Mazes
From Maze
The Magic of Mazes, from the Greeks to the Geeks.
10 PRINT produces a pattern that the manual calls a maze. Of course, it does not have to use the word maze. It could call it the randomly alternating pattern of diagonal lines. Although that description does capture the output of the program, it does not capture the magical power of the program to create out of a simple alternation a visual pattern recognizable as a maze. The amazing turn of this program is the clever and concise operation by which it produces a maze seemingly by the flip of a coin.
Mazes have an iconic place in the world of early computers and, of course, a much longer place in cultures around the world. They are heavily charged symbols that appear to call the viewer into entering their pathways either physically or visually.
Arguably one of the most intriguing characteristics of 10-Print is the maze-like pattern it produces. Or is this output actually a maze? The history of mazes, particularly in Western culture, does not answer that question easily. Nor does the attempt to call this a maze as distinct from a labyrinth, though the latter term seems to be sedimenting with the meaning of elaborate and twisting unicursal passageway. Calling this pattern "maze-like" raises complexities: it cannot be traversed (though Michael Mateas' program traverses it), it has no ending (though stopping the program terminates the maze drawing), it was not designed as a puzzle (though mazes are not necessarily solvable).
Nonetheless, calling this program something other than a maze generator, for example, a random-line-pattern generator, quickly drains it of at least a portion of its mystique. Mazes are bewildering puzzles, places of terror, amusements, challenges, organizing structures, and pleasing patterns. So what does it mean for a home computer in the early 1980s to display a maze in the way the 10 PRINT program does? Computers could and did display many other things. What did the maze, specifically, signify and connote? This chapter examines the role the concept of "maze" plays in making this one line program so tantalizing.
The first part of the chapter will examine the conceptual permutations of the word "maze." From ancient Greece, the legendary labyrinth of Knossos establishes the maze as terrifying and life-threatening space. Even so architectural spaces called labyrinths appeared in descriptions and ruins in Ancient Egypt. The labyrinth found its way into the spiritual centers on the floors of cathedrals. However, mazes have also served as directions for dances. Hedge-row mazes bring the maze into the realm of public shared diversion. In puzzle-books, mazes became an even more common-place diversion, one in which the depiction and the structure were conflated. In psychology the maze becomes the tool of examining behavior. In role-playing games, the maze became the structural frame of the encounters. Finally, and growing out of all of these traditions, in computer games, the maze became one of the central concepts used in the design of levels.
Consistent throughout these various concepts of maze is a sense of providing a structure (whether navigable with body, pen, or joystick) to organize or constrain a person's encounter with a space (whether by setting them on a track, offering them a puzzle, or merely deciding pathways and dead-ends).
The second part of the chapter explores the degree to which the program generates mazes and how permutations in the code can affect that status. How does, for instance, changing the thickness of the lines affect a viewer's perception of the maze? How does the single-line of code present itself as a maze for the novice programmer encountering this code in the beginner section of a manual?
The last considers the kinds of mazes produced by the program.
What is a Maze?
One objection to calling the output a maze is the lack of a solution or single correct path through this visual pattern. However, the OED lists two related senses, the first of which requires that there is *exactly* one correct path, the second of which has no such requirement. Consider the following definitions:
A labyrinth, and related senses.
- 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.
- 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. In the 16th and 17th centuries often in to tread a maze, perh. with allusion to sense
There are quotations for the second of these senses from 1531 to 1994, including:
1542 H. BRINKELOW Lamentacion sig. Cviii, Leadyng them in an endlesse Maze of dyrtye tradicyons and folish ceremonyes.
So, there is an early occurrence of a maze which presumably (being endless) has no correct path through it ... and furthermore, it is endless.
The relevant definition from the 1913 Webster's Revised Unabridged Dictionary is:
perplexed with error. Addison. Syn. -- Labyrinth; intricacy. See Labyrinth. Again, nothing there requires that the maze have a solution.
- A confusing and baffling network, as of paths or passages; an intricacy; a labyrinth. Quaint mazes on the wanton green." Shakespeare.
- Or down the tempting maze of Shawford brook. Wordsworth.
- The ways of Heaven are dark and intricate, Puzzled with mazes, and
Nothing in these definitions requires mazes to have a solutions.
Certainly all of the definitions of maze attend the perception of this particular program, but these definitions demonstrate that the output does qualify as a maze. But what if one wanted to insist on the strictest possible view of the constructed puzzle-maze with a single solution, denying that the output of this program is a maze at every moment? Even then, what could the output possibly suggest, what could it evoke in the viewer, if not the concept of the maze? 10 PRINT is a maze-generator, but even if there are some who deny this, they will have to grant that it is a program that is associated with and falls under the shroud of the myths of mazes and labyrinths.
