Mazes

From Maze

Contents [hide] 1 The Meanings of Mazes 2 Maze vs. Labyrinth 3 What is a Maze? 4 Death and Danger 5 Ritual and Allegory 6 Experimentation 7 Claude Shannon's Theseus 8 The Computerized Maze 8.1 First Person Mazes 8.2 Second Person Mazes 8.3 Third-Person Mazes 8.4 Computer Generated Mazes 9 Context of Expectations: Computer Graphics and Games 9.1 Isometric Games 10 Bibliography

The Meanings of Mazes

This is as strange a maze as e'er men trod

--Alonso, The Tempest (3.3.1)

In discussing the version of 10 PRINT found in the 1982 Commodore 64 User’s Guide, the manual points to the two graphical characters "that the program is using for the maze" (53). So, the output of 10 PRINT was called a maze from the beginning, from the program's first appearance in print. The programmer who submitted the one-line version found in Run also described it as "drawing a continuous maze." (13) Whether or not the 10 PRINT pattern that shows on the screen is solvable at every instant, it was consistently identified as a maze in the early 1980s. If everyone were to see the output simply as a pattern of alternating diagonal lines it surely would not be as interesting to execute, to understand, and to discuss this program. The maze is the central visual trope used to read 10 PRINT's output.

Cryptic, compelling, and cabalistic, the maze invites many modes of interpretation and understanding. Mazes can pique our curiosity and elicit a range of emotions: amusement, excitement, confusion, trepidation, calm, and hopelessness among others. They are approachable as visual objects, as textual artifacts, and as horticultural and architectonic spaces. A full account of the cultural significance of mazes would need to traverse the fields of art, history, literature, religion, architecture, and even music and dance. This chapter makes no pretense of offering a comprehensive account of what mazes mean. (For in-depth historical accounts of mazes and labyrinths, see Doob, 1990; Kern, 2000; and Matthews, 1922.) Rather, it highlights those mazes and representations of mazes throughout history that bear on what Commodore 64 users in the 1980s would plausibly associate with the output they saw after running 10 PRINT. This can help to explain 10 PRINT and also the computing context in which it existed -- one in which mazes were very often represented and simulated.

Whether perceived as amusing puzzles, places of terror, or invitations to contemplative meanderings, our current cultural ideas of the maze (certainly in the Unites States and in much of the West) date back to the legend of Theseus and the Minotaur in the labyrinth of Knossos, a bewildering and life-threatening space. Mazes have since appeared on coins, on walls, and in spiritual centers. Hedge-row mazes have presented public, shared diversions. In more recent times, mazes have served as spaces for movement and dance and as commonplace diversions in puzzle-books. Sometimes, mazes are abstract mathematical objects or scientific tools for studying animal behavior. And in computer games, the maze takes on an archetypal, structural frame for adventure, chase, and combat.

Indeed, the computer has provided new ways of experiencing mazes. In particular, the experience of the maze shifts with the different perspectives commonly associated with video games: first-person, second-person, and third-person. Each entails a different form of embodiment, a different form of subjectivity, and a different perception of space. Experiencing a maze one corridor at a time from a first-person point of view is markedly different from experiencing the same maze through the "you" of a text adventure or through a third-person omniscient or overarching view. By considering how 10 PRINT relates to computer mazes of these types in games, it is possible to understand more about what 10 PRINT's maze means, and what makes this program inviting to try out and to modify.

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Maze vs. Labyrinth

SIDEBAR

The terms "maze" and "labyrinth" are generally synonyms in colloquial English, and indeed, many Western languages only have one word to designate the concept of a path-structure. Despite this common usage, over the past century many scholars and historians have argued for (or against) a careful distinction between these two terms. In this proposed distinction, "labyrinth" refers to only to single-path (unicursal) structures, while "maze" refers only to branching-path (multicursal) structures.

In this discussion, the terms "maze" and "labyrinth" are not used to distinguish two different categories of structure or image. In our view, such a distinction does not accurately reflect the history of Western consciousness of the maze as a single conceptual category, in particular our recent popular imaginary in which the environments of Theseus and Pac-Man are related structures. For this reason, we favor the use of "maze" as a general term.

Nevertheless, it is important to clearly distinguish between unicursal and multicursal path-structures, as these often arise in different cultural contexts, have different uses, and produce different experiences while being used. We term these two types the "unicursal maze" (offering a single path along which walkers proceed, never making a choice about where to turn) and the "multicursal maze" (which invites wrong turns, has dead ends, and may even have multiple paths to the exit or center).

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What is a Maze?

The Oxford English Dictionary offers two definitions:

• A structure designed as a puzzle, consisting of a complicated network of winding and interconnecting paths or passages, only one of which is the correct route through; a labyrinth; (occas. in pl.) the windings of a labyrinth. Also (as in quot. 1903): a structure comprising two points joined by a single winding line much greater in length than the direct line between the two points.</li>
• In extended use: a complex network of paths or streets; a bewildering mass of things (material or immaterial), in which the individual components are difficult to separate or make out. </li>

The first definition describes one particular type of puzzling network; the second, more metaphorical, allows us to name mazes representations of paths with certain characteristics. In popular use, the term’s meaning has been stretched to cover intellectual puzzles, tangled legal code, and confusing, labyrinthine situations, such as the one Alonso refers to near the end of The Tempest. 10 PRINT's output, by representing a maze, can suggest many different things.

