Time Flies like an Arrow: A Mind Puzzle
Jacob Roeland
The puzzle
Suppose you have two points, A and B, where A is the location of a bow-and-arrow and B is the location of a target. Now since any two points make a line, you also have a line AB. Now suppose you take the arrow and shoot it into the target. How much time did the arrow spend at each point between points A and B?
The puzzle: Broken down
- Two points, A and B
- A is a bow-and-arrow and B is a target
- A and B are two points and any two points make up a line
- A line is defined as "An infinitely extending one-dimensional figure that has no curvature; one that has length but not breadth or thickness" made of an infinite number of points.
The question
How long does the arrow stay at each point on line AB when fired from its starting point (A) to the target (B)?
Three Possible Solutions
- The arrow spends a set amount of time at each point.
- The arrow spends an infinite amount of time at each point.
- The arrow spends zero time at each point.
Solution 1
- The arrow spends a set amount of time at each point.
- Any set time x infinite points = infinity
- It will take an eternity (infinite amount of time) for the arrow to reach the target
- In other words, the arrow will never reach the target.
Solution 2
- The arrow spends an infinite amount of time at each point.
- Any infinite time x infinite points = infinity
- It will take an eternity (infinite amount of time) for the arrow to reach the target
- In other words, the arrow will never reach the target.
Solution 3
- The arrow spends zero time at each point.
- Any zero time x infinite points = zero
- Zero time means the arrow will travel zero distance per the distance formula (D=rt)
- In other words, the arrow will never reach the target.
Therefore
- The arrow will never hit the target
Well...
- All solutions are incorrect because the arrow does indeed hit the target. A simple test proves this.
- So what is the correct answer?
- There is none. Tis a paradox.
YAY!
PARADOXES RULE!!!