TEMPORAL OSCILLATIONS IN HUMAN PERCEPTIONS

7/30/2019 TEMPORAL OSCILLATIONS IN HUMAN PERCEPTIONS

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PSYCHOLOGICAL SCIENCE

Research ReportTEMPORAL OSCILLATIONS lN HUMAN PERCEPTION

Stanislas DehaeneI.N.S.E.R.M.. C.N.R.S., and E.H.E.S.S., Laboratoire de Sciences Cognitives et Psycholinguistique, Paris. France

Abstract-The notion that human per-ceptual decisions are based on discreteprocessing cycles rather than a continu-ous accumulation ofinformation was ex-amined experimentally. Significant peri-odicities were found in hwnan responsetimes (RT) to feature and conjunctiondiscrimination tasks in the visual and au-ditory modalities. Individual RT histo-grams were multimodal. with regularlyspaced peaks and troughs. indicatingthat responses were emitted more fre-quently at regularly recurring time inter-vals following stimulus presentation. Onaverage, responses were initiated afterfour to seven discrete processing stepswhose "quantum" duration Il'as propor-tional to task difficulty.Measurement of human responsetimes (RT) is a widespread technique in

cognitive psychology (Luce, 1986; Pos-ner, 1978). It is commonly assumed thatmental processing time has a large sto-chastic component and may vary contin-uously, on a millisecond scale, as a func-tion of stimulus characteristics and taskdemands (Luce, 1986). Psychologicalmodels postulate a series of consecutiveprocessing stages (Donders, 1969; Stern-berg, 1969), each with variable duration.RT, which is the sum of these durations,is therefore expected to be broadly dis-tributed, and in general only its mean ormedian is considered significant.A number of authors have consideredthe alternative possibility of a temporalquantification in mental processing.Stroud (1955) proposed the "perceptualmoment hypothesis," according towhich perceptual inputs are chunkedinto discrete temporal intervals accord-ing to the regular oscillations of a "cen-tral intermittence." Since then, data sug-gestive of an "internai dock" or subjec-The author is on leave at the Institute of

Cognitive and Decision Sciences. StraubHall, University of Oregon, Eugene, OR97403, where correspondence should be ad-dressed; e-mail: [email protected]

tive "time quanta" have been reportedoccasionally (Allport, 1968; Augenstine,1955; Collyer, Broadbent, & Church,1992; Rarter & White, 1968; 10keit,1990; Kristofferson, 1967a, 1967b, 1980;Latour, 1967; Michon, 1967; Pppel,1970; Shallice, 1964; M. Treisman,Faulkner, Naish, & Brogan, 1990; M.Treisman, Faulkner, & Naish, 1992).Several of these studies have reported-multiple discrete peaks in histograms ofa few hundred reaction times or ocularmovement times. The observed period-icities have sometimes been tentativelylinked to physiological events, such asthe alpha rhythm of the electroencepha-logram (Callaway & Yeager, 1960; Kris-tofferson, 1967a, 1967b; Latour, 1967).Most of those data were collected be-fore computer facilities existed. and theirstatistical reliability has been criticizedseverely (Vorberg & Schwarz, 1987;Vroon, 1970, 1974). However, more re-cently, eIectrophysiological recordingsfrom auditory and visual brain areashave revealed stimulus-dependent oscil-lations in the range of 30 to 80 Hz (Basar-Eroglu & Basar, 1991; Eckhorn et al.,1988; Engel. Knig, Kreiter, & Singer,1991; Engel, Kreiter, Knig, & Singer,1991; Engel, Knig, & Singer, 1991;Galambos, Makeig, & Talmachoff. 1981;Gray, Knig, Engel, & Singer, 1989;Gray & Singer, 1989;Pantev et al., 1991;Ribary et al., 1991). These results haveagain suggested that the neuronal encod-ing of sensory information may be dis-crete in time.The present study investigated

whether a temporal periodicity or dis-creteness might be perceptible in individ-ual subjects' distributions of RTs duringperceptual discrimination tasks. To thisend, 1,600 RTs were collected from eachof five highly trained observers in eachof four two-choice tasks. It was reasonedthat the period or phase of the putativeoscillatory processes might differ be-tween subjects or between tasks,thereby hindering any meaningful analy-sis of composite data sets. The experi-

Copyright (0 1993American Psychological Society

mentaldesign and the statistical analysestherefore focused on studying RT distri-butions from single subjects performinga fixed task.Four tasks were used to explore sys-tematically the effect of two variables,stimulus modality and attention, thatprevious work suggested might affectinternai oscillatory processes. First,stimulus modality was manipulated bycontrasting two tasks of auditory dis-

crimination with two tasks of visual dis-crimination. Electro- and magneto-encephalographic recordings of 40-Hzoscillations in humans have mainly usedauditory stimuli (Galambos et al., 1981;Pantev et al., 1991;Ribary et al., 1991),whereas most related electrophysiologi-cal experiments in animais have usedsimple visual stimuli (Eckhorn et al.,1988;Engel, Knig, Kreiter, & Singer,1991; Engel, Knig, & Singer, 1991;Engel. Kreiter, et al., 1991; Gray &Singer, 1989; Gray et al., 1989). It wastherefore of interest to examine the pres-ence of periodicities in RTs to stimuli inboth modalities. Second, attention andtask difficulty were manipulated by con-trasting, in each modality, simplefeaturediscrimination tasks with more complexconjunction discrimination tasks. Thefeature tasks required simple discrimina-tion along one stimulus dimension: ori-entation for visual stimuli and pitch forauditory stimuli. The more difficult con-junction tasks required identification of aspatial or temporal relation between thesame elementary features. Several au-thors have theorized that temporal oscil-lations may play a role in attentive fea-ture binding (Crick & Koch, 1990;Eck-horn et al., 1988;Engel, Knig, Kreiter,& Singer, 1991;Engc1,Knig, & Singer,1991;Engel, Kreiter, et al., 1991;Gray &Singer, 1989;Gray et al., 1989;Sporns,Tononi, & Edelman, 1991; von derMalsburg & Schneider, 1986; see alsoDamasio, 1989).Ifthis hypothesis is cor-rect, then oscillations might be foundonly in the conjunction tasks, but not inthe more simple feature tasks.

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Stanislas DehaeneMETHOD

Design and Stimuliln order to examine the distributionsof individual subjects' RTs. 1.600 RTswere collected fromeach of tive observ-ers in each of four tasks: visual feature(VF), visual conjunction (VC), auditoryfeature (AF), and auditory conjunction(AC). ln each task, one of two alterna-tive stimuli was presented on each trial.and the subject had to respond as fast aspossible by pressing a correspondingright-hand or left-hand Morse key. Thestimuli were as follows:

. Visual feature task: vertical versushorizontal 7-mm bars, centered on acomputer screen (bright orangeagainst a black background), subtend-ing approximately 50. of visual anglefrom a viewing distance of about50 cm.

. Visual conjllnction task: leuers T andL made up of two such 7-mm bars.The stimuli were centered and ran-domlyoriented at O.,90., 180..or 270.from upright and therefore differedonly in the spatial disposition of theircomponent lines.

. Auditory feature task: computer-generated square-wave sounds of 100msduration. witha pitch of440Hz (A)or 1,245Hz (0#). The stimuli weregenerated on-line via the computer'sinternalloudspeaker, withan intensityof 60dB.

. Auditory conjllnction task: sequencesof the same tones, shortened to 50 msduration, with two possible orders (A-0# YS.O#-A).

On each task, total stimulus durationwas 100 ms, and the response-to-stimulusinterval was 1.300ms. Stimuluspresentation and RT measurement werecontrolled with IBM-compatible porta-ble computers. Visual presentation wassynchronizedwith the 6O-Hzrefresh cy-cle of the plasmascreen. Each task com-prised 1,600trials split into eight consec-utive sessions of 200 trials each, with anequal number of the two target stimuliwithin each session. No precise controlwas imposed concerning the time of dayat which the experiment was run. Theeight sessions were generally run over aVOL. 4, NO. 4. JUL Y 1993

few consecutive days, with two to foursessions per day.

SubjectsFive observers with considerable ex-perience in RT tasks, including theauthor, served as subjects. ln order tocontrol for possible hardware-inducedperiodicities. difTerentcomputers wereassigned to difTerent subjects, and thecomputers' internai timers were pro-grammed to a I.ms accuracy using twodifTerent software methods.1ObserversS.O. (male. age 26) and G.O. (female,age 31) passed the experiments usingTimingMethod Ion a ToshibaT-5Ioo, inmatched order (AF, AC, VC, VF forS.O.; AC, AF, VF, VC for G.O.); ob-servers C.P. (male, age 23) and P.G.(male, age 22) passed the experimentsusing Timing Method 2 on a ToshibaT-52oo, in matched order (AC, AF, VF,VCfor C.P.; AF. AC, VC, VF forP.G.);and observer A.C. (female, age 24)usedTiming Method 1 on a Toshiba T-21oo(order AC. AF. VC. VF).

