WEBVTT - How Zero Works 0:00:00.280 --> 0:00:02.840 Brought to you by the reinvented two thousand twelve camera. 0:00:03.160 --> 0:00:07.560 It's ready. Are you welcome to Stuff You Should Know? 0:00:08.160 --> 0:00:16.360 From house stock Works dot Com. Hey, and welcome to 0:00:16.360 --> 0:00:19.599 the podcast. I'm Josh Clark, This Charles W. Chuck Bryant, 0:00:19.840 --> 0:00:25.640 and this is a rare, unusual mathematical uh episode of 0:00:25.640 --> 0:00:27.800 the Stuff you Should Know? Yes, And I'm just gonna 0:00:27.800 --> 0:00:29.520 step out of the room and I'll be back in 0:00:29.600 --> 0:00:33.080 what going to do this? This is not gonna be 0:00:33.120 --> 0:00:36.519 another yo yo episode. I I just hate math. This 0:00:36.560 --> 0:00:39.000 was this was This is not math heavy at all. 0:00:39.800 --> 0:00:42.599 It's about the history of zero. It's about the weirdness 0:00:42.640 --> 0:00:48.200 of zero, my hero zero exactly until you people counted 0:00:48.240 --> 0:00:51.479 on their fingers and toes. I posted that to down Facebook. 0:00:51.600 --> 0:00:54.240 I don't know what that is. The Schoolhouse rock. I 0:00:54.280 --> 0:00:57.360 don't know. He Rosiero. I don't remember that one until 0:00:57.440 --> 0:01:00.320 you came along. Keep going it on her fingers and those. 0:01:00.800 --> 0:01:04.600 It's basically you would appreciate it because it sings what 0:01:04.640 --> 0:01:08.280 you wrote. Oh, that's great in a much more basic way. 0:01:08.319 --> 0:01:11.120 But basically trying to teach kids how amazing zero is 0:01:11.240 --> 0:01:14.800 and don't discount it as just it's a number. It's 0:01:14.800 --> 0:01:18.319 not the absence of something. Well, there's a lot, there's 0:01:18.319 --> 0:01:20.640 a bunch to it. It's many many things. It's a 0:01:20.760 --> 0:01:29.280 multi faceted uh number, the multifaceted entity. Well, nol is 0:01:29.480 --> 0:01:33.600 German for zero, did you know that? But kiss is 0:01:33.680 --> 0:01:39.039 I believe Spanish for zero, zilch zilch is cajun. I 0:01:39.080 --> 0:01:44.800 did actually get a little etymology research. Originally Sanskrit was sonya, 0:01:45.160 --> 0:01:50.000 which meant empty. Then later arabrick was sepia or nothing. 0:01:50.720 --> 0:01:53.600 Then Italian was the foh, and then finally French gave 0:01:53.680 --> 0:01:57.920 us zero, right, and it wasn't you know we represent 0:01:58.040 --> 0:02:01.800 zero as something that looks confusingly like an oh yeah right. 0:02:02.240 --> 0:02:05.280 That was the Europeans who did that. Prior to that, 0:02:05.480 --> 0:02:09.840 the Arabs and I believe the Indians too, um represented 0:02:09.919 --> 0:02:14.440 zero with a heavy dot. You know where that might 0:02:14.440 --> 0:02:18.800 have come from Robert Kaplan's book The Nothing That is 0:02:19.200 --> 0:02:22.680 a Natural History of Zero. He speculates that the shape 0:02:22.720 --> 0:02:26.200 comes from the round depression left in the sand a 0:02:26.280 --> 0:02:29.280 sand counting board. Once you remove a stone from it, 0:02:31.560 --> 0:02:34.160 sence would be a round thing. That's what he he thinks, 0:02:34.160 --> 0:02:37.920 he speculates, But that wouldn't nevern't have been the Europeans 0:02:38.400 --> 0:02:40.600 because the Europeans that came up with that. Well no, 0:02:40.760 --> 0:02:43.639 but you said, uh, like a heavy dot. Yeah, a 0:02:43.680 --> 0:02:47.799 heavy dot could be the depression where a stone was insane. 0:02:48.160 --> 0:02:52.320 That's a good one. Who is that Robert Kaplan? Thanks? 0:02:52.400 --> 0:02:57.080 Mr Kaplan? Um? Well, I guess I feel like we've 0:02:57.160 --> 0:02:59.079 kind of done a pretty good set up here, Chuck. 