A Problem Squared - 088 = Tired Tires and Curvy Cubes

Episode Date: July 1, 2024

🚘 What happens when tires get tired? 🧊 What is the equation for the curve on a spinning Ruibik’s cube? 📜 And there’s some pin related AOB! Find out more about the counting crows here: https://www.science.org/doi/10.1126/science.adl0984 You can hear Bec on Ali Plumb’s podcast ‘Screen Time’ here: https://www.bbc.co.uk/programmes/p02r4zfx/episodes/downloads If you want to learn more about the EMF Festival, follow this link: https://www.emfcamp.org/ To read ‘Where the tire meets the road: Emerging environmental impacts of tire wear particles and their chemical cocktails’, go here: https://doi.org/10.1016/j.scitotenv.2024.171153 For more information on the cones, ruled surfaces, hyperbolic paraboloids and more, have a look at the links below! https://mathworld.wolfram.com/Hyperboloid.html https://mathworld.wolfram.com/RuledSurface.html https://mathworld.wolfram.com/HyperbolicParaboloid.html You can see some nice hyperboloid structures here: https://en.wikipedia.org/wiki/Hyperboloid#Hyperboloid_structures As always, send your problems and solutions to our website: www.aproblemsquared.com. And, if you want more from A Problem Squared, you can also find us on Twitter, Instagram, Discord and on Patreon.

Hello and welcome to A Problem Squared, the podcast which is a lot like a crow in that we can make rudimentary tools with which we can solve simple problems. Yeah, like crack a nut. Like crack a nut. Get an ant out of a anthill, that kind of thing. Get an ant out of a ant. That's what crows do. I'm joined by my crow host, Bec Hill.

Thank you. Did you come up with that first and went backwards? No, I didn't. You know, I had the crow thing first and then I realized crow host was right in front of me. Yeah, nice. So Bec Hill, looked like a crow. If you feed her often enough, she'll become your friend and occasionally bring small shiny gifts in exchange for food. Yeah, I also take a lot of shiny gifts.

You do take a lot of shiny gifts away. That's also very true. And I am Matt Parker. I look like a crow in that it's been proven I can count and I can communicate vocally a specific quantity. Yes. Only animals other than humans that can vocalize a specific quantity. Unlike crows, we are not direct.

Are crows direct? Well, as the crow flies. As the crow flies, good point. Also, unlike crows, we probably don't have a great memory for faces. I'm glad we're workshopping my introduction. Dude, you opened up, like you started with Crowhost and then I was like, oh God, this is all I can think of now. On this episode. What happens when tires get tired?

Oh, that's nice. I've got a new spin on the Rubik's Cube. Nice. And any other birdness. Caw, caw. Nice. And any other birdness? Caw-caw. So, Bec, how have you been? I'm great.

Oh, my gosh. I've had such a great day. You know when you just have a good day? Yeah. You talk about today specifically. Yeah. It has been good. It has been good.

But even before I saw you, and you were a highlight, Matt. Thank you. You continued an already great day. That's day. But I have a lot of issue with time management, which you are aware of. It is something I'm working on. Yesterday I showed up for a podcast record doing Ali Plum's movie podcast. And I got there absolutely on time. And then Ali realized that he'd meant to say 4 o'clock, not 2 o'clock. Oh. Yeah, rare occasion where I was not the problem. And he felt awful. But honestly, I just felt relieved it wasn't me who made the mistake. And you were there early. Yeah.

So I was actually thrilled. He felt awful. I was thrilled. Because suddenly, I'm two hours early. So I did a bunch of life admin. And then I and like looked for some stuff in the shops and everything. I felt amazing. Like a gift of time. Yes.

So to get there and suddenly had the gift of two hours. Yeah. That's pretty special. Because at first the part of me was like, oh, I should have brought my laptop or something. But I was like, no, actually this really limits me to what I can do. And that's actually what I need because I get the workload paralysis. And so that really helped me get a few things done. And then also I bumped into two lovely friends and comedians,

Joss Norris and Howard Reed. I also ran into Robin Ince on the way out. Oh, wow. So I love the day of seeing friends. Anyway, this morning, as I was on my way just down my street, there was a woman in her car. She was looking for a mechanic. Now, annoyingly, I'm on a cul-de-sac, but there's bollards at the end.

So there is another street, but cars can't get to it. You can only walk through it. And there's a mechanic around the corner. And it's such a long convoluted way to get to the other street. Like it is a series, like it's basically driving backwards for quite a long time. And then a lot of. All the way around the houses. Yeah. And I was explaining and she was like, basically the reason she had to get the mechanic is because her car won't reverse.

Oh. It stopped reversing. But I could tell she was really panicked and stressed. So she's like, could you push my car? Because she couldn't turn the car around it was really really tight and i tried but i'm i'm i can push it a tiny bit but also so then when it got to a point it started to roll back but thankfully someone else was walking around the corner with their like tennis gear and stuff and i was like oh excuse me can you come help me push this car and he was like of course and we start pushing but again it starts to like roll a

bit and then just as we're like oh what are we gonna do and she's so upset this um guy had obviously been watching us and so he he starts walking down going all right i'll come help and we're like oh thanks so the three of us managed to push her car backwards so she can then go forward a bit and then push it back again. And then when I got to the tube, there was a woman struggling with her suitcase. She had a kid in tow. Everyone was just walking past us.

I was like, do you want some help? She was like, oh, yes, please. So I helped carry her suitcase down. And just the endorphins you get from helping people. You've just been wandering London, helping people. Helping people. And look, I wasn't going to tell people all about this,

but it put me in such a good frame of mind. Cause a lot of time we can be very embarrassed and we don't want to bother anyone, but you forget what a gift it is to let people help you. Cause it makes them feel good. And so, yeah. So I,

um, I got to Waterloo 15 minutes to kill before I had to get my train, which is unlike me. Normally I'm like, it's just been a great day. Good day. How about you, Matt? I also had some people push a car that I was in. No. Yeah, like two or three days ago.

Wow. I went to EMF camp. Yes, which is electromagnetic field. That's the one. And it's a lot of fun. It's kind of like hackers and makers and doers and builders. Oh, my. Exactly.

And this is the second time I've been there. The first time I did a big installation, I had 2.4-meter-long bits of wood that I painted different colors to make four intersecting tetrahedra that were then covered in LEDs. So at night they would light up different colors. And there's huge kind of – a lot of like people do installations big sculptures yeah my favorite installation this time there were some great ones my favorite one it was actually quite a small one they have a place called the null sector it's like a lot of shipping containers and it's like that kind of post

apocalyptic industrial-esque place yep and my favorite installation was in one of the shipping containers there was a robot that would generate a complaint letter for you. So what you'd do is you'd walk over to it. That's the most British invention ever. It's so good. You put a bit of paper in and you hit go and it would first of all randomly generate a complaint. Something like, I had to wait too long

for my coffee in the cafe in Shepton Mallet or something like that. Like real niche complaint. I've never heard that place before, but it's a great. Great British place. Yeah. I think that's a real place. I don't care if it is.

I don't want to know if it's not. It should be. Yeah. It would generate a random complaint for you. You don't have to do that yourself. It will then use the ChatGPT API to send it over and tell it to write a complaint letter based on that complaint and often give it like a prose style to do it in.

Yep. That comes back from chat GPT. And then there's a pen with motors attached that will hand write out the complaint letter for you. Nice. And then once it finishes writing, which for the record takes a long time, you then get your official handwritten. That's great.

It's such great. Also the weird ridiculous art installations. They run a copper, like it's super digital, and there's like mains power to every tent and very fast Wi-Fi across the entire site. Like it's such a good festival. That's amazing. And they also run a copper network.

So there's rotary phones. Okay. So you can pick up a rotary phone and like and then dial other phones well that's how you have to dial the organizers if you need anything you've got to use a rotary phone someone this time brought a fax machine put it on the copper network and if you fax it anything it will ocr it so convert it back into text from an image and then assume it's c code so like computer code run the code as it can best work out what it is and then fax you back the output from when the code runs so you can fax it c code for it to run for you and it will fax you back i don't know

what that any of that sentence is so good is it so as an analogy is it like um translating English into French on Google Translate and then translating the French into German and then translating it back into English? Sort of, yes. But what's particularly pleasing about it is way back in the day, early computing, you'd have to put your code into punch cards or whatever, send it off to be run overnight, and then you get sent back the output in any errors or whatever went wrong. So it's going back to that kind of you've got to write your code

then send the code off to someone else. Oh, so you'd write the code for an image or something? Yeah, code to calculate a thing or whatever, and it will go and run the code and send you back whatever the output. God. They run a sneaker net. A sneaker net? So if you want to post something to someone,

you write it on a postcard or whatever, and then you give it to whoever you think is most likely to be able to give it to someone else that's good so so if you get something on the sneaker net you've got to look at where it's meant to go and think who's most likely to be closer to that person than me yeah so it's like a physical representation of six degrees yeah i got sent a postcard do you want to see it i I do. I've got it at my back. Did it come to you via the sneaker net? Yep.

Someone sneaker netted me a postcard. So the address is just Matt Parker EMF. Love that. Just accurate. Matt, thank you for being awesome. Hope you're having a fantastic time at EMF. From a Problem Squared fan. P.S.

Please send heart emoji to Beck. Oh, thank you. So this is me fulfilling the final step in the sneaker net to them. That's so cool. Regards onto you. But when I arrived at EMF, I hired a camper van. Okay, yeah. So I was like, it's like a big

metal tent. Yeah, I know what a camper van is. I can stand up in. So thank you for clarifying. No, this is my justification. I'm like, I don't want to stay in a tent. I want to stay in a big metal tent. Yeah. Because it's not like a normal festival where the camping is like over there and the festival's over here.

It's all mixed in because people camping set up their own villages. There's like the lock picking village. There's a bunch of people into lock picking. All have their tents together. And then they have a marquee and they run workshops. They had one lock. If you could pick it, they'd buy you as much beer as you could drink. That's great.

Anyway, I thought I'd drive the van. But you can't go on site after the sun has set. Right. And I got there with 10 minutes to spare. Okay. I turned to someone from the Middle Ages. I'm like, fellow traveler, the sun is still in the sky. Yes.

Albeit low. Yeah. And then after a lot of negotiating i've never been so close to a do you know who i am in my life yeah i know i was like i'm not gonna do that and i got on with like minutes to spare they let me onto the site yeah it immediately got the van bogged and so i had get again. I forgot how we got to this story. Yes, I bogged the van. But people were so helpful.

Loads of people came out. People just appeared from everywhere to help. There's an above average number of problem solvers at a festival like that. I was like, look, I'll just go use the rotary phone to ring the power people. And they're like, no, no, we can work this out. They were doing a stock tape. We got these cables of these lengths and this here. They're like, these extra activities are great.

Yeah, I know, I know. So they were, I couldn't stop them from trying to solve the problem. They're like, right, we'll put the cable and the fox in the canoe at the same time. And then after a while, Steve messaged me saying he had the same problem and he just reset the breaker that's underneath the box. I was like, what? I turned the box over and there's just four breakers on the back. Great. For the four outputs and one of them had flipped.

So I flip it back. Done. Done. Amazing. I love how many people also went away. No, I can't tell you the number of people putting an undue amount of thought

into solving this problem and nobody turned the box over to see that there are breakers underneath it. Too smart for their own good. 100%. Yeah, yeah, yeah. Anyway, I had a great time at the festival. That's why there are breakers underneath it. Too smart for their own good. 100%. Yeah, yeah, yeah. Anyway, I had a great time at the festival. That's why I'm in a good mood.

Amazing. Our first problem was sent in by, I'm going to say, Pytro. It's spelled Pytro. Pietro, maybe? Pietro. And they say, where does all the rubber go? They elaborate. We use up thousands, millions of tires every year.

So where does all the rubber go? And by that, they mean the dust removed by the friction on the road. The bits coming off. They don't mean the actual leftover tire carcass. They mean the little bits. They want to know how much material is it in terms of tons per year and is it now a significant part of atmospheric dust? Will future geologists be able to identify it in the crust layer?

And Neymar time. Oh, they've got some suggestions. The Michelinic. Nice. Michelinic period or the Goodyeronian. Goodyeronian? Goodyeronian. I think you had it with Michelinic period. Yeah, there's something. So, Bec, you looked into this. Yeah, so I had a quick look into this and I actually found that there's a scientific paper about it. When you said you were

going to do this, yesterday, the same question occurred to me. I was cycling behind some cars and I was like, I wonder how much tire dust I'm inhaling. Because it's got to be like tires constantly wear out. The tire is going somewhere. It's not big chunks. It's not like in racing where you see like whole chunks of tire flying off. It's got to be dust. Well, this paper is titled where the rubber meets the

road emerging environmental impacts of tire wear particles and their chemical cocktails they're so good obviously we'll put a link to it in the show notes so it does cover what happens to full tires yep afterwards but i'm not going to go into that true is specifically said they don't care about the actual carcass. Yes. But one of the things that sort of caught my eye in the abstract of the article is tire particles emitted during use are a major component of microplastics in urban runoff and a source of unique and highly potent toxic substances. Oh, none of this is good.

I know. Tires represent a ubiquitous and complex pollutant that requires a comprehensive examination to develop effective management and remediation. What's it going to be? It's not going to be like, oh, it turns out they become, you know, like sprinkles. Yeah. Yeah. Or it turns out they're a really good fertilizer and support healthy, you know, aquatic ecosystem growth. Yeah.

Well, it's funny you should say that because they were looking into what could happen with tire particles. Yeah. And later in the paper, it says that tire particles may be washed off by stormwater runoff into wastewater treatment systems. There are no current data on fate or volumes of Thai particles specifically in wastewater treatment plants. Oh.

You can also surmise that there's not enough data to say specifically how much. We're not tracking it. Yeah, we're not tracking it. Getting filtered out or anything. And the paper does later have a whole, like, data gaps and research needed segmented as well. But it says data suggests that a high percentage of

other microplastic particles transfer from the water into sewage sludge even with high removal rates significant annual loadings of tire and road wear particles have been estimated in treated wastewater effluent in the uk so it makes it through the wastewater treatment plant yeah sewage sludge is typically incinerated disposed of in landfills or spread on agricultural fields where tire particles may remain in the soil or be mobilized and distributed by wind or by a surface runoff to the aquatic environment. That's not great.

Yeah. So, you know, I know that you're like, oh, maybe it turns into manure and use it. Yeah. No, it's... It does get... Like it does, but it's... Mixed into the field when we grow stuff.

Doesn't help it. Yeah. Not on purpose. Because in the UK... Like it does, but it doesn't help it. Mixed into the field when we grow stuff. Yeah. Not on purpose. Because in the UK, well, London, I'm pretty sure, they got like the final kind of wastewater treatment for the sewage. Then you treat it a bunch, you put the water back, you get leftover, you know, solids. Yeah.

Stuff. I think they used to put it on a barge, take it out to the ocean and just push it over the edge. Wow. I think they were told to stop doing that because they made some places burn it. But I guess you put it on a barge take out to the ocean and just push it over the edge i think they were told to stop doing that because maybe somebody's burn it but i guess you put it on a field i mean i think this is an exactly uh a good example of why that could be a problem yeah i was only aware of this maybe being a problem when where we are now goteming and the surrounding villages it's it's quaint as. You're familiar with how quaint it is around here.

It's very quaint. But there's also the A3 motorway. It's a big, busy road that was cut through here just under 100 years ago. Yeah. Would you say it's the British equivalent of a highway? It's a highway light. It's a big road. It's a big road.

It's got no traffic lights or roundabouts or anything. You don't stop. It's highway driving. And it's a very busy road yeah and it just kind of slams through the countryside through villages right across and so i'll often try and walk around and find the vestigial bits of road left from when it just got carved through the country right i'm not saying it shouldn't be done. People have to get places. But now there's a bunch of quaint little villages. They just have constant motorway noise. And I was like, that's a real shame.

And I thought, I wonder, is that a problem that will solve itself once all cars are electric? And so I did a quick bit of research. And it turns out, no, like most road noise above a certain speed is the wind and the tire noise. And then I saw a little bit about how going electric with vehicles is great in terms of carbon, but doesn't solve the tire dust problem. And that's when I was like, ah, great. Now I've learned about a new problem.

Yeah. And look, I understand that I'm citing one paper and that's if I could get yeah get multiple but then they cite multiple sources and to me that feels like that's pretty legit which also then brings me to the fact so i didn't go to university my only experience of reading papers is largely for this point right and even then i've had to like it's it's been a, if it's not something that you're used to, it can be a little bit of a. You're right. It is an acquired skill. Yeah.

That opening sentence that I said at the beginning has so many massively large words that aren't necessarily needed. That's true. They sound smart. Yes. Yeah. I mean, that goes both ways. Sometimes when you read a technical paper that's just outside your

area's knowledge, you're like, oh my goodness, they're just using obscure or obtuse phrasing to be annoying. To sound smart, to be more science-y, which is not untrue. That said, once you're in the discipline, you're like, oh, it's because what we assume are synonyms from the outside are an easy way to say it. Everything's been assigned very specific meanings. And so you're like, oh, I get if you're trying to convey really nuanced things to an audience that you assume is already fluent in what you're talking about, you can use ridiculously complicated language. Yeah. Going through a paper properly and understanding it is a lot of work yeah and if you're not already sufficiently enough of an expert in that area it might even be impossible but you do get good at like reading

you get pretty good at like knowing what to ignore and i find people struggle with this with like math papers now i can skim a math paper and know oh i i understand the essence of the working out they're going to do here right i don't have to follow through and i can just skip right over that and ignore it i think it's just it's survivor bias like you've had to look at so many papers yeah because sometimes i have i've used maths papers to research for this show and i find them this one i actually find is a lot easier to navigate because good diagrams it's got good diagrams and also it's largely verbal like it's it's largely well not verbal it's written yeah yeah prose whereas with maths ones i i will scan but i'll

notice there's a lot of numbers and a lot of symbols. And I'm like, please use words, please. Should I have a little look at this? Yes. Yeah. So what I tend to do is look at the authors. How many? There's a lot of authors.

There's a lot of authors. When I see that on a paper, I'm like, well, that's got to be good. Well, it means it's some kind of big, maybe even a review paper or something. But then more importantly, where are they based? Where is the paper from? So scientific papers, not always, but for most disciplines, will rank the authors in order of importance or involvement in the paper. The first one mentioned, Paul Mayer here.

Paul Mayer is going to be our most important person and they are based at the US Environmental Protection Agency. That sounds good. That sounds good. That's legit. Yeah, that's legit. Obviously it's a government agency so there could be bias. But at the same time, considering the stuff they're talking about, I feel like anytime the government says that something could be bad environmentally, I'm like, well, they're convinced. Yeah, exactly.

Like it's got to be like at the very least it's this bad. Now I'm scrolling through the other places involved. San Francisco Estuary Institute, Department of Fisheries, Wildlife. Oh, more government departments. Oh, wow. What's the government? Department of Environmental Molecular Toxology at Oregon State University. A lot of different universities as well. And some that I recognize the name of, which obviously is my own, brings in my bias of universities I'm familiar

with. I'm not saying research doesn't happen. That's very good in countries where I'm not familiar with it. But in this case, I recognize a bunch of these. So now I'm prone to believe this. It seems like a good paper. It strikes me as a paper that's meant to convince policymakers. So it's been put together in a way and there's good summaries. That doofuses like me can understand. It's been doofus proofed. Yeah, it's because people like me are the sort that would probably get voted to power.

Yes, one day. Because we're not as clued in as everyone else. In power. This episode comes out before the UK not as clued in as everyone else. In power. This episode comes out before the UK election, so we don't know if you become Prime Minister or not. Yeah, yeah. Thanks for everyone who voted for me. So what I'll then tend to do is read

the introduction, scroll through the rest of it to get a sense of it, see if anything's interesting, and then read the conclusion. And there'll be an abstract as well. Sometimes the abstract kind of gives you all you need. Well, because also the conclusion on this isn't necessarily the answer we want for the problem. No.

It's more that the answer we want for the problem is throughout the paper in the research. Conclusions are all doom and gloom now I'm reading it. Yeah. I can answer the first part of the question, which is where does all the rubber go? Yeah. So as I mentioned before, a lot of it

in terms of runoff will end up in sewerage. Because it goes into the waterway. Yeah, exactly. And the stuff that doesn't end up in sewerage will just end up in runoff waterways and end up in like surface waters and stuff. It gets washed off the road when it rains. Yeah. And ends up somewhere in water. It's either in the soil or it's in the water. Some of it is carried by wind. Which again tends to end up in soil or water. Air transport and runoff may

carry tyre particles and associated chemicals into surface water drinking water sources. Drinking water treatment plants draw chemicals into surface water drinking water sources. Oh. Drinking water treatment plants draw water from surface water, groundwater, and or seawater, all of which may contain microplastics, including tire particles. Drinking water treatment typically starts with screening and grip removal, so to get the bigger bits out of the way, followed by addition of... Fish. Yes, the addition of fish. The fish removal.

Oh, right. No, first of all, you filter out the fish. I thought you were going to say what I said with the addition of fish. The fish removal. Oh, right. No, first of all, you filter out the fish. I thought you were going to say what I said with the addition of. Take out the big bits, put in the fish. Vitamin fish. Ooh, salty. With the addition of alum to the raw water for coagulation. Great word.

Don't coagulate. Flocculation. Which, you know, flocculation sounds like it's part of an insult sounds like something medieval monks had to do yes that's anyway it is currently clear that tire wear particles and their chemical cocktails are emerging contaminants of global concern chemical cocktails and that's not scientific wording i don't think i feel like that's talking to you thinking science they wouldn't say cocktail. They probably wouldn't.

Unless cocktail has a very specific meaning in a scientific context. No, I think you're right. I think this is a mix of... I think this is like a deliberate pull quote. Yeah, you're right. What they do say, action should therefore be given to reduce the risks to human health and the environment. I mean, good point.

I agree. So I think basically, where does the rubber go? In the soil, in the water, and in us. Great. given to reduce the risks to human health and the environment i mean good point i agree so i think basically where does the rubber go in the soil in the water and in us great essentially our lungs our systems as we drink and stuff it's it's the same story as microplastics that's the first one how much material is it time per year now that i sort of mentioned earlier they are lacking some research into you know how much is ends up in waste treatment and stuff like this. However, based on relatively limited data, country-specific tire particle generation across size classes, 10 nanometers

to 1,000, this is where you come in useful for me. Is it mu? Sort of a u, but with like a little... Yeah, micrometers. Micrometers. Thank you. See, this is why I have you, Matt. So between 10 nanometers and 1,000 micrometers has been estimated to be as low as 0.23 kilograms per year per capita in India to as high as 5.5 kilograms per year per capita in the US due to its longer per capita annual vehicle travel distances.

Now, that's a very big sentence. So five kilos per person in micro rubber particles. Now, I'm putting that out there for people like you who understand what it means. Thankfully, they then say, thus. Thus. Approximately 1.7 million tons of tire wear particles were produced annually in the US based on 2021 population size.

Where automobile and truck traffic are higher, production of particles may be significantly greater. Based on empirical and extrapolated data synthesized from Europe, Japan, China, Australia, Brazil, India, and USA, annual global tire wear emissions across size classes, 10 nanometers to a thousand. That's the size of the particles? Yeah. We're estimated to be nearly 6 million tons. 6 million tons a year?

Mm-hmm. Of tire wear emissions. Wow. That's a lot. I'm trying to imagine a million tons of microparticle. That's a lot of tons. That's just the particles, which is answering this question. I should also say that it goes on to say a little bit afterwards,

others estimate that globally 1.5 billion tyres are discarded annually, currently with an expected to increase to 5 billion tyres by 2030. So, yeah. Yeah, that's getting rid of the rest of the tyre. 1.2 billion tonnes by 2030. So that's how much material it is per tonne per year for Pietro or Pietro. As they requested. They said, is it now a significant part of the atmospheric dust?

In the same way that microplastics are from, from what I see. So will future geologists be able to identify it in the crust layer and name our time, possibly, there's no signs of it getting better. Well, does it break down or? Certainly not anytime soon. So there's, there's currently discussions going on with geologists about the amount of man-made materials oh stuff that we're going to leave behind yeah permanently in the geological record yeah and a big part of that discussion is

microplastics right of which particles are part of. Oh, okay. Each of the humans, Beck, you have worn this problem down into tiny little pieces. And I think you've successfully answered, I would say, all of it to the best of anyone's ability. Yeah. So I'm going to pretty much give you a ding. Thank you. I think that's dingable.

If Pytro has an opinion and if it's ding-worthy, they should let us know. Yeah. I like to think the answers will one day end up in our waterways and lungs. The point is we have to hurry up and invent hovercasts, because that will solve the noise-ruining quaint villagers problem. Oh, yeah, because I'm sure that they're not loud. Oh, yeah, it's going to be like that.

Have you ever heard a tiny drone, Matt? It's so true. Have you ever heard a helicopter? I Matt? It's so true. Have you ever heard a helicopter? I'm pretty sure a hovercraft is like. A hot air balloon firing, it's burning all the way down the room. A hovercraft is going to sound like a bouncy castle, but with a motor. Yeah, exactly. So tranquil.

Yeah, I will solve the sound problem. Okay. I was making like a Jetsons-esque. That's what you're expecting. That's a bit loud sound problem. Okay. I was making like a Jetsons S. That's what you're expecting. That's a bit loud. Yeah. Keep it down. Our next problem is from Michael who says,

when you spin a Rubik's cube between your thumb and middle finger, as you must every time you solve it. Okay, so I've just filmed you spinning it. Yep. And Michael points out the silhouette forms a diamond with a curved concave equator. Yes. Now I can see that when I pause the video. And you can see it in the video as well.

We'll put the video up online. What is the equation for this curve? What is the name for this family of curves and how do you get curves from straight lines so is this kind of a bit like the rubik's cube version of the rubber pencil trick what oh the rubber pencil trick where it looks like it's bending yeah so you hold a pen or a pencil from one end and you sort of like bounce your arm as you're waving it it looks like it's made of rubber that's really impressive i did it a lot as a kid what you're doing there is moving a straight thing around and you're making

it look like the actual straight thing's flexing whereas the shape made when you spin a rubik's cube is actually curved what it is a curved surface what so the rubik's cube itself is all straight yeah so imagine just the edges. I'm going to use the phrase straight line a bunch. That just means like the edge is a straight line. If you move a straight line around, you can make curved surfaces. Like how the equator is a straight line, but it goes around a circle. Oh, yeah. No.

It's a bit like. I'm still struggling. If I got, I'm going to borrow your pen. Holding it vertically. Yep. I'm moving around and I'm tracing out a cylinder. Yes, you are. That it vertically. Yep. I'm moving around and I'm tracing out a cylinder. Yes, you are. That's a curved surface. A surface made by taking a straight line and moving it around.

