Information theory and figure perception: The metaphor that failed
Post on 22-Aug-2016
INFORFVIATION THEORY AND FIGURE: PERCEPTS
THE IvlETAPH8R T FAlLED
IR. T. GREEN AND M. C. CCKJRlliIS Wnivemity College, London, Englmd
When, in its omnivorous way, information theory got its teeth into the probEem of figure: perception it looked as if the struggle was all over bar the shouting and, of course, a bit of data collection to round out the pictme. ATTSEAVE (1954j made an exciting contribution along these lines, and later developments, ATTNEAVE (1955, 1957), ATTNEAVE and ARNQULT (195&j., did not seem to run counter to the signposts first planted. Related contributions were being made at :ibout the same time by WOCHBERG and MCALTSTER (l953), and WEINSTEIN and F~TTS ( 1954).
More recently, ho-Never, tLrere have been indications that all is not well, and that this type of approach, although interesting methodologi- cally, has its limitations. The basic premises undfxpinning the appli- cation of information theory to figure perception, and the specific predictions made by the theory are both now receiving closer attention.
obliquely so far as CR~NBACH (1995), It has been pointed be brought to bear met. Among these
The basic position has been undermined, albeit figure perception is concerned, by GRANT (1954), TOIM (W56) and C%ENRY (I!?57 a, b) in particukr. out that before infornlation theory can legitimately on any problem certain requirements have to be requirements are:
(1) There is an agreed alphabet of signs with known and constant prob3bihtiles of occuaence,
(21 These probabihties are objective. (E.g. the probability of occx- renc~: of a given lets:r in written English can be established by standard
ng procedures to arrive at an estimate that is in principle ndent of the person conducting the operation).
Both requirements are readily fulfililed in the original context in which information theory was developed by WIENER (1948J and SHANNQN and WEW~~~ (1949), w ich arose from the problems connected with
pacities of comm ication channels. ement, however., 1s manife?t?y not fulfilled in the eption unless the ._ y :yerimenter intervenes. To meet ent the experimeii-a- is obliged to impose certain
conditions upon the task presented to the subject. Firstly, he must Deane the alphabet; that is, brea,k the figure up into a mosaic of elements and specify the possible attributes of those elements. In ~T~N~A~E~s (1954) ca these elements are small squares, each of which may take tine of ree colourq. Then, he must impose a temporal sequence on the prcse~tation of these elements to the subject. This procedure leaves Attneave open to two kinds of criticism: (a) the task as presented to the subject no longer has anything to do with figure perception, Ib) the conditions imposed are entirely arbitrary, producing artifacts pertaining onIy to those conditions, rather than leading to the formulation of general principles.
As for the second rsquirement, this is flagrantly violated. It is tacitly assumed that subjective PiJbabilities mirror objective probabilities. That subjective probabilities are related t,o objective probabilities is demonstrable; that there are systematic discrtzpancies between objective and subjective probabilities is just as firmly established by a wealth of experimental material. Ironically enough, ATTNEAVE (1953) has done his share in this direction.
Before analysing these arguments in greater detail there is something to be said for testing several of the more direct assertions made by Attneave. If in fact his approach makes the right predictions, and can be shown to be independent of the arbitrary conditions imposed by the experimenter, then there is less need to cavil at the desecration of information theory.
One of the assertions made by ATTNEAW (1954, p. 184) is !!r;lt the information contained in a figure is concentrated along its contours, par:icularly at those points where the contlour changes direction mo:;t sharply. The first part of this assertion is little more than the rephrasing of the common sense statement that a homogeneous area has, by defi-
14 8. T. GREEN AND P/I. C. COURT.IS
nition, no shape. Only the edges of a lomcgeneot7s area can tell us anythkag about the shape of that area. This would appear to be a truism -incontestable, but not very illuminating. aradolically, as we shall see, it also happens to fall some way short of the tmth.,
The second part of the assertion is highly questionable. Information is here. meant to be selecti.ve information and corresponds to the predictability of a given state of affairs. For corners to have a high information content they must have a low probability o be d&cult to predict from other parts of the figure. not so. On the contrary, corners become highly predictable once infor- mation is available about other parts of the contour.
In his origina! demonstration Attneavr: used a figure and a scanning sesluence that lent credence to his assertions. The figure used represented * a bottle of ink (black) on a table (brown), laid out in a 50 ?( 80 matrix. (See fig. 1). Starting at the tom left hand corner the subject was required to gues: the colour each square in turn (black, white or brown), proceeding from left to right in ascending rows until he reached the top right hand corner. This procedure r*nakes the prediction of the corner of the table practically impossible. Any corner on the left hand side of the figure is just as impossible to predict, although, due to symm&ry, corners on the right hand side become highly predictable.
Attneave was not entirely unaware of the dangers inherent in this particular scanning sequence. e states (1954, p. 184): Our scanning procedure introduces a certain artifact here, in that a particular subjec::
1. Illustration of redundant visual stimulation (after Attneave 1954).
lNFORMATION T EORY AND FIGURE PERCEPTION 15
make errors a linear contour only the first few times he crosses t is fairly ob he starting point of the sequence and the
direction of scan randomly over a large number of sub- jects, su ated errors would e distributed evenly along suieh a
oes not, however. draw the further conclusion that the unpre- e table is largely an arzifact of this same
Ai172. o show that the distribution of errors made in building up a re is dependent on t e guessing sequence used, and in particular
that errors do not necessarily accumulate at points where the contour of the figure changes direction most sharply.
Appuram. A wooden board, with a surface divided into a matrix of 400 half inch squares (20 X 2Cj. Each subject was provided with half inch wooden blocks and half inch per;pex blocks which were to fo the figure and ground of the pattern rSzspectively.
Subjecrs. Eight men and eight women fr a college populntion. PPoceQure. Two kinds of guessing seque were compared. Group L. Linear scanning. A guessing sequence very similar ~3
Attneaves in which successive guesses were adjacent and in whiL!k the subject started guessing at the bottom right hand corner of the board and guessed from right to left along each row until he arrived at the top left hand corner.
Group R. Randomised scanning. A guessing sequence in which * tccessive guesses were dispersed over the whole :Irea of th.c boa!,d in a random manner.
The pattern which the subjects were required to build up by guess- work was chosen for its lack of symmetry and its straight line contours
The naure of the task was explained to the subject, who guessed whether each square was part of the figure or ground as it was presented to him, trying to make as few errors as possible, After each guess; the appropriate block was put in place.
Results. The distribution of errors for the two groups are given ifl figs. 3a and 3b. As may be selen, group L produces errors in hne with
- / -
Fig. 2. A less redundant pattern.
-I- \ r .- [ -
-- :--- ---
1 . ..^
-1. I .~--
g. 3. Ia) Distribution of errors, group E.
~wever. reveal9 an tircly diflcrent picture. sequence pro-
racteristic: that rrors to occur
e contour rather than the areas.
ake significanrly more errors at corners than
onstration makes it clear that: (a) errors do not necessarily collect at the corners of a figure, (b) the number and location
errors is a function of the scanning procedure, so that general state-
18 R. T. GREEN ANTI M. C. COURT.IS
men,ts about the location of information cannot be derived from an experimental technique of this sort.
Attneave (1954) supported his assertion about information being concentrated at points of maximum curvature with another kind of argument. He displayed irregular closed line figures and required his 80 subjects (1954, p. 185) . . . . to draw, for each of sixteen outlined sl~pcs, a partern of ten dots which would resemble the shape as closely as possible, and then to indicate on the original outline the exact places which th: dots represente,d. There was a definite tendency for dots to be placed corresponding to points of maximum curvature.
This technique, too, may readily be shown to be a vehicle for artifacts. By choosing suitable figures and numbers of dots it is possible to con- firm or refute Attneaves assertion. Show your subject a square and allow him four dots and he will place them at the four corners, precisely according to ahe principle. Give him eight dots and he nearly always places the other four smack in the middle of each side, precisely opposing the same prlncipte. Display an ellipse and his behaviour is slightly more variable. Four dots are usually placed as in fig. 4a, thereby confirmitlg aJud refuting the principle. Out of 57 subjects, 49 gave this responsti_ Occasionally, they are placed as in fig. 4b, which is a kind GF compromise between the principle and its converse. Six subjects did this. The remainiug two subjects gave schizoid responses, their dots bearing no obvious relation to the figure. When allowed eight dots the most common response is to place them at roughly equal intervals round the perimeter. In thr. example given by Attneave the fi.gure has certain characteristics that may help to account for his results. It is irregular, has no straight linet, nor smooth curves. Again, it would seem, the results are task specific and do not lead unequivocally to the formulation of a general principle of the type asserted.
