WEBVTT 00:00:00.000 --> 00:00:02.299 Imagine an alternate timeline for just a second, 00:00:02.459 --> 00:00:06.200 like really picture it. Imagine human beings 00:00:06.200 --> 00:00:09.960 evolved with four fingers on each hand instead 00:00:09.960 --> 00:00:12.560 of five. Right, so eight fingers total. Exactly, 00:00:12.759 --> 00:00:14.859 eight fingers total. If that had happened, I 00:00:14.859 --> 00:00:18.160 mean our entire global concept of mathematics, 00:00:18.699 --> 00:00:21.559 our currency, our science, our culture, all of 00:00:21.559 --> 00:00:23.640 it would revolve around the number eight. Yeah, 00:00:23.679 --> 00:00:25.929 top 10 list wouldn't even exist. No. You'd be 00:00:25.929 --> 00:00:28.850 listening to a top eight list and it would feel 00:00:28.850 --> 00:00:32.090 entirely complete and satisfying to you. The 00:00:32.090 --> 00:00:35.490 very foundation of what we consider a round number 00:00:35.490 --> 00:00:38.049 would completely shift. It really is the ultimate 00:00:38.049 --> 00:00:41.590 example of human anatomy kind of masquerading 00:00:41.590 --> 00:00:44.420 as an absolute law of nature. Yes. We assume 00:00:44.420 --> 00:00:47.179 our math is objective, but it's actually heavily 00:00:47.179 --> 00:00:49.659 biased by the literal shape of our own hands. 00:00:49.759 --> 00:00:51.759 Which is wild. And welcome to this deep dive 00:00:51.759 --> 00:00:54.200 crafted just for you. Whether you are catching 00:00:54.200 --> 00:00:56.859 up on some fascinating historical trivia, maybe 00:00:56.859 --> 00:00:58.780 prepping for a wildly specific conversation, 00:00:58.979 --> 00:01:01.899 or you're just insanely curious about the invisible 00:01:01.899 --> 00:01:04.319 structures of the world around you, you are in 00:01:04.319 --> 00:01:06.780 the right place. Today, our mission is exploring 00:01:06.780 --> 00:01:10.299 a massive stack of source material. all centered 00:01:10.299 --> 00:01:12.739 around something so ubiquitous, so constantly 00:01:12.739 --> 00:01:15.719 in front of our faces, that we have basically 00:01:15.719 --> 00:01:17.920 completely stopped seeing it. We are diving into 00:01:17.920 --> 00:01:20.640 the number 10. And looking at the research we've 00:01:20.640 --> 00:01:22.640 gathered, I mean, this isn't just a basic mathematical 00:01:22.640 --> 00:01:25.439 overview. Not at all. The documentation here 00:01:25.439 --> 00:01:28.379 covers the birth of spoken language, the mechanics 00:01:28.379 --> 00:01:32.180 of ancient warfare, structural chemistry, and 00:01:32.180 --> 00:01:35.620 even ancient mysticism. Everything radiates out 00:01:35.620 --> 00:01:38.939 from this single foundational integer. OK, let's 00:01:38.939 --> 00:01:40.340 unpack this because I want to frame this right 00:01:40.340 --> 00:01:42.719 off the bat. This is not going to be some boring 00:01:42.719 --> 00:01:44.879 math lesson from middle school. Right. This is 00:01:44.879 --> 00:01:48.280 a journey into how a really simple biological 00:01:48.280 --> 00:01:51.319 baseline, basically shaped all of human civilization. 00:01:51.819 --> 00:01:54.579 So where does this all begin? Like before we 00:01:54.579 --> 00:01:56.879 even had written numbers, how did human beings 00:01:56.879 --> 00:02:00.159 first conceptualize 10? Well, to find that, the 00:02:00.159 --> 00:02:02.840 sources trace the actual spoken word 10 back 00:02:02.840 --> 00:02:04.939 through this massive linguistic family tree. 00:02:05.319 --> 00:02:07.400 It originates from the Proto -Indo -European 00:02:07.400 --> 00:02:11.800 root, which is pronounced roughly as dekem. Now 00:02:11.800 --> 00:02:15.169 Proto -Indo -European is the ancient totally 00:02:15.169 --> 00:02:17.889 unwritten ancestor of most modern languages across 00:02:17.889 --> 00:02:21.389 Europe and South Asia. And that root, Decum, 00:02:21.770 --> 00:02:24.949 meant quite simply ten. Decum. It almost sounds 00:02:24.949 --> 00:02:27.449 like a, I don't know, like a drum beat or heavy 00:02:27.449 --> 00:02:29.710 footstep. It definitely has a weight to it, certainly. 