Arnheim wrote extensively about perspective and percepts that were “in between” correct perception of objects and projected shapes. We apply Arnheim's views to a Renaissance piazza of square tiles. We show the kind of formalization to which the analysis leads and give a formula applicable to a perspective picture as an example. We argue that Arnheim was answering the Gestalt phenomenological question “why the world looks as it does” with comments that, happily, are also a solution to the Realist question “how perception lets us know about the world.” Like Renaissance writers, Arnheim recognized that perspective had strict limits. Both the Gestalt and the Realist perception theories give accounts of the effects of perspective and both argue perspective constancy is widespread in perception, but Arnheim is correct that it operates within strict limits. We conclude that perception uses an approximation to perspective. The approximation is close under many circumstances but it produces what Arnheim called “in-between” percepts in more extreme conditions. We conclude it is very inaccurate as conditions become quite extreme.