I also found it interesting that, though in passing, they expressed some of the questions in the mind of many mathematicians and philosopher. Will an alien race be able to appreciate our Mathematics? Being a mathematician, I know several people who believe any sentient being would be able to appreciate our mathematics. So, in some sense, they view mathematics as the ultimate form of art. Other art forms obviously will not be appreciable to a being which does not share similar sense organs. For example, we cannot expect an organism which has no auditory capacity to appreciate music. The makers of this film do not share this idea. In fact, there was a passing mention that the aliens are able to follow some of the ideas in mathematics but not others. I would also like to believe that Mathematics is not holier than other domains.
The climax takes the linguistic-fiction to a whole new level. There is this notion in cognitive linguistics that, our language can influence the way we think. For example, we cannot think about ideas for which we have no words. So adding vocabulary can help us think better. They stretch this idea. Learning the alien language, which is a non-linear language, helps Louise to see time non-linearly. This enables her to see the future, for example. I agree it is stretching it a bit too far. And this might put some people off. But, I enjoyed it. It is an amazing thought, even more so because it is so bizarre. This also gives a brand new explanation to prophecies. In a more scientific world, this gives a theory for the time travel of information - the theme for many science fiction stories like "Stein's Gate". Of course, there is less of science and more of fantasy in this. Nevertheless, it is an interesting idea.
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