 As it may at first appear such an \(n\) is defined in a circular manner, it is also prima facie unclear why such a program must exist. Indeed Soare (2016, 28–29) remarks that the foregoing proof of the Recursion Theorem is “very short but mysterious” and is “best visualized as a diagonal argument that fails”. In order to clarify both this comment and the proof, consider the matrix depicted in Figure 1 whose rows \(R_i\) enumerate not the values of partial computable functions but rather the functions themselves—i.e., the row \(R_i\) will contain the functions \(\phi_{\phi_i(0)}, \phi_{\phi_i(1)}, \ldots\) with the understanding that if \(\phi_i(j) \uarrow\), then \(\phi_{\phi_i(j)}\) denotes the totally undefined function. (Such a depiction is originally due to Owings 1973.)