The theorizing of a southern continent for more than two millennia before the discovery of Antarctica and its long representation in maps are phenomena unparalleled in the history of geography and are well known. However, the epistemological implications of the mapping of this non-existent place have received little consideration. After preliminary remarks about present-day remote imaging of Antarctica and limits to the completeness of all mapping and knowledge, the article discusses the representation of the southern Terra Incognita in examples of mediaeval and Renaissance maps. It is argued that filling in blank spaces both reflected a yearning for complete knowledge and provided an opportunity for non-geographical discourse that is missing in maps today.