084 = Indicators and In Da Cake-ers

Hello, and welcome as we roll the dice on another episode of A Problem Squared, a problem-solving podcast.

Where if you don't want to solve your problems by living 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 in 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 name of the dots on the dice.

Oh, I didn't know that.

Yeah, yeah, yeah.

Pips.

Pips on the dice.

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.

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 afectionatos

on this episode

I'll be looking at what's in a cake I'm gonna indicate when indicators got to indicate in the cake

into cake yeah

you're into cake indicate and there'll be some any other business any other baking

any other bakeness yeah oh no wait no the scene was dice oh too late to change now oh well this is a cake-based episode now.

Good job.

It is.

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 sort of festival here on the weekend.

Bob Baker was a very famous puppeteer.

There's the Bob Baker Marionette 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.

Amazing.

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 like 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

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 theater 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.

100 scoops.

Yes.

So I guess you could have it.

You didn't have to have them all together.

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.

I grabbed a few and noticed that it was for a freestandard ice cream.

I was like, oh, great.

A free ice cream.

A freestander 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 and have themselves ice cream.

So I think between the four of us, we maybe took like 10,

which is quite a lot.

But when you think about it, like that's like you know two to three ice creams per person

a reasonable amount they're gonna use them not all at the same time

and so after after we uh finished the first one we went oh let's go to jenny it's a lovely day let's let's go to jenny's ice cream and get our ice cream is this the same day same

day the four of us we went and got an ice cream each we had a lovely day We're very tough with ourselves.

And this was

about four days ago now, five days ago.

ago.

Okay.

And then last night, just as I'm sort of 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?

We've just helped ourselves to some of the prize because.

You've just skimmed off the top of the prize.

Yeah, but the way that they were sat by the thing, it looked like some had 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, as 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

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

what this company is.

And the way it was presented.

It was a prize on display.

Yeah, exactly.

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

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

like rare marionette puppets.

And those puppets were sitting near the jars so you could actually see what they look like.

And I.

You can 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, and 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 is what I'm saying.

But 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 LA 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 we're 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 sine?

Is it the thing you mentioned on a previous podcast episode, but I think you may have forgotten that you've already mentioned that?

No, no, that is the fact that all the page numbers are the sign of the page number.

Right.

So that's still true.

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 quite pleasingly the phrase a big circle is on page 0.000000

which was nice purely by accident but looks amazing in the index yeah no in addition to giving the page number we uh the index i say we because mate andrew taylor uh does the coding for all my indexes because 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

and 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 know where the words are.

Anyway, 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 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...

the distance and angle from the bottom left-hand corner.

Would you use a pro if you you were if you were doing that, you know, by hand,

would you use protractor?

Yeah, that would be a protractor job.

I think you should do some special edition ones that come with

the

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 if when they run out, there'll be triangle ones for a bit.

And then once they're done, that's it.

No more limited edition.

And I suggest that you make every pre-order and raffle entry.

Oh, yeah.

They could win one of 100 protractors, of which there will be 90 available because

there's certainly still 10.

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?

I'm good.

It's true.

This is our 84th 84th episode.

Of course, I believe that.

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

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 themselves, and it will be a woodland party.

They don't like dark chocolate.

They don't like red velvet.

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 buyers.

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 McDonald'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, I 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.

So

they say.

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.

My guess is definitely wrong.

Let's see if you can.

Were you going to go Marie Antoinette or someone?

I was going to go Queen Victoria.

Oh, because Victoria's sponge cake.

I feel like.

There, see, that's they invented the sponge cake for their birthday.

That's my theory.

That's nice.

I like that.

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 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 a 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.

Wow.

Hmm.

I was off by 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 savoury and nothing like a pudding at all.

It could mean black pudding, which is, again, like a soft.

That's sort of a deal.

Yeah.

So it's sort of one of those terms that it's more in the grey 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.

The ancient Greek called cake placus, 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

to sort of make cakes.

It's got yeast in it.

Yeah.

Makes sense.

Cheesecakes.

They

sort of derive from the ancient Greeks, apparently.

They were using goat's milk, which I'm sure is 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 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 the Intristia 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 used to assume it was quite a recent thing, the more you, 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 that

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 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.

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.

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.

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 by 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, a cake fact.

So I looked into cake mixes, which I thought was really interesting.

You know, pre-packaged 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 with 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 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 mixers became popular and all you had to do was stick some ingredients in a bowl and mix it up and bake it, there was no creativity there.

And so they just weren't weren't interested.

And so the sales dropped.

And the way that marketers got around it was they started to include icing.

Also, 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.

You know, 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 That's cake.

Yeah.

What's your favorite cake, Matt?

I don't know if I have a favorite cake.

I'm partial to chocolate cake, but I'm not a big sweet-tooth kind of guy.

No, you're not.

No, I'm, yeah, 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,

we started a baking competition.

Oh,

and I only entered it once.

There wasn't pies?

No, no,

surprisingly few pies to be honest.

But

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 blocks of cake into an arch.

So I had like a nice catenary-shaped arch built out of wedge-shaped bits of cake.

