The magic words

17 Pages·2017·1.92 MB·English

RESEARCHARTICLE
The magic words: Using computers to
uncover mental associations for use in magic
trick design
HowardWilliams☯*,PeterW.McOwan☯
SchoolofElectronicEngineeringandComputerScience,QueenMaryUniversityLondon,London,United
Kingdom
☯Theseauthorscontributedequallytothiswork.
*[email protected]
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a1111111111 Abstract
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Theuseofcomputationalsystemstoaidinthedesignofmagictrickshasbeenpreviously
explored.Herefurtherstepsaretakeninthisdirection,introducingtheuseofcomputertech-
nologyasanaturallanguagedatasourcingandprocessingtoolformagictrickdesignpur-
poses.Crowdsourcingofpsychologicalconceptsisinvestigated;further,theroleofhuman
OPENACCESS associativememoryanditsexploitationinmagicaleffectsisexplored.Anewtrickisdevel-
Citation:WilliamsH,McOwanPW(2017)The opedandevaluated:aphysicalcardtrickpartiallydesignedbyacomputationalsystemcon-
magicwords:Usingcomputerstouncovermental figuredtosearchforandexploreconceptualspacesreadilyunderstoodbyspectators.
associationsforuseinmagictrickdesign.PLoS
ONE12(8):e0181877.https://doi.org/10.1371/
journal.pone.0181877
Editor:SusanaMartinez-Conde,StateUniversityof
NewYorkDownstateMedicalCenter,UNITED
Introduction
STATES
Withmagic,aswithmostcreativedisciplines,thereislittlethatisentirelynew.Mostcreations
Received:March23,2017
aremodifications,orsyntheses,ofexistingartefacts(thetricksthemselves)[1].Theprocessof
Accepted:July7,2017
designinganewmagictrickoftenhighlightsaspectsthatcouldbeautomatedorimprovedvia
Published:August9,2017 acomputationaltechnique—workhasbeendonetousecomputersasmagictrickdesignaids,
assistingwiththecreationofacardtrick,andamagicaljigsawthatexploitspropertiesofthe
Copyright:©2017Williams,McOwan.Thisisan
openaccessarticledistributedunderthetermsof humanvisualperceptionsystem[2].Here,anoveltrickbasedonexistingmagicaltechniques
theCreativeCommonsAttributionLicense,which isdescribed,thecreationofwhichhasbeenaidedbycomputationalsystemsperformingvari-
permitsunrestricteduse,distribution,and oustasksthatwouldusuallybeperformedbyahumandesigner.Thedevelopedcardtrick,and
reproductioninanymedium,providedtheoriginal
thecomputationalsystemusedtohelpdesignit,relyoncertainempiricalobservations,
authorandsourcearecredited.
detailedanddiscussedbelow,aboutthewayinwhichthehumanbrainprocessesandreactsto
DataAvailabilityStatement:Theminimal languageandimagery.
underlyingdatasetnecessaryforreplicationofthis
studyandusedtoreachtheconclusionswithinthe
Gilbreathprinciples
paperareavailableintheSupportingInformation
files. Therearemanyknowntechniquesavailableforuseinthedevelopmentofanewcardtrick;see
Funding:ThisworkwassupportedbyEPSRC Erdnase[3]andHugard[4]fordetaileddiscussions.NormanGilbreathprovided,in1958,an
grantnumberEP/J50029X/1. ingenioussetofobservationsaboutthemathematicalpropertiesofadeckofplayingcardsthat
magiciansareabletoexploitinnumerousways,commonlyreferredtoastheGilbreath[5]
Competinginterests:Theauthorshavedeclared
thatnocompetinginterestsexist. principles.Thesefindingsshowthatadeckofcards(oranysequenceofobjects)orderedin
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categoricalgroups,maintains,afteroneriffleshuffle,thepropertythatallsequentialgroupsin
thedeckareguaranteedtobecomposedofoneofeachcardfromeachgroup,thoughnotnec-
essarilyintheoriginalorder.Tofacilitatethispriortotheshuffle,theorderofoneportionof
thedeckmustbereversed.SeeFig1foranexample.Manycardtricksdetailedby,amongst
others,Mactier[6],usetheseprinciplestogreateffect.
Cardtrickssometimesrelyonsleightofhandtomanipulatecardsthatspectatorshave,sup-
posedlysecretly,selected,orforceselectionofaknowncard.Aperformermayskilfullykeep
trackofcardsinordertolater,seeminglymagically,revealthem.Aclassictypeofeffectisof
thekind‘selectacard,anycard’,whichtheperformerthenreveals.Essentially,thistypeof
trickgivestheparticipanttheillusionofafreechoice,whichtheperformerissomehowableto
divine.Thereareotherwaystodetermineaspectator’schoices,thatdonotinvolvesleightof
hand,whichwillnowbediscussed.
Fig1.Gilbreathprinciple.AnexampleoftheGilbreathprinciple.Eightcardsareorderedred/black
throughout.Afterreversinghalfthedeck,andperformingariffleshuffle,eachsequentialpairstillcontainsa
redandablackcard.
https://doi.org/10.1371/journal.pone.0181877.g001
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Associativethinking
Mentalists(magiciansconcernedwiththepresentationoftricksthatappeartorelyonthe
workingsofthehumanmind)sometimesrelyoncertainthoughtprocessesoftheirspectators
topredictchoicesorbehaviours.Forexample,amentalistmayaskaspectatortomakeadeci-
sionundertimepressure,assumingthatthedecisionmakingprocesswillreducetoselecting
prototypicalmentalrepresentations.Banachek[7]describesanumberofmanipulationsofthis
kind:“It’syouranniversary,andamessengerhasjustdeliveredalargeboxofflowers.What
arethey?Now!”Unsurprisingly,mostpeoplewillnamearoseinthissituation.Duringthe
courseofatrick,thesepredictionsmayerr,thoughshouldthisoccur,theskilledconjurerwill
alwayshaveanalternativemethod,oreventrick,lineduptosavethesituation.SeeCorinda
[8],Earle[9],andAnneman[10]fordiscussionsofthisperformancetechnique.
Mentalobjects—images,sounds,words,concepts,ideas—areoften,inthecognitivesci-
ences,termedrepresentations:cognitivesymbolsthatrepresentphysicalrealities,orcognitive
processesthatmakeuseofsuchsymbols;seeVonEckardt[11]fordetailedanalysis.Howone
representationmaygiverisetoanotherisacomplexareaofstudyforphilosophersandpsy-
chologists.ThesocalledAssociationistschoolofthinkersbelievethatcertainsensations,asso-
ciatedasufficientnumberoftimeswithcertainideas,maygiverisetothosesameideasby
merethoughtalone;seeHartley[12].
Whenmagicianssearchforanasnearaspossibleguaranteedassociationinthemindofa
spectator,theylook,knowinglyorotherwise,foraparticularpropertyofthedesiredmental
representationsthatwilltriggertheother:ifoneexists,theotherexists[13].Magicianswould
likestrongassociationssuchasthosedetailedinPavlov’sfamousexperiment,seeShettleworth
[14]:adogwasconditionedtoassociatetheringingofabellwiththeappearanceoffoodso
stronglythatanattendantresponseofsalivationwasproducedontheringingofthebellinthe
absenceoffood.
Implicitassociationistheideathatsomeconceptsaresubconsciouslyrelatedinhuman
minds—thestrengthoftheseautomaticassociationscanbemeasuredusingtheImplicitAsso-
ciationTest,presentedbyGreenwald[15];aseriesofcomputermonitorbasedcategorisation
tasks,wherespeedofreactioniscorrelatedtostrengthofassociation.
