The Pearl Poet: Professor Condren Responds

Symbol by Early 17th-Century Mystic Jakob Böhme

Names of Jesus

including

Derivation of Pentagrammaton from Tetragrammaton

(Borrowed from Wikipedia)

In my quest to find out more about Professor Condren's theory without incurring pecuniary debt, I sent him an email to inquire and have received a reply, thereby incurring an intellectual debt.

Here's what I wrote to Condren:

Greetings from Horace Jeffery Hodges. I am a professor of Medieval English at Korea University, in Seoul. I am writing because I have recently become aware of your theory concerning the Pearl Poet.

You can see the 'history' of my awakening interest in the numerological symbolism in these posts to my blog (which I paste here only as evidence, not as an invitation to read what is not intrinsically interesting).

Regular readers will note that I exaggerated my expertise. I should have written that I'm an 'accidental' professor of Medieval English ... but that's another story. Anyway, Condren looked at the blog entries and found my two questions:

1. What was the Medieval approximation for the Golden Ratio?
2. Why does Condren drop the "signature twelves" and the "signature 31s"?

Perhaps I should refresh our memories as to why I posed these two questions. In an online query that was posted on Drexel University's Math Forum in June 1999, Condren explained:

The line counts of the four poems [in the Pearl Poet manuscript] are, respectively, 1212, 1812, 531, and 2531. This highly artful arrangement, minus the signature twelves in the first half and signature 31s (the tenth prime as the Middle Ages reckoned primes) in the second half, gives us two halves of 3000 lines each. More intriguing still, the two outer poems divided by the two medial poems give the Golden Section.

I had earlier noted in my blog entry that the Golden Section, aka the Golden Ratio, is an irrational number that can be given a decimal expansion for as far as one wishes: 1.61803398874989484820....

With that in mind, I followed Condren's method and divided "the two outer poems ... by the two medial poems"...

...without the "signature twelves" and "signature 31s" -- a move that already raises some danger signals for me, but okay. If we add 1200 and 2500, we get 3700, and if we add 1800 and 500, we get 2300. If we then divide 3700 by 2300, we obtain 1.60869565217....

That's closer but still no cigar. We can round off Condren's mean and the actual Golden Mean to 1.609 and 1.618, respectively. That's pretty close, but not the same. If we round off a bit more, we get 1.61 and 1.62. Closer yet, but still not the same. If we round off one more time, we get 1.6 and 1.6. The same ... finally.

At this point, I raised my two questions, to which Condren has graciously responded as follows:

The interesting questions you ask could engage me for several pages, much more, in fact, than I included in my book of a few years ago. But I think it would be best to confine myself to a couple of fundamental points as a way of leading you to a less adverse disposition to numerical design than you express in your blog. Indeed, let me begin with that phrase, "numerical design." You call it numerology in one of your blog entries. Believe me, numerical design differs from numerology as much as astronomy differs from astrology in the modern world. To quote from my book, "While numerology assumes that numbers have inherent symbolic meanings related to the divine supervision of the universe, a numerical analysis focuses almost entirely on formal units of text -- lines, stanzas, sections, fitts, books, and the like -- to discover whether the sizes and shapes of these parts, and their interrelationships, do not perhaps communicate the same meaning that the verbal texture of the manuscript conveys" (p. 3).

I'm glad that Condren corrected my terminology, for I sensed that my reference to the "numerological symbolism" didn't quite capture what Condren is describing. So, "numerical design" it is. Condren continues:

Let me jump to another widely accepted truth the Middle Ages held, that the divine creator used number as the "tool" that enabled the first transition from the mind of God to the physical presence of matter, or as the medieval philosophers themselves put it, "from vitrue to essence." Well then, if God created the universe out of number, then the pale parallel of a poet creating his literary world should also call for number as its efficient cause, especially if he believed his highest ambition was immitatio Christi. So the doubt you have that any modern would design a poem on the basis of number cannot accord with either the philosophy of the Middle Ages nor the poems produced then. You might look at a brief, but immensely persuasive, article by Charles Singleton, "The Poet's Number at the Center," MLN 80:1-10, to see only one instance of Dante's devotion to number in his Commedia.

