Mel Bochner is a New York City artist who, despite disliking the term “conceptual art,” is sometimes credited with staging the world's first conceptual art exhibition in 1966 (Bochner, 2008). With a background in phenomenology, an interest in the work of early minimalist artists, and inspiration taken from an artist-in-residence position at Singer Research Labs, Bochner's sculptures and installations took a turn toward spatial, numerical, and linguistic themes from 1968 through the 1970s. The common thread connecting his early work is a preoccupation with the kinds of abstract categories that relate objects to one another (rather than to the objects themselves) and how the mind represents such relations in distinct formats (e.g., boundaries, numbers, words). At that time, Bochner articulated a desire to create art “that did not add anything to the furniture of the world.” In part, this was a response to an art world “dominated by the equation ‘art = objects’” as promoted by pop artists like Andy Warhol and minimalists like Donald Judd (Field, 1996). Rather than creating art objects that people could take home, Bochner wanted to provide his audience with a kind of mental tool kit. That is, he sought to make art that compelled viewers to attend to, and reflect on, the most basic cognitive processes involved in seeing the structural relations between objects.

More recently, empirical research in cognitive neuroscience has also moved beyond a neuroscience of objects (faces, words, tools, etc.). Interest in basic abstract categories like space, time, number, and causality has increased, as the systems that subserve these relational processes have come to be understood as particularly important and potentially interrelated (Kranjec, Cardillo, Lehet, & Chatterjee, 2012; Bueti & Walsh, 2009; Walsh, 2003). Such basic categories of experience serve well as model domains for developing integrated theories of mental representation and semantics. To illustrate this, consider the semantics of space. On the face of it, the language of space, namely prepositions, may seem relatively insignificant, but this is not the case. On the one hand, the simple meanings of spatial words present an opportunity to investigate the structure of a distributed semantic system in very stark form. Locative prepositions represent a closed set of frequently used spatial categories with meanings constrained by perception and ecology. On the other hand, the meanings of basic spatial categories serve as a foundation on which more complex concepts are built; we think and talk about more abstract conceptual categories like emotions and morality using the language and structure of space (e.g., “I'm feeling high/low.”). But the semantics of prepositions is not the only thing that makes them important with respect to grounding relational thinking. In part, prepositions are special because they are semantically and grammatically flexible in a manner that is unique in human language. Not only can the semantics of prepositions be both concrete and abstract, they also often serve very different functions in language (Kranjec, Cardillo, Schmidt, & Chatterjee, 2010; Frederici, 1982). Prepositions frequently serve a prescribed functional role as syntactic relational units (e.g., “on” alert vs. “in” trouble) seemingly (but not necessarily) empty of semantic content (which may explain why we frequently take them for granted). By investigating how these particularly flexible, ambiguous, and productive units of language are represented in the brain along a semantic–syntactic continuum, we may step closer to both delineating aspects of language that utilize neural structures evolved for perception and action and those that make human language distinct from nonhuman forms of mental representation and communication. The deployment of basic relational language (using prepositions), grounded in fundamentally relational cognitive domains (like space), may make species-specific human abilities like analogy and metaphor possible (Gentner, 2003; Lakoff & Johnson, 1999).

In this way, spatial experience and perception can be seen as a model domain for grounding abstract meaning and relational thinking in the brain. For cognitive neuroscientists, understanding how the neural organization of spatial perception is related to the ways in which we talk about space in terms of prepositions can shed light on the nature of the intermediate representations that link distinct formats (like images and words) and domains (like space and time). Using lesion methods in patients, previous work that I have been involved with has investigated such intermediary structures between perception and language, in a graded model of mental representation (Kranjec & Chatterjee, 2010). For cognitive neuroscientists, describing the structures of “thought” at such an intermediate level can be difficult. When doing so, not only must one develop a verbal vocabulary to unpack complex concepts that can bridge definitions of mind and brain, but also, perhaps more than in other fields, cognitive neuroscientists are frequently required to interpret and develop visual vocabularies and metaphors to further explain novel imaging methods, materials, results, and models.

I became interested in Bochner's art while visiting the National Gallery of Art in the Summer of 2012, where it was suggested to me by my companion that his theory of boundaries (then on display) resembled stimuli from a set of studies I had recently completed exploring spatial representation in stroke patients (Kranjec, Ianni, & Chatterjee, 2013; Amorapanth et al., 2012). I later found myself becoming a quick student of Bochner's work. After recognizing Bochner's general interests in spatial semantics and mental representation, I noticed more fine-grained areas of overlap between his interests and my own. For example, Bochner's work recognizes a well-known neuropsychological distinction between categorical and coordinate spatial information (e.g., the difference between understanding that a shoe is “below the table” vs. “30 in. from the table”). More than anything though, Bochner's particular preoccupation with prepositions as an important window into the structure of thought seemed remarkable to me, as was his interest in depicting related spatial concepts in different representational formats. By providing an opportunity to reflect on the meanings of basic spatial relations while moving between words and images intended to express a common concept, Bochner's art allows viewers to experience the limitations of a particular kind of representation. His work in this respect owes something to “The Treachery of Images” by Rene Magritte who famously painted “Ceci n'est pas une pipe” beneath a picture of a pipe (and remarked, “if I had written on my picture ‘This is a pipe,’ I'd have been lying!” [Torczyner, Miller, & Magritte, 1977]). However, by focusing on relational concepts rather than objects themselves, Bochner moves away from the “furniture of the world” and closer to “the stuff of thought” (Pinker, 2007): The very thing that cognitive neuroscience aims to do by concentrating research on abstract categories like space, time, and number.

