Teacher Guan always talks about "Achilles paradox of chasing turtles" (little-footed old woman), but these four paradoxes have wonderful charm when combined.
1, Dichotomy Paradox: Any object that wants to move from point A to point B must first reach AB midpoint C, then CB midpoint D, then DB midpoint E ... and so on. This dichotomy process can go on indefinitely, and there are infinitely many such midpoints. Therefore, the object will never reach the destination B. Not only that, but we will also come to the conclusion that it is impossible to move, or it is even difficult to start such a trip. Because the first half must be completed before the second half, and before that, the first 1/4 journey must be completed ... so the object can't start moving at all, because it is hindered by the infinite division of the road.
2. Achilles' paradox of chasing turtles: If turtles are allowed to lead by a certain distance, Achilles will never catch up with them.
The tortoise is a little ahead. In order to catch up with the tortoise, Achilles had to reach the starting point A of the tortoise. But when Achilles reached point A, the tortoise had already advanced to point B. When Achilles reached point B, the tortoise had reached point C in front of point B, and so on. Although ............ and his wife got closer and closer, Achilles always fell behind the tortoise and couldn't catch up with it.
3. The flying arrow staying in one place is not a paradox of motion, but doesn't the flying arrow stay in one place at any time? Since the arrow can stay in one place at any time, the arrow is of course motionless.
4. Paradox of sports field. Zeno's paradox may be a theory that there is a minimum unit of time (Planck-Wheeler time now). In this regard, he put forward the following argument: imagine three columns of entities, and initially they are aligned. Imagine that in the minimum unit of time, column C is still, column A is moved one place to the left and column B is moved one place to the right. Compared with B, A has moved two places. That is to say, we have to have a time to let B move one position relative to A. Naturally, this time is half of the unit time, but assuming that the unit time is inseparable, these two times are the same, that is, the smallest unit of time is equal to half of him.
If we analyze these four paradoxes, we can find that they can be divided into two groups. The first two assumptions are that time and space are continuous and can be subdivided infinitely. The last two hypotheses are that time and space are discontinuous. Zhi Nuo intended to show that no matter whether time is continuous or intermittent, it is impossible to move, and absurd things will happen.