I think you might be mis-extrapolating what that article talks about in terms of dimensions. She's not seeing in 4 dimensions. They used the term "dimensions" to mean something more like "more characteristics of color" than others can detect. They're not referring to dimensions like I think you are trying to infer.
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I'm sorry if I was unclear. I do not mean physical dimensions. I mean dimensions of color.
Since most people have three color receptors (rgb), we see color as a three dimensional object. Think of the color cube.
Since she has an additional color receptor, the object to describe how she sees color is 4-dimensional. In other words, most people can see all combinations of 3 colors. She can see all combinations of 4 colors.
This is fascinating to me, actually, because not only am I a photographer, but I'm also colorblind to a degree. I'm referred to as red/green colorblind, but that's not what I experience. My trouble is between green and brown. For example, I can't tell what's brown or green in camo. I can tell both are there, but that's my mind convincing me both are there because I know they should be. To me they just look like different shades of the same brown.
Or green. Dammit I don't know which one it is.
Well you might like this: http://theoatmeal.com/comics/mantis_shrimp
You might also checkout http://enchroma.com/shop/ I'm not sure if they work for every type of color blindness and they are pretty expensive but it'd be cool if they worked for you.