Apparently people are much exercised about this question. Unable to satisfy myself on the point I asked a number of people for their opinion:
Theologians I consulted mostly suggested the church had little to say on the matter of an exact number, but that the angelic essence was concentrated at an indefinable point, while simultaneously permeating the entire universe of heaven and earth. The spokesman for the Church of England suggested that, in the light of this, the answer was whatever I wanted it to be. The Imam said that if by angels I meant djinnis, then they did not dance anywhere at all as it would be contrary to the will of Allah. A Roman Catholic priest said that he had recently attended a party on the head of a pin at which no fewer than 99 angels were present. It was late in the evening, however, and his testimony is open to question. Ian Paisley said the answer was the exact opposite of whatever the Papish infidel had said it was. A passing Salvation Army girl asked me what I was doing that evening but had nothing to say about angels and pinheads.
A noted philosopher prodded me repeatedly in the chest, demanding that I define angel, dance, pinhead and prove the reality of numbers greater than one, rejected the definitions and proofs I gave him, substituted his own, ignored those as well, argued circularly, inductively, deductively, collectively, absurdly and ad hominem, declared at one point that no angels were Scotsmen, invoked and abused the shades of colleagues long dead, argued himself into and out of a corner on at least three occasions, and finally pronounced that the answer was somewhere between zero and infinity, depending on the nature of conceptual reality.
A spokesman for Dave Spart said that the removal of both angel production and dance teaching from the hands of rapacious capitalism had led to ever-increasing numbers of angels dancing on pinheads. He proved this by showing me an envelope which, he said, had that very morning held dozens of such pins with innumerable forms gyrating upon them.
A health and safety officer informed me that no angels could dance on a pinhead because it was forbidden. When I asked her to consider the matter independently of legal restraints she looked at me closely, pressed a leaflet into my hand and said she would around later to inspect my pins and test me on my knowledge of the relevant legislation.
87% of the statisticians I asked returned an answer that was within two standard deviations of 17. However, evidence suggests this is true of almost all questions put to statisticians. (For some value of almost).
A hippy said ‘wow’ repeatedly, while staring, mesmerized, at the head of a pin on which I, personally, could see nothing, Terpsichorean or otherwise. ‘Wow, man, there’s millions of them.’ He would not commit himself to a more precise figure, therefore all we can say is that he might have provided an order of magnitude for the lower bound.
Tony Blair stated through a spokesman who refused to give his name that, after consultation with Peter Mandelson and others, he knew nothing of any angels or pinheads, that it was a matter of collective responsibility in Cabinet subject to the immunity of office and anyway, he wasn’t there. I naturally accept his word on all these points.
Silvio Berlusconi did not feel competent to address the question, but, on being pressed, began to muse, almost to himself, “big enough and wide enough, maybe fifty, maybe sixty; very slim, very little clothes, maybe 70”, and hung up excitedly, thanking me for the idea I had given him for his next orgy.
Richard Dawkins was unavailable for comment.
I conclude from all of this that the field is scandalously under-researched and I have applied for a grant to spend the next three years investigating angels, pinheads, and the spatial and temporal relations between them. Artists can’t answer the question either, but they are in agreement that the clothing of angels is limited to wisps of diaphanous material that drifts across them in not quite random fashion. Between that and the dancing, I expect my research to be exhausting as well as exhaustive. I shall, of course, keep my readers informed.