Game Time: Understanding Temporality in Video Games

By Christopher Hanson

Pausing, slowing, rewinding, replaying, reactivating, reanimating . . . Has manipulating video game timelines altered our experience of time? “Compelling.” —Choice

Video game scholar Christopher Hanson argues that the mechanics of time in digital games have presented a new model for understanding time in contemporary culture, a concept he calls “game time.” Multivalent in nature, game time is characterized by apparent malleability, navigability, and possibility while simultaneously being highly restrictive and requiring replay and repetition. When compared to analog tabletop games, sports, film, television, and other forms of media, Hanson demonstrates, the temporal structures of digital games provide unique opportunities to engage players with liveness, causality, potentiality, and lived experience that create new ways of experiencing time.

Features comparative analysis of key video games titles—including Braid, Quantum Break, Battle of the Bulge, Prince of Persia: The Sands of Time, Passage, The Legend of Zelda: The Ocarina of Time, Lifeline, and A Dark Room.

“The text is well-researched, and the introduction is an excellent, focused overview of video game studies.” —Choice

• Language: English
• Publisher: Open Road Integrated Media
• Release date: Mar 8, 2018
• ISBN: 9780253032836

Book preview

INTRODUCTION

RELEASED IN 2016, SUPERHOT (SUPERHOT TEAM) MIGHT GIVE THE initial impression of being an incomplete game, or perhaps one in which the graphics were never finalized; at the very least, SUPERHOT is strangely anachronistic in its graphical style. Unlike the highly detailed FPS (first-person shooter) games commonly available, SUPERHOT uses a minimalist art style, with the game graphics resembling the wire-frame models found in 3-D design applications before their graphics are fully rendered. But these unpolished and fragmentary graphics belie a complex play mechanic that lies beneath the game’s surface. SUPERHOT reveals its novel twist on the FPS genre as soon as one starts playing. In the game, time barely moves forward as the player stands still and only progresses as the player moves. That is, the enemies in the game are all but frozen if the player does not move the avatar; their movements are slowed to a near-standstill, allowing the player to carefully plot maneuvers through slowly moving bullet trajectories and plan strategies through increasingly complex stages (see fig. 0.1). The player may target enemies in real time while temporality in the game world is slowed, providing a decisive advantage over the numerous enemies. This slow-motion play mechanic is reminiscent of earlier games, such as Max Payne (Remedy Entertainment, 2001), in which the player is able to selectively slow time through the bullet time power. But while games such as Max Payne may feature periodic temporal manipulations, SUPERHOT is a game constructed entirely around a play mechanic of distorted temporality that is linked directly to player movement and agency. The simplified graphics de-clutter the screen, allowing the player to focus on small critical details, such as bullets slowly moving through the air and the movement of enemies, and to maneuver through levels as though with superhuman reflexes. As if to accentuate this, after completing a level, players are shown replays of their actions in real time, apparently making a series of split-second decisions in fluid and continuous fashion, resembling a carefully choreographed gunfight from a John Woo film. SUPERHOT illustrates the pleasures of controlling time, but it is only one of a growing number of games that emphasize temporality in their gameplay.

Figure 0.1. Screenshot: SUPERHOT gameplay depicting slowed bullet trajectories. (SUPERHOT Team, 2016.)

In a video game, the player attains agency over that which cannot be controlled in the real world: time. Video games enable players to experience and manipulate time in ways that transcend other media. The temporalities of video games are numerous: players preserve, pause, slow, rewind, replay, reactivate, and reanimate time as part of the play mechanics of an increasing number of games. This multitude of temporal experiences warrants careful consideration, and not just in the ways in which some game temporal structures correspond to the temporalities afforded by other media forms. Far more importantly, we must examine the remarkable temporal structures that games introduce and invoke and how these ludic temporalities exceed and transcend more familiar temporal experiences.

In this book, I argue that games offer new modes of temporal control that fundamentally alter our experience and understanding of time in contemporary culture. While much of existing games scholarship focuses primarily and almost exclusively on video games, I instead foreground the intermedial linkages among both digital and analog tabletop games, as well as television, film, and performance, to argue that what fundamentally differentiates the temporal structures of video games from other media is their unique engagement with liveness, causality, potentiality, and lived experience. I critically analyze a number of concepts central to game temporality, using key games and play mechanisms that illustrate the numerous complexities of game time. As evinced by these variations in ludic temporality, game time is distinguished by its apparent malleability, navigability, and possibility. But this apparent freedom of game time can be chimerical and is often characterized by replay and repetition. I contend that we must explore both of these polarities in order to better understand games and the extraordinary temporalities that they engender.

