WEBVTT 00:00:00.000 --> 00:00:01.899 So if I asked you to just read a single word 00:00:01.899 --> 00:00:03.700 out loud, you'd probably expect it to take, what, 00:00:03.899 --> 00:00:06.019 a second or two? Yeah, I mean, maybe five seconds 00:00:06.019 --> 00:00:08.240 if it's like a really tough medical term or something. 00:00:08.460 --> 00:00:10.960 Right, exactly. But there is actually a word 00:00:10.960 --> 00:00:14.199 in the English language that will take you three 00:00:14.199 --> 00:00:17.519 agonizing hours to finish speaking. Three hours 00:00:17.519 --> 00:00:22.269 for one word. For one single word. And the reason 00:00:22.269 --> 00:00:25.449 why actually lies in this completely bizarre, 00:00:25.910 --> 00:00:29.329 mostly ignored universe of numbers, because usually 00:00:29.329 --> 00:00:31.649 when we look at a six -digit number, we're not 00:00:31.649 --> 00:00:34.210 exactly thinking about hidden universes. No, 00:00:34.229 --> 00:00:36.359 not at all. We think about data entry. Right. 00:00:36.420 --> 00:00:39.320 You see a number like 400 ,000 on a spreadsheet 00:00:39.320 --> 00:00:42.079 and your eyes just kind of glaze over. Your brain 00:00:42.079 --> 00:00:45.000 categorizes it as this dry utilitarian metric. 00:00:45.119 --> 00:00:46.920 It's just administrative tape, right? Like a 00:00:46.920 --> 00:00:49.820 population count for some mid -sized city or 00:00:49.820 --> 00:00:52.859 a quarterly budget line item. It feels very safe, 00:00:52.859 --> 00:00:55.500 very grounded, completely devoid of mystery. 00:00:55.979 --> 00:00:58.240 But when you actually look closer at this specific 00:00:58.240 --> 00:01:02.079 realm of scale, that mundane spreadsheet just 00:01:02.079 --> 00:01:04.719 shatters. Today, we're bringing you a deep dive 00:01:04.719 --> 00:01:08.260 based on a single wildly detailed Wikipedia article 00:01:08.260 --> 00:01:11.439 that is simply titled 100 ,000. It's quite the 00:01:11.439 --> 00:01:14.019 article. It really is. We are taking you on a 00:01:14.019 --> 00:01:15.859 journey through this strange numeric gateway. 00:01:16.379 --> 00:01:20.859 Think of the numbers from zero to 99 ,999 as 00:01:20.859 --> 00:01:22.739 our familiar neighborhood. You know your way 00:01:22.739 --> 00:01:24.439 around. You can visualize the distances. You 00:01:24.439 --> 00:01:27.359 can picture in your head. Exactly. But today 00:01:27.359 --> 00:01:30.079 we are crossing the county line into the six 00:01:30.079 --> 00:01:32.859 -digit wilderness because as it turns out the 00:01:32.859 --> 00:01:34.959 numbers from a hundred thousand to nine hundred 00:01:34.959 --> 00:01:36.540 and ninety nine thousand nine hundred ninety 00:01:36.540 --> 00:01:40.079 nine contain the little edge of space Vintage 00:01:40.079 --> 00:01:42.560 computer crashing curses and mathematical bridges 00:01:42.560 --> 00:01:44.420 between completely different dimensions And what's 00:01:44.420 --> 00:01:46.400 really fascinating here is that crossing into 00:01:46.400 --> 00:01:48.079 the hundred thousands it fundamentally changes 00:01:48.079 --> 00:01:51.370 how humans perceive scale? How so? Well, when 00:01:51.370 --> 00:01:53.670 quantities get this large, our evolutionary intuition 00:01:53.670 --> 00:01:55.670 just completely fails us. We're actually forced 00:01:55.670 --> 00:01:57.670 to invent new language, new physical boundaries, 00:01:57.829 --> 00:02:00.109 and frankly entirely new mathematics just to 00:02:00.109 --> 00:02:02.090 cope with the cognitive weight of what six digits 00:02:02.090 --> 00:02:04.709 actually represents. Yeah, I mean it makes sense 00:02:04.709 --> 00:02:06.909 that our very first instinct when wandering into 00:02:06.909 --> 00:02:09.310 a new wilderness is to, you know, try and name 00:02:09.310 --> 00:02:11.949 things to feel safe. Definitely. And the sources 00:02:11.949 --> 00:02:14.849 highlight how different cultures wrestle with 00:02:14.849 --> 00:02:17.319 this cognitive weight. For example, South Asia 00:02:17.319 --> 00:02:20.099 doesn't even use the phrasing 100 ,000. They 00:02:20.099 --> 00:02:22.539 use the term lack. Right, the lack. Yeah, and 00:02:22.539 --> 00:02:24.560 they write it uniquely, too. Visually, it's not 00:02:24.560 --> 00:02:27.400 a one, a comma, and five zeros. They write it 00:02:27.400 --> 00:02:30.319 as one, comma, zero, zero, comma, thousand. It 00:02:30.319 --> 00:02:33.460 visually isolates the 100 ,000 mark as