1 00:00:01,370 --> 00:00:04,203 (dramatic music) 2 00:00:12,411 --> 00:00:15,854 -: Is there a mathematical formula for luck? 3 00:00:15,854 --> 00:00:17,902 What about comedy? 4 00:00:17,902 --> 00:00:20,485 Do we live inside a simulation? 5 00:00:21,368 --> 00:00:25,535 I'm Dianna Cowern and this is "Proof of Concept." 6 00:00:28,721 --> 00:00:32,506 In the ancient Greek legends, Zeus, Hades, 7 00:00:32,506 --> 00:00:34,755 and the rest of the Olympian gods are said 8 00:00:34,755 --> 00:00:38,939 to have actually envied humans for their finite lifespans. 9 00:00:38,939 --> 00:00:43,423 This is because despite all of their power and privilege, 10 00:00:43,423 --> 00:00:45,525 the gods' immortality deprive them 11 00:00:45,525 --> 00:00:48,608 of the greatest gift of all, meaning. 12 00:00:49,560 --> 00:00:53,558 Because a human only exists for a brief flash of time, 13 00:00:53,558 --> 00:00:57,056 every choice we make, every meal, every breath, 14 00:00:57,056 --> 00:01:00,091 every moment of laughter is endowed with the meaning 15 00:01:00,091 --> 00:01:03,912 that comes from being an entry on a finite list. 16 00:01:03,912 --> 00:01:07,360 A list that will end up excluding other experiences 17 00:01:07,360 --> 00:01:10,961 and possible paths we might have followed. 18 00:01:10,961 --> 00:01:14,899 Because our time is finite our choices matter, 19 00:01:14,899 --> 00:01:18,662 but considering the profound impact of our finiteness 20 00:01:18,662 --> 00:01:20,496 makes you wonder if there are any ways 21 00:01:20,496 --> 00:01:23,446 in which we are actually infinite. 22 00:01:23,446 --> 00:01:24,446 Is anything? 23 00:01:25,478 --> 00:01:27,195 This image, for instance, 24 00:01:27,195 --> 00:01:31,333 it's an iconic example of an infinite visual effect. 25 00:01:31,333 --> 00:01:34,534 In fact, it's called an infinity room, 26 00:01:34,534 --> 00:01:37,528 but even this isn't truly infinite. 27 00:01:37,528 --> 00:01:41,312 The effect where you see infinite Diannas is the result 28 00:01:41,312 --> 00:01:43,478 of repeated reflections, 29 00:01:43,478 --> 00:01:46,112 light bounces off one wall and then the other 30 00:01:46,112 --> 00:01:49,107 and back and forth over and over. 31 00:01:49,107 --> 00:01:52,520 But technically it only goes so deep. 32 00:01:52,520 --> 00:01:54,614 Think about the first one second 33 00:01:54,614 --> 00:01:57,484 after I walked into this 10 foot cube. 34 00:01:57,484 --> 00:01:59,132 Light moves quickly. 35 00:01:59,132 --> 00:02:01,688 So it's had enough time in that one second 36 00:02:01,688 --> 00:02:05,970 to create 50 million reflections in the image. 37 00:02:05,970 --> 00:02:10,435 But 50 million isn't infinite, not even close. 38 00:02:10,435 --> 00:02:13,699 Not to mention the fact that the light appears to fade 39 00:02:13,699 --> 00:02:16,048 as you look off into the distance. 40 00:02:16,048 --> 00:02:18,399 That's because it does. 41 00:02:18,399 --> 00:02:19,926 For every reflection, 42 00:02:19,926 --> 00:02:23,938 you lose about one to 5% of the light to absorption, 43 00:02:23,938 --> 00:02:26,120 even in the best mirrors. 44 00:02:26,120 --> 00:02:27,600 So that version of me, 45 00:02:27,600 --> 00:02:30,550 30 layers deep is standing in a room 46 00:02:30,550 --> 00:02:34,016 that's about 50% as bright as this room. 47 00:02:34,016 --> 00:02:37,849 That Dianna is 50% as bright as this one. 48 00:02:38,699 --> 00:02:40,612 With all that in mind, 49 00:02:40,612 --> 00:02:44,163 let's kick off our infinity episode with a game, 50 00:02:44,163 --> 00:02:46,992 a game that isn't technically about infinity, 51 00:02:46,992 --> 00:02:50,325 but instead is about really big numbers. 52 00:02:54,892 --> 00:02:56,199 Here's the challenge. 53 00:02:56,199 --> 00:02:59,728 Put this list of numbers in order from smallest to largest, 54 00:02:59,728 --> 00:03:04,664 the number of different ways a 52 card deck can be shuffled. 55 00:03:04,664 --> 00:03:08,097 The number of people currently living on earth, 56 00:03:08,097 --> 00:03:11,373 the number of distinct paths between the most Northeast 57 00:03:11,373 --> 00:03:13,784 and Southwest corners in Manhattan, 58 00:03:13,784 --> 00:03:16,429 without ever retracing your steps. 59 00:03:16,429 --> 00:03:18,845 The number of ants on earth, 60 00:03:18,845 --> 00:03:21,678 the number of stars in our galaxy. 61 00:03:33,925 --> 00:03:35,132 Enough suspense. 62 00:03:35,132 --> 00:03:37,328 Here's the correct order. 63 00:03:37,328 --> 00:03:39,197 The smallest number on the list 64 00:03:39,197 --> 00:03:42,547 is the current human population of planet earth. 65 00:03:42,547 --> 00:03:46,130 Clocking in at approximately seven billion. 66 00:03:47,435 --> 00:03:50,847 Next up is the number of stars in our galaxy. 67 00:03:50,847 --> 00:03:55,084 There are approximately 43 billion or between six 68 00:03:55,084 --> 00:03:58,533 and seven stars for every person on earth. 69 00:03:58,533 --> 00:04:00,953 So go ahead and name one after yourself. 70 00:04:00,953 --> 00:04:02,251 Name six. 71 00:04:02,251 --> 00:04:04,949 There's plenty to go around. 72 00:04:04,949 --> 00:04:08,037 After that is the number of ants on earth. 73 00:04:08,037 --> 00:04:12,704 Estimates place the number at roughly 100 trillion ants. 74 00:04:13,701 --> 00:04:15,752 It is a shocking, but true fact 75 00:04:15,752 --> 00:04:19,767 that the ants on earth actually outweigh the humans. 76 00:04:19,767 --> 00:04:22,396 100 trillion is a big number, 77 00:04:22,396 --> 00:04:23,885 but from here on the number is veer 78 00:04:23,885 --> 00:04:27,355 into an entirely different realm of massive. 79 00:04:27,355 --> 00:04:31,117 The second biggest number on our list is the number of ways 80 00:04:31,117 --> 00:04:34,867 that a standard 52 card deck can be arranged. 81 00:04:35,782 --> 00:04:39,371 This quantity is commonly known as 52 factorial 82 00:04:39,371 --> 00:04:44,245 and is equal to 52 times 51, times 50, times 49, times 48. 83 00:04:44,245 --> 00:04:47,182 And so on, all the way down to one. 84 00:04:47,182 --> 00:04:48,580 Written out in its entirety, 85 00:04:48,580 --> 00:04:51,669 this number is 68 digits long. 86 00:04:51,669 --> 00:04:54,286 To give a sense of just how big this number is, 87 00:04:54,286 --> 00:04:56,499 it's actually larger than the number of seconds 88 00:04:56,499 --> 00:05:01,104 that have passed since the Big Bang 14 billion years ago. 89 00:05:01,104 --> 00:05:03,424 That means that if someone had started shuffling a deck 90 00:05:03,424 --> 00:05:05,153 immediately after the Big Bang 91 00:05:05,153 --> 00:05:08,430 and changed the order of the cards once per second, 92 00:05:08,430 --> 00:05:09,590 from then, until now, 93 00:05:09,590 --> 00:05:11,145 they would still not have had enough time 94 00:05:11,145 --> 00:05:14,479 to run through every possible ordering. 95 00:05:14,479 --> 00:05:17,113 It also means that if you were to pick up a deck right now 96 00:05:17,113 --> 00:05:18,342 and shuffle it, 97 00:05:18,342 --> 00:05:19,833 the most likely result is 98 00:05:19,833 --> 00:05:22,008 that the exact order your deck is in 99 00:05:22,008 --> 00:05:26,944 has never actually happened before, anywhere, ever. 100 00:05:26,944 --> 00:05:29,724 And as huge as 52 factorial is, 101 00:05:29,724 --> 00:05:32,870 it's dwarfed by the final number on our list. 102 00:05:32,870 --> 00:05:36,609 The number of ways to walk from end to end in Manhattan. 103 00:05:36,609 --> 00:05:39,516 The secret here is the concept of choice. 104 00:05:39,516 --> 00:05:41,095 When you're making choices, 105 00:05:41,095 --> 00:05:44,747 the number of ways things can happen gets really huge, 106 00:05:44,747 --> 00:05:46,226 really fast. 107 00:05:46,226 --> 00:05:48,864 It's what's called exponential growth. 108 00:05:48,864 --> 00:05:51,917 Think how internet memes catch fire. 109 00:05:51,917 --> 00:05:54,765 Let's consider the first three blocks you might walk. 110 00:05:54,765 --> 00:05:56,850 All in all, there are 10 different ways you can choose 111 00:05:56,850 --> 00:05:58,139 to walk them. 112 00:05:58,139 --> 00:06:00,353 By the time you've walked 10 blocks, 113 00:06:00,353 --> 00:06:03,732 there are over a thousand paths you might have taken. 114 00:06:03,732 --> 00:06:06,172 Once you've walked a distance of 30 blocks, 115 00:06:06,172 --> 00:06:09,649 there are over one billion possible paths. 116 00:06:09,649 --> 00:06:13,108 Manhattan is about 250 blocks long, 117 00:06:13,108 --> 00:06:15,233 and about 30 blocks wide. 118 00:06:15,233 --> 00:06:17,765 When you consider every choice you might make going 119 00:06:17,765 --> 00:06:19,212 from corner to corner, 120 00:06:19,212 --> 00:06:21,399 the total number of paths you can take turns out 121 00:06:21,399 --> 00:06:23,566 to be over 80 digits long. 122 00:06:25,667 --> 00:06:28,633 That means that it is one trillion times larger 123 00:06:28,633 --> 00:06:32,586 than the number of ways you can shuffle a deck. 124 00:06:32,586 --> 00:06:34,201 It is seriously big in a way 125 00:06:34,201 --> 00:06:36,499 that's hard to begin to imagine. 126 00:06:36,499 --> 00:06:41,499 And yet we live with these sorts of possibilities every day. 127 00:06:42,252 --> 00:06:45,381 Which of the following is an infinite quantity? 128 00:06:45,381 --> 00:06:49,014 A, the number of different possible chess games? 129 00:06:49,014 --> 00:06:52,741 B, the number of different possible songs under five minutes 130 00:06:52,741 --> 00:06:55,569 in length that can be played on a piano? 131 00:06:55,569 --> 00:06:59,401 C, the number of different possible 1000-page novels 132 00:06:59,401 --> 00:07:01,709 written in English? 133 00:07:01,709 --> 00:07:06,209 Or D, the number of different possible Monopoly games? 