Sociable robots, jazz music, and divination: Contingency as a cultural resource for negotiating problems of intentionality



In practices that range from mechanical divination in Central Africa to gamelike interactions among jazz students and the development of a jazz-improvising humanoid robot marimba player in the United States, contextually meaningful contingency is widely used as a cultural resource for negotiating problems of intentionality. Whereas anthropologists have been concerned with the use of contingency mostly as a cultural resource for increasing predictability of intentions in conflictual situations, I highlight contexts pervaded by modern normative ideals of creativity in which predictability of intentions constitutes a problem, for which contextually meaningful contingency is used as a solution.

From the administration of poison to fowls in Central African practices of mechanical divination to the development of jazz-improvising computerized algorithms in two major U.S. institutes of technology, contingency has been used as a cultural resource for negotiating problems of intentionality in a number of distinct ethnographic contexts. A closer look at such disparate contexts, however, reveals variations that cannot be easily accounted for within the framework of many of the anthropological studies that have addressed this topic.

Anthropologists studying the relation between intentionality and contingency have tended to conceptualize the former as something that is pervaded by the latter. Those who are influenced by pragmatism and phenomenology (Csordas 1993; Ingold and Hallam 2007; Jackson 1989), for example, have highlighted the open-ended nature of human action in the world and the ways in which our intentions are themselves evolving projects that unfold in time rather than plans that are formulated in advance. They have thus focused on contingency as the very stuff intentionality is made of. Other anthropologists have highlighted intentionality in relation to the vicissitudes of the external world and of other people's intentions (Becker 1997; Bourdieu 1977; Douglas 1994; Keane 1997; Sahlins 1985). Marshall Sahlins, for example, has emphasized the “double contingency” (1985:145) of agents’ subjective interests and of the material intractability of the objective world, which accounts for the functional reevaluation of cultural categories whenever they are enacted in practice by intentional agents. Similarly, Webb Keane has pointed to the hazards in which “even the most controlled representational practices” (1997:xiv) are thoroughly implicated, adding that agents’ intentions are frequently frustrated or reconfigured because of “the vicissitudes” (1997:208) that result from depending on recognition by others and from the material basis of signs, which frequently subverts what actors intend the signs to mean.

Similar considerations have led philosopher Alasdair MacIntyre to suggest a general principle that stipulates the conditions under which individuals would try to minimize or maximize the contingency of their and other agents’ intentions:

It is necessary, if life is to be meaningful, for us to be able to engage in long-term projects, and this requires predictability; it is necessary, if life is to be meaningful, for us to be in possession of ourselves and not merely to be the creations of other people's projects, intentions and desires, and this requires unpredictability. We are thus involved in a world in which we are simultaneously trying to render the rest of society predictable and ourselves unpredictable, to devise generalizations which will capture the behavior of others and to cast our own behavior into forms which will elude the generalizations which others frame. [2007:104]

In this article, I contribute to the ongoing conversation in anthropology over the relation between intentionality and contingency by discussing a cultural context in which overpredictability of intentions constitutes a problem rather than a desired goal, in response to which individuals produce or harness contextually meaningful contingency as a solution.1 In doing so, I draw on fieldwork I conducted in a number of distinct yet related ethnographic sites: a U.S. academic jazz music program and labs in two major institutes of technology in the United States in which jazz-improvising computerized algorithms are developed.2 For reasons that I explore below, the people I worked with are motivated by mounting concerns about their own, as well as other people's, lack of creative intentionality in jazz improvisation as it is defined within a specific ethnotheory of intentionality.

This lack of creative intentionality finds expression in two key ways. First, some of my interlocutors are unable to align private intentions with public actions, that is, to execute the musical ideas they want to execute in the real time of improvisation. Instead, they fall back on “automatic,” predictable, and noneditorial embodied playing habits. Second, some interlocutors are unable to come up with novel musical ideas or intentions to begin with, regardless of their ability to execute them in the course of performance. In response to this dual predicament, my research participants produce or harness various forms of contextually meaningful contingency. They do so by designing jazz-improvising computerized algorithms that produce contingent yet contextually meaningful outcomes and by producing or picking up random sonic input from the surrounding environment to train themselves and others in being intentional in these two dimensions.

I suggest that, analytically, there is a line connecting, on the one hand, some forms of mechanical divination, a practice that has long been studied by anthropologists (Du Bois 1993; Evans-Pritchard 1991; Moore 1957; Park 1963; Wilce 2001; Zeitlyn 2012), and, on the other hand, the jazz-improvising computerized algorithms and the interactional events between jazz students I discuss below: In all of these contexts, contingency is harnessed or produced as a cultural resource for negotiating problems of intentionality.3 For example, the Azande divinatory practice called the “poison oracle,” famously analyzed by E. E. Evans-Pritchard (1991), has been discussed as an “aleatory” mechanism individuals use to find out who has bewitched them or intends to do so (Du Bois 1993:58). The advantage of this mechanism is that “the meanings arrived at are determined by something other than a volitional, human act” (Du Bois 1993:54). This feature allows the poison oracle to function as a reliable or unbiased “method of revealing what is hidden” (Evans-Pritchard 1991:120), namely, the malicious intentions of one's group members, with which this agonistic cultural context is overflowing. Although individuals do not explicitly treat the poison oracle as a randomizer but, rather, assign it mystical properties (Evans-Pritchard 1991:147–151), the administration of poison to fowls does, in fact, amount to the production of a randomizer (Hacking 2006). To ensure that it acts as such, “as soon as the poison is brought back from its forest home it is tested to discover whether some fowls will live and others die under its influence” (Evans-Pritchard 1991:158). A poison that systematically kills all fowls or has no effect on any of them is tantamount to a die that falls on one face time and again: It is not a proper randomizer in that, all things being equal, it is not “governed by or involving equal chances for each of the actual or hypothetical members of a population”:4 its outcomes are known in advance. Here, then, as in the contexts I am concerned with, contingency, understood as “uncertainty of occurrence” (see N. 1), is mobilized as a cultural resource for negotiating problems of intentionality.

However, Evans-Pritchard argued that, in consulting the poison oracle, individuals harness contingency as a cultural resource for reducing the uncertainty generated by group members’ malicious intentions. Similarly, a recent analysis of the use of divination to help “intentional subjects (the clients) deal with uncertainty” argued that, even when divination is, in fact, “redeploying and possibly increasing uncertainty, rather than reducing it … the uncertainty may be tempered by the possibility of doing something to address the topics raised in the divinatory session” (Zeitlyn 2012:537). The same analytic approach has been prevalent in the long anthropological and folkloristic study of performance, in which scholars have argued that individuals might seek to increase or emphasize the existence of contingency but only for the purpose of publicly displaying their competence in taming, reducing, or resolving it in real time (Bauman 1984:129–130; Berliner 1994:374–383; Gioia 1988; Keane 1997; Lord 2003:37–38; Malaby 2002; Rosaldo 1986:134; Schieffelin 1985:721–722).

In contrast, my interlocutors’ world is suffused with modern normative ideals of creativity that emphasize originality, regeneration, and difference (Wilf 2010, 2011), and it is for this reason that they consider the contingency of their own intentions and that of others as a desirable, albeit rare, feature rather than a problem that needs to be immediately resolved. Their context overflows with overpredictable intentions, and, against this backdrop, they deploy various means of producing and harnessing contingency to reduce that predictability. Furthermore, most of the literature I cite above has approached the ability to engage with contingency as that ability is expressed in its mature state, thus neglecting to study in depth its conditions of possibility and cultivation. In contrast, such conditions of possibility are at the forefront of my interlocutors’ practices. Finally, and most importantly, my interlocutors are concerned with the cultivation of this ability in a context in which they lack the opportunities to apprentice with experienced performers in real-time performance situations because of jazz's changing conditions of existence. This fact forces them to come up with alternative ways of generating and immersing themselves in contextually meaningful contingency. Their self-devised forms of training and the challenges these forms respond to are thus radically different from what one typically finds in descriptions of apprenticeship of neophyte improvisers in various ethnographic contexts (Bryant 2005; Lord 2003; Smith 1998).

To be sure, the use of contingency in art is nothing new. Key figures in aesthetic modernism (such as John Cage in music, Stéphane Mallarmé in poetry, and various visual artists within Dada, surrealism, and abstract expressionism, such as Marcel Duchamp) have used chance procedures in their work. However, as one scholar has argued, much of this “aesthetics of chance” was about “the replacement of the desire to do something with the desire to see what will happen” when contingency is integrated into art (Iversen 2010:24). Reviewing the writings and work of these and dozens more artists, Margaret Iversen argues that this aesthetics was about “limiting authorial control” (2010:13), “refusal of authorial control” (2010:16), “bypassing of intention” (2010:21), “authorial abnegation” (2010:21), and “circumventing intentionality” (2010:23).

My interlocutors, by contrast, harness contingency to buttress their ability to become authors. In the cultural order of jazz, being an author means, in part, being able to align one's private intentions with one's public actions—that is, making sure that one's playing is not arbitrarily but intentionally motivated—and ensuring that one's intentions are creative.5 My interlocutors use contingency to train themselves to be authors in this dual sense. Importantly, the practices by which they harness contingency are meant to be temporary; that is, players are at a preliminary stage in cultivating a specific kind of agency that, at some point, is supposed to function independently of such practices.

My purpose in this article, then, is twofold. First, I analyze the conditions of possibility for frustrated modern creative intentionality. Second, I theorize the use of contingency as a cultural resource for cultivating (rather than circumventing) creative intentionality and overcoming this frustration. In doing so, I highlight the culturally specific logic that motivates my interlocutors to engage in practices toward this end, while I bracket the question of whether these practices are actually successful in bringing about their intended outcomes. Answering the question of impact would require a different kind of a study, for which the present one is a prerequisite.

Lack of creative intentionality #1: Inability to align private intentions with public actions

Notions of intentionality are tied to ethnotheories about the self and personhood, which vary across and within cultural contexts and with respect to specific practices and tasks. Modern normative ideals of agency have revolved around the co-constitution of the self and the materiality of semiotic forms (i.e., when its articulation in words or actions is also the process by which the self comes into being) and around the role of the materiality of semiotic forms in the expression of a presumably pre-existing self (i.e., when already fully formed thoughts or ideas are expressed in words or actions; see Wilf 2011). In the first ethnographic site I examine, the crisis of intentionality concerns the latter: the failure to align private intentions with public actions. The site, a U.S. academic jazz program, is part of the growing academization and institutionalized professionalization of jazz training that have culminated in the establishment of hundreds of programs that grant various degrees in jazz performance (Wilf in press a). I begin with this site because the implications of U.S. academic jazz training also inform the activity of the people I worked with in the two sites I describe below, in which jazz-improvising computerized algorithms are developed.

As an improvised form of music, jazz consists of the real-time generation and execution of musical ideas in accordance with factors such as the basic harmonic structure of a specific tune, stylistic conventions, one's own previously played ideas during the solo, and the ongoing contributions of one's band members (Monson 1996). Compared with the performance of a written score in the classical Western music tradition, then, jazz improvisation entails a higher degree of unpredictability. To function well in such a performance situation, players must be able to flawlessly execute their constantly emerging musical ideas with their instruments and respond to the musical cues provided by their band members in the course of performance. Canonical definitions of “creative thinking” in jazz focus precisely on this skill and the conditions that necessitate it (Berliner 1994:216). To begin from those conditions,

The sense of exhilaration that characterizes the artist's experiences … is heightened for jazz musicians as storytellers by the activity's physical, intellectual, and emotional exertion and by the intensity of struggling with creative processes under the pressure of a steady beat. From the outset of each performance, improvisers enter an artificial world of time in which reactions to the unfolding events of their tales must be immediate. [Berliner 1994:220, emphasis added]

Paul Berliner describes the skill needed to engage in the creative process under such conditions by noting that mature jazz improvisers “attain a perfect unity of conception with the body. The artist becomes intensely focused on thoughts in the language of jazz, and as they come—one upon the other—they are articulated as instantly as conceived. No lead time separates conception from expression, and the gap between intention and realization disappears” (1994:217; emphasis added).6

Charlie, a teacher in the jazz program in which I conducted fieldwork, argued that being able to close the gap between “intention and realization” requires players to master a delicately achieved indexicality between the sounds they hear and how the production of those sounds with their instruments “feels.” He also described a technique for developing this competence:

When you're starting playing things in every key every day you start recognizing the difference between the key of A and the key of C and the key of B-flat on the instrument. You feel it. It's a strange thing. I can't explain it but you start developing a relative pitch from your fingers to your ears, you know. So if I hear somebody playing in a certain key I'll relate [it] to my instrument—whatever it is—tenor or alto [saxophone], and say: “that key feels like that note on my horn.” You know what I mean? So I'll relate [it] to maybe the tenor and say: “yeah, that sounds like it's in the key of A” because I can feel … actually the fingering in my fingers of the horn. It's really a strange thing but it does work. But only if you do it every day. If you only play like in three keys, C, F, and B-flat all the time, you won't get it. But if you do all the keys … you kind of feel it in your hands … You hear something on the radio and it's like: “oh, yeah, that's in the key of E” … I can actually feel that note. The color, yeah, you get the color right. That's what that's like. But it takes time, don't get me wrong.

As I have argued elsewhere (Wilf 2013b), the production of each note on an instrument involves the combination of numerous bodily actions and sensations, such as pressing this finger, breathing this amount of air, tightening the lips to this degree, and so on. Each note produced on an instrument, therefore, entails a distinct configuration of bodily actions and sensations, what I would call its “bodily signature.” Charlie describes one technique for cultivating the needed indexicality between auditory representations and how it feels to execute them with one's instrument: repeatedly playing a pattern in each of the 12 keys without the mediation of a written score (see Berliner 1994:115–116). After practicing this way for a long time, the player begins to form an association between each of the notes heard as produced with his or her instrument and the note's bodily signature. When Charlie refers to “the color, yeah, you get the color right,” he is pointing to this bodily signature. Feeling it “in my fingers,” “in your hands,” is a way of describing this subtle conditioning. Although the skill of aligning private intentions with public actions is not a sufficient condition for creative improvisation (because creative intentions are also required—a point I discuss in the second part of this article), it is a necessary condition. If players do not master this skill, their ability to play editorially—that is, to execute the ideas they want to execute on the spur of the moment and in a way that would make sense given the unfolding situation—is diminished.

Charlie's words make it clear that, to cultivate this skill, players need to condition their playing bodies through intensive listening and playing in real-time performance situations rather than through the mediation of a written score. Indeed, the educators I worked with often warned their students that approaching their instruments solely via the mediation of printed artifacts—books of patterns of improvisation that have proliferated as a result of the growing academization of jazz training—can jeopardize their improvisational skills, especially their creative intentionality. However, because of specific transformations in the conditions for the existence of jazz, it has become more difficult for students to train themselves in live performance situations. Specifically, the dwindling demand for jazz since the 1950s has resulted in the gradual disappearance of performance venues in which neophyte musicians can inform their competence with listening and can apprentice with experienced practitioners in real-time performance situations. Such apprenticeship has gradually given way to abstract, formalized, and rationalized education in the hundreds of academic programs that have come to function as the pillars of the jazz world over the last few decades, in lieu of the commercial jazz scenes of the past (Wilf 2010:572, 2012:35–36, in press a; see also Chevigny 2005:51–52; Rosenthal 1992:170–173). The educators I worked with argued time and again that as a result of these institutional transformations—the shift of jazz training from the clubs to the classroom, where standardized, printed pedagogical aids have become a key mode of acquiring knowledge—students fail to cultivate the embodied indexicality between auditory representations and how it feels to execute them with their instruments. Rather, they cultivate embodied indexicality between the sight of a written note and how it feels to execute it. Students’ heavy reliance on printed artifacts means that they do not necessarily hear what they play before they play it. In the course of performance, when they ought to execute auditory representations with their instruments, they fall back on standardized and predictable embodied patterns of improvisation they learned from method books. In other words, they are unable to harness embodied patterns to editorial playing. Thus, during a workshop, a guest clinician scolded the students who had just finished playing by saying that “they are not thinking of things to play. They are just hoping that their fingers will bring them to a nice place.” Another teacher told his students, “What [do] your ears really control? Not much! … your fingers are playing the eighth notes.” Teachers often described their students as mere “button pushers” and “pattern players,” using tropes that connote the mechanical valves of an engine to describe this lack of intentionality (Wilf 2010:567–568).

If some of Keane's interlocutors viewed “the physical world as overflowing with evidence of purposes … [privileging] the semiotics of intentional meanings over the ‘natural’ meanings of material happenstance and [assuming] the worst” (Keane 1997:32–33)—much like the individuals studied by Evans-Pritchard (1991:21–23), who attribute to witchcraft what many modern subjects would attribute to coincidence—the educators I worked with viewed the classroom as overflowing with evidence of “natural meaning” (Grice 1991) or lack of purposes, in the sense that they understood students’ playing as the result of embodied habits that are not guided by editorial considerations but are “automatic” and nonintentional. In all of these contexts, agents assume the worst, but, in the contexts discussed by Keane and Evans-Pritchard, danger emanates from the uncertainty generated by the malicious intentions of one's group members, whereas, in the jazz school, it results from the overpredictable and noneditorial playing of one's group members.

The inability to play editorially, to align private intentions with public actions and, thus, to be responsible for one's playing, is productive of problems of evidence and verification. In response, the turn to and production of publicly available contingent sonic input by the students I worked with makes sense.

Problems of evidence and verification

A good starting point for unpacking these problems is the productive interrogation conducted in recent years by linguistic anthropologists of whether and to what degree one can have access to other people's private intentions and thoughts and what constitutes evidence of such intentions and thoughts (Duranti 1993; Hill and Irvine 1993; Keane 2002; Robbins and Rumsey 2008). These studies have stressed that one's capacity to know what other people have in mind depends in large part on culturally specific semiotic ideologies and metapragmatic claims about how publicly available semiotic forms such as the words someone utters and his or her bodily gestures are related to his or her private states. This emphasis has been productive in clarifying not only the processuality of “reading other minds” as a semiotically mediated achievement but also the conditions that might frustrate it.

Anthropologists have argued that the act of reading other minds can be frustrated because a person might decide to deliberately hide his or her intentions from others or to lie by intentionally speaking or acting in ways that do not reflect his or her genuine feelings or thoughts. One can also commit an error: In moments of absent-mindedness, a person might say something that does not align with what he or she intended to say (Keane 2002). These circumstances might frustrate people's attempts to accurately impute intentions to one another. In the literature on a number of Pacific societies where scholars have recorded a widespread claim “that it is impossible or at least extremely difficult to know what other people think or feel” (Robbins and Rumsey 2008:407–408), anthropologists have stressed that the difficulty is not to impute intentions to another but, rather, that doing so would infringe on that person's right to be the one who verbalizes his or her thoughts (Schieffelin 2008; Stasch 2008). In a commentary on a series of such studies, Keane has concluded that what is at issue is not so much “whether thoughts can be put in words but who can do it”; not “what is possible but what are the consequences of losing control over these possibilities” (2008:478).

