Re: what is noncommutative geometry?

Traditional geometry defines a structure by a set of points a "space" if 
you will.  We analyze curves and surfaces as a collection, or set, of 
points in Euclidean space.  
   Noncommutative geometry calls upon quantum physics and uses a class of 
functions that are algebraically related to a curve or surface.  It is 
through the algebra of these functions that the aforementioned point sets 
are determined. In effect, it is possible to use only the functions and 
not the actual points to describe your system. Thus you may forget about 
the set, and obtain all useful information from the functions alone.  This 
is where your reading states that you may avoid defining time and space as 
a collection of points, instead determine classes of mathematical 
functions that represent the space.
   In most cases these functions are not algebraically commutative, 
leading to the name of the type of mathematics. That is function A 
multiplied by function B does not equal function B multiplied by function 
A.