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29 A Mental Clock Setting Process Reveated by Reaction Times*
Tutorials i n Motor Behavior G.E. Stelmach and J . Requin (eds.1 0 North-Holland Publishing Company, 1980
29 A Mental Clock Setting Process Revealed by Reaction Times* David A. Rosenbaum and Oren Patashnik Bell Laboratories Murray Hill, New Jersey 07974
To study the preparation of timing for forthcoming movements we require subjects to produce specified time intervals between two responses and also to minimize the simple reaction time (RT) for the first response. RTs are longer when a specified interval must be produced than when no second response is required, and RTs increase as target intervals decrease from 1050 to 50 msec. We reject the hypothesis that these effects are due to "competition" between the two responses, to processing of visual feedback about the intervals, or to a process of adjusting the covariance of the motor delays for the two responses. We argue that the effects can be attributed to a mental clock setting process whose duration is predicted by an analogue of Fitts' Law. That the clock setting process is not used exclusively for timing overt movements is shown in an additional experiment. We infer from the latter result that a central clock is used to time motor and perceptual events. We infer from the applicability of Fitts' Law to mental clock setting that processes of movement prepmarion bear an isomorphic relation to processes of movement execurion, although the former are much faster than the latter. I. Introduction In this paper we describe a series of experiments on how people control time delays between successive movements. The work reported here extends work that we have reported elsewhere (Rosenbaum & Patashnik, in press), and focuses on the preparation of movement timing. We believe that the study of movement timing preparation may help shed light on some issues of long-standing concern in the motor control research area. One such issue is whether motor programs are used to control movement timing when proprioceptive feedback is available ( A d a m , 1977; Cauraugh & Christina, 1978; Kelso, 1978). If one can show that the delay between two movements is prepared before the first movement is executed, even if there is enough time to use proprioceptive feedback from the first movement to time the onset of the second movement, it can be concluded that motor programs are used when proprioceptive feedback is available. Another issue that may benefit from the study of movement timing preparation is the nature of motor programming. If one can discover how the characteristics of timing preparation are related to the temporal characteristics of subsequent movements, it may then be possible to develop detailed models of the programs used for timing control. The experimental procedure we have used to study the preparation of movement timing is shown in Figure 1. In each session the subject's task is to produce one specified time interval between two responses (key presses made with the left and right index fingers). The specified intervals range from 0 to 1050 msec. On each trial we give feedback to help the subject produce an approximation to the specified interval. The feedback takes the form of a vertical line on a CRT screen. The line points up if the produced interval is too long and down if the produced interval is too short; the length of the line shows how large the proportional error is. (More details about the feedback are given in Rosenbaum & Patashnik, in press.) Besides producing the specified interval, the subject is also required to make the first response as quickly as possible after the onset of the reaction signal, that is, to minimize the reaction time (RT). The length of a horizontal line on the
* We thank Ronald L. Knoll, Judith F. Kroll, David L. Noreen, and Saul Sternberg for
suggestions, and Gwen 0. Salyer for assistance with data collection. This paper was formatted with a Bell Laboratories computer phototypesetting system.
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D.A. ROSENBAUM AND 0 . PATASHNIK
screen shows the subject how long the RT is. Our working assumption is that the length of the RT reflects the duration of timing preparation.
REACTION SIGNAL
I
WARNING ;SIGNAL
RESPONSE (LEFT HAND)
RESPONSE (RIGHT HAND)
FEEDBACK
p. 5 I
Fig. 1. Overview of the experimental procedure. “Catch trials” were used 25% of the time to discourage anticipation responses.
Figure 2 shows the results of our first experiment. Here three right-handed women who had had extensive practice in the interval production task participated in eight one hour sessions each. In each session one interval was tested in eleven blocks of 60 trials, with the first block for practice. As is seen in the left panel of Figure 2 , mean RTs declined as target intervals increased, for target intervals greater than or equal to 50 msec. The RT curve dropped at 0 msec, and the subjects said that this condition seemed qualitatively different from the rest in the way the interresponse intervals were controlled.’ An aspect of the RT data that we find particularly interesting is that for every subject RTs were longer when two responses had to be made (regardless of the required interval) than when only one response had to be made -- in the condition we call “infinity“ ( m ) . The panel on the right gives an indication of how precisely the intervals were produced. For all three subjects mean produced intervals were within a few msec of their corresponding target values, and mean interval variances increased linearly with interval means. How can these results be interpreted? One of the first models we developed is shown in Figure 3. We call it an alarm clock model. The model says that after the reaction signal is detected, an internal alarm clock is set to tick n times. Once the value of n has been set to the subject’s satisfaction, the ticking process is begun and the first response is executed after a motor delay, d l . After the nth tick has occurred, an “alarm”goes off, as it were, and response 2 is executed after a motor delay, d2. The linearly increasing variance function is explained by saying that variance accumulates with each delay between successive ticks of the clock. The model says that delays between clock ticks fluctuate randomly about a mean and that successive intertick delays are stochastically independent (see Wing & Kristofferson, 1973). With this type of model, the RT data shown in Figure 2 can be explained by saying that it takes less time to set the clock as the value of n increases. This could come about if the clock’s setting returned to some large value of n after each usage, or if there were fewer possible settings as n increased. In the next section of this paper we will consider some alternatives to the alarm clock model which we have tested and rejected. Then, in Section 111, we will show that the alarm clock model, as described above, fails to explain two of the major results that we obtained in testing alternatives to the alarm clock model. A revised and more specific alarm clock model will then be described. In Section IV, we will address the question of whether the clock setting process is unique to the timing of movements. We will show that it is not. Finally, in Section V, we will review the main results of our experiments and consider some of their theoretical implications.
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MENTAL CLOCK SETTING PROCESS
310
LA
25T,, ,
I
050150 300
I
I
500
750
105d tn MEAN INTERVAL, I
(msec)
Fig. 2. Results of the first experiment> averaged over the three subjects. The values on the abscissa designate the target intervals, and the plotted points, each of which represents a mean of about 1300 observatons, are plotted above the corresponding mean obtained intervals. Errors of responding on catch trials, responding before the reaction signal was presented, or responding first with the right finger when nonzero intervals were required occurred altogether on less than 2% of the trials in each of the eight conditions. ( A ) Mean RTs and estimate of standard error ( t S E ) . The three subjects had similar functions: The mean RT function for the 2-response conditions accounts for 93.7%, 98.4%, and 96.9%of the variance of mean RTs for corresponding conditions for the three subjects, respectively. (B) Mean interval variances, fitted linear function, and estimate of &SE. Linear regression accounts for 98.9% of the variance of mean variances, which is not significantly surpassed by fitting a quadratic function to the same points. Slopes (in msec) and zero-intercepts (in msec') of fitted linear functions for the three subjects are 8.64 and 141.44, 2.57 and 39.80, and 6.87 and 273.90. respectively. Estimates of +SE here and in all other figures are based on mean squares from fits of mean functions to individual subject data.
i i i 1" i h I I II I I
I I
I
II I
rdq
I
I
I
Fig. 3. An alarm clock model for performance in the interval production task.
"
D.A.
490
ROSENBAUM AND 0. PATASHNIK
11. Alternatives to Clock Setting
A. Response Competition One alternative to the clock setting model says that the RT effect we obtained is due to competition between the two responses, where the amount of competition, and hence the RT, increases as the delay between responses decreases (up to values near 0 msec). (For discussions of competition between responses in RT experiments, see Rosenbaum, in press, and Sternberg, Monsell, Knoll, & Wright, 1978.) The response competition hypothesis allows that the delay between triggering of response 1 and response 2 may be controlled by a clock, but it says that any clock setting activity that occurs during the RT takes a negligible or constant amount of time. According to the response competition hypothesis, the RT should depend on the interresponse interval but not on the variability of interresponse intervals. We tested this prediction in an experiment whose results are shown in Figure 4. In one condition we had subjects attempt to produce the same intervals as in the first experiment, with the same accuracy requirements as we had used in the first experiment; we called this the "stringent" condition. In another condition -- the "relaxed" condition we had the same subjects attempt to produce the same mean intervals, but now they were allowed to have much higher interval variances. To get the subjects to do this, we simply reduced the scale of the vertical feedback line so that in most cases subjects could only tell if the intervals they produced were too long or too short
--
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STRINGENT S 2 ( I l =161.96+6.261
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205hl, I I 050150 300 500
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?do
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1050 m MEAN INTERVAL.
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050150 300 500
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Fig. 4. Results of the second experiment. Details of the procedure and results can be found in Rosenbaum and Patashnik (in press).
As is seen in the right panel of Figure 4, interval variances were higher in the relaxedcondition than in the stringent condition. but interval means in the relaxed and stringent conditions were close to one another and also close to the target values. As is seen in the left panel of Figure 4, the pattern of mean RTs in the srrtvgenfcondition was like the pattern of mean RTs in the first experiment (although the range of RTs was smaller here with this different group of subjects). In the relaxed condition mean RTs were significantly shorter than in the sfringen/ condition, and the effect of target interval (including the reduction of mean RTs for the 0 msec target) was virtually eliminated;
MENTAL CLOCK SETTING PROCESS
49 1
an analysis of variance showed that the interaction between target interval and degree of required precision was statistically significant. The results from the reiuxed condition argue strongly against the response competition hypothesis, which predicted that mean RTs should depend on mean interresponse intervals. In general, the data from this experiment indicate that mean RTs depend critically on the precision with which interresponse intervals must be produced.
