A solid sphere is topologically equivalent to a Mobius strip(?)

And a hollow sphere is topologically equivalent to a loop (a Mobius strip without a half turn). This is interesting because a loop has a hole, but a hollow sphere does not. Does the space inside a hollow sphere count as a hole?

Imagine a Mobius strip made out of clay. It could squished and rolled into a ball. And a clay loop could be formed into a hollow sphere. 

The Möbius strip, topological equivalence, and one-way functions

A donut and a coffee mug are topologically equivalent because one can be transformed into the other without cutting, tearing, or adding more holes. It's easier to understand this if you imagine both shapes being made of soft clay or Play Dough. 

However, a Möbius strip and a loop strip are not topologically equivalent even though they have the same number of holes. The first has one side and the other has two sides. A Möbius strip made of clay could be molded into a loop strip, but not the reverse is not possible. 

It seems there are topological transformations that are not reversible. Thus, they are analogous to one-way functions. 

The 4 ways a story can end

At the end of a story, the main character(s) will either get what they want and need or they won't. So the 4 possible outcomes are: 

1. get what they want and what they need

2. get what they want but not what they need

3. don't get what they want but get what they need

4. don't get what they want or what they need

#1 is the most common ending. Disney's Aladdin is a good example. Most Disney movies have such an ending. 

Kafka's The Metamorphosis has a #4 ending. 

Finding examples of #2 and #3 are exercises I leave to the reader.   

Tomb of Hatshepsut, Egypt

 

Norse mythology changed my life

It teaches that it doesn't matter if you win or lose, only if you were brave or not. 

Draken in the North Sea storm

BROTHERS OF METAL - Yggdrasil (2018) // Official Music Video // AFM Records

A man named Bullfinch wrote an excellent explanation of Norse and other mytholgies. 

Bullfinch Norse.pdf

The Project Gutenberg eBook of Bulfinch's Mythology, by Thomas Bulfinch