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NancyLebovitz comments on Other minds and bats: the vampire Turing test - Less Wrong
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I talked with a woman who said she could visualize in four dimensions. I asked her how many corners a tesseract has. A correct answer would have given me very little information, but she didn't give me a correct answer.
Instead, she looked as though she was visualizing something, and then said she was trying to count the corners but couldn't keep track.
I asked her what a hypersphere looked like, and she said, "Like a regular sphere, but rounder".
I can't visualize in four dimensions, but it seems at least plausible that she could.
This seems like it's even harder to test than knowing what it's like to be a bat. On the other hand, your bat test is pretty hypothetical. How would you rate someone who showed bat-like brain activation when imagining being a bat?
I can visualize in 4D by projecting to 3D and keeping the 4th dimension as an "extra parameter". A tesseract has 16 corners, it's rather easy to see it.
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!