1 00:00:19,980 --> 00:00:23,280 Jane: This is But Why: A Podcast for Curious Kids from Vermont 2 00:00:23,280 --> 00:00:26,925 Public. I'm Jane Lindholm. On this show, we take questions 3 00:00:26,925 --> 00:00:32,205 from curious kids just like you, and we find answers. I had a 4 00:00:32,205 --> 00:00:36,105 math teacher for a parent, so for as long as I can remember, 5 00:00:36,165 --> 00:00:39,825 Math has been a part of my life. My stepdad made me and my 6 00:00:39,825 --> 00:00:44,025 brother do math games on long car rides, and he still gives us 7 00:00:44,025 --> 00:00:46,650 math riddles whenever we go visit him now, even though we're 8 00:00:46,650 --> 00:00:51,450 adults. He wishes us a happy Pi Day every March 14, and 9 00:00:51,450 --> 00:00:54,930 suggested we use the Fibonacci sequence for our essential 10 00:00:54,930 --> 00:00:58,830 passcode numbers. Don't know what the Fibonacci sequence is? 11 00:00:58,950 --> 00:01:02,610 You will by the end of this episode. Math and numbers are 12 00:01:02,610 --> 00:01:06,570 fascinating, but I also know it can sometimes get difficult to 13 00:01:06,570 --> 00:01:10,875 wrap your head around big math concepts in school or on long 14 00:01:10,875 --> 00:01:14,475 car rides with a math-loving adult. So today, we're going to 15 00:01:14,475 --> 00:01:19,575 demystify math. You've sent us a lot of mathematical questions, 16 00:01:19,635 --> 00:01:24,555 and our guest today loves all of them. Dr. Melania Alvarez is the 17 00:01:24,555 --> 00:01:27,435 Outreach Coordinator for the Department of Mathematics at the 18 00:01:27,435 --> 00:01:30,915 University of British Columbia in Canada, and she's the 19 00:01:30,915 --> 00:01:33,900 Education Coordinator for the Pacific Institute for the 20 00:01:33,900 --> 00:01:35,280 Mathematical Sciences. 21 00:01:35,660 --> 00:01:39,560 Dr. Melania Alvarez: So my job is to go all around, showing 22 00:01:39,560 --> 00:01:42,560 people how wonderful and interesting and exciting 23 00:01:42,560 --> 00:01:46,880 mathematics really is. If you invite me to your school, I go 24 00:01:46,880 --> 00:01:50,120 to your school and bring some interesting games and puzzles 25 00:01:50,120 --> 00:01:53,540 and things like that to show you, you know, how much fun you 26 00:01:53,540 --> 00:01:54,740 can have doing mathematics. 27 00:01:54,980 --> 00:01:57,200 Jane: Can you give me a puzzle? 28 00:01:57,920 --> 00:02:00,905 Dr. Melania Alvarez: Oh, there are many, but one, one that I 29 00:02:00,905 --> 00:02:06,245 have. So there's a farmer, and he sells chickens. So he goes to 30 00:02:06,245 --> 00:02:10,205 the market, and in the he's going to go to three markets. 31 00:02:10,205 --> 00:02:13,445 And so there goes to the first market, and he sells half of his 32 00:02:13,445 --> 00:02:16,325 chickens plus half a chicken, okay? 33 00:02:16,445 --> 00:02:16,865 Jane: Okay 34 00:02:16,985 --> 00:02:19,445 Dr. Melania Alvarez: And then he goes to the second market and he 35 00:02:19,445 --> 00:02:23,810 sells half of his chickens plus half of a chicken. And then he 36 00:02:23,810 --> 00:02:26,930 goes to the third market and sells half of the chickens that 37 00:02:26,930 --> 00:02:30,770 are left, plus half a chicken. And that's it. And then he has 38 00:02:30,770 --> 00:02:32,630 zero chickens, right? That's it. After that. 39 00:02:32,630 --> 00:02:34,130 Jane: He sold all of his chickens. 40 00:02:34,130 --> 00:02:36,350 Dr. Melania Alvarez: He sold all of his chickens, so yeah, no 41 00:02:36,350 --> 00:02:40,970 chickens left. So how many chickens did he have? When he 42 00:02:40,970 --> 00:02:42,650 sold the chickens, they were all alive. 43 00:02:44,620 --> 00:02:45,460 Jane: I don't know. 44 00:02:48,780 --> 00:02:50,520 Dr. Melania Alvarez: He sold all live chickens, 45 00:02:50,520 --> 00:02:51,480 Jane: All of his chickens, 46 00:02:51,480 --> 00:02:53,580 Dr. Melania Alvarez: All the chickens were alive. Yes, half a 47 00:02:53,580 --> 00:02:57,300 chicken cannot be alive, right? So how many chickens did he 48 00:02:57,480 --> 00:02:58,500 originally have? 49 00:02:58,800 --> 00:03:01,440 Jane: I see, okay, I feel like I need to write it down on paper, 50 00:03:01,440 --> 00:03:05,040 though. So while, while I'm working on this, let me ask you 51 00:03:05,040 --> 00:03:08,100 some of the questions that kids have sent us about math, 52 00:03:08,640 --> 00:03:12,225 starting with some kids who want to understand, who created math? 53 00:03:12,285 --> 00:03:15,465 Sophie: Hi, my name is Sophie, and I'm eight years old, and 54 00:03:15,465 --> 00:03:18,465 live in Arlington, Virginia. Who invented math? 55 00:03:18,540 --> 00:03:22,740 Oonas: My name is Oonas, and I'm six and a half years old, and I 56 00:03:22,740 --> 00:03:26,340 live in Brooklyn, New York. Who invented math? 57 00:03:27,260 --> 00:03:28,820 Dr. Melania Alvarez: Math is something that grew through 58 00:03:28,820 --> 00:03:32,840 thousands of years. It's like a magical tree that was planted by 59 00:03:32,840 --> 00:03:37,640 many, many people, by the Chinese, the Mayans, you know, 60 00:03:37,640 --> 00:03:41,660 so ancient people needed to, needed to count, at some point, 61 00:03:41,660 --> 00:03:45,380 when populations started to grow and we started to have cities, 62 00:03:45,380 --> 00:03:48,440 we people needed to count. We needed, people looked at how 63 00:03:48,440 --> 00:03:50,885 much property they had. There are some cultures where they 64 00:03:50,885 --> 00:03:54,305 only have one, two and many. But you know, the more you have, you 65 00:03:54,305 --> 00:03:57,245 need to, you know, to count. You need to measure. You need to 66 00:03:57,245 --> 00:04:01,145 trade. So we started inventing numbers. Humans started to 67 00:04:01,145 --> 00:04:05,885 invent numbers and systems and symbols and rules and but here 68 00:04:06,125 --> 00:04:09,005 is the twist. So we started to invent that. But at the same 69 00:04:09,005 --> 00:04:12,245 time, math is not just invented, it's also discovered. There are 70 00:04:12,245 --> 00:04:16,010 also things there that are there and we and we discover, like a 71 00:04:16,010 --> 00:04:20,270 triangle has three sides. We didn't, you know, invented that. 72 00:04:20,270 --> 00:04:22,970 You know, it's that's something that is true. So there are 73 00:04:22,970 --> 00:04:26,330 things that we created in order to make sense of a lot of 74 00:04:26,330 --> 00:04:29,690 things, and with that invention, we also discover a lot of 75 00:04:29,690 --> 00:04:35,810 things. So who invented math is we humans started to observe, 76 00:04:35,810 --> 00:04:40,295 started to look for patterns out of need, and we created systems 77 00:04:40,295 --> 00:04:43,595 that allowed us to describe what we were seeing, and that's what 78 00:04:43,595 --> 00:04:44,315 math is. 79 00:04:45,035 --> 00:04:49,415 Jane: So Leilei wants to know who created math problems, and 80 00:04:49,475 --> 00:04:52,595 if we needed to know how to do math as humans, especially as 81 00:04:52,595 --> 00:04:56,255 you say, as we started to have communities and use money or 82 00:04:56,255 --> 00:05:00,500 barter for things. But maybe Leilei is asking, morelike, who 83 00:05:00,500 --> 00:05:04,460 created the study of math, or this idea that we teach people 84 00:05:04,460 --> 00:05:09,320 math and do math problems, not just learn how to count, because 85 00:05:09,380 --> 00:05:10,520 we have to know how to count. 86 00:05:12,040 --> 00:05:15,340 Dr. Melania Alvarez: Well, what happened is that the moment we 87 00:05:15,340 --> 00:05:19,840 are faced with a situation like, okay, I need to get to school, 88 00:05:19,840 --> 00:05:22,780 but first I need to have breakfast, I need to wake up, I 89 00:05:22,780 --> 00:05:25,780 need to brush my teeth. So then you start thinking, okay, how 90 00:05:25,780 --> 00:05:28,480 much time I'm going to take for breakfast, and how much time do 91 00:05:28,480 --> 00:05:31,960 I need to get from here to school? So natural events that 92 00:05:31,960 --> 00:05:35,425 happen to us, and these are problems that we solve in order 93 00:05:35,425 --> 00:05:40,165 to be able to deal with some realities in life. So who 94 00:05:40,165 --> 00:05:43,285 created problems? Well, yes, sometimes you have your teacher 95 00:05:43,285 --> 00:05:46,225 creating tons of problems so that you suffer through them and 96 00:05:46,225 --> 00:05:49,285 stuff like that. But math problems come from the world. 97 00:05:49,945 --> 00:05:53,425 When we start to wonder, you know, the Egyptians, it's like, 98 00:05:53,425 --> 00:05:56,665 Okay, how do I build this pyramid so that it doesn't fall 99 00:05:56,665 --> 00:05:59,950 down, or it doesn't crumble, or a bridge as well, an engineer, 100 00:06:00,070 --> 00:06:03,130 I'm going to build this bridge. How do I build this bridge so 101 00:06:03,130 --> 00:06:07,510 that it will resist trucks going on top? Or how, if this young 102 00:06:07,510 --> 00:06:11,410 girl likes chocolate and she has to divide it equally with 103 00:06:11,590 --> 00:06:14,950 siblings, how do I divide it in a way that is fair for 104 00:06:14,950 --> 00:06:18,910 everybody, you know? Or I strategize perhaps. How do I do 105 00:06:18,910 --> 00:06:23,875 it so that I can get more chocolate than others. So this 106 00:06:23,875 --> 00:06:27,115 is where math, where really math problems come from. Now that 107 00:06:27,115 --> 00:06:31,675 sometimes we create ridiculous problems, like my mother bought 108 00:06:31,675 --> 00:06:35,335 300 watermelons and divided between me and my siblings. 109 00:06:35,515 --> 00:06:38,155 Well, those are weird problems that sometimes I made for 110 00:06:38,155 --> 00:06:42,835 school. But real math problems really come from the world. 111 00:06:43,855 --> 00:06:50,020 Jane: Leilei also wonders, why does one plus one equal two and 112 00:06:50,020 --> 00:06:51,220 not 11? 113 00:06:51,220 --> 00:06:56,140 Dr. Melania Alvarez: We have this system of writing numbers 114 00:06:56,200 --> 00:07:00,220 that is called place value. So it depends where the number is. 115 00:07:00,280 --> 00:07:04,600 So one one means that the one to your right, the first one, is a 116 00:07:04,600 --> 00:07:09,685 one, but the next one is not the one. It's a 10, you see. So for 117 00:07:09,685 --> 00:07:15,445 example, the number 245: in that number, the two is a 200, the 118 00:07:15,445 --> 00:07:20,905 four is a 40, and the five is five. So it depends where you 119 00:07:20,905 --> 00:07:25,945 position the numbers that it changes. So one plus one is two 120 00:07:26,365 --> 00:07:30,130 and one one does not represent two, that one represents a 10 121 00:07:30,250 --> 00:07:33,010 and then a one, so 10 plus one is 11. 