Journal ofExperimental Psychology

VOL. 47, No. 6 JUNE, 1954

THE INFORMATION CAPACITY OF THE HUMAN MOTORSYSTEM IN CONTROLLING THE AMPLITUDE

OF MOVEMENT1

PAUL M. PITTS'

The Ohio State University

Information theory has recentlybeen employed to specify more pre-cisely than has hitherto been possibleman's capacity in certain sensory, per-ceptual, and perceptual-motor func-tions (5, 10, 13, 15, 17, 18). Theexperiments reported in the presentpaper extend the theory to the humanmotor system. The applicability ofonly the basic concepts, amount ofinformation, noise, channel capacity,and rate of information transmission,wil l be examined at this time. Gen-eral familiarity with these conceptsas formulated by recent writers (4,11,20, 22) is assumed.

Strictly speaking, we cannot studyman's motor system at the behaviorallevel in isolation from its associatedsensory mechanisms. We can onlyanalyze the behavior of the entirereceptor-neural-effector system. How-

1 This research was supported in part by theUnited States Air Force under Contract No. AF33(038)-10S28 with the Ohio State UniversityResearch Foundation, monitored by the AirForce Personnel and Training Research Center.Permission is granted for reproduction, publica-tion, use, and disposal in whole or in part by orfor the United States Government.

1 Charles Kelly, Robert Silverman, and Char-lotte Christner assisted in collecting the datahere reported.

ever, by asking S to make rapid anduniform responses that have beenhighly overlearned, and by holding allrelevant stimulus conditions constantwith the exception of those resultingfrom S's own movements, we cancreate an experimental situation inwhich it is reasonable to assume thatperformance is limited primarily bythe capacity of the motor system.The motor system in the present caseis denned as including the visual andproprioceptive feedback loops thatpermit S to monitor his own activity.

The information capacity of themotor system is specified by its abilityto produce consistently one class ofmovement from among several alter-native movement classes. The greaterthe number of alternative classes, thegreater is the information capacity ofa particular type of response. Sincemeasurable aspects of motor responses,such as their force, direction, and am-plitude, are continuous variables, theirinformation capacity is limited onlyby the amount of statistical variabil-ity, or noise, that is characteristic ofrepeated efforts to produce the sameresponse. The information capacityof the motor system, therefore, can be

381

382 PAUL M. FITTS

inferred from measures of the varia-bilit y of successive responses that Sattempts to make uniform.

It is possible to determine experi-mentally the noise associated witheach category of response amplitudeand rate, and to infer the averageinformation capacity per response andthe maximum average rate of infor-mation transmission from the ratio ofthe magnitude of this noise to themagnitude of the possible range ofresponses. This line of reasoningagrees with Miller's (20) suggestionthat the concept of information capac-ity can be interpreted as a sort ofmodern version of the traditionalWeber-fraction and is consistent withTheorem 17 in Shannon (22). 3

The present experiments are limitedto motor tasks in which S is asked tomake successive responses havinga specified amplitude of movement.The information in which we are inter-ested is generated in discrete incre-ments, an increment being added byeach successive "response." The rela-tions to be studied are those holdingamong (a) the average amplitude, (b)the average duration, and (c) the dis-tribution of successive amplitudes(variability) of a series of rapid move-ments that S attempts to produce withuniform amplitude. The thesis to beexamined is that the channel capacityof the motor system, in a task involv-ing a particular limb, a particular setof muscles, and a particular type ofmotor behavior (within limits), is inde-pendent of average amplitude and

8 Theorem 17 states that "the capacity of achannel of band W perturbed by white thermalnoise of power N when the average transmitterpower is limited to P is given by

P+N"(22, p. 67).

W is in cycles per second and takes the form ofthe reciprocal of some value of time. The powerof a band of noise is equivalent to the variance ofits amplitude distribution around its mean value.

of specified permissible variability(movement tolerance).

The need for a unifying concept ofmotor capacity is indicated by theapparent difficulty of reconciling manyof the facts reported in the literatureon motor skill. These difficulties havein large measure stemmed from failureto recognize that the amplitude, theduration, and the variability of move-ments are interrelated.

Early investigators were interestedchiefly in activities such as running, tap-ping with a telegraph key, writing long-hand, and keeping time with a baton inwhich visual monitoring of successivemovement is minimal and in which suc-cessive movements do not have to beterminated precisely. The duration ofthis type of movement is essentially inde-pendent of its extent. Bryan (2), forexample, reported that tapping ratevaried only from 4.6 to 6 cps over anamplitude range from 1 to 40 mm. Not-ing that his results confirmed earlierexperiments by Von Kries, he concludedthat when movements are made at maxi-mum rate ". . . the rate varies slightlywith different muscles; increases withpractice; but is not affected by variationsof the amplitude of motion within widelimits, a certain medium amplitude re-quiring less time than longer or shorterdistances" (2, p. 138). Freeman (9)studied handwriting movement and foundlittl e variation in the total time requiredto write letters as their size was varied.Stetson and McDill state categoricallythat "since the duration of the rapidmovement is fixed, there can be but twovariables, extent and force" (23, p. 25),and Hartson (12) makes fixed durationthe basic characteristic of the ballisticmovement.

Recent investigators (1, 3, 14, 21),studying tasks that require £ to exerciseprecise control of movement amplitudebut rely on his subjective standard ofacceptable movement precision, havereported results that are contrary tothose cited in the preceding paragraph.An example of such a task is moving acontrol quickly so as to realign a spot and

AMPLITUDE OF MOVEMENT 383

a cross hair on an oscilloscope after thespot is suddenly displaced. Typically Sis instructed to make an "exact" adjust-ment by the use of vision. The findingsfor this type of task indicate that theduration of quick corrective movementsis a monotonically increasing function ofamplitude. Studies of eye movements(6, 24) reveal a similar increase of move-ment duration with an increase inamplitude.

Although it has been known for manyyears that the accuracy of quick move-ments decreases with amplitude, the closerelation of speed, amplitude, and accuracyoften has been lost sight of. One of theearliest workers to emphasize the impor-tance of their interrelation was Wood-worth (25). Studying a variety of simplemotor tasks performed with and withoutvisual monitoring, he found that forquick, visually controlled movements var-iable error increases both with amplitudeand with speed. Industrial engineers(19) also have consistently advocatedthat small-amplitude movements be usedwhenever possible in assembly work, onthe grounds that the time required tocomplete a unit of work increases as afunction of its amplitude as well as of theprecision demanded by the task.

The concept of a fixed information-transmission capacity of the motorsystem not only accounts for suchdivergent results but also suggests away of relating quantitatively the am-plitude, duration, and variability ofmotor responses. The concept leadsto the expectation that if repetitivemovements of a fixed average ampli-tude are speeded up, then on the aver-age each movement can provide lessinformation, and movement variabil-ity wil l increase by a specified amount.Similarly, it suggests that if averagemovement amplitude should be in-creased then variability and/or aver-age duration wil l also increase. Thethesis can be tested experimentally inseveral ways.

An accepted method for estimatingchannel capacity in the case of a con-

tinuous signal requires a determinationof the average power of the noise asso-ciated with the output signal. Anexperimental determination of thechannel capacity of the human motorsystem by this method would requirethat the average amplitude and dura-tion (or frequency) of movements becontrolled by E and that the ampli-tude variability of S's movements bemeasured by procedures similar tothose used by Wood worth (25). How-ever, the recording and measurementof successive movement amplitudes arelaborious. Fortunately for the pres-ent purpose man has remarkably goodability to adjust his average rate ofperformance to meet the demands of aparticular task, such as the require-ment that his movements fall withinsome specified tolerance range. Thusit is possible to assess the tenability ofthe thesis of fixed information capacityby means of a test of the following spe-cifi c hypothesis: // the amplitude andtolerance limits of a task are controlled byE, and S is instructed to work at hismaximum rate, then the average time perresponse will be directly proportional tothe minimum average amount of infor-mation per response demanded by theparticular conditions of amplitude andtolerance.