History of Mazes:
Scholars of mazes distinguish the labyrinth as unicursal, offering no choices to one traversing it. Hermann Kern has written the book on labyrinths in his Labyrinthe, Erscheinungsformen und Deutungen 5000 Jahre Gegenwart eines Urbilds, later published in English as Through the Labyrinth: Designs and Meaning over 5,000 Years. However, unlike the more general category of mazes, a labyrinth is “almost completely enclosed by an outerline” and their paths “are not intersected by other paths” (23). Nonetheless, the history of labyrinths is an essential part of the overall mythos of the maze.
When a labyrinth or maze is the visual representation of a dance, it becomes a kind of score or perhaps even a script or program. However, the movements themselves could be said to be the labyrinth enacted in space over time.
Labyrinths can thus be the boundaries of the space to be navigated or the path that is followed. In the latter sense, the labyrinth may be not just the plan of the path but the path in motion across time. In the case of a solvable maze, the solution path is obfuscated by choice points. The pattern presents not the predetermined path but the challenge toward finding that path. However, once that path is known, the maze becomes changed into the solvable path encompassed by wrong turns. Like the labyrinth, it now has one path to its solution and it can no longer be a maze.
This has important implications for how the notion is abstracted and how 10 PRINT itself (not its output) becomes a maze and a labyrinth. Typing in the program, the beginning programmer engages in the ritual. At the same time, the program begins as a maze to the initiated. Unless the programmer is already fluent in C64 Basic and has memorized the PETSCII tables, she is unlikely to recognize the effects of the program. Once the code has been typed in and executed and the programmer sees the maze, there is no returning to the previous status of the line. This is similar to the process of becoming literate, but not exactly. Nonetheless, these are not mazes that have single solutions. When the programmer is encouraged to make changes to the code, new corridors appear, and the maze itself proves to be endless.
Ancient and Mythological Mazes
Of course, the most famous maze is the Cretan Labyrinth, where Theseus slew the Minotaur, finding his way with the help of Ariadne's string.
The Cretan Labyrinth in which Theseus encounters the Minotaur offers perhaps the most famous ancient maze, through which the Ancient Greek hero found his way only with the help of Ariadne’s thread. While such necessity suggests that the structure was a maze, having multiple decision points, early depictions of the structure were labyrinthine, in other words, monocursal. Why would anyone, Greek hero or no, need a string to find their way through a labyrinth, a unicursal twisted passageway without deadends or choices? And yet that is exactly the kind of maze depicted in most of the ancient imagery. Regardless of the depictions, the myth portrays a space of twisting paths that is difficult to navigate, and it establishes the challenge of path-finding puzzle in Western culture.
Plutarch includes in his lives the myth of the labyrinth of Knossos, designed by Daedalus. In the story, in payment for the slaying of his son Angrogeos by the Athenians, Minos required the Athenians send as a tribute to Crete seven men and women who met their fate, whether slain by the Minotaru or "wandering the labyrinth, and finding no possible means of getting out, they miserably ended their lives there" (excerpted in Kern 41). The Minotaur, part man, part bull, was the merciless monster of the maze. Actually, this is merely one of the main competing stories Plutarch recounts.
Theseus set off to end the bloody tribute, by serving as one of the seven. When he arrives at Crete, he wins the affection of Ariadne, the king's daughter, who offers him a technique for defeating the labyrinth by tying a string to the entrance and unraveling it as he proceeded through the maze. Theseus makes his way through the maze, slays the Minotaur, and follows the string back to the entrance. The victorious Greek hero takes Ariadne back with him to Athens.
The Cretan maze may have its origins in Egypt, where Herodotus describes a labyrinthine building: [I won’t be using all of this]
It has twelve covered courts - six in a row facing north, six south - the gates of the one range exactly fronting the gates of the other. Inside, the building is of two stories and contains three thousand rooms, of which half are underground, and the other half directly above them. I was taken through the rooms in the upper storey, so what I shall say of them is from my own observation, but the underground ones I can speak of only from report, because the Egyptians in charge refused to let me see them, as they contain the tombs of the kings who built the labyrinth, and also the tombs of the sacred crocodiles. The upper rooms, on the contrary, I did actually see, and it is hard to believe that they are the work of men; the baffling and intricate passages from room to room and from court to court were an endless wonder to me, as we passed from a courtyard into rooms, from rooms into galleries, from galleries into more rooms and thence into yet more courtyards. The roof of every chamber, courtyard, and gallery is, like the walls, of stone. The walls are covered with carved figures, and each court is exquisitely built of white marble and surrounded by a colonnade.
