A Problem Squared - 060 = Cables Coiled and Water World

Episode Date: May 22, 2023

In this episode...   🎧 How do you stop the wires on headphones from twisting?   🏊🏽‍♀️ If the Earth was a smooth sphere, how much water would sit on it's surface?   🛎 Get ready for some dings!   💼 And the business briefcase is open.   If you'd like to find out exactly why our pockets twist up our wires, follow this link: https://www.independent.co.uk/news/science/why-do-your-earphones-get-tangled-in-your-pocket-science-has-the-answer-9548540.html   For more on the spontaneous knotting of an agitated string, look no further: https://www.pnas.org/doi/full/10.1073/pnas.0611320104#sec-2   To really comprehend the over under technique you have to see it, and even then it's tricky. You can attempt to find out how to do that, here: https://www.youtube.com/watch?v=QwMJHMSmjVY   The Merch Competition is ongoing, so send in your sizes for those T-Shirts! And phone it in if you want THE HAT! Put your down preferences HERE: bit.ly/APSgiveaway   If you'd like to find out which Muppet you are, you can speed ahead of Matt and Bec and find that out here: https://www.buzzfeed.com/jenlewis/which-muppet-are-you.   As always send your problems and solutions to our website: aproblemsquared.com.   And, finally, if you want EVEN MORE from A Problem Squared, find us on Twitter, Instagram or Patreon.  

Hello and welcome to our podcast, A Shroblam Pwed, where, did I say prob? Sorry, sorry. That's very unprofessional. A prob, a problem squared. Sorry. It's normally a more professional codpast pod, it's normally a more professional podcast than that. I apologize. This is a podcast where we polve soblems with my ho-coast, Heck Bill.

She's a canned up comedian and children's author. I'm not doing that one. And I am Pat Marker, a mascot. You're in too deep, Matt. I'm in too deep. I know. I thought this would be funny. And then I'm like, I don't know if I'm over or under doing this.

I suspect it's over. Intro over. I regretted that immensely. On S episode. I'll untangle a particularly naughty situation for one of our listeners. I run the numbers on Waterworld. And we'll have some any other business. I could try and say that in a weird way like Matt, but I'm not going to.

Well, we're just different levels of dedicated. Or different levels of dedicated. If you swap the letters around. Whoa. Well done. Yeah, Del won. I'm Sealy Rory. That sounds awful.

That's the worst. So, Bec, how have you been? I've been better. Oh. As you know, I've been better. Oh. As you know, I've been trying to get fit. Yes. I've talked about trying to get into a regular exercising routine quite a lot.

You've spoken a lot about the correlation of pain to gain. For a few weeks, I kept getting on and off ill. So I decided just to stop because every time I started working out and stuff, I'd get sick again. And I think I just wasn't letting my body fully get better before I jumped back into it. And then what happened is what I thought might happen by doing that is that then I just didn't exercise for a very long time. I'm in a similar lull. Well, don't do what I did, which is to jump into it headfirst. Oh, that sounds like what I'm going to do. Yes, yes, yes.

So the other week I did full workout on a Wednesday, full workout on a Thursday. Already super sore and tired because hadn't done it in like over a month. Then on the Friday, I had a meeting in town at 9am. So I walked into town and then back out not not too bad from where I am but then I decided to walk to the next thing I had which was a five-hour rock climbing course oh I mean which I did and then I walked home after that and then the next day I booked myself a gymnastics class then a a break for lunch, followed by a wrestling class. You go, it's all or nothing from zero to one.

Over those two days, I not only did those things, but also walked the equivalent of 23 miles, which means that in two days I almost did a marathon. The cheeky marathon. Yeah. Yeah. Haven't done any sort of workout since. That's what you want. You want nothing, nothing, nothing, nothing, spike, everything, and then nothing again. That's... Yeah, yeah. That's what they mean by warm up and cool down.

Yeah. It was too hard too soon. Yes, yes. How about you? Good. Well, I'm living the Aussie life. How about you? Good. Well, I'm living the Aussie life. Keeping it real in Australia. I mean, my lull was just that my bike was stolen. I haven't got a new bike yet.

