Thursday, March 21, 2013

On What is Round (ter)

teres atque rotundus
 -- Horace  ('smooth to perfection, to perfection  round')

I saw Eternity the other night
like a great Ring of pure and endless light,
   All calm, as it was bright;
and round beneath it.  Time in hours, days years
   driven by the spheres
Like a vast shadow mov’d …
-- Henry Vaughan, “The World”

Could we but fill to harmony, and dwell
Simple as our thought, and as perfectible, […]
Grow to a radiant round love, and gear
Unfluctuant passion  for some perfect sphere.
-- Rupert Brooke, “Thoughts on the Shape of the Human Body” (1910)

In Vergleichende Anatomie der Engel (1825),  Fechner argued that the angels, as the most perfect beings, must be spherical, since the sphere is the most perfect form.
-- quoted in James R. Newman, ed. World of Mathematics (1956), p. 1152

We have discussed round squares (which do exist, despite everything you’ve ever read)
and round cows (which don’t, and more’s the pity)

G.K. Chesterton wrote a whole book about the subject, called The Ball and the Cross.  As a Christian apologist,  he naturally reveres the Cross, but adds
            There must be some round earth to plant the Cross upon.

He put the case more tartly in Manalive:

“Science!” cried the stranger. “There is only one good thing science has ever discovered -- a good thing, good tidings of great joy -- that the world is round.”

It is difficult to find any passus  in which round  is used in dispraise.  The closest we can come is this:  Brian Greene,  in The Fabric of the Cosmos (2004), p. 294, tells us of “a famously caustic scientist  whose appreciation for symmetry led him to call his colleagues  spherical bastards:  because, he explained,  they were bastards any way you looked at them.”  Still, it sounds nicer than flat bastards.

Why did you do it.  And hearts.  And why was love so round.
-- J. P. Donleavy, The Ginger Man (1955)


Well-rounded (character, education) is another sterling term.  At the simplest level, it contrasts with Fachidiotie -- Merriam-Webster defines it using the terms “broad” and “comprehensive”.  But there is more to it than that -- more than the idea of a well-spread smattering,  jack-of-all-trades (and master of none).  There is the deeper education that all this learning and life experience has -- to borrow the language of topology -- rounded ‘round to form a compact surface.  As such, it gains in structural integrity -- much as a ping-pong ball, though made of inherently thin and flimsy material, shows great spherical strength.


Notions of ‘roundness’ crop up in mathematics as well, well beyond that of straightforward plane or three-dimensional geometry:  for instance, the “unit ball” in a normed linear space. 
The notion is generalized as that of convexity, which has various subtypes, and some surprisingly complex implications in functional analysis.   A lecture at the University of Alberta (Edmonton) in 1982 (Professor Lewis presiding) introduced an especially tasty flavor of this idea:

Definition:   A normed linear space is strictly convex (or ‘rotund’) iff the following holds:
||x|| < 1, ||y|| < 1,  =>  ||(x+y)/2|| < 1

He then added a historical observation:

This sort of thing was introduced by Clarkson in 1936, with  view to integration theorems for functions from the reals to such a space holding also for functions from Euclidean space to such a space.  Community interest switched to linear operators beginning around World War II;  and this remained the case until the late 1960s.  Now we’re back to rotundity.


We leave the last word to C.S. Lewis (English Literature in the Sixteenth Century, 1944):
"Columbus, a man of lofty mind, with missionary and scientific interests, had the original idea of acting on the age-old doctrine of the earth's rotundity, and sailing west to find the east ..."

[Update]  We still leave the last word to CSL, but from a different work, discussing medieval cosmology, and its explanation for the ‘natural’ orbiting-patterns of the celestial bodies:

A modern may ask  why a love for God  should lead to perpetual rotation. [It is because] the nearest approach to His eternal imobility, is eternal regular movement in the most perfect figure … the circle.
-- C.S. Lewis, Studies in Medieval and Renaissance Literature (1966), p. 51

 Does not Saint Thomas remark somewhere, that the most perfect shape, beneath the moon, is the belly of a penguin?  (One feels sure that he did;  yet I cannot  at present  lay my hand upon the passage.)



Further kudos to rotundity:

Dieser rasche Rundgang  durch Schuchardt’s mehr als 50 Jähre umspannende Wirksamkeit  zeigt, daß wir es tatsächlich mit einer  in sich geschlossenen, “runden” Lehre  zu tun haben:  das Bild des Kreises scheint mir am ehesten geeignet, Schuchardt’s Gedankenweben zu versinnbildlichen.
Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2nd edn. 1928), p. 6

Anyone who is up for 'another round', can find more here:


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