[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.53,0:00:07.72,Default,,0000,0000,0000,,In the 1920's,
Dialogue: 0,0:00:07.72,0:00:10.21,Default,,0000,0000,0000,,the German mathematician David Hilbert
Dialogue: 0,0:00:10.21,0:00:12.46,Default,,0000,0000,0000,,devised a famous thought experiment
Dialogue: 0,0:00:12.46,0:00:14.22,Default,,0000,0000,0000,,to show us just how hard it is
Dialogue: 0,0:00:14.22,0:00:18.17,Default,,0000,0000,0000,,to wrap our minds around the concept of infinity.
Dialogue: 0,0:00:18.17,0:00:21.68,Default,,0000,0000,0000,,Imagine a hotel with an infinite number of rooms
Dialogue: 0,0:00:21.68,0:00:24.29,Default,,0000,0000,0000,,and a very hardworking night manager.
Dialogue: 0,0:00:24.29,0:00:27.55,Default,,0000,0000,0000,,One night, the Infinite Hotel is completely full,
Dialogue: 0,0:00:27.55,0:00:31.11,Default,,0000,0000,0000,,totally booked up with an infinite number of guests.
Dialogue: 0,0:00:31.11,0:00:32.42,Default,,0000,0000,0000,,A man walks into the hotel
Dialogue: 0,0:00:32.42,0:00:33.93,Default,,0000,0000,0000,,and asks for a room.
Dialogue: 0,0:00:33.93,0:00:35.47,Default,,0000,0000,0000,,Rather than turn him down,
Dialogue: 0,0:00:35.47,0:00:37.91,Default,,0000,0000,0000,,the night manager decides to make room for him.
Dialogue: 0,0:00:37.91,0:00:38.69,Default,,0000,0000,0000,,How?
Dialogue: 0,0:00:38.69,0:00:41.66,Default,,0000,0000,0000,,Easy, he asks the guest in room number 1
Dialogue: 0,0:00:41.66,0:00:43.32,Default,,0000,0000,0000,,to move to room 2,
Dialogue: 0,0:00:43.32,0:00:46.08,Default,,0000,0000,0000,,the guest in room 2 to move to room 3,
Dialogue: 0,0:00:46.08,0:00:47.16,Default,,0000,0000,0000,,and so on.
Dialogue: 0,0:00:47.16,0:00:49.86,Default,,0000,0000,0000,,Every guest moves from room number "n"
Dialogue: 0,0:00:49.86,0:00:52.20,Default,,0000,0000,0000,,to room number "n+1".
Dialogue: 0,0:00:52.20,0:00:54.41,Default,,0000,0000,0000,,Since there are an infinite number of rooms,
Dialogue: 0,0:00:54.41,0:00:57.03,Default,,0000,0000,0000,,there is a new room for each existing guest.
Dialogue: 0,0:00:57.03,0:00:59.78,Default,,0000,0000,0000,,This leaves room 1 open for the new customer.
Dialogue: 0,0:00:59.78,0:01:01.03,Default,,0000,0000,0000,,The process can be repeated
Dialogue: 0,0:01:01.03,0:01:03.54,Default,,0000,0000,0000,,for any finite number of new guests.
Dialogue: 0,0:01:03.54,0:01:05.39,Default,,0000,0000,0000,,If, say, a tour bus unloads
Dialogue: 0,0:01:05.39,0:01:07.55,Default,,0000,0000,0000,,40 new people looking for rooms,
Dialogue: 0,0:01:07.55,0:01:09.67,Default,,0000,0000,0000,,then every existing guest just moves
Dialogue: 0,0:01:09.67,0:01:11.00,Default,,0000,0000,0000,,from room number "n"
Dialogue: 0,0:01:11.00,0:01:13.66,Default,,0000,0000,0000,,to room number "n+40",
Dialogue: 0,0:01:13.66,0:01:16.79,Default,,0000,0000,0000,,thus, opening up the first 40 rooms.
