Chapter 94 <Scud can't catch up with the turtle>

In ancient Greek mythology, there was a man named Achilles, who was a scud and walked as fast as flying.But the ancient Greek philosopher Zeno believed that although Achilles walked like flying, he could never catch up with a slow-moving tortoise. Zeno argued thus: Let the tortoise crawl for a while, and then Achilles chases it from behind.When Achilles reached the end of the tortoise's path, the tortoise crawled forward again; when Achilles chased to the end of the tortoise's path again, the tortoise moved forward again.And so on, to infinity.Therefore, the tortoise is always in front of Achilles, that is to say, Achilles can never catch up with the tortoise.

Zeno's argument is specious.There is a key problem here that is deliberately hidden, that is, Achilles and the tortoise walk at different speeds.We assume that the speed of the former is ten times the speed of the latter, for example, the former walks 10,000 meters (ten kilometers) per hour, and the latter walks 1,000 meters (1 kilometer) per hour; and let the tortoise go ahead for one hour, that is, it goes one thousand meters first , and then Achilles catches up again. In this way, Achilles only needs one tenth of an hour to cover the distance of one thousand meters, and at the same time the tortoise only crawls forward one hundred meters; in another one tenth of an hour, Achilles moves forward another thousand meters. meters, while the tortoise still advances a hundred meters.By this time Achilles had left the tortoise 800 meters behind.If calculated accurately, Achilles can catch up with the tortoise in only one-ninth of an hour. The calculation formula is one thousand divided by (ten thousand minus one thousand) equals one-ninth. Can't catch up with the turtle?

Zeno's sophistry consists in omitting to say how far Achilles and the tortoise each travel at the same time.It is a kind of sophistry to deliberately avoid key issues in the argument and talk about specific issues in the abstract.