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Journal o Economic PerspectivesVolume 25, Number 4Fall 2011Pages 3156

II magine yoursel lying on your back on a well-oiled high-tech sliding board,magine yoursel lying on your back on a well-oiled high-tech sliding board,rather like the board o an auto mechanic who disappears under the rontrather like the board o an auto mechanic who disappears under the rontend o your car. You too will disappear head frst into the narrow tunnel oend o your car. You too will disappear head frst into the narrow tunnel othe magnetic resonance imaging devicea brain scanner. Unlike a mechanicthe magnetic resonance imaging devicea brain scanner. Unlike a mechanicsliding under a car, however, you are tied with sot constraints around head andsliding under a car, however, you are tied with sot constraints around head andtorso to minimize your movement and hold your head still while areas o yourtorso to minimize your movement and hold your head still while areas o yourbrain are scanned as you play an economic game. Based upon recent neuroeco-brain are scanned as you play an economic game. Based upon recent neuroeco-nomic studies, certain parts o the brain have been ound to be more active innomic studies, certain parts o the brain have been ound to be more active insituations that involve calculation versus trust, or considerations o airness, orsituations that involve calculation versus trust, or considerations o airness, orproblems o ambiguity versus risk, or other actors (or a review, see McCabe,problems o ambiguity versus risk, or other actors (or a review, see McCabe,2008).2008). Like previous studies in behavioral economics, neuroeconomic studiesLike previous studies in behavioral economics, neuroeconomic studieshave established roles or both cognition and emotion in economic decisionhave established roles or both cognition and emotion in economic decisionmaking. But the emphasis o most work thus ar has been to discover their respec-making. But the emphasis o most work thus ar has been to discover their respec-tive spatial locations in the human brain. We begin this essay by describing sometive spatial locations in the human brain. We begin this essay by describing someexamples o this work. We will also discuss some practical concerns suggestingexamples o this work. We will also discuss some practical concerns suggestingthat the fndings o these studies, while an intuitive starting point, should bethat the fndings o these studies, while an intuitive starting point, should betreated as provisional.treated as provisional.An alternative view o the brain has ocused less on spatial locations An alternative view o the brain has ocused less on spatial locationsand more on the brains temporal dimension, using time series data romand more on the brains temporal dimension, using time series data rom

Its about Space, Its about Time,

Neuroeconomics and the Brain Sublime

Marieke van Rooij is a Ph.D. student in Psychology and Guy Van Orden is Professor ofMarieke van Rooij is a Ph.D. student in Psychology and Guy Van Orden is Proessor oPsychology and Director of the CAP Center for Cognition, Action & Perception, all at thePsychology and Director o the CAP Center or Cognition, Action & Perception, all at theUniversity of Cincinnati, Cincinnati, Ohio. The authors email addresses areUniversity o Cincinnati, Cincinnati, Ohio. The authors email addresses are [email protected]@mail.uc.edu [email protected]@uc.edu.. To access the Appendix, visit http://www.aeaweb.org/articles.php?doi=10.1257/jep.25.4.31.doi=10.1257/jep.25.4.31

Marieke van Rooij and Guy Van Orden

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32 Journal o Economic Perspectives

electroencephalography or EEG recordings. The EEG apparatus is sometimeselectroencephalography or EEG recordings. The EEG apparatus is sometimescalled a Frankensteins cap because the head o a participant is covered withcalled a Frankensteins cap because the head o a participant is covered withwires and stickers to record the electrical activity across the scalp, originating romwires and stickers to record the electrical activity across the scalp, originating romneural activity within the brain. EEG signals are less precise in terms o discov-neural activity within the brain. EEG signals are less precise in terms o discov-ering the source location o brain activity, but they accurately record the variationering the source location o brain activity, but they accurately record the variationo brain activity across time. Subsequent patterns o brain activity evolving in timeo brain activity across time. Subsequent patterns o brain activity evolving in timeare studied using methods that derive rom complexity science. These methodsare studied using methods that derive rom complexity science. These methodsdiscover the sel-organizing nature o brain activity, suggesting that the timediscover the sel-organizing nature o brain activity, suggesting that the timedimension o brain activity may deserve ar more attention as the feld o neuro-dimension o brain activity may deserve ar more attention as the feld o neuro-economics develops.economics develops.

Its About SpaceIts About SpacePerceived Unfairness in Economic GamesPerceived Unfairness in Economic GamesWe begin with an early study that used the ultimatum game to determine theWe begin with an early study that used the ultimatum game to determine thebrain areas associated with emotion and decision making (Saney, Rilling, Aronson,brain areas associated with emotion and decision making (Saney, Rilling, Aronson,Nystrom, and Cohen, 2003). The ultimatum game has two players, a Proposer and aNystrom, and Cohen, 2003). The ultimatum game has two players, a Proposer and aResponder, and an opening stake, which in this case was $10. The Proposer decidesResponder, and an opening stake, which in this case was $10. The Proposer decideshow to divide that stake, and i the Responder agrees both players receive theirhow to divide that stake, and i the Responder agrees both players receive theirshare. However, i the Responder disagrees neither player receives any money. Ashare. However, i the Responder disagrees neither player receives any money. Apurely logical Responder would accept any positive oer, because receiving anypurely logical Responder would accept any positive oer, because receiving anyamount o money is better than receiving nothing. Yet ordinary people oten rejectamount o money is better than receiving nothing. Yet ordinary people oten rejectoers perceived as unair (or example, see Thaler, 1988 in this journal; Henrichoers perceived as unair (or example, see Thaler, 1988 in this journal; Henrichet al., 2001; Saney, Rilling, Aronson, Nystrom, and Cohen, 2003, and the reer-et al., 2001; Saney, Rilling, Aronson, Nystrom, and Cohen, 2003, and the reer-ences therein). For instance, splits o $2 or less are rejected about 50 percent oences therein). For instance, splits o $2 or less are rejected about 50 percent othe time.the time.The purpose o scanning the brain while people play this game is to obtainThe purpose o scanning the brain while people play this game is to obtainmore insight into why the ultimatum decisions deviate rom the pure logic o sel-more insight into why the ultimatum decisions deviate rom the pure logic o sel-interest. In this experiment, all the participants play the Responder role and theyinterest. In this experiment, all the participants play the Responder role and theyplay 30 times: ten times with the Proposer identifed as a human partner (partici-play 30 times: ten times with the Proposer identifed as a human partner (partici-pants were introduced to ten Proposers beore the game began), ten times withpants were introduced to ten Proposers beore the game began), ten times withthe Proposer identifed as a computer, and ten times in a ree-money conditionthe Proposer identifed as a computer, and ten times in a ree-money conditionin which people receive money (in amounts ranging up to $10) just or pressingin which people receive money (in amounts ranging up to $10) just or pressinga button. The purpose o the ree-money condition is to control or a reaction toa button. The purpose o the ree-money condition is to control or a reaction tothe monetary reinorcement by itsel, and in actuality, all the Proposer interactionsthe monetary reinorcement by itsel, and in actuality, all the Proposer interactionswere determined by the computer, not by the people met beorehand, so that all thewere determined by the computer, not by the people met beorehand, so that all theResponders aced the same range o oers.Responders aced the same range o oers.Once the scans are taken, the brain images o the players are sorted into theOnce the scans are taken, the brain images o the players are sorted into theree-money, computer, and human Proposer conditions and in each conditionree-money, computer, and human Proposer conditions and in each conditionsorted between air oers, in which the $10 was split evenly, and unair oers,sorted between air oers, in which the $10 was split evenly, and unair oers,in which it was split unevenly. These six piles o images are then collapsed intoin which it was split unevenly. These six piles o images are then collapsed intosix average composites, and the six average composites are in turn morphedsix average composites, and the six average composites are in turn morphedinto a common brain ormat, a standardized brain made by adjusting away theinto a common brain ormat, a standardized brain made by adjusting away the

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Marieke van Rooij and Guy Van Orden 33

idiosyncrasies o each Responders brain size and shape, changing each part oidiosyncrasies o each Responders brain size and shape, changing each part othe Responders brain image to the standard size, and then placing each in thethe Responders brain image to the standard size, and then placing each in thestandard location.standard location.The corrections o the imaging data are meant to put all brains on an equalThe corrections o the imaging data are meant to put all brains on an equalooting. Yet all imagers worth their salt know that these corrections are also distor-ooting. Yet all imagers worth their salt know that these corrections are also distor-tions, and moreover are based on an assumption that the contributions o thetions, and moreover are based on an assumption that the contributions o theindividual parts o the brain are truly distinct such that they add up straightor-individual parts o the brain are truly distinct such that they add up straightor-wardly to the total contribution o the whole brainthe brain can be no more thanwardly to the total contribution o the whole brainthe brain can be no more thanthe sum o its parts.the sum o its parts.The standardized composites o air and unair oers are then contrasted in theThe standardized composites o air and unair oers are then contrasted in theree-money, computer, and human Proposer conditions. In each o these contrasts,ree-money, computer, and human Proposer conditions. In each o these contrasts,the air-oer composite is literally subtracted, point-by-point, rom the unair-oerthe air-oer composite is literally subtracted, point-by-point, rom the unair-oercomposite, yielding an image o dierences. The working assumption here is thatcomposite, yielding an image o dierences. The working assumption here is thatthe most extreme positive dierences mark the parts o the brain that had workedthe most extreme positive dierences mark the parts o the brain that had workedthe hardest during the unair oers.the hardest during the unair oers.The subtraction is made possible because the images are composed o voxels,The subtraction is made possible because the images are composed o voxels,which are not unlike the pixels on your computer screen or television. Voxels which are not unlike the pixels on your computer screen or television. Voxelshave numerical values that estimate a ratio o oxyhemoglobin (HbOhave numerical values that estimate a ratio o oxyhemoglobin (HbO22) to deoxy-) to deoxy-hemoglobin, a ratio which increases as glucose is released rom the blood to anhemoglobin, a ratio which increases as glucose is released rom the blood to anactive region o the brain. This ratio is called the BOLD signal, which estimatesactive region o the brain. This ratio is called the BOLD signal, which estimatesthe glucose sustenance required by an active region ater its hard work. The localthe glucose sustenance required by an active region ater its hard work. The localnumerical values o voxels also lend themselves to the mathematical operations thatnumerical values o voxels also lend themselves to the mathematical operations thatwere necessary to generate the standardized images in the frst place.were necessary to generate the standardized images in the frst place.In this example, the subtraction yielded the largest dierences in threeIn this example, the subtraction yielded the largest dierences in threespecifc regions o the brain: the bilateral anterior insula, dorsolateral prerontalspecifc regions o the brain: the bilateral anterior insula, dorsolateral prerontalcortex, and anterior cingulate cortex. Although raw voxel values o brain activitycortex, and anterior cingulate cortex. Although raw voxel values o brain activityshow all o the brain working all o the time, these three areas worked slightlyshow all o the brain working all o the time, these three areas worked slightlyharderalbeit less than 5 percent harder (Raichle, 2010; Sokolo, Mangold,harderalbeit less than 5 percent harder (Raichle, 2010; Sokolo, Mangold,Wechsler, Kenney, and Kety, 1955)when judging unair oers compared to airWechsler, Kenney, and Kety, 1955)when judging unair oers compared to airoers, establishing an association between these three areas o the brain and theoers, establishing an association between these three areas o the brain and theemotions that bias our judgments o unair oers. (Brain images highlightingemotions that bias our judgments o unair oers. (Brain images highlightingthe location o these parts o the brain, along with a list o other unctions thatthe location o these parts o the brain, along with a list o other unctions thatthese parts o the brain may hold, are available with this paper in the Appendixthese parts o the brain may hold, are available with this paper in the AppendixFigure 1 atFigure 1 athttp://e-jep.orghttp://e-jep.org.).)By comparison, the brain regions highlighted during judgments o computerBy comparison, the brain regions highlighted during judgments o computersplits, or when taking ree money in the control condition, were not the samesplits, or when taking ree money in the control condition, were not the sameareas as those highlighted by the human oers, establishing a dissociation oareas as those highlighted by the human oers, establishing a dissociation obrain areas associated with human oers rom those associated with other oers.brain areas associated with human oers rom those associated with other oers.Also, the magnitude o the dierence between voxel values rom a $9/$1 splitAlso, the magnitude o the dierence between voxel values rom a $9/$1 splitwas greater than the magnitude o dierence rom an $8/$2 split in the bilateralwas greater than the magnitude o dierence rom an $8/$2 split in the bilateralanterior insula, a correlation with the degree o unairness in unair oers.anterior insula, a correlation with the degree o unairness in unair oers.

Saney, Rilling, Aronson, Nystrom, and Cohen (2003) concluded that theSaney, Rilling, Aronson, Nystrom, and Cohen (2003) concluded that theanterior insula represents the negative emotions o someone who is conrontedanterior insula represents the negative emotions o someone who is conrontedwith an unair oera conclusion consistent with previous associations betweenwith an unair oera conclusion consistent with previous associations between

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the anterior insula and instances o pain, distress, hunger, thirst, autonomic arousal,the anterior insula and instances o pain, distress, hunger, thirst, autonomic arousal,and negative emotions generally (Calder, Lawrence, and Young, 2001). The dorso-and negative emotions generally (Calder, Lawrence, and Young, 2001). The dorso-lateral prerontal cortex, on the other hand, represents cognitive processes duringlateral prerontal cortex, on the other hand, represents cognitive processes duringhuman oers, working harder here in unair oers than in air oers, which ishuman oers, working harder here in unair oers than in air oers, which isconsistent with previous associations o this area o the brain to goal maintenanceconsistent with previous associations o this area o the brain to goal maintenanceand executive control, cognitive processing, and memory unctions, but not withand executive control, cognitive processing, and memory unctions, but not withnegative emotions (Levy and Goldman-Rakic, 2000) or with the acceptance rates onegative emotions (Levy and Goldman-Rakic, 2000) or with the acceptance rates ounair oers. Thus, the cognitive work done in the prerontal cortex complementsunair oers. Thus, the cognitive work done in the prerontal cortex complementsthe emotive work done in the anterior insula, the region o the emotions inducedthe emotive work done in the anterior insula, the region o the emotions inducedby unair oers.by unair oers.Trust and AltruismTrust and Altruism

A trust game again begins with a Proposer and a Responder, and in this study,A trust game again begins with a Proposer and a Responder, and in this study,the original stake was $20. The Proposer divided that amount, and then the Propos-the original stake was $20. The Proposer divided that amount, and then the Propos-ers oer was tripled by the experimenter so that the tripled amount was received byers oer was tripled by the experimenter so that the tripled amount was received bythe Responder. Next, the Responder could return some amount to the Proposer. Athe Responder. Next, the Responder could return some amount to the Proposer. Apurely rational Proposer would expect that the Responder would send nothing back;purely rational Proposer would expect that the Responder would send nothing back;thereore, the Proposer would send nothing to the Responder. However, a trustingthereore, the Proposer would send nothing to the Responder. However, a trustingProposer would give some amount to a Responder, and a Responder reacting to thatProposer would give some amount to a Responder, and a Responder reacting to thatimplicit trust with altruism would send something back.implicit trust with altruism would send something back.In a study by King-Casas, Tomlin, Anen, Camerer, Quartz, and MontagueIn a study by King-Casas, Tomlin, Anen, Camerer, Quartz, and Montague(2005), each participant played ten consecutive trust games with the same oppo-(2005), each participant played ten consecutive trust games with the same oppo-nent in the same roles in all ten games. Consequently, i a Responder ailed tonent in the same roles in all ten games. Consequently, i a Responder ailed toreciprocate with a air share o the tripled amount, the Proposer could make areciprocate with a air share o the tripled amount, the Proposer could make astingy initial oer on the next round. Thus, there would presumably be carryoverstingy initial oer on the next round. Thus, there would presumably be carryoverrom each round o the game to the next. Both Proposers and Responders wererom each round o the game to the next. Both Proposers and Responders werescanned simultaneously while playing the multi-round game, one making the initialscanned simultaneously while playing the multi-round game, one making the initialoers and the other deciding the ultimate outcome o each round. The ocus o theoers and the other deciding the ultimate outcome o each round. The ocus o thestudy was on the place and time in the brain during the course o decision makingstudy was on the place and time in the brain during the course o decision makingwherein a person ormulated an intention to trust (p. 80), which determined thatwherein a person ormulated an intention to trust (p. 80), which determined thata generous oer was made.a generous oer was made.Each trials initial oer rom the Proposer was frst characterized in one o threeEach trials initial oer rom the Proposer was frst characterized in one o threeways: generous, which was defned as a larger proportion oered despite a lowerways: generous, which was defned as a larger proportion oered despite a lowerproportion repaid in the previous round (compared to two rounds ago); ungen-proportion repaid in the previous round (compared to two rounds ago); ungen-erous, defned as a smaller proportion oered despite a higher proportion repaiderous, defned as a smaller proportion oered despite a higher proportion repaidin the previous round (compared to two rounds ago); or neutral, which meant thein the previous round (compared to two rounds ago); or neutral, which meant thesame proportion oered as in the previous round. Then the pooled brain images osame proportion oered as in the previous round. Then the pooled brain images oRespondents were compared in a number o dierent ways, including contrastingRespondents were compared in a number o dierent ways, including contrastingResponders who received unexpectedly generous oers with those who receivedResponders who received unexpectedly generous oers with those who receivedunexpectedly ungenerous oers and contrasting immediate brain reactions withunexpectedly ungenerous oers and contrasting immediate brain reactions withthose that happened a ew seconds later.those that happened a ew seconds later.

Four brain regions in the Responders were associated with either generousFour brain regions in the Responders were associated with either generoustreatment or ungenerous treatment (that is, an oer rom the Proposer that wastreatment or ungenerous treatment (that is, an oer rom the Proposer that wasbetter or worse than what would have been expected based on earlier oers): ineriorbetter or worse than what would have been expected based on earlier oers): inerior

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Its about Space, Its about Time, Neuroeconomics and the Brain Sublime 35

rontal sulcus, superior rontal sulcus, thalamus, and inerior/superior colliculli.rontal sulcus, superior rontal sulcus, thalamus, and inerior/superior colliculli.The caudate nucleus (hereater the caudate) was the region that worked hardestThe caudate nucleus (hereater the caudate) was the region that worked hardestollowing generous oers. Also, the magnitude o dierences in voxel values in theollowing generous oers. Also, the magnitude o dierences in voxel values in thecaudate o the Responder produced a larger net change six to ten seconds atercaudate o the Responder produced a larger net change six to ten seconds aterthe Responder received a generous oer, and the magnitude o dierences in thethe Responder received a generous oer, and the magnitude o dierences in thecaudate o the Responder were correlated with that o the Responders anterior-caudate o the Responder were correlated with that o the Responders anterior-cingulate cortex. (Images o brain scans highlighting these particular parts o thecingulate cortex. (Images o brain scans highlighting these particular parts o thebrain, along with a list o other unctions identifed or these parts o the brain, arebrain, along with a list o other unctions identifed or these parts o the brain, arein Appendix Figure 2 available online atin Appendix Figure 2 available online athttp://e-jep.orghttp://e-jep.org.).)Another set o analyses looked at correlations in brain activity o both partici-Another set o analyses looked at correlations in brain activity o both partici-pants and how these correlations changed over time. For example, the magnitudepants and how these correlations changed over time. For example, the magnitudeo dierences in the Responders caudate voxel values were correlated with theo dierences in the Responders caudate voxel values were correlated with thevalues o the Proposers middle-cingular cortex preceding the more generous values o the Proposers middle-cingular cortex preceding the more generousoers by the Proposer. And the magnitude o change in the Proposers middle-oers by the Proposer. And the magnitude o change in the Proposers middle-cingulate cortex region was correlated with the magnitude o change in thecingulate cortex region was correlated with the magnitude o change in theanterior-cingulate cortex o the Responder.anterior-cingulate cortex o the Responder.The maximum or peak correlation between the two brains middle-cingulateThe maximum or peak correlation between the two brains middle-cingulatecortex versus anterior-cingulate cortex trailed the appearance o the initial oercortex versus anterior-cingulate cortex trailed the appearance o the initial oerby about 14 seconds, and the location in time o this peak did not change muchby about 14 seconds, and the location in time o this peak did not change muchrom the frst ew games to the last ew games played. However, the peak correlationrom the frst ew games to the last ew games played. However, the peak correlationbetween the Proposers middle-cingulate cortex with the caudate nucleus o thebetween the Proposers middle-cingulate cortex with the caudate nucleus o theResponder did change over the multiple rounds o the game. Initially, this peakResponder did change over the multiple rounds o the game. Initially, this peakcorrelation between the brain o the Proposer and the brain o the Respondercorrelation between the brain o the Proposer and the brain o the Responderollowed the initial oer by about 18 seconds, but by the fnal rounds o the game itollowed the initial oer by about 18 seconds, but by the fnal rounds o the game ittrailed the initial oer by only 4 seconds.trailed the initial oer by only 4 seconds.A second peak correlation also changed its location in time. The peak corre-A second peak correlation also changed its location in time. The peak corre-lation between the Responders anterior-cingulate cortex and the Responderslation between the Responders anterior-cingulate cortex and the Responderscaudate occurred about 7 seconds ater seeing the initial oer in the frst ewcaudate occurred about 7 seconds ater seeing the initial oer in the frst ewgames. However, by the seventh and eighth rounds o the game, the peak correla-games. However, by the seventh and eighth rounds o the game, the peak correla-tiontion precededthe revealed initial oer by about 9 seconds, which suggests that thethe revealed initial oer by about 9 seconds, which suggests that thedecision to repay an oer generously was made beore the oer was known, at aboutdecision to repay an oer generously was made beore the oer was known, at aboutthe same time that the Proposer appeared to ormulate the initial oer.the same time that the Proposer appeared to ormulate the initial oer.

Plainly, when we look at any one study by itsel, it seems as i a picture oPlainly, when we look at any one study by itsel, it seems as i a picture othe interactions within brains and between brains is beginning to emerge. Andthe interactions within brains and between brains is beginning to emerge. Andyet a number o serious problems remain. For example, i we take the results yet a number o serious problems remain. For example, i we take the resultsconcerning airness and generosity rom the trust game, together with the previousconcerning airness and generosity rom the trust game, together with the previousresults concerning unairness and punishment rom the ultimatum game, it wouldresults concerning unairness and punishment rom the ultimatum game, it wouldappear that responses to airness and unairness are ormulated in dierent partsappear that responses to airness and unairness are ormulated in dierent partso the brain. The anterior insula ormulate the response to unair oers, whereaso the brain. The anterior insula ormulate the response to unair oers, whereasthe response to air oers as an intention to trust is ormulated in the head othe response to air oers as an intention to trust is ormulated in the head othe caudate nucleus. With experience, the intention to trust comes to precedethe caudate nucleus. With experience, the intention to trust comes to precedethe oer, as though a generous response is based on play across earlier games.the oer, as though a generous response is based on play across earlier games.However, i the intention to trust is ormulated in a dierent part o the brain thanHowever, i the intention to trust is ormulated in a dierent part o the brain thanthe response to unairness, it must ollow that some other region or regions in thethe response to unairness, it must ollow that some other region or regions in the

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brain must play the role o dispatcher, to send the correct emotional signals to thebrain must play the role o dispatcher, to send the correct emotional signals to theregion making the brains response. Yet we remain ignorant o how this happens.region making the brains response. Yet we remain ignorant o how this happens.These are some o the kinds o difculties that arise when making comparisonsThese are some o the kinds o difculties that arise when making comparisonsacross studies in neuroeconomics. For example, study conclusions disagree aboutacross studies in neuroeconomics. For example, study conclusions disagree aboutwhich regions o the brain should be counted toward understanding an opponentswhich regions o the brain should be counted toward understanding an opponentsmental states, like a judgment o unairness or an intention to trust. This may bemental states, like a judgment o unairness or an intention to trust. This may bebecause the studies are constructed in dierent ways: such as in their choice o abecause the studies are constructed in dierent ways: such as in their choice o aneutral condition, or choices among linear analyses, or the precise time intuited atneutral condition, or choices among linear analyses, or the precise time intuited atwhich belies exist about an opponents state o mind (or example, Saney, Rilling,which belies exist about an opponents state o mind (or example, Saney, Rilling,Aronson, Nystrom, and Cohen, 2003; King-Casas, Tomlin, Anen, Camerer, Quartz,Aronson, Nystrom, and Cohen, 2003; King-Casas, Tomlin, Anen, Camerer, Quartz,and Montague, 2005; McCabe, Houser, Ryan, Smith, and Trouard, 2001; Tomlin etand Montague, 2005; McCabe, Houser, Ryan, Smith, and Trouard, 2001; Tomlin etal., 2006).al., 2006).Indeed, McCabe, Houser, Ryan, Smith, and Trouard (2001) argue that the basisIndeed, McCabe, Houser, Ryan, Smith, and Trouard (2001) argue that the basisor cooperative behavior appears to be a network o regions that span the wholeor cooperative behavior appears to be a network o regions that span the wholebrain, including sensory and motor regions and both hemispheresnamely rontalbrain, including sensory and motor regions and both hemispheresnamely rontalcortex (middle rontal gyrus, rontal pole), the occipital lobe, the parietal lobe,cortex (middle rontal gyrus, rontal pole), the occipital lobe, the parietal lobe,and the thalamus, but which do not overlap with regions that appeared in imagesand the thalamus, but which do not overlap with regions that appeared in imageso uncooperative participants. Tomlin et al. (2006) also ound that the middleo uncooperative participants. Tomlin et al. (2006) also ound that the middlecingulate regions were important to the Proposer, while the anterior and posteriorcingulate regions were important to the Proposer, while the anterior and posteriorcingulate regions were important to the Responder. The latter regions were notcingulate regions were important to the Responder. The latter regions were notapparently important when the game was played against a computer, only against aapparently important when the game was played against a computer, only against ahuman opponent, but neither were they apparent in the other studies that we havehuman opponent, but neither were they apparent in the other studies that we have

