Henry Ernest Dudeney/Puzzles and Curious Problems/327 - Two Paradoxes/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $327$

$(1): \quad$ Imagine a man going to the North Pole.

The points of the compass are, as everyone knows:

$\qquad \qquad \qquad \begin{array} {ccc} & \text N & \\ \text W & & \text E \\ & \text S & \\ \end{array}$

He reaches the pole and, having passed over it, must turn about to look North.

East is now on his left-hand side, West on his right-hand side, and the points of the compass therefore:

$\qquad \qquad \qquad \begin{array} {ccc} & \text N & \\ \text E & & \text W \\ & \text S & \\ \end{array}$

which is absurd.

What is the explanation?

$(2): \quad$ When you look in the mirror, you are turned right round, so that right is left and left is right,

and yet top is not bottom and bottom is not top.

If it reverses sideways, why does it not reverse lengthways?

Why are you not shown standing on your head?

$(1): \quad$ As you go over the pole, and are facing South, so also are West and East changed over.

So, without turning round to face North, West is already on your right and East on your left.

So when you turn round to face North, West is on your left and East on your right, and all is well with the world.

$(2): \quad$ When you look in a mirror, it is not left and right which are exchanged, but front and back.