The phrase is part of this following line:
普段の生活の中に埋もれている何気ないことなど気にも留めないし、知覚したとしてもすぐに忘れるか、脳が処理をしないかのどちらかなんだ。
Actually I'm also unsure about the role and meaning of the か in the second to last clause too, but, in case it is unrelated to the clause I cited, I thought the meaning would be something on the lines of "The brain decides on what things to remember": I interpreted both か as "nested questions", so it would be something like "the brain thinks どちらか with 処理をしするか処理をしないか as options.
I think the reasoning is pretty convoluted, but it's the only thing I could come up with. I hope somebody may help me. Thanks in advance.