1 00:00:04,280 --> 00:00:06,560 Speaker 1: Hey, and welcome to the Short Stuff. I'm Josh, and 2 00:00:06,559 --> 00:00:08,920 Speaker 1: there's Chuck. Jerry's hanging out and Dave is here in 3 00:00:09,000 --> 00:00:12,160 Speaker 1: spirit as always and this is short stuff. And Chuck, 4 00:00:12,200 --> 00:00:15,520 Speaker 1: I have a question for you about this one. Why 5 00:00:15,520 --> 00:00:20,599 Speaker 1: would you do this to us? Why it gets this math? Yes, 6 00:00:20,760 --> 00:00:24,800 Speaker 1: it's not just math. It's famously incomprehensible math. I'm going 7 00:00:24,840 --> 00:00:26,920 Speaker 1: to talk about it and explain it, so thank you 8 00:00:26,960 --> 00:00:29,920 Speaker 1: for that. Yeah, I will say that uh Lori L. 9 00:00:30,000 --> 00:00:32,600 Speaker 1: Dove from house stuff works dot com did a pretty 10 00:00:32,600 --> 00:00:36,080 Speaker 1: good job of of explaining it, I think. Um, but 11 00:00:36,200 --> 00:00:38,400 Speaker 1: I picked this because let me tell you a little 12 00:00:38,400 --> 00:00:45,240 Speaker 1: story real quick, since it's short stuff. Flashback to um 13 00:00:45,280 --> 00:00:50,640 Speaker 1: seven and a half years ago. Okay, allow me when 14 00:00:51,200 --> 00:00:53,880 Speaker 1: uh Emily and I were waiting on our daughter to 15 00:00:53,960 --> 00:00:57,520 Speaker 1: be born. We were adopting her and just she was 16 00:00:57,600 --> 00:01:00,680 Speaker 1: late and late and late, and I was like, jeez, 17 00:01:00,680 --> 00:01:03,000 Speaker 1: when is this kid going to come out? And finally 18 00:01:03,120 --> 00:01:06,560 Speaker 1: when she was born, I was like, oh, I'm curious 19 00:01:06,720 --> 00:01:10,760 Speaker 1: what celebrities she shares a birthday with. And you know, 20 00:01:10,800 --> 00:01:12,039 Speaker 1: I had a lot in my mind at the time, 21 00:01:12,080 --> 00:01:14,280 Speaker 1: so I wasn't thinking if it I knew anyone personally 22 00:01:14,680 --> 00:01:17,760 Speaker 1: and I went to Celebrity Birthdays dot com or whatever 23 00:01:17,880 --> 00:01:24,120 Speaker 1: the website is, and I saw your face, and two 24 00:01:24,160 --> 00:01:27,399 Speaker 1: things happen. Three things happen. Uh. The first thing that 25 00:01:27,440 --> 00:01:31,639 Speaker 1: happened was you gotta be kidding me seriously. The second 26 00:01:31,680 --> 00:01:35,600 Speaker 1: thing that happened was, oh, that's actually really great because 27 00:01:35,640 --> 00:01:39,520 Speaker 1: I'll never forget Josh's birthday like my whole life, and 28 00:01:39,560 --> 00:01:41,760 Speaker 1: it's kind of cool that you guys share a birthday. 29 00:01:42,400 --> 00:01:44,520 Speaker 1: And then the third thing was what is Josh doing 30 00:01:44,560 --> 00:01:47,800 Speaker 1: on Celebrity Birthdays dot com? And why am I not 31 00:01:47,920 --> 00:01:50,600 Speaker 1: on it? Well, my friend, I have an update for 32 00:01:50,640 --> 00:01:52,760 Speaker 1: you because you told that story not too long ago 33 00:01:53,000 --> 00:01:55,960 Speaker 1: and it got me into action. So I used whatever 34 00:01:56,040 --> 00:01:59,400 Speaker 1: cloud I might have at Famous Birthdays dot com and 35 00:01:59,560 --> 00:02:01,880 Speaker 1: um dominated you to be on the site as well. 36 00:02:01,960 --> 00:02:05,600 Speaker 1: So hopefully I'm hoping that they will listen and then 37 00:02:05,680 --> 00:02:08,519 Speaker 1: get you up there on before your birthday. So that 38 00:02:08,560 --> 00:02:10,720 Speaker 1: could be even more embarrassing and more egg on my 39 00:02:10,760 --> 00:02:14,560 Speaker 1: face if they go, no, you deserve it. I even said, 40 00:02:14,600 --> 00:02:16,720 Speaker 1: I was like, he's at least as famous as I am. 41 00:02:16,720 --> 00:02:18,640 Speaker 1: If I'm from there, he should be on there too, 42 00:02:18,720 --> 00:02:20,760 Speaker 1: So it just seems right, you know. So you guys 43 00:02:20,760 --> 00:02:24,280 Speaker 1: share birthday, which is very cool and awesome and fun, 44 00:02:24,480 --> 00:02:26,680 Speaker 1: and I just think it's lovely. Now. Even though it's 45 00:02:26,720 --> 00:02:30,840 Speaker 1: initially like what because you don't want to, like I 46 00:02:30,840 --> 00:02:33,000 Speaker 1: don't know something about sharing birthdays, some people can get 47 00:02:33,000 --> 00:02:35,600 Speaker 1: a little selfish, be like I want my birthday to myself. 