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SEA DRAGON’S GIFT : Part 4 of 83 : World of Sea

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SEA DRAGON’S GIFT

Part 4 of 83

De Writer (Glen Ten-Eyck)

140406 words

written 2007

Reproduction in any form, physical, electronic or digital is prohibited without the express consent of the author.

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New to the story? Read from the beginning. PART 1 is here

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“Aye, she’s t’e very ane. ‘Ow’d ye know ‘er line an’ folk?”

“My mother, Evanstar Morn Dannav, was her mother’s identical twin. She raised me on stories of their escapades. Twenty-one Gatherings ago, she married onto the Grandalor. I am Tanlin’s cousin, though I’ve never met her before.”

While they were talking, the Princamorn rolled off the coral head and settled down into the crystal waters of the lagoon. She lay on her side about thirty five or forty feet down.

Soon, the divers began to sound and surface, making notes on waterproofed paperfish parchment. In a few hours they had conducted and documented a survey of the wreck for salvage assessment.

While he waited for the divers to finish their work, Barad retired to his cabin. Chena, his cabin-girl was seated on his lap, a two-leaved tallow-slate open before her on the chart table. Her brows were knit as she studied the problem before her. I wish that I could follow this Arrakan arithomatics the way Barad does. He makes it seem so easy. Their crazy writing is easier by far, and it’s a pain. She looked once again at the rows of interrelated figures that Barad was trying to get her to understand. I wish that he’d get his hand off my breast. I can’t concentrate! These Arrakan function things! I’ll never get them to work! A knock at the locked door caused Barad to flip her slate shut and toss it to his bed. He pushed her behind the bed hangings as well. Sliding open the door, he admitted his Purser, Mister Morgu, who was carrying a set of account books, and Master Selked who was bearing the diver’s still wet reports on the condition of the wreck.

Studying the dripping reports, Master Selked, the Grandalor’s chief boat-wright, famous for the quality of the tools that he made, told Barad, “The Princamorn is not that severely damaged, other than the hull breach. She can be easily salvaged. If we are prompt, most of the capital goods in her shops and much of her cargo and stores should be savable as well.

Mister Morgu, the Grandalor’s Purser rubbed his hands together in glee at the thought. “We hold the rights to the wreck, Captain. It is easily worth seventy five thousand Strong Skins. Even after the costs of salvage, we stand to make better than fifty thousand Skins in profit.”

Barad’s pale blue eyes speared Morgu like harpoons. He shook his unruly mop of blond hair, now going gray, and said mildly, “I did say that these folk are not to be looted. We have made easily thrice that amount by trading with them. We shall indeed assert our claim to the salvageable wreck. If the Arrakans recognize our claim, we will return the Princamorn to her survivors at the cost of salvage plus a reasonable sum for our lost ship-time.”

“But Sir,” Morgu started to protest, seeing a large amount of money vanishing from his grasp.

Quelling the protest with a raised hand, Barad looked past his blade of a nose and said coolly, “I expect to gain far more than I lose in this deal, Morgu. Fear not.

“Would you be so good as to go and get Captain P’osettin and Purser Rostow and bring them here to discuss the matter of their ship?”

Am I an errand boy? thought Morgu irritatedly as he said, “Yes, Sir. I’ll attend to it at once.” He slid the cabin door shut behind him and spoke to the ever-present cabin boy waiting in the passageway. “Benj, go get what’s her name, Poset — something and, Rostu is it? You know, the Princamorn’s ex-captain and Purser.”

Benj, irritated at Morgu’s deliberate mangling of the names of people that he had met and liked, said, “Captain P’osettin and Purser Rostow; yes, Sir. I’ll get them,” and ran in the direction of the mess hall, where the survivors were being put up for now. Shortly he returned, leading both Captain and Purser.

Morgu made a show of sliding open the door and escorting them into Brad’s cabin. Captain P’osettin was a tall, rangy woman with black hair, tied back in a complex knot and braid. Purser Rostow was small man, a little over five feet tall, gray of hair and elderly. That he had been crying was obvious.

Barad turned to them and gestured them to comfortable chairs. “Captain P’osettin, Purser Rostow, I regret intruding on your grief. Losing ship and home must be hard. I need help. I know your trade laws well enough but I need information about your salvage laws.”

“Ca’tain Barad,” said P’osettin in a voice roughened by Gatherings of shouting commands, “Rostow ‘as lost more t’an merely ‘ome an’ ship.”

Barad, remembering the death of his own wife, said quietly, “Dragons, please, not Norrin?”

Mutely Rostow nodded. Captain P’osettin, said, “She was foremast lookoot. Tried t’ warn us o’ t’e ‘ead but we couldnae turn in time. Went t’ Iren’s ‘alls when t’e mast went down. ‘er body wa’ nae recovered.”

“My condolences, said Barad sincerely. This was a feeling that he was all too familiar with. “Can you help us or do you need more time to yourself?”

Pulling himself together with a deeply drawn breath, Rostow replied, “‘Aving a task t’ do ‘ll ‘elp. W’at’s yer need?”

Barad turned to Captain P’osettin first. “Ma’am, I ask your permission to open your ship’s Logs and accounts.”

“As salver, ye need nae permission Ca’tain Barad,” she answered. “T’ey’re yers t’ do wit’ as ye see fit. T’e Logs’ll ‘ave t’ be given t’ t’e Arrakan Council for t’e archive,”

“Still, a friend asks,” Barad returned with a serious smile.

That brought a return smile from P’osettin and a ghost of one from Rostow. “We were fortunate t’ ‘ave ye close, Barad. Ye saved many o’ m’ crew from Dark Iren’s ‘alls beneat’ t’e sea.

“W’at ye need now’s a survey o’ t’e wreck, wit’ position. T’at must be filed wit’ t’e nearest Council ship t’ secure yer claim. T’at’ll be t’e Wavenruner. T’en, an’ only t’en, can work begin.

“M’ crew’ll be Scattered over t’e fleet at t’e next Gat’ering. Once t’e Princamorn’s afloat an’ independent ye can put a prize crew on ‘er. She’ll be sold an’ newcrewed at t’e next Gat’ering.”

“Is it legal,” Barad asked with an intense stare, “for me to sell her and recrew her before the next Gathering? And with that, can I appoint her Captain?”

It was Rostow who answered this one. “‘T would be legal t’ do all t’at ye say, t’ough ‘t ‘as never been dune before. T’e Ca’taincy wad be subject t’ Council approval, o’ course. All Ca’taincies are.

“W’ere wad ye find purchasers or crew on such short notice? T’e ‘ole project wad cost on t’e close order o’ twenty or t’irty t’ousand Skins.”

Instead of answering directly, Barad leaned back in his chair and looked up at the web-work of beams and stringers fabricated of glued Strong Skin that made up the support of the afterdeck overhead. He steepled his fingers and said thoughtfully, “Sometimes people do generous things with no thought of return. Last Fall, we were trading in these waters when we were hit by a Coriolis storm. Our damaged mainspar was replaced by folk who said it was but the cost of friendship.

“Consider that spar a down payment. We will do the salvage work in return for a note to cover the cost of salvage and repair. In addition, we will have two full ownership shares in your ship.”

It was P’osettin who with tears in her eyes asked, “After t’is disaster ye wad give us bock our ship? Wye?”

Barad looked at her with a calculating smile, and laid a hand on the Princamorn’s account books. “I have a confession to make. I already did look at your books. They show quality management. I expect to make a handsome, if slower, profit.”

Both P’osettin and Rostow nodded. This they could accept. P’osettin wrung Barad’s hand as they left the cabin and said in a voice thick with emotion as well as accent, “We must bear t’is news t’ t’e rest o’ t’e crew. T’e Articles ‘ave t’ be observed but i’ t’ey dinnae take yer offer, t’ey’re nae wort’y t’ be sailors on a ship o’ mine.”

After the visitors had gone, Chena emerged from the bed hangings, tallow-slate in one hand and a stylus in the other. Timidly, she said, “I got the function thing to work, I think. It must be wrong, though. The answer that I get is a nearly circular ellipse, with the primary focus stationary, the minor focus going about it in a circle, causing a moving point on the ellipse to describe a cycloidal path.”

Barad cocked an eye at her and smiled sardonically. “It sounds basically right. What’s the difficulty?”

Chena quailed, as if in fear of getting hit. “It’s huge! Many times larger than Sea itself! How could something be bigger than the world?”

Barad actually laughed in delight. He dragged Chena by the arm to the open porthole and pointed out at the sky. The largest of the three moons was visible about a hand-span above the horizon. “There is your answer! You have just computed the orbit of Wohan, for about a Wohan ahead. You will become a Calculator yet. Never doubt it.

“Your indenture will net me thrice the value of even a boat-shop apprentice. Your own share of that indenture will be over six times what I get. Look forward to the money and freedom in just a few Gatherings. You will have a safe start in a new fleet. If you do not repeat the mistakes that ruined your life in the Naral fleet you will be secure and respected for the rest of your life.”

Chena looked at Barad in fear, I wish that I could believe that. I’ve heard that your Cabin-girls disappear and are never seen again. A death sentence to be chosen. Well, if you’d not taken me, I’d be dead already. Cast off. No ship, unless one were to chose me. I guess that being taken by the Grandalor is better than drowning.

With the help of the survivors, the Grandalor found the Arrakan fleet Council ship, Wavenruner, easily. It was one of a few ships that were authorized to act for the fleet’s Council until the next Gathering. They took the report of the sinking, along with the precise location and the salvage survey of the wreck. They also issued the necessary salvage claims, and bought much of what had been salvaged already.

Less than a Wohan later a somewhat crippled but now functional Princamorn parted company with the Gandalor. All of her surviving crew went with her, along with Barad’s indentures. The only exception was the gravely injured Tanlin, who was still in a coma.

Captain Barad, descended a companion-ladder to a corridor that lead to the Purser’s scriptorium. A half dozen men and women talented with quill and ink were working industriously by the light of large ports and a few candle lanterns in the brightly lit room. If the fleet Council knew just how talented these folk have been for the last seven Gatherings, the Grandalor would likely have a new Captain and officers, he thought, gleeful at getting away with yet another shady enterprise.

He examined the neatly bound piles of trade scrip. Each one bore the name of a different ship, and had the expertly forged signature of that ship’s Purser. There were several hundred Strong Skins and perhaps four thousand Glue Blocks worth. His brow wrinkled in angry concentration and he looked at the works in progress. “Morgu,” he called softly, voice quietly authoritative.

The Purser got down from his own high stool and work table in the corner of the room, where he could oversee all that was being done. “Yes, Captain?”

“Where is the Longin scrip? I do not see any, nor any in progress. Alor’s signature is no harder to forge than any other.”

“True, Sir. But this is.” Morgu pointed to a number neatly written in Alor’s precise hand.

“So? Copy it. What problem does it present?”

Morgu braced himself to tell Captain Barad the bad news. It was never safe thing to do. “Sir, each scrip, even the quarter block ones, has a separate number. This started last Gathering. Alor keeps a register with all of the numbers. When a scrip is done being traded about and is presented to the Longin for redemption, it is stricken out in her register, with the redemption date marked, and it is destroyed.

“The practical result is that our Longin scrip will be easily detected — and traced — to us.

“We are suspected of the counterfeits already put out.”

“How can you know that? The counterfeits have been discussed in the Captain’s Council but nothing has come of it. I have seen to that,” said Barad, deeply disturbed.

“Sir, a general meeting of the fleet’s Pursers has been called for next Gathering. I was not invited, and when I tried to get invited, I was bluntly told that I was unwelcome and would be ejected if I came.

“It took a number of discreet inquiries, some of them through agents, to find out the secret. The purpose of the meeting is to discuss the counterfeit situation and deal with it at the scrip issuing level, as the Captains’ Council seems unable to do anything.

“If I were you, Sir, I would drop the counterfeiting and wait for at least one or two Gatherings before going back to it.”

Captain Barad scowled, I wish that I could use him for Strong Skin bait. If I do, I will never get a reliable answer from anyone. They will all be afraid to tell me the truth. Dependable advice is the most valuable thing I can get. “I hate to let it go, but though profitable, it is a small trade. I will bow to your expertise and end it, for now,” he said thoughtfully.

“It was a good idea when you brought it to me seven Gatherings ago, when they were about to vote you off the Darok. Your transfer to the Grandalor saved them the embarrassment of admitting how badly you had hoodwinked them. It raised you from a well educated deck-hand to Purser and gave me a good income.

“Do you know why I made you Purser?”

“I have been puzzled by that question.”

Barad smiled, “It is simple. Faced with ruin by the collapse of a small scheme, you thought big enough to forge ahead and come to me with an ambitious proposal.” He smiled at his pun and waited for an answering one from Morgu before going on. “Few people will look to attack when they are being struck by a large opponent. Your ability at forgery has been useful and it will be again someday in some other way.”

Briskly Barad added, “For now, send someone up to my cabin. There are four books there, on the table. Your people should make as many copies as they can. They are the next edition of the Muline’s Moons and Sun Navigational Ephemerides. I got them while we were rendezvoused with Muline. My cabin girl will point them out.”

