A Problem Squared - 015 = Getting Plucky and Feeling Lucky

Episode Date: January 31, 2021

This month Matt and Bec are problem-solving thusly: Can you cast shadow puppets on the Moon? Why do champion cyclists wear such short shorts? Is there such a thing as a lucky person? Here's a useful graphic of how the Moon orbits Earth https://www.nasa.gov/feature/goddard/from-a-million-miles-away-nasa-camera-shows-moon-crossing-face-of-earth And this is the article referenced by Bec in the show about body hair: https://www.theatlantic.com/health/archive/2017/02/the-casualties-of-womens-war-on-body-hair/514983/ Send your problems to our new improved website! www.aproblemsquared.com  

Hello and welcome to A Problem Squared, the podcast that attempts to solve as many problems as possible with medium to decent success rates. In fact, it's kind of the problem solving podcast equivalent of metamorphic rock in that it gradually adjusts and changes depending on the situation around it. My name is Matt Parker, a mathematician and also a bit like metamorphic rock, in that I have a fantastic collection of different types of marbles. And I'm joined by Beck Hill, comedian, who, many have said, responds very well under pressure. How are you doing Beck? It's always a pleasure when you're introducing the show.

Thank you. I put the effort in, you know, I give it a go. Yep, you sure do. You say that like it's not a good thing. You hear what you want to hear, Matt. So true. So true. How are you keeping?

I'm good. I'm very, very good. Just been keeping busy. I'm making new flip charts for the CITV Makeaway Takeaway show. So that's been fun. Getting back to work with me crayons. So this is your, by flip charts, not just pictures you draw, but these are like fully, you know,

physically animated stories in a flip chart. Yeah, yeah. In the show, I'm just going to be doing like a page an episode to sort of show you how the mechanics behind them work, which is really fun. So it's a lot less pressure than the usual ones. But that's been, it's been really nice. And I had a lovely Christmas. Got some good gifts.

A couple of track sets, which is apparently what they're calling track suits now. A track set? Yeah. So right now I'm wearing a lovely sort of fleecy track suit with geometric shapes and dinosaurs on it. And I feel like a baby in that I'm very comfortable and entertained by the colours. What's not to like with geometric shapes and dinosaurs? I mean, I feel like a substantial percentage of our listeners are suitably envious right now. Oh, they should be.

They absolutely should be. Matt, what did you get for Christmas and or your birthday, which happened right after we recorded the last episode? Oh, yeah. So we had the full festive period. I got a lot of beer a lot of drinks I'm I fall into that awkward category where a lot of things if I want a thing I just will buy the thing I either want it and I buy it or I don't want it and I don't get it yeah which is not to say I've got a lot of stuff I just you know I'm into a few niche things and I tend to buy them and so a lot of lucy my wife's family are like oh what do we get matt for like it was my 40th birthday so like i don't know if we're gonna get him um but i like beer

and that's and so and beer doesn't go off and so i um well not in the over the time scales where it's a problem for me and so a lot of people sent me like, you know, unusual coffees and beers and drinks and all sorts of things. And so I basically filled up my drinks cabinet over the festive period. That sounds nice. And we actually, we consumed the 30th birthday present that Lucy got me. That's some old beer. Like, well, an old bottle of port. Oh, nice. when I turned 30.

And I was like, this is amazing. And then initially I just thought, well, we should open it on a special occasion other than my 30th because there's so many other things happening on the actual birthday. You don't want to crack open expensive port as well and just chuck it in the mix. So I was like, well, we'll save that for later. And in the end, I ended up saving it until my 40th birthday. That's nice because after

a while it became a thing i'm like well now we now we can't drink it yeah that's true there's there's always like a bottle of something that you're like oh it's too nice to open exactly yeah so it kind of gained momentum and eventually we're like well the only thing that's going to rival getting it for my 30th is drinking it on my 40th. And so it just sat there. It sat in the kitchen. We moved house. It sat in a different kitchen.

And it was just there the whole time, which was quite nice. And then we opened it. Teasing your guests. Yeah, yeah. Everyone's like, can we have it? Like, don't touch it. That's not for you. That's for the distant future.

But then Lucy, good honor, bought me for my 40th port to drink on my 50th. Nice. She actually went all out. She bought four bottles for my 50th, 60th, 70th and 80th. Oh, so they'll be older and older and older. Exactly. And so the port in theory will get better every decade. And we can add more bottles once a decade.

We can buy port for all the remaining decades yeah and if you die earlier she's got a bunch of port to celebrate with exactly exactly and we're like you know it's a bit morbid that we're like well let's not worry about 90 if that feels like money that may not be well spent yeah but the thing is you're gonna you're gonna get older no matter what happens so So you may as well put some long running traditions into your life because it's going to happen anyway. That's good. So, yeah. I may have mentioned this on a previous podcast, but my dad once taught me the phrase, is there any red port left?

Because obviously port means left in sea terms. And when planes are flying, the left wing has the red light. So is there any red port left is a really handy... Remind you that port is left. Yeah, yep. And which way a plane is flying if you see it's red and blue lights? Red and green? Red and blue.

Oh, I think they're blue, but maybe that's just how I always assumed the other one was blue. Listeners, send us a message at a problem squared. Send us now. Tell us. We could Google it, but we won't. We won't. We're not going to do that. No, that's for you to do right now.

Coming up in this episode. Who wears short shorts? Winners, apparently. I'll be looking at how to cast moon shadows. You'll also be looking at some problems regarding luck, lucky people and Minecraft. We've got a range of updates involving some biscuits and a new way you can send us problems. It's all very exciting. We'll get straight into it.

to it this problem comes from Catherine via email who wants to know if it's possible to cast shadow puppets on the moon from their house their first point they've got several points as well for this question so I'm going to give you the first section which is if it is possible how big would their hands have to be and how big would their torch have to be to cast such shadows right oh i'm glad they broke this into small chunks because there was a lot going on if you want to try and cast shadow puppets on the moon but okay so geometrically the moon is a long way away that's a fake start. Did that answer your question, Catherine? Thank you. Goodbye. There you are. The end. Parker, maths

professional. So, no, so, you could fit 110 moons, give or take, between the Earth and the Moon. Okay. And so, the Moon is further away than anyone ever thinks. So, if the Moon was like a marble one centimeter across, it should be 1.1 meters away from the earth.

And so actually it's quite small and quite far away. I think that people judge the moon's distance the same way people judge my height. Because people always think I'm shorter than I am. Like always. I'll be sitting next to you and if I say stand up and show me how tall you think I am on you, people will always put their hand like just above their waist. Like people think I'm tiny. And not always is a joke. Sometimes that's sincere.

Yeah, yeah, yeah. I'm average height, but apparently give off the feeling that I'm a child. Yeah, exactly. And if you give someone like a tennis ball and you say, how far away should this be? Like if it was the moon away from you if you were the earth. And a tennis ball is about what, seven centimetres? So it should be

over seven metres away, which is a long way. That is a long way. Yeah, it's crazy. But because it looks so big in the sky, we always just assume it's massive and close. It's not. It's medium and far away. There's a lovely line in Red Dwarf where they say that the planets are all like, stay away from Earth.

It's got humans. And I always think that. I feel like that's what it is with the moon. We think it's standing closer to us than it is, but it's actually being socially responsibly distant. It was way ahead of it. Yeah. Way ahead of the curve on that one.

Yeah. So the moon's a fair way away. And it's roughly a hundred times further away than it is big. That's the vague rule of thumb for the moon. Okay. But the actual question here is how big would my hands and torch need to be to cast the such shadows so because the moon is roughly a hundred times further away than it is big if you want to cast shadows that fit on the moon which i'm just taking from this

question how big would the setup have to be? Like, where do you have to put the torch? Where do you have to put your puppets? If you're prepared to use smaller puppets than your hand, like if you make tiny puppets that are like under a centimeter, they need to be, basically the puppets have to be a hundred times further away from the torch than the size of the puppet.

So if you made tiny, tiny puppets, you could hold them like a meter away from a torch and they would cast the right size shadows to fit on the moon. If you want to use your hand, which is like, what, 10, 20 centimeters, give or take, then you need to be a hundred times further away from the torch than the size of your hand, which is like 10 or 20 meters. Yeah, yeah. That's quite a lot. What, a normal size torch?

I'm not, I've, because they've not asked here how bright the torch would have to be. Ah. I mean, depends how you interpret how big would the torch need to be. I've just been looking at the geometry. We'll get to brightness later. Yeah. And spoiler, there are other problems with this. I suspect, see, the way I visualize this is a bit like if you're doing the bat signal. Yes, exactly.

So to me, I imagine you need like a massive spotlight. But what you're saying is it doesn't need to be massive. It just needs to be bright. I've not yet dealt with how bright that light would have to be. When there's a solar eclipse, is that basically the moon casting a hand puppet on the earth? Yes. Aww. And actually, if you look at satellite footage or footage from space of an eclipse,

you just see the moon's shadow move across the earth, like some kind of massive moon shadow puppet. That's so cool. All right, the next segment then is, is there a certain place on the earth that works best? I live in Cheltenham, United Kingdom at the moment. Should I consider moving? Yeah. So this is kind of the reverse problem that astronomers have where they want to observe

things in space. So the light comes down to earth. Whereas what Catherine wants to do here is beam light back up into space. Yeah. And again, we haven't looked at the brightness of the light yet. However, you're going to have the atmosphere in the way and that's going to cause problems with making your image very fuzzy because as light goes through the atmosphere, you get something... In astronomy, it's called seeing. It's why stars look twinkly

because stars should look like static dots. They're not moving. They're not twinkling. They're a point source of light, almost without exception, and they should look like that, but they don't. They look like they're moving around

and they're twinkling and all that jazz, and that's because the light... Oh light because our atmosphere is like a giant instagram filter yes exactly the the it's like a giant instagram filter that's adding sparkly effects to light coming in from space huh and that's the problem and so astronomers have already solved this problem but you know they were they were looking at it in the reverse direction. But the problem is, how can I reliably get light to or from the Earth without the atmosphere and everything else getting in the way?