In performing a given task S mayactually use movements that are lessvariable, i.e., which generate moreinformation, than the minimum de-manded by the task. When only thelimit s of variability are specified, theminimum information condition ismet if all amplitudes within the toler-ance range are used equally often, i.e.,when responses are distributed recti-linearly over the tolerance range,whereas the actual dispersion of re-sponse terminations is an approximateGaussian distribution. The rate atwhich S makes successive responses ina given task, therefore, must be inter-preted as the rate at which he can

384 PAUL M. FITTS

generate, on the average, at least asmuch information per response as thatdemanded by the task. This restric-tion on the interpretation that can begiven to results obtained with thepresent procedure is more than com-pensated for by the fact that the pro-cedure makes it feasible to study awide variety of task conditions withrelatively large samples of Ss andresponses.

EXPERIMENT I:RECIPROCAL TAPPING

In the first experiment two closelyrelated reciprocal tapping tasks werestudied. The Ss were asked to taptwo rectangular metal plates alter-nately with a stylus. Movement tol-erance and amplitude were controlledby fixing the width of the plates andthe distance between them. The taskwas accomplished primarily by move-ments of the lower arm.

MethodApparatus and procedure.—A schematic draw-

ing of the apparatus is shown in Fig. 1. The tar-get plates were 6 in. long and of four differentwidths (2, 1, ,5, and .25 in.). The widths of theplates (hereafter referred to as Wj) establishedthe tolerance limits within which movements hadto be terminated in amplitude. An additionalerror plate was mounted on either side of eachtarget plate. The error plates were wide enoughto catch all overshoots and undershoots. Sixcounters, activated by thyratron circuits throughthe plates and stylus, provided an automaticrecord of hits, overshoots, and undershoots foreach set of three plates. After one of the count-ers in each group of three had recorded, noneof the counters in that group would score againuntil one of the opposite set of plates had been

FIG. 1, Reciprocal tapping apparatus. Thetask was to hit the center plate in each groupalternately without touching either side (error)plate.

touched. Thus the first plate touched on eitherside was always the one scored.

Four center-to-center distances between thetarget plates were studied (2, 4, 8, and 16 in.)giving a total of 16 combinations of amplitude(A) and target size. (For A = 2 in. and W, = 1in. no undershoot errors were possible.)

Two metal-tipped styluses were used. Oneweighed 1 oz. and was about the size of a pencil.The other weighed 1 Ib. and was slightly larger.The use of one or the other of these two stylusespermitted the amount of work to be varied with-out otherwise changing the task.

The S sat with his right arm midway betweenthe plates, which were located at a convenientheight and angle. Each trial lasted 15 sec. andwas followed by a 55-sec. rest period.

The following instructions were read to eachS:

"Strike these two target plates alternately.Score as many hits as you can. If you hit eitherof the side plates an error wil l be recorded. Youwil l be given a 2-sec. warning before a trial.Place your hand here and start tapping as soonas you hear the buzzer. Emphasize accuracyrather than speed. At the end of each trial I shalltell you if you have made any errors."

Subjects.—Sixteen right-handed college menserved as Ss.

Sequence of trials.—Each S was tested at eachof the 16 conditions. A different randomsequence of conditions was used for each S withthe restriction that for the entire group of 16 Sseach condition occur once on each trial. Theexperiment was replicated on the same day byretesting each S on each condition in a reversedsequence.

Each S participated in the experiment for twodays. The lighter stylus was used on the firstday, the heavier on the second day. Al l otherprocedures on the two days were the same. Noattempt was made to equalize practice effectsbetween the lighter and heavier styluses, becauseE was interested chiefly in the effects of ampli-tude and tolerance changes within each variationof the task.

Results

The time and error data for the twovariations of the tapping task are in-cluded in Table 1. The data are ex-pressed as the average time (*), inseconds, between taps (i.e., the timefor each right-left or left-right move-ment) and as the percentage of errors(i.e., movements that were either toolong or too short). Percentages arebased on from 613 to 2,669 movementsper condition.

