How many angels on the head of a pin?

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

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About Quentin

Science Editor, Catholic Herald. Portrait © Jacqueline Alma
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8 Responses to How many angels on the head of a pin?

  1. Emma says:

    This is very interesting, but I have to say I don’t entirely follow Aquinas’ argument. However, I think the broader issue is to make us think about the nature of the realms of the spiritual, and how they interact with the material everyday world.

    We often fail to acknowledge the possibility that there is anything more than the reality of the material, or what we can see in front of us. In thinking about angels we can reconnect with the eternal nature of our existence, and I find it a comfort to remember that we all have a guardian angel looking over us.

    The number of angels one can fit on a pin holds less interest for me. However, the question does have the benefit of encouraging us to make links between the spiritual and material, which can only be a good thing.

  2. I think Aquinas would agree about your “broader issue is to make us think about the nature of the realms of the spiritual, and how they interact with the material everyday world.” In my life I have met a few, very holy, people where I was conscious of only the thinnest veil separating them from the supernatural. And even grimy-souled people like me have occasional moments when God’s presence is almost tangible.
    In my case it happens more often with Our Lady. But then my wife claims that that is because whenever I need anything I always go to a woman first. Too true, I fear!

  3. Emma says:

    I think your wife touches on an important point. How wonderful to have a devotion to Our Lady. Whoever says that the Church oppresses women is so far from the truth. In my experience it is the opposite – Our Lady is an inspirational example of a strong, feminine servant of Christ.

  4. Arnold Lunn in correspondence with Mgr Knox many years ago said that he thought that God approached people via their own personalities. In his case it was the importance he placed on intellectual understanding.
    In another case I know, a young woman, who was a Christian but not a Catholic, suddenly realised – when she happened to be at Mass in the Brompton Oratory – that the congregation was not creating the service but attending what they saw as an objective happening. That was enough to tip the scales in her case.
    All roads may lead to Rome, but each of us has our own way to God.

  5. Blue says:

    Hey! Is this a love-in between Emma and Quentin? Or can anyone join?
    I don’t agree with Emma’s view about Church and women. They are happy about women being holy, and doing useful things like fixing flowers on the altar, but they don’t allow them any real influence. How many women have senior official posisitions at the Vatican?
    Perhaps it’s a hangover from the time when they thought that women were just a source of temptation.
    They won’t allow women deacons let alone priests. Have a look at http://www.womenpriests.org/default.asp. it’s very interesting.

  6. Emma says:

    I’m not bothered by the numbers of women with senior official positions at the Vatican, or that we cannot be priests. I feel that women can be powerful in a different way without having to follow typically male positions of office. Men and women are equal, but different. Why do we have to strive to copy masculine patterns of power and influence? I want my femininity to be of influence.

  7. Blue says:

    OK, that’s how Emma wants to be. It’s up to her, I suppose. But how about women who DO want to bring feminine approaches to being in positions of authority? Perhaps their authority would be more about service and less about ego power. I sometimes think women are their own worst enemies. (All right, before she brings it up, I don’t think Mrs Thatcher was a good example either.)

  8. Emma says:

    I totally agree that women should be able to bring feminine approaches to positions of authority…and Our Lady is an example of how to do this with an attitude of service and humility.

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