copyright 2023 daniel kalak
licensed under cc by nd 4.0
there is a common question about why
mirrors supposedly only swap left and
right and not top and bottom. the question
seems silly to me whenever i hear it.
the key to understand is that in asking
that question, you imagine what it would
be like to physically take the position of
your reflection in the mirror. if you take
the ground as a fixed reference that you
have to walk on, and the pane of the
mirror as something that you have to be
facing, then of course you will think that
a mirror only swaps left and right,
because you imagine yourself walking
around the mirror, turning to face the
unmirrored world, and keeping your feet on
the ground during the process. this feels
natural because this is how we walk around
and turn to face other people.
if, instead, it felt natural to you to
imagine yourself walking straight into the
mirror without turning around to face the
real world, and you stopped right at the
position of your reflection in the mirror
world, then your wristwatch hand would be
where the wristwatch hand of your
reflection is, and your non wristwatch
hand would be where the non wristwatch
hand of your reflection is, but your front
and back have would been swapped, not left
and right. in fact, to reach for something
that is behind you in the real world, you
would have to reach in front of you, i.e.
in the same direction that you have been
walking, in the mirror world.
let us try this trick again, and spin it.
if it felt natural to you to imagine
yourself diving into the mirror and
landing on your head somehow, so that you
would still face the real world from
within the mirrored world, but with your
feet on the air and your head on the
ground, then your back would still face
the same way as the back of your
reflection, and your wristwatch would be
on the same side as that of your
reflection, but the mirror would have
swapped top and bottom instead of left and
right.
if you arent convinced, then observe how
the swapping direction changes in the
following situations
lie down on your side in front of a
mirror.
take an object that you are only used to
holding a certain way, e.g. a newspaper,
and an object where you feel that there
is no right way to turn it, e.g. a ball
or a plate without any writing on it.
turn both in front of you and observe
their reflections.
look up to a mirror that is mounted on
the ceiling instead of on a wall, and
turn to let your feet point in different
directions at a time.
it all comes down to whether or not you
feel like certain axes are fixed.
gemini://dkalak.de/txt/mirror.txt