And so astronomers, first of all, they try to put their telescopes up mountains or somewhere high in the atmosphere, because then you've got less atmosphere, less filter, less Instagram filter for your light to go through. Less Hudson. And so they look for mountains. And they look for places that have very good weather. So maybe this doesn't count for Catherine. If they just want to do a one-off puppet show.

But astronomers will look for locations to put a telescope that has the maximum number of non-cloudy nights to be able to do their observations. Yeah. And my wife, who is a astronomer, has been out to, she went to Tenerife like year before last to do observing. Oh, yeah, sure. And she's been to La Palma and places. Yeah, yeah. I've got to go do some observing.

It's always when I can't go. Yeah, yeah, yeah. I'm like, oh, I'm off with all her colleagues to go and, you. It's always when I can't go. Yeah, yeah, yeah. I'm off with all her colleagues to go and, you know. And then it's cloudy. And so they just have a holiday instead. It's ridiculous. But anyway, astronomers argue, no, we have to put our telescopes in these incredible locations because there's a mountain and there's good weather. And all the things that make a good vacation destination also make a good place to put a telescope that's why she always comes back from holiday like oh i saw

orion that's the name of the pool boy that's the name of the the other consideration for astronomers is you're often constrained geographically like if you you're in america you've got to put it somewhere in America or a European telescope has to go somewhere in Europe, which is why Hawaii is common for US telescopes because that's the best location they've got. And then you'll have, you know, Europe will be putting them down because they've got links to like Tenerife and whatnot.

And so there's other considerations of where you're allowed to build things. And so Catherine needs to factor all these things in and how often they want to put these displays on but the most important thing is the less atmosphere the better and ideally if Catherine could be above the atmosphere because the best observations for astronomy are on spacecraft that are outside the atmosphere and so I mean ultimately that would be the best place just you know even low Earth orbit would probably be sufficient to get above the atmosphere to have a much clearer projection onto the moon.

Catherine also says, if I'm standing on Earth, so let's bring Catherine back down to Earth, with the right equipment, is the distance too great to cast accurate shapes? Would the shadow puppet just become fuzzy beyond recognition? Now we're getting into the real problem because even if there was no atmosphere, which would blur your image, you're still not going to get a sharp shadow over this kind of a distance. Okay. Because, so even if Catherine could get, you know, even without the atmosphere as an issue blurring the image, you've got another problem that light isn't a particle. It's also a wave. Well, it's both.

It's both a particle and a wave, which we're not going to get into right now. But the waviness of light is what causes the problems. Because if photons were solid particles, then you could, in theory, cast a shadow with a pretty sharp edge. Because the particles would either be blocked by the edge of your puppet or your hand or whatever it is or they wouldn't be and they would pass by and if they miss it they miss it and it's fine light however is a wave and so even if it misses it if it doesn't miss it by much it still gets slightly refracted and so even light that goes past the edge of your puppet will have its path uh bent a bit and so when you actually cast a shadow instead of it being a sharp edge

there's a slightly like blurry edge and then you get like bands of bright and dark effects as you go out from the edge of it. And normally in our regular daily existence, this is too small to notice, but it could be a problem when you're projecting something to the distance of the moon. I just realized that even with lunar eclipses, you don't really get the same sort of really slick shadow across the way that we do with a solar eclipse it's sort of from memory whenever i've watched lunar eclipses they tend to just go a bit it the moon just goes a bit murky yeah and that's partly because the moon hasn't got

an atmosphere and so it casts a better shadow whereas the earth has an atmosphere and so it's already a terrible thing to cast a shadow but there are impacts from the distances away because this is actually this is a problem that my wife does have on her spacecraft which is a great sentence that i use at every opportunity yeah i was gonna say you're gonna have to elaborate there because she's a solar physicist the spacecraft she works on have a artificial eclipse basically they have an occulting disc which blocks the sun but the light from the sun and there's a lot of light from the sun um that just misses the disc is refracted and can then be bent around the disc and still ends up on the image when they're trying to look at the faint kind of wispy atmosphere of the sun.

And the way they fixed that, actually, they're planning a new spacecraft where they're going to put the occulting disc on a whole separate spacecraft to get it a long way away from the one with the telescope on it, which is just, the engineering behind that is incredible. It's like the spacecraft equivalent of someone carrying an umbrella around for a rich person. It's exactly. Yes, it's precisely that. I love that.

