Puzzles/Physics puzzles/Eleatic School

Puzzles | Physics puzzles |Problems of the Eleatic School

Some background about these riddles is given on the Puzzles in science page. There is no strict solution to any of these puzzles. So rather than searching for a solution try to find support in favor or against the following postulates.

Achilles and the tortoise
Achilles is racing against a tortoise. Starting the race the tortoise is 10 m ahead. However, Achilles runs 20 times faster than the tortoise which runs at 1 m/sec (or any other positive speed). Shouldn't Achilles overtake the tortoise? In fact we shall see he does not. We start with the tortoise ahead at point A and Achilles behind at point B. When Achilles reaches point B a certain amount of time has passed which allowed the tortoise to move on to point C. Again Achilles reaching point C leaves the tortoise ahaed of some positive length, ad infinitum. Therefore Achilles is not going to catch up with the tortoise which is a contradiction to the initial notion of motion.

Therefore motion does not exist. Do you agree? comment

Here is a variant of the above puzzle:

Reaching point B
Suppose you intend to travel from point A to point B on a straight line. In order to do that you have to reach the midpoint C between A and B. In order to reach point C you have to reach the midpoint of A and C, say D, ad infinitum. Therefore it takes you an infinite amount of finite movements to reach point B which is in contrast with the notion of constant speed.

Therefore motion does not exist. Do you agree?

The flying arrow
Suppose an arrow is being shot from a bow. At any fixed point in time the arrow is motionless at a certain point. This directly contradicts the idea of motion since at any conceivable point in time motion is not present.

Therefore motion does not exist. Do you agree?