Why would you assume that the world would become uniform? Humans have been utterly outclassed by computers in Chess for almost two decades now. In Go, we have lost all hope of defeating the machines last year. If your assumptions are correct, we should've lost all interest in those games. You couldn't be more wrong. Both Chess and Go as competitive sports and subjects of exploration are thriving thanks to AI.
Also, while our basic needs are similar our distractions are nothing of the kind. The differentiation of tastes would probably be mindblowing in a world without scarcity. Consider any arts. Where else have they blossomed the way they have but in royal courts and religious institutions where resources are plentiful and there is all the time in the world for such pursuits?
With artificial superintelligence we'd finally (maybe) have a shot at getting answers to some of the toughest questions in existence. I wouldn't underestimate the universe.
20 years, You are looking very short term, this is generational and will affect our evolution.
At the moment it appears so because the world has over the last few decades been opened up to a view of many other cultures (through gloabalisation/internet) but, we can already see that when it comes to tastes in movies, music etc, there is a globalised popular culture that didn't exist before and it moves rapidly.
The nuances of locality are being lost. Diversity is being lost even as it appears to be increasing. Throw in the competitive cognitive artefacts and the loss of skills to them, in time we will potentially start to devolve, much like the emotional state of the generations.
Indeed they will.
With increased global communication we are indeed seeing a disappearance of local culture. But that would be expected from the globality of mass communication alone. On the other hand, cultural differences arise on a different basis when people interested in similar things can communicate over long distances.
I think that it will expand interests to a point and then eventually stagnate or turn into virtual worlds where skills are illusion.
That's possible. What would be left after the outsourcing of all intelligence and virtue would be an infantile, reactive and self-centered core. :D
Politics?
Something like that but confined to a sandbox limited to things like dog poop along footpaths with all serious matters left for the AI's to take care of.