Kern doubts whether this was the building at all and suggests that the labyrinth of Knossos alludes to a dance, a topic for later discussion.
However, the depiction of this myth include a pattern that as Miller notes has been "conventionalized:
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).
Miller notes that this labyrinth is not a "puzzle." Nonetheless, it appears on coins, walls, and other ancient surfaces including some graffiti scratched on a pillar in Pompeii.
(how this ties to our maze) So while the location or shape of this mythical maze becomes a grail quest, the labyrinth becomes the icon of the story of the maze and the two concepts become entangled. Mazes and labyrinths become places of beastial horror, puzzles that require the collusion of paramours. Mazes become elevated into the pantheon of heroic challenges, literally the stuff of legends. Without a doubt, this mythological status has fueled the search for physical mazes and labyrinths from antiquity to the present.
Other Egyptian Labyrinths date back to 3400 BCE and a labyrinth in the tomb of King Perabsen of the Second Dynasty. In her book, Mazes and Labyrinths of the World, Janet Bord examines appearances of maze in other parts of the globe. For example, she mentions the “long barrows, megalyths, camps and henges of Britain and north-west Europe” as signs that these sorts of patterns, labyrinthine or mazelike, were “not in the first instance diffuse outward from an original birthplace, but developed independently in more than one area” (10). The search for the antecedent to the physical mazes perhaps is the wrong path to pursue. The history of mazes should not start with the earliest mention or depiction of mazes but with the formulation of walled architecture or social spaces with intersecting passages… Furthermore cave structures, for example, the paths modeled in Adventure, offer naturally occurring mazes (more on that in a moment)
Mazes and Labyrinths, however, are not associated only with their physical structures or two-dimensional forms; They can also be patterns of physical movements. In other words, pathways. Dance executions of mazes have been and continue to be performed as areas, such as Italy, Corfu, Munich, Upper Bavaria. There is the Geranos (Crane) dance performed by Theseus performed on Delos. Another commemorates the killing of Hainuwele (divine maiden) on one of the Molucca Islands.
Mazes in Dance
Mazes in Religion
Mazes also have a tendency to turn up in Christian houses of worship, specifically in Italy and France. The earliest labyrinth shows up in the Basilica of Saint Reparata (Algiers) in 324 CE and they continue to be included through today.
These mazes tended to be labyrinths, meant to be walked or crawled on the path to penance. They did not contain dead ends or choice points, until the 15th century, when the aberration appeared as Helmut Birkhan explains, as a "symptom of the secularization of the labyrinth idea" (quoted in Kern 146). The entrances of these labyrinths tended to face the western wall of the church on which scenes of The Last Judgment would be depicted. Thus, these walkable pathways become linked with the idea of the path to Christian salvation.
Labyrinth of Sin The Path to Redemption Easter Dance Images of a Worldview The Path to Jerusalem Maison Dedalus.
Arguably the most famous and largest (approx. 12.3 m) church labyrinth appears in Chartres, and its dimensions have a curious relationship to its symbology. (Kern 153)
Note: Maze as path to be followed as haptic prayer ritual, as allegorical path.
- Note Kern's section on Easter Dance
Mazes in Mass Media
According to Clifford Pickover, the first major maze movie was aptly called The Maze, a 1953 horror film directed by William Cameron Menzies. The maze in the film was the hedgerow kind, like the snowed-under maze of The Shining. Pickover adds Labyrinth and The Man in the Maze to his list movie mazes.
In the 1980s around the time of these early video games, a made-for-TV movie, Mazes and Monsters, presented a young 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. Such a movie spoke to both the moral panic around the rpg Dungeons and Dragons and the relationship between that game and the maze motif.
In these examples, the maze becomes a metaphor of horror and confusion. It is the site for getting lost as opposed to a contrived riddle to be solved.
Computer Generated Mazes
Pickover also includes a section on "the largest computer-generated maze in the world," a title which seems quaint by today's standards. 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). Pickover later adds an followup note from Pullen about a maze he had generated with "@2 miles of passages" that "stretched over 3031 pages" (8).
Needless to say, this quest for the largest computer-generated maze will always be chasing 10 PRINT, whose never ending corridors can be drawn merely by executing and repeating that line. These other mazes, such as Pullen's, are single-solution mazes. However, Moore's law no doubt affects maze production at about the same rate that 1 megabyte diminishes as a sign of large memory and the number of pages in a maze print out approaches absurdity.