134 00:07:20,654 --> 00:07:22,854 All of these are huge quantities, 135 00:07:22,854 --> 00:07:25,949 but the rules of chess, the 88 piano keys, 136 00:07:25,949 --> 00:07:29,485 the speed of sound and the approximately 200,000 words 137 00:07:29,485 --> 00:07:32,457 in English, make three of them finite. 138 00:07:32,457 --> 00:07:36,719 While the game of Monopoly can in fact go on forever, 139 00:07:36,719 --> 00:07:38,504 meaning that there is no finite limit 140 00:07:38,504 --> 00:07:40,039 on the number of different ways 141 00:07:40,039 --> 00:07:42,706 a game of Monopoly might unfold. 142 00:07:44,903 --> 00:07:48,536 Speaking of infinity popping up in surprising places. 143 00:07:48,536 --> 00:07:50,220 There's a picture that I wanna show you, 144 00:07:50,220 --> 00:07:52,786 but it hasn't actually been drawn yet, 145 00:07:52,786 --> 00:07:54,944 because the way we're gonna create this picture 146 00:07:54,944 --> 00:07:57,354 is just about as unusual as the subject 147 00:07:57,354 --> 00:07:59,306 of the picture itself. 148 00:07:59,306 --> 00:08:02,407 We're gonna draw it by rolling this die. 149 00:08:02,407 --> 00:08:03,240 Let's go. 150 00:08:04,775 --> 00:08:05,893 This is Jared. 151 00:08:05,893 --> 00:08:07,408 He's a production assistant, 152 00:08:07,408 --> 00:08:09,687 and I'm gonna make him draw dots all day. 153 00:08:09,687 --> 00:08:10,957 Sorry, Jared. 154 00:08:10,957 --> 00:08:13,584 But what you're gonna do is roll this die. 155 00:08:13,584 --> 00:08:15,199 And if you get a one or a two, 156 00:08:15,199 --> 00:08:17,546 you're gonna go from wherever you are on this triangle, 157 00:08:17,546 --> 00:08:20,743 halfway toward A and draw a dot. 158 00:08:20,743 --> 00:08:23,013 And then if you roll a three or a four, 159 00:08:23,013 --> 00:08:24,442 you're gonna go from wherever you are, 160 00:08:24,442 --> 00:08:27,447 halfway toward B and draw a dot. 161 00:08:27,447 --> 00:08:28,930 And if you roll a five or a six, 162 00:08:28,930 --> 00:08:31,778 you're gonna go halfway towards C and draw a dot there. 163 00:08:31,778 --> 00:08:34,077 And you're just gonna keep doing that. 164 00:08:34,077 --> 00:08:36,383 Keep drawing dots as long as you can. 165 00:08:36,383 --> 00:08:39,047 This is gonna make sense, I promise. 166 00:08:39,047 --> 00:08:40,045 So let's try the first one. 167 00:08:40,045 --> 00:08:42,773 You're gonna start right in that center dot. 168 00:08:42,773 --> 00:08:43,856 Roll the die. 169 00:08:45,287 --> 00:08:46,333 And you got a four. 170 00:08:46,333 --> 00:08:48,398 So you're gonna go halfway toward B 171 00:08:48,398 --> 00:08:49,731 and draw your first dot. 172 00:08:49,731 --> 00:08:51,295 Got it? 173 00:08:51,295 --> 00:08:52,128 All right. 174 00:08:52,128 --> 00:08:53,415 Good luck, Jared. 175 00:08:53,415 --> 00:08:56,498 (light upbeat music) 176 00:09:03,666 --> 00:09:05,583 So how big is infinity? 177 00:09:06,428 --> 00:09:08,317 Well, let's consider one specific number 178 00:09:08,317 --> 00:09:10,930 that's infinite in its own special way. 179 00:09:10,930 --> 00:09:12,914 Despite being finite. 180 00:09:12,914 --> 00:09:17,247 I'm speaking of course of pie, 3.14159265 and so on. 181 00:09:19,197 --> 00:09:21,882 And that's all the digits I've ever memorized. 182 00:09:21,882 --> 00:09:24,169 Pie is the ratio of the circumference 183 00:09:24,169 --> 00:09:25,886 of any circle to its diameter. 184 00:09:25,886 --> 00:09:28,367 But what matters for our purposes here is 185 00:09:28,367 --> 00:09:30,869 that its digits go on forever 186 00:09:30,869 --> 00:09:34,850 and they never settle into any predictable pattern. 187 00:09:34,850 --> 00:09:36,703 That combination of infinity 188 00:09:36,703 --> 00:09:41,450 and the lack of pattern has some astounding consequences. 189 00:09:41,450 --> 00:09:43,017 For Shakespeare. 190 00:09:43,017 --> 00:09:44,311 Let's see what I mean. 191 00:09:44,311 --> 00:09:46,234 According to this coding 192 00:09:46,234 --> 00:09:48,572 that lets us translate the digits of pie 193 00:09:48,572 --> 00:09:51,752 from a string of numbers to a string of letters, 194 00:09:51,752 --> 00:09:53,583 the word "proof" would correspond 195 00:09:53,583 --> 00:09:55,833 to the sequence 1618151506. 196 00:09:57,874 --> 00:10:02,185 The phrase "proof of concept" corresponds to this sequence, 197 00:10:02,185 --> 00:10:05,006 which appears in the digits of pie 198 00:10:05,006 --> 00:10:08,007 here around the 89-billionth digit. 199 00:10:08,007 --> 00:10:12,740 So the title of our show is encoded in the digits of pie, 200 00:10:12,740 --> 00:10:14,533 but we're not special. 201 00:10:14,533 --> 00:10:16,653 Humanity has only ever calculated pie 202 00:10:16,653 --> 00:10:19,653 to around 68.3 trillion digits only. 203 00:10:21,970 --> 00:10:24,974 But we do know that pie goes on forever 204 00:10:24,974 --> 00:10:29,301 and every possible finite sequence does occur somewhere. 205 00:10:29,301 --> 00:10:31,140 That means that somewhere in there are 206 00:10:31,140 --> 00:10:34,391 for sure the complete works of William Shakespeare, 207 00:10:34,391 --> 00:10:36,955 as well as a version of Romeo and Juliet, 208 00:10:36,955 --> 00:10:39,733 where they both grow old and have grandchildren 209 00:10:39,733 --> 00:10:43,645 and a word-for-word transcript of this episode. 210 00:10:43,645 --> 00:10:47,776 And the next conversation you are going to have. 211 00:10:47,776 --> 00:10:49,276 Infinity is weird. 212 00:10:50,322 --> 00:10:52,126 And just when you think you might be starting 213 00:10:52,126 --> 00:10:53,739 to wrap your head around it, 214 00:10:53,739 --> 00:10:56,664 you find out there isn't just one infinity, 215 00:10:56,664 --> 00:10:57,497 but in fact, 216 00:10:57,497 --> 00:11:00,522 there are infinitely many different infinities 217 00:11:00,522 --> 00:11:03,605 of different sizes stretching up to-- 218 00:11:04,572 --> 00:11:06,072 You get the point. 219 00:11:06,928 --> 00:11:09,595 (upbeat music) 220 00:11:10,893 --> 00:11:13,772 I'm very happy to introduce our special guest today, 221 00:11:13,772 --> 00:11:17,959 Dr. Eugenia Cheng, mathematician, concert pianist, 222 00:11:17,959 --> 00:11:20,020 and author of best sellers, 223 00:11:20,020 --> 00:11:23,505 like "How to Bake Pie" and "Beyond Infinity." 224 00:11:23,505 --> 00:11:24,785 Welcome to the show. 225 00:11:24,785 --> 00:11:26,237 -: Thank you so much for having me. 226 00:11:26,237 --> 00:11:29,414 -: Dr. Chang, what is so cool about Infiniti 227 00:11:29,414 --> 00:11:32,733 that inspired you to write an entire book about it? 228 00:11:32,733 --> 00:11:35,831 -: Well, I just love the fact that small children 229 00:11:35,831 --> 00:11:38,485 can get really excited and compelled thinking 230 00:11:38,485 --> 00:11:39,785 about this idea. 231 00:11:39,785 --> 00:11:42,274 But it took mathematicians thousands of years to figure out 232 00:11:42,274 --> 00:11:44,818 how to deal with it in a rigorous way. 233 00:11:44,818 --> 00:11:47,781 And that huge gap between little kids getting excited 234 00:11:47,781 --> 00:11:50,431 about it and mathematicians pinning it down 235 00:11:50,431 --> 00:11:51,950 is so exciting to me 236 00:11:51,950 --> 00:11:54,333 because it's where we can put ourselves to learn 237 00:11:54,333 --> 00:11:58,130 and discover and dream about all these things 238 00:11:58,130 --> 00:11:59,730 and become more intelligent. 239 00:11:59,730 --> 00:12:00,867 That's what this is about really. 240 00:12:00,867 --> 00:12:02,935 -: Yeah, infinity is so complex. 241 00:12:02,935 --> 00:12:05,534 There are different sizes of infinities. 242 00:12:05,534 --> 00:12:06,367 -: Yeah. 243 00:12:06,367 --> 00:12:08,375 And that is very difficult to get our heads around. 244 00:12:08,375 --> 00:12:10,999 And when we try and get our heads around it, 245 00:12:10,999 --> 00:12:14,018 our brains might feel like they're exploding. 246 00:12:14,018 --> 00:12:17,250 -: Well, to understand how there can be different sizes 247 00:12:17,250 --> 00:12:19,572 of infinity, we have to start by learning how 248 00:12:19,572 --> 00:12:21,418 to compare them. 249 00:12:21,418 --> 00:12:23,469 And to help us figure out how to do that, 250 00:12:23,469 --> 00:12:25,719 we're gonna need a simple but powerful technique 251 00:12:25,719 --> 00:12:29,975 that's at the heart of the following contest, mathematics. 252 00:12:29,975 --> 00:12:32,558 Let's bring in our contestants. 253 00:12:34,710 --> 00:12:37,131 -: I'm Asha and I'm a composer. 254 00:12:37,131 --> 00:12:41,178 -: My name is Jason and I'm an artist and a muralist from LA. 255 00:12:41,178 --> 00:12:43,375 I've never played the counting game before. 256 00:12:43,375 --> 00:12:45,292 And they didn't really explain how to play the game. 257 00:12:45,292 --> 00:12:48,187 They said, we're just gonna figure it out on the spot. 258 00:12:48,187 --> 00:12:49,653 -: I'm Ahmad Dami. 259 00:12:49,653 --> 00:12:51,335 I'm a filmmaker. 260 00:12:51,335 --> 00:12:54,002 I did not know what I was doing. 261 00:12:56,658 --> 00:12:57,602 -: For this competition, 262 00:12:57,602 --> 00:13:01,356 we have tasked our three contestants with a counting race. 263 00:13:01,356 --> 00:13:04,439 So each contestant has a jar of blue objects 264 00:13:04,439 --> 00:13:06,207 and a jar of pink objects. 265 00:13:06,207 --> 00:13:07,496 And they simply have to figure out 266 00:13:07,496 --> 00:13:09,789 which jar has more objects 267 00:13:09,789 --> 00:13:12,842 and they can use any of the tools provided here 268 00:13:12,842 --> 00:13:14,714 on the tables. But the goal is to figure out 269 00:13:14,714 --> 00:13:17,156 which jar has the most objects, the fastest. 270 00:13:17,156 --> 00:13:18,359 So you guys ready? 271 00:13:18,359 --> 00:13:19,192 -: Yeah, definitely. 272 00:13:19,192 --> 00:13:20,025 -: All right. 273 00:13:20,025 --> 00:13:21,692 Three, two, one, go! 274 00:13:22,927 --> 00:13:25,510 (upbeat music) 275 00:13:29,112 --> 00:13:29,945 -: Ooh! 276 00:13:35,292 --> 00:13:37,743 I think I see what she's doing. 277 00:13:37,743 --> 00:13:39,817 Dianna: Yeah? 278 00:13:39,817 --> 00:13:44,234 I love that just balls are flying all over the place. 279 00:13:45,995 --> 00:13:47,512 Oh my goodness. 280 00:13:47,512 --> 00:13:49,325 What is Ahmad doing? 281 00:13:49,325 --> 00:13:50,944 -: Looks like this contestant 282 00:13:50,944 --> 00:13:54,278 might actually be counting the blue ones. 283 00:13:54,278 --> 00:13:55,183 Dianna: Oh man. 284 00:13:55,183 --> 00:13:57,094 Individually counting from the different jars. 285 00:13:57,094 --> 00:13:57,927 Eugenia: That's arduous. 286 00:13:57,927 --> 00:13:59,052 Diana: Yeah. 287 00:13:59,052 --> 00:14:00,286 -: I thought I had a plan, 288 00:14:00,286 --> 00:14:04,764 but thinking it through, it wasn't an actual plan. 289 00:14:04,764 --> 00:14:06,431 It was just an idea. 290 00:14:14,566 --> 00:14:17,076 -: This one is trying to weigh them. 291 00:14:17,076 --> 00:14:18,021 -: I chose to weigh the objects. 292 00:14:18,021 --> 00:14:19,241 'Cause I thought that might be faster 293 00:14:19,241 --> 00:14:22,090 than trying to count each object individually. 294 00:14:22,090 --> 00:14:23,222 I was trying to avoid making a mess 295 00:14:23,222 --> 00:14:26,358 so I can actually get an accurate count of the objects. 296 00:14:26,358 --> 00:14:29,097 -: The challenging thing is that there's a lot of different-- 297 00:14:29,097 --> 00:14:29,956 -: Different size. 298 00:14:29,956 --> 00:14:31,134 -: There are a lot of different types 299 00:14:31,134 --> 00:14:32,381 of objects with different weights. 300 00:14:32,381 --> 00:14:33,324 -: So it's not really gonna help. 301 00:14:33,324 --> 00:14:34,966 -: No. 302 00:14:34,966 --> 00:14:37,633 (upbeat music) 303 00:14:49,201 --> 00:14:51,041 -: She's going way faster anyway. 304 00:14:51,041 --> 00:14:52,404 -: She's almost done. 305 00:14:52,404 --> 00:14:53,971 Eugenia: Yeah, right. 306 00:14:53,971 --> 00:14:55,254 -: Before we started the game, 307 00:14:55,254 --> 00:14:57,869 Dianna came to me and told me that we were gonna cheat. 308 00:14:57,869 --> 00:14:59,436 And she told me the strategy. 309 00:14:59,436 --> 00:15:01,587 She told me to take out the same amount of balls 310 00:15:01,587 --> 00:15:02,757 at the same time. 311 00:15:02,757 --> 00:15:06,885 So I was doing two at once and basically until the end 312 00:15:06,885 --> 00:15:11,755 and saw how many balls were left over in each glass jar. 313 00:15:11,755 --> 00:15:13,341 -: Yeah, so Asha has been briefed. 314 00:15:13,341 --> 00:15:14,174 -: I see that. 315 00:15:14,174 --> 00:15:16,857 And were the others told not to, 316 00:15:16,857 --> 00:15:18,027 were they told what to do? 317 00:15:18,027 --> 00:15:18,860 Looks like-- 318 00:15:18,860 --> 00:15:19,693 -: No. 319 00:15:19,693 --> 00:15:20,526 No, they weren't told anything. 320 00:15:20,526 --> 00:15:21,359 Which technique to use. 321 00:15:21,359 --> 00:15:22,351 -: You stacked it. 322 00:15:22,351 --> 00:15:23,250 -: It was stacked. 323 00:15:23,250 --> 00:15:24,201 Yeah, it's true. 324 00:15:24,201 --> 00:15:25,951 We're gonna have to profusely apologize to Jason 325 00:15:25,951 --> 00:15:28,498 and Ahmad after this. 326 00:15:28,498 --> 00:15:30,054 -: Blue! 327 00:15:30,054 --> 00:15:31,221 -: Oh, look, she's done already. 328 00:15:31,221 --> 00:15:32,054 -: She's done. 329 00:15:32,054 --> 00:15:33,554 We have a winner. 330 00:15:34,831 --> 00:15:36,133 We have a winner. 331 00:15:36,133 --> 00:15:38,751 Eugenia: We have a winner by miles. 332 00:15:38,751 --> 00:15:40,555 Director: What would you think if I told you 333 00:15:40,555 --> 00:15:44,637 that we told one of the contestants how to win going in? 334 00:15:44,637 --> 00:15:46,517 So you were always going to lose? 335 00:15:46,517 --> 00:15:47,799 -: All right. 336 00:15:47,799 --> 00:15:51,632 So you told somebody else the actual solution? 337 00:15:54,317 --> 00:15:56,648 -: If one contestant knew how to play the game 338 00:15:56,648 --> 00:15:58,083 or how to figure it out faster, 339 00:15:58,083 --> 00:16:00,041 then that kind of makes it unfair. 340 00:16:00,041 --> 00:16:01,019 -: I felt really good. 341 00:16:01,019 --> 00:16:01,852 I don't feel bad. 342 00:16:01,852 --> 00:16:03,832 I have no remorse for cheating. 343 00:16:03,832 --> 00:16:06,736 -: So how does a chaotic game like this relate 344 00:16:06,736 --> 00:16:09,389 to infinity in any way? 345 00:16:09,389 --> 00:16:11,781 If you were a contestant, is that what you would've done? 346 00:16:11,781 --> 00:16:12,614 -: It is. 347 00:16:12,614 --> 00:16:15,304 Because I know that trick from math, 348 00:16:15,304 --> 00:16:17,488 which is that you don't actually have to know 349 00:16:17,488 --> 00:16:20,211 how many there are in order to know which has more. 350 00:16:20,211 --> 00:16:22,020 The technique that the winner was using 351 00:16:22,020 --> 00:16:24,069 is an important mathematical technique. 352 00:16:24,069 --> 00:16:25,276 'Cause what she was doing, 353 00:16:25,276 --> 00:16:28,023 she didn't actually have to count how many objects were 354 00:16:28,023 --> 00:16:28,987 in each one because-- 355 00:16:28,987 --> 00:16:30,838 -: She's just trying the same number. 356 00:16:30,838 --> 00:16:32,952 -: Right, and so that's a mathematical technique 357 00:16:32,952 --> 00:16:34,085 that we can use on infinity 358 00:16:34,085 --> 00:16:36,664 because you can't tell how big infinity actually is, 359 00:16:36,664 --> 00:16:39,285 'cause it's too big. But what you can do is you can try 360 00:16:39,285 --> 00:16:41,049 and take out the same number. 361 00:16:41,049 --> 00:16:43,955 What you're doing there is you're lining them up in pairs. 362 00:16:43,955 --> 00:16:45,234 You try and match them in pairs. 363 00:16:45,234 --> 00:16:47,152 And if you can match them perfectly, 364 00:16:47,152 --> 00:16:51,529 one to one, on both sides, that's called a bijection. 365 00:16:51,529 --> 00:16:53,763 And if you can do that, then you know they're the same size. 366 00:16:53,763 --> 00:16:54,863 And if you can't do that, 367 00:16:54,863 --> 00:16:57,374 then you know that where there's some leftover, 368 00:16:57,374 --> 00:16:58,853 that one is bigger. 369 00:16:58,853 --> 00:17:00,324 And that's how we show that some infinity 370 00:17:00,324 --> 00:17:01,236 is bigger than others, 371 00:17:01,236 --> 00:17:04,004 because we can't ever match them up with each other. 372 00:17:04,004 --> 00:17:05,530 There's always some left, 373 00:17:05,530 --> 00:17:07,429 which means there's no bijection 374 00:17:07,429 --> 00:17:09,794 and that this infinity must be bigger. 375 00:17:09,794 --> 00:17:14,610 -: So even though every infinity goes onto infinity, 376 00:17:14,610 --> 00:17:17,443 some still have numbers left over. 377 00:17:18,431 --> 00:17:19,343 -: Right. 378 00:17:19,343 --> 00:17:22,743 And this was a huge mind boggling development in math. 379 00:17:22,743 --> 00:17:25,291 It was an argument called the Cantor diagonal argument, 380 00:17:25,291 --> 00:17:27,331 but it was basically this game 381 00:17:27,331 --> 00:17:30,651 and it's a very clever way of avoiding 382 00:17:30,651 --> 00:17:32,363 she having to count things 383 00:17:32,363 --> 00:17:35,263 and just seeing who's got some left over at the end. 384 00:17:35,263 --> 00:17:37,449 It is mind boggling, 385 00:17:37,449 --> 00:17:38,654 but that's the whole point. 386 00:17:38,654 --> 00:17:41,582 We boggle our minds and that's how we stretch our minds 387 00:17:41,582 --> 00:17:42,809 and become more intelligent. 388 00:17:42,809 --> 00:17:44,086 -: So the winning strategy was really 389 00:17:44,086 --> 00:17:46,731 a brilliant mathematical technique. 390 00:17:46,731 --> 00:17:47,564 -: Yes. 391 00:17:47,564 --> 00:17:49,865 And that represented an important development 392 00:17:49,865 --> 00:17:52,576 in the study of infinity in mathematics. 393 00:17:52,576 --> 00:17:53,576 -: Brilliant. 394 00:17:58,352 --> 00:17:59,600 At its core, 395 00:17:59,600 --> 00:18:01,968 the winning strategy in the counting race was all 396 00:18:01,968 --> 00:18:03,973 about attempting to create what is called 397 00:18:03,973 --> 00:18:06,544 a one-to-one correspondence 398 00:18:06,544 --> 00:18:08,738 between the two containers of objects. 399 00:18:08,738 --> 00:18:12,216 So as pairs of pink and blue objects were discarded, 400 00:18:12,216 --> 00:18:14,356 they were associated to each other. 401 00:18:14,356 --> 00:18:15,737 And that process proceeded right up 402 00:18:15,737 --> 00:18:18,088 until it couldn't anymore 403 00:18:18,088 --> 00:18:20,136 because there were no more pink objects to pair 404 00:18:20,136 --> 00:18:22,314 with a remaining blue one. 405 00:18:22,314 --> 00:18:25,525 And while we can never count all the way up to infinity, 406 00:18:25,525 --> 00:18:28,869 we can find ways to create one-to-one correspondences 407 00:18:28,869 --> 00:18:30,749 between infinities. 408 00:18:30,749 --> 00:18:32,883 For instance, this one which shows 409 00:18:32,883 --> 00:18:35,590 that the infinity of all whole numbers is the same 410 00:18:35,590 --> 00:18:39,101 as the infinity of just the even ones. 411 00:18:39,101 --> 00:18:41,954 Or this one, which shows that surprisingly there are 412 00:18:41,954 --> 00:18:45,704 as many whole numbers as there are fractions. 