AUTOMATICITY OF MAGNITUDE AND PARITY

RunningHead:AUTOMATICITYOFMAGNITUDEANDPARITY1

Title:Spontaneousandautomaticprocessingofmagnitudeandparityinformation2

ofArabicdigits:Afrequency-taggingEEGstudy.3

MathieuGuillaume1,AlexandrePoncin2,ChristineSchiltz2,&AmandineVanRinsveld1.4

Thefirsttwoauthors(MGandAP)shareequalfirstco-authorships,andthetwolastauthors(CS5

andAVR)shareequallastco-authorships.6

1CenterforResearchinCognitiveNeuroscience(CRCN),UniversitéLibredeBruxelles,Belgium.7

2CognitiveScienceandAssessmentInstitute(COSA),UniversityofLuxembourg,Luxembourg.8

Correspondingauthor: MathieuGuillaume9

maguilla.ulb@gmail.com +322650203110

Address: UniversitéLibredeBruxelles,11

50,AvenueFranklinRoosevelt,CP191,1050Brussels,Belgium12

ManuscriptWordCount:3,657(excludingabstract,methods,footnotes,andreferences).13

MethodWordCount:1,453.14

NumberofFigures:3 NumberofTables:015

Keywords:Electroencephalography(EEG),SteadyStateEvokedPotential,Numerical16

Cognition,Numericalmagnitude,Parity 17

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AUTOMATICITY OF MAGNITUDE AND PARITY

Abstract18

Arabicdigits(1-9)areeverywhereinourdailylives.Thesesymbolsconveyvarious19

semanticinformation,andnumerateadultscaneasilyextractfromthemseveral20

numericalfeaturessuchasmagnitudeandparity.Nonetheless,sincemoststudiesused21

activeprocessingtaskstoassesstheseproperties,itremainsunclearwhetherandto22

whatdegreetheaccesstomagnitudeandespeciallytoparityisautomatic.Herewe23

investigatedwithEEGwhetherspontaneousprocessingofmagnitudeorparitycanbe24

recordedinafrequency-taggingapproach,inwhichparticipantsarepassively25

stimulatedbyfastvisualsequencesofArabicdigits.Weassessedautomaticmagnitude26

processingbypresentingastreamoffrequentsmalldigitnumbersmixedwithdeviant27

largedigits(andthereverse)withasinusoidalcontrastmodulationatthefrequencyof28

10Hz.Weusedthesameparadigmtoinvestigatenumericalparityprocessing,29

contrastingodddigitstoevendigits.Wefoundsignificantbrainresponsesatthe30

frequencyofthefluctuatingchangeanditsharmonics,recordedonelectrodes31

encompassingrightoccipitoparietalregions,inbothconditions.Ourfindingsindicate32

thatbothmagnitudeandparityarespontaneouslyandunintentionallyextractedfrom33

Arabicdigits,whichsupportsthattheyaresalientsemanticfeaturesdeeplyassociated34

todigitsymbolsinlong-termmemory.35

Abstractwordcount=200words. 36

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AUTOMATICITY OF MAGNITUDE AND PARITY

Spontaneousandautomaticprocessingofmagnitudeandparityinformationof37

Arabicdigits:Afrequency-taggingEEGstudy.38

Numbersymbolsconveyalargerangeofdifferentsemanticproperties,suchasbeinga39

primenumber,beingamultipleofanothernumber,orbelongingtothepowerof40

anothernumber.Whilethesevariouspropertiesneedtobeassimilatedbylongand41

laboriousculturallearningprocesses,someofthemarecriticalforunderstanding42

numbersymbols’essence[1].Amongtheseproperties,cardinality(ornumerosity)and43

parityareofcrucialinterestbecausetheyarebothacquiredatanearlystageof44

numeracylearningandtheyareknowntoincreasinglybecomesalientpropertiesof45

numbersymbols[2:7].Thequestionwhetherandtowhatextentsuchsemanticnumber46

propertiesareautomaticallyactivatedhasoccupiedthenumericalcognitionliterature47

sinceseveraldecades[8:22].Thisissueisessentialbecauseitdirectlyquestionsthe48

natureofsemanticrepresentationofnumbers,aswellasthedevelopmentaltrajectory49

ofnumericalandmathematicallearning[23:29].Forinstance,3rdgraderstypically50

associatedigitsbasedonmagnitudecharacteristicswhentheyareaskedtocategorize51

numbersaccordingtosimilarity,while6thgradersaremoreinfluencedbyparity;adults,52

fortheirpart,equallycategorizedigitsontheirparityandmagnitudefeatures[30].53

Automaticityinmagnitudeprocessing54

Automaticityisusuallydefinedasanunconsciousandunintentionalprocess,thatmight55

occurinparallelwithotherprocesses[31],andthathappenswithoutmonitoring[32,33].56

Fromageneralcognitiveperspective,automatic(andintuitive)processesaregenerally57

contrastedtoslowlogicalreasoningprocesses[95:98].Despitethisduality,ithasbeen58

arguedthataclearerdistinctionshouldbemadewithinautomaticprocesses,between59

twodifferenttypesofautomaticprocesses[21,32,34].Thefirstautomaticprocesstypeis60

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AUTOMATICITY OF MAGNITUDE AND PARITY

