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5.0 out of 5 stars Important, useful but almost un-grokkable, 27 Dec 2013
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This review is from: Methods of Information Geometry (amsns AMS non-series title) (Paperback)
I have a love-hate relationship with this book. As a non-mathematician who cannot properly understand anything without knowing why I would want to, this is one of those books that takes a very long time to get a grip with.

"Yes, OK, great... but why???"

The procession from one equation to the next is completely unmotivated and the text is sparse and badly written. It conforms exactly to the stereotype of mathematics as abstruse and oblivious to practicality.

None-the-less, I have found it to be an indispensable reference, and quite inspiring at times.

The introduction to differential geometry follows the introduction in The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics) very closely - it's concise and thorough. The meat, chapters 2-3 paint a nice, though somewhat obscurely presented picture of divergences and differential manifolds. I have found content of these chapters to be very useful, though as I said, it took me a long time to do so. I have found chapter 4 to have some interesting things to say on testing and estimation. It's definitely a nice way of thinking about statistics (though not a good way of communicating them, as basically no-one will know what you are talking about). I can't say much about the latter chapters, though I have read them they are still beyond my horizon of practicality (barring some of the last chapter) - I can see that one thing follows from the next - but why does it matter?! dammit! There are some examples, but they are still miles from any application.

In summary, I have found it very interesting and helpful, despite it being a completely infuriating read.
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Methods of Information Geometry (amsns AMS non-series title)
Methods of Information Geometry (amsns AMS non-series title) by Shun-ichi Amari (Paperback - 21 Feb 2008)
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