A Problem Squared - 021 = Inharmonics and Skin-harm-tonics

Episode Date: July 31, 2021

This is Inharmonics and Skin-harm-tonics! In this month's episode... How well can the human voice mimic a dinging bell? Bec teams up with a multi-vocalist Beardyman to tackle this one! What is the optimal use of sunscreen to create a tan and protect your skin? Plus: The results from Matt's sunny survey are IN and we have updates from episode 020. As always, if you've got a problem or a solution, hit us up on our website www.aproblemsquared.com, or on social media @AProblemSquared. If you want to master the mysterious art of harmonic singing, you can learn more from Anna Maria on YouTube. And a massive thank you once again to Beardyman. He is on the internet so go check him out! 

Welcome to a problem squared one of the few podcasts that has the decency to put all the words in its name in alphabetical order. My name is Matt Parker, Matt and Parker, of course, also being in alphabetical order. I am an author, mathematician, and YouTuber in that order, alphabetically. I'm joined by Beck Hill, also Beck and Hill in alphabetical order, what we do around here. Beck is first and foremost an artist, alphabetically speaking, also a comedian, performer, and writer. So I had to give you writer Not author because I already used the A For artist

And you write more than just books Exactly It just wouldn't have worked It's actually the reason that I went with Beck Instead of Rebecca Just to re-alphabetize your name My mum's a librarian so Figures. My brother's in Dewey

Decimal order When you said Dewey Decimal Law. When you said Dewey Decimal System, my brain went 526. Which? So I feel like that's probably the Dewey Decimal for science. Natural science and mathematics, 500s. And 526, mathematical geography. Is that from your topography?

I don't know. This would be from actual maths is 510. I don't know why my brain gave me 526. But it's in the sciences. Is 666 about the devil? I'd find that very funny if it was. They've missed a trick if they haven't done that. Ceramic and allied technologies. i've always said that they

are the devil of materials world dewey got his heart broken by a ceramicist and that was that was their revenge introduction to dewey decimal numbers if you'd like to know what dewey decimal systems are look it up we're not going to do it come Look them up. Look them up yourself. Look them up. Yeah. On this episode. Is it possible for a human to actually make a ding sound like a bell? I'll help someone optimize their usage of sunscreen. And we've got some messages from people regarding stuff from last episode. So many messages. There's not so many messages.

There's only two, Matt. You're really making it sound boring. That's two. Some messages. All right. Let's get going so miss hill how how has your month of july been going good busy we finished filming make-away take-away so that's gone into editing now very exciting yeah so still doing like the adr which is like the little voice pickups and stuff like that. But yeah, it's looking good. Super exciting. The clock is ticking, counting down for the time during which you're not a massive TV star.

CITV's finest. Soon you'll be too big for this podcast. So filming the last day was so wonderful. And I won't go into too much because I don't want to give away what we did in the episode. But there will be some bigger art oh craft spoilers yeah yeah there'll be there'll be bigger makes at the end of each episode which is very

exciting and so the last thing we shot was one of these big things and it involved basically a neighborhood and all the neighbors knew each other it was all these families or friends and stuff and it was like really nice there's such a good vibe there and when we had lunch all the crew it was such a nice day that we decided to all sit on the grass outside the houses

and some of the kids from one of the homes came around and they had a little notebook and pen and they took everyone's tea and coffee orders and then they went made tea and coffee for all the crew like a little unlicensed cafe oh it was so cute it was really sweet because quite often in tv you know everything's faked like you would sort of oh yeah get people to pretend that they're happy friendly friendly neighbors that like each other. But they all got on really well. And everyone was so patient because filming is quite lengthy. And it's going to look incredible. But I just, I had an absolute ball.

Really nice time. And yeah, lovely, lovely time. What a lovely end. I'll remember. Remember that when you're a massive diva TV star in the future. Where's my trailer? Exactly. Where's my child waiter? Slapping the notebook out of the kid's

hands. I don't want your... I get my tea specially brought in. I don't know what they're called. Make it happen. I don't know what that is, man. I make the name up. You make that tea happen. Love it.

Yeah. Can't wait till those days. Me too. How's your month been? Oh, good. As you know, I came off my bicycle. You did? Yes.

While moving at a decent speed. Been off the bike now for a good couple of weeks, but I'm healing reasonably well. For the most part, you know what? I've come off my bike twice and both times I had a pannier full of luggage on the back. A pannier is those bike bags, isn't it? Oh no, it's like a toasted sandwich. Or not the Indian cheese. Not the Indian cheese. No, no, no. Yeah. So I had my pannier panini on the back and I brought up my accident when I had some mass people down for some socially distanced outdoor drinks. Like a bunch of us who normally work together doing live shows obviously haven't now for over a year. We all got together outside and I mentioned my accidents. It was no, oh, are you all right?

It's, oh yeah, because your center of mass will be slightly off. So one person's theory, Hugh Hunt, if people watch the videos I've done with Hugh, was like, oh yeah, because you always have it on the same side, you'll be cycling slightly off to the side, which means you will have worn that tread down more than the other side. And both times I was turning right. So turning away from where the mass is. And then the wheels have just slipped out from underneath. I'd cycled over 40 miles. I cycled into some other friends, different gathering, wanted to have a picnic in London. And I was like, I'll come in for that, but I don't want to go on public transport. There's a lot of

coronavirus here in the UK at the moment and a lot of people acting like there isn't. So I did not fancy. So you cycled from Surrey? Yeah. It's not that far. It's pretty far. Yeah. It was like under three hours to cycle in. Right. And you got to come home as well, which is almost a whole working day. Well, okay. So I booked a COVID safe hotel one day cycled in had the picnic stay in a hotel next day cycled home and i cycled the direct way which is like just over 30

miles and i thought on the way home i'd go the more fun way so i went the more long and meandering route just over 40 miles and i was just around the corner from my house i was like within a couple miles of home going around the roundabout, slipped out. Car behind me was two junior doctors. What? So they were like, great,

now we're at work all of a sudden. The cut on my knee was just deeper than I was prepared to go home and just hope for the best. Just let the dog lick it. Yeah, exactly. Yeah. That antiseptic licks.

That's what dogs famously lick things that heal. And so I went to A&E and annoyingly in the accident, I landed on my phone. And so I destroyed my phone. And so I had three and a half hours in the waiting room with no phone or any other way to pass the time while waiting for some poor overworked doctor to glue my knee back together so oh it's so boring i know i'm just laughing at how it's it's like it's a problem that that is such a privilege yeah yeah i had to wait there for my free health care with an injury that's easily going to heal.

And I was a bit bored. Without your tiny pocket-sized computer that you can normally have. Without access to all of humankind's knowledge in case I get bored. FML, Matt. I know. FML. How do I survive? I was going to ask them for some paper so I could do some maths.

And I thought, you know what? I'll just do the maths in my head because i want to go like these are over works in an emergency in a hospital and i'm like um can i have some paper and can i just say that as yeah you're such a living stereotype like i would try and defend you if someone was like, Matt Parker, is he a massive geek? But I could look like if they were using it as an insult. But even then, I wouldn't be able to defend you because only you could fall off a bike, talk to another bunch of mathematicians about physically why the accident occurred.

Like most of the time, people are like, I don't know what happened. And they leave it at that. And then when you're left without a phone, you're like, I know what will pass time. Maths. Yeah. While I wasn't busy doing maths in my head and working out that the waiting music in the A&E at the hospital loops every 21 minutes unless they have an interrupt announcement. Because again, I couldn't write this down or put it on my phone.

I had to mentally keep track of what songs I'm hearing when. And it's all like royalty-free music. I didn't have enough data to know for certainty the rules around when the music repeats. And I don't think they'll let you just sit around after you've been seen to by the doctor. Because you need to get more data. If anyone works in A&E and can tell me that would be great closure if you told them that that's what you were doing they would take you in for more tests they're like how hard did you fall off the bike you said you weren't feeling nauseous or it didn't have a headache but i think you've

i gotta buy to buy a new helmet because once you've had an accident in a bike helmet, you meant to buy a new one. Because you will have, the other one's done its job. It absorbed the impact, but now it's busted. So very happy to buy a new one. What can we do with a leftover bike helmet? Still got it. Hold on to it. And if any listeners can think of what we could do with Matt's leftover helmet.

I mean, deal. I like an arts and crafts thing. I've still got it. Send it to us, a problem posing page. That's at problemsquared.com. And I guess select. I think it's a solution. Solution?

Yeah. But anyway, the final punchline to all of this, I was under instructions to not bend my knee because it had been glued back together and you've got to wait a certain amount of time before you bend it too much. Otherwise, the glue stitches come out posing exactly uh so i had to go up the stairs to go to bed and i was like oh i've got to go up the stairs very carefully and not bend my knee uh

turns out i'm more uncoordinated than i thought because on the way to bed trying to not bend my knee after my bike accident i slipped on the stairs and broke a toe on my other foot no yeah so for the past several weeks now my knee is pretty much healed and all my other grazes are healed but i'm still hobbling because on my other foot the other leg i broke the longest toe and did you have to go back to hospital for it were you like i need more data they're gonna be like wait a minute you could have brought a laptop with a spreadsheet this time to jot down but it turns out the advice is just tape it to the one next to it there's not much we can do so there you are and ever since

then whenever i'm doing something ridiculous and lucy's like you shouldn't be doing that with a tape it to the one next to it. There's not much we can do. So there you are. And ever since then, whenever I'm doing something ridiculous and Lucy's like, you shouldn't be doing that with a broken toe. She's like, if you get a tertiary injury, she will be out of sympathy at that point. Yeah. I don't know what the moral of this story is. I mean, the NHS needs more funding

to get more royalty-free music in the A&E. Because 21 minutes is not enough if people are waiting three hours. Our first problem was sent in via the problem posing page at problemsquared.com by one of our Patreon supporters, although they left the name bit blank. So I'm going to respect that as they didn't want to have their name. But if that was an oversight, get in touch. Person, you know who you are and we can add your name retrospectively in a future episode.

You don't know it's a person. What if a cat is our Patreon? That's a good point. Or algorithm. Whatever the conscious being or very good simulation of a conscious being is, I will happily name or version check them in a future episode. And actually, given the question, it could be a robot, they've said, have you ever felt like your dings were missing something? And just for everyone, whenever we solve a problem, Beck says the word ding a bit like this. Ding! There you go. However, this unnamed entity then says, what's the closest that the human vocal apparatus can get

to mimicking the ding of an actual bell? You know, the more I read this, the more it does sound like a robot trying to learn how to act more human. What is the closest just hypothetically with those human vocal apparatuses that we all have like how close to accurate should i get and still be believable so anyway um but they support us on patreon so hey welcome aboard or it's a problem sent in by a bell that wants to know if it can pass itself off as a human. Exactly. And I've always imagined, if I'm being honest, you know, like the hemispherical ones, like on a counter at a hotel?

Like you get in a hotel lobby? Yeah. That's the ding I imagine. So the question is, what's the closest the vocal cords can get to that back? Okay. Well, first of all, I thought this might be relatively easy. Like I was like, cool. I'll just Google person mimics bell.

Right. Every problem, every problem out of the gate. You're like every problem I think is easy. At last that easy one. This is it. Yeah. So of course I couldn't find human mimics bell. I looked everywhere.

I watched a lot of impressionist videos to see if they happened to do the sound effect mimics bell. I looked everywhere. I watched a lot of impressionist videos to see if they happened to do the sound effect of a bell. I did not have the patience to go through Michael Winslow's complete back catalogue. Quite the back catalogue. I asked several people for help. I asked professors and then I asked our guest who I'll introduce us to soon. Exciting. But when I was speaking to them, I started to realize that I lacked the knowledge necessary

to understand the answer. You know how in Hitchhiker's Guide, they have the answer, but then they actually don't know what the question is? Yep. The meta problem of understanding the answer to the problem. Yeah. So I was like, okay, there's a lot of terms and stuff being mentioned that I don't understand. So let's work out what sound is.

And I spent, I got really into this, Matt. Oh, I know. It's been a long time since I've properly learned stuff and I really enjoyed this. And then I had the problem of trying to communicate what I'd learned. So I have come up with this analogy. Gotcha. And, uh, we'll, we'll see, we'll see if it works. I'm going to step right back.

And I knew you were getting into this because you'd occasionally want to give, you were so excited. You wanted to give me an update, but you had to be so vague because you didn't want to ruin explaining it to me on the podcast. So I've never had such a vague phone calls with you in my life. So I'm very excited. So imagine that you're on your roof. Got it.

And you're going to drop a ball from the roof and see how many times it bounces. Gotcha. And I'm on the other side of the street. Okay. Yep. And you drop a bouncy ball, you know, one of those Super Bowls. Yep.

And it bounces loads, heaps of times. I'm on a two-story house, so there's going to be a lot of bouncing. My drive is on a slope, so... Yeah, I knew you were going to do this. Let me get my analogy across, Matt. Sorry, carry on. You don't have time for your realistic,

confusing driveway tangents. Well, it's such a novel, game-changing analogy. I don't know what aspects are important and what aren't. So I'm trying to give all of it. You'll know when you let me say them. Oh. Oh, good point. Good point. So you drop it.

It's a flat surface. It bounces on completely flat and you're dropping it. It bounces loads of times and you're like, whoa, Beck, did you see that? And I'm like, no, that ball is too small. I don't know what you just did. And you're like, ah, okay, let's try a tennis ball. So then you drop a tennis ball from the same height. Yep. And it bounces not as tennis ball from the same height. Yep.

And it bounces not as many times as the Super Bowl did, as the bouncy ball, but it bounces. It bounces. And I'm like, oh, I think I can see it. Yeah, I can see that. And you're like, oh, we need to make this clearer. All right, I'm going to use a basketball. Gotcha. And then you drop the basketball at the same height.

And again, it doesn't bounce as many times, but I can see it very, very clearly. Got it. That is how pitch and volume work. Okay. Okay. So the amount of times the ball bounces, that represents the frequency. amount of times the ball bounces, that represents the frequency. And for the purposes of this, frequency, pitch and note, when I use those terms, they all mean the same thing.

I'm on board with that. If you get into the nitty gritty of music, there's differences, but for the sake of this, frequency, pitch, notes, same thing. So the more frequently the ball bounces, that would be a higher pitch. So the amount of times it bounces, more frequent, higher pitch. And that's how sounds are created, how frequency is created, because it's how much something vibrates. So if something vibrates very quickly, get a lot of vibrations, high pitch. If it vibrates not as quickly, it's a low pitch.

But of course, the bigger it is, the more energy it would take to get it to bounce as many times oh okay yeah it uses more energy so like i can see the basketball it's bigger but it bounces less it's why deeper sounds can be heard further away than higher sounds okay yeah yeah yeah yeah yeah yeah the bigger the ball the louder the volume. The little bowl, the lower the volume. Got it. That is sound and volume. We've got that. Next, we're going to talk about partials.

Partials? Partials. So. That's new. Basically, everything except, I believe, for a sine wave, which is like an electronic frequency, or a, you pulled a face there, Matt. I mean, I saw the words. It's an electronic thing, an electronic sound.

You're 100% right. You're 100% right that as a mathematician, I think of it as the theoretical sine wave first and foremost, whereas you're right. Like if you actually want to hear one, you'd have to generate it electronically. So, I mean, my problem, not yours. You're doing a great job.

Okay. Or a tuning fork. Basically, everything except for those two things creates multiple frequencies when it's making a sound. Even a tuning fork, depending on the environment. Yeah. Yeah, exactly. Yeah.

Yeah. Even a tuning fork, depending on the environment. Yeah, exactly. Yeah, yeah. So to get back to the ball analogy, if you were dropping your ball from the top, you'd actually have to drop quite a lot of different sized balls. Gotcha. Yep. The bigger the ball, the more clear it is for me to see.

That's the one my eyes are naturally going to focus in on. Gotcha. So just if I may say back to you, what I think you just said, I come up on the roof, I've got a big sack of balls and I dump out that sack of balls and there's balls of different sizes and they all fall, they all bounce, they've all got different frequencies. And for the analogy, let's say that they're all at the exact same height, they're all neatly, you know, in a neat row. You're not worrying about any of the other physics.

Exactly. There's no air. And you're across the street and you probably know, because you've seen the size of the sack of balls, that there's a lot going on, but you can only really see the big dominant ones. If your basketball is the biggest ball of all the balls that you've got i'm gonna you're probably gonna focus on that one how you know i'm serious about

this because i haven't made one joke about your balls yet i i introduced a sack just to bait you even further but carry on and one of your balls is bigger than the others you got multiple balls what's unusual about that on. Let's say the basketball is the biggest one you've got. That's the easiest to follow one. Yeah. To put that back into sound, if you heard a note being played, even though there's a lot of different frequencies, partials, a lot of different partials, frequencies that are happening at the same time, you're going to think you're hearing the

loudest lowest part of that note even though there's actually higher notes happening at the exact same time do you know what i love about your analogy you've you've come up with an analogy to explain like the frequencies and and that kind of side but yet you've kept in the human perception angle obviously super important so you looking from across the road you've still in the human perception angle. Obviously super important. So you looking from across the road, you've still got the brain processing and ignoring and paying attention to things. I don't even know why we bothered getting an expert guest. I feel like you've nailed it. I mean, no bells yet.

I mean, we haven't answered the problem yet. Yeah. So the loudest, deepest note't answered the problem yet. Yeah. So the loudest, deepest note, it's generally the loudest. Sometimes it's not, but we'll go into that later. The loudest part is called the fundamental. That's the note that you perceive. That's what you hear. So your basketball is the fundamental partial.

Gotcha. So that's the one I really wanted to drop from the roof, but a bunch of smaller ones. Yeah. Gotcha. Yeah. And all the other balls, because there's a lot of wanted to drop from the roof, but a bunch of smaller ones. Yeah. Yeah. And all the other balls, because there's a lot of balls that aren't the fundamental, they're called overtones. So now we know about partials and how they work. So let's talk about harmonics.

Okay. You can see my sass drops a lot once you're getting onto musical terms, because I got no idea what you're going to, but now I'm out of my depth. So harmonics are when every ball after your fundamental is in ratio to each other. So for instance, you've got your basketball, but then the next ball is half as small as that,

bounces twice as many times. And the next ball is half as small as that one and bounces four times that. Yep, yep, yep, yep, yep. And the next one, next one, right? Again, I'm just, I'm instantly like, I wonder how bounce speed scales with size of ball. Does Beck mean half by volume or by diameter? And none of these matter. These are all irrelevant.

Don't matter. Don't matter. I got it. Harmonics are just where, instead of having a random collection of ball sizes, they're all in a nice relationship to each other. So you're getting multiples of the frequencies. Yeah. You basically said it yourself just then,

when they're not in relation to the same ratio to the fundamental, that's called inharmonics. Got it. And that's why something like a cough is much harder to understand what note that is because a cough is made up of lots and lots of inharmonics. It's a mess. So inharmonics, like you can vaguely make out what note it is, but it's much more difficult than when you're hearing harmonics because they're all in relation to each other. So we've explained sound. We've got all that. Finally, before I bring on our guest, I'm very excited.