Fig. 4. (a) USUZI~ location cpf dots. (b) Common alternzitive.
INFORMATION THEORY AND FIGURE PERCEPTION 19
. . . *
* . . . . . .
. * 6
Fig. 5. (a) Drawing made by abstracting 38 points of maximum curvature from the contours or a sleeping cat, and connecting these points appropriately with a straightedge (after Attneave 1954). Cb1 Broken contour, corners omitted. (cl Broken contour, corners included. (d) Points of maximum curvature.
Attneaves final argument draws upon the fact that (1954, p. 185): Common objects may be represented with great economy, and fairly striking fidelity, by copying the pointc at which their contours change direction maximally, and then connectiag these points appropriately with a straight edge. This was ihustrated, as in fig. 5a, by a sleeping cat. This same, drawing can be treated rather differently by leaving out the points and retaining the centre portions of the lines, as in fig. Sb. The linkeness to a cat is no longer so orvious as in the original, but is probably little worse than that obtained by omitting the other half of the lines and keeping the corners, as in tjg. 5c. The 38 dots representing points of maximum curvature, fig. Sd, Seem to convey little on their own. A reasonable conclusion to draw from this exercise is that points of maximum curvature carry little information per se. Only when directbn is indicated does the $gure take shape, and this function may be per- formed by various parts of the comour, not necessarily those parts
20 R. T. GREEN AND nc c. COURTIS
encompassing comers. shape and of a on a head is least as drawing in the lower as it be if half enclosing corner were
pursue this of thought may turn the practices professional cartoonists. are three styles in use. The of these the line of heavy with little
to introduce quality. Peunctts, and Donald are f&z in this Then, in more sophisticated comes the drawing with often delicate, to form pattern of and shade in line a photographic
The Rip Carol Day Gun Law are familiar of this of treatment. sophisticated of and
relatively is a patchwork style which shape con- veyed cunningly contrived and patches, being indicated than drawn. Hodson is outstanding exponent
is technique. (See figs, 6a-h.) A comparison of these three styles may throw some light on figure
perception in its natural habitat. The task confronting a cartoonist is to represent in black and white some more or less familiar part of our visual world in a re~ognis;tble form. A photograph does the job exactly, an41 the chiarascuro style is an approximation to this. For this reason it i; the least interesting of the three techniques in the present context. Ht is when the cartoonist aims for a more economical style that we begin to see how complexity may be reduced without loss of vital features- how an impression may be conveyed without supplying all the material. In simple fine drawings subtleties of Bight and shade are ignored or only crudely indicztcd. A set of conventions is adopted whereby a heavy comour, pha several special features, is used to facilitate recognition ,Jf the figure represented. A face, for instance, is conventionalised in terms of eyes, nose, mouth and ears placed within a clear cut boundary. Expressions are conveyed by eye-brows, shape of eyes aud mouth, and an occional line around the mouth, nose or forehead to indicate the ringing into play of particular muscle groups. With this simple equip-
ment a skiLled cartoonist may convey a vast range of facial expressions, remarkably subtle in their overtones.
These simple line drawings seem to support Attneaves contentions
INFORMATIO;J THEORY AND FIGURE PERCEPTION
Fig. 6. (a) Prelate. (b) Outdoor type exercising at bar. (c) On parade.
(d) Businessman. (e) Woman on floor. (f) Woman reclining. (g) Woman walking. (h) Office boy.
22 R. T. GREEN AND M. C. COURTIS
about the location. of information, but even at this stage there is more going on than mleets the eye. There is a selection process involved whereby certain contours are pressed into service, while others, just as clear on a photograph, are dispensed with. Attneaves cat would be drawn by a competent cartoonist using far less of the contour to convey an impression quite as realistic.
Even the contours that are used do not consistently obey the Attneave formula. Points of rapid curvature such as the end of a chin, nose, finger, knuckle, angle of jaw or dome of the forehead are often left out, although perceptually they are not missing. The cartoonist suggests them and the percipient supplies them. It is this economy of line that is regarded as one of the hallmarks of the gifted draughtsman.
