The Geometry of Thinking: From Perception to Language
Before we learn how to speak, we communicate with deictic expressions. For instance, when a toddler points to an object with her finger, she is talking to us by using her body language. She wants us to pick up that object and bring it to her. Since the use of deictic expressions comes before our language acquisition, we subsequently experience a process of translation from using our bodies to the semantics of language. This process of translation continues in later stages of human development when it expands from deictic expressions to spatial cognition—our ability to connect with our physical and social environment. It is my argument that the forces that operate in our spatial cognition also have the ability to shift perspectives and therefore help us develop empathy.
In development theory, the importance of empathy is frequently emphasized, but in architectural discourse empathy is much less studied. As an architect, I have been investigating how physical environments can facilitate the development of empathy, particularly in learning environments.
Learning environments exist within social, cultural, and environmental contexts, and therefore, the specifics of these contexts play an active role in the development of human beings. Context is not a mere vessel that is impartial to the life that takes place within it. Likewise, architecture is not a mere shelter. According to Christian Norberg-Schulz, each space carries a distinct character and “the task of the architect is to create meaningful places.” (Norberg-Schulz, 1979, p.5) In other words, placemaking has its own semantics, and when we experience a place, we are also experiencing the narratives embedded in the language of architecture. It is the power of these narratives that can be transformative in the development of empathy.
Perceptual Space (P-Space) and Language Space (L-Space)
In the early stages of human development, our awareness of things or people outside ourselves is connected to the world that we can directly experience with our senses. Only the objects or people that are within this perspectival space exist, and when they disappear from that perspectival space, not only do they disappear from perception, but their entire existence seemingly vanishes. Early learning specialists correlate a baby getting upset and crying at a nursery during a parent drop-off with the understanding that for a baby, the disappearance of her parents from her sightline is associated with their loss from her life. Consider this common occurrence: a baby sits in her highchair, and she throws an object, like her toy or spoon, on the floor. She starts crying when the object she just threw away disappeared from her sightline. An adult interferes with this situation and grabs the object from the floor, cleans it, and puts it back on her highchair. The baby smiles at first, and then throws the object back out again. In this scenario, the baby is not testing the parent’s patience, but rather, she is learning something important. She is learning that [this] object in front of her continues to exist even when she throws it on the floor, which is outside of her sightline. The reappearance of the object with the assistance of an adult reassures the baby that the object that she threw away is still there even when she can no longer see it. Piaget calls the realization that something continues to exist—even when it’s no longer sensed—“object permanence.” (Garhart Mooney, 2013, p.82) Even though the baby cannot talk, she uses gestures of pointing, as she cognitively develops object permanence. Before the acquisition of language, she uses the deictic gestures of being [here] and seeing [this] object.
As children start to talk, how do they acquire deixis in language—pointing with words—when they have encountered it, thus far, only by pointing their fingers? Unlike categorical words like “spoon” or names like “Joe” that do not change depending on who speaks and where they speak from, the correct use of deictic terms is dependent on the speaker’s position and the proximity of the subject matter to the speaker.
In an essay on how a child acquires English expressions for space and time, psycholinguist Herbert H. Clark (1973) argues that the child acquires them “by learning how to apply these expressions to the a priori knowledge [that the child] has about space and time.” (Clark, 1973, p.28) This a priori knowledge comes from a space Clark calls “P-space,” the perceptual space the child is born into. He writes:
The child is born into a flat world with gravity, and he himself is endowed with eyes, ears, an upright posture, and other biological structure. These structures alone lead him to develop a perceptual space, a P-space, with very specific properties. Later on, the child must learn how to apply English spatial terms to this perceptual space, and so the structure of P-space determines in large part what he learns and how he quickly learns it. The notion is that the child cannot apply some term correctly if he does not already have the appropriate concept in his P-space. (Clark, 1973, p.28)
As a baby discovers the phenomena of gravity that forces the objects she throws toward the floor, into disappearance from her vision, she is developing a broader world than her innate P-space, where objects exist beyond her immediate vision (object permanence). The baby expresses herself using deictic expressions in absence of spoken language. As she acquires the language expressions that relate to the concepts of P-space, she enters what Clark calls “L-space,” the concept of space underlying English spatial terms. L-space coincides with P-space, as such that “any property found in L-space should also be found in P-space.” (Clark, 1973, p.28)
Clark summarizes the characteristics of the P-space of a person, in upright position—what he calls the canonical position—as “the optimal position to perceive other objects visually, auditorily, tactually, etc.” (Clark, 1973, p.34) And he defines these in geometric terms: “P-space consists of three reference planes and three associated directions: (1) ground level is a reference plane and upward is positive; (2) the vertical left-to-right plane through the body is another reference plane and forward from the body is positive; and (3) the vertical front-to-back plane is the third reference plane and leftward and rightward are both positive directions.” (Clark, 1973, p.35) (See Figure 1)
Figure 1. P-Space. The diagram is created based on Herbert Clark’s definition.
