Stuff You Should KnowFew numbers have as storied a past as zero. Even fewer have had as great an impact on our ability to understand our universe. Yet zero is a relatively recent arrival in math. Find out all about this surprisingly fascinating number with Chuck and Josh.
Learn more about your ad-choices at https://www.iheartpodcastnetwork.com
Hi there, how there, It's me Josh, your friend with this week's edition of s Y s K Selects. And for this week I've selected How Zero Works, a surprisingly riveting episode about Zero. You know, Zero, made famous by the phrase you better lose that zero and get yourself a hero. Well, it turns out Zero is pretty great in its own right. Just listen to this episode. Okay, enjoy. Welcome to Stuff you Should Know, a production of My Heart Radios How Stuff Works. Hey, and welcome to the podcast. I'm Josh Clark. There's Charles W. Chub Bryant, and this is a rare, unusual mathematical uh episode of the Stuff you Should Know. Yes, And I'm just gonna step out of the room and I'll be back in what minutes. You to do this? This is not going to be another Yo yo episode. Oh I just hate math. This was this was This is not math heavy at all. It's about the history of Zero. It's about the weirdness of Zero, my hero Zero. Exactly until you came a people counted on their fingers and toes. I posted that to down Facebook. I don't know what that is. The Schoolhouse rock, I don't know he ro Zero. I don't remember that one until you came along. Keep going it on her fingers and toes. It's basically you would appreciate it because it sings what you wrote. Oh, that's great in a much more basic way. But basically trying to teach kids how amazing zero is, and don't discount it as just it's a number. It's not the absence of something. Well, there's a lot, there's a bunch to it. It's many, many things. It's a multifaceted uh number, not the multifaceted entity. Well, nol is German for zero. Did you know that bub kiss is I believe Spanish for zero zilch silch is cajun. I did actually get a little etymology research. Originally sanscrit was sonya, which meant empty. Then later Arabriic was sepia or nothing, then Italian was sapio, and then finally French gave us zero, right, and it wasn't you know we represent zero as something that looks confusingly like an oh yeah right. That was the Europeans who did that. Prior to that, the Arabs and I believe the Indians too, um represented zero with a heavy dot. You know where that might have come from Robert Kaplan's book The Nothing That Is a Natural History of Zero. He speculates that the shape comes from the round depression left in the sand a sand counting board once you remove a stone from it, sence would be a round thing, That's what he he thinks, he speculates. But that wouldn't have haven't have been the Europeans. It was the Europeans that came up with that. Well no, but you said, uh like a heavy dot. Yeah, heavy do could be the depression where a stone was insane. That's a good one. Who was that, Robert Kaplan? Thanks? Mr Kaplan. Um, well, I guess I feel like we've kind of done a pretty good set up here, Chuck. We've talked about how zero is multifaceted, um, and you we talked about the Arabs and the Indians, right yeah, um, And we have to go back even further. Two first find when Zero made itself known? Should we get the way back machine? Let's I think, let's blow the dust off of this thing. Sorry, wow, that was right at you. I think this thing still works. Let's find out you're ready? Yeah, hey, look at their wow lit up like a flex capacitor. Is nice. Um, we're back in ancient Sumer and these baked clay tablets haven't even been baked yet. They're still wet. Look, wow was here? Um so Chuck. If you'll look at this clay tablet, do you see these two U diagonal lines, there's little wedges. Yeah, those, my friend, represent nothing really, And the reason they're there is because round about this time somebody figured out they ran into a problem and when they were making some sort of tax record or grain inventory that um, you know, showing that basically writing out three thousand lines for the three thousand heads of cattle doesn't make any sense. But let's say you have, um, three hundred, you have three thousand heads of cattle, and all you have are the ways to represent three hundred heads of cattle. There's a big difference, right, there's an extra digit in there, and that those two diagonal lines were used to represent one of those digits when there was not any digits there. But there's something to the left of it and something to the right of it, that's right. And Caplan also said that before that even they just would leave a blank space sometimes before they even came up with the little wedges, right, So what what this is all based on is basically our numerical system, where if you look at a string of numbers right, starting from the right, you have the ones column, the tens column, the hundreds, the thousands, the ten thousands, the hundred thousands, and so on. You want me to keep going ad infinitum um. And in each of these columns there may or may not be numbers present. So when there are numbers present, we have our friends zero to serve as what's considered a place holder. Yeah. Makes I mean it's very easy to just say, well, the