[ WP ] The Hilbert 's Hotel is a math thought experiment to understand infinity . You accidentally book a night there .

The universe is composed of indefinable and infinite sequences of hallway. Along each wall are twenty rooms, and at the end of each hallway is an intersection of never more than three walkways. Halfway along each hallway is either an elevator, or a communal bathroom. Elevators are separated by three bathrooms in each latitudinal direction. The elevators go up three-hundred and fourteen floors. On the last floor the elevator opens up into a hallway, across which is another elevator and so on. I call the universe the Hotel. 
 
 I once operated the elevators for other guests. Like many I have moved through the Hotel. My job was a constant. My arthritis now prevents me from shoving the lever and every press of the button seems to send pain up my arm and straight to my heart. 
 
 This does not dishearten me. My grave will be my room and I will turn to dust. What purpose my room will serve in the future I do not know. It may be used by others, but it too is winding down. The sheets are old. The stove barely functions. The floorboards creak. 
 
 Idealists argue that the Hotel is unending. Idealists argue that the elevators finiteness prove the opposite. Let it suffice now for me to repeat the classic dictum: The Hotel is a sphere whose exact center is any one of its rooms and whose four'final' walls are inaccessible. 
 
 The elevators move by a magnetic system that is mysterious. Originally it was hoped that the elevators held scientific and even moral truths that could be exposed with time and effort. Eventually, however, residents concluded that their details were no more or less than any other material of the Hotel. Out of this disappointment came an outpouring of rage as guests attempted to destroy the elevators. In many parts of the Hotel there are no working elevators, merely shafts. 
 
 In part that is why I retired. 
 
 Some believe that the Hotel is a mathematical necessity. We do not know what the Hotel means, but there is something in the image of the hotel that is congenial to man ’ s imagination, and thus the Hotel arises in many, probably all, universes in some form or image. 
 
 In each room there is a bathroom, a small kitchen and a bedroom. Connected to neighboring rooms are two doors, one for each adjacent room along the hallway room. According to social protocol, which has survived the centuries nearly intact, when a neighbor from another room requests to move the current resident must oblige and request lodging in the next room. That present resident then obliges and requests lodging from the next resident. So humanity travels through the universe like a centipede, taking each step no sooner than the last foot has been set down. When there is no room on one floor, they take the elevator to the next, higher floor and begin there. 
 
 The movement of people has never stopped, as far as I know. When it began and where it ends has never been known by any traveler, no matter how fecund. Guests have tried many ways to arrive at the first guest. But more on that, later. 
 
 Gravity—as we perceive it—neither increases nor decreases as we move up or down in the Hotel. These two observations spawned a series of conclusions and hypothesis. I will give no commentary on their accuracy or sincerity beyond mentioning, briefly, that they are not universally held. First, that the Hotel is in fact infinite and therefore there is no center to the Hotel. Some have gone as far as to say the Hotel is constantly expanding. Second, every possible person is present in the Hotel at any one time. 
 
 The contradiction in the first claim and second claim is bridged by the assumption: any single person ’ s permutation is also present in the Hotel. For the Hotel to be infinite there must not only be every possible person, which very well may have been reached at the inception of the Hotel, but every possibility of every possible person. To these acolytes the Hotel means that every decision they have reached and will ever reach has already been anticipated by the Hotel thousands, even millions, of years ago. They have already lived their life, with one small exception, thousands of years ago. By meditation and prayers to obscure gods they can reach their past lives, their future lives and—most of all—commune with their lives already present in the Hotel. 
 
 When it was proclaimed that the Hotel contained all lives, the first impression was one of extravagant happiness. There was no personal or societal problem whose eloquent solution did not exist in some room. Thousands of the greedy abandoned their sweet native rooms and rushed up the elevators, urged on by the vain intention of finding their opposites. Preferably their more successful opposites. These pilgrims disputed in the narrow corridors, proferred dark curses, strangled each other, flung the deceptive into the elevator shafts. 
 
 The deceptive may not be an appropriate word here. Reflect, if the only practical difference between hundreds, thousands and even millions of guests is a small change of decision, it means that the same person is reflected infinitely throughout the hotel and each reflection reflected further and further. With each person the Hotel adds, added and will add a new person in a new room to compensate for every alternate decision that a current guest makes—if guests can be talked about in any particular tense—and thereby grows larger. 
 
 If this is the case then there must be lives that have taken inexplicable and unforgivable turns because some decisions are more important than others. There are lives that have been trapped by decisions they did not make. Resentment, then, naturally, grows.