RESULTSIdentification of a Periodicity1 tirst detail the statistical identitica-tion of oscillations for observer G.O. in

the visual conjunction task. G.O.'s 1,462correct RTs were pooled across the eightsessions and across the difTerent stimu-lus-response conditions. Histogramswere then plotted using a bin size of ei-ther 1 ms (Fig. la) or 6 ms (Fig. Ib).2

1. Both methods involved reprogrammingcounter 0 of the 8254 chip. present in IBM-compatible AT computers, that normallysends an interrupt 08 to the microprocessorevery 54.9 ms. ln Timing Method l, the 8254chip was reprogrammed to send an interruptevery millisecond, and this interrupt was usedto increment the RT counter. ln Timing'Method 2. the 8254chip was reprogrammed toallow access to an internai register that dec-remented continuously at a rate of 1.193MHz. The accuracy of this second timer wasbelow 0.2 ms. The accuracy and lack of biasof both timers were checked with signaIs ofknown accuracy.2. Histograms with a bin size of 6 ms andthe corresponding cross-correlograms wereused only for illustration. AIl statistical anal-

Visual inspection of the 6-ms histogramrevealed a regular pattern of peaks andtroughs. The interval between peaks wasapproximately stable at 30ms. An auto-correlogram of the 6-ms histogram afterhigh-pass filtering at 20Hz confirmed thepresence of rhythmicity (Fig. Ic). Tomeasure the oscillation frequency, a fastFourier transform (FFT) was performedon the millisecond-by-millisecond histo-gram, using a 256-ms window centeredon the median RT. Over the intervalfrom 20 to 100 Hz,3 the periodogramshowed a large coefficient at 35.2 Hz,corresponding to an oscillation period of28.4ms (Fig. Id).

Significance TestsSampling from a unimodal distribu-tion is likely to yield a histogram withmultiple paks, especially when thenumber of samples is smal!. Chancealone might explain the regular spacingof these spurious peaks, thus mimickinga periodic process. 1 therefore used anonparametric Monte-Carlo method toevaluate, separately for each individualdistribution, the null hypothesis that theobserved peaks were due only to finitesampling from a smooth, nonoscillatorydistribution. The millisecond-by-

millisecond histogram of n correct RTswas low-pass filtered at 20 Hz (Fig. la)and then used for the computer genera-tion of 10,000 sets of n simulated RTs.Each of these 10,000 control sets wasthen treated in the same way as the orig-inal data. An RT histogram was tabu-lated, and an FFT was used to quantifythe presence of periodicities. Thismethod yielded an evaluation of the ex-pected range of FFT coefficients whenthe underlying distribution was known toyseswere based on the raw data gathered intomillisecond-by-millisecond histograms. Thepresent method does not require the selectionof an arbitrary bin-size parameter (Pppel.1970;Vorberg & Schwarz. 1987).3. With the present technique, only fre-quencies in this interval could be studiedreliably. Frequencies below 20Hz were con-taminatedby the slow rise and fallof RT dis-tributions, whereas frequencies above 100Hzwere masked by the minimum intrinsic vari-ance of RTs. which is approximately 30to 50ms2 (Hopkins, 1984; Hopkins & Kristoffer-son, 1980).

