All human communication, in its widest sense, involves the use of signs to share information and to express oneself [1
]. Communication refers to the act of conveying intended meanings from one entity or group to another through the use of a mutually shared set of signs and semiotic rules. Although all species communicate, human communication is notable for its precision and flexibility, allowing one “to formulate an unlimited number of meaningful novel messages that are not tied to the immediate present” [2
] (p.1). Through language, people are able to refer to and think about concrete objects and abstractions, past events and experiences, and affairs remote both in space and time or those which exist only in the imagination [1
To communicate, humans use signs (i.e., signifiers) which can take the form of words, images, speech sounds, objects, etc. When humans imbue signs with meaning, they become meaningful because they stand for something (i.e., the signified) [3
]. Yet, the relation between signifier and signified may reflect a wholly arbitrary connection [1
], constructed individually, socially, or culturally, based on experiences, knowledge, or shared norms. In other words, the physical means of communication, such as language and maps, do not carry meaning per se, but rather trigger or release meaning [4
]. And yet, despite their similarities, maps are unlike language; their elements are unlike words. The elements of a map are independent associative symbols with a reference fixed by convention but not by fixed associations or single, unequivocal reference [5
]. Maps are cultural artifacts, based on an accumulation of choices, each of which reveals particular values [7
In his famous work Semiology of Graphics
, Jacques Bertin stresses that visual variables (i.e., shape, color, hue, size, texture, and orientation) must be carefully selected in a way corresponds with the information they represent [5
]. With his semiotic theory, Bertin provided a theoretical framework for cartographic visualization, suggesting how to apply visual variables with respect to the thematic content, such as how to depict information which is selective, associative, ordinal, or quantitative [5
]. Yet, the variety of methods available for representing information through cartographic representations allow for strikingly different results created from a single set of data [9
]. While a map may be designed to convey a single focus of interest, it does not convey a single universal message [9
]. The influence of cartographic representations on the perception and interpretation of maps is therefore significant [10
]. Chandler even claims that “changing the form of the signifier while keeping the same signified can generate different connotations. Changes of style or tone may involve different connotations, such as when using different typefaces for exactly the same text, or changing from sharp focus to soft focus when taking a photograph” [3
Empirical research from related domains supports this notion. Loftus and Palmer, for example, showed that a simple change in the wording of a question can markedly and systematically affect individuals’ associations and responses, like judgments of speed estimation and memory [11
]. Sianipar et al. argue that as constituents of language, words do not only have abstract semantic or referential meanings but also convey the emotional quality of their underlying concepts or references, i.e., they also have connotative, affective meaning [12
]. A word’s affective dimensions thus modulate cognitive processes, such as learning, memory, and attention. Such connotative, affective dimensions may not only refer to language alone but be present in any human-stimulus interaction [13
]. The Gestalt psychologist Wolfgang Köhler claimed that objects and situations imbue a particular “Anmutungsqualität” (“appearance quality”), which refers to an object or situation’s vague effect on a viewer through perception [15
]. Köhler tested this claim and found that in the majority of cases, participants assigned the soft-sounding word maluma
to round shapes while assigning the word takete
to angular-shaped figures. This intuitive, non-arbitrary correspondence between the different channels of human perception has been replicated in different contexts [16
] and cultures [18
Recent research in cartography has also begun to study the influence of design decisions on human responses. Findings support the notion that changes in visual map style influence the map readers’ judgments, trust, liking, recall [20
], and emotional responses [22
]. Likewise, the style of line shapes in origin-destination flow maps (e.g., curved versus straight flow lines) influence people’s preferences and accuracy of judgments [24
]. In recent years, the impact of cartographic representations has most profoundly been studied for the depiction of uncertain phenomena. Findings strongly imply a significant influence of the type of uncertainty visualization on intuitiveness, uncertainty judgments, and people’s preferences [8
]. Research moreover emphasizes the importance of visual saliency in cartographic communication which influences the effectiveness (e.g., detection time) and efficiency (e.g., accuracy) of map reading [28
]. Salient information draws the attention of the reader, while visualizations of greater cognitive fit will produce faster and more effective decisions [29
]. Such cognitive fit can already be found in school children, indicated by the associative and metaphorical use of signs and symbols even at an early age [30
Such empirical research in the field of cartography, however, is still scarce. There still remains the need for a differentiated perspective in terms of the “identification and articulation of the basic visual variables that can be manipulated to encode information” [8
] (p.2496). Inasmuch as Jacques Bertin’s Semiology of Graphics
provides a shared set of signs and rules [5
], cartographic semiotics does not address how the depiction of information through a particular graphic variable may lead to different associations, interpretations, or judgments. Semiotic rules provide a framework to adequately select between the types of visual variables in order to correspond with the particular information they aim to represent, such as when to depict information by shape, color, or size. These rules, however, do not further differentiate within each type of visual variable, such as regarding the effects of different shapes on people’s associations and map interpretation.
