Wednesday, June 14, 2006

Professor Edward Condren: On the Pearl Poet

Professor Edward Condren
English at UCLA
(Borrowed from UCLA, June 14, 2006)

By Googling, I located online an enquiry posed by Professor Condren on Drexel University's Math Forum back in June 1999 when he was researching the material that became his book. Here are some details that he provided on his interpretation of the entire manuscript of the Pearl Poet's four poems:
A unique fourteenth century manuscript, British Library Cotton Nero A.x., has four poems, two of which are the brilliant Pearl and Sir Gawain and the Green Knight. It has always been thought to be a mere anthology, probably by the same author. My book argues that it is in fact a single artifact unified by the same mathematics that, from the Neo-Pythagoreans onward, have been held to demonstrate the unity of all creation. The line counts of the four poems 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. The first poem, Pearl, has 20 sections of 5 stanzas each, with each stanza containing 12 rhyming lines. Moreover, the first line of each stanza replicates the last line of the preceding stanza, with the first line of the poem echoing the last line of the poem. It seems clear to me that this poem's 1212 lines create a verbal dodecahedron: 20 vertices; 12 faces; each face a five-sided pentagon. The pentagon, of course, is highly dependent on the phi ratio. The three remaining poems seem 2-D, rather than 3-D. In other words, the poet may have conceived them as the three inscribed planes. The first of these remaining three, Purity, is constructed almost entirely of phi-related sections which encode a five-pointed star -- another phi-dependent figure -- which happens to be the main symbol on Sir Gawain's shield. The next poem I haven't entirely cracked yet (hence my query about the size of the inscribed rectangles). It's a retelling of the story of Jonah. But its 5 sections have intriguing sizes: 60, 184, 60, 104, 123. When we remove the overages, which total 31 (4 + 4 + 23), we are left with two 60s, two 100s, and 180. This last is the radius of the circumscribed circle surrounding the five-pointed star laid out in Purity.
Obviously, this is technical stuff, and I haven't had time to delve into it beyond checking just enough to learn that the "Golden Section" and the "phi ratio" are two names for the same thing, the "Golden Ratio," which was known as the "Divine Proportion" in the Middle Ages. Assuming that the Pearl Poet really was encoding this into his poem, the question then becomes: What does it all mean?
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I presume that Condren tells us in his book. From the book description at Amazon, I infer that the Pearl Poet's manuscript of four poems is intended to reflect the cosmos, though what this means in its particulars would require my reading Condren's book, which I may well do

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15 Comments:

At 6:33 AM, Blogger eshuneutics said...

A good question. I remain unconvinced by this mathematical "mumbo jumbo" since it neglects the social, political, religious context of poetry. I have attempted a personal reading which I will place on my blog site after reflection.

 
At 9:56 AM, Blogger Horace Jeffery Hodges said...

Well, Condren was speaking to mathematicians and asking for help on some technical points, so this selection might not reflect the details of his book, which probably doesn't neglect these things (from what I can gather on the Amazon site).

But I still have a bit of difficulty imagining that the Pearl Poet was thinking in terms of two- and three-dimensional geometry as he structured his poem.

Perhaps that's merely my own ignorance.

Jeffery Hodges

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At 6:44 PM, Blogger eshuneutics said...

I am with you on this one. There was not the difference between disciplines in the medieval and renaissance worlds that there are now. I cannot imagine any contemporary poet sitting down and writing an advanced mathematical poetry, even though there is a greater range of mathematics and poetries to work from. It would have no audience. Condren's range of learning is admirable, and it had me intrigued, just a little, until I read the Amazon reviews. A Da Vinci code for Pearl. Oh, no. The guide book you have to have to read the poem? Oh, no. It is tempting, however, to see the dodecahedron as an image: it does tanatalisingly fit: Pentagon=5 lines stanzas. OK 12 faces=12 line stanzas. OK. 20 vertices=20 groups of poems. And the dodecahedron,as a Platonic solid, represented the Universe beyond the 4 elements. A lovely insight, but a sort of "grace note", a final flourish unitng mathematics and poetry and paying homage to the Creator. Numbers are an important part of Pearl and show the poet's sophisticsted learning. But sometimes with hermetical ideas you can get a bee in the bonnet and try to get honey from the wrong hive...Highly intriguing, but not as beautiful as the poetry of Pearl.

 
At 9:25 PM, Blogger Horace Jeffery Hodges said...

Eshuneutics, perhaps you should get this article first:

"Numerical Proportion as Aesthetic Strategy in the Pearl-Manuscript," Viator, 30 (1999), 285-305

If there's anything to Condren's argument, this should make it clear.

Jeffery Hodges

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At 5:23 AM, Anonymous Ian Myles Slater said...

Amazon offers a pdf of a published review by Nick Davis of Condren's "The Numerical Universe, from the well-established "Modern Language Review" -- for a fee.

The less prestigious, but extremely useful, "The Medieval Review" offers one by William F. Klein, for free: it is accessible at http://www.hti.umich.edu/cgi/t/text/text-idx?c=tmr;idno=baj9928.0402.025;rgn=main;view=text

For those not familiar with it, TMR, formerly "Bryn Mawr Medieval Review," is "a moderated distribution list," run by and for medievalists. It offers a searchable collection of reviews going back to 1993. You can have new ones delivered by e-mail by subscribing (free). You can also jointly or separately subscribe do its one-time sister, "Bryn Mawr Classical Review" (http://ccat.sas.upenn.edu/bmcr/). (Although they now operate independently, BMCR continues to offer e-mailed TMR reviews selected for relevance as well; which can get confusing.)

 
At 5:40 AM, Anonymous Ian Myles Slater said...

If the TMR link provided doesn't work (and a second test just failed), try the home page at

http://www.hti.umich.edu/t/tmr/

The review ID is 04.02.25. And a search using "Condren" or "Klein" as the key word should also turn it up, although the search function is a bit slow and awkward.

 
At 8:29 AM, Blogger jj mollo said...

Once upon a time, mathematics and the arts were not so rigorously self-segregated. Mathematics retained a mystical allure that usefulness has besmirched. Although scientists and mathematicians will dabble in the other kingdom, they do so with little respect from their counterparts. Certainly, a self-respecting practitioner of the liberal arts today is inclined to forswear allegiance to the idea of truth itself, much less express an interest in physical fact.

There are interesting exceptions.

 
At 11:28 AM, Blogger Kate Marie said...

Hey -- Professor Condren taught my undergraduate Chaucer class at UCLA! One of the beauties of his class was that we didn't "interrogate" or "deconstruct" anything. We actually read and studied Chaucer' work. Imagine that.

(Sorry this is off-topic -- I was just tickled to see my old Professor's picture on your blog.)

 
At 12:01 PM, Blogger Horace Jeffery Hodges said...

Ian, thanks. The review was complimentary to Condren but didn't go into details about the numerology.

I'll look at it again and perhaps post something.

Jeffery Hodges

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At 12:06 PM, Blogger Horace Jeffery Hodges said...

JJ Mollo, I recall when Sokal's article came out and embarassed Stanley Fish. That whole affair was quite amusing despite my admiration for Fish's analysis of Paradise Lost and my enjoyment of what he writes.

Jeffery Hodges

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At 12:08 PM, Blogger Horace Jeffery Hodges said...

Interesting, Kate Marie. I guess the world is small. You seem to have had a positive impression of Condren. That is certainly a recommendation of the man.

Jeffery Hodges

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At 7:18 PM, Anonymous Annie Hamilton said...

I'm a maths teacher (yes, you can tell from the plural I'm from Down Under) who has an abiding interest in phi in literature. I've actually read Prof. Condren's book very recently - and been highly impressed by his efforts at slogging through some complex maths, even though at first his premise seemed a little dubious to me. It was the very complexity of the mathematics that troubled me to start with, since any mathematician worth their salt loves a simple, elegant solution, not a complicated one. So I wasn't entirely convinced of his premise, until the very last page when the final number dropped out. It was so obvious and so logical a starting point for the poet that I was surprised it was left without much comment. By back-formulation from the final number, the entire structure of the poem was laid bare and the various significant line numbers of the poem appear so simply, it's utterly obvious how they arise. (Unfortunately, Condren didn't think to back-formulate - i.e. to start with the number he proposed as the cross-beam number and work out how the poet set the original mathematics up.) Forget the whole business of the 10th and 25th prime. The numbers, 31 and 101, as well as 1212 and others, arise much more simply as a result of the application of the golden ratio to 490. Condren in fact missed the significance of the number 490 in association with the Cross. I would interpret it as a numerical symbol of forgiveness: 70 x 7, the answer Jesus gave Peter when he asked how many times he should forgive a brother who sins against him. Even a cursory look at 490 lines in the manuscript (particularly from the very end) show up some fascinating details that go way beyond any reasonable level of coincidence. (Believe me, I can calculate how likely what Condren's found is likely to occur by random chance - it's more probable I will win the lottery several times in my lifetime.) If the golden ratio is applied to 490, then it's really easy to come up with the set of numbers that looks so odd. It took me a while to be convinced of the dodecahedron, but I looked at other aspects from a mathematical point of view and now definitely agree it's there. I don't advise anyone to use phi (unless you simply want to reproduce what Condren's done), because unless you understand it very well, you're likely to overlook some really luscious mathematical-spiritual-artistic-social symbols. Obviously I'm differentiating between the golden ratio and phi, but I won't bore you with the subtleties. Mind you, there's lots of "mathematical signposts" that are really so simple you don't need to do any calculation anyway. For some really interesting mathematical-spiritual-religious-social allusions, try Lines 618 and 666 of Sir Gawain and the Green Knight. They are a real buzz when you have any serious knowledge about the history of mathematics at all.

