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gwern comments on Harry Potter and the Methods of Rationality discussion thread, part 24, chapter 95 - Less Wrong Discussion
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Hyperventilation's primary effect is to reduce CO2 levels in your blood, although it also increases oxygen. Decreasing CO2 beyond normal levels makes blood bicarbonate combine with hydrogen ions to form more CO2, which increases blood alkalinity, which makes blood vessels constrict and reduce blood supply to the brain, which makes you lightheaded. So hyperventilation is low-quality evidence about the effects of extra oxygen on your brain.
...Now I kinda want to put Gwern into a hyperbaric chamber and have him record his dual-n-back and math performance for comparison.
I don't think that's necessary. Besides oxygen being poisonous and dangerous, it's been studied before, and it seems to be less oxygen that matters after a point than carbon dioxide. This was discussed somewhere on Greg Cochrane's blog.