WEBVTT 00:00:00.000 --> 00:00:03.759 Right now, there's a key on your keyboard that 00:00:03.759 --> 00:00:06.459 ancient philosophers literally believed would 00:00:06.459 --> 00:00:09.080 destroy the fabric of reality if they acknowledged 00:00:09.080 --> 00:00:11.880 it. Which sounds completely wild, right? It really 00:00:11.880 --> 00:00:13.919 does. I mean, you probably use it a dozen times 00:00:13.919 --> 00:00:16.239 a day to type out a number or check your bank 00:00:16.239 --> 00:00:19.179 balance. But for centuries, humanity actively 00:00:19.179 --> 00:00:21.219 pretended it didn't exist. Yeah, they just ignored 00:00:21.219 --> 00:00:23.579 it. I am of course talking about the number zero. 00:00:23.660 --> 00:00:26.460 The literal concept of nothingness sitting right 00:00:26.460 --> 00:00:29.739 there in the middle of our most precise systems. 00:00:30.280 --> 00:00:33.219 Exactly. So today we are taking a deep dive into 00:00:33.219 --> 00:00:36.439 the surprising history of nothing. We're pulling 00:00:36.439 --> 00:00:39.299 entirely from a single comprehensive Wikipedia 00:00:39.299 --> 00:00:42.759 article simply titled Zero. Just the digit. Just 00:00:42.759 --> 00:00:44.740 the digit. Yeah. And our mission today is to 00:00:44.740 --> 00:00:48.759 explore how this one seemingly innocent symbol 00:00:49.000 --> 00:00:51.659 broke ancient philosophies, revolutionized global 00:00:51.659 --> 00:00:54.560 trade, and became the absolute bedrock of modern 00:00:54.560 --> 00:00:56.939 computing. It really is the foundation of everything 00:00:56.939 --> 00:00:59.880 digital. Okay, let's unpack this. Where do we 00:00:59.880 --> 00:01:02.799 even begin the story of a number that, well, 00:01:02.920 --> 00:01:05.299 isn't really there? Well, chronologically, we 00:01:05.299 --> 00:01:07.900 kind of have to begin by looking at how ancient 00:01:07.900 --> 00:01:10.480 civilizations wrestled with the physical reality 00:01:10.480 --> 00:01:13.480 of empty space. Because for a very long time, 00:01:13.579 --> 00:01:15.959 humanity functioned perfectly well without a 00:01:15.959 --> 00:01:17.959 true mathematical zero. Right, they didn't need 00:01:17.959 --> 00:01:21.439 it. Exactly. Instead, early cultures utilized 00:01:21.439 --> 00:01:24.319 placeholders. And a placeholder is just, what, 00:01:24.379 --> 00:01:26.780 a way to keep a seat warm for a real number so 00:01:26.780 --> 00:01:29.810 your columns line up? Pretty much, yeah. In ancient 00:01:29.810 --> 00:01:34.829 Egypt, around 1770 BC, papyrus records show scribes 00:01:34.829 --> 00:01:37.109 keeping track of the pharaoh's daily incomes 00:01:37.109 --> 00:01:39.870 and expenditures. Basic accounting. Right. And 00:01:39.870 --> 00:01:42.090 when the amount of goods received perfectly matched 00:01:42.090 --> 00:01:44.370 the amount dispersed, meaning a zero balance, 00:01:44.810 --> 00:01:47.230 they marked the ledger with a specific hieroglyph 00:01:47.230 --> 00:01:50.579 called NFR. A symbol for nothing. Wait, so what 00:01:50.579 --> 00:01:53.420 did NFR literally translate to in their language? 00:01:53.680 --> 00:01:56.420 It actually meant beautiful or pleasant or good. 00:01:56.579 --> 00:01:59.260 Oh, wow. I mean, a perfectly balanced accounting 00:01:59.260 --> 00:02:01.900 ledger being literally beautiful makes perfect 00:02:01.900 --> 00:02:04.260 sense to anyone who has ever done their taxes. 00:02:04.359 --> 00:02:07.239 It's very relatable. And they applied that same 00:02:07.239 --> 00:02:09.719 NFR symbol to physical space and construction 00:02:09.719 --> 00:02:12.879 too. Like building the pyramids. Exactly. When 00:02:12.879 --> 00:02:15.680 drawing plans for tombs and pyramids, NFR indicated 00:02:15.680 --> 00:02:18.099 the base ground level. Every other measurement 00:02:18.099 --> 00:02:21.139 was calculated as either above or below that 00:02:21.139 --> 00:02:23.419 beautiful baseline. That's super practical. It 00:02:23.419 --> 00:02:26.300 was. But crucially, this was just a marker. It 00:02:26.300 --> 00:02:28.460 wasn't a number they were manipulating in complex 00:02:28.460 --> 00:02:30.180 equations. Well, you can't multiply beautiful 00:02:30.180 --> 00:02:33.020 by 10. Right. And the Babylonians did something 00:02:33.020 --> 00:02:36.360 similar with their base 16 numeral system. How 00:02:36.360 --> 00:02:38.199 did that work? Well, by the middle of the second 00:02:38.199 --> 00:02:41.889 millennium BC, The Babylonians had a highly sophisticated 00:02:41.889 --> 00:02:45.469 numbering system, but to indicate an empty positional 00:02:45.469 --> 00:02:49.270 value, like the zero in our number 101, they 00:02:49.270 --> 00:02:51.789 initially just left a physical blank space on 00:02:51.789 --> 00:02:54.490 the clay tablet. Wait, leaving a literal gap 00:02:54.490 --> 00:02:56.550 in a string of numbers? That seems like a recipe 00:02:56.550 --> 00:02:58.870 for a massive clerical error. I mean, you wouldn't 00:02:58.870 --> 00:03:02.069 know if the scribe meant 11, or 101, or 1001. 00:03:02.210 --> 00:03:04.189 Yeah, and the Babylonians eventually realized 00:03:04.189 --> 00:03:07.729 the exact same thing. So by around 700 BC, a 00:03:07.729 --> 00:03:11.050 scribe named Bell Bonaplew started using three 00:03:11.050 --> 00:03:13.330 hooks to mark that empty space. OK, that's better. 00:03:13.500 --> 00:03:17.520 Yeah, and that evolved by 300 BC into a punctuation 00:03:17.520 --> 00:03:19.879 symbol made of two slanted wedges. You know, 00:03:19.879 --> 00:03:22.560 that feels a lot like the space bar on a keyboard. 00:03:22.780 --> 00:03:25.460 How so? Well, the space bar is absolutely essential 00:03:25.460 --> 00:03:28.259 because it creates the necessary separation between 00:03:28.259 --> 00:03:31.699 words so that a sentence actually makes sense. 00:03:31.979 --> 00:03:33.879 But you don't consider the empty space itself 00:03:33.879 --> 00:03:37.879 to be a letter. It's just the structural absence 00:03:37.879 --> 00:03:40.199 of a letter. That's a perfect analogy to the 00:03:40.199 --> 00:03:42.620 Babylonians. Those slanted wedges function the 00:03:42.620 --> 00:03:45.060 exact same way you wouldn't just write the wedges 00:03:45.060 --> 00:03:47.520 by themselves to say you know I have zero apples 00:03:47.520 --> 00:03:49.639 because they weren't a standalone value right 00:03:49.639 --> 00:03:51.860 because of that limitation we really can't call 00:03:51.860 --> 00:03:54.840 it a true concept of the number zero which brings 00:03:54.840 --> 00:03:57.699 us to a civilization that could have easily developed 00:03:57.699 --> 00:04:02.500 it but actively chose not to the Greeks yes the 00:04:02.500 --> 00:04:05.300 Greeks the archaic Greeks had no symbol for zero 00:04:05.300 --> 00:04:08.280 and they refused to even use a placeholder digit 00:04:08.280 --> 00:04:10.990 why That seems backwards for them. They looked 00:04:10.990 --> 00:04:13.669 at the concept of nothing and asked a fundamental 00:04:13.669 --> 00:04:17.089 philosophical question. How cannot being be? 00:04:17.430 --> 00:04:20.689 Ah, so it was a philosophical block. If a number 00:04:20.689 --> 00:04:23.389 represents a quantity of something that exists, 00:04:24.470 --> 00:04:27.189 then a number representing nothing implies the 00:04:27.189 --> 00:04:30.410 existence of a void. Exactly. And the Greek philosophical 00:04:30.410 --> 00:04:33.350 model, going all the way to Aristotle, held that 00:04:33.350 --> 00:04:36.069 nature abhors a vacuum. Right. The whole universe 00:04:36.069 --> 00:04:38.649 is filled. The whole of the Greek universe rested 00:04:38.649 --> 00:04:42.540 on that one pillar. There's no void. So to accept 00:04:42.540 --> 00:04:45.720 zero mathematically was to accept the void philosophically, 00:04:46.060 --> 00:04:48.139 and that just shattered their entire understanding 00:04:48.139 --> 00:04:50.240 of reality. I have to push back on the practical 00:04:50.240 --> 00:04:52.839 side of this, though. The Greeks were legendary 00:04:52.839 --> 00:04:55.139 astronomers. They were. They were mapping the 00:04:55.139 --> 00:04:58.019 cosmos, predicting eclipses, calculating these 00:04:58.019 --> 00:05:00.540 complex planetary movements. How could the Greeks 00:05:00.540 --> 00:05:03.939 do advanced astronomy without a zero? You can't 00:05:03.939 --> 00:05:05.779 calculate the mechanics of the solar system with 