The second time I sat down to read this book I decided to really give it a try as a story and not so much as "math". This approach worked much better for me. I also checked out an annotated version of the story, but only used it as a reference on a couple of occasions,
I have no idea why it is a "romance of many dimensions". To me, it seemed to be more about aristocratic society and possibly religion than anything else. I say religion because things in the "3rd dimension" is more like believing in God than a mathematical concept. The way that the 3rd dimension is talked about in the aristocratic world of Flatland reminds me of Russia outlawing all Christianity.
In all I found it interesting as a science fiction work. I give this book 3 out of 5 stars.
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