That makes far more sense because before you're like, you're creating a curved surface and I'm like, no, you're not. So the mathematical name for this is a ruled surface and a ruled surface isn't like a ruler surface. It means the surface can be thought of entirely as straight sections or taking a straight pen and moving it around to map out that surface. Actually, I was sounding like I was understanding you, and I'm still not. And the reason is because we're talking about a shape that is not physically present, aren't we?

No. It's the total shape traced out by the cube moving through space. I can't. Well, I mean, you can make any shape moving something straight. The definition of a ruled surface is you get a straight line and move it through space. Okay. Now.

But we're not talking about like when you create that curve. Yep. It's not creating a curve on the cube, is it? No, the cube is just moving through. It's tracing through. Yeah. It's called a hyperboloid is the name of that shape made by the Rubik's Cube. You know what?

A hyperboloid is the perfect name for it because it sounds like a pain in my butt. I love a hyperboloid. So the diamond. Yep. Moving on from your hyperboloid is the perfect name for it because it sounds like a pain in my butt. I love a hyperboloid. So the diamond, moving on from your hyperboloid chat, the tops and bottoms are cones. We're tracing out a cone shape. So if you follow just one edge as it goes all the way around. Okay, so in the way that when you're making a circle with a compass, there's two straight lines.

So you have the point in the center comes up and then back down and then you turn it and that creates a circle. And what you're doing is essentially your top finger is on the corner. So pretend that that's you holding the top of the compass. Your bottom finger is what it is rotating around. Yes, but instead of just the very tip of the compass drawing a circle on a flat bit of paper, I'm talking about if you took the whole edge as like. So if you were drawing a circle with a compass, you've just created a cone shape.

Yes. If you keep one of them. As long as the central one is completely vertical. Correct. Yep. Yeah. So you're creating a cone and that's essentially what you're doing with the top corner and then the middle. Exactly that. Okay. Same thing in the bottom. So there are two cones facing each other. Yep. Nailed it. So you're creating a cone and that's essentially what you're doing with the top corner and

then the middle. Exactly that. Same thing in the bottom. So they're two cones facing each other. Yep. And then the joiny bit, the equator, the curvy looking bit is a hyperboloid. Yes. Right.

Okay. Yeah. And that's because I'm seeing the top cone, which is between the top and the next corner down. And then the bottom cone, which if you're looking at a cube at the angle that it's a hexagon yeah then the bottom corner coming up to the two corners you would see on the left or the right of it that's the other cone and we're talking about the space between the two cones correct excellent all right i love this podcast is called between two cones

yeah let's get mich Michael Cera on here. Is it Michael Cera who's emailed us? It's not. I can see their surname. So, yeah, the middle bit is hyperboloid. But I love ruled surfaces because they look like a very smooth flowing surface. But actually, they're made entirely out of straight lines, which I find very counterintuitive. I find very exciting.

And the reason I specifically asked on the group WhatsApp. To get props? To get Pringles. Well done, everyone. I wasn't sure if producer Lauren had already sourced Pringles. Yep. And so I got ready salted because I know that no one ever buys plain Pringles. But I love them.

Pringles. Pringles. Pringles. Pringles. Is it because it's a plain surface? Whoa. And then, sure enough, Lauren also picked up a tub, but it was the sour cream. Which I think is a subpar flavor.

Come fight me. I don't care. You do say it vocally and often just spontaneously. It's the first time it's been relevant. So I'm glad this lined up. Yes. I'm now going to pop. All right.

After which we're going to struggle to stop. Legally not allowed. We're now in. A Pringle is a hyperbolic paraboloid. This is a ruled surface. Oh, you put a dot anywhere on this Pringle. With pleasure. Oh, she ate it.

Oh, my goodness. This is going to take so long. It's not even a flavor that I like. Okay, Becca's drawn a dot on the Pringle, and I have a ruler here. I should be able to find a straight line that goes through that dot. There will be a line there. The ruler contacts all the way across the Pringle. Yes.

But yet goes through that dot. Yeah. Because I'm so, you know, this morning as we were getting ready to leave the house, Lucy's like, oh, I can't be late. I've got NASA visiting today. And I'm like, well, I have to go put a ruler on a Pringle. So, you know, we're all got real good important careers. So, you know, we're all got real good, important careers.

Anyway, as I've just demonstrated, this Pringle is a ruled surface. Yes. So you can make this. I'm going to take a photo because this is very visual. You do have a habit of choosing very visual things for an audio-based show. People send in very visual problems. Can you hold it up so that it's level? Oh, yeah, down the line.

There we go. You know, I'd never tried that before. I just thought, you know what? I know a hyperbolic paraboloid is a ruled surface, and that's what a Pringle is. And so I figured if you put a dot on it, I should be able to find a line. And I could, because it's maths. That's very cool.

It's maths. Yeah. So that's a hyperbolic paraboloid, Pringle. So, yeah, so at any point I can put a dot and I will be able to find a straight, I will be able to put a ruler on it, basically. Yeah. When you get a line like one of these edges on the Rubik's Cube and rotate it around while fixing the angle it's on, that maps out a hyperboloid. Yes. So that means there are two things.

Number one, I can give you the equation for a hyperboloid because that was requested. Okay. And all ruled surfaces are kind of the combination of two curves. And if you work out what the curves are, you can then work out what the equation of it is. Now, a hyperboloid actually has quite a neat little equation. Okay. The equation for the surface of a sphere, like a ball,

Yes. is for the x, y, and z axes, it's all the coordinates such that the x coordinate squared plus the y coordinate squared plus the z coordinate squared equals one or a constant, whatever the radius is. If you make one slight change, if it's the x-coordinate squared plus the y-coordinate squared,

subtract the z-coordinate squared. Instead of adding it, you subtract it. Yes. Equals one, all the radius. Radius in quotes now. That's a hyperboloid. Okay. There's a whole family of them. So in fact, you can divide all of the X, Y, and Z coordinates squared by a constant,

and that will stretch it in different directions. So you'd have to, like, there's like the, it's like a ball, but you could stretch it into like an egg shape looking thing or whatever. Yeah. So you'd have to distort like the standard hyperboloid to be the one specifically traced out by this rubik's cube but you can do that and that's the equation for it can i ask a question so pringles i mean it is sort of it's uh it's not two-dimensional because it it curves but

that would be um a crisp called a thins yes yeah but they. But they are very thin. But it's very, yeah, it's very thin. And for anyone who's done the duck thing where you put two Pringles facing different directions into your mouth. To make it look like a duck. And to look like a duck. You'll know that it's not easy to join up the edges of a Pringle. No. Is it possible to have a hyperboloid that is more chunky three dimensions?

Ah. Like as a stacked, if a stack of Pringles was one massive crisp. Yeah. Is that one? It's the surface. We're ignoring the thickness of the crisp. Okay. Lastly, I looked up buildings that are shaped like a hyperboloid.

Now, a building is generally much thicker than a crisp. The surface of the building is the shape of a hyperboloid. Not a hyperboloid paraboloid like the Pringle. Now it's the hyperboloid. Oh right, that's where I'm getting confused. So if you spent this whole time thinking, what does it look like? I mean, how would you describe what these buildings have in common? They're a bit like the stalk of a mushroom cloud. Yeah, a cooling tower, like a cooling tower. Yeah, like a nuclear cooling tower.

I've been to one of them, the Ray Thompson Hall in Toronto. I've done a show there. And there is a bridge in Manchester, the Coronation Street Bridge. And the reason that they're often used in architecture is you can build them out of straight beams because it's a ruled surface. So you can make the surface by putting a bunch of metal beams together. Yeah. There's a whole family of them because they're all stretched different ways. We'll link to the Wikipedia page.

But if you flick through the pictures of the various buildings that are all hyperboloids, you're like, oh, I get a sense of the shape that we're talking about here. So that's it. It's a ruled surface. It's a hyperboloid. That's it. It's a ruled surface. It's a hyperboloid. Its equation is x squared divided by something plus y squared divided by something else. Subtract z squared divided by something else again. Equals one. I feel like you answered that.

And it involves snacks. Pringles are a ruled surface shaped crisp packaged in a different ruled surface-shaped tube. I'm going to give that a dingles. A dingles? Well done. Yeah, thanks. I feel like we're giving them far too much advertising. I know, yeah.

What are they, for a Rocher? They're going to be like, what's this spike in sales this month? I would love that. It is now time for any other birdness where we pick through shiny things left behind from previous episodes. What have we got this time, Bec? We have some feedback about the what to get someone on their billionth second birthday. Oh, yeah, their billionth second birthday.

Yeah. So we heard from. I suggested a book with a billion letters printed in it. You did. Which I called a birthday card. We heard from Fakhrudin, F-A-K-H-R-U-D-D-I-N, who said, may I recommend getting a billion of some very low value currency? For example, at official rates.

It may be much cheaper at unofficial rates. currency. For example, at official rates. It may be much cheaper at unofficial rates. You can get one billion Venezuelan Boliva for about $273. I'm guessing that's USDs? Or thereabouts. It may be too much for a single person to gift, but if multiple friends band together, it could work and there's even cheaper currencies out there, I'm sure. Well, here's my problem with that. Okay, yep. Would you have to get a billion one currency unit notes for that to count?

Or would you accept a single note that says this is worth one billion units? Oh, because, again, that was your issue with the one billion micro-hams, micro-shams. Yeah, it's one thing. I want a billion separate things. Yeah, like in itself is a whole thing on its own. It's not a part of a whole thing.

Yeah. Yes. And I know me saying individual letters printed in a birthday card is in the mix because it is just one birthday card, albeit tens of thousands of pieces of paper. But there's a billion discrete letters printed on them. And you can look at one and go, there's one, there's one, there's one. I mean, I would argue that different parts of a ham. Okay, we know your micro ham argument.

We're very familiar with that. But this does also remind me of a problem that I have, if anyone wants to help solve it for me. Oh, stealth problem. Stealth problem. I'm just tacking this on now because, you know, obviously getting a billion Venezuelan bolivar, let's say it was notes. Yeah.

That's a lot of notes. Yeah. That's a lot of notes. I had a similar thing recently where I was gifting someone, there was a whip round and we ended up with $700 American. And it was all through electronic payments. Obviously, I can just transfer it. But what I wanted to do was give them 700 individual bills.

Very funny. Until someone who used to be a bank teller pointed out to me that that actually won't look that impressive. It's not that many. It's not actually that many when you, like, if you're presenting it in like a case. Open a briefcase. There's just like a few notes in the corner. Well, it's 700. Yeah, but it's not.

They're kind of going to swish it around. It's not like it's stacked in the way that you would expect. No one's going to have a good time. So what I did was I then bought 700 fake bills that he used for like educational purposes. And then they were like, what's this? And I'm like, it's representative of 700. And my friend was like, brilliant. And immediately went to put them in the recycling.

And I was like, wait, wait, they're not worth nothing. That was like $30 worth of paper there. Give me that back. It's a prop for me. I have no idea what to do with it. What to do with $700? I don't know what to do with $700. $700 fake.