its own 00:02:33.460 --> 00:02:36.419 foundational unit. Which is honestly a brilliant 00:02:36.419 --> 00:02:38.680 psychological tool. I mean, they're creating 00:02:38.680 --> 00:02:41.560 a dedicated linguistic anchor for this massive 00:02:41.560 --> 00:02:44.639 scale. And they are far from alone in meeting 00:02:44.639 --> 00:02:47.740 that anchor. Oh, for sure. If you look at Thai, 00:02:48.180 --> 00:02:51.300 Lao, and Khmer, they all use the word sun to 00:02:51.300 --> 00:02:54.960 represent 100 ,000. Vietnamese uses ac. The Malagasy 00:02:54.960 --> 00:02:57.780 language in Madagascar uses Hetzi. Wow. So it's 00:02:57.780 --> 00:03:01.120 everywhere. Yeah. And even historically, if we 00:03:01.120 --> 00:03:04.560 look at historical Cyrillic numerals, this specific 00:03:04.560 --> 00:03:08.409 quantity was known as a legion. It's as if all 00:03:08.409 --> 00:03:10.969 these disparate cultures collectively recognize 00:03:10.969 --> 00:03:13.349 that once you hit six digits, you're no longer 00:03:13.349 --> 00:03:15.610 just counting objects. Right. You've arrived 00:03:15.610 --> 00:03:18.270 at a completely different tier of reality that 00:03:18.270 --> 00:03:21.090 requires its own vocabulary. Exactly. And I notice 00:03:21.090 --> 00:03:23.250 it pops up in everyday conversational shorthand 00:03:23.250 --> 00:03:27.849 too. Like in the Netherlands, they use the colloquialism 00:03:27.849 --> 00:03:31.770 ton to mean 100 ,000 monetary units. Oh, really? 00:03:31.909 --> 00:03:34.370 Yeah. It used to refer to 100 ,000 guilders and 00:03:34.370 --> 00:03:37.750 now means 100 ,000 euros. It is incredibly common 00:03:37.750 --> 00:03:39.710 in their real estate market to say a house costs 00:03:39.710 --> 00:03:43.000 five ton. That's fascinating. But the catch is, 00:03:43.300 --> 00:03:45.620 they literally cannot use that word in official 00:03:45.620 --> 00:03:47.740 legal documents because it sounds exactly like 00:03:47.740 --> 00:03:49.819 the metric weight, the ton. Oh, that makes sense. 00:03:49.860 --> 00:03:51.960 You definitely do not want to contract ambiguity 00:03:51.960 --> 00:03:54.199 where you accidentally buy a house that weighs 00:03:54.199 --> 00:03:56.379 a ton instead of costing a ton. Yeah, exactly. 00:03:56.379 --> 00:03:58.060 That would be a terrible real estate deal. Yeah. 00:03:58.219 --> 00:04:01.159 And beyond commerce, we actually see this scale 00:04:01.159 --> 00:04:04.400 used to convey an overwhelming emotional abundance, 00:04:04.719 --> 00:04:07.479 too. In the Irish language, the famous phrase 00:04:07.479 --> 00:04:11.189 sed mili felt literally translates to A hundred 00:04:11.189 --> 00:04:13.550 thousand welcomes. A hundred thousand welcomes. 00:04:13.770 --> 00:04:16.889 I love that. Okay, let's unpack this. Why do 00:04:16.889 --> 00:04:20.170 some cultures invent these dedicated, entirely 00:04:20.170 --> 00:04:23.730 new terms for 100 ,000, like the lack or the 00:04:23.730 --> 00:04:26.449 saying, while English just stacks existing words 00:04:26.449 --> 00:04:28.810 together, we just say 100 and then bolt the word 00:04:28.810 --> 00:04:31.069 thousand onto the end of it. If we connect this 00:04:31.069 --> 00:04:33.269 to the bigger picture, it really comes down to 00:04:33.269 --> 00:04:36.769 how human language systems handle data compression. 00:04:36.990 --> 00:04:39.110 Data compression, like computers. Basically, 00:04:39.250 --> 00:04:42.649 yeah. English uses a highly modular base 10 block 00:04:42.649 --> 00:04:45.410 system. We build larger numbers out of smaller 00:04:45.319 --> 00:04:48.139 reusable linguistic parts. The problem is, as 00:04:48.139 --> 00:04:50.399 the numbers grow, that modular system becomes 00:04:50.399 --> 00:04:52.620 incredibly inefficient. Right, because the names 00:04:52.620 --> 00:04:55.040 just get longer and longer. Exactly. Cultures 00:04:55.040 --> 00:04:57.720 that invented terms like the LAC created compression 00:04:57.720 --> 00:04:59.939 algorithms. They realized that without a shortcut, 00:05:00.360 --> 00:05:02.420 speaking these massive numbers becomes a literal 00:05:02.420 --> 00:05:05.120 physical chore. Which perfectly explains some 00:05:05.120 --> 00:05:07.699 of the hilarious syllable counts the sources 00:05:07.699 --> 00:05:10.550 pointed out for English. And if you want a physical 00:05:10.550 --> 00:05:12.790 chore, try speaking some of these six -digit 00:05:12.790 --> 00:05:15.990 numbers out loud. What was the one that breaks 00:05:15.990 --> 00:05:18.389 the syllable record for its size? Oh, that would 00:05:18.389 --> 00:05:24.449 be 111 ,777. Yes, that's the one. Due to our 00:05:24.449 --> 00:05:27.250 modular language system, that is the smallest 00:05:27.250 --> 00:05:29.889 natural number that requires a staggering 17 00:05:29.889 --> 00:05:31.870 syllables to say out loud in American English. 