|In the futuristic 1980's, a math student graduates from multiversity and gets a job with a megacorporation which is trying to do the impossible, literally. Along with his friends (a psychologist and an electrical engineer), he is working on a project to make it possible to do things that are logically impossible. The project involves sensory deprivation and raising children with extra senses whose minds can handle alternative logical systems. There is a definite "Cold War" feel to the whole thing. Mathematically, the protagonist has the job of testing mathematical models using an aleph sub zero computer and using "Urbont matrices" to analyze brain activity in the children. (The aleph sub zero is made by IBM, just like all of the computers in this story.) And, of course, there is discussion of symbolic logic as well since the project involves attempting to realize an alternative.
As with many SF stories from this era, it is appallingly sexist. Someone could probably write a thesis on this paragraph alone:
|(quoted from Four Brands of Impossible)|
All the co-eds are hot for someone they can discus the Great books with, not some barbarian science of engineering major with a slide rule swinging from his belt. I've seen these Zenish girls, with their long hair and thongs and SANE buttons, wild for motorcyclers and African exchange students. Rotten snobs! Though I've got to admit that some of my friends in the engineering school depend more on force than persuasion for their pleasure. Ha-ha!
One of his friends also argues that black Americans are genetically inferior...although the protagonist does counter that with rather strong sounding arguments to the contrary.
There is some discussion of the difference between pure and applied math, and quite a bit about the way that mathematicians (and all scientists in this story) burn out young. Another tiny bit of math thrown in, for no good reason, is the popularity of Möbius movies in "the future". These movies are looped so that you can begin and end at any time and the story still makes sense (sort of...although people do tend to be their own great-grandparents and so on).
Originally published in Fantasy and Science Fiction Magazine in 1964 and reprinted in Rucker's collection Mathenauts.