There is the implied assumption that divergent evolutionary traditions eliminate convergent features. I am of the opinion that despite divergent traditions, some features may converge if there is a common ancestor, and the feature has a large enough survival potential.
Where this comes in, is the question of consciousness of invertebrates specifically the cephelopods. While we can argue about the consciousness of vertebrates, there has been some question as to the higher invertebrate brains, that is as a default against them being conscious.
The assumption is that because they have spent so long as a divergent tradition evolutionarily speaking, there is no room for convergent evolution.
If my counter assumptions are correct, an early invertebrate ancestor to both vertebrates and invertebrates may have created a common convergent trend that has reached over a significantly large period of time to give both cephalopods and vertebrates the potential to be conscious. However this flies in the face of conventional wisdom about divergent evolution, so I ask the question, is it out of range to ask whether the afforementioned assumption is accurate? What is your opinion?