A Problem Squared - 030 = Genetic Draws and Wheels vs Doors

Episode Date: March 28, 2022

In this episode...   * What are the odds of having the same child twice?   * Wheels or Doors?   * And Bec recommends some new nerdy podcasts!    Don't forget too send in your Blue Dot Festival problems to us on the website below - we might just do it live!    And, as always, if you've got a problem or a solution, hit us up on aproblemsquared.com.   And if you want want even more from A Problem Squared (and who doesn't) find us on Twitter and Instagram

Hello, and welcome to A Problem Squared, the podcast equivalent of a hot dog, in that it's satisfying but should only be consumed as part of a balanced and well-informed diet. It can also get a bit messy if its sources are inaccurate. Yes. The bun in this analogy is your host, Matt Parker, who holds everything together and is very long and surprisingly high in sugar. Oh, I just measured my height in sugar cubes.

If we were to measure you in sugar, it would be surprisingly high. Are you saying I'm sweeter than people expect? Is that the angle you're going for? You know, like normally people say that about mean people. Oh, they're sweeter than you expect. Well, I have got resting sarcasm voice, which can be a problem. Where if I say, I say most things, I'm like, Beck, that was just a great introduction. It's so true. Like introduction it's so true like it's so true

i need to be careful because if i just state a fact i sound sarcastic and so i'm aware there have been multiple times where i've thought that you were taking the mickey and uh you've been like no i'm genuinely impressed by something you've done exactly exactly oh just let me have this one matt and you're like i'm trying really hard so i will accept uh sweeter than people expect i mean you're not now because you've ruined my intro the bun in this analogy is your host but, Matt Parker, holds everything together, is very long and sarcastic. And I'm your other host, Bec Hill. The catch-up.

By no means the star of the show, but without me, the whole thing can get a bit dry. Matt, for the listeners, Matt just stared at me blankly while slow clapping. It was impressive. I meant that genuinely. In today's episode. I answer the question of can you have the same offspring twice? We answer the question, doors or wheels. And we've got some podcast recommendations,

which is the answer to a problem that we'll send in. And then so many other business. Matt, before I ask you how you are, we've had some lovely reviews. Thank you to everyone who sends us in reviews as well. We really appreciate some more five stars these are very helpful for making sure that other people find and listen to this podcast but i wanted to highlight this review from phil chater who made that headline vet killer's incredible and the maths dude isn't too shabby either. Waiter. You got real resting sarcasm review there, Phil. And that's just the title to his review. I think Phil felt sorry for me. Yeah.

Yeah, to be fair, Phil then doesn't expand on that any further. Phil then says, if you only get to listen to one podcast this month, you probably should learn to manage your time better. Failing that, give a problem squared a listen. Oh, opens with a joke. Yeah. And closes. It's entertainment and education in one show.

Ding. There are two things I love about this. Insulting me aside. One is everyone's just putting ding in their reviews, which makes no sense to anyone who has not yet listened to the podcast. But hopefully that's intriguing. And we seem to have strayed into, and this is becoming a theme in the reviews, that they are complimenting one of us and insulting the other. Yeah.

How, how major can we go with this? You need to, you need to subtly compliment one of us and insult the other, right? But nothing that's going to get us You have to start reporting people. Matt, how have you been? You know what, Beck? I have been, well, a little bit sad. Why have you been sad? Because you, you were unable to join myself and my dear wife at an event that we were looking forward to immensely. Yes, that I invited you to.

That you invited, you got us invited to this event. And do you want to tell all the listeners why you were unable to join us? I, uh, I got COVID. I got COVID from my stupid husband. Yeah. We're skipping ahead to to the how are you Beck section. Yeah, I am. I am still, I am COVID-y. I will try my best not to cough during the record, but if I sound a bit off, that is why. Yeah.

That's your dedication to the podcast. I was like, no Beck, we'll take, we'll skip an episode. And you're like, the listeners depend on us. Exactly. But it does mean for our listeners depend on us. Exactly. But it does mean for our Patreon listeners, I'm a Wizard will be coming out in the next episode. Yes. We've delayed everything apart from this one episode. Yeah.

Let's not push it. So, yeah. I couldn't make the event. I was gutted. I was very, I called you as soon as I got the invite to this event and said, if I can get you guys in, will you come? You did. And you, and you guys, you, you had theater tickets that night and you canceled. I re, I rescheduled our theater trip to do the event.

