Mazes
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===Mazes in Mathematics=== | ===Mazes in Mathematics=== | ||
| − | The problem of solvability in mazes has become part of the purview of mathematics, particularly in the area of "critical path analysis" (CPA). Critically CPA has its origins not in hedgerows or darkened hallways but the twisty little corridors of project management. | + | Adventurers, dancers, and the penitent are not the only travelers of mazes. Their pathways are also full of mathematicians. The problem of solvability in mazes has become part of the purview of mathematics, particularly in the area of "critical path analysis" (CPA). |
George Dantzig, the developer of the simplex algorithm and linear programming, if often credited with playing a pivotal role in the creation of maze solutions. The simplex algorithm addresses the shortest path problem and was originally put in service of minimizing cost on large-scale, Cold War airforce projects. | George Dantzig, the developer of the simplex algorithm and linear programming, if often credited with playing a pivotal role in the creation of maze solutions. The simplex algorithm addresses the shortest path problem and was originally put in service of minimizing cost on large-scale, Cold War airforce projects. | ||
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Curiously, Dantzig himself as acquired legendary status as the student who upon arriving late to a class mistook the historically unsolved problems on the board as his homework. Needless to say, his professor was surprised when he turned in the solutions several weeks later. If nothing else, the story reflects the status of this modern day Theseus. | Curiously, Dantzig himself as acquired legendary status as the student who upon arriving late to a class mistook the historically unsolved problems on the board as his homework. Needless to say, his professor was surprised when he turned in the solutions several weeks later. If nothing else, the story reflects the status of this modern day Theseus. | ||
| − | Around the same time, Critical Path Method, developed by James E. Kelley and Morgan Walker at Dupont offered an algorithmic approach to the shortest path problem in project management. | + | Critically CPA has been used not so much in hedgerows or darkened hallways but in the twisty little corridors of project management. Around the same time that Dantzig was developing his model, Critical Path Method, developed by James E. Kelley and Morgan Walker at Dupont, offered an algorithmic approach to the shortest path problem in project management. |
| − | The shortest-path problem has proven to be one of the grand challenges of the late twentieth century. The puzzle appears in telephone routing, planning routes for driving, and optimizing circuit boards. Solutions to the problem would become part of the crucial machinery of electronic networks, for example in autorouters. | + | The shortest-path problem has proven to be one of the grand challenges of the late twentieth century. The puzzle appears in telephone routing, planning routes for driving, and optimizing circuit boards. Solutions to the problem would become part of the crucial machinery of electronic networks, for example in autorouters. Yet these tools were not so far removed from the physical mazes. According to a site on the history of mazes, "The first autorouter was tested on a map of the maze at Hampton Court Palace about 35 years ago." |
| − | Curiously, one website on the history of mazes reports, "The first autorouter was tested on a map of the maze at Hampton Court Palace about 35 years ago." | + | An interesting reversal happens as math takes up mazes. As maze-solving algorithms are applied to more and more real world puzzles, they in turn prove themselves to be mazes of telephones, rest stops, and resisters. Even more importantly, the terror of the maze is not the minotaur but time itself, time which can be just as easily lost in unproductive paths. |
| − | An interesting reversal happens as math takes up mazes. As maze-solving algorithms are applied to more and more real world puzzles, they in turn prove themselves to be mazes of telephones, rest stops, and resisters. | + | Of course, the celebrity of 10 Print... grows out of the quest for optimization, where the clever distillation of a solution to one line becomes the sign of mastery. The mathematical grand challenge of finding the shortest path thus introduces the aesthetic of optimization into the lore of mazes. Mazes become the basic structure of the challenges to modern computing, business, and civic life. 10 PRINT... in this light pays tribute to a most fundamental structure of contemporary life and the obstacle to commercial profits, traffic flows, and the coursing of information over networks. |
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| − | Even more importantly, the terror of the maze is not the minotaur but time itself, time which can be just as easily lost in unproductive paths. | ||
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| − | Of course, the celebrity of 10 Print... grows out of the quest for optimization, where the clever distillation of a solution to one line becomes the sign of mastery. | ||
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| − | The mathematical grand challenge of finding the shortest path thus introduces the aesthetic of optimization into the lore of mazes. | ||
James E. Kelley, J., & Walker, M. R. (1959). Critical-path planning and scheduling. In Papers presented at the December 1-3, 1959, eastern joint IRE-AIEE-ACM computer conference (pp. 160-173). Boston, Massachusetts: ACM. doi:10.1145/1460299.1460318 | James E. Kelley, J., & Walker, M. R. (1959). Critical-path planning and scheduling. In Papers presented at the December 1-3, 1959, eastern joint IRE-AIEE-ACM computer conference (pp. 160-173). Boston, Massachusetts: ACM. doi:10.1145/1460299.1460318 | ||