10 PRINT fits some of the criteria that William Henry Matthews establishes for mazes in his definitive Mazes and Labyrinths (1922): they are "works of artifice,” not "'labyrinths’ of nature, such as forests, caverns, and so forth; they are endowed with "an element of purposefulness in the design" (182); and betray "a certain degree of complexity" (183). Finally he requires "communication" among the maze’s component parts and between its "interior and exterior" (183).

10 PRINT is, indeed, a complex work of artifice. Ironically -- and Matthews could hardly have foreseen this -- the compelling and captivating quality of 10 PRINT is due to the lack of an obvious, purposeful designer. Someone wrote the line of code, certainly, but that human artificer of the program is not credited. The particular pattern that is produced is due entirely to the RND function in BASIC, which is also by some anonymous author and was designed to be unpredictable. Furthermore, in 10 PRINT, communication among the component parts is established by the regularities of the “blank” spaces between slashes, which in the aggregate also establishes a sense of inside and out that is rather more muddled than in the cases that Matthews discusses.

A material, architectural structure is necessarially of finite size. There is no limit to how long 10 PRINT can be left running, however. Can a boundless structure be a maze? There is a very early warrant that it can, found in one of the example sentences from the Oxford English Dictionary': "1542 H. BRINKELOW Lamentacion sig. Cviii, Leadyng them in an endlesse Maze of dyrtye tradicyons and folish ceremonyes." As an endless maze, 10 PRINT tantalizes viewers, but offers no set path or solution, which is quite in keeping with the definition of "maze" given by Webster's Revised Unabridged Dictionary (1913): "a confusing and baffling network, as of paths or passages; an intricacy; a labyrinth."

All mazes offer at least one path; the key structural difference is whether they offer more than one, whether they are unicursal or multicursal. This is true whether mazes be physical structures, mathematical constructions, drawings, dances, or games. In unicursal mazes the space to be navigated is bounded and the single path followed; users have no directional decisions to make, save to follow the meanderings of the path, leaving their attention, mind, or emotions free to wander or focus elsewhere, while continuing along, guided by the path itself, to the end at the center of the maze or to a unique exit. The unicursal maze has often been understood as defining motion across time, offering a spiritual and contemplative space to the walker. Understood this way, the path can be taken repeatedly and ritualistically, again and again offering new insight, peace, and spiritual comfort each time. In unicursal hedge mazes, where the hedges often limit one’s vision to an immediate and foreshortened horizon, one is particularly enclosed and protected.

For children over the centuries, unicursal hedge and turf mazes have offered curling lanes for running but less puzzling pleasures than the seemingly endless grounds for playing hide-and-seek out of doors in multicursal mazes. For in multicursal mazes, which are solvable mazes, the solution is complicated by the possibility of making wrong choices at key nodes where directional choices are required. Instead of following the unicursal maze’s predetermined path, walkers in a multicursal maze risk getting lost on their way. They are challenged to find the path that reaches the exit. Once that path is known, though, the one correct path can be seen as a unicursal maze that is fraught by the possibility of wrong turns.

The distinction between unicursal and multicursal mazes bears important implications for how 10 PRINT itself, not its output, can be seen as unicursal and multicursal. Typing in this program, beginning programmers engage in a ritual that has them trace a string of characters without variation. At the same time, this program is, initially, a puzzle to those who have some understanding of BASIC but lack a complete command of the Commodore 64 and a full knowledge of the PETSCII table. Once the code has been typed and executed and the programmer witnesses the maze, there is no returning to a naive view of this line of code -- it is impossible to read the line without imagining its output. From the many possible outputs that a Commodore 64 user might imagine, one line emerges between input and output. With some study, it becomes clear how the program produces this output, and the single path through this short but initially tangled program becomes clear. All the same, this program holds more opportunities than this single path. Since the programmer is encouraged to make changes to the code, newly shaped corridors can appear, and the forms that the maze itself takes prove be practically endless.

Death and Danger

The Cretan Labyrinth in Knossos, in which Theseus encountered the Minotaur, is the most famous ancient maze, one which deeply influenced cultural perceptions of the maze into the 1980s, the era of 10 PRINT. That mythical maze held the part-man, part-bull Minotaur, the cursed child of Pasiphae’s unnatural love. This early maze, like a basement or attic in more recent folklore, was the hiding place for a defective, dangerous family member, a hybrid horror. Theseus arrived at Crete and won the affection of Ariadne, the king's daughter, who offered him a means of returning from the labyrinth after he entered it to defeat the Minotaur. She suggested he tie a string to the entrance and unravel it as he proceeds through the maze so that he can follow this thread back to the entrance of the labyrinth. Theseus made his way through the maze, slew the Minotaur, and escaped thanks to Ariadne's thread. The victorious Greek hero took Ariadne with him, only to abandon him (in most tellings of the legend) on the island of Naxos.

The need for the thread to serve as a “clue” -- the word “clue” (from “clewe”) refers to the skein of yarn “employed to guide any one in ‘threading’ his way into or out of a labyrinth” (OED) -- seems to strongly suggest the false paths and complexity of a multicursal maze, with decision points and false paths to trick the walker. Yet traditional depictions and descriptions of the Cretan labyrinth suggest a unicursal, if very threatening, edifice from which nobody attempting to slay the Minotaur has returned alive. A study of allusions to and descriptions of labyrinths in Homer, Ovid, and other writers of Western antiquity provides a range of interpretations of mazes as structures and edifices, dance or ritual pathways, or representations on coins and armor (Homer’s daidala) too long to describe in any detail here. Suffice it to say the depictions of the Cretan labyrinth as a dark, complex structure (see Ovid via Doob) and the need for a pointer toward the entrance, to distinguish in from out, may suffice to explain why anyone, Greek hero or otherwise, would want to thread his way along even a unicursal path. Even an experienced programmer can benefit from a one-line thread like 10 PRINT.