Time in Video Games

This book is by no means the first exploration of game time. Game temporality is an inherently complex subject, as several theorists have illustrated (see Crogan 2003; Juul 2004, 2005; O’Grady 2013; Ruggill and McAllister 2011, 51–62; Wolf 2001; Zagal and Mateas 2007). While digital game studies comprise a fairly nascent discipline, consideration of the function of temporality is evident even in foundational theories games and play. Johan Huizinga (1950, 9, 13), Roger Caillois (2001, 6, 22), and others argue that play is defined in part by a clearly delineated temporal duration. Games create separate temporalities from our everyday lived experience and allow us to experience time in new and previously inaccessible ways. When we play a game, we are already subject to multiple temporalities. There is real-life time in which we operate as humans. There is also the temporal structure of the game, which may be intervallic if the game is turn-based or continuous if the game is based in real time, such as soccer or Tag. Additionally, there may be a historical time period in which the game diegetically (i.e., within the fictional narrative of the game) takes place: for example, a game might be based on the American Civil War as in Ultimate General Gettysburg (Game-Labs, 2014), broad past history as in Sid Meier’s Civilization (MicroProse, 1991), or a hypothetical future setting such as in The Resistance (Don Eskridge/Indie Boards and Cards, 2012). And all of these temporalities do not account for the loss of time that a player may experience when immersed in a game, as when looking up from the screen of a game of Tetris (Alexey Pajitnov, 1984) to discover that several hours have passed without notice. And, as I discuss throughout this book, players may exercise agency over these various temporal structures via pausing and saving mechanisms or gameplay elements that make temporal manipulation and navigation a core gameplay mechanic. I should note that I do not, however, extensively examine audience and fan practices in this book, as some others do far more comprehensively for both media in general and games specifically (Anthropy 2012; Atkins and Krzywinska 2007; Avedon and Sutton-Smith 1971; Crawford 2012; Gee 2003; Jenkins 2000, 2006a, 2006b; Jenkins 1992; Juul 2010; Kline, Dyer-Witheford, and De Peuter 2005; Shaw 2015). While I closely examine the role of games and their temporal structures in shaping player experience, I do not deeply consider the central role of identity in shaping understandings and experiences of temporality, as scholars such as Jack Halberstam (2005) have brilliantly explored.

As is true of numerous early examinations of interactive digital texts and games, Espen Aarseth’s (1997) seminal work that defined such texts ergodic (i.e., requiring a nontrivial effort to traverse on the part of the reader or player) was strongly influenced by narratology and literary theory (see also Genette 1980; Ryan 1999, 2001). The influence of these fields is evident in the range of discussions of digital game temporality that have emerged since the late 1990s, with some placing a particular emphasis on the interaction between the sequencing of game events and the sequences of narratives (e.g., see Davidson 2008; Lindley 2005). Of course, the field of digital games studies fairly rapidly distanced itself from the consideration of games as narratives with the turn to ludology and a focus on games as games. Greg Costikyan (2016) has been particularly critical of the consideration of games as narratives (see also Greg Costikyan 2007). Separately, Gonzalo Frasca (2003) and Henry Jenkins (2004) supply helpful overviews of the debates between ludology and narratology in game studies. Well before such debates, Brenda Laurel (1991, 1986) described player experience of possible, potential, probable, and necessary outcomes using a flying wedge, wherein player behavior is shaped by past experience and what is offered in an interactive experience. Aarseth (1999, 36–39) offers one of the earliest explicit engagements with temporality in games (or, for him, ergodic texts) by critically linking the sequencing and temporality of events in a game to the successful and unsuccessful actions of the player.

Markku Eskelinen (2001, 178) further theorizes game temporality by arguing that the dominant temporal relation in digital games is between what he calls user time (the player’s actions) and event time (the game’s happenings).¹ Similar to Eskelinen’s model, Jesper Juul (2004, 131) delineates the function of time within games as built around a basic duality of play time (the time the player takes to play) and event time (the time taken in the game world).² Juul terms the relationship between play time and event time as mapping, noting that in arcade games this is a one-to-one relationship, as play time corresponds directly to event time (i.e., the game takes place in real time). Juul proposes that this mapping between the time in the player’s real world and the time in the game world infuses games with a persistent present: In this way, there is a basic sense of now when you play a game; the events in a game, be they ever so strange and unlike the player’s situation, have a basic link to the player. Thus, whether the game constantly emphasizes speedy reactions in real time (as in the case of an action or sports game) or instead slows time to a turn-based structure (as in a strategy game such as chess), the significance of the player’s action at the moment of play is linked to the now (134).

Juul’s model has proven influential, and has been further developed in multiple ways. For example, Michael Nitsche (2007) provides a more thorough understanding of mapping this model of time. Michael Hitchens (2006) usefully adds to Juul’s model by arguing for four aspects of game time via the addition of engine time and game progress time, both of which help to account for complications presented by the processes of saving and pausing, mechanisms that I discuss in greater detail in the second section of this book (chaps. 3 and 4). Hitchens emphasizes the challenges to temporality effected by the nonlinearity of games, a theme that I address in my discussions of contingency and indeterminacy.

While game temporality has only recently been examined more thoroughly, there are already a wide range of approaches to the topic, using a variety of disciplinary methods. Nitsche (2007), José P. Zagal and Michael Mateas (2010), Tychsen and Hitchens (2009), and others have provided highly useful and comprehensive surveys of some of these differing approaches to game temporality. Within these studies there is a marked trend toward categorizations and frameworks that classify, describe, and analyze the multivalent and remarkably diverse range of temporalities that games can manifest. The complexity of game temporalities is evident in the diagrams found in a number of theorizations, which one can trace from Laurel’s (1986, 1991) flying wedge, Eskelinen’s (2001) story/discourse/event/user, and Juul’s (2004) early mapping model to later iterations of Juul’s (2005) model and others, including Michael Hitchens’s (2006) examination of temporality in games and his work with Anders Tychsen (2009) on time in multiplayer games. Despite the steady progression of intricacy in these visualizations, they are profoundly helpful in illustrating and explicating just how perplexing and convoluted game time can be, particularly in relationship to our lived experience of temporality.

The numerous categorizations, classifications, and frameworks for game temporality found in these approaches are invaluable tools for both analysis and explication of the many valences of game time. However, category and classification systems are often necessarily restrictive in their attempts to clearly define and delineate, sometimes unnecessarily. Such top-down structures are also prone to revision and refinement, as the evolution of Juul’s influential model shows; they must inevitably be revisited and adapted. As genre studies shows us, there are many inherent challenges to creating categorizations that are able to describe all past, present, and future texts in a satisfactory manner, and it is almost impossible to definitively establish neatly delimited categories into which specific texts—or, in this case, temporal structures—will neatly fit.

Nitsche (2007, 145) suggests that theories and models of game temporality can be divided into two groups, formal and experiential.³ Formalist approaches stress the importance of time evolving in a reference between the game state and the play time, while experiential approaches are more driven by cognitive and emotional aspects and players’ understanding of the game world. Nitsche then argues that a combination of these approaches might be more effective and emphasizes the role of spatiality in determining aspects of temporality. I agree with Nitsche in his inclination toward a combined approach but do not privilege spatiality in the ways that he does. I find it more challenging to neatly separate existing and ever-expanding theorizations of game time, particularly along a boundary of formal and experiential approaches. Games by their interactive nature are necessarily experiential, and thus formal aspects of games are necessarily bound up in experiential ones and vice versa.⁴

Unpacking Game Time

Expanding on the focus of many existing considerations of game temporality, this book takes up the project of exploring game time in a more holistic fashion. Just as game studies constitute a truly interdisciplinary field, I leverage concepts from multiple disciplines in considering game temporality; for example, like Janet Murray, Brenda Laurel, and others, I draw from performance studies in examining games as structures that are enlivened through player interaction (see Auslander 2002; Cameron and Carroll 2009; Dixon 2007; Laurel 1986, 1991; Murray 1997; Saltz 1997; Wardrip-Fruin and Harrigan 2004). I unpack concepts essential to studying game temporality by exploring links to media studies, performance studies, and critical theory. In parsing game time through frameworks and categorizations, many discussions of game temporality do not push hard at the question of precisely when a game’s temporality is activated and how its temporal structures are linked to the presence of its player(s). I foreground concepts from television studies and presence studies in my exploration of the activation—and inherent complications—of game temporality (e.g., Couldry 2003, 2004; Crisell 2006, 2012; Marriott 2007). I examine how games become enlivened and activated by players, functioning as a medium through which players experience and understand time. I also carefully consider the underlying technologies, such as hardware and software mechanisms, which have made temporal manipulation and navigation commonplace practices of the play of digital games.

