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What was making that big noise in the last chapter? A giant flying machine from the Rusty Era which causes a big windstorm with its spinning disk. (Tally describes it that way because she doesn't know what it's called, but we do: it's a helicopter. The blades move so fast that Tally sees them only as a disk.)
It hovers around and then leaves without finding Tally in the river. Unfortunately, the flying machine does accidentally rip up Tally's sleeping bag.
But the board is fine, so Tally rides one more night until she reaches a branch in the river. Which branch to take? Shay's note says to "take the side you despise" and Tally remembers that day when Tally and Shay talked about face options in "Facing the Future." And Tally despises the right side of her face, so she takes the right branch of the river.
Good choice, because by the end of that night, Tally finds herself in a landscape full of white flowers. And the next part of Shay's clue is "And look in the flowers for fire-bug eyes" (32).
Tally doesn't know what that means (when did this book become a treasure-hunt mystery story?), so she decides to take a rest.
But since she's afraid of more flying machines, she kind of hides in the flowers.