Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Situating Emotions: From Embodied Cognition to Mindreading

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Basic social cognition without mindreading: minding minds without attributing contents

This paper argues that mind-reading hypotheses (MRHs), of any kind, are not needed to best describe or best explain basic acts of social cognition. It considers the two most popular MRHs: one-ToM and two-ToM theories. These MRHs face competition in the form of complementary behaviour reading hypotheses (CBRHs). Following Buckner (Mind Lang 29:566–589, 2014), it is argued that the best strategy for putting CBRHs out of play is to appeal to theoretical considerations about the psychosemantics of basic acts of social cognition. In particular, need-based accounts that satisfy a teleological criterion have the ability to put CBRHs out of play. Yet, against this backdrop, a new competitor for MRHs is revealed: mind minding hypothesis (MMHs). MMHs are capable of explaining all the known facts about basic forms of social cognition and they also satisfy the teleological criterion. In conclusion, some objections concerning the theoretical tenability of MMHs are addressed and prospects for further research are canvassed