In a sense, then, Theseus’s adventure at Knossos involves the metamorphosis of an effectively multicursal maze to unicursal maze, which itself reflects the change in experience from challenging, mysterious, threatening, and deadly to easy, known, reasonable, and tamed. It also illustrates how some puzzles have sequential solutions: it was not enough for Theseus to kill the Minotaur; he had to find an exit from the labyrinth afterwards. The story of Hansel and Gretel shows that bread crumbs don’t always solve the problem of finding one's way back home; they may not have solved the Cretan problem. Finally, this original labyrinthine myth reflects the reality of many puzzles: when the solution is known, the puzzle seems simpler if not trivial. The pleasure of finding one more, perhaps more efficient, effortless, more elegant, or faster solution can compel players to continue working at puzzles, however. The morphing of the maze from complex to simple (or at least understandable) is part of the Commodore 64 user's ideal encounter with 10 PRINT, and it is what allows this puzzle to lead on to other explorations and different routes.

An interesting aspect of the early maze of Knossos is that legend celebrates not merely the man and woman who overcame it but also the one who devised it. Daedalus was the artful architect of confusion and master designer of the labyrinth at Knossos, and has consequently one a place of honor as puzzle-maker supreme: Genre fiction and Joyce both nod to him, for instance. Daedalus was the first in a long and living history of maze designers and programmers to understand that planning, intentionality, and construction are integral characteristics of the mystique of the maze. 10 PRINT is culturally resonant because it is a blueprint for a maze and a system for constructing a maze, not just a structure or image that appears without any history or trace of its making. And yet it presents a maze without an architect, or rather in 10 PRINT, the process itself becomes the producer. Such a transformation will have larger ramifications for the study of programming culture where the cult of the author, though arguably persisting in the study of algorithms, is eclipsed by the potential for any programmer to become a Daedalus on his or her own.

This equation of the maze with danger and horror would continue to haunt the form even in contemporary film. A snowed-over hedge maze, for example, adds to the horror hiding within "The Shining" (1980). Also in the '80s as adolescent boys and girls busied themselves with 24-sided dice playing Dungeons and Dragons, a made-for-TV movie, Mazes and Monsters (1982), presented Tom Hanks as a young man who had gone over the edge into a psychosis where he could no longer separate his role-playing game from reality. The movie spoke to both the moral panic around Dungeons & Dragons and underscored the popular conceptual relationship between mazes and dungeons. More importantly, it suggested that an (evidently) harmless maze within a game could become the threatening and potentially fatal maze that, in legend, Theseus faced.

It is not actually known whether the labyrinth in Knossos was real or mythology; no ruins of the edifice remain. Yet the telling of this myth includes a pattern that, as Matthews notes, became convention over the centuries:

Starting from the exterior, the "path" runs inwards a short distance, turns so as to run parallel with the other wall until nearly a full circuit has been completed, then doubles back on itself and runs round in the opposite direction, doubles upon itself again, and so on until it finally comes to a stop in a blind end, having traversed all of the space within the outer walls without covering any part twice and without forming any branches or loops. (45).

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In this way, 10 PRINT does not put the user in the role of clever Ariadne, heroic Theseus, or the hunted maze inhabitant, the Minotaur. Rather, the programmer becomes an apprentice to Daedalus. Initially, as the user types the program in and runs it without much of an idea of what it will do or why, the user is simply shoveling characters from page to screen like an enslaved Cretan brought on to build a maze. But as the user traces the path of the program and resolves its many twists into an understanding, a solution of sorts, 10 PRINT offers the person at the Commodore 64 the opportunity to collaborate with Daedalus and to fashion new mazes.

Ritual and Allegory

The associations evoked by 10 PRINT may begin with the Minotaur's maze, but they continue through history, adding to the complex symbology and sacred rites of Christian churches and then rising in the turf and hedges of the countryside. Mazes take on religious import on the floors of cathedrals and basilicas, which are themselves already highly allegorical spaces, with the earliest appearing in the Basilica of Saint Reparata (Algiers) in 324 CE. Among the most famous and one of the largest (approx. 12.3 m) church labyrinths is at Chartres (ca. 1200 CE). It is a walkable 11-circuit labyrinth ornamented around its outer-ring with “lunations” (Kern 153). Called “Domus Daedali” (The House of Daedalus) it has been the object of endless speculation, from rumors of treasure buried under its center to its functioning as a lunar calculator. No wonder, since mazes and labyrinths, as loci of convoluted meaning, consistently invite decoding and interpretation.

Church mazes tend to be labyrinths to be walked or crawled on the path to penance, allegorical pathways with names like Labyrinth of Sin, The Path to Redemption, Easter Dance, Images of a Worldview, and The Path to Jerusalem. These walkable pathways symbolized paths to Christian salvation, telling not a Minoan mystery but a Paschal one. Their entrances typically face the western wall of the church on which scenes of The Last Judgment are depicted. As with a rosary and the stations of the cross, the Christian labyrinth is unicursal. None contained dead-ends or choice points until the 15th century, when the multicursal aberration appears, as Helmut Birkhan explains, as a "symptom of the secularization of the labyrinth idea" (quoted in Kern 146).

