Jones rational coincidences

Coincidences and Rational Cognition 2 Coincidences: A Fundamental Consequence of Rational Cognition* Accepted postprint for New Ideas in Psychology

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...

The Atiyah–Jones conjecture for rational surfaces

is minimal precisely when the curvature FA is anti-self dual, i.e. FA = −∗FA, in which case A is called an instanton of charge k on X. Let MIk(X) denote the moduli space of framed instantons on X with charge k and let Ck(X) denote the space of all framed gauge equivalence classes of connections on X with charge k. In 1978, Atiyah and Jones [AJ] conjectured that the inclusion MIk(X) → Ck(X) indu...

Remodified Bessel Functions via Coincidences and Near Coincidences

By considering a particular probabilistic scenario associated with coincidences, we are led to a family of functions akin to the modified Bessel function of the first kind. These are in turn solutions to a certain family of linear differential equations possessing structural similarities to the modified Bessel differential equation. The Stirling number triangle of the second kind arises quite n...

Causes , Coincidences , and Theories

Sequences , Patterns and Coincidences

This article provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with sequences and patterns in iid multinomial trials, the birthday problem, and the matching problem. The section on patterns includes the classic distribution theory for waiting time for runs and more general patterns, and their means and moments. It also includes the centr...