When a circular coin is rotated in depth, is there any sense in which it comes to resemble an ellipse? While this question is at the center of a rich and divided philosophical tradition (with some scholars answering affirmatively and some negatively), Morales et al. (2020, 2021) took an empirical approach, reporting 10 experiments whose results favor such perspectival similarity. Recently, Burge and Burge (2022) offered a vigorous critique of this work, objecting to its approach and conclusions on both philosophical and empirical grounds. Here, we answer these objections on both fronts. We show that Burge and Burge’s critique rests on misunderstandings of Morales et al.’s claims; of the relation between the data and conclusions; and of the philosophical context in which the work appears. Specifically, Burge and Burge attribute to us a much stronger (and stranger) view than we hold, involving the introduction of “a new entity” located “in some intermediate position(s) between the distal shape and the retinal image.” We do not hold this view. Indeed, once properly understood, most of Burge and Burge’s objections favor Morales et al.’s claims rather than oppose them. Finally, we discuss several questions that remain unanswered, and reflect on a productive path forward on these issues of foundational scientific and philosophical interest.