Isomorphism in Gestalt Theory: Comparison of Wertheimer's and Köhler's Concepts (3)

by Abraham S. Luchins and Edith H. Luchins


Isomorphism in Gestalt psychology is sometimes regarded as strictly KÖHLER's psychophysical isomorphism. Thus, in Solomon E. ASCH's (1968) encyclopedia article on Gestalt theory, the only mention of isomorphism was to KÖHLER's psychophysical isomorphism.

KÖHLER proposed a fundamental change in the conception of cortical functioning-A region such as the optic sector may be considered an electrolyte; the processes within it occur according to physical laws of self-distribution rather than according to the microanatomy of neural networks. Local states of excitation are surrounded by fields that represent these states in their environment and interact with other local states similarly represented. On this basis KÖHLER put forward the hypothesis that there are physiological processes which are special instances of physicochemical gestalten and that these are the correlates of phenomenal gestalten.
Implicit in the preceding examination is the assumption of psychophysical isomorphism, or the proposition that brain processes include some structural features that are identical with those of organized experience. Isomorphism refers not to metrical but to topological correspondences; brain processes are assumed to preserve the functional relations of symmetry, closedness, and adjacency, not the exact sizes and angles of patterns projected on the retina. This formulation diverges from the widely accepted view that phenomenal and physiological events are lawfully correlated but have no further likeness between them. The postulate of isomorphism is intended as a heuristic guide to investigation. In this manner KÖHLER sought a unified explanation for facts in neurophysiology and psychology among certain facts of physics. (ASCH, 1968, p. 161)

ASCH discussed the study of apparent movement but did not refer to the physiological short-circuit hypothesis, perhaps because he knew that WERTHEIMER regarded it as a footnote, rather than as essential in understanding the phi phenomenon. Under the heading of "Perceptual Organization," ASCH wrote:
... WERTHEIMER took the radical step of denying the reality of sensory elements as part of perceptual experience. His study of apparent movement ([1912-1920], 1925, pp. 1-105), which marks the formal beginning of gestalt theory, provides a specific illustration of this thesis .... WERTHEIMER pointed out that apparent movement is not a series of sensations but an effect of two stimulus events cooperating to produce a new, unitary outcome; perceived motion cannot be split up into successive stationary sensations.-From the assumption that experience consists of having one sensation followed by another, one cannot account for the experience of change inherent in motion, a conclusion that applies equally to the perception of real motion. (p. 159)
A further and more important step in this development was the gestalt account of grouping, or unit formation, in perception .... WERTHEIMER described certain fundamental principles of grouping, or unit formation, in perception, among them those of proximity, similarity, closure, common fate, and good continuation.-WERTHEIMER considered one principle, that of Prägnanz , fundamental and inclusive of the others. The principle of Prägnanz maintains that grouping tends toward maximal simplicity and balance, or toward the formation of "good form." (pp. 159-160)

Under the heading "Physical and physiological gestalten," ASCH wrote:
The concept of gestalt received a fundamental elaboration in the work of KÖHLER (1920, 1940). As a first step KÖHLER called attention to a striking similarity between certain aspects of field physics and facts of perceptual organization. He pointed to certain instances of functional wholes in physics that cannot be compounded from the action of their separate parts. There are macroscopic physical states that tend to develop toward an equilibrium and in the direction of maximal regularity. (p. 161)

Under "Nativism," ASCH wrote:
Gestalt theory holds that organization in accordance with general principles of physical dynamics is present from the start in psychological functioning. This position leaves wide scope for unlearned processes. At the same time, the widespread view that gestalt theory underestimates the effects of past experience is oversimplified. It is more important to note that the concept of organization determines the treatment of both unlearned and learned functions. Gestalt theory refers unlearned operations mainly to relationally determined physiochemical processes rather than to the action of specific anatomical structures. Similarly, it holds that the effects of past experience are also products of organization, or determined by structural requirements. (p. 169)

In the conclusion section, ASCH returned to isomorphism:
It is ... appropriate to stress that gestalt theory is not a completed system, that many of the issues it raised await resolution, and that it might be best described as a program of investigation or a region of problems. Thus, there is as yet little understanding of the physiological foundations that gestalt theory sought for psychology, and the postulate of isomorphism remains a heuristic principle. (p. 173)


In his book, A History of Experimental Psychology (1950, original 1929), BORING wrote about the phi phenomenon and isomorphism in Chapter 13, entitled "Gestalt Psychology."

