1 00:00:00,190 --> 00:00:04,070 OK, Pactis right away. I want you a Picture, a number. 2 00:00:04,910 --> 00:00:08,350 È una roba in normal big number light the National dad or the 3 00:00:08,350 --> 00:00:11,510 number Stars the Galaxy thusere cute this are franky. 4 00:00:14,040 --> 00:00:16,320 Zero in. The Grand Scheme. 5 00:00:16,440 --> 00:00:22,440 A number so catastrofica mind bandingly collasso there if you 6 00:00:22,440 --> 00:00:25,200 try to hold just the bidgets of it in your mind. 7 00:00:25,320 --> 00:00:29,080 Just the budget. If you try to fisica in code 8 00:00:29,240 --> 00:00:32,600 that much information in the nurance of you Brain, your head 9 00:00:32,600 --> 00:00:35,520 with liraly collapse into a. Blackhole. 10 00:00:36,870 --> 00:00:47,230 On the Beckenstein Bound whitch basic dictatis the maximum of 11 00:00:47,230 --> 00:00:50,910 information you can Cream into a fine region of Space givenut 12 00:00:50,910 --> 00:00:54,870 Energy if you pack too much information, too much entrope 13 00:00:54,870 --> 00:00:56,710 entro the volume of the Human School the. 14 00:00:57,270 --> 00:00:59,590 Density exeedes the Swarce Child Radios. 15 00:00:59,630 --> 00:01:01,670 Exactly. You become a sinulary. 16 00:01:01,910 --> 00:01:05,510 Pooh, so we're talking, but Numbers there physicly dangerous 17 00:01:05,510 --> 00:01:08,110 to think about about in Air antirity we are. 18 00:01:08,280 --> 00:01:12,120 Talking about hyper large Numbers, the Absolute heavy 19 00:01:12,120 --> 00:01:15,480 weights of the mothworld, specificly things like grams 20 00:01:15,480 --> 00:01:18,200 number. Grams number is the poster Child 21 00:01:18,200 --> 00:01:21,280 for this Hall concept. It's a number so large de the 22 00:01:21,280 --> 00:01:26,240 intere observable Universe far forse molto right it down even 23 00:01:26,240 --> 00:01:29,480 if you wate a single digit on every single plank volume. 24 00:01:29,680 --> 00:01:31,840 Witch is a smalles Misurable unite of Space. 25 00:01:33,390 --> 00:01:35,110 Makes this Deep dice Today. So? 26 00:01:35,110 --> 00:01:43,790 Fascinating eventual this number is too big for the Universe. 27 00:01:43,790 --> 00:01:48,030 Contain Eventhing now the definize all standard Scientific 28 00:01:48,270 --> 00:01:52,230 notation we action know exactly. How itance we do we know the 29 00:01:52,230 --> 00:01:54,390 lest, we know the lest, we know the last Billy and digits 30 00:01:54,390 --> 00:01:55,230 action. There. 31 00:01:55,350 --> 00:01:59,150 The very, very bom of this infinite Towers of Sher, math, 32 00:01:59,150 --> 00:02:02,080 Medical caos there. There is a rigido totali 33 00:02:02,080 --> 00:02:05,240 deterministic structure. A paterna è giusto lax in the 34 00:02:05,240 --> 00:02:07,520 Place. It's a phenomen Matmeticians 35 00:02:07,520 --> 00:02:11,120 Call of Frozen digits, or sometimes the years stable 36 00:02:11,120 --> 00:02:13,080 digits. So Welcome to the Deep dife. 37 00:02:13,480 --> 00:02:16,560 Today we're going on a serious Journey into the infinite. 38 00:02:17,160 --> 00:02:20,520 We're un packing a stack of Pretty Dance Research Papers 39 00:02:20,880 --> 00:02:24,440 very heavy on the number Theory primary focassing on the 40 00:02:24,440 --> 00:02:29,000 incredible collaborative work of enigmate and mathmation Marco 41 00:02:29,000 --> 00:02:32,040 Ripa. Matics of Tetration. 42 00:02:32,120 --> 00:02:36,680 Tetrational definer second todays to solve a very specific 43 00:02:36,680 --> 00:02:39,630 Mystery. How can a math Medical operation 44 00:02:39,790 --> 00:02:42,590 there? Explodes Tours Infinity ad in 45 00:02:42,590 --> 00:02:46,230 Trillias of Digits millisecondi somehouse down into a 46 00:02:46,230 --> 00:02:49,110 predictable Frozen pattern at the very. 47 00:02:49,110 --> 00:02:53,190 Tailanding can we miser the Speed of a Stability because 48 00:02:53,190 --> 00:02:57,070 than is the key contribution of the source imperiale. 49 00:02:58,080 --> 00:03:00,960 Ripa and his colleghs EN in matematica dingus nodues the 50 00:03:00,960 --> 00:03:04,800 parent dei file spedomater dei developt metric cold congruence 51 00:03:04,800 --> 00:03:07,320 Speed. Wheeve. 52 00:03:07,480 --> 00:03:11,320 This metric basicaly teles the Speed limit of the number system 53 00:03:11,320 --> 00:03:12,760 itself. It's a story. 54 00:03:12,760 --> 00:03:16,920 The takeses from basic aritmetic wet we alnow straight into the 55 00:03:16,920 --> 00:03:20,040 weard underground World of Paiatic Analysis. 56 00:03:20,710 --> 00:03:22,790 Majler aritmetic ed eventualmente. 57 00:03:22,790 --> 00:03:25,910 A really Deep filosofico questionmark Weather we are 58 00:03:25,910 --> 00:03:29,510 inventing Numbers come we do this math or just discovering 59 00:03:29,510 --> 00:03:32,910 locations on a map that's literally always been. 60 00:03:33,070 --> 00:03:36,800 There, the gap. Between Tols and Absolute order. 61 00:03:37,400 --> 00:03:40,440 So buckle up we'ere looking for order in the infinite. 62 00:03:40,600 --> 00:03:44,440 OK. So to understand the end the 63 00:03:44,440 --> 00:03:47,440 Universe realisti and this Monster Numbers, we have to 64 00:03:47,440 --> 00:03:49,400 understand how the your build in the first place. 65 00:03:49,680 --> 00:03:51,720 We need to talk about the later of operations. 66 00:03:51,880 --> 00:03:54,760 Right moseless probabile no the first three runs of the this 67 00:03:54,760 --> 00:03:57,160 later perfettaly you learn the man elemento. 68 00:03:58,990 --> 00:04:03,350 Counting THREE Plus Three. Simple enough than room two is 69 00:04:03,350 --> 00:04:06,750 moltiplication what is just repeated Edition three Times 70 00:04:06,790 --> 00:04:09,190 fours religios three addio. It's of War. 71 00:04:09,670 --> 00:04:11,750 Times THREE Plus Three, Plus Three Plus Three. 