WEBVTT 00:00:00.000 --> 00:00:03.700 Imagine, if you will, an ancient empire that 00:00:03.700 --> 00:00:07.040 was so completely terrified of an empty table 00:00:07.040 --> 00:00:10.839 that they like actively and aggressively banned 00:00:10.839 --> 00:00:14.000 the entire mathematical concept of nothing. Right. 00:00:14.199 --> 00:00:16.739 I mean, an empty table. It just feels so completely 00:00:16.739 --> 00:00:20.239 natural to us today. Yeah, exactly. Usually when 00:00:20.239 --> 00:00:22.100 we talk about counting, we just expect it to 00:00:22.100 --> 00:00:24.379 be obvious. You know, like, it's the most intuitive 00:00:24.379 --> 00:00:26.059 thing in the world. You have three apples on 00:00:26.059 --> 00:00:28.760 a table. You take one away, you have two. You 00:00:28.760 --> 00:00:30.519 take another away, you have one. You take the 00:00:30.519 --> 00:00:33.329 last one away, and you have, well, nothing. Right. 00:00:33.369 --> 00:00:34.890 But then you look back through human history 00:00:34.890 --> 00:00:37.090 and suddenly that empty table is just it's the 00:00:37.090 --> 00:00:40.450 source of absolute chaos. It really is like we're 00:00:40.450 --> 00:00:42.789 looking at a historical and mathematical landscape 00:00:42.789 --> 00:00:45.509 where nothing was honestly a genuinely terrifying 00:00:45.509 --> 00:00:47.549 concept. Oh, absolutely. It was the absolute 00:00:47.549 --> 00:00:50.250 definition of a conceptual blind spot for humanity. 00:00:50.509 --> 00:00:52.810 Well, welcome to the deep dive. Today we are 00:00:52.810 --> 00:00:56.049 looking at a singular massive source that we've 00:00:56.049 --> 00:00:59.090 compiled for you, which is a comprehensive Wikipedia 00:00:59.090 --> 00:01:02.079 article on the number zero, the big zero. Yeah, 00:01:02.219 --> 00:01:05.459 the big zero. And our mission today is to unpack 00:01:05.459 --> 00:01:09.459 how the concept of nothing went from being this. 00:01:11.060 --> 00:01:12.739 philosophical impossibility, something that ancient 00:01:12.739 --> 00:01:15.840 scholars literally violently rejected, to becoming 00:01:15.840 --> 00:01:18.459 the fundamental building block of your modern 00:01:18.459 --> 00:01:20.760 digital world. It's quite the journey. It really 00:01:20.760 --> 00:01:23.120 is. And I just have to say up front, I am in 00:01:23.120 --> 00:01:25.840 sheer amazement that something you and I take 00:01:25.840 --> 00:01:28.299 for granted every single day, something a toddler 00:01:28.299 --> 00:01:31.840 inherently understands, actually had to be, like, 00:01:32.120 --> 00:01:34.299 invented. I know. It is wild when you step back 00:01:34.299 --> 00:01:36.420 and really look at it. Yeah. Because what's fascinating 00:01:36.420 --> 00:01:38.980 here is that zero isn't just a number. Right. 00:01:39.159 --> 00:01:41.819 It is a profound conceptual leap. I mean, it 00:01:41.819 --> 00:01:45.060 completely rewired human logic. If we start at 00:01:45.060 --> 00:01:47.459 the beginning of recorded history, early civilizations 00:01:47.459 --> 00:01:49.799 didn't just forget to invent zero. Right. They 00:01:49.799 --> 00:01:51.939 didn't just overlook it. Exactly. Yeah. They 00:01:51.939 --> 00:01:54.400 actively, almost stubbornly, avoided treating 00:01:54.400 --> 00:01:56.719 nothing as a real mathematical entity. OK, so 00:01:56.719 --> 00:01:58.620 let's unpack this. Because when we say they avoided 00:01:58.620 --> 00:02:00.319 it, we don't mean they didn't know what the word 00:02:00.319 --> 00:02:03.299 empty meant. I mean, if a basket had no grain 00:02:03.299 --> 00:02:05.260 in it, they knew it was empty. Yeah, exactly. 00:02:05.299 --> 00:02:07.680 They understood the physical reality. Let's... 00:02:07.760 --> 00:02:09.719 Let's look at ancient Egypt, for example. They 00:02:09.719 --> 00:02:13.080 had a very robust base 10 numeral system. OK. 00:02:13.560 --> 00:02:16.159 But they did not have a positional zero like 00:02:16.159 --> 00:02:20.000 we do. So when an Egyptian scribe, say around 00:02:20.000 --> 00:02:24.060 1770 BC, was recording daily incomes and expenditures 00:02:24.060 --> 00:02:26.400 for the Pharaoh's court. They obviously needed 00:02:26.400 --> 00:02:28.659 a way to show that the accounts balanced. Right. 00:02:28.879 --> 00:02:31.180 They needed to show that what came in equaled 00:02:31.180 --> 00:02:33.460 what went out. But they didn't use a number zero. 00:02:33.680 --> 00:02:35.780 Instead, they actually used this hieroglyph called 00:02:35.780 --> 00:02:38.639 NFR. Which is such a weird pivot because looking 00:02:38.639 --> 00:02:41.939 at the source, NFR is a symbol of a heart with 00:02:41.939 --> 00:02:44.580 a trachea attached to it. Yeah, it's highly specific. 00:02:44.719 --> 00:02:47.180 And it didn't even mean zero. It translated to 00:02:47.180 --> 00:02:50.340 like beautiful or pleasant or good. Right. So 00:02:50.340 --> 00:02:52.280 if we connect this to the bigger picture, they 00:02:52.280 --> 00:02:54.780 were basically using a qualitative concept like 00:02:54.780 --> 00:02:57.979 beauty or goodness to represent a zero balance. 00:02:58.139 --> 00:03:00.919 That is so strange. It is. And they also use 00:03:00.919 --> 00:03:03.240 this exact same symbol in construction. Like 00:03:03.240 --> 00:03:04.900 if you look at ancient drawings of cooms and 00:03:04.900 --> 00:03:07.599 pyramids, NFR was used to indicate the base level. 00:03:07.639 --> 00:03:09.879 Oh, like the ground line? Exactly. The ground 00:03:09.879 --> 00:03:12.719 line. So distances were measured as above or 00:03:12.719 --> 00:03:16.620 below this NFR line. Ah, OK. So it was a state 00:03:16.620 --> 00:03:19.460 of being. It was a baseline. It wasn't actually 00:03:19.460 --> 00:03:21.759 a number you could add or subtract. Precisely. 00:03:21.780 --> 00:03:25.259 It was a reference point, not a quantity. And 00:03:25.259 --> 00:03:29.009 you see a very similar reluctance when you move 00:03:29.009 --> 00:03:31.289 over to Babylon. Right, the Babylonians. Yeah, 00:03:31.409 --> 00:03:33.830 but the second millennium BC, the Babylonians 00:03:33.830 --> 00:03:37.050 had incredibly sophisticated mathematics. I mean, 00:03:37.069 --> 00:03:39.409 they were using a base 60 system. Which, by the 00:03:39.409 --> 00:03:41.590 way, is exactly why we still have 60 seconds 00:03:41.590 --> 00:03:43.389 in a minute and 60 minutes in an hour today, 00:03:43.430 --> 00:03:44.909 right? Yeah, that's the one. It stuck around. 00:03:45.310 --> 00:03:49.129 But here is the catch. To indicate a zero value 00:03:49.129 --> 00:03:52.530 in a specific position, like distinguishing between 00:03:52.530 --> 00:03:55.710 the number 11 and the number 101. What did they 00:03:55.710 --> 00:03:58.780 do? They just... left a space. Wait, they literally 00:03:58.780 --> 00:04:01.479 just left a blank space on the clay tablet. A 00:04:01.479 --> 00:04:03.500 literal blank space. That seems like a terrible 00:04:03.500 --> 00:04:06.060 system for keeping records. It was. Which is 00:04:06.060 --> 00:04:09.340 why, later on, around 700 BC, scribes started 00:04:09.340 --> 00:04:11.439 using three little hooks as a placeholder to 00:04:11.439 --> 00:04:15.139 make it a bit clearer. And by 300 BC, they evolved 00:04:15.139 --> 00:04:18.529 that into two slanted wedges. But... And this 00:04:18.529 --> 00:04:21.389 is a really crucial distinction. These punctuation 00:04:21.389 --> 00:04:23.949 marks were strictly placeholders. They were never 00:04:23.949 --> 00:04:26.269 used alone. Right. You couldn't just write the 00:04:26.269 --> 00:04:28.209 wedges by themselves to mean the concept of zero. 00:04:28.449 --> 00:04:32.069 It sounds like early civilizations treated zero 00:04:32.069 --> 00:04:34.670 the way we treat a blank space in a crossword 00:04:34.670 --> 00:04:36.529 puzzle. Oh yeah, that's a good way to look at 00:04:36.529 --> 00:04:39.810 it. Like, the black squares separate the real 00:04:39.810 --> 00:04:42.189 words and they give the puzzle structure, but 00:04:42.189 --> 00:04:45.050 the black square itself isn't a word. That is 00:04:45.050 --> 00:04:48.209 a perfect analogy. It's structural. not substantive. 00:04:48.610 --> 00:04:51.329 And that distinction becomes the central conflict 00:04:51.329 --> 00:04:53.930 when we reach ancient Greece. Oh, the Greeks, 00:04:54.089 --> 00:04:56.269 they had some strong opinions. They really did. 00:04:56.670 --> 00:04:59.689 The Greeks had a deep, visceral, philosophical 00:04:59.689 --> 00:05:02.290 opposition to zero. I mean, they were obsessed 00:05:02.290 --> 00:05:05.949 with geometry, with shapes, with tangible realities 00:05:05.949 --> 00:05:07.889 you could actually draw in the sand. Right. So 00:05:07.889 --> 00:05:09.930 they looked at the idea of zero and asked this 00:05:09.930 --> 00:05:13.250 paralyzing question. How can not being be? Which 00:05:13.250 --> 00:05:15.649 honestly just sounds like a late night dorm room 00:05:15.649 --> 00:05:18.569 riddle. Yeah, totally. But for them, it was a 00:05:18.569 --> 00:05:21.790 hard roadblock. The sources say, and I'm quoting 00:05:21.790 --> 00:05:24.649 here, the whole of the Greek universe rested 00:05:24.649 --> 00:05:27.850 on this pillar. There is no void. Because if 00:05:27.850 --> 00:05:30.670 you admit that nothing is something, you essentially 00:05:30.670 --> 00:05:33.709 break their entire understanding of nature. Wow. 00:05:33.790 --> 00:05:36.509 This is actually what led to Zeno's famous paradoxes. 00:05:36.990 --> 00:05:39.670 Zeno essentially argued that motion is an illusion. 00:05:39.910 --> 00:05:42.269 Wait, really? How did he justify that? Well, 00:05:42.550 --> 00:05:44.990 he said to walk across a room, you first have 00:05:44.990 --> 00:05:47.470 to walk halfway. then half of that remaining 00:05:47.470 --> 00:05:49.610 distance, then half of that new distance. Right. 00:05:49.670 --> 00:05:52.509 You're constantly dividing space into infinitely 00:05:52.509 --> 00:05:55.550 smaller fractions. Exactly. And the Greeks feared 00:05:55.550 --> 00:05:59.089 that if an absolute void -like, a true zero existed 00:05:59.089 --> 00:06:01.550 between these fractions, the math would just 00:06:01.550 --> 00:06:03.290 break down. You'd fall into the void. You'd never 00:06:03.290 --> 00:06:05.470 actually reach your destination. So to them, 00:06:05.709 --> 00:06:08.709 admitting zero existed meant admitting that reality 00:06:08.709 --> 00:06:11.629 itself was fundamentally broken. Exactly. Now, 00:06:11.629 --> 00:06:13.629 there was one notable exception in the classical 00:06:13.629 --> 00:06:15.649 world, which was the astronomer Ptolemy around 00:06:15.649 --> 00:06:18.970 AD 150. He was heavily influenced by Babylonian 00:06:18.970 --> 00:06:22.110 data. Ptolemy was doing complex mathematical 00:06:22.110 --> 00:06:25.269 astronomy, trying to measure solar and lunar 00:06:25.269 --> 00:06:29.110 eclipses down to the minute of immersion. That's 00:06:29.110 --> 00:06:31.589 incredibly precise. It is. And to do that math, 00:06:31.769 --> 00:06:34.449 he needed a reliable placeholder. So he used 00:06:34.449 --> 00:06:37.129 the Greek letter Omicron with a line over it. 00:06:37.290 --> 00:06:39.589 Which is funny, because Omicron looks exactly 00:06:39.589 --> 00:06:42.430 like our modern zero. It's just a circle. It 00:06:42.430 --> 00:06:45.410 is. But even for Ptolemy, when calculating the 00:06:45.410 --> 00:06:47.470 exact magnitude of the moon passing over the 00:06:47.470 --> 00:06:49.649 sun, it was still just your crossword puzzle 00:06:49.649 --> 00:06:52.529 black square. Ah, gotcha. It meant an empty column 00:06:52.529 --> 00:06:55.269 in his data, but not nothingness as a standalone 00:06:55.269 --> 00:06:58.060 mathematical quantity. Essentially, the old world 00:06:58.060 --> 00:07:01.399 was stuck. Their philosophy just completely trapped 00:07:01.399 --> 00:07:03.879 their mathematics. So how does humanity actually 00:07:03.879 --> 00:07:05.819 break out of that trap? Because looking at the 00:07:05.819 --> 00:07:07.540 source, we don't just jump forward in time. We 00:07:07.540 --> 00:07:09.620 actually have to completely shift gears in terms 00:07:09.620 --> 00:07:12.439 of human needs. We do. We have to look at societies 00:07:12.439 --> 00:07:15.259 that weren't bogged down by all this Greek philosophy, 00:07:15.560 --> 00:07:18.120 but instead had a desperate practical need to 00:07:18.120 --> 00:07:20.689 measure deep time. We are heading across the 00:07:20.689 --> 00:07:23.370 ocean to the pre -Columbian Americas. It really 00:07:23.370 --> 00:07:25.569 is one of the most striking parallel inventions 00:07:25.569 --> 00:07:28.470 in human history. In Mesoamerica, they developed 00:07:28.470 --> 00:07:30.170 the long -count calendar. Okay, tell me about 00:07:30.170 --> 00:07:32.850 that. This was a vigesimal system, which basically 00:07:32.850 --> 00:07:35.509 means base 20. And if you are trying to make 00:07:35.509 --> 00:07:39.850 a base 20 calendar work across vast mythological 00:07:39.850 --> 00:07:42.709 expanses of time, spanning thousands of years, 00:07:43.430 --> 00:07:45.769 you absolutely require a reliable placeholder. 00:07:45.920 --> 00:07:48.259 just to keep your massive numbers aligned? Exactly. 00:07:48.360 --> 00:07:50.360 And because they didn't have old Greek guys yelling 00:07:50.360 --> 00:07:52.379 at them about the void, they just, you know, 00:07:52.480 --> 00:07:54.199 went ahead and invented it. So when did this 00:07:54.199 --> 00:07:57.439 happen? Incredibly early. The earliest date found 00:07:57.439 --> 00:08:01.019 on a stone stela in Chiapas, Mexico goes all 00:08:01.019 --> 00:08:05.379 the way back to 36 BC. Wow, 36 BC. Yeah. The 00:08:05.379 --> 00:08:08.199 Mayans and possibly the Olmecs before them were 00:08:08.199 --> 00:08:11.160 actively using zero. And what I love is how they 00:08:11.160 --> 00:08:13.990 represented it. They commonly used a glyph shaped 00:08:13.990 --> 00:08:16.610 like an empty tortoise -like shell. See, that 00:08:16.610 --> 00:08:18.750 feels like a massive conceptual upgrade from 00:08:18.750 --> 00:08:21.810 a Babylonian punctuation mark. A shell is a physical 00:08:21.810 --> 00:08:24.230 container. It's meant to hold something. Right. 00:08:24.410 --> 00:08:26.589 So showing it empty implies that the absence 00:08:26.589 --> 00:08:28.709 of something is actually a state worth measuring. 00:08:29.029 --> 00:08:31.529 It's a brilliant visual metaphor. And further 00:08:31.529 --> 00:08:34.049 south, the Incan Empire developed an entirely 00:08:34.049 --> 00:08:37.570 different, incredibly tactile system to solve 00:08:37.570 --> 00:08:40.149 the exact same problem. Yeah, this part of the 00:08:40.149 --> 00:08:42.570 source blew my mind. They didn't use writing 00:08:42.570 --> 00:08:45.309 as we know it. They used the kipu, which is a 00:08:45.309 --> 00:08:48.009 complex device made of knotted chords, to record 00:08:48.009 --> 00:08:50.350 accounting and data. This is just wild to me. 00:08:50.370 --> 00:08:53.149 It's a base 10 positional system, but it's literally 00:08:53.149 --> 00:08:55.389 made of string. Right. It's a spreadsheet made 00:08:55.389 --> 00:08:57.210 of string. Yeah. And how do you think they represented 00:08:57.210 --> 00:08:59.690 zero on a piece of string? I mean, following 00:08:59.690 --> 00:09:03.809 the logic, no string. Close. It was represented 00:09:03.809 --> 00:09:06.370 by the simple, deliberate absence of a knot in 00:09:06.370 --> 00:09:08.370 the appropriate position on the chord. Oh, I 00:09:08.370 --> 00:09:10.110 see. So if the hundredth position had a knot, 00:09:10.240 --> 00:09:12.860 And the ones position had a knot, but the tens 00:09:12.860 --> 00:09:15.480 position was just smooth cord. That smooth space 00:09:15.480 --> 00:09:18.419 was zero. Exactly. OK, this raises a really speculative 00:09:18.419 --> 00:09:20.600 question for me. If the Mayans and the Incas 00:09:20.600 --> 00:09:23.179 invented zero completely independently from the 00:09:23.179 --> 00:09:25.360 rest of the world just to make their calendars 00:09:25.360 --> 00:09:27.399 and their accounting work, does that mean the 00:09:27.399 --> 00:09:31.159 concept of zero is like a hardwired mathematical 00:09:31.159 --> 00:09:33.419 truth just waiting to be discovered? That's the 00:09:33.419 --> 00:09:35.000 million dollar question. Right. Or is it just 00:09:35.000 --> 00:09:38.500 a cultural invention? Well, that is the eternal 00:09:38.500 --> 00:09:40.159 debate about the nature of mathematics, isn't 00:09:40.159 --> 00:09:43.879 it? Is math invented or is it discovered? The 00:09:43.879 --> 00:09:46.240 fact that isolated cultures developed a placeholder 00:09:46.240 --> 00:09:49.899 for nothing strongly suggests that zero is a 00:09:49.899 --> 00:09:52.120 necessary structural truth of the universe. It 00:09:52.120 --> 00:09:54.919 definitely points that way. But here is the catch. 00:09:55.620 --> 00:09:58.600 To make the leap from a placeholder, like an 00:09:58.600 --> 00:10:02.120 empty shell or a missing knot, to an actual standalone 00:10:02.120 --> 00:10:04.679 mathematical entity that you can add, subtract, 00:10:04.899 --> 00:10:07.899 multiply, and divide for that, we have to travel 00:10:07.899 --> 00:10:11.200 back across the world to ancient India. Right, 00:10:11.340 --> 00:10:14.379 because this is where zero gets its true superpowers, 00:10:14.580 --> 00:10:16.580 where it goes from being just a missing piece 00:10:16.580 --> 00:10:19.179 to being a real player on the board. How does 00:10:19.179 --> 00:10:22.360 that transition actually happen? Slowly, and 00:10:22.360 --> 00:10:24.879 then all at once. We see early glimpses in the 00:10:24.879 --> 00:10:27.480 third or second century BC. There was a Sanskrit 00:10:27.480 --> 00:10:29.860 scholar named Pingala, who was analyzing the 00:10:29.860 --> 00:10:32.840 rhythms of poetry. To do this, he used binary 00:10:32.840 --> 00:10:35.360 sequences of short and long syllables, sort of 00:10:35.360 --> 00:10:37.879 like an early Morse code. And to mark his sequences, 00:10:38.279 --> 00:10:40.840 he explicitly used the Sanskrit word shinya, 00:10:41.100 --> 00:10:44.120 which translates directly to void or empty. Later 00:10:44.120 --> 00:10:46.759 on, we see the Bakhshali manuscript, which is 00:10:46.759 --> 00:10:49.620 an early arithmetic manual, and it used a solid 00:10:49.620 --> 00:10:52.350 black dot for zero. And there's physical evidence 00:10:52.350 --> 00:10:54.929 of this evolution too. Our source highlights 00:10:54.929 --> 00:10:57.950 this stone tablet found in the ruins of a temple 00:10:57.950 --> 00:11:02.830 in Cambodia dating to AD 683. Yes, the Sambor 00:11:02.830 --> 00:11:06.230 inscription. Right. It contains the number 605 00:11:06.230 --> 00:11:09.009 and right there in the middle is the oldest firmly 00:11:09.009 --> 00:11:12.289 dated use of zero as a decimal figure. Just a 00:11:12.289 --> 00:11:14.549 little circle. It's amazing to actually see it. 00:11:14.759 --> 00:11:17.559 But the real breakthrough, the moment zero became 00:11:17.559 --> 00:11:20.259 a true, manipulating number, happened in the 00:11:20.259 --> 00:11:23.019 7th century with the Indian mathematician Brahmagupta. 