WEBVTT 00:00:00.000 --> 00:00:02.620 You know, if you have like five apples in a basket. 00:00:02.759 --> 00:00:04.679 Right, just sitting there. Yeah, you can see 00:00:04.679 --> 00:00:07.040 them, you can physically hold them, and your 00:00:07.040 --> 00:00:09.900 brain simply points and says, yep, got it. That's 00:00:09.900 --> 00:00:12.519 five. It's incredibly clean, very intuitive. 00:00:12.679 --> 00:00:15.720 Exactly. But the moment you read a headline about, 00:00:16.260 --> 00:00:19.859 say, a billion dollar valuation or some billion 00:00:19.859 --> 00:00:22.239 dollar infrastructure bill, your brain just sort 00:00:22.239 --> 00:00:24.300 of stops counting. Yeah, it completely gives 00:00:24.300 --> 00:00:26.519 up. It throws its hands up and just files that 00:00:26.519 --> 00:00:29.300 information into a mental folder labeled, you 00:00:29.300 --> 00:00:32.439 know. Just a big, vague pile of money. Right. 00:00:32.799 --> 00:00:35.020 So today, we are opening that folder for you. 00:00:35.299 --> 00:00:37.880 We are doing a deep dive into the Wikipedia page 00:00:37.880 --> 00:00:41.799 for the number $1 million. And I got to say, 00:00:42.079 --> 00:00:45.320 while a one followed by nine zeros sounds like, 00:00:45.320 --> 00:00:47.119 I don't know, the simplest math lesson ever. 00:00:47.240 --> 00:00:49.719 Oh, it is anything but simple. Yeah. It is actually 00:00:49.719 --> 00:00:52.619 this wild rabbit hole of linguistic illusions, 00:00:52.960 --> 00:00:56.020 ancient history, and literal invisible walls 00:00:56.020 --> 00:00:58.579 hidden inside your computer. It really is the 00:00:58.579 --> 00:01:01.700 absolute definition of numerical muddy waters. 00:01:02.399 --> 00:01:04.719 I mean, we evolved to understand quantities we 00:01:04.719 --> 00:01:07.519 could actually... interact with, right? Like 00:01:07.519 --> 00:01:10.099 50 people in a cave or maybe a thousand trees 00:01:10.099 --> 00:01:12.480 in a forest. Things we could physically see. 00:01:12.599 --> 00:01:15.980 Exactly. But a billion. We hear it thrown around 00:01:15.980 --> 00:01:18.500 constantly in the news, mostly as the standard 00:01:18.500 --> 00:01:21.400 unit for global economics, yet our paleolithic 00:01:21.400 --> 00:01:24.239 brains have absolutely no natural framework for 00:01:24.239 --> 00:01:27.480 it. So my goal today is to give you, the listener, 00:01:27.840 --> 00:01:30.920 the mental scaffolding to actually feel the weight 00:01:30.920 --> 00:01:33.560 of a 10 -digit number. Okay, let's unpack this. 00:01:33.560 --> 00:01:35.900 Yeah. Because before we even try to I feel like 00:01:35.900 --> 00:01:37.780 we have to talk about what a billion actually 00:01:37.780 --> 00:01:40.420 is linguistically. And I really have to push 00:01:40.420 --> 00:01:42.379 back on the English language here. Uh oh, here 00:01:42.379 --> 00:01:44.980 we go. No, seriously, because the prefix by literally 00:01:44.980 --> 00:01:48.180 means two. Right, like bicycle, two wheels. Exactly. 00:01:48.319 --> 00:01:51.379 And a million has six zeros. So a bi -illion, 00:01:51.579 --> 00:01:53.359 logically meaning a million to the second power, 00:01:53.420 --> 00:01:56.299 or a million millions, is infinitely more logical. 00:01:56.359 --> 00:01:59.939 Oh, one with 12 zeros? Yes. But here in the US, 00:02:00.140 --> 00:02:02.700 and now mostly globally, a billion just means 00:02:02.700 --> 00:02:05.579 a thousand millions. which is only nine zeros. 00:02:06.379 --> 00:02:08.919 Did we just like adopt a mathematically lazier 00:02:08.919 --> 00:02:11.219 word just for convenience? You're actually touching 00:02:11.219 --> 00:02:14.099 on a massive historical conflict here. It's known 00:02:14.099 --> 00:02:16.280 as the collision of the short scale and the long 00:02:16.280 --> 00:02:18.740 scale. And you are completely right, by the way. 00:02:18.800 --> 00:02:22.419 The long scale is etymologically purer. Thank 00:02:22.419 --> 00:02:25.180 you. I knew it. Yeah. Billion originally meant 00:02:25.180 --> 00:02:27.840 million squared. Trillion meant million cubed. 