reviewed. Thus, a variety o contradictory results have emerged that remain to bereviewed. Thus, a variety o contradictory results have emerged that remain to besorted out in urther studies. (To view the brain scans showing areas o the brainsorted out in urther studies. (To view the brain scans showing areas o the braincommonly associated with trust and altruism, as well as a list o other brain unctionscommonly associated with trust and altruism, as well as a list o other brain unctionsassociated with these areas, see the Appendix Figure 3 online with this paper atassociated with these areas, see the Appendix Figure 3 online with this paper athttp://e-jep.orghttp://e-jep.org.).)Ambiguity and RiskAmbiguity and RiskThe examples to this point have all had elements o ambiguity and risk, butThe examples to this point have all had elements o ambiguity and risk, butin the context o social situations. What about ambiguity and risk by themselves?in the context o social situations. What about ambiguity and risk by themselves?Medical students at the University o Minnesota were given an initial sum o $190 toMedical students at the University o Minnesota were given an initial sum o $190 tohold in their let hand while they were slid into a doughnut-shaped brain scanner,hold in their let hand while they were slid into a doughnut-shaped brain scanner,this time a positron emission tomography or PET scanner. Inside the scanner theythis time a positron emission tomography or PET scanner. Inside the scanner theywere presented with choices between dierent gambles tailored to vary risk or ambi-were presented with choices between dierent gambles tailored to vary risk or ambi-guity (Smith, Dickhaut, McCabe, and Pardo, 2002).guity (Smith, Dickhaut, McCabe, and Pardo, 2002).Each choice was between two gambles illustrated by dierent numbers o red,Each choice was between two gambles illustrated by dierent numbers o red,yellow, and blue marbles. A marbles color indicated its payo, and the respective yellow, and blue marbles. A marbles color indicated its payo, and the respectivenumber o marbles o each color represented the probability o each payo. Thus,number o marbles o each color represented the probability o each payo. Thus,in an urn containing 30 red, 30 blue, and 30 yellow marbles, each marble o eachin an urn containing 30 red, 30 blue, and 30 yellow marbles, each marble o eachcolor would be equally likely to be chosen. Furthermore, i a red marble pays ocolor would be equally likely to be chosen. Furthermore, i a red marble pays o$50, blue $6, and yellow $4, the expected payo would be (30$50, blue $6, and yellow $4, the expected payo would be (30 $50)$50) ++ (30(30 $6)$6) ++(30(30 $4)/(30$4)/(30 ++ 3030 ++ 30)30) == $20, an expected gain o $20 on average. On loss trials,$20, an expected gain o $20 on average. On loss trials,the same payos would appear with signs reversed rom positive to negative.the same payos would appear with signs reversed rom positive to negative.

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Each gamble was constructed to orce a choice based on either relative risk orEach gamble was constructed to orce a choice based on either relative risk orrelative ambiguitywith equal numbers o gains and losses in both the risk and therelative ambiguitywith equal numbers o gains and losses in both the risk and theambiguity conditions. Risk was varied using the range o payo values. The expectedambiguity conditions. Risk was varied using the range o payo values. The expectedpayo o 30 red marbles each paying $30, 30 blue marbles paying $30, and 30 yellowpayo o 30 red marbles each paying $30, 30 blue marbles paying $30, and 30 yellowmarbles paying $0 is $20, the same expected value as in the previous example, butmarbles paying $0 is $20, the same expected value as in the previous example, butthe range o the payos across the marbles o $0$30 is smaller than in the previousthe range o the payos across the marbles o $0$30 is smaller than in the previousexample o $4$50, and a smaller range is perceived as a less-risky choice (Smith etexample o $4$50, and a smaller range is perceived as a less-risky choice (Smith etal., 2002).al., 2002).Ambiguity was created by providing the exact number o marbles in oneAmbiguity was created by providing the exact number o marbles in onecolor while giving only the sum total o marbles in the other two colors.color while giving only the sum total o marbles in the other two colors.Ater exiting the scanner, each medical school participant realized two actualAter exiting the scanner, each medical school participant realized two actualgambles. One o the two gambles was or a gain and the other was or a loss, andgambles. One o the two gambles was or a gain and the other was or a loss, andboth were drawn rom among the gambles enacted when in the scanner. The sum oboth were drawn rom among the gambles enacted when in the scanner. The sum othe gain outcome and the loss outcome, plus the $190 given at the outset, equaledthe gain outcome and the loss outcome, plus the $190 given at the outset, equaledthe amount o money pocketed by the student (Smith et al., 2002).the amount o money pocketed by the student (Smith et al., 2002).Medical students typically chose the less-risky gamble when choosing betweenMedical students typically chose the less-risky gamble when choosing betweentwo gains, and the more-risky gamble when choosing between two losses. Studentstwo gains, and the more-risky gamble when choosing between two losses. Studentstrended toward choosing ambiguous gambles when choosing between two gains,trended toward choosing ambiguous gambles when choosing between two gains,but showed no preerence or ambiguity when choosing between two losses. Overall,but showed no preerence or ambiguity when choosing between two losses. Overall,the pattern showed larger dierences due to risk by comparison to ambiguity, andthe pattern showed larger dierences due to risk by comparison to ambiguity, andopposite eects o risk or gains versus losses (Smith et al., 2002).opposite eects o risk or gains versus losses (Smith et al., 2002).The imaging contrasts also indicated an interaction eect: the dierence inThe imaging contrasts also indicated an interaction eect: the dierence inimages changed between ambiguity versus risk depending on whether the payoimages changed between ambiguity versus risk depending on whether the payostructure was a gain or a loss. In a frst contrast, the aggregate standardized imagesstructure was a gain or a loss. In a frst contrast, the aggregate standardized imageso trials presenting risky losses were subtracted rom images o risky gains, and theo trials presenting risky losses were subtracted rom images o risky gains, and theaggregate images o trials presenting ambiguous losses were subtracted rom ambig-aggregate images o trials presenting ambiguous losses were subtracted rom ambig-uous gains. In a second contrast, these images o dierences (the two outcomes ouous gains. In a second contrast, these images o dierences (the two outcomes othe previous contrasts) were subtracted rom each other. This second subtractionthe previous contrasts) were subtracted rom each other. This second subtractiono risk minus ambiguity highlighted ventromedial siteso risk minus ambiguity highlighted ventromedial sites11sites in bottom middlesites in bottom middlecortexworking harder in the risky judgments o gains.cortexworking harder in the risky judgments o gains.Starting again with the same images, the scientists then reversed the previousStarting again with the same images, the scientists then reversed the previoussubtractions. They subtracted the images o trials presenting risky gains rom thosesubtractions. They subtracted the images o trials presenting risky gains rom thosepresenting risky losses, and trials presenting ambiguous gains rom those presentingpresenting risky losses, and trials presenting ambiguous gains rom those presentingambiguous losses. Ater that they subtracted again the images o dierences, butambiguous losses. Ater that they subtracted again the images o dierences, butthis time the subtraction was ambiguity minus risk. Thus, instead o gain minus loss,this time the subtraction was ambiguity minus risk. Thus, instead o gain minus loss,loss minus gainand instead o risk minus ambiguity, ambiguity minus risksuchloss minus gainand instead o risk minus ambiguity, ambiguity minus risksuchthat the voxel values highlighted as positive in this latter contrast would have beenthat the voxel values highlighted as positive in this latter contrast would have beenthe extreme negative voxel values in the previous contrast. The results o this lastthe extreme negative voxel values in the previous contrast. The results o this lastcontrast discovered a larger presence o dorsomedial sitescontrast discovered a larger presence o dorsomedial sites22 (top middle cortex)(top middle cortex)1 Using the notational scheme o Brodmann Areas (in parentheses), the discovered areas o the ventro-medial network included the regions orbitorontal cortex (13b), gyrus rectus (14c), medial orbitorontal(1m, r), intraparietal sulcus (7), brainstem, pons, rontal pole (10p), interior rontal gyrus (47/12m, l),

entorhinal cortex (28), and parietal lobe (7/40).2 The brain regions and Brodmann Areas o the dorsomedial network included the regions cerebellum

VIIB, middle temporal gyrus (21), superior rontal gyrus (6), paracentral lobule (5), pre-SMA (6),

