As it happens I'm rereading the Ritz book presently a couple of quotes might show his ideas on parabolic design, while working with cane in France;
... are not dozens of types of actions, but one only, whose rigidity varies according to the length of the rod, and it must work progressively from the point to the handle without the slightest weakness, however used. The action may be more or less powerful, but the curves must be identical. This action which I have called "Parabolic", though the term is only a figure of speech, and the curve of the rod has absolutely nothing whatever to do with a parabola.
This sorta relieves me of trying to make sense of the term parabolic as relating the rod taper or action to a parabola- he says straight up it doesn't.
Then talking about his fifty years of research and his move to Conolon and fiberglass in 1968;
The main defects with split cane rods were weakness in the rod tip and a relative lack of flexibility in the butt. Some rods produced in the first quarter of this century were too soft in the center section. With such equipment no fly-fisher could possibly develop the skills of which he or she may have been capable.
I understand this to say he wanted a stronger tip, stiffer mid and more flexible butt section.
A question does arise in my mind though, in the example of a willow bending being stronger than other trees breaking, is Ritz desiring a stiffer tip or a less brittle tip?