intentional,usedwhenitisnecessaryandbeneficialfortheongoingtask,forinstance61

manipulatinganumberduringcalculationorreadingwordsinasentence.Thesecond62

typeisautonomous,unintentionalandusedevenwhenitsprocessingisirrelevanttothe63

ongoingtask.Itisnoteworthythatpointingoutunintentionalautomaticprocessing64

fromintentionalprocessesisexperimentallycomplicated.Itisactuallynotpossibleto65

disentangleausefulandintentionalprocessfromanautonomousprocesswhenthis66

processisrequiredforthetask[21].67

Despiteofthesedifficulties,threeeffectscoulddepictautomaticprocessingwith68

numbermagnitude.ThefirstistheSNARCeffect(SpatialNumericalAssociationof69

ResponseCodes)whichischaracterizedbyaninfluenceofthemagnitudewhile70

participantsareaskedtocategorizenumbersaccordingtotheirparity[34].Inparticular,71

participantsarefastertocategorizesmallnumberswiththeirlefthandandlarge72

numberswiththeirrighthandindependentlyofthenumber’sparity.Manyauthors73

explainthiseffectbysuggestingtheautomaticactivationofamentalnumberline[36]74

duringthetask,wherethesmallernumbersaremappedontheleftandthelarger75

numbersontheright1.Nonetheless,becauseparityisalsoanumericaldimension,76

experimentalsettingscouldtriggertheautomaticprocessingofmagnitude.The77

triggeringcouldhappenwhentherelevantdimension(i.e.,parityinSNARCeffect)and78

theirrelevantdimension(i.e.,magnitudeinSNARCeffect)arerelated.Inotherwords,79

parityandmagnitudearebothnumeric,thusitisdifficulttoknowifmagnitude80

1 For alternative mechanisms underlying the SNARC effect, please also consider the dual

route model [37,38], the polarity correspondence account [39], and the working memory account [40:45].

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AUTOMATICITY OF MAGNITUDE AND PARITY

activationobservedduringtheSNARCeffectisanautonomousoranintentional81

automaticprocessing2[21].82

Aseconddomainrevealingautomaticnumbermagnitudeprocessingreferstothe83

interferenceeffectsobservedintaskssimilartothewell-knownStroopexperiment[51].84

Onetypeofsuchnumericalinterferenceeffectsisforinstancethesemanticcongruity85

effect.Adultsareindeedfastertojudgethephysicalsizeoftwonumberswhenthe86

biggernumberwasalsothelargerintermsofnumericalmagnitude(e.g.,comparing587

vs.2iseasierthan5vs.2)[13,22,25,52,53].AnotherexampleisthesizeCongruencyEffect88

happeningwhenparticipantsareaskedtochoosebetweentwodisplayswithdigits,the89

displaywiththemorenumerousarrayofdigits.Participantsarefasterduringthistask90

whenthedisplaycomprisingmoredigitsalsocontainsnumericallylargerdigitsandthe91

screenwithfewerdigitsalsocontainsnumericallysmallerdigits[18].However,these92

interferenceeffectsareonlyobservedinnumericaltasksandconsequentlynumerical93

magnitudecouldbetriggeredbythetaskitself[21].Accordingtothislineofreasoning,94

interferenceeffectsarethusnotsufficienttoarguethatnumbermagnitudeisaccessed95

automaticallyinanautonomousmanner.96

Third,thereisthedistanceeffect,whichreferstothefactthatcomparingclosenumbers97

(e.g.,4and6)isharderthancomparingmoredistantnumbers(2and8).Inother98

words,thedifficultyofcomparingtwonumbersisinverselyrelatedtothenumerical99

distancebetweenthesetwonumbers[54].Distanceeffectsarefoundwhenparticipants100

2 Nevertheless some SNARC studies use tasks not entailing any numerical triggering such as

orientation discrimination [46], plural versus singular nouns [47], line bisection [48] or colour

discrimination [49,50]. Significant SNARC effects reported in these studies could therefore be

taken as convincing marks of automaticity of numerical magnitude processing.

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AUTOMATICITY OF MAGNITUDE AND PARITY

areexplicitlyinstructedtocomparenumbers[11],butalsowhenparticipantshadsimply101

tosayiftwoArabicnumberswerethesameornot[13].Nonetheless,suchevidencehas102

alsobeenassumedtobeinsufficienttoacceptthedistanceeffectasaproofof103

autonomousautomaticprocessing[21].Thatistosay,evenifthedistanceeffectoccursin104

non-numericaltasks,processingthemagnitudeinthiskindoftaskswouldbebeneficial105

forthetaskperformance.Distanceeffectscouldthereforebeamarkerofintentional106

automaticprocessingratherthanmarkerofautonomousautomaticprocessing.107

Automaticityinparityprocessing108

Regardingparity,anumbercanonlybelongtooneoutoftwocategories:‘even’or‘odd’,109

indicatingthatanumberisdivisiblebytwoornot.Parityjudgmentsaretypically110

learnedrelativelyearly,aroundthetwofirstyearsofformaleducationinwestern111

cultures[50],andevenearlierineasterncultures[55].Whilesomeauthorsarguedthat112

parityiscomputedbydividinganumberbytwo[56],othersproposedthatparity113

informationisstoredasdeclarativememorycontent[35,57].Accordingtothelatter,114

parityaccesscouldnotbetheresultofcomputationsbecausethereisnosizeeffectin115

paritytasks.Moreprecisely,ifthedeterminationofparitywereuptodividingbytwo,116

smallnumbersshouldbeprocessedfasterthanlargenumbers,whichisnotthecase.In117

thesamevein,certaindigitswithspecificpropertiesarecategorizedfasterasoddor118

even[4].Thisisforinstancethecasefornumbersthatareapoweroftwo(i.e.,2,4and119

8)andforprimenumbers(i.e.,3,5and7).Inparticular,themorespecificitiesagiven120

numberhas,thefastertheirparitywillbeaccessed[35].Thesefindingsareinlinewitha121

recentstudyproposingthattheobjective,mathematicallydefinedparitydifferstoa122

certaindegreefromthe“perceived”parity,assomenumbersseemtobemore123

prototypicalfortheircategories[58].124

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AUTOMATICITY OF MAGNITUDE AND PARITY

