A Problem Squared - 052 = Piping Hot Baths and Predicting With Graphs

Episode Date: February 6, 2023

In this episode... 🛀 How do you keep a bath warmer for longer? 💼 Matt solves a problem about business. 🗞️ We have some AOB. 🪵 And a brand new stumpdate! If you've got a problem or a solution, hit us up on our website aproblemsquared.com. You can buy A Problem Squared 'DING' t-shirts here https://a-problem-squared.teemill.com. And if you want want even more from A Problem Squared, find us on Twitter and Instagram.

Intro Hello and welcome to something that closely resembles and may very well be a podcast. A problem podcast where we take problems, aren't always problems and provide what are not always solutions. But if anyone's prepared to embrace uncertainty, it might be us. Probably. I'm Matt Parker. I am a mathematician, if you're prepared to overlook the error bars, and occasionally have been described as a comedian. Very generous. And my co-host, whose name is Beck Hill, apparently is definitely within two standard deviations of being a comedian on stage and on screen. Oh, that's the nicest thing you've ever said about me.

That was my uncertain intro. I thought so. I think rigorously that's the most nicest thing I've ever... That encompasses the nice thing I've ever said about you. I think that's how that... It does. Somewhere in that range. Yeah. And there's a decent chance that on this episode... I might be able to help you work out how to keep your bath hotter for longer. You're on theme.

I will be doing some business maths. Business maths. And A-O-B. Assumably, other believably. Good work. Any other business. Now, Beck, traditionally we would do our how are you doing catch up chat right now however we said last episode that because by now we will have probably definitely had a million downloads we were going to record multiple options for this section to celebrate

or not my accurate prediction of a million downloads having happened by now that makes sense yeah so for the sake of everyone listening hooray we did it hey we did it i don't know why i'm firing guns ah we should have bought like party poppers or something or we did not think this through but oh my goodness i've only had two slightly deflated balloons with ones drawn on them. Would you believe? You know what? I'm just going to add an M. Give me a second.

For any new listeners, this is in reference to the previous episode where I mentioned that he helped celebrate Fibber New Year as in the 1st of January this year. It was Fibber Natchi Day in the 1st of January this year, was Fibber Natchi Day, as in 1-1-23. And Matt showed that he had two very sad-looking balloons with ones drawn on them. Yay, one million! One million.

Just put a million after the ones now. He's got two of them. You hold on to those for when November comes and we have two million. Oh, one each. Can you bring it to the UK and I can collect it? Fine. I might have to gently untie them and let the air out, but I will. No, I want it to be fully inflated.

I will package it up. I want you to have to smuggle them through customs under your shirt. One million. Yeah, party times party times matt how are we going to celebrate our listeners well we did ask for listener suggestions for how we should appropriately celebrate one million downloads and i don't think we're going to do any of them no none of them thanks for suggesting things like a live episode i mean we will do a live episode at one stage,

but we're not even in the same hemisphere as most of our listeners now, never mind the same city. No, we can't even do a live episode with our producer listening in. No, exactly. Someone suggested a musical episode, which I don't think anyone would enjoy. No, I mean, I like writing musical stuff,

but I don't like listening to it it'd be a fun writing exercise but that's it would just be for us yeah yeah and no one wants to hear us sing i mean you've had you've heard me sing multiple times it always ends up making the cut yeah but it does that's more because i think it's funny she does she thinks it's hilarious that and i i uh hold a knife to her throat and i might put my music on here put it in get me on the waves whereas i never sing for exactly the same reason so tell our lovely listeners how we're gonna celebrate yes we're having a bit of a chat uh before we started recording because we figured we have to do something and then we realized there's no better

way to commemorate like a massive achievement other than a commemorative plate i mean a commemorative bowl yeah a commemorative plate no a bowl well can you fit a spoon in it uh commemorative bowl plate plate bowl you can decide you can order we'll have both you can pick um you're gonna get the same thing no matter what you pick but you can choose a commemorative plate versus a commemorative bowl and whichever one we sell more of will be oh the definitive what it is how's that okay done what i love is that depending because we at the time of recording this we haven't been able to order such a product yet no No. We had the idea and we've done nothing. That's where we're at.

Yeah. On the off chance that we can't find a specific commemorative bowl, I like the fact that people might still buy something labeled a bowl that clearly looks like a plate just to troll you. Well, as we know, there's ample ambiguity. If you would. Yes. When does a troll become a trait?

Ooh. Deep. So we're going to, we'll have a commemorative plate bowl of some description. And I, we're thinking, and again, we have not done any of the research or execution required to make this happen. But by the time you're listening. We think we will give, we will have. Yeah. Hooray, future us.

Thank you, future us us for sorting this out let's lock future us in for a few obligations as the reckless past us we are i'm prepared to say we will give a free one to all our wizard level patreon supporters oh yeah that's our top tier isn't it yeah there's a top tier, which is not particularly high, and we will absolutely lose money in the short term, but I feel like we must reward the patrons and supporters who have got us so far, and we hugely appreciate you all. But then, I don't know, I guess we'll do a limited run

of a total number of N commemorative plate bowls. So if people want to order them. Will we sign them? Oh we sign them oh my gosh oh yeah let's sign a number them they're commemorative so they have to be collectible they're commemorative they're collectors yeah yeah you want to get if you want to get the whole set you got to get in early you don't want to have to like buy one of these later off someone who did get in early they're're going to inflate the price right up. We may even, and this is just giving future us some wriggle room, we may even have to, depending on what it costs to get these things done, pre-sell them, and then we'll get them all made and send them out.

But we will find a way. There'll be a link in the show notes. We'll tweet it. It'll be out there. Get your commemorative plate. You can choose commemorative plate, commemorative bowl. Hooray. bowl hooray moving on beck how have you been i've been good well i had someone i had my first person pretending to be me online um i saw you tweet something about this yeah where you're like i'm the real beck so everyone else can back off but i didn't see the details it was

quite in fact it was a pretty good scam I was it's annoying when they're good scams because you're like oh that's quite easy to fall for um so my Facebook uh forward slash Beck Hill comedian someone had created a Facebook profile using my pictures and then they were going through and replying to people who had left comments on my posts and pictures saying gotcha hey thanks for the comment congratulations you've won the competition check my pinned post for more details and of course what a lot of people will do as a shortcut it's so clever because not everyone would have done this but the shortcut would be to just click on the person to go to their profile people will do that

yeah and then the pinned post was like i'm doing a thousand dollar giveaway for 20 of my followers simply comment on one of my posts and i'll choose them at random yep yep and so all these people like oh yeah maybe i did oh how. I accidentally entered without even realizing. Beck does crazy things. Yeah. It's very sweet that there were enough people out there who think that I have 20 grand to just give away to people. Yeah. So it wasn't like a more recent one.

And they'd like put like the details of the you know fake competition on my photo it was so much effort and then yeah people were replying to them asking them to message them with details so just contact details but also asking for their bank details so that they could transfer money then i saw that people were like commenting with with screenshots of bank details and stuff. And I was like, no. No, no, no, no, no, no. Yeah. And I reported the page as pretending to be me. And then I got an email from Facebook saying, oh, it doesn't go against our community standards.

And I'm like, it should do. It's literally pretending to be me. And so I sent a reply and I haven't heard back. And so I tried it again from the fan page reporting it. And I think I've successfully banned them from the page. So they shouldn't be able to do it again. Gotcha. They can't reply to you.

So people should look for that if they ever converse with me. I get the lazy automated version of that on YouTube where it's not as involved as that. But accounts will automatically steal the youtuber's profile picture make a very similar looking account and reply to comments saying something real generic like oh that's interesting let's discuss this on telegram try and bump them onto a um side channel somewhere else and i don't know what their end game is but because i just i'll be to get them on messenger or whatever so they can eventually ask for their payment yeah they can try and get details or something yeah

i mean youtube would not be pretty good at filtering that stuff out but every now and then there'll be a sudden spate of a bunch of very similar spam messages. Like someone's just found a loophole in the filters and suddenly the same sorts everywhere. So be careful, everyone. Be safe. Be careful, everyone. But that's me. That's my news.

That happened. Good news. Also, between, because as we made it on the last episode, we did need to record these both on the same day. Just due to us traveling, we wouldn't get a chance later. So we finished recording the last episode and then took a little break. And then. Yeah, took a wee break.

You ran late for the last one because you're at the beach. I was running late for the most back problem, which is that I was on the toilet. And I'm quite, look, you will fairly regularly, if you're trying to get in touch with me, get a WhatsApp message saying, I'm on, you know, I'm on the loop, can't talk right now, or I'll call you after. But I forgot. You've got some kind of shortcut. But with Zoom, you turned on your camera

and there's something just very weird. And, like, my camera and mic were on mute, so you couldn't see me. But there's something really weird about sending a message to someone who you can see and telling them that you're on the toilet. Yeah, no. I had to immediately turn the screen off and move my phone away. Because I was like, this is too far from me.

I don't want to look at your face while I'm on the toilet. Thanks. I feel bad enough if I'm in some kind of really boring meeting that I don't have to be involved with. I can easily go to the loo with my headphones on. Oh, yeah. Just to keep my... Even that, I'm like, it's a bit unsettling. Well, you know I've done that occasionally with you guys.

Oh, yeah. I've told you and Lauren that I'll have my headphones on mute. And it's handy because then there's no catch-up period. It feels like I'm listening to a podcast at that stage, but it's like a very specific podcast to do with admin. Well, have I got to change the pace for my catch-up, Beck? I have a stump date. No.

You said that the stump was gone. Correct. In fact, for our new listeners, do you want to give everyone just a quick, as you remember it, stump date recap? At Matt's family home, there was a big stump. And each year they would try to remove the stump through digging or fire, I believe. And each time they could never fully remove the stump.

Correct. Now, it was a bit more frequent than annual. It was just whenever there was a get-together at parker family residence that doesn't make it any better matt this this fact that you weren't able to remove it after multiple attempts per year took multiple burnings multiple banks now i don't know there are probably two types of people in the world people who've had to remove a stump and people who haven't stumps are real difficult to get rid of yeah There's no easy way to, it's not, it's not straightforward. It's a real pain. So my parents moved into their current

place since the last time I was in Australia before the pandemic. So I'd never been to this place and seen the stump. They'd moved in. There was a stump. I then got updates whenever there was a stump burning, which I then passed on to our fine listeners as a stump date. And I was very keen for the day I got to go back for several reasons back to Australia, one of which was to join in the stump burning. However, they did so many burnings over the several years I wasn't there, they got rid of the stump. They had initially left what was remaining of the stump in like a hole in the ground

but then and my mum was keen that i get to come and at least see you know what was left of it sorry can i just i have to stop for a second there because for anyone who ever sees that matt has like over a million subscribers on youtube and his jet set lifestyle and he's this this lecturer that people like, you know, crave. They fly him all around the place. He's having dinner with astronauts, all that sort of thing. It's like you're bigging this up, but carry on. He's doing Zoom calls with Jeff Goldblum at Royal Albert Hall or whatever.

And then your day-to-day life is stuff like your mom insists you come over to look at where a stump was look at the stump remains how the mighty have fallen there's nothing like having family in perth to keep you real yeah this is where this is life life is what happens between the stumps so so but my dad in a fit of gardening buried all evidence of the stump i missed the whole thing i considered digging down when i got there but but then i realized no no matthew you're looking backwards you gotta look forwards and while i've been here this time another tree adventure has started and i was here for the beginning this time, which I'm finding very pleasing. My parents with the property have a lemon tree they don't want.

And my sister and her husband have an unsuccessful lemon tree that they want to get a new one. And so I was like, look, here's what we got to do. We got to transplant across Perth, a fully grown lemon tree. Literally transplant. Operation transplant is what I've been calling it. And it's not a straightforward process, moving a tree. It took a little bit of convincing to get everyone on board. They're famously stationary.

If this was something we could achieve. It's a combination of effort and physics to get a tree out of the ground and across the city and into another hole. But then it turns out, a bit like burning a stump, you want to do it in phases. My sister did some research. And what they recommend you do is initially you dig a trench around it to sever all the roots. And then you fill that back in again and give it a couple months to recover from the initial... In its natural habitat. Then you come back three or four months later,

dig it back up again and then shift it. I'm back in Perth in a couple of months anyway. There's a solar eclipse happening in Western Australia in April this year. And that feels like a compulsory thing Lucy and I have to attend. So we're going to be back to see the family in a couple of months.

So I was like, let's do it. We'll dig the trench now. And then we can backfill it. And then I'll come back. We rig it out again. We move it. And I was so excited that this time I got to be there right at the beginning of a tree adventure. And so me and my brother and my dad, one afternoon, a couple of days ago, set about digging the initial, you know, earthworks to get this thing going. And we dig down through all the roots and you wouldn't believe what we hit. We hit stump. What? Stump. We hit one of the major roots that would have come off the tree

that gave us the stump. Oh, it lives. I was like, what's this? I'm like, this is a bigger root than the lemon tree. Massive jarrow root. I'm like, it's the stump. And so I got to get an axe and cut through one of the roots from the original stump so i got to partake in the clearing of the stump

because i had to i had to cut through one of its roots to liberate the lemon tree and do you have it now do i have the chunk of root i had to cut out? Yeah. You know I do. Right, let me go grab it. Hang on. Wait here. I knew I could rely on you. He's got a root. There it is. Wow.

That's a nice chunk of wood. Thank you. It was Jarrah. The double entendres in this, by the way. This is how amazed I am by what you're showing me, is that i haven't gone for any double entendres even though they're right there there's been very few root jokes very few wood jokes great work thank you um there it is look at that chunk it's bigger than i expected

yeah yeah there you go so so now i've got a massive chunk of original stump wow and i don't know what to do with it so i'm open to suggest what do you think bag what should i do with this well there's several options you know me i love burning stuff so my initial reaction is you do you do take take it back to your your cool um bonfire at home my mass fire pit Your fire pit and burn it in there. But that is a really nice, I can't, that's a nice chunk of material you got there. And that feels, burning it feels like a bit of waste. I like the idea of making something out of it. I was thinking, what if I got it sliced up into like coasters?

Sliced and then varnished or oiled or whatever. Make some jar of coasters you need someone who knows about wood yeah so listeners tell you what i'll get some photos of this we'll share those um i want suggestions what should i do with the stump that i thought was gone and buried and never to be seen again it's a problem.com and select solution and maybe just chuck the word Wood in there or root In capitals so it's easier for us to find

Yeah put stump Make sure you put stump because I'll just search for stump later And then I'll find all the suggestions Stump Yeah so there you are The stump date lives on Piece of the stump This story went way better than I could have ever imagined

But I did think you were going to say that You saw where the stump this story went way better than i could have ever imagined but i did think you were going to say that thanks you saw where the stump had been and then you secretly planted a seed for a jarry tree oh for a new one because that is that is a long game gat like joke that is real long game really long yeah our first problem today back has been sent in on the problem posing page at a problemsquare.com from Anastasia, who says, well, first of all, they say, hey, Beck and Matt, you guys are great. Love the podcast. I love when people send that.

Thanks, Anastasia. Even if we don't answer their questions, their problems, it's nice. They go on to say, also, I have a problem. They're just having a bubble bath. I guess they listen to podcasts in the bath. It's nice. They go on to say, also, I have a problem. They're just having a bubble bath. I guess I listen to podcasts in the bath. That makes sense. And over time, it's obviously gotten colder. That's deep.

That's the universe for you. But also the bubbles have decreased. So I started wondering whether bubbles make a bath stay warm for longer because of the trapped air in them. Thinking face emoji. And the problem is how do I keep my bath warm the longest? Smiley face emoji. So, Beck, the problem is, well, I guess the question is, do bubbles in a bubble bath keep it warmer longer?

And the problem is, how do you keep a bath the warmest for the longest? Oh, well, first of all, Anastasia, thank you for sending a bath-related problem in because I love baths and it gave me an excuse to take baths and call it science. So, first of all, yes, Anastasia's correct. The bubbles do make a bath stay warm for longer because of the trapped air. It creates an insulation that stops the water from evaporating or leaving heat radiation, that sort of thing. Because the way I was thinking of it is normally you'd have hot water and then air contacting it. The air would heat up and then convect away and new cold air would fill its place.

Yes. That would then absorb more heat from the water whereas i guess the bubbles they stop that convection loop because it warms up the air in the bubbles but then it doesn't go anywhere it's like ah it stays here yeah well it certainly slows it because the structure eventually breaks down in the bubbles oh yeah the bubble burst yeah yeah yeah so that will they will eventually stay warmer for longer yeah you do yeah there there is a there's a lot of stuff out there about how actually using bubble bath is you know it's

not so much about making you clean it's just about keeping your bath warmer for longer so you don't have to use as much energy you don't have to refill the bath and i've i've often said this because gavin my husband he doesn't mind some bubbles but he doesn't if i like to have as many bubbles as possible i like to have enough bubbles that i can hide in the bath and that you can't really see me that's my favorite type of of amount of bubbles where like it's just two eyes poking out from a sea of bubbles comedy film levels of bubbles oh totally yeah that's my i just something to play with put in your head pretend it's a beard it's always i've never aged out of that and i hope i never do i hope that even

when i'm at an age where i need a walk-in bathtub i i still want to still bubble sticking bubbles on my head yeah exactly yeah got it love it great there are no downsides for the bubbles is what you're trying to say exactly but gav doesn't like the bubbles. He just finds them annoying. He doesn't like the feeling of too many bubbles. He's just not. So what we tend to do is if I run him a bath, I'll do obviously always too much bubbles. And then we have to use the shower head to sort of water them down a bit so that they. Oh, you de-bubble.

Yeah. They're sort of, they become like condensed. Does that work? Oh. You sort of end up with... As long as you don't re-lather it, then it stays flat. Yeah, kind of like...

So what you're saying is, you're saying that Gav likes a flat white of the bubble bath world and you're in a cappuccino of the bubble bath world. Our baths are the same as our coffee preferences there you go you're both you're consistent in your opinion on foam okay now just as a side quest i need to know if that's a thing for everyone if you if you have a preference you need to have a preference in coffee for this to work i think if you don't really have a preference or if you don't drink coffee i don't

want anyone like oh well i don't normally but sometimes i'm flat white but it's just whatever they give to me i don't i don't care what i want to know is if you have a preference for a type of coffee and a preference for amount of bubbles in the bath do you find that those two correlate are they the same so i can provide one more data point because i'm a flat white kind of person and i'm also not a big bubble bath kind of person i'm i have to admit i'm there with the minimal bubbles as well so yeah what does lucy drink oh that's a good question well she's she's definitely and i hate to run this down gender stereotype lines i think she's pro bubbles she would be a flat white i know she likes bath

salts though she's like yeah it's true i know because i've had a bath at your place and there were bath salts and i was like oh yeah you you put you put our bath salts on the internet if i remember correctly i did because they were called like when they call like dr salt and i was like oh it's like something like that dr pepper's whatever. Yeah, you're like, I didn't study this long to be called Mrs. Salt. Oh, that was it. Yeah. Okay. Go ask her.

Yeah. Lucy does not conform. She's a flat white and lots of bubbles in the bath. So we need more data points. And that's why I love that woman. She bucks the trend. So when this episode comes out, we'll do a poll. Bubble or nubble?

If you have a preference for coffee, the amount of bubbles you have in coffee i.e flat white latte cappuccino does it match the your bubble bath preference in baths yes or no and then if you want to elaborate right and say yes i have flat white and this or no i have a cappuccino but i don't like bubbles then you can do that in replies that would just be extra data got it and so don't partake in the survey unless you have opinions on both bubble bath and coffee milk-based coffee yeah and then just we just want to do does it match or not that's all we're after yeah what about the fact that i traditionally i drink my coffee just black coffee and i tend to rather have a shower

i mean that's no i think no frills either way coffee equivalent is having nothing in your bath you just go and sit in there for a while and contemplate the world yeah i don't want to hear from you if you're a shower like if you don't have baths no your opinion is invalid got it okay all right so now we're away from our side quest. We've got our side quest. Okay. Meanwhile. Meanwhile, I was happy with the amount of evidence out there that bubbles make the bath stay hotter for longer. I wanted to see if you put anything more in the bath. So apparently salts can make the bath stay hotter for longer because salt water holds heat for longer than pure water.

Different specific heat. I can see that. Bath oils act like an insulator as well. And so I thought I'll do a control bath first. So mum's got a massive bath. Very good of you. So I did a control bath. And so I measured the temperature of the bathroom which i know because mom has a

thermostat and so the bathroom is at a very comfortable 26 degrees oh lovely yeah it's very nice and then i filled the bath and i made sure i measured how far the water was from the top so that when i did the experiment again i'd be able to know be consistent yeah nice and so i ran my bath and this is where i started to realize how many variables there are because the way that i run my baths is i tend to run them far too hot and then i let them cool a bit or i then stick in the cold water you overshoot the mark and then wind it back yeah yeah and i'll come back to that as well but i just want to point that out that that's how i do it because i will come back to that so i ran my hot bath and then wind it back. Yeah, yeah. And I'll come back to that as well, but I just want to point that out that that's how I do it

because I will come back to that. So I ran my hot bath and then I put cold water in until it was the right temperature for me. Did you measure the temperature or was this just bed temperature? First I put in my thing, you know, I did the thing where I was like,

oh, this is the temperature that I'd want to get in. And then realized, oh, I need an actual thermometer. So I've used my mom's meat thermometer because there wasn't anything else right yeah that's clean before she roasts thermometer so we put the i'm a meat so we put the meat thermometer in the bath and yep turns out now i'll be honest when i did get in i was like actually i've made this this is now too this

is actually hotter than i wanted but i'd already done all the other measurements. Because normally I wouldn't get in if it was hot. You're not doing more measurements. It was 43 degrees. Oh, dang, that is hot. You know it's hot when you can see the pink line on your arms. And so I was like, okay, I've made a mistake here, but I'm this far ahead and I can't go back. I love the fact that the level of discomfort of sitting in 43 degree water

is less than your discomfort in having to redo a data measurement. This is how I roll. I'm very comfortable in being uncomfortably hot. I get cold real easy. I don't like being cold. I do not mind being too hot so that was not a risk here i had the bath but the problem with that is that it didn't really go down in temperature for ages so i ended up having to sit in the bath for an hour and a half and i got really dehydrated

by the way guys you should definitely drink water before doing any experiments like this and yeah because you're basically in a very wet sauna yeah and then by the time i came out and i did that i made sure like the window was shut so that the the temperature of the bathroom stayed the same and then when i got out an hour and a half later i remeasured the water and it was 37.7 degrees or 37 that's a reasonable bath temperature yeah yeah so by the time i got out it was 37.7 degrees or 37.8. That's a reasonable bath temperature. Yeah, yeah. So by the time I got out, it was like a reasonable temperature because that's like almost body temperature, right? And that's, you know, our ideal.

But that's not a huge shift when you think about it. No, it's not. It's a very small amount. And that's without bubbles or anything. And then I was like, well, again, I've already gone this far. So the next day, 26 degrees, same air temperature in the bathroom. Decided to recreate it, but with a cup of bath salts, half an ounce of bubble bath. And this is all in the same bath?

In the same bath. And then I did two teaspoons of baby oil. So I was like, well, I'll do all of them and see just. Just everything. If everything together. And made sure the temperature was the same getting in. So I scolded myself getting in again. Another scolding bath.

Yeah. And. Only you could have a sunk cost fallacy in a bath. And then an hour and a half later, which I'll be honest, I think I've lost a lot of weight for just two days of baths that are far too hot for me. Sweating in a bath. I measured it and it was the exact same from the day before without bubble.

It was 37.7 degrees. It was at this point that I was like, I think I'm in too warm a temperature, atmosphere, like climate, I should say, to really properly measure this experiment. Because even though the air outside the bath is less than the temperature of the bath itself, it's a pretty comfortable amount. is less than the temperature of the bath itself.

It's a pretty comfortable amount. So it's going to slow that process right down. It's not exactly cold air that the water's coming in contact with. I don't know if this would be the case, but it feels like your body temperature and the bath temperature are just equalizing. So the bath's cooling down to the point where your body is warming it back up again. And so it's just plateauing out once it reaches back temperature. Yeah, possibly.

I think eventually it would get colder because the air outside is less. I feel like, yeah, I don't think a human body is enough to keep a bath warm no it's not i can tell you that from my would a fluffy coat keep you insulated from the heat experiment gotcha in a previous episode my core body temperature will stay the same or should stay the same for a long time but my skin temperature is different and that would do what it could to try and cool itself down so anything that's outside of the water will try and release any heat so both the water and my body are going to try and release the heat everything is getting rid of heat i think because the air temperature

outside of it isn't that much lower than i'm six degrees i'm sort of i'm keeping it warmer for longer because nothing's cooling me down. There was no air movement and, you know, there's nothing to help me cool down, especially. So I sort of gave up the experiment at that point and realized that. Good work, good work. Sorry, I'm having whiplash in your approach to the sunken cost fallacy. At one point you're like, well, I'm in too deep, better push on. And then you're like, act.