00:02:30.270 --> 00:02:32.830 And from that ancient origin, the linguistics 00:02:32.830 --> 00:02:35.629 trace how it evolved into the Proto -Germanic 00:02:35.629 --> 00:02:39.539 root Tehun. Tehun. OK. And from there, it branched 00:02:39.539 --> 00:02:41.919 out, basically seeding the vocabulary of a whole 00:02:41.919 --> 00:02:44.439 host of modern languages. You see the descendants 00:02:44.439 --> 00:02:47.740 of Tehun in Dutch, in German, in Swedish. And 00:02:47.740 --> 00:02:49.639 of course, it eventually morphs into the English 00:02:49.639 --> 00:02:52.860 word 10. Wow. But the core revelation here, the 00:02:52.860 --> 00:02:54.900 reason the decimal system, which is our base 00:02:54.900 --> 00:02:57.439 10 numeral system, became the dominant way humans 00:02:57.439 --> 00:02:59.840 denote numbers globally is purely physical. It's 00:02:59.840 --> 00:03:02.159 the fingers. It's the fingers. It's simply because 00:03:02.159 --> 00:03:04.159 early humans looked down at their hands and feet 00:03:04.159 --> 00:03:06.379 and used their 10 fingers and 10 toes to keep 00:03:06.379 --> 00:03:09.590 track of them. things. It is so stunningly literal 00:03:09.590 --> 00:03:12.810 like we built an abstract universal system for 00:03:12.810 --> 00:03:15.650 measuring the distance to the stars and its baseline 00:03:15.650 --> 00:03:18.310 was established by you know cavemen counting 00:03:18.310 --> 00:03:21.750 on their digits. It is a really remarkable translation 00:03:21.750 --> 00:03:24.689 of the physical into the conceptual. You are 00:03:24.689 --> 00:03:27.710 taking a tangible reality, your literal fingers, 00:03:28.330 --> 00:03:31.310 and abstracting it. The physical reality of human 00:03:31.310 --> 00:03:34.469 anatomy set a cognitive baseline, and that baseline 00:03:34.469 --> 00:03:37.389 just seeped into every corner of human thought. 00:03:37.550 --> 00:03:39.949 And you really see how deeply embedded it is 00:03:39.949 --> 00:03:42.210 in our everyday language, too. I mean, we use 00:03:42.210 --> 00:03:44.969 the word decade to describe a nice, neat, tidy 00:03:44.969 --> 00:03:47.569 collection of 10 years. We use the ordinal adjunct 00:03:47.569 --> 00:03:49.650 decimal, the distributive adjunct of dairy, and 00:03:49.650 --> 00:03:52.289 we see it in Greek prefixes like deca or deca 00:03:52.289 --> 00:03:55.610 and the Latin prefix. It all feels very orderly, 00:03:55.729 --> 00:03:59.530 very structured and safe. It does feel safe linguistically 00:03:59.530 --> 00:04:01.969 speaking, anyway. But history shows us that this 00:04:01.969 --> 00:04:04.810 mathematical neatness can absolutely be weaponized. 00:04:04.969 --> 00:04:07.949 Right. Because as much as 10, is usually a comforting 00:04:07.949 --> 00:04:10.669 concept for organizing quantities today, the 00:04:10.669 --> 00:04:13.449 research reveals a shockingly brutal historical 00:04:13.449 --> 00:04:16.269 application attached to it. So we've seen how 00:04:16.269 --> 00:04:19.069 biology built our math, but how did that math 00:04:19.069 --> 00:04:21.850 get turned into an actual weapon of terror? Well, 00:04:21.910 --> 00:04:24.949 to answer that, we have to look at the true historical 00:04:24.949 --> 00:04:28.759 definition of the word decimate. OK. Today, people 00:04:28.759 --> 00:04:31.680 use it casually, but the literal definition of 00:04:31.680 --> 00:04:35.199 decimate is to reduce something by exactly one 00:04:35.199 --> 00:04:37.399 -tenth. Literally one -tenth. Literally. And 00:04:37.399 --> 00:04:39.579 in ancient Rome, this wasn't just a math problem. 00:04:39.620 --> 00:04:42.079 It was a formal institutionalized punishment. 00:04:42.220 --> 00:04:44.360 A punishment for what, specifically? Like, who 00:04:44.360 --> 00:04:47.040 was getting decimated? Primarily, it was used 00:04:47.040 --> 00:04:49.300 for cowardice or mutiny within the military ranks. 00:04:49.319 --> 00:04:51.779 Wow. The Roman military was highly structured, 00:04:51.939 --> 00:04:54.899 right? Organized into cohorts. If a cohort rebelled 00:04:54.899 --> 00:04:57.060 or fled in battle, the commanders didn't kill. 00:04:57.040 --> 00:04:59.120 everyone, and they didn't just single out the 00:04:59.120 --> 00:05:01.120 leaders either, they used math. They used math. 00:05:01.300 --> 00:05:04.060 Yeah. The punishment was the execution of exactly 00:05:04.060 --> 00:05:07.720 one in ten soldiers chosen by lottery, and the 00:05:07.720 --> 00:05:09.759 nine who survived were often forced to execute 00:05:09.759 --> 00:05:13.259 their own comrades. Oh my god, that is horrifying. 