldBach,whohadalightedathisson'slodgings,wasimmediatelysummonedtothePalace.WilhelmFriedemann,whoaccompaniedhisfather,toldmethisstory,andImustsaythat1stillthinkwithpleasureonthemannerinwhichlierelatedit.Atthattimeitwasthefashiontomakeratherprolixcompliments.ThefirstappearanceofJ.S.BachbeforesegreataKing,whodidnotevengivehimtimetochangehistravelingdressforablackchanter'sgown,mustnecessarilybeattendedwithmanyapologies.Iwillnetheredwellentheseapologies,butmerelyobserve,thatinWilhelmFriedemann'smouththeymadeaformalDialoguebetweentheKingandtheApologist.
ButwhatismereimportantthanthisisthattheKinggaveuphisConcertforthisevening,andinvitedBach,thenalreadycalledtheOldBach,totryhisfortepianos,madebySilbermann,whichsteedinseveralroomsofthepalace.[Forkelhereinsertsthisfootnote:"ThepianofortesmanufacturedbySilbermann,ofFrevberg,pleasedtheKingsemuch,thatheresolvedtobuythemallup.Hecollectedfifteen.IhearthattheyallnowstandunfitforuseinvariouscornersoftheRoyalPalace."]Themusicianswentwithhimfromroomtoroom,andBachwasinvitedeverywheretotrythemandtoplayunpremeditatedcompositions.Afterhehadgeneenforsometime,heaskedtheKingtogivehimasubjectforaFugue,inordertoexecuteitimmediatelywithoutanypreparation.TheKingadmiredthelearnedmannerinwhichhissubjectwasthusexecutedextempore:and,probablytoseehewfarsucharttcouldbecarried,expressedawishtohearaFuguewithsixObligatoparts.Butasitisnoteverysubjectthatisfitforsuchfullharmony,Bachchoseonehimself,andimmediatelyexecutedittotheastonishmentofallpresentinthesamemagnificentandlearnedmannerashehaddonethatoftheKing.HisMajestydesiredalsotohearhisperformanceentheorgan.ThenextdaythereforeBachwastakentoalltheorgansinPotsdam,asliehadbeforebeentoSilbermann'sfortepianos.AfterhisreturntoLeipzig,hecomposedthesubject,whichhehadreceivedfromtheKing,inthreeandsixparts.addedseveralartificialpassagesinstrictcanontoit,andhaditengraved,underthetitleof"MusikalischesOpfer"[MusicalOffering],anddedicatedittotheInventor.'
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