72 00:04:11,750 --> 00:04:14,830 The run three is expanentiation force repeat moltiplication 73 00:04:15,270 --> 00:04:19,230 three de the forth Power is. Three Time, Three Times Three 74 00:04:19,230 --> 00:04:21,680 Times Three. Most people get off the buss 75 00:04:22,280 --> 00:04:24,360 today. We are the forth wrong. 76 00:04:24,920 --> 00:04:29,320 Tetration, tetration it, softcomes from tetra mining Four 77 00:04:29,320 --> 00:04:32,880 and iteration it is iterated exponentiation. 78 00:04:33,480 --> 00:04:35,200 Visuali. If you reading a math paper this 79 00:04:35,200 --> 00:04:37,960 is usaly ritene as a Little superscript number to the left 80 00:04:37,960 --> 00:04:41,080 the bass. So a smallbeefol by a big a we 81 00:04:41,080 --> 00:04:45,880 re that is tetris of hight Bee with base a or sometemes 82 00:04:45,880 --> 00:04:51,910 beattred to a. For you list if i SEE a. 83 00:04:52,270 --> 00:04:57,310 Little Four to the left of the three that is not three tens for 84 00:04:57,310 --> 00:05:00,270 it's night event three to the fourth Power what is eightyone 85 00:05:00,270 --> 00:05:04,630 Four tour three is. The tour of three Race to the 86 00:05:04,630 --> 00:05:09,470 Power three, three Race to the Power three, Race to the Power 87 00:05:09,470 --> 00:05:12,230 of three. And crucialmente in Israele Trip 88 00:05:12,230 --> 00:05:14,790 Up on i try to do this on African. 89 00:05:14,840 --> 00:05:17,960 You have to a. Valuhead from the tampdown. 90 00:05:18,040 --> 00:05:22,240 If you wheels collapse into a sportly larger standard exponent 91 00:05:22,480 --> 00:05:25,320 to get the True scale of tetration, you start at the 92 00:05:25,320 --> 00:05:27,440 penthouse and work your way down to the lobi. 93 00:05:27,560 --> 00:05:29,960 Let's work through the this to give the listener two Sense of 94 00:05:29,960 --> 00:05:36,310 the very go involution. For tetrade to three, high Four, 95 00:05:36,830 --> 00:05:40,830 base three the very tap the Tower is three to the. 96 00:05:41,190 --> 00:05:44,910 Third Power. Seven iseno Stone the Towers One 97 00:05:44,910 --> 00:05:48,830 step Shorder naw we take the next three down e wese it to 98 00:05:48,830 --> 00:05:50,950 the. Twentyseventh Power. 99 00:05:51,000 --> 00:05:54,400 Leaving the Realm of Human Intuition, three three to the 100 00:05:54,400 --> 00:05:58,680 tween seventh Power isley Seven point six trillia specifica 101 00:05:58,680 --> 00:06:01,920 Seven trillion sixdred twenty-five billion five hundred 102 00:06:01,920 --> 00:06:04,520 ninety Seven, Four hundred eighty Four thousand Nine 103 00:06:04,520 --> 00:06:07,320 hundred eighty Seven. OK, Seven point six trileon. 104 00:06:07,640 --> 00:06:10,280 That is a massive number. That's the National DAD of a 105 00:06:10,280 --> 00:06:14,280 mediam size country writer. But i can still somewth all that 106 00:06:14,280 --> 00:06:16,870 concept in my head. Boh, we are. 107 00:06:17,550 --> 00:06:21,390 We sill have One more step we. Hat the boom three. 108 00:06:21,440 --> 00:06:25,480 Calculate three Race to the Power of Seven point six 109 00:06:25,680 --> 00:06:27,600 trillant. Even is a number with. 110 00:06:27,600 --> 00:06:33,600 Refly three point six trilly indigence not the value, the 111 00:06:33,600 --> 00:06:35,000 number. Of diject. 112 00:06:35,080 --> 00:06:39,840 Yes, if you print the number in a standard twelve point font on 113 00:06:39,840 --> 00:06:43,920 normal paper, the stack of paper REACH from the Earth to the Moon 114 00:06:43,920 --> 00:06:46,920 and back moltible Times. Orf, you lad the pagers out flat 115 00:06:46,920 --> 00:06:50,480 side by side e will rapper on the equator. 116 00:06:50,840 --> 00:06:52,040 Hundreds of Times over. The. 117 00:06:52,240 --> 00:06:56,600 Site for this is a baby. Tower, That's. 118 00:06:56,880 --> 00:07:00,560 Nothing's Numbers is define usingus upper annotation witch 119 00:07:00,560 --> 00:07:04,560 intervices a all other Beast of recursion fondamentaly 120 00:07:04,600 --> 00:07:08,080 underneath of the notation it represent part are of threees 121 00:07:08,600 --> 00:07:11,080 where the high itself is a number so big the Universe 122 00:07:11,080 --> 00:07:12,760 breaks toying to Express the high to. 123 00:07:12,840 --> 00:07:16,240 We're effetiva dealing with pow terres of infinite high. 124 00:07:16,680 --> 00:07:19,280 Practical. Perpaces, Yes, infinite. 125 00:07:19,360 --> 00:07:22,880 South Tour the just never stops grawing it's reaching up 126 00:07:22,880 --> 00:07:23,680 Forever. No? 127 00:07:23,760 --> 00:07:27,000 Normaly when we think of things grawing that fast a candid, 128 00:07:27,000 --> 00:07:29,920 explosive runsway growth, we take a pure caos. 129 00:07:29,920 --> 00:07:32,440 Youth of Enterpey. Exactly, you resume. 130 00:07:32,440 --> 00:07:35,520 That is, you Hat another Power three to the very top, the digit 131 00:07:35,520 --> 00:07:38,840 at the beat charning like a blender, everything shifting 132 00:07:38,840 --> 00:07:40,920 left, everything changing constantling. 133 00:07:40,960 --> 00:07:45,760 The intuition, but. Math is Fall of completamente 134 00:07:45,760 --> 00:07:47,280 contorintutive surprises. What? 135 00:07:47,520 --> 00:07:51,280 The Research and this is SOS Central to Marco ripus work with 136 00:07:51,280 --> 00:07:56,360 eny banca is that as the tour get haire and ire the digit on 137 00:07:56,360 --> 00:08:00,160 the Four right Inside the smalls valus this stat moving? 138 00:08:01,390 --> 00:08:04,390 Whatsement. Beenpord by The Truck. 139 00:08:04,390 --> 00:08:13,270 Building. Iron Hiro floors, It's fluid, 140 00:08:13,270 --> 00:08:15,310 It's concentaly changing, but the boom. 141 00:08:15,950 --> 00:08:19,470 The Foundation, IT cures it, Arts it set and the Absolute 142 00:08:19,470 --> 00:08:24,470 Stone. And once it set, it never 143 00:08:24,470 --> 00:08:27,520 changes again nome. Tower, the Botton logic is 144 00:08:27,520 --> 00:08:31,200 completa locting let's. Look at a Simple Exsample Street 145 00:08:31,200 --> 00:08:33,559 from the source material. The Hall visualizes pace, five 146 00:08:33,559 --> 00:08:36,120 pace. Five is a Classic starting point 147 00:08:36,120 --> 00:08:38,880 because it's stabilizes very visibile and very quickly. 148 00:08:39,640 --> 00:08:42,400 Let's look at the sequence. OK, High want is just five. 149 00:08:42,520 --> 00:08:45,670 Simple. High-too is five to the fifth 150 00:08:45,670 --> 00:08:49,870 Power that three thousand One. Hundred twentyfive. 151 00:08:50,760 --> 00:08:54,680 High three is five to the Power of three thousand One hundred 152 00:08:54,680 --> 00:08:57,440 twentyfive. That is a huge number. 153 00:08:57,440 --> 00:09:02,800 We can't rete the hold thing, but you calculate the tailand of 154 00:09:02,800 --> 00:09:06,280 it in Eight Seven. Four to One, Eight, Seven, five. 155 00:09:07,560 --> 00:09:10,320 It. Before the five in the previo 156 00:09:10,320 --> 00:09:14,480 step, Three Thousand One hundred twentyfive it two. 157 00:09:14,480 --> 00:09:17,080 In this New massive step, it is stilla. 158 00:09:17,080 --> 00:09:22,190 Two. As the highght the be value 159 00:09:22,270 --> 00:09:28,590 increces a. Wave of Frozen Stability creepes 160 00:09:28,590 --> 00:09:33,510 from the right. Side of the number to the left 161 00:09:34,270 --> 00:09:44,790 want to digit freeses it is permanent it is etc. 162 00:09:44,790 --> 00:09:47,590 Into the fabbric of the math. Itself. 163 00:09:47,640 --> 00:09:51,360 Us to know the last digital dream's number beghes greams 164 00:09:51,360 --> 00:09:54,600 Numbers essenziale poweretower of threees there is so un 165 00:09:54,600 --> 00:09:57,880 immaginabile high there a huge chunk of the boom digits have 166 00:09:57,880 --> 00:10:04,030 just Frozen solet. Lost in the clows of Infinity, 167 00:10:04,310 --> 00:10:07,830 but we can stand right there in the lobby and look at the serial 168 00:10:07,830 --> 00:10:10,550 number card entro the quornerstone e we can read 169 00:10:10,590 --> 00:10:12,910 perfettamente. OK, so we know the frees 170 00:10:13,390 --> 00:10:17,190 Thephenant's beone for wild this interrally. 171 00:10:17,190 --> 00:10:19,550 New News, the structure to sum extense centuries a. 172 00:10:19,550 --> 00:10:22,310 Goal, but the much deoper questionmark and the Real focus, 173 00:10:22,310 --> 00:10:25,150 the endingc collaboration is how fast? 174 00:10:26,560 --> 00:10:31,520 One DIGIT per step, Tended per step Doest excelerate does it? 175 00:10:32,160 --> 00:10:33,360 Stall out. Is it random? 176 00:10:33,440 --> 00:10:37,760 Todaytoday a Metric Cold Congruent Speed. 177 00:10:38,000 --> 00:10:40,400 Denoted in all the Papers as vievè. 178 00:10:40,480 --> 00:10:44,640 Vie It's a velocity, it is. A velocy represence the Little 179 00:10:44,640 --> 00:10:49,840 wate of Freezing V away telles exactly home Andy New stable 180 00:10:49,840 --> 00:10:52,680 digital we gain for every single step we add to the high of the 181 00:10:52,680 --> 00:10:56,040 Power Tower. Sovie base One we gain One 182 00:10:56,040 --> 00:10:59,360 Frozen digit per step. IV It's five we game five Frozen 183 00:10:59,360 --> 00:11:01,640 digits per step. Ruffle, Yes, that's Practical 184 00:11:01,640 --> 00:11:04,200 Translation and Major Discovery Papers. 185 00:11:04,200 --> 00:11:11,350 The. Fluxuating Wildly ed è settles 186 00:11:11,350 --> 00:11:15,190 into a specific predectable Inter value. 187 00:11:15,430 --> 00:11:17,910 So we are just guessing anymore we can action. 188 00:11:17,960 --> 00:11:20,440 Calculate the Speed Headtime per howl. 189 00:11:20,440 --> 00:11:21,880 Whats Determines of a number free Slow? 190 00:11:21,880 --> 00:11:26,280 Why Space five supportly, fasterd and based three? 191 00:11:26,920 --> 00:11:29,200 Wor is it? The hard we have look at the 192 00:11:29,200 --> 00:11:31,840 Engine of the number system itself, we hath look at the 193 00:11:31,840 --> 00:11:37,520 factors. We are the greek letter no sub 194 00:11:37,520 --> 00:11:40,240 p. OK, Let's On Pack Pyc Valuation 195 00:11:40,240 --> 00:11:43,240 perché onestly it semestre something you need a Phd 196 00:11:43,240 --> 00:11:46,800 Advanced topology to understand, but reading through the source 197 00:11:46,800 --> 00:11:50,360 material I have a feeling you can explane it to us fai in 198 00:11:50,360 --> 00:11:53,240 English. It action very intuitive want 199 00:11:53,240 --> 00:11:56,040 you force yourself to change your prospective on what Numbers 200 00:11:56,040 --> 00:11:59,670 action are. Usally want we do moth 201 00:11:59,670 --> 00:12:02,270 magnitude. We kared how big a Numbers fifty 202 00:12:02,270 --> 00:12:05,310 is begger than. Fosse matters in standard. 203 00:12:12,400 --> 00:12:18,560 DNA in are standard dessimo numer system base TEN. 204 00:12:18,960 --> 00:12:22,080 The fondamental building blocks are the prime Numbers two and 205 00:12:22,080 --> 00:12:29,520 five because two Times five ten. So AP setic valuation Simply as 206 00:12:29,520 --> 00:12:34,480 a based question, how many Times can i divide the specific numero 207 00:12:34,480 --> 00:12:36,760 by a prime? Puoi take the number forty 208 00:12:36,760 --> 00:12:40,550 forse. Forty is Eight Times five or 209 00:12:40,590 --> 00:12:44,230 Britney with primes, it's two to the third Power Times five to 210 00:12:44,230 --> 00:12:47,390 the first Power. So the fiber e valuation of 211 00:12:47,390 --> 00:12:51,270 forty is One because there is esattamente One five in the 212 00:12:51,270 --> 00:12:55,590 prime factorization, and the two Act valutation of forty is three 213 00:12:55,590 --> 00:12:59,470 because two to the third powers Eight and Eight divide forty. 214 00:12:59,470 --> 00:13:03,270 Perfectly OK, Simple 9 It's Reality counting prime Factor. 