A Problem Squared - 016 = Biscuit Tips and Longer Trips

Episode Date: February 28, 2021

In this month's episode, Matt investigates what is the optimal way to share biscuits amongst a group, and Bec explores how you can elongate your holiday time using all manner of creative methods. Plus updates on short shorts and how much Coronavirus is there in the world. Send your problems at www.aproblemsquared.com And here's the study Matt referenced about perceptions of Time: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0001295  

Hello and welcome to A Problem Squared, a podcast where we do our best to solve your problems. Some problems might include, I forgot to write an intro for this. And well... Are you trying to style your way out of this beck i was and then i realized all i did was present a problem that i haven't solved right at the top yeah between us i think we put an average amount of effort into the introduction i'm not i'm not rescuing you you're you're on your own no don't i think that's you know what

i think this is what what our lovely listeners and hello to you all listening right now. This is what you come for, isn't it? Friendship. You don't need rescuing, Bec. You got this. I'm Bec Hill, joined by my wonderful co-host. Matt Parker. Pleasure to be here, Bec. In this episode, we will be exploring problems such as... What is the most efficient way to share cookies between an arbitrary number of people? Where should you go on holiday in order to make the most of your annual leave?

We've got an update to the volume of coronavirus viral calculation we did previously. And an update on short shorts. Listen now. So, Matt, it's lovely to see you again via the power of Zoom. What have you been up to? I spent a lot of the time since our last episode making a YouTube video about the Minecraft speed running luck thing that we discussed last time. Yeah, yeah. And I talked about it on the podcast because it was kind of in the back of my mind thinking I should do a video on this.

And I finally decided to do the video. But being an idiot, I thought, wouldn't it be funny if in the video i am unnaturally lucky oh nice as like a running theme in the video yeah and so the video starts and actually i've still got it set up so you can see it in my office behind me there's a dartboard that i've got rigged up behind me and a basketball hoop yeah and so at the very beginning of the video i'm talking to camera and I throw a magnetic dart over my shoulder and it hits the bullseye on the dartboard. And then later in the video, I'm talking to camera and I'm throwing like four consecutive basketballs over my shoulder

in the same take. And they're all going through the hoop behind me. And I set up some bowling pins. It was very funny, but it took over six hours of filming to get all the different takes for all the lucky things i did that's way better than what i i thought you were going to say it took six days because if it was me it would take six days yeah i spread it out over nine days right and then i just kind of chipped away at it yeah i tried to do one lucky thing a day and i had a few rest days as i went along and so it was six hours the darts took three hours the opening shot took half of the filming time wow and it's because the way the kind of magnetic darts

work and the way you throw it i was gonna say magnetic darts are hard because they have to hit at the right angle or they don't stick yeah so they're way more random and there's a lot less skill whereas the basketball there's a surprising amount of skill that you develop and so actually the longer it takes you the better you get at it whereas the darts is just pure randomness yeah and i did one shot where i was like rolling dice and getting results and that kind of thing so some sometimes there was a skill i could learn and sometimes it was just randomness until it until it worked and when i put the video out initially the internet was just like meh all right and it did kind of okay for a video on my channel for your standards yeah yeah but not consummate with the amount of effort i'd put into this thing yeah but then the minecraft community

got wind of it. Oh, how lucky. And the YouTube algorithm noticed. And the whole video, by the way, was like 40 minutes long, which is too long. But because people were watching it for a decent amount of time, the YouTube algorithm started serving it up to people who watch Minecraft videos, which it turns out there's a lot of. Why?

It's just hit 2 million views of people watching me throw a dart over my shoulder or throw the basketball around. That's not to be sniffed at, is it? That's two Adelaides. That's two Adelaides. Whenever I think of million, I measure it based on the population. You think of Adelaide. Because it's roughly a million.

Great unit. Well, it reminded me, I did, over Christmas, I wired my Christmas tree with 500 LEDs. Yeah. Took me a long time. A lot of electronics, a lot of programming Christmas, I wired my Christmas tree with 500 LEDs. Yeah. It took me a long time, a lot of electronics, a lot of programming. My goodness, that was a lot of effort. Put the video out, half an Adelaide, which is good. Yeah. In absolute terms.

But I was like, I put so much. I thought this one was going to go wild. And then while I had the tree set up, like mid-January, I've got to get rid of the tree. It's falling apart and I go you know what and I filmed unedited 45 minutes of me running other code viewers had submitted on the tree and I just did it for fun I like I just put it on my second channel there's no edits half the code doesn't work I mean part way through I wander off and get a beer during the video. Yeah.

