One small (hopefully not too obvious) addition: the cluster-nature of thing-space is dependent on the distance function, and there is no single obviously corrent one. Is a penguin more like an eagle or a salmon? Depends on what you mean by “more like”. It’s perfectly reasonable to say “right now, the most useful concept of ‘more like’ is ‘last common ancestor’ so penguins are more like eagles and ‘birds’ is a cluster’ and then as your needs change to say “right now, the most useful concept of ‘more like’ is similarity of habitat so penguins are more like salmon and ‘sealife’ is a cluster.”
One small (hopefully not too obvious) addition: the cluster-nature of thing-space is dependent on the distance function, and there is no single obviously corrent one. Is a penguin more like an eagle or a salmon? Depends on what you mean by “more like”. It’s perfectly reasonable to say “right now, the most useful concept of ‘more like’ is ‘last common ancestor’ so penguins are more like eagles and ‘birds’ is a cluster’ and then as your needs change to say “right now, the most useful concept of ‘more like’ is similarity of habitat so penguins are more like salmon and ‘sealife’ is a cluster.”
why yes
clusters can overlap, and the word “more like” uses different clusters of clusters depending on context