B. Some Response Competition and/or Visual Feedback Processing We cannot rule out the possibility that in the above experiment there was some effect of response competition on RT, because mean RTs were longer when two responses had to be made than when only one response had to be made. To determine whether there was some effect on RTs of merely having to make a second response, we conducted the following experiment. Subjects were told to respond as quickly as possible with the left index finger when the reaction signal appeared (as in the previous experiments) and then to respond with the right index finger any time lurer. We told the subjects that the second response was necessary merely "to turn on the feedback signal." In the control condition of this experiment no second response was required. Our aim was to find out whether the RT for the first of two responses could be as small as the RT for just one response when there was no pressure to produce a specific interresponse interval. In this experiment we also wanted to check on the possibility that RTs were longer for two responses than for one because of the need to study the vertical line that gave feedback about the interresponse intervals. To test this hypothesis in the new experiment, we presented a vertical line in the 2-response condition and told subjects that when the vertical line pointed up they should prepare to respond normally in the next trial, but when the vertical line pointed down they should refrain from responding in the next trial, even though the reaction signal would appear. This made it necessary for subjects to attend to the vertical line after making the second response. After trials in which the vertical line pointed up, the following events occurred. On 75% of the trials both the warning signal and reaction signal appeared, and after the second response was made the vertical line again pointed up with 75% probability. On the remaining 25% of the trials (following trials with an upward-pointing line). after the warning signal appeared no reaction signal was presented. In these catch trials no vertical line appeared, but the subject was instructed to get ready to respond on the next trial. The vertical line had a fixed length approximately equal to its mean length in the second experiment reported here. We made it clear to the subjects that the behavior of the vertical line did not depend in any way on the interresponse intervals. There were four subjects, all of whom had been in one or more of our previous experiments. After practicing the 2-response task for 1 hr, each subject returned the next day for a 1 hr session consisting of five 2-response blocks followed by five I-response blocks, or the opposite. Each block had 25 trials, and the first block in each half of the second session was for practice. Catch trials occurred on 25% of the trials in the I-response condition.
For every subject, errors of responding before or in the absence of a reaction signal occurred on less than 2% of the trials in both the 1-response and 2-response conditions. In the entire experiment there were only three errors of failing to respond correctly to the vertical line. The remaining discussion will be concerned with errorless trials only. Table 1 shows the main results of the experiment. Even though in earlier experiments each of the subjects had produced longer RTs for the first of two responses than for just one response, here mean RTs were the same when just one response had to be made and when the first response could be followed any time later by the second response. This result implies that it was not simply the need to make a second response that lengthened RTs. (This conclusion is supported by the fact that the mean produced intervals were generally within the range that was required before. Moreover, the produced intervals had higher variances than were found earlier for intervals with comparable means.) A second conclusion we reach with the present experiment is that the need to attend to the vertical feedback line did not cause RTs to be longer in the 2-response conditions than in the I-response condition of our earlier experiments, although we cannot rule out the possibility that earlier there was some effect of having to study the Irtrxth of the line. Notwithstanding the latter possibility, our main conclusion is that in the previous experiments RTs were lengthened by a process responsible for precisely controlling the interresponse intervals.*
D.A. ROSENBAUM AND 0 . PATASHNIK
492
Table 1 Mean Reaction Time (RT) and Interval (1) When 1 or 2 Responses Were Required
Subject 1 2 3 4 Mean
Number of Reauired Resoonses 1 2 RT sd RT sd I sd 201.5 27.8 200.4 26.5 384.6 92.6 199.8 18.9 200.6 21.3 1059.4 149.4 201.8 26.4 200.1 21.2 943.6 186.9 202.3 23.8 202.4 23.7 326.7 187.0 201.3 24.2 200.8 23.1 678.5 153.9
C. Response Delay Covariance
Is there any kind of process other than a clock setting process that could affect the precision of interresponse intervals and also lengthen RTs? One possibility is that during the RT the subject sets the covariance between the motor delays for the two responses ( d , and d2), possibly by adjusting muscle tensions in the two arms. The rationale for this response delay covariance model is that as cov(dl,d2) increases, vur(f) will decrease. Therefore, it is to the subject’s advantage to maximize cov(dl.dz). Suppose, however, that it takes time during the R T t o set rov(d1, d2) for a forthcoming response sequence, such that the time needed to set c o v ( d l , d 2 ) increases with the level of c o v ( d l , 4 ) that is actually achieved. If we assume that the RT effects obtained in the first two experiments reflected differences in the time spent setting c o v ( d l , d z ) , and did not reflect differences in the time spent setting a clock that may have been used to control the delay between the triggering of response 1 and response 2, the response &lay covariancr model predicts that cov(d1, 4 ) should increase as mean RTincreases. We tested this prediction as follows. Suppose the following two relations hold:
where P i s a random variable representing the time to prepare a forthcoming interresponse interval f (that is, P includes the time to detect the reaction signal, set c o v ( d l , d 2 ) and , carry out all other aspects of preparation that precede response 1). and C i s a random variable representing the total duration of clock ticking. The covariance of RT and I, c o v ( R T , I ) , is then
cov(RT,I) = cov(P,C)
rov(d1,Cf
+ cov(P,d2) - cov(P,dl) + + COV(dl,d2)- cov(dl.dl)
(2)
If we assume that all the random variables in (2) are independent except dl and d2, and also that c o v ( d l , d 2 ) is independent of mean d2, we have cov(RT,/) = c 0 v ( d l , d 2 ) - c o v ( d l , d l ) = cov(dl,d2) - var(d,) .
(3)
For the stringentcondition of the second experiment, where mean RTs decreased to an asymptote as mean interresponse intervals increased (to approximately 1050 msec), the prediction of the response deluy covariance model is that as mean interresponse intervals increase, cov(dl.d2) should approach 0, so that c o v ( R T , / ) should approach -vur(d,) as an asymptote. Of course, we cannot independently measure -var(dl),so the specific prediction stated above cannot be tested. Nevertheless, we can see whether c o v ( R T , f ) approaches an asymptote less than 0, where this asymptote is assumed to approximate -var(dl). Figure 5 shows cov(RT.I) in the sirinKent condition of the second experiment. As is seen in the figure, cov(RT,f) remained fairly constant at about -56 msec’ in the 50-1050 msec range. The slope of the best-fitting straight line for these points was only .005, and did not differ significantly from zero. The flatness of this curve contradicts the prediction of the response drlay covuriance model. Since the mean c o v ( R T . I ) in the 50-1050 msec interval range was negative, the simplest
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MENTAL CLOCK SETTING PROCESS
explanation of the data seems to be that cov(d,.d2) in this range was approximately zero, in which case cov(RT, / ) = - v a r ( d l ) . One reason why this seems like a reasonable explanation is that Wing and Kristofferson (1973) and Vorberg and Hambuch (1978) obtained estimates of response delay variance quite close to 56 msec2.
