Decoding Amanda, Symmetry

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Welcome to weekend writing warriors. Many fine authors, and me, contribute short snippets for your delectation.

Since it seems that our Regency spy romance is much more popular than our science fiction, this post introduces the sequel to The Art of Deception. Amanda’s reading was interrupted by a summons to attend on her mother. Amanda’s mother made it clear that she must attend the assembly. After a short carriage journey, it only being six or so miles between Coalpit Heath and Chipping Sodbury, they have arrived. Mr Jameson just asked Amanda to dance, despite her interest in a mathematics problem. The set over, Amanda wants to return to her usual pursuits when her mother stops her. Amanda has just said a biting remark about the mysterious Mr Jameson, and her friend Louisa wonders why she is so sour. After the break for refreshments, the story resumes on the dance floor, where Amanda has agreed to another dance with Mr Jameson.


“Tell me, Miss Bentley about those figures; are you a devotee of the cossack art?”
“Until Mother took my copy of Hutton, I was,” Amanda paused, swept away by the figure; shen she returned to speaking distance, she continued, “I was working on symmetric polynomials, not that I’d expect a divinity student to … “
“Interesting area, I feel there is some deep structure there, but…”
“You know about them?”
“Surprised; I wasn’t always … studying for orders; before I received my calling.”
“You were a mathematician?”
“The way to perdition is paved … with equations, determinants and integrals.”
Amanda guffawed; then she blushed as heads turned to her, “No it isn’t and you know it.”
“That’s true, and I retain some interest in the field.”


My sincere apologies for abusing semi-colons. (The cossack art was the study of ‘x’s’ and ‘y’s’ i.e. Algebra.)

There are a couple of non-obvious links to my day job in this snippet. The most interesting is the idea of “Symmetric Polynomials.” The study of these led a certain Evariste Galois to develop group theory of polynomials in the late 1820’s. He wrote a formidable exposition on the theory the night of May 30th 1832 and promptly was shot in a duel in the morning of the 31st.

Galois theory forms the basis for much of modern communications and cryptography. The error correcting codes that allow us to pump gigabits of information through grotty fibre lines or watch DVDs come from his work. As does the mixing step in Rijndael or AES.

The idea itself is strikingly simple, albeit rather tricky to construct in practice. Prime numbers form simple rings or groups that are closed under multiplication and addition in modular (clock arithmetic). For example, if we keep multiplying by 3 mod 7 we have 1,3, 2 (9 mod 7), 6, 4 (18 mod 7), 5 (12 mod 7), and 1 (15 mod 7). It repeats forever after that and every number from 1 to 6 is a power of three mod 7. Therefor 3 is a generator in the ring mod 7. Cool (at least I think it’s cool). Most of the ways we exchange secret keys on the internet use this math, but with rather larger prime rings (where the primes requires 2000 bits or so).

Galois asked the rather simple question, “what happens if we use polynomials instead of numbers?”

This leads to the idea of irreducible polynomials and polynomial rings. Unfortunately the theory is too large to fit in the margins of this post.

The featured image shows a working modern reconstruction of a Turing “bombe” from Bletchley Park.

This snippet continues formal connection to the previous book in the series (the art of deception). Mrs Hudson’s academy doesn’t just teach deportment and other social skills.


I’ve put up a couple of things on instafreebie. The first is a short story, To Court a Dragon.

The second is the start of a science fiction story in the same universe as Cynthia the Invincible, but set in 1893 Dartmoor, The Curious Case of Miss James. It’s available on Amazon.

The Art of Deception, first in a series of late Georgian/early Regency spy novels is now up.. You can get the first part here.

You can find my, well our, works here.

Incoming. Extract from my next one. Steam and Secrets?

The weekend warrior post is here

This is a regency-punk? work set in 1809. It combines steam, ciphers, codebreaking, and espionage, with a chase and sweet romance. Still working on a title.  I’ve just crossed the 50K barrier, so it’s approaching the intensive edit stage.

In any case I’d love to hear what you think.

Lady Caterham’s Difficult Daughter.