And I put the whole thing up and YouTube's like, no, that's a winner. And it's just gone past three and a half Adelaides. What? Me just literally messing around. Oh, my gosh. No effort whatsoever. See, this is like what frustrates me about the internet. Yeah, fair enough.

You handcraft something for the internet, you throw it out there, and it just plonks in without a trace. Barely a ripple. But then occasionally, by accident, I try and guess what the internet is doing. But that aside, how are you doing? How are you doing back? Well, it actually comes quite nicely because as of the recording of this, I recently had my debut appearance on 8 Out of 10 Cats Does Countdown. Oh, yes. Yeah.

It just happened. So it aired, which was very exciting. And that was interesting because loads of people started following me and saying really lovely things and stuff. It was nice to know that TV still works. That's what I said last night i was like oh yeah oh good to know that people because people they don't have my name on like my name popped up in the credits but it's not like on a name card or anything they don't have like a prompt so people were watching and like actively they had to search you out they had to look you up

yeah yeah which was really cool and really nice. And I'm very thankful. I mean, if any of them are listening to this episode, hello. Thank you. Oh, yes. They might have found their way deep into the Beck ecosystem. Yeah. To a problem squared.

There you go. Yeah. It's nice. At least I have a body of work for them to look at as opposed to being like, oh, yeah, no, that was the first thing I did. Well, it's the inside view of the overnight success where it's an awful lot of work, but then one thing suddenly catches somehow the public's attention and you're an overnight success having put in years of arduous effort. Yeah. This problem comes from Rafi or Rafi apologies if I am mispronouncing your name via email and they said both of my parents are teachers and they're teaching from home via zoom in the current lockdown. One of them has asked every member of the class to bake some biscuits for their math

lesson measuring units etc. My question is what's the best way for them to share the biscuits with one another? They've provided some more details as well for your mathematics there, Matt. Excellent. And I mean, that's classic math teacher straight off the bat. Instead of doing it themselves, they've set it as a homework challenge for their own child. Yeah. Who's then come to us. Yeah. Perfect. I applaud every step of this. Love it. So, and I then got to us yeah perfect i applaud every step of this love it so and i then got to solve it which was nice and in the interest of full disclosure we were going to do this problem last episode in 015 but i contacted you before the recording to say i'm in too deep in the maths

i'm not going to have this together before the recording we're going to have to push it back a month because oh my goodness i had a great time trying to solve this so if anyone wants to work out the most efficient way to share biscuits or cookies as we know we can go either way on that between a number of people and i visualized it as like a network how you would link who gives cookies to who. Yeah. And then I minimized the number of links required to achieve that. It was a lot of fun working it out. So if anyone wants to skip this bit of the episode and try it themselves, I highly recommend it.

For people who don't want to, here's how I went about it. So like a lot of things in mathematics, my first thought was, what is the worst way to do this? Give them to Beck. Give them all to beck yeah they all go to beck and that's uh one journey for everyone to get them to beck and then one journey for beck to consume them no biscuits no in my belly problem over exactly so that's given us like an upper bound so but actually that could be one way of solving this. Because if everyone gave them to Beck, but then Beck did not eat all of them, everyone could then come back to Beck and pick up everyone else's cookies. And that would be everyone doing two journeys.

So there's one journey to drop them off, and then one journey later to come and pick up everyone else's cookies. But you couldn't do that all at once, because when you're dropping off your cookies to back you may not already have everyone else's yet so you can't hand them all back over to the person dropping them off yeah so let's say let's say you're a member of the class and so for the example from raffi there are 30 people so all 29 other people would come to your house drop them off individually for important social distancing reasons yeah and then all 29 people would have to come back a second time and pick up the cookies and so that would be 29 twice so that's 58 or for any number of people

it's twice the number of people subtract two because you don't have to go anywhere everyone else has to do two journeys. Yeah. And so I was like, okay, there's like a starting point. Although actually the last person could drop off their cookies and now you've got everyone's. So they could take them straight away. So that would save a journey. And so now it's twice the number of people subtract three because one person doesn't go anywhere.

That's you. And one person does one journey instead of two because they were last. and that's kind of where i got to straight away i went okay i'm pretty sure i can see twice the number of people subtract three is achievable yeah and then i thought could it be done better and actually a cookie party is a real thing in america which is why i keep saying cookie even though traditionally i'd say biscuit friends of mine in california introduced me to the idea of a cookie party where they in non-pandemic times all go around to the one person's house and everyone brings cookies yeah so everyone bakes one type of cookie this sounds like what this sounds more like you're using code word for something else it does doesn't it it's got a real euphemism.

