Belevedere is a painting by Maurits Cornelis Escher (1898 - 1972), a Dutch graphic artist, that contains many impossible figues and impossible elements. The print was created in 1958, and the original version is now in the National Gallery of Canada, in Ontario.
Belvedere depicts objects which could not possibly exist. It is impossible for the building to exist because in order for it to exist, the rules of Euclidean geometry would have to be violated. For example, there are pillars of the building which are represented as being at the front of the building at their top and at the back of the building at their bottom (and vice versa) and yet being completely vertical. Moreover, the ladder in the picture seems to start inside the building, slope further in towards the building, and yet ends up on the outside of the building. The boy sitting outside the buiding in the picture is also holding an impossible cube.
Escher and other artists such as Oscar Reutersvärd have frequently used impossible figures of varying types in their work, and mathematicians have studied the mathematical and computational properties of impossible figures to try and develop formulas and algorithms for modelling impossible objects, for use in such things as computer vision. Cognitive scientists have been interested in the processes involved in continuing to see impossible figures as possible even when we know them to be impossible. Why, for instance, do we not see the Belvedere building just as some lines on a page once we realise that it can’t exist in three dimensional space? In answering this question, debates about modularity and cognitive penetration are of central importance. To explain: on the hypothesis that the mind is modular, a mental module is a kind of semi-independent department of the mind which deals with particular types of inputs, and gives particular types of outputs, and whose inner workings are not accessible to the conscious awareness of the person – all one can get access to are the relevant outputs. So, in the case of impossible figures, a standard way of explaining why experience of the impossible figure persists even though one knows that one is experiencing an impossibility is that the module, or modules, which constitute the visual system are ‘cognitively impenetrable’ to some degree – i.e. their inner workings and outputs cannot be influenced by conscious awareness.
Philosophers have also been interested in what impossible figures can tell us about the nature of the content of experience (Macpherson 2010). For example, impossible figures seem to provide examples of experiences with content that is contradictory, which some philosophers have taken to count against the claim that perceptual states are belief-like because if they were, when experiencing Belvedere one would simultaneously believe that such as figure could exist and that it could not. This would seem to entail that one was being irrational, because one would simultaneously be holding contradictory beliefs. But it seems highly implausible that one is being irrational when under going this illusion. For discussion of this general point about whether perceptions are like beliefs, see Crane & French (2016).