now, but way back then before there was a zero that you know, we take it very much for granted. Yeah, this is huge. That's changed everything, changed everything, um, all of a sudden now because I mean we said there's a big difference between three thousand head of cattle and three head of cattle, and by putting a zero there right saying this this column is represented, there's just not any in here. You're not going to find the two cattle that should be in this right, that changed everything. It changed everything. I mean there was frustrating before that, Yeah, like if only there was something to put there. Yeah, And I guess when they like, just trust me, I have two thousand cattle. And I guess when they left the blank space that got confusing because they could have thought it was an error. So they figured we have to put something there so they know it's not just an oversight, right exactly. And that's the diagonal lines. Well in this, uh, I think before it even became that standardized, it was they used different things. Because they found a tablet from seven BC and a dude to use three little hooks to represent zero. Well that would have been after that, because the Sumerians were doing this like five thousand years ago. Well, it's probably hard to get the word around, right, you know, three hooks? What is this crowd? Exactly? Um. So the Sumerians are the first documented to to come up or stumble upon zero as a placeholder, and then it was um codified with the invention of the abbacus, which uses you know, our numerical column system, right we used today, um, which was invented by the Babylonians about three hundred BC. Wow, right, smart folks back then, So we have zero as a placeholder. We have this understanding now that there's there's something out there, like we can represent nothingness, but It wasn't until um, the fifth century a d in India where zero first comes about as a concept as a number, which is equally groundbreaking. Yeah. Well, this nothingness, we should point out, was not something that people were comfortable with back then. True, oddly now it seems odd, but to have something representing nothing made people very uncomfortable. It was associated with chaos and the great void and even the sign of the devil. Yes, it was. Well. I mean that if you look at the Christian theology, um, the void, which is represented by zero or nothingness, was the state of the universe before the creation of man. Humans. Uh seeks feel the same way too, although I don't know how they felt about zero, but that was there there. That's their conception as well. There was nothing, there's void, um. And then also void fits well with chaos, which is the Christian conception of hell, right, like no one's in charge, right. So yeah, it was avoided. I don't know. I went back and look, Chuck after I wrote this article, Um, when we were studying today, I went back and looked, and I didn't find a lot of support for that, didn't I did see that like the during the Dark Ages, monks kind of were Probably they feared zero. Well Kaplan mentioned it in his book, so, but I mean it was out there, but there's no well these people did this. They killed this guy for saying the word zero. There was nothing like that out there. I think. More more to the point, it was the Romans who just didn't use zero, and the West was built by Rome and um that's I think where the shunning of zero came from, not necessarily from fear, but just because the Roman numeral system doesn't have zero. Yeah. I found where. They flirted with it at first, with nulla in U l l A, which they would represent with a little inn, but it clearly didn't take. No, they said it, We're not gonna use it as zero. No, why would we ever need zero? We don't need it as zero? Right did they talk like that back then too? Yeah, like Vinny from Brooklyn, Sure, I think so. Uh So where are we in India? Yeah, we're in the fifth century a d in India and a guy named um Ariba is possibly the person who invented zero really possible or discovered as you like to say, thank you, yes, thank you for correcting me with my own words. That's when they are your articles. So UM, it is pretty pretty much universally accepted that zero was created or discovered in India, and then it spread pretty quickly over for UM two UH Islamic nations, Arab nations, UM, and the It was the Arabs who taught a guy named Fibonacci Leonardo Pizza, who was a great mathematician of the West in the I think the twelfth century or the thirteenth century. You know, people are gonna say, do the Fibonacci number. Go ahead, Well, no, no, no, people are gonna ask for that podcast. In fact, they've already been asking for that podcast. Do you want to do that one? Do you want to maybe? Probably not? Well, Fibonacci was um, the son of a customs officer in Algeria, Chuck, and he had Arabic tutors, and they said, hey, kid, we're gonna teach you how to really do math. Because by this time, by the I think the twelve hundreds UM or the eleven hundreds of the Salt century, UH, the Arabs were very well versed in mathematics and the West was still just complete idiots. Fortunately, Fibonacci was over there getting tutored and he figured out, wow, this is really really important, and introduced our Arabic numeral