When corresponding with Bochner in advance of this interview, I sent ahead some questions in line with my specific research interests. Although he made it clear that he would reflect on what I had sent, he replied, “Remember I'm an artist not a neuroscientist. I go on hunches and intuitions, not theories.” This is an important distinction and something that I kept in mind during the interview. Although there is precedent for Bochner's art serving as inspiration for scientists (see the anecdote regarding Bochner's collaboration with an organic chemist below), it remains to be seen if an examination of Bochner's work will offer cognitive neuroscience-specific insights. Regardless, the more general idea that conceptual artists have something to offer cognitive neuroscientists remains very compelling. Although an artist like Bochner may not work using the scientific method, the idea that conceptual artists set out to systematically visualize cognitive structure may guide cognitive neuroscientists to notice previously unseen connections between art and our science. Bochner has written elsewhere regarding the mistake of believing that “systematic thinking” should be “considered the antithesis of artistic thinking” (Bochner, 2008). I am of the opinion that, despite the starkly different methods used by both fields, conceptual art and cognitive neuroscience have some interesting common ground. Namely, both disciplines use methods that can be described as systematic or analytic, and both are deeply engaged in the project of describing, abstracting, and visualizing facts about basic categories of mind and experience. Moreover, whereas the emerging field of neuroaesthetics is gaining momentum (Chatterjee, 2011), cognitive neuroscientists have mostly neglected conceptual art (Bullot & Reber, 2012). This is because empirical investigations in aesthetics typically focus on perceptual preferences for visual art (i.e., “what is beauty?”). Ontologically, conceptual art often goes further “upstream” than this (e.g., “what is art?”) in a manner that shares features of scientific inquiry. (A general process that may involve reducing a concept or function to its most basic properties via an analysis of previous work and phenomenology. A cognitive neuroscientist might be said to engage in something like this when utilizing cognitive subtraction techniques or considering the distinction between an experimental task and a cognitive function.) By focusing particularly on the spatial relations between objects, Bochner's art addresses not only deep questions regarding the meaning of art and art objecthood but also topics of more general interest to cognitive scientists. Those interested in how the mind represents objects and abstract concepts, both with and without language, could learn much from how visual artists like Bochner choose to represent such subjects in their work.

Alexander Kranjec: How do you explain the general philosophical and scientific nature of your art and, specifically, your interest in space?

Mel Bochner: That's a complicated question. I think it would be easiest to start at the beginning of my career as an artist. After graduating from the Carnegie Institute of Technology (now Carnegie Mellon University), I couldn't see a way out of an artistic dilemma I was facing at the time, trying to reconcile all my student influences, and was more or less at the point of giving up. I was in correspondence with an old friend who was studying philosophy at Northwestern. He said, “Well if you're interested in philosophy, why don't you come here. You could audit courses and see if maybe you want to come back to school and study philosophy.” So that's what I did. I moved to Chicago, but it didn't take very long to see that that's not what I wanted to do. Sitting around the library reading all day wasn't my idea of something interesting. Also, at that point, I was playing catch up. Everybody else in the program had actually, you know, read Plato (laughs). So, I used to get on the elevated train, go down to the city, and spend the whole day at the Art Institute, because Pittsburgh and San Francisco didn't have great museums and I'd never seen a real El Greco. Actually, I'd never seen a lot of things. And it rekindled my interest. I realized that I really did want to be an artist. So, jumping forward 6 months, I arrived in New York, still without any real direction in my work, just a group of small, all-over gray paintings that represented all my frustrations, in paint.

One day, I ran into a friend on the street who told me there was a Jasper Johns show at the Jewish museum, who I'd vaguely heard of but had no real idea of what he was doing. She said, “Oh, he does all gray paintings, too,” and for some reason, that really annoyed me.

AK: (laughs)

MB: You know, in my naiveté, I thought I was the only one doing all gray paintings. Anyway, I went there and saw he had been doing it for 10 years already and he had done it much better. But, what fascinated me about his work was not the grayness but the introduction of language, alphabets, numbers, and things like that. In one painting, the only image was the word “the.” They were very beautifully painted paintings, but there was this enigma of the word. What did it mean? Why would the word “the” be floating in the middle of this gray surface? And, it seemed to me that he had tapped into some other part of the brain.

AK: That reminds me of a psychological effect (semantic satiation): If you start to repeat a word over and over and over, you more or less start to focus on the phonology or the orthography of the word, the form of it, and the meaning becomes lost. A word can start to feel very strange to you, like nonsense.

MB: Warhol said, if you repeat something often enough, it loses it's meaning, which is basically the secret of his work.

Thinking about Johns' work, I discovered Rauschenberg, and it seemed to me…belatedly, because this wasn't news anymore in 1964…to offer a direction out of the corner that I had painted myself into. My objective was to find something that was my own. I thought, “What can I do that belongs to me and to no one else?” I decided it would have to be like an activity. And the thing that came into my mind was counting, just counting. When you're counting, you didn't have to make anything up. Two always follows one, three always follows two, four always follows three. Then, it became a question of what to count. At that same moment, minimalism, which was the work of (Donald) Judd, (Dan) Flavin, and (Sol) LeWitt, was just breaking, and I was very struck by them. I liked their ideas. Their work was not about geometry in any conventional way. I was beginning to see or understand that, to do something original, you had to question existing thought structures.

