A Problem Squared - 019 = Wetness, Trees and Pet Mysteries

Episode Date: May 31, 2021

How did a hamster end up in a listener's apartment on the other side of the world? How many leaves would humans need to photosynthesise all our energy? Plus, an update on Dish Splatters: Why don't plastic things dry in the dishwasher? If you've got a problem or a solution, hit us up on our website www.aproblemsquared.com, or on social media. It's Pudding, on the 'gram For Bec's hamster habitat, look no further. And, welcome to the world of Hamster-tube. Here are some of Bec's favourite hamster moms, Malica and Victoria.   In the Catch Up segment Matt talks about solving a mathematical quandary: whether all nets of the 4D Hypercube can tile 3D space. The answer is yes! Here is the link to that video  

Hello and welcome to A Problem Squared, a podcast where two dorks take problems that very few people have and then provide solutions that even few people use. We're like the unnecessary kitchen gadget of the podcast world. We of course, as always, have Beck Hill, who is the slap chop of the problem solving podcast, where there's a lot more noise and activity and fun than you think the mundane activity would otherwise require. And myself, mathematician Matt Parker, I'm a bit like one of those orange juicing machines with a lever in so much as I enjoy de-juicing things from first principles. What's a slap chop?

What's a slap chop? It's like one of those meme, like it's a real thing, I think, where you put like the thing you want to cut in a cylinder and then there's like several parallel blades above it on like a handle and you like slap it down to chop whatever is underneath it. Does it like dice, chop, slice and grate or something? It's like playing Hungry Hungry Hippos, but you're using that to slice up some kind of kitchen thing. Yeah. Do you know what? I like to think that I would be one of those corkscrew wine bottle openers so that when you move the head up and down, the arms go up and down.

That's what I am. We've got one of those. I refuse to use it. It caught my flesh in at one time when I was using it, and then I had to unwind it to lower my finger back out again. I've held a grudge against a kitchen utensil ever since and I refuse to use it. I like to think that it's like sort of dramatic music and then we zoom in on the head of that little corkscrew. You know how the bottle top opener always looks like a little face? Yep, yep.

I think it would just zoom in so it's like the eyes are looking at you across the kitchen. Oh, you know what? I'll take a photo of it afterwards. But I will say, when you use those things, like the little arms go up like they're going, yay! Yeah, yeah. So. It looked like it was really happy it got you. I know, little jerk. So anyway, coming up on this week's episode.

How did a hamster end up in a listener's apartment on the other side of the world? I work out how many leaves humans would need to photosynthesize all our energy. And we spoke to a chemist about how dishwashers work. Let's get going. Bec, how are you doing this fine month of May? I'm good. I'm good. We're still filming Make Way, Take Way. You've continued to be incredibly busy. Yes, yeah.

But I love it. Good. I got to make a picture out of horse poo the other day, and there was a lightning storm. And not a small quantity of horse manure either. It's not like you got enough to do a canvas with or something. No, it was an entire massive wheelbarrow full of the stuff. One thing I didn't tell you, horse poo, very heavy.

So heavy. Things I didn't know about the manure arts. Yeah, it was quite the workout. You're just flat out all day working on this show. But the end's in sight, right? Yeah, in about a month's time. Still got to go at the time of recording i've still gotta go up to manchester and do about eight days straight recording with some lovely kids up north

and then a few more of our final sort of big makes that we do at the end i get to go to a skate park on monday yeah in Gloucester. I don't want to give away what we're doing, but it's very exciting. You grind the rails? Oh, I'm all about the ollies, Matt. All about the kickflips. Can you do a kickflip? Yeah, there you go. I'm doing one right now.

I'm a little bit exhausted. I mean, the listeners will just have to use their imagination, but I'm kickflipping in the cupboard right as I talk. There we go. Oh, good kickflip. in the cupboard right as I talk. There we go. Oh, good kick flip. Just did a 180. I can do a heel flip. I can't do a heel flip.

Do you know, I wonder how many listeners feel like this as well and do feel free to hit us up on social media at A Problem Squared. Is the only reason that you know any skateboarding terms is because of Tony Hawk Pro Skater? Actually, no, it's watching like Tony Hawk on youtube that's that's pretty much it you're so much cooler than me well which one is cooler actually watching the videos on youtube or playing the video games hard to say i think they tie for dorkiness don't they but the reason i love skateboarding is it's like there there are two pursuits life, two hobbies where you have to use a lot of degrees to define circles and rotations. And it's pretty much mathematics and skateboarding. They're the only two scenarios where you're like, oh yeah, well we'll do a, we can probably do a 540,

but you know, the 720 is going to be a bit of a challenge. Which one am I talking about? And so I find that deeply pleasing that it's the other area where people talk about degrees in a circle. That's true. I bet there's a ton of maths when it comes to velocity and half pipes and everything. Oh, you know it. Yeah. So that's what you'll be doing for Makeaway Takeaway, I believe. Yeah.

I think I'm on a scooter, to be fair. Got a little handlebars. Oh, right. Okay. What about you, Matt? What have you been up to? I just had a crazy run of videos. Like, it just continues. Yeah. What about you, Matt? What have you been up to? I just had a crazy run of videos. Like, it just continues.

Yeah, you've been insanely busy. Too many. Too many YouTube videos. I've been putting out pretty much a video a week, and they've all been ones where I get too excited. Ambitious. Adventurous, yeah. Well, I get an idea for a video, and then I'm like, oh, wouldn't it be funny if i design and print a ridiculous version of the game where there's like 10 000 cards required or or learn to do a perfect card shuffle or something but my recent one i was looking at the ways you

can unfold a four-dimensional cube which i won't into here, but the short version is there's 261 ways that you can unfold a 4D cube, and they all just look like someone has glued eight small cubes together in some kind of arrangement. Sorry, did you say a four-dimensional? A four-dimensional cube, yeah. What's the fourth dimension? Time. Oh, no. Classic physicist physicist no it's uh four spatial dimensions are you including diagonal then yeah yes that's yes you know what pretty much it's

another direction so i'm i'm using four spatial dimensions you'll hear a lot about the fourth dimension being time in physics right and that's because physics come to the maths department and they look around for new tools and techniques that mathematicians have worked out. And then they go apply them to physical situations. And so they have three spatial dimensions where you can move, which are the ones that we live in. And then they add time as the fourth dimension. Whereas mathematicians originally didn't have the fourth one as time. They did it as another spatial direction you can move in,

but one that our brains can't process it. So it's like orthogonal to our reality. You can do the maths around it, but you can't picture it. And one of the ways you can look at a higher dimensional cube is by unfolding it. So we can understand the net. So when you're at school, people do nets of a cube where you cut out six flat 2D squares and you fold them up into a 3D cube. And you can do the same thing in dimension higher. You start with 3D cubes and they fold up into a 4D cube. And who's a net? A net.

They name a lot of mathematical breakthroughs. She's your auntie. Yeah, someone's aunt, an incredible mathematician, counted the number of unfoldings of the hypercube. And just for anyone who's listening who's tempted to switch off because it sounds very confusing, don't worry, I'm confused too. And we'll go back into the less confusing stuff shortly. Yeah.

In the meantime, continue, Matt. To be honest, in my head, I was like, oh, a quick story about how we discovered a thing. And then I started telling it and then realized there's a lot of background involving high dimensional shakes before you get to the fun. People glued dice together to tile all of the unfoldings of the hypercube. And so we had a breakthrough in mathematics. Wow. all of the unfoldings of the hypercube. And so we had a breakthrough in mathematics. And now we know it is possible to tile all 261 nets of a 4D cube. So I apologize if it doesn't make sense. Well, that's all you have to say, Matt.

You know, I should have opened with that. But it doesn't make sense to anyone, by the way. If everyone's confused going, oh, I can't follow that. No one can. So don't worry. But, you know, there's more on YouTube. But we found a thing. Me and hundreds of people just playing around with cubes discovered a new thing in mathematics.

And I will now check if any of them were named Annette, because that would be amazing. I think I've worked out that that's the key, isn't it? What we're doing is we're asking people to send their problems and only two people are trying to solve them. And it seems to be that we should be asking the problems and getting everybody else to solve them. Yes, we got this the wrong way around, but too late to change now. Let's get solving. We have a problem sent in on our problem posing page on a problem squared.com, which says six months ago, I found a hamster in my apartment. Great problem.

They go on to say, none of the neighbors claimed him. They clarify. They don't know if it's definitely a him. And they say, I don't know if it's really a hamster or a mouse with its tail cut off. Wow. Sneaky mouse.

I don't know how old he is, but most importantly, I still have no idea where he came from. I live in Pakistan. We don't have hamsters. Where did he come from? That's all caps followed by two question marks. And that is from Hammy's mom.

They've evidently named the hamster Hammy. Okay, So, Bec, you had a stab at this problem. I did. Yes. I enjoyed every second of it. I actually spoke to Hammy's mom via email to get some clarification. I needed some more details in order to answer it. The first thing I got was a photo and a video of Hammy. And I can confirm, I can answer this part of the problem immediately,

that Hammy is definitely a hamster, not a mouse with its tail cut off. Oh, that's good. And that's just your innate knowledge of hamsters led you to this conclusion. Yes, yes. So for any listeners who have been with us for a while, you might know that I own a hamster, a lovely little Russian dwarf hamster called Pudding. Pudding even has their own section on the show called Pudding Squared, and it's where we ask problems for our listeners' children to solve.

They're all hamster-based challenges for kids. Yes. Yeah. So I was able to have a look at the videos in the image, and it looks to me that Hammy is a short-haired Syrian hamster. Do they come in a long-haired variety? They do. This is like a sub. Oh, okay.

Wow. Yeah. Yeah. You can get them with long hair as well. I mean, it's worth having a look. They look like tiny little mops or like little hairbrushes. It's very, very cute. But Hammy is very cute as well.

Another part of Hammy's mom's problem was that they didn't know if Hammy was a hymn. And I can't fully tell from the images or the video. From my limited knowledge, I believe Hammy's a hymn because it appears that they might have testicles. And that's kind of the main way you can tell the difference. That's a pretty sure sign. Yeah. way you can tell the difference. Pretty sure sign. Yeah.

If you have a look online, you'll see that there's a few videos about gendering hamsters and the sort of biggest giveaway is that the male hamsters tend to have sort of a pronounced, two pronounced lumps just under their tail. It's usually covered by fur, but it is undeniably hamster balls. But if you're not sure, another thing you can do is you can pop your hamster into a clear container and hold it up above you. And then you can get a little bit of a better look. Female hamster usually has nipples. So if they've got nipples, it's probably a female hamster. Obviously you might have a better look to see if they've got

testicles. And there's usually a difference between where their scent gland and where their butthole is. I love the way you're flipping between medical terminology and butthole. Yeah, well, you know, for some reason, butthole sounds less offensive than anus. That's a good point. I wish I hadn't brought it up. Carry on. So I believe that might be Hammy's gender but I have also sent some links to various videos from hamster owner youtubers who I thoroughly recommend in fact I'll pop some links up on Twitter or maybe in the show notes if you have a hamster and you'd like to follow some people who do some good stuff online so Hammy's mom is happy with that part of the answer and the other thing they said is they

don't know how old he is Now that is a tricky one because hamsters aren't like trees You can't just cut them in half and count the rings You can do some of that It's not going to help work out how old they are I wouldn't advise it With hamsters the general lifespan tends to be about two years Which is sad because they're such sweet creatures

But it does mean that you know that he's probably not more than two years. Oh, you've put an upper bound on it. That's a good point. There's a range. Yep. Hammy's somewhere. And they found Hammy six months beforehand and was running around and stuff. So I would say that Hammy is somewhere between seven months and two years old.

So what you're saying is wait until hammy dies of natural causes, and then you can work backwards to work out how old they were when they were first found. Yeah, exactly. Got it. Got it. That makes sense. Now, this is great, Bec, and I think you've solved some of the more practical problems of unexpected hamster ownership. But I think a lot of us, the intriguing part of the problem, the all caps in the question backs this up. Where did this hamster come from? How did it appear in a house in Pakistan? Yeah. And this bit I found very fun because

as Hammy's mom said in the problem, I live in Pakistan, we don't have hamsters. Now you and I are from Australia, Matt. Correct. And we don't have hamsters in Australia either. We do not. They're very strict about their fauna and fauna. They were deemed too dangerous for Australia, which is quite a high bar. So the first thing I wanted to check was whether it was the same sort of rule where hamsters were actually illegal in Pakistan, like if Hammy had been illegally smuggled. Because illegally smuggled animals are not cheap so it would be really strange if a hamster showed up because that means that someone who's probably paid a lot of money for one has lost it

and you'd think that if you paid a lot of money for a hamster you would yeah but you also want you wouldn't want to blow your cover you can can't put up posters saying, hey, I own this illegal animal. Please bring back my illegal contraband. That sort of occurred to me, actually, because they said that none of my, they said none of their neighbors claimed it. You might put up a sign saying, I lost my mouse without a tail. If anyone's seen my mouse without a tail, let me know. Yeah, exactly. So I had a quick look. If anyone's seen my mouse without a tail, let me know.

Yeah, exactly. So I had a quick look. It doesn't look like they're illegal in Pakistan. I could be wrong if you do know, let us know. But from what I could see, they're not actually illegal. They're just not sort of common. There are hamster breeders online. I found a few sites where you can buy a hamster in various cities in Pakistan. I hope Pudding didn't catch you Googling how to buy another hamster. I mean, I would feel

very uncertain in my role as the house hamster if you're secretly looking up other international hamsters. It's like having a secret wife in another town. You've got another hamster family in a different country. Well, I like to think that Hammy and Pudding will become pen pals now. They should send each other postcards. That feels plausible. And in fact, I did find some breeders that were in the same city

that our listener is from. So it is quite likely that Hammy was someone's pet. How much does a hamster run you in this part of Pakistan? So they're about the same price they would cost from a pet shop in the UK, which is over here around about 10 pounds. Oh, okay. A little bit more expensive in the city that our listeners from, but not so expensive that, you know,

you'd be putting up reward posters if they went missing. Obviously there's the emotional cost and investment. Yes, that's what I was about to say. Obviously someone might be heartbroken. Another clue, though, was that apparently Hammy wasn't in the best condition. Sometimes their fur is quite rough. They could be quite antisocial. Basically, weren't exhibiting that they were a particularly happy hamster when they arrived.

