As we have seen here, understanding the spiral structure of galaxies took many twists and turns even in the hands of Bertil Lindblad who seems rightly regarded the main father of this whole subject. By the early 1960s, with the arrival of computers, plasma physics and several fresh investigators, it entered a new period of unusually vigorous activity, not always very united or monothematic, but broadly grouped under the umbrella marked `density-wave theory'. Its foremost enthusiast and proponent was undoubtedly C.C. Lin, whose 1964 and 1966 papers with Shu had a big and immediate impact upon other astronomers, at least as a welcome sign that genuine understanding of the spiral phenomenon seemed in some sense to be just around the corner.
In retrospect, even Lin occasionally let himself get carried away with too much enthusiasm as for instance when he wrote in his 1967 review article that his relatively exploratory work with Shu had already led to a "theory free from the kinematical difficulty of differential rotation", or that it "enables us to provide a mechanism to explain the existence of a spiral pattern over the whole disk while allowing the individual spiral arms to be broken and fragmentary" (Lin 1967b, p.462). Already at the time such optimism was not entirely shared by other experts. And by the late 1960s - as we shall see in Paper II - it had become very clear to everyone that much hard work still remained to explain even the persistence, much less the dynamical origins, of the variety of spirals that we observe.