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TusiorNotTusi

ArthurShapiroandAlexRose-HenigDepartmentofPsychology,AmericanUniversity

ThetitleofthisentrytakesitsnamefromNasiral-DinTusi,a13th-centuryPersianastronomer.

Tusishowedhowtocreateastraightlinefromcircularmotion.

Theprincipleisillustratedinthefiguretotheleft.Ifcirclewithdiameter

Arotatesontheinnerboundaryofacirclewithdiameter2A,thenapointonthecircumferenceoftheinnercircletracesastraightline.Thefigureis

fromaTusimanuscriptintheVaticancollection(alsopostedon

Wikipedia).(http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Greek_astro.html)

Hereweexplorelocalmotionversusglobalmotionwithtwodifferentconstructions:

TusiMotion:motionfromelementsthattravelinlinearpaths,and

NotTusiMotion:motionfromelementsthattravelincircularpaths.

1. TusiMotion:Inthetwofigurestotheleft,eachcoloreddotmovesonastraightpathalongtheradiallineslikethepointonthe

circumferenceofthecircleinthemanuscriptillustrationabove.Changingtherelativephaseofthecoloreddotsmakestheglobal

perceptappearasradiatinglinesorasaspinningcircle.

2. NotTusiMotion:Inthetwofigurestotheleft,eachcoloreddotmovesonacircularpathverydifferentfromthemotionTusi

described.Changingtherelativephaseofthedotsmakestheglobalperceptappearaslinesspinningaroundthecircleorasacirclethat

movesaroundinsidetheoutercircle,butunlikeTusimotionthe

innercircledoesnotspin.

TusiorNotTusi:ThemotionfromTusiandNotTusicanbemadeto

overlap.Inthefiguretotheleft,allthedotsareblackexceptfor

two.Thebluedotfollowsastraightpath(asintheTusimotion

demonstration);theorangedotfollowsacircularpath(asinthe

NotTusimotiondemonstration).Whenanobserverattendstothe

bluedot,theinnercircleappearstospinasitmovesinsidethe

outercircle,andwhenanobserverattendstotheorangedot,theinnercircledoesnotappeartospinasitmovesinsidetheouter

circle.

Purpose,andwhytheseeffectsareinteresting:Theseeffectsshowhowtheperceptionofthesame

localpathscanbeinterpretedasdifferentglobalstructures.Ourperception,therefore,dependsuponthestatisticalrelationshipbetweenmotionelements,notjustuponthemotionoftheindividual

elements.Inthefinalexample(TusiorNotTusi),weshowhowattentioncanswitchbetweentwo

differentglobalperceptseventhoughbothtypesofmotionarepresent.