0:02:59.160 --> 0:03:03.360 I think so. Do We've talked about how zero is multifaceted, um, 0:03:03.400 --> 0:03:08.560 and you we talked about the Arabs and the Indians, right, yeah, um, 0:03:08.639 --> 0:03:12.919 and we have to go back even further. Two. First, 0:03:14.000 --> 0:03:17.440 find when Zero made itself known to get the way 0:03:17.440 --> 0:03:21.000 back machine. Let's I think, let's blow the dust off 0:03:21.000 --> 0:03:26.119 of this thing that was right at you. I think 0:03:26.120 --> 0:03:30.800 this thing still works. Let's find out you're ready. Yeah, hey, 0:03:30.800 --> 0:03:37.640 look at their wow lit up like a flex capacitor. Um. 0:03:37.720 --> 0:03:41.440 We're back in ancient Sumer and these baked clay tablets 0:03:41.440 --> 0:03:43.920 haven't even been baked yet. It's still wet. Look, wow, 0:03:44.360 --> 0:03:50.480 Jo was here? Cool? Um, so Chuck, if you'll look 0:03:50.680 --> 0:03:54.640 at this clay tablet, do you see these two uh 0:03:54.880 --> 0:04:01.040 diagonal lines, these little wedges, those, my friend, represent nothing 0:04:01.600 --> 0:04:05.520 really and the reason they're there is because round about 0:04:05.520 --> 0:04:08.480 this time somebody figured out they ran into a problem 0:04:08.560 --> 0:04:11.480 and when they were making some sort of tax record 0:04:11.720 --> 0:04:17.520 or grain inventory that um, you know, showing that basically 0:04:17.680 --> 0:04:21.240 writing out three thousand lines there's a three thousand heads 0:04:21.240 --> 0:04:24.440 of cattle doesn't make any sense. But let's say you 0:04:24.480 --> 0:04:27.960 have UM three hundred. You have three thousand heads of cattle, 0:04:28.520 --> 0:04:31.200 and all you have are the ways to represent three 0:04:31.400 --> 0:04:35.240 hundred heads of cattle. There's a big difference, right, there's 0:04:35.240 --> 0:04:39.040 an extra digit in there, and that those two diagonal 0:04:39.080 --> 0:04:41.719 lines were used to represent one of those digits when 0:04:42.080 --> 0:04:44.760 there was not any digits there. But there's something to 0:04:44.800 --> 0:04:46.440 the left of it and something to the right of it. 0:04:47.000 --> 0:04:50.159 That's right. And Kaplan also said that before that even 0:04:50.920 --> 0:04:53.880 they just would leave a blank space, sometimes before they 0:04:53.880 --> 0:04:58.400 even came up with the little wedges. So what what 0:04:58.440 --> 0:05:02.280 this is all based on is basically our numerical system, 0:05:02.560 --> 0:05:04.880 where if you look at a string of numbers right, 0:05:05.600 --> 0:05:09.560 starting from the right, you have the ones column, the 0:05:09.640 --> 0:05:14.599 tens column, the hundreds, the thousands, the ten thousands, the 0:05:14.680 --> 0:05:16.680 hundred thousands, and so on. You want me to keep 0:05:16.720 --> 0:05:20.640 going at infinitum um and in each of these columns, 0:05:20.720 --> 0:05:23.280 there may or may not be numbers present. So when 0:05:23.360 --> 0:05:26.640 there are numbers present, we have our friends zero to 0:05:26.720 --> 0:05:30.039 serve as what's considered a placeholder. Yeah. Makes I mean 0:05:30.200 --> 0:05:35.920 it's very easy to just say, well, the now, but 0:05:36.120 --> 0:05:39.840 way back then before there was a zero that you know, 0:05:39.960 --> 0:05:42.320 we take it very much for granted. This is huge. 0:05:42.320 --> 0:05:45.360 That's changed everything, changed everything, um, all of a sudden 0:05:45.360 --> 0:05:47.320 now because I mean we said there's a big difference 0:05:47.360 --> 0:05:49.640 between three thousand head of cattle and three hundred head 0:05:49.680 --> 0:05:54.280 of cattle. And by putting a zero there right saying this, 0:05:54.279 --> 0:05:57.640 this column is represented, there's just not any in here. 0:05:57.680 --> 0:05:59.839 You're not gonna find the two cattle that should be 0:05:59.839 --> 0:06:03.800 in this, right, that changed everything. They changed everything. It 0:06:03.920 --> 0:06:06.479 made there was frustrating before that, Yeah, like if only 0:06:06.520 --> 0:06:10.240 there was something to put there. Yeah. And I guess 0:06:10.279 --> 0:06:12.760 when they like, just trust me, I have two thousand cattle. 0:06:13.160 --> 0:06:14.960 And I guess when they left the blank space that 0:06:15.080 --> 0:06:17.760 got confusing because they could have thought it was an error. 0:06:18.200 --> 0:06:21.200 So they figured we have to put something there so 0:06:21.240 --> 0:06:24.000 they know it's not just an oversight, right exactly. And 0:06:24.040 --> 0:06:27.440 that's the diaging the lines well in this Uh, I 0:06:27.440 --> 0:06:31.520 think before it even became that standardized. It was they 0:06:31.560 --> 0:06:34.640 use different things because they found a tablet from seven 0:06:35.320 --> 0:06:39.600 and a dude use three little hooks to represent zero. Well, 0:06:39.600 --> 0:06:42.120 that would have been after that, because the Sumerians were 0:06:42.120 --> 0:06:44.960 doing this like years ago. Well it's probably hard to 0:06:44.960 --> 0:06:48.000 get the word around, right, you know, three hooks. What 0:06:48.200 --> 0:06:52.240 is this crud? Exactly? Um, So the Sumerians of the 0:06:52.279 --> 0:06:56.680 first documented to to come up or stumble upon zero 0:06:56.720 --> 0:07:00.359 as a placeholder, and then it was codified with the 0:07:00.360 --> 0:07:04.080 invention of the advocus, which uses you know, our numerical 0:07:04.120 --> 0:07:07.440 column system like we used today, um, which was invented 0:07:07.440 --> 0:07:13.360 by the Babylonians about three right, smart folks back then. 0:07:13.520 --> 0:07:16.240 So we have zero as a placeholder. We have this 0:07:16.400 --> 0:07:19.040 understanding now that there's there's something out there like we 0:07:19.080 --> 0:07:23.960 can represent nothingness. But it wasn't until um, the fifth 0:07:23.960 --> 0:07:28.160 century a d in India where zero first comes about 0:07:28.160 --> 0:07:32.640 as a concept as a number, which is equally groundbreaking. Yeah. Well, 0:07:32.680 --> 0:07:35.120 this nothingness, we should point out, was not something that 0:07:35.160 --> 0:07:39.360 people were comfortable with back then. True, oddly now it 0:07:39.400 --> 0:07:44.080 seems odd, but to have something represent nothing made people 0:07:44.200 --> 0:07:47.840 very uncomfortable. It was associated with chaos in the Great 0:07:47.920 --> 0:07:51.800 void and even the sign of the devil. Yes, it was. Well, 0:07:51.840 --> 0:07:56.240 I mean the if you look at the Christian theology, um, 0:07:56.760 --> 0:08:01.120 the void, which is represented by zero or nothingness, was 0:08:01.200 --> 0:08:03.800 the state of the universe before the creation of man. 0:08:04.760 --> 0:08:07.960 Humans Uh seeks feel the same way too, although I 0:08:07.960 --> 0:08:10.400 don't know how they felt about zero, but that was 0:08:10.440 --> 0:08:13.040 there there. That's their conception as well. There was nothing, 0:08:13.040 --> 0:08:18.000 there's void. Um. And then also void fits well with chaos, 0:08:18.120 --> 0:08:21.440 which is the Christian conception of hell, like no one's 0:08:21.440 --> 0:08:25.240 in charge. So yeah, it was avoided. I don't know. 0:08:25.360 --> 0:08:28.320 I went back and look, Chuck after I wrote this article. Um, 0:08:28.360 --> 0:08:30.320 when we were studying today, I went back and looked, 0:08:30.320 --> 0:08:33.199 and I didn't find a lot of support for that. 0:08:33.880 --> 0:08:37.199 I did see that, like, um, the during the Dark Ages, 0:08:37.559 --> 0:08:41.280 monks kind of were probably they feared zero. Well Kaplan 0:08:41.280 --> 0:08:43.600 mentioned it in his books. But I mean, it was 0:08:43.640 --> 0:08:46.240 out there, but there's no well these people did this. 0:08:46.320 --> 0:08:48.600 They killed this guy for saying the word zero. There 0:08:48.679 --> 0:08:52.360 was nothing like that out there. I think. More more 0:08:52.400 --> 0:08:56.040 to the point, it was the Romans who just didn't 0:08:56.160 --> 0:09:01.600 use zero. And the West was built by Rome and um, 0:09:01.679 --> 0:09:05.319 that's I think where the shunning of zero came from 0:09:05.360 --> 0:09:08.800 not necessarily from fear, but just because the Roman numeral 0:09:08.840 --> 0:09:12.360 system doesn't have zero. Yeah. I found where they flirted 0:09:12.360 --> 0:09:16.280 with it at first, with the nullah in U l 0:09:16.400 --> 0:09:18.600 l A, which they would represent with a little N. 0:09:19.200 --> 0:09:22.360 But it clearly didn't take no, and they said it 0:09:22.400 --> 0:09:25.720 We're not gonna use it at zero. Why would we 0:09:25.760 --> 0:09:28.520 ever need zero? We don't need it as zero? Right 0:09:29.240 --> 0:09:31.720 Did they talk like that back then too? Yeah, like 0:09:31.800 --> 0:09:36.800 Vinny from Brooklyn, Sure, I think so. Uh So, where 0:09:36.840 --> 0:09:39.800 are we in India? Yeah, we're in the fifth century 0:09:40.080 --> 0:09:45.599 a d in India and a guy named um Arita. 0:09:45.840 --> 0:09:51.560 Arita is possibly the person who invented zero really possible 0:09:51.640 --> 0:09:54.480 or discovered as you like to say, thank you, Yes, 0:09:55.040 --> 0:09:57.640 thank you for correcting me with my own words. That's 0:09:57.720 --> 0:10:02.160 weird when they are your articles. So um, it is 0:10:02.240 --> 0:10:07.320 pretty pretty much universally accepted that zero was created or 0:10:07.520 --> 0:10:12.880 discovered in India, and then it spread pretty quickly over 0:10:13.440 --> 0:10:21.120 to uh Islamic nations, Arab nations, um and the It 0:10:21.200 --> 0:10:26.080 was the Arabs who taught a guy named Fibonacci Leonardo Pizza, 0:10:27.120 --> 0:10:30.200 who was a great mathematician of the West. In the 0:10:30.559 --> 0:10:33.160 I think the twelfth century or the thirteenth century. You know, 0:10:33.200 --> 0:10:38.000 people are gonna say, do the Fibonacci number. Well, no, no, no, 0:10:38.040 --> 0:10:41.080 people are gonna ask for that podcast. In fact, they've 0:10:41.120 --> 0:10:43.320 already been asking for that podcast. Do you want to 0:10:43.320 --> 0:10:48.280 do that one? Do you want to maybe? Probably not. Well, 0:10:48.320 --> 0:10:52.600 Fibonacci was um the son of a customs officer in Algeria, Chuck, 0:10:53.559 --> 0:10:56.760 and he had Arabic tutors and they said, hey, kid, 0:10:57.160 --> 0:10:59.680 we're gonna teach you how to really do math. Because 0:10:59.679 --> 0:11:03.040 by this time, by the I think the twelve hundreds 0:11:03.280 --> 0:11:06.839 UM or the eleven hundreds of the talt century, uh, 0:11:07.000 --> 0:11:10.000 the Arabs were very well versed in mathematics and the 0:11:10.040 --> 0:11:15.360 West was still just complete idiots. Fortunately, Fibonacci was over 0:11:15.360 --> 0:11:18.440 there getting tutored, and he figured out, wow, this is 0:11:18.600 --> 0:11:23.040 really really important and introduced our Arabic numeral system which 0:11:23.040 --> 0:11:25.959 we used today, uh, to the West through a book. 0:11:26.160 --> 0:11:27.920 So you said he wrote a book. Did he write 0:11:27.960 --> 0:11:31.719 the book? No, he wasn't the only one. Okay, no, 0:11:31.880 --> 0:11:34.960 that's not true for the West. Yes, he wrote the book, 0:11:35.000 --> 0:11:37.640 and then other people wrote treatises on his book. He 0:11:37.720 --> 0:11:43.559 pretty much he was the the fulcrum, the hinge between 0:11:43.720 --> 0:11:47.640 West and Middle East. Zero is a fulcrum, Yes, it 0:11:47.760 --> 0:11:51.240 is um. So he was the one who introduced it 0:11:51.320 --> 0:11:53.880 to the West. But again, I mean we say that 0:11:53.880 --> 0:11:57.160 because we're Western writers, chuck. But it was very well 0:11:57.280 --> 0:12:00.000 established for hundreds of years by the time Fibonacci heard 0:12:00.000 --> 0:12:02.920 about zero yeah. And you also point out interestingly that 0:12:03.040 --> 0:12:07.959 simultaneously and completely independently of India uh, in Central America, 0:12:08.040 --> 0:12:12.400 the Maya were also uh beginning or already using zero 0:12:12.880 --> 0:12:15.680 yeah to uh, mainly for their calendar, right, yeah, it 0:12:15.800 --> 0:12:19.400 was there. It was the base of counting um, which 0:12:19.400 --> 0:12:21.719 makes sense. It totally makes sense, and it makes for 0:12:21.760 --> 0:12:25.400 a more accurate calendar. Right. So like for mine calendars, 0:12:25.440 --> 0:12:27.520 like the day of the month would be zero day, 0:12:27.920 --> 0:12:30.040 then one day, than two day, than three day and 0:12:30.080 --> 0:12:32.160 so on. How would you say that though, because you 0:12:32.200 --> 0:12:35.199 say first, second third, how would you say they had um? 0:12:35.360 --> 0:12:39.960 They had