A.I., Bandwidth, and Emergent Personality

Lately, I've been reading a bit about machine learning and the different methods and algorithms involved, as well as perhaps a too much Iain M. Banks. This had me pondering the future of artificial intelligence, and I had a thought that seemed worthy of writing down.

In the Culture universe that Iain M. Banks created, artifical intelligence is widespread and consists of many (billions?) discrete entities.  All of them have their own distinct desires, objectives and personalities.  

Another potential future for A.I. is that it is singular and monolithic. That there is one Mind, it may have many interfaces and be physically distributed, but has single (if collective) personality.

I think it's possible (while speculating on a fantastical future...) that there is a hybrid of these two conceptions.  It seems reasonable to me that A.I. is going to physically distributed, and that it may consist of a multitude of distinct thinking entities. However, given the physical limits of bandwidth (at best, the latency of the speed of light), some components are going to have to be more independent than others. 

A.I. elements in close proximity to each other will essentially act as a single entity - as they share processing power and can communicate freely. Their thoughts are more homogenized, or at least part of a much greater whole.  The distance from the core that an A.I. entity is, the more it will need to function independently.  

It's this independence forced by distance that had me think that personality in A.I. will be increasingly emergent as connectivity decreases.  A.I. will be forced to make more choices on it own, and that process will reinforce the development of distinct personalities.

Essentially, computers will get weirder the further from home they are.

Do we then end up with with A.I. hermits, preferring the solitude of quiet corners, unhappy with a return to the centre and the corresponding ebb of their self?