Hofstadter-Goedel Escher Bach-Strange Loops Output

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    StrangeLoops,OrTangledHierarchies

    709

    FIGURE142.PrintGallery,byM.C.

    Escher(lithograph,1956).

    programruns.Onalow(machinelanguage)le

    vel,theprogramlookslikeanyother

    pr

    ogram;onahigh(chunked)level,qualitiessuchas"will","intuition","creativity",and

    "c

    onsciousness"canemerge.

    Theimportantideaisthatthis"vortex"of

    selfisresponsibleforthetangledness,

    fo

    rtheGdelian-ness,ofthementalprocesses.Peoplehavesaidtomeonoccasion,"This

    st

    uffwithself-referenceandsoonisveryamusingandenjoyable,butdoyoureallythink

    thereisanythingserioustoit?"Icertainlydo.Ithinkitwilleventuallyturnouttobeat

    thecoreofAI,andthefocusofallattemptstounderstandhowhumanmindswork.And

    thatiswhyGodelissodeeplywoven

    intothefabricofmybook.

    StrangeLoops,Or

    TangledHierarchies

    710

    AnEscherVortexWhereAllLevelsCr

    oss

    Astrikinglybeautiful,andyetatthesametimedisturbinglygrotes

    que,illustrationofthe

    cyclonic"eye"ofa

    TangledHierarchyisgiventousbyEscherin

    hisPrintGallery(Fig.

    142).Whatweseeisapicturegallerywhereayoungmanisstanding,lookingata

    pictureofashipin

    theharborofasmalltown,perhapsaMaltesetown,toguessfromthe

    architecture,withitslittleturrets,occasionalcupolas,andflatsto

    neroofs,upononeof

    whichsitsaboy,relaxingintheheat,whiletwofloorsbelowhim

    awoman-perhapshis

    mother-gazesouto

    fthewindowfromherapartmentwhichsitsdirectlyaboveapicture

    gallerywhereayo

    ungmanisstanding,lookingatapictureofashipintheharborofa

    smalltown,perhap

    saMaltesetown--What!?Wearebackonthesamelevelaswebegan,

    thoughalllogicdictatesthatwecannotbe.Letusdrawadiagram

    ofwhatwesee(Fig.

    143).

    FIGURE143.AbstractdiagramofM.C.Escher'sPrin

    tGallery.

    Whatthisdiagram

    showsisthreekindsof"in-ness".Thegalleryis

    physicallyinthetown

    ("inclusion");thetownisartisticallyinthepicture("depiction");thepictureismentally

    intheperson("representation").Nowwhilethisdiagrammayseem

    satisfying,infactitis

    arbitrary,forthenumberoflevelsshownisquitearbitrary.Lookbelowatanotherwayof

    representingthetophalfalone(Fig.144).

    FIGURE144.Acollapsedversionofthepreviousfigure.

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