Write the whole thing off. Well, because I was like, because what I was going to do is then try it like with just bubble bath or just bath salts or just body oil. But after doing like what felt like the two extremes and then comparing them and they're getting the same result i was like well this isn't this isn't helpful at all i then realized because i did some research that one of the solutions for keeping a bath hotter for longer is to preheat the bathtub because the bathtub itself will start to disperse the heat depending on how well insulated

the bathtub is obviously some not all baths are created equal and if you have a bath that doesn't have any proper insulation around it then that bathtub itself will cool down quicker or if you're putting hot water into a cold bathtub then it will take on some of that and disperse it more quickly whereas if the bathtub is already hot then it will take longer for the hot water inside to disperse the heat because it's like making a coffee you want to preheat your coffee making equipment so you don't lose all the temperature from the water if you're a nerd sure correct it is like a coffee we're always bringing it back to coffee and so i just i've only got one thing and i'm making it work i love it no it's perfect it does work it's it's a really good comparison so then i realized that's the way that

i run my baths where i run all hot water first that's what i'm doing i'm preheating the tub because i'm making it hotter than it needs to be before cooling it down. So then in that time, it's heating up the bathtub. And I was like, oh, there's all these variables, and it's not even easy for me to measure them all. Also, my home is in a state that is quite prone to droughts, and while they did have a pretty wet season this year, I can't keep having baths.

Bath after bath after yeah it's a lot of yeah so in order to help answer anastasia's question i'm gonna need the help of our listeners and i'm aware that we've asked a lot of our listeners already but if anyone like me loves a bath and you're having them regularly and it's a lot colder over there right now yeah you know it's a lot colder in the uk i say over there but it depends where you're listening but if you're based in the uk or anywhere that's cold especially anywhere that's colder than the uk and you have a bath and you are able to measure the temperature of the room the temperature of your bath i would love to know i don't want people to do too much obviously do what you like

the more data the better but if you wouldn't mind having two baths where you change our variable to see what keeps it hotter for longer so what I'll need from you if you're wanting to help out with this experiment is I need to know the air temperature of your bathroom, the temperature of your bath before you get in, the temperature of your bath after you get out. Yeah. Yeah. Sometime later. How long your bath was for and your bath technique. So whether you fill up the hot water first and then cold water, whether you try and get the water, the perfect temperature from the start, whether anything, anything that you do that might be different and then if you could do the same again but change variables that are within your bath

and let me know if the results differ so everyone get on over to the problem posing page at problemsquared.com and give us your bath results. At some point in the future, we'll report back. Yeah. And then hopefully you'll have your answer then, Anastasia. I'm going to withhold the ding for now until we have some more dingable data. This wing ding slash dinglet comes from Cedric who says, Say you are a salesman tasked with acquiring new customer accounts throughout a year. Now, at the end of the year, you are tasked with planning for your next year's sales numbers.

You need to estimate how much more these new customers will buy next year compared to this year. You know, however, that accounts that were acquired in January had the whole year's worth of sales on the books, while accounts opened at the end of the year only bought for one month so you expect early accounts to increase very little and accounts open later to increase significantly what i want to calculate is if all other things remain constant what would the overall percentage increase be just due to the variance and when the accounts started buying matt i didn't understand any of that i didn't i read the whole thing. And I was thinking about halfway through.

I don't know what any of this means at all. Yep. There's business for you. Business. So Cedric manages salespeople. That's the short version of this. And so he hires someone as a salesperson and says right we make great products here or whatever they do i don't know actually you go sell those products get us new customers yeah

they find a customer they're like hey you want to be our customer and the person's like you're right i do and then you assume henceforth they put all their business through you. And so just as an assumption to make life a bit easier, we're assuming once one of these salespeople gets a new customer, they're just now constantly ordering through their company to get these things. So the spend is, you can just assume it's just a constant rate. The problem is when you've got salespeople, there's like, obviously you get new customers and they spend money. But then you want to know, are they spending more? Are they spending less? Like you want to be able to track the amount of spending they're doing.

The issue is if in the first year you got a new customer halfway through the year, across the entire year, they're only buying for six months. And the next year they're buying for 12 months. So on paper, they've doubled their spend. But you're like, well, hang on. But, you know, that wasn't because they're buying any more. It's just because they've been buying for longer. That's an assumption there that whenever you do the, and I'm sure it is the case, but when you do these calculations, you're always doing it on like a yearly basis

would it not make more sense just to have a different thing for each customer i suspect and again i'm not a business person so i don't know the full details i think it's probably things like annual bonuses end of year accounts i think the business world lives and dies by the four quarters of the business year. So I think they want to be able to chunk things into years. And you're right. It would be better if every customer had their own separate cycle because then you could compare it a lot better. But I guess customers come customers go they want some kind of just sense of um how do you compensate or allow for the just the natural increase because they've been a customer for more of the year than they were before versus any genuine increase in the amount of spend

because maybe you got a particularly good salesperson and cedric did send me through they they had a stab at trying to work this out mathematically and hit a dead end. It's not a straightforward thing to work out. But if I know one thing about business, again, not a business guy, if I know one thing about business, you want to make a slide deck. So I actually made a one-slide presentation to send back to Cedric with my results. Oh, great. On when I work this out for them.

But I thought I'd try and, given this is an audio medium, describe it to you and then see if that works. And then we can always make the deck available if people want to have a look at what I actually did. Okay. But I imagined drawing like a bar to represent a customer buying things. So, if they were buying things for the whole year, that the bar would be the length of the whole year if they were only buying things for half a year the bar would be half as long quarter of a year be much shorter again and so i imagine that a new salesperson is bringing on clients at a regular rate like a new client every month let's say and this is within the assumptions that cedric said

kind of work with their business and so i was like well you're gonna let's say you bring on 12 clients one a month your first client's going to be a bar that's the whole length of the year the next one's going to be a bit shorter but i then i drew that kind of above it next one's going to be a bit shorter again and then a bit shorter again a bit shorter again a bit shorter again you're actually making like a triangle you've got a long one at the bottom and then each one above it gets a bit shorter again, a bit shorter again. You're actually making like a triangle. You've got a long one at the bottom and then each one above it gets a bit shorter. Then the second year, they're all full length bars. So you've got a massive rectangle. And actually the triangle is half the area of the rectangle.

Because they're getting consistently shorter all the way up. And so it's half. So in fact, if you, and this goes, it's not just salespeople, it's not just clients. If you've got anything where things start consistently, and once they start running, they produce consistently, then if they're gradually starting up over the course of some time period, let's say a year, and then they continue running for another time period, the second time period will have double the output of the first one. Yeah.

Just by a nature of their coming online gradually, and then they continue running. And it's such a quick, simple, geometric way of doing it. And the answer drops out and is quote-unquote obvious. Whereas if you try and do it algebraically or working it out, it's a mess, absolute nightmare. And that's one of the things I love about mathematics. Sometimes it's just the way you approach the problem, the way you think about it makes a difference to how hard or how easy it is.

And a lot of the time when people say, oh, that person's good at maths or, oh, they solve things quickly. They've just seen more problems and they know more ways of going about it and ways to think about it. And so I'm like, when I heard the problem, I'm like, I bet there's a geometric way to picture this, which will make sense. Does that only work if the new customer is being acquired? Is it also at a constant rate? Yes, it requires that assumption. You'd have a different shape if they were coming in a different rate.

Yeah. But what's interesting is if you think about it, because I already kind of gave part of the game away when I said imagine one customer starting in the middle of the year. Yeah. Because that straightaway doubles. You see it doubles. Yeah.

I've only just managed to understand what the problem is, I think, because basically what they want to know is let's say the customer, if we're going to keep this customer for the oncoming years, how many commemorative plates are we going to need to have in stock in order to supply the customer next year? So is it not similar to how you worked out when we would hit a million listeners? Like, are you not just looking at previous data? So if a customer came on in November, so they've only been buying for two months, wouldn't you just take what they bought in that two months and then go, okay, well, let's times that by a six because that's 12 months. But what the difficulty lies in, how do you then sum that up across a bunch of customers

and where cedric got caught in a knot was they were like oh ones that start in january will be the same there will be a zero percent increase and the ones that start in february well they've got 11 12ths so they're going to have one more it's an extra 11th because of the length of the year and so what cedric was trying to do is take that approach of the same rate but over more time but then work it out for a bunch of different ones and find a way to how do you how do you combine them how do you do it for all the customers as opposed to just doing each individual customer yeah okay whereas geometrically you don't have to do any of that you just look at it and you're like oh it doubles and that that's the same result you'd get if you

then did a whole bunch of individual hypothetical customers and then add them all up and then work out what the total percentage increase would be you get the same answer but what would happen complicated journey if the customers being acquired were at non-normal nothing that creates a nice gym like geometrical shape yeah then you'd have to i mean what you could do in reality is get a bunch of previous data which is what i kind of did last episode when i was doing the prediction for a million was not try and work out what the shape was just look at the data that and just know like i had to know over what interval to average to then get the previous shape not try and name it or work out what it is and then just duplicate it to predict the future so so in a messier situation

that's what you would do whereas um cedric gave me a bunch of assumptions saying there they come on roughly evenly and they they continue to spend about the same but in reality what's actually happening is they are hoping the customers will buy more over time because the commemorative plates are just so good and what they want to be able to do

is work out how much of that their good product, their good sales their good whatever and how much is just they've been customers for a longer amount of the year and so this doubling as a kind of a baseline means they can kind of compensate for that and anything above that is is a genuine increase that's not just um the effect of having more customers and over a big enough company with enough customers the variations will all kind of average out. And so that's just kind of a nice, you know,

handy way to know what's a genuine increase and what's just they've been buying stuff for longer increase. Yeah. Do you want to see the slide? Yeah, of course I do. I'm curious to know how close, I labeled it year one and year two, and then you got customers coming on making a

triangle and then you got a rectangle yeah that's yeah that's pretty much what I envisaged that's very pleasing that was my my solving a business problem using a diagram it was a very nice diagram yeah yeah that's very satisfying you should put that on a t. You should put that on a t-shirt, Matt. Put that on a commemorative plate. That's your solution. I should. Oh, commemorative plates at the time I solved that problem with the diagram. We're not doing that, everyone. I feel like commemorative plates are going to be a slippery slope.

Like your diagram. Not my diagram. Number of plates. Number of hilarious joke-related plates released in a year. Slash bowls. Slash bowls. Well, I'm going to give that a ding. Hey, a business ding.

Geometric business ding. GBD. Now, I know you're thinking that was a lot of business, but what about if there was any other? And there is. Thank you to everyone who sends in comments, feedback, and add-ons, additions to our previous solutions, including David, who jumped on to the Problem Posing page at problemsquared.com and flagged up. Well, actually, Bec, I'll let you handle this one because it was when you were talking about the reviews of the Bell Tower in Perth on TripAdvisor. Yeah, so David said during a Problem Squared 050,

you briefly mentioned the circle rating for the Bell Tower in Perth on TripAdvisor and gave a small chuckle about it, because we were laughing about how it's five circles. It's like dots, yeah. how it's five circles like dots yeah yeah now david pointed out that the reason for the circles is so that people don't get confused with the star ratings for hotels because if you were to you know give something a five star rating on tripadvisor that's not the same as the you know the proper star rating that is given to hotels and so you don't want people getting confused and i think that's fair enough i think it makes sense yeah if someone sees a hotel and trip advisor with a four star rating it doesn't mean they're going to have a hot food service menu

across certain hours as is required of a four star hotel or whatever the case might be yeah exactly but david also pointed out that the internal name for them are bubble ratings isn't that cute yeah bubble bubbles i feel like david if that is their name is a uh you know anonymous source from within the trip advisor machine seems to be wow well i give david a five bubble rating. So thank you, David. And someone else chipped in to let us know that the Scottish tune played on the bells is called Craglia. How would you pronounce that, Bec? So that was the. Oh, wait. Oh, so that.

Right. I was thinking Scottish tune as in the Robert Burns one in Perth. Yep. But they're pointing out that Waltzing Matilda is a Scottish tune. Oh. Yeah, so apparently it's called the Craigie Lee, written in around the 1800s and was adapted

to be the music for Waltzing Matilda by Banjo Patterson. I did not know it was a Scottish tune. There's your Scottish link again. Again. Classic Perths. And finally, a huge thanks to everyone who listens to this podcast, particularly those of you who give us a five bubble rating on whatever your bubble rating platform of choice may be.

And particularly, particularly those of you who put your money where your bubbles are and you support us on Patreon. This has been a bubble heavy episode, hasn't it? Thanks. We hugely appreciate all our Patreon supporters. Not only are we giving free commemorative plates to the top tier, the wizard tier of our Patreons, but we pick three names at random every time to thank,

which this time includes... Remo. Craig Anderson Erland Bakbu So thank you very much to them and everyone else on Patreon. And that's it for the podcast. Or is it? I think it is. It probably is. I've been

Matt Parker for the vast majority of the time and I'm fairly certain I was joined by Beck Hill, if that is your name. So, Matt. Yeah? You know how we didn't have anything for our post-credits? So, Matt. Yeah. You know how we didn't have anything for our post-credits? No, there was a real void at the end of the show last time. Yeah.

Well, I think it'd be nice if the listeners can get to know us a bit better. Oh. So, I thought I would find out. I feel like we overshare enough in the main episode, but carry on. I thought you might want to know what tree sign you are. What? Yeah. There's a quiz online. What kind of tree are you? Find out your

tree astrology with Celtic Tree Astrology. That's great. You can always trust the sign that repeats itself. Yep. You don't have to do anything. No, you don't have to do anything No you don't have to do anything actually But I thought you know You did your stump date

So I thought you might want to know what tree sign you are So I know that your birthday is in December Correct So you're an elder tree The seeker An elder tree Elder types tend to be freedom loving And sometimes appear to be a bit wild

Compared to the other Celtic tree astrology signs. In younger years, you may have lived life in the fast lane, and as a thrill-seeker, you and your boogie board, you are often misjudged as an outsider, and you have a tendency to be withdrawn despite your extroverted nature. You tend to be very considerate of others and genuinely strive to be helped.

These acts of assistance are sometimes thwarted by your brutal honesty. Elder signs fit well with older and holly signs. What a series of wide sweeping statements that would apply to anyone. I haven't had a cold reading that good all week.

Do you want to know what I am? I want to guess you tend to be extroverted except for times when you just want to be by yourself. Is that right? Am I getting that right? No, actually. What tree are you, Bec? It's not bad.

First of all, mine's not even a tree. I'm a reed. That's not even a tree. What? I'm a grass. You're not even a tree. Dang. Reeds among the Celtic tree astrology signs

are the secret keepers. Now that's a lie. I cannot keep a secret to save my life i i nearly gave away precious secrets on this very podcast you dig deep inside to the real meaning of things and discover the truth hidden between beneath layers of distraction nope i never get past the layers of distraction i am constantly stuck in the layers of distraction famously undistractable when there is a need to get to the layers of distraction. Famously undistractable. When there is a need to get to the heart of the matter,

the read sign will most certainly find the core. That's, to be fair, you know me, I love a deep dive. I will get distracted, but, you know, I will do the deep dive. You love a good story and can be easily drawn in by gossip. Correct. Scandals. Sure. Legend and law.

Yes. These tendencies also make you an excellent historian. No. Journalist. Detective or archae law. Yes. These tendencies also make you an excellent historian. No. Journalist? Detective or archaeologist? Nah. Maybe detective, but archaeologist? Nah.

I do like digging things up, though. You love people because they represent a diversity of meanings for you to interpret. Well, I am. That's what I'm doing right now. Read signs join well with ash or oak signs. You's what I'm doing right now. Read signs join well with ash or oak signs. Whoa. You know what, Beck?

If I was you, I wouldn't read too much into it. Hey! Hey!