WEBVTT 00:00:00.000 --> 00:00:03.359 You know, it is, it's funny how we go through 00:00:03.359 --> 00:00:05.740 our days completely surrounded by these invisible 00:00:05.740 --> 00:00:07.940 rulers. Oh, absolutely. Like just think about 00:00:07.940 --> 00:00:10.560 your morning. You look at your phone and you 00:00:10.560 --> 00:00:13.900 see that little battery icon hit 100 % and I 00:00:13.900 --> 00:00:17.079 mean instantly. your shoulders drop, you feel 00:00:17.079 --> 00:00:19.179 safe. Right. You know your device isn't going 00:00:19.179 --> 00:00:22.120 to just die on you during your commute. Exactly. 00:00:22.239 --> 00:00:24.300 Or, you know, you step outside and someone says 00:00:24.300 --> 00:00:26.140 it's going to be 100 degrees out today, and you 00:00:26.140 --> 00:00:28.879 immediately know it's an absolute scorcher. Yeah, 00:00:28.879 --> 00:00:31.000 or even going back to when you were a kid. Oh, 00:00:31.000 --> 00:00:33.799 getting 100 on a spelling test. Yes. You felt 00:00:33.799 --> 00:00:36.000 like you were totally flawless. It's the best 00:00:36.000 --> 00:00:39.979 feeling. But we interact with this specific number, 00:00:40.200 --> 00:00:43.500 100, every single day of our lives. But we... 00:00:44.010 --> 00:00:47.070 we rarely stop to consider why. Like, why does 00:00:47.070 --> 00:00:49.950 this one specific integer command so much authority 00:00:49.950 --> 00:00:52.469 in the way we view the world? It's just so ubiquitous 00:00:52.469 --> 00:00:54.810 that it becomes essentially invisible. We don't 00:00:54.810 --> 00:00:57.030 question it. We just accept it as the ultimate 00:00:57.030 --> 00:00:59.149 finish line. It's like it's the ceiling of our 00:00:59.149 --> 00:01:03.340 everyday experiences. And that is exactly our 00:01:03.340 --> 00:01:05.859 mission for you today. Welcome to our deep dive. 00:01:06.219 --> 00:01:09.040 We are taking a magnifying glass to a single 00:01:09.040 --> 00:01:12.219 remarkably dense topic today. We're looking at 00:01:12.219 --> 00:01:14.239 the Wikipedia article for the number 100. Which 00:01:14.239 --> 00:01:16.239 sounds simple, but it really isn't. Not at all. 00:01:16.459 --> 00:01:18.799 We're going to look at why this specific number 00:01:18.799 --> 00:01:21.120 sits on the throne of our numerical universe. 00:01:21.719 --> 00:01:24.480 And trust me, the reasons go way beyond basic 00:01:24.480 --> 00:01:26.959 math. Yeah. To set the tone for you as we get 00:01:26.959 --> 00:01:29.359 started, it is crucial to understand that this 00:01:29.359 --> 00:01:32.819 exploration isn't just about digits on a chalkboard. 00:01:33.060 --> 00:01:35.459 It is really a story about human psychology. 00:01:35.980 --> 00:01:38.480 We are looking at how a simple integer became 00:01:38.480 --> 00:01:41.799 human society's absolute benchmark for perfection, 00:01:42.019 --> 00:01:45.590 for completion, and for value. OK, let's unpack 00:01:45.590 --> 00:01:47.530 this, starting right at the bedrock of our modern 00:01:47.530 --> 00:01:49.609 world, which is math and measurement. The foundation 00:01:49.609 --> 00:01:51.950 of it all. Exactly. The number 100 is the square 00:01:51.950 --> 00:01:55.310 of 10. 10 times 10. It's this massive base 10 00:01:55.310 --> 00:01:58.390 powerhouse. And think about why base 10 feels 00:01:58.390 --> 00:02:00.849 so naturally solid to us. Because of our hands. 00:02:01.349 --> 00:02:04.670 Exactly. We have 10 fingers. Early human counting 00:02:04.670 --> 00:02:08.389 was inherently tied to our own biology. So 10 00:02:08.389 --> 00:02:10.550 squared 100 feels like the ultimate realization 00:02:10.550 --> 00:02:12.919 of our natural counting system. It just makes 00:02:12.919 --> 00:02:15.000 sense to our primate brains. It really does. 00:02:15.520 --> 00:02:18.259 And from that biological and mathematical foundation, 00:02:18.840 --> 00:02:21.539 100 became the basis for percentages. I mean, 00:02:21.719 --> 00:02:23.560 the word percent itself comes from the Latin 00:02:23.560 --> 00:02:27.159 percentum. Literally translates to by the hundred 00:02:27.159 --> 00:02:29.280 right when you tell someone you're giving a hundred 00:02:29.280 --> 00:02:31.419 percent effort You were telling them you are 00:02:31.419 --> 00:02:33.599 providing a full complete amount. There's nothing 00:02:33.599 --> 00:02:36.560 left in the tank It's the whole pie and and it 00:02:36.560 --> 00:02:39.300 doesn't stop at just percentages That feeling 00:02:39.300 --> 00:02:41.680 of completeness is baked into how we measure 00:02:41.680 --> 00:02:44.120 the physical world to oh the entire metric system 00:02:44.120 --> 00:02:46.419 relies on it Yeah, you have a hundred centimeters 00:02:46.419 --> 00:02:49.300 making up a meter you have the standard si prefix 00:02:49.300 --> 00:02:52.539 Hector which designates a factor of 100 I always 00:02:52.539 --> 00:02:55.699 think of the number 100 like the VIP bouncer 00:02:55.699 --> 00:02:58.639 of numbers. A VIP bouncer? Yeah, like it sets 00:02:58.639 --> 00:03:01.060 the standard for what gets into the club of completeness. 