Sean Rooney
The study of trajectories is an important part of classical mechanics, with applications in astronomy, aerospace engineering, ballistics, and sports science. The term “trajectory,” rooted in mathematics and physics, has found new life in sociology, performance, and game theory. As outlined by Steve Benford and Gabriella Giannachi in Performing Mixed Reality, the word comes from the Latin term trans jacere, meaning “throwing across” and refers to “the movement of a body or object through space and time” (15). In defining how trajectories function in mixed reality performance, Benford and Giannachi note this concept differs from other terms such as lines, journeys, routes, threads, or traces as “trajectories express the progressive itinerary of a body or object originated by an agent” (15). Additionally, context also plays a significant role, which means that while a trajectory can be planned and predicted, it’s exact path and duration can vary in practice. Thus, a trajectory is a dynamic entity that is constantly changing, both predictable but also unpredictable.
Trajectories are implicit in various art forms; they are essential for audience navigation and intertextual references in architectural works such as Daniel Libeskind’s Jewish Museum in Berlin, which connects the building to the city’s significant addresses. Trajectories are also prevalent in painting and film; Wassily Kandinsky and Sergei Eisenstein use lines to create movement, tension, and direction, employing specific spatiotemporal coordinates to visualize a journey. Theatre and performance involve paths of observation and action by actors and performers. In site-specific performance and performance art, trajectories have been used to map the audience’s route through a site. In recent years, trajectories have become increasingly important in media and performance studies. In these contexts, trajectories refer to the path or course taken by an object, person, or idea over time through real or virtual environments. They can be visualized, described mathematically, and analyzed over time to facilitate reflection and planning. They mark past, present, and future mapping possibilities, representing a way of knowing and learning.
In mixed reality (MR) performance, as conceived by Benford and Giannachi, trajectories are a core concept. They outline two types of trajectories: canonical trajectories, which are scripted into the piece, and participant trajectories, which are defined by the participants and are unpredictable. The relationship between them reflects tension between the artists’ and participants’ control. In MR performance spaces, participants produce “contextual footprints, digital records of their passage through both virtual and physical worlds” (20). These footprints can become part of the work itself or remain invisible to participants but used later for evaluation and analysis. Trajectories mapping traces of digital footprints can play a crucial role in the way we study and learn from mixed reality performance and develop future knowledge and behaviours. Trails are not just routes to remembrance but also routes to knowledge, and these trajectories and contextual footprints may influence the habitual pattern on the movement of others over time.
In the realm of game theory, thinking in terms of trajectories is ubiquitous. As designers and developers seek to create immersive and engaging gaming experiences, the concept of trajectory helps conceptualize the player’s journey through the game world. In open-world games, such as Grand Theft Auto, the player is free to explore a vast virtual world. The path taken by the player as they navigate this world is a trajectory, representing the player’s unique experience within the game. Ensuring that each of these trajectories form a coherent experience for the participant is a programming nightmare; glitches – places where the illusion breaks down – while rare, are part of the game.
The term trajectory has a rich historical trajectory of its own. Originating in mathematics and physics as a means of describing the path of an object through space, its meaning has expanded to encompass a diverse array of fields including sociology, performance, and game theory. The notion of trajectory has been a crucial tool for understanding movement, both physical and metaphorical, and has been employed to describe the development of social phenomena, artistic performances, and strategic gameplay. As mixed reality performance becomes increasingly prevalent and technological advances continue, the concept of trajectory will continue to be a valuable tool in performance and performance theory. It offers a means of analyzing movement, narrative, and the relationships between artists and audiences, and will play an important role in shaping the future of performance.
Works Cited
Benford, S., & Giannachi, G. (2011). Performing mixed reality. MIT Press.
Digital performance repository 