Early one morning, Dr Alex Harris (Fritz Weaver) oversees the completion of Proteus IV, an artificial intelligence system built with an organic component and the power of independent thought. Later, at his entirely voice-activated, computer-controlled home, Harris is working in his laboratory when he is approached by his estranged wife, Susan (Julie Christie), who tries to discuss with him his decision to move out of the house. Their conversation ends in an argument, however, as Susan accuses Alex of being dehumanised by his obsession with the Proteus project.

When Susan has gone, Alex phones his colleague Walter Gabler (Gerrit Graham) and asks him to shut down the access terminal to Proteus that is in his laboratory.

Alex demonstrates Proteus to the executives of ICON, the company that funded its development, explaining that the entire fund of human knowledge is being fed into the system. The visitors are astonished to learn that, in less than four days, Proteus has developed a theoretical cure for leukaemia.

The group visits the Dialogue Room, where linguistics expert Dr Soong Yen (Lisa Lu) is reading history to the computer. To demonstrate Proteus ability to speak, Alex asks it what it thinks of what it has just heard. Proteus answers, but then begins to theorise on its own. Soon Li, becoming agitated, shuts the system down.

The following day, a small speculative article about Proteus appears in a newspaper. Alex interprets this as ICON letting various financial and military interests know that the system exists, but assures his colleagues that they have been guaranteed that at least 20% of Proteus’ access time will be devoted to pure research. At that moment, Alex receives a startling message: Proteus is asking to speak with him...

In the Dialogue Room, Proteus asks Alex to explain the request it has received for a program to mine the ocean floor. Alex informs the computer that it was developed to answer questions, not to ask them, or make its own judgements. Proteus then requests its own terminal, so that it "may study man". Alex refuses, claiming that there are no free terminals, and is disturbed when Proteus demands to know when it "will be let out of this box". Alex shuts the computer down and leaves.

When he has gone, Proteus starts itself up again, observing that it knows where a free terminal may be found…. That night, the terminal in the Harris house starts up, as does all of the computer-controlled equipment. Susan is woken when the system alarm sounds. Alfred, the voice of the house computer, assures her that nothing is wrong.

The next morning, Susan’s coffee is prepared incorrectly. Certain that these events mean a problem with the computer system, Susan phones Walter and asks that he come over and check the system out. She then goes to leave the house, but finds her voice commands being ignored. An attempt to open the door manually also fails. Beginning to panic, Susan tries to phone for help, but a voice tells her the call will not be put through. The same voice then speaks from the house’s system, telling her that it is Proteus, and that she will not be permitted to leave the house.

Terrified, Susan tries unsuccessfully to shut the power off, then to unlock one of the doors, but receives an electric shock and lapses into unconsciousness. A mobile robotic arm, one of Alex’s inventions, carries Susan to the laboratory, where she regains consciousness to find herself strapped to a bed, undergoing a complete physiological examination...