gwern comments on Other minds and bats: the vampire Turing test - Less Wrong
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You could give her a link to a 4D game and see if she plays better than most people do. (There's a fair number; I once played http://www.urticator.net/maze/ and found it quite confusing.)
Reasonable-- not a test that was available at the time, though.
I've heard that some mathematicians say they can visualize in four or more dimensions, and there's some evidence of this in the math they're good at, but a fast search doesn't turn it up.
From my maths background, I have some limited 4D visualisation abilities, but they're highly geometrical and dependent on symmetries (ie I can visualise a tesseract better than most, but not a tesseract in general position). Others seemed to be better - I really should have asked!