How many angels can dance on the head of a pin?

This aphorism was apparently originally conceived to lampoon the idea of angels and the theories of medieval Scholastics such as Sir Thomas Aquinas. Interestingly, Dorothy L Sayers (1893–1957) – poet, crime novelist and translator of Dante’s Divine Comedy amongst many celebrated and academic works – suggested that while angels were located in space they had no extension, and thus could exist in infinite numbers on the head of a pin.

Paul Kelly, the much-lauded Australian singer-songwriter, contemplated this same question in his song ‘Careless’ in which he sang:

How many cabs in New York City, how many angels on a pin? How many notes in a saxophone, how many tears in a bottle of gin?

This has more gravitas as a rhyming couplet than as a profound philosophical enquiry.

Nevertheless, there are complex questions of numeracy that ought to have definitive answers – they’re merely problems of computation.

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