Mazes

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.

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.

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: 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.

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 her (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 a 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.

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

<blockquote>

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). </blockquote> [Image]

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.

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 representations 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).

=== Bibliography ===

----

“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.

Scraps: