The Quotient Space

I don't claim any originality to the discovery that the torus is indeed the quotient space (under appropriate quotienting) of the square. That fact in itself is nice, and it is indeed a fun exercise to try and derive a function that gives the desired quotienting. The joy of the exercise is lost, however, when something like this comes in the exams. Such is the nature of this exercise, that to a casual observer, the people in the exam room might seem in need of urgent psychiatric attention. A common scene might involve people drawing imaginary axes in the air, then rotating their fingers so as to form a circle and then with each of the remaining fingers, they might try and

draw more circles. The more athletic in the room might stand up and bend half way down, then cup their hands behind their back and do semi-uncoordinated somersaults. The rest might get busy filling sheets of paper though it is only the rare intellectual who can solve such a problem in the heated tension of the exam.

It often amazes me that while science fiction has drawn from almost every sphere of scientific advancement and played on almost every insecurity of the human race regarding these advancements, the immense possibilities from mathematics have yet to find their way into the imagination of the authors. They are willing to talk about artificial intelligence to the extent that all of science fiction has now come to be identified with AI. Movie after movie is made on the extent to which AI can replace humans in society, indeed, even replace a human civilization with a machine dominated one. Pathetic movies are made on alien invasions of the earth (notably, these aliens land in the US in some obscure countryside, are a threat to the world, are good for nothing, are scientifically more advanced, and it is only the philanthropy of the US that the world survives yet another crisis). Automation finds its way into slick movies involving suave thieves and superheroes. Yet mathematics remains a subject as far removed from fiction as it seems from reality.

The only movie I have seen that dealt tangentially with something mathematical, and I must admit that it was a horrible movie, so horrible that I don't even remember what its name was, dealt with something called hyperspaces. The idea was nice, but it was lost in the execution. The story, which made little sense to me, was about a few people stuck in some sort of a structure that existed in more than three dimensions, though, at any place inside the structure, more than three dimensions were not perceivable. As a result of this, the people, as they were trying to find their way out, kept traveling between periods of time. I don't remember much of what happened later, but the lasting image from the movie is of this gigantic man gorging out the eye of another and stealing his watch...So much for math fiction.

At times one gets the feeling that there is so little by way of fiction writing in math because to be able to use some of the concepts to make credible fiction, one has to be familiar with a fair amount of mathematics. To attain this familiarity, as a first step, one needs to get over the paranoia math invokes in most. This in itself is a Herculean task. But then what about the fiction once it is written? Will it find readers? Will purple nosed people sit in drawing rooms over scotch and say, "have you read 'Annihilators of the Hyperspace'", or will we ever overhear school kids talk, "You know, I felt really bad when that basis got transformed"? Probably not.

Ok, I guess I got my answer. There is probably a good reason there is no fiction in mathematics.