I just watched Jeff Han's TED presentation. Very cool stuff indeed. Here is where it takes me.
One of the things I've always wanted to be able to do was to estimate the density of a multidimensional dataset. I've never been able to explain the process very well, but I have a very clear way of visualizing it in my head. I have been working with multidimensional data for about 15 years now.
As soon as I saw how he did his fuzzy dots animation and showed how he created objects at multiple scales, I had my aha. Anyway, there are cubes within cubes and that's how you can visualize n-dimensional data. Furthermore you can have anchor points in the sky and then you move through those anchor points as you drill out. In n-space you can navigate that way and you can add time and color as additional dimensional visual attributes. I'm also thinking that you can add sound as well, chords representing some combination of values. I think you can hear a multidimensional histogram.
So solving a density problem of multidimensional databases is a cool application but it's also a visual data mining paradigm. Automatically. The trick is to make it fast.