Morgu shuddered slightly at the thought of the Captain’s cabin girl. I pity her, truly I do. Having to take care of his cabin, and other needs. She won’t last long, they never do. Aloud, he said, “Will you accompany me to my cabin, Captain? I’ve something I’d like to discuss privately.”

“Of course, Morgu, let’s go.”

The Purser’s cabin was small and completely orderly, like its occupant. There was a small table, a chair, a shelf for books and a shut-bed. A small port-hole, open but equipped with a tightly fitting shutter, let in light. Morgu opened the folding door of the shut-bed so that he would have a place to sit, and let the Captain have the chair.

After sitting, Captain Barad demanded, “What did you want to discuss, that needs such privacy?”

Morgu steepled his hands and gathered his thoughts. “I want to ask something that may be personal. I don’t want to snoop into your affairs, but the answer may assist me in helping you with your goals. The question is about the Longin. I know how they cheated you when you tried to take over their crabbing waters, but your dislike for that ship goes further back than that. If I understand the situation better, perhaps I can help you to devise a fitting revenge.”

It was Barad’s turn to gather thoughts. “Way back, over twenty Gatherings ago, a few Wohans after the fire cough epidemic, old Captain Morthan, took ill and died suddenly, I took the helm of the Grandalor. There was not time for a popular election from fleet qualified men, by the Articles because a Coriolis storm was nearly on us. I and a few supporters took the job because someone had to. People took my commands and we got through the storm in good order. After that, they were used to my rule, and my men made it easier and safer to keep on doing so. Very few had to be logged as lost in the storm.

“I forged documents of election for the Captain’s Council. I am not as practiced in that art as you, I admit. Some of the officer’s signatures were questioned by Captain Mord, (a curse on all Halyns!) and I near lost my command and life right there. It took some fancy footwork to keep what I had bought and it cost several more lives.

“To this day I don’t understand why he opposed me. I could easily forgive being outmaneuvered, like with the crabbing waters. That’s a game with a winner and a loser.” He threw up his hands and went on, “There was no reason in it! Neither he nor the Longin could profit by it in any way!”

Morgu listened in rapt attention. Several more lives? There’s more to this story than I’m getting. Aloud he said, “I see. You only barely beat them then, and the real grievance is that they near wasted all your work for no real end. That they have managed to come out even or ahead on every try for revenge since only twists the knife.

“The best that you have done since amount to small nibbles that they barely feel.” Morgu paused before going on, “You don’t want to hit them like a hungry Strong Skin. Big as Strong Skins are, the Longin catches those. You need to strike at them like a big Wing Ray leaping from the deeps onto a small boat! You must smash something that they can’t replace!”

Captain Barad looked at the savage expression on his Purser’s face fascinated by what he saw, “What do you hold against the Longin? Such anger is well past the loss of a few counterfeit notes.” He was well aware of the answer but wanted to hear Morgu’s version from his own lips. Due to the machinations needed to get him to come to the Grandalor, Barad never had this opportunity before.

“There are two things that I hold against that Dragon-haunted ship!” Morgu paused and took a few deep breaths and regained his composure. “The first is not unlike your own. I was just making a few of the Darok’s own scrip for my own use, and none really hurt by it. The Darok found out because Captain Mord Halyn brought it to their attention and then the Longin’s crew helped to trap me. There was nothing in it for them. They just prated of honesty.

“The other thing was even worse. I was near ready to marry a fine young lady from the Muline at the time. Not only did I not get Suze, she married onto the Longin! Now do you understand why I want to hurt them?”

Sympathetically, Barad laid a hand on Morgu’s shoulder. She was going to follow him to the Grandalor but I fixed that! It has paid off better than I could have guessed. “I see why you hate them so and now you know why I do, too. What shall we do about it? How shall we smash them? Captain Mord and Alor are both too well guarded and too prominent to reach safely. I had thought of that.”

“Captain, whose name do you hear everywhere that Longin sailors gather? They talk about the girl Kurin …”

TO BE CONTINUED

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#SEA DRAGON’S GIFT #Part 4 of 83 #World of Sea #Written by De Writer

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thousandmaths · 7 years

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Day 39: Talk with Vic VI

This is the last Talk with Vic post that I will be making on the blog! One of the reasons that I’ve been working so intently recently is not just because it’s exciting to finally have an advisor, but also because I needed to cram as much in before he goes to Berkeley for the semester. Of course we won’t completely lose contact during that time, but the next time we meet will be at the end of September. And that should be after the last post goes up on OTAM, assuming that everything goes according to plan :)

The citation for today’s post is “Notes on a Conjecture of Molchanov”. I would link it, except that it’s actually a pre-preprint, not even on the arXiv yet, and he explicitly asked me not to circulate it, so :3

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Vic

This meeting kind of went all over the place. We actually didn’t talk much about the new idea I’d had yesterday. I mean, I got to say my piece, and he basically said “yeah you should probably keep thinking about that” and we moved on.

One thing Vic reminded me of (which I felt very stupid for not thinking of myself) is that $\binom n2$ is $1+2+3+\cdots + (n-1)$, and so if we wanted to find a sequence of “local moves” that take us between the two extreme bracelets, the natural thing to do is to try to break it into one bead moving once, another moving twice, and so on.

Of course, the idea of local moves had come up before— that’s essentially asking for the covering relations in the poset structure (which, again, we don’t actually know exists). But the numeric idea for identifying a potential “main stem” was something that I should have come up with on my own. Perhaps I shouldn’t have been so hard on myself, though: we tried two very natural ideas, and both of them failed spectacularly.

During that discussion, Vic talked to me about a nifty, if somewhat unrelated, idea: an explicit construction for a symmetric chain decomposition of the Boolean lattice (I may write about it at some point, since it is quite pretty and not too hard to explain).

The ‘somewhat’ could maybe use some clarification: the ultimate endgame of this branch of project would be to find the poset structure on the necklaces, and then to produce an explicit symmetric chain decomposition for it. But this is a very ambitious goal: the Boolean lattice is not the only poset for which we know a symmetric chain decomposition, but it’s close. In particular, the existence of a symmetric chain decomposition for a poset implies that it is strongly Sperner, and proving even much weaker Spernerity properties are notoriously difficult problems in combinatorics.

But one of the reasons that I chose Vic in the first place is because I knew he would always push me to be...

Aiming Higher

We also talked about some other possible branches. In particular, he wanted to talk about a generalization of the (MacMahon) Catalan polynomials called the Fuss-Catalan polynomials:

$$ \frac{1}{[mn+1]_q} \begin{bmatrix} (m+1)n \\\ n\end{bmatrix}_q . $$

[ Take $m=1$ to recover the Catalans. ]

If this strikes you as a strange generalization of the Catalan polynomials, you are not alone, but the Kirkman polynomials have a remarkable pedigree as well. In particular, one (very ahistorical :P) way to understand the Catalan polynomials is as the Frobenius characters of the rational Cherednik algebra representation $M_{1,\frac{n+1}{n}}$. The Fuss-Catalan polynomials are the Frobenius characters of $M_{1,\frac{mn+1}{n}}$. These are also known to have some combinatorial interpretation, so it’s not algebra all the way down, but we didn’t discuss this side much.

(It’s not clear to me whether Vic actually prefers to think of things in terms of rational Cherednik algebra modules but this isn’t the first time he’s mentioned the connection.)

The Armstrong-Reiner-Rhodes paper lives on a different branch, which concerns the so-called Kirkman polynomials:

$$ \frac{q^{r(r+1)/2}}{[n+1]_q} \begin{bmatrix} n-1\\\ r\end{bmatrix}_q \begin{bmatrix} 2n+r\\\ n\end{bmatrix}_q. $$

[ Take $r=0$ to recover the Catalans. ]

The Kirkman polynomials have independent interest (they count “partial triangulations”, in particular), but one particularly exciting bit is that they extend well into other Weyl groups— and possibly to Coxeter groups more generally. The ARR paper, in fact, deals with the Kirkman polynomials (and their corresponding “parking functions”) at this level of generality.

These two branches actually meet up again, where they create the “Fuss-Kirkman polynomials” (this is not standard terminology), which is what the pre-preprint paper is about :)

We finished up the meeting with doing some Mathematica computations, trying to find some of the “even Fuss-Catalan numbers” and the “even Kirkman numbers” on the OEIS.

We actually found one match: the even Kirkmans at $r=1$ are, it seems, the number of winning positions for Player 1 in a Maori game called mu torere, according to the 1987 analysis of Marcia Ascher. (link goes to @jstor)

#math #maths #mathematics #mathema #algebra #combinatorics #algebraic combinatorics #polynomials #everywhere #ethnomathematics #maybe?#can i get some of that sweet sweet interdisciplinary funding somehow?#is the real question #advised reading #2h #0p

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