Tothebestofourknowledge,thereareonlyalimitednumberofinvestigations125

concerningtheautomaticityofparityprocessing.Astudyofparitycategorizationusing126

subliminalprimingofArabicnumbers(i.e.,participantscouldnotconsciouslyseethe127

primeddigits)beforetheonsetofagiventargetnumberwordshowedthatparticipants128

werefastertocategorizethetargetwhentheprimeddigitandthetargetnumberhad129

thesameparity[59].Theseresultsareinfavourofanautomaticaccesstotheparity130

informationofdigits.Thisisinlinewithotherstudiesthatassessedarithmeticalfact131

verificationsbasedontheparityofthemultipliersoraddends[60].Inparticular,those132

tasksconsistedinjudgingthecorrectnessofadditionsormultiplicationsfacts.Ifthe133

parityrules(suchas:additionormultiplicationoftwoevennumbersgivesaneven134

number)werenotrespected,participantswerefastertosaythatarithmeticalfactswere135

false[57].Someauthorsarguedthattheapplicationoftheparityrulesisunconsciousand136

automaticbecausesomeoftheirparticipantsreportedthattheywereunawareofusing137

theparityrules,whiletheirresultsindicateditsutilisation[60].Nevertheless,inboth138

previousparadigms,theexperimentaltaskrequireddirectmanipulationofthenumber139

symbolandthereforecanonlypointtowardsintentionalautomaticprocessing[21],140

leavingopenthequestionwhetherautonomousunintentionalautomaticparity141

processingmightalsoariseinsomecircumstances.142

Neuralcorrelatesof(automatic)numberprocessing143

Neuroimagingstudiesconsistentlyindicatedthattheparietalcortexandmore144

specificallytheintra-parietalsulcus(IPS)playsapivotalroleintheprocessingof145

numericalinformation[61:65].Indeed,thisregionhasbeenassociatedtoavariousrange146

oftasksinvolvingthemanipulationofnumericalmaterial[66,94].Magnitudecomparison147

ofnumbersymbolsactivatemorepredominantlytherightIPS,forconjointsymbolicand148

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AUTOMATICITY OF MAGNITUDE AND PARITY

non-symboliccomparison[92],butalsoforexclusivelysymboliccomparison[64,91].149

Moreover,thesamebilateralIPSregionwasactivatedduringnumericalmagnitude150

comparisonaswellasparitycategorizationinaPETstudy[63],inwhichtheauthors151

consequentlyproposedthatparityandmagnitudeareprocessedinneighbouringareas.152

Itwasalsoproposedthatboththeoccipitoparietalnetworkusedforperceptualand153

representationalprocessingofArabicdigitsandthefrontoparietalnetworkusedfor154

semanticprocessingareinvolvedinnumericalprocessingsuchasmagnitude155

comparisonsandarithmeticalfactsretrieval[64,65].156

Theparietalcortexisalsoassociatedwithautomaticprocessingofnumbersymbol157

semantics.Tasksrequiringthesimpledetectionofvisualnumeralsornumberwords158

activatetheIPSsignificantlymorethanthesametaskswithnon-numericalstimuli(e.g.,159

detectionoflettersorcolours[69]).Tothebestofourknowledge,onlyafewstudies160

furtherinvestigatedautomaticresponsestonumbersymbolmagnitudes,andnone161

examinedautomaticparityprocessing.Noticeably,usingfMRI,astudyreported162

strongerBOLDresponsesforlargedigits(8or9)thanforsmalldigits(1or2)within163

twobilateralparietalregions(i.e.,theinferiorparietallobuleandtheIPS),when164

investigatingtheneuralcorrelatesofnon-predictivenumbercues[70].Otherstudies165

reportedgreaterERPamplitudesacrossparietalelectroderegionsforsmalldigits166

comparedtolargedigits,inataskwherenumberswereusedasnon-informative167

attentionalcues[71,72].Nonetheless,imagingevidenceinfavourofunintentional168

processingofmagnitudeorparityiscurrentlylacking.169

Currentstudyandexperimentaldesign170

Inthepresentstudy,weaimatassessingtheautonomousunintentionalautomaticityof171

magnitudeandparityprocessing,carefullyavoidinganytriggeringofnumerical172

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AUTOMATICITY OF MAGNITUDE AND PARITY

informationprocessing(suchthattheexistenceofautonomousunintentional173

automaticitycanbeprobed[21]).Forthatpurpose,weusedasensitivefrequency-174

taggingapproach–FastPeriodicVisualStimulation(FPVS)–torecord175

electrophysiologicalresponsestaggedatthefrequencyofexperimentallymanipulated176

magnitudeandparitychanges,inapassiveviewingsetting.SimilarFPVSparadigms177

relyingonpassiveviewinghavesuccessfullybeenusedtostudyhigh-level178

discriminationoffaces[73],tools[74],aswellasreading(wordrecognition[75],andletter179