Well, it's interesting because you say that and that actually talking about eclipses and everything, I think runs on to the final section of Catherine's question, which is what's the best time of the month or year to do it? Because obviously trying to cast a shadow puppet onto something that is already reflecting a huge source of light is really difficult. It's like when you try and have a cheap projector on the wall when you've got all the lights on in the room. So surely the best time to do it would be when the moon is the opposite of a full moon an empty moon the empty moon the well-known empty moon it's called uh ironically the new moon oh yeah that's right even though you can't see it yet which i always thought was a

terrible name yeah but yeah no yeah you've you've done two things perfectly there beck oh you've both nailed the exact correct time to do this because you're right you want the screen you're projecting on to be as dark as possible and that happens when there's a new moon which is when the moon is between the earth and the sun and so we're looking at the dark unlit side of the moon not the dark side of the moon that's something subtly different but anyway and you've moved the conversation on because the physics

and maths behind refraction and if you'll get a sharp edge or not is super complicated and so I didn't bother doing it and I wanted to I was going to move on to this point anyway so I love what you've done oh hooray

yeah so the only other issue is the moon is just a bad surface to use as a screen i'm sorry catherine uh to break it to you the moon is not very reflective in fact the earth is is more reflective than the moon there's a fantastic photo of a spacecraft took looking at the moon and the earth it's similar to when you'd have an eclipse where the moon they're both fully lit by the sun and the moon is just super dark so you can measure how reflective something is and there's different types of measuring this because it depends if you care if the light that's reflected off something comes straight back towards you or if it's just reflected off in any direction and during the lunar landings the apollo missions they left a retro reflector

on the moon which is designed that if you hit it with a laser it directly sends the photons back in the direction they came from so you can actually bounce and collect light off the moon which is just incredible but if all you care about is just how much of the light that hits it gets reflected the earth is about 31 reflective so about a third of the light that hits the earth gets reflected back the moon is only about 12 reflective whoa so if all the light that hits it only 12 gets reflected off the rest of it gets absorbed i guess if it was more reflective it would have like it would be a bit closer to looking like the sun wouldn't it yeah yeah and we always assume the moon's bright and you know very

reflective because it looks so bright in the sky but that's because we're comparing it to other things that are dark and it's being lit up by the sun which is super bright so it's in an incredibly bright source of light yeah that's true and during the day it's really hard to see during the day because everything else is bright and we can't see it it's only at night that it looks bright because everything else is so dark around it oh yeah relatively speaking yeah it's actually the moon is roughly as reflective as bitumen so it's like having shadow puppets on a road it's not a good surface for shadow puppets because it reflects so little light and that's before we get into you how bright your torches you'd have to so much light at the moon you're only going to get 12 of it back and that's in every direction let alone coming straight back at you and then

the distances involved it spreads out so much it's just sadly not possible so i didn't even bother i mean i probably should have sat down and worked out the amount of brightness you would need but then you start getting into is it a point source light what directions the torch shining in and so sadly the moon is just not reflective enough and it's too far away to be a good screen for shadow puppets there you go I think in all angles you've dinged this or whatever the opposite of dinging it i've managed to prove that it can't be solved well the solution is no solution is no yeah ding thanks one of our patreon supporters david says hello very nice you david i have a problem for you in the past several years i've taken to running road races. From observation and participating in many races,

I've noticed that the winners always wear the shortest shorts. And then they've put, think five centimeter inseam. I don't think I will, David. Thanks for suggesting it. And they then point out that the people who come last tend to wear shorts that are 30 centimetres or longer. They want to know, is there any possible correlation between running speed and short lengths? And Beck, you looked into some five centimetre inseams, I believe.

Yep. And I want you to quote me on that, wherever you like. I mean, by looking into, I've just got some thoughts on this. First of all, I suspect that longer shorts get in the way. You know, I reckon they'll create some friction. And so I think just generally shorter shorts, you know, will be a little less flappy. Less drag. Less drag. But I don't think that's the only reason why there's a difference. I don't think that's the only thing causing a difference in speed. What I suspect is that more like full-time runners or professional runners are going to go for running specific shorts

because they're like, I run a lot. I don't want any chafing. I don't want any friction. I just, you know, I want my legs to be free in the air. So they will invest in shorts for running. Whereas the people who come in at the end of a marathon are probably people who are like a bit more like me, who are like, oh, I'm going to give this a go. And they're not at the stage where they're going to invest in a proper pair of running shorts. They're just going to wear like, you know, their daggy multi-purpose shorts. I can be one extra data point. The one time I did some running, I was like, I own some basketball shorts. That's, you know, close enough.

Yeah, exactly. Exactly. I think that's it. I mean, because otherwise, theoretically, if you didn't wear any pants at all, you could be the fastest man alive or woman alive. So you're saying that the causal relationship is not wearing shorts makes you faster, but if you happen to be faster, you're more likely to want to wear shorter shorts because they make you faster. Yeah. Yeah yeah otherwise you're saying bolt would just run everything you know everything free-flowing well that would be uh quite traditional from an olympics point of view i think yeah but not with a top on top oh okay oh you keep that yeah yeah i'm sorry i just figured it just works its way up the body i thought i didn't just you know

just the line above which there's no clothing works up so like you're running in just a crop top or something yeah yeah you'll have like you'll be half half covered like a centaur but with clothes that's that's the one that's the one like a centaur but with clothes which which if i heard that sentence i would imagine just a centaur wearing a pair of trousers but i'm sure for many other people that cleared it right up for them. What do you reckon, Matt? What do you... Well, it made me think of, because I'm now a cycling guy, when I was getting into cycling, a lot of people shaved their legs

and I was like, I wonder why. I should look into this. Why do people shave their legs? And there's no real practical reason why cyclists shave their legs, which I find really weird. It's not like a chafing thing or like the hairs get caught in the gears? Because mine would. Not hairs in the gears, not a chafing thing. It's not like they've all been ripped out by being caught in the gears.