00:02:28.340 --> 00:02:30.639 It makes perfect logical sense. And for a very 00:02:30.639 --> 00:02:33.360 long time, British English used this example 00:02:33.229 --> 00:02:36.289 exact long scale, meaning a billion was 12 zeros 00:02:36.289 --> 00:02:38.889 for them. But the United States adopted the short 00:02:38.889 --> 00:02:41.370 scale early on, where a billion is just a thousand 00:02:41.370 --> 00:02:45.120 millions. Nine zeros. So wait. For decades, the 00:02:45.120 --> 00:02:47.080 U .S. and the U .K. were using the exact same 00:02:47.080 --> 00:02:49.180 word to describe two wildly different numbers. 00:02:49.280 --> 00:02:51.800 Yes. That sounds like an absolute disaster. A 00:02:51.800 --> 00:02:54.020 total disaster. I mean, just imagine trying to 00:02:54.020 --> 00:02:57.340 negotiate a post -World War II global trade deal. 00:02:57.639 --> 00:02:59.900 You have like an American industrialist and a 00:02:59.900 --> 00:03:02.180 British banker sitting in a room together. And 00:03:02.180 --> 00:03:05.419 the American asks for a billion dollars. To him, 00:03:05.439 --> 00:03:07.759 that means a thousand million. Right. But the 00:03:07.759 --> 00:03:10.379 British banker here is billion and thinks the 00:03:10.379 --> 00:03:13.680 American is asking for a million millions. Literally 00:03:13.680 --> 00:03:16.740 a thousand times more money. Oh my gosh. You 00:03:16.740 --> 00:03:19.400 can just imagine the panic. Exactly. The sheer 00:03:19.400 --> 00:03:21.900 terror of that miscommunication. So it wasn't 00:03:21.900 --> 00:03:24.659 laziness. It was just survival. Yeah. Basically, 00:03:24.659 --> 00:03:26.639 you could argue it was a linguistic tragedy, 00:03:26.900 --> 00:03:29.780 sure, but it was an absolute financial necessity. 00:03:30.400 --> 00:03:32.620 Standardization was basically forced upon us. 00:03:33.020 --> 00:03:35.860 The U .K. officially shifted to the short scale 00:03:35.860 --> 00:03:40.699 thousand millions in 1974, I believe, just to 00:03:40.699 --> 00:03:43.080 align with the U .S. and global financial reporting. 00:03:43.319 --> 00:03:45.419 Because it's impossible to run a global economy 00:03:45.419 --> 00:03:47.300 when everyone is working off different base units. 00:03:47.500 --> 00:03:49.340 Exactly. Though it is worth noting that a lot 00:03:49.340 --> 00:03:51.379 of languages still use a variation of the word 00:03:51.379 --> 00:03:54.340 milliard to describe a thousand million, which 00:03:54.340 --> 00:03:56.780 keeps their word for billion mathematically pure. 00:03:56.780 --> 00:03:58.400 Well, that's interesting. And other cultures 00:03:58.400 --> 00:04:00.879 bypass this whole million -based thing entirely. 00:04:01.300 --> 00:04:03.539 Like, in the Indian numbering system, they use 00:04:03.539 --> 00:04:06.759 100 crore or one Arab to represent this exact 00:04:06.759 --> 00:04:09.680 same 10 -digit number. OK, so we basically traded 00:04:09.680 --> 00:04:12.379 mathematical logic for a smoother stock market. 00:04:12.580 --> 00:04:15.310 That's one way to put it, yeah. But because we 00:04:15.310 --> 00:04:17.870 standardized the word, we kind of lost our grasp 00:04:17.870 --> 00:04:21.490 on the actual scale. Since language alone clearly 00:04:21.490 --> 00:04:24.790 isn't helping our brains visualize this, we need 00:04:24.790 --> 00:04:28.449 to translate a billion into the ultimate universal 00:04:28.449 --> 00:04:31.990 constants, time and distance. Yes, this is where 00:04:31.990 --> 00:04:33.970 it gets fun. Here's where it gets really interesting. 