AMPLITUDE OF MOVEMENT 385

TABLE 1

TASK CONDITIONS AND PERFORMANCE DATA FOR 16 VARIATION S OF ARECIPROCAL TAPPING TASK

(N = the same 16 Ss at each condition)

Tolerance and AmplitudeConditions

W,

.25

.25

.25

.25

.50

.50

.50

.501.001.001.001.002.002.002.002.00

A

248

16248

16248

16248

16

id

4567345623451234

l-oz. Stylus

/

.392

.484

.580

.731

.281

.372

.469

.595

.212

.260

.357

.481

.180

.203

.279

.388

Errors(%>3.353.412.783.651.992.722.052.730.441.092.381.300.000.080.870.65

ir

10.2010.3310.349.58

10.6810.7510.6610.089.43

11.5411.2010.405.569.85

10.7510.31

Rank

1198

1453.56

1215127

16133.5

10

l-lb. Stylus

/

.406

.510

.649

.781

.281

.370

.485

.641

.215

.273

.373

.526

.182

.219

.284

.413

Errors(%)

3.803.834.044.080.882.162.322.270.130.851.171.320.000.090.651.72

1,

9.859.809.248.96

10.6810.8110.319.369.30

10.9910.729.505.499.13

10.569.68

Rank

78

13ISI26

111213

10161459

Note.—Wi is the width in inches of the target plate. A is the distance in inches between the centers of thetwo plates. * is the average time in seconds for a movement from one plate to the other. The performance Index,IP, is discussed In the text.

The average number of errors madein this task was small, only 1.2% withthe lighter stylus and 1.3% with theheavier one. The low incidence oferrors indicates that Ss successfullyadjusted their rate of performance tomeet changed task conditions.

The largest proportion of errors,3.6% with the lighter stylus and 4.1%with the heavier stylus, was madeat the most difficul t task condition(W, - | in., A = 16 in.). At eachamplitude step the percentage of errorsfor more exacting tolerances was con-sistently slightly larger than for lessexacting tolerances; this indicatedthat Ss did not slow down their move-ments quite as much as necessary toeffect the required accuracy at themore exacting conditions. Nor werethe errors symmetrically distributedover the error plates. The Ss wereuniformly more accurate in terminat-ing flexor than extensor movements.With the lighter stylus over- andundershoot errors were equally fre-quent, but with the heavier stylus

undershoots were about twice asfrequent. However, in spite of suchconsistent trends, the relatively smallincidence of errors justifies an analysisof the data in terms of the total num-ber of movements made under thevarious task conditions.

Practice led to relatively small im-provement in performance. The meantime per movement for all Ss and alltask conditions decreased by 3% fromthe first to the second block of trialswith the light stylus, and by 5% withthe l-lb. stylus. The total numberof errors made by all Ss was almostexactly the same for the first as for thesecond block of trials.

For each category of W,, movementtime increased progressively as move-ment amplitude (A) increased. Like-wise for each amplitude, movementtime increased progressively as toler-ance was decreased. The relationsamong the various conditions forthe lighter and heavier styluses weresimilar.

386 PAUL M. FITTS

EXPERIMENT II : Disc TRANSFER

The second task was to transferplastic washers from one pin toanother. Again, the amplitude andtolerance of the positioning move-ments were varied through a series ofgeometric steps, and the rate of per-formance was measured. This task dif-fered from the previous one in that noerrors were permitted. Some amountof finger activity was involved ingrasping a washer by the edges beforeremoving it from the pin.

MethodApparatus and procedure.—A schematic draw-

ing of the apparatus is shown in Fig. 2. Roundplastic discs, | in. thick and 1.5 in. in diameter,were drilled with four sizes of holes. Eight discsof uniform size were placed over a J-in. pin.The task was to transfer the discs, one at a time,to another pin. The transfer of eight discsconstituted a trial.

The difference between the diameter of thepins and the diameter of the center hole of thediscs was varied in four geometric steps (J, J, i,and ^g in.). Four amplitudes of movement(4, 8, 16, and 32 in.) were used, making a totalof 16 conditions. The S touched a switch platebeside the empty pin as he began the task. Thisstarted a 1/100-sec. timer. The S touched theswitch plate as soon as he had transferred thelast disc. This stopped the timer. Discs werealways moved from right to left.

Subjects.—Sixteen right-handed college menserved as Ss. They were different Ss from thoseused in Exp. I.

Sequence of trials.—Each S worked at all 16task conditions in a restricted randomizedsequence corresponding to that used in the previ-

ous experiment. The entire procedure was thenreplicated on a second day using a differentsequence of trials for each S.

Results

The transfer of a disc involves atransport-empty plus a transport-loaded movement, and the times givenare an average of these two aspects ofeach transfer cycle. There was asmall (6%) decrease in time per move-ment on the second set of 16 trials.The average times per movement foreach condition, averaged over all 16Ss and over both days, are given inTable 2 in the column labeled t.The variations in movement time withincrease in movement amplitude andchanges in tolerance correspond tothose found in Exp. I.

EXPERIMENT III : PIN TRANSFER

The third task was to transferpins from one set of holes to another.Grasping and releasing movements ofthe fingers were required in addition

TABLE 2TASK CONDITIONS AND PERFORMANCE DATA

FOR 16 VARIATIONS or ADISC-TRANSFER TASK

(N = the same 16 Ss at each condition)

FIG. 2. Disc transfer apparatus. The taskwas to transfer eight washers one at a time fromthe right to the left pin. The inset gives thedimensions for the W, «= J in. condition.

Tolerance and AmplitudeConditions

W,

.0625

.0625

.0625

.0625

.125

.125

.125

.125

.25

.25

.25

.25

.5

.5

.5

.5

A

48

163248

163248

163248

1632

li

789

10678956784567

Performance

(

.697

.771

.8961.096.649.734.844

1.028.607.672.771.975.535.623.724.902

I,

10.0410.3810.04!;9.12*:9.249.549.488.758.2418.939.08 '"8.20J7.47$8.028.297.76

Rank

2.512.5764S

101298

1316141115

Note.—Wi is the difference in inches between thediameter of the post and the diameter of the center holeof the disc. A is the center-to-center distance betweenthe two posts. t is the average time in seconds for amovement between two posts.

AMPLITUDE OF MOVEMENT 387

to arm movements. No errors werepermitted. The task was varied infour geometric steps of movement tol-erance and in five geometric steps ofamplitude. The time for completinga series of eight responses was recorded.The data for this task are somewhatmore extensive, and somewhat morepractice was given on this task than inthe two preceding experiments.

MethodApparatus and procedure.—The pin-transfer

apparatus is shown in Fig. 3. Four sizes ofpins(J, J, ^g, and -fa in. in diameter) and fiveamplitudes of movement (1, 2, 4, 8, and 16 in.)were employed, thus making a total of 20 taskconditions. Each set of pins was used with aset of holes whose diameter was twice that of thepins. The difference between the two diametersdetermined the tolerance (IF,) required in trans-ferring a pin from one hole to another. The tipsof the pins were tapered to one-half their diam-eter as shown in the inset of Fig. 3.

The S started and stopped a timer as in thepreceding task, in order to record the over-alltime for making eight transport-empty plus eighttransport-loaded movements. A trial consistedof the transfer of eight pins from one side to theother followed after a short rest by the transferof the same pins in the opposite direction.

The instructions were similar to those em-ployed in the preceding experiments.

Subjects.—Twenty college students, ten menand ten women, served as Ss. These were dif-ferent Ss from those serving in Exp. I and II.

Sequence of trials.—Each S served under alltask conditions. The sequence of conditionswas randomized, with the restriction that for thegroup of 20 Ss each condition occur once on eachtrial and once for each S. The experiment wasrepeated three times with the same Ss on threeseparate days. The sequence of trials for each Swas different each day.