00:03:01.280 --> 00:03:03.580 If you don't hit 100, you are just a fraction. 00:03:03.919 --> 00:03:06.099 You're still waiting in line outside. That is 00:03:06.099 --> 00:03:09.120 a great analogy. And that gatekeeping role is 00:03:09.120 --> 00:03:11.719 perfectly illustrated in how we measure temperature. 00:03:11.819 --> 00:03:14.259 Oh, the Celsius scale. Particularly with the 00:03:14.259 --> 00:03:16.580 Celsius scale. But the history of that scale 00:03:16.580 --> 00:03:18.819 is actually quite surprising. This completely 00:03:18.819 --> 00:03:20.979 threw me for a loop when I read the source. Yeah. 00:03:21.159 --> 00:03:24.300 Because we all grow up learning that 100 degrees 00:03:24.300 --> 00:03:26.500 Celsius is the boiling point of water. Right. 00:03:26.639 --> 00:03:29.319 And zero degrees is the freezing point. And it 00:03:29.319 --> 00:03:33.680 feels clean, neat, naturally perfect. But Anders 00:03:33.680 --> 00:03:35.840 Celsius, the astronomer who actually invented 00:03:35.840 --> 00:03:39.240 the scale in the 1740s, he originally defined 00:03:39.240 --> 00:03:42.199 100 degrees as the freezing point. And zero degrees 00:03:42.199 --> 00:03:44.580 is the boiling point. It is wild. He had the 00:03:44.580 --> 00:03:47.599 entire thermometer completely inverted compared 00:03:47.599 --> 00:03:49.580 to how we use it today. Just imagine checking 00:03:49.580 --> 00:03:51.610 the weather and seeing temperature going up to 00:03:51.610 --> 00:03:53.650 80 degrees and realizing that means you need 00:03:53.650 --> 00:03:56.009 to put on a heavy winter coat because you're 00:03:56.009 --> 00:03:57.889 approaching freezing. It hurts my brain just 00:03:57.889 --> 00:04:00.150 thinking about it. It really does. And it wasn't 00:04:00.150 --> 00:04:01.830 until a couple of years later, shortly after 00:04:01.830 --> 00:04:04.810 Celsius actually died, that the taxonomist Carl 00:04:04.810 --> 00:04:07.590 von Linnae reversed the scale to the modern standard 00:04:07.590 --> 00:04:10.780 we use today. And I want to push back a little 00:04:10.780 --> 00:04:13.319 here. This makes me want to push back on this 00:04:13.319 --> 00:04:16.620 idea of 100 being this naturally perfect universal 00:04:16.620 --> 00:04:19.459 standard. Oh, so? Well, if the guy who invented 00:04:19.459 --> 00:04:21.699 the scale originally had 100 as the freezing 00:04:21.699 --> 00:04:24.879 point, doesn't that prove how completely arbitrary 00:04:24.879 --> 00:04:27.319 our so -called perfect benchmarks actually are? 00:04:27.680 --> 00:04:29.959 Like we just decided one day to flip the numbers 00:04:29.959 --> 00:04:32.079 because it felt better. If we connect this to 00:04:32.079 --> 00:04:34.139 the bigger picture, it absolutely proves how 00:04:34.139 --> 00:04:36.579 arbitrary it is, but it also reveals something 00:04:36.579 --> 00:04:39.199 really fundamental about the human brain. What 00:04:39.199 --> 00:04:41.839 do you mean? Well, we exist in a highly chaotic 00:04:41.839 --> 00:04:45.019 universe. Temperatures fluctuate wildly. Physical 00:04:45.019 --> 00:04:48.139 distances are vast and incomprehensible. Humans 00:04:48.139 --> 00:04:50.980 crave these base 10 anchors to make that chaos 00:04:50.980 --> 00:04:54.040 feel orderly and quantifiable. Oh, I see. Yeah. 00:04:54.220 --> 00:04:56.060 Linnae likely flipped the Celsius scale because 00:04:56.060 --> 00:04:58.920 intuitively, Humans associate the number 100 00:04:58.920 --> 00:05:01.860 with a maximum state. With high energy. Exactly. 