Henry is an only child and a lonely child, leading a life of quiet academic endeavour to please his parents until one evening, chased by bullies in the middle of a thunderstorm, running along a canal towpath, he slips and twists, and finds himself trapped in a different plane of existence – the sideways dimension. Still able to see others, he can no longer interact with them or with anything. All objects are rock solid and immovable to him: a dog can trample him like a steamroller, and a blades of grass can stab him like tiny daggers.
Gradually he learns how to survive in this alien shadow of the normal world. He learns ways to uproot small objects and twist them into the sideways dimension, allowing him to feed himself, until one day he meets Miriam, who looks like a five year old but speaks like a professor. He's not the only child in the sideways dimension, and they're not aging.
The two of them form an unlikely partnership, with her wisdom and his physical strength keeping them alive, until one day they happen upon a larger gang of children, all trapped in the sideways dimension, but protected and enslaved by a man in the real world who can somehow see them, and forces them to steal valuables for him, twisting them out of the world for him to pull them back later, in return for just enough food to survive.
Henry and Miriam infiltrate the gang to sow the seeds of a rebellion amongst the other dislocated children, bringing down their Fagin-like exploiter, but creating a greater enemy in the process.