00:05:05.779 --> 00:05:08.589 just philosophy. You've hit on the exact tension 00:05:08.589 --> 00:05:10.230 they face between their philosophy and their 00:05:10.230 --> 00:05:12.329 science, and the solution they found was essentially 00:05:12.329 --> 00:05:15.149 to cheat. To cheat. Yeah. Greek astronomers, 00:05:15.370 --> 00:05:18.589 like Ptolemy around AD 150, realized they couldn't 00:05:18.589 --> 00:05:21.230 make their complex base 60 calculations work 00:05:21.230 --> 00:05:23.610 without a placeholder. So they caved. Pretty 00:05:23.610 --> 00:05:26.050 much. For his work on mathematical astronomy, 00:05:26.529 --> 00:05:29.329 Ptolemy swallowed his philosophical pride and 00:05:29.329 --> 00:05:32.089 borrowed the placeholder concept from the Babylonians. 00:05:32.610 --> 00:05:35.410 He used a symbol that looked like the Greek letter 00:05:35.410 --> 00:05:38.790 Omicron. with an overline. Oh, so they did use 00:05:38.790 --> 00:05:42.050 a zero when the math demanded it. Yes, but only 00:05:42.050 --> 00:05:44.829 during the rough calculations. Ptolemy used it 00:05:44.829 --> 00:05:46.990 to figure out the magnitude of solar and lunar 00:05:46.990 --> 00:05:49.930 eclipses. But after doing the heavy lifting to 00:05:49.930 --> 00:05:52.230 find the answers, the Greeks would stubbornly 00:05:52.230 --> 00:05:54.610 convert the final numbers back into standard 00:05:54.610 --> 00:05:58.250 Greek numerals. Wait, really? Yeah. They refused 00:05:58.250 --> 00:06:00.709 to leave a zero on the published page. That is 00:06:00.709 --> 00:06:03.730 wild. They used the forbidden math and the rough 00:06:03.730 --> 00:06:06.649 draft, but systematically erased it for the final 00:06:06.649 --> 00:06:09.569 copy. They mathematically airbrushed the void 00:06:09.569 --> 00:06:11.629 out of existence. That's exactly what they did. 00:06:11.910 --> 00:06:14.009 But while the Greeks were actively running from 00:06:14.009 --> 00:06:16.970 the void, other cultures, unburdened by that 00:06:16.970 --> 00:06:19.709 specific philosophy, were independently embracing 00:06:19.709 --> 00:06:21.670 it. Right, because if you're handling the mass 00:06:21.670 --> 00:06:24.709 of logistics of building a civilization, eventually 00:06:24.709 --> 00:06:26.310 you have to deal with the concept of an empty 00:06:26.310 --> 00:06:28.870 space. And our sources show this happening, like, 00:06:28.970 --> 00:06:31.670 all over the globe. Absolutely. The need for 00:06:31.670 --> 00:06:34.990 a placeholder is so universal that isolated cultures 00:06:34.990 --> 00:06:38.009 on completely opposite sides of the world conceptualized 00:06:38.009 --> 00:06:40.569 it independently. Like in the Americas. Right. 00:06:40.850 --> 00:06:43.449 In the pre -Columbian Americas, the Mesoamerican 00:06:43.449 --> 00:06:46.449 long count calendar was under development. This 00:06:46.449 --> 00:06:49.410 calendar used a base 20 positional numeral system. 00:06:49.589 --> 00:06:52.550 OK, base 20. And to track time accurately across 00:06:52.550 --> 00:06:54.970 centuries, they absolutely needed a placeholder 00:06:54.970 --> 00:06:58.089 to keep their base 20 columns aligned. And the 00:06:58.089 --> 00:07:00.879 Maya and the Olmecs saw this by using various 00:07:00.879 --> 00:07:04.100 glyphs right sometimes a partial quatrefoil but 00:07:04.100 --> 00:07:07.410 most famously an empty tortoise -like shell shape. 00:07:07.569 --> 00:07:09.629 Yes, the shell shape. And they figured this out 00:07:09.629 --> 00:07:11.689 incredibly early. There's a stone monument called 00:07:11.689 --> 00:07:15.009 Stela II at Chiapas de Corzo that features a 00:07:15.009 --> 00:07:17.569 long count date with a zero placeholder corresponding 00:07:17.569 --> 00:07:20.949 to the year 36 BC. 36 BC. That's so early. It 00:07:20.949 --> 00:07:23.290 really is. And further south, the Inca Empire 00:07:23.290 --> 00:07:25.449 engineered a completely different physical system 00:07:25.449 --> 00:07:28.149 called the Kipu. Oh, the knotted strings. Exactly. 00:07:28.350 --> 00:07:30.350 It was a device made of knotted cords used for 00:07:30.350 --> 00:07:32.930 recording accounting and digital data in a base 00:07:32.930 --> 00:07:35.129 10 positional system. So how do you knot a string 00:07:35.129 --> 00:07:38.579 to show? For the Incas, zero was brilliantly 00:07:38.579 --> 00:07:41.009 simple. It was represented by the deliberate 00:07:41.009 --> 00:07:43.189 absence of a knot in the appropriate position 00:07:43.189 --> 00:07:45.610 on the string. Just an unknotted piece of string 00:07:45.610 --> 00:07:47.810 to hold the empty place. That's elegant. Right. 00:07:48.069 --> 00:07:50.410 And over in Asia, the Chinese had a similar physical 00:07:50.410 --> 00:07:53.290 approach. They did positional decimal calculations 00:07:53.290 --> 00:07:55.990 using counting rods on a board. So physical sticks 00:07:55.990 --> 00:07:58.670 basically. Right. Moving the physical rods designated 00:07:58.670 --> 00:08:02.069 tens, hundreds, and thousands. And if a column 00:08:02.069 --> 00:08:05.009 was empty on the board, that empty physical space 00:08:05.009 --> 00:08:07.490 denoted zero. But they didn't write it down as 00:08:07.490 --> 00:08:10.540 a zero? Not initially. It wasn't until much later 00:08:10.540 --> 00:08:14.860 in an AD 1247 mathematical treatise by Qin Juxiao 00:08:14.860 --> 00:08:17.100 that we see the introduction of a round symbol 00:08:17.100 --> 00:08:21.319 for zero in Chinese texts. Okay, so 1247. Yeah, 00:08:21.439 --> 00:08:23.480 but even then it was still primarily treated 00:08:23.480 --> 00:08:26.459 as a vacant position rather than a standalone 00:08:26.459 --> 00:08:30.790 number you could like add or multiply. Is necessity 00:08:30.790 --> 00:08:32.950 always the mother of invention here? I mean, 00:08:33.169 --> 00:08:35.210 did the Maya need an empty shell just to make 00:08:35.210 --> 00:08:37.750 their complex calendar work, or did the act of 00:08:37.750 --> 00:08:39.830 tracking the stars lead them to naturally discover 00:08:39.830 --> 00:08:42.159 the concept of zero? What's fascinating here 00:08:42.159 --> 00:08:45.139 is that these completely isolated cultures, the 00:08:45.139 --> 00:08:47.440 Maya with their calendars, the Incas with their 00:08:47.440 --> 00:08:49.399 knotted cords, the Chinese with their counting 00:08:49.399 --> 00:08:52.179 rods, they all developed the architecture of 00:08:52.179 --> 00:08:55.299 zero to solve highly practical physical problems. 00:08:55.360 --> 00:08:57.860 Right, real world issues. Exactly. By creating 00:08:57.860 --> 00:09:00.399 a physical representation of an empty space, 00:09:00.740 --> 00:09:03.039 they proved that the human mind naturally seeks 00:09:03.039 --> 00:09:05.759 a way to quantify the invisible. Giving a shape. 00:09:06.029 --> 00:09:08.370 to the shapeless, it's an incredible leap. But 00:09:08.370 --> 00:09:10.429 I mean, a placeholder is still just a placeholder. 00:09:10.970 --> 00:09:13.210 Yeah. Doing actual mathematical operations with 00:09:13.210 --> 00:09:16.169 nothing as a standalone number requires an entirely 00:09:16.169 --> 00:09:18.330 different level of abstract thinking. It does. 00:09:18.590 --> 00:09:20.889 And that conceptual leap finally happened in 00:09:20.889 --> 00:09:23.110 India. And surprisingly, it didn't start with 00:09:23.110 --> 00:09:25.600 accounting or astronomy. No. What did it start 00:09:25.600 --> 00:09:27.980 with? It started with poetry. Wait, poetry? Yeah. 00:09:28.320 --> 00:09:31.480 As early as the third or second century BC, a 00:09:31.480 --> 00:09:34.220 Sanskrit scholar named Pingala was studying the 00:09:34.220 --> 00:09:37.460 metrics of poetic verse. He used binary sequences 00:09:37.460 --> 00:09:40.159 of short and long syllables to identify valid 00:09:40.159 --> 00:09:42.000 Sanskrit meters. Oh, kind of like a notation 00:09:42.000 --> 00:09:44.360 system. Very similar to modern Morse code, maybe. 