AK: Understanding this part of the story, about the development of your work and eventually where it ends up, is very interesting to me because it reminds me a little of the trajectory of the cognitive neurosciences as well. When neuroimaging (fMRI) became very popular, one of the first things that people started investigating concerned where certain kinds of objects are represented or processed in the brain. You know, where's the tool part of the brain, or the face part of the brain, or the word part of the brain? Much of it was very good work, and we gradually accumulated all of this knowledge about where stuff gets processed, that is, objects. But, no one really thought about this kind of abstract relational information that your work addresses until later. It's sort of a second-order question to think of the relations between objects as objects of thought themselves. It's also neat to hear about your struggle to distinguish your art from that of your peers, because as a scientist, too, we're all trying to find our own territory (Figure 1).

Figure 1. 

(A) “Measurement Five” (1969) and (B) “Cardinal Versus Ordinal” (1972). Works from Bochner's “Measurement” and “A Theory of Sculpture” series highlight the conceptual distinction between number (an abstract symbolic representation) and numerosity (a concrete analog representation) that is central to the work of several prominent cognitive neuroscientists. Stanislas Dehaene and colleagues have provided evidence for notation-independent coding (dots, digits, and number words) of numerical quantity in the intraparietal sulcus (IPS; Piazza, Pinel, Le Bihan, & Dehaene, 2007). The work of Jessica Cantlon further suggests that the right IPS plays a preferential role in nonsymbolic numerosity coding during early childhood (Cantlon, Brannon, Carter, & Pelphrey, 2006). Daheane suggests that the left IPS develops its role in number processing as a function of experience with symbols. Several pieces from “A Theory of Sculpture” also capture the difference between quantity and sequence and the representational ambiguity involved when the same number symbols serve two cognitively distinct functions. Of this series Bochner (2013) recently wrote, “Number constitutes a mental class of objects. Numbers do not need concrete entities in order to exist. In Latin, the word for counting is ‘calculus,’ which translates, literally, as stone. By juxtaposing the numbers with the stones, “A Theory of Sculpture” forces a confrontation between matter (“raw” material) and mind (categories of thought)” (Bochner, 2013).

Figure 1. 

(A) “Measurement Five” (1969) and (B) “Cardinal Versus Ordinal” (1972). Works from Bochner's “Measurement” and “A Theory of Sculpture” series highlight the conceptual distinction between number (an abstract symbolic representation) and numerosity (a concrete analog representation) that is central to the work of several prominent cognitive neuroscientists. Stanislas Dehaene and colleagues have provided evidence for notation-independent coding (dots, digits, and number words) of numerical quantity in the intraparietal sulcus (IPS; Piazza, Pinel, Le Bihan, & Dehaene, 2007). The work of Jessica Cantlon further suggests that the right IPS plays a preferential role in nonsymbolic numerosity coding during early childhood (Cantlon, Brannon, Carter, & Pelphrey, 2006). Daheane suggests that the left IPS develops its role in number processing as a function of experience with symbols. Several pieces from “A Theory of Sculpture” also capture the difference between quantity and sequence and the representational ambiguity involved when the same number symbols serve two cognitively distinct functions. Of this series Bochner (2013) recently wrote, “Number constitutes a mental class of objects. Numbers do not need concrete entities in order to exist. In Latin, the word for counting is ‘calculus,’ which translates, literally, as stone. By juxtaposing the numbers with the stones, “A Theory of Sculpture” forces a confrontation between matter (“raw” material) and mind (categories of thought)” (Bochner, 2013).

MB: I remember having the idea as a young artist that I wanted to take the knowledge that's in art…because I think art is about knowledge, not about objects…and somehow push that further. But, where to push it that it hadn't already been? The first thing I did, which I felt was my own, was the “Working Drawings and Other Visible Things On Paper Not Necessarily Meant To Be Viewed As Art” exhibition.

AK: Which is often cited as the first exhibition of conceptual art.

MB: My idea was that, instead of worrying about the object, what if we look at the thinking process behind it? In other words, the genetics of the artwork, or what I was calling at that time, the upstream. Where's the source? Where does the water come out of the rock? How far upstream can you get? Is there a limit? So, I went to other artists and asked them for their working drawings and notes, things that they didn't consider artworks, and through a series of events, I wound up Xeroxing the drawings and presenting them as a book. The book became the artwork. That was very hard for certain people to swallow. You walked into the gallery, there was nothing on the walls, and you stood there reading a book.

AK: Is that the bigger idea or your motivation for what got you where you are today…perhaps something that is a common feature of anyone who calls themself a conceptual artist? That a conceptual artist needs this explicit awareness of the history of ideas preceding them in order to make a novel contribution? Is that why people that are more interested in theory and criticism might be more attracted to conceptual art?

