CheriAnne Toledo, the daughter of the King of Ohio, uses her mathematical skills (and the assistance of Nikola Tesla) to build a device that is supposed to be able transport people instantaneously from one location to another. However, when forced by desperate circumstances to use it before it is ready, she finds that it transports her seven years in the future to an alternate reality, one in which the history of Ohio is different and Tesla does not know her. In this new world, her only friend is an uneducated but sincere workman helping to build New York City's first subway tunnels.
Many of the plot devices in this book will be familiar to some readers: alternate realities justified by vague references to quantum physics, explanations of time machines in terms of mathematical analogies involving the concept of dimension, transporters, conspiracy theories revolving around Tesla and Edison, etc. However, Flaming managed to keep my interest (for me, this was a "page turner") and present a few interesting twists.
One of the most unusual thing about this book is the way it blends genres. Some of it takes place in contemporary Los Angeles. The majority is historical fiction in turn of the 20th Century New York City. Considering the science fiction aspect, however, it cannot be considered as straight historical fiction either. In the way that it tries to tie together disparate facts (the building of the subway, the conflict between Edison and Tesla, the failed Roanoke Colony, etc.), it reminds me of The Da Vinci Code and other recent conspiracy theory novels. Often it takes the form of pseudoscholarship (with so many footnotes citing references regarding the Kingdom of Ohio that I had to keep reminding myself that, in this reality at least, there was never such a place). Then, it slides (sometimes a bit too jarringly and not always convincingly) into traditional narrative fiction. Moreover, there is a hint of selfconscious postmodernism to the way the mysterious narrator addresses his writing of the book. Though not perfect, this was creative and artfully done. My only real complaint concerns the end of the book, which I felt was not quite as good as the setup...but then I am very picky about endings.
Although math is not discussed frequently in the book, it is quite important as it not only is used to explain how the heroine travelled between realities but moreover is used by her as lure to get the attention of the Tesla who does not know her. In fact, there are few enough explicit references to math in the book that I can essentially address them all below.
 The first bit of mathematics does not show up until Chapter V, quite a ways into the book. There we see a young CheriAnne in her kingdom of Ohio discussing mathematics with her tutor.
(quoted from The Kingdom of Ohio)
Mr. Coulter clears his throat, picks up his glasses, polishes them, and affixes them to his perfectly straight nose. "Well." He shuffles the pages of her work and takes the glasses off again. "I understand the math, but my dear girl"  he chuckles  "honestly, I can't make head or tail of what you're trying to do. These equations simply don't work."
"Yes, exactly!" She realizes that her voice is too loud and lowers it. "You see? They're both true and false  or rather, it seems impossible to demonstrate they are either."
He nods patiently. "Yes, but obviously they're false. They problem is just in the way that you've written your maths."
"But " She struggles to find a way of explaining this most recent inspiration that kept her awake and sitting at her desk all through the previous night, filled with racing thoughts until dawn. "It seems to me as if some paradox about the numbers themselves in this proof. As if"  she struggles for an analogy  "as if I were to tell you `The next sentence is true. This sentence is false.' You see? There is a fundamental inconsistency. And here"  she points at the paper  "given this class of recursive formulae, there must also be a set of recursive signs for which..." she gazes at him hoping she has conveyed some inkling of the beautiful, selfannihilating, logical perfection she imagines.

On the next page, she considers sending a description of her discovery to Bernhard Riemann in Göttingen, to whom she has apparently written before. On the page after that she decides that the proper description of this phenomenon is that it is an "imperfection" within mathematics.
Clearly, the intention of this scene is to convince us that CheriAnne is an unappreciated mathematical genius. Having read many such scenes as part of my "hobby" of reading mathematical fiction, I can say that this one is not bad. I have two problems with it, only one of which is mathematical. I suspect that what Flaming had in mind when he wrote this was that she had independently discovered Gödel's Theorems. It does vaguely sounds like it ("impossible to demonstrate that they are either"). In fact, it is a common misconception that Gödel's proof amounts to showing that there is a contradiction within mathematics. Fortunately that is not the case. (See Division by Zero.) Rather, what he did is quite a bit more involved as it necessarily requires the introduction of metamathematical notation. I am not too bothered by the fact that Flaming gets this wrong, as it would really have been too complicated to introduce all of the tools that would have been necessary to get it right, but I fear it reflects an actual misunderstanding and might reinforce that misconception among readers. Actually, I was bothered more by the nonmathematical problem that the narrator (who was not there and does not have the necessary expertise) could not possibly have written this as we are supposed to believe he did.
 Chapter VI opens with a discussion by the narrator about the relationship between ndimensional geometric objects and their (n+1)dimensional counterparts (e.g. points to lines, lines to polygons, etc.) which is supposed to enlighten us as to how time machines might work. It was not particularly enlightening, but one could imagine this is because the narrator does not fully understand it himself and is only trying his best to understand CheriAnne Toledo's mathematics.
 A brief mathematical metaphor in Chapter IX explains how CheriAnne is feeling:
"She thinks of how she has nothing left anymore  not a family, not a home, not even a name; as if all the variables and crosscanceled equations of her life have been returned to some primordial zero."
 In Chapter XI, CheriAnne relates how and when she first became interested in math. (Both she and Peter, the workman, demonstrate amazing inductive abilities in that they each supposedly recognize the connection between plant growth and Fibonacci numbers with a very small sample and no prior knowledge.)
(quoted from The Kingdom of Ohio)
"I must have been eleven or twelve years old," she says, speaking slowly. "It was not long after my mother died. I had a tutor  Mr. Driggs  who was passionate about botany.
"He had given me a sunflower to study, and I remember counting the florets at the center of the flower. They grow in a spiral and at a certain point I realized something about the number of florets in each ring. There was a shape to them, a progression to their growth: three in the first ring, then five, then eight, thirteen, twentyone, thirtyfour "
"It's totaling up the numbers," Peter breaks in, "isn't it? If you add the first and second you get the third number, then the second and third number to get the fourth "
"Exactly. The Fibonacci sequence, although of course I did not know it at the time. When I told my tutor, he became very excited and gave me a book on mathematics." She shakes her head, eyes unfocused. "When I read those books it was as if I'd already known everything inside them, and had simply forgotten. As if I were remembering these things, rather than learning them for the first time. And I suppose the rest, as they say, is history..."

 Later in Chapter XI, CheriAnne sends a note to Tesla containing only a time and location to meet along with "two lines of mathematical formula".
(quoted from The Kingdom of Ohio)
It is a miracle, he thinks. It is impossible. Studying the equation, he realizes that it is only a fragment of some larger theorem, a partial solution  but it is still more than he could have dreamed. He suppresses the urge to laugh out loud; with this one stroke he has more than Edison and all his lackeys, an affirmation that his years of effort have not been in vain.


Finally, in Chapter XIII, there are references to "the apex of conic projection" and "equations" describing "a spherical magnetic field" in explaining the significance of the new subway tunnels to the transportation device.
I definitely enjoyed reading this book, but the mathematical and science fiction aspects of the book are going to be "old hat" to anyone who has read much mathematical fiction before, and the most interesting aspect of the book  the way it bends genres  is somewhat flawed.
That, anyway, is my opinion. If you have read this book, please use the link below to vote and post your own comments about it! 