The logic of media usage is determined by the self-blinding of the materiality of the medium in the act of its transmitting function. According to the traditional topos of the ‘dying messenger’, a messenger-oriented model of mediality is developed. Contrary to the appearance of the ‘vanishing’ medium, a critical media philosophy has to depict that and how media always shape and constitute what they represent. One phenomenon mostly being invisible in our normal use of texts and pictures is the medium (...) of ‘artificial flatness’ within the framework of a ‘cultural technique of flattening’: scientific, technical and artistic creativity is inconceivable without two-dimensional inscriptions in the form of writings, graphs, diagrams and maps. But how can this imprinting power of inscribed and illustrated surfaces be grasped if at the same time the role of media is understood in terms of transmission, connection, intermediation? Our suggestion is to describe the shaping power of media by the concept of ‘transfiguration’: From a transfigurative perspective, the medium only reveals itself as a trace on its content. Traces are visible transformations in the mode of latency. To manifest this latency, to make the implicit explicit, is then a task of media philosophy. As examples of such a critical-epistemological reflection, the relationship between writing and language, as well as between map and territory, is discussed. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...) computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)