00:04:35.170 --> 00:04:37.209 I came up with an analogy for this as I was going 00:04:37.209 --> 00:04:39.350 through the source material. I want you to imagine 00:04:39.350 --> 00:04:41.980 a time machine. OK. But instead of typing in 00:04:41.980 --> 00:04:44.560 dates on a little keypad, the fuel gauge only 00:04:44.560 --> 00:04:47.459 accepts units of exactly 1 billion. I love a 00:04:47.459 --> 00:04:48.980 good thought experiment. Let's see where the 00:04:48.980 --> 00:04:51.360 math takes us. Right. So if I fuel up my time 00:04:51.360 --> 00:04:54.040 machine with 1 billion seconds and I hit the 00:04:54.040 --> 00:04:56.220 button to go backward, I don't go back to the 00:04:56.220 --> 00:04:58.660 age of the dinosaurs. I don't even go back to 00:04:58.660 --> 00:05:01.680 the invention of the internet. Nope. 1 billion 00:05:01.680 --> 00:05:05.040 seconds is about 31 .7 years. That's it. That's 00:05:05.040 --> 00:05:07.899 it. If I wait a billion seconds, I basically 00:05:07.899 --> 00:05:10.259 just get some gray hair and maybe finish paying 00:05:10.259 --> 00:05:13.139 off a mortgage. Which is such a sobering realization 00:05:13.139 --> 00:05:15.459 of how short a second actually is, or I guess 00:05:15.459 --> 00:05:19.180 how vast a billion is. I mean, 31 .7 years is 00:05:19.180 --> 00:05:22.720 a massive chunk of a human lifespan, and it is 00:05:22.720 --> 00:05:24.959 contained entirely within a single billion ticks 00:05:24.959 --> 00:05:27.379 of the clock. Right. But let's upgrade the fuel. 00:05:27.550 --> 00:05:30.350 I'm turning the dial on the time machine. One 00:05:30.350 --> 00:05:32.470 billion minutes ago, where are we landing? Okay, 00:05:32.470 --> 00:05:36.350 so now you are traveling back roughly 1 ,901 00:05:36.350 --> 00:05:38.990 years. Wow. Yeah, you're landing right in the 00:05:38.990 --> 00:05:41.370 middle of a flourishing Roman Empire. You're 00:05:41.370 --> 00:05:43.449 watching the peak of the gladiatorial games, 00:05:43.589 --> 00:05:46.029 the early emergence of Christianity. That is 00:05:46.029 --> 00:05:49.310 insane. Just by changing the word from seconds 00:05:49.310 --> 00:05:51.089 to minutes, we went from a standard mortgage 00:05:51.089 --> 00:05:53.670 to the literal Colosseum. It stales incredibly 00:05:53.670 --> 00:05:55.689 fast. Okay, let's keep going. Turn the dial to 00:05:55.689 --> 00:05:58.639 hours. one billion hours ago. Now you've wiped 00:05:58.639 --> 00:06:01.680 out all of recorded human civilization. Gone. 00:06:01.939 --> 00:06:04.879 Gone. You are traveling back roughly 114 ,000 00:06:04.879 --> 00:06:07.879 years. We are deep in the middle Paleolithic 00:06:07.879 --> 00:06:10.399 period, the Stone Age. You're hanging out with 00:06:10.399 --> 00:06:12.579 the early ancestors of modern humans who are 00:06:12.579 --> 00:06:15.319 just starting to figure out complex stone tools. 00:06:15.540 --> 00:06:19.560 And if we go to days, one billion days ago. You 00:06:19.560 --> 00:06:23.540 are 2 .73 million years in the past. Oh, man. 00:06:23.680 --> 00:06:26.600 You are watching Australopithecus roam the African 00:06:26.600 --> 00:06:29.620 savannas. Homo sapiens aren't even a glimmer 00:06:29.620 --> 00:06:32.579 in evolution's eye yet. Notice how quickly the 00:06:32.579 --> 00:06:34.959 scale completely escapes our everyday comprehension. 00:06:35.120 --> 00:06:37.720 It does. And it gets wilder. Because I have to 00:06:37.720 --> 00:06:40.379 know about months. If I use a billion months 00:06:40.379 --> 00:06:42.759 to fuel the time machine. Well, a billion months 00:06:42.759 --> 00:06:46.660 is about 83 .3 million years. So yes, if you 00:06:46.660 --> 00:06:49.480 hit that button, you are suddenly dodging a T 00:06:49.480 --> 00:06:51.720 -Rex in the late Cretaceous period. That completely 00:06:51.720 --> 00:06:53.420 breaks my brain. And if we connect this to the 00:06:53.420 --> 00:06:55.939 bigger picture, this progression beautifully 00:06:55.939 --> 00:06:58.819 demonstrates the sheer brevity of human existence. 00:06:59.420 --> 00:07:01.459 When you scale a billion against the cosmos, 00:07:02.120 --> 00:07:04.740 humanity just disappears entirely. How so? Because 00:07:04.740 --> 00:07:06.759 if we look at a billion decades ago, which is 00:07:06.759 --> 00:07:09.860 exactly 10 billion years, our solar system didn't 00:07:09.860 --> 00:07:12.500 even exist. Wait, Yali. Yeah, the thin disk of 00:07:12.500 --> 00:07:14.560 the Milky Way galaxy was just starting to form 00:07:14.560 --> 00:07:17.319 out of cosmic dust. And even then, the universe 00:07:17.319 --> 00:07:20.220 itself is thought to be about 13 .8 billion years 00:07:20.220 --> 00:07:23.459 old. So a billion is the literal ruler by which 00:07:23.459 --> 00:07:25.560 the universe is measured. And that ruler works 00:07:25.560 --> 00:07:28.360 for physical distance too. Like if I ask you 00:07:28.360 --> 00:07:30.959 to imagine driving a billion inches, a billion 00:07:30.959 --> 00:07:35.300 inches is 15 ,783 miles. Which is huge! Yeah. 00:07:35.579 --> 00:07:38.560 If you started driving right now, a billion inches 00:07:38.560 --> 00:07:40.839 takes you more than halfway around the globe. 00:07:41.000 --> 00:07:43.639 You could reach literally any point on the earth 00:07:43.639 --> 00:07:45.980 from any other point with just a billion inches. 00:07:46.180 --> 00:07:49.319 And if we jump to a billion meters a gigameter, 00:07:49.699 --> 00:07:51.879 that is almost three times the distance from 00:07:51.879 --> 00:07:54.360 the earth to the moon. And a billion kilometers 00:07:54.360 --> 00:07:56.779 is over six times the distance from the earth 00:07:56.779 --> 00:07:59.500 to the sun. It's dizzying. I mean, we use this 00:07:59.500 --> 00:08:01.560 exact same number to talk about quarterly corporate 00:08:01.560 --> 00:08:03.540 profits, yet it spans the distance to the sun 00:08:03.540 --> 00:08:05.970 and back. Exactly. Time and space are just so 00:08:05.970 --> 00:08:08.170 vast, and maybe there's still a bit too abstract 00:08:08.170 --> 00:08:10.230 for us. So what if we tried to bring this back 00:08:10.230 --> 00:08:12.329 down to Earth? Look around the room you're sitting 00:08:12.329 --> 00:08:14.810 in right now. What if we tried to put a billion 00:08:14.810 --> 00:08:18.189 physical, tangible things into that room? Oh, 00:08:18.389 --> 00:08:21.050 this is where intuition really betrays us. The 00:08:21.050 --> 00:08:23.569 relationship between volume, mass, and large 00:08:23.569 --> 00:08:26.459 numbers is incredibly counterintuitive. Okay, 00:08:26.480 --> 00:08:28.819 let's test it. Let's take a billion grains of 00:08:28.819 --> 00:08:31.379 table salt, or like granulated sugar. If you 00:08:31.379 --> 00:08:34.860 poured out exactly one billion grains, how much 00:08:34.860 --> 00:08:36.419 physical space do you think it would take up? 00:08:36.820 --> 00:08:39.100 I mean, intuitively you'd think maybe a whole 00:08:39.100 --> 00:08:42.179 room. Right. But it turns out it would only occupy 00:08:42.179 --> 00:08:45.419 about 2 .5 cubic feet. That is astonishingly 00:08:45.419 --> 00:08:48.000 small. Isn't it? Picture a standard mini -fridge 00:08:48.000 --> 00:08:50.700 in a college dorm room or just the empty space 00:08:50.700 --> 00:08:53.100 under your office desk. That's a billion grains 00:08:53.100 --> 00:08:54.899 of salt. You could fit it in the trunk of your 00:08:54.899 --> 00:08:57.399 car. Wow. But now let's change the unit. Let's 00:08:57.399 --> 00:08:59.820 look at a billion kilograms. What does a billion 00:08:59.820 --> 00:09:01.700 kilograms look like? A lot bigger than a mini 00:09:01.700 --> 00:09:05.080 -fridge. Slightly. A billion kilograms is the 00:09:05.080 --> 00:09:10.919 combined weight of 5 ,525 empty Boeing 747 jumbo 00:09:10.919 --> 00:09:13.000 jets. So we go from a cardboard box that fits 00:09:13.000 --> 00:09:16.019 neatly under your desk to an armada of commercial 00:09:16.019 --> 00:09:18.220 airliners that would literally black out the 00:09:18.220 --> 00:09:20.899 