It's like you see some people like, oh, you're more aerodynamic. Don't get me wrong. I mean, being aero, that's a big, big deal in road cycling. But it doesn't make much. It's not making a difference. And then there's, oh, it's easier if you fall off to clean the wound or whatever. Oh, yeah. If you get gravel in it.

But that's not really the case. It's easy enough to do it. From what I can tell, the only reason that cyclists shave their legs is because it shows their dedication to cycling. Right. So it's just a display of how committed you are to the sport that you shave your legs. In the same way that if you're a barista and you have a top knot. Very similar. Yeah, yeah, yeah.

Okay. Yeah, yeah. Because the top knot doesn't make the coffee better, but it tells everyone that you like coffee i bet there's a correlation between how complicated to maintain or difficult or investment in a barista's hair facial hair head hair all of it i bet the quality of the coffee does correlate but just because they're so committed to the look they must be pretty serious about making coffee yeah and that's the deal with cyclists you're doing that to show you're not just some you know casual cyclist who does it occasionally it's part of your identity you shave your legs and you want to show off your legs from cycling i guess yeah right and so cycling is all about the legs i can kind of see

how it started because conceivably an argument over aerodynamics or something yeah it's become way more than that and so i refuse to do it it's interesting you raise it actually because one of my new year's resolutions this year was to become more accepting of the parts of my body that don't need to change you know because obviously it's not i'd like to become healthier and fitter and things like that but there's other elements of my body that i don't like and I realized for no real reason other than my brain tells me that I shouldn't like them and one of them is the fact that I'm quite a huge woman and my legs and feet are really dark and hairy if I don't get rid of the hairs

and I I'm fine with that at home though like Gav's fine with it you know like no one around me has ever cared uh about seeing my uh my leg hair but it's something that i realized that i wouldn't dream of going out in public without either removing the hair or hiding them which means that if i don't want because it takes me like i use an epilator which is, it's like a thing that tears out each hair individually. An epilator. Yeah. So it sort of is like a thing that rolls around and plucks all the hairs. Oh, wow.

So it takes longer than waxing, but is much cheaper. And you don't have to keep buying waxing strips or anything like that. But it lasts longer than shaving. So if you're willing to spend three hours in pain, then you can then not worry about removing your leg hair for another two weeks as opposed to a couple of days. That's a terrible trade-off. It is. It's awful. It's like an I'm a wizard episode.

It's no fun. And also then you've got aftercare as well. So if you don't constantly exfoliate your legs or moisturize and stuff like that, you can get ingrown hairs, infections. So then you end up like in pain or it's not, it's really awful. There's no good solution to removing. It's like your legs want to have hair. Yes. And there's no way, there's no easy solution to stop them from doing

that no and you can get like laser treatment and stuff like that but it's expensive and time consuming and again one of those things where i'm kind of like why do i have to spend my money making it so that other people don't look at my legs so So I decided that I want to get over the fact that I don't like seeing my legs because every summer and stuff, but even when I go back to Australia, I'll wear tights in summer and it's so hot and uncomfortable, but I'd rather that than people be distracted by my leg hair. I don't want people to look at my legs and make assumptions about me that aren't necessarily true or indicative of who I am. And so I'm trying to get past that and sort of not care as much about what other people think, which is really hard because like, especially when

you're a performer, it does matter what people think. And so I have been doing more and more research into it. I've started following Instagram accounts where people of all genders actually post photos of them with their hairy legs, which has actually been incredible for my self-confidence. I'd never seen so many people like a lot of women with legs as hairy as mine. And I realized I'd never seen it. I actually cried when I first started seeing it because that's how much I realized other women hide their legs as well. And so it was really emotional. And I also found out, getting back to my point, sorry, I've gone off on a tangent, but getting back to my point is that I found out that I always thought that shaving or removing leg hair came from marketing. You know, it's like a way to sell more razors or to sell waxing.

Like with most beauty stuff, I just assumed it was all led by the market. And I actually found that it sort of became that way because women from non-white backgrounds tended to have darker body hair. And so it was seen as a way of showing racial superiority for white women to remove their body hair to show that they were different from other races because it was believed that Darwin's evolution had been misquoted as saying that people of other races were less evolved than white people, which is obviously not correct. But they saw the body hair as a link between sort of Neanderthal stuff.