This is a tangent I went on, but I really want to talk about it. You've got your fundamental and then you've got your overtones. So overtones singing is a thing. Oh, yeah, yeah. You're singing more than one note at once. Different types around the world. So I'm going to try and do it. I'll try. I've been practicing a lot and it's not particularly good, but I'm going to try and give an example.

I apologize because there might be a couple of goes at this until we hear it. What you're listening for is you'll hear me doing a low voice, like a low sort of sound. And then you'll start to hear quite a high note, like a whistle. like a whistle and that's because I'm trying to use my vocal apparatus to hone in on one of the partials to give it almost an equal amount of volume as the as the low note so I'm going to try it okay hang on I mean, Beck, of all the practical, life-changing skills you've learned over the years, that's got to be up. And what you're doing, you're inflating the tennis ball. You've got the basketball doing its business, and you're picking another ball,

and you're focusing in on upping its volume. That's right. Yeah, exactly. Exactly. And in fact, because I wanted to know how it would sound if like an actual professional singer did it. So I tracked down Ana Maria Jalefe. Okay. I hope I'm pronouncing it right.

Hello. Back here. Just jumping in quickly to say it's pronounced Hefala. Hefala. Apologies, Ana Maria. Every time anyone hears me mispronounce it, remember it's pronounced Heffler. Heffler. Apologies, Anna Maria. Every time anyone hears me mispronounce it, remember it's actually Heffler. We will be putting the correct spelling of her surname in the show notes. She's given me permission to play this little clip on the podcast so everyone

can hear what you can actually do. Now, remember, this is all coming from one person. She's singing with her one voice. Yep. And all the sounds you hear it's just her so producer luring can you play the clip please That sounds like someone whistling over someone else singing. Right? Yeah. It's just one person. Blows my mind. So I know that that isn't necessary in order to

solve the problem, but I thought it was a really fun tangent that people might enjoy. But nevertheless, I digress. Let us get onto this problem. So to help answer the question, I enlisted the help of beatboxer, rapper, comedian, musician extraordinaire, It's Beardy Man. Hello. Oh, hello. I am none of those things, but it's lovely of you to say. I've sometimes pretended to be a rapper for a joke, and I think some people didn't realize I was joking. I used to be a beatboxer, and now I'm just a very tired dad I think just a very tired man who is afraid of going outside mostly that's what I am but thanks for thinking of me oh well you know I really appreciate we had a good chat and it was when we were talking that I was like I need to find out how sound works

I asked you on Twitter whether it was possible to make a bell sound and you had a go at it. I don't know if you want to do that now or whether you would like to... No, I want you to do it because I taught you how, remember? You did, but I don't think I did it. Beg for me the other day. Come on. Alright. Okay, beg for me.

She was like, is it possible to do a bell? I was like, what do you mean, like this? And she was like, how did you do that? And I was like, okay okay you just sort of whistle and say but at the beginning it's not a good impression of a bell but it's like the closest i have ever been able to have it again it's far from perfect because you can still hear like the hiss on it because it's a whistle so it's shit but you know what if i if we played that every time we solved something if we played that sound, people will go,

oh, that's the sound effect of a bell. They're not going to be like, oh, that's a person. No, it's close enough to a bell that you'd be like, I think that's supposed to be a bell. I can see Matt on his video. He's trying to work out whether he can do it. No, no, no. I was just like, what makes it bell-like?

And I think it's like the decay. I'm not using that phrase word correctly, but the way it- No, that's the correct phrase. Oh, okay. Oh, amazing. So yeah, the way it sounds- The decay stage of the envelope. You just got to get, and also like making it a kind of a sine wavy in terms of its timbre as possible, but I can't seem to get rid of like the white noise. I'm going noise translate for beardy man timbre uh correct me if i'm wrong is the mathematical formula of the difference between

all of your partials yeah that decides the timbre of the note so yes and the timbre is what tells you whether something sounds different to something else so if the balls are all in relation to each other because it's like twice and twice and twice and twice and twice, that'll create very specific sound. But if every ball was a third smaller, a third of the smaller, a third going on, your sound will be different, have a different timbre, and it might be because it's from a different instrument.

Well, it's interesting you're talking about partials. So in a resonating cavity like human vocal tract, it is trivial to produce partials. So like in a resonating cavity like human vocal tract, it is trivial to produce partials which are, they have like an integer multiple relationship to the fundamental. Because that's how resonating cavities tend to produce like amplified resonations. However, in a metallic surface like that of a bell or any kind of metal sheet or anything like that, it's just vibrating and it has multiple different vibration nodes which will kind of cross-modulate with each other so you get what's called inharmonicities, which if you hear a bell… Can you see why I had to look up how sound works?

Yeah. I mean, Matt will probably know what I'm talking about because you get these kind of vibration modes in a sort of metallic object which you can't reproduce with human voice, really. Yeah, so if I can say back what I think you're saying. So when you're, the human vocal apparatus is basically a gas-filled resonating chamber. And so it will select out the harmonics which are whole multiples of each other because that's just how that kind of resonating chamber works whereas if you're hitting a lump

of metal there's far less selection on what frequencies will hang around and so you end up with just a whole load of harmonics which are all all over the place. And you're not picking out the nice- In harmonics, Matt. Oh, same thing. In harmonics is just harmonics you don't like. Get that on a t-shirt. Well, from a mathematical point of view, I would just use harmonics to mean all the other frequencies that showed up. But that may not be a rigorous way to do that in any discipline. So you're saying you're getting a lot more interference and you're getting a lot more

frequencies there. There's a more complex relationship between the different sort of resonating frequencies that will be produced in a metallic object than there are between a resonating chamber. And yeah, you're exactly right. The resonating chamber selects for And they are between a resonating chamber. And yeah, you're exactly right. The resonating chamber selects for those which are in multiple relationships with each other. At the heart of it, I guess any instrument, a bell, a violin, a guitar, a trombone, you're throwing a whole bunch of frequencies at it

by hitting it or blowing into it or whatever. And it somehow, particular frequencies are amplified or retained, they're resonant, and others aren't. And so that's just a much more complex process. Because when you're hitting a bell, you're still getting a note out of it, but you're getting a much more complex collection of smaller frequencies than you would from a classic gas-in- in a pipe resonator. I think in a metallic object, there'll still be resonances which will be a result of the shape and size of the metal and the density of it and it's sort of…

Because it's like echoing inside it, right? It's like a tuning fork. Yeah, exactly. And Matt, we talked about in a previous episode, we talked about phase, phase inversion. Is that what you get? Is that what we're getting? Like when those frequencies bounce into each other? Are some of them cancelling each other out?