Results

There was some improvement in therate of task performance from the firstto the second day, but littl e furtherimprovement on the third day. Theover-all means for the three days were.613, .585, and .578 sec. per movement,respectively. The average movementtimes computed for the combined trialsof the second and third replications ofthe experiment are given in Table 3in the column labeled t. The relations

FIG. 3. Pin transfer apparatus. The taskwas to transfer eight pins one at a time from oneset of holes to the other. The inset gives thedimensions of pins and holes for the W, = \ in.condition.

among the data correspond closely tothose found in the previous experi-ments. Movement times increasedprogressively as the tolerance require-ment was made more stringent and asamplitude was increased.

INFORMATION ANALYSISThe rate of performance of all the

tasks studied increased uniformly asmovement amplitude was decreasedand as tolerance limits were extended.These results agree qualitatively withthe predictions from the hypothesis.

In order to test the results against aquantitative prediction that the infor-mation output of the human motorsystem in any particular type of taskis relatively constant over a range ofamplitude and accuracy requirements,a difficulty index is needed that wil lspecify the minimum information re-quired on the average for controllingor organizing each movement.

The rational basis for this estimateof task difficulty is the maximum rela-tive uncertainty that can be toleratedfor a "correct" movement in a serieshaving a specified average amplitude.4

Thus the minimum organization re-4 Although only amplitude is considered here,

the present rationale can be extended to thequestion of the rate of information involved inthe selection of the direction, the force, or theduration of movements.

388 PAUL M. FITTS

TABLE 3

TASK CONDITIONS AND PERFORMANCE DATAFOR 20 VARIATION S OF A PIN-

TRANSFER TASK(N = the same 20 Ss at each condition)

Tolerance and AmplitudeConditions

W.

.03125

.03125

.03125

.03125

.03125

.0625

.0625,0625.0625.0625.125.125.125.125.125.25.25.25.25.25

A

1248

161248

161248

161248

16

u

6789

10567894567834567

Performance

t

.673

.70S

.766

.825

.959

.484

.518

.580

.644

.768

.388

.431

.496

.557

.668

.326

.357

.411

.486

.592

IT

8.929.93

10.4410.9110.4310.3311.5812.0712.4211.7210.3111.6012.1012.5711.989.20

11.2012,1612.3411.82

Rank

20181413151611629

1710517

1912438

Note.—Wi is the difference in inches between thediameter of the pins and the diameter of the hole intowhich they were inserted. A is the center-to-centerdistance between the holes, t is the average time inseconds for a single movement.

quired of a particular movement isdefined by the specification of one fromamong k possible categories of ampli-tude within which the movement is toterminate.

If we follow the above reasoningand conventional information nota-tion, a binary index of difficult y (/,;)is defined as

WId = —logs Jbits/response, (1)

where W, is the tolerance range ininches and A is the average amplitudeof the particular class of movements.The choice of the denominator for thisindex is arbitrary since the range ofpossible amplitudes must be inferred.The use of IA rather than A is indi-cated by both logical and practicalconsiderations. Its use insures thatthe index wil l be greater than zero forall practical situations and has the

effect of adding one bit ( — logs f) perresponse to the difficulty index. Theuse of IA makes the index correspondrationally to the number of successivefractionations required to specify thetolerance range out of a total rangeextending from the point of initiationof a movement to a point equidistanton the opposite side of the target.

The index of difficult y (la) is givenin Tables 1, 2, and 3 for each of thetasks. Since the index takes intoaccount only the information neces-sary to specify the amplitude of amovement, it is insensitive to theweight of the stylus used in the firstexperiment and hence to the physicalwork required by the task. In itspresent form, the index is also insensi-tive to the information required forspecifying the direction of a movement,or for specifying additional manipula-tory acts such as the finger movementsrequired to grasp and release objects.

Also shown in Tables 1, 2, and 3 isa binary index of performance (7P),which expresses the results as a per-formance rate. For a task in whichW, and A are fixed for a series ofmovements, Ip is defined as

1 WIP = - - Iog2 bits/sec., (2)

where t is the average time in secondsper movement. This index has someresemblance to one by Goldman (11,p. 157, Formula 29) for maximum in-formation rate, although Goldman'scriterion for determining the numberof possible categories is based on amean square criterion.