Dialogue: 0,0:01:16.79,0:01:19.20,Default,,0000,0000,0000,,But now an infinitely large bus
Dialogue: 0,0:01:19.20,0:01:21.77,Default,,0000,0000,0000,,with a countedly infinite number of passengers
Dialogue: 0,0:01:21.77,0:01:23.70,Default,,0000,0000,0000,,pulls up to rent rooms.
Dialogue: 0,0:01:23.70,0:01:25.92,Default,,0000,0000,0000,,Countedly infinite is the key.
Dialogue: 0,0:01:25.92,0:01:28.22,Default,,0000,0000,0000,,Now, the infinite bus of infinite passengers
Dialogue: 0,0:01:28.22,0:01:30.54,Default,,0000,0000,0000,,perplexes the night manager at first,
Dialogue: 0,0:01:30.54,0:01:32.03,Default,,0000,0000,0000,,but he realizes there's a way
Dialogue: 0,0:01:32.03,0:01:33.37,Default,,0000,0000,0000,,to place each new person.
Dialogue: 0,0:01:33.37,0:01:34.99,Default,,0000,0000,0000,,He asks the guest in room 1
Dialogue: 0,0:01:34.99,0:01:36.42,Default,,0000,0000,0000,,to move to room 2.
Dialogue: 0,0:01:36.42,0:01:38.55,Default,,0000,0000,0000,,He then asks the guest in room 2
Dialogue: 0,0:01:38.55,0:01:40.46,Default,,0000,0000,0000,,to move to room 4,
Dialogue: 0,0:01:40.46,0:01:41.54,Default,,0000,0000,0000,,the guest in room 3
Dialogue: 0,0:01:41.54,0:01:42.83,Default,,0000,0000,0000,,to move to room 6,
Dialogue: 0,0:01:42.83,0:01:44.13,Default,,0000,0000,0000,,and so one.
Dialogue: 0,0:01:44.13,0:01:47.34,Default,,0000,0000,0000,,Each current guest moves from room number "n"
Dialogue: 0,0:01:47.34,0:01:50.53,Default,,0000,0000,0000,,to room number "2n",
Dialogue: 0,0:01:50.53,0:01:54.08,Default,,0000,0000,0000,,filling up only the infinite even-numbered rooms.
Dialogue: 0,0:01:54.08,0:01:55.95,Default,,0000,0000,0000,,By doing this, he has now emptied
Dialogue: 0,0:01:55.95,0:01:58.89,Default,,0000,0000,0000,,all of the infinitely many odd-numbered rooms,
Dialogue: 0,0:01:58.89,0:02:00.31,Default,,0000,0000,0000,,which are then taken by the people
Dialogue: 0,0:02:00.31,0:02:02.83,Default,,0000,0000,0000,,filing off the infinite bus.
Dialogue: 0,0:02:02.83,0:02:05.11,Default,,0000,0000,0000,,Everyone's happy and the hotel's business
Dialogue: 0,0:02:05.11,0:02:06.90,Default,,0000,0000,0000,,is booming more than ever.
Dialogue: 0,0:02:06.90,0:02:08.40,Default,,0000,0000,0000,,Well, actually, it is booming
Dialogue: 0,0:02:08.40,0:02:10.44,Default,,0000,0000,0000,,exactly the same amount as ever,
Dialogue: 0,0:02:10.44,0:02:12.92,Default,,0000,0000,0000,,banking an infinite number of dollars a night.
Dialogue: 0,0:02:13.72,0:02:16.38,Default,,0000,0000,0000,,Word spreads about this incredible hotel.
Dialogue: 0,0:02:16.38,0:02:18.57,Default,,0000,0000,0000,,People pour in from far and wide.
Dialogue: 0,0:02:18.57,0:02:20.87,Default,,0000,0000,0000,,One night, the unthinkable happens.
