This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.

This anthology, the largest collection of Pythagorean writings ever to appear in English, contains the four ancient biographies of Pythagoras and over 25 Pythagorean and Neopythagorean writings from the Classical and Hellenistic periods. The material of this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization.

Explores Thales’s speculative philosophy through a study of geometrical diagrams. Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato’s Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn’s book will enrich the study of ancient philosophy and mathematics alike.

This book is a commentary on the Pythagorean Golden Verses, a neglected, but once very popular poem of the Hellenistic period. The goal of the poem is to introduce its readers to the basic moral, religious and philosophical doctrines of the Pythagorean sect and to guide them to spiritual maturity. The first part of the book treats still unresolved introductory matters such as the date, authorship, genre, composition, and the historical locus of the poem. This is followed by a text with translation on facing pages, and a detailed commentary containing a wealth of comparative material from the Greco-Roman period, including early Christianity and Judaism. Particularly valuable are the extensive discussions of the moral topoi and religious themes encountered in the poem.

Frontmatter --Contents --List of Color Plates --Preface --Prologue: Cambridge, England, 1993 --1. Mesopotamia, 1800 BCE --Sidebar 1: Did the Egyptians Know It? --2. Pythagoras --3. Euclid's Elements --Sidebar 2: The Pythagorean Theorem in Art, Poetry, and Prose --4. Archimedes --5. Translators and Commentators, 500-1500 CE --6. François Viète Makes History --7. From the Infinite to the Infinitesimal --Sidebar 3: A Remarkable Formula by Euler --8. 371 Proofs, and Then Some --Sidebar 4: The Folding Bag --Sidebar 5: Einstein Meets Pythagoras --Sidebar 6: A Most Unusual Proof --9. A Theme and Variations --Sidebar 7: A Pythagorean Curiosity --Sidebar 8: A Case of Overuse --10. Strange Coordinates --11. Notation, Notation, Notation --12. From Flat Space to Curved Spacetime --Sidebar 9: A Case of Misuse --13. Prelude to Relativity --14. From Bern to Berlin, 1905-1915 --Sidebar 10: Four Pythagorean Brainteasers --15. But Is It Universal? --16. Afterthoughts --Epilogue: Samos, 2005 --Appendixes --Chronology --Bibliography --Illustrations Credits --Index.

Modern research has demonstrated that many stars are surrounded by planets—some of which might contain the right conditions to harbor life. This has only reinforced a question that has been tormenting scientists, philosophers and priests since Antiquity: Are there other inhabited worlds beyond our own? This book analyzes the many ways that humans have argued for and depicted extraterrestrial life over the centuries. The first known texts about the subject date from as early as the 6th century BC. Since that time, countless well-known historical characters like Lucretius, Aristotle, Thomas Aquinas, Cusanus, Bruno, Kepler, Descartes, and Huygens contributed to the debate; here, their lesser known opinions on the subject are studied in detail. It is often difficult for the modern mind to follow the thinking of our ancestors, which can only be understood when placed in the relevant context. The book thus extends its scope to the evolution of ideas about cosmology in general, as well as the culture in which these great thinkers wrote. The research is presented with the author's insights and humor, making this an easy and enjoyable read.

The World's Religions offers a fascinating insight into a wide range of faiths, their history and their followers. In the richly illustrated new edition of this popular book, religions are described through their symbols, rituals, followers, architecture and art. References, statistics, maps and pictures have been updated and added. The text has been thoroughly revised to highlight recent developments, such as the spread of Islam, African-American and Hispanic-American religious experience, and women priests.

The timeless brilliance of this exhaustive survey of the best classical writers of antiquity on Pythagoras was first published in 1687 in Thomas Stanley’s massive tome, The History of Philosophy. It remains as contemporary today as it was over three hundred years ago. The text of the 1687 book has been reset and modernized to make it more accessible to the modern reader. Spelling has been regularized, obsolete words not found in a modern dictionary have been replaced, and contemporary conventions of punctuation have been used. Biographical sketches of Thomas Stanley and Pythagoras by Manly Palmer Hall, founder of the Philosophical Research Society, have been included, along with a profound overview of Pythagorean philosophy by Platonic scholar Dr. Henry L. Drake. The extensive Greek language references throughout the text have been corrected and contextualized, and reset in a modern Greek font. Each quotation has been verified with the source document in Greek. An extensive annotated appendix of these classical sources is included. A complete bibliography details all the reference works utilized, and a small Glossary defines a number of terms, especially those from musical theory, which may be unfamiliar to the non-technical reader.