Speaker 1: Hey, and welcome to the Short Stuff. I'm Josh, and
Speaker 1: there's Chuck. Jerry's hanging out and Dave is here in
Speaker 1: spirit as always and this is short stuff. And Chuck,
Speaker 1: I have a question for you about this one. Why
Speaker 1: would you do this to us? Why it gets this math? Yes,
Speaker 1: it's not just math. It's famously incomprehensible math. I'm going
Speaker 1: to talk about it and explain it, so thank you
Speaker 1: for that. Yeah, I will say that uh Lori L.
Speaker 1: Dove from house stuff works dot com did a pretty
Speaker 1: good job of of explaining it, I think. Um, but
Speaker 1: I picked this because let me tell you a little
Speaker 1: story real quick, since it's short stuff. Flashback to um
Speaker 1: seven and a half years ago. Okay, allow me when
Speaker 1: uh Emily and I were waiting on our daughter to
Speaker 1: be born. We were adopting her and just she was
Speaker 1: late and late and late, and I was like, jeez,
Speaker 1: when is this kid going to come out? And finally
Speaker 1: when she was born, I was like, oh, I'm curious
Speaker 1: what celebrities she shares a birthday with. And you know,
Speaker 1: I had a lot in my mind at the time,
Speaker 1: so I wasn't thinking if it I knew anyone personally
Speaker 1: and I went to Celebrity Birthdays dot com or whatever
Speaker 1: the website is, and I saw your face, and two
Speaker 1: things happen. Three things happen. Uh. The first thing that
Speaker 1: happened was you gotta be kidding me seriously. The second
Speaker 1: thing that happened was, oh, that's actually really great because
Speaker 1: I'll never forget Josh's birthday like my whole life, and
Speaker 1: it's kind of cool that you guys share a birthday.
Speaker 1: And then the third thing was what is Josh doing
Speaker 1: on Celebrity Birthdays dot com? And why am I not
Speaker 1: on it? Well, my friend, I have an update for
Speaker 1: you because you told that story not too long ago
Speaker 1: and it got me into action. So I used whatever
Speaker 1: cloud I might have at Famous Birthdays dot com and
Speaker 1: um dominated you to be on the site as well.
Speaker 1: So hopefully I'm hoping that they will listen and then
Speaker 1: get you up there on before your birthday. So that
Speaker 1: could be even more embarrassing and more egg on my
Speaker 1: face if they go, no, you deserve it. I even said,
Speaker 1: I was like, he's at least as famous as I am.
Speaker 1: If I'm from there, he should be on there too,
Speaker 1: So it just seems right, you know. So you guys
Speaker 1: share birthday, which is very cool and awesome and fun,
Speaker 1: and I just think it's lovely. Now. Even though it's
Speaker 1: initially like what because you don't want to, like I
Speaker 1: don't know something about sharing birthdays, some people can get
Speaker 1: a little selfish, be like I want my birthday to myself.
Speaker 1: But what we're talking about is sharing birthdays. And what
Speaker 1: are the odds of sharing birthdays with someone? You would
Speaker 1: think it would be one in three d and sixty Yeah,
Speaker 1: And actually I think if you, um put two people
Speaker 1: in a room together, that is the odd although I'm
Speaker 1: sure I'm wrong about it right out of the gate. No,
Speaker 1: I am wrong. I was. There's a one in three
Speaker 1: hundred and sixty four chance if you put two people
Speaker 1: in a room together. The thing is, um, if you
Speaker 1: start putting more people in the room together, the chances
Speaker 1: don't increase linearly. It's not if you put three people
Speaker 1: in the room. It's not like there's a three in
Speaker 1: three hundred and sixty four chance. Man, math, It's not
Speaker 1: like it just increases linearly, like one after the other
Speaker 1: after the other. It starts to increase exponentially, and what
Speaker 1: you end up with is what's called the birthday paradox,
Speaker 1: which if you say that to anyone who knows anything
Speaker 1: about math, they will laugh at you and say, it's
Speaker 1: not actually a paradox. It's just that most people don't
Speaker 1: understand it. We really call it the birthday problem. Yeah,
Speaker 1: because here's the thing. And the more you read about this,
Speaker 1: and the more mathematicians you talk to, they all kind
Speaker 1: of very like they kind of pat you on the
Speaker 1: head and laugh a little bit and say, oh, you
Speaker 1: norms are not very good at calculating things exponentially correct
Speaker 1: like we are. We are very good at it because
Speaker 1: we have studied it and trained to do so. But
Speaker 1: you people, just your little p brains just don't think
Speaker 1: that way, and so you do very rudimentary math that
Speaker 1: is completely wrong when it comes to figuring out like
Speaker 1: the odds of sharing or odds of a lot of things,
Speaker 1: but the odds of sharing your birthday, right and there.
Speaker 1: It's true. They don't have to say it, but it
Speaker 1: is true. It is true. I say, we take a
Speaker 1: break and then we come back and explain what the
Speaker 1: heck is going on here? How about that? Let's do it, okay, Chuck,
Speaker 1: So we should set up the birthday problem or birthday
Speaker 1: paradox to you and me, The question is this, how
Speaker 1: large is a group of people, random people where every
Speaker 1: day of the year, excluding leap years, has an equal
Speaker 1: chance of, um being somebody's birthday, and there are no twins,
Speaker 1: it's all individual people. How many people do you have
Speaker 1: to get in the group before two of them will
Speaker 1: share a birthday? That's right? Wow, did you do that
Speaker 1: off of off of your dome? Know that that's the answer.
Speaker 1: The larger the group you have, the greater the odds
Speaker 1: are obviously, um. So it Yeah, it's an exponential math problem,
Speaker 1: and our brains don't generally think that way. So what
Speaker 1: you have to do is you have to look at
Speaker 1: the number of people in a room. Let's say you
Speaker 1: got your twenty three people, and if you're comparing just
Speaker 1: yourself to the under other twenty two people in the room,
Speaker 1: then you're just gonna end up with those twenty two comparisons.
Speaker 1: But when you're talking about exponential math, you can't just
Speaker 1: look at the one person in that room. You have
Speaker 1: to compare that probability for all the people in the room.
Speaker 1: So the first person would say, all right, I have
Speaker 1: those twenty two comparisons. Then the next person would step
Speaker 1: up and do the comparison, but there would be one
Speaker 1: less because they've already been compared to the one first person.
Speaker 1: And so on and so on until you get to
Speaker 1: the last person. Yeah. Our syllopsism uh misguides us in
Speaker 1: this case because we fail to think about all the
Speaker 1: other people who connect with other people. Right. So I've
Speaker 1: seen a couple of ways to do this. One way
Speaker 1: is to say, um that if you have twenty three
Speaker 1: people in a in a room, Um, you have twenty
Speaker 1: three people times twenty two um possible pairings. Divide that
Speaker 1: number by two, and what you end up with is
Speaker 1: two and fifty three. Okay, that's a really simple easy
Speaker 1: way that Ted Ed taught me to do it. But
Speaker 1: you have to get to the number. Let me put
Speaker 1: it in a different way, Chuck. For that formula, Let's
Speaker 1: say you have five people. Five people have UM twenty
Speaker 1: possible pairings, right, Okay, because if you if you connect
Speaker 1: each person one time, you're gonna come up with twenty
Speaker 1: possible pairings. But half of those are redundant. Right, So
Speaker 1: connecting A to B in person B two A is
Speaker 1: the same thing. That's why you divide that number by two, right,
Speaker 1: so you got five times four equals twenty divided by two,
Speaker 1: which means you have ten genuinely possible pairings in total.
