 Close attention to analogical arguments in practice can also provide valuable challenges to general ideas about analogical inference. In an interesting discussion, Steiner (1989, 1998) suggests that many of the analogies that played a major role in early twentieth-century physics count as “Pythagorean.” The term is meant to connote mathematical mysticism: a “Pythagorean” analogy is a purely formal analogy, one founded on mathematical similarities that have no known physical basis at the time it is proposed. One example is Schrödinger’s use of analogy  (Example 14)  to “guess” the form of the relativistic wave equation. In Steiner’s view, Schrödinger’s reasoning relies upon manipulations and substitutions based on purely mathematical analogies. Steiner argues that the success, and even the plausibility, of such analogies “evokes, or should evoke, puzzlement” (1989: 454). Both Hesse (1966) and Bartha (2010) reject the idea that a purely formal analogy, with no physical significance, can support a plausible analogical inference in physics. Thus, Steiner’s arguments provide a serious challenge.