Let’s Finally Count

This question is well-known in a bad way. It often serves as example of a meaningless debate. Popular atheist writers like to use it as evidence of the Church’s obscurantism and the degeneracy of scholastic thought, in contrast to “real science”.

But is that really so?

If those authors toned down their arrogance and tried to reflect on the wording of this question they mock, they would quickly realize that things are not as straightforward as they seem.

How could angels “dance”? Aren’t they incorporeal? Why the head of a pin? Is that meant to imply that angels are extremely small or thin? What does any of this even mean?

Since these poor souls seem to lack the intellectual capacity, let us think for them instead.

1. To Begin With

Such a question is not found in the works of Thomas Aquinas, Duns Scotus, Bonaventure or any other scholastic theologians. It is a later satire that took shape in the 16th-17th centuries, mostly among Protestant authors such as Keith and Wood, then Voltaire and his followers.

However, the discussions of similar topics did exist – within the broader framework of how to understand the notions of place, movement and action when applied to immaterial beings.

For example, St. Thomas discusses (STh I q.52–53; all further citations are from this source) utrum plures angeli possint esse simul in eodem loco – “whether several angels can be in the same place at the same time.”

So, the modern question is a kind of caricature. Nevertheless, we will answer it in earnest, and exactly as it is typically posed. To achieve that, let’s start with unpacking it.

2. Language of Scholastics

By the head of a pin we may understand the smallest indivisible particle of matter, a quantum – the minimal element of the created world that can be influenced. This part is relatively simple.

However, the “dance of angels” is harder to grasp. To dance, one must be present in the material world in a certain place. Yet “place” is a physical concept, a set of certain X/Y/Z coordinates of a material object on the universal grid of space. But angels have no physical bodies and therefore they cannot occupy any place, large or small.

Yet angels do sometimes appear and act in the world – they move objects, speak to people and so on. The scholastic consensus holds that an angel’s place in the material world is wherever he applies his power to matter.

St. Thomas puts it as follows: angelus dicitur esse in loco per contactum virtutis, non quantitatis – “an angel is said to exist in a place not by the contact of [corporeal] quantity, but by contact of power.”

In other words, an angel does not occupy a place as a physical volume, but as a force acting upon matter in that location.

Then the original question can thus be rephrased as:

“How many angels can simultaneously act upon a single quantum of matter?”

Suddenly the question seems far less foolish, even though we have not fully deciphered it yet.

3. Celestial Congestion

Why not answer “infinitely many”, then? Angels are essentially transparent, aren’t they? So, any number wishing to act could do so at that point.

However, the place of all these angels in the material world would become the same “head of a pin”. But the very meaning of “place” implies that two or more objects cannot occupy the same point in space at the same time.

Or is it different for angels? After all, what exists in a certain location is not the body of an angel but rather his power.

There have been varying opinions, but the prevailing view holds that no, two angels cannot occupy the same place. St. Thomas: si plures angeli essent in eodem loco, oporteret quod essent unus actus applicandi virtutem ad locum – “if many angels were in the same place, they would have to be one act of applying force to that place.”

Thus, the identities of angels would blur, and that is impossible – angels are as unique as humans.

Ergo, two angels cannot occupy the same place secundum idem genus actionis – “by the same kind of action”.

We can reach the same conclusion if we consider teleology. Angels act in the world not out of boredom but because they serve as actors of God’s will – it is the Lord who directs them to perform something.

For instance, if God willed some pebble to move 1.414 cm northwest, he would not send two angels, one to move the pebble 1 cm north and another 1 cm west.

That would not only be inefficient but would also imply a division within God’s will, which is always one and simple. Surely the omnipotent God can do anything, but far more likely he would send a single angel, who would perform a single diagonal motion.

4. The Home Stretch

So, angels cannot act upon a particle of matter in the same modus. But that suggests several angels could influence the same object simultaneously, provided that their powers differ in kind.

Cardinal Cajetan wrote (commentary on St. Thomas, paraphrased): it may be that two angels act upon one corporeal object diverso ordine virtutis – “with differing orders of power”.

For instance, one angel might act locomotive (by moving the object), while another illuminative (by lighting it). Then their places would not metaphysically overlap.

Then, after one more translation step, our original question takes this form:

“How many modes of power, or kinds of action, can be simultaneously applied to a quantum of matter?”

Or:

“How many fundamental interactions exist in the universe?”

Modern physics identifies four: gravity, electromagnetism, weak interaction, and strong interaction.

Meaning we have finally reached the answer:

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

– According to the consensus of modern science, four angels.

🙂

5. Postscriptum

It is arrogant to underestimate people of the past and dismiss them as “simpletons”. True, they knew far less than we, and their reasoning was inevitably shaped by the paradigm of their time. But their minds were just as sharp as ours.

Perhaps people of the 25th century will mock us as primitives – and they will be just as wrong.

Let’s be honest: of course, scholasticism did not directly bring us internet or plumbing. It preferred to contemplate heavenly mysteries over earthly concerns. Yet in doing so, it taught humanity the method of logic and discussion – from which the vast, branching tree of science eventually grew.

For that alone, scholasticism deserves our respect. A wise person never despises their childhood home, even if they think they have “outgrown” it. Yet to me, even that seems doubtful: sometimes it feels that we haven’t outgrown anything at all – but rather that we have not yet grown into it.