Von Neumann's work on self-reproduction concerned the question of how machines might be able to evolve increased complication in order to perform increasingly complex tasks. This is why his design for a self-reproducing machine had to be capable of universal construction, and why it was designed in such a way that it could withstand some kinds of mutations.
It has already been stated that much confusion exists over von Neumann's goals, and it is often assumed that his work was a general treatment concerning the topic of self-reproduction as a whole (i.e. concerning the entire space of possibilities depicted in Figure 7.1). By reading his lecture notes and papers (e.g. [von Neumann 66], [Aspray & Burks 87]), however, it is quite clear that he was primarily interested in self-reproduction that could lead to open-ended evolution (i.e. the rear portion of the lower plane in Figure 7.1).
This confusion has led to considerable debate over the `problem' of trivial reproduction. The problems arise when the issue of trivial versus non-trivial reproduction is taken as relating to the implicit-explicit axis. If we adopt von Neumann's own suggestion that it is the limited-indefinite heredity axis which defines the most interesting distinction, most of the arguments over trivial reproduction in the literature can be seen as irrelevant, or at best subsidiary, to the real issues. Of course, new issues arise when we adopt this new viewpoint. I will discuss some of them in the remainder of this section.