The eccentric exam in the far future for engineers exposes candidates to tales of three impossible machines and asks them to evaluate their deeper meaning.

Trapped in captivity, a Mongolian engineer creates a machine to remind him of his beloved's face, only to realize his creation's lethal ability to distort physical world. With the machine's help, he is able to escape and reunite with his love. Years later, however, the machine begins to deteriorate his wife's health. He sets out to destroy the machine, promising to return when he succeeds. But his lover grows old without seeing him again.

A mysterious Italian church tile is a portal to another world, sending a zealous mathematician on a lifetime of adventures, but with no way home to her artist girlfriend. Years later, she returns an old woman to her lover's doorsteps. Before she passes away, she relies her stories to her lover, who then dedicates her life to painting her tales.

A lonely archaeologist and her students set out to study a commune in Mali, where members are telepathically connected to each other. The researchers protect themselves from this power by wearing metal hats, until one day, the lead archaeologist decides to remove her gear and join the community. She experiences euphoria. Her students, however, in wishing to go home, force the protective gears back on her, severing her connections with the tribe. After years of recovering at home, the archaeologist sets out to find her people again. Unable to find her people again, she theorized the existence of a machine that could dissolve boundaries between self and other, writing finally that she must return to this place.