The Alexandrian Solution

A lot of people have a very famous story … wrong.

The story is that of the Gordian Knot and precisely how Alexander the Great loosened it. Most people imagine Alexander slashing the knot with his sword, as pictured above. But he did not.

In the nuance of how he really untied the knot lies hidden a worldview: the supremacy of simplicity and elegance over brute force and complexity. The true “Alexandrian Solution” was, for example, what Albert Einstein was looking for in his search for a Grand Unified Theory — a formula that was simple enough (!) to explain all of physics.

I’ll give you the background and the nuance of the story in a moment, but first another fist bump to Thomas for reminding us to make the association.

We are, remember, talking about complexity. The Gordian Knot is the archetypal metaphor for mind-numbing, reason-defying complexity; Alexander’s triumph over the knot is the archetypal metaphor for triumphing over complexity. Now read on…

I) Background

a) Phrygia

The Gordian Knot was, as the name implies, a knot in a city called Gordium. It was in Phrygia, an ancient kingdom in Anatolia (today’s Turkey).

The Phrygians lived near (and may have been related to) those other Anatolians of antiquity: the Trojans and the Hittites. They were Indo-European but not quite “Greek”. Their mythical kings were named either Gorgias or Midas (and one of the later Midases is the one who had “the touch” that turned everything into gold). Later, they became part of Lydia, the kingdom of Croesus. And then part of the Persian Empire. And then Alexander showed up.

b) The knot

Legend had it that the very first king, named Gorgias, was a farmer who was minding his own business and riding his ox cart. The Phrygians had no leader at that time and consulted an oracle. The oracle told them that a man riding an ox cart would become their king. Moments later, Gorgias parked his cart in the town square. In the right place at the right time. 😉

So fortuitous was this event and Gorgias’ reign that his son, named Midas, dedicated the ox cart. He did so by tying the cart — presumably by the yoke sticking out from it — to a post.

And he made the knot special. How, we do not know. But Plutarch in his Life of Alexander tells us that it was tied

with cords made of the rind of the cornel-tree … the ends of which were secretly twisted round and folded up within it.

It was a very complicated knot, in other words, and seemed to have no ends by which to untie it.

Lots of people did try to untie it, because the oracle made a second prophesy. As Plutarch said,

Whosoever should untie [the knot], for him was reserved the empire of the world.

II) Alexander, 333 BCE

Alexander, aged 23 and rather ahead of me at that age, arrived in (Persian) Phrygia in 333 BCE. The knot was still there, un-untied.

Alexander had already subdued or co-opted the Greeks, and had already crossed the Hellespont. But he had not yet become divine or conquered Egypt and Persia. All that was to come in the ten remaining years of his short life. And it began with the knot, since he knew the oracle’s prophesy.

Here he his, his sword drawn, approaching the knot:

Did he slash?

No, says Plutarch (ibid,. Vol. II, p. 152, Dryden translation):

Most authors tell the story that Alexander finding himself unable to untie the knot, … cut it asunder with his sword. But … it was easy for him to undo it, by only pulling the pin out of the pole, to which the yoke was tied, and afterwards drawing off the yoke itself from below.

III) Interpretation

I leave it to the engineering wizards among you to re-create the knot as it might have been. But what we seem to have here is a complex pattern that was nonetheless held together by only one thing: the beam.

It was, Einstein might say, like quantum physics and gravity: intimidatingly complex and yet almost certainly reducible to one simple reality.

Alexander, being Great, understood this. He saw through the complexity to the simple elegance of its solution, and pulled the peg.

This is how I understand “the Alexandrian Solution.” I intend to look for it in all of my pursuits. 😉

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47 thoughts on “The Alexandrian Solution”

  2. Thanks for the attribution!

    I hadn’t heard the whole story before–that makes it even more applicable to your complexity discussion.

    On a separate note, and germane to absolutely nothing, I wonder if the Gordian Knot might have been what is today called a “stay mouse” on a tall ships. Old sailing ships (until the 18th century) used big black ropes called stays to support the masts. Some fastenings were done with a slip-knot sort of arrangement and to prevent the short end from coming through the loop they would fatten the end of the rope. The process was called mousing and the end result a mouse. No one knows exactly how it was done–they look like a woven ball of rope with “the ends secretly twisted round and folded up within it” just like Plutarch says.

    Greek biremes had stays but I don’t know if they used the stay mouse. In any event, it is a practical way of securing things with rope and would have been a good way to tie up your ox cart as well.

    The reason I know a little about this is because model ship builders go crazy trying to figure out ways to realistically render stay mice on models. Aside from the problem of working them in scale there is the additional challenge of not knowing how they were woven. If you aren’t aready bored to death you can find out a little more here:

    http://books.google.co.nz/books?id=c_sJIeR0jeIC&pg=PA98&lpg=PA98&dq=mousing+%2B+ship+rigging&source=bl&ots=S6DibMG61Q&sig=6r5mq3IylvvSrK7uaY1agJ7vcok&hl=en&ei=6vb6S4a2IImQNrLN6JsK&sa=X&oi=book_result&ct=result&resnum=6&ved=0CCwQ6AEwBQ#v=onepage&q&f=false

    Reply

  3. seems like even more important than untying a knot is knowing whether or not it needs to be untied. was the purpose of untying only that of proving oneself competent to rule the world?

    also, i think i’ve seen my first typo in the hannibal blog. if not a typo, it’s odd wording at least:

    “Alexander… arrived in (Persian) Phrygia in 333 BCE. The knot was still there, untied.”

    i think it should read “the knot was still there, tied.” or much better because of the repetition involved, “the knot was still there, un-untied.”

    Reply

    • Collaborative writing at its best. Un-untied it is, as you can see. 🙂

      Regarding the “telos” of untying the knot: You should think of it as part of the archetype of the hero’s test. Think Excalibur. (Theseus also had to get a sword to prove himself, like Arthur.) It’s as though we need to establish somebody’s identity or credibility, story-wise, in order to trust him.

    • It’s such a burden, this feminist whining, but here goes: Notice how when we give our girl heroine a test (think the Princess and the Pea) she can only win by failing.

    • Or, worse, she must, in order to pass her test, fit into … a shoe (Cindarella), and not a “comfortable” one either.

      Actually, no, I take it back. Penelope passed her test: keeping suitors at bay with cunning and perseverance (weaving a shroud every day for years, then undoing what she’s woven at night); and then testing Odysseus in turn (the thing with the bed, one of whose legs is an olive tree).

      And you remind me of Jeanne d’Arc. I was just going to post about her anyway….

    • You can include Siegfried in the sword acquisition pantheon. Jenny’s comment reminds me that credentializing a hero by having him win a sword definitely has phallic overtones. As does use of the sword for cutting knots, knighting other heroes, etc.

    • Heroes get metaphor-laden swords, heroines get what?

      SUPER POWERS OF FIDELITY!

      I can hear the promo now: It’s PENELOPE! See her keep suitors at bay with cunning and perseverance! She can weave all day and then surreptitiously undo the weaving at night! SHE’S GOT SUPER FIDELITY POWERS! (Shroud and loom sold separately.)

      Not much of an action figure. More like a no-action figure.

      She’s great. I love her. And I’m all about fidelity, but as a credentializing test for heroines, it’s kinda guysville.

      Don’t know much about Jeanne D’Arc, I guess I always thought she was sort of lacking in the flashy and fun department, but I hear she had a great personality.

      I’m done being snarky now.

    • @Jenny:

      Jeanne d’Arc: girl with big sword. Need more? (Post upcoming)

      You have an assignment herewith: In 20 seconds, 100 words or fewer, name your favorite heroines. My hero thread needs some yin….

    • @ jenny,

      after a while the reply button disappears. find where it was last. the post “should” land right.

      please stay tuned and respond. this blog needs more poets, artists lauded – i think this is a female point of view.

    • Ha! @ you, Andreas! Heroines don’t live by other people’s rules. I’ll stick to the 100 words or less, but I’m going to think a bit beyond 20 seconds. Sprezzatura, y’know, is an illusion.

      But, a very big favorite is Shakespeare’s Rosalind from As You Like It. Smart, funny, sexy, self-deprecating. I love her. (that’s 18 words)

    • Andreas–don’t forget Brunnhilde. Plus you might want to have a look at Zenobia, who took Egypt from the Romans in around 250. Zenobia claimed to be a descendant of Dido, so she might fit well with your Pantheon.

    • aren’t we up to near-modern/modern heroines?

      since i know how much you relish controversy, i nominate Hillary Clinton and Imelda Marcos.

      on the David Byrne you might find a plethora of modern heroines. check it out: “here lies love”

    • I’m still befuddled by the placement of the reply buttons, so, somewhat schizophrenically now, I reply to my own cheap self.

      Just two more heroines (keeping it simple, fearing collapse):

      1. No explanation: Daw Aung San Suu Kyi

      2. Anna Akhmatova. A poet’s poet. She wrote so beautifully on personal themes and the Stalinist purges. She lived through hell along with her countrymen, never abandoned them–a true patriot. I wonder how many people survived years in the gulag or the siege of Leningrad because they knew her verses. No dopey I-am-woman sisterhood feminism in her: When women began to flog their poetry all over Russia following her example, she wrote (it has meter in Russian): I taught women how to speak, but, my god, who will make them be quiet? And she was elegant. Many gorgeous portraits of her.

      They are real heroines, both of them–brave and smart and elegant.

      I have so much more to say in defense of Rosalind’s candidacy, but I’m over word limit as it is. Just hope teach won’t notice.

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  6. “A lot of people have a very famous story … wrong.”

    so many that when i looked to see if there was a mathematical description of the knot, only references to “cutting the knot” came up.

    not that i doubt, but can you provide a link that tells the story correctly?

    Reply

    • My source was not a link but Plutarch. Ancient Greek dude … I usually go with him rather than what Google spits up. 😉

      Also, I meant “wrong” very tongue-in-cheek. With these old stories, there are always several versions, and we shouldn’t pass judgment. Part of interpretation is choosing one that suits you. So my use of “wrong” in the first sentence was mainly … to get you to pay attention.

  7. Gilbert and Sullivan’s operetta, “The Gondoliers”, has these lyrics:

    In a contemplative fashion,
    And a tranquil frame of mind,
    Free from every kind of passion,
    Some solution let us find.
    Let us grasp the situation,
    Solve the complicated plot —
    Quiet, calm deliberation
    Disentangles every knot    .

    Reply

    • uh, kvetch… didn’t i say that (or try to) with the quiet mind posts? oy, i want a fist bump.

      high five to phil 😉

    • soooooo, what took you so long, busy guy with important things to do? an hour ago it might have meant something… even a few minutes ago, but now, nothing. don’t concern yourself with me, i’ll be fine.

      talk amongst yourselves.

      (you softy ;), can’t believe you fell for it. let that be a lesson in kvetching)

    • and, Phil, how about Viola’s fabulous words in Twelfth Night:

      O Time, thou must untangle this, not I;
      It is too hard a knot for me t’ untie.

  9. So I summarize:

    1) Rosalind
    2) Brunhilde
    3) Zenobia
    4) Hillary Clinton
    5) Imelda Marcos
    6) Aung San Suu Kyi
    7) Anna Akhmatova

    Right away, we notice an issue: In my heroism thread so far, I’ve only featured mythical/fictional heroes. Not even Alexander, Hannibal or Scipio (yet)!
    I’ve even been pondering whether Jeanne D’Arc would be a step too far into non-fiction.

    My initial hunch was that only the mythical hero/heroine can tell us what our idea of heroism is. Real people are too, ahem, complex.

    A second issue for me: I need to find something to say about heroes or heroines to post about them. (Ie, I can’t “just” retell stories, I need to advance our understanding.)

    So, will ponder. And do homework. Long time since “As you Like it”, no exposure yet to Akhmatova.

    Good thinking guys.

    Reply

    • how about staying with the mythical/fictional since they represent the ideal?

      then see how close our nominees come to that ideal.
      i’m still new to your blog, but didn’t you do something similar with greatest minds/thinkers?

    • Is it too late to add to the list? Hmm … OK, how about:

      Boudicca
      Elizabeth I
      the Suffragettes
      … Cleopatra?
      Lady Godiva (hey-oh!)

      Alright, so that last one is a tad self-indulgent. How many acts does a hero make? What about Judith of “Judith and Holofernes” fame? I’ll throw Scathach out here again for a strictly mythological one. Ummmm, that’s what I got.

  10. Regarding the mysterious “reply” buttons here:

    WordPress lets me set how many layers to “thread” comment conversations. I used to have it at unlimited, but the comments became tiny columns and unreadable.