00:09:44.509 --> 00:09:48.129 That's a great comparison. In this binary system, 00:09:48.490 --> 00:09:51.110 Pingala used the Sanskrit word shunya, which 00:09:51.110 --> 00:09:55.090 means void or empty, explicitly as a marker to 00:09:55.090 --> 00:09:58.710 refer to zero. Wow. And from poetry, it slowly 00:09:58.710 --> 00:10:00.789 started to take the physical shape we recognize 00:10:00.789 --> 00:10:03.529 today. Right. For example, the Bakhshali manuscript, 00:10:03.769 --> 00:10:06.409 which is an ancient manual for merchants, used 00:10:06.409 --> 00:10:09.649 a black dot for zero. Just a solid dot. Yeah. 00:10:09.799 --> 00:10:12.919 And later, there's an undeniable stone inscription 00:10:12.919 --> 00:10:15.820 at the Chaturboj Temple in Gwalior, India, dated 00:10:15.820 --> 00:10:19.820 to 8876, clearly showing the digit zero is a 00:10:19.820 --> 00:10:21.679 small circle. So the circle is finally there. 00:10:21.860 --> 00:10:24.710 Yes. But the true mathematical breakthrough arrived 00:10:24.710 --> 00:10:26.889 in the seventh century with an Indian mathematician 00:10:26.889 --> 00:10:29.450 named Brahmagupta. What did he do? He was the 00:10:29.450 --> 00:10:31.549 first to establish the formal rules for zero. 00:10:32.070 --> 00:10:34.009 He stated mathematically that the sum of zero 00:10:34.009 --> 00:10:36.649 with itself is zero. He defined how it interacts 00:10:36.649 --> 00:10:38.809 with negative and positive numbers. He gave it 00:10:38.809 --> 00:10:41.409 rules. Exactly. But when he tried to push the 00:10:41.409 --> 00:10:44.570 logic to its absolute limit, he hit a wall. Brahmagupta 00:10:44.570 --> 00:10:47.559 tried to define division by zero. Oh boy. I mean, 00:10:47.639 --> 00:10:49.879 treating nothing as a standalone number breaks 00:10:49.879 --> 00:10:52.240 basic arithmetic pretty quickly. You can't just 00:10:52.240 --> 00:10:55.259 divide a physical pi among zero people. Exactly, 00:10:55.600 --> 00:10:58.940 and Brahmagupta couldn't quite solve it. He incorrectly 00:10:58.940 --> 00:11:01.259 stated that a number divided by zero results 00:11:01.259 --> 00:11:04.379 in a fraction with zero as the denominator. Which 00:11:04.379 --> 00:11:06.179 doesn't really answer the question. No, it just 00:11:06.179 --> 00:11:09.279 shifts the problem. It wasn't until the 12th 00:11:09.279 --> 00:11:12.620 century that another Indian mathematician, Bhaskara 00:11:12.620 --> 00:11:15.759 II, realized that dividing by zero creates a 00:11:15.759 --> 00:11:18.759 paradox. Bhaskara wrote that dividing a number 00:11:18.759 --> 00:11:22.200 by zero creates an infinite quantity. Here's 00:11:22.200 --> 00:11:24.980 where it gets really interesting. because just 00:11:24.980 --> 00:11:26.940 like a physical black hole breaks the laws of 00:11:26.940 --> 00:11:29.559 gravity, dividing by zero breaks the laws of 00:11:29.559 --> 00:11:31.580 arithmetic. It totally shatters them. Right, 00:11:31.600 --> 00:11:33.480 the closer you get to zero in the denominator, 00:11:33.860 --> 00:11:36.080 the larger the result gets until the math just 00:11:36.080 --> 00:11:38.440 collapses entirely into infinity. And Bosker 00:11:38.440 --> 00:11:40.759 recognized that collapse. He actually compared 00:11:40.759 --> 00:11:43.620 this infinite quantity to the divine. He wrote 00:11:43.620 --> 00:11:46.480 that in this quantity divided by zero, no change 00:11:46.480 --> 00:11:49.080 takes place in the infinite and immutable God 00:11:49.080 --> 00:11:53.179 when worlds are created or destroyed. Wow. Moving 00:11:53.179 --> 00:11:55.759 from a practical tool for keeping columns straight 00:11:55.759 --> 00:11:59.139 to a reflection of the infinite nature of God, 00:11:59.879 --> 00:12:03.120 that is a profound philosophical shift. It really 00:12:03.120 --> 00:12:05.139 is, and that transformative knowledge traveled 00:12:05.139 --> 00:12:08.580 quickly to the Islamic world. The Sanskrit concept 00:12:08.580 --> 00:12:12.019 of Shinya, the void, was translated into Arabic 00:12:12.019 --> 00:12:16.720 as alf. During the Islamic Golden Age, the brilliant 00:12:16.720 --> 00:12:19.460 Persian mathematician Al -Khwarizmi synthesized 00:12:19.460 --> 00:12:23.539 Greek and Hindu knowledge. In 8813, he used that 00:12:23.539 --> 00:12:27.419 little circle, the Afr, to keep the rose in the 00:12:27.419 --> 00:12:29.500 Ten's places. Which leads directly to the word 00:12:29.500 --> 00:12:32.259 algorithm, right? Yes. Originating from Al -Khwarizmi's 00:12:32.259 --> 00:12:34.240 name when his work was later translated into 00:12:34.240 --> 00:12:36.679 Latin. That's right. And it's through this Islamic 00:12:36.679 --> 00:12:39.139 transmission that the Indian zero finally knocked 00:12:39.139 --> 00:12:41.480 on the extremely stubborn doors of Europe. And 00:12:41.480 --> 00:12:43.519 Europe did not want to open that door. Not at 00:12:43.519 --> 00:12:45.179 all. Because to understand how you and I use 00:12:45.179 --> 00:12:47.840 zero today, you have to track how this knowledge 00:12:47.840 --> 00:12:49.980 broke through centuries of European traditionalism. 