413 00:18:46,672 --> 00:18:48,045 And I'll spare you the details, 414 00:18:48,045 --> 00:18:49,580 but it turns out there's a way to show 415 00:18:49,580 --> 00:18:52,930 that there's no way to create a one-to-one correspondence 416 00:18:52,930 --> 00:18:55,723 between the whole numbers and the full set 417 00:18:55,723 --> 00:18:57,174 of real numbers 418 00:18:57,174 --> 00:18:59,757 or that continuum of numbers you need to fill 419 00:18:59,757 --> 00:19:02,887 in all the gaps between the fractions. 420 00:19:02,887 --> 00:19:03,907 So just like in the counting race, 421 00:19:03,907 --> 00:19:04,954 if you try to pair them up, 422 00:19:04,954 --> 00:19:08,717 you'll always find that there are some numbers left out. 423 00:19:08,717 --> 00:19:11,457 We're talking about problematic ones like pie 424 00:19:11,457 --> 00:19:14,613 and its other irrational cousins like E. 425 00:19:14,613 --> 00:19:17,746 so even though the number of whole numbers is infinite 426 00:19:17,746 --> 00:19:21,019 and the number of numbers on the continuum is infinite, 427 00:19:21,019 --> 00:19:22,925 it turns out that one of these infinities 428 00:19:22,925 --> 00:19:25,758 is actually bigger than the other. 429 00:19:28,049 --> 00:19:30,845 One of these infinities is bigger than the others, 430 00:19:30,845 --> 00:19:32,370 which is it? 431 00:19:32,370 --> 00:19:35,615 A, the number of possible whole numbers? 432 00:19:35,615 --> 00:19:40,615 B, the number of positive whole numbers divisible by 17? 433 00:19:41,048 --> 00:19:43,990 C, the number of different possible circles 434 00:19:43,990 --> 00:19:45,994 that can be drawn? 435 00:19:45,994 --> 00:19:48,914 Or D, the number of seconds between now 436 00:19:48,914 --> 00:19:50,664 and forever from now? 437 00:20:07,581 --> 00:20:11,431 A, B and D are all countable infinities. 438 00:20:11,431 --> 00:20:14,292 But since the area of a circle can in theory be equal 439 00:20:14,292 --> 00:20:16,690 to any irrational number, 440 00:20:16,690 --> 00:20:18,697 there are actually uncountable 441 00:20:18,697 --> 00:20:22,864 many different possible circles that can be drawn. 442 00:20:24,423 --> 00:20:25,933 Speaking of things that go on forever, 443 00:20:25,933 --> 00:20:28,183 let's check in on our dots. 444 00:20:29,577 --> 00:20:31,991 How's it going, Jared? 445 00:20:31,991 --> 00:20:33,574 -: Great. 446 00:20:33,574 --> 00:20:35,142 -: This is actually coming along. 447 00:20:35,142 --> 00:20:35,975 Yeah. 448 00:20:35,975 --> 00:20:37,158 I'm starting to see the patterns. 449 00:20:37,158 --> 00:20:38,877 Do you feel like you're noticing anything? 450 00:20:38,877 --> 00:20:40,997 -: Yeah, definitely a triangular shape. 451 00:20:40,997 --> 00:20:42,046 -: Yeah. 452 00:20:42,046 --> 00:20:44,154 The points on the edge. 453 00:20:44,154 --> 00:20:46,544 Those came from just this rolling process? 454 00:20:46,544 --> 00:20:47,377 -: Yeah. 455 00:20:47,377 --> 00:20:48,210 -: That's so cool. 456 00:20:48,210 --> 00:20:49,043 -: Did not put them there deliberately. 457 00:20:49,043 --> 00:20:50,875 It all happened naturally. 458 00:20:50,875 --> 00:20:52,117 The will of the die. 459 00:20:52,117 --> 00:20:52,950 -: Amazing. 460 00:20:52,950 --> 00:20:55,148 Well, you still have a long way to go. 461 00:20:55,148 --> 00:20:56,194 -: Oh, great. 462 00:20:56,194 --> 00:20:57,359 -: So keep it up. 463 00:20:57,359 --> 00:20:58,192 Good luck. 464 00:20:58,192 --> 00:20:59,192 -: Thank you. 465 00:21:00,609 --> 00:21:04,535 (light upbeat music) 466 00:21:04,535 --> 00:21:06,317 -: Welcome to the "Proof of Concept. 467 00:21:06,317 --> 00:21:09,083 "Infinite Fun with Kyle Hill" segment. 468 00:21:09,083 --> 00:21:10,252 This is Kyle Hill. 469 00:21:10,252 --> 00:21:11,378 -: That's me, baby. 470 00:21:11,378 --> 00:21:13,044 Hello, Diana. Thank you so much for having me. 471 00:21:13,044 --> 00:21:14,696 -: Kyle, it's so great to have you. 472 00:21:14,696 --> 00:21:15,663 -: Hello, my name is Kyle Hill. 473 00:21:15,663 --> 00:21:17,815 I'm a award-winning science communicator 474 00:21:17,815 --> 00:21:20,426 based in Los Angeles, California. 475 00:21:20,426 --> 00:21:23,093 (upbeat music) 476 00:21:29,704 --> 00:21:31,314 -: So excited to have you here. 477 00:21:31,314 --> 00:21:33,618 Before we even get started with the segment, 478 00:21:33,618 --> 00:21:35,474 I wanna play a game with you. 479 00:21:35,474 --> 00:21:36,803 -: Some sort of infinite game? 480 00:21:36,803 --> 00:21:38,185 -: Some sort of infinite game. 481 00:21:38,185 --> 00:21:39,638 -: I'm excited to talk about infinity 482 00:21:39,638 --> 00:21:43,310 because it's such a layered, complex concept. 483 00:21:43,310 --> 00:21:46,569 It can have applications in everything from mathematics 484 00:21:46,569 --> 00:21:48,923 to the number of possible universes 485 00:21:48,923 --> 00:21:51,507 and beyond my excitement for all of that of course, 486 00:21:51,507 --> 00:21:54,889 I love working with my friend, Diana. 487 00:21:54,889 --> 00:21:57,556 (upbeat music) 488 00:21:59,542 --> 00:22:00,737 -: We're gonna play now, 489 00:22:00,737 --> 00:22:03,065 but we're gonna reveal who wins later. 490 00:22:03,065 --> 00:22:03,898 -: Ooh. 491 00:22:03,898 --> 00:22:04,731 -: Okay. 492 00:22:04,731 --> 00:22:06,397 So here's the game, Kyle. We're just gonna get a card. 493 00:22:06,397 --> 00:22:07,230 Kyle: Okay. 494 00:22:07,230 --> 00:22:09,369 -: And we're gonna write the biggest number we can think of. 495 00:22:09,369 --> 00:22:11,051 We're just trying to get a bigger number 496 00:22:11,051 --> 00:22:12,505 than the other person. 497 00:22:12,505 --> 00:22:13,338 -: I don't know, Diana. 498 00:22:13,338 --> 00:22:14,774 I can think of some pretty big numbers. 499 00:22:14,774 --> 00:22:16,323 -: As can I. 500 00:22:16,323 --> 00:22:18,371 -: Well, Diana is the physics girl 501 00:22:18,371 --> 00:22:20,705 and she's very used to big numbers. 502 00:22:20,705 --> 00:22:22,163 Like the number of atoms in the universe 503 00:22:22,163 --> 00:22:22,996 or something like that. 504 00:22:22,996 --> 00:22:25,785 So I expect she's gonna have some large exponent, 505 00:22:25,785 --> 00:22:29,368 but I don't know how large that's gonna be. 506 00:22:31,625 --> 00:22:33,123 Can it go-- 507 00:22:33,123 --> 00:22:33,956 Yeah. 508 00:22:37,870 --> 00:22:39,990 -: I don't even know if this makes mathematical sense, 509 00:22:39,990 --> 00:22:41,593 but who cares? 510 00:22:41,593 --> 00:22:44,691 -: I don't even know if this is legible. 511 00:22:44,691 --> 00:22:46,313 -: Why are you writing so much? 512 00:22:46,313 --> 00:22:48,749 -: Biggest number you can think of. 513 00:22:48,749 --> 00:22:50,374 -: Hmm. 514 00:22:50,374 --> 00:22:52,691 In my mind you can write a big number 515 00:22:52,691 --> 00:22:54,858 with just a few numerals. 516 00:22:56,230 --> 00:22:57,614 Well, my strategy, 517 00:22:57,614 --> 00:22:59,227 I know a little bit about mathematics 518 00:22:59,227 --> 00:23:00,646 and big number notations. 519 00:23:00,646 --> 00:23:03,065 So if I do this correctly, 520 00:23:03,065 --> 00:23:07,331 no matter what number Diana gives, I should be victorious. 521 00:23:07,331 --> 00:23:08,164 -: Okay. 522 00:23:08,164 --> 00:23:08,997 You got it? 523 00:23:08,997 --> 00:23:10,663 -: I do. I think I have something spicy. 524 00:23:10,663 --> 00:23:12,329 -: Okay. So go ahead and put it in here. 525 00:23:12,329 --> 00:23:13,162 -: Don't look at it. 526 00:23:13,162 --> 00:23:13,995 -: I'm not looking. 527 00:23:13,995 --> 00:23:14,828 No peeking. 528 00:23:14,828 --> 00:23:16,560 All right, I'm going to put this aside for now, Kyle. 529 00:23:16,560 --> 00:23:17,833 So we'll open those in a bit. 530 00:23:17,833 --> 00:23:20,002 We're about to play some infinite Tic-Tac-Toe, Kyle, 531 00:23:20,002 --> 00:23:23,198 but first I wanna pick your brain about infinity. 532 00:23:23,198 --> 00:23:24,031 -: Yeah. 533 00:23:24,031 --> 00:23:26,878 Get the juices flowing before we play weird games. 534 00:23:26,878 --> 00:23:27,711 -: So Kyle, 535 00:23:27,711 --> 00:23:30,347 what is your go-to example of explaining the concept 536 00:23:30,347 --> 00:23:32,246 of infinity to people? 537 00:23:32,246 --> 00:23:33,079 -: Yeah. 538 00:23:33,079 --> 00:23:36,131 Infinity is inherently a hard concept to even think about 539 00:23:36,131 --> 00:23:38,654 because necessarily it's the most of everything, 540 00:23:38,654 --> 00:23:42,046 but one topic that's particularly salient today 541 00:23:42,046 --> 00:23:46,046 in the public is the idea of infinite universes. 542 00:23:46,886 --> 00:23:48,995 Now, a lot of quantum physicists believe 543 00:23:48,995 --> 00:23:51,281 that the many world's interpretation 544 00:23:51,281 --> 00:23:53,465 of quantum mechanics is the correct one. 545 00:23:53,465 --> 00:23:54,663 That sounds very complicated, 546 00:23:54,663 --> 00:23:58,945 but all it is is every possible interaction, 547 00:23:58,945 --> 00:24:02,753 spawns a new universe, every single possibility happens. 548 00:24:02,753 --> 00:24:05,475 So there's a universe in which I'm speaking Portuguese 549 00:24:05,475 --> 00:24:06,779 to you right now. 550 00:24:06,779 --> 00:24:09,450 There's a universe in which I never existed. 551 00:24:09,450 --> 00:24:12,963 There are an infinite array of possible choices, 552 00:24:12,963 --> 00:24:17,963 and we are only following one of those world lines. 553 00:24:18,001 --> 00:24:19,355 If you want to say it like that. 554 00:24:19,355 --> 00:24:23,065 -: Another universe like ours, but somewhere else. 555 00:24:23,065 --> 00:24:24,214 And another one. 556 00:24:24,214 --> 00:24:25,047 -: Exactly. 557 00:24:25,047 --> 00:24:26,918 -: And another one and on and on to infinity. 558 00:24:26,918 --> 00:24:30,894 -: And it gets so granular that one universe, 559 00:24:30,894 --> 00:24:34,637 I did this with my hands and another universe I did that. 560 00:24:34,637 --> 00:24:37,705 Now, if you extend that out to absolutely everything 561 00:24:37,705 --> 00:24:40,935 that could possibly be from, you know, 562 00:24:40,935 --> 00:24:44,083 someone else won World War II to my hair color is different. 563 00:24:44,083 --> 00:24:47,915 You get an infinite array of universes out there 564 00:24:47,915 --> 00:24:49,714 where you are doing a different thing, 565 00:24:49,714 --> 00:24:51,234 or you may not even exist. 566 00:24:51,234 --> 00:24:53,521 Or I could have hair as nice as yours, 567 00:24:53,521 --> 00:24:55,611 but we don't live in that universe. 568 00:24:55,611 --> 00:24:58,335 -: That's your go-to explanation for infinity? 569 00:24:58,335 --> 00:25:00,648 -: It's a bit long-winded. 570 00:25:00,648 --> 00:25:03,596 -: Do you think that infinity truly exists 571 00:25:03,596 --> 00:25:05,925 physically somehow in our universe? 572 00:25:05,925 --> 00:25:07,426 -: Now I know I kind of just talked 573 00:25:07,426 --> 00:25:09,545 about having an infinite number of universes, 574 00:25:09,545 --> 00:25:12,422 but in terms of just living in our own 575 00:25:12,422 --> 00:25:14,740 and what we can see, what we can observe, 576 00:25:14,740 --> 00:25:16,025 what we can experiment with, 577 00:25:16,025 --> 00:25:20,025 it seems unlikely to me that there's an infinity 578 00:25:21,109 --> 00:25:23,625 within this universe. 579 00:25:23,625 --> 00:25:26,427 And that stems from the fact that 580 00:25:26,427 --> 00:25:29,776 from the very moment you begin to exist, 581 00:25:29,776 --> 00:25:31,367 there are a number of constraints. 582 00:25:31,367 --> 00:25:34,294 There's only a set number of particles in the universe, 583 00:25:34,294 --> 00:25:35,994 as far as we know, 584 00:25:35,994 --> 00:25:38,042 and with all those constraints 585 00:25:38,042 --> 00:25:40,603 on what could possibly take place 586 00:25:40,603 --> 00:25:43,158 inside of our own experience, in our universe, 587 00:25:43,158 --> 00:25:45,183 it seems unlikely to me that there's 588 00:25:45,183 --> 00:25:49,183 a true physically infinite thing happening here. 589 00:25:50,043 --> 00:25:53,298 -: If I tell you, you can count one, two, three, four, five, 590 00:25:53,298 --> 00:25:56,821 but you can't count in between, some constraining, 591 00:25:56,821 --> 00:25:59,099 you can still have infinite numbers. 592 00:25:59,099 --> 00:26:00,393 -: Yes. 593 00:26:00,393 --> 00:26:04,497 Conceptually, I could count as high as I wanted to, 594 00:26:04,497 --> 00:26:06,030 but not before I die. 595 00:26:06,030 --> 00:26:06,946 -: Right. 596 00:26:06,946 --> 00:26:07,923 -: So I can't. 597 00:26:07,923 --> 00:26:09,515 -: There are physical human constraints. 598 00:26:09,515 --> 00:26:10,348 -: Yes. 599 00:26:10,348 --> 00:26:11,181 -: Yeah. 600 00:26:11,181 --> 00:26:12,694 -: While infinity is a mathematical concept 601 00:26:12,694 --> 00:26:13,527 that we know about, 602 00:26:13,527 --> 00:26:16,118 that we can work with, that's useful in mathematics. 603 00:26:16,118 --> 00:26:19,729 I couldn't give this interview an infinite number of times. 604 00:26:19,729 --> 00:26:21,418 -: It's hard to imagine a way 605 00:26:21,418 --> 00:26:24,344 you could physically experience infinity. 606 00:26:24,344 --> 00:26:26,010 -: Yeah. And I don't even know if 607 00:26:26,010 --> 00:26:28,414 that's the right way to frame infinity as a concept. 608 00:26:28,414 --> 00:26:30,201 -: That's the type of explanation in infinity 609 00:26:30,201 --> 00:26:33,081 that people just freeze and say, 610 00:26:33,081 --> 00:26:36,478 "Oh my God, this concept is beyond my comprehension." 611 00:26:36,478 --> 00:26:37,311 -: Yeah. 612 00:26:37,311 --> 00:26:38,144 -: It really is. 613 00:26:38,144 --> 00:26:38,977 -: No, yeah, yeah. 614 00:26:38,977 --> 00:26:41,382 -: But I think most infinities are beyond our comprehension. 615 00:26:41,382 --> 00:26:42,215 -: No, absolutely. 616 00:26:42,215 --> 00:26:43,953 I think a lot of us, when we were kids, 617 00:26:43,953 --> 00:26:46,683 at least maybe learning mathematics for the first time 618 00:26:46,683 --> 00:26:48,567 had that experience with, 619 00:26:48,567 --> 00:26:51,785 I'm plus one better than you, I'm plus two better than you. 620 00:26:51,785 --> 00:26:54,233 And then at some point when we're learning, say like, 621 00:26:54,233 --> 00:26:56,486 well, I'm infinity better than you. 622 00:26:56,486 --> 00:26:57,319 -: Yes. 623 00:26:57,319 --> 00:27:00,283 -: And that seems like some unbeatable concept 624 00:27:00,283 --> 00:27:02,358 or number where the conversation kind of stops. 625 00:27:02,358 --> 00:27:05,496 And I think the fact that so many of us have had 626 00:27:05,496 --> 00:27:07,115 an experience like that, 627 00:27:07,115 --> 00:27:10,279 I think it shows that this as a concept 628 00:27:10,279 --> 00:27:12,150 is inherently interesting. 629 00:27:12,150 --> 00:27:13,321 And then the math nerd was like, 630 00:27:13,321 --> 00:27:16,416 "Well, I'm Infinity plus one, which is technically bigger." 631 00:27:16,416 --> 00:27:19,808 And you're like, "Go, go read a book." 632 00:27:19,808 --> 00:27:21,564 -: The fact that this conversation's happening 633 00:27:21,564 --> 00:27:23,911 on elementary school playgrounds 634 00:27:23,911 --> 00:27:27,287 shows you how it's such a human concept to think of 635 00:27:27,287 --> 00:27:28,879 and to conceptualize infinity, 636 00:27:28,879 --> 00:27:31,159 even when we can't fully grasp it. 637 00:27:31,159 --> 00:27:31,992 Right? 638 00:27:31,992 --> 00:27:34,562 -: Yeah, it's kind of analogous to, you know, 639 00:27:34,562 --> 00:27:37,515 how long humans have been thinking about what zero means, 640 00:27:37,515 --> 00:27:38,797 what nothing means 641 00:27:38,797 --> 00:27:40,663 in the same way at the other end of the spectrum, 642 00:27:40,663 --> 00:27:42,398 what does everything mean? 643 00:27:42,398 --> 00:27:44,191 What does infinity and it's yeah-- 644 00:27:44,191 --> 00:27:47,998 It's probably just a product of how our brains evolve. 645 00:27:47,998 --> 00:27:50,258 That it's just fascinating, no matter what. 646 00:27:50,258 --> 00:27:51,940 -: It's so hard for computers 647 00:27:51,940 --> 00:27:54,223 to deal with the concept of infinity. 648 00:27:54,223 --> 00:27:56,945 And yet kids arrive at this on the playground. 649 00:27:56,945 --> 00:27:57,778 -: Yeah. 650 00:27:57,778 --> 00:27:59,248 Computers today still have to use 651 00:27:59,248 --> 00:28:01,898 when they're randomly generating numbers, for example, 652 00:28:01,898 --> 00:28:03,800 they still have to use seeds. 653 00:28:03,800 --> 00:28:06,279 It's not an actually infinite number of things. 654 00:28:06,279 --> 00:28:07,126 Computers can't do that. 655 00:28:07,126 --> 00:28:09,276 And yet the human mind very quickly goes 656 00:28:09,276 --> 00:28:12,132 to what is the biggest, what is everything? 657 00:28:12,132 --> 00:28:14,041 And that's occupied human minds 658 00:28:14,041 --> 00:28:17,362 for as long as we were humans with minds. 659 00:28:17,362 --> 00:28:20,565 So yeah, it's infinitely interesting. 660 00:28:20,565 --> 00:28:23,044 -: It is, it is in fact. 661 00:28:23,044 --> 00:28:25,424 There are conceptually infinite things 662 00:28:25,424 --> 00:28:27,178 about human experiences. 663 00:28:27,178 --> 00:28:29,878 Like there are games that are infinite. 664 00:28:29,878 --> 00:28:30,711 -: Sure. 665 00:28:30,711 --> 00:28:31,544 -: Some that are not, 666 00:28:31,544 --> 00:28:33,551 like there's a finite number of checkers games. 667 00:28:33,551 --> 00:28:34,384 -: Yes. 668 00:28:34,384 --> 00:28:36,497 -: But there's an infinite number of poker games. 669 00:28:36,497 --> 00:28:37,330 -: Yeah, it's interesting. 670 00:28:37,330 --> 00:28:40,262 Once you insert the human element into it 671 00:28:40,262 --> 00:28:42,549 and you have all these outside variables, 672 00:28:42,549 --> 00:28:45,049 then infinity comes into play. 673 00:28:45,049 --> 00:28:48,128 Like there's a set number of cards that you could have, 674 00:28:48,128 --> 00:28:50,007 a set number of hands you could be dealt, 675 00:28:50,007 --> 00:28:52,991 but once you have the human element inserted into it 676 00:28:52,991 --> 00:28:55,227 in decision and choice, 677 00:28:55,227 --> 00:28:57,832 then it can become an infinite array of things. 678 00:28:57,832 --> 00:28:59,967 And that's true of many card games 679 00:28:59,967 --> 00:29:01,077 like "Magic: The Gathering." 680 00:29:01,077 --> 00:29:03,887 Many computer games are infinite in that way as well, 681 00:29:03,887 --> 00:29:08,242 just because human choice is not necessarily rational 682 00:29:08,242 --> 00:29:09,802 or predictable. 683 00:29:09,802 --> 00:29:10,635 -: All right, Kyle. 684 00:29:10,635 --> 00:29:11,853 So speaking of infinite games, 685 00:29:11,853 --> 00:29:16,686 we are going to now play an infinite game of tic-tac-toe. 686 00:29:17,813 --> 00:29:19,480 -: Like, how long is that gonna take? 687 00:29:19,480 --> 00:29:23,647 Because I have lunch with a very important person. 688 00:29:24,853 --> 00:29:25,936 It's not you. 689 00:29:27,736 --> 00:29:30,403 (upbeat music) 690 00:29:31,934 --> 00:29:33,166 -: All right, Kyle, we are going 691 00:29:33,166 --> 00:29:35,654 to play infinite tic-tac-toe. 692 00:29:35,654 --> 00:29:37,886 Obviously this board is not infinite. 693 00:29:37,886 --> 00:29:38,720 -: That's true. 694 00:29:38,720 --> 00:29:39,974 -: But it's big enough for our purposes 695 00:29:39,974 --> 00:29:41,501 because the way you play this game 696 00:29:41,501 --> 00:29:45,587 is you wanna get five X's in a row or O's in a row 697 00:29:45,587 --> 00:29:47,579 instead of the normal three. 