Thehumanmindisapowerfulassociativemachine.Representationscanveryeasilybecon-
nectedtooneanother,evenwhentheyareofdifferenttypes.Magictricksbasedonthesekinds
ofmentalassociation,suchasthetrickunderdiscussioninthispaper,canbeseenasconcrete
instantiationsofthistypeoftheoryofmentalactivity.Thesuccess,orotherwise,ofthetrick,
maybeseenasakindofpsychologicaltestofthestrengthoftheassociationofthemental
objectsdeployedinthetrick.
Automaticthinking
Kahneman[16]hasshownthatthehumanmindappearstorelyontwodifferentpsychological
systems,whichhetermsSystem1andSystem2.System1,inKahneman’sview,takescareof
muchoftheseeminglyautomatic,yetsophisticated,mentalprocessingthatgoesonindayto
daylife.Abasicexampleofthisinaction,isthementalcalculationrequiredtoevaluatethe
simplesumxinx=2+3.Thiscalculation,adding2and3together,happenssorapidlyasto
appeartoourconsciousmindsasbeinganautomaticprocess.Similarlyautomatically,the
complexsetofmentalandphysicalprocessesrequiredtopoursomewaterintoaglassand
drinkthecontentsisperformedeffortlessly,withouterror.
Incontrast,considercalculatingthevalueofthesumxinx=373+259.Thisadditionis
easilycalculable,withalittleeffort.Thesmallamountofmentaleffortrequiredtoaddthetwo
numbersisanexampleofSystem2typethinking:active,conscious,appliedthoughtfor
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problemssuchascalculation,orplanning.System2isthetypeofthinkingthatisableto,for
example,solvepuzzlesbywayofrational,contemplativethought.Thesametypeofthinking
canbeappliedbyaspectatorwitnessingamagictrick,andmayleadthemtoanunderstanding
oftheunderlyingmethod,spoilingtheeffect.Itisthistypeofthinkingthatamagicianwill
wanttominimiseduringaperformance.Equally,aperformerwillwanttomaximisethe
amountofSystem1typeautomaticthinking,asitisfarmoreeasilymisled.Kahnemanshows
thatgivenachoicebetweendeployingthetwosystemstosolveagivenproblem,mostpeople
willbecomfortableacceptingtheimmediatelyavailablesolutionpresentedbySystem1.
Thetrick
Amindreadingpredictioneffectreliantonasetofcustomplayingcardsispresentedhere.
Thetrickhasbeendesignedwiththeassistanceofacomputationalsystemconfiguredwith
psychologicalconstraintsderivedfromthekindofobservationsofassociativeandautomatic
thinkingdiscussedabove.
Duringtheperformanceofthetrickthespectatorisaskedtomakeaseeminglyfreechoice
betweencertainpresentedoptions.Afteracardhasbeenselected,theperformerisableto
revealthatthischoicehadbeenpreviouslypredictedbythem.
Toachievethiseffect,theperformerusesaphysicalsetofplayingcardsthatcanbemanipu-
latedaccordingtotheGilbreathprinciples.Further,Kahneman’sobservationsaroundSystem
1thinkingarebuiltintothepresentationofthetrick,toengineerasituationforaparticipant
wherebytheywillbeaskedtoquicklymakeachoicebetweensomeassociativeoptionspre-
sentedtothem—indoingso,applyingakindofpsychologicalforce.
Foreaseofreference,thetrickwillbereferredtoastheAssociationtrick.Inamagicbook,
itcouldbedescribedas:
Fromtwoshuffleddecksofcards,thespectatorfreelychoosesawordandarelatedimage,
whichtheperformerseemstohavebeenabletopredictinadvance.
0.0.1TemplatefortheAssociationtrick. Thetrickusestwodecksofcustomplaying
cards.Onedeckcontains16distinctimages,theother16distinctwords,onepercard.The
wordsandimagesarederivedfrompre-defined,crowdsourced,conceptualcategories.In
eachdecktherearefourseparatecategories,withfourimages,orfourwords,ineach.
