An arbitrary polarity which has no monopoly on 'up'?

What does "an arbitrary polarity which has no monopoly on 'up'" mean?
It seems to me "arbitrary" is the manner of a dictator why has much monopoly. So the expression "an arbitrary polarity which has no monopoly on 'up'" sounds ambivalent to me.

Context:

NATURAL SELECTION AS A
CONSCIOUSNESS-RAISER
In a science-fiction starship, the astronauts were homesick: 'Just to
think that it's springtime back on Earth!' You may not immediately
see what's wrong with this, so deeply ingrained is the unconscious
northern hemisphere chauvinism in those of us who live there, and
even some who don't. 'Unconscious' is exactly right. That is where
consciousness-raising comes in. It is for a deeper reason than
gimmicky fun that, in Australia and New Zealand, you can buy
maps of the world with the South Pole on top. What splendid
consciousness-raisers those maps would be, pinned to the walls of
our northern hemisphere classrooms. Day after day, the children
would be reminded that 'north' is an arbitrary polarity which has
no monopoly on 'up'. The map would intrigue them as well as raise
their consciousness. They'd go home and tell their parents - and, by
the way, giving children something with which to surprise their
parents is one of the greatest gifts a teacher can bestow.