Non-Euclidean geometry

1829 Non-Euclidean geometry

The book of science

Tom Sharp

Nicolai Lobachevsky, János Bolyai, Bernhard Riemann geometry

Non-Euclidean geometry

Non-Euclidean house


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:

Readings on wikipedia: