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 *x⃗* = [3.1, 4.2, −10.3, −9.1] ∈ ℝ⁴ is close to [3, 4, 2, 3] in the _x₁-x₂_ plane, but also close to [−8, −9, −10, −9] in the _x₃-x₄_ 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 *x⃗* = [3.1, 4.2, −10.3, −9.1] ∈ ℝ⁴ is close to [3, 4, 2, 3] in the _x₁-x₂_ plane, but also close to [−8, −9, −10, −9] in the _x₃-x₄_ plane.