Yeah. This is very reminiscent of when Louis Theroux went to a swingers party. It's not far off. They told you it was cookies, but really. I've not been invited to one, so I don't even know the full detail. They're like, what you do is you bring over these cookies. You're not allowed any clothes. You put the cookies in a bowl.

So anyway, but now in the pandemic pandemic time they can't do that anymore so they still they didn't do the full cookie exchange they just baked cookies for all their friends and then dropped them off to to all of them separately but they weren't picking them up at the same time and so they were doing effectively the worst case they were doing a single journey for every single person to then drop the cookies off. And then now they're looking into it. I've asked them because they're both mathematicians, my friends who do this.

They're now trying to find out if anyone in the US has taken their cookie exchange party online to see if there's a, what the practical solution in the real world is, which I think would be quite interesting. I, however, only cared about the theoretical solution and so i was kind of thinking that was the whole thing and then i thought you know what i'll just play around with an easier case so i drew a little diagram of five people and thought i would see if i could find a better

solution than seven which is what you would get with our current solution where everyone drops them off and picks them up. And just by drawing a little diagram, I found a solution for six. And you know what? I've actually got the bit of paper here. So, I mean, you can see it over Zoom. Hold that up to the mic so the listeners can hear it.

They can hear you're working out. There it is. That's my working out. Yeah. So, but there, I'm just pointing out, it looks like a pentagon with a line through the middle. And I was labeling who's got whose cookies. Oh, yeah.

Yeah. And I suddenly realized, and I've numbered the order that it happens in, because if you drop cookies off to someone, anyone else who visits them in the future can then pick those cookies up. Yeah. And so it's important, the order in which you do all these links. Yeah. And I suddenly realized it was possible to do better.

I did one better than what I thought was the theoretical minimum. And then I was like, great. That's when I contacted you. I said, Beck, I've just blown the mathematical lid right off this thing. I now need to investigate this. And so that's why the moon answer I did last time, not my finest work. It was adequate, but I was talking about the moon, but I was thinking about cookie sharing networks, if I'm being honest.

All my intellectual energy was going into this. And so what I ended up doing was I tried to then solve six just on paper. Yeah. And I got a better number for six. And then I was like, this is getting ridiculous. Like seven is quite complicated to do by hand. So I wrote some software to solve them automatically for me and it was able to find it was able to verify my solutions for five and six and it found a solution for seven but it couldn't then find

a solution for eight because there were just too many different combinations of ways you can pass cookies around to rate people and so then what I did was I took my solutions for the ones so far and I put them into the online encyclopedia of integer sequences, which is a big online database of number sequences. And the idea is if you want to find out if someone else has already discovered something that you just found in maths, you work out the logical way to

describe it as numbers and then you search in like i don't know it's like the wikipedia for number sequences okay and a result came up an exact match oh to my numbers i thought i found a whole new solution to a whole new problem yeah someone had solved exactly the same problem in 1972. What? So I'm like half a century late. I was like, hey, I found a new thing. I'm like, Beck, clear the schedule for next episode. There's a mathematical breakthrough.

Turns out, no. So in 1972, but back then, it was called the telephone problem. Oh, yeah. And the idea was if you've got a number of people who all have an individual bit of gossip to share and sometimes it's called the gossip problem in my research what's the minimum number of phone calls so everyone knows everything that everyone else knew yeah and it's exactly the same problem and the kind of thing also works with the same of like trying to work out isn't it very similar trying to work out who could be infected or whatever with uh contagious stuff

yeah because if if everyone had an infection then this would tell this would be the worst case scenario for everyone to then have a chance to catch everything that everyone else has i hadn't thought of that you're absolutely right so a lot of times in maths it's different context same underlying logic um however the person who did this in the 1970s with phone calls and information if you share it you haven't got any less because you can give someone information and you're not losing it whereas cookies you're handing them over you've got to know how many to give the next person yeah and so i then set about thinking how would i describe the most efficient way for people to actually share their cookies and i'd be curious to know

what your theory is beck because there's a number of ways you can do it. They've always got the same number of links, but it changes who you give the cookies to depending on what you would rather minimize. Because you can minimize the number of journeys per person. So you can try and keep the average down as low as possible. You can try to minimize the number of times cookies get passed around you could try to minimize the number of other people everyone has to interact with because you can do i think what raffi said not to do you could have someone who's like the cookie repository who just takes in all the cookies and then redistributes all the cookies, which is like we were saying before, if everyone gave the cookies to Beck. But that's not very socially responsible.

It's not very socially responsible. So that's one person interacts with everyone else. Can I say what I think my way of doing it would be? Yeah. And this is without really thinking about it. I have overthought about it. So that's probably good. So how many cookies have they made each?

