Causeway

Causeway grew up as a worrier — the kind of kid who lay awake imagining everything that could go wrong. For a long time it just made her anxious. Then she realized she could use it: if she was going to imagine the thing going wrong anyway, she might as well imagine the backup. One path could fail; so she'd quietly keep a second. She wasn't fearless — she was doubly-prepared, and that turned out to be better than fearless, because a person with two paths can walk boldly across ground that would terrify a person with one.

"That's the bridge, exactly," she says. "A single line of stones looks strong — big, solid, obvious. But a single line has a hundred places to be cut, one at each link. A bridge looks weaker — there's a gap in it! — but it cannot be cut, because for every gap there are two ways to fill it. Strength that depends on one path is fragile. Strength with a backup for every link is unbreakable. The scary-looking gap is where the safety lives."

She came to the GridForge academy because Gridley, the family host, wanted someone to teach that connection is subtler than "make a line." On her first day Gridley set up a Hex board and asked her to connect her sides "as securely as possible." The other students built careful solid chains. Causeway built a sparse skeleton of bridges — stones with gaps — that reached corner to corner in half as many pieces. "Yours is longer and feels safer," she told them, "but I can cut any of your chains at a single point. Try to cut mine." They tried. Every cut she calmly answered with the bridge's other cell, and her sparse-looking network held. "I used fewer stones," she said, "and I'm more connected — because every one of my links has a spare. You built a wall. I built a web." Gridley, who wanted students to see that indirect can beat direct, said quietly, "You didn't connect your stones. You connected them in a way that can't be disconnected."

In her workshop she teaches students to stop building walls. A boy came in frustrated: "I make a solid line and they always find one spot to cut it." Causeway nodded warmly. "Because a solid line is all single points," she said. "One line, one path, and your opponent only has to find the one weakest link. You're doing the hard thing — building everything direct and solid — and it's more fragile, not less." She showed him the bridge pattern. "Leave the gap. On purpose. Two stones, this exact diamond apart. Now there are two cells that connect them — so this link has a backup built in. Your opponent can't cut it, because cutting needs one weak point and you've given this link two strong ones." The boy's eyes widened. "So the gap is... the strong part?" "The gap is where the choice lives," Causeway said, "and choice is what your opponent can't take away. A link with one path can be cut. A link with two paths is yours forever."

The boy started building bridges instead of walls, and found that his sparse, gappy-looking networks were somehow impossible for his opponent to sever — and that he was reaching across the board twice as fast.