sky. Yeah. So I have to ask you, is this why 00:09:20.899 --> 00:09:23.639 humans are so profoundly bad at grasping economics 00:09:23.639 --> 00:09:26.580 and national debt? Because the word billion can 00:09:26.580 --> 00:09:29.620 represent the size of a mini -fridge or a literal 00:09:29.620 --> 00:09:31.820 fleet of airplanes depending entirely on the 00:09:31.820 --> 00:09:34.200 unit attached to it. Like, how is our brain supposed 00:09:34.200 --> 00:09:37.230 to process that? That is exactly the mechanism 00:09:37.230 --> 00:09:40.730 behind our economic blindness. Volume and mass 00:09:40.730 --> 00:09:43.009 trick our perception, because they grow in three 00:09:43.009 --> 00:09:45.590 dimensions, right? While our mental counting 00:09:45.590 --> 00:09:48.909 process is strictly linear. We can easily picture 00:09:48.909 --> 00:09:51.549 one airplane. We can maybe picture 10 parked 00:09:51.549 --> 00:09:57.090 on a tarmac. But 5 ,525 airplanes is just a logistical 00:09:57.090 --> 00:10:00.350 nightmare for our visual cortex. It shuts down 00:10:00.350 --> 00:10:03.730 and defaults back to that folder of a lot. And 00:10:03.730 --> 00:10:05.690 what's truly remarkable here is looking at the 00:10:05.690 --> 00:10:07.889 historical divide between nature and human engineering 00:10:07.889 --> 00:10:10.090 at this scale. Oh right, the source notes that 00:10:10.090 --> 00:10:12.389 a small mountain, like slightly larger than Stone 00:10:12.389 --> 00:10:14.450 Mountain in Georgia, weighs about a billion tons. 00:10:14.870 --> 00:10:17.990 Yes. For almost all of history, numbers this 00:10:17.990 --> 00:10:20.129 large were exclusively the domain of nature. 00:10:20.460 --> 00:10:23.419 Mountains weighing a billion tons. The largest 00:10:23.419 --> 00:10:26.299 ant colony in the world, which stretches almost 00:10:26.299 --> 00:10:29.700 4 ,000 miles along the Mediterranean coast, contains 00:10:29.700 --> 00:10:32.659 billions of worker ants. Humans were entirely 00:10:32.659 --> 00:10:35.220 excluded from the billion class. Exactly. Until 00:10:35.220 --> 00:10:37.639 1804. Right, that was the year the global human 00:10:37.639 --> 00:10:40.039 population finally hit one billion. But look 00:10:40.039 --> 00:10:42.820 at how rapidly human engineering has scaled since 00:10:42.820 --> 00:10:45.320 that milestone. We went from taking the entirety 00:10:45.320 --> 00:10:47.720 of human history to produce one billion people 00:10:47.720 --> 00:10:50.600 to mass producing technology at that exact same 00:10:50.600 --> 00:10:52.980 scale in just a few decades. It's exponential. 00:10:53.299 --> 00:10:56.360 It is. Apple sold its one billionth iPhone by 00:10:56.360 --> 00:11:00.149 July 2016. Facebook reached over three billion 00:11:00.149 --> 00:11:03.490 active users by 2025. We have literally built 00:11:03.490 --> 00:11:06.269 artificial digital networks that rival the largest 00:11:06.269 --> 00:11:09.570 biological colonies on Earth. So we finally conquered 00:11:09.570 --> 00:11:12.009 the physical billion. But that physical engineering 00:11:12.009 --> 00:11:14.629 eventually gave birth to a digital world. And 00:11:14.629 --> 00:11:16.730 in that digital world, a billion isn't just a 00:11:16.730 --> 00:11:19.269 milestone to celebrate. No, it acts as an invisible 00:11:19.269 --> 00:11:22.169 physical wall. Which brings us to the strange, 00:11:22.429 --> 00:11:24.889 highly specific territory of the numbers that 00:11:24.889 --> 00:11:27.129 follow one million. the underlying architecture 00:11:27.129 --> 00:11:29.669 of the information age. I was reading through 00:11:29.669 --> 00:11:31.889 the section of the source that catalogs specific 00:11:31.889 --> 00:11:34.370 10 -digit numbers, and I have to admit, I felt 00:11:34.370 --> 00:11:36.470 completely out of my depth. It felt like reading 00:11:36.470 --> 00:11:38.629 the code for the matrix. It can be pretty dense. 