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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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