September 20, 2023 • 11 mins
Have you ever stopped mid-pencil mark and realized to your astonishment where the plus sign came from? Then this one’s for you.
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Speaker 1 (00:04):
Hey, and welcome to the Short Stuff. I'm Josh, and
there's Chuck, and this is short Stuff, and we are
going to talk about something that has been overlooked for
far too long, which is the origins of the plus
minus multiplication, division and equal symbols.
Speaker 2 (00:19):
I thought this was really cool by the way you
put this together with help from FASCO, cal Tech, Science ABC,
among other places. And I had never thought about this
stuff because I'm not a math person, but I love
origin stories, and I thought this is really neat, especially
the fact that these symbols came about to begin with,
(00:41):
because people before they had these. You wrote out a
math problem like this long word problem, but not like
you know, a train's traveling in this direction kind of thing.
It's more like I have divided ten into two parts
and multiplying one of these by the other. The results
was twenty one. Then you know that one of the
(01:03):
parts is thing and the other is ten minus thing.
Speaker 1 (01:07):
Right. That was an excerpt from a ninth century algebra
book by the mathematician Mohammed ibn Musai al Kharazmi. I'm
pretty sure that's his name. Today you would take that
same formula and write it out as x times ten
minus x equals twenty one.
Speaker 3 (01:27):
Yeah, so simple, that's it.
Speaker 1 (01:29):
And that reveals why these things were so important. It
just saves you so much time. So not only did
it make writing an algebra book that much more attractive,
it made teaching it that much faster. You might not
have necessarily learned it any faster, but you definitely could
teach these things faster with these notations rather than writing
(01:51):
it out. And I also saw check that some of
those sentences that they would write, some people would put
it into verse metered verse like poems. That takes a
lot of time, and it's unnecessary.
Speaker 2 (02:03):
Yeah, and especially at the time when you're writing with eagles,
feather and an ink. Weell sure, you know what I mean.
Speaker 1 (02:12):
That really drags too.
Speaker 3 (02:13):
It's not like you're just dashing this stuff off with
a pencil.
Speaker 1 (02:16):
Nope.
Speaker 3 (02:17):
So some folks came along and changed all that.
Speaker 2 (02:20):
According to the v NR Concise Encyclopedia of Mathematics hot Read,
the origin of the equal sign goes like this. A
man named Robert record or record A was the royal
court physician for King Edward about six and Queen Mary,
(02:40):
and a very influential mathematician in Wales, and he got
tired of writing out equals over and over, so he
thus proposed the equal sign because it is two little
equal lines, and that's parallel equal lines.
Speaker 3 (02:59):
And this I never thought it, but it's brilliant.
Speaker 1 (03:01):
Yeah, he said, a pair of parallels or twin lines
of one length, and then he spelled. He shows what
he's talking about, because no two things can be more equal.
And there's a lot of extra vowels in those words,
but yeah, he gets the point across. And he was saying, like,
this is such a great time saver. I'm so tired
of saying is equal to? And he wrote it in
(03:23):
a book called The Wetstone of Wit, And of course
a whetstone is what you sharpened things with, so it
sharpens your wit to read this book. I love that title,
and it actually became very influential and well read as
far as sixteenth century math books go. And Robert Record
is credited with coming up with the minus symbol and
introducing it to his people back then.
Speaker 3 (03:43):
The equal sign.
Speaker 1 (03:44):
You mean what I say?
Speaker 3 (03:45):
Minus sign? Oh just wait, chuck, all right, well we're there.
Speaker 2 (03:50):
Plus and minus are what we use to indicate adding
something and subtracting something. As everyone knows they come. The
terms themselves come from Latin, where plus means more and
minus means less. And the other thing is the plus
symbol itself is also from the Latin word et et,
(04:12):
meaning and like this and that equals that, which is
pretty great. So at one point there was a French
philosopher named Nicole ors Me from the fourteenth century who
used that plus sign as a shorthand for et, which
is what they used to write. And at first it
(04:33):
didn't take right, I think, like people weren't universally accepting this.
Speaker 1 (04:38):
Yeah, it wasn't until like the sixteenth or seventeenth century
that it started to really kind of take off. I
think the sixteenth century, Okay, And apparently there was competition
at first too, that it wasn't just the plain old
plus sign that equal cross, that there were other crosses
in the in the running too, including the Maltese cross.
It's a great looking cross, yeah, but it takes a
(05:00):
lot more time to write the Maltese cross out than
it does to make a plus symbol, and the whole
point of these things was to save time. So everybody said, yeah,
Maltese cross, we like you. But we're gonna go with
the plus sign.
Speaker 3 (05:12):
That's right.
Speaker 2 (05:12):
So that's plus, we got equals, we got plus minus.
Now in Europe there was an Italian mathematician named Luca Pacioli,
and Luca was using the symbol P with a little
line over it for plus, an M with a little
line of it over it for minus. And no one's
exactly sure, but it seems to be that the M
(05:37):
was just dropped right, and then the minus sign, because
we already had a plus sign, became the minus sign.
Speaker 1 (05:43):
Yeah, so you don't need the plus sign forget you
P with the tilbey over it. We're gonna take the
M instead. And it was it wasn't Robert Record who
came up with that, but he was the one who
introduced it.
Speaker 3 (05:56):
To England, right, And I never knew it was called
it tild.
Speaker 1 (06:01):
I didn't either that line over the P or the M. Yeah,
I think that's what they call it, so yeah, And
I don't know if it's the minus sign itself is
called that, or if it has to be over the
letter to be called that.
Speaker 2 (06:14):
All right, Well, there are a couple of other words
that I did not know coming up right after the break,
(06:41):
all right, we're gonna wind it out with the multiplication
symbol and the division symbol multiplication. If you say it's
a little X, you're incorrect because it is not an X.
It's actually called the Cross of San Andreas because X.
Well not because, but it would be very confusing because
X is already a thing in math, Like you're solving
(07:02):
for X. X represents something in math, So it's it's
actually incorrect to say it's a little X.
Speaker 1 (07:08):
Yeah, if you do that at a math conference, they
will find the nearest fire hose and flood you mercilessly
with it.
Speaker 3 (07:14):
They will.
Speaker 1 (07:15):
So, yeah, that makes total sense. And it was a
guy named William Autred who was writing in I think
the sixteenth century, like the sixteen thirties, and he was
the one who introduced it. He's credited with this. But
the people at Science ABC went to the trouble of
digging up the fact that there's an anonymous appendix in
(07:39):
a translation of another book of logarithms from sixteen eighteen
where the Cross of San Andreas is first used.
Speaker 2 (07:48):
Okay, so, but he introduced it in before that, right, no.
Speaker 1 (07:53):
After, But since it was anonymous in the appendix, they
don't know who to credit it with, and I said,
you need to win today. We're going to with that.
Speaker 2 (08:05):
I mentioned before the break that there were a couple
of more words that I didn't realize were words, and
that is the the division symbol that apparently I didn't
even know this is not even really used anymore officially,
which is to say, the line like the minus symbol
with a dot above it and a dot below it
(08:25):
in the center, that is actually called an obelis.
Speaker 1 (08:29):
Yeah, that symbol. You know what, it reminds me of
of that calculator that was shaped like a big plastic owl. Oh,
that's what I associate that with. I remember those, But
I didn't know it was called an obelis either. And
I also didn't know that obelis is an old Greek
word for sharpened stick, and that that division symbol, the
obelis is supposed to represent a small dagger.
Speaker 3 (08:49):
Yeah, it looks like one.
Speaker 1 (08:51):
So I guess what it's doing is it's cutting in half.
It's cutting a portion out. Ah, that's the only thing
I can come up with.
Speaker 3 (08:58):
Okay, I like that though, sure.
Speaker 1 (09:00):
And we can thank Johann Ron, who's Swiss not Swedish,
who started using it all the way back in sixteen
fifty nine.
Speaker 3 (09:07):
That's right.
Speaker 2 (09:08):
The other word I did not know is the what
is now the backslash symbol for division is called a
either a fraction bar or a solidus.
Speaker 1 (09:19):
Yeah, didn't know that either.
Speaker 2 (09:21):
I didn't know that that was the exclusive thing. Now,
this is how out of touch with matth iron.
Speaker 1 (09:25):
Yeah. Apparently the ISO, the International Organization for Standardization, who
aren't familiar with how to create an acronym. They said
that you could only use the solidus or the fraction
bar to indicate division, and that the obelis is out
out out. But Science ABC said, don't worry everybody. Listen,
(09:46):
if you go on to your keyboard, you know what's weird.
I haven't tried this. Did you try it?
Speaker 2 (09:50):
No?
Speaker 1 (09:51):
I'm going to try it right now. Why don't you
go ahead and tell everybody what you're supposed to do
and I'm going to try it myself.
Speaker 2 (09:56):
Chuck, Well, what you do is you hold the alt
key on your keyboard and then press two four to
six on the number pad.
Speaker 3 (10:05):
And what do we got? My friend?
Speaker 1 (10:07):
I think maybe you have to press it at once,
hold on two four six. You got lies? That's what
you got Chuck thirty lies.
Speaker 2 (10:15):
Oh well, let me try then you talked for a second.
Speaker 1 (10:18):
Okay, So I'm going to do it again, two four
six with all pressed at the same time in Microsoft Word.
The current version of Microsoft Word won't do it.
Speaker 3 (10:32):
I don't even know if I have Word on this laptop.
Speaker 1 (10:35):
The thing that gives it away for why I think
this might not be correct any longer, is that they
mentioned that you press the numbers two four six on
your number pad. Remember when numbers used to be off
to the side on a keyboard and their own thing.
Speaker 2 (10:50):
Well, I've got a keyboard like that. Okay, let me
let me try it for you. So all to two
four six.
Speaker 1 (10:55):
Yeah, I think at the same time.
Speaker 2 (10:58):
Oh that's hard to do. I'm trying to, like fingering
a weird guitar chord that didn't work alt two for six.
Speaker 3 (11:05):
Right, this is just bs.
Speaker 1 (11:09):
They got us, Chuck. They got us as good as
Debbie Ranka did with that whole thing about Judas spilling
the salt shaker in the Last Supper.
Speaker 2 (11:17):
Wait, let me try one more thing, two for six.
Now it's not working.
Speaker 1 (11:21):
Okay. Well, I'm sorry everybody that we misled you, but
I'm glad we worked it out so you don't have
to email us about it.
Speaker 3 (11:27):
Yeah.
Speaker 2 (11:27):
Maybe someone knows though, and can tell us what we're
doing wrong.
Speaker 1 (11:31):
Yeah, we love hearing that, and while we wait for
you to write in short, stuff is out.
Speaker 3 (11:41):
Stuff you Should Know is a production of iHeartRadio. For
more podcasts my heart Radio, visit the iHeartRadio app, Apple Podcasts,
or wherever you listen to your favorite shows.
Hey, and welcome to the Short Stuff. I'm Josh, and
there's Chuck, and this is short Stuff, and we are
going to talk about something that has been overlooked for
far too long, which is the origins of the plus
minus multiplication, division and equal symbols.
Speaker 2 (00:19):
I thought this was really cool by the way you
put this together with help from FASCO, cal Tech, Science ABC,
among other places. And I had never thought about this
stuff because I'm not a math person, but I love
origin stories, and I thought this is really neat, especially
the fact that these symbols came about to begin with,
(00:41):
because people before they had these. You wrote out a
math problem like this long word problem, but not like
you know, a train's traveling in this direction kind of thing.
It's more like I have divided ten into two parts
and multiplying one of these by the other. The results
was twenty one. Then you know that one of the
(01:03):
parts is thing and the other is ten minus thing.
Speaker 1 (01:07):
Right. That was an excerpt from a ninth century algebra
book by the mathematician Mohammed ibn Musai al Kharazmi. I'm
pretty sure that's his name. Today you would take that
same formula and write it out as x times ten
minus x equals twenty one.
Speaker 3 (01:27):
Yeah, so simple, that's it.
Speaker 1 (01:29):
And that reveals why these things were so important. It
just saves you so much time. So not only did
it make writing an algebra book that much more attractive,
it made teaching it that much faster. You might not
have necessarily learned it any faster, but you definitely could
teach these things faster with these notations rather than writing
(01:51):
it out. And I also saw check that some of
those sentences that they would write, some people would put
it into verse metered verse like poems. That takes a
lot of time, and it's unnecessary.
Speaker 2 (02:03):
Yeah, and especially at the time when you're writing with eagles,
feather and an ink. Weell sure, you know what I mean.
Speaker 1 (02:12):
That really drags too.
Speaker 3 (02:13):
It's not like you're just dashing this stuff off with
a pencil.
Speaker 1 (02:16):
Nope.
Speaker 3 (02:17):
So some folks came along and changed all that.