MB: That's a good question. First, I don't like the term “conceptual art.” It's an oversimplification and leads to bizarre formulations like “dematerialized art,” as if there was something in the world that wasn't made up of matter. As far as I'm concerned, even a thought is a material. There was no cohesive group that called themselves the “minimalists.” The same is true of the conceptualists. In minimalism, what was at stake was could constitute the minimal conditions of interest? Can you just put a box in the middle of the room and have it be interesting? And if you can, “Why is it interesting?” The people who were against it came up with some interesting ideas about why it wasn't interesting. A critic named Michael Fried developed his theory of absorption. He said a cube sitting in the middle of the gallery is basically performative, whereas a real work of art is absorptive. If you look at a Rembrandt, you're absorbed into the reality of that artwork. The cube is the exact reverse of that, which he accused of being theatrical. And, he did have a point. But, the best work was not theatrical in the superficial sense, although it did force you into a recognition of the space, of the context. In other words, when you look into a picture, you don't think that you're in a museum or a gallery, you're in the picture. Whereas if you're looking at a monochrome canvas, or a cube by Donald Judd, you start to look around the room and you think about the context. And then, you think about the experience of looking itself, which leads to all kinds of other critical and phenomenological thoughts.

AK: So, is this how you got into space then? When you talk about your intellectual process of reduction and looking upstream, you get to this place where space as a basis or context for experiencing art is at the source, you can't get further upstream than that?

MB: Yes, but that was only one factor. The concept of measurement came to me when I was an artist-in-residence at the Singer Research Labs, talking to the scientists who worked there. The conversations always arrived at the notion of objectification. To them, truth had to be verifiable by experiment, which, in turn, had to be verifiable by measurements. That's when the trust, or distrust, of language became interesting to me; I began to see measurement as a language that contained as much ambiguity as any other language. Although these scientists didn't want to recognize it….

AK: And by scientists, these were engineers, these were scientists engaged in producing useful things?

MB: Yes, they were object-oriented scientists. They couldn't figure out what I was doing there (laughs). At the time, my artwork was involved with photography—studying cognitive structures like perspective. Then, the measurement thing sort of took over. But, the background for this goes back to when I was at Northwestern, which at that time was the center for phenomenological studies in America. They were passing around a recently translated typescript of Merleau–Ponty's “Phenomenology of Perception.”

AK: Do you know Duquesne University (where AK is an Assistant Professor) is widely regarded as the current center for phenomenology in America? (It is home to the Silverman Center for Phenomenology.) It's one of the last holdouts in this regard. There are psychologists in my department who primarily refer to themselves as phenomenologists (Figure 2).

Figure 2. 

(A) “Notecard” (Merleau–Ponty; 1969) and (B) “Language Is Not Transparent” (1970). There are signs of both self-education and didacticism in Bochner's early work. Whereas his “Notecards” suggest the notetaking of a graduate student searching for an original project, in “Language Is Not Transparent” the numbered statement, written on a surface that resembles a dripping blackboard, suggests a theoretical foundation for a project that has become more refined and personal. Both pieces reflect Bochner's preoccupation with the limits of a given representational format. Respectively, photographic images bleach visual percepts of their dynamism, and language as inherently symbolic (and nonanalog) is necessarily ambiguous because it abstracts away the details of a more concrete reality. Bochner told me, “All of those early works, actually all of my work, I see as a form of self-education. To learn things you have to look in unexpected places.”

Figure 2. 

(A) “Notecard” (Merleau–Ponty; 1969) and (B) “Language Is Not Transparent” (1970). There are signs of both self-education and didacticism in Bochner's early work. Whereas his “Notecards” suggest the notetaking of a graduate student searching for an original project, in “Language Is Not Transparent” the numbered statement, written on a surface that resembles a dripping blackboard, suggests a theoretical foundation for a project that has become more refined and personal. Both pieces reflect Bochner's preoccupation with the limits of a given representational format. Respectively, photographic images bleach visual percepts of their dynamism, and language as inherently symbolic (and nonanalog) is necessarily ambiguous because it abstracts away the details of a more concrete reality. Bochner told me, “All of those early works, actually all of my work, I see as a form of self-education. To learn things you have to look in unexpected places.”

MB: In the late ‘60s, the linguistic philosophy guys had taken over the Harvard Philosophy department. All the phenomenology professors moved to Northwestern where Merleau–Ponty was the god. My friend, who introduced me to this whole area, was writing his PhD on Heidegger, who I had not heard of before. In short, all these ideas were very much in the air. This served as the background when I started doing my first measurement pieces.

At some point, I read a book about different concepts of space, and there was one sentence that stuck with me: “You can't make space, you can only divide space.” This was a revelation. Space is a given. We know that from Kant. That's the whole idea of innate structures, that space and time are a priori. I was playing with measurement, and I realized at a certain point I've got to measure something. I had sheets of paper and cardboard lying around the studio. Standard size sheets of paper come 8 ½ × 11 in. (or sometimes 8 × 10 in.). Standard-size sheets of cardboard come 36 × 48 in. Lumber came in 6- or 8-ft lengths. Materials are governed by standard sizes. I came to understand that everything is modular as a factor of mass production. Architecture was based on these modules, so that every room has a secret—a hidden measurement system. I asked myself, “What would be the largest space I could measure?” Well, the room itself. The room becomes the envelope for whatever action occurs inside it. That envelope is the projection of an idea, which is based on available materials, which are based on measurements. It's a self-enfolding structure.