[In 1912] WERTHEIMER was describing seen movement under the conditions of discrete displacement of the stimulus, as it occurs in the stroboscope or in the cinema. Wundtian elementism would have required him to say that a sensation of given quality changes its location in time ... Such [apparent] movement is not sensation as the word has been used by WUNDT and KÜLPE. It could properly be called a phenomenon, as that word had been used by the phenomenologists, and thus WERTHEIMER called it phenomenal movement or simply the phi-phenomenon.
Suppose you have a stimulus which is discretely displaced from position A to position B, and then back to A again, and to B again ... If the time-interval between the exposures at the two positions is long, you see simply discrete displacement, no movement. If the time-interval is shortened, you begin to see some movement at A or at B or both. If it is still further shortened, you come to the optimal rate at which perfect movement back and forth is perceived between A and B and in which the phi-phenomenon marks the movement ... Such phi is a visual perception, localized in space, with given extension ... Phi is, moreover, an emergent. It pertains to a whole psychophysical situation and not to any of the separate factors that enter into it. In that it is as much a founded characteristic as is shape, melody, or any other Gestalt.
Because Gestalt psychology tends to deal with wholes it frequently finds itself concerned with fields and field theory. A field is a dynamic whole, a system in which an alteration of any part affects all the other parts .... Because perception seems often to follow laws of physical dynamics, KÖHLER has supposed that there are neural brain fields which underlie and account for the dynamics inherent in the phenomenon of perception. KOFFKA has supposed that you must understand human action in terms of a behavioural field which includes, not the stimuli and the physical environment, but the outer world and its objects as perceived and conceived by the actor. (1950, pp. 590-591)
... There is much more to be understood about Gestalt psychology than that it deals with wholes and phenomena. Usually it works in terms of field theory, as we have noted. The important Gestalt psychologists have accepted a special theory of relation between experienced phenomena and the underlying brain processes, the theory called isomorphism, and to that we shall return. (p. 593)

Returning to the isomorphism concept in Chapter 25, "Brain Function," BORING wrote:
In the twentieth century the Gestalt psychologists have argued for isomorphism. WERTHEIMER suggested this relation for seen movement in 1912, but KÖHLER has been its most effective supporter since 1920 .... Isomorphism is not projection but it implies it. The Gestalt theory is that a spatial pattern of perception is isomorphic with the spatial pattern of the underlying excitation in the brain. Isomorphic means corresponding topologically, but not topographically. Shapes are not preserved, but orders are. In-betweeness is preserved .... It seems pretty clear that WERTHEIMER and KÖHLER got this view, not from the results of research, but from the atmosphere of the times, perhaps from G.E. MÜLLER's axioms, which, like all axioms, ask for acceptance without proof. [Does history support BORING s conjecture? Was this conception of isomorphism not the result of research?] On the other hand, the belief in both visual and somesthetic cortical projection was growing and the two theories, projection and isomorphism, support each other. The stimulus-object and the peripheral excitation are isomorphic. The perception and the stimulus-object are isomorphic. If perception and the cortical excitation are isomorphic, then the cortical and peripheral excitation must also be isomorphic, since patterns isomorphic with the same pattern would be isomorphic with each other.
It is true that WERTHEIMER went out of his way to object to isomorphism between peripheral excitation and perception because he had in mind the many instances, like the perceptual constancies, where the correspondence is not exact topographically; but these arguments deal with gross approximations. There is no doubt that the reason that KÖHLER's contention seemed so plausible was due in part to the growth of the belief in projection. For the same reason some of KÖHLER's more recent experimental demonstrations of the isomorphic relation between perception and brain excitations are consistent with the theory of central projection or at least with central isomorphic reduplication if projection is not the physiological means which the organism employs. (Ibid., pp. 681-682)

The index to BORING's 1950 book listed projection, discussed on pages 680-682, only in relation to isomorphism. BORING's statements raise interesting questions about the relationship. Does isomorphism imply projection? Do projection and isomorphism support each other? Also of particular interest to us are BORING's remarks that WERTHEIMER went out of his way to object to isomorphism because he had in mind instances such as the perceptual "constancies," where the correspondence is not exact topographically; unfortunately, references were not cited.
For more detailed discussion of perception, BORING referred the reader to his 1942 book, Sensations and Perceptions in the History of Experimental Psychology. In Chapter 2, "Physiology of Sensations," the section entitled "Projection," included the following:
The receptor-fields of the sense-organs are projected upon the central nervous system in the sense that the afferent fibers lead to the central system. Indirectly by way of synaptic connections in nuclei, the tracts of all five senses establish in man connection with the cerebral cortex, although they also make other connections at subcortical reflex levels which do not involve the cortex. Thus neural anatomy has come to support Johannes MÜLLER's theory of specific nerve energies, which eventually became .... a projection theory of sensory quality. Sight is not hearing because the optic fibers are projected upon the occipital lobes and the auditory upon the temporal lobes. If you could cross-connect the optic and auditory nerves, you could, du BOIS-REYMOND imagined, see tones and hear colors. (p. 78). [fn 2]