00:05:02.439 --> 00:05:05.500 Boiling water at 100 feels vastly more psychologically 00:05:05.500 --> 00:05:09.699 correct to us than freezing water at 100. We 00:05:09.699 --> 00:05:11.920 essentially molded the physical world to fit 00:05:11.920 --> 00:05:13.959 our preferred mathematical anchor. We really 00:05:13.959 --> 00:05:16.199 do mold the world to fit that number, which actually 00:05:16.199 --> 00:05:18.339 leads us right into biology and nature, because 00:05:18.339 --> 00:05:20.620 we don't just do this with temperature. We project 00:05:20.620 --> 00:05:23.720 this perfect number onto living things that do 00:05:23.720 --> 00:05:26.379 not naturally fit the mold at all. We want 100 00:05:26.379 --> 00:05:28.600 to be everywhere, even when nature just flat 00:05:28.600 --> 00:05:31.959 out refuses to cooperate. Case in point. The 00:05:31.959 --> 00:05:34.240 centipede. Oh, the centipede is a classic example. 00:05:34.360 --> 00:05:36.540 Right. The word centipede falls under the zoological 00:05:36.540 --> 00:05:40.019 group Ketopoda. Centi means hundred. Pide means 00:05:40.019 --> 00:05:43.360 foot. It literally translates to 100 feet. But 00:05:43.360 --> 00:05:45.860 centipedes do not actually have exactly 100 legs. 00:05:46.060 --> 00:05:48.360 Not even close. In fact, according to the source, 00:05:48.439 --> 00:05:50.240 they were categorized as having anywhere from 00:05:50.240 --> 00:05:54.420 15 to 191 pairs of legs. The centipede is basically 00:05:54.420 --> 00:05:56.639 nature's version of false advertising. What's 00:05:56.639 --> 00:05:59.240 fascinating here is how humans handled that specific 00:05:59.240 --> 00:06:03.699 chaotic range. Because 15 to 191 pairs of legs 00:06:03.699 --> 00:06:07.160 is wildly variable. It's a huge spread. Huge. 00:06:08.079 --> 00:06:10.379 And yet, instead of calling it a variable ped 00:06:10.379 --> 00:06:13.680 or a mini -ped, whoever named it looked at this 00:06:13.680 --> 00:06:16.519 scurrying creature and just rounded to the nearest 00:06:16.519 --> 00:06:19.040 satisfying baseline. They just needed a clean 00:06:19.040 --> 00:06:21.899 number. The human brain wanted a clean, dramatic 00:06:21.899 --> 00:06:24.720 number to convey a whole lot of legs and a hundred 00:06:24.720 --> 00:06:27.339 was waiting right there. We just slap the label 00:06:27.339 --> 00:06:29.620 on the bug and call it a day. Pretty much. But 00:06:29.620 --> 00:06:32.000 it goes beyond just naming things, right? We 00:06:32.000 --> 00:06:35.839 actually use 100 as an invented scientific baseline 00:06:35.839 --> 00:06:39.120 to measure completely unrelated things, like 00:06:39.120 --> 00:06:42.959 take dietary protein. Ah, yes. There's a metric 00:06:42.959 --> 00:06:45.540 called the biological value of a protein. This 00:06:45.540 --> 00:06:48.399 is a really crucial metric in nutrition science. 00:06:49.139 --> 00:06:51.800 Biological value basically measures how well 00:06:51.800 --> 00:06:54.259 the protein you consume from food is actually 00:06:54.259 --> 00:06:56.279 absorbed and incorporated into the proteins of 00:06:56.279 --> 00:06:58.480 your own body. Right. And scientists needed a 00:06:58.480 --> 00:07:00.379 baseline to compare all these different foods 00:07:00.379 --> 00:07:02.000 against the... So what did they do? They took 00:07:02.000 --> 00:07:04.740 the chicken egg. They took the egg and they arbitrarily 00:07:04.740 --> 00:07:07.699 set its biological value at exactly 100. Just 00:07:07.699 --> 00:07:11.740 drew a line in the sand. Literally. Then every 00:07:11.740 --> 00:07:16.500 other protein on Earth like beef, soy, way is 00:07:16.500 --> 00:07:20.579 evaluated relative to the egg. But why 100? I 00:07:20.579 --> 00:07:22.579 mean, it's not like the egg is some perfect mathematical 00:07:22.579 --> 00:07:25.139 absolute. They just needed a clean number to 00:07:25.139 --> 00:07:27.540 make the comparative math easier for every other 00:07:27.540 --> 00:07:30.100 food on the planet. It becomes the ultimate comparative 00:07:30.100 --> 00:07:32.759 tool. In early nutrition science, you couldn't 00:07:32.759 --> 00:07:35.180 just look at protein in a vacuum. You needed 00:07:35.180 --> 00:07:37.240 a measuring stick for human absorption. Right, 00:07:37.300 --> 00:07:39.699 something practical. And the egg was highly efficient, 00:07:39.819 --> 00:07:42.680 so pinning it at 100 avoids using messy decimal 00:07:42.680 --> 00:07:44.980 fractions to measure everything else. We round 00:07:44.980 --> 00:07:48.459 up, we round down, or we entirely invent a baseline 00:07:48.459 --> 00:07:51.279 like the egg, just so we can utilize that satisfying 00:07:51.279 --> 00:07:53.579 three -digit number. It is all about the psychology 00:07:53.579 --> 