Some of them will be cancelling each other out and some of them will be peaking because they're adding to each other. So you're still getting a bell making sort of a few dominant frequencies and some are being cancelled out. So you get sort of resonating notes. If you've ever stood in a room in a club, let's say, and you're standing in the shower, you'll notice that a particular point points in the room

where you'll sing a particular note. Maybe only I notice this kind of stuff, but you'll be in part of the bathroom because it's a very sort of resonant chamber where you'll sing a particular note and that will resonate in a sort of bell-like manner so that it'll have like a long tail on it and if you ever stop to think about why there are different resonant nodes at different points in that room so if you put a microphone that isn't feeding back at one point of the room you can move

it a couple of feet to the left let's say and then it will suddenly feed back and feedback if you don't know is where you get a resonation So you'll have the distance between the speakers and the microphone, meaning that a particular frequency, given the speed of sound in the temperature of that room, that will give you just the tiniest little kick. It will just amplify and amplify and amplify and amplify. So it's that same kind of thing. And that's why you get that, woo, like that on the microphone when you're...

Yeah. And that's why it's called feedback, because it's literally the signal's feeding back on itself and being amplified each time. But that doesn't happen all that well at every point in the room. But where you get the distance between the mic and the speakers being kind of with a sort of integer multiple relationship to, say, the walls,

you'll find yourself in a kind of resonant node in that room, which is, it's all kind of part of the same thing we're talking about kind of resonances that are being sort of amplified or cancelled out the reason why humans can't do that as well is because metals generate these inhominicities but i've got a handy tool to help me kind of illustrate what can happen if you introduce inhominicity so there's something called a frequency shifter so i've got one here so yeah so my voice should sound sort of normal at this point.

But as I start to introduce the frequency shifter, you should have the relationship between the frequencies and the frequency. That wouldn't have sounded like a bell, but it does introduce inharmonicity so if i managed to get the the envelope which is to say sort of the transient at the start and then the kind of fall off oh hang

on at the end of the sound so we get the word envelope and transient transient what is an envelope uh if you're making a synthesizer let's say and you want someone to press a note and you want a sound to start when they press the note and then finish when they lift their hand. Pianos don't sound like that. They don't go boop with a hard start and a hard stop. They have a fairly hard start, which has particularly sonic characteristics. And then as the string that has been hit by the hammer,

as its vibrations kind of fade away and get absorbed into heat energy, you will hear this tail off as the energy in the string kind of dissipates into the surrounding air. That you would call the sort of tail off as the energy in the string kind of dissipates into the surrounding air. That you would call the sort of tail section of the envelope

or the decay. Or you could call it the release. No, so yeah, so the way that an oscillator tends to work in an electronic circuit in a synthesizer

is that it's always on. It's always making that noise and you're just gating that sound so that you can either hear it or not to a greater or lesser extent. So like with an envelope on a synthesizer you'll have like an attack phase which is you're just gating that sound so that you can either hear it or not, to a greater or lesser extent.

So with an envelope on a synthesizer, you'll have an attack phase, which is how long it takes to go from zero to one. Takeoff. Yeah, exactly. So a slow attack would be like... But a fast attack would be like... That's a massive attack. Yeah, exactly. So a bell... That's a massive attack. That's a massive attack. Yeah, exactly.

So yeah, so a bell will sort of always do that. You could cause a bell to resonate by kind of rubbing it like a wine glass around the outside, which would cause it to sort of slowly meet its resonant nodes. But like, that would be a slow attack. So anyway, that's the attack phase. And then the sustain phase is...

Cruising altitude. Cruising altitude, altitude exactly you've hit the the peak which is a sort of maximum volume you then have a decay phase where it sort of settles back down to your sort of sustained level then your release stage is when you lift the key how long does it take for the sound to be gone right so that's your little journey with an envelope it's like if you had a plane if it was a fast attack big attack whatever it was massive attack if you had that and then a quick release it would be like if the plane already started in the air flew and then just fell it's like if you like shot a glider out of a cannon that would be

the yes yeah but then the glider hits a wall. That's what it would be. Yeah. Then if you've got the decay, that would be if it was landing nicely. So let's see if I can make a bell by sort of going like that, but with some inharmonicity. So let's reintroduce this frequency shift. Those are bells. Oh my goodness.

That's amazing. So they're bell-like. They're more bell-like because you've got those in-hominesties. So the shift you're doing is not preserving the whole number ratio between the frequencies in your voice. Exactly. Because they're now, you know, irrational distances, our brains are like, oh, that sounds like someone hitting some metal. There you go.

That's it. There is a bird that can do it, and it comes from your native country. It's the lyrebirds, and it's amazing. It does lie. But it can perfectly mimic sounds that it's heard. So the lyrebird, as far as I understand it, has two throats, essentially. Well, not two throats. essentially. Well, not two throats, two resonating flaps, and they can sort of cross-modulate each other. So it's able to do weird things like ring modulation, which is where you sort of chop into

the sound with a sine wave a bit like that, which again gives you inharmonicities and stuff like that. You can hear it doing that in some of its impressions of things right so to recap everything that we've just discussed it is not possible for the human vocal apparatus to completely mimic the sound of a bell due to the way that inharmonics are created. I'm not saying it's impossible. There's probably some kid out there, some crazy beatboxer who's figured out a way. Oh, I like this.

So I'm not saying the human voice can't do wild things like that. It's just it's very hard to tune it and keep that tuning perfect so that it would sound like a bell. And you would also need to do it with a a quick attack and then it has the yeah slow release yeah so i mean the thing is if you are going to sort of force your voice to sing two notes at the same time they're going to wobble a bit because your voice isn't designed to do that and also yeah trying to get it to have like a perfect envelope isn't going to be possible well i thought it was interesting the effect you were putting on your voice before to make it sound more bell-like by messing with the frequencies also made you

sound more like a robot yes and so our original theory that the person asking this question is some kind of artificial intelligence or algorithm clearly that stands to reason it was i i asked the question. See? And sounding like a bell and sounding like a robot are in the same family that are very different to sounding like a human. Before we let you go, Beardy Man, thank you so much. This has been so helpful.