H
t=
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40
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8 z
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a w
5
t
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050 150 300
I
500
I
750
1
1051
MEAN I N T E R V A L , I ( m S e C ) Fig. 5. Mean c o v ( R T , / ) , averaged over the three subjects, in the sir~~igenfcondition of the second experiment. For the 0 msec target condition, algebraic values of I were used to compute c o v ( R T , / ) ;that is, intervals where the right finger led the left were considered negative. The resulting estimate of c o v ( R T , I ) did not differ significantly from zero. (When absolute values of I were used, the estimate of c o v ( R T , I ) did not differ significantly from zero or from the estimate obtained with algebraic values.) For the nonzero conditions, slopes (in rnsec) and mean covariances (in msec2) were .01 and -72.06 -.003 and -21.86, and ,008 and -74.81 for the three subjects, respectively. If we examine c o v ( R T , / ) for the relaxedcondition of the second experiment, we find similar effects to those described above. In the relaxedcondition, the .slope of the best-fitting straight line for values of c o v ( R T , I ) in the 50-1050 msec interval range was ,001 (not significantly different from zero), and mean c o v ( R T , I ) was -60 msec2, The fact that mean c o v ( R T , I ) in the relaxedcondition was close to (and not significantly different from) mean c o v ( R T , I ) in the stringenrcondition violates the prediction of the response delay covauatice model that c o v ( R T . / ) should depend on RT. For the first experiment, the slope of the best-fitting straight line for values of c o v ( R T , / ) in the 50-1050 msec range was only -.008 (not significantly different from O ) , and mean rov(RT.1) in this range was -51 msecC2. The flatness of this slope, like the flatness of the slope in the sfringenicondition of the first experiment. militates against the response delqv covariance model. (It is interesting to note that c o v ( R T , I ) for / = 0 was markedly different from the other values. This finding appears to support subjects’ introspective reports that the simultaneous response condition was qualitatively different from the other conditions.) 111. Clock Setting Models So far we have explained why we do not favor a simple response cornpetifion model or a simple wsponse del0.v covariancr model. Now we turn to the kind of model we favor -- an alarm clock
modeL
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D.A. ROSENBAUM AND 0. PATASHNIK
Earlier, we proposed one kind of alarm clock model which we can now reject. This model said that the time required to set the alarm clock during the RT decreased as the desired set time Le., the desired value of n) increased. We can now reject this model because in the reluxpdcondition of the second experiment we found mean RTs to be essentially unrelated to interval means, and also because the second experiment showed that interval prerwon was the key determinant of mean RTs. What other kind of alarm clock model can be considered then? As a way of addressing this question, let us consider how a mental clock setting process might differ from the process of setting an external clock, say, the alarm clock in one's bedroom. In setting a conventional bedroom alarm clock, once the clock has been set it can be made to go off at its set time on future occasions without being reset. For example, if such an alarm clock is set to go off at 6 o'clock one morning, all that has to be done to make the alarm clock go off at 6 o'clock some later morning is to turn on the alarm system the preceding night; the alarm clock does not have to be reset. Now if all that was involved in reusing a mental alarm clock was reactivating the alarm system, one would not expect the time required to start the clock to depend on the clock setting. Suppose that unlike the bedroom alarm clock the mental alarm clock stores its previous set times, but it does so imperfectly (see the left panel of Figure 6 . ) Suppose that after the alarm clock has been used in an experimental trial its setting driftsrandomly so that at the start of the next experimental trial the setting is some expected amplitude, A , away from the clock's target setting, TI, for desired interval /. (We will assume that A is the same for all values of 1.) As a result of this random drift, before the clock can be used again for the production of interval l the clock's "pointer" must be moved back through A, that is, the clock must be reset at T,.
50150 300
L
I
500
1
750
1
1050
Fig. 6. Schematic diagram of a clock whose "pointer" drifts randomly over an expected amplitude A after being positioned within a window of size W, around a target setting T, [left panel]. Obtained RTs (empty and filled points for the sfrimen[ and relaxed conditions of the second experiment, respectively) and RTs predicted by applying Fitts' Law to mental clock setting [right panel].
Now, we found that RTs are affected by the precision of produced intervals. This fact leads us to suggest that the subject places a "tolerance window" of size W , around the target setting for I. W, is important for two reasons. First, if we assume that the clock does not have to be reset if the pointer is within the window, then as W, decreases, the likelihood of having to reset the clock will increase. Second, if we assume that W, defines the range of settings to which the pointer can be returned before the clock is reused. the precision required to return the pointer to within the window will increase as W, decreases.
We assume that W, depends both on the size of l a n d on the subject's motivation for precision. The nature of these dependencies can be established as follows. Let the random variable N be the number of clock ticks between the triggering of response 1 and 2 . Let the time between ticks I - 1 and (1 < I < n ) be a random variable X , , where the random variables X , are independent of Nand identically distributed as a random variable X with finite mean and variance. The interresponse interval, 1, is
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MENTAL CLOCK SETTING PROCESS
I-X,+...+X,+D
(4)
,
where D is a random variable representing the difference between response delays d , and d2, and where X , , N, and D a r e mutually independent. Using the expression for the variance of a random sum (Parzen, 1962. p. 561, we have Vur ( / )
=
E ( N ) Vur (XI
+ Vur ( N ) E 2 ( X ) + Vur (0) .
(5)
Recalling that we found Vur(/) to be linearly related to E ( I ) , and noting that E(I)-E(D) E") = E(X) ' we have
(6)
As stringency and I are varied, all the terms in (7) are assumed to be constants except for Var ( N ) and E ( / ) .. Therefore, we can rewrite (7) as
+ c 2 E ( / ),
Vur ( N ) = c,
(8)
where and c2 are constants. In view of the fact that a qualitatively different kind of timing control seemed to be used in the 0 msec condition and in the other 2-response conditions, it seems reasonable to assume that for the 0 msec target interval the clock is not used. Thus, for E f l ) = 0, Y u r ( N ) = 0, in which case we can set cl = 0. We also assume that when there are n clock ticks the clock is initially set at ti Ke., that there is perfect correspondence between the number of ticks that are set and that occur). We can now characterize the range of clock settings used in repeated attempts to produce a desired interval / by the standard deviation of clock settings, (9)
W , = A r n ,
where h
= ,/q.
With the above assumptions, we can liken the process of setting a mental alarm clock to the process of positioning a clock pointer to a setting within W,. I n order to characterize how the time required for such repositioning could depend on W,, let us turn briefly to studies of owrrpositioning movements, in particular to manual positioning movements. When the hand must be moved to a target of width Wover a distance A, the movement time is found to be a linearly increasing function of log2(2A/ W ) . This relationship is known as Fitts' Law (1954). We will now show that mean RTs in our interval production task can be accounted for with the following analogue of Fitts' Law: a.
RT,=
a
for W, 2A
+ 6 log2 -,
W,
>> A
otherwise.
(10)
Here a represents the time to make a response to the reaction signal when the clock does not have to be reset (i.e.? when the clock pointer is already within W , ) , and 6 represents the time per bit of information transmitted, where the number of bits is given by log2(2A/ W,). When W, is very large relative to A (i.e., W > > A ) , and if the clock pointer is initially set near T,. the pointer will rarely drift outside of W,. Consequently, the number of occasions on which the pointer will have to be repositioned to a setting within W, will approach zero as W, increases. In the rchcdcondition of the second experiment, where theoretically W, was very large relative 10 A , mean RTs were roughly constant across changes in I . Thus, we can set a equal to the mean R T i n the reluscd condition3.
In the w i t i w n / condition of the second experiment, where W, theoretically was much smaller than in the rrluxedcondition, there would have been many more occasions on which the clock pointer had to be repositioned to within W,. For the sn.//~~r/iicondition, therefore, we must describe how repositioning times would vary across changes in I. To do so, we turn to the second line of (10). We note first that the second line of (10) can be rewritten as
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D.A. ROSENBALM AND 0. PATASHNIK RT/
=
u
1 + b(l+/og2A--l0g2k---log2E(I)) 2
The observed range of mean RTs in the between RTlO5O and RTso, which is
StringEnt condition
.
(11)
can then be expressed as the difference
(The obtained mean intervals in the 1050 and 50 msec conditions were so close to their corresponding target values that we use the target values here and in all other computations involving E ( / ) . ) The value of bcan then be estimated as 7.74 msec/bit (or 129 bit/sec). In order for RTIflSoto equal 230 msec (the observed value of RTloso in the srringentcondition), we must make 1 6(1+/og2A-/oK2k--10g21050) = 230 - 222msec . (13) 2 Thus, (1+/0~2A-l0g2k)
=
6.05 b/t ,
(14)
in which case ! i = .03 A. We can now predict RTs for the remaining intervals, and those predicted RTs are contained in the upper curve in the right panel of Figure 6. The predicted RTs account for 97.4%of the variance among mean RTs in the stringent condition. With our application of Fitts’ Law we can account for interval variance data as well as mean RT data. By making use of Eqs. (6) and (8), we can rewrite Eq. ( 5 ) as
+
V a r ( / ) = ~ ( / ) [ c j k2c4I
+ c5,
(15)
where c3, c4, and c5 are constants. We have assumed that /+the factor that determines how large W /is in relation to E(I)--was much larger in the rrluxrdcondition than in the stringentcondition of the second experiment. Thus, according to (15), the slope of the interval variance function should be larger in the relaxedcondition than in the stringent condition, and the zero-intercepts of the two functions should be equal. This is essentiallywhat we found (see Fig. 4B). It should also be noted that the assumptions and results concerning coov(RT,/), presented in Section IIC, are consistent with the Fitts’ Law model. (According to the model, the time to prepare any particular interval whose corresponding target setting is within W,should be no different, on the average, than the time to prepare any other such interval having the same target setting. Thus, the model assumes cov(P,C)=O, which is necessary for the covariance results to be consistent with the model.) Because of the success of the Fitts’ Law model, we believe that the model is a reasonable way of conceptualizing preparation in the interval production task. Later, we will consider the possible implications of this development for interpretations of Fitts’ Law and for an understanding of the relation between the preparation and execution of movements.