Oh no! More articles to purchase! I suppose that these are the interest payments on my intellectual debt. By the way -- and just for the record -- I believe that not I but one of the commentors referred to the unlikelihood of a Modern poet structuring a poem according to numerical design. Anyway, Condren now broaches the first of my two questions:

You sound a little triumphant in noting that the Pearl poet never quite got it right when he was trying to reach the magic number of the Golden Section, a failure that makes you even more skeptical that you formerly were. Well, first, no one ever gets it right. Only geometry can reach a perfect golden cut. But the measurement of this geometry in whatever numerical system one chooses to use, fails to capture this precision. The closest our measurement can come is with an irrational number. But while the concept of "incomensurability" nearly broke up the neo-Pythagorean circle, efforts to demonstrate this concept would elude mathematics until long after the fourteenth century. The breakthrough came when the West discovered Indian decimals. Thus the Pearl poet did not have the luxury of the precise numbers you were looking for in the calculations I presented. Just think of the challenge such mathematicians faced: the formula you show on your web site uses the sq.rt. of 5, and leaves it at that. But a medieval mathematician only had at his disposal a rational convergent, namely 20/9, to work out the equation you cite. These days one can hit a key for 5, press the sq.rt. key and in a nanosecond learn that the sq.rt. of 5 is 2.236067977.... The medieval mathematician, on the other hand had only 20/9, or 2.222222... in modern terms, an unavoidable error of 0.01384... To my mind it is astonishing that the Pearl poet achieved such precision despite beginning with a huge inaccuracy. Yet you find fault with him for missing his mark by only 0.02051.

I apologize for sounding triumphant. I intended only to sound amusing as I presented my otherwise rather tedious calculations. Ordinarily, I have better control over my literary style. At any rate, what I wanted to understand -- though perhaps lost in my calculations -- was how the Medieval world approximated the Golden Section and what their approximation was. I'm still not quite clear on these two interrelated points, but let me see if I understand. For the sq. rt. of 5, the Medievals used 20/9, or 2.222222.... If I plug this into the Modern formula, i.e., 1/2(1 + 20/9), then I obtain 1.6111111.... I take it that this was the Medieval approximation of the Golden Section? If so, then dividing 3700 by 2300 -- to obtain 1.60869565217... as the Pearl Poet's approximation of the Golden Section -- does come a lot closer than I could previously see. But this again raises my question as to why one should use 3700 and 2300 rather than 3743 and 2343 for the line numbers, to which Condren responds:

You wonder as well why I discounted the "signature twelves" and the "signature 31s." [Editorial note: 12 + 31 = 43, as reflected in 3743 and 2343.] I argue at some length that these units and tens columns show how the manuscript is to be read, as in music the bass and treble "signatures" are not themselves played, but only indicate the time and key with which the notes are to be played. To my mind the fascinating thing about these particular signatures is the tension they show between the duodecimal system and the decimal system, the implications of which would take too long to illustrate. I'll give just one tease: the expansion of the tetragrammaton (the four-letter name for God) into the pentagrammaton (the five-letter name for God, or Jesus) parallels the expansion of the two Hebrew-era poems (Purity and Patience) at the center of the manuscript into the two Christian-era poems (Pearl and Sir Gawain) at the manuscript's extremes, for which the geometric demonstration of the divine proportion--"division into mean and extreme ratio"--with its compelled expansion, is a perfect analogue.

Not knowing much about music theory, I'm now far beyond my ken. (If only my family could have afforded those piano lessons that I wanted to have as an adolescent...) I guess that I'll have to buy Condren's book to even broach an understanding of this.

I want to thank Professor Condren for his gracious reply to my query. Naturally, his explanation has led to still more questions, as always happens, but I think that I should now probably shell out the money for the book and satisfy my expensive curiosity in the proper fashion rather than incur further intellectual debt at the expense of Professor Condren's time.