(If this is not a suitable question in here, I will delete it.)
I am new to noncommutative geometry. I know the motivation is to try to generalize the Gelfrand duality to noncommutative $C^{*}$ algebra, so we can study the algrbra of noncommutative functions on some "noncommutative space".
However, it seems that the concept of "noncommutative space" is only taken as an intuition, one can said it does not exist in real sense. Then I am confused, what is the purpose of studying noncommutative geometry? Is this subject only a disguise of studying operator algebra and quantum group, but somehow involving geometrical picture? If that is the case, what is the geometrical part?