A subsequent quotation summarizes "Ulam's central concern" in his own words as follows:

Is there a true infinity of structures going down into smaller and smaller dimensions? It is not a precise problem, or recognized as such. In physics there has always been an atomistic or a field point of view. If there is a field, then points are mathematical points and they are all the same. But another possibility is a very strange structure of successive stages, each stage different. The topology or the scene on which they exist, that is, space and time themselves, need not be the uniform, smooth Euclidean topology. The miracle is that physics would not be possible if protons and electrons were not very much the same. If this similarity or identity of subsets of the universe did not exist, there would be no physics. It may be that in reality for phenomena in the small and involving high energy, there may be an underlying true infinity that does not allow for similarities. It may be that at the present stage of evolution of the universe a sufficient number of identical situations has not yet been produced. If this is so, then physics will become fundamentally more complicated.

The earlier comment re Hertz is "a general observation" made by Ulam:

The behavior of a truly infinite system is not necessarily obtainable as a limit of the behavior of a finite approximating configuration.

This is from Augenstein's exploration of the role that set theory plays in mathematical physics; it seems to be a citation of something from Stanisław Ulam:

... [there is a] notion that if there are physical structures which increase in complexity indefinitely (see the earlier comment re Hertz), the set-theory axiom of regularity would not hold. This phenomenon has been rediscovered several times; see Scheibe [57].

Augenstein's exploration in Links between physics and set theory mentions Ulam relating complexity and regularity:

There are several sources for appreciating Ulam’s ideas and interests. A collection of his papers in Beyer et al. [80]... discusses the issue of whether one might expect meaningful undecidable statements in physics (Ulam’s answer, yes), and the notion that if there are physical structures which increase in complexity indefinitely (see the earlier comment re Hertz), the set-theory axiom of regularity would not hold. This phenomenon has been rediscovered several times; see Scheibe [57].