However, it turns out that whether the platonist can indeed explain the success of the application of mathematics is, in fact, controversial. Given that mathematical objects are abstract, it is unclear why the postulation of such entities is helpful to understand the success of applied mathematics. For the physical world—being composed of objects located in space-time—is not constituted by the entities postulated by the platonist. Hence, it is not clear why the correct description of relations among abstract (mathematical) entities is even relevant to understand the behavior of concrete objects in the physical world involved in the application of mathematics. Just mentioning that the physical world instantiates structures (or substructures) described in general terms by various mathematical theories is not enough (see, e.g., Shapiro 1997). For there are infinitely many mathematical structures, and there is no way of uniquely determining which of them is actually instantiated—or even instantiated only in part—in a finite region of the physical world. There is a genuine underdetermination here, given that the same physical structure in the world can be accommodated by very different mathematical structures. For instance, quantum mechanical phenomena can be characterized by group-theoretic structures (Weyl 1928) or by structures emerging from the theory of Hilbert spaces (von Neumann 1932). Mathematically, such structures are very different, but there is no way of deciding between them empirically.