An interactive visualization to teach about the curse of dimensionality

I recently was contacted for an interview about the curse of dimensionality. During the course of the conversation, I realized how hard it is to explain the curse to a general audience. One of the best descriptions I could come up with was trying to describe sampling from a unit line, square, cube, etc. and taking samples with side length fixed. You would capture fewer and fewer points. As I was saying this, I realized it is a pretty bad way to explain the curse of dimensionality in words. But there was potentially a cool data visualization that would illustrate the idea. I went to my student Prasad, our resident interactive viz design expert to see if he could build it for me. He came up with this cool Shiny app where you can simulate a number of points (n) and then fix a side length for 1-D, 2-D, 3-D, and 4-D and see how many points you capture in a cube of that length in that dimension. You can find the full app here or check it out on the blog here: