JREF IN THE CLASSROOM MODULE 004 / v 1.0 / 07/2013

Illusions: Our Visual System

©2013 JAMES RANDI EDUCATIONAL FOUNDATIONALL RIGHTS RESERVED

© 2013 James Randi Educational FoundationAll Rights Reserved

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about the JREFThe James Randi Educational Foundation is a not-for-profit organization founded in 1996. Its aim is to promote critical thinking by reaching out to the public and media with reliable information about paranormal and supernatural ideas.

The Foundation’s goals include the following:

• Providingeducationalresourcesandgrantstoeducatorsandstudentswhoareworkingtoadvancecriticalthinkingandskepticismintheircommunities.

•Demonstratingtothepublicandthemedia,througheducationalseminarsandworkshops,theconsequencesofacceptingparanormalandsupernaturalclaimswithoutsufficientevidence.

•Maintainingacomprehensivelibraryofbooks,videos,journals,andarchivalresourceswhichareavailabletothepubliconline.

• Supportinglocalskepticalorganizationsbyprovidingspeakers,grants,promotionalandeducationalresources,andtrainingingrassrootsorganizing.

• Supportingandconductingscientificresearchintoparanormalclaimsandpublishingthefindingsonlineandinskepticperiodicals.

Toraisepublicawarenessoftheseissues,theFoundationoffersa$1Millionprizetoanypersonorpersonswhocandemonstratepsychic,supernatural,orparanormalabilityofanykindundermutuallyagreeduponscientificconditions.

SUPPORTING THE WORK OF THE JAMES RANDI EDUCATIONAL FOUNDATION

TheJamesRandiEducationalFoundationreliesonthesupportofpeoplelikeyouinordertocarryoutitsmission.Whetheritisoursupportofgrassrootsskepticoutreach,ourinvestmentinresourcesforeducatorsandstudents,ourexpandingdigitaleducationalofferings,orourspeakingengagements,whichpromoteskepticismwithtopthinkersaroundtheworld,yourfinancialsupportmakesourprogramspossible.

YoumaysupporttheJREFthroughacharitabledonationandbybecomingamemberatrandi.org.Youcanensurethatyoursupportismosteffectiveinpromotingskepticismforyearstocomebymakingapledgeofmonthlysupport.Formoreinformationaboutpledges,pleasecontactusatdevelopment@randi.orgor(213)293-3092.

*DonationsaretaxdeductibleforU.S.residentstothefullextentofthelaw.

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about this module This module from the James Randi Educational Foundation explores the development of human perception and a few of the ways in which this development leads to incorrect interpretations of visual information. The module is designed to prompt students to consider the implications of misperception and to critically examine their own views of images and events in a way that promotes open-minded inquiry of current knowledge. Open-mindedness, in terms of one’s ability to accept that current knowledge may be inaccurate, has been shown to be a key component of good reasoning.

GRADE LEVEL AND TIME COMMITMENT

ThetextinthismodulewaswrittenforstudentsinGradeSevenandabove.Teachersareencouragedtomodifytheexercisesforuseinlowergrades.

Thetimerequiredtocompletethismodulewillvarywithdepthofinstructionandspecificassignmentsgiven.

NATIONAL SCIENCE STANDARDS

UnifyingConceptsandProcesses

ScienceasInquiry

ScienceinPersonalandSocialPerspectives

AAAS SCIENCE LITERACY BENCHMARKS

TheScientificWorldview

ScientificInquiry

TheScientificEnterprise

ACKNOWLEDGEMENTS

ThismodulewasdevelopedbyBarbaraDrescherwiththeassistanceofJamesRandi,D.J.Grothe,ThomasDonnelly,DanielLoxton,ChipDenman,MattLowry,andKylieSturgess.

SomeofthetextinthismoduleisadaptedfromotherJREFeducationalmaterials.

ABOUT THIS MODULE

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to the reader . . .As a magician, I must have a good working knowledge of all methods of creating deception, and that’s done by many different means. The words I speak, where and how I look, what’s going on onstage, my gestures, and the way I move, are several elements that contribute to my performance of a trick – though I want you to know that as a performer, and entertainer, I’m very careful to always leave my audience knowing that they have seen a show, not a miracle.

Whatyou’llseein thismoduleisacollectionofverybasic illusions,and I think that as a student, you’ll be able to see for yourself howthesethingshappeninnature,andhowtheyareproducedpurposelytodeceiveyou.You’llbemuchbetterequippednowtoapplyyournewknowledge tomanyof the flimflams that so-called “psychics” and”healers” use to dishonestly take money from innocent people who–unlikeyou!–arenotequippedwith the facts thatarewrittenherebeforeyou.

I suggest that you read and learn about each of these illusionaryfactors,and thenbegan lookingaboutyou toseehow theyapply inadvertising, in literature, and on television. I think you’ll be verysurprisedtoseethatyou’vebeenmissingthesethingsandmayevenhavebeenconvincedofsomeclaims thatwerebasedentirelyuponfalseinformationthatwaspresentedtoyou.

Enjoythislesson,butlessonsaretobelearnedfrom,they’renotjustforentertainment.Thisisseriousbusiness,startingoutthefactsfromthefiction.IhopethattheJREFhassucceededinconvincingyouthatyoucanbefooled,andtherearepeopleoutthere,allaroundtheworld,whowilltrytomisdirectyourattention.

James Randi

 

TO THE READER

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introductionHuman beings are not the biggest, strongest, or fastest creatures in the animal kingdom. We do not have the best eyesight, the best hearing, or the best sense of smell. Yet human beings have managed to survive and thrive in a dangerous world. We avoid obstacles and predators, communicate with other humans, and find food, thanks to an extraordinary brain that uses information from all of the senses to figure out the world around us.

Thehumaneye,forexample,isatrulyamazingorgan.Itisabletosenselightandmeasureitsenergy.Yet,theeyecannotsee.Seeingisaprocessoftheentirevisualsystemandmostoftheworkisdoneinthebrain.

Wetakeinanenormousamountofinformationthroughoursenses,butnotasmuchasmostofusthink,especiallythroughoureyes.Ourbrainfillsinthegapssothatweappeartoseeeverything.Forexample,thereisasmallsectionatthebackofeacheyecalled“theblindspot”becauseitdoesnotcontainreceptors.Youdon’tusuallynoticethisspotbecauseyourbrainfillsitin,butifyoupayattentiontoit,youwillseeit.

INTRODUCTION

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try it!TEST IT YOURSELF

Holdthebookletdirectlyinfrontofyourface,aboutafootawayfromyournose.Closeyourlefteyeandstareatthedogontheleft.Slowlymovethebooktowardyourfaceuntilthecatontherightdisappears.

Whenthathappens,thecathasmovedtothepartofyourvisionthebrainusuallyfillsin.Youcanalsocloseyourrighteye,stareatthecat,andwatchthedogdisappear.

Thebrainalsofillsindetailswhentheeyedoesnotprovideenoughinformation.Forexample,you“see”colorinthecornerofyoureyewhenyouarelookingdirectlyforward,butmostofthiscomesfromthebrain.Youcansensecolorfromobjectsveryclosetoyou,butanythingmorethanafootortwofromyoureyemustbenearthecenterofyourvisionforyoutodetectitscolor.Thecoloryouthinkyouseeinthecornerofyoureyeisyourbrain’sbestguessormemoryofwhatwasthere.Anytimeyouneedthatinformation,youwillmoveyoureyestogetit.

Usingvision,wearebetteratidentifyingpeople,places,andobjectsthanevenourmostpowerfulcomputers.Butasgoodasweareatthis,wesometimesmakemistakes.Scientistsstudythesemistakesinordertolearnmoreabouthowthesesystemswork.

Itisimportantforallofustounderstandhowoftenoursensesfoolusandtorecognizethatwhatwethinkweareseeingandhearingissometimeswrong.Itisnotnecessarilybadtobewrong,buthumanbeingsdislikebeingwrongsomuchthatweoftenrefusetobelievethatwecouldbe.

Thatstubbornnesscankeepusfromlearningorbelievingthetruth.Knowingourlimitationsisafirststepinbeingopen-minded.

MORE LIKE A PAINTING THAN A PICTURE

Ingeneral,yourbrainwantstoidentifywhatisintheworldaroundyousothatyoucantakeactiontoavoidit,interactwithit,orignoreit.Ittriestomakesenseoftheinformationitgetsfromthesenseswithoutusingmoreenergythanisnecessary.Thisinformationislimited,soyourbrainusespastexperiencestohelptheprocessalong.Itassumesthatthethingsyouencounterarealotlikethingsthatyouhaveencounteredinthepast.

Inotherwords,whatwethinkweareseeing,hearing,touching,tasting,andsmellingisonlyourbrain’sbestguessaboutwhatisoutthere.Ourperceptionsoftheworldareconstructedfromsensoryinformation,expectations,andmemory.Theyarenotreflectionsoftheworld,likephotographs.Theyarerepresentationsoftheworld,muchlikeapaintingisarepresentationofaperson,object,orscene.

ASK...If the best your brain can do is guess what a shape, object, or scene is, then why is it usually right? How do you think we are we able to figure out what most things are?

THE BRAIN AND ILLUSION

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HOW WE LEARN TO “SEE”Humanshavesomeabilitieswhichappeartobebuilt-in.Forexample,newborninfantswillstarelongeratdotsiftheyarearrangedtolooklikeaface(seeFigure1).Wealsohavebuilt-inresponsessuchasfearofsudden,loudsounds,andheights.Butwearenot

bornwiththeabilitytofullyrecognizesoundsandobjects.Instead,itdevelopsasweexperienceandinteractwithourenvironment.Wedonotrecordourexperienceslikeacameradoes.Instead,eachexperiencechangesthephysicallandscapeofourbrainjustalittlebit.

Imagineaneighborhoodwithafieldoftallgrassinthemiddle.Anewschoolsitsononesideofthefieldandhousesareontheotherside.Thefirstchildtowalktoschoolwillchooseaplacetoen-terthefield,perhapswherethereisanopengate,andwalkinthegeneraldirectionoftheschool,butshewillhavenopathtofollow.Thenextchildtostartinthesameplaceismorelikelyfollowthepathofthefirstchild,whomashedthegrassdownasshewalked,thantowalkanentirelydifferentpath.Hemaywanderabit,especiallyifhegetslostinthought,buthewillmashthegrassdownalittlemorethanthechildbeforehimandaddsomechangestothepath.Asmorechildrenstartatthesameplace,theywillcoverthesamegrounduntilthereisawell-worn,clearpathacrossthefield.Youmayhaveseengrasslesspathslikethisatyourownschool—placeswherepeoplechoosetocutacrossthelawninsteadoffollowingthesidewalk.

Eachchildwhofollowsthatpathwillfinditeasiertowalkthanthechildbeforeaslessandlessgrassisintheway.Iftherearemanyplacestostartandmanychildren,thefieldwillbefullofpaths,crossing,merging,anddividing.Well-usedpathswillbeeasiertofollowthanthepathsthatonlyafewchildrenhaveused.

Sensoryinformationislikeachildsettingouttowalktoschoolthroughafield.Thecloserthatinformationmatcheswithapreviousexperience,theeasieritisforthebraintomakesenseofitasitfollowsanestablishedpathway.

Thesepathwaysarehowexperienceteachesus“rulesofthumb,”calledheuristics,whichallowustomakequickguessesaboutwhatislikelytobeouttherebyrecognizingfamiliarpatterns.Themorefamiliarapatternistous,themorelikelywewillrecognizeitandthelesstimeitwilltaketodoso.

Forexample,imaginethatyouaretalkingtoateacherwhoissittingbehindadesk.Youcanonlyseehisbodyfromthewaistup.Doesitcrossyourmindthathisbodyendsatthewaistorthathemightbefloatinginmid-airoverthedesk?Youhavelearnedthatobjectsintheworldaroundyoudonotusuallyinteractthatway.Yourbrainassumes that the teacher is sitting in a chair that youcannotsee.Youalsoassumethatthedeskisclosertoyouthantheteacherisandtheteacheriscloserthanthebackofthechair.Itmayseemsillyandobviousnow,butyouhadtointeractwithobjectsintheworldmanytimesasababytolearnthesepatterns.

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Fig. 1: Infantswillstarelongerattheconfigurationontheleftthantheywilltheright(Goren,Sarty,&Wu,1975).

VISION AND ILLUSION

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THE ONE-MINUTE MÜLLER-LYER ILLUSIONThisisafastandeasyexercisethatcanbedonebyagrouporindividualinaclassroom,ataconference,orevenatarestaurant.Allyouoryouraudiencewillneedisapieceofpaperandsomethingtodrawwith.

Ideally,thisshouldbedoneusingunlinedpaper,butitworksjustfinewithstandardruledpaper.Ifyouareaddressingaclassroomorconferenceattendees,remindtheaudiencethatiftheydomorethanisasked,suchasusethelinesonthepapertomeasuredistance,thedemonstrationisuselessastheywillnotbeabletoseetheeffectsoftheillusion.

1. Draw an arrow with roughly the same size tip and tail, as shown. Make it large, but do not draw to the edge of the paper.

2. Without thinking too much about it, mark the spot along the arrow’s shaft which you believe is the center—the point at which the shaft would be broken in half.

3. Draw two dots where the shaft meets the fins—the tip of the arrow and base of the tail.

4. Fold the paper so that the two dots meet, then make a crease.

5. Unfold the paper.

6. Compare the placement of your mark to the crease you just made, which is the actual center of the shaft.

Mostpeoplemisjudgethecenterbyanoticeableamount.Thedirectionoferrorisalmostalwaystowardthetailofthearrow.Are you like most people?

try it!WHAT DO YOU SEE?Scientists study illusions because they can show us how we use the information from our senses to figure out what is around us. We have learned a lot this way, and we know that sometimes it is not possible for us to interpret that information correctly.

The following exercises are designed to show you first-hand how our senses and brain can fool us in ways that we may not expect. After each exercise, take time to think about and discuss what you experienced. Why do you think humans perceive each of these incorrectly?

VISION AND ILLUSION

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Fig. 2: Fig. 3:

VISION AND ILLUSION

MÜLLER-LYER:

WHAT IS GOING ON?FranzCarlMüller-Lyerpublishedthisillusionin1889,andscientistshavetriedtofullyexplainiteversince.Theoriginalformoftheillusionisacomparisonoftwolines,onewithfinsthatformanarrow on each end and the other with fins on each endthatlooklikethetailofanarrow (seeFigure2).Thelinesaresamelength,butthefigurewiththearrowsoneachendappearstohaveashortershaft.

Oneofthemostinterestingthingsthatscientistshavelearnedisthatsomepeopledonotmisjudgethelengthsofthelinesasmuchasothers.Forexample,peoplewholiveinsomeregionsofAfricaseenodifferenceatallbetweenthetwo

lines.Comparisonsacrossculturessuggestthatwemaymisjudgethelengthsofthelinesbecauseweareusedtoseeingbuildingsandotherstructureswithsquarecorners (seeFigure3). Insidecornersformlinesthatlooklikethetailsofarrowswhileoutsidecornerslooklikearrowpoints.

Thisdoesnotfullyexplainwhywemisjudgethelengthofthelines,butitdoesstronglysuggest that the illusion is not something we arepreprogrammedtoexperience.Instead,itdevelopswithourabilitytoperceiveandunderstandourenvironment.

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VISION AND ILLUSION

try it!SIZE AND DISTANCE

SIZE AND DISTANCE: WHAT IS GOING ON?Thisillusionisonethatwecannoteasilyovercome,butitiswellunderstoodbyscientists.Experiencehastaughtusthathowbigobjectsappearisrelatedtohowfarawayfromusthoseobjectsare.Ingeneral,thesmallertheobject,thefartherawayitprobablyis.

Youcanseethisyourself.Askafriendtoholdabookabouttwofeetfromyourface,thenslowlymoveitclosertoyou.Ifyoudidnotknowthesizeofthebookandcouldnottellthatitwasmoving,itwouldappeartogrow.However,becauseyoudoknowthebook’ssizeandthatbooksdonotgrow,yourbrainmakesadjustments.Itholdsthebook’ssizeconstant,meaningyoudonotperceiveachangeinsize.Instead,youperceivetheobjectasmovingclosertoyou.

Whenwedonotknowexactlyhowlargesomethingis,wecompareittofamiliarobjects.Eventhen,weneedtoknowhowfarawayeachobjectisinordertosortallofthisinformationout.Tofigureouthowfarawaythingsare,weuseanumberofotherperceptualcues.Intheimagewiththemonsters,thelinesinthebackgroundsuggestthatthemonstersarelinedupalongthewall of a room so that the monster on the right isfartherawaythanthemonsterontheleft.Ifitisfartheraway,itshouldappearsmaller.Sinceitdoesnot,themonsteritselfmustbelarger.Withoutthelinesinthebackground,manyofthecuesfordistancearegoneandthemonstersappearmoresimilarinsize(theyarereallyidentical).