00:05:32.850 --> 00:05:36.850 111 ,777. It's a mouthful. And if you're speaking 00:05:36.850 --> 00:05:39.250 British English, the inclusion of the word and 00:05:39.250 --> 00:05:42.290 bumps it up to 19 syllables. The number literally 00:05:42.290 --> 00:05:44.829 dictates the physical breath required to speak 00:05:44.829 --> 00:05:46.889 it. It's exhausting. And there's another weird 00:05:46.889 --> 00:05:49.250 linguistic quirk out there in the 700 ,000. Yeah, 00:05:49.550 --> 00:05:53.670 777 ,777. It takes 20 syllables to speak, but 00:05:53.670 --> 00:05:56.110 its true claim to fame is that it is the absolute 00:05:56.110 --> 00:05:58.029 largest number in the English language that does 00:05:58.029 --> 00:05:59.990 not contain the letter I in its written name. 00:06:00.470 --> 00:06:03.769 777 ,000. Wow, yeah. Not a single I. Not one. 00:06:03.990 --> 00:06:06.670 So we create these linguistic anchors to try 00:06:06.670 --> 00:06:08.850 and make sense of the scale. But then we take 00:06:08.850 --> 00:06:12.009 those numbers and use them to define the actual 00:06:12.009 --> 00:06:14.410 boundaries of our physical reality. Right. We 00:06:14.410 --> 00:06:17.509 project our need for clean six -digit anchors 00:06:17.509 --> 00:06:19.689 right onto the natural world. Which brings us 00:06:19.689 --> 00:06:22.170 to the edges space. Because, I mean, if you look 00:06:22.170 --> 00:06:24.850 up at the sky, it's just a smooth gradient fading 00:06:24.850 --> 00:06:27.370 into black, right? There's no dotted line up 00:06:27.370 --> 00:06:29.709 there. No. The universe doesn't care about our 00:06:29.709 --> 00:06:32.529 borders. Right. But... The Federation Aeronautique 00:06:32.529 --> 00:06:35.230 International, the governing body for aeronautics, 00:06:35.649 --> 00:06:38.029 they had to draw a line somewhere, and they chose 00:06:38.029 --> 00:06:41.149 exactly 100 ,000 meters. And 100 kilometers up. 00:06:41.430 --> 00:06:43.509 Exactly. That is the Karman line. If you cross 00:06:43.509 --> 00:06:45.930 100 ,000 meters, you are officially in space 00:06:45.930 --> 00:06:48.649 flight. And it is vital to understand why they 00:06:48.649 --> 00:06:51.720 chose that specific altitude. Theodore von Karman 00:06:51.720 --> 00:06:54.240 calculated that around this altitude, the Earth's 00:06:54.240 --> 00:06:57.180 atmosphere becomes so incredibly thin that for 00:06:57.180 --> 00:06:59.500 an aircraft to generate enough aerodynamic lift 00:06:59.500 --> 00:07:02.000 to stay up, it would have to travel faster than 00:07:02.000 --> 00:07:03.959 orbital velocity. So it's basically falling into 00:07:03.959 --> 00:07:06.680 space at that point. Exactly. It's the precise 00:07:06.680 --> 00:07:09.060 mechanical transition point where aerodynamics 00:07:09.060 --> 00:07:12.500 gives way to astronautics. But the actual calculation 00:07:12.500 --> 00:07:15.240 is messy. I mean, it fluctuates based on solar 00:07:15.240 --> 00:07:18.120 activity and atmospheric drag. It's not a hard 00:07:18.120 --> 00:07:21.040 line. No, not at all. But the governing body 00:07:21.040 --> 00:07:23.839 rounded it to exactly 100 ,000 meters because 00:07:23.839 --> 00:07:27.079 human beings crave the authority of a clean six 00:07:27.079 --> 00:07:29.160 -digit threshold. We just force the universe 00:07:29.160 --> 00:07:31.279 into our spreadsheets. We really do. And we do 00:07:31.279 --> 00:07:34.259 the exact same thing with deep time. The source 00:07:34.259 --> 00:07:36.579 has mentioned something in paleoclimatology called 00:07:36.579 --> 00:07:40.459 the 100 ,000 -year problem. Now, I know scientists 00:07:40.459 --> 00:07:42.639 look at historical temperatures trapped in ancient 00:07:42.639 --> 00:07:45.519 ice cores, but what exactly is the problem here? 00:07:45.680 --> 00:07:47.959 So the problem is a glaring mismatch between 00:07:47.959 --> 00:07:50.879 cause and effect. Earth's climate is heavily 00:07:50.879 --> 00:07:53.019 influenced by Milankovitch cycles. Which are 00:07:53.019 --> 00:07:54.959 what exactly? They're changes in the Earth's 00:07:54.959 --> 00:07:57.540 orbit and tilt that affect how much solar radiation 00:07:57.540 --> 00:07:59.879 we receive. And the most significant changes 00:07:59.879 --> 00:08:03.019 in solar radiation actually occur on a 41 ,000 00:08:03.019 --> 00:08:06.259 -year cycle. Okay, 41 ,000 years. But when scientists 00:08:06.259 --> 00:08:09.339 examine the ice cores from the last million years... 00:08:09.199 --> 00:08:11.459 the dominant climate response like the major 00:08:11.459 --> 00:08:14.740 ice ages, they occur roughly every 100 ,000 years. 00:08:14.920 --> 00:08:17.519 Wait, wait. So the sun is hitting us with a 41 00:08:17.519 --> 00:08:20.579 ,000 year rhythm, but the Earth's ice is dancing 00:08:20.579 --> 00:08:23.459 to a 100 ,000 year rhythm. Precisely. And it's 00:08:23.459 --> 00:08:25.839 baffling because the amount of solar radiation 00:08:25.839 --> 00:08:28.459 changing on the 100 ,000 year cycle of orbital 00:08:28.459 --> 00:08:31.639 eccentricity is actually quite weak. Oh, really? 00:08:31.779 --> 00:08:34.580 Yeah. It shouldn't be the primary driver of massive 00:08:34.580 --> 00:08:37.519 glacial shifts. Yet for some reason, the Earth's 00:08:37.519 --> 00:08:41.000 climate system amplifies this specific six -digit 00:08:41.000 --> 00:08:43.600 cycle over the stronger ones. It remains one 00:08:43.600 --> 00:08:45.919 of the great scientific mysteries regarding deep 00:08:45.919 --> 00:08:48.840 time. Which is wild, considering how deeply we 00:08:48.840 --> 00:08:51.559 rely on this scale to track our own lived experience 00:08:51.559 --> 00:08:54.240 of time. I mean, a standard non -leap year is 00:08:54.240 --> 00:08:58.639 exactly 525 ,600 minutes. A standard week is 00:08:58.639 --> 00:09:02.299 604 ,800 seconds. And noticing those translations 00:09:02.299 --> 00:09:05.259 reveals a massive flaw in human intuition. Oh, 00:09:05.259 --> 00:09:06.980 completely. If I tell you, hey, I will see you 00:09:06.980 --> 00:09:09.779 in exactly one week, your brain instantly maps 00:09:09.779 --> 00:09:11.779 out that distance. It feels totally manageable. 00:09:12.340 --> 00:09:16.059 But if I say, I will see you in 600 ,000 seconds? 00:09:16.679 --> 00:09:19.240 That triggers genuine panic. It sounds like you're 00:09:19.240 --> 00:09:21.980 gonna be waiting for a decade. The quantity is 00:09:21.980 --> 00:09:25.000 identical, but the perception is completely warped. 00:09:25.039 --> 00:09:27.860 This is exactly why the six -digit realm is so 00:09:27.860 --> 00:09:30.799 treacherous for us. Without the safety net of 00:09:30.799 --> 00:09:33.639 aggregate units, you know, like weeks or years, 00:09:34.559 --> 00:09:37.460 our brains cannot natively process the magnitude. 00:09:37.679 --> 00:09:40.620 We literally lose our grip on physical reality. 00:09:40.879 --> 00:09:43.019 And speaking of losing our grip on physical reality, 00:09:43.200 --> 00:09:45.100 we have to circle back to that three -hour word 00:09:45.100 --> 00:09:46.779 I mentioned at the very beginning of the deep 00:09:46.779 --> 00:09:50.240 dive, because this is the ultimate physical limit 00:09:50.240 --> 00:09:52.700 of the human body clashing with a six -digit 00:09:52.700 --> 00:09:55.750 scale. According to the sources, the longest 00:09:55.750 --> 00:09:57.629 word in the English language is the chemical 00:09:57.629 --> 00:10:00.470 name for the protein titan. It's passive. It 00:10:00.470 --> 00:10:05.570 contains exactly 189 ,819 letters. If you sit 00:10:05.570 --> 00:10:07.690 down and try to pronounce the single word, reading 00:10:07.690 --> 00:10:09.870 letter by letter, syllable by syllable, it will 00:10:09.870 --> 00:10:11.889 take you a staggering three hours to finish. 00:10:11.950 --> 00:10:14.490 It transforms language from a simple tool of 00:10:14.490 --> 00:10:17.090 communication into a grueling endurance marathon. 00:10:17.490 --> 00:10:20.090 The six digit scale manifests as literal physical 00:10:20.090 --> 00:10:23.009 exhaustion. So human brains and human bodies 00:10:23.149 --> 00:10:26.129 breakdown when confronted with this scale. But 00:10:26.129 --> 00:10:28.070 what happens when we feed these massive numbers 00:10:28.070 --> 00:10:30.929 into machines? I want to pivot from physical 00:10:30.929 --> 00:10:33.289 boundaries to digital ones. OK, let's do it. 00:10:33.450 --> 00:10:35.529 Because in the early days of computing, specific 00:10:35.529 --> 00:10:38.190 six -digit numbers acted like hidden traps. Yeah, 00:10:38.190 --> 00:10:40.610 the hardware limitations of early microprocessors 00:10:40.610 --> 00:10:43.470 created some incredibly strange digital geography. 00:10:43.649 --> 00:10:45.809 So let's talk about the Apple II Plus and the 00:10:45.809 --> 00:10:48.110 Apple Teak. If you were sitting at the basic 00:10:48.110 --> 00:10:50.429 programming prompt on one of these vintage machines, 00:10:50.769 --> 00:10:56.059 and you typed in any number, from 437 ,760 all 00:10:56.059 --> 00:10:59.580 the way to 440 ,319. The computer would instantly 00:10:59.580 --> 00:11:01.440 crash. Yes, it would just drop you right out 00:11:01.440 --> 00:11:03.659 to a machine language monitor prompt. Why did 00:11:03.659 --> 00:11:06.779 that specific block of the 400 ,000s completely 00:11:06.779 --> 00:11:08.659 break the computer? Well, it really comes down 00:11:08.659 --> 00:11:11.700 to the clash between software ambition and hardware 00:11:11.700 --> 00:11:14.820 constraints. These Apple computers ran on 16 00:11:14.820 --> 00:11:18.039 -bit architecture. And in a 16 -bit system, the 00:11:18.039 --> 00:11:20.460 absolute maximum whole number the hardware register 00:11:20.460 --> 00:11:24.539 can natively understand is 65 ,535. Okay, so 00:11:24.539 --> 00:11:26.620 a six digit number is already well beyond what 00:11:26.620 --> 00:11:29.370 the chip wants to handle natively. Exactly. So 00:11:29.370 --> 00:11:31.909 to handle larger numbers, the AppleSoft BASIC 00:11:31.909 --> 00:11:35.350 software used floating point math routines. When 00:11:35.350 --> 00:11:37.750 a user typed a number at the prompt, the software 00:11:37.750 --> 00:11:40.210 had to convert that text string into a mathematical 00:11:40.210 --> 00:11:43.029 value. OK, making sense so far. During that conversion, 00:11:43.110 --> 00:11:45.409 it multiplied the digits. And for that highly 00:11:45.409 --> 00:11:52.909 specific range, 437 ,760 to 440 ,319 years, the 00:11:52.909 --> 00:11:55.110 intermediate multiplication result caused an 00:11:55.110 --> 00:11:57.809 overflow in a specific 16 -bit internal register. 00:11:57.679 --> 00:12:01.299 Ah, an overflow. Right. And the error checking 00:12:01.299 --> 00:12:03.879 routine meant to catch this overflow was flawed. 00:12:04.279 --> 00:12:06.399 So instead of giving the user a polite syntax 00:12:06.399 --> 00:12:09.059 error, it caused a fatal logic fault that dumped 00:12:09.059 --> 00:12:11.340 the user entirely out of the environment. But 00:12:11.340 --> 00:12:13.480 early computer hackers were incredibly resourceful. 00:12:13.559 --> 00:12:16.539 They found this weird esoteric math flaw, and 00:12:16.539 --> 00:12:18.620 they essentially weaponized it. They did. They 00:12:18.620 --> 00:12:21.519 figured out that typing exactly 440 ,000 at the 00:12:21.519 --> 00:12:24.960 prompt was a guaranteed or reliable way to intentionally 00:12:24.960 --> 00:12:26.919 trigger this crash. And you might be wondering... 00:12:26.960 --> 00:12:28.620 Why would you want to crash your own machine? 00:12:28.919 --> 00:12:31.080 Because it acted like a digital crowbar to bypass 00:12:31.080 --> 00:12:33.720 copy protection on loaded video games. Exactly. 00:12:33.960 --> 00:12:36.820 You type 440 ,000, the system stumbles, the protection 00:12:36.820 --> 00:12:38.919 scripts drop, and boom, you have access to the 00:12:38.919 --> 00:12:41.240 code. It is a perfect example of a number transforming 00:12:41.240 --> 00:12:44.080 from a measurement into a mechanical lever. In 00:12:44.080 --> 00:12:47.720 the digital space, 440 ,000 was a physical key 00:12:47.720 --> 00:12:50.080 turning a lock. Here's where it gets really interesting. 00:12:50.990 --> 00:12:54.309 because we see these highly specific mechanical 00:12:54.309 --> 00:12:58.049 numbers pop up in the purest realm of all. Yeah. 00:12:58.049 --> 00:13:00.490 Theoretical mathematics. There are six digit 00:13:00.490 --> 00:13:02.809 numbers that act like structural anomalies in 00:13:02.809 --> 00:13:04.870 the universe itself. Oh, absolutely. Take the 00:13:04.870 --> 00:13:07.990 number 998 ,000 to one, which is the largest 00:13:07.990 --> 00:13:11.330 possible six digit square, since it's 999 squared. 