Points of the compass limit of the compass point. By the middle of the 18th century, the 32-point system had been further extended by using half- and quarter-points to give a total of 128 directions. These fractional points are named by appending, for example east, east, or east to the name of one of the 32 points. Each of the 96 fractional points can be named in two ways, depending on which of the two adjoining whole points is used, for example, NE is equivalent to NbEN. Either form is easily understood but alternative conventions as to correct usage developed in different countries and
How many angels can dance on the head of a pin? about how many could perch at the same time on the head of a pin"". Dorothy L. Sayers argued that the question was "simply a debating exercise" and that the answer "usually adjudged correct" was stated as, "Angels are pure intelligences, not material, but limited, so that they have location in space, but not extension." Sayers compares the question to that of how many people's thoughts can be concentrated upon a particular pin at the same time. She concludes that infinitely many angels can be located on the head of a pin, since they do not occupy any space there: