Decoding Amanda, Symmetry

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.

Author: Amelia

A mild-mannered professor of computer science in real-life, I remove my glasses in the evening to become, well, a mild-mannered author in my alternate reality. I mostly write sweet romantic fiction, although with an occasional science-fiction or paranormal angle thrown in. I have interests in history, mathematics (D'oh), and cryptography. I'm also something of an Anglophile, and know that country pretty well. In addition to writing, research, and more writing, I volunteer with the scouts. I'm something of a nature-nut, enjoying long walks in the country with almost ultra-light gear, boating, and identifying wildlife.

14 thoughts on “Decoding Amanda, Symmetry”

    1. I’m imagining what Bletchley Park and Churchill’s ‘ministry of ungentlemanly warfare’ would have been like in a regency/late Georgian context. In reality, Napoleon, unlike the German’s of WW2, wasn’t particularly clueful about codes and message security. He took the ‘Rossignol’ ciphers from the mid-1600’s that had been used under the Bourbon kings and kept using them. So the Brits didn’t have too much trouble breaking them. It didn’t help that the French sent messages in plaintext on their semaphore system, which was visible from England. This was especially useful to the British when Napoleon spent a winter preparing for his planned invasion at Boulogne sur Mer and all the messages had to go within easy reach of British observers. Fortunately for him, the British, and about 500000 Frenchmen, Napoleon declared victory, erected a monumental pillar (which still stands), and went off to fight with Austria.

  1. I loved his reaction. She’s thinking he won’t understand then, whammo, he gets it, gets her. Cool. While the math stuff is waaay over my head, you make it fun to read.

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