00:05:13.379 --> 00:05:15.620 It gets worse because it wasn't strictly limited 00:05:15.620 --> 00:05:19.120 to the military. The texts detail how decimation 00:05:19.120 --> 00:05:22.019 was also used as a calculated form of retribution 00:05:22.019 --> 00:05:25.279 against rebellious agrarian villages. You civilians! 00:05:25.500 --> 00:05:28.300 Yes. The Roman legions would enter a village 00:05:28.300 --> 00:05:31.339 and kill exactly one -tenth of the able -bodied 00:05:31.339 --> 00:05:33.639 men. They would just line up the farmers, count 00:05:33.639 --> 00:05:36.220 to ten, and execute the tenth man. Precisely. 00:05:36.329 --> 00:05:38.509 And I mean, think about the mechanics of that 00:05:38.509 --> 00:05:41.069 in an agrarian society. Right, the farming. Exactly. 00:05:41.290 --> 00:05:44.069 If you remove exactly 10 % of an able -bodied 00:05:44.069 --> 00:05:46.790 workforce, you don't instantly wipe out the town, 00:05:47.029 --> 00:05:49.610 but you create an immediate catastrophic labor 00:05:49.610 --> 00:05:52.149 shortage that crops can't be harvested in time. 00:05:52.449 --> 00:05:55.329 It introduces the very real threat of mass starvation 00:05:55.329 --> 00:05:57.990 for the following winter. Wow. What's fascinating 00:05:57.990 --> 00:06:01.670 here is how a purely abstract mathematical concept 00:06:01.670 --> 00:06:05.149 division by 10 was utilized as a highly precise 00:06:05.149 --> 00:06:07.569 cold instrument for social control. Yeah, it's 00:06:07.569 --> 00:06:10.769 so calculated. It wasn't about blind rage or 00:06:10.769 --> 00:06:13.410 totally wiping out a population. It was about 00:06:13.410 --> 00:06:15.930 mathematically calibrating the exact amount of 00:06:15.930 --> 00:06:18.610 trauma necessary to break a society's spirit 00:06:18.610 --> 00:06:21.990 while leaving exactly enough of them alive to 00:06:21.990 --> 00:06:25.230 suffer the long -term consequences. It is chilling. 00:06:25.519 --> 00:06:29.220 Just bureaucratic mathematical terror, but you 00:06:29.220 --> 00:06:31.519 know, I really want you the listener to think 00:06:31.519 --> 00:06:33.699 about how we actually use the word Decimated 00:06:33.699 --> 00:06:35.899 today, right? It's totally different completely 00:06:35.899 --> 00:06:38.639 different if you hear someone say The opposing 00:06:38.639 --> 00:06:41.939 team was decimated on the field or the coastal 00:06:41.939 --> 00:06:44.420 town was decimated by the hurricane We usually 00:06:44.420 --> 00:06:47.600 mean it was completely wiped out utterly destroyed 00:06:47.600 --> 00:06:50.569 totally gone. Yeah But mathematically, historically, 00:06:50.889 --> 00:06:53.350 if something was decimated, 90 % of it actually 00:06:53.350 --> 00:06:55.610 survived. Here's where it gets really interesting 00:06:55.610 --> 00:06:58.709 because our modern use of the word has completely 00:06:58.709 --> 00:07:01.589 lost that cold calculated math of the Roman original. 00:07:02.230 --> 00:07:04.610 We've basically replaced the precise fractional 00:07:04.610 --> 00:07:06.949 terror with just a general sense of total annihilation. 00:07:07.170 --> 00:07:10.360 It's a profound semantic shift. We took a word 00:07:10.360 --> 00:07:13.139 that meant a highly structured 90 % survival 00:07:13.139 --> 00:07:16.019 rate and culturally redefined it to mean total 00:07:16.019 --> 00:07:18.980 destruction. It just shows how language can entirely 00:07:18.980 --> 00:07:21.360 grift away from its numerical roots over centuries. 00:07:21.839 --> 00:07:23.860 So the Romans turned this mathematical concept 00:07:23.860 --> 00:07:27.360 into a literal weapon. But if you strip away 00:07:27.360 --> 00:07:29.620 all that human baggage, like the language, the 00:07:29.620 --> 00:07:33.040 history, the bloodshed, how does this number 00:07:33.040 --> 00:07:35.569 actually behave in a vacuum? Like if we look 00:07:35.569 --> 00:07:38.310 at the pure math, does the number 10 actually 00:07:38.310 --> 00:07:41.120 hold up as a perfect structure? Well, in pure 00:07:41.120 --> 00:07:44.240 abstract mathematics, 10 is simply the even natural 00:07:44.240 --> 00:07:46.600 number that directly follows 9 and precedes 11. 