1 00:00:03,120 --> 00:00:06,000 Speaker 1: Welcome to Stuff to Blow Your Mind from how Stuff 2 00:00:06,000 --> 00:00:13,119 Speaker 1: Works dot com. Hey, you're welcome to Stuff to Blow 3 00:00:13,160 --> 00:00:15,800 Speaker 1: your Mind. My name is Robert Lamb and um Julie Douglas, 4 00:00:15,840 --> 00:00:18,479 Speaker 1: and this is our second episode on infinity. If you 5 00:00:18,520 --> 00:00:20,560 Speaker 1: missed the first one, if you recommend you go back 6 00:00:20,600 --> 00:00:22,160 Speaker 1: and listen to that one. But we are going to 7 00:00:22,239 --> 00:00:24,119 Speaker 1: do a little recap here in case any of the 8 00:00:24,160 --> 00:00:28,000 Speaker 1: information has fallen out of your head in the time being. Yeah, 9 00:00:28,040 --> 00:00:31,080 Speaker 1: so let's talk about what infinity is and what it 10 00:00:31,160 --> 00:00:34,440 Speaker 1: is not, because that's our nice little baseline there. It 11 00:00:34,600 --> 00:00:37,680 Speaker 1: is not a real number, because we discussed before. You 12 00:00:37,720 --> 00:00:40,599 Speaker 1: can't say that infinity is X number. You can't write 13 00:00:40,640 --> 00:00:42,640 Speaker 1: it on a check. You can use a symbol, I guess, 14 00:00:42,640 --> 00:00:46,240 Speaker 1: but good luck cashing it. Uh, why have I never 15 00:00:46,320 --> 00:00:50,600 Speaker 1: done that? Uh? It cannot be measured. Of course, that 16 00:00:50,840 --> 00:00:52,880 Speaker 1: is tied back to it not being a real number. 17 00:00:53,360 --> 00:00:56,960 Speaker 1: It's not something that's growing, it's not doing anything. It's 18 00:00:57,000 --> 00:01:02,000 Speaker 1: the ultimate Zen concept. It just is yes. And of 19 00:01:02,000 --> 00:01:06,479 Speaker 1: course this has been an important topic to philosophers, uh, theologians, 20 00:01:07,000 --> 00:01:09,840 Speaker 1: great thinkers throughout time, and that's one of the primary 21 00:01:09,840 --> 00:01:13,080 Speaker 1: things we discussed in our last episode because Ultimately you 22 00:01:13,120 --> 00:01:17,119 Speaker 1: get into discussions about the boundless, about the limits of things. 23 00:01:17,200 --> 00:01:21,000 Speaker 1: I mean, you're dealing with everything from the basic human experience. 24 00:01:21,720 --> 00:01:23,480 Speaker 1: You know, how do I deal with the fact that 25 00:01:23,680 --> 00:01:26,120 Speaker 1: my life only stretches on until so so long? How 26 00:01:26,160 --> 00:01:27,480 Speaker 1: do I deal with the fact that I can only 27 00:01:27,480 --> 00:01:31,120 Speaker 1: perceive the universe with a certain bubble of perception. And 28 00:01:31,120 --> 00:01:34,039 Speaker 1: then you start imagining a god and you're trying to 29 00:01:34,160 --> 00:01:37,280 Speaker 1: figure out how that works. Is God is God? Infinite? 30 00:01:37,400 --> 00:01:41,160 Speaker 1: Is God physically infinite? Is God infinite in quality as 31 00:01:41,160 --> 00:01:44,640 Speaker 1: opposed to quantity. It's to say the biggest idea is 32 00:01:44,680 --> 00:01:47,440 Speaker 1: it is the the the infinite idea that the humanity 33 00:01:47,520 --> 00:01:51,000 Speaker 1: has tackled with over the ages. Yeah, and we talked 34 00:01:51,040 --> 00:01:54,440 Speaker 1: about George Tvorski writing for Ion nine, and he used 35 00:01:54,520 --> 00:01:58,320 Speaker 1: the chess board to illustrate this idea, saying that all 36 00:01:58,360 --> 00:02:01,800 Speaker 1: the other pieces having number assigned to it except for 37 00:02:01,840 --> 00:02:07,840 Speaker 1: the king, whose number value is infinite. Yeah, that chess 38 00:02:07,920 --> 00:02:10,760 Speaker 1: is It is interesting because we mentioned before, you have 39 00:02:10,840 --> 00:02:14,400 Speaker 1: a finite number of playable games for chess, and then 40 00:02:14,480 --> 00:02:17,760 Speaker 1: you then you have this king that has an infinite 41 00:02:18,120 --> 00:02:21,119 Speaker 1: importance within the game, So you have two different types 42 00:02:21,160 --> 00:02:23,480 Speaker 1: of infinity going on there. Yeah, you lose, you lose 43 00:02:23,520 --> 00:02:26,200 Speaker 1: the king, You lose the game because zer or some 44 00:02:26,240 --> 00:02:27,960 Speaker 1: game if you get rid of the king, and so 45 00:02:28,000 --> 00:02:30,639 Speaker 1: again it ties back to this whole idea about eternity 46 00:02:30,680 --> 00:02:35,320 Speaker 1: even consciousness uh embedded in there with infinity. So of 47 00:02:35,360 --> 00:02:40,079 Speaker 1: course it becomes with this great uh media area for 48 00:02:40,240 --> 00:02:44,280 Speaker 1: philosophers to really tussle with, because it's got the afterlife there, 49 00:02:44,280 --> 00:02:47,720 Speaker 1: it's got the idea and the question of God, and 50 00:02:47,840 --> 00:02:51,040 Speaker 1: by its very nature, it's an idea that we cannot 51 00:02:51,080 --> 00:02:55,160 Speaker 1: fully contain and we cannot really completely grasp it, and 52 00:02:55,240 --> 00:02:57,880 Speaker 1: yet we try to and so did philosophers as we 53 00:02:57,919 --> 00:03:00,760 Speaker 1: discussed the last episode, and they used to try to 54 00:03:00,880 --> 00:03:03,440 Speaker 1: prove this out or try to make their arguments even 55 00:03:03,480 --> 00:03:06,320 Speaker 1: more persuasive. So today we're gonna look at some examples 56 00:03:06,440 --> 00:03:10,079 Speaker 1: in math and physics to see how well we can 57 00:03:10,320 --> 00:03:14,959 Speaker 1: contain the idea of infinity and reach some sort of meaning, 58 00:03:15,440 --> 00:03:17,800 Speaker 1: which we already talked about as sort of impossible, like 59 00:03:18,000 --> 00:03:22,720 Speaker 1: meaning is infinite in itself for various reasons. To just 60 00:03:22,760 --> 00:03:27,480 Speaker 1: to recap mathematics and infinity, you voluencountered numbers like twelve 61 00:03:27,560 --> 00:03:32,520 Speaker 1: point one to nine, eight, seven, six, five, three, two, one, zero, one, 62 00:03:32,680 --> 00:03:34,960 Speaker 1: just on on and on forever. You just have to 63 00:03:35,040 --> 00:03:37,920 Speaker 1: stop counting those numbers. After a while, you have to 64 00:03:37,920 --> 00:03:41,680 Speaker 1: stop recording them because it becomes a pointless exercise. You 65 00:03:41,800 --> 00:03:44,880 Speaker 1: just round up, right. Is that because humans are finite 66 00:03:45,000 --> 00:03:49,680 Speaker 1: and we kind of continue to count infinitely. Yeah, that's 67 00:03:49,720 --> 00:03:53,560 Speaker 1: that's Uh, that's kind of the big topic of discussion here. 68 00:03:53,760 --> 00:03:57,160 Speaker 1: And so you kind of have two schools of thought 69 00:03:57,200 --> 00:04:00,960 Speaker 1: in mathematics, right when when it comes to to struggling 70 00:04:01,040 --> 00:04:02,880 Speaker 1: with the infinite, and it kind of comes down to 71 00:04:02,920 --> 00:04:06,760 Speaker 1: some of the core arguments with mathematics itself. So is 72 00:04:06,760 --> 00:04:11,360 Speaker 1: is mathematical infinity? Is this a mere human creation, an 73 00:04:11,360 --> 00:04:14,200 Speaker 1: extrapolation into the world where there's no truth? Or does 74 00:04:14,280 --> 00:04:18,200 Speaker 1: mathematical infinity actually exist? Well, this comes down to the 75 00:04:18,279 --> 00:04:21,839 Speaker 1: question of God to rite. There are some observable things 76 00:04:21,920 --> 00:04:26,280 Speaker 1: of how infinity works in mathematics, um, and I say observable, 77 00:04:26,279 --> 00:04:30,039 Speaker 1: but you can it's just as we discussed in your example. 78 00:04:30,120 --> 00:04:32,919 Speaker 1: There numbers can go on and on forever, and we 79 00:04:32,960 --> 00:04:37,840 Speaker 1: have finite lives. Uh, we can't see God in Therefore, 80 00:04:38,000 --> 00:04:40,960 Speaker 1: some people would say he or she or it does 81 00:04:41,000 --> 00:04:44,080 Speaker 1: not exist. So you're grappling with some of the same 82 00:04:44,120 --> 00:04:47,920 Speaker 1: concepts in math and in infinity. So if you were 83 00:04:47,960 --> 00:04:52,600 Speaker 1: to ask the constructivists or the institutionists, they would say 84 00:04:52,640 --> 00:04:55,560 Speaker 1: that classical mathematics, well, they deal with the sort of 85 00:04:55,560 --> 00:04:58,640 Speaker 1: math that God would do. An infinite God he can 86 00:04:58,680 --> 00:05:02,599 Speaker 1: tackle with infinite numbers. Uh, and and and the idea 87 00:05:02,640 --> 00:05:05,840 Speaker 1: of a mathematical infinity. But we are humans, we are finite, 88 00:05:05,880 --> 00:05:09,280 Speaker 1: and we would rather focus with human mathematics with finite 89 00:05:09,440 --> 00:05:12,400 Speaker 1: numbers because that ultimately is what relates to what we do. 90 00:05:12,440 --> 00:05:15,000 Speaker 1: You know what I hear with that, my brain hurts. 91 00:05:15,080 --> 00:05:18,479 Speaker 1: I'll just I'll just leave it to God. He or 92 00:05:18,520 --> 00:05:20,560 Speaker 1: she or it can deal with it. Yeah, I mean, 93 00:05:20,560 --> 00:05:24,719 Speaker 1: it's kind of the idea that infinity is an interesting 94 00:05:24,720 --> 00:05:27,720 Speaker 1: topic to tackle with as an abstraction, but does it 95 00:05:27,839 --> 00:05:30,680 Speaker 1: really relate to the work that I'm doing here, the 96 00:05:30,720 --> 00:05:33,880 Speaker 1: work that mathematics needs to do in the world. And 97 00:05:33,880 --> 00:05:36,800 Speaker 1: then they're the formalist Now. Formalism is a theory that 98 00:05:36,839 --> 00:05:39,600 Speaker 1: holds that statements of mathematics and logic can be thought 99 00:05:39,600 --> 00:05:42,479 Speaker 1: of as statements about the consequences of certain certain string 100 00:05:42,520 --> 00:05:46,839 Speaker 1: manipulation rules. Um systematic formulation of the concept of mathematical 101 00:05:46,880 --> 00:05:50,400 Speaker 1: formulism arose directly as a reaction to the paradox discovered 102 00:05:50,440 --> 00:05:54,120 Speaker 1: within set theory, which studies the concept of infinity. According 103 00:05:54,120 --> 00:05:59,200 Speaker 1: to twenty century mathematician Abraham Robinson, infinite totalities do not exist, 104 00:05:59,320 --> 00:06:03,559 Speaker 1: either really or ideally. Any mentioned of infinite totalities is meaningless. Still, 105 00:06:03,600 --> 00:06:06,960 Speaker 1: the business of mathematics must continue as if infinite totalities 106 00:06:07,000 --> 00:06:10,240 Speaker 1: actually do exist. Right, we said, there are a couple 107 00:06:10,240 --> 00:06:12,480 Speaker 1: of things that we're talking about. A system here in 108 00:06:12,480 --> 00:06:16,200 Speaker 1: this idea that you can again capture infinity. You can 109 00:06:16,320 --> 00:06:21,760 Speaker 1: define it um and then set theory, which is something 110 00:06:21,920 --> 00:06:25,440 Speaker 1: that a man named Georg Cantor came up with. And 111 00:06:25,480 --> 00:06:29,120 Speaker 1: he's sort of the rabble rouser here. According to Natalie 112 00:06:29,200 --> 00:06:32,760 Speaker 1: while cover writing for Quantum magazine, infinity was boxed and 113 00:06:32,839 --> 00:06:35,960 Speaker 1: sold to the mathematical community in the late night concentury 114 00:06:36,000 --> 00:06:40,360 Speaker 1: by the German mathematician Georg Cantor, who invented a branch 115 00:06:40,440 --> 00:06:45,039 Speaker 1: of mathematics dealing with sets collections of elements that ranged 116 00:06:45,160 --> 00:06:48,560 Speaker 1: from empty the equivalent of the number zero to infinite. 117 00:06:49,000 --> 00:06:52,200 Speaker 1: So Cantra stepped in there really and began to define 118 00:06:52,320 --> 00:06:57,520 Speaker 1: infinity in a much more specific way. Yeah, and uh 119 00:06:57,560 --> 00:06:59,840 Speaker 1: he was he was a one of these individuals who 120 00:06:59,880 --> 00:07:03,120 Speaker 1: was hated as well as love, depending on who you're asking, 121 00:07:03,200 --> 00:07:06,520 Speaker 1: because he was bringing up some really mind blowing, disturbing 122 00:07:06,760 --> 00:07:13,320 Speaker 1: takes on infinity. Yeah. Natalie Walquiver says that other mathematicians 123 00:07:13,360 --> 00:07:18,680 Speaker 1: initially despise what they called this mess of infinities. And 124 00:07:18,680 --> 00:07:21,200 Speaker 1: we'll talk more about this because it's largely due to 125 00:07:21,280 --> 00:07:24,760 Speaker 1: his ideas of set theory, and one of his colleagues 126 00:07:24,880 --> 00:07:28,600 Speaker 1: called them a grave disease. Another called him a corrupter 127 00:07:28,960 --> 00:07:33,120 Speaker 1: of you. Uh. Sadly, he was so vilified that he 128 00:07:33,080 --> 00:07:37,600 Speaker 1: actually um fill into a lifelong depression after that. Um. 129 00:07:37,640 --> 00:07:39,920 Speaker 1: But I think it tells you how radical some of 130 00:07:39,960 --> 00:07:43,040 Speaker 1: these ideas were at the time and still are really, 131 00:07:43,800 --> 00:07:46,680 Speaker 1: because what it does is it just sets minds ablaze 132 00:07:47,200 --> 00:07:52,160 Speaker 1: as to what what reality is and isn't. Essentially, Yeah, 133 00:07:52,160 --> 00:07:54,000 Speaker 1: I mean, one of the core concepts to come out 134 00:07:54,000 --> 00:07:56,840 Speaker 1: of it is that there are different kinds of infinity 135 00:07:57,000 --> 00:07:59,800 Speaker 1: and some are bigger than others. Well, that that's thinking 136 00:07:59,840 --> 00:08:01,760 Speaker 1: for a second. Yeah, let me let's get into the 137 00:08:01,760 --> 00:08:05,000 Speaker 1: math sweats here. I'm having the math sweats right now. Uh. 138 00:08:05,080 --> 00:08:11,600 Speaker 1: Set theory is essentially a useful language for describing mathematical objects. 139 00:08:11,720 --> 00:08:14,600 Speaker 1: And what we're talking about is a nine item list 140 00:08:14,680 --> 00:08:18,600 Speaker 1: of rules that Cantor came up with called Zermelo Frankel 141 00:08:18,720 --> 00:08:21,880 Speaker 1: set theory with the axiom of choice or the z 142 00:08:22,200 --> 00:08:26,240 Speaker 1: f C, established and widely adopted in math by the 143 00:08:26,320 --> 00:08:30,320 Speaker 1: nineteen twenties. Okay Um. One of the axioms says that 144 00:08:30,400 --> 00:08:34,120 Speaker 1: two sets are equal if they contain the same elements. 145 00:08:34,800 --> 00:08:38,520 Speaker 1: Another simply asserts that infinite sets exist. So you can 146 00:08:38,559 --> 00:08:41,280 Speaker 1: have these infinite sets that are one to one equal 147 00:08:41,280 --> 00:08:43,600 Speaker 1: to each other, and you have them going on forever 148 00:08:43,640 --> 00:08:45,880 Speaker 1: and ever and ever and ever. And Cantor showed that 149 00:08:45,920 --> 00:08:48,640 Speaker 1: for any infinite set, forming a new set made of 150 00:08:48,679 --> 00:08:52,280 Speaker 1: all the subsets of the original sets represents a bigger 151 00:08:52,440 --> 00:08:57,360 Speaker 1: infinity than that original set. So once you have one infinity, 152 00:08:57,400 --> 00:08:59,480 Speaker 1: you can always make a bigger one by creating a 153 00:08:59,520 --> 00:09:02,400 Speaker 1: subset the original set, and then an even bigger one 154 00:09:02,440 --> 00:09:04,320 Speaker 1: by making a set of all the subsets, and so 155 00:09:04,400 --> 00:09:07,000 Speaker 1: on and so forth. And there are an infinite amount 156 00:09:07,040 --> 00:09:10,840 Speaker 1: of infinities in different sizes. And he also proved doubt 157 00:09:11,040 --> 00:09:13,360 Speaker 1: that an infinite set of even numbers like two, four, 158 00:09:13,400 --> 00:09:15,560 Speaker 1: or six could be put in that one to one 159 00:09:15,559 --> 00:09:19,880 Speaker 1: correspondence with all counting numbers like one to three. So 160 00:09:20,080 --> 00:09:22,760 Speaker 1: that came to this idea that there are as many 161 00:09:22,840 --> 00:09:27,520 Speaker 1: evens as there are odds and evens in an infinite set. 162 00:09:28,000 --> 00:09:32,760 Speaker 1: There's one problem with this, though, real numbers, yes, like 163 00:09:32,840 --> 00:09:34,840 Speaker 1: the one that you talked about earlier. You know that 164 00:09:34,920 --> 00:09:38,000 Speaker 1: for example point zero zero zero one or pie right 165 00:09:38,040 --> 00:09:39,719 Speaker 1: three point one four or so on and so forth, 166 00:09:39,760 --> 00:09:41,960 Speaker 1: blah blah blah blah. They go on for an ever 167 00:09:42,160 --> 00:09:45,640 Speaker 1: and they are uncountable, and they don't correspond in a 168 00:09:45,679 --> 00:09:48,040 Speaker 1: one to one fashion with counting numbers. But hold on 169 00:09:48,080 --> 00:09:50,080 Speaker 1: because we will get back to that. If that didn't 170 00:09:50,080 --> 00:09:54,400 Speaker 1: thinking completely. Will return to the unccountability of real numbers 171 00:09:54,640 --> 00:09:57,520 Speaker 1: in a minute, once we have a structure in which 172 00:09:57,559 --> 00:09:59,800 Speaker 1: to house them. All right, I am going to dab 173 00:10:00,080 --> 00:10:03,920 Speaker 1: at the infinite number of sweat molecules dripping off of 174 00:10:03,960 --> 00:10:06,520 Speaker 1: me right now. Uh No, it's not too bad actually, 175 00:10:06,840 --> 00:10:09,040 Speaker 1: Uh And let's take a break. When we get back, 176 00:10:09,559 --> 00:10:19,360 Speaker 1: you'll talk more about the infinite hotel. If you're out 177 00:10:19,360 --> 00:10:21,280 Speaker 1: there and you're thinking, I don't know what they're talking 178 00:10:21,320 --> 00:10:23,640 Speaker 1: about there, they're losing me. I'm sinking beneath the waters 179 00:10:23,720 --> 00:10:26,120 Speaker 1: here in the It is the in the deep end 180 00:10:26,280 --> 00:10:32,679 Speaker 1: of the mathematical, philosophical, theological, physical pool. I need help, 181 00:10:32,720 --> 00:10:35,079 Speaker 1: while we need help to for the love of infinity, 182 00:10:35,120 --> 00:10:37,920 Speaker 1: give me an example. Yes, we do have, We do 183 00:10:37,960 --> 00:10:40,680 Speaker 1: have an example. We have a flotation device. And it 184 00:10:40,760 --> 00:10:43,120 Speaker 1: is a thought experiment, because the thought of experiments, as 185 00:10:43,160 --> 00:10:47,320 Speaker 1: always they can take some very difficult to grasp ideas 186 00:10:47,360 --> 00:10:51,960 Speaker 1: and concepts and put them into into a metaphorical form 187 00:10:52,000 --> 00:10:55,160 Speaker 1: that we can latch onto and then and then actually 188 00:10:55,160 --> 00:10:59,319 Speaker 1: explore the concept a little more easily and sometimes a 189 00:10:59,360 --> 00:11:02,520 Speaker 1: little a little deeper. Right, And what could be more 190 00:11:03,320 --> 00:11:06,840 Speaker 1: of a form inaccessible than a building, which is essentially 191 00:11:06,880 --> 00:11:10,200 Speaker 1: what we're talking about. Um, this is an infinite building, 192 00:11:10,240 --> 00:11:13,760 Speaker 1: an infinite hotel. And this was created by German mathematician 193 00:11:13,840 --> 00:11:17,800 Speaker 1: David Hilbert who was obsessed with cantors work and and 194 00:11:17,920 --> 00:11:20,880 Speaker 1: came up with us little ditty to try to explain 195 00:11:20,920 --> 00:11:23,920 Speaker 1: a hotel with an infinite number of rooms. All right, 196 00:11:24,160 --> 00:11:26,520 Speaker 1: it's so it's a hotel, infinite number of rooms? How 197 00:11:26,559 --> 00:11:28,440 Speaker 1: many how many rooms? Does it have to like an 198 00:11:28,480 --> 00:11:33,560 Speaker 1: infinite amount? Oh but accountable infinite amount, which is going 199 00:11:33,600 --> 00:11:35,520 Speaker 1: to turn out to be important. All right, So let's 200 00:11:35,559 --> 00:11:38,440 Speaker 1: say just to just to roll out the basic entry 201 00:11:38,520 --> 00:11:42,000 Speaker 1: level portion of the thought experiment. I show up to 202 00:11:42,160 --> 00:11:45,640 Speaker 1: the Infinity Hotel, all right, and and I need a 203 00:11:45,720 --> 00:11:48,439 Speaker 1: room for the night. I know there's a convention in town. Uh, 204 00:11:48,559 --> 00:11:52,439 Speaker 1: the local set theory convention maybe, and uh, and I 205 00:11:52,640 --> 00:11:54,120 Speaker 1: I know that all the hotels are booked, but I 206 00:11:54,120 --> 00:11:56,800 Speaker 1: really need a room. So the Infinity Hotel sounds like 207 00:11:56,800 --> 00:11:59,080 Speaker 1: a good place to go, all right, So let me 208 00:11:59,559 --> 00:12:04,480 Speaker 1: a my jaunty little manager's bellhop cap here. What I 209 00:12:04,520 --> 00:12:07,160 Speaker 1: am going to do is, I'm going to ask the 210 00:12:07,240 --> 00:12:10,120 Speaker 1: guests in room do you have vacancy? Always? We have 211 00:12:10,160 --> 00:12:12,920 Speaker 1: an infinite amount of rooms. Okay, I see a lot 212 00:12:12,920 --> 00:12:15,839 Speaker 1: of cars in the parking lot. Hold up, okay, just 213 00:12:16,840 --> 00:12:19,040 Speaker 1: look at a magazine or something. We'll figure this out. 214 00:12:19,160 --> 00:12:21,280 Speaker 1: I'm going to ask the guests in room one to 215 00:12:21,480 --> 00:12:24,480 Speaker 1: move to room two, and then the guests in room 216 00:12:24,520 --> 00:12:27,440 Speaker 1: two to move to room three, and so on and 217 00:12:27,480 --> 00:12:32,600 Speaker 1: so forth. Every guest moves to room N plus one. 218 00:12:33,240 --> 00:12:36,080 Speaker 1: And since there are an infinite amount of rooms here, 219 00:12:36,640 --> 00:12:39,280 Speaker 1: then there's room for every guest to move into a 220 00:12:39,320 --> 00:12:41,920 Speaker 1: different room. So you're saying that even though they're already 221 00:12:42,040 --> 00:12:46,600 Speaker 1: infinite guests at the infinity hotel. Occupying the infinite rooms, 222 00:12:46,880 --> 00:12:49,840 Speaker 1: you can still make everyone move over one room and 223 00:12:49,920 --> 00:12:53,040 Speaker 1: thus open up a single room for me to stay 224 00:12:53,040 --> 00:12:56,360 Speaker 1: in this evening. You, a whole person, a whole number, 225 00:12:56,720 --> 00:13:00,320 Speaker 1: a natural person, a natural number, may and are into 226 00:13:00,320 --> 00:13:03,160 Speaker 1: this hotel in fact, and if forty other people want 227 00:13:03,200 --> 00:13:05,880 Speaker 1: to join you, they can, I mean not in your room. Obviously, 228 00:13:05,920 --> 00:13:07,480 Speaker 1: you don't want to sleep with forty other people in 229 00:13:07,480 --> 00:13:10,160 Speaker 1: your room. But forty other people would like to get 230 00:13:10,200 --> 00:13:13,760 Speaker 1: forty rooms. Well, hey guess what they can. And all 231 00:13:13,800 --> 00:13:16,640 Speaker 1: I have to do is have everybody gather their luggage 232 00:13:16,720 --> 00:13:20,280 Speaker 1: and move to room N plus forty. So if you 233 00:13:20,320 --> 00:13:24,400 Speaker 1: are in room two, now you move to room two. 234 00:13:25,880 --> 00:13:27,679 Speaker 1: That sounds reasonable. I'm gonna pick up my bags, I'm 235 00:13:27,720 --> 00:13:29,520 Speaker 1: gonna move on in and hopeful I'm gonna be a 236 00:13:29,520 --> 00:13:32,000 Speaker 1: sleep in an hour or two. Oh. By the way, 237 00:13:32,120 --> 00:13:34,480 Speaker 1: I see a bus coming around the corner. Looks like 238 00:13:34,520 --> 00:13:39,480 Speaker 1: some more guests are arriving. Thus containing a countardly infinite 239 00:13:39,559 --> 00:13:43,240 Speaker 1: number of people arriving. No problem. All I have to 240 00:13:43,280 --> 00:13:46,800 Speaker 1: do is ask each guest to move to room N 241 00:13:47,160 --> 00:13:50,160 Speaker 1: to room number two N. So room one moves room 242 00:13:50,160 --> 00:13:53,360 Speaker 1: to room two to four Room three to six and 243 00:13:53,440 --> 00:13:55,920 Speaker 1: four to eight, and this fills up all the infinite 244 00:13:56,000 --> 00:14:00,480 Speaker 1: rooms and empties all the infinite odd rooms. So you're 245 00:14:00,520 --> 00:14:05,160 Speaker 1: telling me that the Infinity Hotel, which is currently filled 246 00:14:05,240 --> 00:14:09,000 Speaker 1: up with infinite number of guests, has room to take 247 00:14:09,040 --> 00:14:12,280 Speaker 1: care of the guests the infinite number of guests arriving 248 00:14:12,360 --> 00:14:14,640 Speaker 1: in an infinity bus. That's right, because all it is 249 00:14:14,640 --> 00:14:19,000 Speaker 1: is shifted to everybody to the infinite even number rooms 250 00:14:19,400 --> 00:14:22,440 Speaker 1: to accommodate all the infinite amount of people coming off 251 00:14:22,440 --> 00:14:25,080 Speaker 1: the infinite buses. I'm gonna put them all in odd 252 00:14:25,120 --> 00:14:28,160 Speaker 1: number rooms. And you remember Cantor in his infinite sets. 253 00:14:28,160 --> 00:14:30,480 Speaker 1: This is an example of those one to one matches, 254 00:14:30,560 --> 00:14:34,200 Speaker 1: not to mention, underscoring the idea that Cantor had that 255 00:14:34,320 --> 00:14:38,360 Speaker 1: there are an infinite odd and even amount of numbers. 256 00:14:38,960 --> 00:14:42,320 Speaker 1: So so, so far, the Infinity Hotel thought experiment is 257 00:14:42,360 --> 00:14:45,800 Speaker 1: holding up. But of course, one of the the fun 258 00:14:45,840 --> 00:14:50,280 Speaker 1: things about thought experiments is that you can continue to 259 00:14:50,320 --> 00:14:52,800 Speaker 1: experience with them in an attempt to break them, to 260 00:14:52,920 --> 00:14:56,720 Speaker 1: push them to the absolute limits. Break come on, Okay, Well, 261 00:14:57,240 --> 00:15:00,280 Speaker 1: so far the Infinity Hotel has been able to deal 262 00:15:00,320 --> 00:15:02,960 Speaker 1: with one new occupant. It's been able to deal with 263 00:15:03,480 --> 00:15:06,480 Speaker 1: a bus full of infinite new occupants. But what does 264 00:15:06,520 --> 00:15:10,560 Speaker 1: it do of coming around the corner? Are infinite buses 265 00:15:10,760 --> 00:15:16,320 Speaker 1: and each bus has infinite yes, I mean just an 266 00:15:16,320 --> 00:15:22,520 Speaker 1: infinite line of infinitely filled buses. All right, well, maybe 267 00:15:22,560 --> 00:15:25,560 Speaker 1: I remember that youklid said that they're an infinite number 268 00:15:25,560 --> 00:15:29,080 Speaker 1: of prime numbers. Yep, I just remembered that. And so 269 00:15:29,440 --> 00:15:33,200 Speaker 1: current occupants of rooms are assigned the prime number two. 270 00:15:33,600 --> 00:15:36,160 Speaker 1: So for instance, the current occupant of room number seven 271 00:15:36,160 --> 00:15:40,880 Speaker 1: goes to two to the seventh power or room. Then 272 00:15:41,240 --> 00:15:44,040 Speaker 1: the next group they're all assigned to the prime number three, 273 00:15:44,520 --> 00:15:48,280 Speaker 1: and they take their bus seat numbers to figure out 274 00:15:48,360 --> 00:15:52,080 Speaker 1: their room numbers. So seat number seven goes to three 275 00:15:52,080 --> 00:15:55,520 Speaker 1: to the seventh power or room two thousand and seven. 276 00:15:56,040 --> 00:15:57,760 Speaker 1: And I want to throw in it. This is important 277 00:15:57,800 --> 00:16:00,520 Speaker 1: because if you just did them bust by bus, you 278 00:16:00,520 --> 00:16:03,920 Speaker 1: would never finish onload owning the first bus. Well, yeah, 279 00:16:03,960 --> 00:16:06,360 Speaker 1: first you gotta take uh, you gotta take care of 280 00:16:06,400 --> 00:16:08,880 Speaker 1: your career that's already in in the hotel, right that 281 00:16:08,920 --> 00:16:10,800 Speaker 1: you've given that prime number two, And then yes, you 282 00:16:10,840 --> 00:16:13,760 Speaker 1: have to start referring to bus seat numbers to begin 283 00:16:14,680 --> 00:16:17,960 Speaker 1: applying all the infinite number of prime numbers, so you 284 00:16:18,000 --> 00:16:20,480 Speaker 1: can do this. Each each new group gets a new 285 00:16:20,560 --> 00:16:25,200 Speaker 1: prime number, so you know, you go to the you know, 286 00:16:25,200 --> 00:16:28,640 Speaker 1: prime number five, then prime number seven, eleven, and thirteen, 287 00:16:28,680 --> 00:16:31,360 Speaker 1: and everybody just has to reference that number on their 288 00:16:31,440 --> 00:16:35,480 Speaker 1: bus seat. So again, this is just really it's it's messy, 289 00:16:35,560 --> 00:16:40,320 Speaker 1: but there's an elegant system to take place or to 290 00:16:40,400 --> 00:16:43,480 Speaker 1: make sure that everybody gets their place, and that ensures 291 00:16:43,520 --> 00:16:46,360 Speaker 1: that there are no overlapping room numbers for the infinite 292 00:16:46,360 --> 00:16:49,040 Speaker 1: amount of people filing out of the infinite number of buses. 293 00:16:49,200 --> 00:16:52,480 Speaker 1: Here's here's the thing, though, here's the thing. Okay, here's 294 00:16:52,480 --> 00:16:54,360 Speaker 1: what I don't want to see coming out of those buses. 295 00:16:55,360 --> 00:16:59,240 Speaker 1: I don't want to see any irrational numbers. I'm talking 296 00:16:59,240 --> 00:17:01,680 Speaker 1: about you, pie. I don't want to see you tumbling 297 00:17:01,760 --> 00:17:04,280 Speaker 1: off the bus because this is not going to work. 298 00:17:04,520 --> 00:17:08,160 Speaker 1: I don't need to see a negative seven a representation 299 00:17:08,720 --> 00:17:13,040 Speaker 1: human representation of a negative seven. First, you're you're negative, right, 300 00:17:13,119 --> 00:17:15,679 Speaker 1: you're killing the vibe here in the hotel. Second, I 301 00:17:15,720 --> 00:17:21,000 Speaker 1: don't have negative numbers. I don't have basement number rooms, 302 00:17:21,320 --> 00:17:24,880 Speaker 1: you know, extending infinitely down into my my building here, 303 00:17:24,880 --> 00:17:29,359 Speaker 1: and I don't have half fractional rooms available, because that 304 00:17:29,480 --> 00:17:33,120 Speaker 1: ultimately breaks the hotel, that brings everything crashing down, because 305 00:17:33,160 --> 00:17:35,879 Speaker 1: there's one infinity that's too big, and that's the infinity 306 00:17:35,920 --> 00:17:39,160 Speaker 1: contained in a continuous flying, a continuous line of real 307 00:17:39,280 --> 00:17:41,720 Speaker 1: numbers that goes on forever. If it showed up at 308 00:17:41,720 --> 00:17:43,959 Speaker 1: the hotel, they wouldn't be room for everyone. You wouldn't 309 00:17:43,960 --> 00:17:46,119 Speaker 1: be able to, uh to take that real number and 310 00:17:46,119 --> 00:17:47,320 Speaker 1: count it. You wouldn't be able to put it on 311 00:17:47,320 --> 00:17:51,960 Speaker 1: the guest list. Yeah, and that's yeah exactly, that's the problem. 312 00:17:51,960 --> 00:17:54,600 Speaker 1: I mean, because we can deal with this lowest level 313 00:17:54,680 --> 00:17:59,120 Speaker 1: of infinity, the countable infinity of the natural numbers, but 314 00:17:59,440 --> 00:18:04,720 Speaker 1: that's uh, that real number, that continuum that Cantor had 315 00:18:04,760 --> 00:18:08,920 Speaker 1: described before, that is uncountable, that doesn't behave in that 316 00:18:09,040 --> 00:18:12,680 Speaker 1: one to one set way. And that's what I love 317 00:18:12,720 --> 00:18:17,600 Speaker 1: about the Infinity Hotel is that it describes both these 318 00:18:17,760 --> 00:18:22,800 Speaker 1: different levels of infinity, these larger amounts of infinity, but 319 00:18:22,920 --> 00:18:27,640 Speaker 1: how certain numbers don't work within it or are uncountable. 320 00:18:27,800 --> 00:18:32,080 Speaker 1: Plus you've seen being John Makovitch, right, you know what 321 00:18:32,240 --> 00:18:35,680 Speaker 1: happens when you have a half demension, right, you had 322 00:18:35,760 --> 00:18:39,480 Speaker 1: the half floor of the buildings right where where everything's 323 00:18:40,160 --> 00:18:42,560 Speaker 1: cut in half and you have to stoop. And what happens, 324 00:18:42,960 --> 00:18:47,119 Speaker 1: people will will use that as a vessel to somehow 325 00:18:47,359 --> 00:18:51,000 Speaker 1: infiltrate your mind and hijack your body if you're placed 326 00:18:51,040 --> 00:18:53,600 Speaker 1: in a half room or a half floor. Yeah, and 327 00:18:53,640 --> 00:18:55,919 Speaker 1: that nobody wants that. It's gonna hard hard to retain 328 00:18:55,960 --> 00:18:58,560 Speaker 1: tenants when you have that going on. Exactly, so again 329 00:18:58,600 --> 00:19:01,359 Speaker 1: you have Cantor's continum hype offices. Fit says that there's 330 00:19:01,440 --> 00:19:04,560 Speaker 1: there's no set whose cardinality is strictly between that of 331 00:19:04,640 --> 00:19:06,720 Speaker 1: the integers and the real numbers. Can't prove it's true, 332 00:19:06,760 --> 00:19:09,199 Speaker 1: can't prove it's false, can't measure it, can't hunt for 333 00:19:09,240 --> 00:19:12,240 Speaker 1: a particle or measure anything about it. Yes, those real 334 00:19:12,320 --> 00:19:16,880 Speaker 1: numbers are uncountable in this scenario of infinity. And then 335 00:19:16,920 --> 00:19:20,880 Speaker 1: along uh of of and about nine gun named Goodill 336 00:19:22,000 --> 00:19:25,040 Speaker 1: has a pair of proofs that are just spectacular to 337 00:19:25,080 --> 00:19:29,240 Speaker 1: the math community because essentially he shows that you can 338 00:19:29,280 --> 00:19:33,520 Speaker 1: never prove that the continuum hypothesis is false. And this 339 00:19:33,560 --> 00:19:37,320 Speaker 1: feels like, uh, you're like you're moving the needle here 340 00:19:37,600 --> 00:19:39,960 Speaker 1: on infinity just a bit right, Like we think we've 341 00:19:39,960 --> 00:19:43,440 Speaker 1: grabbed onto something here. The problem is that in nineteen 342 00:19:43,600 --> 00:19:47,239 Speaker 1: sixty or they're about Paul J. Cohen shows that you 343 00:19:47,240 --> 00:19:51,640 Speaker 1: can never prove that the continuum hypothesis is true. And 344 00:19:52,119 --> 00:19:54,639 Speaker 1: why does it all of this matter is because it 345 00:19:54,680 --> 00:19:59,679 Speaker 1: shows that there are unanswerable questions in mathematics, particularly dealing 346 00:19:59,760 --> 00:20:03,560 Speaker 1: with infinity, which just is really a microcosm of the 347 00:20:03,560 --> 00:20:10,080 Speaker 1: macrocosm problem of the unknowability of life in general. So 348 00:20:10,119 --> 00:20:12,720 Speaker 1: if your brain is exploding right now, don't worry, because 349 00:20:12,760 --> 00:20:15,040 Speaker 1: now we're going to take it back to physics. We're 350 00:20:15,040 --> 00:20:19,080 Speaker 1: gonna take it to discussions of the physical world as 351 00:20:19,160 --> 00:20:22,399 Speaker 1: complicated and mind blowing is that whole realm can get 352 00:20:22,480 --> 00:20:26,200 Speaker 1: at least we're dealing with observable physical reality, right, Sure, 353 00:20:26,240 --> 00:20:28,280 Speaker 1: you say that, And now I have the physics sweats, 354 00:20:28,280 --> 00:20:31,680 Speaker 1: which is an entirely different stench here. And that's understandable. Yes, 355 00:20:31,760 --> 00:20:36,160 Speaker 1: but because certainly physics gets very complicated as well. But 356 00:20:36,280 --> 00:20:41,080 Speaker 1: when but here's the thing. When we see infinities in physics, generally, 357 00:20:41,280 --> 00:20:43,159 Speaker 1: it means that we have a problem and means that 358 00:20:43,400 --> 00:20:47,399 Speaker 1: something's really catastrophic wrong unless you get into theoretical physics, 359 00:20:47,480 --> 00:20:49,840 Speaker 1: as we will in a second. Yes, but you know 360 00:20:49,920 --> 00:20:53,560 Speaker 1: basic physics, you're trying to use somebody that's designing. You know, 361 00:20:53,600 --> 00:20:56,240 Speaker 1: you know a new building and you look at the plans. 362 00:20:56,240 --> 00:20:59,000 Speaker 1: If you see infinity on there, you know that something 363 00:20:59,119 --> 00:21:02,000 Speaker 1: is wrong. You do not want to try and stand 364 00:21:02,040 --> 00:21:04,959 Speaker 1: in that building or or or or certainly have an 365 00:21:05,000 --> 00:21:08,639 Speaker 1: office in it. Um it's never an actual measurement. It 366 00:21:08,680 --> 00:21:12,959 Speaker 1: doesn't correspond to to to reality as as we we 367 00:21:13,040 --> 00:21:15,840 Speaker 1: deal with it in our lives right today, for instance, 368 00:21:16,119 --> 00:21:20,040 Speaker 1: quantum mechanics okay um and and and in such an 369 00:21:20,040 --> 00:21:23,800 Speaker 1: important area of studies. So many of our greatest technological 370 00:21:23,800 --> 00:21:27,720 Speaker 1: achievements in recent memory have arisen out of quantum mechanics. 371 00:21:27,720 --> 00:21:30,840 Speaker 1: But even here we see this crisis. The crisis being 372 00:21:30,840 --> 00:21:33,920 Speaker 1: that even though we can predict the the light heat 373 00:21:34,000 --> 00:21:37,600 Speaker 1: power emission of a lamp, it's a finite amount of energy, 374 00:21:37,640 --> 00:21:43,560 Speaker 1: but the various wigglings of waves and atoms creates this 375 00:21:43,640 --> 00:21:47,520 Speaker 1: answer infinite energy, which which we simply can't deal with. 376 00:21:47,680 --> 00:21:50,239 Speaker 1: Right we know that there's not infinite energy coming out 377 00:21:50,240 --> 00:21:53,199 Speaker 1: of off of a lamp, so we afterwards we have 378 00:21:53,280 --> 00:21:56,240 Speaker 1: to begin applying quantum physics to the forces of our universe. 379 00:21:56,280 --> 00:22:00,600 Speaker 1: Quantum field theory, which is of course initially played infinities 380 00:22:00,640 --> 00:22:03,000 Speaker 1: as well, and it takes ends up taking decades to 381 00:22:03,200 --> 00:22:05,520 Speaker 1: flog through it all. You end up, you know, having 382 00:22:05,720 --> 00:22:08,480 Speaker 1: all these infinities, all of these problems in the in 383 00:22:08,560 --> 00:22:12,359 Speaker 1: the theory that have to be eradicated, like like enemies 384 00:22:12,359 --> 00:22:15,639 Speaker 1: floating around in a video game, or which becomes incredibly 385 00:22:15,680 --> 00:22:19,119 Speaker 1: important if you're looking at particle physics, right, because if 386 00:22:19,160 --> 00:22:23,040 Speaker 1: you're trying to isolate the Higgs boson, you're taking these 387 00:22:23,200 --> 00:22:26,520 Speaker 1: finite number of particles that we know and have named 388 00:22:26,600 --> 00:22:30,360 Speaker 1: in seeing how they behave right, you do not need 389 00:22:30,440 --> 00:22:33,640 Speaker 1: infinity in the mix if you're trying to figure out 390 00:22:33,680 --> 00:22:37,359 Speaker 1: the composition of the universe, both from the time in 391 00:22:37,400 --> 00:22:40,760 Speaker 1: which it became to now I mean, take the Higgs 392 00:22:40,760 --> 00:22:43,119 Speaker 1: for example, the search for the Higgs boson, this was 393 00:22:43,680 --> 00:22:47,080 Speaker 1: such the so called god particle, right. Uh. This uh, this, 394 00:22:47,200 --> 00:22:50,040 Speaker 1: this of course been one of the predominant science stories 395 00:22:50,359 --> 00:22:54,280 Speaker 1: in recent years, because the whole idea was that we 396 00:22:54,320 --> 00:22:56,800 Speaker 1: had infinities in the theory, we had to remove them, 397 00:22:57,040 --> 00:23:00,480 Speaker 1: and the thing that could remove it would be this 398 00:23:00,680 --> 00:23:03,919 Speaker 1: Higgs particle. Right, So the whole quest for the Higgs 399 00:23:03,960 --> 00:23:08,200 Speaker 1: particle comes out of this, this this necessity, this need 400 00:23:08,520 --> 00:23:14,280 Speaker 1: to eradicate the infinities from the theory, because again, infinite's 401 00:23:14,359 --> 00:23:17,680 Speaker 1: just don't work in the set and the infinities here 402 00:23:17,680 --> 00:23:19,920 Speaker 1: in the theory said said, all right, we have an infinity. 403 00:23:19,960 --> 00:23:22,679 Speaker 1: That means there's something finite in the world that we 404 00:23:22,720 --> 00:23:25,199 Speaker 1: haven't discovered yet, and if we discover it, then we 405 00:23:25,280 --> 00:23:28,480 Speaker 1: find our way around that answer. Now, if you sort 406 00:23:28,480 --> 00:23:30,920 Speaker 1: of back up and then begin to take the large 407 00:23:31,000 --> 00:23:33,439 Speaker 1: view of the universe and not just try to contain 408 00:23:33,440 --> 00:23:36,199 Speaker 1: it in this this one model, right, you know that 409 00:23:36,240 --> 00:23:40,800 Speaker 1: the universe is expanding how much infinitely? These are questions 410 00:23:40,880 --> 00:23:42,800 Speaker 1: that come up, and then you begin to say, well, 411 00:23:42,840 --> 00:23:44,879 Speaker 1: how how far does space go? Anyway? And this is 412 00:23:44,920 --> 00:23:50,280 Speaker 1: where theoretical physicists get into infinity and they really have 413 00:23:50,440 --> 00:23:54,520 Speaker 1: some fun um And it's fascinating because here you see 414 00:23:54,960 --> 00:23:59,960 Speaker 1: some examples of infinity played out in ways that you say, 415 00:24:00,000 --> 00:24:03,879 Speaker 1: this is a possibility, because infinity otherwise we just see 416 00:24:03,960 --> 00:24:05,800 Speaker 1: is this sort of you know, the line on the 417 00:24:05,800 --> 00:24:08,840 Speaker 1: piece of paper and mathematics that goes on forever. But 418 00:24:08,880 --> 00:24:13,320 Speaker 1: then you've got these ideas like multiverse existing. Now, when 419 00:24:13,320 --> 00:24:15,879 Speaker 1: I think of the multiverse, I always think of Jorey 420 00:24:15,960 --> 00:24:20,080 Speaker 1: Lewis Borges the Library of Battle, the library that first 421 00:24:20,080 --> 00:24:23,120 Speaker 1: of all contains all books, all written books, but then 422 00:24:23,200 --> 00:24:26,960 Speaker 1: beyond that also contains all possible books, and and and 423 00:24:26,960 --> 00:24:29,399 Speaker 1: and and so being is is ultimately kind of a 424 00:24:29,520 --> 00:24:34,440 Speaker 1: model for a multiverse. Uh, an existence that contains everything 425 00:24:34,480 --> 00:24:37,199 Speaker 1: that is and everything that could be. Again, you go 426 00:24:37,280 --> 00:24:40,240 Speaker 1: back to Cantor, and you're talking about larger infinities, right, 427 00:24:40,280 --> 00:24:42,960 Speaker 1: And essentially that's what we're talking about with multiverses. And 428 00:24:43,000 --> 00:24:46,240 Speaker 1: I'm going to read this from Brian Green's The Elegant Universe. Um, 429 00:24:46,280 --> 00:24:49,160 Speaker 1: we could talk about multiverse in its very own episodes. 430 00:24:49,280 --> 00:24:52,640 Speaker 1: We won't go too deep here, he says, Imagine that 431 00:24:52,680 --> 00:24:55,760 Speaker 1: what we call the universe is actually only one tiny 432 00:24:55,800 --> 00:24:59,639 Speaker 1: part of a vastly larger cosmological expanse, one of the 433 00:24:59,760 --> 00:25:03,160 Speaker 1: nor almost number of island universes scattered across a grand 434 00:25:03,200 --> 00:25:08,639 Speaker 1: cosmological archipelago. Although this might sound rather far fetched, and 435 00:25:08,840 --> 00:25:12,560 Speaker 1: in the end it may well be, Andrei Lynd has 436 00:25:12,600 --> 00:25:15,720 Speaker 1: suggested a concrete mechanism that might lead to such a 437 00:25:15,760 --> 00:25:19,879 Speaker 1: Gargangan universe. Lynn has found that the brief but crucial 438 00:25:20,000 --> 00:25:24,160 Speaker 1: burst of inflationary expanse may not have been a unique 439 00:25:24,200 --> 00:25:27,960 Speaker 1: one time event. Instead, he argues the conditions for inflationary 440 00:25:28,000 --> 00:25:32,520 Speaker 1: expansion may happen repeatedly in isolated regions and the peppered 441 00:25:32,560 --> 00:25:37,400 Speaker 1: throughout the cosmos, which then undergo their own inflationary ballooning 442 00:25:37,480 --> 00:25:42,080 Speaker 1: and size, evolving into new separate universes. And each of 443 00:25:42,080 --> 00:25:46,160 Speaker 1: the universes, the process continues, with new universes sprouting from 444 00:25:46,200 --> 00:25:49,560 Speaker 1: far flung regions in the old, generating a never ending 445 00:25:49,600 --> 00:25:53,320 Speaker 1: web of ballooning cosmic expanses. And this is what he 446 00:25:53,359 --> 00:25:57,400 Speaker 1: calls the multiverse. And that's pretty mind blow I mean, 447 00:25:57,440 --> 00:26:02,600 Speaker 1: even if you you shrink back down to are single universe. Um. 448 00:26:02,640 --> 00:26:04,679 Speaker 1: There was an interesting point that was brought up by 449 00:26:04,720 --> 00:26:08,919 Speaker 1: physicist Raphael Bosso in that World Science Festival talk I 450 00:26:09,000 --> 00:26:11,840 Speaker 1: was mentioning earlier. We will include a link to in 451 00:26:11,880 --> 00:26:14,639 Speaker 1: the landing page for this podcast episode. But he pointed 452 00:26:14,680 --> 00:26:17,320 Speaker 1: out that that when you start start looking at the 453 00:26:17,320 --> 00:26:19,840 Speaker 1: way light travels across the universe, when you start looking 454 00:26:19,880 --> 00:26:22,520 Speaker 1: at this expansion of the universe, you end up with 455 00:26:22,600 --> 00:26:26,679 Speaker 1: a universe that's arbitrarily large. Light can never reach you 456 00:26:27,200 --> 00:26:30,880 Speaker 1: from rapidly expanding regions regions, and so any given observer 457 00:26:31,080 --> 00:26:35,160 Speaker 1: is trapped within a finite sphere of observable universe within 458 00:26:35,200 --> 00:26:38,960 Speaker 1: an expanding infinite. So you kind of get this again. 459 00:26:39,000 --> 00:26:42,080 Speaker 1: You get these ideas of here's this, here's the sphere 460 00:26:42,160 --> 00:26:46,200 Speaker 1: of the finite within the infinite. You can think about 461 00:26:46,200 --> 00:26:49,320 Speaker 1: the infinite, but you're ultimately trapped within that sphere of 462 00:26:49,359 --> 00:26:52,760 Speaker 1: the finite. Yeah, and this is a similar idea that 463 00:26:52,920 --> 00:26:55,480 Speaker 1: Lee Smollen has in terms of the perception of the 464 00:26:55,560 --> 00:26:59,520 Speaker 1: infinite at least. Smallen, by the way, is a cosmologist 465 00:26:59,640 --> 00:27:03,880 Speaker 1: at and State, and his idea is that the conditions 466 00:27:03,920 --> 00:27:06,880 Speaker 1: at the Big Bang and at the centers of black holes, 467 00:27:07,200 --> 00:27:10,920 Speaker 1: each being characterized by a colossal density of crushed matter. 468 00:27:11,880 --> 00:27:14,639 Speaker 1: I suggested that every black hole is the seed for 469 00:27:14,680 --> 00:27:18,199 Speaker 1: a new universe that erupts into existence through a Big 470 00:27:18,640 --> 00:27:22,359 Speaker 1: Bang like explosion, but is forever hidden from our view 471 00:27:22,520 --> 00:27:26,120 Speaker 1: by the black holes event horizon. And of course, any 472 00:27:26,119 --> 00:27:29,160 Speaker 1: of these discussions of the physical universe are are even 473 00:27:29,320 --> 00:27:31,359 Speaker 1: more twisted when you when you have coorse draw in 474 00:27:31,400 --> 00:27:33,240 Speaker 1: the fact that time and space are one, and if 475 00:27:33,280 --> 00:27:36,880 Speaker 1: you play with space, you're playing with time, and if 476 00:27:36,880 --> 00:27:38,600 Speaker 1: it were to be flat, then it could stretch out 477 00:27:38,600 --> 00:27:40,720 Speaker 1: for an infinity, right, And then you get all these 478 00:27:40,720 --> 00:27:44,680 Speaker 1: different ideas of well maybe in this case that supports 479 00:27:44,680 --> 00:27:48,359 Speaker 1: this idea