Books in the Series on Knots & Everything series

It is not uncommon for the Principle of Complementarity to be invoked in either Science or Philosophy, viz. the ancient oriental philosophy of Yin and Yang whose symbolic representation is portrayed on the cover of the book. Or Niels Bohr's use of it as the basis for the so-called Copenhagen interpretation of Quantum Mechanics. This book arose as an outgrowth of the author's previous book entitled "Knots, Braids and Moebius Strips," published by World Scientific in 2015, wherein the Principle itself was discovered to be expressible as a simple 2x2 matrix that summarizes the algebraic essence of both the well-known Microbiology of DNA and the author's version of the elementary particles of physics. At that point, the possibility of an even wider utilization of that expression of Complementarity arose.The current book, features Complementarity, in which the matrix algebra is extended to characterize not only DNA itself but the well-known process of its replication, a most gratifying outcome. The book then goes on to explore Complementarity, with and without its matrix expression, as it occurs, not only in much of physics but in its extension to cosmology as well.

A collection of essays that stand on their own but are also connected. Part I examines how numbers and geometry arise in nature and several cultural contexts. Part II shows how many of the same numbers and number sequences are related to the study of numbers, dynamical systems, chaos and fractals.

These pictures illustrate standard examples in low dimensional topology. The text starts at the most basic level (the intersection of coordinate planes) and gives hands-on constructions of some beautiful examples in topology, including Poincare's example of a homology sphere, and knotted surfaces.