00:07:56.000 of that number. Exactly. And you see this exact 00:07:56.000 --> 00:07:58.519 same psychological need for a clean baseline 00:07:58.519 --> 00:08:01.680 in technology, too. HTTP status codes when you 00:08:01.680 --> 00:08:04.040 were browsing the web right when your computer 00:08:04.040 --> 00:08:06.480 talks to a website server There's this invisible 00:08:06.480 --> 00:08:10.040 digital handshake that has to happen HTTP status 00:08:10.040 --> 00:08:13.319 code 100 is the specific signal that tells a 00:08:13.319 --> 00:08:16.199 client browser to continue with its request It 00:08:16.199 --> 00:08:18.480 is the foundation of the communication. So it 00:08:18.480 --> 00:08:21.040 basically says I am listening Everything is functioning 00:08:21.040 --> 00:08:24.060 perfectly. Keep talking. Precisely. Similarly, 00:08:24.180 --> 00:08:26.360 in the early days of networking, 100 megabits 00:08:26.360 --> 00:08:29.019 per second became the definitive speed standard 00:08:29.019 --> 00:08:31.500 for fast Ethernet. I said that magic number again. 00:08:31.560 --> 00:08:34.019 Early computer engineers relied on the number 00:08:34.019 --> 00:08:37.440 100 as a signal of trust, a sign that a system 00:08:37.440 --> 00:08:40.059 is whole, stable, and working at peak capacity. 00:08:40.519 --> 00:08:43.059 So we see computer engineers relying on 100 as 00:08:43.059 --> 00:08:46.480 a signal of trust. And I think that psychological 00:08:46.480 --> 00:08:49.100 need for wholeness and trust is exactly why we 00:08:49.100 --> 00:08:51.629 use it. to measure the thing we rely on most 00:08:51.629 --> 00:08:54.330 in our daily societal interactions. Our money. 00:08:54.490 --> 00:08:56.990 Our money. Almost every major global currency 00:08:56.990 --> 00:08:59.669 is divided into 100 subunits. The economic weight 00:08:59.669 --> 00:09:02.110 of the number 100 is profound. It really is. 00:09:02.350 --> 00:09:05.090 One euro is broken down into 100 cents. One British 00:09:05.090 --> 00:09:07.389 pound sterling is made up of 100 pence. And in 00:09:07.389 --> 00:09:09.450 the United States? Yeah. The largest bank note 00:09:09.450 --> 00:09:13.169 currently in circulation is the $100 bill. The 00:09:13.169 --> 00:09:15.980 Benjamin. featuring Benjamin Franklin. It's the 00:09:15.980 --> 00:09:18.480 ultimate symbol of having cash. And dividing 00:09:18.480 --> 00:09:21.860 currencies into a hundred subunits is not a strict 00:09:21.860 --> 00:09:25.700 mathematical necessity at all. Really? No, historically, 00:09:26.259 --> 00:09:29.000 currencies were often divided into 12 or 20 parts. 00:09:29.620 --> 00:09:31.559 Think of the old British system with shillings 00:09:31.559 --> 00:09:34.639 and pence. Oh, right. Dividing by 12 is actually 00:09:34.639 --> 00:09:37.440 incredibly practical for trade, because you can 00:09:37.440 --> 00:09:39.799 easily divide a shilling into halves, thirds, 00:09:39.940 --> 00:09:41.960 or quarters without getting a messy fraction. 00:09:42.080 --> 00:09:43.679 That actually makes a lot of sense for a merchant. 00:09:43.950 --> 00:09:46.629 But moving to a decimal system, dividing a currency 00:09:46.629 --> 00:09:49.470 into 100 cents, creates a psychological sense 00:09:49.470 --> 00:09:52.250 of a completed progress bar for the consumer. 00:09:52.429 --> 00:09:54.289 A progress bar. That is exactly what it feels 00:09:54.289 --> 00:09:56.990 like. Right. When you accumulate 100 cents, your 00:09:56.990 --> 00:09:59.529 brain registers that you have achieved a complete 00:09:59.529 --> 00:10:02.169 whole unit. It's that VIP bouncer again, letting 00:10:02.169 --> 00:10:04.710 you into the club of a whole dollar. And you 00:10:04.710 --> 00:10:07.230 see this prestige outside of money, too. Like, 00:10:07.230 --> 00:10:09.549 look at the world of sports. Oh, the 100 meter 00:10:09.549 --> 00:10:12.830 sprint. Yes. It is widely considered one of the 00:10:12.830 --> 00:10:15.129 most prestigious Olympic events in the world. 00:10:16.409 --> 00:10:18.789 Which makes me wonder, and I want to pose this 00:10:18.789 --> 00:10:21.690 to you. Sure. Is the 100 meter sprint so highly 00:10:21.690 --> 00:10:24.850 regarded just because it's a grueling, explosive 00:10:24.850 --> 00:10:27.870 physical distance that requires ultimate athletic 00:10:27.870 --> 00:10:31.049 exertion? Or is it because winning a race that 00:10:31.049 --> 00:10:33.289 happens to have the number 100 attached to it 00:10:33.289 --> 00:10:36.129 carries a deeper psychological weight of absolute 00:10:36.129 --> 00:10:38.559 perfection? I mean, it is almost certainly the 00:10:38.559 --> 00:10:40.440 psychological weight. You think so? Definitely. 