Adventures in Geometry, a guest post by Dianne K. Salerni

Math was never my favorite subject in school (reading was), but I did enjoy what might be called the speculative aspects of mathematics. I loved changing base ten numbers into other bases and back, as well as imagining who might structure their numerical system that way. (Aliens with six fingers would use base six, right?) And I became fascinated with dimensional geometry after reading Flatland (Edwin A. Abbott, 1884) and Sphereland (Dionys Burger, 1957). 

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The main character of these books is a Square who lives on a flat plane. His wife is a Line; his sons are Pentagons. The Square is visited by a mysterious being, a Sphere from a three-dimensional universe. Together, they visit a one-dimensional world (Lineland), where the inhabitants can only move forward and backward, and a zero dimension where a single contented Point is his own world and universe. Later, the Sphere is surprised by a visit from an Over-Sphere and learns about the existence of the fourth dimension.

I probably would never have thought about writing my own multi-dimensional adventure if I hadn’t come across YA science fiction and horror author William Sleator sometime in the nineties and read his book The Boy Who Reversed Himself (1986). Sleator introduced me to ana and kata, the two extra directions in 4-space that exist at right angles to all of our directions. As there was no Google at the time, I assumed Sleator invented those words until, a decade later, I read Spaceland (Rudy Rucker, 2002). It turns out that ana and kata are real mathematical terms describing movement in the fourth dimension. They were coined by British mathematician Charles Howard Hinton in 1880, along with tesseract, which is not a wrinkle in time after all, but the 4-space analogue of a cube. 

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Another decade would pass before I started planning the four-dimensional setting of my own story. First, I dug deeper into dimensional geometry (Knots don’t work in 4-space; did you know that?) and blundered my way into theoretical physics. Gravity is considered a weak force in our universe—10⁴⁰ times weaker than the force that holds atoms together. What if that’s not true in the fourth dimension? Sound waves and electromagnetism could work differently too. Gradually, I came to understand why beings from 4-space might want to influence events in 3-space and need the assistance of humans to achieve their goals. This is when the 4-space Seers entered my outline along with their human Agents, including Jadie Martin, an abandoned baby rescued by the Seers and placed with a loving, adoptive human family. (At least, that’s what the Seers claim happened.)

When I finally started writing in 2014, describing people and objects in 4-space was a challenge. We can’t see ana and kata. It’s hard to bend our minds around the concept of directions that don’t exist for us. To create visual images, I relied on the example of my mentor texts, Flatland and Sphereland. The Square sees the Sphere as a series of flat cross-sections when it passes through his plane.  First there is a point that grows into a circle, and the circle expands until it reaches the Sphere’s greatest diameter before shrinking back to a point. Accordingly, the Sphere perceives the Over-Sphere as a changing 3D cross-section: a tiny ball that swells into a large one, then reverses the process and disappears. 

Following this example, I described four-dimensional people using three-dimensional cross-sections: disembodied fingers, eyeballs, teeth, and whiskers—randomly growing, shrinking, and morphing like shapes inside a kaleidoscope. Artist Kristina Kister did a splendid job conveying this visual element in the jacket art. The viewing crystal front and center on the cover provides three-dimensional glimpses of Miss Rose, Jadie’s 4-space friend and rescuer. (At least, that’s what she claims to be.)

Three-quarters of the way through my first draft, I began to worry I’d written myself into a corner. I’d created an oppressive four-dimensional universe crushed by gravity where humans can barely see or function, filled with 4-space adversaries capable of looking ana into our universe the way we study a blueprint—and crushing us like bugs. I could see no way for my human protagonists to defeat them in our universe or theirs. 

I took my problem to my chief sounding board (my husband) and our preferred brainstorming spot (a hot tub under the stars). As usual, he came at the problem from an unexpected direction. “Why don’t you …” I’ll redact his solution for the sake of avoiding spoilers, although the title of the book may give you a clue.

That’s the story behind the development of Jadie in Five Dimensions. For simplicity’s sake, I’m leaving out the six years of revisions and the elimination of three unnecessary points of view. (What was I thinking?!) Jadie Martin’s story is full of monsters, kidnappers, spies, and betrayals—and hopefully enough theoretical geometry and physics to make you wonder: Who’s watching us and from where?

Meet the author

Dianne K. Salerni is the author of middle grade and YA novels, including Eleanor, Alice, & the Roosevelt Ghosts, The Eighth Day Series, The Caged Graves, and We Hear the Dead. Her seventh book, Jadie in Five Dimensions, is a multi-dimensional adventure steeped in science and math. Dianne was a public school teacher for 25 years before leaving the profession to spend more time hanging around creepy cemeteries, attending ghost hunting classes, and climbing 2000 year-old pyramids in the name of book research.

Website: https://diannesalerni.com/

Facebook: https://www.facebook.com/DianneKSalerni

Twitter: https://twitter.com/diannesalerni

About Jadie in Five Dimensions

A thirteen-year-old girl seeks answers about her past in the fourth dimension—and beyond—in this think-outside-the-box adventure.

What do you do when it turns out your whole life has been a lie? 

Jadie Martin was always told she was abandoned by her parents. Creatures from the 4th dimension rescued her and placed her with a loving adoptive family. Now, Jadie acts as an agent for the beings, also known as Seers. She uses the 4th dimension as a short-cut to travel anywhere on Earth, performing missions calculated to guide the world toward a brighter future.

But then Jadie discovers that her origin story is fake. In reality, her birth family has suffered multiple tragedies and disasters engineered from 4-space, including the devastating loss of their baby girl. Her! 

Doubting the Seers, Jadie starts anonymously observing her long-lost family. Why are they so important? What are the true intentions of the Seers? And what will all-powerful four-dimensional beings do to a rebellious human girl when they realize she’s interfering with their plans? 

A Wrinkle in Time meets Flatland in this thrilling journey that challenges the meaning of family, loyalty, and our universe at large.

A Junior Library Guild Gold Standard Selection

ISBN-13: 9780823449095
Publisher: Holiday House
Publication date: 10/05/2021
Age Range: 9 – 12 Years

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