How Many Angels Can Dance on the Head of a Pin?

This is a question that is supposed to have been hotly debated throughout the Middle Ages. The idea is that instead studying questions that might be of some use to people, the scholastic philosophers and theologians of the High Middle Ages debated abstruse questions that could not be decided by any evidence and made no difference to anyone living in the real world. This question has become a byword for any intellectual endeavor that is abstract and meaningless.

In fact, the Scholastics specialized in using logic and reason to discuss all sorts of philosophical issues and to reconcile contradictions in philosophy and theology. They were particularly concerned to resolve the differences between ancient Greek philosophy, especially the newly discovered teachings of Aristotle, and the doctrines of the Catholic Church. Their method was usually to ask a question concerning some philosophical point. Arguments contrary to official dogma would first be given, then the official or generally accepted position would be stated, with arguments in its favor, and finally the opponents arguments would be rebutted. These arguments often took the form of citations from the Bible or writings of the Church fathers, but a rigorous system of logic was used to explain and expound on the citations and logic was used to reconcile or reject positions. The doctrines of the Catholic Church were not upheld by faith alone or the authority of the Church. Since the Scholastics held that reason and faith both pointed to the same Truth, reason could and should be used to defend the faith. Perhaps the best example of the Scholastic method would be Thomas Aquinas‘s Summa Theologica. In his masterpiece, he examines point after point of Catholic doctrine in the way I explained.

This Scholastic method could be used with other subjects, including the natural sciences. The work that the Scholastics did was not quite what we call science. They were more interested in abstract reasoning about observations than in performing experiments. While the Scholastics made many contributions to mathematics, including introducing Arabic numerals to the West, the extensive use of mathematics to describe and explain  the natural world generally had to wait until the time of Galileo.  Modern science is only possible if you believe that the universe is an orderly, reasonable place that can be studied using reason and observation. By emphasizing rather than rejecting the use of reason, the Scholastics laid the foundation for the scientific revolutions of the seventeenth and eighteenth centuries.

To get back to the subject, although medieval theologians were much concerned about angelology, including the question of whether angels take up physical space and whether an angel traveling from point A to point B travels through the points between, there is no evidence that the questions of how many angels dance on the head of a pin or the point of a needle was ever seriously debated. It is most likely that the question was made up by later critics of Scholastic philosophy to demonstrate the supposed stupidity and triviality of Medieval thinking. It might also have been a joke among the Scholastics or the type of riddle that students might ask to trip up their professors, perhaps something like the question, “what happens when an irresistible force meets an immoveable object”.

So, how many angels can dance on the head of a pin? I had always thought that the number must be infinite since angels   are not composed of mass or energy and do not take up any physical space. I may be wrong, however, since I have not taken quantum effects into account. Recent research in quantum angelology, a field of theological physics, indicates that the number is, in fact, finite. The Pauli exclusion principle prevents any two angels from occupying the same quantum states. Angels may not have any mass, but they do contain information and any individual angel cannot be smaller than the Planck length of 1.616 X 10 -34  meters. According to the  article I linked to, the maximum number of angels who can dance on the head of a pin is 8.6766 X 10 49 angels.

angels-on-pin
8.6766X10 49 angels are dancing on this pin.

 

 

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Saint Patrick’s Day

Today is St. Patrick‘s day and I thought it might be appropriate to write about St. Patrick. So, who is St. Patrick and why does he get a day? Not very much is known for certain about his life. It is possible that his story has been confused with one Palladius, a missionary who became the first bishop of Ireland. Still, Patrick wrote a short autobiography called “The Declaration” or “The Confession” as part of a letter which seems to be genuine.

Get out snakes!

Patrick, or Patricius was a Roman who lived in Britain. He may have been born around 387 and lived until 460 or possibly 493, so he lived during the twilight of the Roman Empire in the West. At the age of 16 he was captured by raiders and enslaved. He worked as a shepherd in Ireland for about six years. He managed to escape and return to his home, but then he became a priest and returned to the land where he was a slave and worked to convert the pagans to Christianity. He seems to have been very successful during his lifetime, though there were many other missionaries in Ireland. He helped to organize the Church in Ireland and is supposed to have traveled to Rome to seek the Pope’s assistance in this endeavor.

According to legend, Patrick died on March 17, so that date has become his feast day. He has never been officially canonized by the Roman Catholic Church. He became known as a saint long before the modern procedure for canonization was developed. He is, obviously, the patron saint of Ireland, and also Nigeria, Montserrat, engineers, paralegals, and the dioceses of New York, Boston, and Melbourne.

There are many legends about St. Patrick. The most widely known is that he chased all the snakes out of Ireland, thus ruining the local ecology. Another is that he used the example of the three-leaved shamrock to illustrate the trinity.

Happy St. Patrick’s Day to all the Irish, and Irish at heart, out there!

Sorry about the green text. I couldn’t resist.

 

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