Given that, what additional value is The Tensor Cookbook providing such that it is worth learning an entirely new notation (for me)? It would probably require long term usage to really benefit from these visual depictions.
In the Tensor Cookbook I aim to show the same formulas using tensor diagrams, in a way that (hopefully) make them seem so obvious you don't even need the book afterwards.
In contrast, the Tensor Cookbook was my first introduction to tensor diagrams, so I didn't have any prior experience with them to lean on.
It certainly looks like a useful and powerful technique, but it seems like something that warrants almost a crash course in the topic with some exercises rather than just jumping in.
I guess my personal crash course was writing a book on the topic. And a software library... Ironically this makes it harder for me to appreciate the level of explanation needed for others.
Thus I rely on people like you to tell me where the chain jumps off, so I can expand the sections. Please let me know what sections were too quickly skipped through!