    If people get confused, I could get rid of threading (ie, direct replies) altogether. Then we would all leave comments in chronological order. Perhaps that is … simpler… less complex… >better.

    Reply

    • @Andreas

      If people get confused, I could get rid of threading (ie, direct replies) altogether. Then we would all leave comments in chronological order. Perhaps that is … simpler… less complex… >better.

      I happen to like the direct replies but I also have struggled with the Reply function and its seemingly capricious disappearance. Still, using the @[whoever] and/or quoting in some manner should limit confusion.

  11. The story of Alexander and the Gordian Knot sounds like his press release. So how does a Gordian Knot really get loosened? — or, in the following case, sliced? 

    Here is an analysis exerpted from: 

    Breakout From the Hedgerows: A Lesson in Ingenuity 
    by Walter S. Zapotoczny, 

    a detailed account of the many frustrated attempts to break out of Normandy’s hedgerow country in 1944, and the Alexandrian “saw teeth” solution proposed by some unknown U.S. soldier (please excuse its length):

    A significant tactical dilemma facing the U.S. Army in Normandy was the local terrain, called Bocage in French. Bocage refers to farmland separated by thick coastal hedgerows. These hedgerows are denser, thicker, and higher in Normandy than elsewhere along the French coast or in the British countryside on the opposite side of the English Channel. From a military perspective, they were ideal for defense, since they broke up the local terrain into small fields edged by natural earthen obstacles. They provide real defense in depth, extending dozens of miles beyond the coast. The Bocage undermined the U.S. Army’s advantages in armor and firepower, and the hedgerows gave the German defenders natural shelter from attack. … 

    The Bocage presented a substantial obstacle to tanks. While it was possible for tanks to charge the hedgerows and push over the top, this exposed their thin belly armor to German anti-tank weapons. Some hedges were so entangled with foliage and small trees that a tank could become trapped if attempting to push through, or could shed a track, effectively immobilizing it. … 

    During a discussion between some of the 102nd’s officers and enlisted men, someone suggested that they get saw teeth, put them on their tanks, and cut through the hedgerows. Many of the troops laughed at the suggestion, but Sergeant Curtis G. Culin took the idea to heart. Culin designed and supervised the construction of a hedgerow-cutting device made from scrap iron pulled from a German roadblock. …

    On July 14th, General Bradley attended a demonstration of Culin’s hedgerow cutter. Bradley watched as Sherman’s mounting the hedgerow device plowed through the hedgerows “as though they were pasteboard, throwing the bushes and brush into the air.” …

    Welding teams used scrap metal from German beach obstacles to construct most of the hedgerow cutters. In a remarkable effort from 14th to the 25th of July, the First Army Ordnance Section produced over 500 hedgerow cutters …

    Ideas on how to achieve better results against the Germans came from a wide variety of sources. In general, ideas flowed upward from the men actually engaged in battle and were then either approved or rejected by higher commanders. Within the bottom ranks of the Army, individual soldiers suggested ways that enabled their units to move against the enemy. Sergeant Culin’s hedgerow cutter is the best example of a single soldier’s idea that influenced all of the First Army. 

    http://www.militaryhistoryonline.com/wwii/articles/hedgerowbreakout.aspx

    In the ensuing one-sided battle, Operation Cobra, the “saw teeth” equipped Shermans could effortlessly slice through hedgerows that the German tanks had to go around, and the Allies soon encircled and destroyed large numbers of the German army; General Montgomery’s D-Day plan had worked.

    Reply
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  13. I submit you proffer a somewhat fanciful interpretation of symbolism. Plutarch may offer a historical source for biographical research but as he wrote a depiction of the events from a time hundreds of years after I think it’s presumptuous to take his word as fact. Whatever the real events of the day the “Alexandrian Solution” has come to mean a bold decisive stroke that slices through a complex problem…not a delicate teasing of a simple answer to a complicated issue.

    Reply

    • Oh, you’re absolutely right about that, Hal. He did write many years after the fact, and the phrase does, today, mean what you say.

      But that wasn’t of interest to me here. Plutarch is interesting (in general, not just in this case) for the meaning he, and thus the ancient world, ascribed to certain events.

      And as to how words and phrases have changed over time, well, I like knowing where things came from, and what mutations might have arisen over time.

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