The possibility that the opacity of another person's mind might result from that person's actual inability to align private intentions with public actions has not received as much attention as these other factors. And yet the ability to align private states with public actions is precisely what the students I worked with lack because they have had little training that would have allowed them to acquire it. Intentional hiding, deception, momentary negligence and error, or the imperative to avoid imputing intentions to others do not factor in here. Students often find it impossible to execute their musical ideas in the real time of improvisation and, instead, fall back on standardized embodied playing habits over which they have very little editorial control.

This context is rife with problems of evidence and verification of intentionality. If Mary cannot assume that John has the ability to align private intentions with public actions even when he wishes to do so, how can John prove to Mary that he can, in fact, produce nonnatural meaning, that is, be creatively intentional in the sense that he can shape his actions in accordance with his intentions? To be convinced of John's ability to be intentional, Mary must have access to John's private intentions. However, if Mary doubts John's ability to convey his private intentions because he might lack the very ability to do so, how can Mary even test John's ability to be intentional in the context of this specific ethnotheory of intentionality?

In the next section, I discuss the strategies devised by the students I worked with to negotiate this predicament. These strategies function as public forms of verification of one's ability to align private intentions with public actions and as a training ground to cultivate this ability.

Turning to publicly available, random sonic proxies for private intentions

One cold February night, I was walking down a street in Cambridge, Massachusetts, with Sarah, a vibraphone student in her midtwenties. As we were approaching Inman Square, a person sitting in a parked car next to us suddenly honked twice. Immediately, in complete synchrony with one another, Sarah and I whistled in an attempt to imitate the exact pitch of the car horn. However, each of us whistled a different pitch. I did not give the incident a second thought and intended to continue on my way, but Sarah abruptly stood still. She turned to me and asked, “What did you whistle?” I whistled again, repeating the exact pitch I had whistled a second before. Sarah then repeated her whistle. Mine was a few steps below hers. Sarah looked at me for a second and then told me, “Go and ask them to honk again.” I looked at the car. The engine was running and I could see three people sitting inside. I walked to the car and knocked on the driver's window. The two men in the front seats and the woman in the back seat looked at me. The driver had a cell phone in his hand and was apparently calling someone to come down to the car. The window rolled down. “Can you honk again, please?” I asked, hesitantly. “You see,” I continued, trying to figure out what to say, “we had a bet.” I did not explain any further. As I said these words I pointed with my head toward Sarah, who stood watching me. The car's passengers looked at me with suspicion. After a minute of silence, the driver, almost hastily, honked the horn again and quickly rolled up the window. “Thanks,” I managed to say before it was completely sealed again. I turned around to face Sarah, who was standing motionless, an almost unperceivable smile on her lips. She said, “Let's go?”

A similar interaction took place one Friday night as I met with Pierre, a guitar student, for our weekly playing session in the guitar department of the jazz program. Sarah, the vibraphone student, and Carla, a singer, were present too. We played together a couple of tunes, I on trumpet, Pierre on guitar, Sarah on percussion, and Carla singing. After an hour, we decided to take a break. I went to a corner and played random lines for a few seconds. One note I played at the end of a phrase was cracked. I stopped and tried a couple of times to play it properly. Hearing me, Pierre took his guitar and tried to play the exact same pitch. He missed my note by two whole steps above. He then hesitantly descended in a glissando until he found the correct pitch. I could not keep from laughing, saying, “Man, that was funny!” I then imitated the glissando with my voice. As I was about to continue with my playing, Carla stood up and interjected, “Oh yeah? Let's see you do better than him!” “What do you mean?” I asked. Carla went to Pierre and pulled him toward me. “Come, you stand here,” she said, directing him with her hands. Pierre was laughing. “And you,” she said to me, turning me around with her hands, “you stand with your back to him.” Pierre and I were now standing back to back. “Pierre, play some notes. I don't want him to remember what you [just] played,” Carla said. Pierre was confused and asked, “What?” Carla then used her hand to move Pierre's hand over the guitar's neck, producing a cacophony of sounds. She thus hoped to disorient me so that I would not remember what Pierre had played when he had tried to match my cracked note. “Now play one note,” she told Pierre, “and you,” she turned to me, “you need to nail it on the trumpet. Let's see you do better than him.” There was silence. Sarah looked at us attentively from her seat. I stared forward, trying to focus, preparing myself. Do I know my trumpet that well? My thoughts were abruptly cut short. Pierre plucked a string, and a note sounded in the air. I pondered for a second, trying to figure out where to place it on the trumpet, what note on my trumpet would match it. I played a D, then immediately, with urgency, like the reflex reaction when one pulls one's hand away from fire, I changed it a whole step below to a C, only to realize that Pierre had actually played a C-sharp, which I then quickly played. “It doesn't count, it doesn't count,” Carla exclaimed, waving her hands in dismissal, and Sarah, shaking her head, muttered, “No, no, no.”

I argue that these gamelike interactions constitute a strategy students devised to negotiate the problems of evidence and verification of intentionality I discussed above, in addition to other concerns.7 When students pick up random disembodied sonic stimuli from the environment or provide one another with such stimuli, they negotiate these problems by having these stimuli play the role of private intentions, now made publicly available, thus allowing everyone present to ascertain whether they can indeed align private intentions with public actions. In doing so, they also provide one another with the ground on which to train themselves in being intentional in this specific sense. Indeed, that these interactions are directly related to one of the key pedagogical concerns voiced by teachers, namely, students’ inability to align private intentions with public actions, became evident in one of the few courses in the jazz program that were dedicated to the cultivation of this skill. The teacher of this course would often play a note or a chord on the piano, and the students would have to match his notes with their instruments. Significantly, he would not allow them to “slide” toward the right note when they missed it, as I did in the interaction I describe above. In an interview I conducted with this teacher, he explained,

To me they are just digging around. I want them to actually hear it first. If they do that [search the note on their instruments] then they don't trust their ears. I want them to trust their ears … I think it develops your inner ear … Like if you get to know what's the sound of a certain chord progression, if you hear that progression in your ear, then you can know where to find it [on the instrument].

