This comes out of the latest issue of a full page ad
in a major fitness journal by a competitor's brand of Pilates:

"In any well-balanced workout it is important to create comprehensive programing that will challenge the body in all planes of motion such as flexion, extension, rotation and lateral flexion. Brand XXX offer examples of spinal extension to add variety to your workout."

What is good:
They actually acknowledge planes of movement.
(I wonder where that comes from?)

What is bad?
They fail to acknowledge Pilates is a progressive pattern of movement,
and that lateral flexion comes BEFORE rotation.

Before you can come close to understanding Pilates, real Pilates, the essence of Pilates, one of the critical components is the progressive pattern embedded in the work.

That's why the definition of Michael Miller Pilates as an idea is:
Uniform eccentric loading flowing through progressive patterns of movement.
You can pick variety in expression of the pattern, but you can not change the nature of progression, either from simple to complex or complex to simple.