Speaker 1: Another way to do it, to get to the number
Speaker 1: is you take that one the first comparison, three hundred
Speaker 1: and sixty four to three hundred and sixty five divided
Speaker 1: by three sixty five, and then for the next person,
Speaker 1: three hundred sixty three divided by three sixty five, and
Speaker 1: the next person three sixty two, and so on and
Speaker 1: so forth. And if you do that for twenty three
Speaker 1: different people and you take each to the products of
Speaker 1: those equations, all those little little tiny percentages, and multiply them,
Speaker 1: what you come up with is forty nine point eight
Speaker 1: three percent, which means that what you've just done is
Speaker 1: show that there is a forty nine point three percent
Speaker 1: that they're not going to have a birthday. And then
Speaker 1: you just figure out the inverse of that, and you
Speaker 1: come up with a fifty point seventeen percent chance with
Speaker 1: twenty three people that um two of them are going
Speaker 1: to share the same birthday. And again it's because you're
Speaker 1: not coming up with twenty three comparisons, there's two hundred
Speaker 1: and fifty three comparisons, and of just three hundred and
Speaker 1: sixty five days in a year. That's right, I guess.
Speaker 1: The last part of because there's sort of the third
Speaker 1: way to do it, which I kind of started but
Speaker 1: didn't even really finish, is you know, you make those
Speaker 1: twenty two comparisons that first person does, and then the
Speaker 1: next person makes twenty one comparisons, next person makes nineteen
Speaker 1: again because they've already made those other comparisons, and all
Speaker 1: you do is add those numbers all up, you know,
Speaker 1: so on on so on, and adding those together will
Speaker 1: eventually lead to those two hundred and fifty three comparisons
Speaker 1: or combinations of comparisons. Rather, so there's something that escapes me.
Speaker 1: We just generally explained it well. Although I'm sure there's
Speaker 1: some people out there cringing, laughing, crying, who who know
Speaker 1: about this kind of stuff. They're like, this is just
Speaker 1: the saddest thing I've ever heard. We generally explained it.
Speaker 1: I still don't understand how two hundred and fifty three
Speaker 1: comparisons for a possible pool of three hundred and sixty
Speaker 1: five dates leads to a fifty percent chance for three people.
Speaker 1: It doesn't make sense. I'm just airing a grievance really
Speaker 1: more than anything, I don't understand it at all. Um.
Speaker 1: The upshot of it, though, is that, um, when you
Speaker 1: get to seventy people, the pairings have grown so exponentially that, um,
Speaker 1: there's a ninet greater than a ninety nine percent chance
Speaker 1: that there will be a pair of people that share
Speaker 1: a birthday. Again, though we're talking about more than two thousand,
Speaker 1: um comparisons for three hundred and sixty five days. Why
Speaker 1: is that not like five percent chance that there's going
Speaker 1: to be two people that have the same birthday? Yeah,
Speaker 1: I don't know. Uh. With another kind of cool thing
Speaker 1: that was um that Laurie from the House Stuff Works
Speaker 1: article included, which is just another kind of fun example
Speaker 1: of how exponential growth works is and this is I think, um,
Speaker 1: I think she might have interviewed a mathematician. Yeah, his
Speaker 1: name is Frost. Oh yeah, he was laughing at you
Speaker 1: and me the whole time and he doesn't even know us. Yeah,
Speaker 1: he's the one that was like, yeah, you guys just
Speaker 1: aren't very good at this. Uh. Is if you're like,
Speaker 1: if you think of it in terms of money, and
Speaker 1: the example that he used is, um, if you're going
Speaker 1: to be offered a one penny on the first day,
Speaker 1: then two pennies on the second, three pennies on the third,
Speaker 1: and then so on so on for thirty days. It
Speaker 1: might not seem like much money, but at the end
Speaker 1: of the thirtieth day, that is ten point seven million dollars. Right.
Speaker 1: Millionaires who are good at math love to do that
Speaker 1: to people because they turned down this good deal, and
Speaker 1: then they explained to them how it was a great
Speaker 1: deal and they're so dumb. That's how the robber barons
Speaker 1: hoodwinked the generation of people. That's right. Uh, can we
Speaker 1: please end this torment? Yeah, I'm done, Okay, Choice stuff
Speaker 1: is out. Stuff you Should Know is a production of
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