According to Clark, “the perceptual features in the child’s early cognitive development (his P-space) are reflected directly in the semantics of his language (his L-space).” (Clark, 1973, p.30) The critical role that the P-space plays in the development of the individual’s L-space is an important hinge in the interrelationship between deixis, architecture, and empathy. P-space is innate to the person’s experience; it is phenomenological; and it is directly relatable to the physical environment. Architects shape the P-space, and as such, they have an influence on the development of the L-space for both the individual and society. Therefore, in theory, if we can design the P-space purposefully, we can shift the semantics (meaning) and potentially create a place that catalyzes empathy.
Visual Echo in the Perspectival Space (Personal-Deixis & Empathy)
My theory is that spatial deictic words like [here], [there], [this], or [that] and personal deictic words like [I/we], [you], or [he/she/they] can be acquired by children easier in a space that deliberately constructs the deictic depth in the P-space. As seen in Figure 2, the construct of the P-space can make proximity and non-proximity explicit and hence the correlation between the language and the space can be made more direct.
Figure 2. Avenues Shenzhen Early Learning Center three niches conjecture.
For Avenues Early Learning Center project in Shenzhen, we created a purposefully choreographed series of niche spaces for the students. Here, three identical frames are arranged on the same axis, across a space that is open to below. Each frame creates a seating niche, lined with the same green fabric, marking its presence clearly within its respective white wall. The niches look almost identical with small variations. The first one, shown in the foreground, has a keyhole shape and features a writable glass surface that allows for a visual connection to the double-height atrium below. The middle niche also features writable glass, but its shape is square. The third niche, which is the farthest away in Figure 2 and visible only through the middle niche, is open to the student commons located in front of it and has a solid back wall.
All three frames create their own deictic centers but share the same axial arrangement of a single-point perspective. This creates a strong visual connection between each of these individual deictic centers. But the critical element of this design is the visual echo, created by the “three-niches” arrangement. For the children in the foreground, their perspective-taking—based on their own deictic center—is contextualized by the students directly across from them. In the acquisition of personal deictic words like [I] or [we], the impact of the three niches P-space on the cognitive development of the children is to help develop an awareness of the perspective of [others] that co-exist with them in the same perspectival space. Such awareness can catalyze empathy in learning environments. In broader terms, by facilitating the acquisition of language in a specially constructed P-space, we can encourage a shift in the egocentric bias of young children toward a more empathic worldview.
Figure 3. Three Niches Conjecture Diagrams showing different locations of first person and the relative positioning of the second and third person.
