The Mathematical Theory of Black Holes (1983)

Summary

This book is not "The Mathematical Theory of Black Holes" by Subrahmanyan Chandrasekhar. The provided passages are from "A Budget of Paradoxes (1872)" by Augustus De Morgan, a collection of writings on eccentric and paradoxical works in mathematics, science, and theology. De Morgan’s central argument is that many historical works—from mathematical theology to proposed solutions of the longitude problem—represent logical vagaries or overreaching claims, often mixing right and wrong ideas. He critiques figures like Richard Jack, who attempted to geometrically demonstrate God’s existence, and M. Hoene Wronski, who promised the Absolute and a definitive solution to the longitude problem through obscure mathematics. De Morgan also traces the lineage of scientific instrument makers and discusses the Baconian method, noting that Sir John Herschel insisted on sound mathematical knowledge as essential for independent scientific opinion. A reader takes away a skeptical, historically grounded view of scientific and mathematical claims, learning to distinguish genuine advances from paradoxes.

Key concepts

• Mathematical theology — The attempt to prove the existence of God using geometric or mathematical propositions, as in Richard Jack’s work.
• The Jacotot method — A teaching principle summarized as "Tout est dans tout" (everything is in everything), where one learns something and relates everything else to it.
• The Absolute — A transcendental philosophical concept that M. Hoene Wronski claimed to have at his fingers’ ends, but which he would not reveal without prepayment.
• Baconian philosopher — A type of inquirer derived from Francis Bacon’s inductive method, exemplified by William Herschel, though his processes were considered vague by Baconian standards.
• The longitude problem — A historical challenge to determine a ship’s longitude at sea, which Wronski claimed to have definitively solved through his new celestial mechanics.

From the book

Title: The Mathematical Theory of Black Holes (1983) by Subrahmanyan Chandrasekhar

Popular questions readers ask

• Imagine you are explaining to a friend what the editor of 'A Budget of Paradoxes' found most challenging about preparing De Morgan's manuscript for publication. What was the central problem, and how did the editor attempt to balance preserving De Morgan's vision with making the work publishable?
• De Morgan aimed to 'scrutinize and castigate' both 'heterodox ignorance' and later 'orthodox learning.' What do these two targets suggest about his underlying definition of a 'paradox,' and how might addressing both types of 'inconsistencies' shape the overall philosophical message of his work?
• The editor states that alterations were 'slight and few,' yet also mentions 'one rather large omission.' How can both these statements be true, and what does this apparent contradiction reveal about the editor's understanding of their role versus the integrity of the original text?
• If De Morgan had completed his intended second part, scrutinizing 'orthodox learning,' how might this addition have fundamentally altered the book's intellectual impact and its place within academic discourse, beyond just expanding its content?
• Given the 'miscellaneous and discursive character' of 'A Budget of Paradoxes,' described as a 'receptacle for the author's thoughts on any literary, scientific, or social question,' what does this unique structure suggest about the predominant methods or aims of intellectual inquiry during De Morgan's era?