stringsdiscrimination[65,76]),andnon-symbolicquantities[77],withoutengaging180

participantsinanykindofexplicitprocessingofthepresentedstimuli.181

WecombinedtheFPVSparadigmwithastandard/deviantprocedure(oddballmethod182

[79]).Moreprecisely,duringone-minutesequences,wedisplayeddigitsattheveryfast183

rateof10Hz(tenstimulipersecond)followingasinusoidalcontrastmodulation.184

Withinthestreamofstandarddigits,aperiodicdeviantwasintroducedeveryeight185

trialssuchthatdigitsfromthedeviantcategoryappearedat1.25Hz(seeFigure1).The186

digitsusedasstandardsordeviantsvariedaccordingtothecondition:Inthemagnitude187

condition,digitssmallerthanfivewerepresentedasstandardanddigitslargerthanfive188

asdeviants,ortheotherwayaround.Intheparitycondition,odddigitswerepresented189

asstandardsandevendigitsasdeviants,ortheotherwayaround.Finally,inacontrol190

condition,halfofthedigitswerearbitrarycategorizedasstandardsandtheotherhalfas191

deviants(seeFigure1).192

Wepostulatethatweshouldrecordanelectrophysiologicalresponsesynchronizedat193

thedeviationfrequency(i.e.,1.25Hz)ifthebrainissensitivetothechangesfromone194

categorytoanother.Inotherwords,ifmagnitudeand/orparityareprocessedinan195

autonomousunintentionalautomaticway,thenthecategorychangesshould196

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AUTOMATICITY OF MAGNITUDE AND PARITY

systematicallyelicitaspecificbrainresponseatthefrequencyofthechangesforthe197

respectivecondition(s),whilenosuchresponseshouldariseduringthecontrol198

conditionasthelatter'sdigitcategorieswerearbitraryandnotrelatedtoanysemantic199

content.Doingso,wecanobjectivelymeasurewhetheragivensemanticnumber200

informationisautomaticallyandunintentionallyprocessedbythebrainalthoughno201

numericaltaskwasrequestedfromtheparticipant. 202

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AUTOMATICITY OF MAGNITUDE AND PARITY

Results203

Figure2aillustratesthetopographicalmapsoftheaveragedoddballamplitudesfor204

everycondition,expressedastheSignal-to-NoiseRatio(SNR)ofthefrequencybinof205

interestanditsharmonicsuptotheseventh(i.e.,1.25,2.50,3.75,5.00,6.25,7.50,and206

8.75Hz).Thesemapshighlightthatthestrongestrecordedresponsesineachcondition207

werelocatedoverabilateralregionencompassingoccipitoparietalareas.Itisworth208

noticingthattherewasasubstantialoverlapofthelocationofthebrainresponses209

betweentheexperimentalconditions,whichallowsdirectcomparisonofamplitudes210

recordedwithintheseregions.211

Figure2brepresentstheEEGspectrarecordedontheelectrodesfromtheleft(A9,A10,212

A11)andright(B6,B7,B8)occipitoparietalregionsofinterestcorrespondingtothe213

topographicalmaps.Thespectra,expressedasSNRs,areaveragedacrossparticipants214

foreverycondition.Ineachcondition,therewereclearpeaksat10Hz,withZ-scores215

systematicallyreachingvalueslargerthanfive.Thesefindingssupportthatboth216

occipitoparietalregionsspecificallysynchronisedtothe10Hzbaserateduringthe217

recordingsessions.Note,however,thatneuralsynchronisationtothebaseratemerely218

reflectsbrainresponsetotheperiodicstimulusonsetsat10Hz.219

Morecriticallyforthepurposeofthecurrentstudy,wealsoobservedinFigure2blarge220

peaksinthefrequencybinsthatareharmonicsoftheperiodiccategoryfluctuation(up221

totheseventhharmonic).IntheMagnitudecondition,therewerefewerclearpeaks222

acrossthesefrequencybinswithintheleftelectrodes,butpeakswereclearlydepictedin223

therighthemisphere.FortheParitycondition,weobservedsomeclearpeakswithinthe224

leftregionofinterest,andmanydefinitepeakswithintherightregionofinterest.225

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AUTOMATICITY OF MAGNITUDE AND PARITY

Finally,moreunexpectedly,wealsofoundsomerespondingpeaksinthecontrol226

condition,mostlylocatedwithintherightoccipitoparietalregions.227

Inordertoassesswhetherthesepeakswerestatisticallysignificant,wecomputedthe228

averagesignalamplitudeofthefrequencyofinterestanditsharmonicsuptothe229

seventh,expressedasaZ-score,asafunctionofthecondition(seeFigure3).Withinthe230

threeleftelectrodesofinterest,meanoddballamplitudeduringtheMagnitudecondition231

was0.51,StandardDeviation(SD)=1.52,meanamplitudeintheParityconditionwas232

1.59,SD=1.26,andmeanamplitudefortheControlconditionwas0.69,SD=1.17.233

Withintherightelectrodes,meanamplitudeduringtheMagnitudeconditionwas2.01,234

SD=2.40,duringtheParityconditionitreached2.50,SD=1.85,anditwas1.23,SD=235

1.90,fortheControlcondition.VisualinspectionofFigure3revealsthattheright236

occipitoparietalregionsofinterestweresignificantlysensitivetotheperiodiccategory237