IV. Centrality of Clock Setting We turn now to the issue of whether the clock setting process is used exclusively for timing delays between overt movements. I t is also possible that the clock setting process is used for timing delays between movements and stimuli or delays between two (or more) stimuli. We investigated whether the clock setting process is used for timing the delay between a movement and stimulus by conducting the following experiment. As before, on 75% of the trials a reaction signal appeared and the subject was required to respond as quickly as possible with the left index finger. This response defined the start of the subject’s interval, as was the case in the earlier experiments. Now, however, the end of the interval was defined by the onset of a brief burst of vibration applied to the tip of the subject’s right index finger. The vibration was delivered with a Bimorph bender (Vernitron No. 60572) for 20 msec at 200 Hz. In each session there were several different delays between the response and stimulus which were distributed around a single target interval. The subject’s task on each trial was to say whether the presented delay was longer or shorter than the target interval. For each target interval we presented six equally spaced response-stimulus intervals, using the method of constant stimuli. The mean of these six test intervals was equal to the target interval,
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the range was approximately equal to 98% of the mean range of produced intervals for the corresponding target interval in the sir/ri:eni condition of the second experiment, and the test intervals closest to the target interval were presented three times more often than the test intervals farthest from the target interval and one and a half times more often than the test intervals at the middle distance from the target interval. Each of the three subjects was permitted to take as long as needed to give her verbal time judgment. Feedback took the same form as in the earlier experiments except that the word "Right" or "Wrong" was added to the display. There were five blocks of 48 trials each in every session, with the first block for practice. The results are shown in Figure 7. As is seen in Panel A , mean RTs decreased with target intervals and mean RTs were longer when time judgments were necessary than when subjects simply made one response. As before, mean variances increased approximately linearly with intervals; the slope and zero-intercept of the linear function fitted to the mean variance points were comparable to what we found in the 2-response experiments.
s -E 0
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Fig. 7. Results of the time judgment experiment, averaged over the three SUbjeCtS. Each point represents a mean of about 430 observations. Errors of responding on catch trials or responding before the reaction signal was presented occurred altogether on less than 2% of the trials in each of the seven conditions. (A) Mean RTs and estimate of +SE. For all subjects mean RTs were shortest in the m (no judgment) condition. The mean RT function in the judgment conditions was quite representative of all subjects, as is shown by the fact that the mean function accounts for 99.1% 92.7%, and 98.5% of the variance of mean RTs for the three subjects, respectively. (B) Mean variances (averaged over the three subjects) of the psychophysical functions for each target condition, fitted linear function, and estimate of t S E . The method used to estimate variances comes from Woodworth and Schlosberg (1954, pp 204-210). Linear regression accounts for 98.8% of the variance of mean variances, which is not significantly surpassed by fitting a quadratic function to the same points. Slopes (in msecf and zero-intercepts (in mse& of fitted linear functions for individual subjects are 3.61 and 28.54, 5.15 and 43.89, and 5.71 and 26.73, respectively.
These results add weight to our conclusion that the main RT effects obtained in our earlier experiments were not due to response competition or adjustment of response delay covariance, since in the present experiment there was no overt second response. The main conclusion we can reach with the present experiment is that the clock setting process used for interresponse intervals is also used for timing delays between movements and stimuli. (One could imagine that in the time judgment task the mental alarm clock was set to go off near the target time so that time judgments could be made by judging the order of detection of the alarm and vibration.)
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V. Conclusion The main results of this study can be summarized as follows. First, we have shown that the time to make the first of two responses depends on the required precision of the interresponse interval and does not merely depend on there being a second response or on the requirement to make use of visual feedback. Second, we have shown that this RT effect does not derive from a process of adjusting the covariance of motor delays for the two responses. Third, we have shown that our RT results can be explained by a clock setting process whose duration is predicted by an analogue of Fitts’ Law. Fourth, we have shown that the clock setting process is not used exclusively for the timing of overt movements. What are the theoretical implications of these findings? One implication concerns the use of proprioceptive feedback in movement timing. Many interresponse intervals that we required were long enough for proprioceptive feedback from the first response to be available to control the onset time of the second response. Yet even for such long interresponse intervals, we found that RTs were longer than when no specific interresponse interval had to be made. This result leads us to believe that the availability of proprioceptive feedback does not eliminate the need (or at least the tendency) for motor preprogramming. A second implication of our study concerns the application of Fitts’ Law to the hypothesized clock setting process. To our knowledge, the present study is only the second to use Fitts’ Law to account for RT data. The first such study was by Fitts and Peterson (1964). The fact that Fitts’ Law can be applied to RT data as well as movement time data (see Langolf, Chaffin, & Foulke, 1977, and Schmidt, Zelaznick, & Frank, 1978), implies that Fitts’ Law may be a very general description of the relation between speed and precision in human performance.
We would like to go a step further, however, and propose that the applicability of Fitts’ Law to RT data as well as movement time data (for the motion of a hand to a target) suggests that processes of movement preparation bear an isomorphic relation to processes of movement execution4. One of the identifiable differences between the two kinds of processes, however, is that preparatory processes occur much more rapidly than execution processes. That this is so is implied by the fact that estimates of information transmission rates (llb) for RTsare much higher than for movement times: Fitts and Peterson’s estimate of Ilb for RTs was 185 bitlsec and our estimates of I l b for RTs have ranged from 57.6 to 137 bitlsec in the experiments reported here. By contrast, estimates of llb for movement times are usually around 10 bitlsec (see Langolf et al. and Schmidt et al.). Why are information transmission rates higher for preparatory processes than for execution processes? Perhaps by having rapid preparation processes, it becomes possible for the actor to make.decisions effectively about which of the indefinitely large set of possible movements he or she should perform at any given time. The final implication of our study that we mention here is drawn from our last experiment, where we showed that the clock setting process is not used exclusively for controlling time intervals between movements. In 1961 Hirsch and Sherrick concluded from a series of experiments on temporal-order judgments that the human nervous system possesses a central clock that is linked to different afferent modalities. Our last experiment suggests that this clock (or some clock) may be linked both to afferent and efferent modalities, thereby making it a truly central clock in the central nervous system.
FOOTNOTES In the 0 msec condition subjects were permitted to respond with the right finger before the left, and RTwas defined by the latency of the first response. The RT drop in the 0 msec condition was not attributable to fast RTs when the right finger led the left (which was permitted only in this condition), because right-first RTs were only 3 msec longer on the average than left-first RTs. After completing this experiment, we informally retested two of the subjects in the 1-response condition and in the standard interval production task. In the latter condition we required each subject to produce the same mean interval as she had produced in the experiment, but with reduced interval variance. For both subjects the RT difference between the 2-response and 1response condition reappeared, indicating that practice had not eliminated the RT difference.
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3. The reason why we do not set a equal to the mean RTin the m condition is that the clock is presumably not used in this condition. Consequently, there is no need to check whether the clock pointer is outside W,, and there is no need to activate the clock once it has been set. Either or both of these processes could inflate a. These considerations imply that in the experiment reported in Section IIB, the clock either was not used in the 2-response condition or, if the clock was used, the position of the pointer was almost never checked to see if the clock needed to be reset andactivation of the clock took a negligible amount of time.
4. This idea is reminiscent of the idea that preparation of a movement is mediated by an “anticipatory response image” (e.g., Greenwald, 1970. Kelso & Wallace, 1978) which is thought to bear some s/rirc/ura/similarity to the movement.
REFERENCES
111 Adams, J. A. Feedback theory of how joint receptors regulate the timing and positioning of a limb. Psychol Rev. 84 (1977) 504-523. I21 Cauraugh, J. H. and Christina, R. W. Proprioceptive feedback as a mediator in interlimb timing. 1 Motor Behav. 10 (1978) 239-244. 131 Fitts, P. M. The information capacity of the human motor system in controlling the amplitude of movement. J Exp Psychol. 47 (1954) 381-391. [41 Fitts, P. M. and Peterson, J. R. Information capacity of discrete motor responses. J. Exp. Psychol. 67 (1964) 103-112. [51 Greenwald, A . G. Sensory feedback mechanisms in performance control: With special reference to the ideo-motor mechanism. Psychol Rev. 77 (1970) 73-99. 161 Hirsch, I. J. and Sherrick, C. E., Jr. Perceived order in different sense modalities. J Exp Psychol. 62 (1961) 423-432. 171 Kelso, J. A. S. Joint receptors do not provide a satisfactory basis for motor timing and positioning. Psychol Rev. 85 (1978) 474-481. 181 Kelso, J. A. S. and Wallace, S. A. Conscious mechanisms in movement, in Stelmach, G . E. (ed), Information Processing in Motor Control and Learning (Academic Press, New York, 1978). 191 Langolf, G. D., Chaffin, D. B., and Foulke, J. A. An investigation of Fitts’ Law using a wide range of movement amplitudes. J Motor Behav. 8 (1976) 113-128. 1101 Parzen, E. Stochastic Processes (Holden-Day, San Francisco, 1962). 1111 Rosenbaum, D. A. Human movement initiation: Specification of arm, direction, and extent. J Exp Psychol: Gen. In press. (121. Rosenbaum, D. A. and Patashnik, 0. Time to time in the human motor system, in Nickerson, R. S. (ed.), Attention and Performance VIII (Erlbaum, Hillsdale, New Jersey, In press). 1131 Schmidt, R. A,, Zelaznick, H. N., and Frank, J. S. Sources of inaccuracy in rapid movement, in Stelmach, G. E. (ed.), Information Processing in Motor Control and Learning (Academic Press, New York, 1978). 1141 Sternberg, S., Monsell, S., Knoll, R. L., and Wright, C. E. The latency and duration of rapid movement sequences: Comparisons of speech and typewriting, in Stelmach, G. E. (ed.), Information Processing in Motor Control and Learning (Academic Press, New York, 1978). 1151 Vorberg, D. and Hambuch, R. On the temporal control of rhythmic performance, in Requin, J. (ed.), Attention and Performance VII (Erlbaum, Hillsdale, New Jersey. 1978). 1161 Wing, A. and Kristofferson, A. B. Response delays and the timing of discrete motor responses. Percept & Psychophys. 14 (1973) 5-12. 1171 Woodworth, R. S. and Schlosberg, H. Experimental Psychology (Holt, Rinehart and Winston, New York, 1954).
