Planetary Harmonies

The authors have presented and interpreted Johannes Kepler's Latin text to English readers by putting it into the kind of clear but earnest language they suppose Kepler would have used if he had been writing today.

Students in an introductory physics class learn a variety of different, and seemingly unconnected, concepts. Gravity, the laws of motion, forces and fields, the mathematical nature of the science - all of these are ideas that play a central role in understanding physics. And one thing that connects all of these physical concepts is the impetus the great scientists of the past had to develop them - the desire to understand the motion of the planets of the solar system. This desire led to the revolutionary work of Copernicus and Galileo, Kepler and Newton. And their work forever altered how science is practiced and understood.

Book Five of Johannes Kepler's great masterpiece on planetary motion is presented with an introduction by the ultimate authority on this topic, noted physicist and bestselling author Stephen Hawking. Modifying Copernicus's sun-centered model of the universe, Kepler's 1619 work went on to establish laws of planetary motion, forming the basis for Newton's discoveries some 60 years later. As part of our On the Shoulders of Giants series, this translation of the original edition of Kepler's monumental essay includes an insightful biography and a highly accessible summary putting into context the significance of Harmony of the World.

This volume introduces what has sometimes been called "the third component of western culture." It traces the historical development of those religious traditions which have rejected a world view based on the primacy of pure rationality or doctrinal faith, emphasizing instead the importance of inner enlightenment or gnosis: a revelatory experience which was typically believed to entail an encounter with one's true self as well as with the ground of being, God. The contributors to this book demonstrate this perspective as fundamental to a variety of interconnected traditions. In Antiquity, one finds the gnostics and hermetics; in the Middle Ages several Christian sects. The medieval Cathars can, to a certain extent, be considered part of the same tradition. Starting with the Italian humanist Renaissance, hermetic philosophy became of central importance to a new religious synthesis that can be referred to as Western Esotericism." The development of this tradition is described from Renaissance hermeticists and practitioners of spiritual alchemy to the emergence of Rosicrucianism and Christian theosophy in the seventeenth century, and from post-enlightenment aspects of Romanticism and occultism to the present-day New Age movement.

Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the ?Mathematics of Harmony,? a new interdisciplinary direction of modern science. This direction has its origins in ?The Elements? of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the ?golden? algebraic equations, the generalized Binet formulas, Fibonacci and ?golden? matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and ?golden? matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.