The Battle of Pythagorean Numbers

A goofy story of numbers ...

The morning fog hung low over the battlefield as Commander Square 190 rolled to the front lines, his perfectly square armor gleaming in the early light. Above them all, the giant scoreboard flickered:

"Harmony and goodness: 42 | Chaos and Evil: 64."

Odd squares and equilateral triangles and circles surround the square, listening intently.

"Listen up, Odds! We're behind the Evens!" the Commander Square bellowed, his compass-point helmet spinning nervously. "The evil Evens, the forces of Chaos, have pushed us back with their non-Euclidean tactics!"

Circle Scout darted forward, hyperventilating. "Commander! Eight evil Even enemies approach from the east! Let us all pray for the power of perfect numbers, 6, 28, 496 —" he shouted to the heavens.

"Calm yourself, Scout," Commander Square said, his voice as steady as Euler’s constant. "Remember your training. Breathe to the count of the first five Fibonacci numbers."

Triangle Warrior stomped forward, his blocky shoulders squared perfectly at 60-degree angles. He thumped his Laplacian chestplate. "Let me at 'em, Commander! My 4×4 matrix hammer is ready to seriously smash some decimal points!"

From across the battlefield, a menacing Even General Pyramid with far too many sides and components shrieked. "Your pathetic numerical harmony is doomed! Chaos reigns!"

Commander Square narrowed his radius. "Triangle, take your division battalion and flank them from the right with fluxions. Circle, your fractional forces will create a distraction with those numerator number catapults."

Triangle saluted with his angular arm. "And you, sir?"

"I'll lead the arithmetical assault with our triangular number troop,” Square said. “Those of us who are sums of square numbers will show them the meaning of true mathematical harmony!"

Circle Scout bounced nervously on his diameter. "But Commander, what if they deploy their... unsolvable equations?" He whispered the last words with terror.

Commander Square's circumference stiffened. "Then we'll do what mathematicians have always done—simplify, reduce, and solve step-by-step."

As they moved into position, Circle caught a glimpse of the banner fluttering in the algebraic wind:

"Rithmomachia: Where Math Is Always Right!"

Triangle Warrior hefted his multiplication hammer. "For Pythagoras!" he bellowed.

They charged across the field, geometric shapes of all kinds clashing in a spectacular array of mathematical operations. Square bashed a chaotic trapezoid with a mighty matrix hammer, shouting, "That's 4x4 damage—calculate that!"

Circle Scout leapt over enemies, dropping division symbols like land mines. "Can't step on these without solving them first!" he cackled.

Commander Square rolled through the fray, his geometric ratio shield deflecting diabolical denominators. He engaged the many-sided General Pyramid of Chaos, their weapons clashing in a shower of mathematical symbols.

"Your random numbers can't defeat the power of mathematical harmony!" said Square parrying a fractional number thrust.

The Even General Pyramid cackled. "Fool! There will always be chaos in mathematics! What about imaginary numbers? What about infinity?"

Square smiled. "That's the beauty of it. Even those fit into the patterns. Everything in mathematics connects—you just need to learn the rules!" With a powerful thrust of his compass sword, Commander Square solved the evil General Pyramid's equation.

The chaotic Pyramid's angles collapsed in on themselves as he shouted, "Impossible! My calculations were perfect!"

"No," replied Commander Square. "They were just incomplete."

Above them, the scoreboard flickered and changed:

"Harmony and goodness: 81 | Chaos and evil: 64"

As the remaining chaotic shapes retreated, Circle and Triangle joined their commander.

Circle thumped a round chest plate. "Victory through radial vectors!"

Triangle couldn't stand still. "Did you see me? I was adding and subtracting so fast they couldn't keep up with my calculations!"

Commander Square surveyed the battlefield, where defeated shapes were being tutored in proper mathematical principles by the victors. "Remember, Odds —- in Rithmomachia, we don't just defeat our enemies."

"We teach them," Square nodded solemnly.

"And we learn from them," Triangle added, examining a fascinating fractal pattern left behind by a fleeing chaotic shape.

Circle smiled as new recruits began to gather around them, eager to learn the ways of mathematical harmony.

"That's right," Square said. "Because the real victory in Rithmomachia isn't just winning..."

Triangle and Circle smile and nod.

"...it's understanding!" Square declares proudly.

The End

North by Northwest by Hitchcock (and Ernest Lehman)

When I think of Alfred Hitchcock's North by Northwest (1959), I think of the iconic set pieces (the crop duster chase, the Mount Rushmore scenes, Cary Grant's brilliant performance, but also the screenplay, written with Hitchcock’s occasional feedback, by Ernest Lehman.

