8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

1/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

2/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

3/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

4/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

5/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

6/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

7/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

8/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

9/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

10/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

11/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

12/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

13/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

14/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

15/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

16/18

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.

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

17/18

8/9/2019 Hofstadter-Goedel Escher Bach-Strange Loops Output

18/18