Nicolai Lobachevsky, János Bolyai, Bernhard Riemann geometry |

## Non-Euclidean geometry

- On a flat world
- parallel lines
- never intersect
- but flat worlds
- don’t always intersect
- with the real world
- where some do not believe
- their senses
- accepting odd topologies in which
- mass increases with velocity
- in which gravity bends light
- even though we know
- it has no mass for gravity to pull
- in which the vibration
- of twisted and invisible dimensions
- are what others consider immutable
- in which an infinite universe
- never wraps around us
- as we fail to wrap our minds
- around it.

## Non-Euclidean house

- If all plumbs were true
- all paintings hung straight
- no door or window
- stuck on its jamb
- this house would not be be right
- to house this crooked man.

## Postulates

- It is possible
- to understand each other.
- Like foreigners forced to learn
- by trial and error
- we point to a banana
- and the man says “xorupeet.”
- We indicate two parallel lines
- and say “they never meet.”

Like new math or declarative programming (compared to procedural programming), non-Euclidean geometry might be easier to conceptualize if it were your first. But any geometry is a conceptualization, not a reality. Any mathematics declares its assumptions, which it cannot prove, whereas any reality is its own proof, compared to our perception of reality, which is highly influenced by preconceptions, first teachings.

Fortunately, approximations suffice for us. Unfortunately, approximations suffice for others with conflicting views.

In

Broca’s Brain,Carl Sagan says that he is often asked about UFOs and ancient astronauts, which he regards as thinly disguised religious queries, but that he would accept certain proofs, including an ancient and exotic alloy of aluminum and lead (producable only in weightless conditions), or an ancient record of “the derivation of the Lorentz transformation of special relativity”; however, without such proofs, most of us make up our minds based on incomplete evidence, generally following the procedures that we use to make other decisions in everyday life.See also in

The book of science:Geometry—EuclidNumber system—Leonardo Pisano Bigollo (Fibonacci)Mercator projection—Gerardus MercatorIncompleteness theorems—Kurt GödelReadings on wikipedia: