Saturday, June 17, 2006

The Pearl Poet: Professor Condren Responds

Symbol by Early 17th-Century Mystic Jakob Böhme
Names of Jesus
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.



At 1:00 PM, Anonymous Anonymous said...

Very, very interesting and generous of Professor Condren to elucidate. But let's tease this apart. Astrology=numerology; Astronomy=numerical analysis. So, there is a terminological error. True. Numerology, at a basic level, is sticking numbers into names to arrive at an analysis based on assumed meanings. At an advanced level, it becomes Cabala. But to some minds, this is as scientific as astronomy because it reveals the origins of Creation. The distinction is not quite as clear cut. To distinguish "numerical analysis" from numerology (Science from Occultism?) there is an appeal to a belief that God measured the Universe and all is numbered. But this supporting argument is also the same supporting argument that Pico, Ficino, Milton, Spenser, and the whole tradition of sacred number use. It is the line of Christian Cabala and Neo-Platonism and the whole Hermetical Tradition as expounded by Yates. And of course, it has biblical had to...otherwise it could not have been taken seriously. The metaphorical explanation does not really hold water. Numerical analysis= "discover(ing) 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". That is perfectly put. But how do you derive meaning from these measurements and link them back to
"verbal texture" e.g. Paradise Lost has a 33 day time scheme for the years of Christ on Earth. This actually becomes a 13/3/1/3/13 time scheme: fall of the angels/Creation centering on Lights in Heaven/fall of man. This is "numerical design" where a whole structure follows a belief in 3 as Trinity, 13 as Trinity's Law and Order, 3/1/3 as 3 in 1 and 1 in 3, the composition of the Trinity (Fowler in Triumphal Forms). Sacred meanings have to be used to encode the structure of Paradise Lost. This claim that "numerical analysis" is a modern science (like astronomy)does not mean much without referring to sacred number and inherited meanings. I suppose I am the commentator that could not see a modern poet using abstruse mathematical design. So, I will own up to that. But I did not say that poets would not use mathematics. I know the opposite to be true. I merely speculated what kind of poetry would emerge from using modern mathematics. Since then, I have discovered modern poems using Fibonnaci sequences...and a right load of rubbish they are poetry. Lovely numbers, but 0/10 for verbal structure. For me, the question becomes this: how far can a critic stretch this term "numerical composition" and how far can a poet operate this method before it comes so refined that only the angels can hear it? It is also interesting that Professor Condren refers to 12 and 31 like musical "signatures" i.e, they are a silent notation: they instruct a pianist, say, when to play sharps and flats, and demarcate notes for the left and right hands. Of course "signature" was a key medieval idea...but this word brings with it all kinds of occult terms too: so, the oyster is a "signature" for Mary who bore Christ the pearl. As with the astrology/astronomy metaphor, the suggested concept, which comes over as modern, rational and clear cut, is nothing of the kind. Finally, I think of the astrolabe, yes, the triumph of astronomy, but no, it wasn't split off from astrology.

At 2:54 AM, Blogger jj mollo said...

I think it more than reasonable to conclude that numerical analysis, carried to such lengths, implies a certain underlying numerological mode of thought. You, as a scholar, are fascinated by these numbers precisely because it exposes some secret passion on the part of the poet.

At 3:41 AM, Blogger Horace Jeffery Hodges said...

As Eshuneutics pointed out, fields of knowledge were not as differentiated in the Ancient and Medieval worlds as they ae in our Modern (or Postmodern?) era.

Thus, just as Medieval Christians might have looked to astonomy to learn something of the structure of the universe (though they were skeptical about the real existence of such things as epicycles), so they also looked to astrology to learn something of their individual fates (however they might have understood the term).

A poet intent on using numerical design to structure a poem in the manner that God structured the cosmos might also have used numerology to express meanings in the manner that God did in John's Apocalypse.

Condren's emphasis upon the expression "numerical design" is useful for me in making a distinction that I had felt but hadn't been able to articulate, just as the terms "astronomy" and "astrology" are useful for me in making a distinction.

The Pearl Poet may also have made such a distinction, yet without excluding the use of one or the other.

I'll just have to read Condren's book this summer and see what I think. I suspect that Eshuneutics will be reading it as well and will have a 'number' of things to say about it.

Jeffery Hodges

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At 4:00 AM, Blogger Horace Jeffery Hodges said...

Michael, I'm also curious about the expression "from virtue to essence" and wonder not only where it originated but also what it means, precisely.

I gather that it means something like a "power" (virtue) in the mind of God that can be actualized as the "essence" of a created thing.

But I can't find the expression "from virtue to essence" by Googling (which you probably also attempted). Perhaps Condren (or somebody) will read of our dark ignorance and offer the enlightening knowledge.

Jeffery Hodges

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At 5:25 AM, Anonymous Anonymous said...

I wonder if "virtue"=virtu, as in the courtly love tradition. In that case it would mean "potency" in the mind of the Divine. (Neat pun!)

At 5:32 AM, Anonymous Anonymous said...

Hello Jeffery

Let me begin with an apology for mis-spelling your name last time I was here.

The medieval approximation for the golden ratio is - drum roll please! - 61/99. It isn't consistent (just like spelling wasn't consistent), but it's definitely the one that poets used most often in my opinion and I've looked from Beowulf to the beginning of the 15th century. Beowulf itself uses 61/99, if I'm not mistaken to divide the Grendel storyline from the return to the land of the Geats and all subsequent events. The Pearl poet uses 61/99 sometimes and 62/101 at others, depending on whether the poem is a multiple of 22 lines or not. 22 lines seems to be a common feature of much medieval poetry and I believe it is in-built so that at the 7/22 position the fate of the 'hero' can change. 22/7 is a well-known approximation for pi, thus denotes a circle and thus seems to be a "Wheel of Fate" device.
Let me add one last thing - Condren is definitely right. Here speaks a mathematics teacher who took the poet's word "Patience is a point" in the mathematical sense of that statement and then sat back in awe as the new numbers dropped out. The golden sections once Patience is considered as the mathematical equivalent of angels dancing on the head of a pin are just so amazing I'm still shaking my head in wonder. The total length of the manuscript considered this way is 5555 lines which is a multiple of 101 (and maybe not 22, but at least 11), the change of fate is 555.5 lines into Purity and every golden section is a multiple of 101. The golden ratio works well when Patience is included, but it works superbly when it's not. 'Genius' seems quite an under-rated appellation for the poet actually.

At 10:04 AM, Blogger Horace Jeffery Hodges said...

Annie, thanks for the comment. I'm still struggling through Condren's book, so I'm not yet knowledgeable enough to judge the poet's level of genius in things mathematical, but in literary terms, the Pearl Poet is a genius.

As I get further into Condren's book, I hope that I'll better be able to judge what our poet was doing.

Jeffery Hodges

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