heurnp,o'r7nluyia . 401 . N . No . lit pp x6,-876 . 1992Printed in Great Prilain .

JUDGEMENTS ABOUT NUMEROSITY BY ACOMMISSUROTOMIZED SUBJECT

MICHAEL C . CORRALt .Ist and JUSTINL SERGENTt

*University of Auckland, Auckland . New Zealand ; and tMnntreal Neurological Institute . Montreal, Quebec .Canada

(Received 10 Atuy 1991 : accepted 17 June 1992)

Abstract-A commissurotomized subject . L .B ., was shown asterisks flashed at random locations, tipto four in each field, and attempted either to compare the numbers in the two fields or to report thetotal number . The main results were : (a) Report was more accurate with unilateral than with hi lateralpresentation, suggesting that the difficulty integrating across fields was partly attentional ; (b) inintegrating across fields, attention was focused on one field, with only crude 'one-or-many'information from the other ; (c) in cross-field comparisons . the focus was on the LVF, but in reportingthe number it was on the RVF when report was oral or right-handed, and on the I .V F when reportwas left-handed ; (d) cross-field comparisons were improved when the locations were mirrored acrossthe midline.

INTRODUCTION

JOHNSON [7, 8] HAS shown a dissociation in commissurotomizcd subjects between namingstimuli projected to LVF and judging stimuli presented to the two fields to be same ordifferent . In particular, the subject L .B ., on whom the present paper is focused, was able toname letters and digits presented to the LVF quite accurately (although relatively slowly),but was at chance in deciding whether digits or letters in the two visual fields were the same ordifferent . Johnson inferred that L .B . has developed speech in the right hemisphere, enablinghim to name stimuli without transfer to the left hemisphere .

Against this MYERS and SPERRY [15] have argued that the ability of some commissuroto-mized subjects to name stimuli projected to the LVF depends on subcortical transfer . Using atechnique that allowed prolonged inspection of stimuli, they too found that L .B. accuratelynamed digits or letters presented in the LVF, but he could not name drawings unless he hadpreviously been shown the full set in free vision . Myers and Sperry suggested that the lefthemisphere, through a process of active rehearsal . was able to find matches between theknown pool of letters and diffuse information transferred subcortically from the righthemisphere . This information "consisted of limited arousal or orientational cues and partial,contextual, or ambient impressions (Ref . [15], p. 256) ."

Even so, there is evidence that transfer of information between the hemispheres incommissurotomized subjects may be quite fast, efficient, and precise (e.g. Refs [16] and[17]) . Unlike Johnson, SERCENT [18] found that L .B. was able to judge at better than chancewhether digits simultaneously presented in the two fields were the same or different, as didMYL,RS and SPERRY [15] . In Sergent's study, L .B. was even better when required to judgewhich of two digits, the one to the left or the one to the right, was the larger . When he wasrequired to make a binary choice between either side being larger or there being no difference,

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Ire scored much better than when asked simply to make ajudgement of same vs different . Thisresult is rather paradoxical, since the difference between the two tasks seems merelysemantic . Sergcnt concluded that commissurotomy prevents the transfer of shapeinformation between hemispheres, but does not preclude the subcortical transfer of codedinformation . including information about quantity . When making judgements about the sizeof the numbers, then L .B. could rely on the transfer of numerical information extracted fromthe digits, but he was unable to transfer information about the actual shapes of the digits .

In the present study we again focus on L .B . . and explore his ability to compare the numberof randomly located asterisks in the two visual fields . Where previous experiments have usedcodable stimuli, such as letters and digits, that imply left-hemispheric dominance, the presentexperiments are based on judgements of numerosity, which may depend on the righthemisphere [10, 13, 23] .

EXPERIMENT IIn this experiment L .B. was presented with up to four asterisks in each visual field and

judged whether the numbers in the two fields were the same or different .

MethodSubject . L .B . underwent section oft he corpus callosum and the anterior and hippocampaI commissures at the age

of 13 years for the relief of intractable epilepsy . At the time of the present testing he was 36 . Further details of hisneurological history and status are available elesewliere [2] . Despite earlier doubt [4, 16], recent MRI evidenceshows LB .'s corpus callosum to he completely sectioned [1] .