And so the further you could separate yourself from that. The less hair, more civilized. Yes. But then you're like, hey, but why aren't men taking off their hair as well? And that was because it was believed that the more civilized a race was, the more defined the genders became. So they wanted to show that women and men looked far more different than they do in other races so it was seen that white women were technically hairless over their bodies and uh and very different from white men and so that was seen as a again a racist thing to show that and then it also popped up again and became more even more of a popular

misbelief when women were able to enter the job market and start working there was fewer things to show the difference between men and women because women were suddenly starting to be treated equally to men and so then that's when you saw the marketing forces pushing more to say equally to men. And so then that's when you saw the marketing forces pushing more to say, okay, you can work, but you better stay a woman. And it was like really pushing for women to look different to men to at least show that there was a difference. It's all, so it's all wrapped up in this racial patriarchy type nonsense. And that's how we get to where we are today, where you'll see someone with hairy legs and think, they're dirty or if you see a man with a particularly hairy back you'll be disgusted when there's no reason to be except for the fact that we've all been taught by the structure that we've grown up

in that that is bad and it's just like blow my mind so anyway what I'm saying is to solve your problem Matt about cyclists removing leg hair is that they should read the book Plucked, A History of Body Hair Removal, I think it's called. There's a fantastic write-up about it in The Atlantic. We'll pop a link in the show notes for anyone else who wants to read up more about that. It's really fascinating. Definitely recommend it. But to get back to the original problem, because we have gone off on quite the tangent. Yeah, I think I answered it originally at the beginning, was that about the short shorts. I think it's to do with experience.

What do you reckon, Matt? I agree. We have run a long way from where we started. But in short, ding. Now, Matt, in episode 014, we brought up the concept of luck and in particular lucky people. You said that you don't believe lucky people exist. I do not. Oh, everyone who knows you is lucky.

Lucky, Bec. Ah, see, there we go. End of episode. It's not going to end any higher than that. I asked on our Twitter, which is at a problem squared, what our listeners think. And it was pretty down the line. It was something like 49% think they do.

And 51% think they don't, which, okay. You know what? I think if that's how a vote goes, you should do a re-vote. Yeah. I don't think you want to make major major you know nation-changing decisions on that kind of split no so i uh actually spoke to the luckiest person i know which is another comedian called sarah bonetto and she is genuinely

the luckiest person i know so i asked her if she could tell our listeners about her luck and more importantly tell you about her luck. So she took a moment out of doing her laundry to speak to us. I do believe there is such a thing as a lucky person because I get told all the time that I am one. But that comes with caveats. Like I do kind of believe that I'm dusted with the time that I am one, but that comes with caveats. Like I do kind of believe that I'm, I'm, I'm dusted with the magical fairy dust of luck, but also I do believe in science

and, you know, and research and probability. So I often put myself in the way of luck. So Matt, in particular, I know you're probably sitting there listening, smiling, but wringing your hands thinking, yeah, well, where are the results? Give me some stats. I'll give you some stats. Over the years I've been entering competitions, I've won CDs, DVDs. I've won holidays. I've won festival tickets, concert tickets. I've won wine and cheese hampers, five after this year. I won four this year and one last year. I've won a designer living room rug. I've won the lottery, seven grand. Thank you very much. I won a car on a game show. I mean, the list is a little bit, it's worrisome if you do believe in fact-based science, isn't it? Because

it does look a bit like I'm lucky. But yeah, I do think I do put myself in the way of luck but i have a question for you guys when i won the car on a game show my friend from university cliff who was a big maths and probability fan he used uh used to try and teach himself to card count and things like that he was reading a book on probability and he got really angry at me after i'd won the car because it had a chapter on people that win cars in this probability book. I'm not sure if you can find this book, but this book stated that in your life, you might win a car or someone you know in your wider circle of friends, but there is only one car in your circle of friends. So if that's true and if you can find that research,

does that mean that by virtue of you guys being mates with me, I have stolen your car? Hmm, something to think about. Okay, so, I mean, obviously we'll get to Sarah's stealing our car problem in a moment. Yes. But has any of that managed to convince you that lucky people are a thing? Okay. Maybe I do believe, I believe there's no such thing as luck, but I do think there are

lucky people. Oh. Because I think luck is more than just things that randomly happen to you and they turn out better for you than normal in a way that's predictable and ongoing. I don't think that exists. But I think you do get lucky people because either they make a lot of opportunities for things to randomly go well for them. And because there's just more opportunities, things go well randomly more often. Or they're good at capitalizing on them. So people who use their privilege are gonna experience more luck sort of like if you were born rich which in itself you could argue

as lucky but you know that's because your parents or whatever yeah it's lucky for you yeah and then you've got more money to then invest in stuff so you're more likely to get even more rich oh yeah no a hundred percent there's like if you're already rich and you like invest a bunch of money into random stocks and then some of them do incredibly well you're like i'm just so lucky i made all this money on the stock market you're like yeah but other people didn't even have the opportunity for that to happen only an idiot would end up worse off had they not just sat on the money that they'd given only an idiot would do that and you know not become president i feel like you've got specific people in mind um however like back back to bonetto i suspect she enters a lot of competitions if i'm remembering that's true

so i would say that she is lucky in that she's won a lot of prizes. However, if you took her number of competitions entered and then compared it to prizes won, it would be the same rate as everyone else. So she's lucky in absolute terms because she's won a bunch of prizes, but she's not lucky in terms of she wins more frequently out of the number of times she's entered, if that makes sense. Yeah, I think we'd probably need some more stats, wouldn't we? Yeah, and there's also the flip side of,

if let's say you've got 100 Sarahs or entering lots of competitions. Oh, then I'm the lucky person. Then you're the luckiest friend in the world. Some of them would do worse than average. Some would do better than average. Just because randomly, you're going to have a distribution. It's like if they were all flipping coins or rolling dice, even though the odds are the same for everyone,

just out of sheer luck, some people would do really well and some would do poorly because you've got lots of people trying it at once. But then importantly, if you took the 100 Sarahs and you took like the five luckiest ones who won more often than the others, in the future, they wouldn't then consistently continue to do better. They just happen to be the ones who did better so far. So arguably they're the luckiest. But that's not some innate property they have and means they will continue to be statistically lucky in the future.