This selection process becomes even more obvious when we come to consider the patchwork style. Large and important sections of the illustration are deliberately omitted by the artist in such a way that they are as perceptuahy present as the sections actually drawn. This is a remarkable acbie-lement which will repay closer inspection. Somehow the artist manages to conve,y a sense of spatial relationships in parts of the figure that are objectively empty, homogeneous and unstructured. How is this paradox possible?
The answer seems to be that the artist picks out some salient features of the figure to be represented and draws these with such fidelity that the percipient is compelled to complete the figure according to the prescription suggested by the features presented. By presenting a partial cue of unique precision the artist forces the percipient to draw an his own resources to make senc.e of what he sees. He is obliged to structure certain parts of the empty field according to the demands made by the partial cue, completing the figure to meet the prescription supplied bj the artist.
There is an obvious connection here with Streets (1931) gestalt completion figures, the difference being that a Street figure is designed to confuse the percipient. The relevant partial cues are disguised by arbitrary fragmentation and concealed among other patches that are irrelevant or misleading. (See figs. 7a, 7b). In both cases, however, the role of past experience is crucial. The raw sensory data of a Street figure can be orgznised into a meaningful percept only if it can be made to fit into a schema already built up as a result of commerce with the object represented. There is usually a period during which the percipient searches the display for the partial cues that will enable him to identify
INFORMATION THEORY ANLl FIGURE PERCEPTION 23
Fig. 7. (a) Street gestalt completion figure, a train. (b) Street gestalt completion figure, a man crouching with camera.
24 R. T. GREEN AND M. C. COURTIS
*the schema into which all the patches may be fitted. He can be aided in this by being told Its a train, or completely frustrated by having the fipre presented in the wrong spatial orientation or being given a mis- leading set. Presented upsidedown, or with the spurious information Its a face: the random patches remain random and cannot be mslde to cohere into a meaningful percept.
With Hodsons figures the task is made easier, and the percept is formed almost instantaneously. The partial cues are chosen for their compelling quality and are not concealed by irrelevant or misleading cues. The only way to reduce the figure to meaningless elements is to turn it upsidedown.
Some of Ho&on% comments (private cclrmmunication) are relevant in this connection. When asked to desLribc how he came to develop his special style he referred back to an earlier interest in writing poetry that conveyed its message indirectly. The message was never state& only hinteC at in such a way that the reader was obliged to state the message for himself. By means of this elliptical style Hodson aimed to convey the sort of message that loses its impact if an attempt is made to state it directly. Classical mime uses a similar artifice. The quintessence of a story that would seem banal Yi stated directly is conveyed with a disarming simplicity by gestures alone.
In his drawings Hodson is intent on making the percipient do the work, as he puts it. He aims to structure the field in such a way that the percipient is obliged to supply the missing parts. Obliged, in fact, to see something that is not there. A nose ;S often missing, presumably because it so rarely carries vital info, alation, and because we know where it belongs anyway. By way of analogy Hodson refers to his fascination with trapeze artists who draw curves in space that arent there.
Sometimes a whole face is left almost blank, and yet we feel we know exactly what expression the sporting type in fig. 6b is wearing as he downs his pint. In fig. 6c we see the sergeant majors shapeless chin lost in rolls of invisible fat, and the wooden expression of the faceless businessman stares lout from fig. 6d. The women in figs. 6e, f, and g have no costours to their faces at all, yet the bone structure and set of the facial muscles are plain emough. Fig. 6g is especially remarkable fog the sparseness of the cues the percipient is given to work on and tfiz amount that has to be perceptually filled in. Nevertheless, the: im- plied posture obliges us to see the missing arm, shoulders, theft cage and foot, along with the faintly simpering expression. Fig. 6h is worth
INFORMATION THEORY AND -2IGuRE PERCEPTION 25
including for the apparently arbitrary way in which Attneaves second principle has been flouted. Some points of maximum curvature, such as the shoulders, elbows, nose and forehead, have been drawn, while others equally sharp, such as tingertips, lower lip, cuffs and back of the collar have been left to the imagination. Ankles are drawn, but wrists are not.
Hodson is not unique in this. He has simply developed a particular attribute of the cartoonists craft to the point where we may become aware of the demands that are made of us. Any cartoonist worth his salt tries to make us do the work and see with conviction something that is only hinted at in the actual display.