different names for today, like Zula would be 0:12:40.160 --> 0:12:43.720 zul or you know, mon or something like that. It 0:12:43.800 --> 0:12:47.120 was like the rather than first, second third. They didn't 0:12:47.160 --> 0:12:50.440 have numerals like that, right, like first, second third that's Arabic, right, 0:12:50.880 --> 0:12:53.560 So to the Maya, it was like zul day, didn't 0:12:53.559 --> 0:12:57.080 that Ghostbusters. I think so, but that was what Sumerian 0:12:57.800 --> 0:13:01.559 Oh yeah, zul was Sumerians all come together. Um. So 0:13:01.720 --> 0:13:04.160 that does make for a lot more accurate counting UM. 0:13:04.240 --> 0:13:07.400 And that's one of the big flaws in our calendar, 0:13:07.480 --> 0:13:10.439 the Gregorian calendar, is that there is no zero year. 0:13:10.800 --> 0:13:13.719 Well and we all got that pointed out to us 0:13:13.800 --> 0:13:17.880 quite uh through the to the media, especially when the 0:13:17.960 --> 0:13:21.719 millennium turned because there's no year zero. Our decades in 0:13:21.800 --> 0:13:25.120 our centuries and our millennia um actually occur at the 0:13:25.240 --> 0:13:27.560 end of that year and at the beginning, like when 0:13:27.559 --> 0:13:30.800 the clock struck midnight at two thousand and we all went, yeah, 0:13:30.920 --> 0:13:33.960 new millennium, Not so, have we still had a year left? 0:13:34.559 --> 0:13:38.160 Have we started counting from zero? Then? Yeah? In January first, 0:13:38.160 --> 0:13:40.000 two thousand, that would have been the start of the 0:13:40.000 --> 0:13:43.560 new millennium. But the the we started counting from one, 0:13:43.679 --> 0:13:48.120 so one to two thousand nine years rather than two 0:13:48.160 --> 0:13:50.240 thousand years. And there was one guy in every bar 0:13:50.840 --> 0:13:52.880 trying to point out to as many people as he 0:13:52.920 --> 0:13:56.120 could do you realize it's not even true, and he's like, 0:13:56.160 --> 0:14:00.280 why isn't anyone buying me drinks? Why did are they 0:14:00.280 --> 0:14:04.880 going to beat me up? Um. And I put a 0:14:04.880 --> 0:14:08.520 little a little notation in there because I have trouble 0:14:08.559 --> 0:14:11.760 wrapping my head around that sometimes. But the point is 0:14:11.880 --> 0:14:17.640 there's ten single digit numbers in the Arabic numerical system 0:14:17.679 --> 0:14:21.280 that we use, and it's zero through nine. Anything beyond 0:14:21.360 --> 0:14:23.920 that isn't in the tens column er above, and thanks 0:14:23.960 --> 0:14:28.160 to zero, we have a ten column exactly. Take it, 0:14:28.280 --> 0:14:33.600 chuck uh. Well, Western astronomers they came up with a 0:14:33.680 --> 0:14:38.760 system late seventeenth and early eighteenth century that designated calendar 0:14:38.880 --> 0:14:42.120 year one b C is zero and then basically anything 0:14:42.200 --> 0:14:45.560 above or below that would either be plus or minus. 0:14:45.840 --> 0:14:49.480 So a B C or a D. Right, so uh 0:14:49.880 --> 0:14:52.960 two a D would be minus one or no two 0:14:52.960 --> 0:14:56.520 BC would be minus one BC. Yes, since we're not 0:14:56.640 --> 0:14:58.960 living in a D, they just kind of screwed with 0:14:59.000 --> 0:15:00.920 the BC a little bit. So right now we're in 0:15:00.960 --> 0:15:05.640 plus two thousand twelve, yes, which also makes I mean 0:15:06.320 --> 0:15:09.080 it's not just calendars. I mean zero lies between negative 0:15:09.120 --> 0:15:11.720 one and one and serves as a fulcrum point for 0:15:12.320 --> 0:15:16.400 basically all numbering, yeah, positive and negative. And that was 0:15:16.480 --> 0:15:19.920 Jacques Cassini who came up with that um astronomical calendar. 