Believers tend to view the experience of coincidences as evidence for a variety of paranormal beliefs in mind and mysterious causal mechanisms out in the world. On the other hand, skeptics (e.g. most psychologists) tend to dismiss the psychological experience of coincidences as just yet one more demonstration of how irrational people can be. Irrationality in this context means an association be...

In this paper, we apply Pad e approximation methods to derive completely explicit measures of irrationality for certain classes of algebraic numbers. Our approach is similar to that taken previously by G.V. Chudnovsky but has some fundamental advantages with regards to determining implicit constants. Our general results may be applied to produce speciic bounds of the avour of 3 p 2 ? p q > 1 4 ...

The Schrödinger equation for a quantum particle in a two-dimensional triangular billiard can be written as the Helmholtz equation with a Dirichlet boundary condition. We numerically explore the quantum entanglement of the eigenfunctions of the triangle billiard and its relation to the irrationality of the triangular geometry. We also study the entanglement dynamics of the coherent state with it...