But also, I'd like to know, what is your favorite sound to do with your voice which surprises people? I've always liked this one. It's not really my voice, it's just my cheeks. But it's lots of fun. Oh, but it's a creepy sound and I love it. Yeah, it's pretty cool. There's more where that came from. Check me out on the internet. We'll link to things in places. Yeah. Excellent. Great stuff. You're just at BeadyMan, aren't you, on most socials? Yeah, this has been really fun. Thanks guys. Thank you. I hope that helped. I hope

any of this was worthwhile. Safe guys. Bye! So it sounds like the answer is that the human voice might be able to mimic a bell exactly, but we haven't found conclusive proof of this yet. Got it. So technically we have an answer. That is the answer. Oh, I mean. So I've solved it. Are we going to crack out our new and improved ding sound effect this quickly?

Well, I'm going to, I think we've solved it, but. You know what, I'm convinced. I'm, yeah. I would love to hear if anyone has been able to naturally recreate the sound of the bell using their voice. Okay. So if any listeners think that they can do it. Or find examples of people doing it.

Let us know via the problem posing page. Select the solution dropdown. Send us whatever details we need and we'll go from there. Excellent. But in the meantime meantime we've found that it can sort of mimic a bell if you do the that's pretty good or you can run your voice through a inharmonic modulator well but even if just for sheer completeness i feel and extensive research. I'm going to give you a ding for this

one. Our next problem comes from Florian via the problem posing page. And Florian says, now that the weather is getting better, I need to use sunscreen. Otherwise I get burnt, but I don't want to use too much sunscreen. Otherwise I don't get a tan at all. And I'm therefore more susceptible to sunburn. How do I optimize my usage of sunscreen? Thanks, Matt. You were going to take this one. Yeah, I'm all over it. So, I mean, we should say I'm evenly distributed on this one. We should say we're both from Australia. Yeah.

Which has a long history of encouraging people to not get sunburnt and to not tan recreationally, I guess. Yeah. Because you die. You die. It's dangerous. You get skin cancer and you're in trouble. And I remember when I first came to the UK in the late 90s, this was before I moved here, but when I first came over here for a while,

I'd meet people my own age here and it was summer and they wanted to put on some kind of sunscreen and my poor brain couldn't, they're like, oh, what's the rating? Like the SPF rating, but they wanted something not too high. They're like, oh, I don't want to have SPF 15. How am I going to tan?

And I just couldn couldn't like it was one of the more acute bits of culture shock i had it doesn't calculate the first time i came to the uk yeah i was like but what huh well the term here is healthy tan which for us is very uh like an oxymoron that's like a relaxing concussion it's, it doesn't work like that. No, it's zero. Zero is the healthy amount of tan. You know, I've actually started, I never used to wear fake tan, but I've started wearing fake tan over here because it stops me from getting comments from people over a certain generation and above saying, oh, are you all right? Because they think I look poorly or sickly. They're like saying oh are you all right because they think i look

poorly or sickly they're like oh you're very pale and it's like this is my skin like this is because i've looked after it i mean lucy had the flip side the first time she went to australia everyone's like oh you got such good skin it's just because she's had no no sun damage yeah like she's she's lived under a cloud for all of her life. And so she's fine. And you go to Australia and you forget how you get to just seeing people with skin damage because that's just the life over there. And I burn super easy.

And actually, before we get into any of this, a bunch of it does depend on genetics and different people, depending on what your skin does, burns different amounts. And different people, depending on what your skin does, burns different amounts. So I'm going to be talking consistently from a very pasty white individual who burns near immediately when exposed to sunlight, or rather when exposed to ultraviolet light, which is the bit that actually burns us. So the kind of visible spectrum, not so bad. The infrared, that's the warm, actually the warmth you feel, that's not your skin burning as such, that's the other end of the spectrum. So you've

got like the heat waves at one end, and then you've got the UV at the other end of the range of frequencies of light. And it's the high frequency ones that are dangerous. So it's a bit like, so you go out in summer and imagine there's someone nearby on a roof. Yeah. And they've got a whole bunch of balls, right? But when they throw the beach ball at you, you're like, that's fine, right? And all the big balls just bounce off

and you're like, this is just good summer fun. But it's the little bouncy balls. They're the ones that really hurt. Yeah. And for a long time, we thought it was just, past our little bouncy balls. They're the ones that really hurt. Yeah. And for a long time, we thought it was just, actually, the super small- That's because they hit you more fast. They hit you more fast, more energy. And actually, for a long time, we thought it was only the tiny,

tiny ones that were an issue. Actually, the super small ones don't even make it to you. They're so small that the air slows them down. They don't even get to you, which is the equivalent of the atmosphere and ozone stop the very high frequency ultraviolet, which is known as UVC from even making it to the surface of the earth. So the incredibly dangerous radiation from the sun doesn't even make it. Thank you, ozone. Then UVB, that's like the highest frequency that makes it through. And most of it gets stopped, but a bit of it still makes it all the way down.

And that's what sunscreens mainly stop from getting into your body. You've also got UVA, which is the bulk of the uv radiation which for a long time people were less worried about but it turns out while uvb is what causes cancers uva can indirectly cause cancers like it still messes um with your cells and bits and pieces but it's more it does things that then have knock-on effects that cause you to have an increased risk of cancer whereas uvb just goes straight into the DNA and is like, I'm just messing up the joint. So sunscreen is an attempt to stop that from happening.

And I did a quick look into the chemistry and you can either block it or you can absorb it. And I didn't realize, and we'll go into this and more details in a moment, there's a technical difference between a sun block and a sunscreen. So the block is using things like zinc oxide.

Zinc sticks you put on your nose. Yeah. I don't want to get burnt specifically here and here at my school sports day. That's how zinc works. And then when I said here and here, was just indicating two little stripes going kind of going or just one line down my nose that's yeah zinc your other option is to use something that will absorb chemically absorb the uv frequencies and so now there are so many different substances that do this i looked up a bunch you get like your oxybenzone, you get your homosalate, you get your oxalmethoxinamate.

And they're all just organic molecules, but because of the bonds, different frequency photons will be absorbed by the molecule and heated up. And so some of them will block UVB, some will block UVA, some will block both, depends what atomic bonds they've got going on. And some of them will block UVB, some will block UVA, some will block both. Depends what atomic bonds they've got going on. And some of them break down. Like when they absorb photons, they break down, which is why you've got to reapply a lot of sunscreens. It's not just that you're sweating and it's coming off.