00:10:40.899 --> 00:10:43.740 Historically, track distances varied wildly based 00:10:43.740 --> 00:10:45.759 on the size of the specific stadium or field 00:10:45.759 --> 00:10:49.139 being used. But standardizing the premier sprinting 00:10:49.139 --> 00:10:52.360 event on exactly 100 meters creates a mythic 00:10:52.360 --> 00:10:54.840 quality. It's just a... Clean, perfect number. 00:10:54.980 --> 00:10:58.000 Right. It's about 10 seconds of explosive, maximum 00:10:58.000 --> 00:11:00.360 human power. But if that exact same physical 00:11:00.360 --> 00:11:03.340 exertion happened over a 97 -meter race or a 00:11:03.340 --> 00:11:06.100 103 -meter race, it simply wouldn't hold the 00:11:06.100 --> 00:11:07.759 same cultural reverence. People wouldn't care 00:11:07.759 --> 00:11:11.240 as much. Exactly. The number elevates the physical 00:11:11.240 --> 00:11:14.340 act. And if you want the ultimate modern proof 00:11:14.340 --> 00:11:17.779 of how 100 has completely transcended math and 00:11:17.779 --> 00:11:20.480 physical measurement to become a cultural synonym 00:11:20.480 --> 00:11:23.500 for absolute excellence, you just have to look 00:11:23.500 --> 00:11:25.799 at how we communicate today. Oh, you mean the 00:11:25.799 --> 00:11:29.990 100 emoji? Yes. The bright red double underlined 00:11:29.990 --> 00:11:33.850 100. The O emoji. We use it constantly in digital 00:11:33.850 --> 00:11:36.409 culture to represent something that is authentic 00:11:36.409 --> 00:11:39.590 or excellent or just perfect. People say keep 00:11:39.590 --> 00:11:42.169 it 100. Right. Meaning to stay completely true 00:11:42.169 --> 00:11:43.909 to yourself. You don't tell someone to keep it 00:11:43.909 --> 00:11:47.070 99. Never. The number has evolved linguistically 00:11:47.070 --> 00:11:49.889 to become a symbol for absolute truth and maximum 00:11:49.889 --> 00:11:52.269 effort. OK, here's where it gets really interesting, 00:11:52.350 --> 00:11:54.450 though, because we have spent this entire time 00:11:54.450 --> 00:11:57.779 talking about human constructs, right? and society. 00:11:58.299 --> 00:12:01.080 Yeah. Human money, human sports, human emojis, 00:12:01.360 --> 00:12:04.419 human invented protein scales. It makes it sound 00:12:04.419 --> 00:12:06.840 like 100 is just a totally random integer that 00:12:06.840 --> 00:12:09.299 happens to have a really good PR team. That's 00:12:09.299 --> 00:12:11.820 a funny way to put it. But if we strip all of 00:12:11.820 --> 00:12:15.039 that human bias away, like if we take away our 00:12:15.039 --> 00:12:17.919 culture and our obsession with counting on our 00:12:17.919 --> 00:12:22.059 10 fingers, The number 100 actually possesses 00:12:22.059 --> 00:12:25.019 intrinsic, almost magical mathematical properties. 00:12:25.299 --> 00:12:28.500 The pure mathematics of 100 are staggering. They 00:12:28.500 --> 00:12:30.820 really are. Once you dig into the structural 00:12:30.820 --> 00:12:32.980 logic of the number itself, you start to see 00:12:32.980 --> 00:12:35.340 why it feels so special to us. Let's walk through 00:12:35.340 --> 00:12:36.919 some of these because they genuinely blew my 00:12:36.919 --> 00:12:38.860 mind when we were prepping for this. Let's start 00:12:38.860 --> 00:12:41.139 with prime numbers. Okay, primes. So a prime 00:12:41.139 --> 00:12:43.519 number is a number that is only divisible by 00:12:43.519 --> 00:12:47.200 one and itself. So numbers like 2, 3, 5, 7, and 00:12:47.200 --> 00:12:50.590 11. Right. If you take the first nine prime numbers 00:12:50.590 --> 00:12:53.929 in existence, all the primes from 2 through 23, 00:12:54.269 --> 00:12:56.230 and you add them together, the sum is exactly 00:12:56.230 --> 00:12:58.809 100. Just perfectly 100, yeah. 2 plus 3 plus 00:12:58.809 --> 00:13:02.710 5 plus 7 plus 13 plus 17 plus 19 plus 23 equals 00:13:02.710 --> 00:13:05.730 exactly 100. It is a beautiful symmetry, but 00:13:05.730 --> 00:13:07.750 the relationship with primes goes even further. 00:13:07.850 --> 00:13:09.730 Oh yeah, tell them about the division part. So 00:13:09.730 --> 00:13:12.470 how many prime numbers exist below the number 00:13:12.470 --> 00:13:16.639 100? There are exactly 25 primes. Okay. And what 00:13:16.639 --> 00:13:19.179 happens when you divide 100 by that exact number 00:13:19.179 --> 00:13:22.399 of primes beneath it? 100 is perfectly divisible 00:13:22.399 --> 00:13:26.000 by 25. It equals exactly 4. It's just so clean. 