of some sort of repeating going on because 480 00:27:48,359 --> 00:27:50,679 Speaker 1: you have a finite number of particles that you have 481 00:27:50,920 --> 00:27:56,159 Speaker 1: infinite space and time, and maybe that repeating pattern creates 482 00:27:56,560 --> 00:28:01,320 Speaker 1: more universes, right, And then you have ever many worlds 483 00:28:01,359 --> 00:28:05,560 Speaker 1: interpretation that says that the universe branches off into distinct 484 00:28:05,680 --> 00:28:10,639 Speaker 1: worlds to accommodate every single possible outcome. And so maybe 485 00:28:10,640 --> 00:28:13,480 Speaker 1: we live in an infinite web of alternate timelines. I mean, 486 00:28:13,480 --> 00:28:17,640 Speaker 1: it gets crazy and crazy as you go along. So yes, 487 00:28:17,960 --> 00:28:20,280 Speaker 1: I mean I don't even have to everyone else's mind 488 00:28:20,359 --> 00:28:23,080 Speaker 1: is extrapolating the possibilities on that. I don't have to 489 00:28:23,320 --> 00:28:25,320 Speaker 1: push you in that direction. And if you guys would 490 00:28:25,359 --> 00:28:29,080 Speaker 1: like some articles to accompany this, uh, we have ever 491 00:28:29,400 --> 00:28:32,960 Speaker 1: many worlds interpretation on how stuff works, and we also 492 00:28:33,040 --> 00:28:37,479 Speaker 1: have some good amount of string theory and multiverse um, 493 00:28:37,560 --> 00:28:39,400 Speaker 1: so we definitely have some stuff for you guys to 494 00:28:39,440 --> 00:28:43,240 Speaker 1: dive into. Yes, on the Internet, which is of course 495 00:28:43,720 --> 00:28:47,520 Speaker 1: a finite world. Even though it is it is a 496 00:28:47,520 --> 00:28:50,880 Speaker 1: finite world. But yet we we can't even grasp what 497 00:28:51,000 --> 00:28:52,960 Speaker 1: We can't even put a number on it. We can't 498 00:28:52,960 --> 00:28:55,440 Speaker 1: say how many pages there actually are on the Internet. 499 00:28:55,640 --> 00:28:59,040 Speaker 1: We can't actually even comprehend it's a finite thing we've created, 500 00:28:59,400 --> 00:29:01,320 Speaker 1: and it is already, at least as far as human 501 00:29:01,320 --> 00:29:04,800 Speaker 1: perception goes, bordering the infinite. Let's supposed to just fine, 502 00:29:04,840 --> 00:29:07,240 Speaker 1: since we can see its growth and we can put 503 00:29:07,240 --> 00:29:11,600 Speaker 1: a number on it. But it feels infinite at times. Alright, 504 00:29:11,680 --> 00:29:15,160 Speaker 1: So we're gonna walk you guys out of this um 505 00:29:15,200 --> 00:29:17,240 Speaker 1: and we're gonna take a little walk into something called 506 00:29:17,600 --> 00:29:21,760 Speaker 1: the infinite monkey theorem to end this section. Yeah good. 507 00:29:21,760 --> 00:29:24,680 Speaker 1: This is an you know, a thought experiment that I 508 00:29:24,720 --> 00:29:28,280 Speaker 1: often forget even really entails infinity, maybe because I just 509 00:29:28,320 --> 00:29:30,760 Speaker 1: get too caught up on the idea of monkeys banging 510 00:29:30,760 --> 00:29:33,520 Speaker 1: on typewriters and now awful that writing room, let's be, 511 00:29:33,640 --> 00:29:37,480 Speaker 1: and I've I've written in some awful rooms before. Uh. 512 00:29:37,560 --> 00:29:40,920 Speaker 1: This states that a monkey hidden keys at random on 513 00:29:40,960 --> 00:29:45,240 Speaker 1: a typewriter keyboard for an infinite amount of time will 514 00:29:45,320 --> 00:29:50,160 Speaker 1: almost surely type a given text, like say, the complete 515 00:29:50,160 --> 00:29:54,760 Speaker 1: works of William Shakespeare. Okay, okay, And so in this context, 516 00:29:54,800 --> 00:29:57,840 Speaker 1: almost surely is a mathematical term, alright, and it has 517 00:29:57,840 --> 00:30:01,160 Speaker 1: a precise meaning, And that monkey is not an actual 518 00:30:01,240 --> 00:30:04,520 Speaker 1: monkey but a metaphor for an abstract device that produces 519 00:30:04,640 --> 00:30:09,680 Speaker 1: a random sequence of letters for an infinity. In the 520 00:30:09,680 --> 00:30:13,240 Speaker 1: theorem illustrates the perils of reasoning about infinity by imagining 521 00:30:13,240 --> 00:30:17,760 Speaker 1: this vast that finite number, and vice versa. So the 522 00:30:17,840 --> 00:30:21,920 Speaker 1: probability is really tiny, right, The probability exists that a 523 00:30:21,960 --> 00:30:26,400 Speaker 1: monkey could eventually write a work as cohesive as say 524 00:30:26,440 --> 00:30:30,000 Speaker 1: Shakespeare's Hamlet, just by pure dumb accident of banging on 525 00:30:30,120 --> 00:30:35,320 Speaker 1: the keys forever and ever and ever endever, which gives 526 00:30:35,360 --> 00:30:38,640 Speaker 1: my fiction writing some hope. Oh you're you're better than 527 00:30:38,640 --> 00:30:42,400 Speaker 1: a monkey. I don't know. I don't know about that, 528 00:30:43,840 --> 00:30:47,760 Speaker 1: and I'm fine with that actually, all right, So if 529 00:30:47,760 --> 00:30:51,720 Speaker 1: you're still with us, then hopefully you have you maybe 530 00:30:51,720 --> 00:30:54,640 Speaker 1: you have a better idea of what infinity is all about. 531 00:30:54,720 --> 00:30:58,040 Speaker 1: Maybe you have more nuanced idea, more expansive idea. Maybe 532 00:30:58,080 --> 00:31:01,080 Speaker 1: this is uh forced you to sort rearrange your your 533 00:31:01,280 --> 00:31:04,560 Speaker 1: contemplation of the infinite and of the boundless, in terms 534 00:31:04,600 --> 00:31:07,960 Speaker 1: of of our human experience, in terms of our cosmos, 535 00:31:07,960 --> 00:31:10,640 Speaker 1: in terms of our ideas of God. So we'd love 536 00:31:10,640 --> 00:31:12,560 Speaker 1: to hear from you. We'd love to hear your thoughts 537 00:31:12,600 --> 00:31:16,320 Speaker 1: about infinity, your personal takes on infinity, your favorite uses 538 00:31:16,360 --> 00:31:20,000 Speaker 1: of infinity and fiction. All of that is fair game. Yeah, 539 00:31:20,080 --> 00:31:22,320 Speaker 1: and before you do that, make sure you stopped at 540 00:31:22,360 --> 00:31:24,520 Speaker 1: Stuff to Blow your Mind dot com. That's right, That's 541 00:31:24,520 --> 00:31:27,160 Speaker 1: where you'll find all the podcast episodes, all the videos, 542 00:31:27,480 --> 00:31:30,200 Speaker 1: all of the blog posts, a finite amount of all 543 00:31:30,240 --> 00:31:33,400 Speaker 1: of those, but certainly plenty of stuff to keep you occupied. Yeah, 544 00:31:33,680 --> 00:31:35,520 Speaker 1: So share those thoughts with us, why don't you? And 545 00:31:35,600 --> 00:31:38,000 Speaker 1: you can do that at below the mind house to 546 00:31:38,120 --> 00:31:45,160 Speaker 1: works dot com. For more on this and thousands of 547 00:31:45,200 --> 00:31:55,000 Speaker 1: other topics, visit how stuff works dot com