When it comes to deciding what parts to leave out there seem to be few hard and fast rules. The newspaper bzing read by the prelate in fig. 6a, for instance, has lost its bottom corners while retaining the upper ones. There seems to be no special reason for this-the upper corners may be removed without making nonsense of the picture. Possibly the lines chosen help to make the top edge of the newspaper loom over the percipient, emphasising the angle at which it is being held. Such judgements have an intuitive quality that defy exact for- mation, and it may be that a line is left in because it keeps the balance of the composition- which is an aesthetic principle, not necessarily in line with the principles of economy and the compelling partial cue.
It may be thought that the habits and idiosyncracies of cartoonists provide a somewhat laboured and homely way of discussing the refined technicalities of information theory. All this loose talk about partial cues sounds less untidy when referred to the concept of redundancy. Bu! this is precisely the point. There are in fact two languages in vogue using a common vocabulary to conceal their fundamental differences. It is misleading to talk about the information content of a figure and the location of information within a figure as if this were the same kind of information introduced by Wiener, Weaver and Shannon. There can be no objective transition probabilities from element to element when the elements are undefined, perhaps undefinable, and in any case unique to the person perceiving thi* figure, along with the scanning sequence and transition probabilities.
To use the language of information theory in this context is to
36 R. T. GREEN kND M. C. COURT.IS
employ a metaphor. Metaphors can be exciting, illumina+ing, and use- ful, but metaphors they remain. Unless we are very careful we shall find ourselves trying to roll back the frontiers of science with a bull- dozer. Ihis would be unprofitable as well as faintly ridiculous-like ha&g a close shave with Ckcams razor.
There are times when ATTNEAVE (1959) seems almost to concede this point. Drawing on the distinction between metrical and rtructural information tist put forwzd by MACKAY (1950), it is suggested I-hat the metron content can be inferred from the logon content. In the case of figure perception this is alleged to obviate the difficultie,; ar;sxiated. with defining the grain of the stimulus array, and the 1o;;on content (1959, p. 83) . . . will almost certainly be proportional to i lformation- in-bits, to a first approximation, once a:ny particular grain is specified. I2 other words, the amount of selective information is tierred from some other measure. This idea might pass muster if specifying the grain were the only bar to obtaining a measure of selective information, Since, however, the scanning procedure is of crucial importance we arc left with a model that has scant bearing on the problem of figure perception as it normally occurs.
in the model it still makes sense to talk about the amount and location of information contained in a figure as an informat ion source. In real !ife the amount and location of the information is a function of the percipient. What has to be measured is not something VI the source, but something about the process of perceiving. ATTNEAVE (1959, p. $3) still talks as if the model were more than B metaphor. It may be demonstrated (for instance, by the guessing game technique) that angles and intersections are regions of high informational content m the visual field. This discovery, we have seen, is an artifact of the task imposed.
As it so happens, informat? n often is concentrated at th corners of a figure because distinctive features commonly involve shq changes in the direction of the contour. l5ut this is fcrG:ous. For an-f particular
re among a given set of figures the distinctive features may or may not be provided by corners- to discriminate: between a set of snakes, for example, it would be necessary to rely
lINFORMATION THEORY AND FIGURE PERCEPTION 27
dot at 12 oclock is discriminable from one with a dot at 10 oclock. If we are going to borrow a language from another discipline we
wmhl probably do better to draw on game theory rather thzn infor- mation theory. By using this conceptual framework we can direct our attention to the process of perception as it occurs in its natural envi- ronment-the human ethology of perception, so to speak. 0ur efforts would be more gainfully directed if we considered how information (loose sense) is utilised by the percipient, instead of trying to measure . the amount and locus of information (technical sense) in the display. What we might profitably concern ourselves with is defining, analysing, and eventually understanding, the perceptual strategies and categories actually used by percipients. Doubtless, KELLY (1955) and BANNISTER (1962) would be only too ready to accord perception a place of this kind under the general rubric of personal construct theory.
BINDER (1955) and BRUNER (1957a, b) have already gone, some way lowards establishing a bridgehead in this territory without having seen through the metaphor or abandoned the speudo-language cribbed from information theory. Nevertheless, they are on the right track and are riot hopelessly committed to the concepts or mathematics of infor- mation theory. Provided that the terminology is handled with more circumspection this approach need not suffer from the fatal flaws inherent in the application of information theory to the problems of figure perct:$on. The guessing game then falls naturally into place as one of the available techniques for investigating search procedures and perceptual strategies, along with a number of others reviewed by Binder.
As a final exercise we can construct a general model of the game as it is played naturally. This is not intended as an ex cathedra pro- nouncement on the nature of figure perception. The aim is simply to offer a convenient framework within which fruitful research may proceed.
IIn real life two distinct stages may often be distinguished. In seeking to identify a particular person at a distance we first have to establish any candidate as belonging to the required class, for example, human femde. At this stage we direct our attention to those attributes that are most typical of members of this Llass. (Skirt, long hair, etc.). Having established that we are dealing with a member of the required class we turn our attention to those features most unique to the idi- vidual we wish to identify. (The characteristic pose, profile, or article
28 R. 7. GREEN AND M. C. COURTIS
of dress, &c.). So the locus of information will be a functilon of the task and will change with it- not a fixed attribute completely inherent in the figure itself. Similarly, the locus of information will be a function of the percipient, depending on how well and in what capacity he happens tlo know the particular person he is tqing to identify.
The schema that we use to classify the candidate as a human female is a gener,gZ one, and that to identify the individual a special one. At either stage the percipient is engaged in a kind of hypothesis :esting game in which the information (loose sense) is matched against the variou; schemata to allow acceptance, rejection or modification of the hypothesis, and further direct the search pl*ocedure. OLDFIELD (1954), although more concerned with the Bartlett type of recall phenomena than with figure perception, puts forward some interesting suggestions as to just how such schemata might be subjected to an encoding process y the organism cum computer. In this connection it is worth noting
that B,ARTLE ITS (1932) account of remembering as a process of recon- struction within schemata provides a far closer and more illuminating parallel for the perceptual process than does information theory, a p3inz made by VERNON (1957).
In any event the search procedure will be determined largely by the percipient rather than by the display, and will almost certainly be Lzdqendent of the grain or mosaic of the display, even assming that such a grain could be specified. In genuEne figure perceptrL_I infor- mation (loose sense) is gathered in localised blocks corresponding to the fixation points associated with saccadic eye movements. This much has long since been established by BWWELL (1935) who also noted the tlvo main stages of the perceptual process in the same study. LEEPER (1335) put forward some similar ideas.
This account of the perceptual process echoes the controversy tween GI~SQN and GIBSON: (1955) and POSTMAN (1955) concerning
the role of expe,ience in learning to perceive. The view being put ard here is more in line with Postmans enrichment theory, with
phasis on the central importance of meaning as a factor shaping cepts, than with the Gibsons view that perception becomes ridical as stimulus differentiation takes place. In fact it is
essary to go back to TITCHENERS (1915) context theory, with its t distinction between sensation and g>crception. to see how easy
come these days to overlook simple facts in an attempt to r igno. :nce with a spurious scientific air. This is not to say
INFORMATION THEORY AND FIGURE PERCEPTIOK 29
ibsons views are utterly irrelevant. It is quite possible that their account of rceptual learning applies during the earliest stage
fore being su~~lenlented by a more sophisticated ingful concepts begin to shape our percepts. 2) deals at some length with the problems of applying
measurements to attern perception, but very wisely he ion between meaning as structure and meaning as sig-
oughly speaking, this runs parallel to the distinction perception and figure perception. Figures are meaning-
ful in that we have learned their significance and can refer them to :!n object or event in the real world. atterns may have predictable structures, but do not in general look like a familiar object. ,.he easiest way of illustrating the main feature of the distinction is to turn the pattern in fig. 8 upside down. To quote ARNER (1962, p, 142) Thus meaning as structure can be quantified, and the information concepts are quite appropriate for its quantification. On the other hand, meaning as signification cannot be quantified other than to say that it exists or does not exist.
Garner, however, has still failed to appreciate the full extent of the
Fig, 8. The distinction between a pattcm and a figure.
30 R. T. GREEN AND M. C. CGL%TIS
di&uIties inherent in applying informa&ion theory even to pattern perception. He tends to overlook a number of problems in this area because he is mvre o&n cm %&h Stibi& k3!b%Stti kl language sequences than with pattern perception. In his chapter on pattern perch-@on, whether he is talking about discrimination, re- dundancy, noise, or goodness of form, the problems associated with defining the alphabet of signs, the grain of the array, the subjective nature of the transition probabitities involved, and the scanning sequence are all unresolved. In particular, the last of these is lmost completely ignored. There *are points at which Garner comes bAL~e to openly recognising the subjective nature of the information being measured. For instance, in dealing with the problem of the variables involved in redundancy he states (1962, p. 186) There are many ,:xperiments in which a proper analysis of the amount and form of redundancy requires careful consideration of the variables as the subject sees them . . . I[f the total constraint for the subject is lower due to his seing fewer variables, then, clearly, the redundancy which we would assume to be operating for any fixed nul lber of selected stimuli would also be lower. It is necessary, in other words, to use a considerable amount of good judgment in applying these principles and concepts to an actual experimental problem. Or again, (1962, p. 189) In other words, redundancy increases the discriminability of the stimuli actually used, but this increased discriminabjility can be of value only if it is perceived. (Our italics).
Fundamentzgy there is no way out of this dilemma. Information theory is concerned with transitIon probabilities, while perception, whether of figures or patterns, is essentia.Jly non-sequential, or at least non-linear. A linear sequence may be imposed, but the data no longer hrtwe much bearing on problems of perception, Garner appreciates the diBculty, but seems to suggest that it might be overcc+me, at least with regard to mittens (1962, p. 205). With two-dimensional geometric J patterns, the problem is more complex because of the several irections of movement possible on the plane surface. With a time
sequence of stimuli, for example, there is no doubt about which stimu- lus comes after any given stimuIus; but with tiled cells on a matrix, each stimulus ha Eight adjacent stimuli, if each call is considered a stimulus. Perhap this fact suggests the possibility that as a first order analysis, we f=olrld use a multi-variate analysis of patterns of cells on a matrix, in w&ich each cel3 is predicted from the eight ad¢ cells
INFORiMATION THEORY AM) FIGURE PERCEPTION 31
ATTTJEAvE (1954) has suggested a more restricted procedure of this sort+ by having subjects guess along horizontal rows whether the next ceII will be blat us Attneave converted the two-dimen- sional problem rmensional problem so that it could be handled more easily.
Unft,rtunately, once the problem is cast in these terms it is no longer the Saran problem. Pattern perception may involve a kind of guessing game, but not the kind used by Attneave. To Fee just how far this hope of Gamer% fails short of reality it is necessary to take in turn each of the four requirements already discussed. t then become? app%arent that not only is it impossible to meet all four requirements-. in a genuine perceptual task it is not possible to meet aqy one of them.
The personal, idiosyncratic nature of the scanning sequence, and the subjective nature of the transition probabilities involved have al- ready been dealt with. Defining the alphabet of signs and the elements of the mosaic pose difficulties quite as intractable. An abstract picture or design can be broken up into half inch squares, or whatever mosaic the experimenter decides, but this is not how it is seen by the percipient. A three colour reproduction of the display will provide a natural grain and alphabet, in thaw there is a definite number of dots each of which can have only one of three possible colour values., but even if the display is blown up sufficiently for the subject to resolve each dot and discern its coiour, this stiil has nothing to do with pattern perception. Viewed under normal conditions a mixture of red and blue dots is seen as a shade of purple, which is not included in the alphabet of signs as already specified. By blowing up the display to create a discriminable mosaic the experimenter has destroyed the quality of the percept, And the same argument holds, of course, for the spatial relationships between the parts of the display. The quality that makes a pattern into a pattern is lost when elements are presented in isolation, just as surely as the quality of significaStion is lost if a meaningful picture is presented in this way. Perception of a sequence of relation- ships between points is a very different process from that of the per- ception of simultaneous relationships between parts. If the Gestal; school said this ages ago this is no excuse for imagining that the facts will disappear simply by muttering the hermetic formulae of inter- mation theory.