BORING traced the history of projection in vision, noting that spatial differentiation has long been recognized as the basis of spatial perception:
The anatomy of the optic chiasma was known even to GALEN (ca. 175 A.D.) who explained the singleness of binocular vision by assuming that some of the optic fibers from each eye cross at the chiasma and join corresponding fibers from the other eye. The discovery of the horopter (the locus in space of points seen singly in binocular vision) by AGUILONIUS in 1613 certainly supported some such view, and NEWTON in 1717 assumed that half the fibers cross at the chiasma to join the corresponding fibers from the other eye either at the chiasma or at the brain. WOLLASTAN in 1824 observed hemianopia in himself; half the field of his vision disappeared when he was greatly fatigued, indicating that NEWTON s notion of visual projection was correct, that the fibers from the left halves of both retinas lead to the left half of the brain, and conversely. Thus, when [Johannes] MÜLLER came to the problem of vision in 1826, he had little choice about the matter. His nativism, furthermore, also led him to assume that spatial difference on the retina must mean spatial difference in the Sensorium. (pp. 79-80)

MÜLLER offered a formal theory of "specific sense energies" ... or "specific energies of nerves" ... In 1871 Julius BERNSTEIN offered an explicit projection theory involving sensory circles. Although there were many criticisms of his theory. BORING concluded: "Altogether the theory was convincing in 1871 and remains plausible today after seventy years" (p. 81).
It cannot be said, in fact, that we have advanced much beyond BERNSTEIN. It is no longer necessary to assume sensory circles at the periphery or irradiation at the center, for it is clear that all stimulation spreads in the peripheral organ, much or little according to its degree. In vision the spread is partly optical dispersion and partly retinal and neural spread: the brightest stars have the greatest magnitudes. On the skin, the dispersion comes about by way of pressure gradients or thermal gradients. In the inner ear, a loud tone affects more of the organ of Corti than does a weak tone. Thus central irradiation may be given up; but projection stands.
Projection is, of course, in this sense one-to-one. The receptor field and the cortical field are held to be isomorphic, that is to say, the spatial orders at the periphery are supposed to be reconstituted topologically in the brain - not the exact shapes, but the orders. (On the nature of isomorphism, see the next section.) ...
Some degree of isomorphic projection is also required by KÖHLER s theory of the isomorphic relation between perception and the patterns of excitation in the brain (see the next section). If the pattern of perception, being, in general, correct in spite of all the exceptions which Gestalt psychology has exhibited, resembles the pattern of stimulation, and if, as KÖHLER's theory asserts, it also resembles the brain pattern, why then the pattern in the brain must also resemble the pattern of stimulation. (pp. 82-83)

[The last sentence is reminiscent of WERTHEIMER's brief description of KÖHLER's isomorphism concept: How stimulation is and how it is in the brain (K). Note that BORING described projection as one-to-one. He went on to also describe isomorphism as one-to-one, whereas this point-to-point correspondence was not required in either WERTHEIMER's or KÖHLER's conception of isomorphism.]
The next section, called "Isomorphism," began as follows:
One system is said to be isomorphic with another in respect of their spatial relations if every point in the one corresponds to a point in the other and the topological relations or spatial orders of the points are the same in the two .... perception and stimulus are spatially isomorphic in as far as the perceived spatial orders correspond with the spatial orders in the stimulus. Projection of the stimulus field upon the cortex tends to be isomorphic .... If perception and brain field are both isomorphic with the stimulus field, they must be isomorphic with each other. It is to this solution of the mind-body problem that KÖHLER has applied the term isomorphism - meaning psychoneural isomorphism. The simplest test of such isomorphism is to see whether adjacencies and inbetweennesses are preserved from one system to the other.
This word has sometimes been extended to other sensory attributes than space. There would be temporal psychoneural isomorphism if the time-order of perceived events is the same as the time-order of the neural events underlying them. Intensive isomorphism would mean that sensory intensity always corresponds with degree of the total underlying excitation. Qualitative isomorphism, at which KÖHLER has hinted, implies that difference in sensory quality implies difference in excitatory quality, as if different kinds of ion-concentrations in the brain could explain the difference between yellow and blue or between sweet and sour - a rather improbable assumption in view of the uniformity of nervous actions.
Psychoneural isomorphism, however, is a special case of psychophysical parallelism and of the mind-body problem in general. It was believed to be axiomatic long before the anatomical and physiological knowledge of projection was sufficient to justify it. How did psychologists come to hold this view? Why did it seem axiomatic to them? (pp. 83-84)

BORING went on to conjecture about how KÖHLER came to the concept of psychoneural isomorphism:
When KÖHLER participated in the founding of Gestalt psychology (1920), he made over [George E.] MÜLLER's [1897] axioms in accordance with the new unanalytical dynamic conceptions. It was he, indeed, who applied the term isomorphism to this psychoneural relation, he and his colleagues who made the concept so important in Gestalt psychology that it is not always possible in their writings to distinguish between the phenomenal field and the correlated brain field. He was, nevertheless, explicit. The relationship is one of topological order, not of identity of size or shape (BORING, 1942, p. 90).

BORING continued by quoting KÖHLER s statements in his Gestalt Psychology (1929, pp. 64-66):
all experienced order in space is a true representation of a corresponding order in the underlying dynamical context of physiological processes (p. 64)-.experienced order in time is a true representation of the corresponding concrete order in the underlying dynamical context (p. 65). And the law for phenomenal organization is similar: to a context, experienced as "one thing" belonging together, there corresponds a dynamical unit or whole in the underlying physiological processes (p. 66). "In this respect again, the order of experience is a true representation of a corresponding functional order in the processes upon which it depends" (Ibid.).

BORING also discussed isomorphism in relation to WERTHEIMER's experiments on the phi phenomenon in a section called "Perceived Movement" (pp. 595-596). Using a tachistoscope, WERTHEIMER arranged for a single discrete displacement of a simple geometric object, such as a line segment.
The first member presented he designated a, the second b. When the time interval between a and b was relatively long (about 200 millisec.), the subject perceived succession, first a, then b. When the interval was very short (less than 30 millisec.), the perception was one of simultaneity, a and b together. In between successivity and simultaneity he got movement, the optimal interval for which was about 60 millisec. [This gave rise to] the case of pure movement, which WERTHEIMER named phi-movement which connects the objects and has direction between them, but seems not in itself to be an object.
... For optimal movement one sees a single object moving, not an a turning into a b. In this contention WERTHEIMER was following out the tradition of MACH and EXNER, but he went further. He insisted on the validity of movement as an immediate experience without reference to basic constituents, on the "givenness" of and its irreducibility in terms of space and time. Out of such an intransigent phenomenology arose Gestalt psychology.
There is one other item of importance in WERTHEIMER's paper. He suggested that seen movement may be the consequence of a "physiological short-circuit" in the brain. Given exactly the right time-interval, the excitation at one point may be drawn over to become the excitation at the other, the process being - not a retinal process... - but a cortical process which is the physiological substrate of apparent movement. This form of psychophysical parallelism follows the axioms of MACH and G.E. MÜLLER, and anticipates the isomorphism of KÖHLER which has become so nearly an indispensable of Gestalt psychology.
WERTHEIMER's paper, supported presently by the enthusiasm of the growing school of Gestalt psychology, was a great success, for it was the starting point of well over a hundred papers on apparent movement during the next thirty years. At first there were but a few studies by Gestalt psychologists in Germany under the influence of KOFFKA and KÖHLER, but the Americans took up the topic in the 1920 s with considerable zeal. (BORING, 1942, pp. 595-596)
He noted: "So well does WERTHEIMER s cortical short circuit fit the isomorphism of Gestalt psychology that KÖHLER elaborated and modified the theory in 1923, shortly after he had laid down his general principles for isomorphic brain fields in his Physische Gestalten of 1920" (1942, p. 599).