30. 30 cookies for 30 people. Yeah. So they keep one of their own and then they give them to the other 29. So I imagine you would keep one cookie and you'd give 29 to someone. And then that person would keep their own cookie and keep one of the 29 and then pass the remaining to the next person until they've all gone around and then everyone's only made one journey yes and that is the second best possible solution because what happens is you think of it like a cycle so you imagine everyone basically in a circle

yeah and you're right the first person gives 29 to the next person who keeps one and passes on the other 28 and 29 of theirs. Yeah. Oh, actually, no, but they can give one to the person who dropped off their 29. So they give one back to the first person. Oh, yeah. But then as you pass around the chain, everyone gets all the cookies from everyone before them in the chain, but only one person after them when they get that cookie, when they hand over their allotment to the next person.

Yeah. So then what happens is you get right to the end of passing them all the way around, and then you've got to pass them all the way back. So, because once you get to the very last person, their cookie has to get back to the very first person. Yeah. And so you pass all the way around the chain to the last person.

And then you pass all the way back. And you get the same result we had before. It's exactly the same as everyone giving them to Beck and then everyone taking them back. So it's twice the number of people subtract three. Gotcha. You can do one better. And so what you do is you do exactly the Beck idea. The first person passes to the

next person. They keep one. They pass it on. You get all the way around until you've got three people left who haven't got any cookies yet. And then what you do is the person who's like fourth last, and there's still three more people, before they pass the cookies on, the last two people swap with each other so one of them goes to the other one and gives them their cookies and one person gives them like 29 but they only take back two from the other person they take back the cookie that they want plus one spare yeah then the person who's fourth last does their swap with the person who's third last, but they only give them two cookies of each. They don't give them the rest.

And then you get the person who's fourth last does a swap with the person who was last, and the person who was third last swaps with the person who was second last, and they've all got enough cookies to match that up, and then you reverse your way back around the chain. And that little bit of extra complication at the end saves you one journey ha it's a bit of extra faff but it's

now the theoretical minimum and so i was so pleased that i realized that one bit of extra faff where you have a pair trading and then the last two people in the main chain both trade in parallel with the other pair yeah saves you one journey i was amazed that you can't do better than that oh you can drones drones sorry it's always i'm not thinking outside the network that's my problem outside the cookie box tech solution anyway the short version is you can save a single journey and the the downside is it doesn't get better when you've got more people so if you've only got five people trading cookies saving one journey going from seven to six might be worthwhile yeah if you're trying to wrangle 30 students the added complication of explaining how to save one journey to go from 57 to 56 might not be worth it and so as you have

more people the number of journeys increases consistently but the savings don't you still only ever save one additional journey so potentially it's not worth it but it's been proven you cannot do better than that that's the absolute minimum number of journeys wow yeah is there a diagram that um for the more visual of us that we can um see how this looks in action oh i have actually kept all my working out as i was going along because i've been chipping away at this for a while can we pop that up on the problem squared instagram yeah you know what there's the journey network i was working through for seven because my computer code found it but it didn't it just tells me the pairs and the order and i went through and manually worked

out yeah for the listeners it looks a bit like uh someone tried to draw the bat signal and and gave up it's not far off that yeah and actually i'm not even bothered drawing all the links all the implied ones i didn't bother sketching yeah it also looks like a overly complicated dot to dot yeah i'd give you that but you can actually, there's the chain going around. Yeah. And then you get this pair and swap business. Yeah. And then you go back around the chain.

But instead of going back around the chain, what you could do is everyone from the swap pairs could just visit a single person over here. But you've got to work out the more complicated the network, the harder the instructions for how many cookies to hand over in each exchange. And so I suspect as much as I love my theoretical minimums, there's my sketch for eight. It was a bit more comprehensive. For the listeners, Matt is holding up a picture that looks a bit like a cookie wearing a pair of pants, like underpants. That is, I'm, I cannot articulate how much I had not seen that before you said that sentence and how much I cannot unsee a cookie wearing a pair of pants now that you've, you've, uh, you've put that in my head.

Yeah. We'll chuck them all up on the Problem Squared Instagram. And I guess if anyone can find a better way of doing it, we're not against hearing them. You're pretty confident that there isn't though, right? Oh, it's proven. Thankfully, the people back in the 70s were able to prove that you can't do better than this.

And they proved some other weird stuff about the networks. The bit I've added is trying to work out the number of cookies you got to hand over and the logistics around that and minimizing stuff like that. But that wasn't the question. No, exactly. Yeah. So. 56. 56.