Equipment and stinndi . The stimuli were asterisks displayed on a fast-fade screen connected to an Apple IIBcomputer . They were presented in text mode at selected locations among 25 possible locations in each visual field .The 25 locations were defined in text mode on lines 9-13 (from the top of the screen) ; the LV P locations ranged frompositions 12-16 and the RVF locations from positions 25 to 29, where position is measured from the left of thescreen . These 25 locations in each field elTectively constituted a 5-by-5 virtual grid 2 .6 cm wide and 3 .0 cm tall . withthe inside edge 2 .7 cm from the vertical meridian . The subject sat with his chin in a chin rest and his eyes 57 cm fromthe screen, so that I cm on the screen corresponded to I' of visual angle .

The fixation dot was located midway between the two grids, in line with the middle row of locations . The asteriskswere randomly located in the 25 locations, with the restriction that, within a field, no two asterisks could appear inthe same row or the same column . The locations were randomized separately for each field on each trial . The numberof asterisks i n each field varied from trial to trial, as described below : Examples arc shown in Fig . 1 . The stimuli wereshown for five frames, or approx . 83 msec .

Procedure .'I'lie subject received four sessions of 4g trials, 24 in which the same number of asterisks appeared in thetwo fields and 24 in which different numbers appeared . The "sanne" trials consisted of six trials each in which therewere 1 . 2, 3 and 4 asterisks in each field, and the "different" trials consisted of two presentations of each of the 12possible pairings of different numbers of asterisks . The order of presentations was randomized .

L .B . responded by pressing the N and B keys of the computer keyboard . On the 1st and 4th session he used hisright hand, and on the 2nd and 3rd trials his left hand, in each case using the forefinger to signal -Same" and themiddle finger to signal "different" . The experimenter triggered each trial by saying "Ready'?" and pressing a key, andthe display appeared 500 msec later .L .B . placed the paint of the hand he was not using face down on the table and sat with his logs apart to minimize

the possibility of cross-cueing . lie was also monitored to make sure that he did riot vocalize prior to response . Wealso visually monitored his eye fixation from time to time .

Results and discussionOverall, L,B, was correct on 55 .7% of trials, which did not differ significantly from chance

Lr 2 (1)=2 .53 ; n .s .] . When responding with the right hand he scored 58 .3% correct[y 2 (1)=2 .74 ; n .s .], and with the left hand 53 .3% [y2 (1)=0.38 ; n-s .] . He reported "same" on52.6% of trials, but this bias was not significant [y 2 (1)=0.52 ; n .s .] .

The fact that LB.'s performance did not rise significantly above chances does not precludethe possibility that he was responding systematically . Had he been responding totally

JUDGEM&S'IS ANOUI NEMEROSTY BY A ('OMMISSIIROTIlMI/11D SUB FIT

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.T.

Pig.I .Examplesofpossiblestitnuliineachexperiment :(A)'same'pairfromExperiment ((Jr 2 . I B] astimulus requiring the response "four" from Experiment 3 ; (C) a repeated 'same" pair from

Experiment 1 ; (D) ,I mirror-image 'different" pair from Experiment 4 .

randomly, the relative proportions of "same" and "different" responses would have beenrelated neither to the number of asterisks in the LVF nor the number in the RVF, and norwould there have been any interaction. Totally correct responding would likewise haveyielded no main effect of the number in either field, but in this case the number in the twofields would have interacted to determine the "same" and "different" responses .

Table 1 shows the proportion of "same" judgements as a function of the numbers in thetwo fields . A chi-squared analysis showed that the relative proportions of "same" and"different" responses depended systematically on the number of asterisks appearing in theLVF [y 2 (3)=40.00, P< 0.001], and also, though less markedly, on the number in the RVF[;(l (3) = 15 .94, P<0.011 . The proportion of "same" responses peaked when there were twoasterisks in the LVF and declined systematically as the numhcr declined from two, suggestingthat the judgements may have based primarily on the number on the left and that L .B .assumed that the numbers were most likely to be the same when there were two on the left .Dependence oil the number on the right was more dichotomous, with the proportion of"same" responses being above 0 .5 for one and two asterisks and below 0 .5 for three and fourasterisks (see Table I ) .