Dialogue: 0,0:02:20.87,0:02:23.43,Default,,0000,0000,0000,,The night manager looks outside
Dialogue: 0,0:02:23.43,0:02:25.06,Default,,0000,0000,0000,,and sees an infinite line
Dialogue: 0,0:02:25.06,0:02:27.54,Default,,0000,0000,0000,,of infinitely large buses,
Dialogue: 0,0:02:27.54,0:02:30.35,Default,,0000,0000,0000,,each with a countedly infinite number of passengers.
Dialogue: 0,0:02:30.35,0:02:31.41,Default,,0000,0000,0000,,What can he do?
Dialogue: 0,0:02:31.41,0:02:32.91,Default,,0000,0000,0000,,If he cannot find rooms for them,
Dialogue: 0,0:02:32.91,0:02:34.23,Default,,0000,0000,0000,,the hotel will lose out
Dialogue: 0,0:02:34.23,0:02:35.98,Default,,0000,0000,0000,,on an infinite amount of money,
Dialogue: 0,0:02:35.98,0:02:37.98,Default,,0000,0000,0000,,and he will surely lose his job.
Dialogue: 0,0:02:37.98,0:02:39.08,Default,,0000,0000,0000,,Luckily, he remembers
Dialogue: 0,0:02:39.08,0:02:41.81,Default,,0000,0000,0000,,that around the year 300 B.C.E.,
Dialogue: 0,0:02:41.81,0:02:44.75,Default,,0000,0000,0000,,Euclid proved that there is an infinite quantity
Dialogue: 0,0:02:44.75,0:02:47.22,Default,,0000,0000,0000,,of prime numbers.
Dialogue: 0,0:02:47.22,0:02:49.68,Default,,0000,0000,0000,,So, to accomplish this seemingly impossible task
Dialogue: 0,0:02:49.68,0:02:51.00,Default,,0000,0000,0000,,of finding infinite beds
Dialogue: 0,0:02:51.00,0:02:52.31,Default,,0000,0000,0000,,for infinite buses
Dialogue: 0,0:02:52.31,0:02:54.32,Default,,0000,0000,0000,,of infinite weary travelers,
Dialogue: 0,0:02:54.32,0:02:56.61,Default,,0000,0000,0000,,the night manager assigns every current guest
Dialogue: 0,0:02:56.61,0:02:59.07,Default,,0000,0000,0000,,to the first prime number, 2,
Dialogue: 0,0:02:59.07,0:03:01.89,Default,,0000,0000,0000,,raised to the power of their current room number.
Dialogue: 0,0:03:01.89,0:03:04.56,Default,,0000,0000,0000,,So, the current occupant of room number 7
Dialogue: 0,0:03:04.56,0:03:07.56,Default,,0000,0000,0000,,goes to room number 2^7,
Dialogue: 0,0:03:07.56,0:03:09.93,Default,,0000,0000,0000,,which is room 128.
Dialogue: 0,0:03:09.93,0:03:11.64,Default,,0000,0000,0000,,The night manager then takes the people
Dialogue: 0,0:03:11.64,0:03:13.78,Default,,0000,0000,0000,,on the first of the infinite buses
Dialogue: 0,0:03:13.78,0:03:15.83,Default,,0000,0000,0000,,and assigns them to the room number
Dialogue: 0,0:03:15.83,0:03:18.32,Default,,0000,0000,0000,,of the next prime, 3,
Dialogue: 0,0:03:18.32,0:03:21.75,Default,,0000,0000,0000,,raised to the power of their seat number on the bus.
Dialogue: 0,0:03:21.75,0:03:25.28,Default,,0000,0000,0000,,So, the person in seat number 7 on the first bus
Dialogue: 0,0:03:25.28,0:03:28.38,Default,,0000,0000,0000,,goes to room number 3^7
Dialogue: 0,0:03:28.38,0:03:31.63,Default,,0000,0000,0000,,or room number 2,187.
Dialogue: 0,0:03:31.63,0:03:34.09,Default,,0000,0000,0000,,This continues for all of the first bus.