Tell you what, I'm going to ding it. Thanks. I'll then pass that ding on to Rafi, who can pass it on to raffy's parents that's the most efficient way of doing that i think that's what i've heard we have a problem sent in by tim on our new problem posing page at a problem squared.com tim says they'd like to be efficient with their annual leaves. That's like their vacation time. And they want to make the most of the time they have off. Can you please help suggest some interesting ways to elongate the days I have off work in 2021?

They're going to say that they're happy for creative solutions. They're originally thinking of taking the day off when the clocks go back to get a 25-hour day. But that's always on the weekend. And so, Bec, you've looked into how Tim can maximize their days off. Yes. Like, I think I realized all too late that when this problem came in, I was like, oh, yeah, that's a great problem. And didn't consider any, like, cause I just went, oh yay. I can now talk about that thing about the two islands on either side of the international dateline.

And now I'm like, I think I've bitten off more than I can chew. And we haven't even gotten into the problem, Matt. No, no. I do think that there's maybe easier ways that we could do this that don't involve as much travel, which is the psychological element. And I know this from previous chats that you said that there was an experiment where people falling were asked to time themselves. Oh, yes. Yes.

So this was someone. Oh, I don't. I've forgotten their name. Yes. So this was someone, oh, I don't, I've forgotten their name. I'm about to double faux pas because I was at a conference and I met someone at this conference and it was like a, just let's get a bunch of nerdy people together and see what happens conference. It's called Saifu and Google host it. And literally Google are like, we've got a bunch of money. Let's get nerds together and see what comes of it and i was and so people are from all different disciplines and i was chatting to someone and they said they research human perception of time and i started doing the classic science faux pas i'm like oh that's really interesting i was reading a thing the other day where they got people and i was like wait a minute was this your research and they were like yeah

that you're literally about to describe my own experiment back to me and i was like okay i'm embarrassed i started but i'm relieved i pulled out of that nosedive yeah um before i made an absolute fool of myself an absolute fool of yourself an absolute fool of myself anyway that's where the name comes from so they did research research where people, I'm trying to, I'm half remembering this. People were dropped from a height into like a trampoline or a foam pit or something. And they had a way. I'm glad you said that. I thought you were like dropped from a height into lava.

Just dropped from a height. Yeah. And so they then were looking at their watch and they did something clever to try and work out if people's perception of time changed when they were in a, you know, fight or flight adrenaline panic

at being dropped from a height. And our human perception of time, this is my headline stat. I should, I will look this. Someone look this up and send it in for next episode. The human perception of time does change depending on what's going on around you. So if you could holiday perpetually falling.

Oh, skydive. That would feel like a much longer vacation. Yeah. What if Tim skydives over the international deadline? That would work. It would either work really well or cancel out. I'd have to run the numbers.

You seem to hire someone to occasionally panic you throughout your holiday at random points in time. And it would feel like a much longer break. Yeah. Well, I mean, that's the other answer I had, which was that Tim should take me with them.

For anyone who's had to share a car journey with me they'll be fully aware of just how long that journey might take tim won't enjoy their time off having done that i can confirm that beck continues to be a hundred percent beck for the duration of an up to seven or eight hour car journey. Yeah, there's no dwindling. No, you don't taper off and then like have a nap. No. It's Beck, Beck, Beck, Beck, Beck at, you know, full, full, which is a delight, obviously. If you need to be kept awake. Yeah, that's true.

That was not a problem. of problem well to be fair so matt is referring to the time that we um drove back from edinburgh uh fringe down to london and in fairness that that trip did take a lot longer than expected uh due to various roadworks and things we got back to london in a at about 2 a.m. And then you dropped off the van and walked back to our place. So you got back at about 3. Yep. After about 14 hours of driving. You're skipping over the bit where I smashed my phone getting out of the van. Oh, yeah, you did.

At like 2 in the morning. I'd put my phone in one of those spring clamp things so i could have it like on a mini tripod on the dash so we could use it for navigation and what i did was i i i pulled back the spring to release the phone but then accidentally let go and it catapulted it slingshot my phone clear across the van bounced once on the passenger seat and shot out the far side onto the road smashed oh yeah 14 hours of driving two in the morning smash phone and then and then i went and dropped the van off and walked back to your place and walked back yeah so that would be my advice if you want a day to really drag on drive drive from Edinburgh, encounter Roadworks, smash your phone before you have to return the van.

I think my answer is that Tim should just come with us to the next Edinburgh Fringe when it's on and do all of our props. Yeah. Yeah, do all the driving, do all the props. And time ceases to exist at the edinburgh festival fringe so that would be a that's true very good um vacation i feel like i could i feel like this particular problem could be answered in a lot more depth and um uh the problem i had was that i thought it was far well i did the same thing you did with with the cookie one where i went oh

yeah that'll that'll be an easy this This'll be easy. Easy, and it's not. So I think I don't think I deserve a ding for this, unless Tim really likes that. Tim, if you really like that answer, give us a ding. Tim, don't feel peer pressured into liking that answer.

Tell us, Twitter or Instagram, at a problem squared. However, if you believe that that could be better solved, or indeed if any other listeners say, oh, no, actually, I happen to know the perfect response to that, then please let us know at a problem squared. Or go over to the a problem squared.com page and let us know in the little problem posing stuff there tell us that

you're answering tim's question we'll get back to it you know i'll add a drop down menu so instead of problem you can select solution oh that's doable oh my gosh this is happening you guys i'll get that done. So we're moving on to the Any Other Business section of the podcast now where we refer back to previous problems that we've had. And Matt,

I believe that you have some business. I do. I have some recently reopened business. A lot of listeners got in touch, by which I mean about three, and said, hey, someone's ripped off your calculation and so people may recall back oh goodness what episode was this i think it was like october last year i did a calculation for the volume of all the coronavirus particles in the world at the time and it came out to eight milliliters.

And like you said, it was roughly like a teaspoon's worth. And the news media picked up on this. And we had an update the following month that we were in all sorts of national papers and whatnot because of this. It's happened again. But a different mathematician has calculated the volume of all the coronavirus particles in the world. And it's now been picked up again by all the national media, including some of the same ones. So exactly the same newspapers that covered my calculation have some kind of journalistic amnesia and have covered this whole new calculation.

Well, this did well last time. Let's give it a reboot. Yeah. Also, it's bigger. Right. So this mathematician got a value of 160 milliliters. That's a lot. That's a big change.

That's a big change. Well, interesting. And they also did. So this is part of what makes the podcast so much fun for me, Bec. I showed up with this calculation saying it's like 7.9 something milliliters. And you then said, oh, about a teaspoon. And all the media picked up on it because they could have images of teaspoons and all this stuff. Yeah, yeah, yeah.

Right. And so you humanized my calculation. Obviously, people have learned from this. And the new calculation is about half a soda can oh that's a messy measurement i know half a half another measurement what is this but they've all got pictures of like soda cans and they've done tv interviews where like they wave a can around and talk about how it fills into half a can so i just thought i'll do a little update first of all to say i don't think they have deliberately ripped off what we did no the mathematician in question

is a fantastic maths person called kit yates who i know and is a wonderful human being and they're more qualified than me they've been doing some great stats and keeping the numerical and data reporting of the coronavirus in the media honest by providing a good mathematical commentary to it. Okay. So they're pretty qualified. They're more qualified than me. Yeah. Yeah.

And I found out where it came from. So a listener of the BBC Radio 4 program, more or less, went to them with the same question that one of our listeners came to us with. They asked them, what is this? I mean, and there's one of two options there. Either it's convergent evolution and just someone else had the same question. Well, we were surprised when it came to us that we couldn't find anything on it, weren't we?

Because we were like, oh, someone's done this and we didn't see anything. Someone's done this and no one had done it. Interestingly, this means that the person didn't Google it at all. Wow. That's one of two options. They either didn't bother Googling it at all and they just went straight to a radio program to solve it for them, or they were already aware of my calculation, potentially our listener to this podcast, but didn't believe me and decided to get an independent verification. But you know what? That's what you should do. Double check your sources. Fair.

So true. So true. And the BBC, so more or less, then went and asked Kit if they could do the calculation for them. But during that process, Tim Harford, who is the presenter of More or Less and friend of A Problem Squared, went, wait a minute, Matt Parker's already done this for A Problem Squared. And so they got me onto the same episode that Kit was on, on More or Less, to go through our different calculations and why Kit got an answer which is 20 times the size of what I got. So it's thank you everyone who was rushing in to say,

hey, this person's ripping you off. It turns out it was a separate question from someone else. And more or less when they realized I'd already done this, got me involved to present my side to it. Interestingly, I would say the answers aren't that different because they got a value of 160 mil. I got eight mil. And from a mass point of view, if you're estimating something, they're both about the same. It's not like one of us got a small quantity that you could hold in your hand and the other person got a swimming pool or one of us got something too small to see they're both about the size of something you can hold is this your way of saying that kit's answer

was more correct but you got close enough well actually what happened i looked i looked into it and i did a stress test where i used all the upper bounds of all the biggest possible values and that gave me 210 milliliters so kit's number was within the range of my total range but then i picked the middle of the road values for eight mil they also the big thing that changed their calculation theirs is identical to mine other than well first of all it was more thorough so they actually worked out how the level of infection in a person changes over time and they worked out the average amount and they really went into it yeah way more than me the big difference was i took the who infection rates at face value which last october were 300 000 new cases a day. They're currently 500,000 a day.

So it's going to be a bit higher anyway. Kit then went, wait a minute. They wanted to factor in all the cases that they thought were being missed by the WHO reporting. I'm not in a position to question the WHO. I went with their numbers. Kit was like, please. And they multiplied it by six. They decided the true number was six times bigger than what the WHO had in their figures. Oh, that's terrifying. And so that factoring in, we both assumed slightly different sizes for the virus.

We both assumed slightly different amounts in the human. But they all kind of averaged out. The one major difference was Kit factoring in all these people. different sizes for the virus we both assumed slightly different amounts in the human but they all kind of averaged out the one major difference was kit factoring in all these people and then i picked middle of the road and kit's middle of the road was you know within my upper bound but much bigger and so that's that's where they came up um but the one new thing that came out of it a friend of mine hugh hunt got in touch because i also talked about how same as we did in the podcast i think it's amazing that a virus is just data and what's amazing about all these calculations is just how small it is because it's no machinery it's just the data to repurpose

what what cells are doing they can take over the machinery in a human cell a friend of mine was like give it how much data as that got us thinking if you did have let's say 200 milliliters of coronavirus particles so we're going for the kind of upper bound how much data is there in there and we worked out a single viral particle has in its RNA, you know, not DNA, but the RNA in the virus, roughly seven and a half kilobytes of data per cell. Right. Which means that that half a can of soda, which apparently is the new measure we're going for here, let's say 200 mils, is the equivalent of over 600 million one terabyte hard drives whoa all in the same can isn't that insane how do we harness this power well exactly how do we make itty bitty tiny phones and that's the issue because i mean that's incredibly dense data it is just the same pretty much obviously there are mutations it's largely the

same seven and a half kilobytes in every single particle and there's no way to access it like a lot of a hard drive is the machinery to locate and access individual bits of data yeah so if you actually took a like if you have a hard drive or a USB stick, if you removed all the stuff that's not the actual data, it'd be way smaller. But still, I mean, RNA, DNA, incredibly efficient way to store data. It was pointed out, we also realized that actually only about 2% of the RNA in the coronavirus is actively used to encode for proteins it's actually only got 24 genes in the whole viral particle which is insane and it encodes for like 27 different proteins like it's incredibly simple machinery and so actually only two percent of the rna actually has meaningful

data in it and so if you follow through, then the half a can of soda is the equivalent of 12.5 million one terabyte hard drive. So it's still insanely efficient, even if you factor in that most of it is just junk RNA not doing anything. So there you are. Viruses, like, ah,

they wreak havoc and have caused untold suffering, but they're incredibly efficient data storage. I just want everyone to be aware, and especially Kit, if you're listening, just to check up on Matt, see what Matt's saying about you, that the smallest version of a bottle of Corona beer is 210 mils. Really? Yeah, you could have an actual bottle of Corona. No one's made that reference yet. So a bottle of Corona is the actual volume of all coronavirus.

A small bottle of Corona is your upper limit. See, Beck, once again, us mathematicians are all in with a number, but you turn it into a stat. Do you reckon we could get a third dip? Surely not. Like, what if we put a press release out saying all coronavirus is the size of a bottle of Corona? Let's try it. It's good to go.

I don't know where we'd put it. Use drones. That's your solution to everything. Yeah. Use drones. That's your solution to everything. Our last piece of business for this episode is regarding the short shorts one that we looked at in episode 015, which was about whether the length of running shorts affects running times and we got a message from Dom via Instagram who said that

I would like to throw a spanner in the works with the first two record holders that come to mind Courtney DeWalter famous for her knee-length shorts and winning races over 100 miles in the mountains and Sabrina Virgie who ran every wainwright in six days with only a few hours sleep and wearing knee length and full length running tights. I would 100% agree for any of the record holders on track and road events up to 100 kilometers. They get shorter the quicker people get obviously some exceptions there but once you go over 100 kilometers and then off-road to the trails mountains deserts etc the length then seems to increase again with distance and that is an interesting thing because we didn't really talk about distance did we no because this came out

