### Other 2D universes

2D: only a **few universes**.
For a 2D creature, these are spaces to live in, and if our creature is slightly self-centered, it will never discover that the universe is not the plane.

Some spaces are
**orientable** (e.g. the plane,
sphere and torus, where "left" and "right" make sense),

others are
**non-orientable**
(e.g., the
Klein bottle).

What is it like to live on a Klein bottle?

The Klein bottle won't fit in 3D without self-intersections.

3D space is simply to small: in 4D the Klein bottle fits nicely.
Similar phenomenon: the **Borromean rings**. No two are linked, but together they can't be pulled appart.

**However** these 3D and 4D spaces have nothing to do with our 2D universe: for 2D creatures these are **totally abstract** (only occuring in the ravings of theoretical physicists).

A cute book (and a movie) called
Flatland is about 2D creatures.