Angels on a Pin


The following essay is frequently referred to, and often reprinted in textbooks on writing. I recall it was also reprinted in one of the Project Physics supplementary readers. Few people recall its source, or its author.

As a bit of humor it is nicely constructed. As a parable with a moral, it falls flat. What is the author's point, one wonders? Is it an argument against a particular kind of pedantry in teaching? Is it a demonstration that exam questions can be subject to multiple interpretations? Is it an example of how a clever student can find ingenious ways to answer a question?

Just what is the difference between exploring `the deep inner logic of the subject' and teaching `the structure of the subject'. Callandra doesn't make that difference clear, yet his student seems not to like the first, but would rather have the second.

The title (which most people forget) is a clue. Medieval scholastics were fond of debating such meaningless questions as "How many angels can dance on the point of a pin," "Did Adam have a navel," and "Do angels defecate." The emerging sciences replaced such `scholarly' debates with experimentation and appeals to observable fact. Callandra seems to be suggesting that "exploring the deep inner logic of a subject in a pedantic way" is akin to the empty arguments of scholasticism. He compares this to the `new math', so much in the news in the 60s, which attempted to replace rote memorization of math with a deeper understanding of the logic and principles of mathematics, and he seems to be deriding that effort also. So it still seems to me that we get no clear and useful message from this essay.

On almost every level, this essay falls apart on critical analysis. I wonder why it has become such a legend in the physics community?

-- Donald Simanek

Angels on a Pin

A Modern Parable
by Alexander Callandra
Saturday Review, Dec 21, 1968.














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