The interaction between the number in the LVF and the number in the RVF was alsohighly significant LX 2 (9)=34.46, P<0.001], indicating at least some degree of interhemis-

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Notes: Diagonal entries represent "same" trials and tire each based on 24presentations . Off-diagonal entries represent "different" trials and arc each based oneight presentations .

pheric communication. To probe this interaction further we examined the influence of thenumber on the right separately for each number on the left . This effect was highly significantwhen there was one asterisk on the left [x 2 (3) =17.67. P<0.001], but not when there weretwo, three or four on the left [g 2 (3)= 3 .81, 3 .35 and 5 .58, respectively] . Moreover, with onlyone asterisk on the left, L .B . was correct on 78 .2% of trials (19/24 "same" and 19/24"different"), which was significantly above chance [y 2 (1)=16.33, P<0 .001] . His perform-ancedid not deviate from chance, and averaged 47 .9% correct, when there were two, three orfour asterisks on the left .

These analyses suggest that L .B, focused primarily on the LVF, tending to respond "same"when there were two asterisks there . but that he also had access to diffuse information as tothe number on the right . This information appears to have been in the form of "one-or-many", so that he was reasonably accurate when there was one on the right, but tended tounderestimate the number on the right when it exceeded two . Thus he was correct on 23 ofthe 24 "same" trials on which there were two on each side, but persisted in responding "same"when there were two on the left but three (75% "same") and four (87 .5% "same") on the right .

This analysis does not necessarily contradict the fact that overall performance did not risesignificantly above chance, since the tendency to underestimate the number on the rightwould have caused systematic error that may have offset any gain from the transfer itself .Thus if we examine his performance for each number on the right, we see that it peaked at75% [ye (I )=12, P<0 .0001] when there were two on the right, and was also significantlyabove chance when there was one on the right [y 2 (I)=5 .33, P<0.05], but fell to 35 .4%,which was significantly below chance [ ;t 2 (1)=4 .08, P<0.05], when there were four on theright. This pattern of results is again consistent with L .B. having based his judgementsprimarily on the number in the IN F, but with access to "one-or-many" information from theRVF.

In summary, then, the results suggest that L, B . generally responded largely on the basis ofthe number of asterisks on the left, perhaps because the right hemisphere is the morespecialized for judgements of numerosity [10, 13, 23], but that crude information as to thenumber on the right had some influence . He appeared to know reasonably accurately whenthere was a single asterisk on the right, but when there were more than two he generallyunderestimated the number . One possible reason for this may be that, while the righthemisphere evaluates numerosity by a holistic process of "subitization" [14], the lefthemisphere does so by counting sequentially, and the limited exposure duration may haveprevented the count from going beyond two on most trials .

'fable l . Proportion of "same' judgements as a function of the number in eachvisual field in Experiment I

No . No . in RVFin FVF 1 2 3 4 Mean

1 0 .792 0 .375 0 .125 0 .125 0.5002 0 .750 0.958 0.750 0 .875 0.8753 0 .625 0.500 0.333 0 .625 0-4584 0 0 .500 0 .375 0 .250 0.271

Mean 0 .625 0,708 0.375 0.396 0.526

JUDGEMENtS AHOU'r NCMEROSITY BY A COMMISSUROTOMtzrD SUR1F(T

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EXPERIMENT 2In this experiment, we provided three response alternatives-"same", "left greater" and

"right greater" . We were prompted in part by SERGFNT'S [18] demonstration that L .B . wasbetter able to judge the relative size of two digits in the two visual fields than to judge whetherthey were the same or different .

MethodThe only difference between this experiment and Experiment I lay in the response requirements . On the first and

fourth sessions of 48 trials L. B . responded with his right hand, pressing the M key with his middle linger to signalthat there were more asterisks on the right, the N key with his forefinger to signal equal numbers on the two sides . Onthe second and third sessions he used his left hand, pressing B with his forefinger to signal 'right greater', V with hismiddle finger to signal "left greater" and the space bar with his thumb to signal "same' .

