The story has some nice and unique ideas, but for me it didn't really form a full story (on the level expected from a short story), and it also has some flaws. It has value, but didn't make me part of the fan group. 
 Some of my problems, as spoilers follow. 
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 Experiencing free will has nothing to do with the world being deterministic or not. A chess program will make decision, but in practice, it will follow a deterministic path. (A curve in the memory phase space.) Consequently, the fact that we perceive free will says nothing about our world being non-deterministic. 
 Similarly, a deterministic universe would not imply the existence of a 'Book of Ages' and create the kind of paradox described. A deterministic universe would obviously only exist if it didn't have an internal paradox and the 'Book of Ages' is one. The philosophical section related to the 'Book of Ages', only proves that there could be no Universe with free will AND a 'physically' existing 'Book of Ages'. Again, this is of no value to prove anything within the story. 
 'Variation' variations: The fact that the path of the light between two points can be found by means of variations, has nothing to do with the 'light knowing in advance where it will go'. Light will go where the laws of physics will take it. If you shoot a laser beam from point A, it will travel according to these rules even if it's vacuum all along, or you decide to push a prism into its path after it has left point A. 
 I don't see the relationship between being able to 'get the hang of Heptapod B' and 'seeing the future'. Just because I understand an equation that describes the working of the Universe (let's call it Unified Equation), I won't automatically able to put in all existing information and process it. Just because you acquire the capability to read a book with a single glance (absorb the story at once), won't make you an Oracle, just a superfast reader... Not all human languages are completely linear either, but not everyone is a lottery winner. 
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