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closeMaps, Mappings and Animal Models
Posted by mapologist on 17 Dec 2009 at 20:11 GMT
In Category Theory (see e.g., Lawvere & Schanuel 1997), the most important issue is maps and mappings (as corroborated by these authors as well).
However, for being able to correlate the ongoing mapping processes in the human mind with real neural maps (i.e., neural activity patterns in vivo), we may turn to smaller animals first (e.g., zebrafish, fruit flies), where we can really see the synaptic networks in action and in real-time and during the whole ontogenetic development.
Hence, it would be interesting to have a cross-talk between these authors and zebrafish (or fruit fly) experts, because transitive inference and class inclusion could also be studied in these (more transparent and better investigable) model animals.
But when these mapping processes will be demonstrated (or "unveiled") by experimental mappings, then a big step in modern neuroscience will have been done indeed...
RE: Maps, Mappings and Animal Models
steven1 replied to mapologist on 14 Jan 2010 at 08:36 GMT
Though we agree that much is to be gained by integrating animal and human studies, we think that the (implicit) form of Transitive Inference demonstrated by non-humans is fundamentally different from the (explicit) form acquired by older children and adults. Adults also perform transitive inference without being explicitly aware of the structure (see Frank et al 2005), and one characteristic difference between the two is the many more trials required to achieve criterion in the implicit form.
Category theory also provides another perspective on this difference, alluded to in the third and second last paragraphs of our paper. That is, Transitive Inference is modeled as a product in the category Set, but more succinctly as a composition in the category Rel. However, Class Inclusion cannot be modeled as a composition in Rel. Hence, if the non-human and infant examples of Transitive Inference are indeed the same as the explicit form demonstrated by older children and adults, then these groups should also be capable of Class Inclusion.
Reference
Frank MJ, Rudy JW, Levy WB, O'Reilly RC. (2005). When logic fails: Implicit transitive inference in humans. Memory and Cognition, 33(4), 742-750.