1. Look at Fig. 4a to the right and quickly decide which of the three monsters is tallest.

2. Use a ruler to measure the height of each of the monsters.

3. Were you right about which was the tallest? If not, why do you think your perception was not accurate?

Fig. 4a:

Answer is in Fig. 4b on page 17.

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SIZE PERCEPTION

Fig. 5ThePonzoIllusion.

Whichlineislonger?

Fig.6Gnomeswalkingontheboardwalk?Arethe gnomes in the lower left smaller than thegnomesintheupperright?

Forexample,inmostpartsoftheworld,roadsarecommon,asarerectangularobjectssuchasboxesorboards.Welearnthatthesidesoftheroadareparallel;however,werarelylookatroadsfromabove.Instead,whenwelookdownaroadfromtheground,thefartherawayasegmentofroadis,theclosertogetherthesidesappear.Thisiscalledlinearperspectiveanditisusedbyartiststocreatetheillusionofdepth.

Becauseweknowthattheroadisnotshrinking,ourbrainrecognizesthatdistanceiswhatmakestheroadappeartoshrinkanditmakesadjustmentstoourjudgmentsofsize.ThisisdemonstratedbyanotherillusioncreatedbyMarioPonzo(Fig. 5).Inthisillusion,twoidenticalhorizontallinesareplacedbetweenverticallineswhicharetiltedtowardthecenteratthetop.Thetoplineappearslargerthanthebottomlinebecausethetiltofthevertical lines is similar to what we would see if lookingdownaroad.Ifthelineswereplacedonaroad,thetoponewouldbefartheraway,soitshouldappearsmallerthanthebottomifthelinesarereallyidentical.

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BRIGHTNESS COLOR AND CONTRAST

AnothergoodexampleofhowperspectiveaffectsjudgmentsofsizeisSander’sParallelogram(Fig.7)(createdbyFreidrichSander).Wearesousedtoseeingobjectsinthreedimensionsthatweperceivetheparallelogramasarectanglethatweareviewingfromanangle.Imagineatheaterticketwiththestubattached:theredlineshouldbeshorterthantheblueline.However,thisisatwo-dimensionaldrawingandtheredlineisthesamelengthastheblue.

try it!BRIGHTNESS AND COLOR CONTRAST

To create this illusion, you will need scissors and a copy of Fig. 8 on page 19. It does not need to be in color, but it must be a clean, sharp copy with no areas faded.

1. Carefully cut out the grey circles. They do not need to be perfect, but make sure none of the background remains.

2. Place one circle on each of the “+” markers in the middle of the bars.

3. Do the circles look the same? If the circles on the lighter bars appear darker than the circles on the darker bars, pick them up and shuffle them, then try again.

4. Why do you think the circles appear to be darker or lighter depending on where they are placed?

Look at the two pictures of birds below (Fig. 9a).

1. Which of the grey birds is darker? Which of the orange birds is more red? Is one darker?

2. Now look at the picture of blue and yellow stripes on the next page (Fig. 10).

3. Compare the reddish squares on the left to the squares on the right. Does one set look more orange than the other? Is one set darker?

Fig. 7Sander’sParallelogram.Istheredor

bluelinelonger?

Fig. 9a

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BRIGHTNESS AND CONTRAST

BRIGHTNESS AND COLOR CONTRAST: WHAT IS GOING ON?Experiencetellsusalotabouthowbrightsomethingsaroundusshouldbe.However,wealsolearnthathowbrightsomethingisdependsonhowmuchlightisshiningonit.Whenwearelookingattwo-dimensionalimages,ourbrainsattempttoidentifylightsourcesandmakeadjustments.Whennolightsourceisavailable,themostusefulinformationishowbrightthesurroundingobjectsare.

Returningtothebarsandcircles,comparedtotheblackbarontheleft,thegreycircleismuchlighter.Comparedtothewhitebarontheright,thegreycircleismuchdarker.Thedifferences betweenthecirclesandthebarsinthemiddlearemuchsmaller,butourbrainsexaggeratethosedifferencestoallowustoseetheedgesbetter.Asaresult,thecirclesappeardarkerorlighterdependingontheshadeofthebackground.