Oh, and even our producers now screaming, what was the event? And we haven't said what it was. It was a deeply, deeply ridiculous, silly event. No, it was high class and highbrow and I shan't hear anything worse. It was, I was there Beck. It was deeply ridiculous, but I had a fantastic time. So even without you, who knows if you and your stupid husband have been able to come along, who knows the giddy heights of fun we would have had. Even missing you, we still had a great time.

I've been letting you just say it, Matt. Now you're driving me crazy. Okay. So we were at the launch event for a new season of a reality TV show. And some people may watch this. I suspect not many, but there is a show called Below Deck, which is a reality TV show where they follow super yachts. Oh, our producer is losing her mind in the chat. I take it, Lauren, that you watch Below Deck.

We did not warn her we're going to be discussing this in the episode today. So they follow super yachts and part of the episode is following the crew who work on the super yacht. And part of the episode is following the rich people who have charted the super yacht and they have different people each time and uh reality show shenanigans go from there basically is that is that an accurate summary beck i mean it's the sort of summary that i think would speak most to our listeners yeah yeah yeah it's it ridiculous TV. And they had a series set like in the Caribbean. And then they had a spinoff series set in the Mediterranean. And we were there at the launch of Below Deck Down Under. Which also, that's kind of like a, that's, that's like the opposite of an oxymoron, isn't it? It's two of the same thing. It's even further Below Deck.

Below Deck and down under. It should be down under below deck is what it should be called. I think we're in the ocean at this point. If we're down under being below deck, you're right. Do belows and down unders, do they add or do they multiply? That's my question. We're in the hull. Right.

So they've obviously thought we've got to do the UK version of an Aussie show launch. We need like the Rent an Aussie crowd. We need all the Australians who are going to come and love this show. And so they went to TV's Beckhill. Yeah. I like to think influencers. The internet. Yeah.

You influence things and people. I mean, electric sleeping bags, those sales have just, you know, they're heating up. Whereas you then invited the internet's Matt Parker. Yes. And then you neglected to show up. I did not neglect I was so sad about not going to the point that poor Gav was genuinely

like going through some real guilt feelings because he knew how much I was looking forward to going to Below Deck and because he'd tested positive because I actually got COVID like technically the day after the event but he'd tested positive.

Yeah. And so we were like, let's, yeah, let's not, I don't want to be a wang. I will, I will stay home even though I really wanted to go. And then I felt actually better about the fact that I got COVID because the next day I was like, oh, that's it. I've got it. I've tested positive. I would have felt really awful if I'd gone and then tested positive the next day and

knowing that I could have given it to other people. So yeah, I really wanted to go. So we had a great time. They had free cocktails and they had free Vegemite and cheese on toast. Oh my goodness. The only people who could stomach it, and I say people, it was just me, were those with a very high tolerance for Vegemite and a very keen instinct for free food. So you're actually surprisingly high in salt rather than sugar now.

So you're actually surprisingly high in salt rather than sugar now. Yeah, I am. I was definitely high in yeast extract and salt. And so I had more cheese and Vegemite on toast than I think I've ever had in one sitting previously. I was standing, but you get the idea. To the point where the waitstaff were like, hey, if you want anything, just let us know. We'll grab it from the kitchen for you. Like, if no one else was there for the free food, it turns out.

And even if they would, they couldn't stomach it. Yeah, so I had a direct line to the kitchen. I was like, just keep it coming. And I stole you a goodie bag. What? And I've got it right here. So here it, ready? Here's your goodie bag. Oh my gosh, it's like a proper beach bag. On the front. Yeah. On the front it says below deck and on the back it says primary charter guest.

So there you are. Oh, Matt. If you want socks that say below deck, you're in luck. I do. Where are those? Where are they? Well, here you go. There we are. There we are.

There's your below deck socks. There's a hat. I don't know why the hat, the brand of the hat is budget smuggler. And I don't. Is it the brand or is it a phrase? If it's the phrase, I think they're insulting us. Now, there are two things that I think are the peak of the bag. And I'm going to show them the one I think you're going to enjoy more followed by the one I'm going to enjoy more.

Full packet of Tim Tams. Amazing. So I don't know how they did that, but Beck, you get your full packet of Tim Tams and jar of Vegemite. Yes! I don't have any Vegemite at the moment. Which I'm super excited because I ran out literally two days before we went to this party. I finished my stock of Vegemite because it's been so long since I last got to Australia. I've not managed to stock up on my catering sized Vegemite. And I'm going back in about a month.