Results and discussionIf "right greater" and "left greater" responses are combined as "different" responses, L .B .

again failed to score significantly above chance ; his percentage correct was 55 .2[y a (I)=2 .32; n .s .] . When he responded with his right hand he scored 61.5% correct, whichwas significantly above chance [g 2 (1)=8.22 ; P< 0.01], but his left-handed responses yieldedan accuracy of only 49 .0%, which is slightly below chance . 58.85% of the responses were"different" (i .e . either "left greater" or "right greater"), which was a significant bias

(I)=6.02, P<0.05] . Within the "different" category, 62.8% of the responses were "leftgreater", which was a significant bias [x 2 (1)=7.44, P<0.01], perhaps again reflecting atendency to systematically underestimate the number on the right when it exceeded two .

Although the same-different judgements were not significantly above chance, L,B.'scorrect "different" responses nearly always correctly identified the side containing the largernumber of asterisks . On 31 of these trials the larger number was on the left and on all of thesetrials L .B. correctly responded "left greater" . On 32 of these trials the larger number was onthe right and on 28 (87 .5%) of these he correctly responded "right greater" . Table 2 gives adetailed breakdown of L,B .'s responses to the various conditions .

Table 2 . Frequency of judgements of' left greater" (L > ), "same' (5), and "right greater" (R >) for eachallocation of asterisks in Experiment 2

It may seem paradoxical that relative judgements on "different" trials should have been atwell above chance level, while same different judgements themselves did not rise significantlyabove chance. However this is readily resolved once it is understood that it is possible toscore well on relative judgements by considering only the asterisks in a single field .

"Same" conditions "Different" conditionsMore on right More on left

Hemifield

ResponseR>

Hemifield ResponseL> S R>

Hemifield ResponseL> S R>L R L R L R L> S

I I II 12 1 2 1 I 6 2 I 3 5 02 7 17 0 I t 0 0 8 3 I 7 1 03 9 14 1 I 4 0 0 8 4 I 7 1 04 19 4 I 2 0 6 2 3 3 5 0

7 0 4 4 4 2 6 2 03 3 5 0 4 3 5 3 0

Totals 36 46 4 t6 28 31 17 0

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For example, focusing only on the asterisks on the left, the optimal strategy would be torespond "right greater" when there were one or two, and "left greater" when there were threeor four . This would result in correct decisions on 80 of the 96 "different" trials . Indeed, of the63 "different" trials on which L .B . responded "left greater" or "right greater", the optionalstrategy would have produced 57 correct, whereas L .B .'s actual score was 59 correct. And asin Experiment I, the data suggest that he did indeed base his judgements largely on thenumber appearing on the left, but with some crude "one-or-many" information from theright .

The relative proportions of `left greater" and "right greater" responses depended almostentirely on the number on the left ; among the "different" responses . the relative proportionsof "left greater" were 0 .056, 0.625, 0 .956 and 0 .974 for one, two, three and four asterisks onthe left [y 2 (3)=8030, P<0 .001], while the corresponding values for asterisks on the rightwere 0.600,0.739, 0 .560 and 0 .629 [y Z (3)=1 .84, n .s .] . This shows that L .B. did indeed adopta strategy of responding "right greater" when there was one on the left, and "left greater"when there were three or four on the left . The only anomaly was the slight tendency torespond "left greater" when there were only two on the left, but this can be attributed in partto L .B .'s limited knowledge of the number on the right .

The relative proportions of "same' and "different" responses again varied more sharplywith the number of) the left [y 2 (3) 28 .63, P<0 .001] than with the number on the right[y` (3) = 7 .46, P<0-050] . A significant interaction between the numbers on the left and right[y 2 (9) = 19.10, P<0.05] suggests that there was some degree of interhemispheric transfer,and the pattern is again consistent with L .B . attending primarily to the number on the leftand receiving diffuse "one-or-many" information as to the number on the right . As inExperiment 1, when performance was examined for each number on the left, L .B. scored70.8% correct when there was one on the left, which was significantly above chance[y 2 (1)=8.33, P<0.01], but his performance did not differ significantly from chance whenthere were two, three or four on the left .

In this experiment, then" the addition of "left greater" and "right greater" responsesprovided even stronger evidence that L .B . was basing his judgements primarily on thenumbers in the LVF. so that these judgements were presumably under the control of the righthemisphere . As in Experiment 1 . however, there was evidence for access to some informationfrom the RVF . And while overall accuracy in same different judgements did not risesignificantly above chance in either Experiment I or Experiment 2 alone, it was significantlyabove chance when the data from the two experiments were combined [;{ 2 (1)=4.58,P < 0 .051 .

EXPERIMENT 3Experiments I and 2 suggested that L .B. had only limited access to information about the

number of asterisks on the right in comparing the number in the two fields . One possiblereason for this is that the left hemisphere was generally unable to enumerate more than twoasterisks in the RVF, perhaps because of a reliance on a sequential "counting" mode .Experiment 3 tests this . Up to four asterisks were flashed in one or other or both fields, but nomore than four altogether, and the subject was simply asked to report the total number-

Vanod BThe experiment was run under three condition,, One oral and two manual . In each condition there were two

sessions, each consisting of 48 trials, to make a total of 96 trials per condition . I here 96 trial consisted of 24

JUDGEMENTS ARUUT NUMEROSITY BY A COMMISSUROTOMI7ED SUBJECT

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presentations each of one, two, three and four asterisks . Table 3 shows how the asterisks were allocated to the twovisual fields for the different numbers of asterisks, and the frequency of each allocation . Within these constraints, thedifferent allocations were presented in random order .

Under the oral condition, the subject was simply asked to call Out the number of asterisks, and the experimentertyped his answers on the keyboard . Under the manual conditions, the subject responded by typing in the answerswith one hand, using four adjacent keys on the bottom row of the keyboard . With the left hand, the keys V, C, X andZ stood for the answers "one" . "two", "three", and "four", respectively, and with the right hand the correspondingkeys were V, B . N and M, respectively . These options were chosen by the subject, and were such that the index fingerserved to signal "one" and the little finger "four" . lie was able to respond without looking at the keyboard by restinghis fingers lightly on the keys between trials .

The two sessions of oral trials were given first, then sessions with the right, left, left and right hands, in that order .Presentations were again signalled by the experimenter and the stimuli flashed 500 msec later . The subject was toldto fixate the central fixation point on hearing the "ready" signal .

Results and discussion

Table 3 shows the number correct for each allocation under each condition . Performancewas higher under the oral than under the manual conditions [y' (1)=4 .33 ; P<0.05], butthere was no significant difference between the hands . Performance was also generally higherwhen the asterisks were in a single visual field than when they were presented in both fields .This difference was significant for oral [g' (l)=5 .00; P<0.05] and right-hand responses[y' (1)=5 .93; P<0.05], but not for left-hand responses [y' (1)=1 .59 ; ns .] .

Table 3 . Presentation conditions, and number correct under each condition, inExperiment 3

With unilateral presentation, there were slightly more errors in reporting asteriskspresented in the LVF alone (17/90 than in reporting those in the RVF alone (11/90) .Although the difference was not significant [y' (1)= 1 .52 ; n .s .], it should dispel any notionthat the LVF (right-hemispheric) bias evident in Experiments 1 and 2 was due to poorerability of the left hemisphere in enumerating the asterisks . Note in particular that L .B. wasalways correct in reporting four from the RVF, so there was no indication that the stimulusduration was too short for the left hemisphere to count to four, or that the left hemispheretended to underestimate the number when it exceeded two .

Number in :LVF

RVFPresentationfrequency Oral

Number correctL Hand R Hand

1 0 12 12 8 110 1 12 12 11 P2 0 8 7 4 61 l 8 6 1 40 8 7 7 53 0 6 6 5 22 1 6 3 3 31 2 6 4 50 3 6 4 64 0 4 4 43 1 4 3 42 2 8 7 81 4 4 30 4 4 4 4Totals 96 82 71 72

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The RVF advantage applied to both left-hand and right-handed responses, and did notinteract significantly with hand. Curiously, there was a slight LVF advantage with oralresponses (LVF : 29/30 correct, RVF : 26,130 correct) but this was not significant .With bilateral presentation, L .B. was correct on 73 out of 108 trials . While this is clearly

above chance, it is not so very much higher than would be predicted by a sophisticatedguessing strategy based on the number appearing in one field, and the appreciation that atleast one asterisk appeared in the other . For example, if one asterisk appears in the attendedfield, the only possible responses are "two", "three", and "four", but if three appear than theonly possible response is "four" . From these considerations it may be calculated that anoptimal guessing strategy would have yielded 51 correct out of 100 . L .B .'s score of 73 correctwas significantly above this value [y" (1)=19 .37, P<0.001], indicating some degree ofinterhemispheric transfer .