00:12:50.379 --> 00:12:52.460 You can actually see the resistance in the etymology, 00:12:52.759 --> 00:12:55.039 the journey of the word itself. How so? Well, 00:12:55.120 --> 00:12:57.279 the Arabic aphor was translated into medieval 00:12:57.279 --> 00:13:01.419 Latin as zephyrum. In Italy, that became zevro 00:13:01.419 --> 00:13:04.679 or zephyro, heavily influenced by the existing 00:13:04.679 --> 00:13:07.700 Italian word for the west wind. And finally, 00:13:08.159 --> 00:13:10.820 that contracted into the word we use today, zero. 00:13:11.220 --> 00:13:14.019 I love that. And the individual responsible for 00:13:14.019 --> 00:13:16.039 finally getting Europe to adopt it was the great 00:13:16.039 --> 00:13:18.519 Italian mathematician Fibonacci. A sequence guy. 00:13:18.659 --> 00:13:21.580 The very same. He grew up in North Africa, learned 00:13:21.580 --> 00:13:23.860 the Hindu -Arabic numeral system from Arab merchants, 00:13:24.139 --> 00:13:26.519 and brought it back to Europe in his 1202 book, 00:13:26.659 --> 00:13:29.350 Libra Baci. He explicitly wrote that with the 00:13:29.350 --> 00:13:32.370 nine Indian figures and with the sign zero, any 00:13:32.370 --> 00:13:34.590 number may be written. I mean, think about this 00:13:34.590 --> 00:13:37.350 for a second. Europe's most valuable world changing 00:13:37.350 --> 00:13:40.409 import from the East was quite literally nothing. 00:13:40.690 --> 00:13:43.509 It's extremely poetic. But even after Fibonacci 00:13:43.509 --> 00:13:46.789 laid out a clearly superior system, Europeans 00:13:46.789 --> 00:13:49.700 still resisted. I mean, why cling to Roman numerals 00:13:49.700 --> 00:13:51.879 for hundreds of years? Try multiplying the Roman 00:13:51.879 --> 00:13:55.080 numeral 14th by x7 on paper. It's impossible, 00:13:55.279 --> 00:13:57.000 because there's no place value. You can't carry 00:13:57.000 --> 00:13:59.610 a 1. It's just an alphabet soup. If we connect 00:13:59.610 --> 00:14:01.909 this to the bigger picture, you have to remember 00:14:01.909 --> 00:14:04.429 what Roman numerals were actually designed for. 00:14:04.830 --> 00:14:07.789 They were a system of recording a final tally, 00:14:07.850 --> 00:14:10.750 not a system of calculating. Like a receipt system, 00:14:10.750 --> 00:14:13.509 basically. Exactly. If you were a European merchant 00:14:13.509 --> 00:14:16.129 in the Middle Ages, you didn't do math on paper. 00:14:16.350 --> 00:14:19.090 You did your math physically, manipulating beads 00:14:19.090 --> 00:14:21.629 on an abacus. Right, the abacus. And the abacus 00:14:21.629 --> 00:14:23.830 was controlled by specialized mathematicians. 00:14:24.389 --> 00:14:26.409 Once you figured out the answer on the physical 00:14:26.409 --> 00:14:29.350 board, you simply recorded that final tally using 00:14:29.350 --> 00:14:32.350 Roman numerals. The adoption of the Hindu -Arabic 00:14:32.350 --> 00:14:35.169 system with its true zero completely eliminated 00:14:35.169 --> 00:14:37.649 the need for the physical abacus. Because zero 00:14:37.649 --> 00:14:40.309 holds the empty place for you on the page. You 00:14:40.309 --> 00:14:42.309 don't need a physical bead on a wire to represent 00:14:42.309 --> 00:14:44.629 an empty column. The zero does the heavy lifting 00:14:44.629 --> 00:14:47.250 right there in the ink. Yes. It fundamentally 00:14:47.250 --> 00:14:50.570 democratized mathematics. Manuals called algorithmists 00:14:50.570 --> 00:14:53.409 started to spread rapidly. By the 16th century, 00:14:53.490 --> 00:14:55.870 math moved from a physical tool gate kept by 00:14:55.870 --> 00:14:58.740 specialists to an abstract concept that absolutely 00:14:58.740 --> 00:15:01.759 anyone could do using just ink and paper. That 00:15:01.759 --> 00:15:04.799 is huge. And once math moves from the physical 00:15:04.799 --> 00:15:08.039 abacus to the abstract page, zero is perfectly 00:15:08.039 --> 00:15:10.279 positioned to become the invisible bedrock of 00:15:10.279 --> 00:15:13.539 the modern scientific age. It forces us to distinguish 00:15:13.539 --> 00:15:16.519 between arbitrary human scales and the fundamental 00:15:16.519 --> 00:15:19.659 laws of nature. Take physics, for example. Zero 00:15:19.659 --> 00:15:22.419 degrees Celsius is an entirely arbitrary human 00:15:22.419 --> 00:15:24.440 scale. It's just the freezing point of water. 00:15:25.000 --> 00:15:27.379 The atoms are still vibrating. Energy still exists. 00:15:27.720 --> 00:15:30.039 Right. But absolute zero, measured in Kelvin, 00:15:30.059 --> 00:15:32.700 that is a true physical zero. It's the lowest 00:15:32.700 --> 00:15:35.399 possible energy state where a quantum mechanical 00:15:35.399 --> 00:15:38.379 physical system hits its ground state and atomic 00:15:38.379 --> 00:15:41.460 movement essentially ceases. It is the absolute 00:15:41.460 --> 00:15:43.759 limit of physics. And it's also the absolute 00:15:43.759 --> 00:15:46.000 foundation of computer science. Oh, absolutely. 00:15:46.279 --> 00:15:48.659 Modern computers obviously run on binary. in 00:15:48.659 --> 00:15:50.539 the ears representing the presence or absence 00:15:50.539 --> 00:15:52.759 of electrical current. But where zero really 00:15:52.759 --> 00:15:55.659 causes modern headaches is in programming languages 00:15:55.659 --> 00:15:57.799 and something called array indexing. Right. This 00:15:57.799 --> 00:16:00.139 is a classic problem. Throughout human history, 00:16:00.179 --> 00:16:02.279 when we count a physical list of objects, we 00:16:02.279 --> 00:16:05.980 start at one. One, two, three. Early classic 00:16:05.980 --> 00:16:08.460 programming languages like Fortran did exactly 00:16:08.460 --> 00:16:11.649 that. Makes sense. But in the late 1950s, languages 00:16:11.649 --> 00:16:15.610 like LISP and later C introduced zero -based 00:16:15.610 --> 00:16:18.570 numbering. If you have an array, a list of items, 00:16:19.110 --> 00:16:21.750 the sequence of indices runs from zero up to 00:16:21.750 --> 00:16:24.590 n minus one. So what does this all mean for your 00:16:24.590 --> 00:16:28.509 daily life? It means massive unseen logic puzzles 00:16:28.509 --> 00:16:31.529 for the people building the apps you use. I mean, 00:16:31.669 --> 00:16:33.889 why would anyone look at a list of items and 00:16:33.889 --> 00:16:36.509 call the very first thing item zero? It goes 00:16:36.509 --> 00:16:38.899 completely against human intuition. Well, it 00:16:38.899 --> 00:16:41.200 is counterintuitive to a human, but perfectly 00:16:41.200 --> 00:16:43.000 logical from the perspective of the machine. 00:16:43.460 --> 00:16:45.700 To a computer, zero in an array isn't just a 00:16:45.700 --> 00:16:48.259 count, it's an offset. An offset? Yeah. It tells 00:16:48.259 --> 00:16:50.340 the computer exactly how far away a piece of 00:16:50.340 --> 00:16:52.720 data is from the starting point of memory. The 00:16:52.720 --> 00:16:54.700 first item in the list is zero steps away from 00:16:54.700 --> 00:16:57.440 the start of the list. Ah. OK. It makes sense 00:16:57.440 --> 00:16:59.440 mechanically, but the lack of standardization 00:16:59.440 --> 00:17:02.340 causes endless confusion. For example, the programming 00:17:02.340 --> 00:17:05.099 language Java uses zero -based indexing. But 00:17:05.099 --> 00:17:08.059 Java's database connectivity tool JDBC indexes 00:17:08.059 --> 00:17:11.119 from one. It's a nightmare for developers. And 00:17:11.119 --> 00:17:13.440 speaking of databases, the concept of null introduces 00:17:13.440 --> 00:17:15.720 another layer of complexity that is critically 00:17:15.720 --> 00:17:17.759 different from zero. Which is funny, because 00:17:17.759 --> 00:17:20.720 in my mind, a null value and a zero are the exact 00:17:20.720 --> 00:17:23.619 same thing. Most people think that. But in a 00:17:23.619 --> 00:17:27.000 database, if a numeric field is zero, that is 00:17:27.000 --> 00:17:30.220 a known specific quantified value. You know for 00:17:30.220 --> 00:17:32.940 a fact that you have zero dollars. But if a field 00:17:32.940 --> 00:17:35.799 is null, it means the value is completely undetermined. 00:17:35.880 --> 00:17:37.720 You don't know if you have zero dollars or a 00:17:37.720 --> 00:17:40.119 million dollars or if the bank account even exists 00:17:40.119 --> 00:17:43.259 at all. Oh, wow. It leads to what computer scientists 00:17:43.259 --> 00:17:46.779 call three -valued logic. A condition isn't just 00:17:46.779 --> 00:17:49.799 true or false anymore. It can be true, false, 00:17:50.039 --> 00:17:53.089 or undetermined. Any computation that includes 00:17:53.089 --> 00:17:55.970 a null value delivers a null result. Exactly. 00:17:56.210 --> 00:17:58.089 It's almost like the philosophical void the Greeks 00:17:58.089 --> 00:18:00.809 were terrified of has come back to haunt modern 00:18:00.809 --> 00:18:02.829 data architecture. It really is the ghost in 00:18:02.829 --> 00:18:05.430 the database. And zero even dictates time itself 00:18:05.430 --> 00:18:08.069 for a digital infrastructure. The Unix epoch, 00:18:08.289 --> 00:18:10.630 which is the foundational moment from which all 00:18:10.630 --> 00:18:13.069 subsequent computer time is measured, is set 00:18:13.069 --> 00:18:15.410 to a zero time stamp. So the ultimate anchor 00:18:15.410 --> 00:18:18.309 of the digital world is midnight. just before 00:18:18.309 --> 00:18:21.410 January 1st, 1970. That is computer time zero. 00:18:21.710 --> 00:18:23.609 Well, to recap the incredible journey we've been 00:18:23.609 --> 00:18:26.829 on today, we started with an Egyptian hieroglyph 00:18:26.829 --> 00:18:29.930 for a beautiful baseline. We saw the void become 00:18:29.930 --> 00:18:32.549 a philosophical terror that forced Greek astronomers 00:18:32.549 --> 00:18:35.170 to erase their own math. We witnessed it transform 00:18:35.170 --> 00:18:37.789 into an infinite mathematical revolution in India. 00:18:38.039 --> 00:18:41.039 Right, face fierce resistance from abacus -wielding 00:18:41.039 --> 00:18:44.880 Europeans, and finally emerge as the offset logic 00:18:44.880 --> 00:18:48.460 and binary lifeblood of our modern digital devices. 00:18:48.740 --> 00:18:51.039 It truly is the most powerful tool ever born 00:18:51.039 --> 00:18:53.839 from human imagination. It is. But I want to 00:18:53.839 --> 00:18:56.400 leave you, the listener. with a final provocative 00:18:56.400 --> 00:18:58.420 thought from the biology section of our source 00:18:58.420 --> 00:19:00.859 material. Oh, this part is fascinating. It really 00:19:00.859 --> 00:19:03.900 is. Cognitive scientists and comparative zoologists 00:19:03.900 --> 00:19:06.359 have discovered that some animals actually display 00:19:06.359 --> 00:19:09.339 an awareness of the concept of zero. They show 00:19:09.339 --> 00:19:11.700 the capability for numerical abstraction early 00:19:11.700 --> 00:19:14.180 in the evolution of species. Which is just mind 00:19:14.180 --> 00:19:16.380 -blowing. Right. If animals innately understand 00:19:16.380 --> 00:19:19.440 nothing, if the concept of an empty set is hardwired 00:19:19.440 --> 00:19:22.079 into the brains of other species, it raises a 00:19:22.079 --> 00:19:24.339 totally mind -bending question for you to ponder. 00:19:24.539 --> 00:19:28.259 Did humanity actually invent the concept of zero 00:19:28.259 --> 00:19:31.519 with our knotted strings and counting rods? Or 00:19:31.519 --> 00:19:33.859 did we simply discover a fundamental law of nature 00:19:33.859 --> 00:19:36.559 that the animal kingdom inherently knew all along? 00:19:37.259 --> 00:19:38.859 The next time you sit down at a keyboard and 00:19:38.859 --> 00:19:41.720 see that oval -shaped key or look at a bank balance 00:19:41.720 --> 00:19:43.619 that isn't quite what you want it to be, look 00:19:43.619 --> 00:19:45.740 differently at those empty spaces. You aren't 00:19:45.740 --> 00:19:48.200 just looking at nothing. You are looking at the 00:19:48.200 --> 00:19:50.599 beautiful, terrifying, infinite concept that 00:19:50.599 --> 00:19:52.480 built the modern world. Thank you for taking 00:19:52.480 --> 00:19:54.039 this deep dive with us. See you next time.