RHA Books

Books by Ralph H. Abraham

This is the comprehensive list of English editions. The most recent editions in reverse chronological order, with links to amazon.com. Titles available as ebooks marked ***.

Books, History

Schism: The Madness of Crowds, Toxicity of Social Media, Social Polarization, and Political Violence; A Cybernetic Approach, Epigraph Books, Rhinebeck, NY, 2023. This book targets the crisis in regulating the mechanisms of violence. It's goal is to bring modern mathematics, specifically catastrophe theory, to bear on the problems of social polarization, division, and the onset of civil war in the United States of America at the time of writing, Fall 2022. We will try to connect catastrophe theory to these problems with a minimum of mathematical mystification. Bolts from the Blue: Art, Mathematics, and Cultural Evolution, Epigraph Books, Rhinebeck, NY, 2011. Six episodes from the history of mathematics. This book is about the role of mathematics in the evolution of culture, and the evolution of mathematics itself. It aims to clarify the question: What is mathematics, and who is a mathematician? We believe that everyone has a native mathematical talent, before it is tainted in school by math anxiety. Chaos, Gaia, Eros: A Chaos Pioneer Uncovers the Three Great Streams of History, Epigraph Books, Rhinebeck, NY, 2011. Reprint of the 1994 edition. This book collects evidence for a theory. Rather than expand this collage of information into a pretense of normal narrative, for you to recondense in your own mind, I have kept it in condensed form. The information is not in linear (one-dimensional) order. Its natural order is multidimensional: one-dimensional time, two-dimensional space, plus many-dimensional ideas. Thus the same theme may be traced through time, over space, or through an evolution of ideas or myths. Wittgenstein wrote in the Preface to his Philosophical Investigations, The very nature of the investigation . . . compels us to travel over a wide field of thought criss-cross in every direction. Thus this book is really only a collection. Revised 8 March 2024 by Ralph: Epigraph Books, Rhinebeck, NY, 2023.; This book targets the crisis in regulating the mechanisms of violence. It's goal is to bring modern mathematics, specifically catastrophe theory, to bear on the problems of social polarization, division, and the onset of civil war in the United States of America at the time of writing, Fall 2022. We will try to connect catastrophe theory to these problems with a minimum of mathematical mystification.