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working harder in the risky judgments o losses, completing the parallel with theworking harder in the risky judgments o losses, completing the parallel with thebehavioral interaction eect (Smith et al., 2002).behavioral interaction eect (Smith et al., 2002).On the basis o these fndings, Smith, Dickhaut, McCabe, and Pardo (2002,On the basis o these fndings, Smith, Dickhaut, McCabe, and Pardo (2002,p. 717) concluded they had discovered two distinct and complementary choicep. 717) concluded they had discovered two distinct and complementary choicesystems, a dorsomedial network associated with loss processing when evaluatingsystems, a dorsomedial network associated with loss processing when evaluatingrisky gambles and a more primitive ventromedial system related to processingrisky gambles and a more primitive ventromedial system related to processingo other stimuli. A ew years later, a dierent study o risk and ambiguity oundo other stimuli. A ew years later, a dierent study o risk and ambiguity oundcontradictory results, examining specifc areas o the brain predicted rom previouscontradictory results, examining specifc areas o the brain predicted rom previousstudies: the striatum (rontal middle primitive subcortical structure associated withstudies: the striatum (rontal middle primitive subcortical structure associated withreward anticipation), orbitorontal cortex (rontal lobes just behind and abovereward anticipation), orbitorontal cortex (rontal lobes just behind and abovethe eyes associated with uncertainty), and the amygdala (site in middle outsidethe eyes associated with uncertainty), and the amygdala (site in middle outsidetemporal cortex associated with ambiguous acial cues and vigilance) (Hsu, Bhatt,temporal cortex associated with ambiguous acial cues and vigilance) (Hsu, Bhatt,and Adolphs, 2005). (Brain images highlighting these parts o the brain, along withand Adolphs, 2005). (Brain images highlighting these parts o the brain, along withother unctions that have been associated with these parts o the brain, are availableother unctions that have been associated with these parts o the brain, are availableonline in the Appendix Figure 4 together with this paper atonline in the Appendix Figure 4 together with this paper at http://e-jep.orghttp://e-jep.org.).)The Hsu, Bhatt, Adolphs (2005) study used two tasks based on a gamble meta-The Hsu, Bhatt, Adolphs (2005) study used two tasks based on a gamble meta-phor o drawing cards rom a deck, rather than marbles rom an urn, and a thirdphor o drawing cards rom a deck, rather than marbles rom an urn, and a thirdtask that varied risk and ambiguity in knowledge judgments. Ambiguity imagestask that varied risk and ambiguity in knowledge judgments. Ambiguity imageswere subtracted rom risk images, and then risk rom ambiguity. Regions workingwere subtracted rom risk images, and then risk rom ambiguity. Regions workingharder due to ambiguity included the orbitorontal cortex and the amygdala, andharder due to ambiguity included the orbitorontal cortex and the amygdala, andthe dorsomedial prerontal cortex. Regions working harder due to risk includedthe dorsomedial prerontal cortex. Regions working harder due to risk includedthe dorsal (top) striatum (caudate nucleus), and the work demands o the dorsalthe dorsal (top) striatum (caudate nucleus), and the work demands o the dorsalstriatum were ound to be correlated with the average payo o the gambles chosen,striatum were ound to be correlated with the average payo o the gambles chosen,which was not the case or the orbitorontal cortex or the amygdala.which was not the case or the orbitorontal cortex or the amygdala.A point o convergence o Smith et al. (2002) and Hsu et al. (2005) is thatA point o convergence o Smith et al. (2002) and Hsu et al. (2005) is thatboth discovered a harder-working orbitorontal cortex, and both sets o authorsboth discovered a harder-working orbitorontal cortex, and both sets o authorssee this region as a part o a larger unctional network. While the unction o thissee this region as a part o a larger unctional network. While the unction o thisventromedial network was only vaguely stated in Smith et al.s hypothesis, Hsu et al.ventromedial network was only vaguely stated in Smith et al.s hypothesis, Hsu et al.were more precise, proposing a network spanning two interacting systems, a systemwere more precise, proposing a network spanning two interacting systems, a systemor vigilance and evaluation o uncertainty (the amygdala and the orbitorontalor vigilance and evaluation o uncertainty (the amygdala and the orbitorontalcortex) and a second system downstream in the striatum that anticipates rewards.cortex) and a second system downstream in the striatum that anticipates rewards.A point o divergence was that the vigilanceevaluation plus rewardanticipationA point o divergence was that the vigilanceevaluation plus rewardanticipationsystems were discovered in the condition that emphasized ambiguity, whereas thesystems were discovered in the condition that emphasized ambiguity, whereas theless-precisely described system o Smith, Dickhaut, McCabe, and Pardo (2002) wasless-precisely described system o Smith, Dickhaut, McCabe, and Pardo (2002) wasdiscovered in the condition that emphasized risk. Hsu, Bhatt, and Adolphs (2005)discovered in the condition that emphasized risk. Hsu, Bhatt, and Adolphs (2005)ailed to corroborate the harder-working orbitorontal location in their contrastailed to corroborate the harder-working orbitorontal location in their contrastthat emphasized risk.that emphasized risk.O course the feld o neuroeconomics is quite young, and these difcultiesO course the feld o neuroeconomics is quite young, and these difcultieshave been acknowledged. Possibly, as the neuroimaging technology improves andhave been acknowledged. Possibly, as the neuroimaging technology improves andas the literature builds, studies will be sufciently cross-reerenced to convergeas the literature builds, studies will be sufciently cross-reerenced to convergeupon a map o the brain with reliable locations or each type o emotional or logicalupon a map o the brain with reliable locations or each type o emotional or logicalcerebellar vermis VI, precuneus (7), inerior parietal lobe (39/40), precuneus (7/31), and cerebellumcrus I.

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decision (Roskies, 2010).decision (Roskies, 2010).33 Certainly some association must exist between the brainCertainly some association must exist between the brainand decision making! However, a skeptical view holds that it has not been the lackand decision making! However, a skeptical view holds that it has not been the lacko exotic imaging technology that has delayed the development o lasting insightso exotic imaging technology that has delayed the development o lasting insightsabout brain unction, cognition, and behavior. Rather, it has been a wrongheadedabout brain unction, cognition, and behavior. Rather, it has been a wrongheadedlogic that seeks to equate spatial locations in the brain with the causes o behaviorlogic that seeks to equate spatial locations in the brain with the causes o behavioror mental unctions (Uttal, 2001).or mental unctions (Uttal, 2001).James and the Psychologists FallacyJames and the Psychologists FallacyThe pioneering psychologist William James (1890) coined the termThe pioneering psychologist William James (1890) coined the termpsychologists allacy: the tendency to make attributions to others based on ourpsychologists allacy: the tendency to make attributions to others based on ourfrst-person experience o cognition and behavior. In one version o this allacy,frst-person experience o cognition and behavior. In one version o this allacy,the frst-person experiences o reasoning or emoting, or example, become third-the frst-person experiences o reasoning or emoting, or example, become third-person categories or components o cognition and behavior (Ashworth, 2009).person categories or components o cognition and behavior (Ashworth, 2009).We reason, so there must be a seat o reason, and we emote, so there must be a seatWe reason, so there must be a seat o reason, and we emote, so there must be a seato emotion. In cognitive neuroscience, we may take the allacy one step urthero emotion. In cognitive neuroscience, we may take the allacy one step urtherin placing the seats o reason or emotion in the brain. We emote, thereore wein placing the seats o reason or emotion in the brain. We emote, thereore wecan isolate the cause o emotion in the brain, and so on.can isolate the cause o emotion in the brain, and so on. The psychologistsThe psychologistsallacy seems to be built on logic o cause and eect. However, the conictingallacy seems to be built on logic o cause and eect. However, the conictingoutcomes discussed here illustrate a general state o aairs across many studiesoutcomes discussed here illustrate a general state o aairs across many studiesusing unctional neuroimaging. Many o the studies that seek to trace particularusing unctional neuroimaging. Many o the studies that seek to trace particularkinds o decisions to particular areas o the brain have reached contradictory orkinds o decisions to particular areas o the brain have reached contradictory orinconsistent conclusions.inconsistent conclusions.

Early on, the scientists using subtractive brain imaging discovered that theirEarly on, the scientists using subtractive brain imaging discovered that theirresults were not usually replicable, at least in the strict sense o producing over-results were not usually replicable, at least in the strict sense o producing over-lapping active voxels in overlapping brain regions or the same brain unctionlapping active voxels in overlapping brain regions or the same brain unction(Jennings, McIntosh, Kapur, Tulving, and Houle, 1997; Poeppel, 1996; Van Orden(Jennings, McIntosh, Kapur, Tulving, and Houle, 1997; Poeppel, 1996; Van Ordenand Paap, 1997). These ailures to replicate led scientists to relax the standards oand Paap, 1997). These ailures to replicate led scientists to relax the standards oevidence or what counts as a replication. For example, in some studies two brainevidence or what counts as a replication. For example, in some studies two brainimages that contain at least one active voxel in the same brain region can be countedimages that contain at least one active voxel in the same brain region can be countedto be equivalent. The respective voxels need not overlap; they must only appearto be equivalent. The respective voxels need not overlap; they must only appearin the same region o the standardized brain (Knoch, Gianotti, Baumgartner, andin the same region o the standardized brain (Knoch, Gianotti, Baumgartner, andFehr, 2010; McCabe, Houser, Ryan, Smith, and Trouard, 2001).Fehr, 2010; McCabe, Houser, Ryan, Smith, and Trouard, 2001).The act that similar tasks or methods highlight dierent brain regions hasThe act that similar tasks or methods highlight dierent brain regions hasanother interpretation: that mental unctions must be distributed across networksanother interpretation: that mental unctions must be distributed across networkso brain regions. This network hypothesis makes (apologetic) sense o the ailureso brain regions. This network hypothesis makes (apologetic) sense o the ailuresto replicate, but it runs into other problems. The extent o a brain network canto replicate, but it runs into other problems. The extent o a brain network cangrow with each new studyat least until it flls the whole brain, which deeats thegrow with each new studyat least until it flls the whole brain, which deeats theunderlying assumption o the analysis (or example, see Anderson, 2010). Also,underlying assumption o the analysis (or example, see Anderson, 2010). Also,studies inevitably discover spurious brain regions associated with spurious idiosyn-studies inevitably discover spurious brain regions associated with spurious idiosyn-cratic task eects or strategies, present in one task contrast but no other. Coherentcratic task eects or strategies, present in one task contrast but no other. Coherent

3 A related but dierent point o view is that the dierent entailments inherent in brain processes,behavior, or conscious experience can become a basis or triangulation, yielding a reliable empirical andphenomenological convergence (Roepstor and Jack, 2004).

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criteria have not yet emerged to reliably distinguish unctional networks romcriteria have not yet emerged to reliably distinguish unctional networks romunctional anomalies.unctional anomalies.When one considers the spatial methodology, the difculty o fnding alse When one considers the spatial methodology, the difculty o fnding alsepositives seems all too realthat is, fnding regions o the brain that seem to bepositives seems all too realthat is, fnding regions o the brain that seem to beidentifed with a certain task in one study, but not in other studies. Ater all, a brainidentifed with a certain task in one study, but not in other studies. Ater all, a brainin these studies becomes an image landscape o measured voxel values, a topographyin these studies becomes an image landscape o measured voxel values, a topographyundulating up and down in local variation. With any two non-identical images, iundulating up and down in local variation. With any two non-identical images, ione is subtracted rom the other, the results will include a region o maximumone is subtracted rom the other, the results will include a region o maximumpositive dierences and a region o minimum negative dierences. In this way, anypositive dierences and a region o minimum negative dierences. In this way, anycontrast using brain images can be counted on to make discoveries (Uttal, 2001).contrast using brain images can be counted on to make discoveries (Uttal, 2001).In the most notorious example o how discovery can go astray, Bennett, Baird,In the most notorious example o how discovery can go astray, Bennett, Baird,Miller, and Wolord (2010, p. 2) presented a dead (!) salmon with a series o photo-Miller, and Wolord (2010, p. 2) presented a dead (!) salmon with a series o photo-graphs o humans in social situations, and using standard analyses o the imagesgraphs o humans in social situations, and using standard analyses o the imagesthat resulted, they discovered a hard-working region o human social perception inthat resulted, they discovered a hard-working region o human social perception inthe salmons brain. They point out that a standard MRI produces 130,000 voxels,the salmons brain. They point out that a standard MRI produces 130,000 voxels,and so, depending on how one analyzes this mass o data and the inevitability oand so, depending on how one analyzes this mass o data and the inevitability onoise in the data, the possibility o a alse positive outcome can be very high. Theynoise in the data, the possibility o a alse positive outcome can be very high. Theysuggest that standard statistical tests may ail badly in this setting. The positive fnd-suggest that standard statistical tests may ail badly in this setting. The positive fnd-ings o their study, despite the previous death o the salmon, should perhaps humbleings o their study, despite the previous death o the salmon, should perhaps humblethe conclusions drawn rom any single neuroimaging study and rein in some othe conclusions drawn rom any single neuroimaging study and rein in some othe hype that so oten accompanies a new neuroimaging result.the hype that so oten accompanies a new neuroimaging result.In eect, the spatial approach to studying the brain assumes that the brain canIn eect, the spatial approach to studying the brain assumes that the brain canbe treated as the sum o its parts. The assumption is called component-dominantbe treated as the sum o its parts. The assumption is called component-dominantdynamics, meaning interactions within the components dominate the interactionsdynamics, meaning interactions within the components dominate the interactionsamong the components (Van Orden, Holden, and Turvey, 2003). Component-among the components (Van Orden, Holden, and Turvey, 2003). Component-dominant dynamics are necessary i components are to remain causally distinct. Todominant dynamics are necessary i components are to remain causally distinct. Todo so, components must interact only locally. For example, an emotion componentdo so, components must interact only locally. For example, an emotion componentresponding to fduciary transactions could interact with a cognitive component thatresponding to fduciary transactions could interact with a cognitive component thatrationally evaluates transactions without having the guts o either response changedrationally evaluates transactions without having the guts o either response changedin the process. The component-dominant dynamics assumption encapsulatesin the process. The component-dominant dynamics assumption encapsulateslocal eects o components such that they can be recovered in linear analyses olocal eects o components such that they can be recovered in linear analyses othe measurements o the brain. This approach underlies what is oten called thethe measurements o the brain. This approach underlies what is oten called theGeneral Linear Model o the brain.General Linear Model o the brain.One reason to assume component-dominant dynamics is to justiy theOne reason to assume component-dominant dynamics is to justiy thesubtraction o one image o the brain rom another, or to justiy more complicatedsubtraction o one image o the brain rom another, or to justiy more complicatedactorial analyses o brain or behavior (Van Orden, Pennington, and Stone,actorial analyses o brain or behavior (Van Orden, Pennington, and Stone,2001). The assumption requires that brain dynamics are uniorm uctuations2001). The assumption requires that brain dynamics are uniorm uctuationsaround equilibriums, even when contrasting average values rom two dierentaround equilibriums, even when contrasting average values rom two dierentpoints in time. The existence o such equilibriums in the brains behavior couldpoints in time. The existence o such equilibriums in the brains behavior couldbe turned around to corroborate component-dominant dynamics and wouldbe turned around to corroborate component-dominant dynamics and wouldjustiy pooled values, means, and the standardized images so prominent in justiy pooled values, means, and the standardized images so prominent insubtractive analyses. But brain dynamics are not uniorm and do not containsubtractive analyses. But brain dynamics are not uniorm and do not containstable equilibriums (Buzski, 2006; Kelso, 1995). Consequently, we believe thatstable equilibriums (Buzski, 2006; Kelso, 1995). Consequently, we believe thatwhile some kind o spatial approach to analyzing the brain will eventually chalkwhile some kind o spatial approach to analyzing the brain will eventually chalk

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up reliable successes (Freeman, 2007), it will ultimately ail to capture, in a ullup reliable successes (Freeman, 2007), it will ultimately ail to capture, in a ullway, how the brain works, unless it gives sufcient emphasis to the dimension oway, how the brain works, unless it gives sufcient emphasis to the dimension otime (Freeman, 2006).time (Freeman, 2006).

Its About TimeIts About TimeUntil recently, it was not clear how to envision brain activity without theUntil recently, it was not clear how to envision brain activity without theaccompanying notion that certain areas o the brain were the home o partic-accompanying notion that certain areas o the brain were the home o partic-ular unctions. A clear alternative has emerged, however, rom a contemporaryular unctions. A clear alternative has emerged, however, rom a contemporaryunderstanding o complex systems, inspired originally by ar rom equilibriumunderstanding o complex systems, inspired originally by ar rom equilibriumthermodynamics (Gregoire and Prigogine, 1977). The nature o voxel valuesthermodynamics (Gregoire and Prigogine, 1977). The nature o voxel values

in brain images suggests a look in this direction because voxel values directlyin brain images suggests a look in this direction because voxel values directlyreect local thermodynamics (Davia, 2006). Voxel values estimate metabolism,reect local thermodynamics (Davia, 2006). Voxel values estimate metabolism,the uel required by the thermodynamic engine that is the brain. Given this act,the uel required by the thermodynamic engine that is the brain. Given this act,it seems at least potentially appropriate to borrow rom thermodynamics andit seems at least potentially appropriate to borrow rom thermodynamics andcomplexity theory (Hollis, Kloos, and Van Orden, 2009).complexity theory (Hollis, Kloos, and Van Orden, 2009).Repeatedly measuredRepeatedly measuredvoxel values reveal distinct patterns o change over time, as do other measures ovoxel values reveal distinct patterns o change over time, as do other measures obrain activity, giving access to the dynamics o the brain in terms o how activitybrain activity, giving access to the dynamics o the brain in terms o how activityuctuates over time.uctuates over time.How Do the Components of the Brain Interact?How Do the Components of the Brain Interact?

Measuring the behavior o the brain over time allows us to pose hypotheses aboutMeasuring the behavior o the brain over time allows us to pose hypotheses aboutthe dynamics o the brain. An alternative to the assumption othe dynamics o the brain. An alternative to the assumption ocomponent-dominantdynamics discussed earlier is calleddiscussed earlier is called interaction-dominant dynamics, a hypothesis, a hypothesisbased on the claim that the brain is dierent than the sum o its parts. Interaction-based on the claim that the brain is dierent than the sum o its parts. Interaction-dominant dynamics allow the interacting components to change each othersdominant dynamics allow the interacting components to change each othersintrinsic dynamics as they interactat least within limits (Jensen, 1998; Van Orden,intrinsic dynamics as they interactat least within limits (Jensen, 1998; Van Orden,Holden, and Turvey, 2003).Holden, and Turvey, 2003).Interaction-dominant dynamics and component-dominant dynamics predictInteraction-dominant dynamics and component-dominant dynamics predictdierent patterns in the time series o measured values o brain activity.dierent patterns in the time series o measured values o brain activity.Component-Component-dominant dynamics predict that a time series o measured values o the brain shoulddominant dynamics predict that a time series o measured values o the brain shouldexhibit a uniorm random pattern around a mean value (so long as all else remainsexhibit a uniorm random pattern around a mean value (so long as all else remainsequal). Large or small changes in one component will not be systematically relatedequal). Large or small changes in one component will not be systematically relatedto large or small changes in other components. Brain components are coupled onlyto large or small changes in other components. Brain components are coupled onlyloosely, or not at all (Newell, 1990; Simon, 1973).loosely, or not at all (Newell, 1990; Simon, 1973).Interaction-dominant dynamics imply that the brain is composed o inter-Interaction-dominant dynamics imply that the brain is composed o inter-dependent components that inect each other with changes, and the changesdependent components that inect each other with changes, and the changescan be amplifed or damped in the interactions among components. Instead o acan be amplifed or damped in the interactions among components. Instead o apattern o random variation, there exists an unstable balance between two dierentpattern o random variation, there exists an unstable balance between two dierenttendancies a tendency among interdependent components to be dominated bytendancies: a tendency among interdependent components to be dominated bychanges due to a ew stronger components versus a tendency or each componentchanges due to a ew stronger components versus a tendency or each componentto behave independently. The actual activity o the brain diers in quality romto behave independently. The actual activity o the brain diers in quality romeither o these two tendenciesand a ractal pattern is predicted to emerge.either o these two tendenciesand a ractal pattern is predicted to emerge.