I emphasize the aspects of digital games that differentiate them from other forms, and much of this book is built on an underlying argument about the medium specificity of games: that games are something that, while existing among a nexus of time-based media forms, are singular and thus can offer extraordinary and unparalleled experiences of temporality. This access to newfound temporalities is not without precedent, as other time-based media have similarly reconfigured understandings of time. The capacity of cinema to record the everyday allowed for viewers to re-experience and revisit the past, just as it allowed filmmakers to reconstruct and reconfigure temporality.⁵ For example, the 1896 Lumière brothers’ film Démolition d’un mur (Demolition of a Wall) depicts a wall of their factory being knocked down by several men with sledgehammers. After showing the film played normally, the projectionist could then depict the wall’s magical reconstruction from rubble by reverse-cranking the projector, providing access to temporal reversals that were only previously imagined. I illustrate how digital games greatly expand on these early experiments, offering entirely new experiences and understandings of temporality. I detail the tendency of games to emphasize repetition and their replay, imposing particular temporal structures of repetition on players. Finally, I address the ways in which games afford new experiences of time through innovative mechanisms for temporal manipulation and navigation, and even via unusual recursive temporalities.

State Machines

In order to fully understand the mechanisms of game temporality, it is necessary to consider the digital structures on which they are built. At the most fundamental level, computational structures are binary-based logical systems, as almost every computer-based device is governed by the flow of electrically charged particles through a series of simple gates. Much like a light switch, these gates effectively operate as switches that can be set to one of two states, on or off. The elementary duality of this logical structure is at the core of all computer processors, from a rudimentary electronic device to the most profoundly complex supercomputer. The alignment and continuous reconfiguration of these switches essentially means that computers are in a constant state of flux, shifting from one state (a specific configuration of switches) to another. This succession of discrete states as principal function explicates a term applied to these processors: finite state machines, or, more simply, state machines.

The ability to change or preserve the given state of a system is instantly recognizable to anyone who has ever used a word processor. As we enter data into a document, we change its state. When we save the document and close it, we preserve the document in its given state, which then allows us to return later to further modify it; the Undo function of word processors acts in a comparable fashion, allowing the user to iterate through earlier states. The Back button of a web browser operates in much the same manner, allowing a user to return to a previous state, an earlier web page in the browser’s history.⁶ In a fundamental sense, principles of difference dictate basic notions of interactivity. As a user inputs data into the state machine of a computational system, the state of the system changes, changing output in response to input. This input/output cycle constitutes interactivity—as we input data via the interface (most commonly today via a keyboard or mouse), this data alters the system, and the system correspondingly outputs data (e.g., moving the mouse moves the corresponding cursor, or pressing the letter k produces the character k on-screen). It should be noted that changes to the state machine may be made explicit to the user (such as the appearance of k on-screen) or, more often, remain hidden to the user (the addition of the k to the current file in the computer memory and/or hard drive).

The rapid development of the graphical capabilities of video games and their increasingly lifelike depictions and capacity for representation means that it is easy to forget the processes on which these systems are built. In simplified terms, games are assembled from data structures and algorithms that are then processed through the hardware on which they run. As software code being run through processors, games are built and operate on the aforementioned minute electrical currents that navigate the tiny physical spaces of circuits, constantly changing the state of countless switches between the binary state of 1 and 0 in a rule-based temporality. In essence, these electrical currents are the physical manifestation of the computational bits to which they correspond. Thus, the electrical pulses of computer circuits representing bits of data (in their larger allegorical representation of time and space within games) are also regulated by real-world time and space in the physical circuits in which they are generated and function. In this manner, the virtual representations rendered in games correlate to physical elements in the material function of computer hardware.

Given their construction as computational structures, it is helpful to build from Juul’s articulation of the game as a state machine: "The more fundamental part of games is a change of state, the movement from the initial state (the outcome has not been decided) to another state (the outcome has been decided) . . . a game is actually a state machine: it is a system that can be in different states; it contains input and output functions, and definitions of what state and what input will lead to what following state."⁷ In the most rudimentary sense, both analog and digital games are rule-based systems governed by changes in states. Video games process data input by the player in accordance with these rules and output a change in the game state in response to this data. In turn, the player inputs more data, and the loop continues, with the player constantly responding to the changing game state. Successful play of a game requires proper response to the game’s state, and it should be noted that even nondigital games are almost entirely state machines in which a state or finite set of conditions exists and then is continuously altered by the player(s). Consider a game of chess. To begin play, the pieces for both sides are arranged in a predetermined pattern, on opposite sides of a board. When the first player moves a piece, the board and game’s state changes in a discrete fashion, altering both the configuration of pieces on the board and the next possible moves (as defined by the rules of the game). Thus, games of chess may be expressed in a shorthand form using descriptive or algebraic notation (i.e., the movement of the queen to a specific square may be represented by Q-QB3 in descriptive notation or c1 c3 in algebraic notation). A player’s ability to precisely reproduce a specific set of moves written in such notation evinces the capacity of the game to be represented discretely; in so doing it illustrates its function as a discrete state machine.

Almost any game’s structure is reliant on an explicitly bounded space or arena in which the play occurs. That which occurs within the boundaries of this space is considered to be governed by the rules of the game, and that which exists outside of this bounded space is not. Huizinga (1950) refers to the arena and conventions of play agreed on by players as the magic circle—the social contract to which participants in the game must abide, typically delineating the boundary between the play world and the real world. His magic circle articulates the occasionally nebulous area in which players agree to follow the rules, within reason. The bounds of this circle can be broken by players refusing to play or by a physical danger. For instance, a game of Tag takes a lower priority when crossing a busy street or other such dangerous area.⁸ This bounded space is vital to a game’s definition as a state machine: by defining the limits of the game, one makes the number of variables in a game finite and thus defines the game within discrete units. It goes without saying that some nondigital games are more readily translatable to discrete modes of representation than others. For example, while algebraic notation may be well suited to describing and reenacting a chess game, developing a similar system for a playground game of Tag would be considerably more complex, given the lack of distinct spaces, pieces, and a host of other variables that resist simple mathematical representation. That some games are more suited to digital forms is readily apparent; the vast number of video-game versions of chess compared to the dearth of digital games based on Tag demonstrates this spectrum of the capacity for quantification of game systems.

(In)Determinacy and Games

The operation of digital games as rule-based structures and their basis in discrete and finite systems engender pleasures specific to their play that stem from the recognizable patterns of game mechanics. The game world typically behaves in a predictable manner in response to the player’s input. By playing and replaying a game, a player begins to learn how the game works; this is what Elizabeth and Geoffrey Loftus (1983, 55–56) describe as the function of expectancy of the player in video games. In some ways, this predictability mirrors that of the real world. For example, the use of a realistic physics model allows a game world to behave in a way familiar to the player: gravity may be simulated, or a rock thrown into the water in a 3-D game may create ripples on the water’s surface.