00:13:26.259 --> 00:13:28.860 And it gets even wilder when we look at the sum 00:13:28.860 --> 00:13:30.919 of the cubes. This is a great one. If you take 00:13:30.919 --> 00:13:33.980 the first four positive integers, 1, 2, 3, and 00:13:33.980 --> 00:13:36.980 4, if you cube them, meaning you multiply each 00:13:36.980 --> 00:13:39.279 number by itself three times and add them up, 00:13:39.659 --> 00:13:41.659 they hit our magic number. Let's do the math. 00:13:41.879 --> 00:13:46.360 1 cubed is 1. 2 cubed is 8. 3 cubed is 27. 4 00:13:46.360 --> 00:13:50.159 cubed is 64. 1 plus 8 plus 27 plus 64 adds up 00:13:50.159 --> 00:13:52.340 to exactly 100. Which brings us to something 00:13:52.340 --> 00:13:55.240 called Nicomachus' theorem. Okay, yes. Break 00:13:55.240 --> 00:13:57.600 this down. This is one of my favorite mathematical 00:13:57.600 --> 00:13:59.539 connections to explain because it feels like 00:13:59.539 --> 00:14:02.460 a magic trick, but it is pure logic. I love that. 00:14:03.039 --> 00:14:04.980 Nicomachus' theorem states that the sum of the 00:14:04.980 --> 00:14:07.539 cubes of the first n numbers is equal to the 00:14:07.539 --> 00:14:10.179 square of the sum of those exact same numbers. 00:14:10.340 --> 00:14:11.759 Wait, wait. Walk me through what that actually 00:14:11.759 --> 00:14:13.620 looks like in practice. Okay, take those same 00:14:13.620 --> 00:14:16.789 four numbers. One, two, three, and four. We just 00:14:16.789 --> 00:14:18.710 established that if you cube them and add them 00:14:18.710 --> 00:14:21.149 together, you get 100. Now, instead of cubing 00:14:21.149 --> 00:14:23.429 them, just add them together normally. One plus 00:14:23.429 --> 00:14:26.610 two plus three plus four equals 10. Now, square 00:14:26.610 --> 00:14:31.149 that result. 10 squared is 100. Wow. So the sum 00:14:31.149 --> 00:14:33.870 of their cubes perfectly mirrors the square of 00:14:33.870 --> 00:14:36.509 their sum. To me, looking at these interlocking 00:14:36.509 --> 00:14:39.580 properties, it's like a cosmic math puzzle. clicking 00:14:39.580 --> 00:14:41.820 perfectly into place. It makes you feel like 00:14:41.820 --> 00:14:44.059 math is something we discover out in the universe, 00:14:44.639 --> 00:14:46.539 rather than something we just invented in a classroom. 00:14:46.860 --> 00:14:49.299 That is the core of it, really. We can talk all 00:14:49.299 --> 00:14:51.480 day about how arbitrary the Celsius scale is, 00:14:51.580 --> 00:14:54.519 or how we force the centipede's name, but the 00:14:54.519 --> 00:14:57.519 elegance of pure mathematics underpins the natural 00:14:57.519 --> 00:15:00.019 order of the universe. It's beyond us. Exactly. 00:15:00.480 --> 00:15:03.320 Being the sum of the first nine primes, or resting 00:15:03.320 --> 00:15:06.990 perfectly inside Nicomachus' theorem. These aren't 00:15:06.990 --> 00:15:09.409 human inventions. They are fundamental properties 00:15:09.409 --> 00:15:12.850 of logic, and 100 is uniquely situated at the 00:15:12.850 --> 00:15:14.970 crossroads of all these patterns. The Wikipedia 00:15:14.970 --> 00:15:17.590 article goes into some incredibly dense classifications 00:15:17.590 --> 00:15:20.970 as well. Things like harshad numbers and Euler 00:15:20.970 --> 00:15:22.990 totions. But there was one that really stood 00:15:22.990 --> 00:15:25.110 out to me as another beautiful puzzle, and that 00:15:25.110 --> 00:15:28.059 was Leyland numbers. Oh, yes. Leyland numbers 00:15:28.059 --> 00:15:30.340 are a great example of this hidden elegance. 00:15:31.000 --> 00:15:32.700 A Leyland number is what you get when you take 00:15:32.700 --> 00:15:35.600 two integers, raise them to each other's powers, 00:15:35.700 --> 00:15:38.059 and then add the results together. So how does 00:15:38.059 --> 00:15:41.159 that work for 100? So to get 100, you take the 00:15:41.159 --> 00:15:45.320 numbers 2 and 6. 2 to the power of 6 is 64. 6 00:15:45.320 --> 00:15:49.220 to the power of 2 is 36. Add 64 and 36 together, 00:15:49.220 --> 00:15:52.360 and you get exactly 100. It is just endless. 