changesduringbothexperimentalconditions,withz-scoredamplitudesexceedingthe238

unilateral95%thresholdof1.64.239

Weadditionallyperformedarepeated-measuresANOVAwiththeregionofinterest(two240

levels,eitherleftorright)andthecondition(threelevels)asfixedfactors.Therewasa241

significantmaineffectofthecondition,F(2,88)=14.409,p<.001,partialη2=.179,and242

asignificantmaineffectoftheregionfactor,F(1,44)=5.468,p=.024,partialη2=.111.243

Althoughtheinteractiondidnotreachthesignificancelevel,F(2,88)=1.761,p=.178,244

partialη2=.038,weconductedpairwisetwo-sidedWilcoxontests(sinceassumptionof245

normalitywasrejected)todirectlycomparetheamplitudeswithineachhemisphere.246

Thesepost-hoctestsrevealedthat,fortheleftelectrodesofinterest,Parityyielded247

significantlygreaterresponsesthanbothControl,Z=56,p=.011,andMagnitude248

conditions,Z=43,p=.003.Ontheotherhand,ParityandControldidnotdifferfrom249

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AUTOMATICITY OF MAGNITUDE AND PARITY

eachother,Z=168,p=.377.Fortherightelectrodesofinterest,ParityandMagnitude250

weresignificantlygreaterthanthecontrolcondition,respectivelyZ=35,p<.001,andZ251

=65,p=.025,buttheexperimentalconditionsdidnotdifferfromeachother,Z=91,p=252

.160. 253

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AUTOMATICITY OF MAGNITUDE AND PARITY

Discussion254

Magnitudeandparityareverysalientfeaturesofnumbersymbols[5,30].Whilethereare255

severalstudiesdemonstratingtheexistenceofautomaticnumbersymbolsprocessingin256

educatedadults,onlyafewstudiescouldunequivocallydemonstratetheexistenceof257

autonomousandunintentionalnumbermagnitudeprocessing.Therefore,itisstill258

necessarytoprovidefurtherevidencebytriggeringmagnitudeaslittleaspossiblein259

ordertodisentangleautonomousfromintentionalautomaticprocessing[21].Moreover,260

dataconcerninganautomaticprocessingofparityarecurrentlylacking.261

ThecurrentFPVSparadigmallowsinvestigatingthespontaneousandautonomous262

natureofspecificcognitiveprocessesduringpassiveviewingofrapidsequence[87].This263

techniquehasnotyetbeenusedtoinvestigatenumbersymbolprocessing,thoughitis264

veryrelevantforourobjectivesinceitisanobjectivemeasureofthebrainresponseata265

frequencydefinedaprioribytheexperimenter,whichallowsdirectandstraightforward266

analysisoftheneuralsynchronisation.Moreover,therecordedresponsesquantifythe267

processingofdigits’magnitudeandparitywithoutanactivetaskandthus,withoutthe268

implicationofdecision-makingprocesses[78].Takentogether,thecurrentdesign269

avoidedanyconscioustriggeringofmagnitudeorparityduringtherecordingsession270

andthusprobetheautonomousnatureofthesenumericalprocesses.271

Weobservedasignificantneuralsynchronisationtochangesinnumericalmagnitude272

andparitywithinrightoccipitoparietalareas,whereasnosuchsynchronisationwas273

foundduringthecontrolcondition.ItisnoteworthythatvisualinspectionofSNRs274

suggeststhatsomebrainresponsespeakedatsomeharmonicsofinterestinthecontrol275

condition,wherecategorywasbasedontemporarilyconstructedrules,butthesepeaks276

didnotreachthestatisticalsignificance.Incontrast,thestrongresponseswithinthe277

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AUTOMATICITY OF MAGNITUDE AND PARITY

rightoccipitoparietalelectrodesindicatethatparticipantsimplicitlyprocessedthe278

categorytowhichnumericalstimulibelongandreactedtochangeswithrespecttothe279

category.Additionally,parityyieldedsignificantlylargerbrainresponsesthantheother280

conditionsinthelefthemisphere.281

Wethusmeasuredsubstantialimplicitresponsestothetwomanipulatedsemantic282

features,butnottoshort-termarbitraryassociations.Thismeansthatwecanexclude283

thatthebrainsynchronisationsrecordedinbothexperimentaltaskswereonlydueto284

therarenatureofthedeviantstimulus.Theseevidencessupporttheviewthatboth285

numericalmagnitudeandparitywereautomaticallyaccessedandprocessedduring286

passiveviewingsessions.Inotherwords,bothsemanticfeaturesarespontaneouslyand287

unintentionallyextractedfromArabicdigits,whichcorroboratespreviousobservations288

thatseveraldeliberatetasksonArabicdigits(suchasnaming)arenecessarily289

semanticallymediated[14].Itisnoteworthythattheautomaticityofparitythatwe290

observedheredoesnotsupportthehypothesisarguingthatparityiscomputedby291

dividingthenumberbytwo[56],butourfindingsareratherinlinewiththeideaofa292

directretrievalfromsemanticmemory[35,57].293

Thetopographyofthefrequency-taggedresponsescorrespondswithseminalmodelsof294

numericalcognition,suchasthetriple-codemodel[66,80],sincewefoundsignificant295

responsesoverrightoccipitoparietalelectrodesspecificallyrelatedtobothmagnitude296

andparitychanges.Thisisinlinewiththehypothesisthatthesemanticofnumber297

representationsarehousedinparietalregions[98].Theoccipitoparietalresponsesthat298

weobtainedduringMagnitudeandParityconditionsaretypicalinERPstudies299

investigatingtheneuraldistanceeffectwithArabicnumbers[64,67,68].Thesestudies300

highlightedaneuraldistanceeffectillustratedbyamodulationofthepositivityofP2p301

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AUTOMATICITY OF MAGNITUDE AND PARITY

recordedoveroccipitoparietalelectrodesasafunctionofthenumericaldistanceduring302

numericalcomparison.Thesestudies,except[68],alsofoundadominanceoftheright303

hemispherefornumericalmagnitudecomparison.Intheabsenceofanactivetask,we304

similarlyfoundsignificantright-sideddominancefornumericalsymbols’processing.305

Wedidnot,however,observeanysignificantdifferencesbetweenrighthemisphere306

electrodesrespondingtoparityandmagnitude,whichispartlyinlinewithaPETstudy307

indicatingthatparityandmagnitudeinformationareprocessedinneighbouringarea308

insidetheIPS[81].309

Finally,itisnoteworthythateachdigitpresentationonlylasted100msinthecurrent310

experimentaldesign(sinceourbaseratewas10Hz,seeFigure1).PreviousERPstudies311

showedthatnumberprocessingactuallyfollowsatimecoursethatinvolvesdistinct312

stagesofneuralprocesses[99].Critically,numericalmagnitudewasalreadyreportedto313

beearlyextracted(within200ms)fromdigitsymbols[99].Duetothefastdisplayperiod314

inthecurrentFPVSparadigm,fewerthan100ms,wecanassumethatourmethod315

mostlycapturedearlycognitiveprocesses.Becauseweobservedsignificantbrain316

synchronizationtomagnitudeandtoparity,ourresultsconsequentlysupportthatnot317

onlymagnitude,butalsoparityinformation,canbeextractedandprocessedveryearly318

inthebrain.Thetimecourseoftheautonomousprocessingofnumericalfeaturescould319

beinvestigatedinfuturestudiesby,forinstance,varyingthebaserateofsimilarFPVS320

paradigms.Moregenerally,thecurrentparadigmprovidesstrongevidenceof321

unintentionalandautonomousprocessingofsemanticinformationfromdigits,andit322

couldbeeasilyimplementedtofollowhowsymbols’semanticprocessingbecomes323

automaticacrosstypicalandatypicaldevelopment.324

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AUTOMATICITY OF MAGNITUDE AND PARITY

Insummary,weobservedsignificantbrainresponsestaggedatthefrequencyof325

magnitudeandparityperiodicchangesoveroccipitoparietalelectrodesduringpassive326

viewingofarapidstreamofArabicdigits.Wedemonstratethatnumericalmagnitudeis327

spontaneouslyprocessed,andwealsoprovideevidencethatparityisasemanticfeature328

thatisunintentionallyactivatedbyArabicdigitsinnumerateadults.Thecurrentstudy329

thusprovidesevidencethatculturallylearnednumbersymbolsbecomeautomatically330

processedbythehumanmind. 331

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AUTOMATICITY OF MAGNITUDE AND PARITY

Method332

Participants333

Twenty-nineundergraduatestudentsfromtheUniversityofLuxembourgparticipatedin334

thestudy.Anyhistoryofneurologicalorneuropsychologicaldiseaseoranyuncorrected335

visualimpairmentconstitutedexclusioncriteria.Toensureparticipantshadnomajor336

mathematicaldifficulties,participants’arithmeticfluencywasevaluatedwiththe337

Tempo-TestRekenen[82],whichisatimedpen-and-papertest(fiveminutes)consisting338

inarithmeticproblemsofincreasingdifficulty.Allparticipantsreachedtheinclusion339

criterion,whichwas100correctitemsoutof200,andwereincludedintothepresent340

study.Sixparticipantswereexcludedfromthefinalsampleduetosubstantialnoisein341

theirEEGsignal(mostlyduetotranspiration).Thefinalsamplethusconsistedin23342

adults,withameanageof24years(SD=3.5).Participantsreceived30eurosfortheir343

participation.344

Experimentalsetup345

WeusedMATLAB(TheMathWorks)withthePsychophysicsToolboxextensions[83:85]to346

displaythestimuliandrecordbehaviouraldata.TheEEGrecordingtookplaceina347

shieldedFaradaycage(288cm×229cm×222cm).Participantswereseatedat1meter348

fromthescreen,withtheireyesperpendiculartothecentreofthescreen(24’’LED349

monitor,100Hzrefreshrate,1msresponsetime).Screenresolutionwas1024×768350

px,withalightgreybackgroundcolour.TheorderoftheconditionsduringtheEEG351

recordingsessionwascounterbalancedacrossparticipants.352

MaterialandProcedure353

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AUTOMATICITY OF MAGNITUDE AND PARITY

AlthoughFPVSparadigmtheoreticallyonlyinvolvespassiveviewingofthestimuli,we354

introducedabasicorthogonalactivetaskduringtherecordingsessionsinorderto355

ascertainthatparticipantswerelookingatthecomputerscreen.Participantswerethus356

instructedtofixatethecentreofthescreenwhereasmallbluediamond(12pxsize)was357

displayed,andtheywereaskedtopressabuttonwiththeirrightforefingerwhenthey358

detectedthatthediamondchangeditscolourfrombluetored.Thiscolourchangewas359

notperiodicandcouldrandomlyoccursixtoeighttimesinagivensequence.360

Participantswerealsoinformedthatblackdigitsrangingfrom1to9–excluding5–361

wouldquicklyappearonthescreen.Theywereexplicitlyinstructednottoactivelylook362

atthedigitsbuttokeeptheirgazeonthecentraldiamond.Onaverage,participants363

took640ms(SD=121ms)torespondtothecolourchangethataffectedthefixation364

diamond.Misseswereveryrare,occurringonlyin1.5%ofthetrials.Suchhigh365

detectionrateindicatesthatparticipantsfollowedtheinstructionandkepttheirgazeon366

