The mirrors are place one unit apart, then one-half, then one-fourth...
Is the photon travelling upwards or downwards when it exits the series of mirrors?
What is wrong with the following argument?
1. When the arrow is in a place just its own size, it is at rest. [This means that if you measure the location of the back of the arrow at one instant in time, and the tip at the next instant in time, it occupies an interval of greater length than its own length.]2. At every moment of its flight, the arrow is in a place just its own size.
3. Therefore, at every moment of its flight, the arrow is at rest.
What is wrong with the following argument?
A lamp is initially on at time t=0.1. After 1 second the lamp is turned off.
2. AFter 1/2 second the lamp is turned on.
3. AFter 1/4 second the lamp is turned off.
...
After 2 seconds, it cannot be on, since each time I turned it on, I then turned it off shortly thereafter. It cannot be off, since each time I turned it off, I turned it on shortly thereafter.
What is the final state of the lamp after 2 seconds, since the lamp is obviously on or off!
A photon enters a series of mirrors as shown below (the photon makes an angle of 45 degrees with each mirror).The mirrors are place one unit apart, then one-half, then one-fourth...
Is the photon travelling upwards or downwards when it exits the series of mirrors?
A gambling casino has a new game:
A fair coin is tossed. If it comes up heads, you win 2$.If it comes up tails first, then heads, you win 4$.
If it comes up tails twice, then heads, you win 8$.
...
The expected value is clearly
(1/2)*2 + (1/4)*4 + (1/8)*8 + ... = infinity The casino charges 10,000$ to play. Being a good student of mathematics, why wouldn't you pay 10,000$ to play this game?
here is the answer from "Ask Dr. Math."
A slightly weaker form of the paradox can be found here