00:07:46.680 --> 00:07:49.759 Very basic. Very basic. In geometry, if you draw 00:07:49.759 --> 00:07:52.060 a polygon with 10 sides, it forms a decagon. 00:07:52.540 --> 00:07:54.480 But what the sources illustrate beautifully is 00:07:54.480 --> 00:07:57.199 how the actual identity of 10 completely changes 00:07:57.199 --> 00:07:59.480 depending on the mathematical language or the 00:07:59.480 --> 00:08:01.540 base system you are using to look at it. Right. 00:08:01.620 --> 00:08:03.379 It's like the number wears different disguises 00:08:03.379 --> 00:08:05.610 depending on who is doing the counting. Yes, 00:08:05.790 --> 00:08:09.410 exactly. So in our standard decimal system base 00:08:09.410 --> 00:08:14.240 10, it's a 1 followed by a 0. But in the binary 00:08:14.240 --> 00:08:16.819 system, which is base 2, and the foundational 00:08:16.819 --> 00:08:19.180 language of all modern computers, the number 00:08:19.180 --> 00:08:22.579 10 is written as 1010. OK, I have to stop you 00:08:22.579 --> 00:08:24.639 there because we hear about binary code all the 00:08:24.639 --> 00:08:27.500 time, right? Just ones and zeros. But how does 00:08:27.500 --> 00:08:30.220 the physical quantity of 10 actually translate 00:08:30.220 --> 00:08:33.159 into 1010? Like, how does that work? It's all 00:08:33.159 --> 00:08:35.960 about place value. So in our normal base 10 system, 00:08:36.039 --> 00:08:38.259 you have the ones place, the tens place, the 00:08:38.259 --> 00:08:41.190 hundreds place. Each step up. multiplies by 10. 00:08:41.830 --> 00:08:44.350 In binary, you only have zeros and ones, so each 00:08:44.350 --> 00:08:46.750 place value multiplies by two instead of 10. 00:08:47.250 --> 00:08:48.950 You have the ones place, the twos place, the 00:08:48.950 --> 00:08:50.929 fours place, and the eights place. Oh, I see. 00:08:50.970 --> 00:08:53.950 So instead of ones, tens, hundreds, it's ones, 00:08:53.970 --> 00:08:56.389 twos, fours, eights. Exactly. So to build the 00:08:56.389 --> 00:08:58.649 physical number 10 in binary, you need one, eight, 00:08:58.730 --> 00:09:01.629 zero, fours, one, two, and zero, ones. OK, let 00:09:01.629 --> 00:09:03.789 me follow that. An eight plus a two is 10. Right. 00:09:03.990 --> 00:09:07.120 So reading those places from left to right. 1, 00:09:07.120 --> 00:09:10.539 0, 1, 0, 10, 10. Oh wow. That makes perfect sense 00:09:10.539 --> 00:09:12.000 when you break down the machinery of it. Yeah, 00:09:12.019 --> 00:09:14.590 it's very elegant. But the sources also mention 00:09:14.590 --> 00:09:17.250 hexadecimal and duodecimal systems. And there, 00:09:17.549 --> 00:09:19.850 the number 10 isn't even a number at all, right? 00:09:19.889 --> 00:09:22.190 It's just represented by the letter A. And the 00:09:22.190 --> 00:09:24.509 mechanics behind that are actually equally logical. 00:09:24.750 --> 00:09:27.870 Hexadecimal is a base 16 system. Base 16, OK. 00:09:27.970 --> 00:09:30.769 Right. That means you need single distinct characters 00:09:30.769 --> 00:09:33.809 to represent every value from 0 all the way up 00:09:33.809 --> 00:09:36.129 to 15 before you carry over to the next place 00:09:36.129 --> 00:09:39.350 value. But we only have digits up to 9. Exactly. 00:09:39.590 --> 00:09:42.710 Since our normal numbers run out at 9, mathematicians 00:09:42.710 --> 00:09:45.149 just started using the alphabet. So 10 becomes 00:09:45.149 --> 00:09:49.309 A, 11 is B, 12 is C, and so on. That is so practical. 00:09:49.549 --> 00:09:52.409 It really is. And in Roman numerals, 10 is the 00:09:52.409 --> 00:09:55.269 familiar X. In Greek numerals, it is represented 00:09:55.269 --> 00:09:57.690 by the symbol iota with a small stroke, so it 00:09:57.690 --> 00:10:00.049 looks like an I with an accent mark. It is a 00:10:00.049 --> 00:10:01.909 complete chameleon, depending on the system. 