And suddenly the universe gave me a tiny jar of Vegemite to tide me over. I also just need to point out for the listeners that the jar that Matt is holding is not tiny. It is like a standard jar of Vegemite. It's tiny. Matt gets such big jars normally. Oh yeah, yeah, yeah. I can't be buying these on the regular.

Come on. So I fly back with a few of the big ones in my case. So Beck, next time we do an in-person recording, I will hand over this free swag bag. Yeah. Okay, Matt, this problem comes from Andrew Smith, who says, So I was driving in my car today and had the following thought. What are the odds of having the same child twice? Not twins.

Giving birth to a child, getting pregnant, then having the exact same child again. I'm guessing they mean like just genetically. By the same parents. And they said it's infinitesimal. That's how you pronounce that, isn't it? I don't know. Infinitesimal. Infinitely small. Infinitesimal. That's how you pronounce that, isn't it? I don't know. Infinitesimal. Infinitely small.

Infinitesimal? That's it. It's infinitesimal. But how much so compared to other infinitesimally unlikely occurrences? All right. So they're right to rule out twins because identical twins are identical. They have the same DNA, let's say. And I need to just warn everyone.

I am a mathematician about to just go blundering into biology. And it has previously been established. Biology is a mess. no one's sure of anything everything has exceptions i get upset however i have done my best to wade through the biological chaos and work out the probability that instead of having twins where you start with like one egg that's been fertilized so it's got all its chromosomes and then it duplicates into two. So that's where you start with one, you know, potential human. And then very early on, it splits into two identical humans, right? That's a whole separate thing. And non-identical twins, that's just where you had two humans at the same time.

This case, you have a human and then you have another identical human, because to make that first human, you're combining the genetic information of two humans and you're shuffling it around and putting it together. But there's only a certain amount of genetic information to start with, and there's only a certain number of ways you can combine it. So two people who are going to produce a child is only a finite number of possible humans they can produce. You say only. Well, for one definition of only. Why do I get the feeling that this is going to involve an exclamation mark? Both literally and punctuationally, there will be, and by literally, I mean, there's some factorials.

It's a big old number, just as a heads up. However, we're going to have to make a bunch of approximations along the way. And so I just want to say, before we go anywhere, I will occasionally say things like, I'm ignoring mutations, or I'm not worrying about this situation or that situation. And that's because all I want to get to is kind of the rough size of the number. I want to know roughly how many distinct humans can a pair of humans create with their DNA. And there's a bunch of stuff I'm just going to rule out

because it doesn't make a big difference. And I thought I'd actually start just by establishing it's okay to do that. By looking, first of all, let's say I was asked a much easier question, which was, what's the probability of winning the lottery in the UK at the moment? And I can calculate that because there are 59 possible numbers you can pick.

You choose six of them and I can work out how many ways there are to do that. So I'm just working out the combinatorics. How many ways can you choose six numbers from 59? And then that gives us the probability. And actually there are 45 million, roughly just over 45 million possible ways you can choose six numbers out of 59 possible numbers. But let's say, oh, and the probability, by the way, is 0.00000022%.

Very small. Five zeros and then 22% time. But let's say along the way, while I'm working it out for strange reasons, I go, I go, Oh, you know what? I'm going to ignore all the options, which are all square numbers. You know, I just can't be bothered including them. Yeah. They're legitimate lottery tickets, but just to make the math easier, I'm going to ignore them. And people are getting up in arms and they're like, you can't ignore them. They're real options. Well, that changes the probability from being five zeros, two, two, one, nine, three, nine percent to being five zeros, two, two, one, nine, three,

nine percent. It's identical. Just because I ruled out those options. Even if I said, ruled out those options. Even if I said, I'm going to ignore all the tickets, which are all odd numbers, it's still five zeros, two, two percent. It hasn't changed. Even if I say, I'm going to ignore all the lottery tickets that have a seven on them, the number seven, which is a lot, over half a million, it's still five zeros, 2%. A little bit different. Wow. Instead of being two, two, it's two, five.

So that changes it a little bit. Ooh. Doesn't change the- Hey, you round up, get that one to a three. But if you round them both, they're the same. So the point is, if all you care about is the rough answer or even a very accurate answer, you can still ignore a lot along the way. So I'm going to be ignoring a lot along the way.

So things like mutations and whatnot, they're all going to go. Okay. I thought I'd overemphasize that. I mean, you have just likened people to the lottery, but. Same thing. What's being born if not winning the lottery? I'm not going to oversimplify though, because at a very, very simple level, when two humans want to make a new human, they've each got cells that have.

Are you giving me the talk? I'm giving you the talk. You know, we sometimes have young listeners. It's the bits, the bits and the bees. So a human has a cell with 23 pairs of chromosomes. So you got 46 chromosomes in total, but they're in pairs. So you got redundancy, which is very useful. So if anything goes wrong, you got backup genes, basically.

So when your cells decide to, and I'm not going to use this, like biologists have named every single step and part of this so there's a name for the cell when it's got all the pairs there's a different name when they're separated there's a different i mean there's a big difference between naming things and knowing what's going on and they've done a lot of naming things but you things. But you start with the 23 pairs, your body splits them apart and then has to pick one of the two to put in the reproductive cell. So you're making a sperm or you're making a cell. They only have single chromosomes. They don't have pairs. And so your cell basically takes each of the pairs and is like, do I put in this one or this one? This one.

And then they get the next pair. This one or this one? That one, right? And then they go through all 23 of them and they pick one from each pair and put it in. I just need to explain for the listeners that every time Matt says this one or this one, he's like weighing them up in his hand. Yeah. Like he's a little character. I'm the selector.

This one or this one? Enzyme? I don't know, right? But also your weighing up looks a bit like someone milking a cow. It's not dissimilar. Yeah. Or someone choosing which udder to milk. This one or this one?

This one. This one. And so if you just run the numbers on that, the number of ways you can choose one of the chromosomes from each of the 23 pairs is two to the power of 23, which is just over 8 million. It's 8,388,608. So if you start with a single human cell and you choose one chromosome from each pair, you've got just over 8 million possible, like either eggs or sperm that you can make by choosing those combinations. You've then got the other human doing the same thing.

So they've got another just over 8 million possible cells that they can produce. And then you've got all the possible ways to combine all of those. Just to get an analogy going in my head. Yep. If I went to a popular sandwich chain restaurant yep gotcha and they only gave me two choices each time so they were like what bread do you want wholemeal or white yep and then i chose one yeah and then they were like you know chicken or tofu and then they were like you know lettuce or spinach yep uh high sugar bun low sugar bun. Yeah, all the way down.

Yeah. High in salt, high in sugar. Long. Yeah. A little bit of Vegemite, too much Vegemite. They're all your options. Yeah. And if there were 23 of those steps, there are just over 8 million possible sandwiches you can walk away with.

Amazing. And that's not including, but you have to have, you have to make a choice of each one, right? You can't have a missing one. There's no null option. You've got to have one of every single one. We're ignoring all the perfectly valid fringe cases. Very valid. Yeah, exactly.

But we're just trying to get a headline stat across the total number. But now you've got two people because I hate to have the talk, but two people both buy a sandwich and then they put their sandwiches together. And because there's 8 million sandwiches the first person can have, there are 8 million distinct sandwiches the second person can have. There are now 8 million squared sandwich combinations where people mush their sandwiches together. Yeah, like a double-decker sandwich. To make a new Yeah, like a double-decker sandwich. To make a new sandwich.

Like a double-decker sandwich. If that was the whole story, then a pair of humans could produce just over 70 trillion possible distinct humans. 70 trillion, 368 million and a few possible humans. That's a lot of baby showers. It's a lid, yes. But we are just talking about the same two people, right? We're not saying that someone on the planet might have the same kid as two other people on the planet.

What it means is that if two humans have a child, first of all, that's one of those 70 trillion possible kids. And then they have a second one. There's a one in 70 trillion chance they have the same kid again. Yeah, yeah, yeah, yeah, yeah. And so every time, every time a family has two kids, there's a one in 70 trillion they have a match. There's a one in 70 trillion they have a match. But now you think, what if there's been 70 trillion human families or breeding pairs in existence? Who've been alive. Exactly.

Then suddenly it's more likely than not. And again, there's some more complicated math going on here. It's on the same order of the possible number of human pairs that there might have been or will be in the future of the human species. Or is it like, is it the Murphy? That's the Monty Hall problem. It's not the Monty Hall problem. No, there's no. Yeah.

Yeah. Okay. Every time in this show. It's not like the chances. No. You always win a kid. You don't get a sports car occasionally. I'd like to point out.

That's a very funny pun involving the word kid. Anyway. It is good. Thank you. It's very good. So good. I thought I would underline it because that makes it funnier. So now the reason I'm being a bit vague is I didn't bother carrying on the exact calculations. I went, I got, I got, I did this, you know, the rough approximation got 70 million possible humans per pair of humans. And I was like, oh, that's weird because that's not far off the number of humans there are or will be, etc. However, I knew in my limited biological knowledge, that is not the whole story because your cells don't just choose between the two possible chromosomes.

What they do is, first of all, they duplicate them all. So they've got twice as many as they need. There's now two copies of everything that was already in pairs. So actually there's like technically four of each one, but two identical pairs, that pair. And then they take one of each of those and they do a crossover. So it's like in the sandwich version, if they're like, do you want the whole meal or the plain bun? The white bread.

Yeah. You can actually choose. I want, I actually want, I want the first, I want the first 10 centimeters of the whole meal and then I want you to cut it. And then I want the rest of the white after that. Yeah. Half and half. Yeah.

Half and half. So they cut both the buns and then swap the ends over. What actually happens in your cell, give or take complicated enzymes and all those things, two of the strands of the DNA kind of cross over each other. Oh yeah. And then they cut and separate at the crossover point and it can happen more than once. So you can have zero crossovers, you can have one, you can have two, you can have, it seems up to four. And there's some complex

biology going on where it's not totally random, like you won't have like arbitrary crossovers, but also you'll always have one or two. You don't often have none because it's a really useful way to shuffle the genes around by mixing and matching across the chromosomes. Suddenly you have a lot more options. So is this where recessive genes comes from? Recessive genes comes from the fact that, and that would happen in the simplified version, you get pairs of genes, one from one parent, one from the other parent. And if they've all got duplicate genes on them, and so if one of them is faulty, or you've got the backup one, or if one of them is dominant, it will overpower the other one.

And that's the recessive one. If you have two recessives, there's no dominant one, you know, shout over them. And so they get to do a thing, which is why it's called 23andMe, not 46 and... Us. Us. Yeah. So, um, because we ha you have technically got 46 chromosomes, but they're all paired up and the pairs are, you know, they're not duplicates of each other, but they do the same job. You don't say I've got 23 pairs of socks. You don't say I've got 46 socks. Exactly. Exactly. Yeah. Yeah. But in this case, the socks aren't identical, but they do the equivalent job to the other one in the pair. And so if one sock's got a hole in it, you can wear the other one.

I think that works. Oh, yeah. Okay. That makes sense. And what about a crossover? Is that when you've got odd socks? A crossover is where you take, you cut the end off two socks and swap them over. So they still match.

They still match. They still do the same things, but now you'll swap them over. So they still match. They still match. They still do the same things, but now you'll swap them over. And there's, oh, there's, there's, I don't want to get too distracted in how and why cells do this, but it's a very clever way that you duplicate and then you cross the non-duplicate chromosomes. So let's say you've got pair chromosomes. So you've got A and B. You duplicate both of them. So now you've got AA and BB. Right. So I've got a pair of chromosomes. So you've got A and B, you duplicate both of them. So now you've got AA and BB.

Right. So I've got a pair of socks and then I duplicate those. Yep. Yep. And then you leave one A and B alone effectively, and you cross the other A and B, and then you partner them up with the one that wasn't crossed. So you've got the best way of shuffling around the genes. It's super clever. But being biology, there's no clear, here's how many different sites there can be a crossover event, right? It's just like, it happens a bunch and it happens normally four or fewer, normally one

or more, but then it starts to get a bit vague. And so what I did was, first of all, I found out it happens on average once every 100,000 base pairs of DNA. So the longer your chromosome, the more likely you are to get a crossover, which makes sense. The longer your socks. And I've, the longer the sock, the more likely you're going to cross over. But because it can happen more than once, you might cut the toe off and then swap that, but then cut it again near the heel and then swap again.

So you can have multiple swaps on the same sock chromosome, but the longer it is, the more likely you are to have multiple swaps. And you tend to do a swap for every 100 million stitches, base pairs, in the sock chromosome. But you can have more, you can have fewer. So what I've done is I've, okay, bear with me here. I've taken all 23 possible chromosomes that humans have. 24 actually, because I had to deal with the X and Y separate. Oh, and me.

24 and yours. That's what it should be called. Yeah. I've then assumed an upper bound of the number of possible crossover events at one per 50 million base pairs. Because I just want to have the range of what could possibly happen. And so this means the shorter ones have one and the longer ones can have up to five. So I'm just trying to cover every possible option. And then I've worked out how many ways there can be zero crossover events, which is one, how many ways there can be zero crossover events, which is one, how many

ways there can be two crossover events, how many ways there can be three, four, up to however many the maximum number is. And I've assumed the crossover of points are always between the genes that are on the chromosomes. So your chromosomes are basically the DNA is a series of genes which encode for making one or more proteins. And so I've assumed the crossovers happen between those. Not a biologist. That seems to be the way it works. People, please correct me if I'm wrong. the way it works. People, please correct me if I'm wrong. So what it means is, let's say, what's your favorite human chromosome? They're numbered. So I'm asking you, what's the number between one and 24? Seven.

Seven. The seventh chromosome is just over 159 million base pairs. So that's 159 million, you know, A, G, T's, et cetera. It contains 989 working genes, which means there's 988 places between them where you could have a crossover event. Oh my goodness. And it's long enough that there's going to be up. There could be none. There could be like, there could be zero. There could be one, there could be two, there could be three crossover events in the extreme. There's probably only going to be one or two. But it means you can go through and calculate the number of

possible ways that those combinations can happen. And if you add up the number of ways you can have zero, which is one, the number of ways you can have one, the number of ways you can have two, you can have three. You then go to grand total. There are 161,227,770 ways you can have crossover events to mix and match chromosome number seven. And I've done that for every single chromosome. And then I've gone through and combined them all

to work out the number of possible reproductive cells that you can produce, assuming every possible crossover event. And if you are starting with an XX configuration, starting with an XX configuration, there's 3 times 10 to the 166 possible cells you can produce. If you're starting with an XY configuration, because the Y is a bit smaller than the X, you've got fewer, there's 2 times 10 to the 160. Now these are outrageously big numbers. 2 times 10 to the 160. Now these are outrageously big numbers. So for the XX starting position, it's 3 followed by 166 more digits. So the number is 166 digits long. It's just ridiculous because you still got to combine one sperm with one egg and then you combine them to work out

how many possible options there are. And again, that varies depending on if you're getting an XX or an XY at the other end, but they're both on the order of a number with over 300 digits in it. Just stupidly big numbers. And there are other complications in reproduction that I haven't even factored in. These are just crazy, crazy big. And Andrew Smith did say, is there a way to compare that to other infinite simile unlikely occurrences? So here's the crazy thing.

The probability of having one child and then having another identical child is so unlikely, it's the equivalent of, out of the entire observable universe, picking out a single proton and going, oh, that's cool, mixing it back into the observable universe, and then choosing another single proton at random and getting the same one again, purely by coincidence. And in fact, doing that four times. So are you saying that it's more likely that someone will pick up a grain of sand and then

the next day, like pick up a grain of sand. Pick up the same grain of sand. The exact same grain. Yep. And do that three more times. So you've done it four times in total. It's more likely they will do that than have the same child twice. Correct.

It's because combinatorics, once you start combining things, the number gets real big, real fast. And so it's not going to happen, is the short answer. Like there is a chance, but it's so ridiculously slim that it's basically impossible. I mean, mathematically though, it's still finite. There's still only a certain number of humans, distinct humans that two humans can produce. And I've not gone into any of the way genes are expressed.

And, you know, are we just talking humans or who are indistinguishable to our human perception? Like biology is a mess. human perception. Biology is a mess. I've taken the problem as stated to be the equivalent of identical twins, which means the chromosomes are all the same. And in that, it is one in 10 to the power of 333. And that is just ridiculously unlikely. I prefer the term slim possible. I think we

should make that a thing. It's slim possible. It is impossible, but there's a slim chance, but it's impossible. It's slim possible. I will just say for everyone who's like, there's no way they're probably having the same human is less likely than finding the same proton in the universe. The difference is in one case, you're just trying to find a single thing. In the other case, you're looking at not even pairs of things, but incredible overlapping combinations of things and combinations just get so big, so fast. But yet intuitively we're like, but the universe is so big. I'm like, yeah, but combinatorics like can be even bigger.

Do you know what's amazing is that, and I know it's different, but despite all those, despite how slim possible it is. Yeah. How you can still have two separate kids that look heaps the same. Oh yeah. Yeah. you can still have two separate kids that look heaps the same. Oh yeah. Yeah.

