She hurried across the tracks then up the steps. She glanced back at Erasmus: he seemed to be in no hurry, but at least he was moving.
A whistle shrilled. She looked round, and down. Erasmus stood on the platform below her, panting, clearly out of breath. "No reservations," grumbled a fat man in a violently clashing check jacket. He shook his newspaper ostentatiously and made a great show of shifting over a couple of inches.
Miriam reached down and took Erasmus's hand. It felt like twigs bound in leather, light enough that her heave carried him halfway up the steps in one fluid movement. She stepped backwards and sat down, and he smiled at her briefly then tugged the door closed. The whistle shrilled again as the train lurched and began to pull away. "I didn't think we were going to make it," she said.
Burgeson took a deep breath and held it for a few seconds. "Neither did I," he admitted wheezily, glancing back along the platform towards the two running figures that had just lurched into view. "Neither did I..."
Chapter 8
You couldn't world-walk if there was a solid object in your position in the destination world. That was why doppelgangering worked, why if you wanted protection against assassins for your castle in the Gruinmarkt you needed to secure the equivalent territory in the United States-or in any other world where the same geographical location was up for grabs. That explained why the Wu family had been able to successfully murder a handful of Clan heads over the years, triggering and fueling the vicious civil war that had decimated the Clan between the nineteen-forties and the late nineteen-seventies. And their lack of the pattern required to world-walk to the United States explained why, in the long run, the Wu family had fallen so far behind their Clan cousins.
"There are a bunch of ways the knotwork might work," he'd tried to explain to the duke. "The fact that two different knots let us travel between two different worlds is interesting. And they're similar, which implies they're variations on a common theme. But does the knotwork specify two endpoints, in which case all a given knot can do is let you shuttle between two worlds, A and B-or does it define a vector relationship in a higher space? One that's quantized, and commutative, so if you start in universe A you always shuttle from A to B and back again, but if you transport it to C you can then use it to go between C and a new world, call it D?"
The duke had just blinked at him thoughtfully. "I'm not sure I understand. How will I explain this to the committee?"
Huw had to give it some thought. "Imagine an infinite chessboard. Each square on the board is a world. Now pick a piece-a knight, for example. You can move to another square, or reverse your move and go back to where you started from. That's what I mean by a quantized commutative transformation-you can only move in multiples of a single knight's move, your knight can't simply slide one square to the left or right, it's constrained. Now imagine our clan knotwork is a knight-and the Wu family's design is, urn, a special kind of rook that can move exactly three squares in a straight line. You use the knight, then the rook: to get back to where you started you have to reverse your rook's move, then reverse the knight's move. But because they're different types of move, they don't go to the same places-and if you combine them, you can discover new places to go. An infinite number of new places."
"That is a very interesting theory. Test it. Find out if it's true. Then report to me." He raised a warning finger: "Try not to get yourself killed in the process."