Yet, shapes—in particular, geometric shapes—are considered as core visual variables over a wide range of disciplines [5
]. In cartography, geometric shapes are prevalently applied as point symbols in thematic maps to represent nominal data and to locate spatiotemporal occurrences. To this day, the cartographer still faces the challenge of near infinite variations of shapes to choose from. This challenging fact is acknowledged by Bertin’s semiotic rules, which further help guide the selection process, such as by recommending to choose shapes which are associative to the content they represent [5
]. While this provides helpful guidance in the cartographic communication process, the selection for the most adequate visual signifier can still be a difficult task [34
]. Besides following conventions, such decisions may be based on the map maker’s individual associations, knowledge, and preferences. Hence, inasmuch as cartographic semiology does provide a theoretical framework for geospatial communication, it does not further explain the effects of shape characteristics on the map reader’s responses and judgments. While empirical findings strongly support the notion that variations in visual representation can change the map reader’s responses on multiple levels, it still remains obscure why some shape symbols emerge as more effective than others in conveying particular information.
The present study will therefore explore the qualities assigned to two-dimensional, geometric shapes – such as triangle, point, or square – and examine their similarities. The concept of similarity (or sense of sameness) is pivotal to theories in cognitive sciences. By identifying similarities between two stimuli, part of the stimuli’s cognitive structure and relatedness can be revealed. Shapes that are perceived as more similar can be regarded as more cognitively related. Besides studying perceived similarities, the present study will further explore strategies and processes underlying the similarity judgments. With a better understanding of why some shapes are perceived as more similar, shapes can be more accurately be discriminated [35
], allowing for more effective and associative visualization of information.
Human communication is notable for its variability and flexible use of signs to share and express information, both verbally and visually. The choice of signs, however, must be selected carefully, since the selection will influence how people perceive and respond to the information. Research in visual communication, for example, shows that visual signifiers can be processed more intuitively, faster, and with less cognitive effort, when associative to the information they convey. In the field of cartography, in particular, such an associative and intuitive communication process is aimed for. Yet, the selection for visual variables which are most effective to convey particular information still remains a challenge. With a better understanding of why some shapes are perceived as more similar, however, shape symbols can more accurately be discriminated [35
] and then using more informed choices, allowing for more effective and associative information visualization, such as in cartography. By unraveling core qualities of shapes, the findings of this research aim to contribute to such a better understanding of why some shapes may be more suitable to represent particular content than others.
The present study, therefore, focused on exploring qualities assigned to geometric shape symbols by assessing their proximities (i.e., similarities) to uncover part of their cognitive structure and relatedness. The present study further explored the strategies and processes underlying these similarities. With its multi-method approach, this empirical research aimed to contribute a differentiated perspective on shape proximities, cognitive relations, and hierarchies, as well as on underlying concepts and processes involved in similarity judgments.
In detail, the findings from cluster analysis strongly imply that even simple, geometric shapes imbue qualities which distinguish them from one another. The study discovered three independent similarity clusters based on a set of 12 geometric shapes: polygons, round shapes, and star-like shapes. These clusters may not be surprising since qualitative content analyses, moreover, revealed that predominantly visual strategies were applied when grouping shapes according to their similarities. In addition, findings from cluster analysis indicate not only the shapes’ cognitive proximities but also a hierarchical order. In particular, the clusters of round shapes and polygons suggest a shared meta-concept; distinguishing both clusters from star-like shapes. The result of a three-cluster solution is further supported by the distribution of the geometric shapes in the two-dimensional semantic space illustrated in this research. By identifying the similarities of the 12 shape stimuli, part of the stimuli’s cognitive structure and relatedness is disclosed. It is particularly beneficial to have a quantitative estimate of the proximity between two concepts, which allows appropriate discrimination between them. The concept of similarity is therefore pivotal in theories in cognitive and communication sciences.