of what park runs which are you know they're not sprints but they're not endurance race yeah yeah or like just those sort of marathon type fun run things yeah yeah so we both chatted about this in our downtime and found out that we've both got people who can we can compare because matt you've got a connection with yep long distance running don't you yeah a friend of mine kenny does or used to do ultra marathons which is just ridiculous distances we're talking this is the over 100 kilometers races where you're doing like multiple marathons it's just insane and so Kenny would do these you know super super long distance runs and so I thought that would be a good data point to get one person's experience for what it's like what would you wear what kind of shorts are you wearing attire in general for that kind of distance so i

asked kenny if they could record some of their thoughts on what they wear for ultra marathons and this is what they had to say so when i used to run ultra races as an amateur i was out there for a long distance a long time and potentially a multitude of weathers assuming the weather was good i'd usually wear very light fabrics something thin and light that is breathable and lets you dissipate heat and takes the moisture away from your skin. You also have to carry waterproofs and a layer for warmth in your backpack but I'd always be trying to make those as light as possible. I wasn't too worried about aerodynamics, you're unlikely to be moving at a speed much above a walk by the end so shaving an extra second off your running place isn't crucial. In terms of shorts I would almost certainly go for a longer short because often

these races are in bright blazing sunshine for a whole day and the more skin you cover the less skin gets sunburned. Sunblock only goes so far and nobody wants to keep stopping during a race to reapply it. But I would say there's an argument for wearing shorter shorts in most races. The more surface area of skin that's exposed to the air the more evaporative cooling as in sweating your body can do legs can really add to that surface area and i definitely know of marathon runners who follow that logic personally i've never noticed a difference so there that kind of confirms it that if you're running a long distance you do want longer shorts in kenny's case it's partly sun protection which i thought was interesting yeah stopping to reapply sunscreen as much and i imagine that there's also in in other types of

races as well if you're going off-road there's going to be like nettles and just things that you don't want rubbing up against your legs and stuff like that so yeah protection and everything when i was chatting to kenny as well after that he did separately say it's a bit different if you're doing something like a 24 hour race where you're just doing the same circuit on a track over and over and over again because then you're back in more of a controlled environment but i figured for this data point we want super long distance out in the wilderness and in that case we can confirm the shorts go long again yep and then just for balance i contacted the most successful runner i know which is my sister-in-law um who was originally caroline innes she's now caroline

baird and she's won four gold medals in the Paralympics for sprinting I mean that's pretty qualified yeah I thought I was doing all right bringing an ultra runner to the party I brought some ruddy gold medals mate yeah yeah and I asked her what factored in with what she wore when she was when she was competing and she said she never really thought about it in terms of the length and stuff. For her, she said, obviously, there's like the comfort factor, you know, like you want to be comfortable and you don't want things to be baggy and stuff while you're running. Relaxed and not worried about it. But one of the other factors that she mentioned, which I just never take it into consideration, and it's so obvious, was that she said she liked wearing the little short lycra shorts and little lycra top because she looked great. Like she'd been training really hard. Her body looked amazing.

But it's not just about showing off. It's the psychology of it. It's showing you it's showing your competitors yeah look how look how fit i am look at like she said it was so great because sometimes your fellow competitors would like comment on your physique and you've been working really hard you want people to see like oh she's going to be good and it's almost like that sort of self-fulfilling prophecy type thing. If you're thinking, oh yeah, they're scared of me,

then you've got that edge, that confidence, and then you're going to run better because you feel better. So I just never considered the actual fashion choices, but it made so much sense. It is fashion. Yeah. I mean, we're all humans.

Yeah. That's amazing. It's fashion. Yeah. I mean, we're all humans. Yeah. That's amazing. It's almost pushing back into the cyclist shaving their legs just to show how hardcore they are. Yeah. I've got a lot more respect for that suggestion that you made now because that does, it seemed a bit silly at first, but I think you're right.

There you go. And it still does. But yeah, humans, there's no accounting for humans. I'm also going to pop up a picture of Caroline in her gear so you can see her in her prime up on Instagram at a problem squared. I'll pop it on Twitter as well. That's it for this episode of a problem squared. Thank you very much for tuning in.

We want to thank you everyone who has been you conclude as slick as how you start yeah i like a top and tail great work i like to bookend these shows yeah consistent yeah i do want to thank everyone who continues to recommend us to their friends and stuff it's so lovely welcome to listeners, of course. And if you are in a position where you'd like to support us as a Patreon, do be aware that we have our bonus podcast available for Patreons only,

which is a wizard-level Patreon where you can get our show, I'm a Wizard, where Matt and I talk a lot less sense, but a lot more silliness. Oh yeah. Also, thank you to our producer, John Harvey, and our problem curator, Steph Keegan. Thanks for listening. Bye.