Could the acquisition of a non-linear language distort the mind into a condition where it can see 'the future', and use information gained in future events to make decisions in present events? If we can truly think of the events in our lives holistically, understanding how our choices are interconnected and influence each other without needing to place them in a linear context, could this enable us to imagine our future so clearly that we can actually read additional detail back out of it, and use that to steer our present actions? I don't mean just seeing what we'll do; I'm talking about seeing what other people will do. Exact words they will say, in an exact place and time, in the future -- like what happens in this movie.
According to the movie, if you spend a lifetime working to truly understand the non-linear visual language of the heptapod creatures (like the main character will do), you not only gain this ability but the ability becomes retroactive and starts intruding on your brain even before you fully comprehend it. There is a chicken-and-egg problem here, as well as the usual time paradox issues, but I want to set all those aside and ask a more fundamental question:
Is there such a thing as a non-linear communication method at all?
The movie makes a big deal of the discovery that the heptapod's spoken language is totally unrelated to their written language, and their written language is unique because it is "non-linear" - i.e. there is no proper beginning or end to their "sentences". But I don't think that difference actually matters.
Think of all the flowcharting tools there are out there, connecting boxes with lines to show operations and sequences visually. They can convey both linear and non-linear information. An example with all non-linear information might be a diagram of a database schema. There is common grammar for that, using double-arrows and lines and other markup, and if you know it you can get a good understanding of a very complicated database structure.
But whether these charts are linear or non-linear, our process of interpreting them is still the same linear one we use for spoken language. We focus on a piece that is relevant to our train of thought and follow its connections in the visual structure until the question we have is answered, and as we go we internalize the structure so subsequent linear readings create more connections at once.
Even a completely grammar-free visual communication, like a photograph of an event, is still interpreted by constructing an impression in the mind one concept at a time. The visual information triggers a cascade of reactions, with some happening sooner or later than the others. It's not discrete, but it's still definitely linear.
That's the physiological basis for language. Anywhere we must involve the act of interpretation we must involve linearity. A visual communication method - even one that deliberately refuses to express linear concepts - is not enough, in itself, to escape this.
I think there must be something more in play.
Take a human, evolved to see color. Studiously prevent them from internalizing any objective descriptors for it - "red", "blue", "paisley". Are they now somehow closer to perceiving colors their eyes cannot even detect? (The equivalent of "seeing the future" in the movie.) Of course not. (Well, perhaps in the sense that they have a more direct understanding of what it's like to lack that knowledge... Handy for your spiritual awakening, but not actually what I could call actionable data.)
Take a human evolved to see color. Provide them with glasses that can detect the entire electromagnetic spectrum, and translate it into colors their eyes can see. Train them from birth to use the glasses effortlessly, to filter and interpret the whole spectrum around them. Now that's a new paradigm.
Take a human evolved to depend on various physiological means to remember past events. Give them a pair of glasses that automatically records everything they see, for all time, with fidelity so high they cannot tell the difference between live input and playback. Teach them from birth to use these glasses, to use the highly-compex object and scene recognition and tagging software that comes with the glasses, to augment their own physiological memory. Even better!
Provide every human with these glasses. Embed them surgically a few years after birth. Now give every human the ability to access the full recordings of every other human, living or dead, since the invention of the first pair. Are we headed for dystopia or utopia? I'm not sure.
Invent a supercomputing device made of billions of distributed nodes, with access to these archives, and other archives from passive recording devices spread all over the planet. Train it to predict the outcome of future events, starting from one second in the future, and then increasing that limit to ten seconds, then a minute, as the system ratchets up in accuracy. It won't make us heptapods, but it will give us a vision of the future without breaking any laws of causality...
But look out: Now the system needs to factor in the results of its own future predictions, when it makes future predictions. The Red Queen effect. Perhaps only give a few powerful people the ability to see those predictions, limiting their potential impact. Might help with accuracy. Might also tip the balance towards horrible dystopia.
Pardon me, I've been reading too much scifi lately. :D
But anyway, the point I'm trying to make is, you cannot escape the linearity of interpretation, and if you want to see the future, standard human hardware just ain't enough.