To determine the relative contributions of the two fields tinder bilateral presentation, wesubjected the actual responses to multiple-regression analysis, where the predictors were thenumbers of asterisks on each side . Had L.B. responded with perfect accuracy, the responsewould have been the simple sum of the two numbers (i .e . the regression weights would eachhave been 1 .0) . With oral responses the regressions weights were 0 .967 [t (35)=8 .38,P<0.001] for the RVF and 0.603 for the LVF [t (35)=5 .23, P<0 .001], and for right-handresponses they were 0 .867 [t (35)=6 .44, P<0.001] for the RVF and 0 .413 [t (35)=3 .06 ;P<0.005] For the LVF . Thus although there was significant contribution from each field, theRVF made the larger contribution. With left-hand responses, this was reversed ; theregression weights were 0 .369 [t (35)=3 .19, P<0.005] for the RVF and 0 .641 [t (35)=5 .56,P<0.001 1 for the LVF .

The data therefore suggest that responses in this experiment were controlled primarily bythe hemisphere contralateral to the hand used in the manual conditions, and by the lefthemisphere in the oral condition . In all cases however there was a significant contributionfrom the number on the other side, again suggesting a degree of interhemisphere transfer .

EXPERIMENT 4In this experiment we return to L .B .'s ability to judge whether the numbers of asterisks in

the two fields are the same or different, and explore the effect of introducing structuralconstraints between the patterns in the two fields . Under the repeated condition the "same"patterns were in fact identical ; that is, the positions occupied by the asterisks in the 5-by-5locations grids in the two fields were the same . Under the mirror-image condition the "sane"patterns were in fact left-right mirror images of one another .SERGENT [17] has shown that some correspondences between the visual fields are

accurately detected by commissurotomized subjects (including L.B .), and there is otherevidence that these subjects are sensitive to mirror-image relations between the visual fields[21, 22]. It has also been shown that commissurotimized subjects accomplish mirror-imagecompletions of half-pictures of familiar symmetrical objects presented in a single field [12] .These findings suggest the possibility that L .B .'s ability to make "same"judgements might beenhanced by structural correspondences between the fields .

Method

The basic procedure was the same as in Experiment I, except that the stimuli were constrained to conform toeither repeated or mirror-image patterns between fields . L.B . received eight sessions of48 trials . four with repeatedand four with mirror-image configurations . For the repeated condition . "same" patterns formed the same (randomly

JUDGEMENTS ABOUT SUMEROSITY BY A COMMISSUROTOMIZGD SIonFCI

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chosen) configuration within each 5-by-5 block .- Different" patterns were such that the smaller set was d uplicated inthe other field, and that the extra position or positions filled out at random . For the mirror-image condition . "same"patterns were mirror images about the vertical meridian . "Different' patterns were such that the smaller set wasmirrored in the other field and the remaining position(s) filled out at random . Examples are shown in Fig . 1 .

The repeated condition was presented on the first, second, seventh and eighth sessions, with the mirror-imagecondition on the intervening sessions . L .B . used his right hand for response on the first, fourth, fifth and eighthsessions, and his left hand on the remaining sessions . He was not told about the patterning across fields, and whenlater asked reported that he had not noted anything different or unusual .

Results and discussion

Under the repeated condition, L.B . scored 53 .13% correct, which did not differsignificantly from chance [y 2 (1)=0.87 ; n .s .] . Under the mirror-image condition, however,his performance rose to a significant 61 .45% [y 2 (1)=10.88 ; P<0.01] . Although thedifference between these scores was significant only on a directional test [yx (1)=2 .98 ;one-tailed P<0 .05), this result does suggest that symmetry across the meridian may haveenhanced L .B.'s ability to detect sameness . However there was a strong bias to respond"same" under both conditions, and the difference in accuracy between conditions occurredlargely on "different" trials . Accuracy under the repeated and mirror-image conditions on"same" trials was 72 .88 and 75 .0%, respectively, while on "different" trials it was 34 .38 and47.92%, respectively .