00:11:23.440 --> 00:11:25.360 Brahmagupta, what did he do differently? He didn't 00:11:25.360 --> 00:11:27.580 just write a symbol for zero. He established 00:11:27.580 --> 00:11:30.299 the actual mathematical rules for it. Oh, wow. 00:11:30.519 --> 00:11:32.659 He stated clearly that the sum of zero with itself 00:11:32.659 --> 00:11:35.519 is zero. He defined how it interacted with positive 00:11:35.519 --> 00:11:37.679 and negative numbers. He did have one little 00:11:37.679 --> 00:11:39.840 hiccup though, according to the article. Brahmagupta 00:11:39.840 --> 00:11:42.639 actually got division by zero wrong. He claimed 00:11:42.639 --> 00:11:45.379 that zero divided by zero was zero. He did, yeah. 00:11:45.620 --> 00:11:48.039 Division by zero is a notoriously tricky mechanism. 00:11:48.600 --> 00:11:51.019 It actually took until the 12th century for another 00:11:51.019 --> 00:11:54.179 Indian mathematician, Bhaskara II, to correct 00:11:54.179 --> 00:11:57.259 this. And what did he say? Bosco II stated that 00:11:57.259 --> 00:12:00.139 a quantity divided by zero actually becomes an 00:12:00.139 --> 00:12:02.120 infinite quantity. Okay, stop right there. I 00:12:02.120 --> 00:12:04.279 have to push back on this because this always 00:12:04.279 --> 00:12:08.139 hurts my brain. How can dividing a normal number 00:12:08.139 --> 00:12:11.320 by nothing magically equal infinity? Explain 00:12:11.320 --> 00:12:13.379 that to me like I'm five. Okay, think about it 00:12:13.379 --> 00:12:16.059 as a shrinking fraction. If you divide 1 by 0 00:12:16.059 --> 00:12:19.860 .1, you get 10. Right. You divide 1 by 0 .01, 00:12:19.860 --> 00:12:24.120 you get 100. If you divide 1 by 0 .0001, you 00:12:24.120 --> 00:12:26.950 get 10 ,000. OK, I'm a following. As the number 00:12:26.950 --> 00:12:29.269 you are dividing by gets closer and closer to 00:12:29.269 --> 00:12:32.370 absolute zero, the result just explodes. It gets 00:12:32.370 --> 00:12:35.269 closer and closer to infinity. Wow. OK, so the 00:12:35.269 --> 00:12:37.149 smaller the piece I'm trying to carve out, the 00:12:37.149 --> 00:12:39.129 more pieces I end up with, until I'm literally 00:12:39.129 --> 00:12:41.049 carving out nothing and I end up with everything. 00:12:41.649 --> 00:12:44.629 Exactly. And what's really amazing is how Bhaskara 00:12:44.629 --> 00:12:47.980 II explained this to his contemporaries. He didn't 00:12:47.980 --> 00:12:51.639 just use fractions, he used a really poetic theological 00:12:51.639 --> 00:12:54.480 analogy. Oh really? Yeah, he compared dividing 00:12:54.480 --> 00:12:57.799 by zero to the infinite and immutable God who 00:12:57.799 --> 00:13:00.440 remains unchanged no matter how many worlds are 00:13:00.440 --> 00:13:03.250 created or absorbed. That is fascinating. Wait, 00:13:03.409 --> 00:13:05.610 so the definitive mathematical rule for dividing 00:13:05.610 --> 00:13:08.830 by zero was explained using theology. Yep. It's 00:13:08.830 --> 00:13:10.909 like they needed the concept of an infinite god 00:13:10.909 --> 00:13:13.110 just to make sense of the math of nothing. It 00:13:13.110 --> 00:13:15.549 perfectly illustrates why the concept thrived 00:13:15.549 --> 00:13:18.049 in India while it struggled so hard in Greece. 00:13:18.629 --> 00:13:21.090 Indian philosophy already had a very comfortable, 00:13:21.090 --> 00:13:23.909 profound relationship with the concepts of the 00:13:23.909 --> 00:13:26.710 void. nothingness, and the infinite. Right. They 00:13:26.710 --> 00:13:28.450 weren't terrified of the void like the Greeks 00:13:28.450 --> 00:13:30.750 were. They embraced it. And because they embraced 00:13:30.750 --> 00:13:33.169 it culturally, they could finally define it mathematically. 00:13:33.889 --> 00:13:35.669 So we have this fully functioning number zero 00:13:35.669 --> 00:13:37.789 in India tied to the divine and the infinite. 00:13:37.950 --> 00:13:40.429 How does it get from there into, you know, my 00:13:40.429 --> 00:13:42.509 bank account today? Well, it followed the trade 00:13:42.509 --> 00:13:45.429 routes. Practicality usually wins out over philosophy 00:13:45.429 --> 00:13:48.600 in the end. In the 9th century, during the Islamic 00:13:48.600 --> 00:13:51.759 Golden Age, a Persian mathematician named Al 00:13:51.759 --> 00:13:55.039 -Khwarizmi was tasked with synthesizing Greek 00:13:55.039 --> 00:13:57.799 and Hindu knowledge. Al -Khwarizmi, wait, I know 00:13:57.799 --> 00:14:00.600 this. His translated name in Latin was algorithm, 00:14:01.179 --> 00:14:04.120 which is literally where the modern word algorithm 00:14:04.120 --> 00:14:06.620 comes from. That's the one. He wrote a groundbreaking 00:14:06.620 --> 00:14:09.080 book explaining the use of Hindu numerals, including 00:14:09.080 --> 00:14:12.519 zero. Okay. He instructed that if no number appears 00:14:12.519 --> 00:14:15.159 in the place of tens, a little circle should 00:14:15.159 --> 00:14:17.580 be used to keep the rows. And he called this 00:14:17.580 --> 00:14:20.399 little circle ifr, which was the direct Arabic 00:14:20.399 --> 00:14:23.279 translation of the Sanskrit word shunya, meaning 00:14:23.279 --> 00:14:26.500 empty. And then the baton gets passed to Europe, 00:14:26.980 --> 00:14:30.200 but not by a philosopher. by a guy named Fibonacci. 00:14:30.259 --> 00:14:32.980 Ah, yes. It's the year 1202. Fibonacci is an 00:14:32.980 --> 00:14:34.980 Italian mathematician, but he actually grew up 00:14:34.980 --> 00:14:37.940 in North Africa because his dad was a state official 00:14:37.940 --> 00:14:40.120 working in the customs house for merchants. Right, 00:14:40.159 --> 00:14:42.980 he had that exposure. So Fibonacci learns this 00:14:42.980 --> 00:14:45.779 Hindu -Arabic numeral system from Arab merchants, 00:14:45.899 --> 00:14:47.860 and he brings it back to Europe in his famous 00:14:47.860 --> 00:14:50.860 book, Lieber Abaci. Because he realized, quite 00:14:50.860 --> 00:14:53.759 rightly, that calculating with nine digits and 00:14:53.759 --> 00:14:57.539 this new sign for zero, was vastly superior to 00:14:57.539 --> 00:15:00.440 the clumsy Roman numerals everyone in Europe 00:15:00.440 --> 00:15:02.840 was still using for their accounting. I mean, 00:15:02.980 --> 00:15:05.080 put yourself in their shoes for a second. Imagine 00:15:05.080 --> 00:15:08.080 trying to do your taxes using Roman numerals, 00:15:08.279 --> 00:15:11.340 trying to multiply 7 by 14. It's an absolute 00:15:11.340 --> 00:15:14.299 nightmare. Your accountant would quit. Exactly. 00:15:14.720 --> 00:15:17.120 The merchants didn't care about the philosophical 00:15:17.120 --> 00:15:19.620 dread of the void. They just cared about balancing 00:15:19.620 --> 00:15:21.840 their ledgers quickly. Which is such an amazing 00:15:21.840 --> 00:15:24.220 irony. You have Greek philosophers agonizing 00:15:24.220 --> 00:15:26.320 over whether nothing can exist for centuries. 00:15:26.899 --> 00:15:29.299 But ultimately it was just traveling merchants 00:15:29.299 --> 00:15:32.100 and a customs official's kid who forced Europe 00:15:32.100 --> 00:15:34.860 to accept zero simply because it made bookkeeping 00:15:34.860 --> 00:15:37.240 easier. And we can actually trace the linguistic 00:15:37.240 --> 00:15:39.440 journey of this practical tool right into the 00:15:39.440 --> 00:15:42.000 English language. It's a really fascinating evolution. 00:15:42.440 --> 00:15:44.799 You start with the Sanskrit shunya. Right, meaning 00:15:44.799 --> 00:15:47.500 void. That gets translated to the Arabic eifer. 00:15:48.240 --> 00:15:51.269 Then when Fibonacci writes his book, He translates 00:15:51.269 --> 00:15:54.669 afer into Latin as zephyrum. Influenced by Zephyrus, 00:15:54.809 --> 00:15:57.610 the west wind, right? Correct. Then in the Venetian 00:15:57.610 --> 00:16:01.009 dialect, zephyrum contracts into zevro. And finally, 00:16:01.149 --> 00:16:02.690 they get shortened to the word we use today, 00:16:02.830 --> 00:16:05.840 zero. What a massive game of historical telephone. 00:16:06.419 --> 00:16:10.299 Shinya, Ifir, Zefram, Zevaro, Zero. So what does 00:16:10.299 --> 00:16:13.299 this all mean for us today? Because zero has 00:16:13.299 --> 00:16:15.440 completely transitioned from an accounting trick 00:16:15.440 --> 00:16:18.399 into something much bigger. It is essentially 00:16:18.399 --> 00:16:21.720 the DNA of our modern reality. Oh, without zero, 00:16:22.059 --> 00:16:24.580 higher mathematics simply collapses. It is the 00:16:24.580 --> 00:16:26.940 origin of the complex plane. It is the only real 00:16:26.940 --> 00:16:29.820 function that is both even and odd. Right. And 00:16:29.820 --> 00:16:32.039 one of the most beautiful quirks of math, the 00:16:32.039 --> 00:16:34.279 factorial of zero, which is written as a zero 00:16:34.279 --> 00:16:36.759 followed by an exclamation point, actually equals 