00:13:11.909 --> 00:13:13.490 If you take the reciprocal of this number, so 00:13:13.490 --> 00:13:16.570 one divided by 998 ,001, and you look at the 00:13:16.570 --> 00:13:19.320 infinite decimal expansion, It does something 00:13:19.320 --> 00:13:22.019 seemingly impossible. It organizes chaos into 00:13:22.019 --> 00:13:24.740 a perfect sequence. It perfectly lists out every 00:13:24.740 --> 00:13:26.580 single three -digit number in numerical order, 00:13:26.940 --> 00:13:31.279 because .0000001002003, all the way up into the 00:13:31.279 --> 00:13:34.259 900s. But it skips exactly one number. Just one. 00:13:34.399 --> 00:13:38.860 Just one. It lists 997, skips 998 completely, 00:13:39.000 --> 00:13:42.600 and goes straight to 999. Why would a decimal 00:13:42.600 --> 00:13:45.980 expansion just casually count to a thousand, 00:13:46.440 --> 00:13:48.809 but skip a single number? It feels like a prank, 00:13:49.029 --> 00:13:50.710 doesn't it? It totally does. But it's actually 00:13:50.710 --> 00:13:53.110 a beautiful consequence of how base 10 mathematics 00:13:53.110 --> 00:13:55.929 and series expansions work. It's rooted in the 00:13:55.929 --> 00:13:58.470 algebraic formula for 1 divided by 1 minus x 00:13:58.470 --> 00:14:00.990 squared. When you scale that underlying logic 00:14:00.990 --> 00:14:03.970 up to specific values close to 1 ,000, the mathematical 00:14:03.970 --> 00:14:06.490 structure inevitably produces an ordered sequence. 00:14:06.629 --> 00:14:08.690 So the skip number isn't a mistake? No, the skip 00:14:08.690 --> 00:14:11.570 number, 998, is not a mistake at all. It is the 00:14:11.570 --> 00:14:14.210 mathematical artifact of the overlapping carryover 00:14:14.210 --> 00:14:16.970 digits when the sequence reaches the denominator's 00:14:16.970 --> 00:14:19.409 threshold. OK, so it's deeply structural. And 00:14:19.409 --> 00:14:21.370 we see similar structural weirdness with the 00:14:21.370 --> 00:14:25.240 number 956 ,619. If you square that specific 00:14:25.240 --> 00:14:27.980 number, the result is a massive 12 -digit integer, 00:14:28.259 --> 00:14:32.120 915119991161. If you look at the digits of the 00:14:32.120 --> 00:14:34.220 root 9561 and then look at the digits in the 00:14:34.220 --> 00:14:36.259 massive square, it's an exact match in terms 00:14:36.259 --> 00:14:38.139 of the ingredients used. Both the root and the 00:14:38.139 --> 00:14:40.340 massive square use only the digits 1, 5, 6, and 00:14:40.340 --> 00:14:43.179 9. Nothing else. This raises an important question. 00:14:43.779 --> 00:14:46.580 When we see anomalies like this, do these specific 00:14:46.580 --> 00:14:49.240 six digit numbers possess some inherent mystical 00:14:49.240 --> 00:14:52.620 property? Or is the universe of numbers simply 00:14:52.620 --> 00:14:56.480 so incredibly vast that highly specific coincidences 00:14:56.480 --> 00:14:59.139 are statistically inevitable? That's the million 00:14:59.139 --> 00:15:01.299 dollar question. Right. I mean, when you have 00:15:01.299 --> 00:15:03.259 nine hundred thousand different combinations 00:15:03.259 --> 00:15:06.759 to play with in this tier, the sheer volume guarantees 00:15:06.759 --> 00:15:09.360 that eventually you will stumble upon a sequence 00:15:09.360 --> 00:15:12.039 that looks deliberately engineered. But to answer 00:15:12.039 --> 00:15:14.519 that question, we have to look past the coincidences 00:15:14.519 --> 00:15:17.240 and look at the actual load -bearing beams of 00:15:17.240 --> 00:15:19.500 this mathematical universe. We have to look at 00:15:19.500 --> 00:15:21.740 the prime numbers. The prime numbers. So in our 00:15:21.740 --> 00:15:23.899 six -digit wilderness, the grand tally is this. 00:15:24.600 --> 00:15:27.399 Between 100 ,000 and 1 million, there are exactly 00:15:27.399 --> 00:15:31.659 68 ,906 prime numbers. The very first one you 00:15:31.659 --> 00:15:34.220 hit after crossing the county line is 100 ,003. 