This question has been used many times as a dismissal of scholasticism, which used such questions in dialectical reasoning to extend knowledge by inference, and to resolve contradictions. In modern times, it has been used as a metaphor for wasting time debating topics of no practical value, or questions whose answers hold no intellectual consequence, while more urgent concerns pile up.
It has been suggested that the first reference to angels dancing on a needle’s point occurs in an expository work by the English divine, William Sclater (1575-1626). Sclater claimed that scholastic philosophers occupied themselves with such pointless questions as whether angels “did occupie a place; and so, whether many might be in one place at one time; and how many might sit on a Needles point; and six hundred such like needlesse points.”
Thus the question became a symbol for the silly and pointless sophistry of medieval scholastics. But as modern scholarship has shown, scholastics was not such a thoughtless desert.
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.
The comic Saturday Morning Breakfast Cereal poses an answer derived from physics to this question: between one and 30 vigintillion angels.
In the seventh episode of the fifth season of the science-fiction series Babylon 5, the recurring character Byron Gordon, in a conversation about a rebellion among Human Telepaths against a despotic government, both asked and answered the question with a confident but cryptic: “As many as want to.” He thus suggested that the specific number of angels is irrelevant; it is the existence of angels (and by way of analogy, the Telepaths and allies that follow the message of freedom and peace against tyranny) that is important.
In the satirical novel Good Omens by Neil Gaiman and Terry Pratchett, the angel Aziraphale is said to be the only angel who could dance on the head of a pin, as he learned the gavotte in the 19th century. Also in Carpe Jugulum by Terry Pratchett, Granny Weatherwax says the answer is 16, if it’s an ordinary house pin.
Modern physicists, of course, have settled to the billionth of a millimetre every movement and position in the dance of electrons.
The question reminds me of Zen koans, of which the most famous is probably, “What is the sound of one hand clapping?” There’s no sensible answer to either question.