Hall of Infinite Doors
"Now then," the professor says. "Let's say I want to approach this wall," he says, pointing at the wall to his left. You look over and see that it is, in fact, a nice wall, before you divert your gaze back to the professor.
"But what if I can only walk half of the distance I have previously walked? The wall is one foot away. So, I walk six inches toward it." The professor does so. "But now, I can only walk half of the distance I just did. So, I move three inches closer." He does so. Is there a point to this?
"But how will I ever reach the wall? As I move closer and closer, the distance I can travel becomes smaller and smaller! It is impossible for me to reach this wall, even though it's so close!"
That's just dumb, you think to yourself. It almost reminds you of...yes, one of the dragon's quotes! "Shoot for the moon. Even if you miss, you'll land among the stars."
"Hey, professor!" you yell. "What if you tried to travel beyond the wall?"
"Well, that's impossible," he says, sulkily. "You can't travel through the solid-"
"But when you travel at an exponentially decaying distance beyond what you want to reach, it will be possible to actually reach it!" you say triumphantly, interrupting him. "If I were a foot away from the wall, and I wanted to travel two feet away, my distance would take me a foot, where I would then touch the wall!"
The class begins to stir, but for the most part they're still paying close attention to the professor.
"But what if I can only walk half of the distance I have previously walked? The wall is one foot away. So, I walk six inches toward it." The professor does so. "But now, I can only walk half of the distance I just did. So, I move three inches closer." He does so. Is there a point to this?
"But how will I ever reach the wall? As I move closer and closer, the distance I can travel becomes smaller and smaller! It is impossible for me to reach this wall, even though it's so close!"
That's just dumb, you think to yourself. It almost reminds you of...yes, one of the dragon's quotes! "Shoot for the moon. Even if you miss, you'll land among the stars."
"Hey, professor!" you yell. "What if you tried to travel beyond the wall?"
"Well, that's impossible," he says, sulkily. "You can't travel through the solid-"
"But when you travel at an exponentially decaying distance beyond what you want to reach, it will be possible to actually reach it!" you say triumphantly, interrupting him. "If I were a foot away from the wall, and I wanted to travel two feet away, my distance would take me a foot, where I would then touch the wall!"
The class begins to stir, but for the most part they're still paying close attention to the professor.