The present empirical study, moreover, discovered four particular processes involved in the participants’ similarity judgments: visual, associative, affective, and behavioral strategies. Most frequently, visual strategies were applied when grouping geometric shapes according to their similarities. This finding corresponds with existing literature, claiming that visual qualities are the most powerful of all, which “reach us most directly and deeply” [48
] (p.97). At the same time, findings of the present study suggest that not only visual characteristics guide similarity judgments but that associations and affective-evaluative judgments also account for the (dis)similarities of visual stimuli – although to a less significant extent. The participants’ affective-evaluative responses emerged to correspond to the three dimensions of semantic and affective space theories: valence, arousal, and dominance [45
]. Affective strategies, however, were mentioned least often by the participants of the study to explain grouping decisions. While female and male participants used visual and affective strategies similarly often, associative strategies were expressed twice as often by males than by females. However, due to the small sample size, these differences cannot claim statistical significance. Besides the three cognitive-affective strategies identified through qualitative content analysis, a fourth, behavioral strategy was found which was shown to influence shape similarities, i.e., shape rotation. According to J.J. Gibson’s Affordance Theory [49
], the environment and the stimuli therein are not merely perceived in terms of shapes and spatial relationships but also in terms of their possibilities for action (i.e., affordances). Present findings from rotation analysis support this notion as being applicable to static, two-dimensional geometric shapes. The results indicate that a shape’s line features (edges) may serve as cues used to rotate a shape towards a particular orientation. It appears that a shape’s edges may serve as “baselines”, along which shapes are more likely to be aligned to. With its results, the present study provides empirical evidence of geometric shapes more and less prone to be rotated. While these findings are of relevance for design decisions, the possibility to rotate the geometric shapes in the present study must be treated as a constraint at the same time. As Arnheim claims, orientation may change a shape’s character [33
]. While participants were allowed to freely group and rotate the 12 geometric shapes, results have not been further subjected to rotation-dependent analyses. Future research is, therefore, needed to explore the influence of shape rotation on shape characteristics in more detail. Future studies are also needed to expand upon the variety and number of shapes and to further explore the different facets which account for the perceived (dis)similarities between and relatedness of such visual stimuli. While the present study aimed to embrace the most basic and prominently used two-dimensional, geometric shapes, its results are limited to these shapes.
Inasmuch as the present research aims to advance our understanding of shape similarities and underlying processes, the results’ transferability to more applied scenarios are nonetheless limited. When people make choices, they always do so in particular mindsets and contexts. Research has long recognized the power of situation and context [50
] and have demonstrated many ways in which situations activate particular contents of memory, making related constructs more accessible [51
], and by doing so, influencing associations and behaviors, even without an individual’s awareness [52
]. Despite the attempt to deprive the present study of context, the prevailing associations towards cartography indicate an influence due to the participants’ and research study’s background of cartography. Associations found in this research through retrospective verbalization must therefore not be treated to be exhaustive. The perceived similarity between two shapes may change given different environments, cultures, or contexts [35
]. In cartographic research, this challenge has been widely acknowledged, stressing that by focusing on the effects of map elements in an isolated way, the criterion of ecological validity may not necessarily be met, i.e., that results may not be transferable to cartographic representations due to their more complex, holistic nature [4
]. At the same time, “changing the nature of the map task or the precise design of the test materials often led to variability in the results” [54
] (p.295). Thus, both research approaches – controlled and applied studies – have merits and limitations: “the lack of careful isolation of variables in user studies makes it difficult if not impossible to determine whether the results can be generalized to any scenario without identical design and tasks. Without an explanation for why an effect occurs, there is rarely an indication of what and how much can change while maintaining the benefits of a particular design” [55
] (p.3). Hence, both approaches are needed to allow for conceptual replications of each other [55
This research studied shape qualities at their most fundamental and purest level. This controlled approach allowed for the exploration of shape proximities and underlying processes fairly independent of context. In doing so, this research revealed shape proximities and four strategies which accounted for similarity judgments found in the study. While future research is needed to further explore the distinct qualities of individual shapes, the four groups of strategies identified can provide a useful framework for future studies. With profound knowledge of shape qualities and their relatedness, hypotheses about their communication effects can more deliberately be generated and tested, such as in applied scenarios, with different levels of visual complexity, in different contexts, and in different visual disciplines. Current findings, therefore, aim to be expanded upon. With a profound understanding of shape qualities and their effects on perception and communication, design decisions can likewise be supported, such as to allow for deliberate choices on whether two shapes are similar enough to be acted upon as the same, or whether they are dissimilar enough to require different decisions. Being able to more accurately discriminate between graphic variables, can help to make more informed decisions and better tailor information visualizations in cartography and beyond.