So when you say block just before, sorry, when you're saying block, you actually mean absorb. Absorb. Sorry. Yes. Not absorb. Yes. Right.

when you're saying block you actually mean absorb absorb sorry yes no absorb yes you're right and that actually brings me to what people call the thing that you put on your body to stop the sun from damaging you because and this is why we did a call out last episode for people who've heard the previous episode zero two zero because i had a thesis that the more sun a country has, the more negative the name of the thing you put on to block the sun. I first started thinking this when I realized when I moved to the UK, I would still call it sunscreen because it's screening you from the sun. But a lot of other people would call it suntan lotion. And it got that kind of positive you put this on because you want to go out and get a tan which i think historically and this is why we asked you to put their age in as well

historically you would have put on a tanning cream like an oil yes like an oil so i spoke so a friend of mine they remember their parents, and so this is only going back a couple of decades, like factor two tanning oil. And when you say factor, because we've talked about SPF, is factor the same? Factor, you'll see it sold two different ways. Some people will say it's the fraction of UV light that makes it through. And some people will say it's how much longer you can stay in the sun. And it turns out both are technically true in so much as let's say factor 30, it's a perfectly reasonable way to understand factor 30 as it lets one 30th of the light through the actual burning light compared to not having any on at all.

Or factor 50 would let through a fiftieth. Factor 2 would let through half. And that does then mean if you're wearing factor 30, technically you can be in the sun 30 times as long before you'll be as burnt as one thirtth at the time with nothing on no no protection yeah so if you went out for 30 minutes it'd be the same as standing in the sun for one minute exactly now yeah yeah the issue here is blocking it is not like a super simple process it depends how it's put on the skin how it's distributed very much it includes how often you reapply. And so in terms of compliance, like the SPF is like the best case. If you put it on properly and you reapply it frequently

and you don't sweat or go swimming or any of these things, then that's your optimal protection, but it's never going to be quite that good. Can you get that with blocks or the absorbing types? Yeah, both. it's the same well this is where it gets interesting because the actual score i thought it would have been like some property of whatever the substances were or it would have been some lab test on the sunscreen but it's not the way they calculate the spf rating for a sunscreen is to get someone with pasty skin to come into the lab and then they sunburn them. So they put on the sunscreen in like little regulation sized patches. They have different intensity amounts of UV light. They see how long it takes to burn this poor

volunteer through the sunscreen compared to the same intensity light burning them without any sunscreen. And that's where the SPF value comes from. And there are, depending on the country, there's different maximums. So I'm pretty sure most places, 50 is the most you're allowed to put on sunscreen because above that, it's getting ridiculous. And it gives people a false sense of security. Like you'd slather on SPF 100 or something and then be super nonchalant. And there's a whole other world of people exposing themselves to

more risk because they've taken safety precautions such that it undoes all the good provided by the safety precautions, which is a very interesting aspect of human psychology and safety. Oh, and sunscreen is just adjacent to conspiracy theory, big pharma, scare. It's not a vaccine, but there's still people online going, ah, but what about the nanoparticles? And actually, there's a big debate on the Wikipedia discussion page about should the Wikipedia page say, no, putting on sunscreen won't introduce nanoparticles into your cells, or should it remain silent on the topic and all these things? So researching it was not quite as straightforward as I thought, because it's just in that kind of people making things up online and scare stories.

So the SPF or factor, or it's all the same measurement, it is technically how much longer you can stay in the same amount of UVv radiation to get the same burn compared to if you didn't have any sunscreen on you at all and that's just because that's how it's tested and that's where the number comes from but you could also understand it as that's the fraction of light it's letting through gotcha and so thank you very much to everyone who from the previous podcast went through and told us what they call sunscreen or sunblock in the country they're in. I went through all the data and I tried to tidy it up as always and I had to decide what counts as a positive, a sun positive name versus what counts as a sun negative name. And what I totally had missed

is actually in the UK, it's almost overwhelmingly called sun cream. In fact, most of Europe, it's either sun cream or variations on that, obviously in whatever the local language may be. I think some German people were like, it's probably, it's like sun milk. And I did Australia, the UK and the USA separately. And then I just did an overall, all countries. Yep. Does US mainly call it sunscreen? Yep. Correct. Because, I mean, it's not because of that song, but that song where sunscreen was such a big thing. Oh yeah. In the 90s. And I feel like there was a generation

of kids who heard that in other countries and went oh it's called sunscreen the Australian one I just be like where sunblock yeah block and also the USA have a few blocks too sunblock and then yeah the difference between sunblock and sunscreen I'm guessing is it's like the difference between having a bin lid and they all bounced off of the bin lid like a shield yep yep yep but sunscreen would be like if i held up a mattress and the balls just flooded into the mattress a velcro one of like a velcro balls and they yeah they stick to the protective layer versus swatting them away. Now, we'll do my first thesis about countries with more sun,

have a more sun-negative name for their sun lotion names. So if you assume that cream counts as a positive name, then the UK is like 92% of people replying gave a sun positive name. However, that feels a little bit unfair because it's such a generic name and I think people would understand it to mean it's a protective thing you're putting on. Yeah, because you put on an antiseptic cream. Yeah. That's to help things.

You're right. It's more medicinal than sun embracing. So I switched the word cream into the negative column as well. And so in Australia, it was overwhelmingly negative, like over 95% negative. Likewise, in America, it was only 6% positive responses. It was three from 49. In the UK, however, it was 21% positive. It was 13 from the 62 responses. And that's getting rid of cream. That's taking cream out. That's just counting things like suntan lotion as being positive.

Still one in five people were using a positive name. There wasn't as big a skew by age as I expected. The average age, and this is worldwide now, of someone using a negative name about the sun was about 29, 28.8 years old. And the average age of someone embracing the sun with the name of their lotion was about 32, so 31.7. So there's only a couple of years in it. And the median ages where sun negative was median age 28, sun positive was a median age of 30. And I plotted them and there are, they're just way more positives to be honest. So I don't think this is necessarily statistically significant. There's an ever so slight bias.

The older you are, the more likely you are to use a sun positive name for the substance you put on your skin when you go out in the sun. Yeah. I feel like all you've solved so far is potentially where Florian comes from and how old they are. Exactly. So they're very likely to be from Europe and they're ever so slightly more likely to be younger than older, but not much.

Also, we're going by people who listen to this podcast. Oh. These are not conclusive. Let's not. Like what we're saying. podcast oh these are not conclusive let's not like what we're saying let's not start pulling the thread on survey design and you know uh integrity of my data it's a mess no no no no no i will not be releasing my data for further review or analysis because it's just a finger in the air so that's i guess is i guess our problem is from Europe. And their actual wording was they don't want to not get a tan at all

because they're therefore more susceptible to sunburn. And this I thought was very interesting. So I looked it up and it seems having a tan compared to not having a tan is somewhere in the region of SPF 2 to 4 ballpark. So having a tan does provide some protection against being burnt. Is that to do with melanin then? Yeah. So having a tan.