Very fake looking pieces. Bright green. Yeah. Educational money. Yeah. Wow. So if anyone has any suggestions. Send in a solution at the problem posting page.

Yes. But we also heard from Eris in regards to the billion second thing. And Eris said, now this was from episode 86. Eris suggested, alternatively, to give a billion of something is to give a gigabyte USB stick or file. And then you've given one billion bytes. I just assumed that that was right. Well, here's the problem. Computers use base two for a lot of things.

And so I forget the distinction because sometimes like a megabyte is a million bytes. Yeah, no. Sometimes a kilobyte is a thousand bytes and sometimes it's a thousand and twenty-four because that's a power of two. Stanford website says one gigabyte is about one billion bytes. About, yeah. So maybe. Does that appeal to you more? That appeals to me more because I know in the memory all the bits are in there

and in groups of eight. But now you're actually giving them eight, you're really giving them eight billion bits. Is anything worth one byte? Was there ever a file that was worth one byte? Oh, yeah, definitely. Back in the day. What would it have been? Like a Unicode character.

So, yeah, so you could have a billion Unicode characters. I don't know if it would count as a file, but yeah. Yeah. Yeah, you could make a real, I don't know, could you even make. Could you make a file, yeah. You couldn't, no, no't know could you even make is that you make a file you couldn't no no i take it back you couldn't make a file that is a single byte no you would never room for the header and stuff to say this is a file yeah yeah yeah okay i'm gonna put that in the maybe pile but still i do like the idea of being like here's a billion bytes it's a useful

gift i'm a big fan of things that are also practical a document on it a gigabyte is still not like we're still in a stage where a gigabyte is it's a decent amount useful yeah i don't think it's even have space to do a billion characters because you're gonna need more than a byte each yeah exactly yeah oh you're thinking i've gone right off the idea put the file file on there. Yeah, yeah, yeah. No, no, no. I'm saying the USDC... Just email them the birthday card. They can print it themselves. At EMF camp.

Oh, yeah. Someone called Olivia. Mm-hmm. She came with a backpack that was displaying a lot of enamel pins. Excellent. So there's like a transparent section. There's like a zippable giant pocket on the back of the backpack. And inside that, she'd put all the pins like through the backpack fabric

and then had the clasp holdy bits on the inside of the backpack. I took photos. We will share the photos. And one of the benefits, Olivia explained to me, was this way if a pin falls out, unlike your case where it just vanishes, it's gone. Now it just falls to the bottom of that section. And also what was great was Olivia and her partner Robin

were driving to EMF camp, and they happened to listen to that episode of the podcast, heard the problem, and realized they were already bringing the solution with them. That's awesome. To EMF, and I was going to be there, and so they closed that loop. You got some photos?

I got photos of the bag. I got a photo of Olivia holding the bag. Amazing. In fact, we have another listener who's done precisely that. Zef said, I just finished 085 and have a good solution for not wanting to take pins outside in case you lose them or they get damaged. I have a collection of over 30 enamel pins and badges and I sewed a pocket onto my backpack with a clear panel. There it is.

So that the pins can be seen but will be caught in the pocket if any fall off. I think that's a great. Olivia did say the backpack she's got is just purchased off Jeff Bezos' website. Oh, yes. Bezos Backpacks, I think it's called. Bezos Backpacks. That's the one. Little upstart.

Yeah. So you can either do a Zeph and make it yourself or you can have a chat time. Jeff. Yeah, Zeph or Jeff. Yeah, Zeph. They're your options in life. You go the Zeph way or the Jeff way. Thank you so much to everyone listening to this podcast.

We really appreciate it. Whichever hacker and maker festival you may be driving to, we particularly want to thank our murder of supporters. Nice. Who make this whole thing work by funding it on Patreon. We really appreciate that. We pick three names at random from all our supporters to mispronounce over the course of thanking them,

which this episode includes... Oatray Orangay. Key Ith. Roe. Ben. Ben. Thank you so much to everyone else who's posted on Patreon, everyone who listens and interacts, sends us problems,

sends us solutions and the like. I've been Matt Parker. You've been listening to Beck Hill. Everyone who listens and interacts, sends us problems, sends us solutions and the like. I've been Matt Parker. You've been listening to Beck Hill. And I originally wrote the fun fact about Lauren was going to be that she can recognize human faces. You already brought that up at the beginning. I'm sorry. I had to frantically Google fun facts about crows because I use them all up at this point.

I love you because if that had been me, I would have gone. No, you can't say that. You have to pretend that you didn't say that. No, I know the podcast happens the way the podcast happens. I'd like to thank our producer Lauren who can solve puzzles on par with a toddler. Perfect. Bye. Bye. That's the end of the episode, by the way.

Yeah. I don't know why we're still here. We, yeah. We haven't got anything else to do. We're done. Yep. We've picked cards. haven't got anything else to do. We're done. Yep. We've picked cards. Yeah.

We've eaten twisties. We are a Muppet. We, yep. And. You guessed how many dice were in the jar. Yes. That's all of the things. Do you know that was originally a suggestion?

Someone said. Someone sent in, you should, at the end of the episode, the post-credit little bit, see if Beck can guess how many dice were in that jar that they see in the background of my videos. Did I know this? Has it been that long since we started? It's been that long. I'd forgotten too. I came across it by accident. And I was like, that's why we were doing that. Because I was like, why are we even doing this? That was why. Well, I mean, who knows? Maybe by next episode. We have something else. We'll find out.