When I put the measurements on the wall, I'm forcing the architecture to reveal itself, to surrender its transparency. When I did the first installation in Germany, I had another revelation: In the “Measurement: Room” there is no center, because the artwork surrounds you. As you move around the room, it constantly appears and disappears. It's always simultaneously in front of and behind you. You are the center of the work, a mobile center.

AK: I'm following you. So, how you got to be interested in measurement was fairly straightforward, and then, it led to this sort of bigger idea that was the result or the effect of your interest in measurement; you made the ground the focus of your artwork rather than the figure. And by doing that, you make explicit these figure–ground relations in a very interesting way. And once you make figure–ground relations explicit, then you get to this idea of boundaries and these other kinds of spatial relations that you depict in the “Theory of Boundaries.” Does that make sense? (Figure 3)

Figure 3. 

(A) “Measurement Room” (1969), (B) “Actual Size” (Face; 1968), and (C) “Theory of Boundaries” (1969–1970). Bochner first started to measure things while at Singer Labs. The resulting “Measurement” pieces simultaneously draw attention to certain kinds of objects (e.g., faces and places) and away from them, as the viewer is encouraged to consider the abstract spatial constraints that structure and unify our discrete experiences. In a historical context, they “canceled the ironic commentaries on the arbitrariness of measurement” (Field, p. 34), suggested by a work like Marcel Duchamp's “Three Standard Stoppages” (1913–1914). And although his actual size portraits would seem to play with the idea that measurement is distorted when objects are represented in photographs, the knowledge that Bochner instructed the printer to develop the 12” measurement “actual size” further toys with this expectation, creating an analog metric relation between the representation and the thing it represents. “Theory of Boundaries” dates from 1969, the same year as “Measurement Room.” Here, Bochner depicts four word–image relations or what he calls “language fractions” (at/in, over/in, /in, at/out). In the preliminary sketch notes for the piece, first published in Arts Magazine (1970) titled “No Thought Exists Without a Sustaining Support,” Bochner explains that, “the first term of the language fraction refers to the contingency of the film [surface paint] to the border. [The] second term…refers to the position of the film as regards the sense of enclosure.” For example, in the first square on the left, the color is both at the boundary and in the enclosure created by that boundary. In contrast to the metric relations depicted in his “Measurement” works, in “Theory of Boundaries,” word–image relations are explicitly ambiguous. (It is perhaps no coincidence that “Language Is Not Transparent” also comes out of this same year or that “No Thought Exists Without a Sustaining Support” is presented as axiom number two as part of that series.) Bochner's work during this period seems to recognize the neuropsychological distinction between categorical and coordinate spatial information. Kosslyn (1987) originally proposed a hemispheric bias for processing two types of spatial information. Categorical relations refer to discrete spatial relations frequently lexicalized by locative prepositions like “above,” “below,” and, “in.” Coordinate relations are finer-grained metric relations not as readily coded by language, usually involving distance information. Categorical representations specify abstract, equivalent (but perceptually ambiguous) classes of spatial relations and are preferentially processed in the left hemisphere, whereas coordinate representations specify the exact locations of objects in space, information important for reaching and navigation and processed in the right hemisphere (Kosslyn, Thompson, Gitelman, & Alpert, 1998; Kosslyn et al., 1989; Kosslyn, 1987). In Kosslyn's later thinking on the subject (Kosslyn & Jacobs, 1994), he hypothesizes that low-level perceptual biases in left hemisphere structures important for abstraction (and categorization) served as a precursor for the development of language in proximate cortical areas (see Postma & Laeng, 2006, for a short review).

Figure 3. 

(A) “Measurement Room” (1969), (B) “Actual Size” (Face; 1968), and (C) “Theory of Boundaries” (1969–1970). Bochner first started to measure things while at Singer Labs. The resulting “Measurement” pieces simultaneously draw attention to certain kinds of objects (e.g., faces and places) and away from them, as the viewer is encouraged to consider the abstract spatial constraints that structure and unify our discrete experiences. In a historical context, they “canceled the ironic commentaries on the arbitrariness of measurement” (Field, p. 34), suggested by a work like Marcel Duchamp's “Three Standard Stoppages” (1913–1914). And although his actual size portraits would seem to play with the idea that measurement is distorted when objects are represented in photographs, the knowledge that Bochner instructed the printer to develop the 12” measurement “actual size” further toys with this expectation, creating an analog metric relation between the representation and the thing it represents. “Theory of Boundaries” dates from 1969, the same year as “Measurement Room.” Here, Bochner depicts four word–image relations or what he calls “language fractions” (at/in, over/in, /in, at/out). In the preliminary sketch notes for the piece, first published in Arts Magazine (1970) titled “No Thought Exists Without a Sustaining Support,” Bochner explains that, “the first term of the language fraction refers to the contingency of the film [surface paint] to the border. [The] second term…refers to the position of the film as regards the sense of enclosure.” For example, in the first square on the left, the color is both at the boundary and in the enclosure created by that boundary. In contrast to the metric relations depicted in his “Measurement” works, in “Theory of Boundaries,” word–image relations are explicitly ambiguous. (It is perhaps no coincidence that “Language Is Not Transparent” also comes out of this same year or that “No Thought Exists Without a Sustaining Support” is presented as axiom number two as part of that series.) Bochner's work during this period seems to recognize the neuropsychological distinction between categorical and coordinate spatial information. Kosslyn (1987) originally proposed a hemispheric bias for processing two types of spatial information. Categorical relations refer to discrete spatial relations frequently lexicalized by locative prepositions like “above,” “below,” and, “in.” Coordinate relations are finer-grained metric relations not as readily coded by language, usually involving distance information. Categorical representations specify abstract, equivalent (but perceptually ambiguous) classes of spatial relations and are preferentially processed in the left hemisphere, whereas coordinate representations specify the exact locations of objects in space, information important for reaching and navigation and processed in the right hemisphere (Kosslyn, Thompson, Gitelman, & Alpert, 1998; Kosslyn et al., 1989; Kosslyn, 1987). In Kosslyn's later thinking on the subject (Kosslyn & Jacobs, 1994), he hypothesizes that low-level perceptual biases in left hemisphere structures important for abstraction (and categorization) served as a precursor for the development of language in proximate cortical areas (see Postma & Laeng, 2006, for a short review).

