WEBVTT 00:00:00.000 --> 00:00:03.240 So there is this hidden 10 ,000 number stretch 00:00:03.240 --> 00:00:07.700 of mathematics that secretly controls everything 00:00:07.700 --> 00:00:10.019 from the physical limits of vintage computer 00:00:10.019 --> 00:00:13.740 hardware to the underground language of early 00:00:13.740 --> 00:00:16.059 internet hackers. It's honestly kind of wild 00:00:16.059 --> 00:00:19.000 when you think about it. Right. And today, we 00:00:19.000 --> 00:00:22.519 are completely ignoring the millions, the billions, 00:00:22.579 --> 00:00:24.920 and the trillions to go looking for it. So I 00:00:24.920 --> 00:00:26.820 actually want you to do something for me. Yeah, 00:00:27.000 --> 00:00:29.239 play along with this. Right now, wherever you 00:00:29.239 --> 00:00:31.660 are, I want you to picture a completely random 00:00:31.660 --> 00:00:35.100 number. But let's narrow it down to this specific 00:00:35.100 --> 00:00:38.159 block. Pick a number somewhere in the 30 ,000s. 00:00:38.340 --> 00:00:44.359 Like maybe 34 ,212? Yeah, or 38 ,999. Got one. 00:00:44.640 --> 00:00:46.579 Keep that number right in the back of your mind. 00:00:46.820 --> 00:00:49.479 Hold onto it tightly, because usually, When we 00:00:49.479 --> 00:00:51.320 think of a number like that, it just, you know, 00:00:51.520 --> 00:00:54.039 it feels like filler. It's not a nice, clean 00:00:54.039 --> 00:00:56.840 milestone like 10 ,000 or 100 ,000. Right. They're 00:00:56.840 --> 00:00:58.920 not the big round numbers we usually celebrate. 00:00:59.320 --> 00:01:01.920 Exactly. The 30 ,000s just feel like the flyover 00:01:01.920 --> 00:01:04.219 states of the number line, just like a blur on 00:01:04.219 --> 00:01:06.829 a spreadsheet. But for today's deep dive, we 00:01:06.829 --> 00:01:09.569 are pulling from a single, incredibly dense source, 00:01:10.069 --> 00:01:12.370 which is the Wikipedia article for the number 00:01:12.370 --> 00:01:15.209 30 ,000. And specifically, we're looking at the 00:01:15.209 --> 00:01:18.090 block of integers sitting directly between 30 00:01:18.090 --> 00:01:23.420 ,001 and 39 ,999. Which, I mean, sounds on the 00:01:23.420 --> 00:01:25.379 surface like reading a phone book. It really 00:01:25.379 --> 00:01:28.420 does. But our mission today is to prove to you 00:01:28.420 --> 00:01:32.319 that what looks like a dry, endless list of integers 00:01:32.319 --> 00:01:36.420 is actually a secret map. Because numbers are 00:01:36.420 --> 00:01:39.120 never just quantities, right? They are a reflection 00:01:39.120 --> 00:01:42.120 of the systems, the machines, and, well, the 00:01:42.120 --> 00:01:44.120 human cultures that rely on them. I got to say, 00:01:44.140 --> 00:01:46.480 I went into the source material expecting a very 00:01:46.480 --> 00:01:49.540 straightforward kind of dry math textbook. But 00:01:49.540 --> 00:01:52.090 instead, I found what feels like an undiscovered 00:01:52.090 --> 00:01:54.310 country. Oh, absolutely. We've got the fundamental 00:01:54.310 --> 00:01:57.170 building blocks of mathematical theory, the literal 00:01:57.170 --> 00:02:00.049 physical walls of early computer science, and 00:02:00.049 --> 00:02:03.090 some truly bizarre pop culture trivia, all just 00:02:03.090 --> 00:02:05.810 living in this exact 10 ,000 number stretch. 00:02:06.129 --> 00:02:08.729 It really is a microcosm of how humans interact 00:02:08.729 --> 00:02:11.710 with the universe. But before we can understand 00:02:11.710 --> 00:02:14.289 how humans and machines twist these numbers for 00:02:14.289 --> 00:02:16.669 their own use, we have to look at their natural 00:02:16.669 --> 00:02:19.629 state in the mathematical wild. The pure math. 00:02:19.770 --> 00:02:22.009 Exactly. We have to look at the pure math. The 00:02:22.009 --> 00:02:24.789 wilderness. And out in this specific wilderness, 00:02:25.210 --> 00:02:29.150 between 30 ,000 and 40 ,000, there are exactly 00:02:29.150 --> 00:02:33.069 958 prime numbers. Which is a pretty solid chunk. 00:02:33.169 --> 00:02:35.229 Yeah. And just as a quick refresher for anyone 00:02:35.229 --> 00:02:38.650 whose high school math is a little rusty, prime 00:02:38.650 --> 00:02:41.210 numbers are numbers that can only be divided 00:02:41.210 --> 00:02:44.310 by one and themselves. They're the absolute bedrock 00:02:44.310 --> 00:02:46.250 of math. Right. You can't break them down any 00:02:46.250 --> 00:02:49.090 further. Exactly. But what the source reveals 00:02:49.099 --> 00:02:52.919 is that in the 30 ,000s, these primes start doing 00:02:52.919 --> 00:02:55.900 some really weird, highly structured things. 00:02:55.939 --> 00:02:58.280 I absolutely do. Let's start with a concept called 00:02:58.280 --> 00:03:01.259 the primorial. OK. Lay it on me. So most people 00:03:01.259 --> 00:03:03.639 are familiar with factorials, right? If you see 00:03:03.639 --> 00:03:06.000 a number with an exclamation point next to it, 00:03:06.159 --> 00:03:08.620 like 5 factorial, that means you multiply the 00:03:08.620 --> 00:03:11.020 number by every integer below it. So 5 times 00:03:11.020 --> 00:03:14.219 4 times 3 times 2 times 1. Exactly. Which gives 00:03:14.219 --> 00:03:18.120 you 120. Right. But a primorial is a slightly 00:03:18.120 --> 00:03:20.580 different beast. Instead of multiplying every 00:03:20.580 --> 00:03:23.479 consecutive integer, you only multiply consecutive 00:03:23.479 --> 00:03:26.060 prime numbers together. Oh, OK. So it's 2 times 00:03:26.060 --> 00:03:30.219 3 times 5 times 7 times 11 times 13. And if you 00:03:30.219 --> 00:03:33.020 run that calculation, the math lands you perfectly 00:03:33.020 --> 00:03:37.599 on 30 ,030. Making 30 ,030 a primorial number. 00:03:37.770 --> 00:03:40.370 I mean, it's like this massive, mathematically 00:03:40.370 --> 00:03:43.270 perfect intersection on the highway. It really 00:03:43.270 --> 00:03:45.449 is. And what I love is the neighborhood built 00:03:45.449 --> 00:03:48.270 around it because right next door you have 30 00:03:48.270 --> 00:03:52.039 ,029. which is a primorial prime. And on the 00:03:52.039 --> 00:03:55.099 other side, 30 ,000 and 31, which is the smallest 00:03:55.099 --> 00:03:57.560 composite number that is exactly one more than 00:03:57.560 --> 00:04:00.780 a primorial. It's so tidy. It is. You step into 00:04:00.780 --> 00:04:03.500 the 30 ,000s, and immediately you are greeted 00:04:03.500 --> 00:04:06.000 by this highly organized little mathematical 00:04:06.000 --> 00:04:08.960 suburb. And the architecture only gets stranger 00:04:08.960 --> 00:04:11.840 as you venture deeper, because mathematicians 00:04:11.840 --> 00:04:15.379 scour this specific range, looking for extreme, 00:04:15.639 --> 00:04:18.790 almost unbelievable patterns. Like what? Well, 00:04:18.930 --> 00:04:23.529 for example, 32 ,043, it is the smallest number 00:04:23.529 --> 00:04:26.389 where, if you square it, the resulting number 00:04:26.389 --> 00:04:30.149 is pandigital. Pandigital meaning it contains 00:04:30.149 --> 00:04:34.040 every single digit from 0 to 9. Yes. Exactly 00:04:34.040 --> 00:04:36.899 once, or at least encompassing all of them. Wow. 00:04:37.300 --> 00:04:40.540 And then you have 32 ,045, which can be expressed 00:04:40.540 --> 00:04:43.800 as the sum of two squares in more ways than any 00:04:43.800 --> 00:04:46.279 smaller number before it. Okay. Or you stumble 00:04:46.279 --> 00:04:50.040 across 30 ,240, which is classified as a harmonic 00:04:50.040 --> 00:04:52.879 divisor number and is also the smallest four 00:04:52.879 --> 00:04:54.699 -perfect number. Okay, wait, let me stop you 00:04:54.699 --> 00:04:56.540 there. I can feel my eyes starting to glaze over 00:04:56.540 --> 00:04:58.120 a little bit. Fair enough, fair enough. Because 00:04:58.120 --> 00:05:00.339 harmonic divisor number and four -perfect number, 00:05:00.660 --> 00:05:03.089 that's exactly the kind of dense math jargon 00:05:03.089 --> 00:05:05.350 that usually loses me that just feels too abstract 00:05:05.350 --> 00:05:07.329 like why are mathematicians actually hunting 00:05:07.329 --> 00:05:10.709 for these things that is a completely fair pushback 00:05:10.709 --> 00:05:13.509 let me translate the jargon into the actual goal 00:05:13.509 --> 00:05:15.990 here please do mathematicians are essentially 00:05:15.990 --> 00:05:19.490 hunting for symmetry in a landscape the number 00:05:19.490 --> 00:05:22.110 line that is notoriously chaotic and unpredictable. 