With this secular turn, the maze became a space of leisure as well as ritual, and was lined with hedges, marked by rocks, and surrounded by grooves. Church-like mazes and mazes that invite a ritual attitude surfaced on the turf of Europe, although several of these were more related to pagan rites of spring than to Christianity. In A Midsummer Night’s Dream, the faerie queen, Titania, ponders the ghostly outlines of abandoned turf mazes:

The nine men's morris is fill'd up with mud,
And the quaint mazes in the wanton green
For lack of tread are undistinguishable. (2.1.98-100)

As more and more pagan and secular mazes emerged alongside church and other labyrinth traditions, they retained some of their profound, sacred nature while also offering puzzle-play and leisure.

The introduction of hedge mazes, in particular, is noteworthy, for they have characteristics also found in 10 PRINT. Like all mazes, hedge mazes need to be planned and plotted, but unlike most other mazes, they grow to fulfill their plan. 10 PRINT's maze does as well, albeit in a different way: Once seeded, the computer-generated maze requires none of the tending and nurturing the hedge mazes need, growing until the viewer interrupts it. It's also resonant that among the many ways of experiencing hedge mazes, the most exhilarating is “running” the maze. This way of encountering the maze was carried into video games such as Doom and Pac-Man In a different way, the cascading display that results from running 10 PRINT offers some of the playful zig-zagging of the side-to-side motion of children gamboling through the hedges. Of hedge mazes facilitating this sort of play, a particularly famous one is that of the Hampton Court Palace in London. The Daedalus of this maze has been said to be Christopher Wren, though the maze may date back to the time of Cardinal Thomas Wolsey, the palace's first occupant (Kern 261). Miller writes of its roughly half-mile of path: "It may be a sad sight to the 'highbrows' of horticulture, but to the unsophisticated many it is a never-failing source of merriment" (129). He describes the maze as an "undiluted delight" to "scores of hundred of children, not to mention a fair sprinkling of their elders" (129).

As a running display, 10 PRINT retains a dimension of mystery, baffling the viewer with its playful invitation to follow its paths with the eye. 10 PRINT offers no path to religious practice, but the association of mazes and mysterious rituals does attend the later use of the program. As code, 10 PRINT taps into the maze-like mystery that visual symbols evoke: to type in a program from a manual is to follow the twisted line from code to output and back again. The programmer follows the single path of the code from ignorance to knowledge, a pilgrim's path. 10 PRINT may not help programmers attain Christian salvation or welcome the pagan coming of Spring, but it does offer an accessible means by which novice programmers can trace the steps of writing code and being initiated into the mysteries of a magic box, the personal computer.

While Mazes have been rendered in stone, hedge, and turf, mazes do not require high, mossy walls or lines drawn on marble. Dancers have created the pathways of mazes through their movements since the earliest tales of Theseus. Dancers weave their steps and movements in space and through time and, in so doing, create an invisible fabric in and of space. The oeuvre of the choreographer, the Daedalus of dance, plays out on the dance floor through sequences of dancers’ steps. These maze dances have followed a similar trajectory through ancient myth, Christian and pagan rituals, and secular cultural expression in art.

In The Iliad, Homer credits Daedalus both with a dance floor and the labyrinth. Kern speculates that labyrinth was a choros, which has the double meaning of dance and dance surface. Since no labyrinthine building in Crete survives, the depictions of labyrinths on coins may indicate the path of the dance rather than an architected structure. Though the Cretan labyrinth did not survive into the present, the maze dances based on it have. Theseus met the Minotaur in a Minoan maze, but he and his men immortalized that adventure in dance on the way back from their mission. As Miller explains, "on the island of Delos they performed a peculiar dance called the Geranos, or 'Crane Dane,' in which they went through the motions of threading the Labyrinth, and ... this dance was perpetuated by the natives of that island until fairly recently" (19). These dances have continued to be performed in Italy, Corfu, Munich, Upper Bavaria, and as far from Greece as the Molucca Islands.

The Crane Dance is just one of many ancient labyrinthine dances. Several Roman writers, including Virgil, Suetonius, and Tacitus, recount a "Game of Troy" or simply "Troja", which is described sometimes as a ritual around a grave site and at other times as a kind of formal demonstration performed by youths, perhaps a sort of military review. Other labyrinthine dances appear as part of an exclusion right, in which "movements ....are intended to weave a magical entanglement and spread a field of magical force to exclude all that is not wanted to enter the guarded place" (Knight qtd. in Bord)". Still more appear to be tied to rites of spring.

In the Twentieth Century, Martha Graham adapted the motifs of the Cretan maze story in “Errand into a Maze” (1949). In this adaptation, Ariadne is the one tapped by the minotaur. After contemplating her escape from the labyrinth represented by a rope on the floor, as Roberta E. Zlokower notes, “she breaks her pattern and breaks her tormentor. The maze of rope reflects the maze of her mind and the maze of the myth ...”

Early on, the maze may have been one of the locations in which the dance was performed (Bord 13). However, more than likely the labyrinth is produced by the movement of the dancers. Kern notes that a consistent feature of Games of Troy is the demarcation of inside and outside. It is as if we can see through the walls to Theseus on his way through the Cretan trap. As a result, rather than a set of walls or lines, "maze" names a series of constraints to movement, a set of paths to be traversed, a procedure.

In the sense of labyrinth as a set of constrained enacted movements, another connection with 10 PRINT arises as the programmer becomes dancer. The novice programmer prepares to face the minotaur Commodore 64, offspring of the Commodore PET (half-companion, half-machine), with only one line of code as a clue leading to safety. Treading that line across the keyboard, the techno-Theseus travels safely through the convolutions of code by staying true to each symbol. Though that ritual seems to produce an aporia, the careful adherence to the path ultimately leads to mastery. At the same time, like the maze dance, it is in tracing this labyrinth, that its very corridors are created -- daunting hallways where PETSCII numbers obfuscate graphical elements and a simple loop conceals an endless string of instructions. To type the precious few characters of 10 PRINT and then to be amazed by its output is to participate in the creation of that wonder, to enact that dance that establishes the maze. It is in typing the line and executing the code that the programmer comes into contact with the mystery of concision in code and will thereafter be even more tantalized by the opportunity to build such a clever maze.

The maze dance has not been forgotten in digital media. It may seem odd to think of Dance Dance Revolution as a maze game, but its arrows do show a labyrinthine path that the dancer, standing in place, is supposed to navigate. Missing a step is allowed, but the perfect performance will be as ritualized a motion through space as a Pac Man pattern. Diana Slattery has created a work called The Maze Game that brings together the maze as a site of meaningful dance. In her digital work and companion novel, moving through a lethal maze takes grace and “literacy,” since the maze is constructed out of glyphs from Slattery’s created visual language “glide.” Slattery’s work stands at the intersection of dance, maze, and narrative, but it is in figuring the maze as an utterance of a language that her work offers the most evocative exploration of mazes as semiotic systems in which communication and literacy are dependent on navigation. In its own way, 10 PRINT also functions at this juncture, a means of evoking literacy by compelling the user, learning to program, to trace the path of its execution and determine how it accomplishes its effect.

Maze in dance illuminates the relationship between the unicursal path of a program and the multicursal possibilities for programmers. The choreographer’s multi-dimensional vision is invoked, interpreted, and performed by bodies in motion through space. The canvas takes shape in world where there are many choices about how to move; the dancers on stage, in performance, run through this world from beginning to end as though moving through a unicursal, fully plotted path. The labyrinth becomes multicursal for dancers when the plot thickens with improvisation.

Experimentation

The maze also has cultural resonance because of its role in behavioral research. Mazes have been used as laboratory environments for rats and mice, and as means of testing these rodents. The depiction of mazes in certain cultural productions reflects this aspect of the maze. For instance, images of rats in a maze are prominent in Alex Proyas' 1998 film Dark City. Dr. Schreber, a captive human who works with his alien captors, is shown looking down on a rat in a large, intricate maze; the rat and the maze connect figuratively to the people in the film and the titular city, which is constructed for the purpose of an experiment. In Daniel Keyes' novel Flowers for Algernon (1966; first published as a short story in 1959), a white mouse with augmented intelligence demonstrates its abilities by traversing a maze. Algernon parallels the novel's protagonist, Charlie, in many ways: the success of the intelligence-enhancing procedure performed on him leads to its being done to Charlie. This sort of maze has been important in less mainstream literary practices, too. The co-founder of the influential French group Oulipo, Raymond Queneau, famously described the members of this group, who set writing constraints for themselves, as "rats who build the labyrinth from which they plan to escape." The experimenter's maze can also frequently be seen in many other contexts, including advertising and cartoons.

The first maze constructed for rats by researchers was built in the late 1890s -- but, intriguingly, it was not for testing the creatures. Willard Small of Clark University built a maze environment to allow rats to eat and exercise when they weren't taking part in experiments. Small wanted the environment to simulate the burrows that rats inhabited in nature, but he modeled the first laboratory rat maze "after the Hampton Court Palace maze, a trapezoidal hedge maze that dates in its present form to 1690 but was probably built in the early sixteenth century by the first owner of the palace, Cardinal Thomas Wolsey" (Lemov 2005, p. 25). The maze was for restorative purposes quite consonant with the purposes for which the Hampton Court Palace maze was built.

But John B. Watson used maze environments for quite different purposes. He sought to determine whether rats could make their way through a maze under different conditions. Watson continued his work by systematically blinding rats and maiming them in other ways to deprive them of different senses after they had learned their way through a maze. His work attracted public attention, and he was denounced in a New York Times editorial as a torturer. Watson, however, was sure of his behavioral science agenda and that the same principles that applied to rats applied to people. By 1916 he had moved on to experiments with infants. In a 1920 experiment that became famous he conditioned one baby, "Little Albert," to fear a furry white rat and furry white things in general. The use of mazes in experiments with rats increased greatly during the 1920s. We now associate behaviorism, the perspective that all animal and human actions are behaviors, mainly with another American scientist, B. F. Skinner. Skinner's operant conditioning chamber, also known as the Skinner box, is another famous environment for laboratory animals that was built decades after Watson's mazes. While Skinner's name is better known today, Watson's maze remains emblematic -- and similar environments are still used for experiments today.

In 1959, one of the earliest computer programs written for fun - an example of "recreational computing" - depicted an experimenter's maze. The program, which is possibly the first computer program to draw a maze of any sort, was written for the TX-0 at MIT by Douglas T. Ross and John E. Ward. The TX-0 was an experimental computer that, when loaned out from MIT's Lincoln Laboratories, provided one of the first opportunities for people to program when not working on an official project. It also allowed programmers to work on the machine interactively, much as Commodore 64 programmers later would, rather than submitting batch jobs in the form of decks of punched cards. In the program that became known as "Mouse in the Maze," a mouse would move through a maze, eating cheese. The mouse could also consume martinis, which would cause it to become disoriented. Here, the environment implemented was not the hedge maze of diversion and fun, but a more staid experimenter's maze. This was then made playful by the implementation of an amusing reward for the mouse and the simulation of appropriate behavior.

10 PRINT's output is a regular arrangement of "walls" in a grid -- akin to the arrangement of the stereotypical laboratory maze. Instead of suggesting that the computer is creating structures or drawings for pure amusement, the idea of the laboratory maze offers a concept that is more serious and scientific. It also brings in the idea of the experimenter -- indifferent to the struggles of the creatures lost in the maze, at least, and perhaps cruelly impairing those creatures -- and the subject of the experiment, trapped in a bewildering structure created by powers and for purposes beyond comprehension.

When 10 PRINT runs, it relentlessly provides a maze, but it does not not trap the user in it like a rat. Instead, given the top-down view and the lack of a user-controlled maze walker, the computer may be offering to collaborate with the user in experimenting on virtual rats. This would be a different suggestion than the cinematic, literary, and cartoon representation of behavioral science mazes that encourage people to identify with the rat or mouse. In any case, amid the playful and religious connotations of the maze are those things the experimenter's maze hints at: That the computer is a scientific instrument, for instance, and that the recent history of science has certain dark corners.

Claude Shannon's Theseus

In the early 1950s the mathematician and engineer Claude Shannon designed a mechanical mouse that appeared to solve the same kind of maze a real mouse might be have been expected to navigate in one of Watson’s behavioral experiments. A foundational figure in modern computing, Shannon named the mouse Theseus, after that mythological explorer of the Cretan labyrinth. Featured in both Time and Life in 1952, Theseus was not a sophisticated piece of artificial intelligence, however. It was simply a wooden mouse on wheels, with a bar magnet inside and copper wire whiskers. The true magic of this mouse resided underneath the maze, in a system of electronic relays that switched position when the mouse’s whiskers touched corresponding walls in the maze above. The first time through a maze, Theseus blundered randomly, propelled by its magnet, flipping the relays underneath the maze whenever it encountered a passage. The next time, Theseus would navigate the maze perfectly, thanks to the relays underneath, which recorded the correct route. This means of negotiating the twisting passages of Shannon’s maze was not mere novelty. As Time explained in 1952, Theseus was “useful in studying telephone switching systems, which are very like labyrinths.” Indeed, George Dyson argues that Theseus inspired the RAND Corporation engineer Paul Baran’s “adaptive message block switching” — the precursor to what is now known as packet switching, the protocol that defines the way data flows on the Internet (150).

Aside from its significance to network computing, Theseus serves as a vivid example of an early connection between mazes and computers. Furthermore, Theseus shares a procedural resonance with 10 PRINT. Theseus “learned” through a repetitive process the fundamental process that draws the 10 PRINT maze. And like a computer program, the mouse in Shannon’s maze was only the surface level signifier of much deeper processes. Theseus in fact was dumb, inert. The “brain” of Theseus lay in the relays hidden underneath the surface of the maze, much in the same way the on-screen design of 10 PRINT is generated by an piece of code, initially not very clear, which depends upon an invisible, low-level call to generate pseudo-random numbers.

“Better Mouse: A Robot Rodent Masters Mazes.” Life, July 28, 1952.

Dyson, George. Darwin among the Machines: The Evolution of Global Intelligence. Da Capo Press, 1998.

“Mouse with a Memory.” Time, May 19, 1952.

The Computerized Maze

A clear line can be drawn from the physical and visual mazes of earlier times to the mazes of the digital age. It is here, in the computer culture that has arisen in the past thirty years, that mazes once again become part of daily life. With the arrival of the computer in the 1960s and graphical displays in the 1970s, the maze has entered a kind of renaissance. There are two important developments that contributed to the prevalence of the maze as a cultural production: (1) the ability to easily generate complete maze-like structures on a screen or, with older computers, printed output; and (2) the appearance of procedural mazes, that is, mazes traversed not through physically walking through space nor through tracing a pencil on a page, but through navigating representations of convoluted virtual space that are generated by mathematical algorithm.

It would be a mistake to assume that all computer and video game mazes operate according to the same principles. A useful way to think about the differences between various digital mazes is to consider the perspective each maze affords—and which consequently structures the encounter with the maze. Roughly speaking, it is possible to conceive of mazes as first-person, second-person, or third-person mazes, a framework with roots in narratology but which has also been commonly applied to videogames (for example, the first-person-shooter):

• First-person mazes are partially represented mazes, in which the maze walker is confronted with a subjective perspective of the maze; nothing can be seen of the maze except the wall or passageway directly in front of the maze walker;
• Second-person mazes are textually represented mazes, in which the maze walker is hailed by a second-person mode of address (“you”), and is fully at the mercy of the textual descriptions on the screen; nothing about the maze can be known unless “you” are told it;
• Third-person mazes are fully represented mazes, in which the maze walker maintains an omniscient view of the maze, a panoptic perspective that nonetheless does not guarantee safety or solvability.

First Person Mazes

Early on, Maze and Mazewar presented a first-person view of a confusing environment. ...

