The Greek philosopher Plato is famous for writing his teachings in the form of dialogues. But there are additionally a series of seven letters attributed to Plato. Over the centuries much ink has been spilt in arguments over their authenticity. My guest today argues that these letters are actually epistolary philosophical novel which are if nothing else a “ripping great yarn”.

“In the pages of Plato’s letters,” writes Ariel Helfer, “we find Plato the teacher, the counselor, the ally, the statesman; intrigue and faction in the court of a tyrant; grand political hopes dashed as famous utopian dreams become living nightmares—it is a stunningly dramatic and dynamic portrait of Plato and his philosophy.” An alll this is set in the exotic setting of Hellenized Sicily during the 5th century BC, which has a cultural and political complexity that makes the head spin uncontrollably.

Ariel Helfer is Associate Professor of Philosophy at Wayne State University, and the most recently editor and translator of Plato’s letters in an edition titled Plato’s Letters: The Political Challenges of the Philosophic LIfe . He was last on Historically Thinking to discuss Plato’s dialogue Alcibiades, and the broader subject of political ambition, in a conversation that was published on September 30, 2020.

For show notes, resources, and our archive, go the Historically Thinking Substack

Chapters

1. Introduction and Background — 00:22
2. The Authenticity Debate of Plato's Letters — 03:25
3. Arguments for Authenticity and Unity — 11:27
4. Textual History and Preservation — 18:36
5. Historical Context: Plato in Syracuse — 26:19
6. Themes in the Letters — 33:55
7. Letter One: A Dramatic Opening — 40:51
8. Letter Six: Philosophy, Law, and Playfulness — 47:35
9. Philosophy vs. History: Different Perspectives — 56:24
10. The Herculaneum Scrolls and Future Discoveries — 1:03:20

On October 16, 1843, William Rowan Hamilton was taking a walk with his wife Helen. He was on his way to preside over a meeting of the Royal Irish Academy. As Hamilton came to Broome Bridge, over the Royal Canal, the solution to a vexing problem finally emerged in front of him. He was so excited, and perhaps so afraid that he might forget, that he pulled out his penknife and carved the equation he had so suddenly conceived on the stonework of the bridge.

That might not seem like such a revolutionary moment. But as my guest Robyn Arianrohd explains, Hamilton’s equation was the result of long centuries of mathematical effort. And its consequences would be immense. Because Hamilton’s thought made possible the concepts known as vectors and tensors. And vectors and tensors underlie much of modern science and technology, because they are used whenever a scientist or an engineer wants to use locations in space–everything from designing a bridge, to predicting the path of a gravitational wave; and there’s quite a lot of territory in between those two applications. That moment by the Broome Bridge ushered in a new era.

Robyn Arianrohd is a mathematician, and a historian of science. Her previous books include Thomas Harriot: A Life in Science, which she and I discussed in a conversation that was published on April 30, 2019. Her latest book is Vector: A Surprising Story of Space, Time, and Mathematical Transformation.

For show notes, resources, and our archive, go the Historically Thinking Substack

Chapters

1. Thomas Harriet and the Birth of Modern Algebra
2. Navigation, Collisions, and Early Vector Concepts
3. Newton's Definition of Force and Direction
4. Augustus De Morgan and the Formalization of Algebra
5. Hamilton's Breakthrough: Quaternions and Four Dimensions
6. The Non-Commutative Revolution
7. James Clerk Maxwell and Electromagnetic Theory
8. Maxwell's Equations and the Nature of Light
9. The Vector Wars: Quaternions vs. Vectors
10. Tensors: Beyond Vectors to General Relativity
11. The Playful Seriousness of Mathematical Discovery
12. Conclusion: The Journey into History of Mathematics