We want to test the hypothesis thatmovement time varies with task diffi -culty in such a way that Ip is constantover a wide range of movement ampli-tudes and tolerances. It is apparentfrom the data in Tables 1, 2, and 3that even though the index is not pre-cisely constant, the hypothesis is sub-stantially confirmed.

For the eight best (out of the 16)

AMPLITUDE OF MOVEMENT 389

conditions of tapping with the lightweight stylus, the rate of performancevaried between 10.3 and 11.5 bits/sec., a range of only 1.2 bits. Per-formance fell off markedly only for theleast exacting bits/sec., condition stud-ied (A = 2 in., W, = 2 in.).

Performance rate with the 1-lb. sty-lus also was relatively stable over acomparable range of amplitudes andtolerances. The rate at all but twoconditions was reduced slightly by theadded work, and the region of maxi-mum performance was shifted towardsmaller amplitudes of movement. ThePearsonian correlation between the 16IP values for the two variations in thetapping task was large however(r = .97).

For the 16 conditions of the disc-transfer task, on which the difficultyindex ranged from 4 to 10 bits/re-sponse, the rate of performance variedfrom 7.5 to 10.4 bits/sec. Over theeight best conditions the range wasonly 1.3 bits/sec.

Performance on the pin-transfertask varied from 8.9 to 12.6 bits/sec,for the 20 conditions studied, but therange of variability was only 1.0 bit/sec. over the ten best conditions.

In all tasks it was found that move-ment amplitudes and tolerances couldbe varied within limits without mucheffect on performance rate, but thatperformance began to fall off outsidethese limits. This is readily apparentfrom an inspection of Fig. 4, which isa three-dimensional representation ofthe performance data for the pin-transfer task. Movements of 1- and2-in. amplitude were consistently lessefficient than movements of 4 to 8 in.In the pin-transfer task in particular,both the smallest amplitude (1 in.)and the smallest tolerance (1/32 in.)resulted in relatively low rates of per-formance. In most cases performancerate also fell off at the largest ampli-tudes and tolerances. Throughout allthe tasks, movement amplitudes of 4

t

FIG. 4. Three-dimensional representation ofperformance rate (7P) in bits per second for thepin-transfer task as a function of amplitude andtolerance requirements

to 8 in. were more consistently asso-ciated with good performance thanwas any particular tolerance or anyparticular difficult y index.

DISCUSSIONAlthough the four tasks thus far anal-

yzed are a small sample of perceptual-motor activities, the results are suffi-ciently uniform to indicate that thehypothesized relation between speed,amplitude, and tolerance may be a gen-eral one. It is not surprising to find thatperformance, measured in informationunits, is relatively constant over a centralrange of amplitude and accuracy condi-tions and falls off outside these limits.Such a relation holds for most perceptualand motor activities and has recentlybeen found (16) in a study of the opti-mum relation between the amplitude oflever movement and observed displaymovement.

The absolute level of capacity of themotor system probably varies consider-ably for different movements, limbs, andmuscle groups. For example, the arm,which in the present experiments wasasked to generate information only inrespect to successive movement ampli-tudes, may have a lower informationcapacity than the hand. Using all of hisfingers singly and in combinations, S canproduce one bit of information per re-

390 PAUL M. FITTS

sponse per finger. Quite likely he cansustain higher level performance by usingfinger rather than arm movements. Morecomplex movement patterns than thosestudied may also have a higher informa-tion capacity since in this case infor-mation can be generated along severaldimensions simultaneously.

The estimates of information capacityarrived at by the present procedures givelower values than would be obtained byother and perhaps equally tenable as-sumptions regarding the number of pos-sible categories. However, the estimatesare of similar magnitude, in fact slightlyhigher, than the figures reported for theaverage S in a perceptual-motor task,such as pressing keys in response to flash-ing lights (18), in which responses toa series of discrete stimuli have beenstudied.