The difference between the conditions cannot be attributed simply to their ordering . L.B .received two sessions under the repeated condition, then two under the mirror-imagecondition, then two more under the mirror-image condition, and finally two under therepeated condition . His accuracy on these pairs of sessions was 54 .17, 61 .45, 61 .45 and52 .08%, respectively . He was therefore consistently better under the mirror-image condition .

Table 4 shows the proportion of "same" judgements as a function of the number in eachfield under each conditions . In both the repeated and the mirror-image conditions, thepattern is similar to that of Experiment 1, except for the stronger tendency to respond"same". Taken over both conditions, the relative proportion of the "same" judgements againvaried significantly with the number on the left [y 2 (3)=41 .97, P<0.001], and this effect did

Table 4. Proportion of 'Same" judgements as a function of the number in eachvisual field under each condition in Experiment 4

No .in LVF I

No. in RVFMean2 3

Repeated condition0 .958 1 .0W 0,175 0 .500 0 .7920 .875 0.917 0 .875 0 .875 0 .8960 .625 0.750 0 .542 0 .750 0 .625

4 0 .250 0.375 0 .625 0 .500 0 .458

Mean 0 .771 0 .813 0583 0 .604 0 .693

0 .958Mirror-image condition

0.250 0 .6880 .625 0 .3751.000 0 .958 0.750 0.750 0 .8960 .250 0 .750 0 .667 0.500 0 .5830 .125 0.375 0.500 0.417 0 .375

Mean 0.708 0,771 0.604 0.458 0 .635

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not interact significantly with condition[ ;(' (3)=5 .34] ; in both conditions, the proportion of"same" judgement peaked with two on the left . And as in Experiments I and 2, the effect ofthe number on the right was less marked, though significant [X' (3)=12 .29, P<0.01], andthe interaction with condition again just failed to reach significance [z' (3)=6 .14] . Howeverthe interaction between the number on the left and the number on the right was highlysignificant [<' (9)=212 .78, P<0.001], indicating that interhemispheric transfer did occur .The triple interaction between condition, the number on the left, and the number on the rightdid not reach significance [;t' (9)=12 .50] . However, if we examine accuracy as a function ofthe number on the right, we see that for the repeated condition the percentage correct was68 .75, 60.42, 45.83 and 39 .58 for one, two, three and four asterisks on the right, while thecorresponding values for the mirror-image condition were 66 .67, 60 .41 56 .25, and 50.00 .That is, accuracy in the repeated condition fell from above chance to below chance, while inthe mirror-image condition it remained at or above chance .

It may seem odd that the mirror-image configuration had a greater effect on the accuracyof "di fferent" judgements than of "same" judgements . Even in the case of a difference betweenthe fields, however, the mirror-image relation held for the asterisks in common between thetwo fields, and may have helped the subject detect the "excess" on one or other side .

GENERAL DISCUSSIONThese experiments confirm previous evidence that L .B . is relatively poor at integrating

information across the two fields, both in judging the sameness or difference of quantities inthe two fields (Experiments 1, 2, and 4) and in enumerating the number of asterisks whenthey straddle the fields (Experiment 3) . By contrast, he is relatively accurate in enumeratingthe number in a single field (Experiment 3) ; others have similarly found that L .B . has littledifficulty in verbally reporting information in the EVE when the number of responsealternatives arc relatively few and arc known in advance [7, 8, 15] . This suggests that theproblem of integration is in part one of attention rather than one of interhemisphericcommunication per se .

Although commissurotomy may reduced the ability to allocate attention to both visualfields, L .B . seems to have had little difficulty switching attention to one or other field . InExperiment 3 lie was able to report the number of asterisks quite accurately when they werepresented to one side only. regardless of which side, suggesting that control was quicklyallocated to the hemisphere corresponding to the side containing the asterisks; this musthave been dependent on rapid appreciation that one field was blank . Even when presentationwas bilateral, attention could be allocated to either hemisphere (cf. Ref. [11]) . InExperiments 1, 2 and 4 it was evidently the right hemisphere that assumed control, perhapsbecause enumeration of elements tends to be right- rather than left-hemispheric [10, 13, 23] .But in Experiment 3 control seemed to be left-hemispheric when L .B . responded orally orwith the right hand and right-hemispheric when he responded with the left hand . Thisdependence on hand, not evident in the other experiments, may have arisen because the fourresponse alternatives required more exacting control over distal musculature, favouring thecontralateral hemisphere [4] .

