1 00:00:04,360 --> 00:00:06,280 Speaker 1: Hey, and welcome to the Short Stuff. I'm Josh, and 2 00:00:06,320 --> 00:00:08,479 Speaker 1: there's Chuck, and this is short Stuff, and we are 3 00:00:08,560 --> 00:00:11,840 Speaker 1: going to talk about something that has been overlooked for 4 00:00:11,920 --> 00:00:15,400 Speaker 1: far too long, which is the origins of the plus 5 00:00:15,440 --> 00:00:19,560 Speaker 1: minus multiplication, division and equal symbols. 6 00:00:19,880 --> 00:00:22,880 Speaker 2: I thought this was really cool by the way you 7 00:00:22,920 --> 00:00:27,440 Speaker 2: put this together with help from FASCO, cal Tech, Science ABC, 8 00:00:27,640 --> 00:00:31,240 Speaker 2: among other places. And I had never thought about this 9 00:00:31,240 --> 00:00:33,480 Speaker 2: stuff because I'm not a math person, but I love 10 00:00:33,560 --> 00:00:37,480 Speaker 2: origin stories, and I thought this is really neat, especially 11 00:00:38,040 --> 00:00:40,519 Speaker 2: the fact that these symbols came about to begin with, 12 00:00:41,280 --> 00:00:47,080 Speaker 2: because people before they had these. You wrote out a 13 00:00:47,120 --> 00:00:51,400 Speaker 2: math problem like this long word problem, but not like 14 00:00:51,520 --> 00:00:54,200 Speaker 2: you know, a train's traveling in this direction kind of thing. 15 00:00:54,600 --> 00:00:58,200 Speaker 2: It's more like I have divided ten into two parts 16 00:00:58,240 --> 00:01:00,560 Speaker 2: and multiplying one of these by the other. The results 17 00:01:00,640 --> 00:01:03,520 Speaker 2: was twenty one. Then you know that one of the 18 00:01:03,560 --> 00:01:07,520 Speaker 2: parts is thing and the other is ten minus thing. 19 00:01:07,920 --> 00:01:10,920 Speaker 1: Right. That was an excerpt from a ninth century algebra 20 00:01:10,959 --> 00:01:17,160 Speaker 1: book by the mathematician Mohammed ibn Musai al Kharazmi. I'm 21 00:01:17,160 --> 00:01:20,200 Speaker 1: pretty sure that's his name. Today you would take that 22 00:01:20,280 --> 00:01:24,119 Speaker 1: same formula and write it out as x times ten 23 00:01:24,280 --> 00:01:26,760 Speaker 1: minus x equals twenty one. 24 00:01:27,000 --> 00:01:29,120 Speaker 3: Yeah, so simple, that's it. 25 00:01:29,680 --> 00:01:34,240 Speaker 1: And that reveals why these things were so important. It 26 00:01:34,400 --> 00:01:37,160 Speaker 1: just saves you so much time. So not only did 27 00:01:37,200 --> 00:01:39,720 Speaker 1: it make writing an algebra book that much more attractive, 28 00:01:40,480 --> 00:01:43,400 Speaker 1: it made teaching it that much faster. You might not 29 00:01:43,440 --> 00:01:47,280 Speaker 1: have necessarily learned it any faster, but you definitely could 30 00:01:47,360 --> 00:01:51,440 Speaker 1: teach these things faster with these notations rather than writing 31 00:01:51,480 --> 00:01:54,440 Speaker 1: it out. And I also saw check that some of 32 00:01:54,480 --> 00:01:57,440 Speaker 1: those sentences that they would write, some people would put 33 00:01:57,440 --> 00:02:01,680 Speaker 1: it into verse metered verse like poems. That takes a 34 00:02:01,720 --> 00:02:03,560 Speaker 1: lot of time, and it's unnecessary. 35 00:02:03,960 --> 00:02:08,320 Speaker 2: Yeah, and especially at the time when you're writing with eagles, 36 00:02:08,320 --> 00:02:11,839 Speaker 2: feather and an ink. Weell sure, you know what I mean. 37 00:02:12,200 --> 00:02:13,280 Speaker 1: That really drags too. 38 00:02:13,600 --> 00:02:15,320 Speaker 3: It's not like you're just dashing this stuff off with 39 00:02:15,360 --> 00:02:15,840 Speaker 3: a pencil. 40 00:02:16,360 --> 00:02:16,600 Speaker 1: Nope. 41 00:02:17,200 --> 00:02:19,600 Speaker 3: So some folks came along and changed all that. 42 00:02:20,200 --> 00:02:26,000 Speaker 2: According to the v NR Concise Encyclopedia of Mathematics hot Read, 43 00:02:27,040 --> 00:02:30,160 Speaker 2: the origin of the equal sign goes like this. A 44 00:02:30,200 --> 00:02:34,640 Speaker 2: man named Robert record or record A was the royal 45 00:02:34,680 --> 00:02:39,880 Speaker 2: court physician for King Edward about six and Queen Mary, 46 00:02:40,520 --> 00:02:46,400 Speaker 2: and a very influential mathematician in Wales, and he got 47 00:02:46,480 --> 00:02:50,640 Speaker 2: tired of writing out equals over and over, so he 48 00:02:50,760 --> 00:02:55,880 Speaker 2: thus proposed the equal sign because it is two little 49 00:02:55,960 --> 00:02:59,120 Speaker 2: equal lines, and that's parallel equal lines. 50 00:02:59,160 --> 00:03:01,079 Speaker 3: And this I never thought it, but it's brilliant. 51 00:03:01,160 --> 00:03:04,239 Speaker 1: Yeah, he said, a pair of parallels or twin lines 52 00:03:04,280 --> 00:03:06,480 Speaker 1: of one length, and then he spelled. He shows what 53 00:03:06,560 --> 00:03:10,520 Speaker 1: he's talking about, because no two things can be more equal. 54 00:03:11,040 --> 00:03:13,240 Speaker 1: And there's a lot of extra vowels in those words, 55 00:03:13,360 --> 00:03:17,280 Speaker 1: but yeah, he gets the point across. And he was saying, like, 56 00:03:17,360 --> 00:03:20,080 Speaker 1: this is such a great time saver. I'm so tired 57 00:03:20,120 --> 00:03:22,680 Speaker 1: of saying is equal to? And he wrote it in 58 00:03:23,000 --> 00:03:25,799 Speaker 1: a book called The Wetstone of Wit, And of course 59 00:03:25,840 --> 00:03:28,160 Speaker 1: a whetstone is what you sharpened things with, so it 60 00:03:28,280 --> 00:03:31,000 Speaker 1: sharpens your wit to read this book. I love that title, 61 00:03:31,560 --> 00:03:34,480 Speaker 1: and it actually became very influential and well read as 62 00:03:34,480 --> 00:03:38,240 Speaker 1: far as sixteenth century math books go. And Robert Record 63 00:03:38,320 --> 00:03:40,520 Speaker 1: is credited with coming up with the minus symbol and 64 00:03:40,560 --> 00:03:43,119 Speaker 1: introducing it to his people back then. 65 00:03:43,520 --> 00:03:44,160 Speaker 3: The equal sign. 66 00:03:44,200 --> 00:03:45,480 Speaker 1: You mean what I say? 67 00:03:45,760 --> 00:03:49,800 Speaker 3: Minus sign? Oh just wait, chuck, all right, well we're there. 68 00:03:50,400 --> 00:03:54,560 Speaker 2: Plus and minus are what we use to indicate adding 69 00:03:54,600 --> 00:03:58,720 Speaker 2: something and subtracting something. As everyone knows they come. The 70 00:03:59,040 --> 00:04:03,440 Speaker 2: terms themselves come from Latin, where plus means more and 71 00:04:03,600 --> 00:04:08,200 Speaker 2: minus means less. And the other thing is the plus 72 00:04:08,240 --> 00:04:12,080 Speaker 2: symbol itself is also from the Latin word et et, 73 00:04:12,360 --> 00:04:16,520 Speaker 2: meaning and like this and that equals that, which is 74 00:04:16,560 --> 00:04:19,000 Speaker 2: pretty great. So at one point there was a French 75 00:04:19,040 --> 00:04:25,760 Speaker 2: philosopher named Nicole ors Me from the fourteenth century who 76 00:04:26,040 --> 00:04:30,200 Speaker 2: used that plus sign as a shorthand for et, which 77 00:04:30,200 --> 00:04:33,359 Speaker 2: is what they used to write. And at first it 78 00:04:33,440 --> 00:04:38,400 Speaker 2: didn't take right, I think, like people weren't universally accepting this. 79 00:04:38,839 --> 00:04:41,760 Speaker 1: Yeah, it wasn't until like the sixteenth or seventeenth century 80 00:04:41,800 --> 00:04:43,520 Speaker 1: that it started to really kind of take off. I 81 00:04:43,560 --> 00:04:47,240 Speaker 1: think the sixteenth century, Okay, And apparently there was competition 82 00:04:47,320 --> 00:04:50,719 Speaker 1: at first too, that it wasn't just the plain old 83 00:04:50,960 --> 00:04:54,800 Speaker 1: plus sign that equal cross, that there were other crosses 84 00:04:54,800 --> 00:04:57,280 Speaker 1: in the in the running too, including the Maltese cross. 85 00:04:57,760 --> 00:05:00,880 Speaker 1: It's a great looking cross, yeah, but it takes a 86 00:05:00,880 --> 00:05:03,680 Speaker 1: lot more time to write the Maltese cross out than 87 00:05:03,720 --> 00:05:05,640 Speaker 1: it does to make a plus symbol, and the whole 88 00:05:05,680 --> 00:05:09,000 Speaker 1: point of these things was to save time. So everybody said, yeah, 89 00:05:09,040 --> 00:05:11,120 Speaker 1: Maltese cross, we like you. But we're gonna go with 90 00:05:11,160 --> 00:05:11,719 Speaker 1: the plus sign. 91 00:05:12,320 --> 00:05:12,720 Speaker 3: That's right. 92 00:05:12,760 --> 00:05:16,000 Speaker 2: So that's plus, we got equals, we got plus minus. 93 00:05:16,040 --> 00:05:20,640 Speaker 2: Now in Europe there was an Italian mathematician named Luca Pacioli, 94 00:05:21,440 --> 00:05:25,200 Speaker 2: and Luca was using the symbol P with a little 95 00:05:25,200 --> 00:05:27,839 Speaker 2: line over it for plus, an M with a little 96 00:05:27,880 --> 00:05:32,200 Speaker 2: line of it over it for minus. And no one's 97 00:05:32,320 --> 00:05:37,279 Speaker 2: exactly sure, but it seems to be that the M 98 00:05:37,680 --> 00:05:40,640 Speaker 2: was just dropped right, and then the minus sign, because 99 00:05:40,640 --> 00:05:43,039 Speaker 2: we already had a plus sign, became the minus sign. 100 00:05:43,200 --> 00:05:45,560 Speaker 1: Yeah, so you don't need the plus sign forget you 101 00:05:45,640 --> 00:05:48,200 Speaker 1: P with the tilbey over it. We're gonna take the 102 00:05:48,480 --> 00:05:52,720 Speaker 1: M instead. And it was it wasn't Robert Record who 103 00:05:53,320 --> 00:05:55,640 Speaker 1: came up with that, but he was the one who 104 00:05:55,680 --> 00:05:56,599 Speaker 1: introduced it. 105 00:05:56,480 --> 00:06:00,240 Speaker 3: To England, right, And I never knew it was called 106 00:06:00,240 --> 00:06:00,599 Speaker 3: it tild. 107 00:06:01,880 --> 00:06:05,640 Speaker 1: I didn't either that line over the P or the M. Yeah, 108 00:06:05,720 --> 00:06:07,640 Speaker 1: I think that's what they call it, so yeah, And 109 00:06:07,720 --> 00:06:10,039 Speaker 1: I don't know if it's the minus sign itself is 110 00:06:10,080 --> 00:06:12,000 Speaker 1: called that, or if it has to be over the 111 00:06:12,279 --> 00:06:13,440 Speaker 1: letter to be called that. 112 00:06:14,080 --> 00:06:16,039 Speaker 2: All right, Well, there are a couple of other words 113 00:06:16,040 --> 00:06:33,359 Speaker 2: that I did not know coming up right after the break, 114 00:06:41,040 --> 00:06:43,760 Speaker 2: all right, we're gonna wind it out with the multiplication 115 00:06:43,880 --> 00:06:48,240 Speaker 2: symbol and the division symbol multiplication. If you say it's 116 00:06:48,279 --> 00:06:52,320 Speaker 2: a little X, you're incorrect because it is not an X. 117 00:06:52,360 --> 00:06:56,599 Speaker 2: It's actually called the Cross of San Andreas because X. 118 00:06:56,839 --> 00:06:59,480 Speaker 2: Well not because, but it would be very confusing because 119 00:06:59,680 --> 00:07:02,440 Speaker 2: X is already a thing in math, Like you're solving 120 00:07:02,480 --> 00:07:05,880 Speaker 2: for X. X represents something in math, So it's it's 121 00:07:05,880 --> 00:07:07,800 Speaker 2: actually incorrect to say it's a little X. 122 00:07:08,080 --> 00:07:10,640 Speaker 1: Yeah, if you do that at a math conference, they 123 00:07:10,680 --> 00:07:13,760 Speaker 1: will find the nearest fire hose and flood you mercilessly 124 00:07:13,840 --> 00:07:14,120 Speaker 1: with it. 125 00:07:14,440 --> 00:07:14,920 Speaker 3: They will. 126 00:07:15,440 --> 00:07:18,600 Speaker 1: So, yeah, that makes total sense. And it was a 127 00:07:18,640 --> 00:07:23,760 Speaker 1: guy named William Autred who was writing in I think 128 00:07:23,800 --> 00:07:29,000 Speaker 1: the sixteenth century, like the sixteen thirties, and he was 129 00:07:29,040 --> 00:07:31,280 Speaker 1: the one who introduced it. He's credited with this. But 130 00:07:32,000 --> 00:07:34,680 Speaker 1: the people at Science ABC went to the trouble of 131 00:07:34,680 --> 00:07:39,160 Speaker 1: digging up the fact that there's an anonymous appendix in 132 00:07:39,200 --> 00:07:44,040 Speaker 1: a translation of another book of logarithms from sixteen eighteen 133 00:07:44,440 --> 00:07:48,040 Speaker 1: where the Cross of San Andreas is first used. 134 00:07:48,760 --> 00:07:52,880 Speaker 2: Okay, so, but he introduced it in before that, right, no. 135 00:07:53,040 --> 00:07:56,720 Speaker 1: After, But since it was anonymous in the appendix, they 136 00:07:56,720 --> 00:08:00,320 Speaker 1: don't know who to credit it with, and I said, 137 00:08:00,440 --> 00:08:02,920 Speaker 1: you need to win today. We're going to with that. 138 00:08:05,120 --> 00:08:07,080 Speaker 2: I mentioned before the break that there were a couple 139 00:08:07,080 --> 00:08:13,120 Speaker 2: of more words that I didn't realize were words, and 140 00:08:13,320 --> 00:08:17,040 Speaker 2: that is the the division symbol that apparently I didn't 141 00:08:17,040 --> 00:08:19,520 Speaker 2: even know this is not even really used anymore officially, 142 00:08:20,120 --> 00:08:23,320 Speaker 2: which is to say, the line like the minus symbol 143 00:08:23,360 --> 00:08:25,240 Speaker 2: with a dot above it and a dot below it 144 00:08:25,320 --> 00:08:28,200 Speaker 2: in the center, that is actually called an obelis. 145 00:08:29,080 --> 00:08:31,119 Speaker 1: Yeah, that symbol. You know what, it reminds me of 146 00:08:31,120 --> 00:08:35,319 Speaker 1: of that calculator that was shaped like a big plastic owl. Oh, 147 00:08:35,559 --> 00:08:38,160 Speaker 1: that's what I associate that with. I remember those, But 148 00:08:38,320 --> 00:08:40,080 Speaker 1: I didn't know it was called an obelis either. And 149 00:08:40,160 --> 00:08:42,720 Speaker 1: I also didn't know that obelis is an old Greek 150 00:08:42,760 --> 00:08:46,680 Speaker 1: word for sharpened stick, and that that division symbol, the 151 00:08:46,720 --> 00:08:49,480 Speaker 1: obelis is supposed to represent a small dagger. 152 00:08:49,840 --> 00:08:51,000 Speaker 3: Yeah, it looks like one. 153 00:08:51,280 --> 00:08:53,680 Speaker 1: So I guess what it's doing is it's cutting in half. 154 00:08:53,720 --> 00:08:57,160 Speaker 1: It's cutting a portion out. Ah, that's the only thing 155 00:08:57,200 --> 00:08:58,160 Speaker 1: I can come up with. 156 00:08:58,400 --> 00:09:00,280 Speaker 3: Okay, I like that though, sure. 157 00:09:00,120 --> 00:09:03,920 Speaker 1: And we can thank Johann Ron, who's Swiss not Swedish, 158 00:09:04,080 --> 00:09:06,280 Speaker 1: who started using it all the way back in sixteen 159 00:09:06,400 --> 00:09:07,040 Speaker 1: fifty nine. 160 00:09:07,600 --> 00:09:08,080 Speaker 3: That's right. 161 00:09:08,480 --> 00:09:10,920 Speaker 2: The other word I did not know is the what 162 00:09:11,080 --> 00:09:16,360 Speaker 2: is now the backslash symbol for division is called a 163 00:09:16,559 --> 00:09:18,800 Speaker 2: either a fraction bar or a solidus. 164 00:09:19,120 --> 00:09:20,400 Speaker 1: Yeah, didn't know that either. 165 00:09:21,000 --> 00:09:23,080 Speaker 2: I didn't know that that was the exclusive thing. Now, 166 00:09:23,080 --> 00:09:24,760 Speaker 2: this is how out of touch with matth iron. 167 00:09:25,160 --> 00:09:30,480 Speaker 1: Yeah. Apparently the ISO, the International Organization for Standardization, who 168 00:09:30,640 --> 00:09:34,440 Speaker 1: aren't familiar with how to create an acronym. They said 169 00:09:34,480 --> 00:09:36,800 Speaker 1: that you could only use the solidus or the fraction 170 00:09:36,920 --> 00:09:40,760 Speaker 1: bar to indicate division, and that the obelis is out 171 00:09:40,960 --> 00:09:45,920 Speaker 1: out out. But Science ABC said, don't worry everybody. Listen, 172 00:09:46,600 --> 00:09:48,720 Speaker 1: if you go on to your keyboard, you know what's weird. 173 00:09:48,760 --> 00:09:50,160 Speaker 1: I haven't tried this. Did you try it? 174 00:09:50,679 --> 00:09:50,760 Speaker 2: No? 175 00:09:51,640 --> 00:09:53,120 Speaker 1: I'm going to try it right now. Why don't you 176 00:09:53,120 --> 00:09:55,120 Speaker 1: go ahead and tell everybody what you're supposed to do 177 00:09:55,240 --> 00:09:56,440 Speaker 1: and I'm going to try it myself. 178 00:09:56,520 --> 00:09:59,839 Speaker 2: Chuck, Well, what you do is you hold the alt 179 00:10:00,679 --> 00:10:03,160 Speaker 2: key on your keyboard and then press two four to 180 00:10:03,160 --> 00:10:04,960 Speaker 2: six on the number pad. 181 00:10:05,640 --> 00:10:06,960 Speaker 3: And what do we got? My friend? 182 00:10:07,320 --> 00:10:08,800 Speaker 1: I think maybe you have to press it at once, 183 00:10:08,800 --> 00:10:13,360 Speaker 1: hold on two four six. You got lies? That's what 184 00:10:13,440 --> 00:10:14,880 Speaker 1: you got Chuck thirty lies. 185 00:10:15,160 --> 00:10:17,880 Speaker 2: Oh well, let me try then you talked for a second. 186 00:10:18,120 --> 00:10:20,280 Speaker 1: Okay, So I'm going to do it again, two four 187 00:10:20,360 --> 00:10:23,960 Speaker 1: six with all pressed at the same time in Microsoft Word. 188 00:10:24,520 --> 00:10:27,880 Speaker 1: The current version of Microsoft Word won't do it. 189 00:10:32,559 --> 00:10:35,000 Speaker 3: I don't even know if I have Word on this laptop. 190 00:10:35,720 --> 00:10:38,160 Speaker 1: The thing that gives it away for why I think 191 00:10:38,200 --> 00:10:41,920 Speaker 1: this might not be correct any longer, is that they 192 00:10:42,000 --> 00:10:44,560 Speaker 1: mentioned that you press the numbers two four six on 193 00:10:44,600 --> 00:10:47,160 Speaker 1: your number pad. Remember when numbers used to be off 194 00:10:47,200 --> 00:10:49,200 Speaker 1: to the side on a keyboard and their own thing. 195 00:10:50,080 --> 00:10:52,320 Speaker 2: Well, I've got a keyboard like that. Okay, let me 196 00:10:52,600 --> 00:10:54,920 Speaker 2: let me try it for you. So all to two 197 00:10:55,000 --> 00:10:55,960 Speaker 2: four six. 198 00:10:55,960 --> 00:10:57,720 Speaker 1: Yeah, I think at the same time. 199 00:10:58,559 --> 00:11:00,640 Speaker 2: Oh that's hard to do. I'm trying to, like fingering 200 00:11:00,640 --> 00:11:05,640 Speaker 2: a weird guitar chord that didn't work alt two for six. 201 00:11:05,920 --> 00:11:08,920 Speaker 3: Right, this is just bs. 202 00:11:09,240 --> 00:11:12,040 Speaker 1: They got us, Chuck. They got us as good as 203 00:11:12,040 --> 00:11:14,560 Speaker 1: Debbie Ranka did with that whole thing about Judas spilling 204 00:11:14,600 --> 00:11:16,760 Speaker 1: the salt shaker in the Last Supper. 205 00:11:17,000 --> 00:11:19,560 Speaker 2: Wait, let me try one more thing, two for six. 206 00:11:20,280 --> 00:11:21,160 Speaker 2: Now it's not working. 207 00:11:21,280 --> 00:11:24,240 Speaker 1: Okay. Well, I'm sorry everybody that we misled you, but 208 00:11:24,240 --> 00:11:25,920 Speaker 1: I'm glad we worked it out so you don't have 209 00:11:25,960 --> 00:11:27,079 Speaker 1: to email us about it. 210 00:11:27,400 --> 00:11:27,679 Speaker 3: Yeah. 211 00:11:27,800 --> 00:11:31,199 Speaker 2: Maybe someone knows though, and can tell us what we're 212 00:11:31,240 --> 00:11:31,680 Speaker 2: doing wrong. 213 00:11:31,880 --> 00:11:35,160 Speaker 1: Yeah, we love hearing that, and while we wait for 214 00:11:35,200 --> 00:11:40,200 Speaker 1: you to write in short, stuff is out. 215 00:11:41,000 --> 00:11:43,880 Speaker 3: Stuff you Should Know is a production of iHeartRadio. For 216 00:11:43,960 --> 00:11:48,160 Speaker 3: more podcasts my heart Radio, visit the iHeartRadio app, Apple Podcasts, 217 00:11:48,280 --> 00:11:50,120 Speaker 3: or wherever you listen to your favorite shows.