Actually, Andrew did have another question about how percentage overlap, how similar siblings can be, but the genetics just gets so crazy that the way you go from your DNA and your genes to your human is not a nice, crisp mathematical calculation that I can crunch. And you're absolutely right. You'd be amazed how similar siblings or even people in different generations can be because, you know, humans, humans, man, humans. I, I, um, I mean, my head's to be, with COVID, my head is already blown. But I am very impressed. So I, from my angle, I'm giving it a D.

Our next problem, which has been sent in by everyone, is are there more wheels or more doors in the world? Apparently everyone's asking this question. Everyone's definitely been asking us. So, Beck, wheels or doors? I got doors. Oh, me too. Excellent.

Doors it is. Ding. Ding, ding, ding. Now, Beck, we have a dinglet, a mini problem. And this was sent in by Ava on the Problem Posing page at problemsquared.com, who says that Problem Squared is the first podcast they've listened to regularly, and they've discovered they really like the format. That's nice.

They want to listen to more. However, they don't know how to find more good ones, like other podcasts. So they're asking, here we go. Do you have any recommendations for other fun and nerdy podcasts? I do, actually. Good. One is called A Podcast of Unnecessary Detail.

Oh, that rings a bell. I don't know if you've heard of it, Matt. Yeah. Wow. I hear they're also afflicted by having and some mask guy. But other than that, it's quite a great podcast. Not too shabby, though. Not too shabby.

I tell you what, I've been listening to it, but it does weird me out when i hear you saying hello at like as if you're just introducing our podcast i feel like i get it suddenly you're like oh yeah i haven't prepared but that's not the problem the problem is not fun so a podcast by necessary detail recommend that while we're plugging it we're just about our second series of a podcast of necessary detail, which, just in case people aren't aware, I do with Helen Arney and Steve Moult. First of all, The Spoken Nerd. We are known as collectively. And season two out soon.

Yeah. So yeah. If you enjoy this, check that out. Yeah. I mean, it's not as good, but sure. Go check it out. It's not as good, but sure. Go check it out. It's not as good. Not nearly.

No. Other nerdy podcasts. Science Versus. Big fan of that one. If you haven't listened to it, it's just Science VS. It's hosted by another Aussie, Wendy Zuckerman. They did a brilliant episode recently about the Joe Rogan interview regarding vaccinations and everything like that. So that was absolutely fascinating.

But it's a really, really solid podcast at Science Versus. I also recommend Mathematical Objects, which is hosted by a friend of ours, mathematical friend of ours, Katie Steckles and Peter Rowlett. I am on an episode either now or coming out soon. If anyone wants to hear me talk about whether a joke can be counted as a mathematical formula. Yeah. People show up, talk about an object. Progressively less and less strict definition of the word object.

Yes. Yeah. Mine was far more conceptual. Another one I've always been a big fan of is Reply All. Most people probably already listened to that. If you like Reply All and you wish it was nerdier, then make sure you check out the Darknet Diaries. Some really fascinating stuff there about programming, coding, hacking, all that sort of thing. Very interesting. And one that isn't as nerdy but I thoroughly recommend and I would love so much if everyone that listens to this suddenly went and listened to it is a show called the

dream factory if you like all the puns that we do on this show and you're like I would like that but with none of the learning the The Dream Factory is really adorable. It's two lovely guys. People tweet them pun-based movie titles. I think one that I sent them recently was The King Kongsman. The Fast and the Spurious. That kind of thing. Yeah, they love that stuff.

Yeah. Ah, there you go. People send them stuff like that. I would watch the Fast and the Spurious. Okay. Well, what we'll do is we'll, I'll tweet it to them. I'll say that you've mentioned it and see if they can, basically they come up with what they think that film is and it's just them having a little think about what they think the films are. It's really enjoyable.

It's very pleasant. I think it's PG. I don't recall hearing them swear, but don't, you know, don't quote me on that. But it's one of those podcasts that I can recommend, a comedy podcast I can recommend that I don't believe will offend anyone. I think for any media we mention or recommend in this show, legal guardians should just have a quick check themselves before they pass them on to any offspring.

Yes, absolutely. But I highly recommend, yeah, the Dream Factory. Everyone go and listen. That's a good list, Beck. And given all Ava said is, do you have any recommendations? They didn't make any comment about the quality or if they will enjoy them or not. Well, they said fun and nerdy. Well, you think they're fun and nerdy.