00:05:22.529 --> 00:05:24.470 Because primes are just everywhere. Exactly. 00:05:24.709 --> 00:05:28.189 Prime numbers pop up seemingly at random. Multiplication 00:05:28.189 --> 00:05:31.389 can spin off into wild directions. So when a 00:05:31.389 --> 00:05:34.089 mathematician finds a perfect number or a harmonic 00:05:34.089 --> 00:05:37.149 divisor, what they're really finding is a rare 00:05:37.149 --> 00:05:40.230 moment of perfect symmetrical balance. Oh, I 00:05:40.230 --> 00:05:42.750 see. It's like hacking through a wild overgrown 00:05:42.750 --> 00:05:45.569 jungle of random digits and suddenly finding 00:05:45.569 --> 00:05:48.519 a perfectly symmetrical crystalline leaf. It 00:05:48.519 --> 00:05:51.060 proves there is underlying order in the chaos. 00:05:51.600 --> 00:05:53.160 OK, I see where you're going with that. It's 00:05:53.160 --> 00:05:56.259 the thrill of the hunt. But instead of the perfect 00:05:56.259 --> 00:05:58.000 symmetrical numbers, I actually want to talk 00:05:58.000 --> 00:05:59.819 about a number that rejects all of that. Oh, 00:05:59.899 --> 00:06:02.000 I think I know the one. It is my absolute favorite 00:06:02.000 --> 00:06:04.279 number in this entire source, the one that feels 00:06:04.279 --> 00:06:06.180 like it actually has a personality. You must 00:06:06.180 --> 00:06:12.819 be talking about 38 ,501. Yes. 38 ,501. Mathematically, 00:06:13.079 --> 00:06:15.860 it's known as a Friedlander -Iwaniak prime. Which 00:06:15.860 --> 00:06:18.540 is a mouthful. It really is. And it means it 00:06:18.540 --> 00:06:21.220 can be expressed as a very specific elegant formula, 00:06:21.540 --> 00:06:25.060 which is 7 to the power of 4 plus 190 squared. 00:06:25.279 --> 00:06:28.379 Right. But that's not why I love it. I love it 00:06:28.379 --> 00:06:31.279 because of how it lives. The source describes 00:06:31.279 --> 00:06:34.560 it as an isolated prime. It sits completely alone. 00:06:34.699 --> 00:06:39.240 Yes. I like to think of 38 ,501 as this grumpy 00:06:39.240 --> 00:06:41.920 hermit living in a remote cabin in the mathematical 00:06:41.920 --> 00:06:44.339 woods. Just yelling at kids to get off his lawn. 00:06:44.620 --> 00:06:47.800 Exactly. It is actively maintaining a strict 00:06:47.800 --> 00:06:50.600 40 -acre buffer from its nearest mathematical 00:06:50.600 --> 00:06:53.220 neighbors. Yeah. The closest prime number before 00:06:53.220 --> 00:06:57.279 it is 38 ,416 -1. And the closest prime after 00:06:57.279 --> 00:07:02.379 it is 38 ,543. There is a gap of at least 40 00:07:02.379 --> 00:07:04.600 in either direction where absolutely no other 00:07:04.600 --> 00:07:06.959 primes exist. It just wants everyone to stay 00:07:06.959 --> 00:07:10.519 away. It's a fantastic analogy. And if we look 00:07:10.519 --> 00:07:13.740 at why mathematicians care about your grumpy 00:07:13.740 --> 00:07:18.259 hermit, it's because these massive gaps prove 00:07:18.259 --> 00:07:21.879 that the number line isn't just a smooth, uniform 00:07:21.879 --> 00:07:25.839 highway. It has intense terrain, it has densely 00:07:25.839 --> 00:07:28.920 populated cities, and it has these empty wastelands. 00:07:29.000 --> 00:07:31.500 Like the prime quadruplets. Yes. The source points 00:07:31.500 --> 00:07:36.800 out that right at 31 ,721, and again at 34 ,800, 00:07:37.459 --> 00:07:40.519 you have the start of prime quadruplets. Which 00:07:40.519 --> 00:07:43.180 are tight little clusters of four prime numbers 00:07:43.180 --> 00:07:45.860 packed incredibly close together. The bustling 00:07:45.860 --> 00:07:48.699 cities to our hermit's remote cabin. Exactly. 00:07:49.060 --> 00:07:52.060 And you also have these strange delicate structures 00:07:52.060 --> 00:07:56.360 like the Leyland primes. Take 32 ,993. To build 00:07:56.360 --> 00:07:58.560 a Leyland prime you take a number to the power 00:07:58.560 --> 00:08:00.959 of a second number and add it to that second 00:08:00.959 --> 00:08:05.019 number to the power of the first. So for 32 ,993 00:08:05.019 --> 00:08:08.079 you take two to the power of 15 and add 15 to 00:08:08.079 --> 00:08:10.920 the power of 2. Precisely, x to the y plus y 00:08:10.920 --> 00:08:14.060 to the x. That is so cool. It's a prime number 00:08:14.060 --> 00:08:17.160 built entirely out of a mirrored equation. And 00:08:17.160 --> 00:08:19.439 then As you navigate through these structures, 00:08:20.079 --> 00:08:24.339 you eventually hit 38 ,807. The Goldbach partitions. 00:08:24.680 --> 00:08:28.379 Yeah, this is a heavy one. 38 ,807 represents 00:08:28.379 --> 00:08:30.980 the exact number of non -equivalent ways you 00:08:30.980 --> 00:08:33.700 can express the number 10 million as the sum 00:08:33.700 --> 00:08:36.860 of two prime numbers. Let's break that down for 00:08:36.860 --> 00:08:38.419 a second, because I know the Goldbach conjecture 00:08:38.419 --> 00:08:41.279 is one of those legendary unsolved math puzzles, 00:08:41.460 --> 00:08:44.090 right? It is. The conjecture simply states that 00:08:44.090 --> 00:08:46.889 every even whole number greater than two is the 00:08:46.889 --> 00:08:49.649 sum of two prime numbers. Right. So four is two 00:08:49.649 --> 00:08:52.789 plus two. Six is three plus three. Eight is three 00:08:52.789 --> 00:08:55.870 plus five. Exactly. It sounds incredibly simple, 00:08:56.149 --> 00:08:58.549 but no one has ever been able to mathematically 00:08:58.549 --> 00:09:02.629 prove that it holds true to infinity. So mathematicians 00:09:02.629 --> 00:09:05.529 test it by taking massive numbers like 10 million 00:09:05.529 --> 00:09:08.029 and figuring out how many different pairs of 00:09:08.029 --> 00:09:10.190 primes can add up to it. And the answer for 10 00:09:10.190 --> 00:09:16.110 million is 30. It's just staggering to think 00:09:16.110 --> 00:09:18.350 about. It really is. You look at a number like 00:09:18.350 --> 00:09:20.429 that on a piece of paper, and you just assume 00:09:20.429 --> 00:09:23.490 it's meaningless filler. But it's actually a 00:09:23.490 --> 00:09:26.269 specific coordinate in a centuries -old puzzle. 00:09:26.970 --> 00:09:29.129 It holds the structural blueprint for how to 00:09:29.129 --> 00:09:31.450 build the number 10 million. It's amazing to 00:09:31.450 --> 00:09:34.149 think about these numbers stretching out to infinity 00:09:34.149 --> 00:09:37.269 with endless hermit primes and sprawling equations. 00:09:37.429 --> 00:09:40.940 But, well, Infinity is a luxury of pure math. 00:09:41.440 --> 00:09:44.460 In the real world, infinity doesn't exist. Especially 00:09:44.460 --> 00:09:46.600 not when you try to cram these numbers into a 00:09:46.600 --> 00:09:49.500 computer chip. Okay, yes. This is where the story 00:09:49.500 --> 00:09:52.480 pivots from the abstract into the physical. Because 00:09:52.480 --> 00:09:54.840 when humans try to force these infinite numbers 00:09:54.840 --> 00:09:57.500 into the actual physical constraints of computer 00:09:57.500 --> 00:10:00.600 hardware, things break. They really do. Or at 00:10:00.600 --> 00:10:02.740 least they hit a very rigid wall. And that wall 00:10:02.740 --> 00:10:05.139 happens to sit. right smack in the middle of 00:10:05.139 --> 00:10:07.679 the 32 thousands. We are talking about the digital 00:10:07.679 --> 00:10:10.919 boundary of the 16 -bit signed integer. Let's 00:10:10.919 --> 00:10:13.399 unpack this for the listener. If you're programming 00:10:13.399 --> 00:10:16.419 an early computer, so think vintage arcade cabinets, 00:10:16.720 --> 00:10:20.360 early PCs, classic game consoles memory is incredibly 00:10:20.360 --> 00:10:22.779 precious. Oh, absolutely scarce. You can't just 00:10:22.779 --> 00:10:25.149 tell the computer to remember a number. You have 00:10:25.149 --> 00:10:27.830 to tell it exactly how much physical space to 00:10:27.830 --> 00:10:31.009 set aside to store that number. And a very common 00:10:31.009 --> 00:10:33.909 format was the 16 -bit integer. Right. And to 00:10:33.909 --> 00:10:37.289 really visualize this, think of a bit as a literal 00:10:37.289 --> 00:10:39.789 microscopic light switch on a circuit board. 00:10:40.370 --> 00:10:43.669 It can only be in one of two states. off, which 00:10:43.669 --> 00:10:47.309 the computer reads as a zero, or on, which the 00:10:47.309 --> 00:10:49.950 computer reads as a one. If you have a 16 -bit 00:10:49.950 --> 00:10:52.970 system, you have a row of 16 physical light switches 00:10:52.970 --> 00:10:55.070 to store your data. But the crucial word here 00:10:55.070 --> 00:10:58.960 is signed. a 16 -bit signed integer. Which means 00:10:58.960 --> 00:11:00.960 the computer needs a way to remember if the number 00:11:00.960 --> 00:11:03.480 is positive or negative. And because the computer 00:11:03.480 --> 00:11:06.320 only understands those switches, it has to use 00:11:06.320 --> 00:11:09.259 the very first switch in that row of 16 just 00:11:09.259 --> 00:11:12.299 to store the plus or minus sign. So if that first 00:11:12.299 --> 00:11:14.139 switch is off, the number is positive. If it 00:11:14.139 --> 00:11:16.220 flips on, the number is negative. Which leaves 00:11:16.220 --> 00:11:19.200 exactly 15 switches to store the actual size 00:11:19.200 --> 00:11:21.779 of the number. Mathematically, if you turn all 00:11:21.779 --> 00:11:24.220 15 of those remaining switches to the on position, 00:11:24.600 --> 00:11:27.440 you calculate two to the power of 15 minus one. 00:11:27.639 --> 00:11:31.799 Which gives us a magic number. Yes. 32 ,767. 00:11:32.080 --> 00:11:34.700 That is the absolute largest positive number 00:11:34.700 --> 00:11:37.259 you could physically store in that system. It's 00:11:37.259 --> 00:11:39.659 a hard physical ceiling built right into the 00:11:39.659 --> 00:11:42.320 silicon. So to make this relatable, think of 00:11:42.320 --> 00:11:46.620 32 ,767 like the mechanical odometer on a really 00:11:46.620 --> 00:11:49.559 old rusty car. Oh, I like this. Right. You're 00:11:49.559 --> 00:11:54.320 driving along, adding miles. 32 ,765, 66, 67. 00:11:55.039 --> 00:11:57.980 And the odometer is entirely maxed out. Every 00:11:57.980 --> 00:12:00.559 dial is showing its highest possible value. The 00:12:00.559 --> 00:12:02.960 bucket is completely full of water. Exactly. 00:12:03.419 --> 00:12:05.320 But what happens when you drive one more mile? 00:12:06.080 --> 00:12:08.220 What happens when you add one single drop of 00:12:08.220 --> 00:12:10.539 water to that completely full bucket? Well, see, 00:12:10.539 --> 00:12:12.879 on a car, it just rolls over to all zeros. Right. 00:12:13.399 --> 00:12:15.740 But computers use a system called Two's Complement. 00:12:16.320 --> 00:12:20.399 When you add one to 32 ,767, the current cascades, 00:12:21.620 --> 00:12:24.299 all 15 of those switches flip back to zero. But 00:12:24.299 --> 00:12:26.919 the momentum spills over. And it hits that 16th 00:12:26.919 --> 00:12:30.639 switch. Yes. The sign bit. It flips that switch 00:12:30.639 --> 00:12:33.620 from off to on. From positive to negative. Instantly. 00:12:33.820 --> 00:12:39.100 You add 1 to positive 32 ,767 and the computer 00:12:39.100 --> 00:12:41.600 violently throws you into the maximum negative 00:12:41.600 --> 00:12:43.799 number. You plunge straight down to negative 00:12:43.799 --> 00:12:46.679 32 ,768. Which is why we call it a boundary. 00:12:46.919 --> 00:12:49.720 The 30 ,000s are literally the invisible fences 00:12:49.720 --> 00:12:53.960 of early computing. It's crazy. Negative 32 ,768, 00:12:54.059 --> 00:12:56.759 which mathematically is exactly 2 to the power 00:12:56.759 --> 00:13:01.179 of 15, or 8 to the 5th, or 32 cubed, it acts 00:13:01.179 --> 00:13:03.960 as the absolute floor of reality for that machine. 00:13:04.659 --> 00:13:09.519 And positive 32 ,767 acts as the ceiling. Exactly. 