00:10:02.090 --> 00:10:03.710 And when you look at the calculation tables and 00:10:03.710 --> 00:10:07.129 the research, multiplication and exponentiation 00:10:07.129 --> 00:10:09.289 by 10 are just deeply satisfying. I mean, to 00:10:09.289 --> 00:10:12.110 multiply, you just add zeros, 10, 100, 1 ,000, 00:10:12.149 --> 00:10:14.860 10 ,000. It scales perfectly. It does. It defines 00:10:14.860 --> 00:10:17.200 what we call an order of magnitude. And I want 00:10:17.200 --> 00:10:19.500 to give you, the listener, an analogy for how 00:10:19.500 --> 00:10:22.120 powerful that is. Multiplying by 10 isn't just 00:10:22.120 --> 00:10:24.919 taking a step forward. It's entirely changing 00:10:24.919 --> 00:10:27.039 the dimension of what you're looking at. Yes. 00:10:27.419 --> 00:10:29.179 It's the difference between looking at a single 00:10:29.179 --> 00:10:31.779 house and then zooming out to see the entire 00:10:31.779 --> 00:10:34.279 city and then zooming out to see the entire globe 00:10:34.279 --> 00:10:37.820 from space. Each zero completely changes the 00:10:37.820 --> 00:10:41.759 scale of reality. That is a perfect way. to visualize 00:10:41.759 --> 00:10:44.379 an order of magnitude. It is an exponential leap, 00:10:44.580 --> 00:10:46.679 not just a linear progression. But you know, 00:10:46.679 --> 00:10:49.019 I'm going to push back on this idea that 10 is 00:10:49.019 --> 00:10:51.700 the perfect mathematical VIP. Oh, really? Yeah, 00:10:51.720 --> 00:10:53.779 because when you look at the division table in 00:10:53.779 --> 00:10:55.820 the source material, the neatness completely 00:10:55.820 --> 00:10:58.460 falls apart. It gets messy. Very messy. You divide 00:10:58.460 --> 00:11:01.120 10 by 2, you get a clean 5. You divide 10 by 00:11:01.120 --> 00:11:04.100 3, you get 3 .33 repeating into infinity. Divide 00:11:04.100 --> 00:11:07.379 10 by 7, you get this chaotic string of decimals, 00:11:07.480 --> 00:11:12.360 1 .428. 571? So from a purely practical standpoint, 00:11:12.539 --> 00:11:14.519 10 is actually a terrible number for everyday 00:11:14.519 --> 00:11:17.220 division. And that is a very mathematically sound 00:11:17.220 --> 00:11:20.220 critique. In fact, many mathematicians and historians 00:11:20.220 --> 00:11:22.519 argue that we locked ourselves into the wrong 00:11:22.519 --> 00:11:25.620 base system purely because of our fingers. Really? 00:11:25.879 --> 00:11:28.980 So what should we have used? A base 12 system, 00:11:29.139 --> 00:11:32.620 which is also known as a dozenal system, is mathematically 00:11:32.620 --> 00:11:36.019 vastly superior for human use. Because 12 divides 00:11:36.019 --> 00:11:39.019 so much cleaner. Exactly. The number 12 can be 00:11:39.019 --> 00:11:42.320 cleanly divided by 2, 3, 4, and 6. The number 00:11:42.320 --> 00:11:45.460 10 can only be cleanly divided by 2 and 5. That 00:11:45.460 --> 00:11:47.820 makes so much sense. Yeah. If you are a carpenter 00:11:47.820 --> 00:11:50.419 trying to divide a board into thirds, or just 00:11:50.419 --> 00:11:52.860 a person trying to divide a pizza among three 00:11:52.860 --> 00:11:56.259 friends, a base 10 system creates messy fractions. 00:11:56.840 --> 00:11:59.360 The ancient Sumerians and Babylonians actually 00:11:59.360 --> 00:12:01.740 used a base -60 system for this very reason, 00:12:01.820 --> 00:12:04.759 which is highly divisible. Base -60. Yes. It's 00:12:04.759 --> 00:12:07.039 why we still have 60 seconds in a minute, 60 00:12:07.039 --> 00:12:09.480 minutes in an hour, and 360 degrees in a circle. 00:12:09.940 --> 00:12:13.279 We force our biological base -10 quirk onto a 00:12:13.279 --> 00:12:16.000 universe that probably prefers base -12 or base 00:12:16.000 --> 00:12:18.500 -60. So we're just stubbornly dragging our ten 00:12:18.500 --> 00:12:20.940 fingers into advanced mathematics. Pretty much. 00:12:21.220 --> 00:12:23.100 And speaking of advanced math, this is where 00:12:23.100 --> 00:12:25.159 the research throws some serious jargon at us. 00:12:26.059 --> 00:12:29.919 translate it. The text classifies 10 as a, quote, 00:12:30.559 --> 00:12:33.539 composite number, a happy number, and the smallest 00:12:33.539 --> 00:12:37.259 non -catotient number. Yes. That is quite a list. 00:12:37.399 --> 00:12:39.500 Now, an encyclopedia will just drop those terms 00:12:39.500 --> 00:12:41.899 and expect you to know them. But we can't leave 00:12:41.899 --> 00:12:44.340 you hanging like that. What on earth makes a 00:12:44.340 --> 00:12:46.059 number happy? Like, does it have a good credit 00:12:46.059 --> 00:12:48.740 score? What does that mean? A happy number is 00:12:48.740 --> 00:12:51.399 essentially a mathematical puzzle. Here's how 00:12:51.399 --> 00:12:54.539 it works. You take a number, like 10. and you 00:12:54.539 --> 00:12:58.179 separate its digits, so a 1 and a 0. Then you 00:12:58.179 --> 00:13:00.379 square both of those digits and add the results 00:13:00.379 --> 00:13:02.440 together. Okay, let me do the math. 1 squared 00:13:02.440 --> 00:13:07.340 is 1, 0 squared is 0, 1 plus 0 is 1. Right. In 00:13:07.340 --> 00:13:09.720 number theory, any number that eventually boils 00:13:09.720 --> 00:13:12.580 down to exactly one through that repeating process 00:13:12.580 --> 00:13:15.360 is classified as a happy number. It's just a 00:13:15.360 --> 00:13:18.399 fun, quirky behavioral trait of certain integers. 00:13:18.639 --> 00:13:20.419 That's amazing. OK, so what about a composite 00:13:20.419 --> 00:13:22.539 number? That one is much simpler. A composite 00:13:22.539 --> 00:13:24.559 number is just any positive integer that can 00:13:24.559 --> 00:13:27.000 be formed by multiplying two smaller positive 00:13:27.000 --> 00:13:29.480 integers together. Oh. Because 10 is made by 00:13:29.480 --> 00:13:32.379 multiplying 2 and 5, it's composite. It's basically 00:13:32.379 --> 00:13:34.600 the opposite of a prime number, which can only 00:13:34.600 --> 00:13:37.340 be made by multiplying itself. and one. All right, 00:13:37.419 --> 00:13:40.340 now the final boss of the jargon, non -cototient. 00:13:41.419 --> 00:13:43.659 Doesn't even sound like a real word. It is a 00:13:43.659 --> 00:13:46.240 dense concept, admittedly, relying on something 00:13:46.240 --> 00:13:49.480 called Euler's totient function. But to strip 00:13:49.480 --> 00:13:51.860 away the complex formulas, just think of it this 00:13:51.860 --> 00:13:54.940 way. In math, there's a specific equation used 00:13:54.940 --> 00:13:57.039 to figure out how many numbers below a certain 00:13:57.039 --> 00:14:00.360 threshold share no common factors with the starting 00:14:00.360 --> 00:14:03.179 number. It's a way of mapping out relationships 00:14:03.179 --> 00:14:05.580 between numbers. Most numbers can be generated 00:14:05.580 --> 00:14:08.480 as an answer to this equation. But 10 is a non 00:14:08.480 --> 00:14:11.059 -kotoshin, meaning 10 is the smallest number 00:14:11.059 --> 00:14:13.639 that never appears as an answer in this specific 00:14:13.639 --> 00:14:16.549 relationship mapping. Wow. Yeah, it is prominently 00:14:16.549 --> 00:14:18.830 locked out of that particular mathematical club. 00:14:19.049 --> 00:14:21.509 So it's not just a bland placeholder. In the 00:14:21.509 --> 00:14:24.490 higher realms of number theory, 10 possesses 00:14:24.490 --> 00:14:27.509 these only unique, distinct architectural properties. 00:14:27.529 --> 00:14:30.210 Yeah. But here is the massive question that raises. 00:14:31.090 --> 00:14:34.490 If 10 is so mathematically clunky for division 00:14:34.490 --> 00:14:37.889 and has all these weird quirks, how did it become 00:14:37.889 --> 00:14:41.190 the absolute dictator of modern science and physics? 00:14:41.529 --> 00:14:44.299 Enter the metric system. Oh, of course. While 00:14:44.299 --> 00:14:47.019 base 10 might struggle with division into thirds, 00:14:47.419 --> 00:14:50.299 it is unparalleled for scaling up and down rapidly. 00:14:50.799 --> 00:14:53.179 During the French Revolution, the world was a 00:14:53.179 --> 00:14:56.259 chaotic mess of local weights and measures. A 00:14:56.259 --> 00:14:58.259 foot in one city might be a completely different 00:14:58.259 --> 00:15:01.179 length than a foot in a city 20 miles away. That 00:15:01.179 --> 00:15:03.460 sounds like a nightmare for trade. It was. So 00:15:03.460 --> 00:15:05.919 the metric system was designed to create a universal 00:15:05.919 --> 00:15:08.399 standard for physical measurement, and it was 00:15:08.399 --> 00:15:10.919 entirely fundamentally built on the number 10. 00:15:11.080 --> 00:15:13.139 Which is why converting units in the metric system 00:15:13.139 --> 00:15:15.200 feels almost like cheating compared to the imperial 00:15:15.200 --> 00:15:17.940 system. Like in Imperial, you have to memorize 00:15:17.940 --> 00:15:22.200 that there are 5 ,280 feet in a mile, 16 ounces 00:15:22.200 --> 00:15:24.960 in a pound. It's chaos. It really is. But in 00:15:24.960 --> 00:15:27.179 the metric system, converting units is done simply 00:15:27.179 --> 00:15:30.080 by shifting that decimal point, utilizing those 00:15:30.080 --> 00:15:32.480 orders of magnitude we discussed earlier. One 00:15:32.480 --> 00:15:35.559 centimeter is 10 millimeters. One decimeter is 00:15:35.559 --> 00:15:39.440 10 centimeters. One meter is 100 centimeters. 00:15:39.899 --> 00:15:43.399 One kilometer is 1 ,000 meters. You literally 00:15:43.399 --> 00:15:45.840 just slide the zero left and right. It's so easy. 00:15:45.950 --> 00:15:48.570 If we connect this to the bigger picture, the 00:15:48.570 --> 00:15:50.730 metric system's strict reliance on the number 00:15:50.730 --> 00:15:53.409 10 is arguably one of the greatest collaborative 00:15:53.409 --> 00:15:56.299 tools ever invented in human history. It brings 00:15:56.299 --> 00:15:58.820 the tidiness of the multiplication table directly 00:15:58.820 --> 00:16:00.799 into physical reality. That's a great way to 00:16:00.799 --> 00:16:02.740 put it. It is the infrastructure that allows 00:16:02.740 --> 00:16:06.000 a structural engineer in Tokyo to share physical 00:16:06.000 --> 00:16:08.960 data with an aerospace engineer in Paris without 00:16:08.960 --> 00:16:11.679 catastrophic measurement errors. That shared 00:16:11.679 --> 00:16:15.240 base -10 reality creates a unified global language 00:16:15.240 --> 00:16:17.820 of physics. And the number 10 pops up in the 00:16:17.820 --> 00:16:20.570 physical world itself. Yeah. Naturally. not just 00:16:20.570 --> 00:16:22.309 in how we choose to measure it. Oh, definitely. 00:16:22.570 --> 00:16:24.649 The sources note some great elemental trivia. 00:16:24.750 --> 00:16:26.990 Like if you look at the periodic table of elements, 00:16:27.210 --> 00:16:29.730 the 10th element is neon. And if you're looking 00:16:29.730 --> 00:16:32.429 at transition metals, the 10th one is zinc. But 00:16:32.429 --> 00:16:34.330 before we wrap up this journey, I have to bring 00:16:34.330 --> 00:16:37.029 up one final detail from the research that takes 00:16:37.029 --> 00:16:40.110 us from hard objective science straight into 00:16:40.110 --> 00:16:43.970 ancient cult -like metaphysics. Ah, the Pythagorean 00:16:43.970 --> 00:16:47.070 mysticism. This is a really fascinating pivot. 00:16:47.210 --> 00:16:50.179 Yes. When we think of Pythagoras today, We just 00:16:50.179 --> 00:16:52.639 think of the Pythagorean theorem from high school 00:16:52.639 --> 00:16:56.299 geometry, right? Triangles and hypotenuses. But 00:16:56.299 --> 00:16:59.399 in ancient Greece, Pythagoreanism was practically 00:16:59.399 --> 00:17:02.220 a religion. It was a full -blown worldview. Yeah. 00:17:02.700 --> 00:17:05.099 And to them, the number 10 wasn't just useful. 00:17:05.200 --> 00:17:08.519 It was revered as divine. It played a deeply 00:17:08.519 --> 00:17:11.079 mystical role. It was symbolized by something 00:17:11.079 --> 00:17:13.859 they called the tetractis. The tetractis is a 00:17:13.859 --> 00:17:16.640 powerful ancient symbol. Visually is a triangular 00:17:16.640 --> 00:17:19.039 figure consisting of 10 points arranged in four 00:17:19.039 --> 00:17:21.480 rows. The top row has one point, the second has 00:17:21.480 --> 00:17:23.200 two, the third has three, and the bottom row 00:17:23.200 --> 00:17:26.259 has four. One, two, three, four. Right. If you 00:17:26.259 --> 00:17:28.460 add those rows together, one plus two plus three 00:17:28.460 --> 00:17:31.180 plus four, it perfectly equals 10. And the Pythagoreans 00:17:31.180 --> 00:17:33.180 didn't just draw this in the sand. They swore 00:17:33.180 --> 00:17:36.480 their sacred oaths upon it. They did. To them, 00:17:36.700 --> 00:17:39.059 the four rows represented the classical elements, 00:17:39.299 --> 00:17:43.380 fire, air, water, and earth. of ten represented 00:17:43.380 --> 00:17:46.279 the entire organization of space, harmony, and 00:17:46.279 --> 00:17:49.400 the universe itself. To the Pythagoreans, ten 00:17:49.400 --> 00:17:52.160 was the literal shape of divine perfection. So 00:17:52.160 --> 00:17:54.240 what does this all mean? If you take a step back 00:17:54.240 --> 00:17:56.380 and look at what we've just traversed. in this 00:17:56.380 --> 00:17:59.059 deep dive. I mean, we have gone from cavemen 00:17:59.059 --> 00:18:00.759 looking down at their hands and counting their 00:18:00.759 --> 00:18:05.220 thumbs to the brutal mathematically calibrated 00:18:05.220 --> 00:18:08.440 punishments of the Roman military. Right. We've 00:18:08.440 --> 00:18:11.240 decoded the 1010 of binary computer language. 00:18:11.279 --> 00:18:13.960 We've debated the flaws of dividing by three, 00:18:14.460 --> 00:18:16.259 explored the flawless scales of the universal 00:18:16.259 --> 00:18:18.859 metric system and ended up in the religious worship 00:18:18.859 --> 00:18:21.319 of ancient Greek triangles. It is a remarkable 00:18:21.319 --> 00:18:23.599 synthesis of human history, honestly. Ten is 00:18:23.599 --> 00:18:26.759 not just an integer following nine. It is perhaps 00:18:26.759 --> 00:18:29.720 the ultimate scale in a mechanism for human understanding. 00:18:30.099 --> 00:18:32.559 It gives us a way to conceptualize immense stretches 00:18:32.559 --> 00:18:35.220 of time through decades. It gives us the cognitive 00:18:35.220 --> 00:18:37.519 tool to comprehend the vastness of the universe 00:18:37.519 --> 00:18:39.920 through orders of magnitude. And it provides 00:18:39.920 --> 00:18:43.099 a universal metric system that binds all of global 00:18:43.099 --> 00:18:45.960 science together. It is the invisible scaffold 00:18:45.960 --> 00:18:49.079 we built our entire modern reality on. This raises 00:18:49.079 --> 00:18:51.599 an important question though about how entirely 00:18:51.599 --> 00:18:54.220 dependent our modern world is on this single 00:18:54.220 --> 00:18:57.319 framework. We are locked into a base 10 reality 00:18:57.319 --> 00:19:00.000 because the evolution of our biology and we have 00:19:00.000 --> 00:19:03.000 built a global infrastructure so reliant on it 00:19:03.000 --> 00:19:05.980 that to change it now to a superior system like 00:19:05.980 --> 00:19:09.119 base 12 would be fundamentally impossible. It's 00:19:09.119 --> 00:19:11.619 completely baked into the code of human civilization 00:19:11.619 --> 00:19:14.299 and that leads me to a final provocative thought 00:19:14.299 --> 00:19:16.599 for you the listener. Throughout this whole deep 00:19:16.599 --> 00:19:18.650 dive we've talked about how 10 is the universal 00:19:18.650 --> 00:19:21.369 human language. The research actually highlights 00:19:21.369 --> 00:19:23.809 that Wikipedia entries about the number 10 are 00:19:23.809 --> 00:19:26.410 translated into 156 different human languages, 00:19:26.750 --> 00:19:29.430 from Africans to Navajo to Zulu. It's everywhere. 00:19:29.869 --> 00:19:33.190 Everywhere. Among humans, base 10 is our absolute 00:19:33.190 --> 00:19:36.150 common ground. But imagine for a moment that 00:19:36.150 --> 00:19:39.319 tomorrow We make first contact with an intelligent 00:19:39.319 --> 00:19:42.880 alien species. Oh, wow. The ultimate test of 00:19:42.880 --> 00:19:45.119 universal concepts. Exactly. We always assume 00:19:45.119 --> 00:19:47.319 that mathematics is the universal language we 00:19:47.319 --> 00:19:49.259 will use to communicate with extraterrestrials. 00:19:49.859 --> 00:19:52.759 We beam binary code and prime numbers into deep 00:19:52.759 --> 00:19:55.359 space expecting them to understand. But what 00:19:55.359 --> 00:19:57.960 if those aliens evolved with, say, seven tentacles 00:19:57.960 --> 00:20:01.259 or 12 digits? Their math would look entirely 00:20:01.259 --> 00:20:03.440 different. Right. Their entire mathematical foundation, 00:20:03.619 --> 00:20:06.069 their physics, their orders of magnitude, would 00:20:06.069 --> 00:20:08.490 be built on a completely different base. Would 00:20:08.490 --> 00:20:11.849 we even recognize their math as math? Or would 00:20:11.849 --> 00:20:14.329 our supposedly universal language of base 10 00:20:14.329 --> 00:20:16.970 get completely lost in biological translation? 00:20:17.369 --> 00:20:19.750 So after you finish listening to this, I invite 00:20:19.750 --> 00:20:21.589 you to just hold your hands out in front of you, 00:20:21.690 --> 00:20:23.890 look at your own digits, and take a moment to 00:20:23.890 --> 00:20:26.109 ponder how those specific 10 fingers not only 00:20:26.109 --> 00:20:28.190 built the mathematical universe you live in today, 00:20:28.650 --> 00:20:30.730 but might just be the very thing that isolates 00:20:30.730 --> 00:20:31.910 us from the rest of the cosmos.