MB: That's pretty close, but I'm summarizing and telescoping it. The progression of my work was more convoluted. The realizations came more slowly.

AK: Right, your measurement pieces are not Experiment 1, and “Theory of Boundaries” isn't Experiment 2. This isn't science.

MB: Art works don't follow each other in any necessary way.

AK: But, you did recognize them as exploring very different kinds of spatial relationships?

MB: They are different, just like “Language is Not Transparent” is a different kind of work too.

AK: The reason I'm harping on this is because something that I and others have studied in cognitive neuroscience for some time now is the distinction between what's called categorical and coordinate spatial relations. Stephen Kosslyn at Harvard has argued for some time in favor of this distinction being particularly important in the evolution of human cognition and that this is reflected in a hemispheric division of labor in processing these two kinds of spatial relations in the brain. Coordinate relations have more to do with measurement, distance, or metric space, and categorical relations have to do more with the sort of discrete categories of spatial relations that are described with prepositions, like “above,” “in,” and “on.” Because categorical relations can be easily verbalized, they can also be ambiguous. There is evidence that the left hemisphere is more important for processing categorical relations that are more verbally mediated and the right hemisphere is more important for processing the kind of spatial information that is less easily described in words. I don't want to get too much into the details of the scientific theory, but I did want to make the general point that the distinction between different kinds of spatial relations that you explore in those two pieces maps fairly directly onto this major overarching theory in the cognitive neurosciences. The fact that these two pieces came out while you were thinking about this stuff is really interesting.

MB: Have you come across a work I did called “Axiom of Indifference”?

AK: I read the Bruce Boice article about it in the Yale Catalog. When I started reading it, I thought we could really make our whole conversation just about rolling over all of the spatial and logical relations expressed in the article. It seems like we could spend hours doing that.

MB: Interestingly, we had never met before he wrote that.

AK: (laughs)

MB: Boice just walked in, saw the exhibition, went home, wrote the whole thing, and sent it to me. It was amazing analytical detective work. He really thought his way through. At that time, I wasn't thinking of my work as consisting of “works of art,” I considered them as tools to think with. And Boice used them that way…I worked on that piece for over a year. Mapping out all of those spatial and logical relationships was complicated. But, even after I thought that I had mapped all of the possibilities, the logical possibilities, I realized I hadn't accounted for the permutations of top and bottom. One day, I was at a friend's house for dinner and I was washing the dishes and they had a little jar where they collected pennies. And, I was washing the dishes and absent-mindedly looking at the pennies, suddenly my head just exploded. Of course, heads and tails! Tops and bottoms. And, that was it (Figure 4).

Figure 4. 

(A) “Prepositional Sculpture” (1970) and (B) “Axiom of Indifference” (1973) with (C) map for Sonnabend Gallery, installation of Axiom of Indifference. “Prepositional Sculpture” illustrates Bochner's interest in the verbal labeling of spatial relations in a relatively direct manner. In this case, the representational link between word and percept is made explicit such that the tape's analog position describes the spatial relation coded by the verbal label printed on the tape (beside, between, over, under). A recent study using voxel-based lesion symptom mapping (Amorapanth et al., 2012) found evidence suggesting that discrete verbal and perceptual representations of such categorical spatial relations show a hemispheric bias. “Axiom of Indifference” is a larger, more ambitious work, but also more complex. In this work, Bochner depicts a number of containment relations using pennies and tape. Logical propositions (e.g., “some are in”) describe each containment relation in a manner that, at first, seems straightforward. However, while moving through the installation, on closer inspection, one becomes aware that the meanings of the propositions are ambiguous depending on the frame of reference employed. Heightening attention to the ambiguity of spatial relations when expressed in distinct visual and verbal formats is a common method used by Bochner. In this instance, he goes further by pointing out that logical structures and reference frames play a role in creating meaningful relations between language and perception.

Figure 4. 

(A) “Prepositional Sculpture” (1970) and (B) “Axiom of Indifference” (1973) with (C) map for Sonnabend Gallery, installation of Axiom of Indifference. “Prepositional Sculpture” illustrates Bochner's interest in the verbal labeling of spatial relations in a relatively direct manner. In this case, the representational link between word and percept is made explicit such that the tape's analog position describes the spatial relation coded by the verbal label printed on the tape (beside, between, over, under). A recent study using voxel-based lesion symptom mapping (Amorapanth et al., 2012) found evidence suggesting that discrete verbal and perceptual representations of such categorical spatial relations show a hemispheric bias. “Axiom of Indifference” is a larger, more ambitious work, but also more complex. In this work, Bochner depicts a number of containment relations using pennies and tape. Logical propositions (e.g., “some are in”) describe each containment relation in a manner that, at first, seems straightforward. However, while moving through the installation, on closer inspection, one becomes aware that the meanings of the propositions are ambiguous depending on the frame of reference employed. Heightening attention to the ambiguity of spatial relations when expressed in distinct visual and verbal formats is a common method used by Bochner. In this instance, he goes further by pointing out that logical structures and reference frames play a role in creating meaningful relations between language and perception.

AK: (laughs) It's incredible to me that you're interested enough in these sorts of ideas to spend a year making a work like this, that someone else was able to walk through the whole thing and, like you said, do this detective work to puzzle out your reasoning. There is this relatively young field called cognitive linguistics. People working in this area and some in psychology are interested in the relationship between basic perceptual processes, cognition, and language. They pursue the same sorts of questions like, “What does ‘between’ really mean?” or “How do different languages parse or carve up spatial relations?” So, you know, in English, we have different words for “in” and “on,” but in Spanish, they use the same preposition collapsing both spatial relations with a single label. In Dutch, they do something different. Cognitive linguists are interested in looking at how all this might relate to the cognitive and perceptual processes involved in experiencing the world.

MB: Prepositions have fascinated me for a really long time. I did a piece called “Prepositional Sculpture” where I took three 4 × 4 pieces of 4-ft-long wood and laid them in a line (one, two, three). I put a strip of 4-in. white tape at the end of piece 1. Then, in the 4-in. space between piece 1 and piece 2, I put another strip of white tape. At the end of the second piece, I put a strip of white tape that starts on the floor, goes up and over the block of wood. And at the end of the third piece, I put the tape underneath it. On the first tape, I wrote “beside”; on the second, “between”; on the third, “over”; and on the fourth, “under.” So, you get these four prepositional possibilities, which are materialized as pieces of tape. At that time, I didn't want to make anything permanent. I wanted everything, at the end of an exhibition, to return to its ordinariness. The works are a demonstration of an idea that hopefully strikes a chord in a viewer: enabling them to use it as a tool to think with as opposed to an object to possess. “Prepositional Sculpture” was the beginning of my thinking about prepositions, which became more refined in “Theory of Boundaries” moving to a tighter formulation of boundary and border relationships. I was reading a lot of things at that time, including Piaget. I'm sure you know in those books, where he conducts interviews with children, asking them what it means for something to be in front versus something else behind.

AK: Just the fact that you're interested in prepositions at all I think is sort of astounding. Even for cognitive neuroscience people that study language, prepositions are marginalized. Language researchers are relatively more interested in nouns or verbs, but very few people are interested in prepositions.

MB: Prepositions are what hold the world together.

AK: Right! I mean, they're incredibly flexible and promiscuous, and they provide the skeletal structure for language and thought in this really fundamental way.

MB: Prepositions and conjunctions—those are the two parts of speech that interest me. I did a series of paintings a couple years ago about conjunctions. A conjunction is a word which actually has no meaning within itself. It has to have partners on both sides, to relate to anything. This “and” this. This “or” that. If, then. All these things are words without weight. They don't exist alone—you don't talk about the word “and”; you don't talk about the word “but.” At the same time, you can't think without using them, and they give all language its interior sense of cohesion.

AK: I think it was very clever of you use prepositions in that way. It's just such a natural way to get away from objects and things. That seems like an important idea for a conceptual artist. Well you don't like that word, but as an artist interested in making a novel contribution to an art of ideas. It was a really very clever insight, and I'm glad that it's still being recognized today.

MB: All of those early works, actually all of my work, I see as a form of self-education. To learn things, you have to look in unexpected places. You can't learn things following the same old ruts in the road. I was always looking for new ways to approach the subject. At that point in my life, I was trying to build a really firm structure for my work, so that anything I did afterward would always have a foundation that I could go back to. But in the beginning, people mostly just looked at my work and shrugged their shoulders.

AK: I'm sure. It's not very different in the sciences, if you study something so abstract, believe me.

MB: Later on, some people began to realize it was not totally arcane. And the reason they woke up is that other artists found that the work was useful to them. Things go in cycles. After the '80s and '90s with neo-expressionism, neo-surrealism, and all that, people were looking for something else, and younger artists were rediscovering these long lost things. Then, someone, like you, comes along from out of the blue. Somebody came to me about 10 years ago. He was an organic chemist who had seen a drawing that I did in the '70s; a combination of adjacent triangles, squares, and pentagons. He got my address, wrote me a letter asking, “Has anyone made a molecule based on one of your drawings?” (laughs) And I said, I don't think so, but why would anyone want to do that?!

AK: (laughs) As if he would be really surprised if they haven't already.

MB: He said, “Because this is the perfect form for a molecular structure and if it's never been synthesized, I would like to be the one who does it!”

AK: I didn't even know such a thing was possible.

MB: Neither did I! You were talking about metric concepts of space, and it's something that fascinated me in the early ‘70s—especially in relation to the pentagon. You can't tile a flat surface with a pentagon because there are always leftover spaces. It's also the shape on which all organic growth is based on. So that immediately made me fall in love with it. I evolved this language of triangles, squares, and pentagons that formed what I called “shape complexes.” And then, 15 or 20 years later, this guy comes along and has his student making molecules out of these shapes. Bochner molecules. (laughs)

AK: That's actually a very good name for a molecule. It has a nice ring to it.

MB: So anyway, you never know where things are going to find resonance. But I guess my question for you is what led you to this? What's your background coming into it?

AK: As far as being interested in space, actually, my dissertation work was more directly about relations between space and time. Ideas in line with some of the things Merleau–Ponty was interested in. About how our thinking about space informs and influences the way that we think about time, especially with respect to language. So, there's all of this language of space that we use to think and talk about time. The future being in front of us, and the past being behind us, that sort of thing. My dissertation work was really about getting people to think about space in a very particular way and seeing if that would influence their temporal reasoning. I think that you're aware of that basic idea because, when I saw your garden (The Kraus Campo) at Carnegie Mellon, I could see that you were playing with it a little bit. Before I puzzled out the text, I was not sure what to think. Once I figured out the strategy, it seemed to really be about relationships between space and time (Figure 5).

Figure 5. 

The Kraus Campo (with Michael Van Valkenburgh, 2005). In the cognitive sciences, there is an abundance of research investigating the links among time, space, and language (Nunez & Cooperrider, 2013). Much of this research suggests that we talk and think about time using spatial representations. Furthermore, many studies suggest that the process of using space to structure temporal thought is embodied or grounded in sensorimotor structure and experience. For example, most languages tend to conceptualize the future as in front, and the past as behind because as ambulatory, front-facing organisms, events in our future tend to involve locations in front of us and those in our past tend to involve locations behind us (Clark, 1973). Cultural conventions like reading direction can also influence temporal thought. For example, a recent study found differences in how readers and writers of left-to-right languages (like English) and right-to-left ones (like Hebrew) make judgments about temporal relations (Fuhrman & Boroditsky, 2010). Despite the abundance of behavioral and linguistic data, there is little neural data supporting the idea that our temporal concepts are grounded in spatial representations (Kranjec & Chatterjee, 2010), although a common area in the parietal cortex may play a role in aspects of temporal and spatial perception (Bueti & Walsh, 2009).

Figure 5. 

The Kraus Campo (with Michael Van Valkenburgh, 2005). In the cognitive sciences, there is an abundance of research investigating the links among time, space, and language (Nunez & Cooperrider, 2013). Much of this research suggests that we talk and think about time using spatial representations. Furthermore, many studies suggest that the process of using space to structure temporal thought is embodied or grounded in sensorimotor structure and experience. For example, most languages tend to conceptualize the future as in front, and the past as behind because as ambulatory, front-facing organisms, events in our future tend to involve locations in front of us and those in our past tend to involve locations behind us (Clark, 1973). Cultural conventions like reading direction can also influence temporal thought. For example, a recent study found differences in how readers and writers of left-to-right languages (like English) and right-to-left ones (like Hebrew) make judgments about temporal relations (Fuhrman & Boroditsky, 2010). Despite the abundance of behavioral and linguistic data, there is little neural data supporting the idea that our temporal concepts are grounded in spatial representations (Kranjec & Chatterjee, 2010), although a common area in the parietal cortex may play a role in aspects of temporal and spatial perception (Bueti & Walsh, 2009).

MB: Yes, and there's a funny story behind it. When Michael Van Valkenburgh, the landscape architect, and I submitted the proposal to the committee at the University, the head of the Engineering Department immediately hated it. He said, “This is absolutely ridiculous. I'm not voting for this. I'm against this whole thing.” (It wasn't going to cost the school a cent because a private donor was paying for it.) I asked him what he found ridiculous. He said, “The text is just a bunch of gibberish. I don't want my students wasting their time on nonsense!” So, somebody who had figured it out said, “Are you sure it's gibberish? Did you try reading it backward?” He said, “I don't read things backward! I'm an engineer!”

AK: (laughs)

MB: So, this other person said, “Well, why don't you try? Just for the heck of it.” So, he starts reading it… “Yeah, yeah, yeah…” he says, “Oh my god…Oh my God…Oh my God! It really means something! This is fantastic!”

AK: The text of the piece is actually a quote from…?

MB: It's (Ludwig) Wittgenstein quoting (Arthur) Eddington on what it might mean if time moved backward. (laughs) Right up his alley. So then he said, “I love this, I love this, we have to have it!” That sealed the deal.

AK: I had a similar experience for a while just being sort of vexed by the text until I got it.

MB: And that's the great thing because suddenly, as a viewer, you are no longer passive, you are writing the text by reading it. And once you've got it, it belongs to you.

Acknowledgments

My special thanks to Mel Bochner for participating in the interview, and for permitting the reproduction of all images included here. I am also particularly grateful to Danielle Kranjec for discovering “Theory of Boundaries” at the National Gallery of Art, and for encouraging the development of this project. Additional thanks to Ashley Galazia for transcription, Ashley Gill for proofreading, and two anonymous reviewers for their comments on an earlier version of the manuscript.

Reprint requests should be sent to Alexander Kranjec, Psychology Department, Duquesne University, 600 Forbes Avenue, 544 College Hall, Pittsburgh, PA 15282, or via e-mail: kranjeca@duq.edu.

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