215 00:13:03,430 --> 00:13:06,470 It's like Doing a Generic test under number forty and counting 216 00:13:06,470 --> 00:13:08,390 home Andy to Chrome zones and five Chrome. 217 00:13:08,830 --> 00:13:17,070 Infinite. Tower, the Congruant Speed è. 218 00:13:17,790 --> 00:13:23,030 Vve comes directly from this valuations, specifically Marco 219 00:13:23,030 --> 00:13:26,070 repast formula show the Speed depens on Homey Times. 220 00:13:26,070 --> 00:13:28,830 You can divide the nabors of the base by this. 221 00:13:28,830 --> 00:13:31,150 Primes the Nabors One and a plus One. 222 00:13:31,430 --> 00:13:34,110 Yes, trivil Manupulation of the base. 223 00:13:35,000 --> 00:13:36,320 Or sometimes even a squirre plus One. 224 00:13:36,760 --> 00:13:41,280 This is genuole fassinate me certifid out how stable a huge 225 00:13:41,280 --> 00:13:43,720 poweretower of aspecific number is gonna be. 226 00:13:44,120 --> 00:13:45,640 You don't action look at the number self. 227 00:13:45,880 --> 00:13:48,880 You look at the guys living next door on the number. 228 00:13:48,880 --> 00:13:52,840 Line you look maniation exactly catagonis this in to what he 229 00:13:52,840 --> 00:13:56,240 calls congruence Classes hebreaks the Hall system down 230 00:13:56,240 --> 00:13:58,880 based on what the based number is magilo twenty. 231 00:13:59,080 --> 00:14:03,520 Module twenty, Witch for anyone resti under mogel aritmetic is 232 00:14:03,520 --> 00:14:07,070 basily just asking W. Suppose your base a and One. 233 00:14:07,270 --> 00:14:14,430 Twenty-One or fourtyone or hundred One. 234 00:14:14,590 --> 00:14:18,270 Ok, if you sub track to One Saw a minus One, what happens to 235 00:14:18,270 --> 00:14:20,510 those Numbers? One because twenty, fortyone 236 00:14:20,510 --> 00:14:22,270 because forty thy all and in zero. 237 00:14:22,470 --> 00:14:26,470 Witch become moltipliles of ten dei sedenly have thus Magic 238 00:14:26,470 --> 00:14:29,470 Factor of two and five repat found there. 239 00:14:29,470 --> 00:14:32,670 This Numbers the congruent Speed Largely depens on how the 240 00:14:32,670 --> 00:14:36,390 visible that a minus One nable is by the specific primes. 241 00:14:36,710 --> 00:14:38,400 So therect. The secret, the infinite 242 00:14:38,400 --> 00:14:42,440 Stability of twenty-one is actly hidden Inside the number. 243 00:14:42,440 --> 00:14:43,400 Twenty. It's Highing. 244 00:14:44,360 --> 00:14:48,000 In Planet site. OK, about the trick, the. 245 00:14:48,440 --> 00:14:52,960 Tricky matmetically speaking here are Numbers hending in 246 00:14:52,960 --> 00:14:55,600 three or Seven, like three, thirteen, Seven, seventeen. 247 00:14:55,720 --> 00:14:58,240 This is classified. Is Peace three in the literature 248 00:14:58,240 --> 00:15:01,240 OK for this? Baces Semply Subtracting One or 249 00:15:01,240 --> 00:15:03,600 add in One doesn't help us all. Take Three, three. 250 00:15:04,720 --> 00:15:07,840 Minus One is two that is not visible by five, no good. 251 00:15:07,840 --> 00:15:10,640 Three. Plus One is Four alton not 252 00:15:10,640 --> 00:15:14,320 visible by five, still no good. We find the hidden factors of 253 00:15:14,320 --> 00:15:17,680 ten for a number like. Three. 254 00:15:17,880 --> 00:15:22,680 What is three dry and what is the immediate? 255 00:15:22,840 --> 00:15:23,920 Right napor of Nine. Nine? 256 00:15:24,120 --> 00:15:28,160 Bing for Baces hding Inter Seven the Congruence Speed Depents on 257 00:15:28,160 --> 00:15:31,280 the five eat valuation of a squareplus One the. 258 00:15:31,280 --> 00:15:34,400 Square Plus One. Why that specific formula? 259 00:15:34,400 --> 00:15:37,440 The why squared? Because the any number and three 260 00:15:37,440 --> 00:15:40,600 or Seven it's Square will inevitabile ent Nine three three 261 00:15:40,600 --> 00:15:43,760 Square is Nine Seven squares fourtynine thirteen squares One 262 00:15:43,760 --> 00:15:45,360 hundred sixty Nine. And. 263 00:15:45,760 --> 00:15:48,320 Hating One to any number ending in Nine. 264 00:15:48,870 --> 00:15:57,550 Su the DNA Stability the. Blueprint for healthfest freeses 265 00:15:57,990 --> 00:16:01,510 is hidden in how easy you can mathematically turn the base 266 00:16:01,510 --> 00:16:04,270 World Square into a moltipli of ten. 267 00:16:06,360 --> 00:16:09,840 Ere essenziali looking for the path of least Math Medical 268 00:16:09,840 --> 00:16:13,040 Resistance to the prime Factor to and five OK. 269 00:16:15,390 --> 00:16:22,440 Libro in Math Grams number. Is fondamentali a Tower of 270 00:16:22,440 --> 00:16:25,400 Threees, so ar base is a ecules Tree se wee define the 271 00:16:25,400 --> 00:16:29,680 congruence Speed of three. We need V three repust formula 272 00:16:29,680 --> 00:16:32,360 live right now. Sense three is congru to three 273 00:16:32,360 --> 00:16:36,160 moodle o ten and moodle twenty we Fall squirry Internet three 274 00:16:36,160 --> 00:16:38,560 we wed about se we look a squareplus One. 275 00:16:38,880 --> 00:16:42,240 OK, so Three Square Plus One, that's Nine plus One, what is 276 00:16:42,240 --> 00:16:44,440 ten? No, we need the five Arc 277 00:16:44,440 --> 00:16:47,760 valutation of ten, remember? Five divide. 278 00:16:48,520 --> 00:16:50,440 Tende. Tennis two Times, five to. 279 00:16:50,440 --> 00:16:57,160 The first Power corrects. Valuratis V Three One. 280 00:16:57,400 --> 00:17:00,320 Precisay One. So a powerpower threees 281 00:17:00,680 --> 00:17:04,680 essenziale the core Architecture of grams number gains exactly 282 00:17:04,680 --> 00:17:08,040 One New stable digit for every single step you go up the. 283 00:17:08,200 --> 00:17:12,880 Towers a very Slow, very stay March One digitati a time it is 284 00:17:12,960 --> 00:17:14,839 perfettay. Linear. 285 00:17:14,920 --> 00:17:18,359 Precision for something soft so grams never is World the tuppler 286 00:17:18,359 --> 00:17:21,880 of semplificare sixty Four tetrade the three ruffleys the 287 00:17:21,880 --> 00:17:23,520 stage of the recution we talking about. 