system which we used today, uh, to the West through a book. So you said he wrote a book. Did he write the book? No, he wasn't the only one. Okay, No, that's not true for the West. Yes, he wrote the book, and then other people wrote treatises on his book. So he pretty much said the basis. Yes, okay, he was the fulcrum, the hinge between West and Middle East. A zero is a fulcrum, Yes, it is interesting. Um. So he was the one who introduced it to the West. But again, I mean we say that because we're Western writers, chuck. But it was very well established for hundreds of years by the time Fibonaci heard about zero. Yeah. And you also point out interestingly that simultaneously and completely independently of India, uh, in Central America, the Maya were also uh beginning or already using zero yeah to uh, mainly for their calendar. Right. Yeah, it was there. It was the base of counting um, which makes sense. It totally makes sense, and it makes for a more accurate calendar. Right. So like for mine calendars, like the day of the month would be zero day, then one day than two day, than three day and so on. How would you say that though, because you say first, second third, how would you say they had um? They had different names for today, like Zula would be zul or you know, mon or something like that. It was like the rather than first second third. They didn't have numerals like that, like first second third that's Arabic. So to the Maya, it was like zul day. Didn't that Ghostbusters? I think so? But that was what Sumerian. Oh yeah, zul was Sumerians all coming together. Um. So that does make for a lot more accurate counting UM. And that's one of the big flaws in our calendar, the Gregorian calendar, is that there is no zero year. Well and we all got that pointed out to us quite uh through the through the media, especially when the millennium turned. Because there's no year zero, our decades and our centuries and our millennia um actually occur at the end of that year and at the beginning, Like when the clock struck midnight at two thousand and we all went, yeah, new millennium, not so we still had a year left, that's right. Have we started counting from zero then? Yeah? In January first two thousand that would have been the start of the new millennium. But the the we started counting from one so one to two thousand years rather than two thousand years. And there was one guy in every bar trying to point out to as many people as he could do you realize it's not even true, and he's like, why isn't anyone buying me drinks? So why did? Why are they going to beat me up? Um? And I put a little a little notation in there because I have trouble wrapping my head around that sometimes. But the point is is there's ten single digit numbers in the Arabic numerical system that we use, and at zero through nine, anything beyond that isn't in the tens columner above, and thanks to zero, we have a ten column exactly. Take a chuck. Uh. Well, Western astronomers they came up with a system late seventeenth and early eighteenth century that designated calendar year one b C is zero and then basically anything above or below that would either be plus or minus so a B C or a D right, so uh two a D would be minus one or no two BC would be minus one bc. Yes, since we're not living in a d They just kind of screwed with the BC a little bit. So right now we're in plus two thousand twelve. Yes, which also makes I mean, it's not just calendars. I mean zero lies between negative one and one and serves as a full corum point for basically all numbering. Yeah, positive and negative. And that was Jacques Cassini who came up with that, um astronomical calendar. What the Italians are all up on this stuff, weren't they. Yeah, it'soking to be French, but yeah it is an Italian. Yeah, who knows, maybe he's Northern Italian. Yeah, exactly. Um, but yeah, so they he basically said, well, wait, why don't we just choose one year to be zero, and then we'll just basically make it. We'll make the calendar based on zero's rightful place in numbering, which is precisely between one in negative one. There's a zero there. It doesn't just go from negative one to one. Zero is, like you said, the full crumb of all numbers. It spreads out infinitely on either side. So it's not positive and it's not negative, and um, so it's the only number that is non positive and non negative. But it's neither a positive number nor a negative number. Wrap your head around that one. Yeah, you college students sitting around here at midnight, just gaze up at the stars and try and figure that out. Start counting, Start counting. It's also an integer whole number, right, Yes, and h is very handy when it comes up to ratios and fractions, because a fraction can be written in a couple of ways, either with the one on top of the other or with a little decimal point. Yes, and without those zeros, you wouldn't be able to do that. No, So this decimal system, um, basically you can look at it as anything to the right of the decimal So that tends the hundreds, the thousands, right, the th ten, hundreds about thank you. Yeah, you're getting as bad as um. They those are all encapsulated in that zero that's up to positive one, right, yeah, because it's less than a whole one. But it's not so much that it's negative one, right, it's encapsulated by that zero. So all of these ratios, all of the decimal system, gives us these incredibly precise numbers. Whereas we can count in whole numbers to the right of zero in positive whole numbers that just goes on and on and on and measures the vastness of the universe. To go the other way, to go in this infinite decimal system that's encapsulated within zero, lets you measure the infantismal right, Yeah, so it's not like, oh it's between two and three, right, I mean, try making like high quality machine parts using whole numbers. You can't know, it can't be done. So there's all sorts of things that would have never taken place. Head zero not given rise to the decimal system, or everything would be really big. Yeah, you know, everything would be like twice as large, Like the ten thousand year clock wouldn't even work. Remember they were using like fractions of an inch that still wouldn't work. Um, what else, Chuck, Well, you point out very astute lee some odd properties of zero, and they are actually called the properties of zero because it's such a weird number that you have to have properties to explain it exactly. So the which is the first one called, is the additive property of zero row addition property. Yeah, add zero to anything and you're gonna get that same thing. That sounds very basic. Same with subtracting. Sure, five plus zeros five. Zero is five, right, and it is very basic. But zero is the only number that doesn't affect another number when it's added or subtracted to it, which is important. It is anytime a number is the only thing of its kind, it's worth mentioning. Like pie. There's um, which by the way, wouldn't exist without zero in the decimal system, or any of those wouldn't exist. To us. Um, there's the additive inverse property of zero, where any numbers that add up to zero are additive inverses of one another. So negative five plus positive five, or just five as they call it in positive land, equal zero. So negative five and five are additive inverses of one another. Multiplying from the time you're I think I learned in the second grade my multiplication tables, if I remember correctly, Ms. Anderson and Ms. Temple, thank you very much. Uh. They taught me that if you multiply any number by zero, you're going to get zero. And as you point out, that multiplication is really just a quicker way of adding things. It's a shortcut. Yeah, it's a shortcut. So uh. The idea that a number can be added zero times uh, or that zero can be added to itself. That's when I get the most. Yeah, it's just doesn't make any sense. Like you like five times zero doesn't mean zero place zero place ero place zero place ero, that doesn't mean anything zero. Yeah, right, what about dividing by zero? Let me ask you? No, let me This is the part where I was like, nobody understands this. I don't feel very bad about this because no one really understands it. Um, there's no So there's these other properties of zero that cover like additive, inverse, addition, subtracting, multiplication. There is no property that says why you can't divide by zero because it's so nonsensical. It doesn't even exist. The concept of dividing by zero doesn't really actually exist except in you know, the imagination of people. I bet mathematicians have tried, though, like frustratingly tried. You can't. There's nothing you can do, and they don't even fully understand why. But the um. The best explanation that I saw was that it has to do kind of with the multiplication property right to where if you divide something, so like six divided by two equals three, So if you can divide a number, Um, the result of that number by the divisor so in this case, three and two multiplied by one another should equal the dividend, which is six. Now if you divide six by zero, right, it doesn't equal anything. It should equal zero. If you multiply it, it's not gonna equal to Uh. That's the best example I could come up with. Yeah, that makes sense, so it shouldn't. Well, I mean, you're completely insane. It makes sense that it doesn't make sense. Okay, that's what I'm saying. And Stephen right head a joke. He said that black holes are where God tried to divide by zero. Wo. Like, that's good, Steven right his Uh, I still did that his one bit Sometimes when um, people get in a car with me, I say, hey, put your seat belt on. I want to try something. That was one of his jokes. He's like, just try that when the someone gets in a car, he's good. Um. And then also there's the property of zero exponent, which also doesn't make any sense. Chuck, there's um you know, there's negative exponents, like numbers to the negative power tend to the negative five. Yes, because of this, mathematically it works out, but I don't understand it. UM numbers to the zero power equal one. That doesn't make any sense because zero multiplied by something should equal zero, not one. That's how it works out, though, magical mysterious number at my hero zero and I ran across one other thing that I thought was pretty cool. Um. The the the evidence of UM Islamic countries comfort with zero concept and Western countries discomfort with it can be found still today on elevators in countries where the Ottoman Turks or UM any other Islamic nation UM conquered and ruled for a while, you're still going to find evidence of a comfort with zero, like in Hungary. If you look in Spain. I here too, if you look on an elevator, the ground floor is zero, and any floor beneath that is a negative number, really like the basement parking, like negative one, negative two. Huh isn't that cool? And apparently that's because of the presence of the Turks who were there for a while. Wow, yeah, I mean they didn't have elevators then, but apparently, like the that's like, you don't see a floor zero in the West, No, you don't. We just don't like zero that much or a fourth thirteen, all right, although it is thirteen. We've had that talk before. I think, yeah, what do we have here? P? One, P two in our building? Definitely not negative. Let's say that from now on, like what love you parked on? I'm on negative four, I will say that. I will say that right now, I'm on negative three. I'm on negative two. Go and chuck um. And also, let's see you can type zero. You got anything else? You're just happy to be done with this one? No, this was actually really good. Um, I don't know about that. Zero is my hero a magic number. If you type in zero and this is the search bar how stuff works dot Com, it will bring up this article, including a cool little story that we didn't get to about a great parent. True. Uh. And also I highly encourage if if this even piqued your interest at all, I highly encourage you to read zero in four Dimensions, which is an article you can find online from two Thou Too by a guy named Hassain Arsham, and he explains in much greater depth in detail like zero and what's so cool about it? Or if you want to really get into it, Robert Kaplan wrote a whole book on it, we should do one on three al right. I pitched that article a long time ago. A long time ago, remember on on three, I remember, so those would be our two. I'd have to write it down, so I don't know if it'll ever happened, get to it. I wrote this so we could do this. You're more of a man than me, um, I think at some point in the not too distant past, Chuck I said search bar, So that means it's time for listener mail. Indeed, I'm gonna call this, uh coffee including coffee song from a listener. Okay, this is from Ashley. Great work on the Coffee podcast, gents. I could have saved my last four years of work at a cafe just by listening to y'all. Really though, it was a splendid way to spend my days getting to know the locals in downtown Edmonton, Alberta, Canada, North America. Have we entered the song yet? Because she rhymed a second in case, no, that is not the song. Okay, that's coming. Uh, She's just a rhymer by nature. I think. While I can't say I'm a total coffee snobber expert, I do have a thought on the old wise Starbucks, so better debate. I think that part of the taste comes from the number of beans used in the blend. For instance, at the cafe I used to run, we served both Milano Coffee and then Umbria. I believe that each of these companies, plus a coffee I now drink called Intelligentsia, contains a blend of beans as many as fifteen different kinds to create that smooth balance I really love. In my americanos, it's her last name Starbuck. No no no, no, she's saying Starbucks doesn't use the blend, so it's more better. Her name is mom and pop her last name. As far as I understand, Starbucks may use this view as one to three types of beans and their espresso blend. Like I said, I think this may be a part of the story, but not likely the whole story. On another note, since leaving the cafe, I now work with a group of software nerds who used to visit my cafe on a regular basis. So now I too, get to go for coffee every day. It's one of the parks of the job, pun intended. We have, uh, we even have a little coffee song. And she recorded this and sent it to us, so we're going to play that right now. Coffee, coffee, coffee, coffee all day long. When I eat some coffee, I sing the coffee song. Well that's the g rated version I learned. So how about that, Josh, that was something else. Thank you Ashley for that. Yeah, thanks a lot, she says, As you can tell, we're a bit mad about our coffee drinking. It's the new smoke break for us. What, um, where where where is that person? She didn't say, Oh no, she did say, I'm sorry, Edmonton, Alberta's earth. That's right. Well, thank you very much for that. We appreciate you and um, your co workers for making that song, for listening, for drinking coffee, indeed for caring. That's great. Yeah. Um, if you have a song, Chuck. We get them from time to time and I feel like we should we should be better about playing them. Yes, Uh, we want to hear it. You can, I guess make it as like an MP three, MP four. MP three is good, right, Jerry? MP three? Uh, and uh you can send it to us. You can tweet to us and tell us it's on the way a s y SK podcast. You can go onto Facebook can tell us it's on the way. At Facebook dot com, slash stuff you Should Know, and you can actually send it to us at stuff podcast at how stuff works dot com. H Stuff you Should Know is a production of iHeart Radios how stuff Works. For more podcasts for my heart Radio, visit the iHeart Radio app, Apple Podcasts, or wherever you listen to your favorite shows. H