Derived from our design study at Avenues Early Learning Center, the “three niches” conjecture is a P-space construct that assists with the acquisition of deictic expressions with empathy in early childhood. The three niches conjecture is constructed as follows: Define three deictic centers and locate them on the same perspectival axis, the positive and negative directions of each being parallel to the axis. On each deictic center, the vertical front-to-back perpendicular plane of the person is visually framed with an identical or similar marker to achieve a visual echo. The framing elements should have conspicuous geometric, textural, and color similarities. (See Figure 3)
If the grammatical first person is located on the deictic center at either end of the axis, all the three personas can be subsequently located in the same direction. This type of arrangement for the P-space will result in the construction of second and third person for the L-space, and hence the perspective taking can be expanded to the [other] in the same directional axis. If the grammatical first person is located in the middle, the second person is visible across, whereas the third person will be behind the first person, or toward the negative direction. The first person located in the middle will need to pivot to visually engage with the third person. (See Figure 4)
The forced perspective construct of the three niches conjecture creates three egocentric reference frames that align toward the same vanishing point. The visual echo of each frame is intended to catalyze perspective taking for each individual, shifting the focus of spatial cognition to social interaction. In this specially choreographed P-space, which allows multiple perspectives in the same narrative, a shift from an egocentric frame of reference to an allocentric frame of reference is intended.
Summary: The Geometry of Empathy
The interdisciplinary connections amongst discourses of spatial cognition, language acquisition, and development theory create an important basis to theorize the transformative potentials between perspectival projections in the physical (architectural) environment and perspective-taking in psychology. Based on these interdisciplinary readings, this essay discussed how the physical environment can influence the development of perspective-taking, and more specifically, how the purposeful design of spatial constructs can nudge us toward being more empathic.
Deixis is the most obvious way language and context relate to each other. (Levinson, 1983, p.54) The decision to explore design concepts based on deixis and empathy sprung from Herbert Clark’s argument that our perceptual space (P-space) influences our language space (L-space). (Clark, 1973) His theory that the properties in P-space can also be found in the properties of L-space led me to the premise that if we can alter the perceptual space purposefully, we can potentially create new narratives, ones that can encourage us to be more empathic.
Geometry is a common ground that deixis and architecture share. The concepts of projective geometry are not merely rules of representation, but a set of forces that are omnipresent in our imagination and spatial perception, and consequently instrumental in the development of social and spatial cognition. Robin Evans, in his seminal work The Projective Cast: Architecture and Its Three Geometries, underlines the indispensable role that geometry plays, “a constitutive part of Architecture.” (Evans, 1995, p.xxvi) He stated: “What connects thinking to imagination, imagination to drawing, drawing to building, and buildings to our eyes is projection in one guise or another, or processes that we have chosen to model on projection.” (Evans, 1995, p.xxvi) The connections listed in Evans’s argument are also the connections that are proposed in this essay between perspective taking in development theory and experiencing spatial perspectives in architecture.
Through the use of projective geometry, we can create spatial nudges that can encourage perspective taking. And furthermore, we can curate specific trompe l’oeil constructs that have the ability to shift deictic center. The premise of this theory is explored in the three niches conjecture. Like the reciprocity of vision described by Michel Foucault in Velasquez’s painting Las Meninas, the three niches conjecture creates juxtapositions of perspectives. (Foucault, 1994, p.4) In this design conjecture, within the field of forced perspective, the egocentric nature of deictic center is challenged, and students are encouraged to take the perspective of the other. The visual echo in this construct encourages cognitive reflections, which moves the first person away from the deictic center and enables her to look at the scene from outside, and hence shift the spatial frame of reference from an egocentric to an allocentric one. The premise of the three niches conjecture is to help develop an awareness of the other person during the acquisition of deictic words and expressions in early learning.
References:
Clark, H.H. (1973). Space, time, semantics, and the child. In T. Moore (Ed.), Cognitive Development and the Acquisition of Language (pp. 27–63). New York: Academic Press)
Evans, R. (1995). The Projective Cast: Architecture and Its Three Geometries. MIT Press.
Foucault, M. (1994). The Order of Things: An Archaeology of the Human Sciences. Routledge.
Levinson, S. C. (1983). Pragmatics. Cambridge University Press.
Mooney, C. G. (2013). Theories of Childhood, Second edition: An Introduction to Dewey, Montessori, Erikson, Piaget & Vygotsky. Redleaf Press.
Norberg-Schulz, C. (1979). Genius Loci: Towards a Phenomenology of Architecture. New York: Rizzoli.
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