288 00:17:23,560 --> 00:17:25,760 Ruffley YES, to give a working moth. 289 00:17:25,839 --> 00:17:28,960 So ripeteres work formally prooves the grants number shares 290 00:17:28,960 --> 00:17:33,240 exactly White termine. The paperly Slug base, Three of 291 00:17:33,240 --> 00:17:36,600 g Mines, One stable digis, the infinite Power Tower Forgbase. 292 00:17:36,800 --> 00:17:42,920 Three the Slog or superlogym? È basabile di inverse of 293 00:17:42,920 --> 00:17:45,480 Tetration accounts the highght of the Tower. 294 00:17:46,110 --> 00:17:50,070 Since the Concorrent Speed VF three is exactly One, the number 295 00:17:50,070 --> 00:17:52,790 of frase and digits is essenziale quial to the high of 296 00:17:52,790 --> 00:17:58,270 the Towers self minus One. But for base three? 297 00:17:58,470 --> 00:18:05,470 It's a one-to-one ratio, the source material. 298 00:18:06,110 --> 00:18:10,750 Something else, but the telegrams number it Mens a 299 00:18:10,750 --> 00:18:14,430 pheshift. Ah Yes, the asanth phyeshift. 300 00:18:14,470 --> 00:18:17,270 This is the DIGIT havent Frozen years. 301 00:18:17,430 --> 00:18:21,550 If I have a Frozen Tele of, say, five hundred complete 302 00:18:21,590 --> 00:18:24,560 stabledigits there. Is a five hundred first digit 303 00:18:24,560 --> 00:18:27,520 just the left that Wall the still changing is the Tower 304 00:18:27,520 --> 00:18:29,840 growse it's on the borderline. Correct. 305 00:18:29,840 --> 00:18:32,960 It's The Act Frontier, and the ovvios questionmark is the 306 00:18:32,960 --> 00:18:35,520 frontier. Interly random is the mathis 307 00:18:35,640 --> 00:18:38,400 Rolling atside die every single time we Hat. 308 00:18:38,560 --> 00:18:40,040 A. Power. 309 00:18:40,280 --> 00:18:45,400 Is abolte Ripa an enigma d'America found the digit gesto, 310 00:18:45,400 --> 00:18:49,840 the left the Frozen tale action. Cycles for base. 311 00:18:49,840 --> 00:18:54,880 Three specificat the difference between the non stable digits of 312 00:18:54,880 --> 00:18:57,600 consecutive haits flips back and forth. 313 00:18:57,840 --> 00:19:00,760 Between What vales? Between Four and six. 314 00:19:00,760 --> 00:19:05,520 Forensics, back and fours. Forever Mogiler Pattern the 315 00:19:05,520 --> 00:19:09,440 Paper descrives this ask faeshift in detail for base 316 00:19:09,440 --> 00:19:14,110 three, the sequence of the Shi. Four Dance six than Four dance, 317 00:19:14,110 --> 00:19:18,910 six to Infinity, it just baunces back and forth like a metronome, 318 00:19:18,910 --> 00:19:20,190 thinking outside the Frozen Wall. 319 00:19:20,590 --> 00:19:25,390 Is wild to think about, so even the socal Keys, just the outside 320 00:19:25,590 --> 00:19:27,030 the Frozen. Digits has a heartbeat. 321 00:19:27,390 --> 00:19:30,830 We Little grimms number down in a physical Universe, but 322 00:19:30,830 --> 00:19:35,030 descrive it Absolute mathmetical Precision and descrive the 323 00:19:35,030 --> 00:19:37,510 behavior of the digits tost Beyond the tall, we have a 324 00:19:37,550 --> 00:19:39,550 Perfect map of the very edge of the. 325 00:19:39,950 --> 00:19:42,320 Number. Love about this Research IT 326 00:19:42,320 --> 00:19:46,480 terrificing Monster number feel almost tame like we have 327 00:19:46,480 --> 00:19:50,400 successivo captured a Cage of margel. 328 00:19:50,400 --> 00:19:55,400 Aritmetics behavior with prouvenist still haste. 329 00:19:55,400 --> 00:19:58,920 To follow usando the Speed of based three, it's Slow. 330 00:19:59,160 --> 00:20:02,880 V of Three is One per the Papers dedicato a lot time to what the 331 00:20:02,880 --> 00:20:07,910 collant inverse problem. Mining inserit taking a random 332 00:20:07,910 --> 00:20:12,190 number entro find it Speed, can we Act build a number that a 333 00:20:12,190 --> 00:20:15,150 specific Speed? Like if I want a base number 334 00:20:15,150 --> 00:20:18,270 that frees One hundred digits per step, can i engineer One? 335 00:20:19,190 --> 00:20:24,710 Perfect, Perfect squares. Perfect cubes. 336 00:20:24,750 --> 00:20:27,950 Yes, Numbers of the General Form X to the Power of Sea. 337 00:20:28,030 --> 00:20:30,510 The Research House è completamente fastina in 338 00:20:30,510 --> 00:20:33,830 Relationship Twein Net Exponent Sea and the result incongruent 339 00:20:33,830 --> 00:20:35,790 Speed. Go One. 340 00:20:36,030 --> 00:20:41,030 Ripa matmetical proves you can find infinitamente many based 341 00:20:41,030 --> 00:20:46,190 Numbers dapperpowers and have a congrurant Speed exactly. 342 00:20:46,390 --> 00:20:49,110 Equal to Sea. Wanna Speed of Five for Perfect 343 00:20:49,110 --> 00:20:50,710 fifth Powers. Essere. 344 00:20:50,760 --> 00:20:55,360 Yes, a very specific algebra Construction, mentre in the 345 00:20:55,360 --> 00:20:59,520 paper to garantied it look something like ten to the Power 346 00:20:59,520 --> 00:21:02,160 of K plus T plus ten to the Power T plus One. 347 00:21:02,480 --> 00:21:04,600 All of art rayse to the Power of c. 348 00:21:04,920 --> 00:21:09,440 Wow OK let's dico da formula bit for the Listner tendo a Power 349 00:21:09,720 --> 00:21:14,200 Plus Tend a Power Plus One all Race to see e Luke scarim paper 350 00:21:14,200 --> 00:21:16,440 but what is it action doing meccanicaly? 351 00:21:17,390 --> 00:21:18,910 Uno structure Inside, thus fantasy. 352 00:21:19,110 --> 00:21:21,830 It's a number constructed interrally of once and zeroes 353 00:21:22,190 --> 00:21:23,910 powers of TEN plus One at the end. 354 00:21:24,430 --> 00:21:28,270 This, the specific Illy engineer structure ensures that when you 355 00:21:28,270 --> 00:21:31,230 look at the thus palatic valuations, the scompcyl prime 356 00:21:31,230 --> 00:21:34,270 Factor we talk about there are perfettaly aline. 357 00:21:34,270 --> 00:21:37,430 Se you are basicly handcrafting a base number, this is perfecly 358 00:21:37,430 --> 00:21:41,070 divisible by exactly the prime Factor. 359 00:21:41,070 --> 00:21:43,670 You need to be divisible your stacking the deck and when you 360 00:21:43,670 --> 00:21:47,510 findly raise thatire prendere structure to the Power of c you 361 00:21:47,510 --> 00:21:52,870 effettivamente. So you are matmatically 362 00:21:52,990 --> 00:21:57,670 rigorosally garanting che the Final congrurant Speed esact sì. 363 00:21:57,830 --> 00:22:00,950 So we Willy Clean Engineer Numbers to freeze whatever rate 364 00:22:00,950 --> 00:22:02,750 we want. We can building custom high 365 00:22:02,750 --> 00:22:05,630 Speed Numbers. Within SER and boundes, yes it's 366 00:22:05,630 --> 00:22:08,350 Perfect highlights at the freesing Effect isn? 367 00:22:08,350 --> 00:22:11,390 Some magical isolated property of the number three of the 368 00:22:11,390 --> 00:22:14,550 number five. It is a fondamental structural 369 00:22:14,550 --> 00:22:18,150 property of how the based interx with the numer System Excel. 370 00:22:18,470 --> 00:22:21,470 Speaking the Numer System system this to. 371 00:22:21,870 --> 00:22:24,430 Writing is World the most mindbending parts of this 372 00:22:24,430 --> 00:22:27,390 intere, Deep dife. The Environment matters. 373 00:22:27,550 --> 00:22:29,990 The. Retix who Space TEN Human have 374 00:22:29,990 --> 00:22:33,430 tenders of evolute ten e una base TEN tetration semestre to 375 00:22:33,430 --> 00:22:35,510 behave Pretty well stabilizes it. 376 00:22:35,710 --> 00:22:38,310 Frees IT have specifically because based tennis World 377 00:22:38,310 --> 00:22:41,110 Square free. Square free to find out, forse. 378 00:22:41,190 --> 00:22:45,830 A number free if it is notvisible by any Perfect Square 379 00:22:45,950 --> 00:22:49,550 other then One se look it's prime Factor are two and five, 380 00:22:49,550 --> 00:22:53,110 two Times five are any Square primis. 381 00:22:53,360 --> 00:22:57,160 One to One five distinct primes nel lockup base x to temps. 382 00:22:57,160 --> 00:23:00,080 Three again distinct PRIMES. It's Square free. 383 00:23:00,320 --> 00:23:06,520 OK of a non Square free number. For is litteraly tosquare it's a 384 00:23:06,520 --> 00:23:10,160 Square or lockabas twelve. Twelve is Four Times three witch 385 00:23:10,160 --> 00:23:13,680 is two Square. Times Tree contains a Square 386 00:23:13,920 --> 00:23:16,280 Factor. Or considerare sixteen witch 387 00:23:16,280 --> 00:23:20,200 computer Scientist love exidesmo sixteen is two. 388 00:23:20,200 --> 00:23:22,520 The fourth Power it is a Square of a Square. 389 00:23:23,360 --> 00:23:25,720 Password. This distinction between Square 390 00:23:25,720 --> 00:23:29,360 free baces and non Square free baces mex a massive difference 391 00:23:29,360 --> 00:23:32,400 in how teatration behaves. A critical fondamental 392 00:23:32,400 --> 00:23:36,240 difference in a Square Free System everyday base TEN 393 00:23:36,520 --> 00:23:40,200 Stability is robust almost every single based number you trial 394 00:23:40,200 --> 00:23:42,560 eventual digital a Constant Speed. 395 00:23:42,960 --> 00:23:46,520 It is a stable math Medical. Universe System. 396 00:23:46,640 --> 00:23:48,360 Retaling with is specific rule in the. 397 00:23:48,440 --> 00:23:52,400 Paper isoling the radical. The radical the number are 398 00:23:52,400 --> 00:23:57,560 denoted is ratevar è sempre the product of it distinct prime 399 00:23:57,560 --> 00:24:01,120 factors ignorang any exponts. Software base sixteen wit is 400 00:24:01,120 --> 00:24:03,280 two. The Forth, the only distinct 401 00:24:03,280 --> 00:24:06,560 prime Factor is two se. The radical sixteen is just two. 402 00:24:06,560 --> 00:24:09,080 Correct. Now here is the instability 403 00:24:09,080 --> 00:24:13,920 criterian ladyscover in any non Square free ratex are if you 404 00:24:13,920 --> 00:24:17,320 tetris base a happens to be thevisible by the radical. 405 00:24:18,310 --> 00:24:20,870 The Congruant Speed never stabilies never it. 406 00:24:21,070 --> 00:24:25,350 Never freesen to a Constant. Rate never IT Excel complete out 407 00:24:25,350 --> 00:24:28,430 of control. Woo, let's Trace that's imagine 408 00:24:28,430 --> 00:24:32,870 we are Alien beans for sixteen finger e we nebbiable counting 409 00:24:32,870 --> 00:24:36,790 exadesimal base sixteen. OKA base Sixteen Universe an I. 410 00:24:36,790 --> 00:24:40,790 Pick a base for my teatration lets a tools devisible by the 411 00:24:40,790 --> 00:24:43,830 radical of sixteen whit we service two. 412 00:24:43,880 --> 00:24:47,560 Soctor building a powter of tools in this base sixteen Alien 413 00:24:47,560 --> 00:24:49,840 World, What action happens to the digis? 414 00:24:50,120 --> 00:24:53,040 The number of stable digits whitful be the trailing zeros, 415 00:24:53,040 --> 00:24:55,120 in questo caso crowes esplosivamente. 416 00:24:55,120 --> 00:24:58,400 It doesn't set on to a nice Constant rate like One digit 417 00:24:58,440 --> 00:24:59,760 per. Step. 418 00:25:00,080 --> 00:25:04,640 E Mike V One Zero on the First and Jump to Four 0, 0 and. 419 00:25:07,360 --> 00:25:09,640 Hundred zero. Caos in the congreens 420 00:25:09,640 --> 00:25:14,160 calculations, the zeros accumulate so unbelevable fast 421 00:25:14,160 --> 00:25:18,080 the paiac valuation never sels down to a flatline jumping 422 00:25:18,080 --> 00:25:21,680 expoly. So grams number witch is a Tower 423 00:25:21,680 --> 00:25:25,680 based on three. World the Frees is nicely, but 424 00:25:25,680 --> 00:25:28,800 if we try to calculare the Tower two in B sixteen. 425 00:25:30,670 --> 00:25:34,550 Productivable Youd find a runaway Train faster investment 426 00:25:34,550 --> 00:25:37,990 the needle Brooks of. Enry Parmix a Pretty Bold 427 00:25:37,990 --> 00:25:39,830 conjecture about this in the material. 428 00:25:39,830 --> 00:25:43,110 Disney he Does he Esplicitaly conception that square-frinness 429 00:25:43,110 --> 00:25:46,790 is the soul criterian he suspects that only in Square 430 00:25:46,790 --> 00:25:50,590 free numero Systems do you get this ironc guarantee of Constant 431 00:25:50,590 --> 00:25:54,190 Speed for all baces. There is profund e basicly 432 00:25:54,190 --> 00:25:58,070 suggeste are entere ability producted hail of a Monster like 433 00:25:58,070 --> 00:26:00,110 grams. Nember realize everyly onde 434 00:26:00,110 --> 00:26:04,630 tolely arbitrary. Sixteen, the. 435 00:26:04,790 --> 00:26:10,430 Math of. Infinite Numbers would look like 436 00:26:10,430 --> 00:26:13,030 a completaly different, much more. 437 00:26:13,390 --> 00:26:16,680 Karic landskake. Implies the this Stability is 438 00:26:16,800 --> 00:26:20,440 purally a property of the number self, but a property of the 439 00:26:20,440 --> 00:26:23,320 specific lands we happen to be viewing it OK. 440 00:26:23,480 --> 00:26:27,480 Speaking of the philosophical applications, we spen a live 441 00:26:27,480 --> 00:26:31,480 time talking about the how the formules, the congruent speeds, 442 00:26:31,480 --> 00:26:35,640 the baces the ratises ma we have reality tesh on the. 443 00:26:36,200 --> 00:26:39,520 Deoper, wy the wis. I know would because the White 444 00:26:39,520 --> 00:26:42,800 is the number, freeze it all. White does it just Channing out 445 00:26:42,800 --> 00:26:46,590 random digits Forever even. What is physical? 446 00:26:46,590 --> 00:26:52,150 Your matmetically. Stopping as quantities the 447 00:26:52,150 --> 00:26:54,350 Groabs physical location. Thing about. 448 00:26:54,350 --> 00:26:57,070 It weally. Think of the poweretowers garing 449 00:26:57,070 --> 00:26:59,430 bigger and begger rushing endless letteras positive 450 00:26:59,430 --> 00:27:01,230 Infinity. It's moving constantly to the 451 00:27:01,230 --> 00:27:04,110 right on the standard numberline. 452 00:27:04,160 --> 00:27:09,680 Sense in the realm of Factor and valuations, rushing Tours a very 453 00:27:09,680 --> 00:27:14,640 specific point. We need introdusse the concept 454 00:27:14,640 --> 00:27:18,720 of the PC manager specificat denoted as Z subscript in for a 455 00:27:18,720 --> 00:27:20,950 based ten. How is AP edic innerture 456 00:27:20,950 --> 00:27:23,310 different from a regular eneater use everyday? 457 00:27:23,550 --> 00:27:26,190 A regular induture is a fine night string of ditests. 458 00:27:26,510 --> 00:27:29,350 One, two, three, or five. It Four it's stops, but the 459 00:27:29,790 --> 00:27:33,070 payat integer can extende infinitamente. 460 00:27:33,070 --> 00:27:36,430 To the left, to the left, usely only thing Infinity is thingor 461 00:27:36,430 --> 00:27:40,510 the right, like pie p point One Four One five Nine under the 462 00:27:40,510 --> 00:27:42,430 right. That's True for Real number. 463 00:27:42,430 --> 00:27:46,270 Yes, Real Numbers fill the infinite microscopic gaping 464 00:27:46,270 --> 00:27:48,920 indags, but. C Numbers go the other 465 00:27:48,920 --> 00:27:51,480 interrally. Thy are sequences of digits that 466 00:27:51,480 --> 00:27:55,160 stret infinitamente into the larger place valerioes like da 467 00:27:55,160 --> 00:27:58,400 da da Nine, Nine, Nine, Nine, Nine, Nine, or data Eight to 468 00:27:58,400 --> 00:28:01,320 One. Eight Seven fivec intetration. 469 00:28:01,910 --> 00:28:04,870 That specific string of stable thegis of the. 470 00:28:05,270 --> 00:28:08,590 Last hours, a fine night Life of One of this infinite pyc 471 00:28:08,590 --> 00:28:12,480 Numbers. Power Tower of Threees and The 472 00:28:12,480 --> 00:28:16,000 Street Mostics frees in the place we are essenziale, just 473 00:28:16,000 --> 00:28:19,080 revealing more more of this preesistenti infinite leftard 474 00:28:19,080 --> 00:28:22,200 number. Yes, we are waping the dirt of 475 00:28:22,200 --> 00:28:27,120 fuscal and this infinite number string of noise it a precise 476 00:28:27,120 --> 00:28:29,520 solution to a specific algebrac equation. 477 00:28:29,520 --> 00:28:30,960 The equation is. Why? 478 00:28:31,120 --> 00:28:33,680 To the Power of teen caolse. Why? 479 00:28:33,680 --> 00:28:38,520 But in base TEN specifically, the stable tale of disdetion 480 00:28:38,520 --> 00:28:43,150 Tares converges to a solution. Quasion White to the fifth. 481 00:28:43,150 --> 00:28:47,590 Power Y White second. If i take a normal number like 482 00:28:47,590 --> 00:28:50,630 two to two, the fifth thirty-the-o that is definita 483 00:28:50,630 --> 00:28:55,270 not to vita three three to the fifth to hundred fourthree 484 00:28:55,270 --> 00:28:57,550 alfont three. The only normal Numbers were wyd 485 00:28:57,550 --> 00:29:00,630 the thirtyckles Wire zero One e maybe negative One. 486 00:29:02,110 --> 00:29:03,870 Regular integers. Yes you are completa right. 487 00:29:03,870 --> 00:29:07,590 But in the World of Tenc integrars this is infinite left 488 00:29:07,590 --> 00:29:10,070 Word strings. There are altre solutions. 489 00:29:10,430 --> 00:29:13,750 There are what i like to col Ghost Numbers leaorking Deep and 490 00:29:13,750 --> 00:29:17,230 the arctecture number number solutions of eurous Works and 491 00:29:17,230 --> 00:29:22,310 Infinity string of zeros ending in a One Works ones. 492 00:29:22,310 --> 00:29:30,150 There is an infinite tenetic number that ens in Nine to zero. 493 00:29:30,460 --> 00:29:32,860 Five Seven. If you Take That Inter infinite 494 00:29:32,860 --> 00:29:37,740 number and raise to the fifth Power, you get the exact same 495 00:29:37,740 --> 00:29:41,070 infinite number back. Il ministero? 496 00:29:41,070 --> 00:29:45,470 Stationar number system a tractors. 497 00:29:45,550 --> 00:29:49,910 A number. Iterating expanentiation over e 498 00:29:49,910 --> 00:29:53,750 over euro, passing a based number into a Illy Dynamic 499 00:29:53,750 --> 00:29:56,430 system and the Gravity the mathmecal Gravity of this 500 00:29:56,430 --> 00:30:00,430 patacle fixed points start polling the number in the 501 00:30:00,430 --> 00:30:03,870 magnetic pollsing. On we see the DIGIT freesing. 