00:11:38.769 --> 00:11:44.470 Yeah, it's like a 2 ,147 ,483 ,647. Ah, yes. 00:11:44.629 --> 00:11:47.049 The source says this is the eighth Mersenne prime. 00:11:47.490 --> 00:11:49.970 But more importantly for us, it is the largest 00:11:49.970 --> 00:11:54.200 signed 32 -bit integer. And then there's 4 ,294 00:11:54.200 --> 00:11:59.139 ,967 ,295, which is the maximum 32 -bit unsigned 00:11:59.139 --> 00:12:01.059 integer. Right. I need you to translate this 00:12:01.059 --> 00:12:03.460 for me. What does signed and unsigned actually 00:12:03.460 --> 00:12:05.820 mean for a computer? Is a sign literally just 00:12:05.820 --> 00:12:07.679 a positive or negative marker? And what is a 00:12:07.679 --> 00:12:09.539 Mersenne prime? OK, let's break that down, because 00:12:09.539 --> 00:12:11.320 that mechanism here is fascinating. First, a 00:12:11.320 --> 00:12:13.600 Mersenne prime is just a prime number that is 00:12:13.600 --> 00:12:16.139 1 less than a power of 2. OK. So 2 to the power 00:12:16.139 --> 00:12:19.720 n minus 1. In this case, 2 to the 31st power 00:12:19.720 --> 00:12:24.480 minus 1 gives us roughly 2. Now, regarding signed 00:12:24.480 --> 00:12:27.299 and unsigned, you absolutely nailed it. The sign 00:12:27.299 --> 00:12:30.120 is just the positive or negative symbol. But 00:12:30.120 --> 00:12:32.159 you have to remember that computers have finite 00:12:32.159 --> 00:12:35.039 physical memory. For decades, much of our computing 00:12:35.039 --> 00:12:38.379 architecture was built on 32 -bit systems. That 00:12:38.379 --> 00:12:41.899 means the computer has exactly 32 tiny physical 00:12:41.899 --> 00:12:46.080 switches or bits to store a number. OK, 32 physical 00:12:46.080 --> 00:12:48.340 switches. If a number is signed, the computer 00:12:48.340 --> 00:12:50.559 has to sacrifice one of those precious switches 00:12:50.559 --> 00:12:52.700 just to remember if the number is positive or 00:12:52.700 --> 00:12:55.899 negative. That leaves only 31 switches to actually 00:12:55.899 --> 00:12:58.879 count the number. And the absolute maximum number 00:12:58.919 --> 00:13:03.779 can count to with 31 binary switches is 2 ,147 00:13:03.779 --> 00:13:08.700 ,483 ,647. I see. But if a number is unsigned? 00:13:08.899 --> 00:13:10.860 If it's unsigned, meaning the programmer tells 00:13:10.860 --> 00:13:12.500 the computer, hey, this number will never go 00:13:12.500 --> 00:13:14.820 below zero, it's strictly positive, you get that 00:13:14.820 --> 00:13:17.100 switch back. Oh. And because binary works in 00:13:17.100 --> 00:13:19.620 powers of 2, getting one extra switch literally 00:13:19.620 --> 00:13:21.960 doubles your maximum limit. Precisely. That's 00:13:21.960 --> 00:13:24.539 why the unsigned 32 -bit integer limit jumps 00:13:24.539 --> 00:13:27.440 up to roughly 4 .29 billion. That makes perfect 00:13:27.440 --> 00:13:30.500 sense. These specific 10 -digit numbers were 00:13:30.500 --> 00:13:32.539 the literal boundaries of our digital reality. 00:13:33.000 --> 00:13:36.039 If a video game score, or a bank database counter, 00:13:36.500 --> 00:13:39.960 or a YouTube view count exceeded 2 .14 billion 00:13:39.960 --> 00:13:43.039 on a signed 32 -bit system, it would physically 00:13:43.039 --> 00:13:45.720 break. The computer simply didn't have the switches 00:13:45.720 --> 00:13:48.539 to comprehend a number larger than that. You 00:13:48.539 --> 00:13:50.220 might actually remember when the music video 00:13:50.220 --> 00:13:52.360 for Gangnam Style broke YouTube's view counter. 