[sionnsar]

I don't see in this a description of any dimension, except those in which:
- there are no bears
- you have no home
- there is no South, East or North
- there is no constant linear metric or other "mile-equivalent"
- the linear metric cannot reach or exceed one mile, or
- you cannot walk.

I'm guessing it's #2, "home". Do I win the prize? *\;-)

[ThomasThomas]

This is the prize for #2

[NicknamedBob]

"Do I win the prize?"

No prize to be given as the answer was provided along with the puzzle. It's a old school puzzle describing a geographic anomaly; the only place it could be true is at the Earth's Pole, and the only color of a bear you might see would be white.

I think it was featured in a movie a few years ago, "Young Sherlock Holmes".