29 A Mental Clock Setting Process Revealed by Reaction Times* David A. Rosenbaum and Oren Patashnik Bell Laboratories Murray Hill, New Jersey 07974
To study the preparation of timing for forthcoming movements we require subjects to produce specified time intervals between two responses and also to minimize the simple reaction time (RT) for the first response. RTs are longer when a specified interval must be produced than when no second response is required, and RTs increase as target intervals decrease from 1050 to 50 msec. We reject the hypothesis that these effects are due to "competition" between the two responses, to processing of visual feedback about the intervals, or to a process of adjusting the covariance of the motor delays for the two responses. We argue that the effects can be attributed to a mental clock setting process whose duration is predicted by an analogue of Fitts' Law. That the clock setting process is not used exclusively for timing overt movements is shown in an additional experiment. We infer from the latter result that a central clock is used to time motor and perceptual events. We infer from the applicability of Fitts' Law to mental clock setting that processes of movement prepmarion bear an isomorphic relation to processes of movement execurion, although the former are much faster than the latter. I. Introduction In this paper we describe a series of experiments on how people control time delays between successive movements. The work reported here extends work that we have reported elsewhere (Rosenbaum & Patashnik, in press), and focuses on the preparation of movement timing. We believe that the study of movement timing preparation may help shed light on some issues of long-standing concern in the motor control research area. One such issue is whether motor programs are used to control movement timing when proprioceptive feedback is available ( A d a m , 1977; Cauraugh & Christina, 1978; Kelso, 1978). If one can show that the delay between two movements is prepared before the first movement is executed, even if there is enough time to use proprioceptive feedback from the first movement to time the onset of the second movement, it can be concluded that motor programs are used when proprioceptive feedback is available. Another issue that may benefit from the study of movement timing preparation is the nature of motor programming. If one can discover how the characteristics of timing preparation are related to the temporal characteristics of subsequent movements, it may then be possible to develop detailed models of the programs used for timing control. The experimental procedure we have used to study the preparation of movement timing is shown in Figure 1. In each session the subject's task is to produce one specified time interval between two responses (key presses made with the left and right index fingers). The specified intervals range from 0 to 1050 msec. On each trial we give feedback to help the subject produce an approximation to the specified interval. The feedback takes the form of a vertical line on a CRT screen. The line points up if the produced interval is too long and down if the produced interval is too short; the length of the line shows how large the proportional error is. (More details about the feedback are given in Rosenbaum & Patashnik, in press.) Besides producing the specified interval, the subject is also required to make the first response as quickly as possible after the onset of the reaction signal, that is, to minimize the reaction time (RT). The length of a horizontal line on the
* We thank Ronald L. Knoll, Judith F. Kroll, David L. Noreen, and Saul Sternberg for
suggestions, and Gwen 0. Salyer for assistance with data collection. This paper was formatted with a Bell Laboratories computer phototypesetting system.
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screen shows the subject how long the RT is. Our working assumption is that the length of the RT reflects the duration of timing preparation.
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Figure 2 shows the results of our first experiment. Here three right-handed women who had had extensive practice in the interval production task participated in eight one hour sessions each. In each session one interval was tested in eleven blocks of 60 trials, with the first block for practice. As is seen in the left panel of Figure 2 , mean RTs declined as target intervals increased, for target intervals greater than or equal to 50 msec. The RT curve dropped at 0 msec, and the subjects said that this condition seemed qualitatively different from the rest in the way the interresponse intervals were controlled.’ An aspect of the RT data that we find particularly interesting is that for every subject RTs were longer when two responses had to be made (regardless of the required interval) than when only one response had to be made -- in the condition we call “infinity“ ( m ) . The panel on the right gives an indication of how precisely the intervals were produced. For all three subjects mean produced intervals were within a few msec of their corresponding target values, and mean interval variances increased linearly with interval means. How can these results be interpreted? One of the first models we developed is shown in Figure 3. We call it an alarm clock model. The model says that after the reaction signal is detected, an internal alarm clock is set to tick n times. Once the value of n has been set to the subject’s satisfaction, the ticking process is begun and the first response is executed after a motor delay, d l . After the nth tick has occurred, an “alarm”goes off, as it were, and response 2 is executed after a motor delay, d2. The linearly increasing variance function is explained by saying that variance accumulates with each delay between successive ticks of the clock. The model says that delays between clock ticks fluctuate randomly about a mean and that successive intertick delays are stochastically independent (see Wing & Kristofferson, 1973). With this type of model, the RT data shown in Figure 2 can be explained by saying that it takes less time to set the clock as the value of n increases. This could come about if the clock’s setting returned to some large value of n after each usage, or if there were fewer possible settings as n increased. In the next section of this paper we will consider some alternatives to the alarm clock model which we have tested and rejected. Then, in Section 111, we will show that the alarm clock model, as described above, fails to explain two of the major results that we obtained in testing alternatives to the alarm clock model. A revised and more specific alarm clock model will then be described. In Section IV, we will address the question of whether the clock setting process is unique to the timing of movements. We will show that it is not. Finally, in Section V, we will review the main results of our experiments and consider some of their theoretical implications.
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Fig. 2. Results of the first experiment> averaged over the three subjects. The values on the abscissa designate the target intervals, and the plotted points, each of which represents a mean of about 1300 observatons, are plotted above the corresponding mean obtained intervals. Errors of responding on catch trials, responding before the reaction signal was presented, or responding first with the right finger when nonzero intervals were required occurred altogether on less than 2% of the trials in each of the eight conditions. ( A ) Mean RTs and estimate of standard error ( t S E ) . The three subjects had similar functions: The mean RT function for the 2-response conditions accounts for 93.7%, 98.4%, and 96.9%of the variance of mean RTs for corresponding conditions for the three subjects, respectively. (B) Mean interval variances, fitted linear function, and estimate of &SE. Linear regression accounts for 98.9% of the variance of mean variances, which is not significantly surpassed by fitting a quadratic function to the same points. Slopes (in msec) and zero-intercepts (in msec') of fitted linear functions for the three subjects are 8.64 and 141.44, 2.57 and 39.80, and 6.87 and 273.90. respectively. Estimates of +SE here and in all other figures are based on mean squares from fits of mean functions to individual subject data.
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11. Alternatives to Clock Setting
A. Response Competition One alternative to the clock setting model says that the RT effect we obtained is due to competition between the two responses, where the amount of competition, and hence the RT, increases as the delay between responses decreases (up to values near 0 msec). (For discussions of competition between responses in RT experiments, see Rosenbaum, in press, and Sternberg, Monsell, Knoll, & Wright, 1978.) The response competition hypothesis allows that the delay between triggering of response 1 and response 2 may be controlled by a clock, but it says that any clock setting activity that occurs during the RT takes a negligible or constant amount of time. According to the response competition hypothesis, the RT should depend on the interresponse interval but not on the variability of interresponse intervals. We tested this prediction in an experiment whose results are shown in Figure 4. In one condition we had subjects attempt to produce the same intervals as in the first experiment, with the same accuracy requirements as we had used in the first experiment; we called this the "stringent" condition. In another condition -- the "relaxed" condition we had the same subjects attempt to produce the same mean intervals, but now they were allowed to have much higher interval variances. To get the subjects to do this, we simply reduced the scale of the vertical feedback line so that in most cases subjects could only tell if the intervals they produced were too long or too short
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As is seen in the right panel of Figure 4, interval variances were higher in the relaxedcondition than in the stringent condition. but interval means in the relaxed and stringent conditions were close to one another and also close to the target values. As is seen in the left panel of Figure 4, the pattern of mean RTs in the srrtvgenfcondition was like the pattern of mean RTs in the first experiment (although the range of RTs was smaller here with this different group of subjects). In the relaxed condition mean RTs were significantly shorter than in the sfringen/ condition, and the effect of target interval (including the reduction of mean RTs for the 0 msec target) was virtually eliminated;
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an analysis of variance showed that the interaction between target interval and degree of required precision was statistically significant. The results from the reiuxed condition argue strongly against the response competition hypothesis, which predicted that mean RTs should depend on mean interresponse intervals. In general, the data from this experiment indicate that mean RTs depend critically on the precision with which interresponse intervals must be produced.
B. Some Response Competition and/or Visual Feedback Processing We cannot rule out the possibility that in the above experiment there was some effect of response competition on RT, because mean RTs were longer when two responses had to be made than when only one response had to be made. To determine whether there was some effect on RTs of merely having to make a second response, we conducted the following experiment. Subjects were told to respond as quickly as possible with the left index finger when the reaction signal appeared (as in the previous experiments) and then to respond with the right index finger any time lurer. We told the subjects that the second response was necessary merely "to turn on the feedback signal." In the control condition of this experiment no second response was required. Our aim was to find out whether the RT for the first of two responses could be as small as the RT for just one response when there was no pressure to produce a specific interresponse interval. In this experiment we also wanted to check on the possibility that RTs were longer for two responses than for one because of the need to study the vertical line that gave feedback about the interresponse intervals. To test this hypothesis in the new experiment, we presented a vertical line in the 2-response condition and told subjects that when the vertical line pointed up they should prepare to respond normally in the next trial, but when the vertical line pointed down they should refrain from responding in the next trial, even though the reaction signal would appear. This made it necessary for subjects to attend to the vertical line after making the second response. After trials in which the vertical line pointed up, the following events occurred. On 75% of the trials both the warning signal and reaction signal appeared, and after the second response was made the vertical line again pointed up with 75% probability. On the remaining 25% of the trials (following trials with an upward-pointing line). after the warning signal appeared no reaction signal was presented. In these catch trials no vertical line appeared, but the subject was instructed to get ready to respond on the next trial. The vertical line had a fixed length approximately equal to its mean length in the second experiment reported here. We made it clear to the subjects that the behavior of the vertical line did not depend in any way on the interresponse intervals. There were four subjects, all of whom had been in one or more of our previous experiments. After practicing the 2-response task for 1 hr, each subject returned the next day for a 1 hr session consisting of five 2-response blocks followed by five I-response blocks, or the opposite. Each block had 25 trials, and the first block in each half of the second session was for practice. Catch trials occurred on 25% of the trials in the I-response condition.
For every subject, errors of responding before or in the absence of a reaction signal occurred on less than 2% of the trials in both the 1-response and 2-response conditions. In the entire experiment there were only three errors of failing to respond correctly to the vertical line. The remaining discussion will be concerned with errorless trials only. Table 1 shows the main results of the experiment. Even though in earlier experiments each of the subjects had produced longer RTs for the first of two responses than for just one response, here mean RTs were the same when just one response had to be made and when the first response could be followed any time later by the second response. This result implies that it was not simply the need to make a second response that lengthened RTs. (This conclusion is supported by the fact that the mean produced intervals were generally within the range that was required before. Moreover, the produced intervals had higher variances than were found earlier for intervals with comparable means.) A second conclusion we reach with the present experiment is that the need to attend to the vertical feedback line did not cause RTs to be longer in the 2-response conditions than in the I-response condition of our earlier experiments, although we cannot rule out the possibility that earlier there was some effect of having to study the Irtrxth of the line. Notwithstanding the latter possibility, our main conclusion is that in the previous experiments RTs were lengthened by a process responsible for precisely controlling the interresponse intervals.*
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Table 1 Mean Reaction Time (RT) and Interval (1) When 1 or 2 Responses Were Required
Subject 1 2 3 4 Mean
Number of Reauired Resoonses 1 2 RT sd RT sd I sd 201.5 27.8 200.4 26.5 384.6 92.6 199.8 18.9 200.6 21.3 1059.4 149.4 201.8 26.4 200.1 21.2 943.6 186.9 202.3 23.8 202.4 23.7 326.7 187.0 201.3 24.2 200.8 23.1 678.5 153.9
C. Response Delay Covariance
Is there any kind of process other than a clock setting process that could affect the precision of interresponse intervals and also lengthen RTs? One possibility is that during the RT the subject sets the covariance between the motor delays for the two responses ( d , and d2), possibly by adjusting muscle tensions in the two arms. The rationale for this response delay covariance model is that as cov(dl,d2) increases, vur(f) will decrease. Therefore, it is to the subject’s advantage to maximize cov(dl.dz). Suppose, however, that it takes time during the R T t o set rov(d1, d2) for a forthcoming response sequence, such that the time needed to set c o v ( d l , d 2 ) increases with the level of c o v ( d l , 4 ) that is actually achieved. If we assume that the RT effects obtained in the first two experiments reflected differences in the time spent setting c o v ( d l , d z ) , and did not reflect differences in the time spent setting a clock that may have been used to control the delay between the triggering of response 1 and response 2, the response &lay covariancr model predicts that cov(d1, 4 ) should increase as mean RTincreases. We tested this prediction as follows. Suppose the following two relations hold:
where P i s a random variable representing the time to prepare a forthcoming interresponse interval f (that is, P includes the time to detect the reaction signal, set c o v ( d l , d 2 ) and , carry out all other aspects of preparation that precede response 1). and C i s a random variable representing the total duration of clock ticking. The covariance of RT and I, c o v ( R T , I ) , is then
cov(RT,I) = cov(P,C)
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+ cov(P,d2) - cov(P,dl) + + COV(dl,d2)- cov(dl.dl)
(2)
If we assume that all the random variables in (2) are independent except dl and d2, and also that c o v ( d l , d 2 ) is independent of mean d2, we have cov(RT,/) = c 0 v ( d l , d 2 ) - c o v ( d l , d l ) = cov(dl,d2) - var(d,) .
(3)
For the stringentcondition of the second experiment, where mean RTs decreased to an asymptote as mean interresponse intervals increased (to approximately 1050 msec), the prediction of the response deluy covariance model is that as mean interresponse intervals increase, cov(dl.d2) should approach 0, so that c o v ( R T , / ) should approach -vur(d,) as an asymptote. Of course, we cannot independently measure -var(dl),so the specific prediction stated above cannot be tested. Nevertheless, we can see whether c o v ( R T , f ) approaches an asymptote less than 0, where this asymptote is assumed to approximate -var(dl). Figure 5 shows cov(RT.I) in the sirinKent condition of the second experiment. As is seen in the figure, cov(RT,f) remained fairly constant at about -56 msec’ in the 50-1050 msec range. The slope of the best-fitting straight line for these points was only .005, and did not differ significantly from zero. The flatness of this curve contradicts the prediction of the response drlay covuriance model. Since the mean c o v ( R T . I ) in the 50-1050 msec interval range was negative, the simplest
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explanation of the data seems to be that cov(d,.d2) in this range was approximately zero, in which case cov(RT, / ) = - v a r ( d l ) . One reason why this seems like a reasonable explanation is that Wing and Kristofferson (1973) and Vorberg and Hambuch (1978) obtained estimates of response delay variance quite close to 56 msec2.
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MEAN I N T E R V A L , I ( m S e C ) Fig. 5. Mean c o v ( R T , / ) , averaged over the three subjects, in the sir~~igenfcondition of the second experiment. For the 0 msec target condition, algebraic values of I were used to compute c o v ( R T , / ) ;that is, intervals where the right finger led the left were considered negative. The resulting estimate of c o v ( R T , I ) did not differ significantly from zero. (When absolute values of I were used, the estimate of c o v ( R T , I ) did not differ significantly from zero or from the estimate obtained with algebraic values.) For the nonzero conditions, slopes (in rnsec) and mean covariances (in msec2) were .01 and -72.06 -.003 and -21.86, and ,008 and -74.81 for the three subjects, respectively. If we examine c o v ( R T , / ) for the relaxedcondition of the second experiment, we find similar effects to those described above. In the relaxedcondition, the .slope of the best-fitting straight line for values of c o v ( R T , I ) in the 50-1050 msec interval range was ,001 (not significantly different from zero), and mean c o v ( R T , I ) was -60 msec2, The fact that mean c o v ( R T , I ) in the relaxedcondition was close to (and not significantly different from) mean c o v ( R T , I ) in the stringenrcondition violates the prediction of the response delay covauatice model that c o v ( R T . / ) should depend on RT. For the first experiment, the slope of the best-fitting straight line for values of c o v ( R T , / ) in the 50-1050 msec range was only -.008 (not significantly different from O ) , and mean rov(RT.1) in this range was -51 msecC2. The flatness of this slope, like the flatness of the slope in the sfringenicondition of the first experiment. militates against the response delqv covariance model. (It is interesting to note that c o v ( R T , I ) for / = 0 was markedly different from the other values. This finding appears to support subjects’ introspective reports that the simultaneous response condition was qualitatively different from the other conditions.) 111. Clock Setting Models So far we have explained why we do not favor a simple response cornpetifion model or a simple wsponse del0.v covariancr model. Now we turn to the kind of model we favor -- an alarm clock
modeL
494
D.A. ROSENBAUM AND 0. PATASHNIK
Earlier, we proposed one kind of alarm clock model which we can now reject. This model said that the time required to set the alarm clock during the RT decreased as the desired set time Le., the desired value of n) increased. We can now reject this model because in the reluxpdcondition of the second experiment we found mean RTs to be essentially unrelated to interval means, and also because the second experiment showed that interval prerwon was the key determinant of mean RTs. What other kind of alarm clock model can be considered then? As a way of addressing this question, let us consider how a mental clock setting process might differ from the process of setting an external clock, say, the alarm clock in one's bedroom. In setting a conventional bedroom alarm clock, once the clock has been set it can be made to go off at its set time on future occasions without being reset. For example, if such an alarm clock is set to go off at 6 o'clock one morning, all that has to be done to make the alarm clock go off at 6 o'clock some later morning is to turn on the alarm system the preceding night; the alarm clock does not have to be reset. Now if all that was involved in reusing a mental alarm clock was reactivating the alarm system, one would not expect the time required to start the clock to depend on the clock setting. Suppose that unlike the bedroom alarm clock the mental alarm clock stores its previous set times, but it does so imperfectly (see the left panel of Figure 6 . ) Suppose that after the alarm clock has been used in an experimental trial its setting driftsrandomly so that at the start of the next experimental trial the setting is some expected amplitude, A , away from the clock's target setting, TI, for desired interval /. (We will assume that A is the same for all values of 1.) As a result of this random drift, before the clock can be used again for the production of interval l the clock's "pointer" must be moved back through A, that is, the clock must be reset at T,.