00:13:09.639 --> 00:13:11.539 I mean, it's a terrifying concept if you don't 00:13:11.539 --> 00:13:14.360 know what's coming. Imagine playing a role -playing 00:13:14.360 --> 00:13:17.139 video game in the 1980s. You've been grinding 00:13:17.139 --> 00:13:21.519 for hours, you finally collect your 32 ,768th 00:13:21.519 --> 00:13:25.000 gold coin, the bucket spills over, that 16th 00:13:25.000 --> 00:13:27.700 switch flips, and suddenly your inventory says, 00:13:28.000 --> 00:13:31.159 you are 32 ,000 coins in debt. It's such a hilarious 00:13:31.159 --> 00:13:33.860 glitch, but it's also profound, you know? It 00:13:33.860 --> 00:13:37.039 bridges the gap between theoretical math, the 00:13:37.039 --> 00:13:39.799 elegant powers of two, and the physical reality 00:13:39.799 --> 00:13:42.779 of how memory was allocated. Right. It's a reminder 00:13:42.779 --> 00:13:45.419 to you, the listener, that our seemingly boundless 00:13:45.419 --> 00:13:47.980 digital worlds actually have physical borders. 00:13:48.379 --> 00:13:52.740 You can only travel 32 ,767 steps before the 00:13:52.740 --> 00:13:55.220 universe just folds in on itself. It's fascinating. 00:13:56.000 --> 00:13:59.389 So once we leave the physical hardware, we start 00:13:59.389 --> 00:14:02.570 seeing humans claim the leftover numbers for 00:14:02.570 --> 00:14:04.909 culture. Oh, yes. We got the pure math, we got 00:14:04.909 --> 00:14:06.769 the computer architecture, but then people step 00:14:06.769 --> 00:14:09.470 in. Yeah. And they turn these sterile digits 00:14:09.470 --> 00:14:13.409 into language, into art, and into tools for measuring 00:14:13.409 --> 00:14:15.470 the physical world. The human imprint. Yeah. 00:14:15.610 --> 00:14:18.929 And there is one number in the 30 ,000s that 00:14:18.929 --> 00:14:20.909 practically defined the culture of the early 00:14:20.909 --> 00:14:25.990 internet, 31 ,337. 31 ,337. I actually know this 00:14:25.990 --> 00:14:29.889 one. I figure you might. on internet forums or 00:14:29.889 --> 00:14:32.730 bulletin board systems, or playing online video 00:14:32.730 --> 00:14:35.629 games in the late 90s or early 2000s, this number 00:14:35.629 --> 00:14:37.950 was everywhere. Right, mathematically the source 00:14:37.950 --> 00:14:41.389 notes it's just a cousin prime, but culturally. 00:14:41.629 --> 00:14:43.950 Culturally it is legendary. It is the numerical 00:14:43.950 --> 00:14:46.889 spelling for the word elite. Yep. The three looks 00:14:46.889 --> 00:14:49.450 like a capital E, the one is an L, the threes 00:14:49.450 --> 00:14:54.440 are Es again, the seven is a T. IT exactly it 00:14:54.440 --> 00:14:58.039 was a foundation of leet speak this entire obfuscated 00:14:58.039 --> 00:15:00.779 alphabet made with numbers and punctuation but 00:15:00.779 --> 00:15:02.500 why go through the trouble of spelling words 00:15:02.500 --> 00:15:04.759 with numbers though like what was the point well 00:15:04.990 --> 00:15:07.450 Originally, it was a practical tool. Early hackers 00:15:07.450 --> 00:15:09.789 and software pirates needed a way to talk to 00:15:09.789 --> 00:15:12.509 each other on public message boards without triggering 00:15:12.509 --> 00:15:14.649 automated text filters. Oh, the filters that 00:15:14.649 --> 00:15:17.250 were searching for words like hacker or elite. 00:15:17.549 --> 00:15:19.529 Exactly. So they just swapped the letters for 00:15:19.529 --> 00:15:22.389 numbers. And over time, it just became a badge 00:15:22.389 --> 00:15:24.669 of honor, you know, a secret handshake for the 00:15:24.669 --> 00:15:27.230 digital age. It's fascinating how a completely 00:15:27.230 --> 00:15:31.269 random prime number just gets co -opted to become 00:15:31.269 --> 00:15:34.370 a cultural shibboleth. Humans are really desperate 00:15:34.370 --> 00:15:36.809 to find meaning in the abstract. Which perfectly 00:15:36.809 --> 00:15:40.070 explains our next stop. Because from underground 00:15:40.070 --> 00:15:44.169 internet hackers, we swing wildly to the Muvvets. 00:15:44.570 --> 00:15:49.850 Ah, yes. The source material brings up 34 ,969. 