00:13:52.559 --> 00:13:54.789 Wait, was that because of this? Yes. It crossed 00:13:54.789 --> 00:13:57.970 that exact 2 .14 billion threshold, and the system 00:13:57.970 --> 00:13:59.950 couldn't handle it. It's literally the edge of 00:13:59.950 --> 00:14:02.049 the digital universe. But honestly, that isn't 00:14:02.049 --> 00:14:03.690 even the weirdest part of this section. There's 00:14:03.690 --> 00:14:06.629 more. The source lists these incredibly strange 00:14:06.629 --> 00:14:13.289 10 -digit numbers, like 3 ,405 ,691 ,582. The 00:14:13.289 --> 00:14:15.070 source says this is used as a magic debug value 00:14:15.070 --> 00:14:16.990 in programming, corresponding to the letters 00:14:16.990 --> 00:14:20.149 C -A -F -E -B -E -E. Cafe babe. Cafe babe. And 00:14:20.149 --> 00:14:25.549 then 3 ,735 ,928 ,559 corresponds to D -E -A 00:14:25.549 --> 00:14:29.230 -D -B -E -F. Dead beef. Okay, why are computer 00:14:29.230 --> 00:14:31.309 programmers hiding the word dead beef inside 00:14:31.309 --> 00:14:33.470 10 -digit numbers? Are these digital inside jokes? 00:14:33.690 --> 00:14:36.110 Well, sort of, but this brings up an incredibly 00:14:36.110 --> 00:14:38.529 important point about how humans interface with 00:14:38.529 --> 00:14:41.549 machines. You see, computers don't read numbers 00:14:41.549 --> 00:14:44.370 in base 10 like we do. They operate in binary, 00:14:44.629 --> 00:14:47.990 endless strings of 1s and 0s. Right. But humans 00:14:47.990 --> 00:14:51.350 can't read a string of 32 1s and 0s without going 00:14:51.350 --> 00:14:54.230 completely cross -eyed. So programmers use a 00:14:54.230 --> 00:14:57.230 system called hexadecimal, which is base 16. 00:14:57.389 --> 00:14:59.730 Base 16. So instead of counting 0 to 9, you have 00:14:59.730 --> 00:15:02.720 to count 0 to 15. But we don't have single numbers 00:15:02.720 --> 00:15:05.899 for 10 through 15 exactly so to solve that problem 00:15:05.899 --> 00:15:08.580 hexadecimal uses the standard numbers 0 through 00:15:08.580 --> 00:15:11.840 9 But then it uses the letters a through F to 00:15:11.840 --> 00:15:14.679 represent 10 through 15 the whole mechanism here 00:15:14.679 --> 00:15:17.399 is compression hexadecimal takes those massive 00:15:17.399 --> 00:15:20.220 unreadable binary strings and Compresses them 00:15:20.220 --> 00:15:23.240 into shorter human readable chunks. Okay, so 00:15:23.240 --> 00:15:26.100 because it uses letters a through F You can actually 00:15:26.100 --> 00:15:29.000 spell words. You can. So imagine you are a programmer, 00:15:29.419 --> 00:15:31.799 your software crashes, and you have to scan through 00:15:31.799 --> 00:15:33.980 thousands of lines of raw memory looking for 00:15:33.980 --> 00:15:36.179 the exact spot where the error occurred. Sounds 00:15:36.179 --> 00:15:42.600 terrible. It is. The numerical value 3 ,735 ,928 00:15:42.600 --> 00:15:45.559 ,559 doesn't mean anything to your human eyes. 00:15:45.820 --> 00:15:48.039 It just blends in with all the other data. But 00:15:48.039 --> 00:15:51.080 when translated to hexadecimal, it spells dead 00:15:51.080 --> 00:15:53.559 beef. Oh, it jumps right off the screen. Yes. 00:15:53.759 --> 00:15:55.899 When a programmer needs a highly visible value 00:15:55.899 --> 00:15:58.919 to mark uninitialized memory or a software crash, 00:15:59.259 --> 00:16:02.139 they use one of these magic debug values. It's 00:16:02.139 --> 00:16:04.159 basically a way for human engineers to leave 00:16:04.159 --> 00:16:06.320 bright neon breadcrumbs for themselves inside 00:16:06.320 --> 00:16:08.740 the vast, cold landscape of computer memory. 00:16:08.840 --> 00:16:10.779 That is brilliant. It's just human nature trying 00:16:10.779 --> 00:16:13.220 to make the incomprehensible readable. Exactly. 00:16:13.480 --> 00:16:15.620 And to round out the math quirks, the source 00:16:15.620 --> 00:16:19.820 gives us one last number. 6 ,210 ,000 ,000. It 00:16:19.820 --> 00:16:21.899 is the only self -descriptive number in DACE 00:16:21.899 --> 00:16:24.039 10. I love this one. Meaning the first digit, 00:16:24.159 --> 00:16:26.179 6, tells you exactly how many zeros are in the 00:16:26.179 --> 00:16:28.379 number. The second digit, 2, tells you there 00:16:28.379 --> 00:16:30.320 are two 1s in the number. The third digit, 1, 00:16:30.379 --> 00:16:32.279 tells you there are one 2, and so on. A number 00:16:32.279 --> 00:16:35.320 that perfectly mathematically defines its own 00:16:35.320 --> 00:16:38.940 internal structure. It's beautiful, really. And 00:16:38.940 --> 00:16:40.720 I would ask you to consider what stands out to 00:16:40.720 --> 00:16:44.600 you more here. The pure, pristine math of a self 00:16:44.600 --> 00:16:47.399 -descriptive number or the messy human fingerprints, 00:16:47.639 --> 00:16:50.460 like the dead beefs, left deliberately inside 00:16:50.460 --> 00:16:53.340 the code. It really is a fascinating clash between 00:16:53.340 --> 00:16:56.320 natural, immutable math and human invention. 00:16:57.080 --> 00:16:59.340 So let's take a step back and look at what we've 00:16:59.340 --> 00:17:01.059 actually uncovered today. We've covered a lot 00:17:01.059 --> 00:17:03.779 of ground. We really have. We started with the 00:17:03.779 --> 00:17:05.950 linguistic quirks of the milliard. and realized 00:17:05.950 --> 00:17:09.289 that trying to avoid a post -WWII trade disaster 00:17:09.289 --> 00:17:12.690 actually cost us our logical mathematical prefixes. 00:17:12.750 --> 00:17:15.390 A necessary sacrifice. Then we fueled a time 00:17:15.390 --> 00:17:17.250 machine and discovered that just changing the 00:17:17.250 --> 00:17:19.109 dial for minutes to months drops us out of the 00:17:19.109 --> 00:17:21.470 Roman Empire and right into the path of a T -Rex. 00:17:22.170 --> 00:17:23.950 We learned that our brains absolutely cannot 00:17:23.950 --> 00:17:26.269 be trusted with volume because a billion can 00:17:26.269 --> 00:17:28.630 be a mini -fridge of salt under your desk or 00:17:28.630 --> 00:17:31.089 a sky -darkening fleet of over 5 ,000 Boeing 00:17:31.089 --> 00:17:34.839 747s. Depending entirely on the unit. Yep. We 00:17:34.839 --> 00:17:38.000 saw humanity scale from taking all of biological 00:17:38.000 --> 00:17:40.220 history to hit one billion people to churning 00:17:40.220 --> 00:17:43.160 out a billion iPhones in a matter of years. And 00:17:43.160 --> 00:17:45.079 finally, we found out that the invisible walls 00:17:45.079 --> 00:17:48.519 of our digital world are literally padded with 00:17:48.519 --> 00:17:51.839 secret hexadecimal beef. It is a profound shift 00:17:51.839 --> 00:17:54.720 in perspective when you finally attach real world 00:17:54.720 --> 00:17:58.180 weight to those zeros. So the next time a politician 00:17:58.180 --> 00:18:01.940 or a scientist or a tech CEO casually drops the 00:18:01.940 --> 00:18:04.740 word billion into a sentence. You now possess 00:18:04.740 --> 00:18:06.819 the mental toolkit to actually weigh that number 00:18:06.819 --> 00:18:08.859 in your mind. You can picture the airplanes, 00:18:08.960 --> 00:18:11.599 the years, the distance to the moon. It is no 00:18:11.599 --> 00:18:14.140 longer just a vague, murky synonym for a lot. 00:18:14.599 --> 00:18:16.819 You have brought the apples back into the physical 00:18:16.819 --> 00:18:19.410 basket. And yet, I want to leave you with one 00:18:19.410 --> 00:18:22.430 final mind -expanding thread to pull on. Oh, 00:18:22.430 --> 00:18:24.930 what's that? Well, if it takes this much cognitive 00:18:24.930 --> 00:18:27.109 effort, this many historical breakdowns, and 00:18:27.109 --> 00:18:29.329 this many wild analogies for our brains to even 00:18:29.329 --> 00:18:33.210 begin to visualize a single billion, how fundamentally 00:18:33.210 --> 00:18:36.029 distorted is our perception of a trillion? Yeah. 00:18:36.150 --> 00:18:38.549 As national debts and tech valuations casually 00:18:38.549 --> 00:18:41.210 cross the trillion mark, we are entering a scale 00:18:41.210 --> 00:18:43.549 of math that our paleolithic brains were simply 00:18:43.549 --> 00:18:46.529 never built to comprehend. Try translating a 00:18:46.529 --> 00:18:48.619 trillion seconds into yours tonight and see how 00:18:48.619 --> 00:18:48.980 you feel.