In the notes BORING provided references, including those that contained criticisms, his own and others, of the concept of isomorphism in Gestalt psychology. [fn 3] He summarized some of the criticisms:
The criticism of psychoneural isomorphism has come from the physiologists and the positivistic psychologists. The physiologists said that the brain is, in general, a net-work of connections, not a field where dynamic forces, such as the Gestalt psychologists find in perception, can exist. The future will decide that point. Even the physiologists know little as yet about the action of the brain. The positivists said that a mere statement of correspondence between mind and body is not enough, that they wished to know how the one affects the other, and that operational analysis of the nature of the available evidence for isomorphism shows that the axioms should be rewritten so as to state relationships between neural events - between events in the brain and the other physiological events involved in the description of experience. In this contention they are expressing a taste of scientific logic and again it is the future that will decide whether their preferences will be fruitful enough to persist. (BORING, 1942, p. 90)

It is now the future, almost six decades later. What does the reader think has been shown about whether the brain is a field with dynamic forces, or a network of connections, and whether isomophism can be meaningful between neural and non-neural events and need not be limited to relationships between neural events?


Some, but not all, of the sources we cited mentioned WERTHEIMER's physiological short-circuit hypothesis for apparent movement. Most of the citations referred only to KÖHLER s principle of isomorphism, usually described as psychophysical isomorphism.
WERTHEIMER would probably not be troubled that this principle was associated with KÖHLER. It seemed that initially both WERTHEIMER and KÖHLER were interested in the physiological or psychophysiological field. But subsequently WERTHEIMER became more concerned with the phenomenal and geographical fields. In his publications, aside from his classical study on apparent movement, he did not introduce a physiological model (but sought for a mathematical model of isomorphism). However, he did not entirely overlook physiology. In a 1937 lecture he talked about the "old view" which held that psychology and physiology (that is, psychological and physiological events) are similar because of associations due to past experience; the "new view" held that psychology and physiology are similar because of similar Gestalt qualities. He also said that he and KÖHLER had different formulations of isomorphism. He wrote: How stimulation is and how it is in the brain (K); how behaviour is and how it appears (W).
We think these words can be clarified by using the letters and schema that KOFFKA suggested. Let B represent the behavioural field, G the geographical (or physical) field, and P the physiological field. Consider the schema BP(G. His formulation of the principle of isomorphism as "characteristic aspects of the physiological processes are also characteristic aspects of the corresponding conscious processes" (1935, p. 109) focused on the relationship between B and P, which he called crucial (p. 53). It might be said that WERTHEIMER focused on the relationships between the behavioural and the geographical world, between B and G, whereas KÖHLER focused on the relationship between the behavioural and the physiological field, between B and P. Both apparently recognized that it sometimes happens that the behavioural field, the geographical field, and the physiological or brain field may be isomorphic, may have similar molar characteristics.
WERTHEIMER stated that isomorphism did not always hold and that the conditions under which it did or did not hold called for research. WERTHEIMER's thesis called for empirical research, for new ways to deal with the question of why things look the way they do. WERTHEIMER also broadened the concept of isomorphism beyond the perception of things to the perception of emotions, movements, language, and other symbols. KÖHLER considered such ideas in his 1938 book on values, which frequently referred to isomorphism.
It seems that there is more than one concept of isomorphism in Gestalt theory to judge by WERTHEIMER's distiction between his and KÖHLER's formulations. {We are reminded of the distinction drawn by GRELLING & OPPENHEIM (1991, 1988, original 1939) between two conceptions of Gestalt: Gestalt as configuration, shape or form, contrasted with Gestalt as "functional whole."]. Neither KOFFKA, KÖHLER nor WERTHEIMER claimed to have introduced the concept of isomorphism in Gestalt theory. Nor is it easy to distinguish clearly between the contributions of one or the other of the founders. We are reminded of what Giovanni B. VICARIO (1994) wrote in a tribute to his mentor, Gaetano KANIZSA:

Curiously enough, Gestalt psychologists are a Gestalt in their own, since you will never be able to make a sure distinction between the ideas that are due to the one and the ideas that are due to the other: Everyone who is acquainted with the papers by WERTHEIMER, KÖHLER and KOFFKA knows very well that they constitute a unique book. In addition to, I noticed the same sort of unselfishness as to the ownership of research starting points that I can testify in the case of KANIZSA. (p. 127)

