Stadium Paradox

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Paradox

Consider three rows of bodies:

$\begin{array} {ccccc} \text {(A)} & 0 & 0 & 0 & 0 \\ \text {(B)} & 0 & 0 & 0 & 0 \\ \text {(C)} & 0 & 0 & 0 & 0 \\ \end{array}$

Let row $\text {(A)}$ be at rest, while row $\text {(B)}$ and row $\text {(C)}$ are travelling at the same speed in opposite directions.

$\begin{array} {ccccccc} \text {(A)} & & 0 & 0 & 0 & 0 & \\ \text {(B)} & 0 & 0 & 0 & 0 & & \\ \text {(C)} & & & 0 & 0 & 0 & 0 \\ \end{array}$

By the time they are all in the same part of the course, $\text {(B)}$ will have passed twice as many of the bodies in $\text {(C)}$ as $\text {(A)}$ has.


Therefore the time it takes to pass $\text {(A)}$ is twice as long as it takes to pass $\text {(C)}$.

But the time which $\text {(B)}$ and $\text {(C)}$ take to reach the position of $\text {(A)}$ is the same.

Therefore double the time is equal to half the time.


Resolution


Historical Note

The Stadium Paradox is one of Zeno's Paradoxes, as famously raised by Zeno of Elea.


Sources