The elevator paradox proves your elevator always goes the wrong wayS

Does it occur to you, when waiting for an elevator, that elevators always seem to be going the wrong way? It occurred to two physicists, too. And, with a little work, they proved that this wasn't just Murphy's Law, it was reality.

George Gamow was a physicist who worked had a celebrated, and action-packed career which included working on radiation research and defecting from the USSR. Busy guy. At one point he found himself in an office on the second floor of a six story building. He was friendly with Marvin Stern, another physicist. Stern had himself an office on the fifth floor of the same building. The two must have been visiting quite a bit, because after a while, they both noticed a strange phenomenon.

Gamow, whenever he used an elevator to go up to Stern's office, found that all the elevators seemed to be going down. Stern, on his way down to Gamow's office, found that elevators were always going up. Two people, in the same building, noticed that the elevators were always moving in opposite directions. Gamow and Stern decided that the only way this could happen is if the elevators were manufactured in the middle of the building, and were constantly be sent up to the roof or down to the basement to be disassembled, then rebuilt in the middle again. After some discussion, probably with the building's maintenance crew, they found that this was not the case. Then they pulled out some writing instruments and got to doing equations.

The math that it took to explain this seemingly impossible set-up is complicated, but the gist is simple. Elevators spend more time traveling one way or another depending on what stage of their journey you happen to be on. If you are just under the top floor, elevators will generally speed by you on their way up, drop off the Top Floor Elite quickly, and then come back down. Unless the elevators get stuck on the top floor, they'll spend more time below you than above you, so you'll only catch an elevator going down if you happen to press the call button in that brief time between when the elevator drops off its passengers on the top floor and when it moves back down. Similarly, if you're one floor above the Morlocks, and you just sit outside the elevator doors (not a good idea with Morlocks around), you'll spend a long time watching the elevator descend, and a relatively short time watching it bounce back up from the basement.

In reality, it takes a lot more finessing to prove that elevators are more likely to pass a given floor on the way up than the way down (or on the way down than the way up). You have to factor in how many people use each floor, and how regularly they do so. Still, it's generally true that, if you and a friend are on different ends of a building, you will notice that the elevators are "always" traveling in a certain direction - and that direction will be opposite of the direction the direction your friend "always" sees them moving

Via The Math Behind the Numbers.