Okay. It's most likely that their original owner wasn't taking great care of them. Or they've been on the streets for a while. Yeah. So one thing is it could have been a neighbor's hamster. They decided they didn't want it anymore, didn't care, let it go, which is obviously why they never claimed it. But as you say, they could have been on the streets for a while. And if you've listened to the show before, you may have heard me talking about the fact that hamsters can run up to nine kilometers a night. It's amazing. I love that stat for two reasons. You both realize how far a hamster can move, which is amazing. And you learn that hamsters use the metric system.

Yes, indeed. Exactly. One of the many great things about hamsters. I agree. I agree. So it's quite possible that hammy has come from a neighborhood nine kilometers away. And that's only if it was in one night. It could have been from even further away for several nights. Now, the listener did tell me that they live in quite a built up area of the city and they didn't think it was likely that a hamster would have survived trying to travel nine kilometers in

it but hamsters are nocturnal so there wouldn't be as much traffic or footfall probably their biggest predators are going to be other animals okay so they could have traveled a decent distance at night yeah and hamsters very very good climbers so our listener is in an apartment block and again wasn't sure how how many had gotten up to their apartment block. They're really good at climbing and they're really bendy. Hamsters are borrowers, so they're very used to getting into really tight spaces and bending around things. Their mouths are incredibly stretchy, so you might see them stuff their pouches in their mouths and then go to sort of bury it somewhere. So they're used to working around tight corners and small things. So it is completely possible that a hamster may have managed to crawl up a

drain pipe or in between the wall cavity or something like that. And did they find this hamster just actually in their apartment? It's not like they opened the door and it was on the doorstep. Like one day it was just wandering around their flat. Yeah, yeah, that's exactly it. Hammy just appeared. Hammy adopted them and Hammy seems much, much happier now. And if you find a hamster, a couple of facts that you should know. They need a lot of space. Most pet shops sell cages that are far too small, even the ones that are marked large. A hamster needs a cage that is sort of minimum recommendations are 75 centimeters by 30 or 40 centimeters.

They need a lot of unbroken floor space because, as I mentioned, they like to run. And because they're climbers, it's best not to give them something that's completely covered in bars, especially if it's tall. Because what they tend to do is they'll climb up the bars and they'll use them as monkey bars. And it is incredibly cute. But more often than not, they tend to slip and break their backs, which is really sad. That's not the direction I thought this cute hamster on the monkey bar story was going. But that's good warning. Yeah. Yeah.

So if anyone wants a cost effective solution, you can get one of those really, really big plastic multi-purpose bins, you know, the big storage containers. Oh yeah, like a box that's really useful and big. Yes, yes. Cut some holes in and attach some wire mesh for ventilation. Obviously, you want to make sure that the edges aren't too sharp or anything like that. You can swap the lid over for some mesh as well. Another thing you can do, which is slightly more pricey, but still a lot cheaper than other options, is to buy a Detolf display cabinet from Ikea and lie it on its side. They're like the glass display cabinets, right?

Yeah. Yep. Yep. There's some beautiful ones out there I'd definitely recommend. There's some good hamster porn. And I mean that in the sense of setting up its habitat and not hamsters breeding yeah so I was able to send our listener all of that information including my theories as to where hammy may have came from how hammy might have ended up there how old hammy might roughly be and what gender hammy might be as well. One thing I did like was that

our listener did suggest that hammy might be a jinn. And what's a jinn? Well, I'd heard of them before, but I am going to quote from Wikipedia because I want to make sure I get the word incorrect. In general, a jinn is a supernatural creature from early pre-Islamic Arabian and later Islamic mythology and theology. So they're sort of these little spirits, sometimes they're sort of demonic. The way that a friend of mine had once told me was that they're sort of mischievous spirits. Like a hamster? Yeah. So that is the other option. Maybe Hammy isn't a hamster after all. So you've answered the additional problem of they've now got a hamster to look after.

You've solved that problem for them with your sage hamster advice. But in terms of their specific problems, as put in the problem posing page on a problemsquared.com, you've narrowed it down to when they found Hammy, they were between zero and two years old. They've got between zero and two testicles and they traveled between zero and nine kilometers. That's where they came from, that kind of travel distance. So, I mean, yeah, I can say with absolute confidence that you deserve between zero and one dings. Definitely in that range for your excellent problem solving on this one. Well, thank you, Matt.

The listener has actually given me a full ding. I'll have you know. Oh, okay. Well, that was in my range. I allowed for that. It was. There you are. One ding.

And all of that has inspired me to bring on a new, a pudding squared. So for any listeners out there with children, this is a problem for you to pose them from my hamster pudding. The pudding's cage is 36 inches by 17 inches. 91.44 centimetres by 43.18 centimetres. Yeah. Just putting that out there. I thought I'd mix it up with some inches because we used centimetres last time.

No, you're right. It's a good point. I mean, we've established hamsters metric, but for the purposes of a pudding squared, we will go imperial. I'll be interested to see if you can keep up with the conversion rates. I undoubtedly cannot. Carry on. Hamsters should have a minimum of six inches of bedding so that they can burrow.

15.24 centimeters. And one bag of bedding that I currently buy is 49.2 liters. You don't really need to know that. I just thought it'd be interesting to say that. The bag says that that equals 3,000 cubic inches. And finally, a hamster's cage should always have a minimum of six inches of bedding. That's because they burrow so much. So if you've got a hamster at home and you can't fit six inches of bedding in their cage, their cages are too small. Get them a bigger one. So that's the depth. The depth of the bedding has to be 15.24 centimetres.

That's right. Yeah. The depth of the bedding is to be what you said. Six inches. Yeah. My question is how many bags or what proportion of a bag of bedding is needed to provide pudding with six inches deep of bedding. That is the problem for you to pass on to your children. We'll pop it up in the show notes as well and on social media.

We love to see working as well. Obviously, Dexter was the child who answered the last pudding squared problem. We got to see all the working out on their whiteboard. They did a great job. In fact, they beat all of the adults who decided to try and answer the question as well and got it wrong. We should make it very clear. This Pudding Square Challenge is open to all listeners with children

and all listeners who are prepared to pretend to be a child. Actually, you know what I say, Matt? If you're a listener who desperately wants to solve this problem and you're like, I'm not a kid and I don't have access to children, but I want to be involved. I'm going to say you're welcome to, but you have to show you're working out as if you're a child. I want to see wonky writing. I want to see it, you know, in crayon or chalk on the sidewalk.

Yeah. I want stick figures. Absolutely. And a nice heading. Yeah. Love it. Yeah. I'll allow it for that. Our next problem is from at mvpetri, or Petri, depending on how you pronounce it, from Twitter. It's one of our older problems before we had the problem posting page. And it says, if humans were able to grow trunks and leaves to use photosynthesis to

harness energy from the sun how big would our human leafy crown have to be to sustain our daily energy expenditure i mean great problem right there i mean to start with we kind of do this already because plants take the energy from the sun the light they turn it into chemical energy and then we either eat the plants or another in between animal eats the plants and then we eat that animal or someone right so all of our energy does come via photosynthesis the question i think what we're getting here is what if we skip out the middle steps yeah you know what if we just had the leaves and so I thought I would just work out what area of leaf would be required for me to get all my energy from just those leaves producing I don't know I don't want to get into the biology here because biology is a mess,

but produce whatever the substances are that the rest of my body can then burn as fuel. So we know how much energy I need, two and a half thousand calories a day, or technically Kcal, which is kilocalories. Very confusingly, people say calories, but the calories that you see on food are actually thousands of calories. So it's either 2.5 million calories or 2,500 calories. Each calorie, which is a calorie is like the amount of energy to heat water or something. I looked it up. It's just, it's 4,184 joules, the correct units for measuring energy. So I was able to work out that you need, so it's 2,500 calories times 4,184 joules each. That is 10,460,000 joules. And actually, I thought I'd switch that to be power. So instead of just straight up amount of energy, I'd switch that to be power.

So instead of just straight up amount of energy, power is energy over time. So it's like the amount of energy per second or hour or something. We measure that in watts. Oh, yeah, yeah. Yeah. It's actually, that's going to make our life a bit easier when we start looking at what leaves can do. And it's a bit counterintuitive to think of plants in terms of watts,

in terms of like energy they're producing, in terms of energy they're producing. But that's what they're doing. They get light from the sun and then they're producing an amount of wattage. And so as humans, we run at around about 121 watts. So that's my energy requirements. So a bit more than like an old school 100 watt incandescent bulb. That's roughly a human. So there you are.

And obviously I'm going off my calorie intake. Other people might need fewer. So I know my wife Lucy, about 2,000 calories a day, give or take. I'm about 2,500, give or take. You can work this out for yourself. I'm doing it for me. So the next question is, how many leaves do you need to get that much energy? And the leaves convert energy from the sun, because I want to work out per area of leaf, we need to work out the amount of solar energy per, let's say, meter squared.

And actually, my wife, Lucy, who's a solar physicist, was chatting to me when I was working on this. I was like, oh, I'm going to work out the energy from the sun. And she's like, oh, you can do that because you get the luminosity of the sun, and you can calculate that from the first principles of the sun. And then you work out for a shell with the radius is the distance to the earth. And then you work out the proportion of the cross section of the earth from the shell. I'm like the earth, and then you work out the proportion of the cross-section of the earth from the shell. I'm like, yeah, you could do that.

Or you can look it up on the NASA website, and it's 1,360 watts per square meter. And she's like, yeah, if you do it her way, you get 1.3 kilowatts, which is the same. So there you are. My wife would have done this much more thoroughly. I looked it up. I've just realized that Lucy is the mat to your back.

It's so true. That's the way that works. My wife consistently out nerds me, but that's why she's the smart half of this relationship, let's be honest. So I, however, I still did some work. I did the conversion from, that's just the energy from the sun coming straight at us, but the surface of the earth is curved. And if you're on a part of the earth that's curved away from the sun, the light that's hitting you is more spread out. So you're getting less energy per area. And the answer would change actually, depending on your latitude. So I just took the average, did the average of the whole latitude. So I just took the average of the whole earth. So I worked out the surface area of the hemisphere facing the sun.

And then I worked out the cross-sectional area, the amount of light. And it's because of the way the equations work, it's a quarter. it's a quarter so it's actually you average 340 watts per square meter of energy from the sun on the surface of the earth okay it won't be that exactly for anyone but that's the average i don't want to grow the leaves for one location and then not work somewhere else i'd rather on average feel sated um from my leaf uh then you got to work out how much of the energy makes it through the atmosphere. Because I was going to say, square meter actually is less than I expected. Oh yeah. No, no, no. It's not going to be enough, it turns out. There's two more factors,

because it sounds like not that many leaves. We've got one issue, which is how much of that light makes it through the atmosphere. So again, looked up the NASA website. Hey, they're bright people over there at NASA. I mean, my wife has literally worked for NASA. So that's, you know, story checks out. 29% of the energy is reflected off the atmosphere. 23% of the energy is absorbed by the atmosphere. And they're things like clouds.

Wait, is that at the same time or is that like at each, you end up with? Yeah, at the same time. Yeah. Love it. Yes, no, of the full 100%, 29 goes reflected, 23 gets absorbed. So that's at once, not one after the other.

Yay, doing a Dexter. Oh, and this is also, this factors in cloud cover and stuff. This is reflection from clouds and whatnot. So people are like, oh, but what about cloudy days? Factored in. 48% of it hits the ground. So we get about half of that energy actually makes it to the ground where your leaves would be.

And then leaves, not that efficient. They don't convert all of the energy into food or into something that your body can burn. Dumb leaves. I know. Useless leaves. So for reference, if you just had a solar panel, like you just want to generate electricity, that runs at about 10% efficiency or take and i believe the theoretical maximum is like 25 percent well that's you know without some advancement in technology that's about as much energy as we can capture based on our current method wow now here's the question plants better or worse than a solar panel turns out plants worse oh worse. They run about, and again, hard to get an exact number,

biology, sort yourself out, 5% or 6% efficiency, depending on what specific chain of reactions a plant's using in its photosynthesis path. A lot of plants are different, hey? Plants are different. And also they've got other priorities because different ways of doing it can make a difference to other nutrients that the plants have available. There's other evolutionary pressures on the chemical reactions involved

in the photosynthesis process. I've gone with the figure of 5% efficiency, which means your leaf is running at about 8.1 watts per meter squared. Oh my. And we need 121 watts. Well, I need 121 watts. Yeah. So that means I need on the order of 15 square meters. I worked out exactly like 14.836 square meters. This is probably not a hard and fast rule, but roughly it's a square twice as big as your height. Yeah. So imagine lying down twice in both directions, that kind of square size, which is a lot. The issue here becomes, though, as our problem poser said, you're going to need some kind of trunk to support all this, some kind of scaffolding to hold all these leaves up. That's going to be heavy.

And that's going to be a lot of energy requirement to move around. You're definitely, like if you were like an athlete you'd easily use twice if not more calories like i know people have gone for bike rides and the bike ride alone is like a 10 000 calorie bike ride so you can you can burn a lot of energy if you've got to do a lot of movement or you've got to carry a lot of mass. And so I think if you had to carry around a big enough trunk or something to support those leaves, you'd easily double your calorie requirements. So you're going to have to have twice as much. You're going to have to carry even more around. But then you end up with more leaves, which means you need a bigger trunk. Which means you've got to carry more mass. It's almost like this is why trees don't walk

around. Exactly. You got it in one. This is why ants are rubbish. So not only does this explain why trees can't walk, it also shows why if you've got solar panels, you put them on a solar farm or you put them on the roof of your house, you don't just carry them around with you. Because there's a thing called the rocket equation, which is the same problem for rockets.

You need more fuel to lift more rocket, but now the fuel's heavier, so you need more fuel to lift that fuel. There is a solution to that where eventually you can make it work. I've not run the numbers on how much energy you would need to carry, because I don't know how much the trunk would weigh, but I'm pretty sure it's not going to work you're never going to get enough energy to carry the amount of mass required to get the energy like it's just not going to work so you're right this is why trees can't walk and this is why we eat plants right they stay still we wander around and then we eat them so you are we had a ridiculous problem about how many leaves to get your energy supply. And we managed to prove that Ent's walking trees are ridiculous. What a flight of fantasy that is. I am very impressed with that, Matt.

You've gone to so much effort to then realize that it's not possible. Can't be done. So I'm going to ding that. I'm a happy man when I solve a problem by proving it can't work. Ding. In our Any Other Business department, we have occasional updates to previous problems, which may not have been satisfactorily solved. And we had one such problem from episode 008. I think actually this was a WhatsApp message from someone I know to me saying that when they open their dishwasher, they're always confused as to why some things are dry, like the bowls, and other things have droplets of water all over them, like Tupperware or plastic things.

Oh, yeah. And do you remember I had an unsatisfactory answer where I basically said, I think it's the amount of energy, the heat energy stored in the different objects. And because there's more heat stored in the bowls, they dry, whereas the plastic hasn't got enough energy to dry itself. Where my theory was that it had something to do

with the texture of the surface and the curvature of the surface as well. And it turns out I think you were closer to the truth, Bec. Yes. Yeah. This is going to be a ding for Bec, I feel. That's all I ever wanted. Hang on, hang on.

Let's just go through the motions before we get too excited. I was this close to quitting the podcast, ending on a high. I'm out. I like to announce my retirement in the problem-solving game. No, no. So we located someone who knew what was going on and we had to find a professor of inorganic chemistry. We found Professor Andrea Seller at UCL, who we both worked with before.

Yeah, he's great. So Andrea is a great chemist. You've done shows with Andrea involving chemistry chemistry and christmas yeah it was a christmas uh what non-panto and i got to set fire to my hands nothing more christmassy than that and i've done i did a show with him about sulfur once so there you go i think i named it like sulfur so good or something ridiculous i thought you said salsa, and I was like, as in the music? No, the condiment or the dance. No, no, it was sulfur.

So we dropped Andrea a line, and they both recorded an answer, and they sent us some homework. But we'll start with an interesting curveball they've thrown into the mix. Hey, Matt. I thought I'd try and answer this question about the dishwasher. Why is the plastic wet while the others are dry? And it's an interesting question. And it all comes down to what you mean by wetting.

Because interestingly, to a chemist, the plastic is dry while the ceramics are actually wet. What? We had it the wrong way around. So the problem posed by Laura going, oh, the ceramics dry, but the plastic doesn't. No. Professor of inorganic chemistry has set the record straight. Technically, the ceramics are the things that are wet

and the plastic is dry. Wait. And yeah. I know. I know. And so to try and help us get our non-chemistry heads around this, Andrea sent us some homework where we had to go and put drops of water on different surfaces of things in the kitchen

and then have a look at the angle the water forms with the surface. So, Bec, what did you do? So, I took a photo of a drop of water on the glass stove top, you know, where you put the glass down over to protect the gas grill. Yeah. Like the lower, like the lid down on top of the stove. So I did a drop on there. I did a drop on my kitchen tiles and I did a drop on top of an upside down plastic container

that I would put like. Oh, I did like a lid. I got like a lid of a Tupperware container and the water on the lid for me I've got a photo of this we'll put all these photos up on social media so you can check them out yeah at a problem squared on Instagram and Twitter at a problem squared on everything um I reckon about 45 degrees give or take angle on the edge of the drop but it definitely formed a noticeable drop on the tupperware i also did like a ceramic plate and that one was pretty pretty flat

like 10 or 20 degrees it spread right out got a photo of that oh in all the photos i'm pointing at the droplet that's not just because i like pointing at things in photos, which is true. It's because for a lot of them, I couldn't get my phone camera to focus on the drop because it was so flat. And so my finger is there to give a focus distance for the camera. I actually learned how to use my phone's manual focus option to take these photos. Oh, that's also a solution uh i found glass was pretty flat that was maybe like another 10 degrees and uh i metal i was surprised i thought metal would spread right out that for me was up 45 50 degrees yeah on cutlery and that that that

does kind of match because i do get water beading on some of the cutlery i've got like bead marks on them and i did like a non-stick frying pan and the non-stick pan that's probably the biggest angle that's probably up i mean i didn't measure this with a protractor i do apologize i did it by eye maybe 60 degrees on my nonstick pan. I don't know if that means I need to get a new nonstick pan or not, but that was definitely the tightest bead. Yeah, right. I had really similar findings as well. So my glass stovetop was pretty flat. The kitchen tiles, pretty flat. I haven't done degrees. I'll let the listeners decide from when they see the pictures on social media. And the plastic container, similar to you, I remember that much stronger beating.

So what we have are surfaces which are either hydrophobic, so they repel water and we get quite a tight droplet. Or we've got surfaces which are hydrophilic which like water and so the water spreads out oh so with the frying pan i think it's the non-stick frying pan that made this start to make sense for me about something being dry and something being wet because obviously non-stick frying pan the whole idea is that it yeah yeah, as you say, it repels stuff. So if it's repelling water, then the drop isn't like touching it. So it's. Yeah.

The water is not on the surface. It's clumped together into a droplet. Yeah. So the dishes are wet, but it's just so fine that we don't pick it up on our fingers. I think, I think you've cracked, you've got it in one, Beck. In terms of which things have different beading of the water, there's three factors that change how much the water beads. There's the forces within like the surface tension.

So that's how much the molecules are trying to cling to each other. You've then got the interaction of the liquid and the air around it which actually doesn't make a big difference but technically that's in the mix and then finally you've got the forces between the water and the actual surface of the dish or the cutlery or whatever it is and it's all they're electrostatic forces so these are the intermolecular forces. Does the water want to cling to itself and minimize its energy like that way? And that's the surface tension as we know it. Or is the water drawn more to the surface

of whatever the dish or cutlery or Tupperware it's on? And it's the balance between those two forces, which means the water either beads or it spreads out. Or as a professor of inorganic chemistry put it. So let's get back to wetting. So what wetting really means is that the water interacts very strongly with the surface and therefore tends to spread out. And the surface structure is key. So with the glass, if you clean the surface really carefully, then you end up with a surface which is covered in OH groups. And that means that the water can really get purchased. It can really adhere to the surface. And so the droplets just spread out to form an invisible film. And the secret to a hydrophilic surface is having those OH groups, which is a common feature of ceramics, of metal oxides.

And so what you're talking about here is an invisible layer. So actually, the stuff that's coming out of the dishwasher is completely wet, but you don't see it, right? is completely wet, but you don't see it, right? Now, on the other hand, Tupperware that you've put into your dishwasher is made of polyethylene or polypropylene, and the surface consists of CH bonds. And CH bonds just don't have that charge difference. And that's part of the reason why oil and water don't mix. So when you open your dishwasher, the water on the ceramics is thinly spread out so you don't even see it. And because the big surface area, right, it evaporates really quickly. On the other hand, the Tupperware, right, causes the water to form little droplets. And because of their smaller surface area, right, they know, they evaporate much more slowly.

So there you are, Bec. You are completely correct. It's what the surface is. And you're right, it's wet, but it's an invisible film of water and then it evaporates. So that means if you do the dishes and then you put them in the drying rack and there's all beads of water on them, if someone someone says can you dry those dishes for me you can be like actually i think you'll find that they're already very dry uh allow me to uh play some supporting evidence from a professor of inorganic chemistry yeah and when in fact i'm going to go one step further this probably means that when you dry dishes with a tea towel you're not drying them you're wetting the tea towel whoa that's deep you're you're a professor of inorganic uh

mind-blowingness well i think that uh laura from episode eight whoa 11 episodes ago we got it within a year come on they must they must give that a ding. I think so. I'm going to give us a ding, I think. And the fact that you called it. There you are. A ding to Beck. And that brings us to the end of another episode of A Problem Squared. Thank you so much for listening. If you enjoyed it, please tell your friends. We're at A Problem Squared on social media, so make sure you tag us in. Or you could leave us a nice review on whatever the thing is that you'd listen to us on.

Yeah, we love having listeners and we like having new ones. Hello if you're a new listener as well. And thanks for sticking with us if you're an older listener listener and huge thanks to all of our patreon supporters who i mean sharing this is super important but um also thank you to those who support us financially and mean that we can do this and we're going to mix it up slightly because we've got two tiers of patreon supporters and we used to have a exclusive bonus episode just for the i'm a wizard tier supporters called i'm a wizard we've decided it's a bit of a shame to not make that more widely available so we're now going to make the i'm a wizard bonus feature available to everyone who supports us on patreon so So any of our Patreon supporters.

And you know what? We will unlock the previous episodes. I think we've been doing it for about a year now. So there's on the order of 12 or so. So we'll make them all, the back catalogue available. And Beck, how would you describe I'm a Wizard in one sentence? All of the things that are too ridiculous to put on a problem squared. That's not far off.

Yes. Maybe you're right. We should manage expectations. I'm saying bonus episode. It's us warming up before the actual recording, but it's good fun. And if you do find yourself missing us between episodes and your Patreon supporter, that means that you've got all 12 of those to get you through. You could listen to three a week. There you go.

And then you'd have the next episode of Problem Squared. And this does leave our wizard level supporters high and dry without their own extra feature. So we're keen to hear from the people who go above and beyond to make this podcast possible, what you would like. where, you know, the Patreon has always been a collaborative effort with people saying what they'd like us to do on there. So we're going to start a forum on there where if you're a wizard level supporter, you can tell us open brackets, no promises, close brackets,

what you would like to see as an extra perk for making this whole thing happen. Bye. Bye. Bec, just before we go. Yes. Is this your card? No. Oh, come on.

One day. One day.