698 00:29:47,579 --> 00:29:48,412 -: Hmm. 699 00:29:48,412 --> 00:29:50,318 So there must be some mathematical reason to that. 700 00:29:50,318 --> 00:29:53,335 And this is practically infinite for our purposes, 701 00:29:53,335 --> 00:29:54,480 as you say. 702 00:29:54,480 --> 00:29:56,082 -: It is practically for our purposes 703 00:29:56,082 --> 00:29:57,487 and you can play anywhere you want. 704 00:29:57,487 --> 00:29:59,304 So even if I start here, 705 00:29:59,304 --> 00:30:03,287 you can play over there while I win on this side of course. 706 00:30:03,287 --> 00:30:05,656 -: Don't be so sure, Dianna. 707 00:30:05,656 --> 00:30:06,705 So what do you wanna be? 708 00:30:06,705 --> 00:30:07,870 -: I'll be X's. 709 00:30:07,870 --> 00:30:08,703 -: That makes me O's. 710 00:30:08,703 --> 00:30:09,536 -: You'll be O's. 711 00:30:09,536 --> 00:30:10,369 All right. 712 00:30:10,369 --> 00:30:11,202 Go ahead and start. 713 00:30:11,202 --> 00:30:12,185 -: I'm gonna go first. 714 00:30:12,185 --> 00:30:14,122 I think everyone in their life has played some version 715 00:30:14,122 --> 00:30:17,820 of Tic-Tac-Toe, but I've never played a version like this. 716 00:30:17,820 --> 00:30:18,903 That's so much larger. 717 00:30:18,903 --> 00:30:21,922 That's practically infinite for the game that we're playing. 718 00:30:21,922 --> 00:30:24,223 So I have no strategy going into it. 719 00:30:24,223 --> 00:30:28,347 I hope something comes to me as we start playing. 720 00:30:28,347 --> 00:30:30,667 I'm gonna go right here. 721 00:30:30,667 --> 00:30:31,500 -: Ooh. 722 00:30:31,500 --> 00:30:32,333 All right. 723 00:30:32,333 --> 00:30:33,166 My territory. 724 00:30:33,166 --> 00:30:33,999 All right. 725 00:30:33,999 --> 00:30:34,832 I will go-- 726 00:30:34,832 --> 00:30:36,351 I'm gonna go close to you. 727 00:30:36,351 --> 00:30:37,470 Right here. 728 00:30:37,470 --> 00:30:38,969 -: I feel like if I stay there, 729 00:30:38,969 --> 00:30:40,671 it's just like a regular game of Tic-Tac-Toe. 730 00:30:40,671 --> 00:30:44,009 So I'm gonna mix it up a little bit and I'm gonna go here. 731 00:30:44,009 --> 00:30:45,621 Now don't be fooled, dear viewer. 732 00:30:45,621 --> 00:30:47,089 It looks like I'm trying something fancy 733 00:30:47,089 --> 00:30:48,290 with this giant board, 734 00:30:48,290 --> 00:30:49,667 but I have no idea what I'm doing. 735 00:30:49,667 --> 00:30:51,605 Instead what I'm trying to do is 736 00:30:51,605 --> 00:30:54,684 if there's something to a giant Tic-Tac-Toe board, 737 00:30:54,684 --> 00:30:56,143 it must be going outside 738 00:30:56,143 --> 00:30:58,555 the normal three by three box, right? 739 00:30:58,555 --> 00:31:02,237 So I'm just gonna try to distract Dianna over here 740 00:31:02,237 --> 00:31:05,237 while I advance my plans over there. 741 00:31:06,251 --> 00:31:07,084 Okay. 742 00:31:08,709 --> 00:31:11,717 So I guess that's starting to force me to do something, 743 00:31:11,717 --> 00:31:15,300 but I also wanna start laying my own plans. 744 00:31:16,680 --> 00:31:18,736 -: Kind of like normal Tic-Tac-Toe so far, 745 00:31:18,736 --> 00:31:22,069 just a lot more squares to think about. 746 00:31:24,453 --> 00:31:26,536 Gotta get in there, Kyle. 747 00:31:35,171 --> 00:31:37,089 Well, obviously. 748 00:31:37,089 --> 00:31:40,637 -: Yes, but I'm forcing you to waste your moves. 749 00:31:40,637 --> 00:31:42,493 -: It's true. 750 00:31:42,493 --> 00:31:43,902 Are you though? 751 00:31:43,902 --> 00:31:45,235 -: I don't know. 752 00:31:46,318 --> 00:31:47,661 Interesting. 753 00:31:47,661 --> 00:31:49,078 Most interesting. 754 00:31:53,003 --> 00:31:54,202 -: If I didn't go right here. 755 00:31:54,202 --> 00:31:55,035 -: Yes. 756 00:31:55,035 --> 00:31:55,868 -: You would win. 757 00:31:55,868 --> 00:31:56,701 -: That would be-- 758 00:31:56,701 --> 00:31:58,618 -: That would be unwise. 759 00:32:01,851 --> 00:32:03,920 -: I mean, this is already more interesting 760 00:32:03,920 --> 00:32:05,920 than normal Tic-Tac-Toe. 761 00:32:07,118 --> 00:32:08,022 Interesting. 762 00:32:08,022 --> 00:32:09,024 -: I made him say, "Hmm," 763 00:32:09,024 --> 00:32:11,357 he thinks I have a strategy. 764 00:32:14,323 --> 00:32:18,490 -: I don't want you to start doing either of those. 765 00:32:24,090 --> 00:32:26,657 -: I like how this just sort of shot off. 766 00:32:26,657 --> 00:32:28,240 -: I feel like the-- 767 00:32:29,206 --> 00:32:30,897 This is my whole strategy. 768 00:32:30,897 --> 00:32:31,730 -: Yeah. 769 00:32:31,730 --> 00:32:32,771 -: Diagonals. 770 00:32:32,771 --> 00:32:34,691 The creeping worry that I have while playing this game 771 00:32:34,691 --> 00:32:37,290 is that because I have no experience with it 772 00:32:37,290 --> 00:32:39,174 and we're kind of just winging it 773 00:32:39,174 --> 00:32:42,169 is that I am completely missing out on something 774 00:32:42,169 --> 00:32:45,257 that should be deducible about this game. 775 00:32:45,257 --> 00:32:47,555 Well, if you have this in this position, 776 00:32:47,555 --> 00:32:51,856 then you just force them to do X or O in that position. 777 00:32:51,856 --> 00:32:54,086 I'm not seeing any of that so I could lose it any moment, 778 00:32:54,086 --> 00:32:55,253 it feels like. 779 00:32:59,297 --> 00:33:01,964 (upbeat music) 780 00:33:05,446 --> 00:33:10,363 -: This is the longest game of Tic-Tac-Toe I've ever played. 781 00:33:13,230 --> 00:33:15,810 -: Oh, I should have put it there. 782 00:33:15,810 --> 00:33:16,643 Dianna! 783 00:33:22,533 --> 00:33:23,909 -: Kyle Hill. 784 00:33:23,909 --> 00:33:25,245 -: Eliminated. 785 00:33:25,245 --> 00:33:26,637 -: Do I get to cross it? 786 00:33:26,637 --> 00:33:29,980 -: Yes, you always get to do the cross if you get it. 787 00:33:29,980 --> 00:33:30,813 Okay. 788 00:33:30,813 --> 00:33:31,920 -: There it is. 789 00:33:31,920 --> 00:33:32,753 Good game, sir. 790 00:33:32,753 --> 00:33:33,935 -: Yeah, I guess. 791 00:33:33,935 --> 00:33:35,815 Well, I think what's fun about games like this is 792 00:33:35,815 --> 00:33:37,383 that you can have a sudden realization 793 00:33:37,383 --> 00:33:39,819 of what the strategy is and how to play it well, 794 00:33:39,819 --> 00:33:42,019 especially if you're playing it for the first time. 795 00:33:42,019 --> 00:33:45,137 So the fact that Diana suddenly realized that 796 00:33:45,137 --> 00:33:47,686 in a certain orientation of her X's, 797 00:33:47,686 --> 00:33:50,765 basically her victory was assured. 798 00:33:50,765 --> 00:33:53,106 So even though losing doesn't feel great, 799 00:33:53,106 --> 00:33:55,322 especially to a colleague of mine 800 00:33:55,322 --> 00:33:59,530 who I very much wanted to embarrass on this show, 801 00:33:59,530 --> 00:34:00,730 I think it's fine. 802 00:34:00,730 --> 00:34:02,717 We learned something. 803 00:34:02,717 --> 00:34:05,335 -: The rules of this game demonstrate the balance 804 00:34:05,335 --> 00:34:09,189 that exists between the finite and the infinite. 805 00:34:09,189 --> 00:34:13,213 Two finite humans playing a potentially infinite game 806 00:34:13,213 --> 00:34:15,887 where boundless possibility is constrained 807 00:34:15,887 --> 00:34:18,054 by just a bit of strategy. 808 00:34:18,935 --> 00:34:21,373 -: Well, that was certainly interesting, wasn't it, Diana? 809 00:34:21,373 --> 00:34:22,383 -: That was fun. 810 00:34:22,383 --> 00:34:23,957 That was fun, Kyle. 811 00:34:23,957 --> 00:34:25,419 -: I can confidently say I've never done anything 812 00:34:25,419 --> 00:34:28,836 like that before, and I'm still confused. 813 00:34:30,186 --> 00:34:31,853 -: You'll have to keep practicing. 814 00:34:31,853 --> 00:34:33,455 But we have one more thing to do. 815 00:34:33,455 --> 00:34:34,418 -: Oh, that's right! 816 00:34:34,418 --> 00:34:38,517 -: We have to reveal who won the infinite game. 817 00:34:38,517 --> 00:34:39,350 -: Yeah. 818 00:34:39,350 --> 00:34:40,668 After all this thinking about big numbers 819 00:34:40,668 --> 00:34:42,637 and infinity and playing around with it, 820 00:34:42,637 --> 00:34:44,321 I wonder where our heads were at 821 00:34:44,321 --> 00:34:46,103 when we started this conversation. 822 00:34:46,103 --> 00:34:46,936 -: Yeah, okay. 823 00:34:46,936 --> 00:34:49,335 You hold my card and I hold your card. 824 00:34:49,335 --> 00:34:51,703 And then on three, two, one, we flip it over. 825 00:34:51,703 --> 00:34:52,649 All right. 826 00:34:52,649 --> 00:34:54,399 Three, two, one, go. 827 00:35:00,242 --> 00:35:03,331 -: So Diana wrote 99 to the 99 to the 99 to-- 828 00:35:03,331 --> 00:35:05,247 So I think this is the biggest, 829 00:35:05,247 --> 00:35:07,445 I mean, this is bigger than a Google. 830 00:35:07,445 --> 00:35:08,373 This is bigger than anything. 831 00:35:08,373 --> 00:35:11,384 What I wrote was the subset of all Diana's numbers 832 00:35:11,384 --> 00:35:13,507 that she gives plus one. 833 00:35:13,507 --> 00:35:14,840 -: He did indeed. 834 00:35:15,696 --> 00:35:17,594 He did indeed say my number. 835 00:35:17,594 --> 00:35:18,523 -: I tried to mitigate. 836 00:35:18,523 --> 00:35:19,395 -: Plus one. 837 00:35:19,395 --> 00:35:22,162 This is like the playground game, Kyle. 838 00:35:22,162 --> 00:35:25,472 This is the classic playground trick 839 00:35:25,472 --> 00:35:28,804 Kyle played on me and I never learn. 840 00:35:28,804 --> 00:35:30,539 -: I know some nerdy viewers of you 841 00:35:30,539 --> 00:35:32,913 at home might disagree with my actual notation 842 00:35:32,913 --> 00:35:35,144 of that number, but the idea was there. 843 00:35:35,144 --> 00:35:37,158 And when you're talking about infinity, the idea, 844 00:35:37,158 --> 00:35:39,559 the concept is what's important. 845 00:35:39,559 --> 00:35:42,726 I feel very good about beating Diana in this game 846 00:35:42,726 --> 00:35:46,080 because I lost in infinite Tic-Tac-Toe, 847 00:35:46,080 --> 00:35:47,697 which was extremely embarrassing. 