00:15:34.320 --> 00:15:36.259 But what is critical to understand is that this 00:15:36.259 --> 00:15:38.860 wilderness is not evenly populated. Prime numbers 00:15:38.860 --> 00:15:41.179 thin out the further you travel into the vastness 00:15:41.179 --> 00:15:43.919 of mathematics. They get rarer. Much rarer. If 00:15:43.919 --> 00:15:46.120 you look at the first block, the 100 ,000s, you'll 00:15:46.120 --> 00:15:50.279 find 8 ,392 primes. But as you journey closer 00:15:50.279 --> 00:15:53.059 to the 1 million mark into the 900 ,000s block, 00:15:53.600 --> 00:15:56.220 the primes become scarce. The count drops to 00:15:56.220 --> 00:16:00.059 just 7 ,224. The fundamental building blocks 00:16:00.059 --> 00:16:02.500 of math literally become harder and harder to 00:16:02.500 --> 00:16:04.799 locate. And some of the primes you do manage 00:16:04.799 --> 00:16:07.399 to find out there in the deep wilderness are 00:16:07.399 --> 00:16:10.519 structurally mind -blowing. Take the number of 00:16:10.519 --> 00:16:15.090 739 ,397. It's a prime number. But it's not just 00:16:15.090 --> 00:16:17.269 any prime. It is the largest prime number that 00:16:17.269 --> 00:16:20.090 is both left and right truncatable. Meaning its 00:16:20.090 --> 00:16:22.649 structural integrity is absolute no matter how 00:16:22.649 --> 00:16:24.889 you deconstruct it. Yes. I picture it exactly 00:16:24.889 --> 00:16:27.460 like a massive mathematical Jenga tower. You 00:16:27.460 --> 00:16:29.059 can pull digits away from the left side, or you 00:16:29.059 --> 00:16:30.940 can pull digits away from the right side, and 00:16:30.940 --> 00:16:33.100 whatever number is left standing is still a perfect 00:16:33.100 --> 00:16:34.980 prime number. It's amazing. Pull the seven off 00:16:34.980 --> 00:16:36.659 the front, it's prime. Pull the seven off the 00:16:36.659 --> 00:16:38.460 back, it's still prime. You can keep pulling 00:16:38.460 --> 00:16:40.419 blocks until there is just a single digit left, 00:16:40.720 --> 00:16:42.740 and the tower never collapses. It's a monument 00:16:42.740 --> 00:16:45.240 standing out there in the 700 ,000s. It really 00:16:45.240 --> 00:16:47.919 is. But perhaps the most incredible monument 00:16:47.919 --> 00:16:51.679 in this entire six -digit tier involves two specific 00:16:51.679 --> 00:16:54.500 adjacent numbers that act as a bridge between 00:16:54.500 --> 00:16:56.700 entirely different dimensions of human thought. 00:16:58.549 --> 00:17:03.990 196 ,883, and 196 ,884. Whoa, hold on. The sources 00:17:03.990 --> 00:17:06.269 get incredibly dense here. You're talking about 00:17:06.269 --> 00:17:09.190 the monster group and the J invariant. I am going 00:17:09.190 --> 00:17:10.670 to need you to break those down, because that 00:17:10.670 --> 00:17:12.490 sounds like pure science fiction. It borders 00:17:12.490 --> 00:17:15.630 on it, honestly. So in the 1970s, mathematicians 00:17:15.630 --> 00:17:18.289 were studying a field of abstract algebra dealing 00:17:18.289 --> 00:17:20.769 with symmetry. OK, symmetry. Think of a snowflake. 00:17:20.890 --> 00:17:23.269 It has a very simple, understandable symmetry. 00:17:23.349 --> 00:17:25.329 You can rotate it a few ways, and it looks the 00:17:25.329 --> 00:17:28.230 same. A three -dimensional cube has 48 different 00:17:28.230 --> 00:17:30.690 symmetries. Right, makes sense. Now, mathematicians 00:17:30.690 --> 00:17:33.670 theorize the ultimate symmetrical object, a structure 00:17:33.670 --> 00:17:36.670 of such immense, incomprehensible complexity 00:17:36.670 --> 00:17:39.109 that the number of its symmetries exceeds the 00:17:39.109 --> 00:17:41.869 number of atoms in Jupiter. I can't even picture 00:17:41.869 --> 00:17:43.930 that. You can't. They called this theoretical 00:17:43.930 --> 00:17:46.829 structure the monster group. To even begin describing 00:17:46.829 --> 00:17:49.730 its most basic geometry mathematically, you need 00:17:49.730 --> 00:17:54.089 a space that has exactly 196 ,883 dimensions. 00:17:55.490 --> 00:17:58.569 196 ,883 is the dimensional coordinate required 00:17:58.569 --> 00:18:00.769 just to start talking about this theoretical 00:18:00.769 --> 00:18:03.849 hyper complex monster geometry. I'm tracking. 00:18:04.079 --> 00:18:06.299 What about the other number? Meanwhile, in a 00:18:06.299 --> 00:18:09.079 completely separate unrelated wing of mathematics 00:18:09.079 --> 00:18:11.599 number theory, which deals with complex analysis 00:18:11.599 --> 00:18:13.380 and calculus researchers, we're studying something 00:18:13.380 --> 00:18:15.680 called the J -invariant. What's that? It's a 00:18:15.680 --> 00:18:17.880 specific function used to understand the geometry 00:18:17.880 --> 00:18:20.920 of elliptic curves. When they wrote out the long 00:18:20.920 --> 00:18:23.200 infinite sequence of coefficients for this J 00:18:23.200 --> 00:18:26.200 -invariant function, the very first major coefficient 00:18:26.200 --> 00:18:30.750 in the sequence was 196 ,884. Wait. Let me get 00:18:30.750 --> 00:18:34.029 this straight. You have 196 ,883 to find the 00:18:34.029 --> 00:18:36.349 