This article examines the case of an observational and a demonstrational armillary sphere confused, one for the other, by fifth‐century historians of astronomy He Chengtian and Shen Yue. Seventh‐century historian Li Chunfeng dismisses his predecessors as ignorant, and in so doing he supplies the reader with additional evidence. Using their respective histories and what sources for the history of early imperial armillary instruments survive independent thereof, this article tries to explain the mix‐up by exploring the ambiguities of ‘observation’ (guan) as it was mediated through terminology, text, materiality and mathematics. Reconstructing the material features of the ‘sight’ (yi) and ‘effigy’ (xiang), the article will reflect upon the mathematics necessary for their operation. The ‘effigy’, as Li Chunfeng defines it, is a substitute for observation; the ‘sight’, however, is so mediated by the material and mathematical sphere as to confound Li's distinction between looking through and looking at. In the end, however, the difference is moot, since the observational model appears to have played a negligible role in the history of astronomy in first‐millennium China, leaving us to wonder what instrument(s) were used for observation.