Speaker 2 (02:20):
According to the v NR Concise Encyclopedia of Mathematics hot Read,
the origin of the equal sign goes like this. A
man named Robert record or record A was the royal
court physician for King Edward about six and Queen Mary,
(02:40):
and a very influential mathematician in Wales, and he got
tired of writing out equals over and over, so he
thus proposed the equal sign because it is two little
equal lines, and that's parallel equal lines.
Speaker 3 (02:59):
And this I never thought it, but it's brilliant.
Speaker 1 (03:01):
Yeah, he said, a pair of parallels or twin lines
of one length, and then he spelled. He shows what
he's talking about, because no two things can be more equal.
And there's a lot of extra vowels in those words,
but yeah, he gets the point across. And he was saying, like,
this is such a great time saver. I'm so tired
of saying is equal to? And he wrote it in
(03:23):
a book called The Wetstone of Wit, And of course
a whetstone is what you sharpened things with, so it
sharpens your wit to read this book. I love that title,
and it actually became very influential and well read as
far as sixteenth century math books go. And Robert Record
is credited with coming up with the minus symbol and
introducing it to his people back then.
Speaker 3 (03:43):
The equal sign.
Speaker 1 (03:44):
You mean what I say?
Speaker 3 (03:45):
Minus sign? Oh just wait, chuck, all right, well we're there.
Speaker 2 (03:50):
Plus and minus are what we use to indicate adding
something and subtracting something. As everyone knows they come. The
terms themselves come from Latin, where plus means more and
minus means less. And the other thing is the plus
symbol itself is also from the Latin word et et,
(04:12):
meaning and like this and that equals that, which is
pretty great. So at one point there was a French
philosopher named Nicole ors Me from the fourteenth century who
used that plus sign as a shorthand for et, which
is what they used to write. And at first it
(04:33):
didn't take right, I think, like people weren't universally accepting this.
Speaker 1 (04:38):
Yeah, it wasn't until like the sixteenth or seventeenth century
that it started to really kind of take off. I
think the sixteenth century, Okay, And apparently there was competition
at first too, that it wasn't just the plain old
plus sign that equal cross, that there were other crosses
in the in the running too, including the Maltese cross.
It's a great looking cross, yeah, but it takes a
(05:00):
lot more time to write the Maltese cross out than
it does to make a plus symbol, and the whole
point of these things was to save time. So everybody said, yeah,
Maltese cross, we like you. But we're gonna go with
the plus sign.
Speaker 3 (05:12):
That's right.
Speaker 2 (05:12):
So that's plus, we got equals, we got plus minus.
Now in Europe there was an Italian mathematician named Luca Pacioli,
and Luca was using the symbol P with a little
line over it for plus, an M with a little
line of it over it for minus. And no one's
exactly sure, but it seems to be that the M
(05:37):
was just dropped right, and then the minus sign, because
we already had a plus sign, became the minus sign.
Speaker 1 (05:43):
Yeah, so you don't need the plus sign forget you
P with the tilbey over it. We're gonna take the
M instead. And it was it wasn't Robert Record who
came up with that, but he was the one who
introduced it.
Speaker 3 (05:56):
To England, right, And I never knew it was called
it tild.
Speaker 1 (06:01):
I didn't either that line over the P or the M. Yeah,
I think that's what they call it, so yeah, And
I don't know if it's the minus sign itself is
called that, or if it has to be over the
letter to be called that.
Speaker 2 (06:14):
All right, Well, there are a couple of other words
that I did not know coming up right after the break,
(06:41):
all right, we're gonna wind it out with the multiplication
symbol and the division symbol multiplication. If you say it's
a little X, you're incorrect because it is not an X.
It's actually called the Cross of San Andreas because X.
Well not because, but it would be very confusing because
X is already a thing in math, Like you're solving
(07:02):
for X. X represents something in math, So it's it's
actually incorrect to say it's a little X.
Speaker 1 (07:08):
Yeah, if you do that at a math conference, they
will find the nearest fire hose and flood you mercilessly
with it.
Speaker 3 (07:14):
They will.
Speaker 1 (07:15):
So, yeah, that makes total sense. And it was a
guy named William Autred who was writing in I think
the sixteenth century, like the sixteen thirties, and he was
the one who introduced it. He's credited with this. But
the people at Science ABC went to the trouble of
digging up the fact that there's an anonymous appendix in
(07:39):
a translation of another book of logarithms from sixteen eighteen
where the Cross of San Andreas is first used.
Speaker 2 (07:48):
Okay, so, but he introduced it in before that, right, no.
