The Paradox of Zeno
According to this paradox motion is impossible. Zeno of Elea, an ancient Greek philosopher, came up with a thought experiment that perplexed mathematicians and philosophers to this present day.
How is motion possible?
“That which is in locomotion must arrive at the half-way stage before it arrives at the goal” – Aristotle’s interpretation of Zeno
thus nothing can reach its goal as the number of half-way points are infinite….resulting in an infinite sequence that must take an infinite amount of time.
Visual explanation
the completion of the distance requires an infinite amount of tasks whether at the beginning or at the end...which Zeno states is impossible.
The Arrow Problem
"In the arrow paradox, Zeno states that for motion to be occurring, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant (dimensionless point) of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. It cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible. This paradox is also known as the fletcher's paradox" -wikipedia
Trying to Resolve the Paradox
YouTube - Refuting Zeno's Paradox-Series on Infinity Part 7
Although this does not resolve the paradox in its entirety it is good enough for me
.
According to this paradox motion is impossible. Zeno of Elea, an ancient Greek philosopher, came up with a thought experiment that perplexed mathematicians and philosophers to this present day.
How is motion possible?
“That which is in locomotion must arrive at the half-way stage before it arrives at the goal” – Aristotle’s interpretation of Zeno
thus nothing can reach its goal as the number of half-way points are infinite….resulting in an infinite sequence that must take an infinite amount of time.
Visual explanation
The Arrow Problem
"In the arrow paradox, Zeno states that for motion to be occurring, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant (dimensionless point) of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. It cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible. This paradox is also known as the fletcher's paradox" -wikipedia
Trying to Resolve the Paradox
YouTube - Refuting Zeno's Paradox-Series on Infinity Part 7
Although this does not resolve the paradox in its entirety it is good enough for me
.