thecentreofthescreenduringEEGacquisition.367

Digitsweresequentiallypresentedatthefastbasefrequencyof10Hz(i.e.,tenstimuli368

persecond)followingasinusoidalcontrastmodulationfrom0to100%[73,77,86](see369

Figure1).Therewasthusforeachstimulusa50msperiodofgradualfade-inand50ms370

ofgradualfade-out.Thesuccessivepresentationofdigitsconsistedinsequencesthat371

lasted64seconds,including60secondsofstimulationand2secondsoffade-inand372

fade-out,whichwedidnotanalyse.373

WeusedtheFPVSvariationoftheoddballdesign[79]inwhichweintroducedaperiodic374

fluctuationwithinthestandardsequence:thestimuluscategorychangedeveryeight375

items(i.e.,at1.25Hz).Ourdesignincludedthreedifferentexperimentalconditions,376

eachconsistinginadifferentcategorychange.Inthemagnitudecondition,periodical377

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AUTOMATICITY OF MAGNITUDE AND PARITY

variationswerebasedonthemagnitudeoftheArabicdigit(i.e.,smallerthan5orlarger378

than5).Forhalfofthesequences,thestandardstimulidisplayedatthebaseratewere379

randomlydrawnamongthesmallestnumbers(1,2,3,4)whereasthedeviantitemwas380

randomlydrawnamongthelargestnumbers(6,7,8,9).Fortheotherhalf,itwasthe381

opposite,thegreatestnumberswerestandardsandthesmallestonesweredeviant.In382

theparitycondition,periodicalvariationwasbasedontheparityoftheArabicdigit(i.e.,383

oddvs.even).Forhalfofthesequences,theoddcategory(1,3,7,9)wasstandardand384

theevencategory(2,4,6,8)wasdeviant,andvice-versafortheotherhalf.Finally,we385

introducedacontrolconditionthatwasbasedontwoarbitrarycategorieswithequal386

amountsofodd,even,smallandlargenumbers(1,4,6,9vs.2,3,7,8).Asthecontrol387

categorieswerearbitrary,andinordertoreducetherecordingtime,weonlypresented388

thefirstsetasthestandardcategoryandthesecondsetasthedeviantcategory.389

Sequencesforeveryconditionwererepeatedfourtimes.Themagnitudeandparity390

conditionseachyieldedeightsequences,foratotaloftwentysequences.391

Followingpreviousrecommendations[87],andtodecreasehabituationtothevisual392

propertiesofthestimuli[9],wedeliberativelyintroducedstochasticphysicalvariations393

withinthestimulistream.Thestimulusfontrandomlyvariedamongfourpossibilities394

(Arial,TimesNewRoman,Cambria,andCalibri),thepositionofthestimulusrandomly395

variedonboththeverticalandhorizontalaxes(withavariationofmaximum10%from396

thecentreofthescreen),andthefontsizevaried(from122to148,withanaverage397

valueof135).Theserandomvisualvariationsoccurredateachonsetandwerethusnot398

congruentwithourfrequenciesofinterest(i.e.,1.25Hzanditsharmonics).399

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AUTOMATICITY OF MAGNITUDE AND PARITY

EEGacquisition400

Weuseda128-channelBioSemiActiveTwosystem(BioSemiB.V.,Amsterdam,The401

Netherlands)tunedat1024HztoacquireEEGdata,asin[77].Wepositionedthe402

electrodesonthecapaccordingtothestandard10-20systemlocations(forexact403

positioncoordinates,seehttp://www.biosemi.com).Weusedtwosupplementary404

electrodes,theCommonModeSense(CMS)activeelectrodeandtheDrivenRightLeg405

(DRL)passiveelectrode,asreferenceandgroundelectrodes,respectively.Weheld406

electrodesoffsets(referencedtotheCMS)below40mV.Wealsomonitoredeye407

movementswithfourflat-typeelectrodes;twowerepositionedlateraltotheexternal408

canthi,theothertwoplacedaboveandbelowparticipant’srighteye;butwedidnot409

furtheranalysetheseelectrodes.410

EEGanalysis411

AnalyseswereconductedwiththehelpofLetswave6412

(http://nocions.webnode.com/letswave).Beforestartingtheanalyses,wedown-413

sampledourdatafileresolutionfrom1024Hzto512Hzforfastercomputerprocessing.414

Weuseda4-orderband-passButterworthfilter(0.1to100Hz)andwethenre-415

referencedthedatatothecommonaverage.Wedidnotinterpolateanyelectrodenor416

correcttheEEGsignalforthepresenceofocularartefacts.Thefade-inandthefade-out417

periodswereexcludedfromtheanalysesleadingtothesegmentationofanEEGsignalof418

60seconds(correspondingtothedisplayof600stimuli).Weaveragedthesignalfrom419

allrepetitions3ofeachconditionforeachparticipant.WethenperformedaFastFourier420

3 We did not expect that brain responses to deviant odd digits within a sequence of standard

even digits would be different than brain responses to deviant even digits within a sequence of

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AUTOMATICITY OF MAGNITUDE AND PARITY

