A Problem Squared - 084 = Indicators and In Da Cake-ers

Episode Date: May 6, 2024

In this episode... 🎂 Where did birthday cake come from?  🚗 How come my indicator is never in sync with other cars waiting to turn? 💼 And, as always, some business from the business briefcase. Nina, here’s that recipe for Greek Honey Cake: https://www.food.com/recipe/greek-honey-cake-428671 And for more cake from around the world, look no further than this infographic: https://i.imgur.com/lhhotIE.png Here’s the Ben Eater video referenced by Matt: https://www.youtube.com/watch?v=kRlSFm519Bo And the fascinating paper about time perception and its illusions: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2866156/ Please do send us your problems and solutions to the website: www.aproblemsquared.com If you want more from A Problem Squared, you can also find us on Twitter, Instagram, Discord and on Patreon.

Hello and welcome as we roll the dice on another episode of a Problem Squared problem solving podcast where if you don't want to solve your problems by leaving it to chance and rolling dice you can contact us and we'll do our absolute best to solve your problem for you and by us i mean me matt parker mathematician i solve problems in a very similar way to rolling dice and that you don't know what you're going to get but it's pretty likely it's going to be covered in numbers and i'm joined by comedian author writer performer beck hill who's also very similar to rolling dice because her solutions will be full of pip yes pip is the like the name of the dots on the dice oh i didn't know that yeah yeah pips pips on the dice oh that's. There you go. Oh, that's cute. When you said full of pip, I was like, wait, the inside of a dice has a name?

I thought it was going to be like- No, I mean, covered in pip, just didn't have the same ring. I was okay with covered in numbers. Yeah. I feel like full of pip was a better way to phrase that. Yeah, I'm full of pip and vinegar. First, I was just filled with vinegar. That is a Simpsons reference that maybe about a third of our listeners will get.

Our listeners will be an above average amount of Simpsons aficionados. On this episode. I'll be looking at what's in a cake. I'm going to indicate when indicators got to indicate. Indicate. Indicate. Yeah. You. Indicate. Indicate. Yeah. You're Indicate.

Indicate. And there'll be some any other business. Any other baking. Any other bakeness. Oh, no, wait. No, the theme was dice. Oh, too late to change now. Oh, well.

This is a cake-based episode now. Good job. Hey, I'm up for pivoting to a cake-based themed episode. So, Bec, how are you doing? I'm great. I'm still in LA. I went to the Bob Baker Anniversary Festival here on the weekend. Bob Baker was a very famous puppeteer.

There's the Bob Baker Marinette Theatre here in LA. Are you saying that just because it's got the word bake in it and that keeps us on a new theme? Oh my gosh, no, I didn't even think of that, but you're right. This is just synchronicity happening. I love this. Yeah, no, we went to this puppet festival, outdoor fair thing, and it was great. All these different creative stalls that have made puppets and sell puppets and everything. In fact, there was a stall for one puppet-based business that I actually follow on Instagram, and I got a little bit starstruck seeing some of the puppets.

Oh, my goodness. Yeah. Hang on, hang on. Is this a trade show for people in the puppet industries? Or is it like something you would go? Okay, right. Yeah, it was a public fair. It was sort of to introduce people to this thing

and tell them about the history of the theatre and everything like that. But it was really fun. The weather was gorgeous. Yeah. Had a lovely time, even though we didn't win the raffle. But I did realize something. I've got to admit to a potential low-level crime that I only realized last night might have happened. So one of the prizes of the raffle was to win 100 scoops of Jenny's ice cream.

And Jenny's ice cream was a- 100 scoops? Yes. So I guess you could have it. You didn't have to have them all together. And Jenny's ice cream is a very nice ice creamery here in LA. And next to the jar with all the tickets in it, there was some little sort of business card things. And I thought, oh great, little like discounts or money off or something. And I thought, oh, great, little like discounts or money off or something.

I grabbed a few and noticed that it was for a free standard ice cream. I was like, oh, great. A free ice cream? A free standard ice cream, yes. I was like, oh, brilliant. So I'll grab a couple. And then my friends can go a couple of times, you know, throughout the year. Yeah. Help themselves with ice cream.

So I think between the four of us, maybe took like 10 which is quite a lot but when you think about it that's like that's like you know two to three ice creams per person a reasonable amount they're going to use them not all at the same time and so after after we uh finished the first one we went well let's go to jenny's lovely day let's let's go to jenny's ice cream and get our ice cream so is this the same day same location the four of us we went and got an ice cream each we had a lovely day we're very chuffed with ourselves and this was um about four days ago now five days ago okay and then last night, just as I'm getting ready to go to bed, I realized, and I don't know why it didn't occur to me earlier, but I was like, oh, do you think there was a hundred of those cards? Was the prize a hundred cards that give you a free ice cream?

Oh. And we've just helped ourselves to some of the prize because you just skimmed off the top of the prize yeah but the way that they were sat by the thing it looked like someone already been taken because they were kind of like there was a cut there was it was they were standing up half of them were like in a little paper wrap thing you know when you get like a thing of business cards or flyers or something there's like a little strip of paper that holds them all together so i would say about paper belt about two-thirds of them were in that paper belt and then there were a couple strewn around so it looked to me like that they chucked

it there as a like oh this is an advertisement for for what this company is and the way it was presented on display yeah exactly was it and i suspect that is down to whoever put them there thinking this is not the prize this is just but when i thought about it i realized the other jars had because the other jars were um for the for the raffle tickets because you would take a raffle ticket and you'd put your ticket in the jar for the corresponding prize right i should have made that clear so there'd be a little sign saying what it was and a picture and that was with all the other jars and some of them were like for a t-shirt pack so you didn't have the t-shirt pack there

you just sort of guessed based on the little sign but some of the others were like for um like rare marionette puppets and those puppets were sitting near the jars so you can actually see what they look like and i didn't help yourself to them no well if there'd been multiple if there'd been hundreds of puppets there that sort of were strewn about as if you could just take one do you think that the was it the fault of the person setting up the jar and prize and they were like oh when they kind of opened them and spread them out a bit or do you think there was like the first person who broke the seal and took a couple and after that everyone's like oh it looks like a take a few situation well i suspect that the person who laid them look either people had

taken them or the person who laid them out because the seal wasn't broken they'd obviously just taken some out and sort of fanned them across yep so it's possible i was the first person to take some but i might not have been either i went back and took several each time though and no one stopped me so whoever was working on the stand didn't seem annoyed by this so i don't know i may have stolen from a charity raffle that's what i'm saying you didn't know at the time you're an accessory to your own crime after the fact yes yeah i feel like you can only get into a medium amount of trouble and you didn't cross state lines while eating the ice cream or anything. So it's not like a felony. Oh, no.

Oh, gosh. I don't know how to break this. But yes, other than that, I'm good. Anyway, how are you? I was also in L.A. until quite recent. Actually, the big part of the trip, I handed in the final outstanding parts of my book, Love Triangle. So it now exists in its entirety at the publishers. There will still be one last check.

I will get to see one more round of the typesetting because I've asked for a few last changes. And so I'll get to sign off on that. But they're not waiting for anything else from me. I've sent in absolutely everything. And the big things that were waiting on the index. Oh, do you want to guess what perfectly normal system I've come up with for the index this time? Is it the degrees of a triangle in sign pretty much there is is it the thing you mentioned on a previous podcast episode but i think you may have forgotten that you've already

mentioned no that is the fact that all the page numbers are the sign of the page number right so that's that's still true but so the index does give you it's like such and such is on page and then it'll be like 0.12748 or whatever yeah quite pleasingly the phrase a big circle is on page 0.000000 which was purely by accident but looks amazing in the index yeah no in addition to giving the page number, the index, I say we because my mate Andrew Taylor does the coding for all my indexes. I know Andrew Taylor.

Andrew's great. Yes. Very, very talented mathematician, coder man. And does all sorts of ridiculous coding for me for different projects. And so he's done all my indexes. So we get together. Each book, we have a think about what would be fun to do in the index.

And this time we decided to, as well as the page number. That's a great sentence. We get together, think about the most fun thing to do. Yeah, like the first book we gave the X and Y coordinates on the page. You don't need to justify it. Anyway, okay okay so this time we also give the angle we give it in polar coordinates so we give you the page number the words the words are on and then we give you the distance and angle from the bottom left hand

corner of the page so so you just need to rotate up by whatever angle we give. And we do it in units of page width. So then you know the distance. Then you can quick and easily find where the words are on the page by using the distance and angle from the bottom left-hand corner. Would you use a protractor? If you were doing that, you know, by hand, would you use a protractor is that the tool you would use i i think you should do some special edition ones that come with come with the a protracted index yeah nice you're right i should give away protractors that'd be kind of fun yeah please pre-order my book i put a lot of effort into the index go to massgear.co.uk pre-order Love Triangle we're currently on the

tetrahedron limited edition covers and when they run out they'll be triangle ones for a bit and then once they're done that's it no more limited edition just check it out and I suggest that you make every pre-order and raffle entry they could win one of

one of a hundred protractors of which there will be 90 available because i accidentally still turn yeah would you believe that would not be the first time i will have made and given away branded protractors i 100 believe that matt how long have i known you good it's true this is our 84th episode of course i believe oh my goodness speaking of which shall we do an episode? Our first problem was sent in by Nina, who went to the problem posing page at problemsquared.com

and they say that they're having their ninth birthday oh on a good square number it's not often you get to turn a square number that's pretty special and they space out as you age fewer and fewer so get ready nina birthday party on sunday the 19th of may and they are not sure what type of cake to have there will be 20 people max it's good to have an upper bound on these things nina including uh themselves and it will be a woodland party they don't like dark chocolate they don't like red velvet uh but they do like all other types of cake and then unlike most people there's a problem they have signed off by saying, Bye, Beck and Matt. As in goodbye, not as in buy us.

As in goodbye, like for sale. Yeah, no, goodbye. Nice sign off. So, Beck, you've solved or have some potential solutions for Nina's birthday cake problem. Yeah, this is a great problem. It was also a terrible problem because I'm so suggestible. I am so highly suggestible. And anytime I do any sort of research, like we were taking notes for the other podcast that I do, Enemy in Paris, and the episode we were watching of Emily in Paris featured McDonaldald's and so i had to order mcdonald's they got right in the way of my research and likewise last night as i was doing some research for this had to stop and go and buy some cake so i thought i should just do some research into the history of birthday cakes.

Oh, nice. Just out of interest. I've never questioned it. Yeah, because you find yourself thinking, like, who was the first person to go, oh, I'm going to have a cake. Can I have a guess? Oh, well, I don't have a specific person, but sure, go for it. In that case, my guess is definitely wrong.

Let's see if you can we're gonna go marie antoinette or someone i was gonna go uh queen victoria oh because victoria's like there see that's they invented the sponge cake for their birthday that's my theory that's nice i like that uh oh look i'll tell you what Do you want to guess what culture they believe the birthday cake tradition might have stemmed from? Germany. You're partially right. Yes. Oh. I would say the more modern version of it does stem from Germany.

