Thinking through other minds: A variational approach to cognition and culture

The processes underwriting the acquisition of culture remain unclear. How are shared habits, norms, and expectations learned and maintained with precision and reliability across large-scale sociocultural ensembles? Is there a unifying account of the mechanisms involved in the acquisition of culture? Notions such as “shared expectations,” the “selective patterning of attention and behaviour,” “cultural evolution,” “cultural inheritance,” and “implicit learning” are the main candidates to underpin a unifying account of cognition and the acquisition of culture; however, their interactions require greater specification and clarification. In this article, we integrate these candidates using the variational (free-energy) approach to human cognition and culture in theoretical neuroscience. We describe the construction by humans of social niches that afford epistemic resources called cultural affordances. We argue that human agents learn the shared habits, norms, and expectations of their culture through immersive participation in patterned cultural practices that selectively pattern attention and behaviour. We call this process “thinking through other minds” (TTOM) – in effect, the process of inferring other agents’ expectations about the world and how to behave in social context. We argue that for humans, information from and about other people's expectations constitutes the primary domain of statistical regularities that humans leverage to predict and organize behaviour. The integrative model we offer has implications that can advance theories of cognition, enculturation, adaptation, and psychopathology. Crucially, this formal (variational) treatment seeks to resolve key debates in current cognitive science, such as the distinction between internalist and externalist accounts of theory of mind abilities and the more fundamental distinction between dynamical and representational accounts of enactivism.

Role of the cut-off function for the ground state variational wavefunction of the hydrogen atom confined by a hard sphere

A variational treatment of the hydrogen atom in its ground state, enclosed by a hard spherical cavity of radius Rc , is developed by considering the ansatz wavefunction as the product of the free-atom 1s orbital times a cut-off function to satisfy the Dirichlet boundary condition imposed by the impenetrable confining sphere. Seven different expressions for the cut-off function are employed to evaluate the energy, the cusp condition, <r^-1>,<r>, <r^2>, and the Shannon entropy, and as a function of Rc in each case. We investigate which of the proposed cut-off functions provides best agreement with available corresponding exact calculations for the above quantities. We find that most of these cut-off functions work better in certain regions of Rc , while others are identified to give bad results in general. The cut-off functions that give, on average, better results are of the form (1- (r/Rc)^n), n=1,2,3

Peculiarities of some classical variational treatments using the maximum entropy principle

We study some peculiarities of the classical variational treatment that applies Jaynes’ maximum entropy principle. The associated variational treatment is usually called MaxEnt. We deal with it in connection with thermodynamics’ reciprocity relations. Two points of view are adopted: (A) One of them is purely abstract, concerned solely with ascertaining compliance of the variational solutions with the reciprocity relations in which one does not need here to have explicit values for the Lagrange multipliers. The other, (B) is a straightforward variation process in which one explicitly obtains the specific values of these multipliers. We focus on the so called q-entropy because it illustratesa situation in which the above two approaches yield different results. We detect an information loss in extracting the explicit form of the normalization-associated Lagrange multipliers.

A Lagrangian–Hamiltonian unified formalism for a class of dissipative systems

Entropy production in classical thermomechanical systems is the result of three sources: transfer of heat; dissipative stresses, such as viscosity; and internal variables. In this paper, a variational treatment for dissipative systems due to internal variables is presented. Specifically, in the context of the theory of internal variables, a novel dissipative Lagrangian–Hamiltonian formalism is developed. Two fundamental thermodynamic functions (the free energy and the entropy production rate) form the basis of this formalism. The Hamiltonian formulation reveals a new structure on the phase space, and is applied to prove large-time solutions for the semilinear problem. Finally, the formalism is applied to the problem of dynamic brittle fracture.