His point is the volume of the unit sphere is tiny. The &quot;volume&quot; of the unit 20-cube is 1. The volume of a 20-sphere is just 0.0258. 100-cube, volume is 1. 100-sphere, 2.36e-40<p>If your algorithm works well for &quot;nearby&quot; meaning 1, i can just keep adding dimensions till you find nothing. If &quot;nearby&quot; on the other hand is related to the number of dimensions, you&#x27;re going to have to grow the &quot;nearby&quot; value exponentially.