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Circle squared

You have undoubtedly heard the term “square circle”, generally used to refer to something that does not exist—perhaps somewhat related to “once in a blue moon” or “pigs might fly”. If you read anything by anyone who esteems the Enlightenment you are bound to find smug references to Scholastics who “vainly tried to ‘square the circle’, along with other peculiar activities such as ‘counting the number of angels on the heads of pins’”. In other words, for a certain set, “square circle” is a by-word for religious obscurantism and foolishness—a problem that is trivially impossible from the geometric perspective; or, at least, not literally possible as you might imagine.

The philosophy club at my university was even called “The Square Circle” as a kind of joke reference to this activity—something that serious people would not attempt, being logically impossible by definition, and therefore a good name for a light-hearted social club (I never attended—have some doubts it was light-hearted, to be frank).

Another vein in “square circles”, more minor, can be found on “mildly schizo” websites that maintain a mid-90s layout and resolutely claim that through geometric transformation “the circle has been squared” within the Great Pyramid (insert suitable pun about Pi-ramids). These always make me feel a bit queazy and as if the walls are closing in on me—there is something a bit depressing about the incipient schizophrenia that reminds me of urinals clogged with tissue paper and stuttering fluorescent lights (perhaps just the general scene in psychiatric triage—I don’t know).

Anyway, the above are all wrong. The “square circle” is perfectly real and not a logical conundrum at all. The square circle is what is depicted above: the mandala with its quaternary—the circle divided into four segments. The above example is from Jung. So those Scholastics—people further back—were not “wasting their time” on childish illogical nonsense; they were interested in quaternaries—and the mandala just happens to represent your soul. So these moderns who chuckle that we have “overcome” such nonsense as trying to “square the circle” inadvertently say that we have given up on the development of our souls—and this was an advance, thanks to the Enlightenment.

As is often the case, the explanation is completely literal not metaphorical or logical. “Square the circle? Nothing easier—just draw two lines that intersect to form quarters on a circle.” It makes me wonder, really, if the Scholastics had a point about angels dancing on the heads of pins—I mean have you ever looked, let alone counted, the angels on the head of a pin? You may be surprised by the result.


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