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500 ms

Fig. 1. Evidence for oscillations in the distribution of response times (RTs) fromobserver a.D. in the visual conjunction task. (a) I-ms histogram of a.D. 's 1,462correct RTs. The ordinate is the number of observations per bin. The smooth curveis the histogram after low-pass filtering at 20Hz, used for the generation of control,random data sets. (b) 6-ms histogram of the same data. The arrow indicates themedianRT. The curve is the histogram after high-pass filtering at 20 Hz. showing ac1earoscillation around 35Hz. (c) Autocorrelogram of the curve in (b). Dotted linesshowthe values of the correlation coefficients that were significantat the .01 and .001levels. (d) Periodogrambased on a fast Fourier transform (FFf) of the I-ms histo-gram. using a 256-mswindow centered on the median RT. Significanceleve\s werecomputed for each Fourier coefficient by drawing 10,000control sets of 1,462simu-lated RTs from a random-number generator using the smooth distribution in (a). AnFFf was performedon each set, and the 10.000Fourier coefficients at each frequencyin the range from 20to 100Hz were sorted in decreasing order. Horizontal curvesshow the value of the 20th. looth. and 500th coefficient for each frequency, corre-spondingto significancelevels of .002. .01. and .05 before Bonferroni's correction.be nonoscillatory. but otherwise ex-tremely similar to the actual data. Forobserver a.D. in the visual conjunctiontask. none of the 10,000simulateddatasets had a Fourier coefficient larger thanthe peak at 35.2Hz in the originaldata(Fig. Id). Since 20frequencies are testedin the interval from 20 to 100Hz. thelevel of significanceof the peak is p


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Table 1.Oscillationfreqllency (Hz) for fil'e obsen'ers in the fOllrdiscriminat ion tasks

Note. Frequency '" most significantpeak of the fast Fourier transform (FFf)periodogram in the range from 20to 100Hz. Bonferroni-corrected significancelevels: * = p < .05; + = P < .02; + + '" p < .01; ** '" p < .002. Since the FFfwas performed on a 256-mswindow over the RTdistributions, only 128estimatesof the complex Fourier coefficients were obtained over the Nyquist range from0to 500Hz. or only 20 estimates over the interval from 20 to 100Hz. Therefore, theperiodogram could be calculated only at frequencies that were integer multiplesof500/128... 3.9 Hz. Hence the identical frequency values in several columns.

(Stroud. 1955).They indicate that on afinetime scale, responses are not distrib-uted randomly with respect to stimuluspresentation. but are emitted more fre-quently at regularly recurring time inter-vals after the stimulus first appeared.Several experimenters have previ-ously claimed to have identified period-icities in RT distributions (Augenstine.1955; Harter & White. 1968; Jokeit.1990;Latour. 1967;Michon. 1967;Pop-peI, 1970;Vroon, 1970).However, theseoriginal studies suffered from a numberofflaws that may explainwhy this lineofresearch has remained marginal. First,until recently, it has been impractical torecord and analyze several thousandRTs. Even Jokeit's relatively recent ar-ticle (1990)includedonly 152RTs from asinglesubject. ln addition, many authorsfailed to mention how their data setswere selected, thus leavingopen the pos-sibility that periodicities were obtainedonlyfrom a few subjects ina large study.and might therefore be a chance event.By contrast, the present study included20 data sets of 1,600 trials each. Al-though periodicities sometimes seemedvisiblewhenanalyzing smallersubsets ofthe data (e.g.. right-hand responses orfirst four sessions only), statistical signif-icance was hardly ever reached whenfewer than 1,000RTs were included inthe distributions.VOL.4. NO. 4, JULY 1993

Second. previous studies often re-sorted to some complexpreprocessing ofthe data in order to demonstrate thepresence of periodicities. ln some cases.the periodicities appeared to be artifactsof the preprocessing rather than genuinepsychological phenomena. For instance.Poppel (1970) plotted histograms ofabout 260RTs. reported the presence ofmultiple peaks, and evaluated the oscil-lation period as the mean interpeak in-terval in a histogram with 10-msbins.However. Vorberg and Schwarz (1987)demonstrated that this procedurewas bi-ased and could "discover" periodicitieseven in artificial data drawn froma uni-modal distribution. Similarly, Jokeit(1990)discovered periodicities in a histo-gram of the RTdifferences between anypair among a set of 152RTs. However.the histogram was both "smoothed andtrend-reduced" in an unspecified waybefore periodicities were at ail visible. Itseems likely that smoothing, whichactsas a low-pass filter, and trend reducing.which is equivalent to a high-passfilter,together contributed to the selective am-plification of random fluctuations in anarrow bandwidth, thereby yielding animpression of periodicity.The present results. by contrast.seem less susceptible to such statisticalartifacts. Regularly spaced peaks wereoften obvious inthe rawRTdistributions

(Fig. 1). ln addition. the possibility thatsampling and statistical proceduresthemselves were responsible for the ob-served oscillations was assessed by sys-tematic comparison to a large number ofrandom data sets drawn from a distribu-tion that was known to be nonperiodic.ln 14 out of 20 data sets. periodicitieswere found more often than could be ex-plained by chance (Table 1).The present study underlines the psy-chological significance of periodicities inRT distributions by demonstrating thatthe oscillation period is systematicallyrelated to task difficulty. The observedcorrelation between median RT and theoscillation period suggests a decomposi-tion of decision time into two compo-nents. one of fixed duration and theother showing discrete temporal oscilla-tions. ln the regression equation RT =225 -t 5.53T, the constantof 225:t 40ms coincides roughly with the minimalvalue for simple RTs (Luce. 1986),andcan be tentatively ascribed to stimulustransduction and motor response. Theregression slope 5.53 :t 1.86 indicatesthat a response isgenerally initiated afterfourto seven processing cycles. This fig-ure remains remarkably constant acrossvariations in task difficulty. Cycle dura-tion. in contrast. varies considerablywith task difficulty and is shorter whenthe task requires simple feature discrim-ination than when the task implies a con-junction of two different features (A.Treisman & Gelade. 1980).The presentresults do not appear to support the viewthat oscillations are present only whenthe task requires a conjunction or "bind-ing" operation (Crick & Koch, 1990),since fast but significant oscillationswere observed in the two simple featurediscrimination tasks.A possible model for the present data.depicted in Figure 3, supposes that per-ceptual information is not transmitted

continually to higher processing stages,but is made available only at regularlyrecurring time intervals following stimu-lus presentation. An adequate metaphoris the notion of information packets thatare transmitted to subsequent stages ofprocessing only when the perceptual in-formation has been appropriately syn-thesized and registered. This "packag-ing" of perceptual information seem-inglytakes longer when a conjunction offeatures is required. Finally, for each in-267

TaskAuditory Auditory Visual VisualObserver feature conjunction feature conjunction

S.D. 85.9 46.9** 82.0+ 66.4**G.D. 74.2** 27.3** 70.3 35.2**A.C. 97.7* 35.2** 50.8+ 46.9c.P. 74.2 + + 27.3** 70.3* 66.4P.G. 85.9 27.3+ + 58.6 54.7*Average 83.6 32.8 66.4 53.9Mean RT (ms) 278 407 312 341Errors (%) 7.7 8.8 11.3 11.8


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Median RT (ms)500

RT=225 + 5.53 T.

Fig.2. Correlation between medianRT and the oscillation period (1). Small symbolsshow data from individual observers. Large symbols show averages over the fiveobservers.formation packet reaching the decisionstage, either a response is initiated im-mediatelyor the decision is postponed tothe next cycle, eventually generatingmultiplediscrete peaks in the RT distri-bution.This model can be formalizedmathe-matically with five free parameters esti-mated from the RT distribution: meanand standard deviation of the constantduration before the first peak, mean andstandard deviation of the number of cy-cles before responding, and the durationof the cycle itself. Figure 3 demonstratesthe reasonable fit achieved with thismodel.

The proposed model may help to de-lineate the assumptions that mustbe sat-isfiedfor periodicities to showup in RTdistributions. First, the postulated pro-cessingcycles must remain in phasewiththe onset or offset of the stimulus; oth-erwise, the peaks and troughs from suc-cessive trials would cancel each other.The present data cannot be explained interms of a central oscillation or internaiclock that would run continuously andindependentlyof sensory inputs (Pppel,268

1970). Rather, the phase of the oscilla-tion must be reset on each trial.A second assumption is that the delayascribable to sensory transduction andmotor response has a low variance. Dis-tinct peaks will appear in the RT distri-bution only if the interpeak interval,which is the period of the oscillation, islarger than twice the standard deviationof the sensorimotor delay. Hopkins andKristofferson (1980; Hopkins, 1984)found that trained subjects showed "ul-trastable stimulus-response latencies"with a standard deviation as lowas 6 to 7ms. This value suggests that, in theory,oscillations withperiods as smallas 12to14ms, or frequencies as highas 70to 85Hz, could be identified from the RT dis-tributions of trained subjects. Indeed, anaverage frequency of 83.6Hz was foundin the auditory feature task. It should benoted, however, that subjects were ex-tremely fast in this task (average = 278ms), and that they therefore respondedafter only a few oscillation cycles. Itseems unlikely that any biologicalmech-anism could maintain a very precise fre-quency over many cycles. For instance,