0:15:20.120 --> 0:15:23.240 What this Italians are all up on this stuff, weren't they. Yeah, 0:15:23.280 --> 0:15:24.960 it's talk going to be French, but yeah it is 0:15:24.960 --> 0:15:30.480 an Italian who knows, maybe northern Italian exactly. Um, but yeah, 0:15:30.560 --> 0:15:33.600 so they he basically said, well, wait, why don't we 0:15:33.640 --> 0:15:36.080 just choose one year to be zero and then we'll 0:15:36.120 --> 0:15:38.840 just basically make it. We'll make the calendar based on 0:15:38.920 --> 0:15:42.920 zero's rightful place of numbering, which is precisely between one 0:15:43.000 --> 0:15:46.000 and negative one. There's a zero there. It doesn't just 0:15:46.040 --> 0:15:48.640 go from negative one to one. Zero is, like you said, 0:15:48.640 --> 0:15:51.200 the full crumb of all numbers. It spreads out infinitely 0:15:51.200 --> 0:15:54.600 on either side. So it's not positive and it's not negative. 0:15:55.080 --> 0:15:58.640 And um, so it's the only number that is non 0:15:58.720 --> 0:16:01.480 positive and non negative if but it's neither a positive 0:16:01.560 --> 0:16:04.280 number nor a negative number. Wrap your head around that one. Yeah, 0:16:04.640 --> 0:16:07.960 you college students sitting around here at midnight, just gaze 0:16:08.040 --> 0:16:09.760 up at the stars and try and figure that out. 0:16:10.240 --> 0:16:15.320 Start counting, Start counting. It's also an integer, a whole number, right, Yes, 0:16:15.640 --> 0:16:18.360 And uh, it's very handy when it comes up to 0:16:18.600 --> 0:16:23.560 ratios and fractions, because a fraction can be written in 0:16:23.600 --> 0:16:25.560 a couple of ways, either with the one on top 0:16:25.600 --> 0:16:29.040 of the other or with a little decimal point. Yes, 0:16:29.320 --> 0:16:32.280 and without those zeros you wouldn't be able to do that. No, 0:16:32.520 --> 0:16:36.200 So the decimal system, um, basically you can look at 0:16:36.200 --> 0:16:41.480 it is anything to the right of the decimal So 0:16:41.560 --> 0:16:46.920 the tens, the hundreds, the thousands, right, the ten hundreds 0:16:46.920 --> 0:16:50.840 about thank you. Yeah, you're getting as bad as um 0:16:51.120 --> 0:16:54.520 they those are all encapsulated in that zero that's up 0:16:54.560 --> 0:16:58.200 to positive one, right, yeah, because it's less than a 0:16:58.200 --> 0:17:01.880 whole one. But it's not so much that it's negative one, right, 0:17:02.000 --> 0:17:05.280 it's encapsulated by that zero. So all of these ratios, 0:17:05.560 --> 0:17:10.199 all of the decimal system gives us these incredibly precise numbers, 0:17:10.200 --> 0:17:12.600 whereas we can count in whole numbers to the right 0:17:12.640 --> 0:17:15.719 of zero and positive whole numbers. That just goes on 0:17:15.800 --> 0:17:18.120 and on and on and measures the vastness of the universe. 0:17:18.640 --> 0:17:22.000 To go the other way, to go into infinite decimal 0:17:22.080 --> 0:17:27.600 system that's encapsulated within zero. Let you measure the infantismal right, yeah, 0:17:27.640 --> 0:17:30.360 so it's not like, oh it's between two and three, right, 0:17:30.400 --> 0:17:35.880 I mean, try making like high quality machine parts using 0:17:35.920 --> 0:17:38.439 whole numbers. You can't know. It can't be done. So 0:17:38.480 --> 0:17:40.600 there's all sorts of things that would have never taken 0:17:40.600 --> 0:17:43.399 place had zero not given rise to the decimal system, 0:17:43.480 --> 0:17:46.480 or everything would be really big, you know, everything would 0:17:46.480 --> 0:17:48.159 be like twice as large, Like the ten thousand year 0:17:48.200 --> 0:17:50.800 clock wouldn't even work. Remember they were using like fractions 0:17:50.840 --> 0:17:55.840 of an inch that still wouldn't work. Um, what else, Chuck, Well, 0:17:56.240 --> 0:17:59.680 you point out, very astute lee some odd properties of 0:17:59.760 --> 0:18:03.360 zero row and they are actually called the properties of zero, 0:18:03.600 --> 0:18:06.240 because it's such a weird number that you have to 0:18:06.280 --> 0:18:10.760 have properties to explain it exactly. So the which this 0:18:10.800 --> 0:18:15.560 person called is the additive property of zero property. Add 0:18:15.680 --> 0:18:17.800 zero to anything and you're gonna get that same thing. 0:18:17.960 --> 0:18:21.560 This sounds very basic, same with subtracting. Sure, five plus 0:18:21.680 --> 0:18:25.439 zeros five zero is five, right, and it is very basic. 0:18:25.520 --> 0:18:29.200 But zero is the only number that doesn't affect another 0:18:29.280 --> 0:18:32.760 number when it's added or subtracted to it, which is important. 0:18:33.119 --> 0:18:35.520 It is any time a number is the only thing 0:18:35.960 --> 0:18:40.160 of its kind, it's worth mentioning. Like pie. There's um, 0:18:40.240 --> 0:18:42.520 which by the way, wouldn't exist without zero in the 0:18:42.520 --> 0:18:47.080 decimal system, or any of those It wouldn't exist. To us, Um, 0:18:47.119 --> 0:18:51.359 there's the additive inverse property of zero, where any numbers 0:18:51.840 --> 0:18:55.920 that add up to zero are additive inverses of one another. 0:18:56.000 --> 0:19:01.199 So negative five plus positive five, or just five as 0:19:01.240 --> 0:19:04.639 they call it in positive land, equal zero. So negative 0:19:04.680 --> 0:19:08.199 five and five are additive inverses of one another. Multiplying 0:19:09.200 --> 0:19:11.240 from the time you're I think I learned in the 0:19:11.280 --> 0:19:15.159 second grade my multiplication tables. I remember correctly. Ms. Anderson 0:19:15.160 --> 0:19:20.040 and MS. Temple, Thank you very much. Uh. They taught 0:19:20.080 --> 0:19:22.880 me that if you multiply any number by zero, you're 0:19:22.920 --> 0:19:25.520 going to get zero. And as you point out, that 0:19:26.160 --> 0:19:31.720 multiplication is really just a quicker way of adding things, shortcut. Yeah, 0:19:31.720 --> 0:19:35.439 it's a shortcut. So the idea that a number can 0:19:35.480 --> 0:19:39.399 be added zero times uh, or that zero can be 0:19:39.440 --> 0:19:42.359 added to itself, that's when I get the most. Yeah, 0:19:42.440 --> 0:19:44.800 it's just doesn't make any sense. Like you like, five 0:19:44.840 --> 0:19:47.840 times zero doesn't mean zero plus zero. Plas zero place 0:19:47.880 --> 0:19:52.080 zero place zero. That doesn't mean anything zero, right, what 0:19:52.200 --> 0:19:56.160 about dividing by zero? Let me ask you. No, let 0:19:56.160 --> 0:19:57.959 me ask you. This is the part where I was like, 0:19:58.400 --> 0:20:01.320 nobody understands this. I don't feel very bad about this 0:20:01.359 --> 0:20:05.199 because no one actually understands it. Um, there's no So 0:20:05.280 --> 0:20:08.440 there's these other properties of zero that cover like additive 0:20:08.440 --> 0:20:12.760 inverse edition and subtracting multiplication. There is no property that 0:20:13.040 --> 0:20:16.120 says why you can't divide by zero because it's so 0:20:16.200 --> 0:20:19.719 nonsensical it doesn't even exist. The concept of dividing by 0:20:19.800 --> 0:20:24.280 zero doesn't really actually exist except in you know, the 0:20:24.320 --> 0:20:28.159 imagination of people. I bet mathematicians have tried, though, like 0:20:28.440 --> 0:20:33.000 frustratingly tried. You can't. There's nothing you can do, and 0:20:33.160 --> 0:20:37.040 they don't even fully understand why. But the um. The 0:20:37.080 --> 0:20:40.280 best explanation that I saw was that it has to 0:20:40.359 --> 0:20:43.240 do kind of with the multiplication property, right to where 0:20:43.280 --> 0:20:46.040 if you divide something, so like six divided by two 0:20:46.400 --> 0:20:50.200 equals three. So if you can divide a number, um, 0:20:50.440 --> 0:20:55.000 the result of that number by the divisor so in 0:20:55.040 --> 0:20:58.800 this case, three and two multiplied by one another should 0:20:58.840 --> 0:21:02.000 equal the dividend, which just six. Now, if you divide 0:21:02.040 --> 0:21:06.679 six by zero, right, it doesn't equal anything. It should 0:21:06.680 --> 0:21:11.760 equal zero if you multiply it, it's like an equal to. Uh. 0:21:11.880 --> 0:21:14.480 That's the best example I could come up with. Yeah, 0:21:14.520 --> 0:21:17.600 that makes sense, so it shouldn't. Well, I mean, you're 0:21:17.840 --> 0:21:21.159 completely insane. It makes sense that it doesn't make sense. Okay, 0:21:21.200 --> 0:21:23.320 that's what I'm saying, and Stephen might had a joke. 0:21:23.400 --> 0:21:25.439 He said that black holes are where God tried to 0:21:25.480 --> 0:21:35.480 divide by zero. You like, that's good Stephen, right his Uh, 0:21:35.600 --> 0:21:38.959 I still did that his one bit. Sometimes when UM 0:21:39.080 --> 0:21:40.920 people get in the car with me, I say, hey, 0:21:40.920 --> 0:21:42.560 put your seat belt on. I want to try something. 