A Carleton computer science professor has co-authored a mathematical study, “The Urinal Problem,” that determines which urinal provides the most privacy, given the possible behaviour of men entering the washroom.
The study was completed by Carleton professor Evangelos Kranakis and mathematics professor Danny Krizanc of Wesleyan University in Connecticut.
The paper concludes that in almost every situation, the stall farthest from the door offers the most privacy.
“Our main conclusion is that when faced with the decision of what urinal to choose upon entering the men’s room, in order to maximize your privacy, you should probably choose the one furthest from the door if it is available and the one next to it is unoccupied,” the paper states.
The study makes the assumption that men are “naturally lazy,” and so there is a higher chance that urinals farther from the entrance will be unoccupied, compared to ones closer to the entrance.
The topic of the paper was inspired by an attempt to calculate the possible configurations of a ribonucleic acid (RNA) protein, Krizanc said.
The RNA question is similar to other problems that have been studied since the 1960s, he said.
“It turns out that a particular version of [the RNA] problem leads to analysis which is equivalent to the following problem: Unfriendly patrons arrive at a bar with n stools and chose one at random in such a way as to have nobody on their right and nobody on their left. How many patrons arrive before no new patrons can be seated?” he said via email.
“Soon after discovering this, we thought of the urinal version of the problem. We thought it was an amusing question that would be perfect to present at a conference called ‘FUN with Algorithms’ which was coming up at just about the same time,” Krizanc said.
The research fits into a larger body of work about bathroom behaviour, he said, but the paper is unique in its algorithmic approach.
It has some practical applications, but Krizanc said a lot of science isn’t exactly practical.
“Most results in science turn out to have very little use. Our hope was this might at least be a little entertaining,” he said.
He quoted from British mathematician G. H. Hardy and said, “’Nothing I have ever done is of the slightest practical use.’”
“His work is the basis for the codes that keep the Internet secure, and all of electronic commerce would be impossible without it,” he said.
