How many angels can dance on the head of a pin? I am reasonably persuaded that the question was never asked by anyone who actually sought an answer. It was the kind of query that medieval scholastics might sink their teeth into. There were even suggestions that theologians hotly debated the question in Constantinople while Turks besieged the city. But there is, in fact, no record that the scholastics ever broached the subject, even though they were known to entertain some pretty abstruse topics. (Thomas Aquinas, for example, asked in the Summa Theologica "whether several angels can be at the same time in the same place.”) However, the first citations of angels dancing on pins don’t crop up until centuries later to impugn the scholastics for being preoccupied with picayune questions.
Now that the subject has come up, we might reasonably ask how it occurred to anyone to ask, even if the sole intention was to impugn the scholastics. Angels are non-corporal beings, which means they don’t actually occupy space in the physical world. Strictly speaking, they could be almost any size. They show up from time to time in the Bible, although there is no indication they are small enough to dance on the head of a pin. For that matter, there is no indication that angels dance at all.
Theology has long since given way to science as humankind’s preeminent intellectual endeavor. So far as I know, science remains wholly unconcerned with how many angels can dance on the head of a pin – and for good reason. As non-corporal beings, angels are not subject to empirical observation and therefore can’t be counted. For Karl Popper, noted philosopher of science, a proposition can’t be considered valid unless it is falsifiable using the scientific method, meaning that it must be capable being proven false. This would exclude virtually any spiritual question.
According to current scientific theory, the entire universe began as a singularity that would fit comfortably on the head of a pin. (Whether this is falsifiable in Popper’s terms, I cannot say.) From its pin-sized beginnings, the universe rapidly got much bigger – immensely larger than anyone would have imagined in Aquinas’ day. At the same time, we are discovering that components of the material world are much smaller than when the ancient Greek philosopher Democritus first suggested the universe was made up of atoms. In recent decades, particle physicists have been using larger and larger machines to detect smaller and smaller particles. A case in point: the Large Hadron Collider, a particle accelerator some 27 kilometers in circumference straddling the Swiss-French border, which was used to prove the existence of the Higgs boson. The Higgs boson is an elementary particle whose existence is considered essential to confirming the so-called Standard Model, the generally accepted framework for everything in the universe other than gravity.
Have physicists reached the limit of how small they can go in identifying the building blocks of the physical world? Apparently not. Scientists seeking to incorporate all four known physical forces, including gravity, have come up a package deal called string theory. This so-called “unified field” theory postulates that the building blocks of the universe are not elementary particles like quarks, gluons and the Higgs boson but something much, much smaller: tiny vibrating strings, so small that they are undetectable. But that’s not all. These strings vibrate in nine or more spatial dimensions, which is at least six more than you would think could be shoe-horned into the three-dimensional universe we can actually picture.
If you do the math, string theory does appear to work. However, there are obvious drawbacks to a theory whose basic component is undetectable – and therefore unfalsifiable in scientific terms. Critics complain string theory makes no predictions that can be empirically tested – or rather that it makes too many of them, potentially trillions. Then again, several thousand years passed before Democritus’ theory of the atom could be empirically verified. In the meantime, string theory has been dismissed in some quarters as metaphysics rather than science. If so, perhaps we should be asking, “How many strings can dance on the head of a pin?