From his mentor, VICARIO wrote (p. 129), he learned the phenomenological attitude so well described by Wolfgang METZGER (1963, p. 12): "to simply accept the facing thing as it is ... to let the thing speak for its own, without indulging in what we know, or we previously learned, or in what is obvious, in the knowledge of the subject, in logical demands, in linguistic prejudices ..." and so on.
... I always appreciated his theoretical minimalism, cause or effect of his exclusive attention for the data of immediate experience ... I saw KANIZSA always attentive to single perceptual phenomena, and in some ways careless of their theoretical arrangement. He was a Gestaltist, I think, because he was an experimental phenomenologist, but during the years I saw him abandon the cumbersome physiological hypotheses of KÖHLER and KOFFKA, and retire to his own view of pure phenomena bounded by phenomenal laws. (p. 130)

METZGER dedicated his Gesetze des Sehens (1975; first edition, 1936) as follows: "Dem Andenken Max WERTHEIMERs und den italienischen und japanischen Freuden, in denen sein Geist lebendig geblieben ist." [In memory of Max WERTHEIMER and of Italian and Japanese friends, in whom his spirit is still alive.] Recalling that WERTHEIMER studied with Christian von EHRENFELS in Praha [Prague], with Carl STUMPF in Berlin, and with Friedrich SCHUMANN in Frankfurt, VICARIO surmised:
That should mean that he was a follower of [Franz] BRENTANO's phenomenology ... According to [Georges] THINÈS (1977) the neurophysiological hypotheses (isomophism) with which WERTHEIMER and KÖHLER stuffed phenomenal evidence represent a backward step in the evolution of phenomenology ... Anyway, I think that, when speaking of the "spirit of WERTHEIMER", METZGER refers to the commandment that [Edmund] HUSSERL synthesized in the phrase: Zurück zu den Sachen selbst! [Back to the things themselves!] ... In short, phenomenology, and experimental, if possible. Exactly what KANIZSA did along his whole scientific life. (p. 130)

WERTHEIMER had what might be called a phenomenon-centered experimental approach to research: letting the phenomenon "speak for itself" and studying it under a variety of conditions [fn 4]. He issued an invitation for experimentation, not argumentation. [Years later KÖHLER issued a similar invitation in his Presidential address to the American Psychological Association (1959).]
WERTHEIMER might have been influenced by HUSSERL's phenomenology. An essay on HUSSERL by Joseph LYONS (1968) stated:
The most direct and specific of HUSSERL s effects on psychology as may be expected, occurred in Europe .... Of the important group who were at the University of Berlin just before World War I, and from whose joint efforts came the school of gestalt psychology, Max WERTHEIMER and Karl DUNCKER were apparently deeply influenced by phenomenology. (p. 30)

Similarly, an essay by Robert B. MACLEOD (1968) on phenomenology, referred to the phenomenological approach to perceptual organization represented by the Berlin group of gestalt psychologists.
The reality of gestalt qualities had been recognized by Christian von EHRENFELS in his article, "Über Gestaltqualitaten " (1890) and by [Karl] STUMPF, but it was Max WERTHEIMER's experimental studies of apparent movement (1912) which set the stage for the gestalt movement. The older theories could not admit as psychologically valid an experience of movement when there is no physical movement in the stimuli; phenomenal movement had to be explained away as an illusion. WERTHEIMER, like [David] KATZ, simply accepted the phenomenal fact as valid, insisting that movement as such must have its direct neural correlate; hence the controversial principle of isomorphism .... While the gestalt theories which emerged, notably the physiological and the psychological field theories, go beyond phenomenology, the basic approach is in each case phenomenological. (p. 71)

While not denying the basic importance of phenomenology, KÖHLER maintained that it was necessary to go beyond phenomenology and consider the brain field. "Beyond Phenomenology" is the title of Chapter IV in his 1938 book, The Place of Value in a World of Facts. The chapter began, "It is not our intention to restrict this investigation to questions of phenomenological description" (p. 102). Although he noted that "all questions of fundamental principle ... can only be solved on phenomenological grounds" (Ibid.), he was concerned with transcending phenomena, with "transphenomenal reality." "Physical nature is generally believed to be of transphenomenal existence " (p. 104). "No matter what our epistemological convictions are, we must recognize, besides pure phenomenology, all the natural sciences, such as physics, chemistry, geology, biology" (p. 106). He added: "only such percepts serve the physicist s purpose as are trustworthy signs of transphenomenal reality" (p. 107). "Practically all research in natural science proceeds, I believe, on the tacit assumption that its subject-matter exists outside the phenomenal world of all observers" (p. 121). Discussing memory, he wrote:
There is only one part of nature which, according to present knowledge, could in this case be intimately in contact with phenomenal data. This part of nature is the circumscribed world of brain-events ... Our conclusion will therefore be that, in trying to remember something and knowing that we know it, our reference is from the point of science reference to a definite neurological, or better: neural entity. (p. 123)

Thus, although one might have been more influenced than the other by phenomenology, both KÖHLER and WERTHEIMER recognized the importance of the phenomenal field. It might be said that KÖHLER focused on its relation to the brain field. WERTHEIMER did not criticize this focus, but apparently was less interested in physiological speculation than in experimental investigations of the relationships between the behavioural and the geographical fields. Such differences in orientation, we conjecture, might help to explain their different conceptions of isomorphism.


What does the word "isomorphism" mean in Gestalt psychology? To attempt to answer the question, a sample survey was undertaken of this concept and related ideas, mainly in the Gestalt psychological literature in English. Our interest was in what had been expressed about isomorphism, the phi phenomenon (whose study is considered to have suggested the concept and to have launched the experimental basis of Gestalt theory), and the relationships among various fields or environments in psychology, including the physiological or brain field. We presented excerpts from some of the writings by the founders of Gestalt psychology: KOFFKA, KÖHLER, and WERTHEIMER, as well as from some of the latter s lectures in seminars at the New School for Social Research, as revisited by the present authors. Also considered were reports by others who had attended WERTHEIMER's seminars: SCHEERER on fields and isomorphism; ARNHEIM on the psychology of perception and art; and a survey article by ASCH on Gestalt theory. We also presented excerpts from HUMPHREY on the Gestalt psychology of thinking. We described BORING's historical accounts of Gestalt psychology and the links that he drew between isomorphism and projection.
WERTHEIMER had referred to differences between his conception and KÖHLER's conception of isomorphism. The discussion section cited VICARIO's description of his mentor, KANIZSA, as an experimental phenomenologist who abandoned "the cumbersome physiological hypotheses of KÖHLER and KOFFKA." We suggested that WERTHEIMER had more of an experimental phenomenological approach, which fostered his concern with the relationship between the behavioural and the geographical fields, and less interest in physiological hypotheses than KÖHLER who was concerned with going "beyond phenomenology" to the physical world and ultimately to the brain field. Such differences might help account for differences in their conceptions of isomorphism.


Was bedeutet das Wort "Isomorphie" in der Gestaltpsychologie? Um diese Frage zu beantworten, wird in dieser Untersuchung - vorwiegend in der englischsprachigen gestaltpsychologischen Literatur - der Verwendung dieses Konzepts und damit zusammenhängender Ideen nachgegangen. Das Interesse der Autoren ist dabei vor allem darauf gerichtet, was über Isomorphie, über das Phi-Phänomen (dessen Untersuchung als Ausgangspunkt für die Entwicklung des Isomorphie-Konzepts betrachtet wird und das für die experimentelle Fundierung der Gestalttheorie den Grundstein legte) und über die Beziehung zwischen verschiedenen Feldern oder Umgebungen, einschließlich des physiologischen oder Gehirnfeldes, in der Psychologie ausgesagt wird. Dabei werden Auszüge aus einigen Schriften der Begründer der Gestaltpsychologie, KOFFKA, KÖHLER und WERTHEIMER präsentiert sowie auch Auszüge aus WERTHEIMERs Vorlesungen in Seminaren an der New School for Social Research, die von den Autoren dieses Beitrags dokumentiert wurden. Auch Ausführungen anderer Besucher dieser Seminare werden dabei miteinbezogen: SCHEERERs Äußerungen über Felder und Isomorphie, ARNHEIMs Gedanken zur Psychologie der Wahrnehmung und der Kunst, ein Beitrag ASCHs über Gestalttheorie. Weiters werden Auszüge aus HUMPHREYs Arbeit über die Gestaltpsychologie des Denkens und BORINGs historischer Beitrag über die Gestaltpsychologie (und die Verbindungen, die er zwischen Isomorphie und Projektion herstellt) präsentiert.
WERTHEIMER selbst hat Unterschiede zwischen seiner und KÖHLERs Konzeption von Isomorphie angesprochen. Im Diskussionsteil dieses Beitrags wird VICARIO zitiert, der von seinem Mentor KANIZSA sagt, dieser hätte in seiner Entwicklung als experimenteller Phänomenologe "die Bürde der physiologischen Hypothesen von KÖHLER und KOFFKA" abgeworfen. Die Autoren kommen zu dem Schluß, daß für WERTHEIMER der experimentelle phänomenologische Ansatz im Vordergrund stand. Dieser veranlaßte ihn zur vornehmlichen Beschäftigung mit der Beziehung zwischen dem behaviouralen und dem geographischen Feld. Sein Interesse an physiologischen Hypothesen war daher geringer als bei KÖHLER, dessen Anliegen es war, über die Phänomenologie hinaus zu Aussagen über die physikalische Welt und letztlich zum Hirnfeld zu kommen. Die Beachtung dieser Unterschiede in ihrem Forschungsinteresse kann zu einem besseren Verständnis der Unterschiede in den Isomorphie-Konzeptionen von WERTHEIMER und KÖHLER beitragen.


