The Music of the Spheres (1984)

Set in the not-too-distant future, when the existing world economy has collapsed, and the new city-states are controlled by computers, many of which require a kind of telepathic linkage with a human counterpart. When the most important of these computers exhibits strange patterns during a crucial operation, its counterpart, a top scientist named Melody, begins having psychic experiences. For a low-budget film, a surprisingly deep exploration of emotions vs. logic and the elusive search for truth.