Transformation(FFT),andweextractedamplitudespectraforthe128channelswitha421

frequencyresolution(thesizeofthefrequencybins)of0.016Hz.Giventhetopography422

ofourresults(seeFigure2a),wemergedsomeelectrodesintotworegionsofinterest:423

wesubsequentlycomputedleft(A9,A10,A11)andright(B6,B7,B8)occipitoparietal424

areasofinterest.425

Basedonthefrequencyspectra,wecomputedtwomeasurestodeterminewhetherand426

howthebrainspecificallyrespondedtothedeviantfrequencyduringthethree427

manipulatedconditions:wefirstcomputedtheSignal-to-NoiseRatios(SNRs)by428

dividingeachfrequencybinbythemeanamplitudeoftheirrespectivetwenty429

surroundingbins(excludingtheimmediatelyadjacentbins,andthetwomostextreme430

values[73,77,88:90]).WeusedSNRstodepictthefrequencyspectraandillustratethe431

topographiesofourresults(seeFigure2).432

WealsocomputedaZ-scoretoassessthestatisticalsignificanceofthebrainresponses433

tothecategorychange.Todoso,foreachconditionandforeachparticipant,we434

croppedtheFFTspectraaroundthefrequencyofinterest(1.25Hz)anditssubsequent435

harmonicsuptotheseventh(i.e.,1.25,2.5,3.75,5,6.25,7.5,and8.75Hz)surroundedby436

theirtwentyrespectiveneighbouringbins(tenoneachside[77]).Wesummedall437

croppedspectraandthenappliedaZ-transformationtotheamplitudes.Wefinally438

extractedfromthisZ-transformationthevalueacrossthefrequencybinsofinterest.439

Thisvaluerepresentsthebrainresponsespecifictotheexperimentalmanipulationat440

1.25Hz,whichcanbeinterpretedastheneuraldetectionofthechangeofthestimulus441

category.AsaZ-score,avaluelargerthanthethresholdof1.64(p<.05,one-tailed,442

standard odd digits in the Parity condition (and similarly for small and large numbers in the

Magnitude condition). We thus aggregated all repetitions for these conditions.

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testingsignallevel>noiselevel)indicatesasignificantresponsetoourexperimental443

manipulation. 444

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AUTOMATICITY OF MAGNITUDE AND PARITY

Ethicalconsiderations445

Allproceduresperformedinthisstudywereinaccordancewiththeethicalstandardsof446

theAPA,andwiththe1964HelsinkiDeclarationanditslateramendmentsorcom-447

parableethicalstandards.TheEthicReviewPanelfromtheUniversityofLuxembourg448

approvedthemethodologyandtheimplementationoftheexperimentbeforethestartof449

datacollection.Informedconsentwasobtainedfromallindividualparticipantsincluded450

inthestudy.451

Authors’contribution452

Allauthorscontributedtodesigningthestudy;CSandAVRdirectedtheproject;MG453

createdtheacquisitionsoftware;MGandAPcollectedthedata;APanalyzedthedata;AP454

andMGwrotethepaperwithinputfromAVRandCS.455

Acknowledgements456

TheauthorswouldliketothankAlietteLochyforheradvisesindataanalysis.457

Conflictsofinterest458

Theauthor(s)declarednopotentialconflictsofinterestwithrespecttotheresearch,459

authorship,and/orpublicationofthisarticle.460

Funding461

Thecurrentresearchwasfundedbythe“LuxembourgNationalResearchFund”(Grant462

AFRPHD-2015-1/9161107). 463

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AUTOMATICITY OF MAGNITUDE AND PARITY

FigureCaptions464

Figure1.IllustrationoftheFastPeriodicVisualStimulationparadigm.(a)Duringfour465

60secondsessions,Arabicdigitsbetween1and9(except5)wereperiodicallydisplayed466

atthebasefrequencyof10Hz.Inallconditions,digitsfromadeterminedstandard467

categorywereperiodicallydisplayedatthebasefrequency,whiledigitsfromanother468

deviantcategoryweredisplayedattheoddballfrequencyof1.25Hz.IntheMagnitude469

condition,categorieswerebasedonthemagnitudeofthedigits(smallerorlargerthan470

five).IntheParitycondition,categorieswereconstructedasafunctionoftheparityof471

theArabicdigit(oddoreven).IntheControlcondition,categorieswerearbitrary.472

Fonts,fontsizes,andpositionsarehereconstantforbetterreadability.(b)Illustration473

oftheonsetandtheoffsetofeachstimulusfollowingthesinusoidalcontrastmodulation474

froma0to100%contrast.475

Figure2.(a)Topographicalmapsoftheperiodicbrainresponsesexpressedasthe476

Signal-to-NoiseRatio(SNR)oftheaverageoftheamplitudeattheoddballfrequency477

(1.25Hzanditsharmonicsuptothe7th).(b)AmplitudesspectraexpressedasSNRfor478

thethreeconditions(magnitude,parity,andcontrol)withintheleftelectrodesof479

interest(A9,A10,A11)andwithintherightelectrodesofinterest(B6,B7,B8).480

Figure3.Meanamplitude,inZ-score,acrosstheoddballfrequencyanditsharmonics481

uptotheseventh,asafunctionoftheconditionandasafunctionoftheelectrode482

lateralisation(lefthemisphere:A9,A10,A11;righthemisphere:B6,B7,B8).Verticalbar483

depictsstandarddeviations.Thehorizontaldashedlinerepresentstheone-sided95%484

thresholdofsignificance(Z>1.64,p<.05,one-tailed). 485

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