Quaquaversal and Procellous

The going is slow, but each word carries meaning with it, meaning that beckons us to "turn aside" and look more closely. Let's begin with procellous. The OED tells us that it is a rare word, and it means "turbulent, stormy." It comes from the Latin procella, which itself is comprised of pro ("forward") and cellere ("throw violently"). That it is/was a sort of pretentious word can be seen from this 1875 quotation: "What man in his senses...would talk of a stormy day as procellous and himself as madefied (i.e., wet)?"

But a quotation from the St. Louis Post-Dispatch in 1992 gave me an idea to develop in this essay. It simply said, "It was a Stygian and procellous night." Of course, this is a take-off from perhaps one of the most unintentionally famous lines in English literature: the beginning of Edward Bulwar-Lytton's undistinguished 1830 novel Paul Clifford. Bulwer-Lytton wrote:

"It was a dark and stormy night; the rain fell in torrents, except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness."

This kind of sentence is all too reminscent of many students' forays into 19th century English literature, which is why that literature remains largely unread today. But, as America is a very creative place, we just haven't let this line lie or simply be taken up by Charles Schultz in Peanuts. The English Department at San Jose State Univ. now has an annual "Bulwer-Lytton Fiction Contest" to celebrate the worst exemplars of this style, which has variously been described at a "self-serious attempt at dramatic flair" or "an extravagantly florid style" full of "redundancies" and "run-on sentences." The contest, in which contestants are asked to "compose the opening sentence to the worst of all possible novels," now receives more than 10,000 entries a year. Here is the 2007 "winner":

"Gerald began -- but was interrupted by a piercing whistle which cost him ten percent of his hearing permanently, as it did everyone else in a ten-mile radius of the eruption, not that it mattered much because for them "permanently" meant the next ten minutes or so until buried by searing lava or suffocated by choking ash -- to pee."

All this from the word procellous. Let's quickly move on.

Quaquaversal

In a word, quaquaversal means "dome-like" or "dome-shaped," but the road down which it might take us is much more interesting than the simple definition. It is derived from two Latin terms, quaqua meaning "wherever," and vertere, meaning "to turn" or "incline." Thus, it is a turning/incline/decline in all directions from a central point. The term has been used in geology in the phrase quaquaversal dip, to describe a dipping in all directions from a central area. You get the picture now, don't you? You have a high point, and then you have a decline all around the point.

But then, as I was researching the word, I ran across the title of a 1995 book: Quaquaversal Tiling, and I knew I was not in Kansas anymore. This has nothing to do with how you finish your kitchen, but is a rather complex concept in pure mathematics. There is a picture of a quaquaversal tiling here. In a nutshell, which is always a dangerous thing into which to put items in pure math, it is a pattern in 3 dimensional Euclidean space, which is generated by rotations about orthogonal axes. I don't really know what is rotated around what at this point, but I wonder if it is called quaquaversal because there is an "every directional" rotation. In any case, this is one for the future.

But the graphic depiction of a pure math concept brought to memory another such depiction which I saw recently when I was visiting the Stanford University Campus. It is called the "Sieve of Eratosthenes" by sculptor Mark di Suvero (b. 1933), and is located outside the Cantor Art Museum on the campus. There is no picture online. Suvero sculpted it in 1999 and dedicated it to the international law expert and Stanford Law Professor John Merryman. Of course, when I learned these things, I spent a good hour researching Merryman, the history of Stanford Law School, the "great steal" of four significant professors from Columbia in 1962, and many many other things that sear that place deeper into my consciousness. But, back to Eratosthenes, the Hellenistic mathematician (ca 275-194 BCE). His "sieve" was a mathematical game/puzzle, a means for finding all prime numbers up to a specified integer. The diagram and explanation here is helpful, but I will try to explain it.

You compose two lists of numbers. The one on the left includes all consecutive integers you want to test for prime numbers. Put it in columns or rows so that the list is easily organized (say the integers from 1 to 100). In the list on the right, begin by writing the number "2." Then, after writing "2" on the right, go to the list on the left, eliminating all numbers that are divisible by two. The number after the first eliminated number is a prime (in this case "3"). Then you write this prime number into the list on the right, so that you have "2" and "3" on the right. Go back to your list on the left, striking off all numbers that are divisible by 3. Your next remaining number on the left list is now "5." It, too, is a prime. Write that number on the right list, and eliminate those which are divisible by 5 in your list on the left. You are left with "7" as the next prime number.

This is a rather cumbersome method, but it is a sure way of determining prime numbers up to a certain number. Another concept learned, even if faster methods of determining primality have been developed since Eratosthenes. I don't know at this point why Suivero's multi-pronged object to the North of the Cantor Art Museum is a likeness of Eratosthenes' sieve, but I suppose I will learn an explanation some day.

Conclusion

Words take you places. Words introduce you to yet other concepts. The number of concepts to which words lead you to is finite (though it sometimes seems infinite). There is joy in discovering almost every new concept. Once you have learned a bunch of them, you become a very interesting person, broadly educated, perceptive, understanding and even fun. Believe me...

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