This works because, empirically, mammals have lots of things in common with each other and water-dwellers have lots of things in common with each other. If we [imagine entities as existing in a high-dimensional configuration space](http://lesswrong.com/lw/nl/the_cluster_structure_of_thingspace/), there would be a _mammals_ cluster (in the subspace of the dimensions that mammals are similar on), and a _water-dwellers_ cluster (in the subspace of the dimensions that water-dwellers are similar on), and whales would happen to belong to _both_ of them, in the way that the vector *xâ* = [3.1, 4.2, â10.3, â9.1] â ââ´ is close to [3, 4, 2, 3] in the _xâ-xâ_ plane, but also close to [â8, â9, â10, â9] in the _xâ-xâ_ plane.
This works because, empirically, mammals have lots of things in common with each other and water-dwellers have lots of things in common with each other. If we [imagine entities as existing in a high-dimensional configuration space](http://lesswrong.com/lw/nl/the_cluster_structure_of_thingspace/), there would be a _mammals_ cluster (in the subspace of the dimensions that mammals are similar on), and a _water-dwellers_ cluster (in the subspace of the dimensions that water-dwellers are similar on), and whales would happen to belong to _both_ of them, in the way that the vector *xâ* = [3.1, 4.2, â10.3, â9.1] â ââ´ is close to [3, 4, 2, 3] in the _xâ-xâ_ plane, but also close to [â8, â9, â10, â9] in the _xâ-xâ_ plane.