00:15:52.649 --> 00:15:55.429 perfect symmetry. It is a mathematical playground 00:15:55.429 --> 00:15:58.250 and I think that is why human beings instinctively 00:15:58.250 --> 00:16:00.129 recognized its importance. Even before we knew 00:16:00.129 --> 00:16:03.090 all the math. Definitely. Long before we understood 00:16:03.090 --> 00:16:06.019 advanced theorems or Leyland numbers. Early humans 00:16:06.019 --> 00:16:08.480 probably sensed that 10 squared was a remarkably 00:16:08.480 --> 00:16:12.100 stable and elegant plateau. We chose 100 as our 00:16:12.100 --> 00:16:14.539 societal benchmark because mathematically, it 00:16:14.539 --> 00:16:16.720 actually deserves the crown. Which makes the 00:16:16.720 --> 00:16:19.200 historical plot twist in our source material 00:16:19.200 --> 00:16:21.639 so absolutely shocking. Quite the curveball. 00:16:21.879 --> 00:16:24.059 Because after establishing all this absolute 00:16:24.059 --> 00:16:26.720 undeniable mathematical perfection, the deep 00:16:26.720 --> 00:16:29.039 dive delivers a massive wrench in the gears. 00:16:29.700 --> 00:16:31.799 Historically, 100 wasn't always a fixed integer. 00:16:31.980 --> 00:16:34.440 This raises an important question about how human 00:16:34.440 --> 00:16:37.200 civilization actually developed and just how 00:16:37.200 --> 00:16:39.159 messy our history really is. Wait, wait, wait. 00:16:39.220 --> 00:16:41.659 You're telling me 100 wasn't always 100? Not 00:16:41.659 --> 00:16:44.360 at all. Because the source notes that in medieval 00:16:44.360 --> 00:16:47.500 contexts, the Germanic and English use of the 00:16:47.500 --> 00:16:49.960 word hundred could actually refer to what they 00:16:49.960 --> 00:16:52.159 called the long hundred. A long hundred, yes. 00:16:52.620 --> 00:16:55.080 And the long hundred was six score. A score is 00:16:55.080 --> 00:16:59.139 20. So 6 times 20 is 120. Right. When medieval 00:16:59.139 --> 00:17:02.860 people said 100, they frequently meant 120. To 00:17:02.860 --> 00:17:05.140 differentiate, they had to specifically describe 00:17:05.140 --> 00:17:08.440 our modern 100 as the short 100, or five score. 00:17:08.940 --> 00:17:12.420 I mean, doesn't a long 100 of 120 completely 00:17:12.420 --> 00:17:14.579 undermine everything we just discussed about 00:17:14.579 --> 00:17:17.640 its perfect base 10 nature? It does undermine 00:17:17.640 --> 00:17:19.799 the base 10 nature, but it perfectly illustrates 00:17:19.799 --> 00:17:22.079 the friction between pure math and practical 00:17:22.079 --> 00:17:25.210 human language. How so? We like to think of mathematics 00:17:25.210 --> 00:17:27.470 and language as these perfectly aligned logical 00:17:27.470 --> 00:17:30.549 systems that grew up holding hands. But in reality, 00:17:31.069 --> 00:17:33.029 language and mathematics evolved on parallel 00:17:33.029 --> 00:17:36.730 but incredibly messy tracks. Messy is an understatement. 00:17:37.309 --> 00:17:39.829 Imagine trying to buy groceries today and having 00:17:39.829 --> 00:17:42.009 to ask the cashier if they are using the short 00:17:42.009 --> 00:17:44.859 or long hundred. It would be chaos. We take for 00:17:44.859 --> 00:17:47.059 granted that numbers are absolute truths today, 00:17:47.460 --> 00:17:50.339 but for centuries, your hundred could have literally 00:17:50.339 --> 00:17:53.380 meant 120 depending on what town you were standing 00:17:53.380 --> 00:17:56.200 in. Exactly. And the reason for this goes back 00:17:56.200 --> 00:17:59.839 to how people actually lived and worked. In early 00:17:59.839 --> 00:18:02.880 Germanic and medieval English societies, trade 00:18:02.880 --> 00:18:06.019 and grouping items often relied on 12s or 20s. 00:18:06.119 --> 00:18:07.740 Oh, like the currency we talked about earlier. 00:18:07.779 --> 00:18:10.000 Right. Think about how we still buy eggs by the 00:18:10.000 --> 00:18:12.980 dozen or pencils by the gross, which is a dozen 00:18:12.980 --> 00:18:15.140 dozens. Yeah, that makes sense. The actual word 00:18:15.140 --> 00:18:17.319 hundred started out as a conceptual grouping. 00:18:17.420 --> 00:18:20.400 It was just a linguistic way to say a very large 00:18:20.400 --> 00:18:22.740 standard batch of goods rather than a strict 00:18:22.740 --> 00:18:25.480 mathematical absolute. So a merchant selling 00:18:25.480 --> 00:18:27.940 fish might count them out in groups of 20 or 00:18:27.940 --> 00:18:32.420 a score. And handing over six groups of 120 fish 00:18:32.420 --> 00:18:36.299 was just their standard large batch. Precisely. 00:18:36.579 --> 00:18:40.380 A long hundred. of 120 made practical, everyday 00:18:40.380 --> 00:18:43.039 sense for merchants counting by dozens or scores. 