Second Person Mazes

While third-person mazes—such as the Pac-Man play field—might seem to be the most "maze-like," because the maze is fully present, fully visible from the outset, the earliest procedural mazes were most often second-person mazes. These second-person mazes were found in early text-based adventure games, now known as interactive fiction. Mazes in these games were not symmetrical spaces to navigate so much as puzzles to solve, non-Euclidean space represented textually.

The genre began with the groundbreaking Adventure, written by Will Crowther for the PDP-10 mainframe in 1977 and expanded shortly after by Don Woods into a full-fledged underground adventure. Basing the game in part on his own caving experience in the Mammoth Cave system, Crowther included in Adventure a ten-room "MAZE OF TWISTY LITTLE PASSAGES, ALL ALIKE." Woods would go on to add a second maze, this time "TWISTY LITTLE PASSAGES, ALL DIFFERENT" (Jerz 2007, 23, capitalized as found in the original source code). This phrase "twisty little passages" has become shorthand for interactive fiction in general, for gamers and scholars alike (see, for instance Montfort's Twisty Little Passages); the phrase abbreviates the sentence that appears when one is playing Adventure:

   YOU ARE IN A MAZE OF TWISTY LITTLE PASSAGES, ALL ALIKE.

The mode of address here—“YOU”—is as important to the game as the cryptic description of the maze that follows. Interactive fiction is one of the few literary genres to consistently use second person narration. Second person narration in interactive fiction closely resembles what Brian Richardson calls the “autotelic” mode of second person address. The autotelic form is distinct from both the “standard” second person found in literature, in which the protagonist is known as “you” instead of “I,” “he,” or “she,” as well as distinct from what Richardson calls the “hypothetical” or “subjunctive” form, in which the narration reads like a guidebook or recipe book (2006, 18). The very Commodore 64 manual that introduces the 10 PRINT maze employs this subjunctive second-person form, telling readers, “Congratulations, on your purchase of one of the best computers in the world. You are now the proud owner of the COMMODORE 64....The Commodore 64 USER’S GUIDE is designed to give you all the information you need to properly set up your equipment, get acquainted with operating the COMMODORE 64, and give you a simple, fun start at learning to make your own programs” (vii).

Unlike the subjunctive, didactic form or the standard, novelistic form of the second-person, the autotelic "you" is not a stable pronoun. Its referent shifts seamlessly between an imagined diegetic "you" and an extradiegetic reader. As Richardson explains, the autotelic form is a "direct address to a 'you' that is at times the actual reader of the the text and whose story is juxtaposed to and can merge with the characters of the fiction" (30). This shifting is evident in an interactive fiction game like Adventure, as the game alternates between addressing the adventurer within the game and the player sitting in front of a keyboard, using "you" in both cases. For example, when Adventure tells the player toward the beginning of the game, "IF YOU PREFER, SIMPLY TYPE W RATHER THAN WEST," the game acknowledges the extradiegetic "you." And without interruption the game shifts back toward addressing the in-game adventurer.

The autotelic second person is "alternately opposed to and fused with the reader" (33), which in the case of Adventure means that the "you" shifts from adventurer, to player, to reader. Richardson suggests that the instability inherent in the autotelic "you" is particularly effective at "revealing a mind in flux" (35). It is a mode of address, then, that is particularly suited for interactive fiction, in which so many of the early games centered upon being lost—and more to the point, lost in a maze. The instable "you" of the games matches the instability of the narrative itself.

Players frequently solved textual second-person mazes by mapping them, generating secondary visual mazes. The manual to the Apple II version of Zork, the famous "prose adventure" game directly inspired by Adventure even told players (using a subjunctive second-person form), "It is essential that you draw a map. Some of the problems in the game (the Maze in ZORK I, for one example), cannot be solved without mapping" (Infocom 1981, 5). The maze in the game requires a map of the maze outside the game: Maze begets maze.

Third-Person Mazes

What's most remarkable about these user-designed maps of mazes in Adventure and Zork is that they transform textually represented second-person mazes into fully-represented third-person mazes. Such maps convey a sense of mastery of the maze, but as noted above, third-person mazes do not guarantee safety or solubility. Perhaps it is this paradox—the pretense of mastery undercut by the promise of difficulty—that makes third-person mazes the most common in computer culture. In fact, one is tempted to pin the advent of maze craze to the release of Pac-Man in the U.S. in October 1980, followed by Ms. Pac-Man in 1981, and the popular (though problematic) subsequent ports of those games to the Atari VCS in early 1982 (Pac-Man) and late 1982 (Ms. Pac-Man). Pac-Man appeared on the Commodore 64 itself in 1983. It was standard to recognize the Pac-Man playing field as a maze: The New York Times called Pac-Man "a circle with a big mouth that eats up dots in a maze while other big mouths try to eat it up" (Latham 1981), while Newsweek mentioned the "maddening Pac-Man maze" (Langway 1981). But even before they hit the mainstream in Pac-Man, mazes were a staple of computer culture, and on-screen maze-like structures abound [1] in the early days of video arcades and home computers.

Procedural mazes are mazes in which the entire structure of the maze does not coherently exist in physical or visual space. The maze resides in code. Or rather, the potential of the maze resides in code. Only a portion of the maze is ever available to be traversed at any given time; the rest remains to be generated by algorithms. There are two types of procedural mazes found in the 1970s and 1980s: textual and visual.

The 10 PRINT program's output is a visual, procedural maze; an on-screen maze generated by an algorithm.

