All these railroads go through flat empty terrain that previously had only a few nomadic inhabitants—and no settlements to define a route.

• Will a given pattern of origami folds yield an object that can be made flat?

In many fields outside of statistics, however, the idea persisted even to the 1990s that block frequencies (or flat frequency spectra) were somehow the only ultimate tests for randomness.

What happens in essence is that the modes of fields in different background spacetime structures differ to the point where zero-point excitations seem like actual particle excitations to a detector or observer calibrated to fields in ordinary fixed flat infinite spacetime.

To get all the familiar properties of additivity one needs an addition operation that is associative ( Flat ) and commutative ( Orderless ), and has an identity element (white or 0 in the cases above)—so that it defines a commutative monoid.