If teachers often portray the classroom as a world overflowing with evidence of lack of purposes, the students I worked with, by weaving this gamelike strategy into their everyday activities, transform their world into one overflowing with evidence of purposes. Now any external sonic stimulus can potentially function as a proxy for a private intention. It can be approached as an intention that students can publicly demonstrate they are able to execute whether by singing, whistling, or with their instruments. Indeed, at different times, I witnessed students taking up the ringing of a cell phone, the sound of an airplane passing overhead, and an ambulance siren as proxies for their own private intentions and then replicating these sonic stimuli with their own instruments, for assessment by the people around them. Their world, then, has become populated with sonic stimuli that function as “intentions without intentions.”

By calling these stimuli “intentions without intentions,” I am appropriating John Du Bois's (1993) analysis of mechanical divination, which he titled “meaning without intention.” Du Bois examined rituals of divination that are based on the use of aleatory mechanisms to challenge the view that intention is a necessary criterion of meaningful language use, a view advanced in the context of speech act theory. At one point in his discussion, Du Bois quotes John Searle's influential discussion of speech acts:

When I take a noise or a mark on a piece of paper to be an instance of linguistic communication, as a message, one of the things I must assume is that the noise or mark was produced by a being or beings more or less like myself and produced with certain kinds of intentions. If I regard the noise or mark as a natural phenomenon like the wind in the trees or a stain on the paper, I exclude it from the class of linguistic communication, even though the noise or mark may be indistinguishable from spoken or written words. [Searle 1969:16–17]

In contrast to Searle's approach, Du Bois argues, with reference to mechanical divination, that the “pragmatic backing—backing of a sort usually thought to require an intending speech actor—here derives from a semiotic mechanism which is apersonal, mechanical, and aleatory” (1993:58). In other words, here is a case of “meaning without intention” or a speech act not produced as a result of intentional behavior.8 Paraphrasing Du Bois, then, I suggest that, in the case of the jazz students, “noise” or disembodied and random sonic stimuli have come to function as proxies for private intentions. They are “intentions without intentions.”

Indeed, the sonic stimuli that serve as proxies for students’ intentions are random. In the first interaction above, the stimulus is a car horn that Sarah and I happened to hear. In the second interaction, it is a note randomly produced by Pierre. Note that Carla asks Pierre to “play some notes” before producing the one I need to replicate with my trumpet. When Pierre fails to understand her, Carla physically moves Pierre's hand up and down the guitar's neck, producing a cacophony of sounds. The randomization of the sonic stimulus is meant to ensure that this stimulus will not be causally tied to any recently played note. In other words, its purpose is to increase the chances that my replication of the note produced by Pierre will be cut off from the conditions of possibility for natural meaning and that it will, instead, be the result of editorial and intentional playing, or nonnatural meaning (Grice 1991).

The usefulness of contingency as a cultural resource for cultivating creative intentionality explains why many of the communicative events in which my interlocutors engaged took the form of gamelike interactions, for “games … are marked by the legitimacy of their indeterminacy; that is, their outcomes are supposed to be contingent” (Malaby 2009:214). However, whereas Thomas Malaby argues that “showing how [games] contain the same kinds of unpredictabilities and constraints that saturate our experience elsewhere … allows us to see how games may be related to a particular mode of experience, a dispositional stance toward the indeterminate” (2009:208), my interlocutors orchestrate gamelike interactions precisely because these interactions are saturated with indeterminacy, which their ordinary experience as jazz musicians lacks. Their purpose, then, is to cultivate “a dispositional stance toward the indeterminate,” with which they have no experience outside of such games.

In the two interactions I describe above, then, individuals harness contingency or “uncertainty of occurrence” to help one another cultivate their ability to align private intentions with public actions, which is necessary for creative jazz improvisation, and thus to reduce the predictability of intentions grounded in standardized, embodied playing habits that are not informed by editorial considerations. In the next two sections, I discuss two ethnographic sites in which individuals develop computerized algorithms that produce contextually meaningful, contingent input to train people in being creatively intentional in the second dimension I have enumerated: the capacity to come up with creative ideas or intentions regardless of one's ability to execute them with one's instrument.

Lack of creative intentionality #2: Having no creative intentions to begin with

In introducing these two ethnographic sites and their cultural specificity, I turn to the book Alone Together (Turkle 2011), which has recently received a lot of media coverage. In it, author Sherry Turkle delineates what she calls the “robotic moment,” by which she means the contemporary advent of sociable robots and the broader societal shifts that have structured it. Turkle argues that a shift has occurred in people's expectations of computational technologies relative to their expectations of the people around them. Three decades ago, Turkle's informants told her that computational technologies would never be able, and should never be allowed, to perform certain decidedly human tasks, such as caring, empathizing, and feeling. Today, this “romantic reaction” has been replaced by “a new pragmatism” that puts a premium on performance. Although they are aware that social robots merely perform emotions, care, and empathy, an increasing number of people—both adults and children—are ready to make do with such a performance against the backdrop of their dwindling demands on and diminishing expectations of the people in their lives. In her conversations with informants, sociable robots such as My Real Baby and AIBO become “evocative robots—they give people a way to talk about their disappointments with the people around them—parents and babysitters and nursing home attendants—and imagine being served more effectively by robots” (Turkle 2011:68). Turkle's informants argue that people are “risky” while robots are “safe” (2011:51). People are unpredictable, they have their own desires and agendas and are prone to disappoint us, whereas “programming means that robots can be trusted” (Turkle 2011:71). For Turkle, this turn to sociable robots instead of relationships with people is bound to jeopardize people's ability to become fully developed human beings:

Dependence on a robot presents itself as risk free. But when one becomes accustomed to “companionship” without demands, life with people may seem overwhelming. Dependence on a person is risky—it makes us subject to rejection—but it also opens us to deeply knowing another. Robotic companionship may seem a sweet deal, but it consigns us to a closed world—the lovable as safe and made to measure. Roboticists insist that the artificial can be made unpredictable so that relating to robots will never feel rote or mechanical. Robots, they say, will be surprising, helpful, and meaningful in their own right. Yet, in my interviews, fantasies about robot companionship do not dwell on robots full of delightful surprises. Rather, they return, again and again, to how robots might … be made to order, a safe haven in an unsafe world. [Turkle 2011:66; see also Suchman 2007]

Turkle's argument is structured around the same idea that has structured many of the approaches to intentionality and contingency, both within and outside anthropology, that I discuss in my introductory section. According to this idea, a large share of the contingency in our lives, which we naturally want to reduce, results from the fact that the people who surround us are endowed with their own unpredictable agendas and desires that often conflict with ours.

However, in fieldwork I conducted in labs at two major U.S. institutes of technology, I discovered very a different form of disappointment with people and a very different use of computerized algorithms and sociable robots in response to this disappointment. The computer scientists I worked with, who are also semiprofessional jazz musicians, are developing computerized algorithms that can improvise jazz in response to the real-time improvisation of a human player. In one lab, the music generated by the algorithms is played by a humanoid robot marimba player. In the other lab, the music generated by the algorithms is played by a digital sound generator. Both are interactive systems, that is, “sociable” in that they produce music in response to the music produced by the human musicians who interact with the systems in real time.9 Although in interviews I conducted with these computer scientists, they made clear that their efforts to develop technologies that can improvise were the result of their disappointment with their fellow musicians, their disappointment turned out to be very different from the disappointment discussed by Turkle. Significantly, they were not disappointed because their fellow musicians were unpredictable and risky. On the contrary, they were concerned that their fellow musicians were too predictable and not risky enough.10 Similar to the criticism instructors directed at the jazz students, my interlocutors in the labs highlighted their discontent with the music played by the majority of jazz musicians in terms of its lack of variety, open-endedness, and creative intentionality. In response, they developed technologies that can provide them with the musical variety their fellow musicians lack. Here too, then, is a context in which people seek to reduce the predictability of intentions by mechanical means against the backdrop of the predictable intentions of the people who surround them. However, if the students I discussed above devised strategies to cultivate their creative intentionality in the sense of enhancing their ability to align private intentions with public actions, the computer scientists I worked with devised strategies to cultivate creative intentionality in the sense of enhancing players’ ability to come up with creative ideas or intentions to begin with.

When I first met James, the director of the lab in which a humanoid jazz-improvising robot was being developed, I explained my interest in studying his lab by describing my previous research on the rationalization of jazz training in U.S. academic jazz education. I told him that his attempt to “train” Syrus, the humanoid robot, to play jazz might be conceptualized as an extension of this rationalization. Yet James immediately made clear that he had a very different interpretation of what he was trying to do in relation to academic jazz education (Wilf in press b). As I was describing my previous research, James interrupted me: “They all sound the same.” “Who?” I asked. “The students! They all sound the same. Like machines!” He laughed. “And all the musicians who come out of the schools, and like 99 percent of the jazz musicians today—they all sound the same. You know what they say: jazz may not be dead yet but it sure smells funny.” He continued,

This is why I built Syrus. Because I wanted to be inspired. I wasn't inspired anymore by—everything that can be written had already been written. Everything that can be played had already been played. I felt that I understood all the genres I was familiar with, like jazz—there was nothing that really caught my interest, a new sound, new ideas. I wanted to develop a device or a tool that would generate new musical ideas that I could not come up with by myself, nor could other people.

The same discontent emerged in interviews I conducted with David, a computer scientist who has developed another jazz-improvising computerized technology at a different institute. David said,

I prefer playing with it [the system] to playing with most people because I get a bigger kick out of how it responds to what I play than out of what people do to what I play when we trade fours [when people musically interact with one another by trading four-bar phrases]. And I get much better ideas listening to it formulating a response than I do by listening to most people because most people play licks [phrases] that they know instead of making something up. It's [jazz] supposed to be about making something up. You would go to a jam session and there's often no [musical] conversation [between players]. Everyone is just playing the licks they learned. You'd get a trumpet player who has OD'ed on Clifford Brown [a legendary trumpet player who passed away in 1956] and this is all he plays. So I get more inspiration from playing with my system than with other people.

Note that both James's and David's disappointment in their fellow musicians is related to their perception that these players’ musical ideas have become predictable and that entering into meaningful musical interaction with them has become impossible. Their discontent does not emanate from the fact that these musicians are too risky. On the contrary, it emanates from the fact that they are not risky enough.

James's and David's responses to their disappointment was to develop computerized interactive systems that can provide them with contextually meaningful, contingent input that is, indeed, risky and less predictable.

Engineering contextually meaningful, creative intentions

One of the principles guiding James in his work on Syrus has been, he told me, to build a robot that would “listen like a human and play like a machine.” Accordingly, his research team developed two types of algorithms: perceptual and generative. Perceptual algorithms enable Syrus to “listen” to the music produced by the human musicians interacting with it through a digital interface and to detect in this music a number of meaningful dimensions.11 These perceptual algorithms, then, are in charge of the “listening like a human” part. More important for my discussion here is the second type of algorithms, the generative. The role of the generative, or improvising, algorithms is to generate the music that Syrus will eventually play in response to the meaningful dimensions it detects in the human players’ music. In a brainstorming session with his research team, James said,

For the improvising, we want to do something that humans will not do. In this case, it's to combine the styles of different jazz masters in a very algorithmic way … which humans will not do, at least not in this way. But then what we also did is genetic algorithms, which is also something that humans don't do—they don't calculate fifty generations of mutations and crossovers in less than a millisecond. We also tried fractals a little bit but we didn't push it enough. Why fractals? We are looking for something that has some promise in creating patterns that are interesting … But I need you to think: what other interesting things can you think of that will inspire us?12

Note that James attributes the added value of his system to the fact that it generates musical ideas that humans could never generate—this is the “playing like a machine” part. Different kinds of algorithms—mainly Markov models (although, as James notes, the team also experimented with genetic algorithms and fractal-based algorithms)—generate music using complicated calculations that incorporate both stochastic and deterministic (nonlinear) processes into their logic.13 Contextually meaningful contingency is a key part of their logic, what allows them to introduce the contingency that human playing presently lacks, according to James. By contextually meaningful, I mean that the contingency generated by the algorithms and played by Syrus is not meaningless. Rather, the music Syrus produces makes sense because it is generated in the context of specific tunes and their harmonic progressions as well as in response to the musical ideas of the people playing with Syrus. Although the algorithms take this context into account, there is no way to know in advance what they will instruct Syrus to play because they are based on chance decisions weighted by functions of likelihood. In conversations I had with him, James emphasized that the purpose of developing Syrus is to inspire humans in what he perceives to be a field that lacks inspiration. When I asked him how he would define inspiration, he answered that “it is to come up with an idea that you didn't previously have, in real time, an idea that results from and is based on the robot's input, the computer's input, the algorithm's. To think of the music differently, to think differently of a given tune, something that will make you respond differently in real time.” James's goal, then, is to develop a system that will generate new creative ideas that will inspire people to modify their own repertoire of hitherto standardized intentions.

The system developed by David is based exclusively on genetic algorithms. The system takes into consideration the input provided in real time by David when he trades four-bar musical phrases with it as well as the harmonic context of the tune on which David and the system improvise together. Significantly, much like James, David highlighted the decidedly nonhuman calculative capacities of his system that allow it to generate the interesting ideas that the humans he plays with fail to generate:

The things that [the system] does to develop what it hears me playing have nothing to do with the things I do to develop what it plays that I hear. I mean, if the dice came out that way, it might take a four-bar phrase that I played and play a retrograded inversion of the entire four bars and hit all the [harmonic] changes for the next four bars and there's no human alive who can do that. There's no way.

Here, again, the rationale for turning to computerized technologies becomes evident: These technologies can transcend the impasse in which humans have found themselves. Key here too are these technologies’ higher calculative capacities and, in this case, emergent outcomes—the “dice” David mentioned—which allow them to generate contextually meaningful variety and, thus, to train players in the generation of potentially more creative intentions than those they presently have.

The various ways the jazz students and the computer scientists I worked with harness contingency to train their creative intentionality mirror some of the ways that mature jazz players encounter and produce contingency in real-time improvisation. First, jazz improvisation is replete with chance decisions and mistakes that mature players integrate into their subsequent decisions; indeed, knowing how to do so has been a key normative ideal in jazz improvisation from the outset (Berliner 1994:374–383; Gioia 1988; Monson 1996:156–170). This aspect is addressed by the form of training the students practice. Yet mature players also intentionally introduce and generate contingency through practices of ironic self-reference, recursion, and “doubleness.” The aesthetic sensibilities expressed in repetitive and imitative musical structures such as riffs and call-and-response (Snead 1981), as well as in the ironic replication and quotation of previous musical structures and other players’ solos (Gates 1988; Monson 1994), have long informed ideals of creativity in jazz. This aspect is mirrored by the self-referential and recursive nature of some of the deterministic nonlinear algorithms the computer scientists use to generate unexpected outcomes—precisely the “retrograded inversion” of a musical phrase that David's system is capable of generating in response to his playing.14

Conclusion: The limits and scope of contingency as a cultural resource for cultivating creative intentionality

The ethnographic material I have presented in this article—from interactional games among jazz students to the development of jazz-improvising computerized algorithms—suggests that contingency or “uncertainty of occurrence” need not always be something that individuals strive to minimize when attempting to implement their intentions in the world. Nor is it always the taken-for-granted stuff of which intentionality is made. Rather, in the context of specific institutional transformations and ethnotheories of intentionality and agency, individuals might understand their world to be problematic precisely because their intentions and their group members’ intentions are not contingent enough. To negotiate this predicament, they might turn to or produce publicly available forms of contextually meaningful contingency in an attempt to cultivate their desired form of intentionality.

At the same time, I do not argue that the culturally specific use and production of contingency in the three related contexts I have examined always achieve their intended goals. Indeed, during my fieldwork in the two labs, I occasionally witnessed the limited usefulness of computer-generated contingency when it exceeded individuals’ capacity to make sense of it. Consider Syrus, the humanoid marimba robot player that is animated by algorithms designed to produce complicated musical responses to the input it receives from the musicians playing with it. At the beginning of my fieldwork, Dan, one of the Ph.D. students in charge of Syrus, demonstrated Syrus's different features to a number of students and visitors to the lab. At one point, Dan put Syrus in a turn-taking mode and then played a very short phrase on the electric keyboard that is connected to the computer that animates the robot. After a few seconds, in response to this phrase, Syrus's four arms moved rapidly across the marimba and played a very long and convoluted phrase. After it finished playing, we all stood in silence. Rick, one of the students, asked Dan in amazement, “That was in response to what you did?” Everybody then laughed. Dan answered, “Yeah, sometimes it's really out there.” Rick continued, “The reason I ask is that, to me, I can't see the relation to what you played.” In a later conversation I had with him, Rick explained his amazement:

I think that because it plays like a machine the human brain is sort of not wired to completely understand what he's doing because of the algorithms that he uses. Sometimes he plays phrases that a human would never play. Which you can consider inspiring. But to me … I hear a lot of haphazard phrases that don't seem to have any sort of intrinsic melody or pattern and I don't think it's a shortcoming of Syrus. I think it's doing something so advanced due to the algorithm that it's completely disregarding the limitations that humans play with and because of that I think that as a listener I am able to connect less with Syrus because, you know, years of listening to music which is based completely on human limitations sort of accustom your mind to expect these things, and your human expectations, what you would describe as pleasant music is completely based on human limitations … So I think that if you bring down the level of Syrus and say, “you know what, I'll take all that information but I'm really going to limit how I analyze it and what I do with it”—not limit it in a bad way but limit it in a more human way, that might sort of make things more interesting.

Rick describes the implications of excessive contingency that verges on meaninglessness, at least for the humans who need to grapple with it. Syrus's musical responses are sometimes so computationally advanced in terms of the contingency that structures them that the players who are supposed to be inspired by it to develop their own creative intentions are baffled, instead. At these moments, Syrus's response becomes meaningless cacophony. Rick suggests that Syrus needs to be programmed to be more predictable and contextually meaningful so that the humans interacting with it can benefit from its responses (see Wilf 2013a for a different critique of Syrus's purported abilities). At stake, then, is finding the sweet spot between uninspiring repetition and incomprehensible contingency.15

The limits and potentialities of the use of contingency as a cultural resource for negotiating problems of intentionality notwithstanding, my interlocutors developed the different strategies I have explored in this article in response to the disappearance from U.S. cities of real-time performance venues where they can apprentice with experienced jazz performers. At stake is an improvisation-based form of expressive culture originally developed within African American communities and today practiced by an increasing number of white middle-class individuals in educational institutions heavily predicated on standardized, abstract, and rationalized curricula. Their response, then, points to a host of concerns that have long stood at the center of anthropological and sociological research, namely, the shifting conditions of possibility for cultural reproduction, which involve educational infrastructures, the politics of race and class, the rationalization of life-forms, and the availability of new technologies of mediation of sociality. Rather than a negligible aspect of social life, then, the use of contingency as a cultural resource for negotiating problems of intentionality—whether in mechanical divination in Central Africa or in the production of jazz-improvising computerized algorithms in the United States—is overdetermined by a host of social factors. Its full theoretical importance can only be unpacked if we tease out its cultural specificity, especially in terms of its relation to the ethnotheories of intentionality that inform the specific fields of practice within which it is a salient feature.