48 00:02:36,960 --> 00:02:39,520 Speaker 1: But what we're talking about is sharing birthdays. And what 49 00:02:39,560 --> 00:02:42,800 Speaker 1: are the odds of sharing birthdays with someone? You would 50 00:02:42,800 --> 00:02:46,600 Speaker 1: think it would be one in three d and sixty Yeah, 51 00:02:46,720 --> 00:02:49,840 Speaker 1: And actually I think if you, um put two people 52 00:02:49,880 --> 00:02:53,040 Speaker 1: in a room together, that is the odd although I'm 53 00:02:53,080 --> 00:02:56,040 Speaker 1: sure I'm wrong about it right out of the gate. No, 54 00:02:56,840 --> 00:03:00,000 Speaker 1: I am wrong. I was. There's a one in three 55 00:03:00,080 --> 00:03:04,000 Speaker 1: hundred and sixty four chance if you put two people 56 00:03:04,200 --> 00:03:07,400 Speaker 1: in a room together. The thing is, um, if you 57 00:03:07,440 --> 00:03:11,280 Speaker 1: start putting more people in the room together, the chances 58 00:03:11,320 --> 00:03:14,160 Speaker 1: don't increase linearly. It's not if you put three people 59 00:03:14,160 --> 00:03:16,600 Speaker 1: in the room. It's not like there's a three in 60 00:03:17,080 --> 00:03:23,240 Speaker 1: three hundred and sixty four chance. Man, math, It's not 61 00:03:23,320 --> 00:03:26,280 Speaker 1: like it just increases linearly, like one after the other 62 00:03:26,320 --> 00:03:30,400 Speaker 1: after the other. It starts to increase exponentially, and what 63 00:03:30,520 --> 00:03:32,960 Speaker 1: you end up with is what's called the birthday paradox, 64 00:03:33,000 --> 00:03:35,440 Speaker 1: which if you say that to anyone who knows anything 65 00:03:35,440 --> 00:03:37,440 Speaker 1: about math, they will laugh at you and say, it's 66 00:03:37,440 --> 00:03:39,839 Speaker 1: not actually a paradox. It's just that most people don't 67 00:03:39,880 --> 00:03:43,360 Speaker 1: understand it. We really call it the birthday problem. Yeah, 68 00:03:43,400 --> 00:03:46,080 Speaker 1: because here's the thing. And the more you read about this, 69 00:03:46,120 --> 00:03:48,840 Speaker 1: and the more mathematicians you talk to, they all kind 70 00:03:48,840 --> 00:03:50,920 Speaker 1: of very like they kind of pat you on the 71 00:03:50,920 --> 00:03:53,520 Speaker 1: head and laugh a little bit and say, oh, you 72 00:03:53,680 --> 00:04:00,440 Speaker 1: norms are not very good at calculating things exponentially correct 73 00:04:00,520 --> 00:04:02,720 Speaker 1: like we are. We are very good at it because 74 00:04:02,720 --> 00:04:04,680 Speaker 1: we have studied it and trained to do so. But 75 00:04:05,320 --> 00:04:08,800 Speaker 1: you people, just your little p brains just don't think 76 00:04:08,840 --> 00:04:11,520 Speaker 1: that way, and so you do very rudimentary math that 77 00:04:11,640 --> 00:04:14,240 Speaker 1: is completely wrong when it comes to figuring out like 78 00:04:14,480 --> 00:04:16,800 Speaker 1: the odds of sharing or odds of a lot of things, 79 00:04:16,839 --> 00:04:19,760 Speaker 1: but the odds of sharing your birthday, right and there. 80 00:04:19,880 --> 00:04:21,640 Speaker 1: It's true. They don't have to say it, but it 81 00:04:21,760 --> 00:04:23,839 Speaker 1: is true. It is true. I say, we take a 82 00:04:23,839 --> 00:04:25,479 Speaker 1: break and then we come back and explain what the 83 00:04:25,520 --> 00:04:50,120 Speaker 1: heck is going on here? How about that? Let's do it, okay, Chuck, 84 00:04:50,160 --> 00:04:52,760 Speaker 1: So we should set up the birthday problem or birthday 85 00:04:52,760 --> 00:04:56,040 Speaker 1: paradox to you and me, The question is this, how 86 00:04:56,160 --> 00:05:00,279 Speaker 1: large is a group of people, random people where every 87 00:05:00,400 --> 00:05:03,880 Speaker 1: day of the year, excluding leap years, has an equal 88 00:05:03,960 --> 00:05:08,640 Speaker 1: chance of, um being somebody's birthday, and there are no twins, 89 00:05:09,120 --> 00:05:12,320 Speaker 1: it's all individual people. How many people do you have 90 00:05:12,400 --> 00:05:16,039 Speaker 1: to get in the group before two of them will 91 00:05:16,080 --> 00:05:22,360 Speaker 1: share a birthday? That's right? Wow, did you do that 92 00:05:22,400 --> 00:05:26,000 Speaker 1: off of off of your dome? Know that that's the answer. 93 00:05:27,120 --> 00:05:29,840 Speaker 1: The larger the group you have, the greater the odds 94 00:05:29,880 --> 00:05:35,880 Speaker 1: are obviously, um. So it Yeah, it's an exponential math problem, 95 00:05:36,000 --> 00:05:39,720 Speaker 1: and our brains don't generally think that way. So what 96 00:05:39,760 --> 00:05:41,600 Speaker 1: you have to do is you have to look at 97 00:05:41,600 --> 00:05:43,560 Speaker 1: the number of people in a room. Let's say you 98 00:05:43,560 --> 00:05:47,320 Speaker 1: got your twenty three people, and if you're comparing just 99 00:05:47,480 --> 00:05:52,599 Speaker 1: yourself to the under other twenty two people in the room, 100 00:05:52,720 --> 00:05:55,800 Speaker 1: then you're just gonna end up with those twenty two comparisons. 101 00:05:56,200 --> 00:05:59,160 Speaker 1: But when you're talking about exponential math, you can't just 102 00:05:59,200 --> 00:06:01,520 Speaker 1: look at the one person in that room. You have 103 00:06:01,600 --> 00:06:05,880 Speaker 1: to compare that probability for all the people in the room. 104 00:06:05,880 --> 00:06:09,039 Speaker 1: So the first person would say, all right, I have 105 00:06:09,120 --> 00:06:12,040 Speaker 1: those twenty two comparisons. Then the next person would step 106 00:06:12,120 --> 00:06:14,880 Speaker 1: up and do the comparison, but there would be one 107 00:06:14,960 --> 00:06:18,080 Speaker 1: less because they've already been compared to the one first person. 108 00:06:18,920 --> 00:06:20,640 Speaker 1: And so on and so on until you get to 109 00:06:20,640 --> 00:06:26,040 Speaker 1: the last person. Yeah. Our syllopsism uh misguides us in 110 00:06:26,040 --> 00:06:28,039 Speaker 1: this case because we fail to think about all the 111 00:06:28,040 --> 00:06:31,920 Speaker 1: other people who connect with other people. Right. So I've 112 00:06:31,920 --> 00:06:34,799 Speaker 1: seen a couple of ways to do this. One way 113 00:06:35,040 --> 00:06:38,719 Speaker 1: is to say, um that if you have twenty three 114 00:06:38,800 --> 00:06:43,479 Speaker 1: people in a in a room, Um, you have twenty 115 00:06:43,520 --> 00:06:50,640 Speaker 1: three people times twenty two um possible pairings. Divide that 116 00:06:50,760 --> 00:06:54,200 Speaker 1: number by two, and what you end up with is 117 00:06:54,200 --> 00:06:58,640 Speaker 1: two and fifty three. Okay, that's a really simple easy 118 00:06:58,720 --> 00:07:01,520 Speaker 1: way that Ted Ed taught me to do it. But 119 00:07:01,600 --> 00:07:03,440 Speaker 1: you have to get to the number. Let me put 120 00:07:03,480 --> 00:07:05,360 Speaker 1: it in a different way, Chuck. For that formula, Let's 121 00:07:05,360 --> 00:07:09,640 Speaker 1: say you have five people. Five people have UM twenty 122 00:07:09,720 --> 00:07:14,880 Speaker 1: possible pairings, right, Okay, because if you if you connect 123 00:07:14,960 --> 00:07:18,400 Speaker 1: each person one time, you're gonna come up with twenty 124 00:07:18,480 --> 00:07:22,400 Speaker 1: possible pairings. But half of those are redundant. Right, So 125 00:07:22,600 --> 00:07:25,640 Speaker 1: connecting A to B in person B two A is 126 00:07:25,680 --> 00:07:29,920 Speaker 1: the same thing. That's why you divide that number by two, right, 127 00:07:30,200 --> 00:07:33,480 Speaker 1: so you got five times four equals twenty divided by two, 128 00:07:33,640 --> 00:07:38,200 Speaker 1: which means you have ten genuinely possible pairings in total. 129 00:07:39,120 --> 00:07:40,880 Speaker 1: Another way to do it, to get to the number 130 00:07:40,960 --> 00:07:44,640 Speaker 1: is you take that one the first comparison, three hundred 131 00:07:44,640 --> 00:07:46,960 Speaker 1: and sixty four to three hundred and sixty five divided 132 00:07:46,960 --> 00:07:49,280 Speaker 1: by three sixty five, and then for the next person, 133 00:07:49,400 --> 00:07:52,320 Speaker 1: three hundred sixty three divided by three sixty five, and 134 00:07:52,400 --> 00:07:54,800 Speaker 1: the next person three sixty two, and so on and 135 00:07:54,840 --> 00:07:57,320 Speaker 1: so forth. And if you do that for twenty three 136 00:07:57,360 --> 00:08:01,840 Speaker 1: different people and you take each to the products of 137 00:08:01,880 --> 00:08:06,680 Speaker 1: those equations, all those little little tiny percentages, and multiply them, 138 00:08:07,000 --> 00:08:09,840 Speaker 1: what you come up with is forty nine point eight 139 00:08:09,920 --> 00:08:13,000 Speaker 1: three percent, which means that what you've just done is 140 00:08:13,040 --> 00:08:15,960 Speaker 1: show that there is a forty nine point three percent 141 00:08:16,000 --> 00:08:18,240 Speaker 1: that they're not going to have a birthday. And then 142 00:08:18,240 --> 00:08:20,800 Speaker 1: you just figure out the inverse of that, and you 143 00:08:20,840 --> 00:08:23,480 Speaker 1: come up with a fifty point seventeen percent chance with 144 00:08:23,520 --> 00:08:25,960 Speaker 1: twenty three people that um two of them are going 145 00:08:26,000 --> 00:08:28,920 Speaker 1: to share the same birthday. And again it's because you're 146 00:08:28,960 --> 00:08:31,960 Speaker 1: not coming up with twenty three comparisons, there's two hundred 147 00:08:31,960 --> 00:08:35,640 Speaker 1: and fifty three comparisons, and of just three hundred and 148 00:08:35,679 --> 00:08:40,080 Speaker 1: sixty five days in a year. That's right, I guess. 149 00:08:40,120 --> 00:08:43,360 Speaker 1: The last part of because there's sort of the third 150 00:08:43,400 --> 00:08:44,800 Speaker 1: way to do it, which I kind of started but 151 00:08:44,840 --> 00:08:47,520 Speaker 1: didn't even really finish, is you know, you make those 152 00:08:47,520 --> 00:08:50,920 Speaker 1: twenty two comparisons that first person does, and then the 153 00:08:50,920 --> 00:08:54,640 Speaker 1: next person makes twenty one comparisons, next person makes nineteen 154 00:08:55,120 --> 00:08:58,439 Speaker 1: again because they've already made those other comparisons, and all 155 00:08:58,480 --> 00:09:00,679 Speaker 1: you do is add those numbers all up, you know, 156 00:09:01,600 --> 00:09:04,360 Speaker 1: so on on so on, and adding those together will 157 00:09:04,400 --> 00:09:07,559 Speaker 1: eventually lead to those two hundred and fifty three comparisons 158 00:09:08,400 --> 00:09:13,200 Speaker 1: or combinations of comparisons. Rather, so there's something that escapes me. 159 00:09:13,280 --> 00:09:16,200 Speaker 1: We just generally explained it well. Although I'm sure there's 160 00:09:16,240 --> 00:09:19,920 Speaker 1: some people out there cringing, laughing, crying, who who know 161 00:09:20,000 --> 00:09:21,960 Speaker 1: about this kind of stuff. They're like, this is just 162 00:09:22,040 --> 00:09:25,400 Speaker 1: the saddest thing I've ever heard. We generally explained it. 163 00:09:26,840 --> 00:09:30,679 Speaker 1: I still don't understand how two hundred and fifty three 164 00:09:31,760 --> 00:09:36,400 Speaker 1: comparisons for a possible pool of three hundred and sixty 165 00:09:36,440 --> 00:09:42,120 Speaker 1: five dates leads to a fifty percent chance for three people. 166 00:09:44,440 --> 00:09:47,640 Speaker 1: It doesn't make sense. I'm just airing a grievance really 167 00:09:47,640 --> 00:09:50,600 Speaker 1: more than anything, I don't understand it at all. Um. 168 00:09:50,640 --> 00:09:53,640 Speaker 1: The upshot of it, though, is that, um, when you 169 00:09:53,679 --> 00:09:59,080 Speaker 1: get to seventy people, the pairings have grown so exponentially that, um, 170 00:09:59,120 --> 00:10:02,840 Speaker 1: there's a ninet greater than a ninety nine percent chance 171 00:10:02,920 --> 00:10:05,559 Speaker 1: that there will be a pair of people that share 172 00:10:05,600 --> 00:10:09,400 Speaker 1: a birthday. Again, though we're talking about more than two thousand, 173 00:10:10,679 --> 00:10:15,680 Speaker 1: um comparisons for three hundred and sixty five days. Why 174 00:10:15,760 --> 00:10:18,640 Speaker 1: is that not like five percent chance that there's going 175 00:10:18,679 --> 00:10:23,080 Speaker 1: to be two people that have the same birthday? Yeah, 176 00:10:23,760 --> 00:10:28,000 Speaker 1: I don't know. Uh. With another kind of cool thing 177 00:10:28,040 --> 00:10:30,400 Speaker 1: that was um that Laurie from the House Stuff Works 178 00:10:30,440 --> 00:10:33,400 Speaker 1: article included, which is just another kind of fun example 179 00:10:33,440 --> 00:10:38,480 Speaker 1: of how exponential growth works is and this is I think, um, 180 00:10:38,520 --> 00:10:41,320 Speaker 1: I think she might have interviewed a mathematician. Yeah, his 181 00:10:41,400 --> 00:10:43,640 Speaker 1: name is Frost. Oh yeah, he was laughing at you 182 00:10:43,679 --> 00:10:45,920 Speaker 1: and me the whole time and he doesn't even know us. Yeah, 183 00:10:45,960 --> 00:10:47,599 Speaker 1: he's the one that was like, yeah, you guys just 184 00:10:47,640 --> 00:10:50,760 Speaker 1: aren't very good at this. Uh. Is if you're like, 185 00:10:50,800 --> 00:10:52,760 Speaker 1: if you think of it in terms of money, and 186 00:10:52,960 --> 00:10:55,560 Speaker 1: the example that he used is, um, if you're going 187 00:10:55,600 --> 00:10:58,160 Speaker 1: to be offered a one penny on the first day, 188 00:10:58,520 --> 00:11:01,760 Speaker 1: then two pennies on the second, three pennies on the third, 189 00:11:02,400 --> 00:11:05,200 Speaker 1: and then so on so on for thirty days. It 190 00:11:05,280 --> 00:11:07,320 Speaker 1: might not seem like much money, but at the end 191 00:11:07,360 --> 00:11:12,000 Speaker 1: of the thirtieth day, that is ten point seven million dollars. Right. 192 00:11:12,200 --> 00:11:14,560 Speaker 1: Millionaires who are good at math love to do that 193 00:11:14,600 --> 00:11:16,760 Speaker 1: to people because they turned down this good deal, and 194 00:11:16,760 --> 00:11:18,480 Speaker 1: then they explained to them how it was a great 195 00:11:18,520 --> 00:11:21,000 Speaker 1: deal and they're so dumb. That's how the robber barons 196 00:11:21,040 --> 00:11:25,120 Speaker 1: hoodwinked the generation of people. That's right. Uh, can we 197 00:11:25,200 --> 00:11:28,880 Speaker 1: please end this torment? Yeah, I'm done, Okay, Choice stuff 198 00:11:28,920 --> 00:11:34,280 Speaker 1: is out. Stuff you Should Know is a production of 199 00:11:34,280 --> 00:11:37,600 Speaker 1: I Heart Radio. For more podcasts my heart Radio, visit 200 00:11:37,640 --> 00:11:40,439 Speaker 1: the i heart Radio app, Apple Podcasts, or wherever you 201 00:11:40,520 --> 00:11:41,800 Speaker 1: listen to your favorite shows.