How many angels can dance on the head of a pin?
The question "How many angels can dance on the head of a pin?" (alternatively "How many angels can stand on the point of a pin?") is a reductio ad absurdum of medieval scholasticism in general, and its angelology in particular, as represented by figures such as Duns Scotus and Thomas Aquinas. It is first recorded in the 17th century, in the context of Protestant apologetics. The question has also been linked to the fall of Constantinople, with the imagery of scholars debating about minutiae while the Turks besieged the city. In modern usage, it therefore 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.
Aquinas's Summa Theologica, written c. 1270, includes discussion of several questions regarding angels such as, "Can several angels be in the same place?" However the idea that such questions had a prominent place in medieval scholarship has been debated, and it has not been proved that this particular question was ever disputed. One theory is that it is an early modern fabrication,[a] as used to discredit scholastic philosophy at a time when it still played a significant role in university education. James Franklin has raised the scholarly issue, and mentions that there is a 17th-century reference in William Chillingworth's Religion of Protestants (1637), where he accuses unnamed scholastics of debating "whether a Million of Angels may not fit upon a Needle's point?" This is earlier than a reference in the 1678 The True Intellectual System Of The Universe by Ralph Cudworth. HS Lang, author of Aristotle's Physics and its Medieval Varieties (1992), says (p. 284):
The question of how many angels can dance on the point of a needle, or the head of a pin, is often attributed to 'late medieval writers'... In point of fact, the question has never been found in this form…
Peter Harrison (2016) has 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). In An exposition with notes vpon the first Epistle to the Thessalonians (1619), 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." Harrison proposes that the reason an English writer first introduced the "needle’s point" into a critique of medieval angelology is that it makes for a clever pun on "needless point".
[D]octors declare that in heaven a thousand angels can stand on the point of a needle. Now rede me the meaning of this.
Other possibilities are that it is a surviving parody or self-parody, or a training topic in debating.
In Italian, Spanish and Portuguese, the conundrum of useless scholarly debates is linked to a similar question of whether angels are sexless or have a sex. Spanish jurist José Antonio Ramírez López (1908–1987) said about the story of the Byzantine empire: "Everybody knows the idiotic and sometimes bloody discussions in that Empire on the sex of angels, 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:
The practical lesson to be drawn from the argument is not to use words like "there" in a loose, unscientific way, without specifying whether you mean "located there" or "occupying space there."
In the humoristic magazine Annals of Improbable Research, Anders Sandberg has presented a calculation based on theories of information physics and quantum gravity, establishing an upper bound of 8.6766×1049 angels. Comparing medieval superstition and modern science, George Bernard Shaw wrote in the introduction to the play Saint Joan that "The medieval doctors of divinity who did not pretend to settle how many angels could dance on the point of a needle cut a very poor figure as far as romantic credulity is concerned beside the modern physicists who have settled to the billionth of a millimetre every movement and position in the dance of the electrons."
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.
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- Franklin 1993 p. 127.
- Peter Harrison, "Angels on Pinheads and Needles’ Points", Notes and Queries, 63 (2016), 45-47.
- Sylla, E. D. (2005). "Swester Katrei and Gregory of Rimini: Angels, God, and Mathematics in the Fourteenth Century". In Koetsier, S.; Bergmans. Mathematics and the Divine: A Historical Study. Amsterdam: Elsevier. p. 251. ISBN 0444503285. Retrieved 7 December 2017.
- "Angelo - Dizionario dei modi di dire - Corriere.it". dizionari.corriere.it (in Italian). Retrieved 2017-07-13.
- Sayers, Dorothy L. "The Lost Tools of Learning". Gbt.org. Retrieved 14 November 2012.
- "Quantum Gravity Treatment of the Angel Density Problem". Annals of Improbable Research. 2001. Retrieved 10 May 2013.
- "Saint Joan – A Chronicle Play in Six Scenes and an Epilogue". Retrieved 22 July 2015.
- Franklin, J., "Heads of Pins" in: Australian Mathematical Society Gazette, vol. 20, n. 4, 1993.
- Harrison, Peter. "Angels on Pinheads and Needles’ Points", Notes and Queries, 63 (2016), 45-47.
- Howard, Philip (1983), Words Fail Me, summary of correspondence in The Times on the matter
- Kennedy, D. J., "Thomism", in the Catholic Encyclopedia
- Koetsier, T. & Bergmans, L. (eds.), Mathematics and the Divine: a historical study, Ch. 14 by Edith Sylla (review)