And I thought, because I've ordered a new bike. Also, I should say, I went, because it's old news that your bike got stolen. Old news. Oh, geez, my bike got stolen. This is not, it's fine. The new bike should have happened by now. The new bike will be, is being assembled as we speak. Ah. But when I went in to order the new bike, they're like, oh, we can get this, you know, to you.

And then they named a date. It was pretty much right after I was planning to leave to go to Australia. There's no rush. I'll get it when I get back. And I just thought, same as you, I'm like, you know what? Maybe just a bit of a rest for a while. Take it easy. I'm worried. I'm just taking it too easy. I did go for one swim. We had some friends from America staying. They wanted to go for a swim. I like to get in the ocean at least once whenever

I'm back. It's technically the end of swimming season on the beach. And so I braved a single, single swim in the seaweed and dumping, dumping waves. But, but actually I have a tiny update. I have an undies update. Not a big one. Can I just say that you talking about it being too cold to go in the sea and that you have a tiny undies update is maybe my favorite. That was occurring to me as I was saying it.

And I was like, Beck is too professional to point that out. And so for people who missed it previously, last time I was in Australia, I bought a two pack of underwear that came with a security tag, holding them together. And it's the kind where if you smash it, ink goes everywhere. And we tried to open it with a very powerful magnet because we figured that was how it should be done. I went back to the same shop. I went back to Big W and I went in and I bought another identical pair of the same underwear,

same two pack. I made sure it had the same security tag on it so i could then take it to the checkout and see how they removed the tag and it turns out they've got a whole device so yeah and it's like of course they do what did you think they did just took it off with their teeth i've seen them before like hold it in a divot in like the the counter like there's a magnet or something that does it or like a clampy thing. They turned around so I could not see what they were doing, walked across to another

bench and inserted it into this device built into the bench. So hang on. So you didn't take the ones that you have with the security tag still on them to them to take off with the big machine? No. I bought new ones to get information about how to remove the tag. I could take... What are you saying?

I just go back with the other one? Yeah. Actually, now I say it out loud. Actually, now I say it out loud, I've now got a receipt for a pair of underwear that matches the description of the ones with the security tag. Yeah. Oh, that's easy. I'll take them back. The fact that you took your undies back to Australia.

I did. I brought them back with me, yes. I think that's the best way to get the tag removed. Like, that's the most amount of effort. You say you went back for the solar eclipse. I say you went back to get your undies unstapled. It's not unrelated. So, well, I mean, I have a photograph of the device they used. Matt, you would have looked so dodged.

I look so suspicious. Like, unimaginably suspicious. But I managed to get, and I've zoomed in and cropped out a shot of the device. No! You can't share it because you're teaching people

how to shoplift. No, it's like lockpicking. It's an academic pursuit. No, if you're saying it's like lockpicking it's like lock picking. It's an academic pursuit. No, if you're saying it's like lock picking, it's like you specifically worked out the lock that this shop uses and now you're letting people know how to create their own key for that shop. See, the problem is you're right. You're right.

I could go in there now with the undies and the receipt and then they would take off the tag, but I still would not know how that tag works. What's the shop? Big W at the Caranup Shopping Center. I had a friend that worked at Big W for years. No. Yeah.

I wonder if he would. You've been holding out of it. They might have changed the system. How about, how about we have a deal here, Beck? I will not distribute my research into what this device may be. I will not put that in a public forum, but I will give it to you. You can pass it on to your friend and we'll see if either of them can give me some additional insight into how this mechanism works. Done.

Right. And failing that, I will just take the undies back with the new receipt. I won't go undercover. Can we get on with the show now? Undercover underwear. No. Okay. Sure. Let's do it.. Get on with the show now. Undercover underwear. No. Okay. Sure.

Let's do it. Undie cover. Undie cover. That's it. First problem is sent in by someone named Jekka. And they say that the wire on their headphones constantly twists and coils on itself, despite them putting it on and off in a normal and they claim non-twisty fashion so they want to know are they inadvertently adding half a twist

on each headphone removal or is there some other cause and i guess more pragmatically how can they avoid the twists and preserve the life of their wire i guess i guess that they're assuming the twists are wearing it out because they do point out that it is looking increasingly threadbare. So that is Jacker's problem, and they have preemptively thanked you for your help, Bec. Well, I was drawn to this one because I used to get through headphone leads so fast, so fast.

And until I discovered there was a brand, their headphone leads not only became less tangled, but also didn't get threadbare or anything too quickly as well. And I figured it had something to do with the cover of the wire, but I never really thought about it. So in one sense, that's your advice. Yeah. Yeah. I think we may have talked about this on a previous episode, but I briefly did a sound

engineering course when I was in high school, of which I remember very little. But the one thing that I came away from that course having learned was the correct and incorrect way of coiling a lead. There's a lot of, a lot of debate. I know you and I have talked about this ourselves. We have. So the incorrect way is when you twist the cord just around, like you loop it around and around as you would.

I don't do that. I'd like everyone to know I don't do that. But the correct way amongst sound industry folk is to do the over-under loop. I don't do that either. So you sort of loop and then you kind of do a reverse loop and it's very hard to explain, but if you look up over and under loop. I do consistent twists. So it all stacks.

Yeah. That's exactly what I said for the first one. The incorrect one. Yeah. Well, no, you were just like, oh, wrap it all up. It's not all wrapped up. It's very systematically twisted. No, it's still looping it.

Look at that. I wanted to go on the record that our sound engineer slash producer, Lauren, nodded when I said that's exactly what I said for the first one. No, you described it in very disparaging terms. It made it sound like. Yeah, because it's still wrong i was doing like this kind of rubbish i'm doing the thing where you loop it around your whole arm or you know what you're essentially doing the same thing matthew i'm not look at it look at it so what matt is

doing for the listeners at home is that he is looping it in the same direction but he's going on either side of the first loop and that was not that's meant. I will go with, um, I will go with producer Lauren's final opinion on this, but it is my naive understanding that if you do it the alternate method way and one end ends up passing through the coil by accident, when you throw it out, it just, you get a series of knots, like the whole thing tangles. And then this way, the reason you do that isn't so that you can go and throw it across and it unravels easily that's not really the point of doing again i feel like i feel like you're saying it in disparaging way but carry on

well first of all you don't want to throw your leads around anyway if they could the second one is that when you do it that way, you're inverting the first loop. So you're undoing the first twist so that when it's uncoiled, it doesn't start to naturally coil itself back up. You're not sort of twisting it in the same direction the whole time. Yeah, because what I'm doing is this is progressively gaining twist. Yeah. And so while you've got a lovely, neat loop there, yours will eventually twist and get more and more twisted over time. But also when, when you call it up the next time, you've got to like feel it and like speak to it and you go, uh-huh. And you got to, you got to,

it's now got a coil, a way it wants to coil. I know because you've twisted it. And what you have to understand as well. I'm trying to sell that as a feature. We're both using charging cables because they are the easiest ones to us. But if you were working with a headphone lead, cable leads tend to be a bit more stiff. Yes. Headphone leads, you don't want them to be too stiff because you're moving around a lot. Your head moves a lot. And so something that is smaller and thinner and goes into pockets and stuff a lot more, if you're looping it that first way, you're doing it a lot more. Right. That said, the over and under technique is not handy if you're taking your headphones

out of your pocket or out of your bag constantly, because each time you're going to have to untangle them. It will slightly tangle them, but it's not going to ruin them. It's not going to break them. Got it. It just means that you can't go and unravel it. I will say, this is a mild distraction. If you clip the two ends together to make a closed loop, you know,

often you get like a little clip on one of the sides, one of the buds that clips to the other cable. I never did because of the sort that I would use. I use headphones, not buds. It's been shown mathematically that if they're jumbled around in a pocket, a closed loop is substantially less likely to become tangled than two open ends. Well, Matt, you're jumping ahead. Oh, I thought I was jumping to the side. Because there is an entire paper on the spontaneous knotting of an agitated string.

There you go. That was used to study the effect of tangling headphones. So essentially what tends to happen is that when there is a loose end, and especially because headphones or earbuds, it's a Y shape, which means you don't have like a single end on the other one either. Yeah. If you've got a loose end, it will weave between the things just with movement. And a lot of that is to do with the friction of the cord itself and the casing of it. So they found that with the string, the stiffer the string, the fewer the knots

generally. Kind of makes sense if you think in terms of if there's anyone listening who's ever had to tease their hair. If you want to make your hair big and voluminous, you don't want to put oil or anything in your hair that's going to stop it from having friction because then it's going to be smoother. It's going to untangle itself much easier. That's why untangling sprays and stuff tend to have like hair oils and things in them. And it's the same with headphone leads. If there's enough friction being caused by that casing, it's going to naturally grab onto itself and work its way around itself within your pocket. So you either want to oil your headphone cable. Yeah.

Or you want it to be like rigid, like coat hanger wire or something. Yeah. I mean, if you want it to be that, I mean, it definitely might not if you're using a coat hanger. Problem solved. Problem solved. They did find that the length made a considerable difference. Oh, okay.

So cables shorter than 46 centimeters rarely, if ever, got knotted. And I guess that's because after a while, they just sort of start to untangle themselves as much as they tangle themselves. But the average pair of headphones or earphones tends to have, it tends to be roughly 140 centimeters long. Oh, that's way longer. And so the fact that those will tend to get put into a space relatively small, a pocket or a bag or something, it all increases the chances of it

getting tangled or twisted or knotted. There's a couple of ways and techniques and hints of trying to combat it. A lot of them involve leaving your Oh. So that the weight of it untwists it. I don't think that's a good idea because I think that might start damaging the cable. But it certainly will stop it from being twisted. Not as convenient to carry around though, is it? Yeah. Some people recommend putting heavy books on it. Lying it out in a straight line and putting heavy books.

What? Basically doing the same thing you would do if you're working with like crinkled paper. Iron it. Yeah, exactly. So... A cool iron? Yeah, it's got sunglasses and everything. In a nutshell, just get some wireless headphones.

Problem solved. I think that's my answer. No wires, no problems. That's what they say. Yeah. I suppose the other option is probably to get those ones that are already coiled. Oh, like the old school telephone. Yeah, yeah.

Okay. I think that's some good advice. So excellent research. The trick is to just make sure you measure out, what was it, 46 centimeters? Just get a really small lead for your headphones so that you don't have to walk around with your phone on your shoulder. Get your phone real close. No, I thought, you know what?

I feel like there's a range of deployable advice there. I'm going to give you an untangled ding for your excellent headphone advice. This next problem is for Matt. It's from Chris. Chris says, the earth is a sphere, sort of. It's got bumps where the land is and big bumps where mountains are and holes where the sea goes in. And it's a bit squashed at the top and the bottom.

But if everything was smoothed out, you could turn it into a proper sphere, but then you'd be left over with the water, and that would basically be a big pond covering the whole land. They think it'd be like Waterworld, a bit like Noah's Flood. Right. But they want to know how deep it would be. It makes sense. There's water on the earth.

It's not everywhere because some bits of land are higher than other bits. And so the water pools in the lower bits. Very straightforward. But if there was no higher or lower bits, one big, shiny, perfectly smooth ball, we would just be, we'd have, the water would just form a layer on the top. So I, first of all, before I tried to solve this problem by running some numbers, Bec, I'm just curious. Do you want to have a guess how deep do you think it would be overall

if all the water was just on the perfectly smooth surface? Well, I know that there are some very deep bits of the ocean, but I also know there's a lot of very tall bits above the ocean. Yep, yeah, good work. I'll have a guess. I think, I don't know, like a couple of meters. Oh, okay, interesting. Between a meter and two.

Well, at first I was trying to think, well, what's the deepest bit of the ocean? And I thought the Mariana Trench, is it like 10.9 kilometers? But there's lots of bits that aren't deep. Like there's obviously a lot of land. Oh, but the Earth's like two thirds water. Like a third of it is like zero. And then the rest of it varies between zero and about 10 kilometers. And so I then thought, you know what, it's probably in the middle somewhere. So I went with five kilometers

of water. Oh, wow. We both went very different. I think actually we're both pretty, a similar amount of incorrect. Right. So either it's in the middle or it is so high that the difference between those guesses is negligible. So let's work this thing out. I decided to not go too detailed, but just to get like a, try and get something as vaguely the right answer. So I looked up the amount of water on earth and there is 1,386,000,000 cubic kilometers of water. That's a lot of water. That's a big old, big old amount of water, but there's also a lot of earth.

So I took the earth's radius to be 6,371 kilometers, which means I can work out its volume. It's just over 1 trillion cubic kilometers, 1.0832 trillion cubic kilometers, which means, and I know I've approximated a bunch there, but you know ballpark figures the earth is 0.128 percent water and that's like surface water and then you got all the rock and everything else inside and so now i know if you were to level out the earth as a giant sphere they'd then be like this shell around the outside of the sphere that makes it a bit bigger. And the volume of that extra shell will be 0.128% of the total volume of the whole sphere. I now know how big that is. And there's several ways you could do this mathematically. What I thought I would do is just work out the percentage change in volume once you add the water and then

take the cube root of that which would be the scaling factor for the diameter or the radius which will give us how much of the depth is water comparedureka moment. It's not, that was yes, sort of. I'm going to go with maybe. If, if instead of a bath. Do you know what? Knowing when I listen back to these episodes and I ask questions like that, and you're very kind and say sort of, or maybe I find myself thinking, no, no, it's not like now that I've listened back and I've really heard what you're saying, absolutely

not. That is not what you're saying. If instead of a bath, there was just a massive glob of water floating in space, and then you inserted the earth into that floating glob of water bath and look at how much it expands out. That's what I'm doing. So that's kind of. Oh, so it's the inverse of it.

No. Rather than Archimedes coming out of the bath and measuring how low the water went down, you're putting Archimedes into the bath and working out how much the water went up. Archimedes went into the bath and measured how much the water overflowed. Oh yeah. Well, that's kind of the same thing. It's the same thing. It's the same thing.

The answer was maybe. So I then worked out that. So then I had to flip, because before I had the percentage of the total earth that was water, I had to change it to be if you've just got the rock and you increase it to include the water, what's the percentage increase? I then took the cube root of that,

and it turns out the radius, if you go from just the rock to including the water as well, it goes up by 0.043%, which is not much at all. But I can now work out what 0.043% of if you increase the Earth's radius. And I got 2.7 kilometers, which is pretty much between our two guesses. Like, weirdly in between. Yeah. So I would say ballparkpark 2.7 kilometers deep the

whole way around give or take a smidgen that's a lot it's a lot like my guess was like it's the deep end of a pool but the reality is is if your pool was that deep you it'd be terrifying yeah it's deep that's deep there's a lot of water. The Pacific Ocean is big is another way of just answering this question. There's a lot of water out there. It would be like Waterworld. It would be Waterworld. Yeah. Not like my guess where it was like.

A fun pool. It's like a theme park. Yeah. So there you go. I don't know what problem they're strictly solving in a practical sense, but if you were ever curious, how deep is the ocean on average, if you include the land, 2.7 kilometers. There you are.

Thanks, Matt. No worries. I'm not smart enough to know whether that's wrong, so I'm going to give you a ding. It's definitely not exactly right, but it's within the fuzzy zone of right enough. It's within two meters and five kilometers. You're going to have to tread water.

We can say with absolute certainty. Get your armbands on. And now it's time for any bother Osness, which we've got a few things to go through this time. We've got a ding has rolled in. Yeah. Yeah, one of yours. Lawrence came back from Bluey's Beats and Undy's Teats. Lawrence had posed the question about the time signature for the Bluey's theme tune

and says, now I can sing along without feeling like I don't know what time signature I'm in. Because any time signature is correct as far as I'm concerned. Excellent. A huge number of people really got involved in the calculating factorials chat. So I talked about the biggest number you can calculate as a factorial on various computing systems. Actually, this one on the Patreon. So we have a Patreon for Problem Squared.

Thank you, everyone who supports us. Don't stress if you're unable to afford it. It's okay. These folks have got you covered. And oh my goodness, everybody was trying to factorialize the biggest number possible on all sorts of calculation devices. Some people on their phone, some people named Chris Adams, said that they got to 13,904 factorial. That's pretty great. Yeah. And Uncle Sweaty on their Android calculator, it kept out at 19,515. Maybe mine was Samsung specific. Wow. Yeah. These are just ridiculous numbers. And then we got some practical advice.

I'd like to thank Frank Knorr, who gave us a step-by-step breakdown. Or Knorr. It's one, nor the other. They gave us a step-by-step breakdown for how to use Excel to calculate bigger and bigger factorials. And someone used the OnePlus default calculator app. Again, I'm not endorsing any specific calculator app, but they're claiming that got up to 48,884 factorial. And on someone's Sharp EL501X, it stopped working at 69 factorial.

That's Jacob Edwards. I don't know why that's funny, but they seem very excited. A 69 factorial. I also wanted to just give a mention. We had a few responses in regards to the trying to predict dates. Oh, yep. What day of the week a specific date is. Yeah.

This was from Michael Chook, who pointed out that it helps to know what dates take place on the same day of the year. So, uh, boxing day, Halloween, 4th of July, Pi Day. So if they all have the same day that they fall on, then it's much easier to remember. Um, it doesn't necessarily help if you're given a different day that you don't know and you have to calculate it from that, but nice little hack. And one extra bit of any other business that we actually didn't have in the agenda, but I just need to say this out loud. I don't think we're going to do anything with it, but I need to offload this fact. We talked about how I calculated if Michael Jackson's

hair catching on fire during the Pepsi commercial was the exact middle point of his life. Someone got in touch and said a friend of a friend was there. They were a costume designer and they were part of the crew when it happened. And they offered to put me in touch to get a more accurate time for exactly when it happened. Now, I don't think we need to do that. I feel like unless we also got a more accurate time for Michael Jackson's birth, we're not going to add any kind of net precision. It's not going to change the results.

But I just had to say out loud, such as the power of a problem squared, that we've now got a direct line to someone who witnessed the event who could give us a more accurate time. I don't think this is a worthy use of pestering them, but I just wanted to go on the record to say thank you. Thank you, you amazing listeners. What an incredible resource you are. And I do not wish to abuse the incredible power

that comes with such a wide ranging and enthusiastic network of problem solvers. I did mention that we have a Patreon. In fact, that's how we fund this entire enterprise. So not only can you engage in conversation about your favorite calculation device, not only do you get a bonus podcast every month called I'm a Wizard, which is Beck and me getting ready for the main recording. And not only do you get a smug sense of warm satisfaction

that you enabled this entire enterprise, but every single episode we pick three names completely at random to thank in the closing credits, which this time includes... Mark Co-Cohi. Co-hi. Coffee. Linus Becker. Would you say Linus or Linus? Linus Becker

Did you say Linus or Linus? Linus. Ellie. That was easy. Good old Ellie. Yeah, thanks Ellie. We'd like to thank them and all our Patreon supporters and everyone else. If you're listening to this at this point at the end of the podcast, we hugely

appreciate your support. But that's it for this episode. I'd like obviously to thank Beck Hill, myself, Matt Parker, and our podcast producer. I did top the P's on that just to continue the opening theme from the episode. We'll make that very clear. Lauren, calm, Beck, we're continuing our Which My Buddy Use survey. I've not looked ahead, so I don't know how many more of these we've got. But this time we've got, what would you want as a pet? And the options are frog, lizard, poodle, chicken, pit bull, fish, cat, gerbil, ant farm. See, this is a tough one because I've had pet chickens and they're awesome. And I love eggs.

Obviously, I do have a hamster now and they're not too dissimilar from gerbils. As with gerbil, I mean, you've kind of put your hamster where your mouth is now. But I've also always wanted a pet bearded dragon and a quite light green tree frogs. I think I'm going to go chicken because I already have a hamster. Okay. I'm going to go ant farm. I've always wanted, I've never successfully had an ant farm. So I feel like that's what I'm going to go for

Do you mean that you've had one and been unsuccessful? I had one as a child that was unsuccessful But the problem was the ant farm did not come with ants And what I didn't realize at the time is when I was putting ants I wasn't putting like a queen ant or anything I was just finding some ants and chucking them in. And then obviously they're not going to, they're not going to do well. But I always thought like an ant farm, like as if it's like a framed picture in a living room would be really cool.

Or even just like in my study, like I think an ant farm would be amazing. So I'm going to, I'm going to go lock in ant farm. I went to Chessington World of Adventure to film something at Makeway Tech for Makeway Takeaway last year. And in the restaurant, they have these clear tubes going along the, uh, wall. And I hadn't really noticed it until I saw something moving and it was a leaf. And I realized they've got some type of ant. Exactly that.

Obviously it goes into its coat, but it, but they were all walking along this tube. Amazing. Like bits of leaves and stuff. That's so good. You get different ant farms joined with tubes. Ah, it'd be great. you you