[fn 2]:Thus, the composer Olivier MESSIAEN, speaking of the union of color and tone in his music, explained to an interviewer: "When I hear music, I see inwardly, in the mind's eye, colors which move with the music. This is not imagination, nor is it a psychic phenomenon. It is an inward reality." And Carol STEEN, a New York artist who, like most synesthetes, has had synesthetic experiences from an early age and who uses her perceptions in her work, says she distinguishes different types of headaches by their colors. "If it s a sinus headache, it's green," Ms. STEEN said. Synesthesia received a flurry of attention from artists and psychologists at the turn of the century. But until relatively recently, modern science largely ignored it. Those who experienced synesthesia rarely complained. And the private nature of the perceptions made investigation difficulty - there was no objective way to tell what, if anything, unusual was taking place.In the past 10 years, however, the arrival of imaging techniques and other new technologies for studying the brain at work is revived interest in synesthesia, capturing the interest of a small core of researchers in a variety of countries and disciplines, PET scanners, electrophysiological recording, DNA analysis and other techniques are increasingly being used. In the current issue of The Journal of Neuropsychiatry and Clinical Neurosciences, for example, German Researchers from the University of Hanover Medical School report electrophysiological findings from a group of synesthetic subjects. An understanding of synesthesia as a perceptual anomaly, researchers hope, may eventually help elucidate normal perception, or even shed light on consciousness itself. Meanwhile, much more remains unknown about the comingling of the senses than is known. Even basic facts about synesthesia - its prevalence, for example - are still less than certain. [back to text]

[fn 3]: For the development of the psychophysical axioms into the isomorphic principle, BORING (1942, p. 96) offered a list of references that included the following: R.H. LOTZE, Medicinische Psychologie, 1852, pp. 206-232, especially pp. 230-232; H. GRASSMANN, Zur Theorie der Farbenmischung, Ann. Phys. Chem., 165, 1853, pp. 69-84 (Eng. trans., Phil. Mag, 4 ser., 7, 1854, pp. 254-264); as well as writings of E. MACH (1865), E. HERING (1878); F.C. DONDERS (1881); G.E. MÜLLER (1896); M. WERTHEIMER (1912); W. KÖHLER (1920, 1929, 1938); and K. KOFFKA (1935).
Also mentioned by BORING (1942, p. 96) were his reports that gave criticisms as well as a positivistic restatement of isomorphism: Psychophysical systems and isomorphic relations, Psychol. Rev., 43, 1936, pp. 565-587, especially pp. 579-586; A psychological function is the relation of successive differentiations of events in the organism, Psychol. Rev., 44, 1937, pp. 445-461, especially pp. 454f; An operational restatement of G.E. MÜLLER s psychophysical axioms, Psychol. Rev., 48, 1941, pp. 457-464.
[back to text]

[fn 4]: We adapted WERTHEIMER s approach in our phenomenon-centered variational approach. This orientation is reflected in our research on Einstellung, e.g., our 1959 book, Rigidity of Behaviour: A Variational Approach to the Effect of Einstellung. The preface notes: "Our research has been guided by a phenomenon-centered variational approach ... that involves centering on a specific phenomenon of behaviour and attempting to vary systematically the conditions under which it is studied" (p. x). The book ends with Chapter XXIV, "The need for a phenomenon-centered variational orientation." This orientation was also used in our other research, for example, "A variational approach to phenomena in social psychology" (1957). [back to text]


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Copyright © 1999 , A.S. Luchins, E.H. Luchins. All Rights Reserved.
This paper was prepared in the context of the 11h Scientific Convention of the international Society for Gestalt Theory and its Applications (GTA), March 1999 in Graz/Austria, and was first published in
GESTALT THEORY - An International Multidisciplinary Journal, Vol. 21, No 3, Nov 1999, pp 208-234.

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