Entropy, information and doubly stochastic transformations

I analyze two inequalities on entropy and information, one due to von Neumann and a recent one to Schiffer, and show that the relevant quantities in these inequalities are related by special doubly stochastic matrices (DSM). I then use generalization of the first inequality to prove algebraically a generalization of Schiffer's inequality to arbitrary DSM. I also give a second interpretation to the latter inequality, determine its domain of applicability, and illustrate it by using Zeeman splitting. This example shows that symmetric (degenerate) systems have less entropy than the corresponding split systems, if compared at the same average energy. This seemingly counter-intuitive result is explained thermodynamically. © 1991.

Visual information and body sway coupling in infants during sitting acquisition

The purpose of this study was to examine if there is any developmental change in the coupling between visual information and trunk sway in infants as they acquire the sitting position. Twenty-four infants distributed in four groups (6-, 7-, 8-, and 9-month-old) were sat inside a moving room that oscillated back and forward at frequencies of 0.2 and 0.5 Hz. The results revealed that trunk sway matched to the moving room at both frequencies but did not differ among the four age groups. Coherence and gain revealed that the coupling was weaker at 0.2 than at 0.5 Hz. Relative phase showed that at 0.2 Hz, infants were swaying with no lag but at 0.5 Hz they were lagging the room. These results showed that the coupling between visual information and trunk sway in infants varies with the visual stimulus but does not change as infants acquire the sitting position. © 2001 Elsevier B.V.

Information and mechanical models of intelligence: What can we learn from cognitive science?

The impact of new advanced technology on issues that concern meaningful information and its relation to studies of intelligence constitutes the main topic of the present paper. The advantages, disadvantages and implications of the synthetic methodology developed by cognitive scientists, according to which mechanical models of the mind, such as computer simulations or self-organizing robots, may provide good explanatory tools to investigate cognition, are discussed. A difficulty with this methodology is pointed out, namely the use of meaningless information to explain intelligent behavior that incorporates meaningful information. In this context, it is inquired what are the contributions of cognitive science to contemporary studies of intelligent behavior and how technology may play a role in the analysis of the relationships established by organisms in their natural and social environments. © John Benjamins Publishing Company.

Experiencing Manipulative Material for the Teaching and Learning of Mathematics

This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.