Jokeit's (1990)findingof a lOO-Hzperi-odicity in a sampie of 152RTs rangingfrom 650 to 1,200ms seems implausible,since the 10-msperiod wouldhave had toremain stable to within a fraction of amillisecond for more than 60 cycles.Finally, a third assumption is that theoscillation period and the sensorimotordelay both remain approximately con-stant throughout the testing sessions.While this assumption seems to hold forthe eight consecutive sessions used here,preliminary results suggest that more ex-tensive training can reduce the minimalstimulus-to-response delay, thereforeleading to an apparent shift of the oscil-lation phase. RT oscillations can there-fore seeminglydisappear if data from toomany trials are compiled. With observerS.D., two sets of 1,600 RTs were col-lected in the auditory conjunction task.The FFT identified a significant oscilla~tion both in Set 1(46.9Hz, p < .002)andin Set 2 (62.5 Hz, p = .014). The cross-correlogram of the 20-Hz through 100-Hz components of the two histogramswas oscillatory at about 50 Hz. How-ever, interestingly, the two componentswere negatively correlated at lag 0, r =-.321, (254) = 5.40, p < 10-6: Thepeaks in the first histogram coincidedwith the troughs of the second. This wasaccompanied by an acceleration of me-dian RT from 379 to 361ms.

Such a phase shift with training wasreplicated in a task of discrimination oftwo natural syllables (lba/ ys. /v,a/)matched for prevoicing and overail dura-tion. Two sets of 1,600RTs were againcollected from observer S.D. Both setsshowed a significant oscillation (respec-tively, 43.0 Hz, p < .002;46.9 Hz, p =.024).The 20-Hzthrough lOO-Hzcompo-nents of the two histograms showed ashiftedoscillatory cross-correlogram andwere negatively correlated at lag 0, r =- .439, (254) = 7.80, p < 10-6. againconcurrent with a decrease inmedian RTfrom 294ms to 287ms. Further researchshould assess more systematically thevariations with training of cycle phase.cycle duration. and mean number of cy-cles before responding.

CONCLUSIONln the present study, a fine-grained

periodic structure was found within re-VOL. 4. NO. 4. JUL y 1993


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. . .. .. .. .. .. .0-0-0-0-0-11111RESPONSE

D ,DECISION

DRT, ,,.

ENCODINGtime

StimulusOnsetFig. 3. Possible model for RT oscillations. Perceptual information is transmitted inpacketsat regulal"moments'ilTtime: FOieach discrete packet of information, a deci-sion is taken either to respond immediately or to check with the next packet. Thenumber of cycles before responding varies stochastically from trial to trial, generatingamultimodal RT distribution. The 6-mshistogram from observer S.D. in the auditoryconjunction task (1,433 correct RTs) is used for illustration. The fitted curve wasobtained by minimizing X2from a model with five free parameters, X2(47)= 46.6.action time distributions. The oscillationperiod was systematically related to taskdiff iculty, and subjects appeared to re-spond after an approximately constantnumber of cycles regardless of the task.These lawful psychological phenomenahave potential significance for cognitivestudies of sensory and decision pro-cesses. Stimulus-induced oscillationshave also beenobserved in the neuronalor brain electrical activity of several spe-des, including humans(Galambos et al.,1981;Pantev et al., 1991; Ribary et al.,1991).These oscillations could provide abiological basis for the results presentedhere. At odds with the present results,however, is the finding that neuronal os-cil lations are often highly variable andnot phase locked to the stimulus (Eck-horo et al., 1988;Gray & Singer, 1989;Gray, Engel, Knig, & Singer, 1992).This may be related to the fact that inneurobiological studies, the animais aregenerally anesthetized, or awake butpassive, and that the stimuli used oftendo not have a sharp onset. Although theassumption of a common mechanism fortemporal oscillations in the psychologi-cal and neurobiological domains istempting, it remains to be convincinglyestablished.VOL.4.NO.4.JULY 1993

Acknowledgments-I thank J.Mehler.J.P.Changeux, and M. Posner for insightfulcomments. This research was supportedby the Institut National de la Sant et dela Recherche Mdicale, Centre Nationalde la Recherche Scientifique. Ecole desHautes Etudes en Sciences Sociales, andNational Science Foundation.

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TEMPORAL OSCILLATIONS IN HUMAN PERCEPTIONS