502 00:30:04,070 --> 00:30:07,150 Yes, the DIGIT lock Inter. Place semplice because the 503 00:30:07,150 --> 00:30:11,230 number in Closer and Closer to that solution and for base TEN. 504 00:30:12,110 --> 00:30:15,070 There only a Handfull of the Solutions available. 505 00:30:15,070 --> 00:30:20,110 The paperlist every. Single time your in base ten you 506 00:30:20,110 --> 00:30:23,310 are inevitabilmente sliding down the gravy wealth words, One of 507 00:30:23,630 --> 00:30:26,710 witch specifica when you hit depens on your starting base and 508 00:30:26,710 --> 00:30:29,230 this underlind structure. Changes if you change the base. 509 00:30:29,230 --> 00:30:33,150 Yes in base. Six, forse the equation isn? 510 00:30:33,150 --> 00:30:36,990 White to the fifth, White to the third equest why the intere 511 00:30:36,990 --> 00:30:40,470 invisible structure changes base on the prime Factor of the base 512 00:30:40,470 --> 00:30:42,860 Your operating. Massive. 513 00:30:42,860 --> 00:30:49,340 Tale stable digits, we know exets it is essenziali a Shadow. 514 00:30:49,340 --> 00:30:53,700 The Shadow ha completamente deterministic Shadow cast by One 515 00:30:53,700 --> 00:31:00,100 of the pinatic fixpoints number three been rollentasi toord a 516 00:31:00,100 --> 00:31:02,700 specific infinite solution of wy to the fith eackles. 517 00:31:02,700 --> 00:31:08,140 Why Congruence Speed of One the V Three Walls One. 518 00:31:08,230 --> 00:31:12,550 Suring the exact velocity with false Internet Gravity well, the 519 00:31:12,670 --> 00:31:15,590 infinite feel. Surprising Structured the 520 00:31:15,590 --> 00:31:18,190 Ultimate. Beauty of it finding order in 521 00:31:18,190 --> 00:31:19,710 the. Infine we normaly think of 522 00:31:19,710 --> 00:31:24,310 Infinity is asmeless che hotic terrifiing expense beh math 523 00:31:24,310 --> 00:31:29,030 Marcon logic actly imposes a very rigid skeleton underneather 524 00:31:29,030 --> 00:31:30,270 event the Monsters Hat follow the. 525 00:31:30,270 --> 00:31:32,590 Rules of the House speciale the Monsters souls. 526 00:31:32,590 --> 00:31:35,510 Recaptis. Incredibley Deep churney we. 527 00:31:35,750 --> 00:31:40,270 Started with the conceptiuly simple operation tetration, the 528 00:31:40,270 --> 00:31:42,900 Tower of Power. Physics of. 529 00:31:42,900 --> 00:31:48,540 The Universe, the farraight Tales of this Numbers freees 530 00:31:48,540 --> 00:31:51,140 complete Solid we learnd about congruent. 531 00:31:51,140 --> 00:31:55,980 Speed VVAE Now Marco Repa and is collaborator enig matematica 532 00:31:56,220 --> 00:32:00,300 manager to quantify exactly how fast at freesing happens, and i 533 00:32:00,300 --> 00:32:03,980 did it using the DNA of the Numbers prime Factor through 534 00:32:03,980 --> 00:32:06,180 patic. Valuations. 535 00:32:06,790 --> 00:32:13,470 We found VF Three One Slow stady linearly feeling in the digit 536 00:32:13,470 --> 00:32:16,870 One step of a time itself. The retics determinent it is Eni 537 00:32:16,870 --> 00:32:19,790 Stability at all base tennis safe because it's perfectly 538 00:32:19,790 --> 00:32:23,110 Square free bayxxteen is pure cats Beats it contense Square 539 00:32:23,110 --> 00:32:25,030 prime Square freeness is the Ultimate. 540 00:32:25,030 --> 00:32:28,310 Key to garante in order freasing process is. 541 00:32:28,310 --> 00:32:31,870 Reality a number falling enevabley tour the piac fix 542 00:32:31,870 --> 00:32:35,510 point a go solution to White to the feat equose why the exysted 543 00:32:35,510 --> 00:32:42,540 Wong before Human even road. Number Theory and Advanced Patic 544 00:32:42,540 --> 00:32:47,620 Analysis into One Beautiful cohern Picture it ready changes 545 00:32:47,620 --> 00:32:49,020 how you. Look at a simple Member like 546 00:32:49,020 --> 00:32:51,740 three. It's not a quantity three things 547 00:32:51,740 --> 00:32:55,300 anymore, it is a seed. What a highly specific 548 00:32:55,500 --> 00:33:00,100 predeterment project through the infinit specific Speed. 549 00:33:00,100 --> 00:33:06,060 Travels so cheers of Final. Provocative, a molover as we up. 550 00:33:06,340 --> 00:33:08,580 We canzone talk about calculato in groms number. 551 00:33:08,900 --> 00:33:13,500 We talk about super Computers charning through algoritms to 552 00:33:13,500 --> 00:33:18,550 find news digits. Pre-exysting paix solutions. 553 00:33:18,670 --> 00:33:21,430 Waiting in the invisibles structure of the paigenagers, 554 00:33:21,830 --> 00:33:25,390 are we trully creading this Numbers when we do the moth or 555 00:33:25,390 --> 00:33:28,550 we semply discovering locations on a mathus aree ritme on the 556 00:33:28,550 --> 00:33:31,030 sealing of the Universe, Discovery invention. 557 00:33:31,030 --> 00:33:34,550 It's the Eternal Questionmark of Mathematics, I think we. 558 00:33:34,550 --> 00:33:38,950 Sorti from enigment the maplice Orly. 559 00:33:38,950 --> 00:33:41,350 We're just finely building tune of Lights to see iTunes. 560 00:33:41,590 --> 00:33:43,790 The structure is always. There, you just have to know 561 00:33:43,790 --> 00:33:45,950 exakry next. Next Time you look at the 562 00:33:45,950 --> 00:33:46,550 number. Three. 563 00:33:47,470 --> 00:33:50,350 Or five for eventus TEN. Remember the Ghost Numbers 564 00:33:50,510 --> 00:33:54,030 waiting Patient at the end. Other infinite hours lock at the 565 00:33:54,030 --> 00:33:57,030 minus One in a Square Plus One differenty for now. 566 00:33:57,030 --> 00:34:02,390 One One Problem there. The actional Keys to unlacking 567 00:34:02,390 --> 00:34:04,910 the Speed of Infinity there is always Deep. 568 00:34:04,910 --> 00:34:07,750 Structure. Thanks for taking this 569 00:34:07,750 --> 00:34:09,590 incredible. Deep 10.