1Expressive qualities have always been a tricky issue for philosophy. What does it mean for a sunset to be melancholic, or for a musical piece to be graceful and for the atmosphere of a party to be cheerful? What kind of qualities are these? Do they really pertain to the objects in which they seem to be located? What kind of access can we have to them?
2The aim of this paper is to give some insight into how Giovanni Piana’s philosophical reflection may contribute to exploring the issue of expressivity, in particular regarding the relation between expressive qualities and the perceptual objects to which they seem to pertain. More specifically, based on Piana’s phenomenological structuralism (Piana 2013a) and his theoretical investigation into Gestalt Psychology theses (Piana 2013b), I would like to argue for the idea that expressive qualities can be considered as qualities of Gestalt structures. Moreover, stemming from Piana’s analysis of the laws governing the structural organization of percepts, I would like to propose the idea that expressive qualities depend, even though arguably not exclusively, on the inner dynamic tendencies between the elements of the perceptual objects to which they seem to pertain.
3The debate about expressive qualities is a crucial one to extend and renew because, far from being just a narrow issue of minor philosophical importance, the phenomenon of expressivity is widespread in many different fields of our everyday life and therefore deserves a careful theoretical analysis, at least from the point of view of phenomenology. As an example, let us just mention two fields in which expressivity turns out to be crucial.
4Firstly, let us consider that expressive qualities can be the basis of the positive and negative valences of several objects in our everyday-life world, which can variously attract or repulse us based on such valences. The creepy and gloomy atmosphere of a cemetery can found the cemetery’s frightening aspect that may discourage one to enter it alone in the middle of the night; contrariwise, the peaceful and calm atmosphere of a Tuscany-hills landscape at sunset time of a middle-Spring evening can found the relaxing aspect of that landscape that may encourage one to sit there and enjoy the view. Language is not always able to describe appropriately the expressive qualities of objects and their positive or negative valences, but the world we live in seems to be full of them and it is easy to see how we are acutely sensitive, even just pre-reflectively, to most of them (Forlè 2017, Griffero 2010, Slaby 2014).
5Secondly, expressive qualities are also central in the social dimension of our everyday life. The expressive qualities of others’ behavior—e.g. gentle or harsh gestures, happy or sad facial expressions, nervous or calm movements—are a crucial way for us to have access to others and, at least, to some of their experiences. In the contemporary philosophical debate on the phenomena of intersubjectivity, too (Baron-Cohen 1995, Carruthers 1996, Gallese and Sinigaglia 2011, Goldman 2006, Gallagher 2008, Zahavi 2014), the crucial role of expressivity has emerged. Several authors, for instance, defend a Direct Perception Theory (DPT) about our access to others’ minds: the thesis is that, at least sometimes, we can perceptually grasp some mental states of others (Gallagher 2008, Krueger 2018, Overgaard 2012, Zahavi 2014). The very general idea is that, since some mental states are (partly) expressed through one’s bodily behavior, by having perceptual access to others’ bodily expressions we can also have perceptual access, at least partly, to the expressed mental states. Obviously, in order to argue that expressions can make mental states themselves perceivable, one needs to provide at least a theoretical clarification of what expressions are and what their relation to the expressed mental states is (Krueger and Overgaard 2012, Overgaard 2014, Forlè 2019). Moreover, other questions can be posed to DPT: even if expressions can make expressed mental states perceivable, are all mental states expressible and perceivable? Is DPT able to maintain that we perceive mental phenomena themselves or is it forced to maintain that we have perceptual access solely to bodily behavior? My aim here is neither to tackle these issues, nor to take a position in this debate. Rather, by making reference to it, I merely wanted to highlight that the debate on this topic may benefit from an accurate analysis of the phenomenon of expressivity, and therefore, for instance, from a renewed interest in the investigation of the main phenomenological aspects of expressive qualities.
6Coming to the main theme of this paper, as anticipated in the beginning, I would like to tackle the issue of expressivity by giving some suggestions about how Piana’s philosophical reflection can help us explore the relation between expressive qualities and the perceptual objects to which these qualities seem to pertain. In order to do so, I will organize this paper as follows.
7Firstly, I will show how Piana criticizes elementarist and associationist theories of perception and I will present Piana’s thesis according to which every perceptual object presents itself as a structured whole—a Gestalt—that is not simply obtained by the sum of its elements (Piana 2013b, 2013a). Stemming from a reflection of this kind on the structural organization of percepts, I will propose the idea that expressive qualities can be considered as qualities of Gestalt structures.
8Secondly, I will highlight that Piana does not just focus on the fact that perceptual objects present themselves as structured rather than unstructured but also makes insightful analyses about the structural laws governing percepts, highlighting that percepts are internally dynamic and governed by forces of attraction and repulsion among their elements (Piana 1991, 2013e). Against this background, I will argue that the expressive qualities of a perceptual object depend, even though arguably not exclusively, on the inner dynamic tendencies of the elements of the object itself.
9In what follows, I will try to clarify Piana’s position on the two aspects mentioned, as well as my proposal about expressive qualities that stems from Piana’s theses.
1 | Gestalts and expressive qualities
10In Piana’s works on perception and perceptual phenomena (Piana 1967, 2013b), attention is constantly paid to looking at the objects of perception for how they appear, and to analyzing them iuxta propria principia, as Paolo Bozzi (1989, 2007) would say—that is, finding at the level of perception the laws and principles that govern objects’ perceptual appearance and avoiding making use of concepts, terms or theoretical posits that cannot find their evidence in the perceptual object itself. Against this background, Piana develops a phenomenological theory of perception that, contra psychological elementarism and associationism, highlights the perceptual priority of unitary wholes. Piana argues that these unitary wholes are not the outcome of a projectivist activity of a subjectivity but depend on the intrinsic conditions of perceptual objects themselves and present themselves as structured (Piana 2013b, 49-50). Indeed, according to Piana (2013a, 8), every kind of experience presents a specific structure, so that phenomenological research itself should be considered as aiming specifically at investigating the structure of different kinds of experience. This thesis is at the basis of what Piana has called “phenomenological structuralism” (Piana 2013a, 7). In the field of perceptual experience, this thesis implies the idea that any perceptual situation presents itself as having a structure, i.e., a form, albeit a very simple one, of organization (Piana 2013b). Even the simplest spot of color, for instance, is given as a figure that is segregated in such and such a way from the background: the perceptual situation is organized in a figure/background structure that defines the relations between the different parts of the perceptual field.
11Based on examples such as this, it is difficult to maintain that something like pure sensations—that is, thin sensory data that can be completely isolated from the ones they are given with—can be ever given. However, an elementarist or associationist psychologist would probably argue that pure sensations constitute the basic materials for perception, and that percepts are obtained by means of addition, so that actual percepts are just the product of sums of single pure sensations that are fundamentally independent of one another (Piana 2013b, 23-24). Piana (2013b) contrasts this theoretical position: starting by criticizing the actual givenness of pure sensations, he also highlights how a conception of perception-by-addition is profoundly wrong. Percepts are immediately given as organized wholes in which at least some of the properties of the composing elements are determined by the context in which they appear, that is by the organized whole in which they are inserted. The single elements cannot be given as such—with all their properties—if the whole itself is not given.1 Therefore, the whole cannot be obtained by adding the single elements to each other, because the elements as such are not completely defined until the whole is in place.
12To clarify this point, let us take for instance the case of a melody. If the notes of a melody are arranged appropriately, a specific tonality is established, e.g. C major. Based on this specific tonality, the single notes acquire new properties. In C major, for instance, the note B becomes the leading tone and can be actually perceived as such, since it is perceived in its tendency to C, which becomes the tonic and can be actually perceived as such in its static quality. Such properties do not pertain to the note B or C as such but they start pertaining to them only when a specific tonality is established, that is, only when a particular structure of notes is in place (De Monticelli 2013, 118). This aspect seems to be confirmed, for instance, by a rule of music composition that every (classic western music) composer, or even educated musician, knows. In western musical pieces, it is common to go from one tonality to another: for instance, a piece can start in C major, moving to G major and ending in D major. The passage from one tonality to another is known as modulation. Now, an important rule of modulation, amongst others, is that once the passage from one tonality to another has occurred, the new established tonality has to be ‘confirmed’ by means of a cadence, which somehow perceptually states that a new tonality, a new context, is in place. The interesting aspect for our purposes is that perceptually, in a modulation, a new whole has to be established, in which the elements of the previous whole change not only their function and harmonic role, but also the very way in which they are perceived. This change cannot depend just on the elements (i.e., the notes), but on the structure of relations between them, that is on the unitary whole (i.e., the tonality). This is the reason why the tonality has to be ‘confirmed’: a sequence of notes (i.e., the cadence) that makes a new context perceptually stable has to be played to allow one to perceive the single elements in a new way. Once the process is completed, the ‘same’ notes of the previous tonal context will acquire new perceptual meanings and new properties, because of the new context they are in. Interestingly, moreover, the tonality of a melody is not only set when an adequate group of notes is in place, but it is also perceptually given as a quality of the melody itself, rather than of the single notes. It is a quality of the whole, not of the elements.
13Given examples such as these, it should be clearer how one can maintain, as Piana does, not just that pure sensory-data are not part of what is actually given in perception, but also that percepts are integrated wholes that, far from being reducible to the sum of their elements, are something different from them, so that the former (i.e., the wholes) can even determine the properties and perceptual meanings of the latter (i.e., the elements). Moreover, what is crucial is that these integrated wholes are such because of their structure—that is, because of the specific relations between the parts that constitute them.
14In this theoretical analysis of percepts and their structuring laws, Piana has fruitfully given philosophical prominence to the multitude of results that have been achieved by Gestalt Psychology, also highlighting the affinity that this psychological school has with phenomenology itself and its results.2 In the same vein, with his work on Husserl’s Third Logical Investigation, Piana (2013d) has prominently contributed to shedding light on the Husserlian theory of parts and wholes that, in a certain sense, can be considered as expanding and revising in a formal ontology some intuitions of Gestalt Psychology itself. Piana has strongly highlighted how the Husserlian theory of parts and wholes finds its own origin in an analysis of experience itself, and specifically in an analysis of perceptual experience (Piana, 2013c). In this way, Piana has particularly underlined how a philosophical theory of perception could benefit from the overall project of Husserlian formal ontology.
15Let us sum up what we have highlighted about Piana’s thought until now with some of his own words:
The main thesis I would like to put forward can be formulated in this way: in any perception of a unitary whole, there are conditions of unity that are embedded within the perceptual situation itself. We can call these conditions laws of form, or Gestalt laws. The term Gestalt recalls the verb gestalten, which means to structure, to organize, to shape, to give form to. Gestalt can be easily considered as another term to indicate the structure. The idea implicated in the use of this word is that every perceptual situation is a structured one and that the operation of gestalten is already working in the act of perceiving. This means, in particular, that we must not think of a perceptual level devoid of forms, which is put into shape afterwards like marble in the hands of a sculptor. This analogy might be misleading for the following reason: as soon as we have a perceptual situation, as soon as the perceptual operations are in place, the structuring operations are in place too. As we have just said, perceiving is itself a gestalten, and—we might say—is subject to specific laws (Piana 2013b, 42, my translation).3
16As mentioned above, my thesis is that highlighting, as Piana does, that every perceptual situation is a structured one and that we are perceptually sensitive to unitary wholes (Gestalts) that are founded on their constituting elements but are not phenomenologically reducible to them is crucial for a proper analysis of the phenomenon of expressivity.4 Indeed, I would like to argue that expressive qualities can be considered as qualities of Gestalts—that is, global qualities of unitary structures of elements—that do not pertain to the single elements but to the entire whole. In this sense, once an expressive quality of a Gestalt is in place, the elements of the Gestalt themselves acquire new perceptual meanings, as in the case of the single notes of a melody once a specific tonality is established.
17To clarify this point, let us briefly consider two paradigmatic cases of expressive qualities—expressive qualities in aesthetic objects and expressive qualities of human bodily behavior. Regarding the first case, I will recall a classic example made by Mikel Dufrenne (1973) in his Phénoménologie de l’expérience esthétique. Dufrenne argues that, in a musical piece, it is the perceptual overall structural organization—the Gestalt, we could say—of many different aspects (e.g. melody, rhythm, harmonic structure, timbre, tempo) that is able to convey the expressive qualities of the piece. Indeed, even though, for instance, the vigor of César Franck’s Prelude, Chorale and Fugue clearly depends on its rhythm and on the modulation from the minor to the major scale, as well as the mysterious grace of Debussy’s The Girl with the Flaxen Hair depends on the uncertainty of rhythm and tonality, we can still argue that, in both pieces, these expressive qualities are founded in (and pertain to) the perceptual overall structural organization of the piece. Indeed, one can modulate from the minor to the major scale without achieving the effects of Franck’s Prelude, Chorale and Fugue, just as one can maintain an uncertain tonality without producing the dreamlike atmosphere of Debussy’s music (Dufrenne 1973, 326-327).
18Similarly, in the case of bodily expressions, we can argue that a specific expressive quality pertains to a structured set of different elements—elements such as facial traits (e.g. posture of mouth, eyes, eyebrows) or bodily postures and movements—not to single elements as such. Moreover, it may happen that, once in place, a Gestalt of bodily elements with its expressive quality is able to disambiguate the expressive meaning of the elements themselves. For instance, if they are perceived on the face of a trembling man standing with clenched fists in front of an aggressive lion, two wide-open, staring eyes may easily be perceived as expressive rather than non-expressive, and as specifically expressing fear or terror. However, if they are perceived on the face of a young child who is smiling in front of a new toy, those eyes will be probably perceived as expressing a joyous surprise. That specific facial trait, therefore, acquires the property of being expressive in one sense or another thanks to the fact that a specific Gestalt of elements is perceptually given. We can even imagine that the mere physical properties of the eyes remain the same but their perceptual meaning is dramatically different in the two cases, being perceived as constituents of an expression of fear in one case and of joyous surprise in the other.5
19Considering expressive qualities as global qualities of Gestalts allows one, on the one hand, not to bind specific expressive qualities to single elements—which would sound as potentially problematic at least in some cases, such as the one of the man/child with wide-open, staring eyes just described. On the other hand, however, it would help to argue for the thesis that expressive qualities pertain to specific structures of elements that cannot be arbitrary, as if expressive qualities were not qualities of the perceptual objects themselves but simply the result of arbitrary subjective projections. Contra projectivist hypotheses, I would suggest that objects have their own ‘rights’, as Andrea Pinotti would say (Pinotti 2005, 15-20): not any atmosphere can be gloomy, nor can any melody be cheerful. We have argued that Gestalts are subject to specific “laws of form” (Piana 2013b, 42), so that they are founded in a specific set of elements, appropriately arranged. Being qualities of Gestalts, expressive qualities can consequently be argued to be founded in the appropriate arrangement of elements, too.
2 | Dynamic tendencies and expressive qualities
20Piana’s phenomenological structuralism (Piana 2013a), as well as his theoretical attention to the heritage of both Husserl’s theory of parts and wholes and the results of Gestalt Psychology, are clearly of the utmost importance for such a project. However, there is at least a second crucial way in which Piana’s work might be useful for the analysis of the phenomenon of expressivity. Indeed, as we mentioned, Piana does not just argue for the idea that every perceptual object presents itself as structured rather than unstructured, but he also makes insightful analyses about the laws that rule such structural organization (Piana 1991, 2013e). In particular, he crucially contributes to highlighting that percepts are internally dynamic and governed by forces of attraction and repulsion.
21For instance, focusing on musical percepts, in his Filosofia della musica, Piana stresses that music appears as a process and its duration in time clearly reveals itself in its perceptual appearances: it is not just the case that music and sounds are in time—because all other material things are—but that their being in time experientially appears as passing. Now, it is worth noticing that this passing appears as the sequence of the phases of one single phenomenon. This means that perceiving a melody does not mean perceiving a static juxtaposition of sounds; rather, it means perceiving the sequence of notes as the dynamic passage—the transition—from one sound to another, or, as Piana says with an Italian expression that explicitly refers to the metaphor of movement and walking, as a kind of avanzare sopravanzando—that is, a kind of moving forward (Piana 1991, 155).
22Now, how can this dynamic effect be produced in a musical piece? Piana seems to suggest that this effect is at least partly due to the internal tendency of some elements towards others (Piana 1991, 167-181). Indeed, when they are arranged according to a particular rhythmic, melodic and harmonic organization, the notes of a melody perceptually appear not as unrelated sounds, but as perceptual unities that are organized according to the scheme of beat and upbeat. This is actually a widespread phenomenon. Even if we listen for a while to the perfectly uniform mechanism of a metronome, for example, we may come to perceive sequences of short rhythmic unities with downbeats and upbeats (Zhok 2012, 133). Now, according to Piana, what we can observe in configurations like these is the fact that the relation between the sounds is perceived as that of impulses and relaxations, openings and closures, questions and answers (Piana 1991, 173). This means that, far from being just a set of sounds in which there is no actual articulation in sequences but a mere juxtaposition of notes that we can arbitrarily choose to group as we prefer, the musical perceptual course appears, on the contrary, as an organized unity that requires a closure when something has been previously perceived as an opening. In other terms, as Helmuth Plessner says in his Zur Anthropologie der Musik, in a musical piece sounds appear as impulses for what comes next and therefore the peculiar character of having a direction, an open connection to something else, is motivated by the sounds themselves (Plessner 2007, 146-150).6
23Far from pertaining just to temporally-extended percepts such as musical pieces, dynamic tendencies also seem to be in place in static percepts such as pictures and visual images. Piana has contributed to shed light on this aspect, too. One paradigmatic example is his paper La nozione di tendenza sintetica illustrata con esempi (Piana 2013e), in which Piana investigates what directionalities are in place in a simple visual image, highlighting how simple modifications in the structure of the different parts of the image can dramatically change the dynamic tendencies in the whole image itself. Through this kind of investigation, Piana also contributes to re-discovering another piece of heritage of Gestalt Psychology that finds, for instance, in the work of Rudolf Arnheim (1954) one of its richest and most interesting examples on this issue. Indeed, Arnheim focused largely on the Gestalt laws structuring the perceptual field and paid particular attention to the visual domain. One of the aspects he stressed is that visual objects are internally dynamic, since they are characterized by “directed tensions” (Arnheim 1954, 11). Such tensions are not something added by the observer, but they are inherent to the visual percept itself: according to Arnheim, such tensions have direction and magnitude, so much so that he also calls them “forces” (Arnheim 1954, 11). Arnheim’s idea is that, when the directed tensions of a visual percept are balanced, then they contribute to conferring an appearance of stability on the perceptual object, as in the case of a black circle in the middle of a white square. On the contrary, when such tensions are more or less un-balanced, then an appearance of dynamicity is produced, as in the case of a black circle that is not in the middle of a white square but slightly de-centered towards the upper-right angle of the square. This latter perceptual object, Arnheim notices, shows a dynamic character since the black circle seems to be “striving towards” the center of the square, as being “attracted” by something that, however, is “not physically present in the picture” (Arnheim 1954, 11).7
24One of the interesting aspects of such a theoretical reflection for an analysis of the phenomenon of expressivity is that the internal dynamics of tendencies between the different parts of a percept can be partly at the basis of some expressive traits. Let us think, for instance, of how two pictures can be expressively different if one is composed of intricate zig-zag lines that break the visual field into several different-sized and sharp-cornered pieces while the other is composed of sinuous, curved lines that draw a set of circular figures. In the two pictures the elements are structured accor|ding to very different internal tendencies and this aspect arguably plays a role in ascribing to the first picture probably a nervous, messy (or vivacious and energetic) trait, and the second one probably a calm and graceful trait. Abstract painters have been great in showing with their art how specific arrangements of simple elements such as lines, points, and colored spots can convey expressive valences, even without representing anything (De Monticelli 2017). In many musical pieces, moreover, some expressive traits seem to depend on the dynamic tendencies between notes and chords: let us think for instance, of the enormous expressive differences between Beethoven’s Funeral March in Piano Sonata op.26 n.12 and Chopin’s Grande valse brillante op. 18. The somehow slow solemn gait of the former can be argued to depend partly on the reduced dynamic tendencies between the notes that are produced thanks to the specific tempo and rhythmic structure of the piece and that convey a perceptual effect of several, somehow disconnected, sonic events. On the contrary, the elegant and cheerful dancing of the latter musical piece can be argued to be obtained also thanks to the strong tendencies between the musical passages produced by the constant perceptual suspensions that are almost immediately resolved afterwards.
25The theoretical hypothesis that expressivity depends, at least to some extent, on the internal dynamic tendencies between the elements of a perceptual Gestalt needs surely to be investigated further. However, if proven to be true, it could support the idea that expressive qualities are linked to the structures of the perceptual objects to which they pertain and that specific expressive qualities cannot pertain to any object, independently of its structural organization.
3 | Concluding remarks
26The aim of this paper was to deal with some phenomenological aspects of expressive qualities, considering in particular the relation between these qualities and the perceptual objects to which they seem to pertain.
27I have tried to show that Piana’s work, and particularly his philosophical reflection on perceptual experience and the laws governing the structural organization of perceptual situations, may be of the utmost importance for such an investigation. Against the background of Piana’s theses, I have argued for two main theses: namely, first, that expressive qualities can be conceived as global qualities of Gestalts and, secondly, that they depend, even though arguably not exclusively, on the inner dynamic tendencies of the elements constituting the expressive object itself.
28Far from being an exhaustive analysis of the phenomenological aspects of expressive qualities, this paper intends to highlight some possible lines of research in the field, stressing, particularly, how Piana’s reflection could be a treasure trove of philosophical analyses for this theoretical enterprise.
- 1 On these points see also Husserl’s Third Logical Investigation (Husserl 2001), which Piana clearly has in mind when elaborating his theoretical position on the structural organization of the perceptual field. See also Piana’s commentary on Husserl’s Third Logical Investigation (Piana 2013d).
- 2 Obviously, Piana is also well aware of the methodological and theoretical differences between a pure phenomenological approach to perception and the one of Gestalt Psychology. On this point, see Piana (2013b).
- 3 “La tesi generale che ora si fa avanti potrebbe invece essere formulata così: data una qualunque percezione di unità vi sono condizioni dell’unità stessa che giacciono all’interno della situazione percettiva. Queste condizioni le chiamiamo leggi della forma o leggi della Gestalt. Il termine Gestalt rimanda al verbo gestalten che significa strutturare, organizzare, plasmare, dare un’articolazione. Gestalt potrebbe dunque essere considerato come un altro termine per indicare la struttura. Nell’uso di questa parola è implicata l’idea che ogni situazione percettiva sia una situazione strutturata, che l’operazione del gestalten sia già da sempre in opera nello stesso atto del percepire. Ciò significa, in particolare, che non dobbiamo pensare ad un livello percettivo privo di forme, che viene poi messo in forma come il marmo ad opera dello scultore. Questa analogia può essere fuorviante proprio per questo motivo: non appena abbiamo a che fare con una situazione percettiva, non appena si attivano le operazioni percettive, si attivano anche le operazioni strutturanti. Come abbiamo detto or ora, il percepire stesso è un gestalten—ed esso, così forse ci potremmo esprimere, obbedisce a determinate leggi.” (Piana 2013b, 42)
- 4 The notion of foundation used in this paper refers to the phenomenological notion of foundation, as it is developed by Husserl in his Third Logical Investigation (Husserl 2001). In a nutshell, phenomenological foundation refers to a relation of dependence of a founded content on a founding one, so that “A content of species A is founded upon a content of the species B, if an A can by its essence (i.e. legally, in virtue of its specific nature) not exist, unless a B also exists […]” (Husserl 2001, 34). Regarding the foundation of a unitary whole on its constituting elements—which I am referring to in this passage—, what is crucial to underline is that, in the Husserlian perspective I endorse, the founded whole is not reducible to the mere sum of the founding parts: rather, it constitutes an entity of a new kind that is also able to make its constituting elements acquire new properties due to the fact that they are parts of that whole. On Husserl’s theory of foundation, see Husserl (2001), Piana (2013d), Sokolowski (1968), Smith and Mulligan (1982), Casari (2000).
- 5 Arguing that the expressive qualities of one’s behavior are global qualities pertaining to a Gestalt of different bodily aspects does not mean implying a form of behaviorism, according to which those mental states that are expressed by bodily expressions are reducible to such expressions. Being expressible by bodily behavior does not make a mental state reducible to that behavior. Indeed, even those who maintain that bodily expressions can be considered as constitutive parts of the expressed mental states (Krueger 2018, Krueger and Overgaard 2012), reject behaviorism, maintaining that bodily expressions constitute just one of the proper parts of the expressed mental state—where the latter is conceived as having a complex hybrid structure, constituted both by internal aspects (e.g. the lived experience of the subject) and external ones (the bodily gestures and expressions) (Krueger and Overgaard 2012, 245).
- 6 I previously dealt with these issues in Forlè (2016) and Forlè and Perani (2013).
- 7 To look at the visual examples discussed by Arnheim, see Arnheim (1954, 10-13).