"Since the first living thing gazed upward through the darkness, Man has seldom been content merely to be born, to endure, and to die. With a curious fervor he has struggled to unlock the mysteries of creation and of the world in which he lives. Sometimes he has won. Sometimes he has lost. And sometimes, in the tumbling torrents of space and time, he has brief glimpses of a world he never even dreams..."
The story begins as policemen investigate the destruction of Dr. Stone's office, the latest in a series of attacks on optometric facilities. After they leave, Dr. Stone realized that his own glasses are broken and decides to try a pair of prescription lenses designed for patients who suffer from double vision, lenses made from meteoric quartz. Putting on the glasses, he recoils in horror as he sees a being that appears to be made of pure light. The being attacks him, destroying his glasses, steals a page from Stone's notebook on which are written the names of patients who have been prescribed the lenses, and quickly vanishes.
Stone ascertains that the being must exist purely in two dimensions, as when it turns sideways it becomes invisible, and is able to move through walls. Stone visits his physicist brother to talk over the idea, but his brother dimisses him as mad. Dr. Stone then has his secretary order several new pairs of the meteoric eyepieces, and tries to track down the patients sought by the two-dimensional creature. One has been injured, another is found dead, and the third, a welder, managed to ward off the creature with his welding torch (later we are told by the creature that he comes from a world in which fire is all powerful because two-dimensional beings, like dry leaves or paper, are easily set aflame). It is also discovered that a large building has been sliced in half. Stone's brother and the police begin to investigate these occurrences. Meanwhile, in the excitement of the moment, Stone suddenly seems to notice his love-struck secretary for the first time, remarking after putting on a different pair of glasses that something about her "looks different," as she glows with adoration towards him. From this point onward, Stone begins to refer to his secretary by her first name and they are physically closer.
Soon, the creature appears again to Stone after he puts on a pair of the meteoric glasses. The creature, the titular Eck, explains that he was trapped in our world when he fell through a time-space rift. He needs to return to his world through the rift and close it, or else the rift could cause the destruction of our entire world. However, Eck is unable to see properly in three-dimensional space, and requires lenses to correct his two-dimensional vision so that he can find the rift. Eck gives Stone one of his eyes, a translucent triangle shaped object, and, building suspense, asserts that a lens must be constructed in 24 hours as he is dying. Stone begins to grind the interdimensional lens.
Meanwhile, the police and Stone's brother have ascertained that Stone is harboring the creature, and break into his office with a flamethrower. They attack Eck with fire, and apparently succeed. After they leave, though, Dr. Stone and Elizabeth find Eck alive, having deceived his attackers. By this time, Stone and Elizabeth have become increasingly intimate, and Stone has his arm around Elizabeth as they speak with Eck. They produce the interdimensional lens, which Eck tries to take with him through a wall but cannot as the lens is three-dimensional. Stone and Elizabeth offer to bring the lens with them to the public square, where the rift is located. Eck exits through the wall, Stone asks Elizabeth if she would like to go to the square to "say goodbye to a friend," and the two exit as a couple, Stone's arm still around Elizabeth's waist.
"Paradoxically, Man's endless search for knowledge has often plundered his courage and warped his vision, so that he has faced the unknown with terror rather than awe, and probed the darkness with a scream rather than a light. Yet there have always been men who have touched the texture of tomorrow with understanding and courage. Through these men, we may yet touch the stars."