50150 300
L
I
500
1
750
1
1050
Fig. 6. Schematic diagram of a clock whose "pointer" drifts randomly over an expected amplitude A after being positioned within a window of size W, around a target setting T, [left panel]. Obtained RTs (empty and filled points for the sfrimen[ and relaxed conditions of the second experiment, respectively) and RTs predicted by applying Fitts' Law to mental clock setting [right panel].
Now, we found that RTs are affected by the precision of produced intervals. This fact leads us to suggest that the subject places a "tolerance window" of size W , around the target setting for I. W, is important for two reasons. First, if we assume that the clock does not have to be reset if the pointer is within the window, then as W, decreases, the likelihood of having to reset the clock will increase. Second, if we assume that W, defines the range of settings to which the pointer can be returned before the clock is reused. the precision required to return the pointer to within the window will increase as W, decreases.
We assume that W, depends both on the size of l a n d on the subject's motivation for precision. The nature of these dependencies can be established as follows. Let the random variable N be the number of clock ticks between the triggering of response 1 and 2 . Let the time between ticks I - 1 and (1 < I < n ) be a random variable X , , where the random variables X , are independent of Nand identically distributed as a random variable X with finite mean and variance. The interresponse interval, 1, is
495
MENTAL CLOCK SETTING PROCESS
I-X,+...+X,+D
(4)
,
where D is a random variable representing the difference between response delays d , and d2, and where X , , N, and D a r e mutually independent. Using the expression for the variance of a random sum (Parzen, 1962. p. 561, we have Vur ( / )
=
E ( N ) Vur (XI
+ Vur ( N ) E 2 ( X ) + Vur (0) .
(5)
Recalling that we found Vur(/) to be linearly related to E ( I ) , and noting that E(I)-E(D) E") = E(X) ' we have
(6)
As stringency and I are varied, all the terms in (7) are assumed to be constants except for Var ( N ) and E ( / ) .. Therefore, we can rewrite (7) as
+ c 2 E ( / ),
Vur ( N ) = c,
(8)
where and c2 are constants. In view of the fact that a qualitatively different kind of timing control seemed to be used in the 0 msec condition and in the other 2-response conditions, it seems reasonable to assume that for the 0 msec target interval the clock is not used. Thus, for E f l ) = 0, Y u r ( N ) = 0, in which case we can set cl = 0. We also assume that when there are n clock ticks the clock is initially set at ti Ke., that there is perfect correspondence between the number of ticks that are set and that occur). We can now characterize the range of clock settings used in repeated attempts to produce a desired interval / by the standard deviation of clock settings, (9)
W , = A r n ,
where h
= ,/q.
With the above assumptions, we can liken the process of setting a mental alarm clock to the process of positioning a clock pointer to a setting within W,. I n order to characterize how the time required for such repositioning could depend on W,, let us turn briefly to studies of owrrpositioning movements, in particular to manual positioning movements. When the hand must be moved to a target of width Wover a distance A, the movement time is found to be a linearly increasing function of log2(2A/ W ) . This relationship is known as Fitts' Law (1954). We will now show that mean RTs in our interval production task can be accounted for with the following analogue of Fitts' Law: a.
RT,=
a
for W, 2A
+ 6 log2 -,
W,
>> A
otherwise.
(10)
Here a represents the time to make a response to the reaction signal when the clock does not have to be reset (i.e.? when the clock pointer is already within W , ) , and 6 represents the time per bit of information transmitted, where the number of bits is given by log2(2A/ W,). When W, is very large relative to A (i.e., W > > A ) , and if the clock pointer is initially set near T,. the pointer will rarely drift outside of W,. Consequently, the number of occasions on which the pointer will have to be repositioned to a setting within W, will approach zero as W, increases. In the rchcdcondition of the second experiment, where theoretically W, was very large relative 10 A , mean RTs were roughly constant across changes in I . Thus, we can set a equal to the mean R T i n the reluscd condition3.
In the w i t i w n / condition of the second experiment, where W, theoretically was much smaller than in the rrluxedcondition, there would have been many more occasions on which the clock pointer had to be repositioned to within W,. For the sn.//~~r/iicondition, therefore, we must describe how repositioning times would vary across changes in I. To do so, we turn to the second line of (10). We note first that the second line of (10) can be rewritten as
496
D.A. ROSENBALM AND 0. PATASHNIK RT/
=
u
1 + b(l+/og2A--l0g2k---log2E(I)) 2
The observed range of mean RTs in the between RTlO5O and RTso, which is
StringEnt condition
.
(11)
can then be expressed as the difference
(The obtained mean intervals in the 1050 and 50 msec conditions were so close to their corresponding target values that we use the target values here and in all other computations involving E ( / ) . ) The value of bcan then be estimated as 7.74 msec/bit (or 129 bit/sec). In order for RTIflSoto equal 230 msec (the observed value of RTloso in the srringentcondition), we must make 1 6(1+/og2A-/oK2k--10g21050) = 230 - 222msec . (13) 2 Thus, (1+/0~2A-l0g2k)
=
6.05 b/t ,
(14)
in which case ! i = .03 A. We can now predict RTs for the remaining intervals, and those predicted RTs are contained in the upper curve in the right panel of Figure 6. The predicted RTs account for 97.4%of the variance among mean RTs in the stringent condition. With our application of Fitts’ Law we can account for interval variance data as well as mean RT data. By making use of Eqs. (6) and (8), we can rewrite Eq. ( 5 ) as
+
V a r ( / ) = ~ ( / ) [ c j k2c4I
+ c5,
(15)
where c3, c4, and c5 are constants. We have assumed that /+the factor that determines how large W /is in relation to E(I)--was much larger in the rrluxrdcondition than in the stringentcondition of the second experiment. Thus, according to (15), the slope of the interval variance function should be larger in the relaxedcondition than in the stringent condition, and the zero-intercepts of the two functions should be equal. This is essentiallywhat we found (see Fig. 4B). It should also be noted that the assumptions and results concerning coov(RT,/), presented in Section IIC, are consistent with the Fitts’ Law model. (According to the model, the time to prepare any particular interval whose corresponding target setting is within W,should be no different, on the average, than the time to prepare any other such interval having the same target setting. Thus, the model assumes cov(P,C)=O, which is necessary for the covariance results to be consistent with the model.) Because of the success of the Fitts’ Law model, we believe that the model is a reasonable way of conceptualizing preparation in the interval production task. Later, we will consider the possible implications of this development for interpretations of Fitts’ Law and for an understanding of the relation between the preparation and execution of movements.
IV. Centrality of Clock Setting We turn now to the issue of whether the clock setting process is used exclusively for timing delays between overt movements. I t is also possible that the clock setting process is used for timing delays between movements and stimuli or delays between two (or more) stimuli. We investigated whether the clock setting process is used for timing the delay between a movement and stimulus by conducting the following experiment. As before, on 75% of the trials a reaction signal appeared and the subject was required to respond as quickly as possible with the left index finger. This response defined the start of the subject’s interval, as was the case in the earlier experiments. Now, however, the end of the interval was defined by the onset of a brief burst of vibration applied to the tip of the subject’s right index finger. The vibration was delivered with a Bimorph bender (Vernitron No. 60572) for 20 msec at 200 Hz. In each session there were several different delays between the response and stimulus which were distributed around a single target interval. The subject’s task on each trial was to say whether the presented delay was longer or shorter than the target interval. For each target interval we presented six equally spaced response-stimulus intervals, using the method of constant stimuli. The mean of these six test intervals was equal to the target interval,
MENTAL CLOCK SETTING PROCESS
497
the range was approximately equal to 98% of the mean range of produced intervals for the corresponding target interval in the sir/ri:eni condition of the second experiment, and the test intervals closest to the target interval were presented three times more often than the test intervals farthest from the target interval and one and a half times more often than the test intervals at the middle distance from the target interval. Each of the three subjects was permitted to take as long as needed to give her verbal time judgment. Feedback took the same form as in the earlier experiments except that the word "Right" or "Wrong" was added to the display. There were five blocks of 48 trials each in every session, with the first block for practice. The results are shown in Figure 7. As is seen in Panel A , mean RTs decreased with target intervals and mean RTs were longer when time judgments were necessary than when subjects simply made one response. As before, mean variances increased approximately linearly with intervals; the slope and zero-intercept of the linear function fitted to the mean variance points were comparable to what we found in the 2-response experiments.