However, they think that the sort of first time that annual cake was presented to celebrate something was potentially back in ancient Egypt when they would celebrate their gods. So the coronation day of their gods was named as their birthday. They would celebrate with this sort of type of cake. The Greeks later adopted the tradition. They added a cake to the celebration for their gods. Way older than I expected. Yeah. So they would create a moon shaped cake, decorate it with candles and present it as a peace offering to Artemis, goddess of the moon.

Once the candles were lit, they were signified as they were shining up at the moon. Hmm. I was off by a millennia. Yeah, you were. But you know, there's a lot. There's a lot of background to it. The term cake itself has a really long history. Because cakes are sort of different in each culture,

there's actually no real defined limits of what a cake specifically is. It's kind of like the word pudding in the UK, because pudding in the UK could mean dessert generally. It could mean a specific type of dessert like christmas pudding or it could mean yorkshire pudding which is savory and nothing like a pudding at all it could mean black pudding which is again like a sausage there's yeah so it's sort of one of those terms that uh it's more in the gray area of what it is but the word itself has a viking origin it's from the old norse word kaka which i'm hoping very much has nothing to do with kaka also being a term for poo um the ancient greek called cake

placas which was derived from the word for flat it was baked using flour mixed with eggs milk nuts and honey they also had a cake called satura which was a flat heavy cake during the roman period the name for cake became placenta which was derived from the greek term so placenta was baked on a pastry base or inside a pastry case the ancient greeks first started adding stuff like beer as a leavener oh okay to make cakes got yeast in it yeah makes sense cheesecakes they uh sort of derived from the ancient Greeks, apparently. They were using goat's milk, which I'm sure was actually very tasty. You're right.

I never realized how varied cakes are. So varied. In ancient Rome, the basic bread dough, you know, that you kind of, you get more for like banana bread, that kind of thing. They added butter, eggs, and honey. So that is how we get sort of closer to the sort of cake that we see today. Yeah. In fact, a birthday party and cake are mentioned in Tristia,

in the first book of exile by Latin poet Ovid. Wow. You know, I don't tend to bother with a cake for my birthday or indeed Lucy's. We're not big birthday cake people. But the more you talk about this history, because I assumed it was quite a recent thing. Now I realize the Greeks did it. Suddenly I'm like, oh, I should have a birthday cake. Like, I feel like this is an ancient tradition.

Yeah. Yeah. It's part of the human condition is having a birthday cake. Absolutely. I mean, one thing that came to my mind immediately as well is the Chinese tradition of moon cakes around the Lunar New Year celebration, which I particularly like. They're sort of closer to, how would I describe them? They're kind of like, imagine a pork pie in terms of the crust, sort of very heavy, stodgy, but instead of the pork filling,

it's like a sweet egg yolk. And there's all sorts of cakes from all around the world. In fact, I will link to it. There's a nice infographic which will pop up on socials and link to in the show notes. But that shows a lot of very famous cakes from all around the world. If you want to expand your knowledge of different types of cakes and how it could be done. But you were right in terms of Germany.

You said that earlier. Yep. I just thought of a culture that does a lot of celebrations, has a bunch of traditions, has a sweet tooth, has been around long enough and i thought germany ticks a lot of those boxes although i reckon i could be off by plus or minus one country and in that kind of region yeah well i mean also when you think of germany like they're pretty good at cake they're pretty good at desserts actually the sort that we get today um so modern birthday parties are said to get their roots from 18th century German celebrations of Kinderfest. So, on the morning of a child's birthday, they would receive a cake with

lighted candles that added up to the kid's age, plus one. Oh, plus one. Yeah. Off by one error. A zeroth candle, you could say. Love it um this extra candle was called the light of life and it represented the hope of another full year lived oh wow it's like oh good luck kid this is all this could be yours yeah if you survive another year now they would light the candles at the beginning of the day and then replace the candles as they burned out throughout the day you weren't allowed to have the cake until after dinner. So you'd just be tortured. Watching this cake.

Yeah. Replacing the candles as required. Yeah. And then as we do today, the kid whose birthday it was would make a wish, try and blow out all the candles in one breath. Standard. Standard procedure. And the reason this didn't really become custom until the 18th century is because ingredients for cakes were really expensive. Sugar was like gold dust.

To get all of the ingredients needed to make a good cake, there was a lot of effort that would go into that. And so it kind of wasn't until the Industrial Revolution where ingredients became more available, therefore cheaper. Do you want a little bit more cake fact before we get on to solving the problem? Yeah, let's have another serving of cake fact. So I looked into cake mixes, which I thought was really interesting. You know, prepackaged box comes in the powder and you might add milk or eggs or something and create your cake. So during the Great Depression, there was a surplus of molasses,

but obviously there was also a need to provide easily made food to millions of economically depressed people in the United States. So there was a company that painted a cake bread mix to deal with the economic situation and they established the first line of cake in a box. When you think about any time of hardship for a country whether it's war depression anything like that quite often that's when you start to get the instant food become a thing but during the post-war boom other american companies notably general mills developed the idea further they marketed cake

mix on the principle of convenience especially to housewives so it became very popular housewives then they found in the 1950s the popularity dropped and they tried to work out why and they realized it was because previously housewives didn't have much opportunity to express their creativity because they were kind of just bound to stuff around the house so a lot of women put their creativity into they were kind of just bound to stuff around the house. So a lot of women put their creativity into their cooking, into their food. So they would invent, they would try different recipes and put it all into what type of cake it was and all this sort of thing. But of course, when cake mixes became popular and all you had to do is stick some ingredients in a bowl and mix it up and bake it, there was no creativity there. And so they just weren't interested.

And so the sales dropped. And the way that marketers got around it was they started to include icing. Oh, so you decorate the cake. So you could decorate the cake. So it became less about what went into the cake and more about the decoration. And I want to lean on that as a potential option because I know, Nina, you're worried about what sort of cake you should choose. I think you should just choose whatever your favorite cake is. It's your birthday. I think you should choose. But if you want it to keep on woodland theme, I think you should think about how you're going to decorate it. That's what you might want to concentrate on. You could have quite a generic cake, which I'm now going to call the filling, and go all out on the decoration.

Yeah. So if you wanted something that technically no one's going to argue with, you could go just a standard sponge cake. It's sort of vanilla. It doesn't really have a huge amount of flavor, but you could choose what sort of icing you have on top. Another option you might want, Nina, is you could look at what the most popular dessert was when the year you were born. I believe you were born in 2015, if it's your ninth birthday this year. In which case, I looked it up for you. Yahoo, which to be fair, might not be the most reliable search engine of that year, but Yahoo said that in 2015, banana bread was the most searched one. So you could have a form of banana bread,

which I would argue is cake. That's cake. Yeah. What's your favorite cake, Matt? I don't know if I have a favorite cake. I partial to chocolate cake but i'm not a big sweet tooth kind of guy so you're not no i'm no yeah i do like elaborately decorated cakes we at the mass jam weekend which is like the big mass jam recreational mass conference i'm involved with um we started a baking competition oh and i only entered it once there wasn't pies no i know uh a surprisingly few pies to be honest but the the competition's judged on how good the maths is and how good the actual cake whatever it is you're eating is so there's two different axes upon which the entries are judged and the one year i entered i did use a cake mix

because i was like i have no interest in the actual content of the cake but then i cut it up into so i could assemble the the blocks of cake into an arch so i had like a catenary shaped arch built out of wedge shaped bits of cake yes so as long as the bottom two i kind of iced onto the board then the rest were self-supporting so i think i mean i'd inadvertently subscribe to the back philosophy of it doesn't really matter what the cake is it's all about how you decorate it and how you express it so i would say you know an engineering marvel is not to be ruled out for your, I don't know if that helps for a woodland cake, but you know, the cake can be a surprisingly versatile material. Yes.

To then express yourself with. Nina's turning nine, as I mentioned, square number. So a three by three grid of cupcakes, a a cube of cakes that's area based nine would work or if everyone had half a cupcake that's 18 portions it was max 20 i think for a woodland themed my main suggestion and i think this might be an answer because i don't know many people it's not one that people necessarily think of this type of because it's not usually the top normally it's chocolate cake or red velvet or as as nina was saying uh or victoria sponge or something but i think if you're going for a woodland theme and you want something that actually people forget about but they're like oh this is really nice and this is my favorite cake

matt this is my favorite type of cake oh Oh, really? Yep. Carrot cake. Carrot cake? I think carrot cake is very, very underrated. It's got a bit more to it than a plain vanilla flavor or whatever. Oh, yeah. And get yourself some of that cream cheese icing. You've got a little bit of a tang to go along with the sweetness of the cake. Oh, you bring us a tang. Yeah.

That's my personal favorite cake. And then I would probably decorate it with some, maybe I'd wash some sticks or something. I don't know. Put some, try and put some nice decorations on there. Or, oh no, do you know what I would do? I would make like trees or logs or stuff, but using pretzel sticks, things like that. Oh, nice. Yeah.

You could have little baby carrots as logs well isn't there a type of cake which is like a yule log that's a christmas christmas thing but couldn't you couldn't you still log i'm using a log as now a category of cake not a mass where you make a very thin not a mass log make a very thin sheet of cake and then you roll it up with icing in the middle is that is that logification of a cake i think so i believe so so if it's woodland themed you could do a log cake yes as a log that'd be quite nice yeah that's true and if you find it hard to roll cake just do it with pancakes just do pancakes yeah I like your idea of finding other edible items to decorate it to make it look like a woodland scene. I think that's really nice. Get some edible flowers.

Now, I don't know this with 100% certainty, but I think I know who Nina is. Oh. I think Nina, and this is going to really close the loop on this one. When we were talking about honey, and I said I spoke to a beekeeper friend of mine about how long honey lasts for, I'm like 99% sure that's Nina's dad that I spoke to. Ooh. So I think this is my neighbor.

Let the record state that I chose this problem. There's no nepotism going on here. But that's why i'm only bringing it up now yeah at the end of the problem solving when i saw nina i'm like wait a minute i think that's my neighbor nina so i suspect that neighbor nina has access to honey from her parents bees oh so if you which live in the woodland so if you want to go full woodland, you could use honey as one of the sweeteners in the cake. It could be a shaped cake.

That also harks back to the very old traditional ones as well. The original Greek cake. Nuts and honey. Yeah, nuts and honey. That's a woodland cake. Well, I tell you what, we may have solved this problem. What? We're going to set an unreasonably high bar for ourselves might i suggest yep nina that if your parents can somehow make or source this greek honey cake greek honey cake yep it tastes uh a lot like baklava

i don't know what that is you don't know what baklava is oh okay matt do not like baklava. I don't know what that is. You don't know what baklava is? Oh, okay, Matt, do not have baklava until I'm back in the UK and you're back in the UK because I know you're going to be in Australia soon. I've managed to avoid it for the first 43 years of my life. Yeah, but I just know that since this came up, you're going to get- That's true. Okay, fine, fine. No one offer me that thing that Beck said.

Baklava. It's all right. I can't wait. You're going to love it. It's like a- Until, can you bring some around next time? Yes. We're recording together?

Yes, I can. Yeah, yeah. There's loads of places near me in Camden that sell it. Anyway, I will add a link for a recipe for Greek honey cake in the show notes. You're going to love this, Matt, because the example that they have has been shaped. I don't know how they've done this, but they've shaped it into hexagons so that it looks like a honeycomb. I don't know. Well, I put the link for Greek honey cake in the show notes. So if any of our listeners want to crack as well, we'd love to see photos. So if you're on Instagram or Twitter, please send them to us, or you can send them to the

problem posing page, which is a problem squared.com. Select solution in the drop down box and pop a link to wherever you've uploaded your photo. You can go and view it. I'd love to see that. And of course, if anyone else has any recommendations of cakes, tweet them to us or X them to us as our new lord and master, you know, must we call it, at Problem Squared. Well, Beck, I don't feel like we can put the ice sting on this problem just yet. If this is neighbor Nina, I'm going to be in Australia when the birthday party is happening, assuming I would have been invited where I around. So I can't check in the moment,

but we will wait. Nina will have a birthday and then she will report back on what cake she ended up with. And if you solve this problem for her and then we will AOB it. Any other bakeness in a future episode. This next problem comes from Charles.

And I've got to say off the top, I love this problem. I would have answered it had I felt like I had the capability to. I'm very glad to know. You spotted it as well in did because i'm posing page database yeah some of my favorite problems are ones where i go yes that's annoyed me too so charles says how come my turn signal or indicator is never in sync with any of the

other cars waiting to turn it always slowly drifts into sync and then out to opposite and then back again is my car's turn signal twin out there somewhere will i ever find oh gotta go traffic is moving don't type problems and drive people yeah i think this is fairly widespread i know i look at well it's difficult now because back in the day when you put an indicator on, you would hear the click, click, click, click of the indicator going on and off. You could audibly hear it. I mean, you're hearing the actual indication. Oh, you're hearing the actual light.

Yes. Yeah. Well, you're hearing whatever the mechanical mechanism is that's turning the light on and off and i don't know i assume that's surprising to me because i imagine that cars are quite are even louder in the past but i suppose if you're just sitting there you're not driving that's a good point you're not revving the engine you're indicating also it was you know partly a byproduct but also a feature so you know your indicator's on as opposed to just driving along with it on all the time yep so i think it was also deliberate

and the old old mechanisms were you'd effectively have a contact like a bit of metal would make a contact but as it warms up from the current flowing through it it would cause the metal to bend and break the contact and then it would cool down because it's not a current going through it and as it cools down it bends down and recreates the contact and then repeat it's so it's not an active on off you know it's not being told to switch on switch off switch on switch off it's actually the the way that the connection's done itself that is a natural yes way that it yep wow you just supply current and it then regulates itself because as soon as the current flows it heats up and breaks the circuit it cools down and makes the circuit and

then by tuning you get like two metals stuck together which expand at different rates and that causes it to bend because one is expanding more than the other and by selecting the right metals for that you can kind of tune the time it takes it to cycle through okay so you think that that was deliberate because my mind immediately goes to at what point did someone try to make just a normal on off switch where it was meant to stay on but it kept turning itself off and they're turning on. And they were like, oh, what use is this? When is this ever going to come in handy? And then cut to someone going, how are we going to do these indicators

where they're really obvious? No, super deliberate. And it's like a very slow version of telephone bells and doorbells ringing. That's where the current turns on an electromagnet that pulls away the strikey thing, which breaks the circuit. So it then goes back towards it and reconnects, which then turns the magnet back on again,

which pulls it away, which turns the signal off, which goes back and hits. And that's the ringing noise. Is that happening super fast? Which is like an electronic version of a bike bell yes yes time you the bell connects it turns on it's obviously kinetic energy with a bike belt but this is yeah cool cool cool all right that's very interesting

and so because of that that kind of system there's a lot of variability so actually the speed at which your indicator goes if you look at the official like traffic code has a lot of range generally speaking anywhere between blinking 60 times a minute up to 120 times a minute. So that's like either once a second or twice a second. Anywhere in that range is kind of fine. And that's quite a big range when you're talking about the rate. It's like, you know, twice. It can either, you know, go once every half second or up to twice that. And so manufacturers apparently of cars would try to aim for the middle where you're doing about 90 blinks a minute.

And then they got lots of leeway above and below that to still be within the official regulations. And that variability means that, you know, the chance of two cars having the same blinking rate is quite low. That has not entirely gone away now cars are much more electrical and you use circuitry for these things but it's not like there's a computer telling the indicator on now off now on now off now you're still using circuitry using capacitors and everything else to do that more often than not i probably entirely now you're using some kind of custom chip you can buy little chips processors that are like timing chips and i looked up if there's like a standard one and there's not different

manufacturers use different chips and there's a whole bunch of these kind of off the shelf timing chips you can buy so there'll be some chip on some bit of circuitry somewhere in the car which is basically doing a very similar thing to the old metal connecting and disconnecting but there'll be a capacitor or something that fills up and discharges and you can use that to um to time it if people are at all interested in how chips and computers actually keep time. Like, how can you use circuitry to do timing? There's a YouTuber called Ben Eater, who I absolutely love. I think Ben's videos are amazing.

Ben builds basic computers on a breadboard, which is like a breadboard's like a prototyping board you're using electronics where you can, it's got a bunch of little holes in it and you can push components in and kind of build it up bit by bit. I never knew that's what that was called. You sort of get one if you get a Raspberry Pi kit, don't you? Exactly that. Yes. So Ben makes breadboard based computers. Which would be another good woodland cake idea, by the way, a Raspberry Pi, just saying. Well done. I feel like we should just end the episode now. Thanks for listening, everyone.

Goodbye. That's the high point that we're going to achieve. Anyway, Benita has a whole thing about building timing circuits and how these chips work. So I will link to one in the description if you want to dive further into that. The point is there's a lot of variation in the frequency your indicators happen to go at.

