I am absolutely loving this book. Everyone has struggled to understand tensor calculus (I mean the real "tensors" with…

I am absolutely loving this book. Everyone has struggled to understand tensor calculus (I mean the real "tensors" with Christoffel symbols, metric etc). Most textbooks just puts out magical definitions for you to memorize without providing any insights or giving you any explanations of where things came from. On the other hand, pop-sci/pop-math books just tells you how amazing things are but without any details on what exactly those things are. The gap is so serious that it has haunted me for decades and I have started to take things in my own hand (I mean put it in AI's hand). 🧵

Arianrhod's book is largely an exception to usual pop-sci genre. This book is so lovingly, caringly and passionately written that it is definitely in my top 5 all-time list. You cannot unsee the labor of love that has gone to produce this amazing marvel. The key thing that makes this book different is that it doesn't shy away from mathematical details. There are so many aha moments, memorable quotes and hilarious facts that my copy is now filled with highlights. But still....

The book is still constrained by the economics of paper, so at times at times you get all the buildup and then the scene cuts. So, how about asking Astra to fill in the gaps? It works marvelously! Here's the example of page Astra inserted in the book:

I think the technique is fairly general. You can insert new sections, sub-sections in your favorite books while not changing any of the original content. The new content is properly demarked so you know its AI generated. In my experience, this has made reading these books 10x more rewarding and enjoyable. Here' the prompt I used that worked very well for this book: The file `xyz.ext` contains excellent and lively historical account of how tensor calculus evolved through the history. However, at times, the book avoids exposing the readers with actual mathematics, the equations it is talking about and other relevant mathematical details that leaves reader in mystery and confusion and only superfluous understanding. Your job is to fix all that by creating a new version of this file. You will assume that the reader is competent high school graduate with understanding of differentiation and integration (but no differential equations etc) as well as 2D vector concepts and basic arithmetic (but no quaternions, vector calculus etc). You will not remove or re-write any existing content in this file but instead you will insert additional information that exposes relevant mathematical details for the context so the reader can fully understand and appreciate the content. You may insert this new content as paragraphs or sub-sections or new entire section as you desire. Note that some of the mathematical content is pushed to endnotes which you may bring it back or duplicate so it is in the flow of the text instead reader having to jump back and forth between endnotes. You may also create links in existing content so user can easily navigate if you feel the links are missing. For any mathematical details you add, you must explain all the symbols if not already explained before and all the steps and make sure user will not have open questions about your writings. You do not need to add additional content for everything but only wher it makes sense or illuminates or enhances the understanding of the context. As an example, the book mentions that Maxwell reformulated previous electromagnetic laws so that he can avoid action at distance but the book does not mention how older formulation looks like, how Maxwell identified the issue of action at distance in those formulations and how exactly Maxwell fixed it. The books frequently mentions such historical formulations and their shortcomings without actually laying out in details what that means and how fixes were created. This is just an example of missing mathematical details but you should find other patterns and add content to fix these issues. You will put yourself in curious reader's shoes and see if you leave wondering or confused or would have liked more details. You will add those details. The content you add should be marked with some sort of red boundary so reader knows that you added them. Outside of that you should not modify any original content (except adding links for navigation). You should preserve the fidelity and style of the book in your writings so it remains cohesive and consistent. You need not worry about chapter or book length increasing too much. You will generate new file `xyz_with_math.ext`.

as this has started to blow up, please do support author by buying this book. If you can manipulate div, grad and curls but never truly understood them, this book is for you: a.co/d/08eyosOY