Becausewealsousecolortoperceiveedges,thesameadjustmentsarewhenwearetryingtofigureoutwhatcolorsomethingis.Thegreybirdsareidentical,asaretheorangebirds.Youcanseethiswhenthebackgroundsareremoved(Fig.9b)

Fig. 9b

Fig. 10

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PERSISTENCE OF VISION

try it!PERSISTENCE OF VISION

For this project, you will need the following:

• A copy of this page (at least the image at the bottom), color or black/white

• A long, round stick. Wooden skewers or chopsticks work well.

• Scissors

• Glue

1. Cut out the circles below.

2. Place one of the circles on the table face-down with the dot toward you.

3. Glue the stick to the circle as shown, with the point at the center of the circle. Make sure the stick goes over the location of the dot so that when you hold it up, the object appears upright.

4. Place the other circle face-up so that the dots are back-to-back and glue in place.

5. After it dries, roll the stick back and forth between your palms while looking at the disk.

DO YOU SEE THE BIRD IN THE CAGE?

What you have made is called a thaumatrope. It was a popular toy more than 100 years ago. You can create more thaumatropes by drawing your own scenes, placing different objects on each side. Be sure to space your objects so that the scene makes sense when combined. Some popular versions include a dog appearing to chase a cat or bird and a fish in a fishbowl.

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PERSISTENCE OF VISION

PERSISTENCE OF VISION: WHAT IS GOING ON?

Youreyeworksbychannelinglighttospecialcells(calledreceptors),whichreacttothatlight,sendingsignalstoyourbrain.Thebrainusesthatinformationtoperceiveedgesandshapes.Someoftheheuristicswedeveloptellushowedgesandshapesshouldbegroupedtoformameaningfulimage.

Forexample,wegroupobjectsthat are closer together than

theyaretootherobjects,especiallywhenthegroupingforms a line or other familiar shape.Thisiscalledthegroupingprincipleofproximity(Fig.11).Wealsotendtogroupobjectsthataresimilartooneanother.Thisisgroupingprincipleisappropriatelycalledsimilarity.

Wedothisbecauseourexperiencetellsusthatitisthewaythingsusuallywork

intheworld.Theprincipleofproximityreferstoobjectsinspace,butitalsoreferstotime.Ourbrainsconnectinformationacross time to form meaningful perceptions.Inourexperience,objectsdonotflashinandoutofexistenceinlessthanasecond.Instead,weseetheimagesoneithersideofthethaumatropeasone.Thissameprocessallowsustoperceivesmoothmotioninaseriesofstillpicturessuchasmoviesorflipbooks.

Fig. 11Groupingprinciplesofproximityandsimilarity.Thetopleftlookslikeasquaremadeupofdots.Bymovingsomedotsclosertogether,weseecolumns(topright)androws(bottomleft).Thebottomrightappearstoberowsofsimilarobjects,buttheobjectsarethesamedistanceapart.

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GLOSSARY

glossaryGrouping Principle:Ageneralruleofthumb(see“heuristics”),whichsuggeststhatobjectsorpartsofobjectsbelongtogether.

Heuristics:General“rulesofthumb”orshortcutsthebrainusestofigureoutwhatisintheworldaroundusortomakedecisions.

Linear Perspective:Whenseenfromtheair,lookingstraightdown,thesidesofroadsandrailroadtrackslookparallel,butwhenseenfromtheground,theyappeartogetclosertogetherastheygetfartheraway.Becauseofthis,whenpeopleseelinesinanimagewhichareclosertogetheratthetopthanthebottom,theytendtoperceivedepth.

Perceptual Cue:Somethingweseeorhearthattellsussomethingaboutanobjectandwhatitmaybedoing.Forexample,ifoneobjectappearstobealotsmallerthananother,thesizedifferenceisacuethatthebiggerobjectisclosertousthanthesmallerone.

Receptors:Specializedcellsthatreceiveinformationfromtheoutsideworld.Examples:tastebudsinthemouthsensechemicalsinfoodandreceptorsintheeyesenselight.

answersFig. 5The Ponzo Illusion (upper): the top line appears larger than the bottom line, but they are the same size. The vertical lines create a familiar pattern (lower) we perceive as depth.

Fig.6Gnomes walking on the boardwalk? The gnomes in the lower left are identical to those in the upper right. Use a ruler to check.

Fig.7Sander’s Parallelogram. The red and blue lines are the same length

Fig. 4b:

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Fig. 8 BRIGHTNESS & CONTRAST