Frogwatch wrote:

Back when I was discussing coord systems for navigating on weird shaped
worlds,

In a really weird shaped world, if you would navigate long
enough you return to your original position and find your
friends have turned to their mirror images. That would
happen to 2-dimensional creatures travelling a (transparent)
mobius band.
http://plus.maths.org/issue26/featur...ndex-gifd.html

someone pointed out that I could actually buy a Kleins bottle
from a company called "ACME Kleins Bottles" so I ordered one. They
also have a great thing called "The Mug of Tantalus" which is a blown
glass beer mug with a siphon built into the handle. You can fill the
mug about halfway with no problem but if you go any higher ALL the
liquid drains out via the siphon. Of course, I bought one for a beer
drinking friend.

A variation of The Mug of Tantalus is known as
Pyhthagoran Mug of Justice.
http://www.mlahanas.de/Greeks/InventionsP.htm
Pythagoras invented this as he thought his friends were
drinkin all too much. They still make those for tourists to
buy - out of clay, as was the original - on Pyhtagoras' home
island Samos in Greek.

The Klein Bottle is not as cool as I thought it would be primarily
because none of my friends know what it is so they do not appreciate it.

Btw, the story in
http://plus.maths.org/issue26/featur...ndex-gifd.html
suggests, that you make a thermometer out of the Klein
bottle, if you don't know what to do with it.

TC