A classic example to illustrate the [[Curse of Dimensionality|curse of dimensionality]] in the n-dimensional hypersphere is that, for a high-dimensional space, the [[Euclidean Distance|Euclidean distance]] of all the random points within the sphere are not evenly distributed but all clumped together in high values, rendering the distance effectively useless: the metric is not measuring anything anymore. This insight is more detailed in [this Stack Exchange answer](https://stats.stackexchange.com/a/200425).