00:16:36.759 --> 00:16:38.440 one. Wait, wait, wait. Full stop. I'm going to 00:16:38.440 --> 00:16:40.440 need another ELI -5 here. You're telling me the 00:16:40.440 --> 00:16:42.679 factorial of nothing equals something. How does 00:16:42.679 --> 00:16:44.620 that work? It sounds like a paradox, but it's 00:16:44.620 --> 00:16:48.019 about combinatorics. Yeah. Basically how we arrange 00:16:48.019 --> 00:16:49.759 things. A factorial tells you how many different 00:16:49.759 --> 00:16:52.149 ways you can arrange a set of items. Okay, track 00:16:52.149 --> 00:16:54.269 it. So the factorial of three is three times 00:16:54.269 --> 00:16:56.809 two times one, which equals six. There are six 00:16:56.809 --> 00:16:59.330 ways to arrange three items. Okay, following 00:16:59.330 --> 00:17:01.289 so and so. The factorial of two is two times 00:17:01.289 --> 00:17:03.250 one, which equals two. Two ways to arrange two 00:17:03.250 --> 00:17:05.910 items. Right. The factorial of one is one. There's 00:17:05.910 --> 00:17:08.529 only one way to arrange a single item. So what 00:17:08.529 --> 00:17:11.930 is the factorial of zero? How many ways can you 00:17:11.930 --> 00:17:15.970 arrange zero items on a desk? I mean, I guess 00:17:15.970 --> 00:17:17.829 there's only one way. You just leave the desk 00:17:17.829 --> 00:17:21.400 empty. Exactly. There is exactly one way to arrange 00:17:21.400 --> 00:17:25.059 nothing. Therefore, zero factorial equals one. 00:17:25.680 --> 00:17:28.339 It maintains the internal logic of the math perfectly. 00:17:28.559 --> 00:17:31.880 That is strangely poetic. And zero is so thoroughly 00:17:31.880 --> 00:17:34.619 embedded in our culture and language now. Like, 00:17:34.619 --> 00:17:36.779 we don't just use the word zero. Oh, definitely 00:17:36.779 --> 00:17:38.779 not. If you're reading a phone number or postcode, 00:17:38.880 --> 00:17:42.339 you'll probably just say, oh, we say zilch, zip, 00:17:42.559 --> 00:17:46.119 nada. In sports, it has its own slang. In cricket, 00:17:46.319 --> 00:17:48.440 a score of zero is a duck, which is short for 00:17:48.440 --> 00:17:50.380 a duck's egg. Yeah. And in tennis, if you have 00:17:50.380 --> 00:17:52.630 zero points, it's called love. Which actually 00:17:52.630 --> 00:17:54.869 likely comes from the French word l 'oeuf, meaning 00:17:54.869 --> 00:17:57.309 the egg. Again, they're referencing the physical 00:17:57.309 --> 00:18:00.170 round shape of the number zero. But where zero 00:18:00.170 --> 00:18:03.089 really flexes its modern superpowers, where it 00:18:03.089 --> 00:18:05.789 literally runs the world you and I live in, is 00:18:05.789 --> 00:18:09.130 in computer science. Modern computers store information 00:18:09.130 --> 00:18:12.130 in binary. The entire digital alphabet is just 00:18:12.130 --> 00:18:15.170 two symbols, one and zero. And that's not arbitrary 00:18:15.170 --> 00:18:17.430 at all. It represents the physical reality of 00:18:17.430 --> 00:18:20.500 the hardware. It's the presence or absence of 00:18:20.500 --> 00:18:23.059 electrical current in a microscopic wire. Exactly. 00:18:23.200 --> 00:18:25.500 One means the switch is on. Zero means the switch 00:18:25.500 --> 00:18:28.380 is off. Every website, every digital photo, every 00:18:28.380 --> 00:18:30.960 single piece of software is built on millions 00:18:30.960 --> 00:18:33.940 of micro decisions between something and nothing. 00:18:34.279 --> 00:18:36.220 And because humans and computers think differently, 00:18:36.500 --> 00:18:39.039 the quirks of zero show up everywhere in programming. 00:18:39.940 --> 00:18:42.059 Our source talks about this famous debate over 00:18:42.059 --> 00:18:44.589 zero based index. Yes, this is a classic. It's 00:18:44.589 --> 00:18:47.130 about how you count items in a list. Normal humans 00:18:47.130 --> 00:18:49.289 start counting at one. First item, second item, 00:18:49.349 --> 00:18:52.150 third item. Early programming languages like 00:18:52.150 --> 00:18:54.690 Fortran mirrored this and started counting at 00:18:54.690 --> 00:18:58.609 one. But languages like C, which heavily influenced 00:18:58.609 --> 00:19:01.170 modern computing, start counting at zero. So 00:19:01.170 --> 00:19:03.690 if you have a list of groceries in a computer 00:19:03.690 --> 00:19:06.990 program, the milk isn't item number one, it's 00:19:06.990 --> 00:19:09.390 item zero. Exactly. It represents an offset. 