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Fractal Time in Brain DataFractal Time in Brain DataThe middle graph in Figure 1 portrays results rom a typical electroencepha-The middle graph in Figure 1 portrays results rom a typical electroencepha-lography or EEG recording rom a data bank available on the Internet (atlography or EEG recording rom a data bank available on the Internet (athttp://http://www.physionet.orgwww.physionet.org, 2011). Specifcally, EEG recordings yield a time series o values, 2011). Specifcally, EEG recordings yield a time series o valuesrom each electrode in the Frankensteins cap, reecting the variation o activityrom each electrode in the Frankensteins cap, reecting the variation o activitywithin the brain. The middle, raw, EEG time series in Figure 1 was recorded romwithin the brain. The middle, raw, EEG time series in Figure 1 was recorded roma healthy participant at an electrode located above the middle-posterior regiona healthy participant at an electrode located above the middle-posterior regionduring a no-task resting condition (see the EEG Motor Movement/Imagery Datasetduring a no-task resting condition (see the EEG Motor Movement/Imagery Datasetatat www.physionet.orgwww.physionet.org or descriptions o experimental conditions and data,or descriptions o experimental conditions and data,www.physionet.orgwww.physionet.org, 2011). The signal consists o 9,760 data points recorded over, 2011). The signal consists o 9,760 data points recorded overthe course o one minute.the course o one minute.EEG outputs may appear quite irregular, but several decades ago researchersEEG outputs may appear quite irregular, but several decades ago researchersdiscovered ractal structure in the brain signals o nonhuman animals (Anderson,discovered ractal structure in the brain signals o nonhuman animals (Anderson,Holroyd, Bressler, Selz, Mandell, and Nakamura, 1993; Freeman, 1989; Grneis,Holroyd, Bressler, Selz, Mandell, and Nakamura, 1993; Freeman, 1989; Grneis,Nakao, and Yamamoto, 1990; Kodama, Mushiake, Shima, Nakahama, andNakao, and Yamamoto, 1990; Kodama, Mushiake, Shima, Nakahama, andYamamoto, 1989a, b; Selz and Mandell, 1991; Yamamoto, Nakahama, Shima, Yamamoto, 1989a, b; Selz and Mandell, 1991; Yamamoto, Nakahama, Shima,Kodama, and Mushiake, 1986). A decade later, these fndings had been replicatedKodama, and Mushiake, 1986). A decade later, these fndings had been replicatedin studies o human brains. For example, a ractal pattern like that illustrated by thein studies o human brains. For example, a ractal pattern like that illustrated by themiddle data in Figure 1 was observed in the EEG recordings rom human partici-middle data in Figure 1 was observed in the EEG recordings rom human partici-pants in a so-called resting state, in which no task was required while being scannedpants in a so-called resting state, in which no task was required while being scanned(Linkenkaer-Hansen, Nikouline, Palva, and Ilmoniemi, 2001).(Linkenkaer-Hansen, Nikouline, Palva, and Ilmoniemi, 2001).Economists have traditionally not worked much with ractal mathematics, andEconomists have traditionally not worked much with ractal mathematics, andso we will provide a quick overview o the concepts and how they apply to brainso we will provide a quick overview o the concepts and how they apply to brainresearch. Benoit Mandelbrot invented the termresearch. Benoit Mandelbrot invented the term ractal in the 1970s to reer to ain the 1970s to reer to anew geometry, synthesizing previously exceptional mathematical monsters withinnew geometry, synthesizing previously exceptional mathematical monsters withina geometry emphasizing the highly irregular phenomena o nature in the rough.a geometry emphasizing the highly irregular phenomena o nature in the rough.Loosely speaking, ractal geometry is about patterns or shapes that have the propertyLoosely speaking, ractal geometry is about patterns or shapes that have the propertythat when divided into partsno matter how smallthe shapes o the parts mimicthat when divided into partsno matter how smallthe shapes o the parts mimicexactly (or statistically) the shape o the whole. Parts and wholes are sel-similar.exactly (or statistically) the shape o the whole. Parts and wholes are sel-similar.Many naturally occurring phenomena are readily analyzed using ractal geometry,Many naturally occurring phenomena are readily analyzed using ractal geometry,ranging rom snowakes and broccoli to cardiovascular networks or kidneys. Butranging rom snowakes and broccoli to cardiovascular networks or kidneys. Butwhile these examples are ractal in space, physiological signals like heartbeat andwhile these examples are ractal in space, physiological signals like heartbeat andEEG readings are ractal in time.EEG readings are ractal in time.In Figure 1, the middle pattern is the EEG brain signal o the healthy, restingIn Figure 1, the middle pattern is the EEG brain signal o the healthy, restingparticipant. The signal below that is the EEG signal o a brain in seizure, whileparticipant. The signal below that is the EEG signal o a brain in seizure, whilethe upper signal represents a random, snythethic white noise signal. All threethe upper signal represents a random, snythethic white noise signal. All threepatterns appear irregular, but even an untrained eye can see that the three signalspatterns appear irregular, but even an untrained eye can see that the three signalsare markedly dierent rom each other. Indeed, it turns out that, with training andare markedly dierent rom each other. Indeed, it turns out that, with training andexperience, the human eye is among the most reliable devices or distinguishingexperience, the human eye is among the most reliable devices or distinguishingamong these patterns.among these patterns.How is the ractal structure o a time series characterized? EEG data have aHow is the ractal structure o a time series characterized? EEG data have astatistical ractal structure, although it is not the ideal repeating structures o thestatistical ractal structure, although it is not the ideal repeating structures o theractals made popular in posters and other popular art. The ractal structure oractals made popular in posters and other popular art. The ractal structure oa time series can be evaluated using several kinds o statistical tools but the mosta time series can be evaluated using several kinds o statistical tools but the most

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Figure 1

Three Examples of Noise in EEG Timeseries

Source:Authors.Notes: Top: a synthetic signal o random white noise with 0. Middle: EEG data rom a healthyparticipant at rest. The time series resembles that o ractal time and 1 (known as pink noise).Bottom: EEG recording during a seizure in which the time series o EEG data resembles brown noise with 2 (www.physionet.org, CHB-MIT Scalp EEG Database).

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common is to use a Fourier transormation, which approximates an irregular andcommon is to use a Fourier transormation, which approximates an irregular andaperiodic series o EEG data with wholly regular and periodic sine waves.aperiodic series o EEG data with wholly regular and periodic sine waves. SimplySimplyadding up sine waves o dierent requencies and amplitudes can closely approxi-adding up sine waves o dierent requencies and amplitudes can closely approxi-mate any complicated curve. The next step is to transorm these sine curves into whatmate any complicated curve. The next step is to transorm these sine curves into whatis called a spectral density unction, which summarizes the relationship between theis called a spectral density unction, which summarizes the relationship between thesize o changes and how oten those changes occur.size o changes and how oten those changes occur.We frst approximate the raw EEG data series at the upper right o Figure 2We frst approximate the raw EEG data series at the upper right oFigure 2using the Fourier transormation, which involves transorming the curve into theusing the Fourier transormation, which involves transorming the curve into theseries o sine waves on the let. Then the sine waves are transormed in turn intoseries o sine waves on the let. Then the sine waves are transormed in turn intothe power spectral density unction at the bottom right. Again, the spectral densitythe power spectral density unction at the bottom right. Again, the spectral densityplot summarizes the relation between the size (amplitude squared) o changes (plot summarizes the relation between the size (amplitude squared) o changes (S))over time in the EEG signal versus how oten or how requently changes o that sizeover time in the EEG signal versus how oten or how requently changes o that sizeoccur (occur (). This relation o size compared to requency,). This relation o size compared to requency, S((), is the typical ocus o), is the typical ocus oa ractal analysis. The mathematics o ractal geometry is defned by invariant rela-a ractal analysis. The mathematics o ractal geometry is defned by invariant rela-tions between the size (or magnitude) o structures and the number (or requency)tions between the size (or magnitude) o structures and the number (or requency)

o structures at that size.o structures at that size.The decomposition o a pattern into sine waves, via the Fourier transorma-The decomposition o a pattern into sine waves, via the Fourier transorma-tion, is portrayed on the let side o Figure 2. Each sine wave has a particulartion, is portrayed on the let side o Figure 2. Each sine wave has a particular

Figure 2

Spectral Plot of an EEG Time Series

Source:Authors.Notes:Data rom the middle panel o the earlier Figure 1, the participant at rest recorded or 60 seconds.On the lower right, the power spectrum is displayed on log-log scales. Four ordered pairs o amplitude

(power) and requency are highlighted with dots and lines that connect to the respective sine waves thatthey represent (see also Holden, 2005.)

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requency and amplitude, and these two values are graphed as an ordered pairrequency and amplitude, and these two values are graphed as an ordered pairwith the (log) requency spectrum on thewith the (log) requency spectrum on the x-axis and the (log) amplitude-squared-axis and the (log) amplitude-squared(power) on the(power) on they-axis, as portrayed in the lower right-hand plot o Figure 2. Arrows-axis, as portrayed in the lower right-hand plot oFigure 2. Arrowsin the fgure connect the illustrated sine waves to their actual point coordinates inin the fgure connect the illustrated sine waves to their actual point coordinates inthe spectral plot.the spectral plot.A ractal pattern is plausible when power or size o change lines up proportion-A ractal pattern is plausible when power or size o change lines up proportion-ally with requency o change on the log-log axes. The regression line portrayedally with requency o change on the log-log axes. The regression line portrayedin Figure 2 expresses this relation, with a slope o in Figure 2 expresses this relation, with a slope o , where, where is called the scalingis called the scalingexponent. The name scaling exponent comes rom the relation oexponent. The name scaling exponent comes rom the relation oS(() = 1/) = 1/,which translates as the size o changes occurring with a particular requency equalswhich translates as the size o changes occurring with a particular requency equalsthe inverse o requency, itsel, raised to the scaling exponent alpha. The relation isthe inverse o requency, itsel, raised to the scaling exponent alpha. The relation iscalled an invariant scaling relation because the proportional relation between sizecalled an invariant scaling relation because the proportional relation between sizeand requency o change is equivalent at big scales o change, small scales o change,and requency o change is equivalent at big scales o change, small scales o change,and all scales in between. The invariant relationship across all scales between sizeand all scales in between. The invariant relationship across all scales between sizeand requency o changes is the defning eature o ractals.and requency o changes is the defning eature o ractals.The straight line o the spectral plot in Figure 2 is also called a power law.The straight line o the spectral plot in Figure 2 is also called a power law.Power laws show up as straight lines when graphed on loglog scales. Power lawsPower laws show up as straight lines when graphed on loglog scales. Power lawsrelating event sizes and event requencies are ound widely in nature, and a varietyrelating event sizes and event requencies are ound widely in nature, and a varietyo power law values have been associated with a wide array o organisms, biologicalo power law values have been associated with a wide array o organisms, biologicalprocesses, and collective social activities (Bak, 1996; Farmer and Geanakoplos,processes, and collective social activities (Bak, 1996; Farmer and Geanakoplos,2005; Jensen, 1998; Jones, 2002; Mitzenmacher, 2003; Philippe, 2000; Van Orden,2005; Jensen, 1998; Jones, 2002; Mitzenmacher, 2003; Philippe, 2000; Van Orden,Kloos, and Wallot, 2011; West and Deering, 1995). Power laws also appear widely inKloos, and Wallot, 2011; West and Deering, 1995). Power laws also appear widely inmeasurements o human perormance (or reviews, see Gilden, 2001; Kello et al.,measurements o human perormance (or reviews, see Gilden, 2001; Kello et al.,2010; Kello and Van Orden, 2009; Riley and Turvey, 2002; Van Orden, Holden, and2010; Kello and Van Orden, 2009; Riley and Turvey, 2002; Van Orden, Holden, andTurvey, 2003; Holden, Van Orden, and Turvey, 2009).Turvey, 2003; Holden, Van Orden, and Turvey, 2009).The power law value oThe power law value o== 1.1 in Figure 2 is close to one, and1.1 in Figure 2 is close to one, and == 1 repre-1 repre-sents a mathematical ideal in ractal geometry. The ideal is here called ractalsents a mathematical ideal in ractal geometry. The ideal is here called ractaltime because the ractal pattern unolds in time instead o space.time because the ractal pattern unolds in time instead o space.44 Resting-stateResting-stateneural activity has been examined in a number o studies, and the general fndingneural activity has been examined in a number o studies, and the general fndingis ractal time (Buzski, 2006). EEG signals that exhibit ractal time are associatedis ractal time (Buzski, 2006). EEG signals that exhibit ractal time are associatedwith healthy brains. Signals that depart rom ractal time, becoming either overlywith healthy brains. Signals that depart rom ractal time, becoming either overlyrandom or overly regular, are associated with aging and disease (Van Orden, 2010;random or overly regular, are associated with aging and disease (Van Orden, 2010;Van Orden, Kloos, and Wallot, 2011; West, 2006).Van Orden, Kloos, and Wallot, 2011; West, 2006).For example, signals resembling the white noise signal in Figure 1 are otenFor example, signals resembling the white noise signal in Figure 1 are otenassociated with aging and, analyzed with these methods, yieldassociated with aging and, analyzed with these methods, yield 0. I the data in0. I the data inthe bottom panel o Figure 1 that came rom a brain seizure were analyzed withthe bottom panel oFigure 1 that came rom a brain seizure were analyzed withthese methods, thenthese methods, then 2. The value2. The value 1 is also the source o other names or1 is also the source o other names orthethe S(()) == 1/1/scaling relation, namely 1/ scaling or 1/ noise. It is also calledscaling relation, namely 1/ scaling or 1/ noise. It is also calledpink noise because noise captures the arrhythmic irregularity o the raw EEG signalpink noise because noise captures the arrhythmic irregularity o the raw EEG signal4 Loosely speaking, the ractal dimension estimates the extent to which the rough irregular raw EEG

curve leaks rom the frst dimension o a straight line into the second dimension o a plane. The powerlaw or scaling exponent o ideal ractal time is 1, and the ractal dimension o ideal ractal time is 1.2.Random white noise has a power law value or scaling exponent o 0 and a ractal dimension o 1.5.

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and because the power spectrum o light with a similar scaling relation appearsand because the power spectrum o light with a similar scaling relation appearspink rom the large amplitudes o reddish light in the low-requency portion opink rom the large amplitudes o reddish light in the low-requency portion othe spectrum.the spectrum.O course, the data that stream rom the Frankenstein cap o EEG recordingO course, the data that stream rom the Frankenstein cap o EEG recordingorm multiple time seriesone or each o the electrodes. Thus, a key questionorm multiple time seriesone or each o the electrodes. Thus, a key questionor studying the behavior o the brain is the extent to which similar patterns oor studying the behavior o the brain is the extent to which similar patterns ochange are observed across the EEG nodes. This area o study was inspired bychange are observed across the EEG nodes. This area o study was inspired byresults rom physics concerning how systems may sel-organize their own behaviorresults rom physics concerning how systems may sel-organize their own behavior(Jensen, 1998). For example, when a pile o rice is ormed by dropping one grain(Jensen, 1998). For example, when a pile o rice is ormed by dropping one graino rice at a time, it will sel-organize to allow access to the widest possible rangeo rice at a time, it will sel-organize to allow access to the widest possible rangeo rice avalanches. The brain analogy to avalanches is the tendency or coherento rice avalanches. The brain analogy to avalanches is the tendency or coherentactivity to spread among the nodes o the Frankenstein cap, the nodes distributedactivity to spread among the nodes o the Frankenstein cap, the nodes distributedacross a persons scalp. Size, in this analogy, is the number or spatial extent oacross a persons scalp. Size, in this analogy, is the number or spatial extent onodes that participate in coherent activity (Allegrini, Paradisi, Menicucci, andnodes that participate in coherent activity (Allegrini, Paradisi, Menicucci, andGemignani, 2010).Gemignani, 2010).In addition, each avalanche begins and ends in an observable rapid transitionIn addition, each avalanche begins and ends in an observable rapid transitionbetween two states o coherent activity, so each avalanche o coherent EEG canbetween two states o coherent activity, so each avalanche o coherent EEG canbe measured in two ways: by the number o nodes participating in the coherentbe measured in two ways: by the number o nodes participating in the coherentdynamics and the duration in time o each avalanche (the time rom the rapiddynamics and the duration in time o each avalanche (the time rom the rapidtransition at the beginning o the avalanche until the rapid transition at the end).transition at the beginning o the avalanche until the rapid transition at the end).Fractal time across the size and duration o EEG avalanches has been observed orFractal time across the size and duration o EEG avalanches has been observed orsome years (Gong, Nikolaev, and van Leeuwen, 2003; Stam and de Bruin, 2004).some years (Gong, Nikolaev, and van Leeuwen, 2003; Stam and de Bruin, 2004).More recent work fnds that both ways o measuring brain avalanches yield powerMore recent work fnds that both ways o measuring brain avalanches yield powerlaw behavior (Allegrini, Paradisi, Menicucci, and Gemignani, 2010), similar to thelaw behavior (Allegrini, Paradisi, Menicucci, and Gemignani, 2010), similar to thepower law illustrated in Figure 2.power law illustrated in Figure 2.Variation in patterns o global synchronization is the paramount scale o Variation in patterns o global synchronization is the paramount scale oglobal change in brain dynamics, and changes in the global organization o centralglobal change in brain dynamics, and changes in the global organization o centralnervous system activity unold in the predicted ractal pattern. Interaction-dominantnervous system activity unold in the predicted ractal pattern. Interaction-dominantdynamics predict that ongoing interdependent changes in each o a systemsdynamics predict that ongoing interdependent changes in each o a systemscomponents participate in the global dynamical pattern. Consequently, no mattercomponents participate in the global dynamical pattern. Consequently, no matterthe scale or direction rom which we enter the system, the repeated measurementsthe scale or direction rom which we enter the system, the repeated measurementsshould bear evidence o the ractal signature. Indeed, ractal characteristics haveshould bear evidence o the ractal signature. Indeed, ractal characteristics havebeen observed rom the smallest to the largest scales o brain dynamics. Fractalbeen observed rom the smallest to the largest scales o brain dynamics. Fractaltime is observed in the variation o current ow through neuronal ion channelstime is observed in the

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