A Thinking machine from another universe, called the Nagha, has sent invaders through a rift in space, in order to expand its reach beyond its (fully conquered) home universe. To counteract this, Singa, the titular Sleeper, a mutant with astounding mental capabilities, commandeers the Enterprise and takes it to destroy the Nagha.
Singa's abilities include some kind of telepathy and the ability to think in multi-valued logic naturally (said to be impossible for normal humans, because neuron, like switches, are either on or off--not accurate).