Monday, January 17, 2005
The Importance of Being Zeno's Paradox
There was this man who enlisted in the army. In fact, he joined the parachute regiment because he had a revolutionary new way of jumping out of planes to test.
"Well," he said to his fellow recruits. "In order to travel from the plane to the ground, you must first travel half way from the plane to the ground. Then you have to travel half of the remaining distance so you are now a quarter of the way to the ground. Then you have to travel half of that distance and then half of the remaining distance and so on. No matter how close to the ground you are, you always have to go half of the remaining distance so you can never actually reach the ground. All I have to do is get sufficiently close and then put my hands and feet out to stop."
He tried his technique on his first jump. Unfortunately, although his jump did indeed consist of an infinite number of bisections of the remaining distance to the ground, each one took an exponentially shorter time to travel than the last and when they were all added up, in accordance with analytical theory the total time was finite. In short, he learned at least two meanings for the phrase "terminal velocity".
Miraculously, our hapless recruit had managed to put his hands and feet out as he planned and the shattering of the bones in his limbs cushioned the fall such that he was otherwise unharmed.
He lay in the hospital bed with all four limbs in plaster. The Colonel of the Regiment called in the Paras' best medical team to look at him. The head surgeon looked him over with a grim expression.
"I'm afraid zere is little hope", he pronounced (he was a Frenchman on exchange and spoke in an outrageous French accent).
"Why?" said the colonel.
"Well, most of our patients seem to land on zere heads. We are very good at reconstructing flattened noses, but not much else."
"So there's nothing you can do?"
"I'm afraid not, it is ze impotence of being ze nose Para docs."
"Well," he said to his fellow recruits. "In order to travel from the plane to the ground, you must first travel half way from the plane to the ground. Then you have to travel half of the remaining distance so you are now a quarter of the way to the ground. Then you have to travel half of that distance and then half of the remaining distance and so on. No matter how close to the ground you are, you always have to go half of the remaining distance so you can never actually reach the ground. All I have to do is get sufficiently close and then put my hands and feet out to stop."
He tried his technique on his first jump. Unfortunately, although his jump did indeed consist of an infinite number of bisections of the remaining distance to the ground, each one took an exponentially shorter time to travel than the last and when they were all added up, in accordance with analytical theory the total time was finite. In short, he learned at least two meanings for the phrase "terminal velocity".
Miraculously, our hapless recruit had managed to put his hands and feet out as he planned and the shattering of the bones in his limbs cushioned the fall such that he was otherwise unharmed.
He lay in the hospital bed with all four limbs in plaster. The Colonel of the Regiment called in the Paras' best medical team to look at him. The head surgeon looked him over with a grim expression.
"I'm afraid zere is little hope", he pronounced (he was a Frenchman on exchange and spoke in an outrageous French accent).
"Why?" said the colonel.
"Well, most of our patients seem to land on zere heads. We are very good at reconstructing flattened noses, but not much else."
"So there's nothing you can do?"
"I'm afraid not, it is ze impotence of being ze nose Para docs."
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# posted by JeremyP : 2:41 pm
