How many angels can dance on the head of a pin?
The question, "How many angels can dance on the head of a pin?" has been used many times as a dismissal of medieval angelology in particular, and of scholasticism in general. The phrase has been used also to criticize figures such as Duns Scotus and Thomas Aquinas. Another variety of the question is: "How many angels can sit on the head of a pin?" In modern usage, this question also serves as a metaphor for wasting time debating topics of no practical value, or questions whose answers hold no intellectual consequence.
That certain renowned medieval scholars considered similar questions is clear. 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, 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, 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. H. S. 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".
The early modern version in English (usually a needle, rather than a pin) dates back at least to Richard Baxter. In his 1667 tract The Reasons of the Christian Religion, Baxter reviews opinions on the materiality of angels from ancient times, concluding:
And Schibler with others, maketh the difference of extension to be this, that Angels can contract their whole substance into one part of space, and therefore have not partes extra partes. Whereupon it is that the Schoolmen have questioned how many Angels may fit upon the point of a Needle?". –Richard Baxter—
Philosopher George MacDonald Ross has identified a close parallel in a 14th-century mystical text, the Swester Katrei. Other possibilities are that it is a surviving parody or self-parody, or a training topic in debating.
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 an infinity of 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.
- "St. Thomas does not discuss the question "How many angels can dance on the point of a needle?" He reminds us that we must not think of angels as if they were corporeal, and that, for an angel, it makes no difference whether the sphere of his activity be the point of a needle or a continent (Q. lii, a.2)." (Kennedy, D. J., "Thomism", in the Catholic Encyclopedia)
- "Supernatural: On the Head of a Pin". SF Universe (B5Media: Entertainment). 27 Feb 2009. Retrieved 2009-03-15.
- Hirsch, E. D. Jr., Kett, Joseph F. & Trefil, James, ed. (2002). The New Dictionary of Cultural Literacy (Third ed.). Houghton Mifflin Co.
- Van Asselt, Willem J. (2011). Introduction to Reformed Scholasticism. p. 65.
- More precisely, in play in the 17th century, and discussed at various levels by the Cambridge Platonists Cudworth and Henry More, and Leibniz.
- Franklin 1993 p. 127.
- Richard Baxter, p530 of The Reasons of the Christian Religion, 1667.
- G. MacDonald Ross, Angels in: Philosophy, vol. 60, 1985, pp. 499–515.
- Sayers, Dorothy L. "The Lost Tools of Learning". Gbt.org. Retrieved 2012-11-14.
- "Quantum Gravity Treatment of the Angel Density Problem". Annals of Improbable Research. 2001. Retrieved 2013-05-10.
- "Saturday Morning Breakfast Cereal". Smbc-comics.com. Retrieved 2012-11-14.
- Franklin, J., "Heads of Pins" in: Australian Mathematical Society Gazette, vol. 20, n. 4, 1993.
- 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)