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Correct me if I'm wrong:

In Frequencies Theo appears to be a determinist (just like the movie's authors), while his father believes in free will and the uncertainty principle.

In the end, when Theo explains "how it all works" and tells his father that as he, Theo, perfects the formula, he'll know everything about the future (no surprises, just enjoying the performance while knowing how it ends), he suggests to his father he should say good-bye; the father agrees and leaves, and seconds later Theo discovers the perfect version of the formula.

Why did his father leave; why the good-bye? Does he hate his son now? Has he renounced him? Why is Theo indifferent? Does his knowledge of the future void all filial emotions somehow?

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His father knows the son is right, in a way, but the conclusion with Zac and Marie is realizing that even if Zack is the "ironic particle" that broke Marie free of the hold of her Frequency, then Nature determined that she needed him to get what she wanted. Therefore, it had been determined that Zack would believe free will was so important that he'd work his whole life to set her free from determinism. Ow, our heads! Theo's father as we know him so far is the spirit of Free Will, so he can tell by looking in his eyes that either Theo knows that he's right about knowing everything, or believes so strongly in it that he will shape the world around him to prove it.

The lines about 'goodbye' make him realize it - it becomes an automatic reaction "So this is where I say goodbye" "Yes" "Goodbye." It's like Marie when she was younger and merely reacting to everything around her perfectly - as further reflected at the party where she and Zack meet as adults and she looks at the other lower-frequency people reacting as if automatons, just like her.

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