Editing 2821: Path Minimization
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You could also fulfill the criteria of reaching the target in finite, but arbitrarily long, time by following a {{w|random walk}}(+swim) or even follow a {{w|space-filling curve}} carefully chosen to be the maximally finite scenario. Or you could simply choose any path, and stop for an arbitrarily long time, or travel at a speed approaching zero. In the comic, however, a requirement for simplicity of path may dictate the use of something close to the opposing {{w|great-circle distance}}, or a variation that has a maximal swim-time even without ''undue'' time-wasting detours, and assume equal speeds of travel on all routes. | You could also fulfill the criteria of reaching the target in finite, but arbitrarily long, time by following a {{w|random walk}}(+swim) or even follow a {{w|space-filling curve}} carefully chosen to be the maximally finite scenario. Or you could simply choose any path, and stop for an arbitrarily long time, or travel at a speed approaching zero. In the comic, however, a requirement for simplicity of path may dictate the use of something close to the opposing {{w|great-circle distance}}, or a variation that has a maximal swim-time even without ''undue'' time-wasting detours, and assume equal speeds of travel on all routes. | ||
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The comic pokes fun at two famous physical/mathematical problems that are usually stated as happening on a beach. The first is the Lifeguard problem, which Richard Feynman, in his book ''QED'', uses to illustrate {{w|Fermat's principle}}, or principle of least time, which states that the path taken by a light ray between two given points is the path that can be traveled in the least time. This is closely related to {{w|Stationary-action principle}} for mechanical systems. In Feynman's words: | The comic pokes fun at two famous physical/mathematical problems that are usually stated as happening on a beach. The first is the Lifeguard problem, which Richard Feynman, in his book ''QED'', uses to illustrate {{w|Fermat's principle}}, or principle of least time, which states that the path taken by a light ray between two given points is the path that can be traveled in the least time. This is closely related to {{w|Stationary-action principle}} for mechanical systems. In Feynman's words: |