Theunderlyingmechanismofthetrickisthat,inall,thereareinfactonlysevendistinct
conceptualcategories.Thereisonefurthercategorythatisdeployedthroughboththedeckof
wordsandthedeckofimages.Notethefundamentalpointthatthereisonecategorythat
appearsinbothdecks;allothercategoriesarerepresentedineitherthedeckofwords,orthe
deckofimages.Thetrickperformancereliesonthespectatorselectingaword,andthencou-
plingitwitharelatedimage,selectedfromaconceptuallysimilarcategoryintheimagedeck.
Thevariouscategoriesthatareusedarecriticaltotheefficacyofthetrick.Eachcategoryused
belongstoanoverarchingsuper-category(or,theme),thatunifiesthedistinctcategoriesin
someway,forexampletheyareallwellknownbusinesses.Anautomatedprocesshasbeen
developedthatallowsacomputertotakeovermanyofthetrialanderrordesigndecisionsin
selectingstrongassociationsandcategoriespreviouslyincumbentonahumandesigner.
Usinganumericaldigit1to7,todenoteacardfromagivenconceptualcategory,thecards
ineachdeckareinitiallyorderedas:
• Worddeck:1,2,3,4,1,2,3,4,4,3,2,1,4,3,2,1
• Imagedeck:1,5,6,7,1,5,6,7,7,6,5,1,7,6,5,1
Therearetwothingstonote:first,thatthesequentialorderingisreversedhalfwaythrough
eachdeck,andsecond,thepresenceofcategory1ineachdeck.ThesecondGilbreathprinciple
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(whichgeneralisesthefirstprinciple)statesthatanysequentiallyorderedsetofobjectswill
retainelementsofstructureafteroneriffleshuffle.
Tobeclear,ariffleshuffleisonesetofrandominterleavingoperationsperformedontwo
partsofadeck;adeckissplitintotwosections,andrandomlyshuffledbacktogetheronce.
Usually,inGilbreathbasedtricks,asequentiallyordereddeckissplitbydealinganynumber
ofcardsfacedownfromthetopofthedeck,whichreversestheirorder.Thesecardsarethen
riffleshuffledbacktogetherwiththeremainingcardsfromthedeck.SeeDiaconis[5]forfur-
therexplanationsandexplorationsoftheseprinciples.
IntheAssociationtrick,halfthefulldeckofthe16imageorwordcardsispre-reversed,as
shownabove.Crucially,thestructurethatremainsinthistotalstackofimageorwordcards
afteroneriffleshuffleisguaranteedtoholdonecardfromeachcategoryineachsetofcardsof
appropriatelength(here,fourcardssets)dealtfromthedeck,thoughtheorderingisnow
unknown.FortheAssociationtrickthismeansthat,ifeachdeck,cardsandimages,isriffle
shuffled,dealinggroupsoffourcardsfromtheWorddeckwillyieldgroupscontainingcards
fromthecategories[1,2,3,4],insomeorder.Similarly,theImagedeckwillyieldgroupscon-
tainingcardsfromthecategories[1,5,6,7],insomeorder.
ThesetupoftheAssociationtrickisthereforetoorderthetwodecksbycategoryas
described.TheperformanceoftheAssociationtrickthenruns:
1. Theperformerwelcomesthespectator,andasksfortheirname,checkingthattheywould
liketoparticipateinamindreadingexperiment.Usingapadofpaper,theperformer
apparentlynotesdowntheirname,usingsomepretence(e.g.‘I’lljustnoteyourname,
sometimesithelpsmeconnectwithpeopleifIwritetheirnameout,Idon’tknowwhy...’).
Thepadofpaperisputaway.
2. Theperformerproducesthetwodecksofcards,explainingthattheycontainWordsand
Images.
3. ToshowthattheWorddeckcontainswords,theperformerdealseightcardsfaceuponto
thetable,thenquicklyfanstheremainingcardsforthespectatortoconfirmthattheyareall
wordcards.Thefaceuphalfofthedeckisplacedfacedownonthetable,nexttotheother
half,alsofacedown.
4. Theperformerasksthespectatortoshufflethedeckbypushingthetwohalvestogether,in
arandomfashion(or,ifthespectatoriscomfortablehandlingcards,toriffleshufflethe
deckbacktogether).
5. AnidenticalprocedureisperformedwiththeImagedeck.
6. Theperformer,emphasisingthatthedecksarenowrandomised,dealsfourpilesoffour
cardsfromeachdeck,facedownontothetable,makingeightpilesintotal,takingcareto
keepthepilesofwordsandimagesclearlyseparated.Eachpileoffourcardsisdealtsequen-
tiallyfromthedeck,beforethedealermovestothenextpile.
7. Theperformerasksthespectatortoselectonepileofwords,andonepileofimages.
8. Theperformernowstatesthatthespectator’staskistoquicklychoose,fromtheeightcards
intheirhand,onewordandoneimagethat‘goreallywelltogether;agood,strongmatch’,
andtoputthepairfaceuponthetable.Theintentionistoputverymildpsychologicalpres-
sureonthespectatortomakeaquick,System1,decision,ratherthanallowingtheirminds
tohavetimetodeploySystem2typethinking,thatmayleadtoidiosyncraticassociationsto
bemadebetweenthecards.
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9. Theperformercanappearinterestedintheselectionatthispoint.Themostlikelychoice
thatthespectatorwillhavemadeisawordfromcategory1,withamatchingimagefrom
category1.Alltheothercategorieshavebeencarefullychosentobequitedistinctfromone
another,thoughstillrelatedinsomewaytothetheme,andsotoallthewordsandimages
ineachdeck.
10. Theperformernowretrievesthepadofpaperfromthebeginningofthetrick,andreveals
that,inadditiontothespectator’sname,theyalsowroteapredictionaboutthecardsthey
wouldchoose.Forexample,ifcategory1containsweatherrelatedimagesandwords,a
spectatormayhavechosenapictureofthesun,andtheword‘Rain’,andtheperformer
couldhavewrittenonthepad,aboutaspectatornamedFred:‘Fredisinterestedinthe
weathertoday’.
Attheconclusionofthetrick,thespectatorshouldfeelthattheperformerhasimpossibly
predictedatotallyfreechoicetheyhavemadeaboutsomerandomshuffledupwordsand
images.Thespectatorrecallsitwasthemthatshuffledthecards,andmadeafreechoiceabout
whichofthesmallerdealtoutpilesofcardstouse,andalsothefinalpairingofcards.
Whathasactuallyhappenedisthattheperformerknowsthat,duetoGilbreath,attheend
oftheinitialshufflingprocessthespectatorwillhaveapileofimagesandwordsguaranteedto
containonewordandoneimagefromcategory1(andnomore).Theperformeralsoknowsin
advancethatthespectatorshouldmakeaquickassociationbetweenanyofthefourwordsand
anyofthefourimagesfromcategory1,inpreferencetomixinganyoftheothercategories,for
exampleawordfromcategory3withanimagefromcategory6.Selectingsuitablydistinctcat-
egoriesisthereforecritical.Thereisofcourseachancethatthespectatormakesanunpredict-
ableassociation,ruiningtheeffect.Wewillseehowlikelythisisinpractise.
Psychologicalfactors
AsseenfromthedescriptionoftheAssociationtrick,itseffectivenessreliesonthecareful
selectionofcategories.Crucially,thesecategoriesmustbechosentominimiseconceptual
overlap.Forexample,whileFruitsandVegetablesaredistinctcategories,itisnotimpossibleto
imagineaspectatorchoosingapictureofaredappletomatchwiththeword‘Beetroot’.The
keyfactoristoreducethepotentialmatchesbetweencategories,leavingoneeasychoice:our
category1.However,thiscategorymustnotglaringlystandoutamongsttheothercategories,
forfearofraisingthespectator’ssuspicionsthatthecardshavebeenmanipulatedinsomeway;
whilethechoicemustbethemostnaturalchoice,itmustalsobemixedinwithotherchoices
thatfeelviablepriortoseriousconsideration.