This is not to suggest that video games are structured around mechanics of predictability alone. Recent scholarship argues quite the opposite: that games are structures in which arbitrariness is an essential component. Thomas Malaby (2007, 107) identifies this trait of games as contingency, which he defines as that which could have been otherwise. Malaby’s description stresses the role that controlled randomness plays in games; he argues that games represent a semibounded arena in which unpredictability is emphasized. Lived experience is dominated by contingency, as everyday life is composed of innumerable possible outcomes for the countless events that constitute each day. But games function as a domain in which game designers may confine and restrict contingency to a finite and recognizable realm.⁹ As players, we may begin to learn game patterns and develop better strategies for play, reducing contingency from an overwhelming amount of possibility to a pleasurable and explicit system. Greg Costikyan (2013) makes a similar claim about the function of games, but prefers the term uncertainty. Costikyan builds from Roger Caillois’s (2001) definition of play as an uncertain activity and a venture in which the outcome must necessarily be uncertain for it to be pleasurable; if a player is so skilled at a game that she is no longer challenged by it, the game will no longer be enjoyable. Costikyan expands on this by pointing out that uncertainty plays throughout a game, rather than merely in its outcome. I emphasize that this unpredictability in games operates in essential tension with the degree of predictability supplied by the rule structure. In order to be pleasurable and immersive, the game must behave in a predictable manner according to the rules governing the game. In the example of chess, a player may move the queen piece any number of spaces horizontally, vertically, or diagonally. Per the rules of the game, the queen may not, however, be moved anywhere on the board on a whim. There is thus a tension between the predictable (that movement of pieces on the board as regulated by the rules) and the arbitrary (that the player may move these pieces in any number of ways per the rules). This tension is further illustrated by the strategies employed by the player. As players become more familiar with the rules and begin to recognize patterns that emerge from the play mechanics of the game, they may begin to develop specific playing strategies.¹⁰ For example, a player may learn that a specific sequence of opening moves in chess proves more successful than other initial moves, or that a particular piece is most effective when in certain positions on the board. After observing these patterns, the player may then develop strategies that capitalize on these patterns. Through play, a player may also learn that particular moves or strategies are less effective and may weaken the player’s position on the board; for example, moving or sacrificing the pawns that protect the queen and king may result in the player losing the game quickly. In chess, particular sequences of initial moves to open the game are characterized and cataloged as openings and are so established that they are given specific names and compiled in books about chess.¹¹ The efficacy and pervasiveness of such precise sequences of moves demonstrate that players may resort to established practices and tested strategies (established by themselves or others) while playing a game. This reinforces predictability, as players adopt particular patterns of play, while also increasing the degrees of uncertainty and contingency of the game, as experienced players may draw from an ever-growing repertoire of opening moves.

The importance of the player’s voluntary involvement is what I wish to stress. By choosing to play a game, the player essentially commits to a particular social contract of the game: the player will abide by the rules, will not intentionally cheat or physically harm other players, and so forth. This tacit agreement aligns with Bernard Suits’s (1978, 41) description: playing a game is the voluntary attempt to overcome unnecessary obstacles. By the mere act of agreeing to play, the player is already engaged in the act of relinquishing a degree of control in order to consent to the rules and the conceits of the game and its world. In some ways, video games elide the degree of make-believe necessary to some traditional real-world games such as Tag or a paper-based role-playing game (RPG) such as Dungeons & Dragons (Gary Gygax and Dave Arneson/TSR 1974). In a video game, the player is almost always presented with a visual and aural representation of the game world, from either the first- or third-person perspective. Simply by playing the video game, the player tacitly agrees to the representational systems used by the game and the avatar or other elements the player controls. In a video game, players submit on multiple levels: to the rules of the game, to the physical-control interface used to play the game, to the game’s play mechanics, and even to the software code on which the game runs. Ted Friedman (1999), in his essay "Civilization and Its Discontents, notes that the players of computer games must internalize the logic of the game’s play mechanics in order to succeed; in essence, the player must think like the game system in order to thrive. Alexander Galloway (2007, 90–91) expands on Friedman’s notion with his own concept of the allegorithm, which I define as the allegorical messages and meanings implicitly contained within the game’s algorithms and play mechanics. Galloway argues, To play the game means to play the code of the game. To win the game means to know the system. And thus to interpret a game means to interpret its algorithm (to discover its parallel ‘allegorithm’)."¹² Both Friedman and Galloway use examples from the Sid Meier’s Civilization series (MicroProse/Firaxis, 1991–). In these games, the player builds and guides an empire from its foundation (several thousand years BCE) to the eventual development of space flight in order to colonize other planets. The game’s various civilizations are loosely based on real-world historical groups, each with its own particular (and often highly problematic) traits. The game is structured such that the player’s civilization is in competition with several others that also originate at the same time. To achieve success in the Civilization series games, the player must prevail over the other civilizations in the game, most often via military domination.¹³ As Friedman and Galloway illustrate, the player must essentially enact Western expansionist imperialism in order to win; one must not only adhere to the game’s rules, but also play in the aggressive style the game dictates in order to win. Of course, the player may choose a nonaggressive posture and play the game in what Stuart Hall (1980) might identify as an oppositional counterhegemonic fashion by resisting the game’s dominant ideological requirement and not attempting to conquer opponents. But such a play style would almost inevitably result in losing the game. As such, the player must play according to the game’s algorithms, and may gain insight to