And I do stupid things like this all the time. Like for one video on YouTube, I flip 10 coin predictions in a row. I flip heads, tails, heads, tails, perfectly alternating 10 in a row. And it's because I just sat there and flipped the coin thousands of times until it happened. row and it's because i just sat there and flipped the coin thousands of times until it happened and just because it happened those 10 in a row it was no more likely to happen the next time than if it was the first time it's statistical distribution you're going to have some freakishly lucky things some freakishly unlucky but there's no ability to predict the future and so when i say i don't think luck exists i mean just because you've had

a run of good luck i don't think that means in the future you will continue to have good luck but i'm also i don't want to rule out people who are just better at seizing opportunities so actually in minecraft speed running circles and some people already know what i'm talking about now there's been a big controversy over a youtuber and video game streamer named dream now i don't play minecraft beck are you in the minecraft world nine craft i am not hey good well done um so i don't i mean i watch uh some speed running but it tends to be like retro video games where the idea is to get through the game as fast as possible and the ones i like are the old nez you know um mario mega drive kind of yeah those how fast can you get through super mario

brothers that kind of stuff right i love them but for a lot of these the ones i like are skill-based and it's always interesting when there's a bit that just requires dumb luck like a certain enemy moves randomly and you know only one time in 10 are they in the perfect position to get through them in the optimal time right and what it means is after then if anyone wants to break the record they have to be as lucky or luckier than the previous person who did it. Gotcha. And I find that a bit boring because you just people just trying it over and over again till they happen to be lucky.

Yeah. Minecraft, because there are versions of Minecraft where you can finish it, but there's so much luck involved. It's crazy. And so I'm like, well, I get why you speed run, but it's so much is down to like one bit. You've got a trade with one of the in-game characters and there's only like a 5% chance they will give you the item you need in return. Or you kill an in-game character and there's a 50-50 chance they drop the item you need. So getting through the speed runs is just a test of how lucky you are, which is just randomness.

And I don't find that very satisfying. And this controversy was that this player, Dream, was way luckier than the statistics indicate they possibly could be. They were just getting outrageously good luck. And I found that interesting because, I mean, statistically, Dream encapsulated both types of luck. Because they were also one of the biggest breakout YouTubers of 2020. Oh. They've now got tens of millions of subscribers.

And they didn't come out of nowhere. They've been doing stuff for a while. But they absolutely exploded in 2020. And you could say, well, suddenly there are a bunch of young kids who like watching Minecraft videos trapped at home with not much to do all of a sudden. Yeah. And this was the perfect opportunity for a YouTuber like this for that to happen to. And some people say, well, they were very lucky that their channel exploded. I think that was where they were making their own luck.

They're in the right place, the right time, but that they capitalized on it and they were producing a good product. And so I think that's that one type of luck where I agree it exists. They saw an opportunity. There was some randomness in them having that opportunity, but they capitalized on it. And so I'd say, yeah, they're definitely a lucky person in that regard. But on the flip side, I don't think that makes a difference to what happens when there's a random number generator deciding when they trade gold if they're going to get you know a pearl or whatever in return because that's a random number generator and some code and so i think it's easy to confuse those because we're humans but one's pure randomness and one's capitalizing on things that happen around you and

so the the now the you know the accusations, this person can't be that lucky. They must have altered the version of the game that they're playing on to change the odds when these things happen. Well, arguably more people have tuned into them and started watching them because they have had an unordinary amount of success with the random results.

Yes. For every YouTuber like Dream, there's like thousands and thousands of other YouTubers not having that luck and therefore not getting a following because they're having the same experience as everyone else. Yep. But this YouTuber happens to be having good experience and therefore is far more watchable. Yes. And you've perfectly nailed the problem with saying this person must have faked their games

or their luck because you say, well, what if there's just thousands of people playing it and you're going to expect some people to randomly do much better than other people? And so then there's a lot of stats behind. Is it within the realms of what conceivably could happen or is it so ridiculously lucky it's outside that so i think this kind of brings us back to sarah's problem with the car as well oh and i should say i tried to find that book that has a section about you or someone you know will win a car oh yeah any luck no i've had no bad luck. I'm just unlucky at these things. I asked around all my maths book experts and people had some guesses,

but no one could confirm what book it was. So if anyone knows the book about probability that talks about the odds of you or someone you know winning a car, please tell us. I'd love to track it down. I found a very similar bit there's a book called why do buses come in threes by rob easterway which is a great book highly recommended and in it rob

talks about the probability of you or someone you know winning the lottery and how that's higher than you expect because the phrase or someone you know that's doing a lot of work, that phrase, because you know a lot of people. Yeah, because I've actually, with the car thing, I was going to say my friend's mum won a car. So if Sarah's won a car as well, I've instantly proved that incorrect. Yeah. There's a lot of people who, if they won the lottery,

I would then be able to say, oh, I've got a friend who won the lottery. And Sarah is now in that category. But do you know anyone else who's won the lottery, I would then be able to say, oh, I've got a friend who won the lottery. And Sarah is now in that category. But do you know anyone else who's won the lottery? I know one other person who's won the lottery. And it was a family friend of my parents won the lottery in the late 1990s. They won like the top level jackpot. Oh, wow. So there you go, you know.

But now we're including Friends My Parents Had in the 90s. Which is a very, very wide net to cast. I don't know if we've cleared up this luck issue at all to be honest. I think if anything we've muddied the waters. I think maybe we could just redefine this as the problem

of just finding that book. I mean, that feels like a much more open and shut problem to deal with. Okay, yeah. I'm willing to ding this problem on the head if someone can tell us what that book is. If we can find that book, that would be good luck. Let's do it. Find us. We're at a problem squared on Twitter. Hit us up. Another problem that we looked at in episode 014 was about cookies and biscuits and what the difference is between them. And I made a staunch opinion that they are the same thing. I am adamant that they are the same thing. Something that has come to my attention from the replies in social media is that it's not necessarily always the same thing. And I think what really did it for me was one of our followers pointed out that a lot of biscuit companies will also refer to some crackers as biscuits, you know, like crackers for cheese and biscuits for

cheese. And they're not necessarily, I mean, the cookie monster might eat them, but you know, they're not necessarily sweet or anything like that. And I realized that it is, it is a difficult one. Yeah. You wouldn't put cheese on a cookie. I mean, you could, and it's probably amazing, but it's not marketed in the same way. And so I've decided that I'm going to try and reassess it. And I think it's not a binary answer. And that is that I think a cookie or a biscuit is whatever it identifies itself as. And that we should respect that instead of trying to point out what the differences are. So whatever it says on the packet,

whatever the product decides, we should respect. Yeah. I just think we should respect the fact that it's cookie and biscuit. There's a spectrum of baked goods and they're more enjoyable if we don't focus on the things that separate them. Rather, we celebrate the fact that they exist at all.

This is a big step forward for you, Beck, and I support your progress. Thank you. As an extra side note, we got a tweet from at underscore Hectors who said about my answer versus that. They said, here in Brazil, there is a big war on a similar problem. Capital big. Bolacha versus Biscoito. It's a thing that divides the country and now and then generates discussion here on Brazilian Twitter. And they've even provided a map.

I'll retweet this for anyone who wants to have a look at it at a problem squared. It's great. And it's a map that shows who calls it a bolacha and a biscoito. Apologies for my pronunciation if that's wrong. The map has both as an option. Yes, which I think the people who go for both are in my camp now, which is that it's whatever you want to label it as. What's super interesting about the map,

just anyone who's not seen it, it's the regions aren't contiguous. It's not like there's like the Biscotto people on one side and the Bellaccio on the other and then both in the middle. There's fragments of all of them all over the place. Yeah. I can see why it's them all over the place. Yeah. I can see why it's a constant source of argument.

Yeah. There's like one tiny corner of both, like surrounded by bolacha. So I'm interested. People, any Brazilian listeners or Portuguese, if you're finding this issue there as well, tell us more. Tell us more about this problem. Let's see if we can help out. That's great. So your problem is just, the problem is not big enough. Let's add to it.

Yeah. I'm wondering if I can fix it with my new message of acceptance. I love it. I'm on board. Before we finish up this episode, Matt, you've been busy. I've made a problem entry form. Yay, a problem posing page. Problem posing page. The PPP. That is a much better name.

Oh, well, there you are. Yeah, so previously we weren't doing anything with the website. So now a problemsquared.com sends you to a page where you can submit a problem and that problem gets injected straight into our database of problems yeah which is very pleasing from a back-end point of view yeah and so we'll be able to categorize and file your problem and then attempt if we can because we could we can't solve every problem but it'll be in our queue to attempt to be solved. Yeah. And that's not to say don't tweet us or anything, but it will very much help us out,

given that there is a very small team of us working in the back end here. If you would like to put your problem in via that, that will be the first place we'll be checking. So if you have a problem, head on over to a problemsquared.com, enter it via the form, and we will more likely see it before the next recording. And if you do tweet it or put it somewhere else, put it in the form as well. There's a free entry box. You can chuck in the link to a tweet or anything else, any supplementary evidence, put it in there, and we'll see what we can do.

Yeah. Thanks for listening we also want to thank obviously our lovely patreon supporters as well as everyone who has recommended us to other people or left us a lovely five-star review on whatever podcasting app you use we also want to thank our wonderful audio producer john harvey and our brand new problem curator, Steph Keegan. Bye. Bye.