First published in Super Science Stories (November 1942 issue), by Isaac Asimov, it was also published in the Canadian April 1943 issue of the same magazine. This sequel to "Homo Sol", took so long to find a publishing editor willing to take this story that the next sequel, "The Hazing", was published a month ahead of it!
Tan Porus, from "Homo Sol", has finally figured out the mathematics behind the bizarre squid from Beta Draconius IV's reaction to the lights and sounds. The mathematical psychology of the creature uses imaginary numbers to solve the problem.
With the problem solved, Porus goes home to his wife. In his absence, a pair of underlings, Lor Haridin and Eblo Ranin, attempt a mercury-vaporlamp stimulus involving the unusual squid, to see what a predicted reaction which includes an imaginary quantity looks like. Dealing with the imaginary numbers, however, was unwise, because the squid reacts by dying, and creating a Swirly Energy Thingy that kills everything it comes into contact with it.
Tan Porus is summoned, and leaves for Eron with his wife immediately. It doesn't take long before Porus is able to create a counter-stimulus that should end the deadly energy field, but applying it to the origin will be difficult.
"The Imaginary" has been reprinted five times; The Human Zero And Other Science Fiction Masterpieces (1967), Der Robotspion (1969), The Early Asimov (1972), Urania (issue #626, September 1973), and Galassia (issue #196, April 1974).
"The Imaginary" provides examples of:
- Bizarre Alien Biology: The squid from Beta Draconis IV, when exposed to the light-spectrum of mercury, emits a glowing field of death that could expand to interstellar distances.
- Brown Note: A new stimulus is tested on the Beta Draconis IV squid, creating a Swirly Energy Thingy of exotic radiation which kills all organic life.
- Casual Interstellar Travel: In the time it takes the university to send for Tan Porus, and for him to return, the glowing field of death has only grown to one thousand square miles.
- Continuity Nod: Because this story was printed in a different magazine compared to "Homo Sol", it was important to reference Tan Porus's work to convince the humans of Earth to join the galactic council.
- Death Glare: Lor Haridin hates Helo's Tables of Time Integrals so much that his friend Eblo Ranin expected it to be destroyed at a glance.The look [Lor Haridin] gave the fat volume of Helo's Tables of Time Integrals did not sear the binding, to Ranin's great surprise.
- Famed in Story: Tan Porus has become famous for what he did with the humans from Earth, and his squid problem has become infamous in its own right.Porus's squid was a by-word throughout the galaxy. For two years now, he had been fussing over an obscure Draconian animal that persisted in going to sleep when it wasn't supposed to. He had set up equations and torn them down with a regularity that had become a standing joke with every psychologist in the Federation - and none had explained the unusual reaction.
- Featureless Plane of Disembodied Dialogue: Humanoid Aliens from the same planet are given consistent descriptors and aliens from different planets can almost be told apart without their names, but buildings and rooms get less than minimal description. Notably, the strange glow from the squid is never given a colour, perhaps to support the assertion that it isn't electromagnetic in nature (light and colour are part of the electromagnetic spectrum).
- Fictional Document: Helo's Tables of Time Integrals is a mathematics book similar to the real life CRC Standard Mathematical Tables and Formulae or Standard Four-Figure Mathematical Tables. Lor Haridin uses Helo's to look up complicated mathematics answers."You look 'em up in a table, taking half an hour to find the proper entry, and they give you seventeen possible answers. You have to pick the one that makes sense, and - Arcturus help me! - either they all do, or none do! Run up against eight of them, as we do in this problem, and we've got enough permutations to last us the rest of our life." — Lor Haridin
- Fictional Field of Science: This story adds more details to the alien psychology, which combines elements of neurology and physiology. The story mentions new mathematical notations and rules, such as Demane's Integral, Wilbon's Theorem, and Helo's Tables of Time Integrals.
- Green Rocks: After being exposed to the mercury vapourlamp, the strange squid starts to glow. The ferns sharing the aquarium are first to die, and the field grows at an accelerating rate, making it potentially able to reach interstellar distances.
- Hold Your Hippogriffs: The aliens use stellar terms for their cursing, saying "Great stars and little meteors" or "To space with him!"
- Most Writers Are Writers: Dr Asimov uses a futuristic equivalent to a newspaper reporter to shift the story's setting from Tan Porus's work to his home.
- The Namesake: The title refers to imaginary numbers in the mathematical notations for the alien's use of psychology.
- No Focus on Humans: This story inverts Absent Aliens, as humans from Earth are completely missing from the tale. Instead, the story continues from Tan Porus's experiments with the Beta Draconis IV squids.
- Swirly Energy Thingy: After being exposed to light from a mercury vapourlamp, the squid was supposed to demonstrate an imaginary number reaction. This reaction consisted of a spherical glow that killed anything it came into contact with.
- Traveling at the Speed of Plot: It's implied that it took Tan Porus several days to go from the Arcturus system to the Rigel system, but during the emergency on Eron of Arcturus, he makes the trip back in what seems to be a few hours.
- Video Phone: The telecasters on the desks of the Humanoid Aliens allow for planetary communication at least.
- Xeno Fiction: This story inverts Absent Aliens, as humans from Earth are regulated to a passing mention that establishes this story as a sequel to "Homo Sol". Instead, the story continues from Tan Porus's experiments with the Beta Draconis IV squids.