848 00:35:47,697 --> 00:35:49,870 As you know, my entire brand is related 849 00:35:49,870 --> 00:35:52,691 to being a Tic-Tac-Toe champion. 850 00:35:52,691 --> 00:35:54,524 And so this felt good. 851 00:35:56,859 --> 00:35:58,832 -: What would've happened if you had done mine plus one 852 00:35:58,832 --> 00:36:00,893 and I had done yours plus one. 853 00:36:00,893 --> 00:36:02,299 We would've broken the game. 854 00:36:02,299 --> 00:36:05,513 -: We would've never left these seats. 855 00:36:05,513 --> 00:36:07,174 You know, even though I didn't win the main game 856 00:36:07,174 --> 00:36:08,637 of this episode, 857 00:36:08,637 --> 00:36:11,704 if true infinity exists somewhere, if there are, 858 00:36:11,704 --> 00:36:15,146 for example, an infinite number of possible universes, 859 00:36:15,146 --> 00:36:19,842 then there is a universe in which I both won that game 860 00:36:19,842 --> 00:36:21,558 and I'm the host of the show. 861 00:36:21,558 --> 00:36:23,028 Thanks for watching. 862 00:36:23,028 --> 00:36:24,282 Does that-- 863 00:36:24,282 --> 00:36:26,168 That doesn't work? 864 00:36:26,168 --> 00:36:27,001 Okay. 865 00:36:27,001 --> 00:36:28,001 That's cool. 866 00:36:32,538 --> 00:36:35,893 -: So far we've been talking about the infinitely big, 867 00:36:35,893 --> 00:36:39,820 but it's just as important to consider the infinitely small. 868 00:36:39,820 --> 00:36:43,489 The Greek philosopher Zeno noticed a long time ago 869 00:36:43,489 --> 00:36:47,322 that infinity can be found in surprisingly mundane places. 870 00:36:47,322 --> 00:36:50,335 And in many cases it can't be avoided. 871 00:36:50,335 --> 00:36:51,429 For example, 872 00:36:51,429 --> 00:36:53,132 he pointed out that even when doing something 873 00:36:53,132 --> 00:36:56,890 as simple as trying to walk from one spot to another, 874 00:36:56,890 --> 00:36:59,721 we have an infinite number of things we have to do 875 00:36:59,721 --> 00:37:01,869 before we can get there. 876 00:37:01,869 --> 00:37:04,656 So before I can get from over here to the other side 877 00:37:04,656 --> 00:37:09,591 of the room, I have to of course, walk halfway there. 878 00:37:09,591 --> 00:37:14,506 And now that I'm here, I have to get halfway again. 879 00:37:14,506 --> 00:37:15,424 And now that I'm here, 880 00:37:15,424 --> 00:37:18,722 I have to get halfway from this spot to the end of the room. 881 00:37:18,722 --> 00:37:22,629 But those first three halfways are only three items 882 00:37:22,629 --> 00:37:24,416 on an infinite to-do list 883 00:37:24,416 --> 00:37:27,976 that includes getting halfway there over and over, 884 00:37:27,976 --> 00:37:30,077 infinitely many times. 885 00:37:30,077 --> 00:37:31,994 But somehow we make it. 886 00:37:34,506 --> 00:37:36,578 How is that possible? 887 00:37:36,578 --> 00:37:38,784 The details of why we make it have something 888 00:37:38,784 --> 00:37:41,175 to do with a calculus concept called limits 889 00:37:41,175 --> 00:37:44,233 and infinite series that basically show 890 00:37:44,233 --> 00:37:46,712 how an infinite to-do list like this one gets done 891 00:37:46,712 --> 00:37:48,959 in a finite amount of time. 892 00:37:48,959 --> 00:37:51,144 As long as the steps take less and less time 893 00:37:51,144 --> 00:37:53,727 and get shorter quickly enough. 894 00:37:55,426 --> 00:37:57,690 Well, that's one solution. 895 00:37:57,690 --> 00:37:59,160 Some people think that sort of explanation 896 00:37:59,160 --> 00:38:01,162 isn't even required 897 00:38:01,162 --> 00:38:03,472 because they endorse theories of physics, 898 00:38:03,472 --> 00:38:06,397 like certain formulations of quantum gravity, 899 00:38:06,397 --> 00:38:09,310 where space and time are discreet. 900 00:38:09,310 --> 00:38:10,469 In other words, 901 00:38:10,469 --> 00:38:13,277 those theories propose a universe where space time 902 00:38:13,277 --> 00:38:15,807 comes in tiny indivisible units 903 00:38:15,807 --> 00:38:18,077 beyond which no meaningful notion 904 00:38:18,077 --> 00:38:21,973 of when and where can even be defined. 905 00:38:21,973 --> 00:38:24,352 This vision of the universe doesn't allow 906 00:38:24,352 --> 00:38:25,962 for Zenos' paradox. 907 00:38:25,962 --> 00:38:28,512 Since you can't keep cutting the distance 908 00:38:28,512 --> 00:38:29,667 in half indefinitely. 909 00:38:29,667 --> 00:38:31,776 You'll eventually hit the basic unit of length 910 00:38:31,776 --> 00:38:33,981 that can't be divided. 911 00:38:33,981 --> 00:38:36,012 But while it solves one paradox, 912 00:38:36,012 --> 00:38:40,037 it potentially introduces another that's even weirder. 913 00:38:40,037 --> 00:38:41,121 Pay close attention, 914 00:38:41,121 --> 00:38:44,010 because I'm about to prove that in a discrete universe, 915 00:38:44,010 --> 00:38:47,653 assuming you can't skip over spots and teleport, 916 00:38:47,653 --> 00:38:50,376 either nothing moves at all or everything would move 917 00:38:50,376 --> 00:38:52,957 at exactly the same speed. 918 00:38:52,957 --> 00:38:54,437 Check this out. 919 00:38:54,437 --> 00:38:56,729 If L is the smallest unit of length 920 00:38:56,729 --> 00:38:59,223 and T is the smallest unit of time, 921 00:38:59,223 --> 00:39:03,176 consider the following speed, L over T. 922 00:39:03,176 --> 00:39:05,399 That is the speed of moving one unit of length 923 00:39:05,399 --> 00:39:07,149 per one unit of time. 924 00:39:09,005 --> 00:39:12,517 If something were to move faster than one L per one T, 925 00:39:12,517 --> 00:39:14,991 then the length of time it would take to move one L 926 00:39:14,991 --> 00:39:18,305 would be less than one T, which is impossible. 927 00:39:18,305 --> 00:39:22,933 Since we said one T is the smallest possible amount of time. 928 00:39:22,933 --> 00:39:25,386 But then if something were to move slower 929 00:39:25,386 --> 00:39:27,104 than one L per one T, 930 00:39:27,104 --> 00:39:30,325 then the distance it would travel in one T would be less 931 00:39:30,325 --> 00:39:32,920 than one L, which is impossible. 932 00:39:32,920 --> 00:39:34,291 Since we agreed one L 933 00:39:34,291 --> 00:39:37,218 is the shortest possible amount of distance. 934 00:39:37,218 --> 00:39:41,512 Therefore everything that moves would move at the same speed 935 00:39:41,512 --> 00:39:42,737 L over T. 936 00:39:42,737 --> 00:39:44,070 One L per one T. 937 00:39:45,077 --> 00:39:47,161 Kind of trippy, right? 938 00:39:47,161 --> 00:39:50,087 So in a quantized version of the universe like this, 939 00:39:50,087 --> 00:39:52,589 everything would move at the same speed. 940 00:39:52,589 --> 00:39:54,138 And as weird as that seems, 941 00:39:54,138 --> 00:39:57,407 we can get even weirder by asking the following question, 942 00:39:57,407 --> 00:39:59,322 is it possible everything's not only moving 943 00:39:59,322 --> 00:40:00,594 at the same speed, 944 00:40:00,594 --> 00:40:04,855 but perhaps everything's also moving the same direction? 945 00:40:04,855 --> 00:40:07,455 Might not be quite as crazy as it sounds. 946 00:40:07,455 --> 00:40:09,773 One of the basic rules you might remember 947 00:40:09,773 --> 00:40:13,713 from geometry class says that parallel lines never cross. 948 00:40:13,713 --> 00:40:16,687 This rule, called the parallel postulate 949 00:40:16,687 --> 00:40:19,159 allows for a little wiggle room. 950 00:40:19,159 --> 00:40:20,475 We can change it slightly to say 951 00:40:20,475 --> 00:40:22,537 that parallel lines do cross, 952 00:40:22,537 --> 00:40:24,471 but they only do so at a special point, 953 00:40:24,471 --> 00:40:28,383 that happens to be infinitely far away. 954 00:40:28,383 --> 00:40:30,305 Adding these points at infinity and saying 955 00:40:30,305 --> 00:40:33,789 that infinitely many parallel lines can meet there, 956 00:40:33,789 --> 00:40:37,445 gives you what's called non-euclidean geometry. 957 00:40:37,445 --> 00:40:38,890 And because in real life, 958 00:40:38,890 --> 00:40:41,573 we can't ever reach those points at infinity, 959 00:40:41,573 --> 00:40:44,063 we aren't entirely sure what sort 960 00:40:44,063 --> 00:40:48,109 of geometry best describes the universe that we live in. 961 00:40:48,109 --> 00:40:51,151 Stay with me now, because this is the extra cool part. 962 00:40:51,151 --> 00:40:54,506 According to Einstein's theory of relativity, 963 00:40:54,506 --> 00:40:57,221 light waves don't experience time the same way 964 00:40:57,221 --> 00:40:59,658 that matter does. In fact, you might even say 965 00:40:59,658 --> 00:41:02,385 that light doesn't experience time at all. 966 00:41:02,385 --> 00:41:05,207 So if one day in the unimaginably distant future, 967 00:41:05,207 --> 00:41:08,613 there comes a time when the last bit of matter reverts back 968 00:41:08,613 --> 00:41:12,081 to being energy in the form of electromagnetic waves 969 00:41:12,081 --> 00:41:13,201 or light, 970 00:41:13,201 --> 00:41:15,164 there would be nothing left in the universe 971 00:41:15,164 --> 00:41:19,581 that experiences time, at least not in the usual way. 972 00:41:20,461 --> 00:41:24,619 At that moment, if the shape of reality is non-euclidean 973 00:41:24,619 --> 00:41:27,348 all of the light would simultaneously meet up 974 00:41:27,348 --> 00:41:29,520 at that point at infinity. 975 00:41:29,520 --> 00:41:31,826 But what's a moment if there's no time 976 00:41:31,826 --> 00:41:36,557 and how can things be simultaneous if there's no time? 977 00:41:36,557 --> 00:41:39,627 Anyway, a whole universe worth of energy, 978 00:41:39,627 --> 00:41:41,875 interacting at the edge of space and time 979 00:41:41,875 --> 00:41:44,794 where being as far away from each other as possible 980 00:41:44,794 --> 00:41:46,361 suddenly loops back into being 981 00:41:46,361 --> 00:41:49,392 as close together as possible. 