So that now leads us to two problems. So there's two things that stand in the way for if... Actually, you know what? Because now I don't 100% know if the noise that's made in the car matches what the indicator is actually doing. Because it's now it's now divorced it's it's a separate noise that's being made probably in the speaker or a custom speaker in the cabin of the car to tell you the indicator's on which i find very funny because it's recreating the old noise used to get yeah from the strip connecting and disconnecting

which means if that if it is the case it's not necessarily the timing and which your indicator is on on the outside so i'm gonna reframe the question because what i always notice is i will look out and see two cars in front of me and then i'll notice if their indicators are in time or not because i'm looking at both the lights at once so i actually think that's the question here. Because I don't think people are that, and maybe I'm wrong. People do correct me. I don't think that many people are kind of looking at the indicator, blinking in front of them and then listening to their thing. No, that's what I do.

Oh, really? Wow. The fastest I've been proven wrong in a while. Just because I'm like, oh, am I hearing their indicator? And then I'll notice that I'm like, oh, no, now it's like... Ah, it's off. Ding, ding, ding, ding, ding. Okay.

And then the listeners can't see this, but I'm sort of using one finger to denote... One finger per car. ...a light. And the other one is the sound that I'm hearing, yeah. Okay. So let's assume the noise made in the car is the same kind of mechanism, like the circuitry, et cetera. So it may or may not match your indicator but it's the same system

for if it's in sync or not with the flashing light of someone else's car or you could be looking at two other cars and seeing if they match let's imagine there are two cars that have by some miracle of manufacturing exactly the same frequency at which their blinkers go that may still not mean that they happen at the same time though because they could be perfectly out of phase it could be one than the other and then one and then the other it doesn't necessarily mean they're going to happen at once so you've now got the probability of are they happening at exactly the same time or are they out of phase and because they're the same frequency they will forever remain out

of phase so yes that's your first but our our listener does point out that sometimes it'll go in and out of phase it'll start off in line and then go opposite well that's the other problem because to stay blinking in unison even if they happen to both be blinking at the same time to start with if they're not precisely the same they will then drift apart from each other so by saying precisely the same we're actually saying close enough such that they don't drift over the period of time you're likely to be paying attention to them yes because the odds of them being exactly exactly the same as vanishingly small so that now gave me a couple problems one was i mean like how long do they have to stay in sync for

so i looked up roughly how long it takes for lights to change and i don't know how much you trust research from insurance companies because it's like they put out a press release because they know they're going to get free advertising because media will cover a fun press release about some ridiculous bit of research but not to get distracted in my complaints about those things but some insurance companies did this as like research that they could do a press release on and they said it's uh in the 60 to 90 seconds range that's the amount of time you tend to be waiting at lights in the UK. I then had to work out what would a human being consider simultaneous. So what's the human perception of things being simultaneous?

I couldn't get a hard number on that. Because so many things vary. You can alter how humans perceive if something is simultaneous or not, which I find very, very interesting. There's loads of things you can do to prime how simultaneous or not we will perceive things to be. Yeah, because I think we may have in our brains means that, I mean, even me talking right now between me thinking the thought and then communicating it out my mouth and you hearing that, there is time difference between that. time difference between that and so you are essentially always a little lagged behind because you're hearing and then processing that and we're weirdly good at ignoring or removing that lag so we don't perceive it so i found an experiment done well it's published in 2008 it's called human time perception and itsusions by David Eagleman, who is a

researcher at a university in Texas somewhere. And they did this experiment. So what they did was they got volunteers or subjects to come in and push a button that would turn a light on. But the light was a reasonable distance away. But the people pushing the button could see the light turn on. And they introduced an artificial lag of 0.1 of a second so 100 milliseconds and so you push the button and there's a tiny lag 0.1 second then the light comes on but they were able to convince over time the subjects that there was no lag that it was simultaneous and after a while the people pushing the button couldn't perceive the lag anymore because their brain had gotten used to it and they'd been primed that it wasn't there they then remove the lag

suddenly between presses and people had the sensation of whenever they went to push the button the light would come on shortly before they pushed the button but every time they went to do it their brain would go the light came on first because it's removing a lag that's no longer there anymore. And I was like, that's such a good experiment. That's so smart. I took that to mean, given that experiment was using a lag of 0.1 second and you could mess around with people's perception of simultaneous

or causality on that kind of scale, I decided that within 0.1 seconds we could perceive things as happening at once so that was like my tolerance for are these things blinking at the same time i rephrase it to be are they blinking within 0.1 second of each other and then you got to work out well how much can the difference be in the time between blinks such that you don't drift by more than 0.1 second over the course of 60 to 90 seconds that you're waiting at the lights? Yes. And I then ran that. seconds and the frequency at which people's indicators are going can vary between once a second or one hertz to twice a second at two hertz and so i i've now got two different things that

have a range of values and i combine them all to find the kind of upper and lower bounds of the the range so in conclusion the zone which two indicators will appear to stay within that 0.1 second difference so they appear to be always blinking simultaneously to the human mind the time between blinks the difference between that timing between the two cars needs to be somewhere in the range of 0.0017 seconds and 0.00056 seconds so that's roughly half a millisecond up to one and a half milliseconds which is less than a percent yeah per blank which is pretty small i then went looking into the sorts of this is why I was looking into what chips cars might use. And there's no consensus. So I looked up like one chip, the 555 chip,

but I couldn't really get good numbers on it. If people know more about what circuitry is actually used in a car and what the tolerances are on those timing chips, but the general vibe I got from quickly researching it is, you know, these chips have a decent amount of variability in them so you will get a wide range of different times across different cars and that feels like they have to be very close together if you want a very crude probability and there's a lot of assumptions I've had to make and I'm averaging across all these different

ranges things could be in I would say about one in a thousand cars have the same frequency as your car for one arbitrary car. So I'd say one in a thousand, give or take across a bunch of things we're assuming. And on top of that, you've got the, are they starting simultaneous in the first place when you see them at once or listen to one and see the other one? Yeah. And I reckon that is around one in 10.