00:18:43.619 --> 00:18:46.619 It proves that our modern, rigid, standardized 00:18:46.619 --> 00:18:49.880 definition of numbers, where the word 100 strictly 00:18:49.880 --> 00:18:52.920 and only means 10 squared, is a relatively modern 00:18:52.920 --> 00:18:56.000 luxury. It took centuries of standardization 00:18:56.000 --> 00:18:58.720 for the pure, elegant math we discussed earlier 00:18:58.720 --> 00:19:01.359 to finally conquer the practical, linguistic 00:19:01.359 --> 00:19:03.940 habits of medieval traders. So what does this 00:19:03.940 --> 00:19:06.940 all mean? We started this deep dive wondering 00:19:07.150 --> 00:19:10.329 Why 100 is the VIP bouncer of our numerical lives? 00:19:10.950 --> 00:19:12.769 And the journey to answer that has taken us all 00:19:12.769 --> 00:19:14.829 over the map. It really has. We've gone from 00:19:14.829 --> 00:19:16.910 the freezing point of water in Sweden to the 00:19:16.910 --> 00:19:19.869 number of legs scurrying on a centipede. We've 00:19:19.869 --> 00:19:22.250 seen its staggering mathematical elegance, the 00:19:22.250 --> 00:19:24.569 sums of primes and cubes and Leyland numbers 00:19:24.569 --> 00:19:26.769 that make it a naturally occurring masterpiece 00:19:26.769 --> 00:19:28.809 of logic. Which is just beautiful. And we've 00:19:28.809 --> 00:19:31.089 seen its biological misnumbers, where we just 00:19:31.089 --> 00:19:33.660 force nature and nutrition science to fit our 00:19:33.660 --> 00:19:36.059 favorite round number. And we've seen its absolute 00:19:36.059 --> 00:19:38.740 psychological grip on our society. From the Benjamin 00:19:38.740 --> 00:19:40.940 in your wallet to the 100 meter sprint on your 00:19:40.940 --> 00:19:43.079 television down to the ovemoji you text your 00:19:43.079 --> 00:19:45.920 friends. It is the ultimate benchmark, even if 00:19:45.920 --> 00:19:48.359 it took our ancestors a while to finally decide 00:19:48.359 --> 00:19:50.180 between the short hundred and the long hundred 00:19:50.180 --> 00:19:52.799 at the market. So for you listening, the next 00:19:52.799 --> 00:19:54.980 time you look down at your phone. and feel that 00:19:54.980 --> 00:19:57.420 wave of relief seeing a 100 % charged battery, 00:19:57.720 --> 00:19:59.819 or you send that Red Thaw emoji in a group chat, 00:20:00.279 --> 00:20:02.799 take a second. Really think about it. Remember 00:20:02.799 --> 00:20:06.200 that you are participating in a massive, rich 00:20:06.200 --> 00:20:09.460 history. You are touching medieval language quirks, 00:20:09.980 --> 00:20:12.980 pure mathematical geometry, and deeply arbitrary 00:20:12.980 --> 00:20:16.279 human psychology. all rolled into one three -digit 00:20:16.279 --> 00:20:18.880 package. And I want to leave you with one final 00:20:18.880 --> 00:20:21.599 thought to mull over, drawing from a small detail 00:20:21.599 --> 00:20:24.039 in the science section of our material. Oh, that's 00:20:24.039 --> 00:20:26.500 a... We talked about 100 in biology and physics, 00:20:26.559 --> 00:20:29.039 but we didn't mention chemistry. On the periodic 00:20:29.039 --> 00:20:31.900 table, the atomic number 100 belongs to an element 00:20:31.900 --> 00:20:34.619 called fermium. Fermium, okay. What is fascinating 00:20:34.619 --> 00:20:37.000 about fermium is that it is a purely synthetic 00:20:37.000 --> 00:20:39.359 chemical element. It does not occur naturally 00:20:39.359 --> 00:20:42.240 in the Earth's crust. It was created by humans 00:20:42.240 --> 00:20:45.529 in a lab. a completely synthetic element sitting 00:20:45.529 --> 00:20:47.970 at the most mathematically perfect number. Yes. 00:20:48.509 --> 00:20:51.410 So as humanity moves into a future where we increasingly 00:20:51.410 --> 00:20:54.069 synthesize our own elements, build our own digital 00:20:54.069 --> 00:20:56.650 realities, and expand beyond our earthly origins, 00:20:57.210 --> 00:20:59.750 you have to wonder, will the number 100 remain 00:20:59.750 --> 00:21:02.210 our ultimate organic benchmark of completion? 00:21:02.519 --> 00:21:05.079 Or, in a vast universe that doesn't actually 00:21:05.079 --> 00:21:07.519 care about human fingers or base 10 math, is 00:21:07.519 --> 00:21:10.220 our obsession with 100 just a temporary milestone. 00:21:10.700 --> 00:21:12.819 When we finally step out into the cosmos, will 00:21:12.819 --> 00:21:14.660 our invisible ruler still measure up?