 I am grateful to Angelique Haugerud and anonymous AE reviewers for their insightful suggestions that have greatly improved this article. I thank E. Summerson Carr, who served as a discussant when I presented some of the material that appears in this article at the Michicagoan conference in May 2009 at the University of Michigan in Ann Arbor, as well as Susan Gal, Webb Keane, and Michael Silverstein, who provided helpful comments during the same event. This research was supported by a University of Chicago Century Fellowship, a Dan David Prize, the Josephine de Kármán Fellowship, a Mellon Foundation Dissertation Year Fellowship, a Marie Curie Career Integration Grant from the European Research Council, and a Faculty Matching Grant from the Hebrew University. Finally, this article would not have been possible without the generosity of my interlocutors in the fields of U.S. academic jazz education and algorithmic music composition.

  1. 1

    By contingency, I mean “uncertainty of occurrence of incidence” or “being open to the play of chance, or of free will” (Oxford English Dictionary, 2nd ed., s.v. “contingency”). Contingency does not necessarily mean complete unpredictability because it is possible to estimate the chance of occurrence of some contingent events on the basis of various considerations. Crucial here, then, is also the notion of “chance,” or “the possibility or probability of anything happening: as distinct from a certainty” (Oxford English Dictionary, 2nd ed., s.v. “chance”). As will become clear in this article, although jazz improvisation—my main ethnographic form of performance—is contingent, that is, “open to the play of chance, or of free will,” it is not completely unpredictable because it is constrained by various factors such as the harmonic structure of a tune, stylistic features, and the real-time contributions of one's group members. (The fact that the contingent input, which my interlocutors generate in different ways, is meaningfully related to these constraints is precisely what makes this input “contextually meaningful.”) Indeed, jazz improvisation is tantamount to “the regulated improvisation” (Bourdieu 1977:79) produced by one's habitus, or one's propensity for or likelihood of acting in a certain way because of specific patterns of socialization. The purpose of the various strategies I explore in this article is precisely to open improvisation “to the play of chance, or of free will” that would allow for innovation within specific constraints. They are not meant to turn improvisation into a completely unpredictable stream of notes. See also N. 5 and this article's conclusion.

  2. 2

    I conducted fieldwork in the school—Berklee College of Music in Boston, Massachusetts—from July 2006 to June 2007 and in the two labs from August through October 2011 (with preliminary fieldwork in May 2011). My ethnographic fieldwork in the two labs was part of a broader, multisited research project on computer-mediated, algorithmic forms of creative agency and sociality, which began in March 2011. To maintain the anonymity of my interlocutors, I have used pseudonyms throughout the article and have abstained from naming the two institutes.

  3. 3

    For an anthropological study of the use of uncertainty or contingency as a resource on an institutional level, that is, unrelated to problems of intentionality, see Samimian-Darash 2013.

  4. 4

    See Oxford English Dictionary, 2nd ed., s.v. “random.”

  5. 5

    Note that one can decide to give up control over one's public actions, for example, by embracing the “aesthetic of chance,” as some modernist artists have done (Iversen 2010:24). This too, of course, is an example of aligning private intentions with public actions, except that the intention in this case is explicitly to relinquish control over the unfolding of one's actions. My interlocutors are not concerned with this specific strand of high-modernist creativity. Indeed, in a sense, they have never had much control over their public actions that they could give up.

  6. 6

    Indeed, mature players often achieve such a high degree of instantaneity between an intention and its execution that “they feel at times like recipients and conveyers, rather than inventors, of ideas” (Berliner 1994:218) and are surprised by their own playing. In these moments, their experience is one of the co-constitution of the self and the materiality of semiotic forms, rather than of the role of the materiality of semiotic forms in the expression of a presumably preexisting self (Wilf 2011).

  7. 7

    Elsewhere I have discussed these interactions in terms of practices of sensory self-fashioning in response to processes of modernization and standardization (Wilf 2013b).

  8. 8

    In a critique of Du Bois, James Wilce (2001) has argued that, in fact, mechanical divination is a communicative event whose success hinges on the real-time negotiation of meaning between intentional human agents.

  9. 9

    For a discussion of a different interactive jazz-improvising computerized system, see Lewis 2000.

  10. 10

    We might say, then, that inasmuch as disappointment is the result of the relation between one's expectations and the reality that is the subject of these expectations, it hinges neither on the former nor on the latter in isolation. Hence, there is nothing inherently disappointing in unpredictable or predictable people. They become so only in relation to specific expectations, which are context dependent.

  11. 11

    At the time of my fieldwork, the algorithms processed mainly note pitch and duration (and, to a lesser degree, volume). The research team was in the process of designing the system to perceive harmonic tension—the relation of notes to the harmonic context in which they are played. The algorithms were indifferent to timbre.

  12. 12

    Part of Syrus's novelty is that it can mix the styles of different players and thus generate new styles. James's notion of “interesting,” then, is not about exploring an already existing style or “conceptual space” (something that the contemporary musicians who disappoint James do quite well) but, rather, creating a new conceptual space or style “so that thoughts are now possible which previously … were literally inconceivable” (Boden 2003:6; see Wilf in press b).

  13. 13

    Markov models are algorithms that the research team uses to simulate the styles of specific past jazz masters and to morph these styles into one another to generate new styles. These algorithms generate music on the basis of probabilities derived from a given corpus such as a jazz master's solos. Genetic algorithms in music composition are based on the stochastic transformation of basic musical phrases through processes modeled on genetic mutation, evolution, and the “survival of the fittest.” Fractal-based algorithms are used to generate music that is self-similar in structure across different scales or levels of magnitude (Nierhaus 2010). On the (often fetishized) value assigned to the emergent outcomes of some of these algorithms (especially genetic algorithms) in a U.S. scientific institution devoted to the study of nonlinear and complex systems, see Helmreich 2000:107–202.

  14. 14

    Thus, whereas Native American trickster traditions rely mostly on the use of stochastic variation to generate unexpected narrative structure, while West African trickster traditions are replete with self-referentiality and recursion that feed back on themselves to generate unexpected narrative structure (Pelton 1989), jazz aesthetics reveals a heightened awareness of both aspects. I thank one of this article's reviewers for directing my attention to this point.

  15. 15

    This topic has been an object of mathematical inquiry in complexity theory (Mitchell et al. 1994).