122 00:07:33,360 --> 00:07:35,760 Jane: Yeah, it's just interesting to think about. 123 00:07:35,760 --> 00:07:40,440 We've created these systems that are supposed to make it easier 124 00:07:40,440 --> 00:07:44,220 for us and easier for us to do these kinds of problems with 125 00:07:44,220 --> 00:07:47,580 other people, so that your brain and my brain can match up, and 126 00:07:47,580 --> 00:07:51,540 we both understand what one plus one equals. I think I see where 127 00:07:51,540 --> 00:07:54,120 Leilei is coming from in that it can be really interesting. It 128 00:07:54,120 --> 00:07:56,760 can kind of blow your mind when you start to think about like, 129 00:07:56,760 --> 00:08:00,165 oh, we had to make this work for all of our brains. 130 00:08:00,285 --> 00:08:01,665 Dr. Melania Alvarez: For everybody, exactly. 131 00:08:02,040 --> 00:08:07,980 Kai: My name is Kai. I live in California, and I'm four years 132 00:08:08,040 --> 00:08:12,000 old. Why is there so many numbers in math? 133 00:08:12,600 --> 00:08:15,120 Dr. Melania Alvarez: Oh, what happened is, as I said, when 134 00:08:15,120 --> 00:08:18,660 counting started, we had very few numbers. You know, it was 1, 135 00:08:18,720 --> 00:08:22,920 2, 3, many, and then somebody, instead of having three sheep, 136 00:08:22,920 --> 00:08:25,980 now tomorrow, they have four sheep or five sheep, and then 137 00:08:25,980 --> 00:08:29,340 they have to add that. So we needed a system that the more we 138 00:08:29,340 --> 00:08:33,000 have, the more needed to be accounted for. And we have a 139 00:08:33,060 --> 00:08:36,525 very, very nice system where, you know, we just basically can 140 00:08:36,525 --> 00:08:38,865 go on forever and ever and ever and ever and ever. 141 00:08:39,165 --> 00:08:40,905 Jane: Well, some of the kids want to know why. 142 00:08:40,905 --> 00:08:45,165 Lily: My name is Lily. I'm nine years old, and I live in 143 00:08:45,165 --> 00:08:48,045 Portland, Oregon. Why don't numbers end? 144 00:08:48,225 --> 00:08:53,865 Isla: Hi, I'm Isla. I live in Clearwater, and why do numbers 145 00:08:53,865 --> 00:08:54,585 numbers stop? 146 00:08:54,585 --> 00:08:58,605 Nicholas: My name is Nicholas. I'm five years old. I live in 147 00:08:58,605 --> 00:09:01,950 Washington, DC. Why do numbers go off forever and ever. 148 00:09:02,160 --> 00:09:06,120 Jane: Why don't numbers end? Why do we never stop adding numbers? 149 00:09:06,120 --> 00:09:08,700 Is there really infinity numbers? 150 00:09:08,780 --> 00:09:12,560 Dr. Melania Alvarez: Yes, yes. You can give me a number and I 151 00:09:12,560 --> 00:09:15,980 can add one to that number, then now you have more numbers. You 152 00:09:15,980 --> 00:09:20,360 know, for example, there's the googol which has a one and 100 153 00:09:20,360 --> 00:09:21,920 zeros afterwards, right? 154 00:09:21,980 --> 00:09:25,340 Jane: That's right before we all knew what the internet was, 155 00:09:25,340 --> 00:09:32,345 googol was just a number. That's googol spelled G, O, O, G O L. 156 00:09:32,885 --> 00:09:37,325 Google, the internet search engine is G, O, O, G, L, E. 157 00:09:37,925 --> 00:09:42,185 Googol, the number, as Melania said, is a one followed by 100 158 00:09:42,185 --> 00:09:42,905 zeros. 159 00:09:43,265 --> 00:09:45,065 Dr. Melania Alvarez: It's a huge number. And then there's the 160 00:09:45,065 --> 00:09:48,185 Googolplex, which is even larger than that. And you say, so 161 00:09:48,185 --> 00:09:51,545 there's a Googolplex, and I can add one to that, and it's bigger 162 00:09:51,545 --> 00:09:54,710 than the Googolplex. And then I can add one to that one. And I 163 00:09:54,710 --> 00:10:01,070 can keep going on and on, adding 1, 1, 1, 1, 1, and 1. And I just 164 00:10:01,070 --> 00:10:06,830 go on, you see. But also infinity can be kind of also 165 00:10:06,830 --> 00:10:11,150 small. Like, for example, I have a mile to go, okay? And so then 166 00:10:11,150 --> 00:10:16,070 I can go half a mile, and then I go half of half of the mile, and 167 00:10:16,070 --> 00:10:19,295 then I get half and half and half of that, and that, do I 168 00:10:19,295 --> 00:10:23,555 ever get there? No, never. And I can go infinitely, going and the 169 00:10:23,555 --> 00:10:27,155 steps are smaller and smaller and smaller. Eventually, in real 170 00:10:27,155 --> 00:10:30,395 life we get there, but mathematically, we just can be 171 00:10:30,575 --> 00:10:33,035 stuck there, trying to get there. But if you always do 172 00:10:33,035 --> 00:10:37,835 half, half, half, half, half, we will not get there. This is what 173 00:10:37,835 --> 00:10:41,720 is amazing about mathematics, is that you can go on with your 174 00:10:41,720 --> 00:10:44,480 imagination, and math is a great companion for that. 175 00:10:44,480 --> 00:10:44,960 Jane: Yeah. 176 00:10:44,960 --> 00:10:47,600 Dr. Melania Alvarez: And it shows you ways that you never 177 00:10:47,600 --> 00:10:50,600 thought that were possible. And that's what is so wonderful 178 00:10:50,600 --> 00:10:51,080 about it. 179 00:10:51,440 --> 00:10:53,780 Jane: It can kind of make your brain hurt when you try to 180 00:10:53,900 --> 00:10:57,200 think, think, you know, all the way out on those things, but 181 00:10:57,200 --> 00:10:59,360 hurt in a good way. I mean, it's just cool. 182 00:10:59,420 --> 00:11:01,760 Dr. Melania Alvarez: So it is true. You talk about the hurt 183 00:11:01,940 --> 00:11:05,780 and about the struggle and all of that, but what happens when 184 00:11:05,780 --> 00:11:09,740 you are able to solve a problem that is really, really hard? How 185 00:11:09,740 --> 00:11:10,940 do you feel about that? 186 00:11:11,000 --> 00:11:12,800 Jane: Really good. Proud of myself. 187 00:11:12,800 --> 00:11:13,520 Dr. Melania Alvarez: Really good. 188 00:11:13,520 --> 00:11:15,020 Jane: Yeah. Like, I figured it out. 189 00:11:15,020 --> 00:11:17,300 Dr. Melania Alvarez: You get this big high, isn't it? You get 190 00:11:17,300 --> 00:11:21,020 like, wow, I'm really smart. I'm at the top of the world. You 191 00:11:21,020 --> 00:11:23,765 know, that's what we mathematicians live for. Do you 192 00:11:23,765 --> 00:11:26,825 know we were working, we struggle, and then when you 193 00:11:26,825 --> 00:11:30,965 finally solve it, and not just solving it, is the beauty 194 00:11:30,965 --> 00:11:34,145 sometimes of those solutions that are just like, how can this 195 00:11:34,145 --> 00:11:37,865 be so perfect? And that's why. And there are mathematicians 196 00:11:37,865 --> 00:11:42,245 that spend a year, two years, eight years, you know, 10 years, 197 00:11:42,245 --> 00:11:44,885 trying to solve a problem, but they think that it's worth it. 198 00:11:45,050 --> 00:11:48,710 So that's another thing. You don't need to be fast to be a 199 00:11:48,710 --> 00:11:51,890 good mathematician. Many kids think that they have to be 200 00:11:51,890 --> 00:11:55,310 really fast problem solvers to be really good mathematicians. 201 00:11:55,310 --> 00:11:58,310 That's not true. You know, you can take your time. 202 00:11:59,210 --> 00:12:03,650 Tryphon: Hi, my name is Tryphon. I'm nine years old, and I live 203 00:12:03,710 --> 00:12:09,455 in Winnipeg, Manitoba, Canada. Why do people hate math so much? 204 00:12:09,600 --> 00:12:13,200 Jane: Why do people hate math so much? And we should say, 205 00:12:13,200 --> 00:12:16,320 certainly not everybody, but math has a reputation, and 206 00:12:16,320 --> 00:12:19,920 people sometimes seem to feel comfortable saying, Oh, I'm not 207 00:12:19,920 --> 00:12:23,220 good at math, or I hate math, in ways that you wouldn't say about 208 00:12:23,220 --> 00:12:24,000 other things. 209 00:12:24,300 --> 00:12:26,640 Dr. Melania Alvarez: That's right. First of all, many times, 210 00:12:26,640 --> 00:12:29,700 is the way that math is presented to us. It's just like 211 00:12:29,760 --> 00:12:33,045 a series of rules, and you're to solve this problem, and that's 212 00:12:33,045 --> 00:12:35,625 it. And that's not math, actually. That's just something 213 00:12:35,625 --> 00:12:40,425 that we call practice. Real math is not that you need to know the 214 00:12:40,425 --> 00:12:43,065 tools. You need to know how to add and subtract and all of 215 00:12:43,065 --> 00:12:47,085 that, yes, but it's like you need a hammer and you need nails 216 00:12:47,085 --> 00:12:51,285 to build a house. So that's what that is. But math is thinking. 217 00:12:51,285 --> 00:12:55,305 Math is strategizing. So math is not just the solution. It's the 218 00:12:55,305 --> 00:12:59,370 way to get there and how and your thinking to get there. So 219 00:12:59,370 --> 00:13:02,790 it's, so many times is how math is... if it is just rote 220 00:13:02,790 --> 00:13:05,730 learning and just memorizing all the time, which we have to do 221 00:13:05,910 --> 00:13:08,550 sometimes. But if that's the only thing that we learn and the 222 00:13:08,550 --> 00:13:11,970 only thing that we do, then is really boring. I'm telling you, 223 00:13:11,970 --> 00:13:15,450 if that was math, there wouldn't be professional mathematicians, 224 00:13:15,450 --> 00:13:18,330 because no, come on, we're not that boring people. We really 225 00:13:18,330 --> 00:13:21,675 like, we're explorers. That's what it is, math is about 226 00:13:21,735 --> 00:13:24,435 exploration. It's about questioning. It's about doing 227 00:13:24,435 --> 00:13:28,515 all that. If you start to dislike math, and this is also 228 00:13:28,515 --> 00:13:31,995 something that happens, is perhaps along the way, and I 229 00:13:31,995 --> 00:13:35,955 find that many people say I like mathematics, but at some point I 230 00:13:35,955 --> 00:13:40,275 start disliking it, because I got lost. So what I tell kids is 231 00:13:40,275 --> 00:13:43,440 this: if you are in class and you understand that everything 232 00:13:43,440 --> 00:13:46,920 and all of a sudden you don't understand something, go and ask 233 00:13:46,920 --> 00:13:50,880 your teacher, but soon. Don't wait a month or two months 234 00:13:50,940 --> 00:13:54,660 afterwards, go immediately and ask your teacher, Hey, I didn't 235 00:13:54,660 --> 00:13:58,500 get this. Could you explain it to me again? Because math builds 236 00:13:58,500 --> 00:14:01,200 on top. You know, it's something that you it's a structure where 237 00:14:01,200 --> 00:14:04,096 you... So if you miss the first floor, then the rest of the 238 00:14:04,096 --> 00:14:07,005 floors are going to be all wobbly and you're not going to 239 00:14:07,005 --> 00:14:10,605 understand. So don't be embarrassed about asking, and if 240 00:14:10,605 --> 00:14:13,485 you're embarrassed in front of the class, then ask after class. 241 00:14:13,725 --> 00:14:16,725 But don't leave something that you don't understand and say, 242 00:14:16,725 --> 00:14:20,025 well later on, I'll catch up. No, no, no, no. So don't get 243 00:14:20,025 --> 00:14:22,665 lost. Go for help as soon as possible. 244 00:14:23,020 --> 00:14:25,300 Jane: That's always good practice. If you don't 245 00:14:25,300 --> 00:14:29,560 understand something, ask a question, get some help. Math is 246 00:14:29,560 --> 00:14:33,160 complicated, and if one explanation of a math concept 247 00:14:33,160 --> 00:14:36,880 isn't working for you and your brain, you can always say, Could 248 00:14:36,880 --> 00:14:40,060 you describe it to me a different way? Or maybe you need 249 00:14:40,060 --> 00:14:43,480 someone to write it out for you, or help you work backwards from 250 00:14:43,480 --> 00:14:47,185 the answer back to the original question. You can ask for 251 00:14:47,185 --> 00:14:50,905 different kinds of help to make sure you understand the math 252 00:14:50,965 --> 00:14:52,945 you're working on in school or at home. 253 00:14:52,945 --> 00:14:58,705 Coming up, why are the numbers in the order they are, and is 254 00:14:58,705 --> 00:15:02,665 there really math in everything? And of course, I still have to 255 00:15:02,665 --> 00:15:05,785 solve that puzzle Melania gave me about the chicken farmer. 256 00:15:06,085 --> 00:15:06,985 Stay with us. 257 00:15:08,050 --> 00:15:12,010 This is But Why: A Podcast for Curious Kids. I'm Jane Lindholm. 258 00:15:12,370 --> 00:15:14,950 Today, we're talking about numbers and math with 259 00:15:14,950 --> 00:15:18,910 mathematician Melania Alvarez. We're going to solve that puzzle 260 00:15:18,910 --> 00:15:22,210 about the chicken farmer in just a little while. But first, some 261 00:15:22,210 --> 00:15:25,270 of your questions about how numbers are ordered and how they 262 00:15:25,270 --> 00:15:26,110 help us count. 263 00:15:26,290 --> 00:15:31,030 Kai: I'm Kai, and I'm six years old, and I live in Saint Paul, 264 00:15:32,035 --> 00:15:35,635 Minnesota. Why is the numbers in order? Why are they in 1, 2, 3, 265 00:15:35,635 --> 00:15:40,075 4, 5, 6, 7, 8, 9, 10, why can't they just be like in different 266 00:15:40,255 --> 00:15:41,275 orders? 267 00:15:41,600 --> 00:15:44,180 Dr. Melania Alvarez: Well, so numbers are like a step ladder. 268 00:15:44,420 --> 00:15:47,300 We make one number, and then we go to the next, and when we go 269 00:15:47,300 --> 00:15:51,380 to the next, and then we go to the next. So, so that's why it 270 00:15:51,380 --> 00:15:54,680 keeps an order, and that order helps us to count. If the 271 00:15:54,680 --> 00:15:58,520 numbers were all over the place, imagine we have here one, and 272 00:15:58,520 --> 00:16:04,220 then comes 25 and they call 36 and how can we count like that? 273 00:16:04,580 --> 00:16:08,885 We can't! So it is like a ladder. We go step by step by 274 00:16:08,885 --> 00:16:12,845 step, and we gave them numbers those names, right? Because we 275 00:16:12,845 --> 00:16:16,265 need them to track things. We need them to trade. We need them 276 00:16:16,265 --> 00:16:19,805 for things in real life. And if we didn't have that order, we 277 00:16:19,805 --> 00:16:22,745 wouldn't be able to do that. We'll be lost in confusion in 278 00:16:22,745 --> 00:16:28,130 the jungle of numbers. So, so that's why there's a rule, why 279 00:16:28,130 --> 00:16:32,030 we have an order. You know, it's like why don't you build a house 280 00:16:32,030 --> 00:16:35,150 upside down? Because then it wouldn't make sense. So that's 281 00:16:35,150 --> 00:16:36,830 exactly the same thing with this. 282 00:16:37,190 --> 00:16:42,230 Miles: I'm Miles and I'm five years old. I live in Quebec, 283 00:16:42,230 --> 00:16:44,990 Canada. Why are numbers for counting? 284 00:16:45,230 --> 00:16:47,450 Dr. Melania Alvarez: Why are numbers for counting? Well, the 285 00:16:47,450 --> 00:16:50,330 numbers are counting because, actually, that's where math 286 00:16:50,330 --> 00:16:54,455 began. Math began with counting, long, long, long, long time ago, 287 00:16:54,455 --> 00:16:58,955 over 20,000 years ago. So this is something that helped people 288 00:16:58,955 --> 00:16:59,915 to survive. 289 00:16:59,960 --> 00:17:02,540 Jane: And you can think about, let's say, you had to get 290 00:17:02,540 --> 00:17:06,020 through a winter, and you're, you needed to have enough crops 291 00:17:06,200 --> 00:17:08,960 for your whole family to get through the winter. Well, you 292 00:17:08,960 --> 00:17:12,260 have to know how many people are there that I'm trying to feed. 293 00:17:12,260 --> 00:17:15,560 So let's say there are four people in my family. How much do 294 00:17:15,560 --> 00:17:19,760 we eat every day? How many days do we need to get through to get 295 00:17:19,760 --> 00:17:22,985 through the winter before we can grow more food. So you need to 296 00:17:22,985 --> 00:17:27,845 be able to count and add and multiply to know how much food 297 00:17:27,845 --> 00:17:30,905 you need to store for the winter, which will take you to 298 00:17:30,905 --> 00:17:34,145 how much you need to grow in the summer, which will take you back 299 00:17:34,145 --> 00:17:37,745 to how much you need to plant and how many plants you think 300 00:17:37,745 --> 00:17:40,565 the animals are going to eat before you get to have them. So 301 00:17:40,565 --> 00:17:43,685 how much more do you actually