00:19:09.690 --> 00:19:12.230 How far away is this item from the start of the 00:19:12.230 --> 00:19:14.890 list? Well, the first item is zero steps away 00:19:14.890 --> 00:19:17.230 from the start. There's also the concept of the 00:19:17.230 --> 00:19:19.609 Unix epoch in computing. This one just blew my 00:19:19.609 --> 00:19:22.190 mind. Ah, yes. When a computer needs to know 00:19:22.190 --> 00:19:24.289 what time it is, it can't just look at the clock 00:19:24.289 --> 00:19:26.690 on the wall. it counts the seconds forward from 00:19:26.690 --> 00:19:29.890 a specific zero time stamp. Right. For Unix systems, 00:19:30.150 --> 00:19:32.869 which run most of the world's servers, time literally 00:19:32.869 --> 00:19:36.150 began at the midnight before January 1st, 1970. 00:19:36.369 --> 00:19:39.710 That is their big bang. January 1st, 1970 is 00:19:39.710 --> 00:19:42.269 zero. Which actually reminds me of another mind 00:19:42.269 --> 00:19:44.170 -bending fact from the dating system section 00:19:44.170 --> 00:19:46.650 of our source. When we look at our own human 00:19:46.650 --> 00:19:49.269 calendar, transitioning from BC to AD... There 00:19:49.269 --> 00:19:51.519 is no year zero. There is no year zero. It goes 00:19:51.519 --> 00:19:54.539 from 1 BC directly to 81. We just skipped it 00:19:54.539 --> 00:19:56.420 entirely. It feels absolutely absurd when you 00:19:56.420 --> 00:19:58.619 think about it. It really is. But it highlights 00:19:58.619 --> 00:20:02.119 how unnatural the concept of zero still was when 00:20:02.119 --> 00:20:05.220 the calendar was originally formalized. The monks 00:20:05.220 --> 00:20:07.920 creating the calendar just didn't have a concept 00:20:07.920 --> 00:20:09.900 for a zero year. So they just didn't include 00:20:09.900 --> 00:20:12.849 one. Nope. It wasn't until modern astronomers 00:20:12.849 --> 00:20:15.430 needed to calculate intervals backward in time 00:20:15.430 --> 00:20:18.490 that they had to force an astronomical year zero 00:20:18.490 --> 00:20:21.029 into existence just to make their math work. 00:20:21.829 --> 00:20:24.250 So, to summarize all of this, if numbers were 00:20:24.250 --> 00:20:27.130 a building, 1 through 9 are the bricks. They 00:20:27.130 --> 00:20:29.509 are the tangible things you can hold, stack, 00:20:29.670 --> 00:20:33.759 and count. But zero is the mortar. I love that. 00:20:33.900 --> 00:20:36.539 It's the invisible stuff, the nothingness, that 00:20:36.539 --> 00:20:38.839 holds the entire structure of mathematics and 00:20:38.839 --> 00:20:41.220 the digital age together. You just can't build 00:20:41.220 --> 00:20:43.480 a skyscraper without mortar. I think that's a 00:20:43.480 --> 00:20:45.700 brilliant way to frame it. I really want you, 00:20:45.720 --> 00:20:48.099 the listener, to think about this the next time 00:20:48.099 --> 00:20:50.779 you check a digital clock or type in a postcode 00:20:50.779 --> 00:20:53.819 or even just pause this audio file. Yeah, exactly. 00:20:53.960 --> 00:20:56.359 This very audio you are listening to right now 00:20:56.359 --> 00:20:59.359 is currently being processed by your device as 00:20:59.359 --> 00:21:01.940 a rapid -fire sequence of binary zeros and ones. 00:21:02.170 --> 00:21:05.890 You were relying on a concept that ancient empires 00:21:05.890 --> 00:21:08.710 actively fought against, that terrified Greek 00:21:08.710 --> 00:21:11.750 philosophers, and that Indian mystics had to 00:21:11.750 --> 00:21:14.470 tie to the concept of an infinite god just to 00:21:14.470 --> 00:21:17.470 make it comprehensible. It is a massive heavy 00:21:17.470 --> 00:21:20.630 legacy for just an empty circle. And I want to 00:21:20.630 --> 00:21:22.809 leave you with one final provocative thought 00:21:22.809 --> 00:21:25.680 from the source material. We've spent this whole 00:21:25.680 --> 00:21:28.680 deep dive talking about zero as a human invention, 00:21:29.000 --> 00:21:31.480 a cultural milestone that took us thousands of 00:21:31.480 --> 00:21:34.119 years to figure out. But cognitive science and 00:21:34.119 --> 00:21:36.240 biology have recently revealed something stunning. 00:21:36.940 --> 00:21:39.539 Certain animals, like crows and honeybees, actually 00:21:39.539 --> 00:21:41.559 display an awareness of the concept of zero. 00:21:41.660 --> 00:21:43.779 It's incredible. They have a numerical abstraction 00:21:43.779 --> 00:21:45.900 for nothing. Which completely upends the narrative. 00:21:45.960 --> 00:21:49.160 It really does. Exactly. So I leave you with 00:21:49.160 --> 00:21:51.859 this. If a tiny honeybee inherently understands 00:21:51.859 --> 00:21:55.099 nothingness, then was zero ever really a human 00:21:55.099 --> 00:21:57.220 invention? Or is it a fundamental law of the 00:21:57.220 --> 00:21:59.559 universe that we simply finally opened our eyes 00:21:59.559 --> 00:22:01.420 to? Think about that the next time you're looking 00:22:01.420 --> 00:22:02.279 at an empty table.