Experiencing data, if done properly, can give the sensation of more than just the 3D world we live in. For example, stress analysis simulations put areas of high stress in red, and areas of low stress in blue - for a 3D object. The color actually gives the model a fourth dimension. Of course, it's not the entire 4D object - in the case of stress analysis there is no such thing - but it is a mapping from 3-space to 1-space. Just as a 3D surface can be represented on a 2D graph with color (a heat map; the two representations can be combined), a 3D model with color can express a 4D surface. Although less common, other orthogonal features of graphs can be used to express other information, taking the visualization into even higher dimensions. An animated heat map (for example, a stress analysis which shows the change as the stress is applied then relieved) is convey 5D data. I can imagine other things - for example, perhaps the thickness of the mesh outline - which can be used to show even more information at once.
On the other hand, sometimes the data can just be in 3D, but the user experiences higher dimensions. One of the authors of The Mathematical Experience talks about a 4D intuition. A project at Brown University allows people to manipulate a tesseract (also known as a hypercube - a 4D structure where all edges are the same length and are orthogonal to every edge it shares a vertice with). By using the controls to rotate the virtual tesseract in different ways, the author suddenly could feel and reason about the tesseract, just as normal people can mentally rotate a cube. I find the possibility of lesser dimensional beings able to have an intuition about higher dimensional objects fascinating.
Another use of data visualization is not so much about the data, but about the visualizer's partition and organization of the world. Randall Munroe, for example, does this rather often, as does Indexed.
I don't have much more to say, but I would like to share some cool data experiences:
- Did You Know - a video with surprising statistics. Notice how the background images are made to convey meaning as well, although this is now very common with newspaper polls and such.
- AlloSphere - an enclosed sphere where sound and images can be used to help scientists explore connections.
- TwitterVision - a simple but elegant way to show not only what people are doing, but where they are doing it.
- Ball Droppings - a Google experiment with interactive AJAX. Not exactly data visualization, but it does link the different senses.
Good ideas, sir. One caveat that does come to mind, however, is to make sure to consider human ability a little closer. For instance, it has been shown that thematic animation is quite difficult for people. So, your 5D example might be better served by two side-to-side cubes.
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