geometry of an abstract multi -dimensional monster 00:18:36.349 --> 00:18:38.630 in one field. Yes. And in a completely different 00:18:38.630 --> 00:18:41.170 field setting, calculus and curves, a core sequence 00:18:41.170 --> 00:18:45.029 relies on 196 ,884. They are just one single 00:18:45.029 --> 00:18:48.130 digit apart. Exactly. And a mathematician named 00:18:48.130 --> 00:18:51.269 John McKay noticed this adjacency. And initially, 00:18:51.289 --> 00:18:53.369 people thought it was a joke. I mean, the idea 00:18:53.369 --> 00:18:56.349 that these two incredibly dense, deeply isolated 00:18:56.349 --> 00:18:58.789 fields of mathematics were secretly talking to 00:18:58.789 --> 00:19:02.670 each other absurd they called the idea monstrous 00:19:02.670 --> 00:19:05.809 moonshine meaning it was a crazy foolish idea 00:19:05.809 --> 00:19:09.470 but it wasn't a joke was it no it wasn't years 00:19:09.470 --> 00:19:11.990 later a mathematician named Richard Borchards 00:19:11.990 --> 00:19:14.289 actually proved that the connection was real 00:19:14.289 --> 00:19:16.589 using the mathematics of string theory to build 00:19:16.589 --> 00:19:20.009 the bridge the moonshine was actually a profound 00:19:20.009 --> 00:19:23.210 hidden architecture underlying the universe and 00:19:23.210 --> 00:19:25.609 those two six -digit numbers were the very first 00:19:25.609 --> 00:19:27.799 breadcrumbs that led us to see it So what does 00:19:27.799 --> 00:19:29.900 this all mean? We started this deep dive by talking 00:19:29.900 --> 00:19:32.099 about how a six -digit number just looks like 00:19:32.099 --> 00:19:35.039 a boring, dry metric on a spreadsheet. A population 00:19:35.039 --> 00:19:38.200 count or a budget. Exactly. But you, listening 00:19:38.200 --> 00:19:40.039 to this right now, the next time you open your 00:19:40.039 --> 00:19:42.539 banking app or look at a population counter or 00:19:42.539 --> 00:19:44.920 see a mundane six -digit figure scrolling across 00:19:44.920 --> 00:19:47.039 the screen, I want you to remember what is actually 00:19:47.039 --> 00:19:49.980 hiding inside that scale. It's an entire universe. 00:19:50.339 --> 00:19:53.380 You are looking at a bizarre universe. A wilderness 00:19:53.380 --> 00:19:56.440 filled with ancient linguistic compression, hackers 00:19:56.440 --> 00:19:58.940 crashing computers to bypass copy protection, 00:19:59.500 --> 00:20:02.339 the aerodynamic edge of space, and prime number 00:20:02.339 --> 00:20:04.920 Jenga towers standing guard over bridges between 00:20:04.920 --> 00:20:07.880 mathematical dimensions. It is a scale that constantly 00:20:07.880 --> 00:20:10.440 forces us to confront our own human limitations, 00:20:11.259 --> 00:20:12.960 which actually leads me to a final thought for 00:20:12.960 --> 00:20:15.019 you to mull over. Let's hear it. Earlier, we 00:20:15.019 --> 00:20:17.480 talked about the protein titan, the longest word 00:20:17.480 --> 00:20:21.079 in the English language at 189 ,819 letters long, 00:20:21.640 --> 00:20:24.019 and we noted that simply reading that one word 00:20:24.019 --> 00:20:26.759 consumes three solid hours of a human life. Right. 00:20:26.880 --> 00:20:29.180 Now imagine the sheer physical exhaustion of 00:20:29.180 --> 00:20:31.380 sequentially speaking every single number from 00:20:31.380 --> 00:20:36.269 a hundred up to 999 ,999. Oh my god, you'd be 00:20:36.269 --> 00:20:38.910 there for years! You would. Mathematics is a 00:20:38.910 --> 00:20:40.769 miracle because it allows us to compress these 00:20:40.769 --> 00:20:43.309 massive scales. We can manipulate numbers like 00:20:43.309 --> 00:20:46.589 998 ,001 with a single pencil stroke, but to 00:20:46.589 --> 00:20:48.890 actually experience that scale physically, to 00:20:48.890 --> 00:20:50.910 count it out in real time, breath by breath, 00:20:51.230 --> 00:20:53.490 is to experience the heavy, undeniable weight 00:20:53.490 --> 00:20:56.430 of human mortality. Our minds can build the hundred 00:20:56.430 --> 00:20:58.670 thousands, but our bodies cannot outlast them. 00:20:58.890 --> 00:21:01.789 We really appreciate you taking the time to cross 00:21:01.789 --> 00:21:04.950 the county line and explore this numerical wilderness 00:21:04.950 --> 00:21:07.430 with us today on the deep dive. Keep questioning 00:21:07.430 --> 00:21:09.690 the numbers around you. There's always a deeper 00:21:09.690 --> 00:21:11.069 structure waiting to be found.