Speaker 1 (07:53):
After, But since it was anonymous in the appendix, they
don't know who to credit it with, and I said,
you need to win today. We're going to with that.
Speaker 2 (08:05):
I mentioned before the break that there were a couple
of more words that I didn't realize were words, and
that is the the division symbol that apparently I didn't
even know this is not even really used anymore officially,
which is to say, the line like the minus symbol
with a dot above it and a dot below it
(08:25):
in the center, that is actually called an obelis.
Speaker 1 (08:29):
Yeah, that symbol. You know what, it reminds me of
of that calculator that was shaped like a big plastic owl. Oh,
that's what I associate that with. I remember those, But
I didn't know it was called an obelis either. And
I also didn't know that obelis is an old Greek
word for sharpened stick, and that that division symbol, the
obelis is supposed to represent a small dagger.
Speaker 3 (08:49):
Yeah, it looks like one.
Speaker 1 (08:51):
So I guess what it's doing is it's cutting in half.
It's cutting a portion out. Ah, that's the only thing
I can come up with.
Speaker 3 (08:58):
Okay, I like that though, sure.
Speaker 1 (09:00):
And we can thank Johann Ron, who's Swiss not Swedish,
who started using it all the way back in sixteen
fifty nine.
Speaker 3 (09:07):
That's right.
Speaker 2 (09:08):
The other word I did not know is the what
is now the backslash symbol for division is called a
either a fraction bar or a solidus.
Speaker 1 (09:19):
Yeah, didn't know that either.
Speaker 2 (09:21):
I didn't know that that was the exclusive thing. Now,
this is how out of touch with matth iron.
Speaker 1 (09:25):
Yeah. Apparently the ISO, the International Organization for Standardization, who
aren't familiar with how to create an acronym. They said
that you could only use the solidus or the fraction
bar to indicate division, and that the obelis is out
out out. But Science ABC said, don't worry everybody. Listen,
(09:46):
if you go on to your keyboard, you know what's weird.
I haven't tried this. Did you try it?
Speaker 2 (09:50):
No?
Speaker 1 (09:51):
I'm going to try it right now. Why don't you
go ahead and tell everybody what you're supposed to do
and I'm going to try it myself.
Speaker 2 (09:56):
Chuck, Well, what you do is you hold the alt
key on your keyboard and then press two four to
six on the number pad.
Speaker 3 (10:05):
And what do we got? My friend?
Speaker 1 (10:07):
I think maybe you have to press it at once,
hold on two four six. You got lies? That's what
you got Chuck thirty lies.
Speaker 2 (10:15):
Oh well, let me try then you talked for a second.
Speaker 1 (10:18):
Okay, So I'm going to do it again, two four
six with all pressed at the same time in Microsoft Word.
The current version of Microsoft Word won't do it.
Speaker 3 (10:32):
I don't even know if I have Word on this laptop.
Speaker 1 (10:35):
The thing that gives it away for why I think
this might not be correct any longer, is that they
mentioned that you press the numbers two four six on
your number pad. Remember when numbers used to be off
to the side on a keyboard and their own thing.
Speaker 2 (10:50):
Well, I've got a keyboard like that. Okay, let me
let me try it for you. So all to two
four six.
Speaker 1 (10:55):
Yeah, I think at the same time.
Speaker 2 (10:58):
Oh that's hard to do. I'm trying to, like fingering
a weird guitar chord that didn't work alt two for six.
Speaker 3 (11:05):
Right, this is just bs.
Speaker 1 (11:09):
They got us, Chuck. They got us as good as
Debbie Ranka did with that whole thing about Judas spilling
the salt shaker in the Last Supper.
Speaker 2 (11:17):
Wait, let me try one more thing, two for six.
Now it's not working.
Speaker 1 (11:21):
Okay. Well, I'm sorry everybody that we misled you, but
I'm glad we worked it out so you don't have
to email us about it.
Speaker 3 (11:27):
Yeah.
Speaker 2 (11:27):
Maybe someone knows though, and can tell us what we're
doing wrong.
Speaker 1 (11:31):
Yeah, we love hearing that, and while we wait for
you to write in short, stuff is out.
Speaker 3 (11:41):
Stuff you Should Know is a production of iHeartRadio. For
more podcasts my heart Radio, visit the iHeartRadio app, Apple Podcasts,
or wherever you listen to your favorite shows.
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