982 00:41:49,392 --> 00:41:51,464 Something like that could be the perfect recipe 983 00:41:51,464 --> 00:41:54,192 for a brand new big bang, 984 00:41:54,192 --> 00:41:58,525 creating a cycle of infinities inside of infinities. 985 00:41:59,613 --> 00:42:03,676 Like I said, unproven and hotly debated, 986 00:42:03,676 --> 00:42:08,676 but definitely cool to think about, which reminds me-- 987 00:42:08,796 --> 00:42:11,963 (light upbeat music) 988 00:42:15,978 --> 00:42:18,781 Let's take a closer look at one example 989 00:42:18,781 --> 00:42:21,330 of the sort of counterintuitive things 990 00:42:21,330 --> 00:42:25,728 that can happen when we try to calculate with infinity. 991 00:42:25,728 --> 00:42:28,427 Consider the number 0.9999 992 00:42:28,427 --> 00:42:32,292 where the nines go on forever and ever. 993 00:42:32,292 --> 00:42:33,664 Surprisingly, it turns out 994 00:42:33,664 --> 00:42:37,484 that this number is actually equal to one. 995 00:42:37,484 --> 00:42:39,495 I'm not just saying that it's very close to one. 996 00:42:39,495 --> 00:42:41,078 It actually is one. 997 00:42:42,380 --> 00:42:46,197 Here's a simple proof of this fact using basic algebra. 998 00:42:46,197 --> 00:42:48,197 Say that 0.999 equals X, 999 00:42:49,126 --> 00:42:52,459 then 10X equals 10 times 0.999 or 9.999. 1000 00:42:56,983 --> 00:43:01,066 So 9X equals 10X minus X equals 9.999 minus 0.999 1001 00:43:04,307 --> 00:43:05,792 equals nine. 1002 00:43:05,792 --> 00:43:07,292 So 9X equals nine. 1003 00:43:09,167 --> 00:43:11,725 And lastly 9X equals nine 1004 00:43:11,725 --> 00:43:14,774 of course means that X equals one. 1005 00:43:14,774 --> 00:43:17,983 But we started out by saying that 0.999 equals X. 1006 00:43:17,983 --> 00:43:19,650 So 0.999 equals one. 1007 00:43:21,380 --> 00:43:22,630 That's a proof. 1008 00:43:23,642 --> 00:43:26,564 Upon close inspection we see that infinity 1009 00:43:26,564 --> 00:43:30,912 is actually playing a subtle but fundamental role here 1010 00:43:30,912 --> 00:43:32,699 because the algebra only works out this way 1011 00:43:32,699 --> 00:43:36,265 if there really are infinitely many nines. 1012 00:43:36,265 --> 00:43:38,805 For instance, if instead of infinitely many nines, 1013 00:43:38,805 --> 00:43:41,305 there were just 10 nines then, 1014 00:43:46,071 --> 00:43:48,754 where the rest is just zeros forever. 1015 00:43:48,754 --> 00:43:51,504 So 9X equals 10X minus X equals-- 1016 00:43:56,233 --> 00:44:00,396 So the proof can't continue in the same way. 1017 00:44:00,396 --> 00:44:04,377 Now that was a 100% legit math, but watch out 1018 00:44:04,377 --> 00:44:05,771 because fooling around 1019 00:44:05,771 --> 00:44:09,145 with infinite calculations can get tricky real quick. 1020 00:44:09,145 --> 00:44:10,479 And if you aren't careful, 1021 00:44:10,479 --> 00:44:12,481 you might end up thinking you've proven something, 1022 00:44:12,481 --> 00:44:14,513 which isn't true at all. 1023 00:44:14,513 --> 00:44:15,598 Like this old trick, 1024 00:44:15,598 --> 00:44:18,764 which looks like a proof that one equals zero. 1025 00:44:18,764 --> 00:44:20,963 But of course it isn't. 1026 00:44:20,963 --> 00:44:22,296 One equals zero? 1027 00:44:23,815 --> 00:44:27,727 Turns out infinity is the problem here. 1028 00:44:27,727 --> 00:44:30,894 That sum is an example of what's known 1029 00:44:32,554 --> 00:44:37,015 as a divergent series and taken on into infinity, 1030 00:44:37,015 --> 00:44:40,497 can't be manipulated using normal algebra. 1031 00:44:40,497 --> 00:44:44,830 Sometimes infinity is just a bit too much to handle. 1032 00:44:49,336 --> 00:44:52,419 (light upbeat music) 1033 00:44:57,139 --> 00:45:00,571 Oh my gosh, Jared, this looks amazing. 1034 00:45:00,571 --> 00:45:02,457 I think that you've done enough dots. 1035 00:45:02,457 --> 00:45:03,817 I think you're done at this point. 1036 00:45:03,817 --> 00:45:05,234 How does it feel? 1037 00:45:06,450 --> 00:45:09,035 -: Satisfying to see it goes so far. 1038 00:45:09,035 --> 00:45:10,156 It actually looks really good. 1039 00:45:10,156 --> 00:45:11,089 -: It looks amazing. 1040 00:45:11,089 --> 00:45:13,916 You really can see all of the triangles popping out 1041 00:45:13,916 --> 00:45:14,985 of the pattern. 1042 00:45:14,985 --> 00:45:18,423 It's very obvious that you followed the directions 1043 00:45:18,423 --> 00:45:20,778 because you would not have gotten this pattern 1044 00:45:20,778 --> 00:45:23,458 if you didn't draw like this using the die. 1045 00:45:23,458 --> 00:45:24,378 -: Of course. 1046 00:45:24,378 --> 00:45:25,211 -: Yeah. 1047 00:45:25,211 --> 00:45:26,044 Amazing. 1048 00:45:26,044 --> 00:45:28,557 So you may or may not be familiar with this picture, 1049 00:45:28,557 --> 00:45:30,488 but this is an approximation of something known 1050 00:45:30,488 --> 00:45:33,061 as the Sierpiński triangle. 1051 00:45:33,061 --> 00:45:34,394 And I say it just an approximation 1052 00:45:34,394 --> 00:45:36,410 because the real Sierpiński triangle 1053 00:45:36,410 --> 00:45:38,155 is a theoretical object. 1054 00:45:38,155 --> 00:45:41,026 That's technically impossible to draw 1055 00:45:41,026 --> 00:45:43,359 as it would require following this process 1056 00:45:43,359 --> 00:45:46,959 or something like it for infinitely many steps. 1057 00:45:46,959 --> 00:45:50,011 So you'd be here for forever. 1058 00:45:50,011 --> 00:45:52,175 That being said, with enough time on your hands, 1059 00:45:52,175 --> 00:45:54,794 this process would yield the image 1060 00:45:54,794 --> 00:45:56,346 to whatever level of complexity 1061 00:45:56,346 --> 00:45:59,096 or resolution you're looking for. 1062 00:46:04,175 --> 00:46:07,192 The process used to draw this image is known 1063 00:46:07,192 --> 00:46:09,394 as fractal encryption. 1064 00:46:09,394 --> 00:46:12,197 It's an alternative method of coding information 1065 00:46:12,197 --> 00:46:15,317 that rather than saving an entire image pixel by pixel, 1066 00:46:15,317 --> 00:46:18,647 instead saves a rule or a process that a computer 1067 00:46:18,647 --> 00:46:23,575 or you can follow to recreate the image from scratch. 1068 00:46:23,575 --> 00:46:25,817 The technique isn't just for images. 1069 00:46:25,817 --> 00:46:26,662 In theory, it could be applied 1070 00:46:26,662 --> 00:46:29,514 to almost any sort of information. 1071 00:46:29,514 --> 00:46:32,533 Using this method, something like the Sierpiński triangle, 1072 00:46:32,533 --> 00:46:35,329 which is technically too large of a concept 1073 00:46:35,329 --> 00:46:38,061 to ever save as a traditional photo 1074 00:46:38,061 --> 00:46:41,251 can be recreated from scratch by an algorithm 1075 00:46:41,251 --> 00:46:44,381 to whatever level of resolution is required 1076 00:46:44,381 --> 00:46:47,881 and is saved in a single line of code. 1077 00:46:47,881 --> 00:46:49,174 It's a lot smaller. 1078 00:46:49,174 --> 00:46:51,679 This method has been used to make image storage 1079 00:46:51,679 --> 00:46:55,381 way more efficient for things like rendering 3D graphics 1080 00:46:55,381 --> 00:46:58,047 for video games and digital sound effects. 1081 00:46:58,047 --> 00:47:00,778 But most compelling of all with this concept 1082 00:47:00,778 --> 00:47:02,119 are the early indications 1083 00:47:02,119 --> 00:47:04,783 from cutting edge neuroscience research 1084 00:47:04,783 --> 00:47:07,775 that our brains may be using something analogous 1085 00:47:07,775 --> 00:47:11,461 to fractal encryption to store memories, 1086 00:47:11,461 --> 00:47:14,922 allowing for some combination of saved information 1087 00:47:14,922 --> 00:47:16,338 and then algorithmic processes 1088 00:47:16,338 --> 00:47:19,199 to be followed in our minds that come together 1089 00:47:19,199 --> 00:47:20,546 to recreate memories. 1090 00:47:20,546 --> 00:47:22,962 whenever we need to recall them, 1091 00:47:22,962 --> 00:47:25,083 rather than pulling up a saved file, 1092 00:47:25,083 --> 00:47:27,737 which would be more akin to looking at a photo 1093 00:47:27,737 --> 00:47:29,820 or watching an old video. 1094 00:47:31,731 --> 00:47:36,015 Which of the following geometrical oddities actually exists 1095 00:47:36,015 --> 00:47:37,869 in theoretical math? 1096 00:47:37,869 --> 00:47:40,601 A, a snowflake with a finite area 1097 00:47:40,601 --> 00:47:43,562 enclosed by an infinite boundary? 1098 00:47:43,562 --> 00:47:45,317 B, a funnel that can only 1099 00:47:45,317 --> 00:47:47,817 hold a finite amount of liquid, 1100 00:47:47,817 --> 00:47:50,706 but would take infinite paint to color? 1101 00:47:50,706 --> 00:47:53,471 C, a sphere that can be cut into pieces 1102 00:47:53,471 --> 00:47:58,471 and rearranged into two spheres of exactly the same size? 1103 00:47:58,669 --> 00:48:00,586 Or D, all of the above? 1104 00:48:10,526 --> 00:48:13,417 The Koch Snowflake, Gabriel's Horn 1105 00:48:13,417 --> 00:48:16,506 and the Banach-Tarski paradox are just a few 1106 00:48:16,506 --> 00:48:18,538 of the strange things that can happen 1107 00:48:18,538 --> 00:48:20,538 when infinity runs wild. 1108 00:48:28,853 --> 00:48:32,933 If our minds are in fact using a form of fractal encryption, 1109 00:48:32,933 --> 00:48:35,489 that would mean that we carry a version of infinity around 1110 00:48:35,489 --> 00:48:37,455 inside of ourselves, 1111 00:48:37,455 --> 00:48:40,048 that our capacity for creativity 1112 00:48:40,048 --> 00:48:43,835 and invention may in fact be unlimited. 1113 00:48:43,835 --> 00:48:47,473 But it makes you wonder which infinity are we? 1114 00:48:47,473 --> 00:48:51,027 The first one or one of the really big ones? 1115 00:48:51,027 --> 00:48:53,371 This has been "Proof of Concept." 1116 00:48:53,371 --> 00:48:55,536 Thanks for watching. 1117 00:48:55,536 --> 00:48:58,203 (upbeat music)