Charterhouse, always at the cutting edge, has succeeding in finally solving a theological problem which has taxed great minds for 700 years. You might think that the number of angels that can stand on the point of a pin is a trivial question; indeed it is taken as a proxy for the absurdity of scholastic discussion. But it was by no means always so: and it is still the subject of discussion today.
Bring on the usual suspect: Thomas Aquinas of course. He started it by arguing that any angel could occupy a point in space and that no other angel could occupy the same point. He added that an angel did not have a dimensional quantity but a virtual quantity: it is not contained by the space in which it is present, rather it contains that space. However “there is nothing to hinder us from assigning a divisible place to an angel according to virtual contact; just as a divisible place is assigned to a body by contact of magnitude.” Plenty of room for argument, once you have worked out what he means. Check it at ST1. 52, 53 if you’ve a mind to.
Nowadays there appear to be two approaches to this vital question. Dr. Phil Schewe, of the American Institute of Physics, assumed, in his 1995 paper, the point of the pin to be one atom across and, by dividing this by the theoretical limit of the divisibility of space, calculated the number of angels to be 1 followed by 25 zeros. Another approach, sidestepping the Aquinas prohibition on overlapping angels, made use of quantum gravity. I cannot say I entirely followed the mathematics, but the answer turned out to be roughly the same. Apparently a larger number can be accommodated if they are dancing, but this causes insuperable problems with friction.
My own solution is, I claim, more elegant than either. We must assume the sharpest pin possible since any degree of bluntness is arbitrary. Therefore its tip must be equal to the limit of the divisibility of space or, if you wish, the smallest point possible. Since, St Thomas assures us, no other angel can occupy the same point, the answer to the question must be one. QED.
From The Catholic Herald, 17 April 2004