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Guest Post: Demonic Mathematics in The Demons of Wall Street by Laurence Raphael Brothers

In my romantic-noir urban fantasy novella The Demons of Wall Street, there’s a lot of mention of mastery of mathematics as a requirement for doing magic. There’s a historical basis for this conceit, with a curious twist to it. In the demon-summoning grimoires of the 15th and subsequent centuries, entries for the demons look something like this (from the Goetia section of the Lemegeton or the Lesser Key of Solomon):

The 8th spirit is called Barbatos he is a great duke & appeareth when ye is in ,2 with four Noble kings and their companions in great troops, he giveth ye understanding of ye singing of Birds, and ye voice of other Creatures and ye barking of dogs &c, he breaketh hidden treasures open, that have been Laid by ye Enchantment of Magicians, & of ye order of vertues, which some part beareth rule still &c he knoweth all things past and to come: and reconsileth friends & those that are in power, he ruleth over 30 Legions of spirits, his seal of obedience is this. wch were before you &c.

Not much math there, apparently. But many grimoires list magic squares along with their respective demons, angels, and planetary spirits. A magic square is a grid of numbers whose rows and columns all add up to the same value, so you can think of it as an early kind of Sudoku puzzle…. This image is from Albrecht Durer, in the 15th century:

Now, if you superimpose a demon sigil on a magic square at the right scale, the intersections and crosses appear over selected numeric values, and you wind up with what could arguably be a vector or matrix of numbers. What application could such numbers have, outside of magic? Well, there’s ciphers and cryptography. During this period (just as today), it was important for merchants and spies to be able to communicate without letting others read their message. Of course letters written in plain text were highly insecure because they had to pass through so many hands along the way while being transported across the breadth of Europe, so there was no telling who might steam open your message, read it, and send it along on its way resealed. So using ciphers and codes was absolutely necessary.

The most crucial element in cryptography is letting your correspondent know the secret key you’re going to use to encipher the message. That key is a number or a sequence of numbers. What better way to do that than to conceal the key within a text which is apparently all about magic and demon-summoning, with no commercial or diplomatic relevance? And lo and behold, there’s a famous grimoire called Steganographia or “secret writing”, written by the mathematician and occultist Jonathan Trithemius in the 15th century, which has only recently been shown to be a book on cryptography.

So if I send you a message with the name Barbatos hidden in it, or even presented in clear text, you can look up the sigil and square for Barbatos in your copy of the grimoire, trace out the pattern of numbers, and use that to generate the mathematical key to the message. But any uninitiated person who sees the message and looks up Barbatos in the grimoire will only see a bunch of mumbo jumbo about demon summoning and what magical powers you’ll gain if you make him your servant.
Of course, in The Demons of Wall Street, demons actually exist, and are in fact used for financial prognostication, a notoriously abstruse field of applied mathematics. So after Trithemius turned magic on its head to use it for cryptography, I’ve turned the old fogey on his head again, to make the math serve magic again….


Welcome to the 1-Week Virtual Book Tour for The Demons of Wall Street (Nora Simeon Investigations #1), an Urban Fantasy, Paranormal Novella by Laurence Raphael Brothers.

About the Book:


Nora Simeon hates demons.


But as an investigator for the secretive Commission, the organization that regulates financial sorcery in New York City, she deals with the creatures a lot more than she’d like. Her latest case has her on the track of a rogue demon, escaped from magical bondage as an analyst for a leading investment bank.


On the demon’s trail, Nora crosses paths with a beautiful young man named Eyre. He’s too pretty and complaisant to be human, and too kind to be a demon in human form, but what else could he be? Together they become embroiled in the secret corruption at the heart of the financial industry. But before Nora can untangle a twisted skein of sorcerous murder and intrigue, she has to untangle her feelings for Eyre. And before she can do that, she has to find out who and what he really is.


Publisher Website:

Mirror World Publishing

Purchase Links:

Mirror World Publishing e-book

Mirror World Publishing paperback

Amazon e-book

Amazon paperback

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Meet the Author:


Laurence Raphael Brothers is a writer and a technologist. He has published over 25 short stories in such magazines as Nature, the New Haven Review, PodCastle, and Galaxy’s Edge. His WWI-era historical fantasy novel Twilight Patrol was just released by Alban Lake. For more of his stories, visit https://laurencebrothers.com/bibliography, or follow him on twitter: @lbrothers.


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