Dialogue: 0,0:03:34.09,0:03:35.76,Default,,0000,0000,0000,,The passengers on the second bus
Dialogue: 0,0:03:35.76,0:03:39.43,Default,,0000,0000,0000,,are assigned powers of the next prime, 5.
Dialogue: 0,0:03:39.43,0:03:41.52,Default,,0000,0000,0000,,The following bus, powers of 7.
Dialogue: 0,0:03:41.52,0:03:42.94,Default,,0000,0000,0000,,Each bus follows:
Dialogue: 0,0:03:42.94,0:03:43.77,Default,,0000,0000,0000,,powers of 11,
Dialogue: 0,0:03:43.77,0:03:44.77,Default,,0000,0000,0000,,powers of 13,
Dialogue: 0,0:03:44.77,0:03:47.19,Default,,0000,0000,0000,,powers of 17, etc.
Dialogue: 0,0:03:47.19,0:03:48.32,Default,,0000,0000,0000,,Since each of these numbers
Dialogue: 0,0:03:48.32,0:03:50.99,Default,,0000,0000,0000,,only has 1 and the natural number powers
Dialogue: 0,0:03:50.99,0:03:53.24,Default,,0000,0000,0000,,of their prime number base as factors,
Dialogue: 0,0:03:53.24,0:03:55.41,Default,,0000,0000,0000,,there are no overlapping room numbers.
Dialogue: 0,0:03:55.41,0:03:58.36,Default,,0000,0000,0000,,All the buses' passengers fan out into rooms
Dialogue: 0,0:03:58.36,0:04:00.87,Default,,0000,0000,0000,,using unique room assignment schemes
Dialogue: 0,0:04:00.87,0:04:03.51,Default,,0000,0000,0000,,based on unique prime numbers.
Dialogue: 0,0:04:03.51,0:04:05.58,Default,,0000,0000,0000,,In this way, the night manager can accomodate
Dialogue: 0,0:04:05.58,0:04:07.87,Default,,0000,0000,0000,,every passenger on every bus.
Dialogue: 0,0:04:07.87,0:04:10.81,Default,,0000,0000,0000,,Although, there will be many rooms that go unfilled,
Dialogue: 0,0:04:10.81,0:04:11.90,Default,,0000,0000,0000,,like room 6
Dialogue: 0,0:04:11.90,0:04:15.12,Default,,0000,0000,0000,,since 6 is not a power of any prime number.
Dialogue: 0,0:04:15.12,0:04:17.54,Default,,0000,0000,0000,,Luckily, his bosses weren't very good in math,
Dialogue: 0,0:04:17.54,0:04:19.18,Default,,0000,0000,0000,,so his job is safe.
Dialogue: 0,0:04:19.18,0:04:22.03,Default,,0000,0000,0000,,The night manager's strategies are only possible
Dialogue: 0,0:04:22.03,0:04:23.98,Default,,0000,0000,0000,,because while the Infinite Hotel
Dialogue: 0,0:04:23.98,0:04:26.20,Default,,0000,0000,0000,,is certainly a logistical nightmare,
Dialogue: 0,0:04:26.20,0:04:29.98,Default,,0000,0000,0000,,it only deals with the lowest level of infinity,
Dialogue: 0,0:04:29.98,0:04:31.75,Default,,0000,0000,0000,,mainly, the countable infinity
Dialogue: 0,0:04:31.75,0:04:33.54,Default,,0000,0000,0000,,of the natural numbers,
Dialogue: 0,0:04:33.54,0:04:36.62,Default,,0000,0000,0000,,1, 2, 3, 4, and so on.
Dialogue: 0,0:04:36.62,0:04:40.54,Default,,0000,0000,0000,,Georg Cantor called this level of infinity aleph-zero.
Dialogue: 0,0:04:40.54,0:04:42.66,Default,,0000,0000,0000,,We use natural numbers for the room numbers
Dialogue: 0,0:04:42.66,0:04:44.79,Default,,0000,0000,0000,,as well as the seat numbers on the buses.
Dialogue: 0,0:04:45.63,0:04:48.18,Default,,0000,0000,0000,,If we were dealing with higher orders of infinity,
Dialogue: 0,0:04:48.18,0:04:49.73,Default,,0000,0000,0000,,such as that of the real numbers,
Dialogue: 0,0:04:49.73,0:04:51.10,Default,,0000,0000,0000,,these structured strategies
Dialogue: 0,0:04:51.10,0:04:52.56,Default,,0000,0000,0000,,would no longer be possible
Dialogue: 0,0:04:52.56,0:04:53.85,Default,,0000,0000,0000,,as we have no way
Dialogue: 0,0:04:53.85,0:04:56.57,Default,,0000,0000,0000,,to systematically include every number.
Dialogue: 0,0:04:56.57,0:04:58.92,Default,,0000,0000,0000,,The Real Number Infinite Hotel has
Dialogue: 0,0:04:58.92,0:05:00.93,Default,,0000,0000,0000,,negative number rooms in the basement,
Dialogue: 0,0:05:00.93,0:05:02.39,Default,,0000,0000,0000,,fractional rooms,
Dialogue: 0,0:05:02.39,0:05:04.51,Default,,0000,0000,0000,,so the guy in room 1/2 always suspects
Dialogue: 0,0:05:04.51,0:05:07.20,Default,,0000,0000,0000,,he has less room than the guy in room 1.
Dialogue: 0,0:05:07.20,0:05:10.33,Default,,0000,0000,0000,,Square root rooms, like room radical 2
Dialogue: 0,0:05:10.33,0:05:11.46,Default,,0000,0000,0000,,and room pi,
Dialogue: 0,0:05:11.46,0:05:14.35,Default,,0000,0000,0000,,where the guests expect free dessert.
Dialogue: 0,0:05:14.35,0:05:15.87,Default,,0000,0000,0000,,What self-respecting night manager
Dialogue: 0,0:05:15.87,0:05:17.17,Default,,0000,0000,0000,,would ever want to work there
Dialogue: 0,0:05:17.17,0:05:19.49,Default,,0000,0000,0000,,even for an infinite salary?
Dialogue: 0,0:05:19.49,0:05:20.80,Default,,0000,0000,0000,,But over at Hilbert's Infinite Hotel,
Dialogue: 0,0:05:20.80,0:05:22.26,Default,,0000,0000,0000,,where there's never any vacancy
Dialogue: 0,0:05:22.26,0:05:23.88,Default,,0000,0000,0000,,and always room for more,
Dialogue: 0,0:05:23.88,0:05:26.95,Default,,0000,0000,0000,,the scenarios faced by the ever diligent
Dialogue: 0,0:05:26.95,0:05:28.72,Default,,0000,0000,0000,,and maybe too hospitable night manager
Dialogue: 0,0:05:28.72,0:05:29.80,Default,,0000,0000,0000,,serve to remind us
Dialogue: 0,0:05:29.80,0:05:31.15,Default,,0000,0000,0000,,of just how hard it is
Dialogue: 0,0:05:31.15,0:05:33.32,Default,,0000,0000,0000,,for our relatively finite minds
Dialogue: 0,0:05:33.32,0:05:37.09,Default,,0000,0000,0000,,to grasp a concept as large as infinity.
Dialogue: 0,0:05:37.09,0:05:38.70,Default,,0000,0000,0000,,Maybe you can help tackle these problems
Dialogue: 0,0:05:38.70,0:05:40.43,Default,,0000,0000,0000,,after a good night's sleep.
Dialogue: 0,0:05:40.43,0:05:42.30,Default,,0000,0000,0000,,But honestly, we might need you
Dialogue: 0,0:05:42.30,0:05:44.70,Default,,0000,0000,0000,,to change rooms at 2 a.m.