So if you're born with pasty skin, and to be fair, a lot of people who responded to the survey are obviously not Caucasian saying things like, I'm fine. I know what you're talking about. So this is for skin that comes with no built-in protection. If you then tan it, you're going to get some protection against burning. And I've got two kind of non professional observations here. And one is, I think it's a dangerous game to play to have your tan and then be putting on less sunscreen because of it. I think that's a false sense of safety and you're going to end up with more damage. On top of, I don't think, and again, dermatologists might want to come in with a more nuanced view, no UV exposure is safe exposure.

If you're exposing yourself to UV radiation, you UV exposure is safe exposure. If you're exposing yourself to UV radiation, you're risking damage to your DNA, you're risking all these things. And so the safest option is just wear sunscreen, reapply it regularly, and minimize the damage to your cells and DNA, and don't get sunburned. Unless you're part of a study into the SPF rating of sunscreens, in which case we thank you for your service. Have you got any good fake tan advice? Genuinely, I use, this isn't a paid ad or anything. It's not sponsorship, but I use a brand called Tanologist.

They do a foam version, which means that it doesn't really streak. Yeah. I'd recommend a fake tan foam quite quite good if you're the sort of person like me who doesn't know much about fake tan there you go good advice so going back to florian's problem yep they want to know how to optimize the usage of sunscreen because they think it has something to do with tan but you've already said tan is bad as bad so how should they optimize their usage of sunscreen because they think it has something to do with tan, but you've already said tan is bad. Tan's bad.

So how should they optimize their use of sunscreen? By using sunscreen. Unless you're at risk of drowning in it, I don't think there's an upper limit. And there's no nanoparticles or anything like this. You just use sunscreen. That's how you optimize it. Put it on.

I think there's one thing you haven't said, Matt. And that is if you want to optimize in terms of uh get the most use out of your sunscreen so that you're not using as much but still staying safe that is uh don't go outside stay indoors stay under a shelter get a uv top long sleeve stuff the the slip of the slip slopslop-slap. Yeah, that's right. Ding. All right, Beck, it's time to take care of any other AOB business we have lying around. And up first, we have closure already on a problem

from last month's episode, episode 020. We had the problem about the funniest way to fall down without hurting yourself. Andrew has sent us a tweet saying that with their dislike of sport, they guess their life is now wearing a Michelin man suit while dressed in full ceremonial Lord Mayor's outfit while kicking puppies on a bouncy castle. There's a lot of references, which will make no sense at all if people haven't listened to the previous episode. However, they said the pain is the same.

They laughed. They've decided it was funny. So they say ding, all caps, ding. Yay. Good job. Thank you, Andrew. Glad I could help. And we have some more, any AOB from Neil, who is responding to a problem that we had

again in 020, this time in regards to whether it would be possible to fix global warming if we were to dilute the atmosphere. Great, great suggestion. Using nitrogen. And Neil says, hi, Matt and Bec, I'm a scuba diver instructor with London Clydive. I think I've pronounced that right. Clydive? C-L-I-'m a scuba diver instructor with London Clydive. I think I've pronounced that right. Clydive? C-L-I-D-I-V-E.

Clydive. Oxygen becomes toxic at a partial pressure of 1.4 bar. So to dive to 60 meters, 7 bar, you need to reduce the oxygen content below the normal 21%. Nitrogen becomes narcotic at a partial pressure of around 3 bar. So below 30 meters, 4 bar, you can reduce the nitrogen percentage to retain a clear head. You can fix this contradiction by adding helium, which is non-toxic and less narcotic, to form a gas called trimix, which I think we mentioned on the podcast.

Saturation divers who live for months at high pressure sound squeaky not because of the helium, but because the speed of sound is higher in denser air. They also suffer from bone necrosis, so this is something to watch out for in your high-pressure utopia. Oh, right. Okay, I'm going to forgive them because the information is so useful for using bar as a measure of pressure.

And the distances they're talking about is underwater, as opposed to, I was looking at the depth of the atmosphere, but we would definitely need pressures way above those to dilute the atmosphere to a point where we can solve global warming. So we would definitely have to dilute it solely with helium. And it's good to know, actually, not just our voices would be squeaky. All noises would be higher pitched because the balls are just closer together. I think that's how that works. And so, but this bone necrosis doesn't sound good. I think they're saying it's not going to work.

No. Yeah. That's a shame. We're not going to work. No. Yeah. That's a shame. We're so close to solving climate change. Not solved. You can't solve climate change by diluting the atmosphere. If you want to keep your bones. I'm going to give you the other half of the ding then, Matt.

Thank you. Full ding. Thank you so much for listening to episode 021 of A Problem Squared. Huge thanks, as always, to all our Patreon supporters who are the sole reason we keep making these episodes. You are all incredible. The bonus episode will be up there. That's not true.

It is. They're not the sole reason. They're number one on the very short list. They're the sole reason why we can. Okay, good point. Okay, right. Okay, right. Okay, fine. It depends on your definition of it.

Thank you for being one of the sole reason why we can do it and a significant reason why we do it. Is that acceptable? Yeah, that's nice. Good, good, good. Yeah, I'll take it. So, yeah, listeners, I guess, again, thanks for listening. A huge thanks to our guest, Darren Foreman,

who's often known as Beardy Man. If you want to look them up online, we will link to them in the show notes. And they're also sometimes known as Jay Foreman's brother. Those of you who watch Jay's YouTube videos, I suspect we have a non-zero number of you listening in. And thank you to Anna Maria Helefe for letting us use the clip from her overtone singing. Again, we'll pop links to more of her singing

or watching more of her stuff in the show notes and on social media. Don't forget, at A Problem Squared on Instagram and Twitter. All the socials. So I've been Matt Parker.

Of course, we've had Beck Hill and our producer slash editor slash everything else is Lauren Armstrong Carter. Bye. Bye. Bye. Oh, actually, Bec, one last thing. We had a free text box on the, what do you call the sun

thing you put on your skin survey. Oh, yeah. And a 34-year-old Italian just put in the box, Bec, is this your card? So I the box, Beck, is this your card? So I guess, Beck, is this your card? That is holding up a card and it is

not my card. Move that one to the bottom. Oh, he's got a system now. I got a system.