If we're saying that's the, you know, it's a 0.1 second window that we're using. Again, super ballpark. Super ballpark. So I would say order of magnitude, it's a one in 10,000 chance that when you're sat at lights, a specific other car that you look at will blink in unison with your car the entire time you're waiting at the lights. Wow. Very hand wavy. It would be interesting to do this experimentally to see if that matches my hand wavy theory. But I'm vaguely confident that's the kind of region I'd expect it to be. One of my assumptions may be wrong. Do you know what?

You've gotten closer to an answer than I ever would. And I'm willing to accept that. I think the only way to test this is for a minimum of a thousand of our listeners. Yeah. What you'd need to do is get, you could get like a Raspberry Pi, as discussed, with a light sensor. And you could stick the light sensor on

or hold it up against an indicator and get someone to turn their blinker on. And then you've got to log the exact timing of that specific car. And then if you sampled enough cars doing that, you'd have to find somewhere you could ask people to turn their indicator on and you hold a thing against it or you wait a traffic light clicky thing on the inside as well i think and that's true that's a

separate experiment is does the clicking inside a modern car match that's something people could maybe do at home if you can when you're not moving put the indicator on wind the window down and get yourself in a position where you can hear the noise inside the cabin but see the indicator outside the cabin or like use a mirror or something i'd be curious to know from people i would have cameras with audio on both things and then find a way of lining that up as closely as possible so it would work because then you're not relying as much on your perception. And maybe I should have done this for my own car before this, but if people want to give that a go, let us know.

You already did a lot, Matt. I think I'm going to give that a ding, ding, ding, ding, ding. That's my impression of an indicator going dings. I love it. It works. A ding-dicator. A ding-dicator. Ah.

Yeah. Every episode we use the ding decader to see if we solved a problem or not. Yeah, that's right. It's like a clapper meter. Yeah, exactly. How many dings for this one? How many units of ding? I love that, Matt.

Thank you. Given you had the same question, I hope that was a satisfying answer. Yeah, it's a good one because it's one of the things that bothers me and now you've thought about it far more than most i believe and i've been proved correct that it's not really worth worrying about but but but i'm satisfied that i don't have to worry about it now okay yeah that's my that's my goal in life it's like it's like wondering if you left the iron on and then finding out you didn't yeah you know that's how i feel about this you don't have to yeah that's right thank you matt my pleasure

now it's the time in the show that we call any other bakedness or business, depending on what we're dealing with, where we take just miscellaneous things that listeners have sent in, which this time we've had a few people responding to when we were talking about clothes dryers. And, Bec, I believe you've looked into what people have sent us. Yes. And Beck, I believe you've looked into what people have sent us. Yes.

Yeah. So this is in response to a problem that I tackled in episode 082, which thank you, by the way, to Kristen, who I'm about to read out the response to, for mentioning that it's episode 082 because it's saved us going back and trying to remember what number it was. So thank you very much, Kristen for that really appreciate it and kristen got in touch with us via the problem posing page by going to your problem square.com and selecting solution in the drop down kristen says hi beck and matt with respect to episode 082 i have access to a tumble dryer and i used it excellent hey matt you know we're all about showing our workings. Very true. Kristen's done a Dexter. There's a lot of working here.

For any new listeners, that is in reference to one of our younger listeners who likes to always go to full detail. The gold standard for showing detail. Doing a Dexter. Kristen says, I have neither the time nor the money or clothes to tumble dry my laundry until it stops existing. or clothes to tumble dry my laundry until it stops existing. However, I figured a reasonable estimate of dryer-related reduction in fabric weight could probably be reached by weighing the dryer lint that is caught by the filters. Very clever. Going in with about six kilograms of laundry, about 50% towels, 50% other cotton stuff,

I gathered a total of 1.1 grams of dryer lint. Assuming that the amount of dryer lint is constant relative to the amount of fabric, we would expect an exponential decrease around 0.02% per cycle. After a bit more than 12,500 cycles, only 10% of the original piece of clothing would be left, which I would consider pretty much non-existent in this context. If the amount of dry lint was related more to the surface area, a linear decrease of the weight of clothes might be more fitting, leading to crossing that 10% left threshold after about 4,900 cycles. Of course, I can't account for any fibers lost while washing the clothes, but I think it is safe to say that it would take a while for the fabric

to disappear completely. Did I use my kitchen scales to weigh my laundry maybe did i buy some precision scales so i could weigh dry lint no comment that's so good welcome to the club of people who have scales that are too accurate in their kitchen christian might be my favorite person right now christian is gunning for my role as co-host they have they have gone to far more effort to answer this problem, deserve an entire episode where they get to do it. They've even bought scales. Christian, I am bowing to you like they do in Wayne's world.

I want to add that this is the level of attention to detail and problem-solving data collection that I expect of all listeners. So I think this is very standard. Well done. and problem solving data collection that i expect of all listeners so yeah not me but i'll listen yeah well done uh kristen then also says did i write some python code to visualize a predictive weight of my laundry over the next 12 551 dryer cycles well yes of course i did the code is below if you feel the need to adjust the definition of no longer existing or any of the other parameters. Cheers, Kristen. And then they've listed a bunch of code in the form. That's great.

