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This book is INCREDIBLE!
I have several years of different kinds of dance and dance-related background (social dancing - swing, tango, etc.; yoga, pilates, ballet, ...) I also have a strong background in mathematics, physics, computer science (will have a Ph.D. in a few months) and related disciplines.
If you have some college-level physics background, or even a solid understanding of high-school physics, chances are that you can work out many of the things in this book on your own. But it takes time, and you may not have the enthusiasm. (In fact, after reading this book you may get the enthusiasm to actually work out a few things.) On the other hand, if you have this kind of background, then reading this book is simple, very enjoyable, and also a great learning experience. You do not have to understand everything. If you understand one idea from each chapter - that is more than enough to read this book. (For example, if the only things you understand from the chapter on pirouettes is that it makes sense to push into the floor with both legs in opposite directions. Another idea you may get from another chapter is - why your body wants to lean in the direction you are starting to fall to actually save you from falling.)
This is great for learning dance on top of your scientific background. In minutes you pick up things that would take months to discover. You start applying them immediately. Very quickly (if you devote some time to thinking over this book) it creates a framework in your mind. You come to a dance class, and you understand so much more, because many of the things can be easily explained in the framework of this book. In other words, the book gives you a quick foundation to build on top, if you have intellect and years of education, rather than years of dance background (then you already do have a foundation).
Besides, this book gives you a better understanding of physics. Especially if you are more of a dancer than a thinker, then, I would assume (not sure though) you can get a lot of physics out of it. That is, you can use the book the other way round. You know how something feels, and then you can relate to the physical explanation.
I am not, however, sure that this book would be of equal benefit to those who don't know much physics. Generally speaking, I would highly recommend to every dancer to actually learn some physics. Especially if you are in college, take a course in basic Newtonian mechanics. (This can make even more sense for a dancer, than learning anatomy or music.) The author of the book stresses it a lot, many dancers without a science background do many things that are counterproductive. It takes just a little scientific thinking to recognize these mistakes and stop wasting time. Just like it is useful to know how your body works to e.g. strech safely and efficiently, it is also useful to know how nature works to dance better.
If you ask "What does it feel like, when you know more physics, how does it help to dance?" --- I can try to answer. You know how it feels when you notice which way you are falling (out of balance or out of alignment) - forward, sideways, etc., right? You notice, then you fix it. After this book, especially if you have some physics background to relate to, but perhaps even without it, you will start to notice how having your feet further apart makes it easier to rotate (e.g. pirouette from 4th), how lifting your leg in Arabesque Pirouette slows you down (unless you lift it higher than 90 degrees), how sacrificing turnout before a grand jete makes your jump longer and higher; how you get more tired when doing slower jumps then when doing faster jumps, and other kinds of things. The world will become more clear for you, easier to understand; it will make more sense.
If you do some other dance style, you would also definitely benefit from this book. (You would benefit much more if you supplmenent your dancing by taking some ballet classes, at least for a year, and then you can apply this book to your dance style.) If you do acrobatics, martial arts, etc., you can greatly benefit from this book as well, but again, you need to be able to relate to this book. You need to know some ballet (better by personal experience) and/or some physics, at least on a basic level (e.g. 2nd Newton's law, F=ma).
If you are a physicist, note that this book is not technical. It has some appendices (still pretty basic) and plenty of references, some, presumably, to more technical materials. So you can use it as a starting point. (Not sure there is much technical research on the physics of dance or related activities.)
Overall, a great book. Standing ovation!