“Amanda Jane Elizabeth Grace, what have you done to yourself?” Lady Caterham wailed at her daughter. “You’re covered in grease, and we must leave for the assembly in an hour.” Amanda stood in the doorway of Lady Caterham’s room, awaiting instructions from her mother. Lady Caterham sat at her dressing table while she gave instructions to her daughter. Lady Caterham’s maid was waiting to put the finishing touches on her mistresses’ gown and hair while Lady Caterham dressed down her slovenly daughter.
“I was just repacking the bearings. We don’t want the wheels to fall off our carriage, do we? The roller bearings Sam and I put together turn so much easier than the old wooden axle, and I think you’ll like the way we’ve sprung the box. It-.”
“And that’s another thing young lady. Playing around with machines. Why, look at those hands. Even if Mary can clean the grime from under your nails, what man would look twice at you with those hands?”
“There’s more to life than men, mother.”
“No there isn’t, at least not for a young lady of refinement like yourself. Do you want to die an old maid, alone and forgotten?”
“No, not as such. It’s just. Well. Oh dash it Mother, the man for me won’t be upset with a little grease and the odd broken nail.”
“One more thing young lady, watch your language. Where did you ever pick up such an expression? Keeping company with that blacksmith?”
“Oh no Mother. Sam is very polite. At least when I’m present. Ask Mary about him if you want confirmation. It’s Freddy and his friends, when they come in from the hunt, who use such expressions. I thought.”
Lady Caterham spat out, “You don’t think. That’s the problem.”
“I do. If my brother can say it, and far worse, then it’s suitable language.”
“Suitable for a man that is. Now go, get cleaned up. We must not be too late for the assembly. Not if you want a dance.”
“Yes, Mother.”
Lady Caterham ignored the tone of that last remark and watched as her eldest daughter, a striking, tall, auburn-haired young woman walked off to change into the dress of a refined and cultured young lady.
“My Lady,” Millicent, her maid, pointed out, “Miss Amanda will have no trouble attracting male attention. She’s a fine looking young woman. As you were at her age.”
“That’s true, but she’d look so much better without that black grease streak covering her forehead and staining her hair, or that house-dress. It’s just so torn and patched, stained with who knows what, and covered in grease. How can she stand to wear it?”
“I don’t know Ma’am, but she’ll be presentable, even elegant. Mary will see to it.”
“I’m sure she will, but I so wish Amanda would focus on the important things in life. Like marriage, men and children. Get her head out of the clouds.”
“Or the steam, Ma’am. I’ve heard that the 20th regiment is stationed nearby. There should be plenty of fine young men, officers in their red-coats. That should catch her eye and turn her thoughts in the right direction.”
Lady Caterham thought for a few moments and then replied, “I hope so. Although last time, she ended up talking all night to an engineering officer from the artillery. A nobody, who was a captain just because he’d been to school at the Royal Military Academy in Woolwich and knew how to move guns and build fortifications. It would have been better to leave her home. What’s the point of going to the assemblies if you don’t flirt with eligible men?”
Much to Lady Caterham’s relief, and fully justifying the expense of hiring her, Mary turned Amanda out dressed in the proper mode of a young lady. The grease was gone from her face and her auburn hair was immaculate, as were her muslins. She wore a simple string of pearls, suitable for a young woman venturing into the wilds of society. While no amount of cleaning could restore her hands and nails to the pristine state that was so important in a fashionable young woman, she would be wearing gloves. They would hide most of the damage. One did not hold hands without something between you and the young man.
Amanda did nothing that spoiled Lady Caterham’s trip. While she may have cast an eye over the bearings, axles and springs, she didn’t stop to play with them. Indeed, without the squeaks, the jarring and the shaking normal in a carriage, Lady Caterham arrived at the assembly in a remarkably refreshed state. When they arrived at the assembly, one of the officers, a captain, swept Amanda away. He led her onto the dance floor for the first country dance of the evening. All in all, it made for an outstanding start to the evening.
The vicar’s wife, Mrs. Peabody, addressed Lady Caterham, while she and the other mothers watched their daughters perform the figures on the floor. “Lady Caterham, I know you suffer in the carriage rides and I was planning to offer to chaperone your daughter, but it looks like you’re well. Did you find a cure for the travel sickness? I only ask because I suffer too.”
Despite her misgivings about Amanda’s mechanical interests, Lady Caterham’s bosom swelled with pride as she said, “It was Amanda’s doing. She redid the springs and the axles on our carriage. It was such a smooth and quiet ride that I barely noticed we were moving.”
“She did? I must say, she is a clever girl.”
“And see, she’s dancing with.” Lady Caterham stopped, “Who is that?”
“Oh, that’s Captain Williams’ cousin. He’s studying divinity, at Oxford.”
“A suitable connection?”
“Absolutely, quite nearly related to the Fairfax’s. They say he will inherit a sizable income. With his family connections, he’s bound to become a bishop.”
Lady Caterham smiled at Mrs. Peabody. “In other words, a connection to be encouraged. I do so hope Amanda will find something other than machines to tinker with.”
“I agree, a husband and children will soon put her head straight. Settle her down.”
Their happy optimism about Amanda’s prospects would have been tempered had they been able to hear her conversation with the young man. While good looking with blue eyes, dark hair and a firm visage, able to dance the figures with a natural athletic grace, polite, educated and well mannered, he was also a serious disappointment.
“Mr. Williams, you’re studying divinity?”
“A suitable study for a gentleman, honorable and in the service of both man and God.”