And you recommended them. I mean, there you are. That's a problem solved. Ding. Yay. It is any A.O o other businesses b a o b excellent so first up with uh any other businesses is uh um a pudding squared we were going to go through the answer today uh but because of my limited brain capacity and everything being filled with phlegm

just a little gargle for proof there we're going to give the answer to a pudding squared in the next episode. This time, however, we will pass on a ding to Beck. Dennis, who asked about the food packaging, has come back with, wow Beck, you went so far to answer my question. Congrats on your certification. Thanks a lot for it. You definitely get an un-gnitable ding.

So that's like a ding backwards is a g-nid, and it's un-gnitable. Or nid? Is it a silent G? Is it a silent G? Nid? Un-nid and it's un-g-nid-able. Or nid. Is it a silent G? Is it a silent G? Nid. Un-nid-able. We'll go with un-nid-able. An unreversible ding.

This ding, Dennis is committing to the ding. It cannot be knitted. So top work, Beck. There's your un-nid-able ding from Dennis. Thank you, Dennis. Although Chris did ask on the problem posing page, does counterfeiting a food naming certificate using the HTML elements count as a food crime?

So there you are. Yeah. Luckily, I haven't done that, but if anyone else does, maybe we'll report you to the food crimes unit. Yeah, you legitimately got that qualification. So you should defend it. Also, I just want to say that when people send us problems, so often they say such lovely things to us in those messages. And I want everyone to know that I read them and they're really lovely and appreciate them. So even if we don't get around to answering

your particular problems, thank you for keeping up the kindness and for going to the effort and time of sending us your problems. We do appreciate it. And you are loved and special. With that in mind, we're going to thank people who give us money. Right. With that in mind, we're going to thank people who give us money. Including on our list of random Patreon supporters this time, Phil Chapman. Jacob Faber.

Kevin Davis. Thank you very much to you and the rest of our Patreon supporters. And of course, a huge thank you to everyone who listens and tells all their friends, all of that stuff. Thank you. We appreciate every single one of you. I'm going to go back to bed. Problem Squared has been brought to you by me, Beck Hill, and a lot of paracetamol,

Matt Parker, and our producer, Lauren Armstrong-Cart. Bec, I'm about to ask you if what I'm showing you is your card. But before I do that, we've got an answer on why we do this. And it's so telling that we didn't know why we were still doing this. But thankfully, our listeners do.

Several people wrote in that it came from episode 018. Oh, yes. Someone named Red probably gave us the most accurate answer. They said it was episode 018 At 30 minutes and 26 seconds in You were answering the problem What's something I can say or do to make a good impression

When meeting other people And they have written out the transcript Of what happened So I mean Good job Red We could just play in that recording but i think you know given that they've actually typed it all out we should do it like a little radio play so should we should we recreate yeah we should yeah let's recreate the um origin and

do an accent then um you can yeah you can do'm going to try and do it as old time radio play. But I, well, also I was assuming you were going to play Beck and I was going to play Matt, but I'm open, open to suggestion. Oh yeah. Yeah. Okay. Let's swap roles. Why not?

I regret this. Yeah. Like a freaky Friday. So I'm Beck. Oh my goodness. I'll try and do your sarcastic voice. You can do resting sarcasm voice. I'm going to do more Australian voice.

I think that's... I'm not more Australian. I'm just happier. A hundred percent. No, we're not. Exactly. One of my co-workers had... Hang on.

Sorry. I came in too strong. Too strong. I don't think you came in strong enough. Okay. This is what happened. Whatever you're thinking, ramp it up. More, more. Okay, okay.

Ready? Let me take you back to episode 018. One of my co-workers had my favorite introduction, which was that as people opened their doors, he would hold his... Chris Knight, actually, and he's a comedian now. Okay, but he would have a pack of cards, and as soon as they opened the door, he would just say, Is this your card? And then hold up a card. I'm trying to do the wheeze that you do when you laugh.

And they'd be so confused that they wouldn't slam the door in his face immediately. That is amazing. And in related news, Beck, is this your card? Ha! Matt has just held up a card, and it's not, I'm afraid. Oh, hang on. I've got plenty more. I suddenly realized I literally had a deck of cards right next to me as you were saying that. And I was like, wow, this is never pass up a chance for unexpected physical comedy that translates well into a podcast. a podcast. See, I can't tell if you're like, how much of that is your impression of me and how much is just you're ill.

Wow. I'm Matt Parker. Which does bring me to my question though, Bec. Is this your card? Matt's just held up three cards. Yeah.

And one of them is my card. Oh boy, oh boy. We're getting close.