April 27, 2019 • 29 mins
Few 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.
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Speaker 1 (00:00):
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
(00:23):
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
(00:45):
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
(01:07):
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
(01:31):
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,
(01:53):
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
(02:14):
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
(02:38):
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
(03:01):
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
(03:22):
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
(03:44):
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
(04:06):
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,
(04:27):
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,
(04:50):
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,
(05:11):
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
(05:34):
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
(05:54):
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
(06:17):
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
(06:38):
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
(07:01):
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
(07:23):
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
(07:44):
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
(08:04):
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
(08:25):
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.
(08:48):
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
(09:08):
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,
(09:30):
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?
(09:51):
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,
(10:25):
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,
(10:49):
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
(11:10):
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
(11:30):
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,
(11:54):
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
(12:15):
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
(12:37):
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
(12:58):
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
(13:19):
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
(13:40):
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
(14:01):
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,
(14:21):
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,
(14:42):
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
(15:06):
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
(15:28):
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
(15:52):
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
(16:14):
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.
(16:34):
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
(16:55):
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,
(17:17):
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
(17:38):
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
(17:59):
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
(18:20):
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,
(18:41):
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
(19:03):
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
(19:23):
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
(19:48):
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,
(20:09):
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.
(20:31):
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
(21:09):
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
(21:30):
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.
(21:51):
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
(22:13):
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,
(22:35):
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.
(22:57):
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
(23:17):
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
(23:43):
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,
(24:05):
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
(24:25):
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,
(24:46):
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
(25:08):
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
(25:28):
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
(25:50):
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.
(26:15):
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,
(26:37):
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,
(26:59):
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
(27:22):
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
(27:44):
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.
(28:07):
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,
(28:29):
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?
(28:52):
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
(29:18):
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
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
(00:23):
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
(00:45):
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
(01:07):
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
(01:31):
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,
(01:53):
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
(02:14):
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
(02:38):
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
(03:01):
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
(03:22):
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
(03:44):
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
(04:06):
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,
(04:27):
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,
(04:50):
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,
(05:11):
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
(05:34):
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
(05:54):
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
(06:17):
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
(06:38):
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
(07:01):
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
(07:23):
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
(07:44):
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
(08:04):
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
(08:25):
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.
(08:48):
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
(09:08):
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,
(09:30):
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?
(09:51):
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,
(10:25):
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,
(10:49):
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
(11:10):
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
(11:30):
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,
(11:54):
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
(12:15):
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
(12:37):
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
(12:58):
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
(13:19):
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
(13:40):
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
(14:01):
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,
(14:21):
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,
(14:42):
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
(15:06):
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
(15:28):
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
(15:52):
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
(16:14):
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.
(16:34):
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
(16:55):
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,
(17:17):
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
(17:38):
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
(17:59):
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
(18:20):
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,
(18:41):
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
(19:03):
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
(19:23):
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
(19:48):
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,
(20:09):
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.
(20:31):
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
(21:09):
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
(21:30):
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.
(21:51):
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
(22:13):
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,
(22:35):
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.
(22:57):
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
(23:17):
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
(23:43):
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,
(24:05):
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
(24:25):
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,
(24:46):
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
(25:08):
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
(25:28):
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
(25:50):
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.
(26:15):
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,
(26:37):
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,
(26:59):
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
(27:22):
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
(27:44):
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.
(28:07):
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,
(28:29):
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?
(28:52):
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
(29:18):
is a production of iHeart Radios how stuff Works. For
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