In the fantasy/SF world of this novel, numerates are special people who are aware of the fact that numbers themselves are alive and can be coaxed or controlled into doing seemingly magical things for them. This plot and the descriptions of the "ecology" of numbers is certainly original. Sometimes, it really worked for me, such as when experienced numerate, Dom, teaches Jenna how to use a pay phone without paying:
(quoted from Napier's Bones)
Jenna looked up, watched a passenger jet cutting across the sky high overhead. "I see circles," she said. "Triangle, other shapes. Some numbers are squeezing their way in, filling gaps between them."
"Good," said Dom. "From what I've heard, it works, or at least looks, different for everybody who does it. Does it seem complete?"
She looked back at the phone, waved a finger in the air and whispered to herself. "They don't want to cooperate," she said, frowning. She reached out a hand, annd Dom watched as a small cloud of numbers tried to break way from her, but with an effort she managed to get them under control. "Okay. got them. I've just added my home phone number. Wow!" She broke into a huge smile. "Everything just fell into place!"
Dom frowned. The numbers were still bouncing in the air around Jenna, but seemed to be doing their level best to keep away from her. But he nodded his head and said, "One more thing to add, then. Pick up the phone and punch in whatever numbers work with the patter you just made. Then add a series of eleven primes, starting with...[s]eventeen. And jump two when you get to the fifth and the seventh."
Jenna screwed up her face, concentrating. Then she punched in a bunch of number, finishing off with the set of primes, the last one seventythree...."It's ringing!" she said.

The use of technical terms like "imaginary" or "irrational" in these contexts can seem poetic, even if unrelated to the real meanings of these words. (The book itself hints explicitly at connections between mathematics and poetry, including Blake and Shakespeare among its famous numerates.) At other times, at least from my point of view, it seemed quite silly, as in this apparent reference to Zeno's paradox and Euclidean space:
(quoted from Napier's Bones)
In panicked response, Dom threw up a wall of Euclidean space between the two of them. The numbers from Ewan quickly found themselves halving the distance between the two men with each second, but the number of halves had stretched out to infinity.

The title of the book refers to a device for performing arithmetical operations which was invented by Scottish mathematician John Napier of Merchiston (1550 – 1617). In fact, Napier (or rather, his spirit or "shadow" preserved in living numerical form and inhabiting the body of a living individual) is the villain in this novel. He is hunting down Dom and Jenna who are collecting physical objects with special numerical properties that will give him power to (you guessed it) take over the whole world.
The "shadows" of mathematicians Isaac Newton and Archimedes also appear in the book, though they are not evil like Napier. In addition, Dom and Jenna are aided by some sentient numerical creatures, made entirely of numbers in the same way that we are made of independently nonsentient cells. The special physical objects are also quite important to the plot, often taking the form sporting memorabilia associated with numerical coincidences, but a special and quite important role is played by the notebooks of Werner Heisenberg.
As the blurb from Peter Watts on the back cover explains, Derryl Murphy does a really impressive job of taking this strange idea for how things could work and seeing where it goes, making it seem real along the way. One certainly does not need to know any actual mathematics to appreciate it. (Dom himself once brags that he has no advanced mathematical training.) Yet, despite being completely fantastical, it does capture some of the feeling of mathematics in addition to being quite entertaining.
Contributed by
John
This story is very well written, but is more fantasy than mathematics (think, in the author's own words, "Donald in Mathmagic Land"). It gives an interesting spin on John Napier, the famous Scottish mathematician and scientist that not all scholars may appreciate. Allinall however, I found it to be an enjoyable read!