00:15:50.009 --> 00:15:54.649 According to the text, 34 ,969 is famously the 00:15:54.649 --> 00:15:56.730 favorite number of the Sesame Street character. 00:15:57.110 --> 00:15:59.289 Count fun count. Which is just incredible. It 00:15:59.289 --> 00:16:01.549 is an amazing piece of trivia. But I have to 00:16:01.549 --> 00:16:03.850 ask you, and I admit I am totally confused by 00:16:03.850 --> 00:16:06.210 this, of all the infinite numbers in the universe, 00:16:06.649 --> 00:16:09.370 why did the creators of Sesame Street pick 34 00:16:09.370 --> 00:16:13.789 ,969 for a puppet vampire? Is there like a hidden 00:16:13.789 --> 00:16:17.360 math joke here? Actually, no. Really? Yeah, the 00:16:17.360 --> 00:16:19.860 source text trickly attributes this as a fact 00:16:19.860 --> 00:16:22.899 cited by a BBC news broadcast back in 2012. It 00:16:22.899 --> 00:16:25.220 doesn't give us a deep mathematical conspiracy 00:16:25.220 --> 00:16:27.600 or a primordial equation for the Muppets. It's 00:16:27.600 --> 00:16:30.259 just random. Well, what it does perfectly illustrate 00:16:30.259 --> 00:16:32.879 is how human beings assign aesthetic value to 00:16:32.879 --> 00:16:37.799 numbers. 34 ,969 isn't special because of its 00:16:37.799 --> 00:16:40.620 factors or its primes. It's special because a 00:16:40.620 --> 00:16:43.230 writer decided it sounded funny. Oh, I see. It 00:16:43.230 --> 00:16:45.850 has a certain bouncy rhythm when spoken out loud 00:16:45.850 --> 00:16:49.049 by a character who loves to count. We literally 00:16:49.049 --> 00:16:51.629 breathe life into these numbers. We use them 00:16:51.629 --> 00:16:54.830 to anchor ourselves. Which brings me to the final 00:16:54.830 --> 00:16:58.549 way. Humans use the 30 ,000s, and that's to measure 00:16:58.549 --> 00:17:01.250 the physical reality of the universe. Weight 00:17:01.250 --> 00:17:03.649 and time are locked right here in this block. 00:17:04.230 --> 00:17:06.269 For instance, did you know there are exactly 00:17:06.269 --> 00:17:10.809 35 ,840 ounces in a long ton? A long ton being 00:17:10.809 --> 00:17:14.650 2 ,240 pounds, and translated down to the ounce, 00:17:14.849 --> 00:17:18.750 you hit exactly 35 ,840. It's such a specific 00:17:18.750 --> 00:17:21.680 anchor for global trade and industry. But I gotta 00:17:21.680 --> 00:17:24.200 say, my absolute favorite measurement in this 00:17:24.200 --> 00:17:27.119 entire deep dive is a number that finally helped 00:17:27.119 --> 00:17:29.480 my brain understand the concept of scale. Oh, 00:17:29.539 --> 00:17:33.519 I know the one. The number is 31 ,688. The time 00:17:33.519 --> 00:17:36.559 conversion. Yes. Because humans are fundamentally 00:17:36.559 --> 00:17:39.900 terrible at understanding large numbers. We really 00:17:39.900 --> 00:17:43.680 are? We throw around words like million, billion, 00:17:43.859 --> 00:17:46.579 and trillion, and to our brains, they all just 00:17:46.579 --> 00:17:48.829 sound like a lot. The difference between a million 00:17:48.829 --> 00:17:51.349 and a billion just feels fuzzy. It's hard to 00:17:51.349 --> 00:17:53.549 visualize. But the source points out a concrete 00:17:53.549 --> 00:17:58.369 fact. 31 ,688 is the approximate number of years 00:17:58.369 --> 00:18:02.390 it takes to equal exactly one trillion seconds. 00:18:02.569 --> 00:18:04.630 And if we break that down to help you really 00:18:04.630 --> 00:18:07.089 grasp the scale we're talking about here? Please 00:18:07.089 --> 00:18:10.170 do, because it's wild. A billion seconds is about 00:18:10.170 --> 00:18:12.789 11 and a half days. Just over a week and a half. 00:18:12.930 --> 00:18:17.420 Okay. A billion seconds is roughly 31 .7 years, 00:18:17.720 --> 00:18:20.539 a sizable chunk of a human life. But a trillion 00:18:20.539 --> 00:18:24.180 seconds, that takes you back 31 ,688 years. It 00:18:24.180 --> 00:18:26.940 is mind -blowing. When you put it in terms of 00:18:26.940 --> 00:18:30.319 seconds, a million is next week. A billion is 00:18:30.319 --> 00:18:33.880 a few decades ago. But a trillion seconds ago, 00:18:34.279 --> 00:18:36.200 Neanderthals were still walking the Earth. It 00:18:36.200 --> 00:18:40.119 really puts it into perspective. And that specific 00:18:40.119 --> 00:18:45.400 number, 31 ,688 lives right here in this unassuming 00:18:45.400 --> 00:18:48.819 stretch of Wikipedia. It acts as the skeleton 00:18:48.819 --> 00:18:51.240 key to understanding what a trillion actually 00:18:51.240 --> 00:18:53.700 feels like. It really highlights the core mission 00:18:53.700 --> 00:18:55.839 we set out on at the start of this deep dive. 00:18:56.279 --> 00:18:57.980 You know, you look at a list of numbers from 00:18:57.980 --> 00:19:02.319 30 ,001 to 39 ,999 and you naturally assume it's 00:19:02.319 --> 00:19:05.519 just raw data. But it's not. No. So let's summarize 00:19:05.519 --> 00:19:07.759 what we've actually uncovered in just this random 00:19:07.759 --> 00:19:10.410 10 ,000 number block. Let's do it. We ventured 00:19:10.410 --> 00:19:13.069 into the math wilderness and found the foundational 00:19:13.069 --> 00:19:15.930 architecture of the universe. We found primorials 00:19:15.930 --> 00:19:18.569 that multiply prime numbers, pandigitals that 00:19:18.569 --> 00:19:21.410 collect every digit, and grumpy hermit primes 00:19:21.410 --> 00:19:24.250 fiercely guarding their 40 -acre voids. We found 00:19:24.250 --> 00:19:26.829 the literal physical walls of early computer 00:19:26.829 --> 00:19:29.130 programming, where adding a single drop of water 00:19:29.130 --> 00:19:31.809 to a full bucket flips a switch and throws a 00:19:31.809 --> 00:19:34.430 machine from its absolute maximum positive value 00:19:34.430 --> 00:19:37.650 into a negative void. We found the exact weight 00:19:37.650 --> 00:19:41.059 of an industrial long -ton. We decoded the underground, 00:19:41.099 --> 00:19:43.940 lengthy slang of early internet hackers. We found 00:19:43.940 --> 00:19:46.559 the punchlines of Sesame Street Muppets. And 00:19:46.559 --> 00:19:49.279 we found the exact number of years it takes for 00:19:49.279 --> 00:19:51.960 a trillion seconds to tick by on the cosmic clock. 00:19:52.380 --> 00:19:56.079 All of that packed into just a tiny microscopic 00:19:56.079 --> 00:19:58.650 sliver. of the number line. Which is exactly 00:19:58.650 --> 00:20:01.029 why the next time you look at a spreadsheet or 00:20:01.029 --> 00:20:02.930 a bank statement or even just a random address 00:20:02.930 --> 00:20:04.769 on the side of a building, I want you to remember 00:20:04.769 --> 00:20:07.069 that you aren't just looking at a quantity. You 00:20:07.069 --> 00:20:09.910 are looking at a story waiting to be unpacked. 00:20:10.230 --> 00:20:12.349 Every single number has a biography. If you do. 00:20:12.650 --> 00:20:14.309 And I want to leave you with one final thought 00:20:14.309 --> 00:20:17.509 to mull over. We've spent this entire time exploring 00:20:17.509 --> 00:20:21.690 just the 30 ,000s, a tiny 10 ,000 number block. 00:20:22.109 --> 00:20:25.549 And look at how much wild, human, and cosmic 00:20:25.549 --> 00:20:29.130 history is packed into it. It's a lot. Now imagine 00:20:29.130 --> 00:20:32.029 the undiscovered digital cultures, the mathematical 00:20:32.029 --> 00:20:34.630 hermits, and the strange human connections waiting 00:20:34.630 --> 00:20:37.069 out there in the millions, the billions, and 00:20:37.069 --> 00:20:40.430 the trillions. Oh, wow. The number line is infinite, 00:20:40.849 --> 00:20:43.069 which means the amount of hidden meaning in the 00:20:43.069 --> 00:20:46.289 universe is infinite too. That is heavy. But 00:20:46.289 --> 00:20:48.829 it's entirely true. Think back to that completely 00:20:48.829 --> 00:20:50.869 random number I asked you to picture at the very 00:20:50.869 --> 00:20:53.470 beginning of this deep dive, wherever it was 00:20:53.470 --> 00:20:55.970 in the 30 ,000s. I bet it doesn't feel like just 00:20:55.970 --> 00:20:58.289 a random face in the crowd anymore. Definitely 00:20:58.289 --> 00:21:00.210 neither. It's got a story. You just have to know 00:21:00.210 --> 00:21:01.009 how to read the map.