The present index of difficult y can beapplied to a wide range of motor tasks.For example the three stick and ruddercontrol movements necessary to make asingle match on the Complex Coordina-tion Test (Model E) require one bit ofinformation to specify each of the threedirections of movement and 3.9 bits tospecify each of the three amplitudes (atotal of 14.7 bits); this assumes that Sstarts his adjustments with the controlsin the neutral position.

Ellson (7) has raised the question ofthe linearity of motor responses, usingthe superposition theorem as the criterionof linearity. This theorem demands thatmovement duration remain constant asamplitude increases. We have notedthat many recent data violate thisrequirement. However, the presentresults indicate that over the range inwhich performance is optimum, move-ments of differing amplitude but of equaldifficult y in terms of information tendto be of approximately equal duration.Man differs from a linear electronic ormechanical system, however, in that hesometimes varies his standard of relativeprecision for a movement at the sametime as he varies its amplitude; unless rel-ative precision remains constant, move-ment time wil l vary with amplitude.

The basis for the uniformity of motorperformance perhaps is to be found in thetime taken for central organizing proc-

esses. Fenn has pointed out that inreciprocal movements made at maximumrate and without any visual control themuscles work at a level far below theirphysical capacity. Since maximum rateof performance in this case is not limitedby the muscles, he has proposed that themaximum rate is limited by ". . . thespeed with which excitation and inhibi-tion can be made to alternate in thecentral nervous system without at thesame time losing precise control of themagnitude of the force" (8, p. 174). Thisconcept of central organizing time isentirely consistent with an informationpoint of view. The finding that rela-tively small differences in performanceresult from the change in stylus weight,and the validity of predictions of per-formance rate from the index of taskdifficult y lend support to the basic thesisof this paper, that it is the degree of con-trol required over the organization of aresponse, i.e., the amount of informationrequired to specify a response, which isthe major factor limiting the rate ofmotor performance.

SUMMARY

The present paper attempts to relate the tra-ditional Weber function (variability of a responseas a function of its amplitude) to the parallelphenomena of variability as a function of responseduration, using certain concepts of informationtheory.

An index of the difficulty of a movement isproposed on the assumption that the averageamplitude, the average duration, and the ampli-tude variability of successive movements arerelated in a manner suggested by informationtheory. The basic rationale is that the minimumamount of information required to produce amovement having a particular average amplitudeplus or minus a specified tolerance (variableerror) is proportional to the logarithm of theratio of the tolerance to the possible amplituderange. The specification of the possible ampli-tude range is arbitrary and has been set at twicethe average amplitude. The average rate ofinformation generated by a series of movementsis the average information per movement dividedby the time per movement.

Three experiments are reported which weredesigned to test the following hypothesis: If theamplitude and tolerance limits of a task are fixedand the S is instructed to work at his maximumrate, then the average duration of responses wil lbe directly proportional to the minimum averageamount of information per response (i.e.,|the

AMPLITUDE OF MOVEMENT 391

degree of behavior organization) demanded bythe task conditions. The conditions studied cov-ered the range from 1 to 10 bits/response.

The results indicate that rate of performancein a given type of task is approximately constantover a considerable range of movement ampli-tudes and tolerance limits, but falls off outsidethis optimum range. The level of optimum per-formance was found to vary slightly among thethree tasks in the range between about 10 to 12bits/sec. The consistency of these resultssupports the basic thesis that the performancecapacity of the human motor system plus itsassociated visual and proprioceptive feedbackmechanisms, when measured in informationunits, is relatively constant over a considerablerange of task conditions. This thesis offers aplausible way of accounting for what otherwiseappear to be conflicting data on the durations ofdifferent types of movements.

The author feels that the fixed information-handling capacity of the motor system probablyreflects a fixed capacity of central mechanismsfor monitoring the results of the ongoing motoractivity while at the same time maintaining thenecessary degree of organization with respectto the magnitude and timing of successivemovements.

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(Received for early publication March 13, 1954)