This "whirling dervish" does indeed turn round, as long as the motor is switched on (it stops in the evening). It stands in front of a mosque of which I show several shots on the next pictures, which has a circular interior, for the dances of the dervishes. In it there are the graves of a number of dervish sheiks. The Ulu Camii is slightly to the right out of the picture.
I have been informed by a Kütahya resident the name of the mosque is Dönenler Cami (the mosque of those who rotate).