A new class of intransitive objects – geometrical and mathematical constructions forming intransitive cycles A>B>C>A – are presented. In contrast to the famous intransitive dice, lotteries, etc., they show deterministic (not probabilistic) intransitive relations. The simplest ones visualize intransitivity that can be understood at a qualitative level and does not require quantitative reasoning. They can be used as manipulatives for learning intransitivity. Classification of the types of situations in which the transitivity axiom does and does not work is presented. Four levels of complexity of intransitivity are introduced, from simple combinatorial intransitivity to a "rhizomatic" one. A possible version of the main educational message for students in teaching and learning transitivity-intransitivity is presented.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.