One example is suppose I'm trying to tune some parameters and I'm going to do this by sampling. If I have only one parameter which is between 0 and 1 to tune, t

One example is suppose I'm trying to tune some parameters and I'm going to do this by sampling. If I have only one parameter which is between 0 and 1 to tune, then I can find the best choice to within .01 by trying 100 values (each .01 increment). Now instead, consider what happens when I have 100 parameters (high dimensionality). Now with 100 samples, I can't really learn much. Even if I wanted to try only 2 values in dimension (say 0 and 1), there would be 2^100 (roughly 10^30) different possibilities to try. I would say the key line from Wikipedia is that, "when the dimensionality increases, the volume of the space increases so fast that the available data becomes sparse."