Here are some examples of borders created by someone else's "own whims instead of how the indigenous people themselves would have divided them up" (to use Vijay's quote) from around Europe.
Yes, in general they are smaller areas than what Vijay is referring to and they were decided by people who were geographically closer to them, but still, I'm not sure that makes any difference to the people who actually live there. (To an individual it doesn't make much difference how large or small the area is if friends and family or livelihood are on both sides of the border; nor does the distance between an individual and the decision-makers have much impact on how they feel about it.)
Brown part is culturally Setu territory (split by Estonian-Russian border).
Saatse (circled) on Estonian-Russian border in the Setu area: "until recently the Estonian villages of Sesniki, Ulitina and Saatse were effectively enclaves, as by road they could only be reached by travelling 900 metres (3,000 ft) through Russian territory"
Podmotsa, Estonia (the photo is the view of Kulje Church in Russia as seen from Podmotsa):
"Podmotsa village is located on the border of Estonia which is also incidentally the border of the European Union; 100 m across the lake, there is Russia. When the border was still open, a priest from Kulje church on the Russian side came to Podmotsa tsässon together with people from Kulje to celebrate Pentecost. Crosses and icons arriving by boat or raft from the other shore of the bay marked the beginning of the feast."
sourceSaami-speaking areas spanning four countries (keep in mind that traditionally theirs is a nomadic culture).
Historical Saami herding districts:
Basque-speaking areas
Berlin 1986
2012 - West and East Berlin as seen from space:
2011 - Western and eastern Germany:
Kaliningrad
Gibraltar (British territory attached to Spain) and Ceuta (Spanish territory attached to Morocco)
Llívia, a bit of Spain surrounded by France - in this case the residents did get to choose and this is how it turned out: