Interesting piece in the NYT today; apparently the US tradition of mineral rights (in most cases) being included with surface ownership is not the norm. This article highlights Ontario, Canada, where mineral rights are (in most cases) independent of surface rights. So a cabin owner goes to his cabin and discovers that a prospector has cut down a tree for stakes, dug a number of exploratory holes and driven heavy equipment all over the place. What is his recourse? Years in court with the outcome unclear.
In addition to a number of startling stories like this, there are moments of humor as well. For example, one landowner got a permit for a private shooting range, then put signs up all over the place that trespassers were in danger of being shot. Accidentally of course.
One family friend many years ago was considering playing this game from the opposite direction; he had a more or less unused woodlot across the road from his house, and had several times caught folks prospecting. He wanted to get an ounce or two of powdered gold and salt the ground with it- a waste of a few hundred dollars up front, but increasing the value of the land several fold to a prospector who took the assays at face value. Don't think he ever followed through, but I loved the idea.
Is This Your Hat?
12 years ago

A Klein Bottle is the equivalent of a Mobius strip, rasied another dimension. A Mobius strip is a two dimensional strip, wrapped into a cylinder, with a twist in the third dimension. So a Mobius strip thus has only one surface and one edge. A Klein bottle is a three dimensional tube, with the ends connected to make a torus (donut), with the mathematically plausible (but physically impossible) "twist" through the fourth dimension. For a "real" Klein bottle, the tubes' piercings of the surface would actually bypass from one side to the other in the fourth dimension, and would not pass through the wall. So A Klein Bottle has no inside or outside, and only one surface. This model would be the equivalent of a Mobius strip with three twists instead of one.

