Reading Lewis Carroll's "Alice in Wonderland" has had a peculiar effect on poor Rhoda. She's afflicted with spells of vertigo, as well as difficulty distinguishing fantasy from reality. The situation is complicated by an unexpected visit from Bob's boss.
It would take a computer to find the right girl for Peter, and Bob has just the tool, Rhoda. He furnishes Rhoda with information on 250 girls working at the space lab, trying to find a match for Peter.
Bob gets off to an inauspicious start as chairman of a road-safety committee by crashing into his neighbor's car, then Rhoda testifies in court about the entire incident.
Dr. Robert McDonald moves the beautiful robot Rhoda Miller into his apartment and begins the task of training her how to function in the human world, while keeping her secret from being discovered, a situation complicated by his interfering sister and his lovesick neighbor Peter.