s -E 0
A
-
230
H
N
? 4000
W
W
9
k
0
z a
220
a 300C
z
3
2
I0 W
J
U
2 200c
210
W + z
a
z
H
U
w
=
5000
c
U
200
1000
w
I I
I
I
I
1 - 1
0
u 150300 500 750 105
TARGET I N T E R V A L , I (mSeC)
Fig. 7. Results of the time judgment experiment, averaged over the three SUbjeCtS. Each point represents a mean of about 430 observations. Errors of responding on catch trials or responding before the reaction signal was presented occurred altogether on less than 2% of the trials in each of the seven conditions. (A) Mean RTs and estimate of +SE. For all subjects mean RTs were shortest in the m (no judgment) condition. The mean RT function in the judgment conditions was quite representative of all subjects, as is shown by the fact that the mean function accounts for 99.1% 92.7%, and 98.5% of the variance of mean RTs for the three subjects, respectively. (B) Mean variances (averaged over the three subjects) of the psychophysical functions for each target condition, fitted linear function, and estimate of t S E . The method used to estimate variances comes from Woodworth and Schlosberg (1954, pp 204-210). Linear regression accounts for 98.8% of the variance of mean variances, which is not significantly surpassed by fitting a quadratic function to the same points. Slopes (in msecf and zero-intercepts (in mse& of fitted linear functions for individual subjects are 3.61 and 28.54, 5.15 and 43.89, and 5.71 and 26.73, respectively.
These results add weight to our conclusion that the main RT effects obtained in our earlier experiments were not due to response competition or adjustment of response delay covariance, since in the present experiment there was no overt second response. The main conclusion we can reach with the present experiment is that the clock setting process used for interresponse intervals is also used for timing delays between movements and stimuli. (One could imagine that in the time judgment task the mental alarm clock was set to go off near the target time so that time judgments could be made by judging the order of detection of the alarm and vibration.)
498
D.A. ROSENBAUM AND 0 . PATASHNIK
V. Conclusion The main results of this study can be summarized as follows. First, we have shown that the time to make the first of two responses depends on the required precision of the interresponse interval and does not merely depend on there being a second response or on the requirement to make use of visual feedback. Second, we have shown that this RT effect does not derive from a process of adjusting the covariance of motor delays for the two responses. Third, we have shown that our RT results can be explained by a clock setting process whose duration is predicted by an analogue of Fitts’ Law. Fourth, we have shown that the clock setting process is not used exclusively for the timing of overt movements. What are the theoretical implications of these findings? One implication concerns the use of proprioceptive feedback in movement timing. Many interresponse intervals that we required were long enough for proprioceptive feedback from the first response to be available to control the onset time of the second response. Yet even for such long interresponse intervals, we found that RTs were longer than when no specific interresponse interval had to be made. This result leads us to believe that the availability of proprioceptive feedback does not eliminate the need (or at least the tendency) for motor preprogramming. A second implication of our study concerns the application of Fitts’ Law to the hypothesized clock setting process. To our knowledge, the present study is only the second to use Fitts’ Law to account for RT data. The first such study was by Fitts and Peterson (1964). The fact that Fitts’ Law can be applied to RT data as well as movement time data (see Langolf, Chaffin, & Foulke, 1977, and Schmidt, Zelaznick, & Frank, 1978), implies that Fitts’ Law may be a very general description of the relation between speed and precision in human performance.
We would like to go a step further, however, and propose that the applicability of Fitts’ Law to RT data as well as movement time data (for the motion of a hand to a target) suggests that processes of movement preparation bear an isomorphic relation to processes of movement execution4. One of the identifiable differences between the two kinds of processes, however, is that preparatory processes occur much more rapidly than execution processes. That this is so is implied by the fact that estimates of information transmission rates (llb) for RTsare much higher than for movement times: Fitts and Peterson’s estimate of Ilb for RTs was 185 bitlsec and our estimates of I l b for RTs have ranged from 57.6 to 137 bitlsec in the experiments reported here. By contrast, estimates of llb for movement times are usually around 10 bitlsec (see Langolf et al. and Schmidt et al.). Why are information transmission rates higher for preparatory processes than for execution processes? Perhaps by having rapid preparation processes, it becomes possible for the actor to make.decisions effectively about which of the indefinitely large set of possible movements he or she should perform at any given time. The final implication of our study that we mention here is drawn from our last experiment, where we showed that the clock setting process is not used exclusively for controlling time intervals between movements. In 1961 Hirsch and Sherrick concluded from a series of experiments on temporal-order judgments that the human nervous system possesses a central clock that is linked to different afferent modalities. Our last experiment suggests that this clock (or some clock) may be linked both to afferent and efferent modalities, thereby making it a truly central clock in the central nervous system.
FOOTNOTES In the 0 msec condition subjects were permitted to respond with the right finger before the left, and RTwas defined by the latency of the first response. The RT drop in the 0 msec condition was not attributable to fast RTs when the right finger led the left (which was permitted only in this condition), because right-first RTs were only 3 msec longer on the average than left-first RTs. After completing this experiment, we informally retested two of the subjects in the 1-response condition and in the standard interval production task. In the latter condition we required each subject to produce the same mean interval as she had produced in the experiment, but with reduced interval variance. For both subjects the RT difference between the 2-response and 1response condition reappeared, indicating that practice had not eliminated the RT difference.
MENTAL CLOCK SETTING PROCESS
499
3. The reason why we do not set a equal to the mean RTin the m condition is that the clock is presumably not used in this condition. Consequently, there is no need to check whether the clock pointer is outside W,, and there is no need to activate the clock once it has been set. Either or both of these processes could inflate a. These considerations imply that in the experiment reported in Section IIB, the clock either was not used in the 2-response condition or, if the clock was used, the position of the pointer was almost never checked to see if the clock needed to be reset andactivation of the clock took a negligible amount of time.
4. This idea is reminiscent of the idea that preparation of a movement is mediated by an “anticipatory response image” (e.g., Greenwald, 1970. Kelso & Wallace, 1978) which is thought to bear some s/rirc/ura/similarity to the movement.
REFERENCES
111 Adams, J. A. Feedback theory of how joint receptors regulate the timing and positioning of a limb. Psychol Rev. 84 (1977) 504-523. I21 Cauraugh, J. H. and Christina, R. W. Proprioceptive feedback as a mediator in interlimb timing. 1 Motor Behav. 10 (1978) 239-244. 131 Fitts, P. M. The information capacity of the human motor system in controlling the amplitude of movement. J Exp Psychol. 47 (1954) 381-391. [41 Fitts, P. M. and Peterson, J. R. Information capacity of discrete motor responses. J. Exp. Psychol. 67 (1964) 103-112. [51 Greenwald, A . G. Sensory feedback mechanisms in performance control: With special reference to the ideo-motor mechanism. Psychol Rev. 77 (1970) 73-99. 161 Hirsch, I. J. and Sherrick, C. E., Jr. Perceived order in different sense modalities. J Exp Psychol. 62 (1961) 423-432. 171 Kelso, J. A. S. Joint receptors do not provide a satisfactory basis for motor timing and positioning. Psychol Rev. 85 (1978) 474-481. 181 Kelso, J. A. S. and Wallace, S. A. Conscious mechanisms in movement, in Stelmach, G . E. (ed), Information Processing in Motor Control and Learning (Academic Press, New York, 1978). 191 Langolf, G. D., Chaffin, D. B., and Foulke, J. A. An investigation of Fitts’ Law using a wide range of movement amplitudes. J Motor Behav. 8 (1976) 113-128. 1101 Parzen, E. Stochastic Processes (Holden-Day, San Francisco, 1962). 1111 Rosenbaum, D. A. Human movement initiation: Specification of arm, direction, and extent. J Exp Psychol: Gen. In press. (121. Rosenbaum, D. A. and Patashnik, 0. Time to time in the human motor system, in Nickerson, R. S. (ed.), Attention and Performance VIII (Erlbaum, Hillsdale, New Jersey, In press). 1131 Schmidt, R. A,, Zelaznick, H. N., and Frank, J. S. Sources of inaccuracy in rapid movement, in Stelmach, G. E. (ed.), Information Processing in Motor Control and Learning (Academic Press, New York, 1978). 1141 Sternberg, S., Monsell, S., Knoll, R. L., and Wright, C. E. The latency and duration of rapid movement sequences: Comparisons of speech and typewriting, in Stelmach, G. E. (ed.), Information Processing in Motor Control and Learning (Academic Press, New York, 1978). 1151 Vorberg, D. and Hambuch, R. On the temporal control of rhythmic performance, in Requin, J. (ed.), Attention and Performance VII (Erlbaum, Hillsdale, New Jersey. 1978). 1161 Wing, A. and Kristofferson, A. B. Response delays and the timing of discrete motor responses. Percept & Psychophys. 14 (1973) 5-12. 1171 Woodworth, R. S. and Schlosberg, H. Experimental Psychology (Holt, Rinehart and Winston, New York, 1954).