It would simply be impossible to use the word "maze" within the semiotic domain of computers and without recalling these games to some extent. The various sources from the early eighties that called the 10 PRINT output a "maze" tapped into a cultural history of mazes that home programmers and game players would be aware of.

Computer Generated Mazes

Clifford Pickover wries of "the largest computer-generated maze in the world," a designation which seems quaint today. Although he notes the program could generate an 1000-page maze, he cites the largest one she had printed to date as a 200-page maze. However, he gives the title to the 1987 maze produced by Walter Pullen. This 23-foot maze had to be stored on "eight floppy disks" and "require one megabyte of disk space" (7). In a note, Pickover mentions a maze Pullen had generated with "@2 miles of passages" that "stretched over 3031 pages" (8).

Some formulation of Moore's Law, which in its first formulation describes how the number of transistors on a chip doubes every 18 months, could surely apply to describe the continual increase in the area of single-solution computer-generated mazes. In the more general space of convoluted structures, solvable or not, the quest for the largest computer-generated maze will always be chasing 10 PRINT, whose never-ending corridors can be drawn with a one-line reductio ad absurdum.

Context of Expectations: Computer Graphics and Games

The representation of mazes in computer graphics was already a staple during the period that finds the 10 PRINT BASIC one-liner appearing in C64 manuals and journals -- in fact, the use of computers to represent mazes conceptually was common even before the advent of home computer graphics.

Gotcha (1973 arcade) a game of tag between two players in a maze-like field of partitions

The Amazing Maze Game (1976 arcade) -- a classic maze

Maze Craze (1978 Atari VCS) -- a large set of games -- complete, race-to-complete, tag, etc. -- all played within classic mazes.

In graphical computer games, one common feature of the many different 2D maze video games from the period is orientation: all are rectilinear and aligned to the Cartesian axes, rather than being diagonal. This similarity, it turns out, constitutes the category -- in fact, it is even more important than the degree to which given games are maze-like, or what impact their maze-ness has on gameplay. Different games have different maze aesthetics. The arcade game Gotcha (1973) stages a game of tag between two players in a maze-like field of disconnected partitions which served as an obstacle course. Conversely, the arcade game The Amazing Maze Game (1976) implements a race (two-player or against a computer) to solve a classic continuous closed maze. A similar implementation on the home Atari VCS, Maze Craze (1978) provides a playable random maze generator as the field for a very a large number of games, including races and tag, and includes modes with invisible walls where the maze must be interactively felt out and remembered.

Pac-Man (1982 Atari VCS)

Pac-Man (1980) is perhaps the most famous classic maze-like arcade game, although, like Gotcha, it is less a maze than a free-form obstacle course, using the free-floating wall partitions to complicate the game of tag rather than obfuscating any path to escape. When Pac-Man was reimplemented for the Atari VCS in 1982, the vertical field was redesigned in horizontal format and for a lower resolution display; the essential topology of the game (partitions, looped corners, and warp gates connecting one side to the other) remained the same.

Another feature shared by all these games (both arcade and for home video game consoles) is their treatment of the screen display as a single complete visual unit, like the board of a board game. An interesting contrast to this aesthetic is a close-up design that puts the player in the maze, the Atari VCS game Adventure (1979) implements a maze as a series of many close-up screens. Adventure was extremely loosely based on the interactive fiction work of the same name, and featured a hero with a sword collecting treasures despite the efforts of four dragons. Unlike Pac-Man, in which the player can guide Pac-Man out a warp gate on one side of the screen and see him enter on the other side, Adventure contains numerous topologically impossible warps that are always hidden from view, and can only be deduced. Instead of an overview map of the total maze, each screen is a claustrophobic close-up of simple paths, often emphasizing discontinuous fragments of other paths that can't easily be reached. This kind of claustrophobic, discontinuous maze-space was later further explored in Haunted House (1981), particularly in the use of darkness and the addition of keys in some modes to restrict and sequence room access.

Isometric Games

Ant Attack (1983 ZX Spectrum)

Whether close up or distant, continuous mazes or partitioned obstacle courses, what all these period maze-games have in common is that, unlike the diagonal orientation of 10 Print, all are constructed of horizontal/vertical walls that are orthogonal to the edges of the screen and the scan line of the display.

Diagonal orientation did have a place in the design of early maze-like games, but not in simple 2D fields -- instead, it emerged through isometric video games that introduced diagonal motion at the same time it challenged the picture plane through the pseudo-3D effect of isometric perspective. In the arcade, two isometric games emerged in 1982: Q*bert, an completion/avoidance platform on an isometric pyramid, and Zaxxon, an obstacle-racer emphasizing pseudo-3D elements. Neither of these game designs is particularly maze-like.

Later games did incorporate maze-like obstacle elements into isometric gameplay. Part of this limitation was due to available resolution at the time, particularly on home systems. Graphics with isometric effects took up a lot of space, which limited the ability to design large complex level structures like mazes on a unified field. Thus, when Ant Attack (1983) and Marble Madness (1984) introduced isometric obstacle course elements on a large field, both did so using scrolling.** By contrast, Knight Lore (1984) follows the design pattern of Adventure for the VCS, showing a close-up view of one room at a time in a maze-like castle.

• • Ant Attack also alters the camera view when navigating behind objects.

Even here, however, we see how extremely different aesthetic of early isometric maze games was when compared to the 10 Print output. While both have a dynamic diagonal orientation, the move from 2D design to volumetric pseudo-3D space leaves them, visually, worlds apart.

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