Recently, in a commentary written for Turner Classic Movies, Guillermo del Toro calls it cinema's only flawless action movie:

North by Northwest, 1959 by Alfred Hitchcock, is a perfect perpetual motion machine and is made by one of the greatest clockwork makers in cinema history – a filmmaker that could blend seamlessly comedy, drama, action, and suspense. … This is one of the canonical films of Alfred Hitchcock, The most perfect action film ever made, in my opinion.

The film follows Roger Thornhill (Cary Grant), a suave yet hapless advertising executive who is mistaken for a government agent and is subsequently thrust into a web of espionage, deceit, and danger. Thornhill's journey—from a mistaken identity at the Plaza Hotel to the climax atop Mount Rushmore—is packed with twists, yet the pacing never feels overwhelming. Lehman’s transitions between action, comedy, and romance are seamless. Thornhill’s evolution from a complacent Madison Avenue executive to an unwilling yet capable hero is one of the screenplay’s greatest strengths. His transformation feels organic, propelled by Lehman’s writing, which keeps him grounded despite the extraordinary situations he faces.

While Hitchcock is the master of suspense, it was collaborating with Ernest Lehman that produced an entertaining thriller, as well as an example of how a well-structured screenplay can become the foundation for cinematic excellence.

By the way, as a writing exercise, I re-typed the screenplay for North by Northwest (as well as The Prize from 1963, Sabrina Faire, released as Sabrina in 1954, The Sweet Smell of Success, co-written with C. Odets in 1957, and Executive Suite from 1954). If you are interested in a pdf for scholarly purposes (e.g, you need to copy and paste into a scholarly article using the Fair Use clause), just send me an email. No promises that it is free from typographical errors (of my own), but the fountain files are also available, for making your own corrections.

Awesome Sauce

Awesome Sauce is a novelette in a story world I call the Avatar Academy universe.

Logline: When their planet faces an energy crisis, a team of flamboyant Venusians use avatar technology to infiltrate Earth and steal our trash, leading to hilarious encounters with Baltimore mobsters and a surprising family reunion.

This image was generated by Gemini (google's AI).

Summary: The Venusians, a secretive underground alien race with a love for spandex, face an energy crisis that threatens their luxurious lifestyle. Their solution? Earth's abundant plastic trash. They launch the audacious "Venusian Environmental Avatar Teleportation Trash 2.0" (VEATT 2.0) plan, using avatar technology to infiltrate Earth and steal plastic. Bevers Sonnof, a hapless but enthusiastic Venusian, takes control of the fearsome El Toro, an enforcer for Victor the Vicious, a Baltimore mob boss. As Bevers searches for plastic and his long-lost father, chaos ensues, involving wood-chippers, surprise parties, and a healthy dose of "awesome sauce." Meanwhile, a team of Venusian trainees uncovers a massive plastic-tracking network called P.L.A.S.T.I.C., leading to a daring heist with interplanetary implications.

Here's an image of what the underground Observation Facility on Venus might look:

I managed to get it onto amazon using publishdrive, so it's now available at amazon as a kindle ebook. (But you can also email me for a free copy:-) Here's the book cover:

The process for writing this was different. I had already written a feature length screenplay version of this, one that had been out for reader's notes and had been revised many times. Now I want a prose version (a detailed "screenplay treatment" as the terminology goes). I should point out that I've done this process many times for many other screenplays I've written. I find it hlpes me "see" the overall plot better than a detailed outline.

This time, I tried something different. This time, to convert to the story form, I used chatGPT, Gemini, and claude to help "translate" the screenplay one scene at a time into prose. (This topic has been discussed before on the internet and this process seems to be best at the current state of AI models.) Building a good prompt for this is a whole blog post in itself, but in each case I told the AI to not change any of the dialogue used in the screenplay. Not surprisingly, the response from these AI models was "off" in many cases (that it, the story line was modified somehow, even if the dialogue did stay the same). This required a lot of proofreading and rewriting on my part, probably more work than simply "translating" the screenplay into prose by myself. More work, true, but I enjoyed the interactive process. These AI models are very polite, even when they aren't doing exactly what you want them to! I also enjoyed the fresh perspective and often the terminology it used was better than my own. It's hard for me to regard this as a collaboration, as opposed to asking a very smart screenwriting expert a large number of questions about my screenplay and then compiling and using the "notes" in my next version. That's the story of how Awesome sauce arose!

I have other screenplays in the VEATT universe and so hopefully there will be more stories like this soon.