 
At 8:52 PM, Blogger Horace Jeffery Hodges said...

Annie Hamilton, thanks for the comment, much of which went over my head since I don't know the mathematics. Perhaps you should contact Professor Condren for an exchange of ideas. His email is available at the UCLA site that I've linked to in the post.

Meanwhile, perhaps you could explain some of the math that you've alluded to?

Or if you have an online page on this stuff, let me know, and I'll go there and read.

Jeffery Hodges

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At 9:27 AM, Anonymous Annie Hamilton said...

Hello Jeffrey

I have in fact already had a delightful and lengthy correspondence with Prof. Condren, who was very gracious and kind enough to suggest that perhaps I might like to write a paper entitled something along the lines of "Five (or Four or Six)Mathematical Curiosities in the Pearl Manuscript". However, I don't feel adequate to such an undertaking, given firstly that my background is maths, not medieval literature, and secondly and more importantly, I don't think of mathematics in isolation. I see it as part of a wider symbolic universe and it's not that I don't think I couldn't explain the maths to an audience of medieval scholars, it's that I don't think I could explain how mathematics can be the symbolic heart of poetic inspiration. To those who fear maths (which is about 90% of the population), there's a unbridgeable chasm between maths and poetry and it's inconceivable to such thinkers that algebra is a rich and resonant symbolic language and it's possible for some numbers to be so evocative that they can be translated into poetic forms or art or even religious imagery. I'm not talking numerology, just about particular numbers. So I just don't see I can adequately convey the sense that I have that "this is not a mere line number, guys: look at what's in it, this is a marvel weighted with glory, suffused with incalculable wonder". Condren basically commented to me that there's more than a few people who see his analysis as simply "counting lines" - while I see instead a vast and gorgeous tapestry of art, poetry, symbolism, social comment, political allusion and spiritual symbolism, encrusted with mathematical gems. Most people seem to think these jewels are unnecessary (and maybe even illusory) but I see that the mathematical adornment makes perfect sense. Moreover I think that not only is the mathematics a major clue to the heart of the matter, but that Condren understood the poet's mind sufficiently to push through the clues relentlessly. His inspired guess was to look for a cross-formation overlaid on a pentagram - and without that, the mathematics looks specious and arbitrary. With it, however, everything becomes explicable - all the line numbers, everything - including the placement of the illuminations to form the Five Wounds on the Cross.

Condren lays a brilliant foundation, but the main problem seems to me that he didn't always understand what he'd found. I hope someone does take his conclusions and examine them on their own merits.

Sorry I don't have a website: I am merely a mathematician-cum-novelist who became curious about Joan Helm's theory concerning the golden ratio in The Knight of the Cart and why it should be symbolised by the word "gold" and the letter E. I thought there might be something in Sir Gawain and the Green Knight to help clear up the mystery - and that's because even a novice like me can see SGGK has heaps of allusions to Lancelot as well as golden ratio maths neon-lighted everywhere (which I knew before ever reading Condren). However, there was never anything I could find to throw light on that enigmatic E.

Condren's book, of course, didn't address this issue (in fact, he didn't know about "gold" being a signal word for the "golden ratio" in The Knight of the Cart) but talking to him, I did find clues to what I was looking to understand. In Pearl, where else? Once you understand it's the whole manuscript you need to look at, not just the last section, it's simple to know where to look. But again the answer was not merely a number for a line placement (the golden section, of course) or an E, it's this mind-blowing jewel-like image with so many facets (mathematical, social, religious, mystical) that I'm reduced to inarticulate awe. The best I can do here - and please forgive me because I'm struggling to explain my vision of this - is that the golden ratio is engraved on Pearl to evoke both the E in The Knight of the Cart and the E engraved on the white navelstone at Delphi. I'm not sure of my wording here, but is this what's called "playing with the meta-text"?

The link here, anyway, is Pythagoras and, unfortunately, it's mostly maths from now on.

 
At 10:00 AM, Blogger Horace Jeffery Hodges said...

Annie Hamilton, thanks for the extra information. I'll look into this when I have some time. Condren intended to have his book delivered to me, but it seems to have been delayed or lost in shipping. I intend to purchase a copy for myself and read it, after which, I'll be able to follow up your leads.

Thanks again. By the way, my name is spelled "Jeffery."

Jeffery Hodges

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