Anthony Smith and William Anti-Aut are full brothers who live in a post-catastrophe world where, due to concerns about humanity's limited genetic diversity, full siblings are rare (and identical twins are nonexistent). Not only are they full brothers, they also look alike, which is totally unheard of.
William pursues a career in genetic engineering, referred to as homology, and has been trying to understand and cure Autism, hence his chosen surname. Anthony has gone into telemetrics, and is working on the Mercury Project, the purpose of which is to send a robot to Mercury. This is a problem because the positronic brain at the time is not yet adapted to such an environment, so a computer on Earth must direct the robot. However, the speed of light communications lag between Earth and Mercury can last up to twenty-two minutes, making computer control difficult. Anthony attempts to solve this problem by recruiting a homologist that can design a positronic brain that resembles a human brain. The leading homologist in this area is his brother William, and much to their mutual embarrassment, the two wind up working together.
William struggles to help form the brain, but when the robot is tested in Arizona, it is terribly clumsy. Anthony sees no hope in the robot, but William argues that it was designed for the environment of Mercury, not Arizona. When the robot is sent to Mercury, it operates smoothly, and the project is a success. The solution, William realized, was to use an autistic human rather than a computer to direct the robot. The story ends with William and Anthony befriending each other after being so long separated.