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Specifically, that the way contiguous levels relate to each other within a hierarchy is similar across different levels. Encoding recursive embedding requires the ability to represent similarities across hierarchical levels (self-similarity). Encoding hierarchical embedding requires the ability to represent dependency or grouping relationships between constituents at multiple levels.
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We focus on detecting what kind of information individuals can represent, rather than on how this information is implemented algorithmically.Įncoding iteration requires the ability to represent the repetition of a certain process, for instance the repeated addition of elements to a structure. In this manuscript we explicitly focus on a third level of analysis, which is the level of representation. However, this isomorphism does not always occur (Lobina, 2011 Luuk & Luuk, 2010 Martins, 2012). Frequently, we find an isomorphism between procedure and structure, i.e., recursive processes often generate recursive structures. Recursion can be defined either as a “procedure that calls itself” or as the property of “constituents that contain constituents of the same kind” (Fitch, 2010 Pinker & Jackendoff, 2005). The second theoretical difficulty is to define the level of analysis useful for empirical enquiries.
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Nevertheless, it is possible to segregate the cognitive abilities necessary to represent the kind of information that each of these processes encode (Fig. Iteration, hierarchical embedding, and recursion are not mutually exclusive processes: in fact, recursion typically involves both hierarchy and iteration. If the hierarchical embedding occurs between constituents of the same category (e.g., such as a noun phrase inside a noun phrase) we classify it as recursive, otherwise as non-recursive. In contrast, “hierarchical” structures always involve the embedding of elements within other elements. For example, putting one marble at a time into a bag is an iterative process, but neither hierarchical nor recursive. An iterative process may or may not generate hierarchical structures or create dependency relationships between different elements. Regarding the first theoretical difficulty, here we adopt a framework (Fitch, 2010 Martins, 2012) in which “iteration” refers to the process of repeating an operation a certain number of times. On the other hand, it has not been clear which level of analysis (process, structure, or representation) is relevant for empirical research (Lobina, 2011, 2014 Martins, 2012). On the one hand, it has proven to be particularly difficult to establish clear distinctions between recursion and similar processes such as hierarchical embedding and iteration (Hulst, 2010). This method opens exciting opportunities to explore the relationship between visual recursion and language.ĭespite considerable agreement about the importance of recursion, many different definitions of recursion are in use (Chomsky, 2010 Corballis, 2007 Gentner, Fenn, Margoliash, & Nusbaum, 2006 Hofstadter, 1980 Kilpatrick, 1985 Odifreddi, 1999 Penrose, 1989) which has hindered consistent interpretation of empirical results (Fitch, 2010).
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We conclude that humans are able to use recursive representations to process complex visuo-spatial hierarchies and that our visual recursion task taps into specific cognitive resources. Compared with embedded iteration, visual recursion correlated positively with other recursive planning tasks (Tower of Hanoi), but not with specific visuo-spatial resources (spatial short-term memory and working memory). We found that adult humans can represent recursion in the visuo-spatial domain, and that this ability is distinct from both general intelligence and the ability to represent iterative processes embedded within hierarchical structures. To investigate this recursion/hierarchy distinction in the visual domain, we developed two novel methods: The Visual Recursion Task (VRT), in which an inferred rule is used to represent new hierarchical levels, and the Embedded Iteration Task (EIT), in which additional elements are added to an existing hierarchical level. With this definition recursion can be distinguished from general hierarchical embedding. We define recursion as the ability to represent multiple hierarchical levels using the same rule, entailing the ability to generate new levels beyond those previously encountered. We describe a new method to explore recursive cognition in the visual domain.