0.0.2Theme:Trademarks. TrademarkswerechosenasathemethattheAssociationtrick
couldbebuiltaroundforthisproofofprincipleexperiment.Athemecanbeseenasconsisting
oflistsofcategories;forexample,thetrademarkthemeconsistsofbrands(‘Nike’,‘Google’,
‘Coca-Cola’,etc).Inadditiontoautomaticallygivingeachimageandwordineachdeckan
overallthemedsimilarity(loosely:companies),choosingtrademarksasathemecapitaliseson
theworkdonebybrandbuilderstocleanlyseparatethetypesofassociativethoughtsabout
eachbrandanygivenpersonmayhave.Thesethoughtsfallintoconceptualspacescraftedby
themarketeers,fromwhichdistinctconceptualcategoriescanbeconstructed.
Fromthesecategories—essentiallypoolsofwordsandimages—sevencanbeselectedfor
useinthetrick.Selectingsevencategoriesthatareconceptuallyfarapartfromoneanother
minimisesthechancesthataspectatorwillmakeanassociationbetweenawordandanimage
acrosscategories,makingiteasiertostaywithincategory1,asrequiredbytheperformer.
Theoverallgroupingeffectmaybequitesubtle,dependingonthewordsandimagesused,
butmaybestrongenoughtogivethedecksofcardsacrediblefeelingofcohesion.
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Conceptualspacing. Trademarksarepowerfulculturalsymbolsthatprovideapre-strati-
fiedsetofconceptualspaces;theyareverycarefullyconstructedbyadvertisersandmarketeers
tocarveoutanicheareaofmentalspace.Thereiscommonalitybetweenthewordsandimages
thatpeoplethinkofwhentheyseethetrademarks,andthesewordsandimagesminimally
overlapwithothersthatrefertodifferenttrademarks.Obviously,thereiscommonality
betweenoverarchinggroups,dependentonthemarketspacethatcompaniesoperatein.For
example,theFordtrademarkislikelytotriggersimilargeneralassociationsaboutvehiclesas
thosetriggeredbytheMercedestrademark;however,theremaybemorespecificassociations
thatdonotoverlap;perhaps‘luxury’fortheMercedes,and‘affordable’fortheFord.
Inadditiontothewordsthatareassociatedwitheachbrand(viathetrademark),theremay
alsobecommontypesofimages(inadditiontothetrademark).Thisideaofconceptualspace
separationcanbeseeninFig2.
Methods
Psychologicaldatabank
Inordertodetermineageneralviewoftrademarksinthisway,anonlineexperimentwasrun,
inwhichparticipants(N=87)wereshown,inarandomorder,tenofthemostfamousone
hundredtrademarks,asdeterminedbyMillwardBrown’sBrandZ[17]statementfor2013,in
theirannualreviewofthemostwellknownbrandsfromaroundtheworld.Allonehundred
brands/trademarkswerecovered,buteachparticipantsawonlyten.Theywereasked,foreach
trademark,towritewordsabouthowthetrademarkmadethemfeel,oranyassociationsatall
thattheyhadaboutthetrademark,andalsotomakealinedrawingofanythingthattheyasso-
ciatedwiththebrand.Thegatheredresponsesformakindofdatabankofwordsandimages
thatpeoplecalltomindwhenaskedabouttrademarks.
Thesewordsandimagescannowbesearched,categorised,andselectedfordeploymentin
decksofcardsforuseintheAssociationtrick.Thesizeofthedatabank(870distinctresponses
ofwordsandimagesfromtheparticipants)makesitadifficulttaskforahumandesignerto
siftthroughandgroupthevarioustrademarksintoconceptuallydistinctcategories,andto
pickoutmeaningfulwordsandimagesforeachcategory.Thistaskcanbeperformed
computationally.
Controlledproblemdomain
Asnoted,choosingthemostconceptuallydistinctcategories,andsubsequentlythewordsand
imagestopopulateeachcategory,presentsachallengeforthetrickdesigner.
Thedatabankgainedfromtheonlinetrademarkassociationexperimentprovidesaseries
ofqueryablerepositories;eachtrademarkhasabodyoftextassociatedwithit,alongwitha
seriesofimages.Viewedinthisway,itispossibletoconstructtheproblemofidentifyingcate-
goriesofwordsandimagesfromthisheterogeneousdataasaninformationretrievalproblem:
analysingdatatofindasetofwords(orimages)thatbestrepresentthatdata.
Themainproblemaddressedhereisthegroupingofcertaintrademarkstogetherintocon-
ceptualspacesbasedonthewordsusedtodescribethem.Theimagesgatheredexperimentally
forthetrademarkthemeprovideadirectsourceforthehumantrickdesignertouse.
Automateddatagatheringandprocessing
Inadditiontotheautomatedidentificationofthebestcategoriestouseforthetrick,thegath-
eringofthedataitselfwasalsoautomatedbyacomputer,reducingtheneedfordirectpsycho-
logicalexperimentstobeperformed.ThepowerofsearchenginessuchasGooglewas
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Fig2.Conceptualspacing.Thewordsthatpeopleusetodescribecertaintrademarksallowtheconceptualspacearoundeachtobe
defined.Somenaturallygrouptogether,somearecleanlyseparated.TheAssociationtrickreliesontheseparatedgroups.
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harnessedtoprovideaccesstodocumentsontheinternetthatbelongtoeachclass(e.g.trade-
marks/brands)ofeachtheme.Insteadofqueryingahumanparticipantinanexperimentto
respondtotrademarksusingtheirownwords,internetsearcheswereperformed—theweb
pageslinkedtobythetoptenresultsforeachtrademarkwerethenaccessedandthewordson
thepagesappendedtothedatabankrepositoriesfortherelevanttrademark.
TheproblemfacedbytheAssociationtrickdesigneristogroupsetsofsimilarclassesfrom
thedata,forexampleGoogleandIBM,(toavoidhavingsimilarclassesindifferentgroups),
andalsotoselectwordsthatbelongtotheseclassesandgroupsthataresignificantand
meaningful.
Thedevelopedalgorithmreliesonthefollowingcomputationalconcepts:
Informationcontent
Informationcontent(IC)isabasicmetricusedincomputationalnaturallanguageprocessing
toconveyhowspecificaconceptaworddescribes.Highervaluesindicatethatamorespecific
conceptisrepresentedbyacertainword(forexample‘pencil’specificallydescribesaparticular
objectthatbelongstothemoregeneralconceptualgroupofwritingimplements);lowervalues
indicateamoregeneralconcept(forexample‘idea’).TheICofawordcanbecomputedinthe
contextofabodyoftext;themorefrequentlyoccurringwordsareseenashavinglowerIC
scores.TheICscoresareusedhereasatextpre-processingtool—toreducethenumberof
wordsinthedocumentstorebypruningwordswithlowICscores(forexample‘the’,‘and’,
etc.).[18]
Wordsimilarity
Akeyprocessincomputationallanguageprocessingistocomparetwowordsforsemantic
similarity.Forexample,theword‘dog’issemanticallysimilartotheword‘cat’,butnottothe
word‘sky’.Providinganumericalmeasureofthiskindofsimilarityiscomputationally
difficult.
TheWordNetsystem,originatedbyMiller[19],isalexicaldatabasethatdescribeshierar-
chicalrelationshipsbetweenwords,andiscommonlyusedinnaturallanguageprocessing
tasks.InWordNet,wordsarearrangedintoatreestructurethatincreasesinspecificitywith
depth;parentnodessubsumemorespecificinstances—forexample,theword‘coin’maybea
parentto‘penny’and‘pound’.WordNetprovidesanumberofdifferentsimilarityscoring
mechanismsfortwowords,basedontheirparentnodes,andthedepthsoftherespective
wordsandparents.WordNetalsoprovidessetsofdatadescribingsynonymsforwords.
Morerecently,workbyMikolovetal[20][21]hasproducedanaturallanguageprocessing
toolcalledword2vec.Thetooloperatesondatasets,learningvectorrepresentationsofwords
usingneuralnetworks.Themodelisabletoprovidegoodwordsimilarityscores.
OkapiBM25scoring
Informationretrievalisafieldofcomputersciencededicatedtofindingspecifieddatain,often
large,datasets.OkapiBM25isarankingfunction,firstdevelopedatLondon’sCityUniversity
inthe1980sand1990sforuseinsearchengines[22][23],thatscoresdocumentsforrelevance
toasearchquery.‘BM’simplystandsfor‘BestMatch’,while‘25’reflectsthefunction’sincre-
mentaldevelopmentthroughBM11andBM15versions.Here,itisreferredtoasBM25.
Itisfeasibletoperforminternetsearchestogathercrowdsourceddataaboutcertain
themes,thatcantheneitherreplaceoraugmentadocumentstorederivedexperimentally.For
thetrademarktheme,thedocumentstorewasgeneratedusingacombinationofthesetwo
methods.
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Fig3.Documentstoreprocessing.Simpleexamplesofwords(queries)withtheirassociatedclasses
(documentsofwordsrelatingtoaparticularbrand)rankedbyBM25score.Categoriesofclassescanbe
pickedoutingroups,byfilteringandmergingtherankedlists.Thegreenwordsareallcloselyrelated,and
existinbothqueries.
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0.0.3Associationtrickstrongassociationselectionalgorithm. BM25canbeusedby
searchenginestoretrieverelevantdocumentsfromadocumentstore,givenaparticularquery.
Weuseitslightlydifferentlyhere.Viewingthegenerateddatabankofwordsforeachclassin
eachthemeasthedocumentstore,whereeachdocumentreferstoaparticularclass(e.g.
‘Nike’,forthetrademarktheme),itispossibletogenerateBM25scoresforeachdocumentin
thedocumentstore,foreachwordinagivendictionary(usingword2vecandWordNetfor
granularwordsimilarityscoring).
Theseonewordqueriesthenhaveasetofrankeddocumentsassociatedwiththem,which
canbesortedwiththehighestscoresatthetop.SettingathresholdfortheBM25score,above
whichdocumentsareseenashighlyrelevanttoaparticularquery,allowsthegroupingofdoc-
umentsintoclassesdefinedbyqueries.
SeeFig3.
Thesescoresalsoalloweachdocumenttobeassociatedwithmultiplerelevantqueries.In
thisway,thedocumentstorecanbecategorised,andasetofwordsgeneratedforeachcategory
(usingBM25scoresforwordsinadictionaryusedasqueriestothedocumentsforeachcate-
gory).Thisprovidesthetrickdesignerwithapre-computedsetofwordsforuseintheAssocia-
tiontrick.
Acompanionsetofimagesmaybegeneratedbytakingasetofwordsforthispurposeand
feedingthemintoanimagesearchengine,orpassingthemtoanartist.Inthecaseofthetrade-
marktheme,empiricallysourcedimagesfromexperimentalparticipantsareavailabledirectly
fromthedocumentstore.
Whiletheoutputsogivenwillwork,togeneratethebesttrickpossible,thehumantrick
designershouldstillsiftthroughthecomputergeneratedsuggesteditems,pickingoutafurther
refinedset.Thecomputeractingasaformofcomputerassisteddesigntool.
AvisualrepresentationoftheprocessisshowninFig4.
Results
0.0.4Associationtrickalgorithmoutputs
Thealgorithmoutlinedisabletooutputsuggestedsetsofcategories,andwordsassociated
withthesecategories,whichthetrickdesignermayusetoconstructanAssociationtrick.The
benefitofusingthisautomatedsystemisthatrapidprototypesofthemedtricksmaybeauto-
maticallyproduced,whichthetrickdesigneristhenabletofinetune,comparingdifferent
themestoeachothertofindasuitablesetfromwhichtoproduceafulltrick.
PLOSONE|https://doi.org/10.1371/journal.pone.0181877 August9,2017 10/17