Superficially, at least, L .B. scored well above chance when required tojudge whether therewere more asterisks on the left or right (Experiment 2), or when reporting the total numberwhen there were one or more asterisks in each visual field (Experiment 3) . However thesedata could be attributed largely to sophisticated guessing . and warn against inferring

JUDGEMENTS ABOUT NIIMFROS]TY BY A COMMISSUROTOMIZGO SUBJECT

87 5

interhemispheric transfer when accurate performance can be achieved by referring to theinformation on one side only .

Conversely, however, performance that does not rise significantly above chance need notimply lack of transfer . In Experiments I and 2 there were highly significant interactionsbetween the numbers of asterisks in the left and right visual fields, indicating interhemis-pheric transfer of information even though accuracy of performance was overall barely abovechance. This transfer seems to have been essentially binary, signalling whether there were"one" or "many" asterisks on the unattended side . The tendency to underestimate thenumber when there were more than two appears to have created systematic errors, so thattransfer is not truly reflected in the accuracy of same difference judgements .

It is conceivable that transfer from the unattended side was based on cross-cueing . Forexample, in making same different or relative judgements, L .B_ may have been able to cuethe presence of a single asterisk on the right . We were at pains to prevent obvious cross-cueing via the hands or feet, or through vocalization, but cross-cueing of, say, the presence ofa single asterisk may still have been possible (e .g . via a tongue movement) . Cross-cueing isperhaps unlikely, however, since it implies attention, whereas our analyses suggest that L .B .had difficulty attending to the side from which transfer occurred . It is perhaps more likelythat limited transfer occurred via the tcctal and pretectal decussations [7], or possibly withinthe cerebellum [6] .*

Although our results suggest some degree of interhemispheric transfer, they neverthelesscontrast with other evidence that interhemispheric integration in commisurotomizedsubjects can be both fast and accurate in certain perceptual tasks . SERCEN I [16] found thatthe L.B. scored well above chance in several tasks requiring the perceptual integration ofinformation across the vertical meridian, such as judging whether two lines are aligned orwhether two lines would meet at an angle of greater or less than 90° . These tasks may be lessdependent on attention to both visual fields than tasks requiring same-different judgements .This might help explain why same different judgements were facilitated by the presentationof bilaterally symmetrical displays in Experiment 4, since symmetry may operate at a pre-attentional level [21, 22] . Jut .rsz [9] has argued that one mechanism of symmetry detectiondepends on point-to-point connections between symmetrical regions of the brain andsuggested that it might be a throwback to a stage in evolution when the eyes were morelaterally placed . This is consistent with a subcortical route for the symmetrical mapping .

In summary, the level at which attention is allocated appears to be an important factordetermining interhemispheric integration following commissurotomy . In making same --dif-ferentjudgements across the fields, it seems that attention to both fields is critical to accurateperformance, and the commissurotomized subject is able to attend effectively to only onefield . The data on the effects of symmetry, as well as SERGENT's [17] data, show that in moreelementary perceptual tasks integration may occur at a more automatic, "implicit" level, sothat attention can then be directed to a percept that has already been unified .

Acknowledgements-We thank .1 . F. Bogen and R . W. Sperry for permission to test the subject, C . R . Hamilton forhelping with the arrangements, and L .B . for his cheerful cooperation .

*In all four experiments, RTs for manual responses were recorded from the offset of the stimuli . but detailedanalyses are not presented in this paper . However responses were fast, and seem to preclude elaborate cross-cueingstrategies, or the sorts or rehearsal processes described by MYERS and SPERRY [12] . The mean RTs were [042 msec,1 t30 cosec and 829 ntsec in Experiments 1, 2 and 4, respectively, and 1116 msec for the manual conditions ofExperiment 3 .

8 7 6 M. C . CORBAI .ras and J . SERGENT

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