“If you say so, but with a chance to meet Dalton or Henry or Davy or,” and here Amanda gave a frisson of excitement, “Even Faraday. You have the chance to study natural philosophy with such masters, and you choose divinity.”
“What’s wrong with divinity?”
“Nothing, except.”
“Except what?”
“It’s so commonplace. I’d cut off my right arm to study with any one of those men and you’re just wasting the opportunity.”
Mr. Williams was nonplussed. Unable to think of anything witty, eventually he replied, “Please don’t do that. You have a pretty, indeed beautiful right arm. It wouldn’t look right, replaced with a hook.”
Amanda smiled back and laughed as she said, “I didn’t mean it literally, but I’d kill someone for the chance you have and are throwing away.”
“Please don’t do that either. I suppose I could try law.”
Amanda’s grimace suggested that option was, if anything, even less appealing than divinity.
“In my defense, none of the masters you mentioned are fellows at Oxford.”
“Still, there must be someone.”
Despite her misgivings about divinity students, Amanda couldn’t help feeling disappointed when the dance drew to a close and it was time for the supper break. Mr. Williams bowed and returned to his cousin’s company, while she found her mother.
Lady Caterham’s interests and hopes were peaked, and she asked, “So, Amanda, what did you think of him? He has real prospects.”
“About Mr. Williams?”
“Who else?”
“He seems a nice enough man. Although I wish he were doing something with his education. Something worthwhile.”
“Damning me with faint praise?” It was Mr. Williams. He had walked up behind them and was carrying two cups of punch. “Miss Caterham, I thought you could use this, after your exertions on the dance floor, and with the crush.”
Amanda blushed at his attention, then curtsied, accepted the punch from him and said “Thank you. I didn’t mean to disparage you.” Her mother beamed at Mr. Williams, but fortunately showed her good sense and stayed silent.
He replied, “You didn’t say anything that you hadn’t told me to my face. It is true, divinity is dull work, but I never had much aptitude for natural philosophy.”
Lady Caterham loudly whispered, cautioning her daughter, “Amanda, behave. Watch that tongue of yours.” Mr. Williams did not fail to notice Amanda rolling her eyes at the admonishment, nor that she kept smiling at him.
He added, “It may be a liberty, but could I ask for a third dance? That is if you are free.”
“She accepts,” Lady Caterham injected.
“Mother, please. That is so fast, to dance three dances with the same man. What about my reputation?”
“What harm can there be when the man is so obviously moral. When do you take orders, Mr. Williams?”
“Early next year, when I finish my studies at Oxford. Miss Caterham, if you would rather not dance with me, I’d be disappointed but willing to release my claim.”
“No, no, I didn’t mean that. Yes, I’d love to dance with you again. Please. Even two more times.”
“Twice more is excessive,” Lady Caterham added.
When the next dance started, another country dance that would let the participants converse between the figures, Mr. Williams asked, “So Amanda, why are you so interested in natural philosophy?”
Amanda blushed, “Not philosophy, engines, power, steam. Ever since I saw Trevithick’s engine in London, I’ve wanted to build one of my own.”
“Indeed? Tell me about it. Have you made much progress?”
“Well, I don’t have any engines, right now. Sam and I are building another one. It will be a corker.”
“Sam?”
“Mr. Perkins, my maid’s husband, a blacksmith.”
“So not a rival.”
Amanda laughed, “Good Lord, no.”
“Good. So if you don’t have an engine, what else are you interested in?”
Amanda paused until the next chance to talk, and then replied, “Bearings, bearings and springs.”
“Bearings?”
“I want to go fast, very fast, so quickly that the axles would smoke and the wheels fall off with a regular carriage. Sam and I can build the engine and the gears, but need a carriage that will handle the power.”
“I suppose your family approves?”
“What they don’t know won’t hurt them.”
“If you say so, Miss Caterham, but I’ve found keeping secrets leads one into sticky situations.”
“What do you know of secrets? Studying for the clergy, I’d assume you lived a tame life.”
Mr. Williams stopped, stunned that she would shoot so near the mark, interrupting the dance figure for a few seconds. “More than I can tell you.” Then he quickly resumed the dance.
Amanda was piqued, “So you have a secret, or are you just offering me a nut to crack open as a puzzle?”
“I hope you’ll find the meat at the heart of this nut to your liking.”
“Are you trying to flirt with me?”
“Yes. Trying, not succeeding.”
“If you’re like most men I’ve met it’s just a conker, hard on the outside, bitter and inedible on the inside. What brings you to the wilds of Sodbury?’
“That I can answer directly. I’m on a repairing lease. Been burning the candle at both ends too long at the ‘varsity.”
“Daily Compline and Evensong too much for you?”
“One might say that.”
“From what my brother Frederick says, it’s probably the all-night drinking and parties on the Cherwell.”
Mr. Williams smiled at her, which she took for confirmation. Then he added, “It’s the all-nighter’s in any case. I was told to rest, and leave off it until I recovered.”
“Have you recovered?”
“I’ve made great strides. Dancing with beautiful women helps immensely.”
The music ended. Mr. Williams and Amanda bowed to each other. Good manners dictated that she dance with other partners. For some reason the officers who were available and willing seemed curiously flat. Good dancers, elegantly mannered, but deficient in conversation.
The evening ended well, at least the dancing did. Partway back to Caterham hall, when the carriage went over a steep bump, there was snap. It was followed by a gentle hiss and the box leaned to the right.
Lady Caterham was startled, “What was that?”
“One of the seals broke. Blast.”
“Amanda! What did I tell you about your language.”
“I’m sorry. It’s just Sam and I put such a lot of effort into building the springs. To have one fail so quickly. It’s highly annoying.”
‘”I just wish, Amanda, that you would pay attention to the important things in life, marriage and men.”
“Mother.”