Shotokan's Secret

All of these actions make the body generate useful momentum in the hara. They are, therefore, conceptually all equivalent. We get the body moving in a straight line (forward, backward, up or down) and then bleed off the momentum into technique. This is the sine qua non of linear technique.

Changing stance is not usually listed in this group, but consider that. Changing from back stance to front stance involves driving the hara almost a foot to the front. We should be alert to the idea that a stance change is a momentum engine and see where it leads us.

Reverting to the older "basic principles" of Chinese karate, it is easy to see that a stance change often generates angular momentum, the storage batter of pure rotation. Much of our linear expertise concerns taking this rotational power and converting it to linear power as we strike. Similarly, there are places in our katas where we launch a linear move and then use it to generate a swift rotation to a new direction. Linear and rotational power are interchangeable.

When reading this article I could immediately see parallels in my training experience. That linear and circular techniques are inseparably interwoven rings true on an instinctual level. In linear karate "sayu" (left and right) switching is taken for granted - when right hand punches left goes into hikite, when left punches right goes into hikite. Yet if viewed from directly above, no matter how stable the stance from waist down is, from waist up the torso and shoulders rotate circularly around the pivotal center of gravity and the 'hara'.
Ergo, even in basic techniques, linear and circular movements are inextricably interwoven.