need to plant to be able to have 302 00:17:43,685 --> 00:17:47,750 enough to harvest... and, uh oh, there's a new baby in the 303 00:17:47,750 --> 00:17:50,690 family. Now you have to do that, but for five people, so you have 304 00:17:50,690 --> 00:17:54,890 to be able to do that math in order to survive, and even if 305 00:17:54,890 --> 00:17:58,310 we're not thinking about growing all of our own food now, as 306 00:17:58,310 --> 00:18:01,610 families, we have to figure out how to budget, how much money we 307 00:18:01,610 --> 00:18:05,270 need, how much money we need if we also want to go on vacation 308 00:18:05,270 --> 00:18:09,335 to the beach at some point. So math is really important, and we 309 00:18:09,335 --> 00:18:13,595 do like it because it helps us get the things that we want and 310 00:18:13,595 --> 00:18:17,375 need, even if we think, or some people think they don't like 311 00:18:17,375 --> 00:18:18,335 math in school. 312 00:18:18,455 --> 00:18:19,835 Dr. Melania Alvarez: You're absolutely right. 313 00:18:20,195 --> 00:18:23,915 Jane: Zoe lives in California and is seven and wonders, why do 314 00:18:23,915 --> 00:18:27,395 you need to do math? We already said math has helped people 315 00:18:27,395 --> 00:18:30,695 survive, but what are some of the other ways math is needed? 316 00:18:30,815 --> 00:18:33,380 Dr. Melania Alvarez: Well, you need to do math for for so many 317 00:18:33,380 --> 00:18:38,660 things. You need to do math to go to the supermarket. You need 318 00:18:38,660 --> 00:18:43,040 to do math to trade with people. You need to do math, to build a 319 00:18:43,040 --> 00:18:48,020 house, to build a pyramid, to study chemistry, to read graphs 320 00:18:48,020 --> 00:18:52,040 about how, who's going to win the presidential election. So we 321 00:18:52,040 --> 00:18:55,805 also need to know, like, for example, if you are in class and 322 00:18:55,805 --> 00:18:58,745 you want to go to recess and you want to know how many minutes 323 00:18:58,745 --> 00:19:01,085 are there to recess? So you can count them. Oh, it's almost 324 00:19:01,085 --> 00:19:05,405 almost five minutes to recess, I want to go there. Also, if you, 325 00:19:05,405 --> 00:19:09,305 if you like, to trade cards. How many cards should I trade for 326 00:19:09,305 --> 00:19:12,665 this card? That card is worth three of these cards. And now, 327 00:19:12,905 --> 00:19:16,925 for example, all this technology, the phones, the TVs, 328 00:19:16,985 --> 00:19:21,350 everything, all of that was created thanks to math. 329 00:19:21,590 --> 00:19:24,770 Saanvi: My name is Saanvi. I'm 10 years old, and I live in 330 00:19:24,770 --> 00:19:28,010 Bothell, Washington. Is there math in everything? 331 00:19:27,980 --> 00:19:31,078 Dr. Melania Alvarez: Math is not just in everything. Math is also 332 00:19:31,149 --> 00:19:35,586 a way to see everything. We can see it in patterns from nature, 333 00:19:35,656 --> 00:19:39,670 flowers. There's a sequence called the Fibonacci sequence 334 00:19:39,741 --> 00:19:44,037 that goes one one, and then what is one plus one, is two. And 335 00:19:44,107 --> 00:19:48,544 then one plus two is three. And then if I add two and three, so 336 00:19:48,615 --> 00:19:53,051 I take the last two numbers and add them up, and then I get the 337 00:19:53,122 --> 00:19:56,643 next sequence. And what's interesting is that that 338 00:19:56,714 --> 00:20:00,798 sequence represents a lot of things that happen in nature, 339 00:20:00,869 --> 00:20:04,742 the petals in flowers, they usually, they are Fibonacci 340 00:20:04,813 --> 00:20:09,109 number. So the really math is like this invisible thread that 341 00:20:09,179 --> 00:20:13,334 connects everything around you, and it is the spiral in the 342 00:20:13,405 --> 00:20:17,137 shell. We have the rhythm in music, when you bounce a 343 00:20:17,208 --> 00:20:21,293 basketball, too. The trees in the branches. But the secret 344 00:20:21,363 --> 00:20:25,729 about this is you can see this if you are curious. You have to 345 00:20:25,800 --> 00:20:30,237 be curious, okay, to see it. So math doesn't necessarily scream 346 00:20:30,307 --> 00:20:34,603 for attention. It whispers to you, says, hey, hey, come check 347 00:20:34,674 --> 00:20:38,758 it out. Well, you have to be curious. You can notice a lot 348 00:20:38,829 --> 00:20:43,900 more if you're curious, and you can have a great time if you're curious. 349 00:20:44,740 --> 00:20:47,140 Jane: Well, you came to the right place, because anybody 350 00:20:47,140 --> 00:20:50,080 who's listening to this podcast is a curious kid. It's in the 351 00:20:50,080 --> 00:20:53,200 name of our show. So all of the kids who are listening, that's 352 00:20:53,200 --> 00:20:55,780 something that we all have in common all around the world. We 353 00:20:55,780 --> 00:20:59,620 are curious kids who want to know more about the world. So if 354 00:20:59,620 --> 00:21:04,900 you have us convinced. Let's wrap up with Alistar's question. 355 00:21:05,020 --> 00:21:08,605 Alistar: Hi, my name's Alistar. How do you become a 356 00:21:08,605 --> 00:21:10,105 mathematician? 357 00:21:10,345 --> 00:21:13,225 Jane: How do you become a mathematician? We all want to do 358 00:21:13,225 --> 00:21:15,805 it now, Melania, how do we become mathematicians? 359 00:21:15,780 --> 00:21:18,437 Dr. Melania Alvarez: So first of all, we are all mathematicians. 360 00:21:18,499 --> 00:21:21,404 You know babies, they immediately can recognize 361 00:21:21,466 --> 00:21:25,175 patterns. When we are playing and we're putting cubes on top 362 00:21:25,237 --> 00:21:28,946 of each other and trying to measure if it's going to fall or 363 00:21:29,007 --> 00:21:32,840 not fall, you know, and how to build things when we're little, 364 00:21:32,902 --> 00:21:36,734 we are all mathematicians, all of us. When we like to say, How 365 00:21:36,796 --> 00:21:40,628 many cookies I need to bake for everybody in my family, I look 366 00:21:40,690 --> 00:21:44,213 at cool pattern, I say, Oh, how does that grow? How can I 367 00:21:44,275 --> 00:21:47,922 continue this pattern, all of that. Now, mathematicians, a 368 00:21:47,984 --> 00:21:51,693 real mathematician, not just answer the questions, they also 369 00:21:51,754 --> 00:21:55,649 ask questions. A mathematician is always asking questions about 370 00:21:55,710 --> 00:21:59,666 how things work, and then tries to answer it. So this is what it 371 00:21:59,728 --> 00:22:03,066 is. Everybody, you know, everybody can do math, and we 372 00:22:03,128 --> 00:22:06,960 all can be mathematicians. Now, if what you want... asking is, 373 00:22:07,022 --> 00:22:10,484 how I become a professional mathematician, usually, most 374 00:22:10,545 --> 00:22:14,316 mathematicians, I mean, there are some who don't, but most of 375 00:22:14,378 --> 00:22:17,530 them go to university, and they... they have become 376 00:22:17,592 --> 00:22:21,548 undergraduates in math or a math related thing, and then they go 377 00:22:21,610 --> 00:22:25,319 for a PhD in mathematics, and they solve problems. Now there 378 00:22:25,380 --> 00:22:28,595 are two types of mathematicians, mainly. The applied 379 00:22:28,656 --> 00:22:31,871 mathematician and the pure mathematician. So I am an 380 00:22:31,932 --> 00:22:35,703 applied mathematician and my husband is a pure mathematician. 381 00:22:35,765 --> 00:22:39,474 So an applied mathematician people come with problems to me, 382 00:22:39,535 --> 00:22:43,430 like I have worked with problems in anthropology. I have worked 383 00:22:43,491 --> 00:22:47,324 with problems in engineering. So engineers come with a problem 384 00:22:47,386 --> 00:22:51,033 and they want, you know, they want someone who does all the 385 00:22:51,094 --> 00:22:54,989 calculations and who creates a model of what they're seeing. So 386 00:22:55,050 --> 00:22:58,945 I do that. So people comes with their problems, and I take care 387 00:22:59,006 --> 00:23:02,653 of their math problems, only their math problems. So that's 388 00:23:02,715 --> 00:23:06,300 right. The pure mathematicians, they ask questions if some 389 00:23:06,362 --> 00:23:10,194 really abstract thing can work or not work, you know, and then 390 00:23:10,256 --> 00:23:13,594 they start, they start working on the on this abstract 391 00:23:13,656 --> 00:23:17,179 mathematics that it looks like they are useless, that who 392 00:23:17,241 --> 00:23:20,826 cares, doing this math, that there doesn't seem to be real 393 00:23:19,005 --> 00:24:21,300 Dr. Melania Alvarez: did he originally have? 394 00:23:20,888 --> 00:23:24,597 application. And lo and behold, 10 years from now, 200 years 395 00:23:24,659 --> 00:23:28,367 from now, 3000 years from now, all of the sudden we find the 396 00:23:28,429 --> 00:23:32,076 application. Isn't it.. it's like magic, and that's what is 397 00:23:32,138 --> 00:23:33,560 so exciting about math. 398 00:24:21,720 --> 00:24:24,840 Jane: So I want anybody who's listening now who wants to solve 399 00:24:24,840 --> 00:24:29,040 it to pause the episode and see if you can figure it out. 400 00:24:37,820 --> 00:24:42,800 Can we go through the answer and how one way that we might be 401 00:24:42,800 --> 00:24:45,500 able to solve it, because I was thinking about it while you were 402 00:24:45,500 --> 00:24:47,840 talking, and I think I have an answer. 403 00:24:47,840 --> 00:24:49,820 Dr. Melania Alvarez: Okay, why don't you tell me what you're 404 00:24:49,820 --> 00:24:50,420 thinking about? 405 00:24:50,540 --> 00:24:53,945 Jane: Okay, I think he had seven chickens at the start. 406 00:24:54,125 --> 00:24:55,445 Dr. Melania Alvarez: And how did you solve that? 407 00:24:55,445 --> 00:24:59,405 Jane: When you said all the chickens were alive and at the 408 00:24:59,405 --> 00:25:04,745 end he had no chickens, it made me realize that when he at the 409 00:25:04,745 --> 00:25:09,005 very end at the last market, he sold half of his chickens plus 410 00:25:09,005 --> 00:25:13,985 half a chicken, he would have to have one chicken to sell, 411 00:25:13,985 --> 00:25:15,725 because no chickens were harmed. 412 00:25:15,725 --> 00:25:16,265 Dr. Melania Alvarez: Yes. 413 00:25:16,310 --> 00:25:21,290 Jane: So then I sort of went from the very end to the 414 00:25:21,290 --> 00:25:24,710 beginning by sort of adding and multiplying rather than 415 00:25:24,710 --> 00:25:28,910 subtracting and dividing. And so I think he had one chicken at 416 00:25:28,910 --> 00:25:29,630 the beginning, 417 00:25:29,630 --> 00:25:30,590 Dr. Melania Alvarez: Yes. 418 00:25:30,590 --> 00:25:33,530 Jane: Three chickens in the middle and seven chickens at the 419 00:25:33,530 --> 00:25:33,890 start. 420 00:25:34,010 --> 00:25:36,170 Dr. Melania Alvarez: And you got it absolutely correct. 421 00:25:36,410 --> 00:25:37,190 Jane: Wow, phew. 422 00:25:37,300 --> 00:25:39,040 Dr. Melania Alvarez: And that's actually, that's the way, 423 00:25:39,100 --> 00:25:42,400 working backwards, you see. So you work backwards. You said, 424 00:25:42,400 --> 00:25:45,400 Okay, I think that the first one is one, and then the next one 425 00:25:45,400 --> 00:25:47,980 will be three, because I will be, calculating what's half, you 426 00:25:47,980 --> 00:25:51,280 know, double of that, and then you calculate what will be sold, 427 00:25:51,280 --> 00:25:53,860 and then that. So you got absolutely right. So in the 428 00:25:53,860 --> 00:25:57,940 first market, he has seven chickens, and half of those 429 00:25:57,940 --> 00:26:01,645 chickens is three and a half plus half a chicken is four 430 00:26:01,645 --> 00:26:06,325 chickens. So seven minus four is three. So we're left with three 431 00:26:06,325 --> 00:26:10,285 chickens. He goes to the second market, half of those three 432 00:26:10,285 --> 00:26:13,525 chickens is one and a half chickens. And then plus half a 433 00:26:13,525 --> 00:26:18,265 chicken, that's two chickens. Three minus two is one. So we're 434 00:26:18,265 --> 00:26:22,765 left with one chicken. And the last market is one chicken, and 435 00:26:22,765 --> 00:26:25,870 then it's half of a chicken is half, and then the other half is 436 00:26:25,870 --> 00:26:30,070 one. And there we are, and oh, there were no chickens hurt in 437 00:26:30,070 --> 00:26:30,730 this puzzle. 438 00:26:33,380 --> 00:26:37,460 Jane: I was so, as you said, I was so pleased when I realized, 439 00:26:37,520 --> 00:26:40,340 oh, I can figure this out and get to the answer. 440 00:26:40,360 --> 00:26:42,580 Dr. Melania Alvarez: So there are many ways that you can solve 441 00:26:42,580 --> 00:26:45,700 a math problem. You can you can guess, and you can do a 442 00:26:45,700 --> 00:26:49,060 systematic guess, not just random numbers, but little by 443 00:26:49,060 --> 00:26:52,480 little, guesses that will give you some information. So you go 444 00:26:52,480 --> 00:26:55,900 on. You can start backwards. You can draw a diagram, too. 445 00:26:55,960 --> 00:26:58,240 Sometimes you can draw a picture, and that will help you. 446 00:26:58,240 --> 00:27:01,000 There are many ways, and that's what mathematicians use. They 447 00:27:01,000 --> 00:27:04,285 have the different ways of approaching and see what work, 448 00:27:04,285 --> 00:27:07,405 what will work, and sometimes it works, and if it doesn't work, 449 00:27:07,525 --> 00:27:09,865 then you start again. And that's all there is. 450 00:27:09,180 --> 00:27:13,320 Jane: Let's end this episode there. Did you figure out the 451 00:27:13,320 --> 00:27:16,680 answer to the puzzle? I will admit it took me a while, and I 452 00:27:16,680 --> 00:27:20,220 had to write myself some notes, and I did start to get really 453 00:27:20,220 --> 00:27:22,740 worried at one point that I wasn't going to get the answer 454 00:27:22,740 --> 00:27:25,920 right. And then my mind started to go blank, and then I thought 455 00:27:25,920 --> 00:27:29,160 of all of you listening, and I thought, oh no, you'll all be so 456 00:27:29,160 --> 00:27:34,200 disappointed in me, or think I'm not very smart. But as Melania 457 00:27:34,245 --> 00:27:38,205 was talking, I realized two things. The first was that I 458 00:27:38,205 --> 00:27:41,205 just needed to take a deep breath and start working 459 00:27:41,205 --> 00:27:45,405 backwards, and I could probably figure it out. And number two, 460 00:27:45,405 --> 00:27:49,485 that if I couldn't figure it out, that's okay. No one is 461 00:27:49,485 --> 00:27:52,725 supposed to just automatically know all the answers to things. 462 00:27:53,025 --> 00:27:55,845 And when we're learning math, part of what we're doing is 463 00:27:55,845 --> 00:28:00,390 learning how to solve problems. So I knew I could ask Melania 464 00:28:00,390 --> 00:28:03,990 for help if I got stuck, and she would steer me to the right 465 00:28:03,990 --> 00:28:08,430 strategy. Thanks to Dr. Melania Alvarez of the University of 466 00:28:08,430 --> 00:28:11,490 British Columbia and the Pacific Institute for the Mathematical 467 00:28:11,490 --> 00:28:15,330 Sciences for answering all of our math questions today. We're 468 00:28:15,330 --> 00:28:18,390 going to add some math puzzles and resources in the show notes 469 00:28:18,390 --> 00:28:22,335 if you want more. As always, if you have a question about 470 00:28:22,335 --> 00:28:25,635 anything, have an adult record you asking it on a smartphone 471 00:28:25,635 --> 00:28:29,175 using an app like voice memos, then have your adult email the 472 00:28:29,175 --> 00:28:34,455 file to questions@butwykids.org But Why is produced by Melody 473 00:28:34,455 --> 00:28:38,355 Bodette, Sarah Baik and me, Jane Lindholm at Vermont Public and 474 00:28:38,355 --> 00:28:42,840 distributed by PRX. Our video producer is Joey Palumbo, and 475 00:28:42,840 --> 00:28:46,200 our theme music is by Luke Reynolds. If you like our show, 476 00:28:46,200 --> 00:28:49,260 please have your adults help you give us a thumbs up or a review 477 00:28:49,320 --> 00:28:54,060 on whatever podcast platform you use, we'll be back in two weeks 478 00:28:54,060 --> 00:28:58,560 with an all new episode. Until then, stay curious.