Linear and nonlinear interactions of an electromagnetic wave with molecules of an isotropic medium induce in them multipole moments which contribute to electric polarization of the system [1]. Out of absorption bands optical rectification (OR) via the second-order susceptibility is forbidden but the fourth-order dipolar electric nonlinearity may cause OR in chiral liquids [2]. However, in absor...

In 1974, Heinz von Foerster articulated the distinction between a firstand second-order cybernetics, as, respectively, the cybernetics of observed systems and the cybernetics of observing systems. Von Foerster’s distinction, together with his own work on the epistemology of the observer, has been enormously influential on the work of a later generation of cyberneticians. It has provided an arch...

Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core...

.................................................................................................................................. iii ACKNOWLEDGMENTS ............................................................................................................. iv TABLE OF CONTENTS................................................................................................................ v L...

This paper introduces the other papers in this issue, describing and arguing for the context in which they were written – a conference that was, unusually, based in conversation rather than reporting through the presentation of papers: and a refereeing process that continued after the initial presentation (at the conference) of the work reported, thus allowing responses to critical comments. Ma...

summing the Boltzmann factor over all spin configurations {si}. The enumeration of all configurations cannot be done for d ≥ 3, and although possible in d = 2 is extremely hard there as well (a problem solved by Onsager). We will use an approximate solution technique known as mean field theory. Last term we solved the problem of noninteracting spins in a magnetic field described by the Hamilton...