An old philosophical problem, the mind-body problem, has not been yet solved by philosophers or scientists. Even if in cognitive neuroscience has been a stunning development in the last 20 years, the mind-body problem remained unsolved. Even if the majority of researchers in this domain accept the identity theory from an ontological viewpoint, many of them reject this position from an epistemol...

In this paper we present a simplified model of a three-body problem. Place three parallel lines in the plane. Place one mass on each of the lines and let their positions evolve according to Newton’s inverse square law of gravitation. We prove the KAM theory applies to our model and simulations are presented. We argue that this model provides an ideal, accessible entry point into the beautiful m...

We review what has been learned recently using N -body simulations about the evolution of globular clusters. While simulations of star clusters have become more realistic, and now include the evolution of single and binary stars, the prospect of reaching large enough N is still a distant one. Nevertheless more restricted kinds of simulations have recently brought valuable progress for certain p...

This selective review is written as an introduction to the mathematical theory of the Schro ̈dinger equation for N particles. Characteristic for these systems are the cluster properties of the potential in configuration space, which are expressed in a simple geometric language. The methods developed over the last 40 years to deal with this primary aspect are described by giving full proofs of...