0:21:43.240 --> 0:21:44.840 That was one of his jokes. Nice, He's like, just 0:21:44.880 --> 0:21:48.320 try that whenever someone gets in a car. He's good. Um. 0:21:48.359 --> 0:21:50.680 And then also there's the property of zero exponent, which 0:21:50.680 --> 0:21:53.119 also doesn't make any sense. Chuck, there's UM. You know, 0:21:53.160 --> 0:21:56.320 there's negative exponents, like numbers to the negative power tend 0:21:56.359 --> 0:22:00.440 to the negative five because of this. Mathematically it works out, 0:22:00.520 --> 0:22:03.720 but I don't understand it. UM numbers to the zero 0:22:03.760 --> 0:22:07.280 power equal one. That doesn't make any sense because zero 0:22:07.400 --> 0:22:11.959 multiplied by something should equal zero, not one. That's how 0:22:12.000 --> 0:22:16.000 it works out. Though it's a magical, mysterious number. At 0:22:16.040 --> 0:22:18.760 my hero zero and I ran across one other thing 0:22:18.800 --> 0:22:22.119 that I thought was pretty cool. UM. The The the 0:22:22.240 --> 0:22:28.600 evidence of um Islamic countries comfort with zero concept and 0:22:28.680 --> 0:22:32.040 Western countries discomfort with it, can be found still today 0:22:32.119 --> 0:22:36.800 on elevators in countries where the Ottoman turks or UM 0:22:36.840 --> 0:22:41.080 any other Islamic nation um conquered and ruled for a while, 0:22:41.440 --> 0:22:43.960 you're still going to find evidence of a comfort with zero, 0:22:44.000 --> 0:22:47.600 like in Hungary. If you look in Spain, I here too, 0:22:47.720 --> 0:22:50.840 if you look on an elevator, the ground floor is zero. 0:22:51.119 --> 0:22:54.480 In any floor beneath that is a negative number, really 0:22:54.760 --> 0:22:59.520 like the basement parking, like negative one, negative two? Isn't 0:22:59.520 --> 0:23:03.239 that cool? And apparently that's because of the presence of 0:23:03.280 --> 0:23:05.480 the Turks who were there for a while. Wow, yeah, 0:23:05.600 --> 0:23:07.840 I mean they didn't have elevators then, but apparently, like 0:23:07.880 --> 0:23:11.159 the that's like, you don't see a floor zero in 0:23:11.200 --> 0:23:14.080 the West, No, you don't. We just don't like zero 0:23:14.160 --> 0:23:17.800 that much. Or a fourth thirteen right, although it is thirteen. 0:23:17.880 --> 0:23:21.119 We've had that talk before. I think, yeah, what do 0:23:21.160 --> 0:23:23.280 we have here? P one, P two in our building? 0:23:24.560 --> 0:23:27.040 Definitely not negatives. Let's say that from now on, Like 0:23:27.080 --> 0:23:29.960 what love you parked on? I'm on negative four, I 0:23:30.000 --> 0:23:32.200 will say that what I will say that right now, 0:23:32.240 --> 0:23:36.639 I'm on negative three. I'm on negative two. Go and 0:23:36.720 --> 0:23:41.480 chuck um. And also, let's see you can type zero. 0:23:41.840 --> 0:23:44.440 You got anything else? You're just happy to be done 0:23:44.440 --> 0:23:47.120 with this one? No, this was actually really good. Um, 0:23:47.160 --> 0:23:49.840 I don't know about that. Zero is my hero a 0:23:49.880 --> 0:23:53.639 magic number. If you type in zero and this the 0:23:53.680 --> 0:23:55.840 search bar how stuff works dot Com, it will bring 0:23:55.920 --> 0:23:58.680 up this article, including a cool little story that we 0:23:58.720 --> 0:24:03.040 didn't get to about a great parent. True. Uh. And 0:24:03.119 --> 0:24:06.119 also I highly encourage if if this even piqued your 0:24:06.160 --> 0:24:08.959 interest at all, I highly encourage you to read zero 0:24:09.080 --> 0:24:11.680 in four Dimensions, which is an article you can find 0:24:11.760 --> 0:24:15.440 online from two thousand to by a guy named Hassain Arsham, 0:24:15.480 --> 0:24:18.679 and he explains in much greater depth in detail like 0:24:19.119 --> 0:24:21.959 zero and what's so cool about it? Or if you 0:24:22.000 --> 0:24:24.720 want to really get into it, Robert Kaplan wrote a 0:24:24.720 --> 0:24:27.320