When starting a new turn, I'm frequently interrupted by factions telling me what technologies they've researched or that they've summoned a shadow warg. There is only one canned response for me to give so it seems a bit pointless.
What if, instead of taking up the entire screen to tell me this, Their (animated?) picture just showed up on the side of the screen with a notification. If the AI is offering a treaty, perhaps I could click on the picture and go to the diplomacy window or whatever.