Do you want me to try and run it? Yes. Yes. Okay. Hang on. I'm opening Visual Studio Code. Let's hit go. Something just blows up near you.

And here we go. Running. Oh, it's returned a number. It's come back and said, oh, it gives the number. So I ran it and it now says cycles until defined threshold, assuming linear decrease, 4,906, assuming exponential decrease, 12,551. So you can put in the threshold at which you think it no longer exists 206, assuming exponential decrease, 12,551.

So you can put in the threshold at which you think it no longer exists, and it will then tell you how many drying cycles it will take until that happens. Oh, it's given me a plot, and it's given me some text. The text says, this is quite a nice little readout. It says cycles until defined threshold. So you can edit the threshold if you want. And it says assuming linear decrease, 4,906. And then assuming exponential decrease, 12,551. There's also a plot that's appeared which shows the decrease over time.

So there's one line, a blue line, showing the exponential decay. And there's another line just showing the linear decay. And then you can see where they go below some threshold to indicate that the clothes no longer count as clothing. So I will make this screen grab available. And I will also, I'll just take a still of the output that we can share as well so if you want to see that perfect uh you can see it and for anyone who skipped forward christian's too long didn't read just says based on weighing dry lint i would predict that 90 of

the fabric will be gone after 5 000 to 10 000 dryer cycles details plus python code for plots below thank you so much, Kristen. That is phenomenal. Absolutely phenomenal. I would argue that that is absolutely made this episode. Yeah. So far, this has been one of my favorite episodes so far. We did receive another piece of feedback from Judah,

who also said regarding episode 082. Again, thank you, Judah. Thank you for numbering it. Love it. While talking about Lint, you left out what, in my mind, is the most important reason for why we use lint traps. So your house doesn't burn down. I mean, that's handy.

The trap catches all of the pieces of lint that are likely to catch on stuff. Without the trap, a lot of that lint gets stuck in the duct between the dryer and the exterior of the building when enough builds up fires will happen all capital letters will even with the lint trap then can build up in the duct and the duct should be checked for proper airflow on a regular basis yeah so i can't help but feel that between all of us, this is very similar to when I thought I very clearly answered the problem about whether a plane could fly along the autobahn. Oh, yes. And loads of people came out from different angles to explain various reasons

why I was wrong. And I love it. I love learning through this. I mean, these people haven't said that I'm wrong. They've just done. I love learning through this. I mean, these people haven't said that I've wrong. They've just done a better job at answering it than I have. So I appreciate that very much. They've built upon the firm foundation you laid to solve this problem. On the shoulders of giants, as they say. That's the one. Thank you so much for listening to A Problem Squared, episode 084. Please refer to that if you want to send in

any other business pertaining to this episode we hugely appreciate everyone who listens to this podcast because that's what gives it meaning but we super extra appreciate the uh strict subset of listeners who make this possible by supporting us on patreon.com slash a problem squared we were unable to name and thank every single patreon supporter every single time but we can name a fraction of them all of the time so we pick three names completely at random i ran a spreadsheet earlier and we thank those people which this episode mispronouncing their names. Oh, we always, yeah, we mispronounce people's names. Just to be fair. And this episode, we'd like to thank...

Aunt Honey. Hey, on brand. Good old Aunt Honey. Your favorite aunt. Cadogan. By the way... Cadogan. I believe might be my cousin.

What? Your cousin? I don't know many people. Cardog-an? I don't know many people with the same surname. So I suspect that might be my cousin. Wow. Which is one of those weird things.

First neighbor Nina, now this. I know. This is an accidental nepo. A nepo-sisode, if you will. The good old ne-pisode. Yeah. Permanently frozen in time. We can have fully, it's like my brother is always going to be a baby, even though he's only three years younger than me.

And I feel very similar about Aaron. So it's weird for me that Aaron's a Patreon supporter, even though Aaron is very much- Aaron's spending all their pocket money on supporting- Aaron is very much old that Aaron's a Patreon supporter, even though Aaron is very much... Aaron's spending all their pocket money on supporting... Aaron is very much old enough to be a Patreon supporter. And if you're not my cousin, you know, you're an honorary cousin now. Oh, and... Christ, Ian. Christ, Ian.

Chum, Aker. Oh, chum. Aker. Oh, s-chum. Good work. Thanks. I didn't even spot that. Nicely done. Thank you. So thank you so much to all three of those people we just named,

as well as everyone else who supports us on Patreon, and everyone who listens, including you. You, listening right now. Thank you very much for listening. This has been a Problem Squared with Beck Hill, Matt Parker and of course our producer Lauren Armstrong Carter, who's a bit like

Rolling Dice in that occasionally we call her Old Snake Eyes. And so... She should be here for the record if she doesn't want it yeah exactly we're gonna call it that's what we are now it feels a bit mean it might be workplace bullying but that's just how these things go uh so thank you so much for listening and that's it bye bye right back neither of us are in the office but i was in there this morning and the big jar of dice that you're trying to guess how many dice are in is still in the office

would you like to last time you said four six six and i said lower do you want to have another guess i'm going to go for four six four lower oh i'm kind of glad we didn't get it i really want it to happen when we're in the all Four. Lower. I'm kind of glad we didn't get it. I really want it to happen when all of us are in the office with the dice. So we can celebrate properly. Which still won't be for a little while. You're going to be in Australia by the time I get back.

That's a good point. Okay, we'll string it out. Well, at this rate, I mean, who knows how close you are? Or far away. Oh, yeah, I mean, who knows how close you are? Or far away. Oh, yeah, I'm driving the main one this time. So have fun with that intro. I haven't written it yet. It's quite the lag, by the way.