Perhaps it is to MILZER (1962) that credit should go for dealing the most devous blow. Up to now we hsvc been considering arguments
32 R. T. GREEN AND M. C. COURTIS
against only the misapplication of information theory to figure and pattern perception, tacitly allowing that language sequences provide legitimate material for an analysis of this kind. MILLER (195 l), origi- nally one of the foremost exponents of information theory applied to langurzige, has since revised his earlier views in a most courageous and forthCght manner. As he says (1962, p. 761) In the course of this work I seem to have becqme a very old-fashioned kind of psycholo I now believe that mind is something more than a four-letter, A Saxon word-human minds exist and it is our job as psychologists to study them. Without going into the arguments in detail it is suaicient to note that language is not just a set of transition probabilities. As soon as we look for meaning in a language sequence (and this is what language is al! about) we discover that the transition probabilities are a function of the reader a& the situation in which he finds himself. Give me the sheet has two entirely different meanings to the sailor and the housewife. Moreover, a word sequence can occur for the first time and yet be entirely predictable. The boy spoke a triangle is an unusual and unexpected sequence, but if it is suggested that the same kind 03; sentence construction can be applied in respect of a regular fous sided fi,gure, then the sequence The boy spoke a square, a!thou never encountered hitherto, is perfectly predictable.
So two of the cardinal requirements of information theory are lost; traasition probabilities are no longer objective, even in principle, and the alphabet of signs is not one of letters or words, but of meaning units, which are again peculiar to the individuti:. What is transmitted may be regiarded by an engineer as simply a string of words, or letters and sr, tes for that matter, but what is conwnunicuted is a set of meanings. To use Millers terminology; the essential property of language is not to be found in Markov chains but in syntactic consti- tuzuts. It is easy to overlook this crucial distinction in print because of the absence of speech melody in the channel. Both the sender and ree:liver of the written message use speech melody to carry the msaming, but the melody itself is not transmitted-it is re-created by the Ireceiver according to a set of rales external to the message itself. MILLER and BARD (1963) and MARKS and MILLER (1964) have taken pains to show the importance of syntactic and semantic rules, but the influence of the speech melody has yet to be systematically investigated. Which leaves information theory right back where it started-a mathematical tool in communication engineering, particu-
My useful 41~ ~e~li~g with the echnieal problems of channel capacity. AT 59, p. SLa) tacitly concedes the main point when he
says: ~~~~t~~t~~ bear in mind, however, that the subject in ~~~~r~~~~~ with the experimenters de-
ram jut these discrepantzies that we about the nature of perceptual processes.
rise to the important distinction e d~sti~~ti(~~ between bits and
d to reveal its limitations. To the point, and possibly, the bus.
Attempts to hrin Mre ~r~~pti~~ within the smbit of intsrmation theory, gh su~r~~iail~ altrac turn 010 on elaser i &ion to be misdirected. nly are some fundam I principles af the th y flagrantly violated, the
data themselves sim do not justifp tile desecration of information theory on matic grounds. veral counter demonstrations are used to reveal previous
findine HS artifacts of the techniques employed and the arbitrary conditions imposed by the experimenter.
It is further argued that it is meaningless to talk af the location of informatioia within a figure as if it were something independent of the percipient or the task imposed. This error stems directly from failing to reco~nise that borrowing the language of information theory to discuss the problems of figure perception is ts employ a metaphor of limited scope. Attention therefore needs to be focussed on the prucess of gxxceiving rather than on the propepties of the figure itself. En terms of the metaphor this means examinin the encoding process instead of the source.
In order to apply information theory 1 imately ts figure perception at least four principles must be! observed: the sea ing sequence, the alphabet of signs, and the grain or mosaic of the display must all th;ec be defined, and the transition probabilities between the elements must be objective. Not one of these conditions can be met in genuine figure perception. Figure perception, ds it occurs naturally, does nor involve the scanning of a mosaic of elements in a manner
ous to a teLvisian camera dealing with a gramcd photographic print. A study of the practice af professional cartoonists indicates that the percipien! is called upon to respond to partial cues, drawing on his past experience to fit the whale inta a schema that makes sense of the display. In other words, We wauld do better to talk of perceptual strategies, as if the percipient were engaged in EL search for the perceptual hyppothesis that will best srganise the raw sensory data. The sorts of hypotheses he entertains, and where he looks within the display for relevant cues, must depend on the task as presented to and conceived by the percipient, and on the percipients past experience.
It is suggested that there are two distinct stages in this perceptual discrimination
34 R. T.. GREEN AND M. C. COURTJS
prwxm. Firstly, to identify the figure as belonging to a particular class. Secondlyay, to establish its unique identity as a member of that class, These stages are thkreftore characterised by a search for those cues that are: (a) Imost typical of that class, (b) most unique to the particular member of that class, The location and the amount of information thus depend, arnk%q\g O&W thin what the percipient thinks he is looking for, and are bound to change d the actuai process of perceiving.
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