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 Beck 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

to then express yourself with.

Nina's turning nine, as I mentioned, square number.

So a three by three grid of cupcakes, 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 Nina was saying,

or Victoria's 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, 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.

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.

Yeah, that's my personal favourite cake.

And then I would probably decorate it with some nice, maybe I'd wash some sticks or something.

Yeah.

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 and 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 log.

Where you make a very thin, not a mass log.

You make a very thin sheet of cake and then you roll it up with icing in the middle.

Is that a is that logification of a cake?

I think so.

I believe so.

So if it's woodland woodland-themed, you could do a log cake

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 it with 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

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.

Ooh.

So, if you which live in a woodland, so if you want to go full woodland, you could use honey as one of the sweeteners in the cake.

And that also be-shaped cake.

That also harks back to the very old traditional ones as well.

The original Greek cake, go go old.

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,

Nina, that if your parents can somehow make or source this, Greek honey cake.

Greek honey cake?

Yep.

It tastes a lot 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.

Bucklava.

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 for 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 it looks like a honeycomb.

I don't...

Oh, so good.

Well, I've put the link for Greek honey cake in the show notes.

So if any of our listeners want a 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 our problemsquared.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 elon musk would call it at problem squared well bec i don't feel like we can put the ice ice sting on this problem just yet.

If this is neighbour Nina, I'm going to be in Australia when the birthday party is happening, assuming I would have been invited were 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 A-O-B-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

be very glad to know.

You spotted it as well, isn't it?

I did.

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 indicator.

Or you're hearing the actual light.

Yes.

Well, you're hearing

whatever the

mechanical mechanism is that's turning the light on and off.

And I don't know, I assume there was.

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 got current going through it and as 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 then turning itself 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?

They're really obvious.

So super deliberate.

And it's like a very slow version of

like 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 the bell connects,

it turns on

energy with a bike belt, but this is, yeah, cool, cool, cool.

All right, very fun.

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 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 metal where you're doing about 90 blinks a minute and then they've got lots of leeway above and below that to still be within the official regulations.

And that variability means that

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 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,

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

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 like, 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.

It's got breadboard.

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.

That was bad.

That's the high point that we're going to achieve.

Anyway, Ben Eater 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 divorced.

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 you used to get

from the strip connecting and disconnecting.

Which means if it is the case, it's not necessarily the timing in which your indicator is on on the outside.

So

I'm going to 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.

Dink, ding, dink, dink, dink.

And

the listeners can't see this, but I'm sort of using one finger to denote

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, circuitry, etc.

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, then 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, that's your first problem.

But 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 is vanishingly small.

So, that now gave me a couple of 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 it's 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 loads of things you can do to prime how simultaneously or not we will perceive things to be.

Yeah, because I think we may have even talked about this on the podcast before, but I've heard it a few times about the

fact that

the way that we process stuff 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.

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 Its Illusions 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 removed 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 I was like, that's such a good experiment to make sure that you're not.

That's so smart.

I took that to mean, given that the 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 rephrased it to be, are they blinking within 0.1 second of each other?

And then you've 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.

So the waiting time is 60 to 90 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've now got two different things that have range of values, and I combine them all to find the kind of upper and lower bounds of

the range.

So, in conclusion, the zone at 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

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 triple five, 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 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.

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

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 better 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 waited traffic lights 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 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

similar to

cameras with audio on both things, and then find a way of lining that up as closely as possible.

That 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 ding.

I love it.

A ding decator.

A ding decator.

Ah.

Yeah.

Every episode we use the ding decator to see if we solved a problem or not.

Yeah, that's right.

It's like a clappometer.

Yeah,

exactly.

How many dings for this one?

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 I'm satisfied that I don't have to worry about it now.

Oh, good.

Yeah.

That's my goal in life.

It's like wondering if you left the iron on and then finding out you didn't.

Yeah.

You know,

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 uh 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 their response to for mentioning that it's episode 082 because it's so helpful 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 problemsquer.com and selecting solution in the dropdown.

Kristen says, hi, Becca Matt.

With respect to episode 0, 8, 2, I have access to a tumble dryer and I used it.

Excellent.

Hey, Matt, you know, we're all about showing our workings.

Kristen's done a dexter.

There's a lot of work in here.

For any new listeners, that is in reference to one of our younger listeners who likes to always

show detail.

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.

However, I figured a reasonable estimate of dry-related reduction in fabric weight could probably be reached by weighing the dry 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 dry lint.

Assuming that the amount of dry 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 will 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 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.

Kristen might be my favorite person right now.

Kristen is gunning for my role as co-host.

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.

Kristen,

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

it's very standard.

Yeah.

Well done.

Kristen then also says, did I write some Python code to visualize a predicted 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 pasted a bunch of code in the form.

That's great.

Shajiba, 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, and it will then tell you how many washes it will take, or 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, 4906, 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,

you can see it.

And for anyone who skipped forward, Kristen's too long didn't read.

Just says, based on Wayne Dryer 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.

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.

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.

Capital letters will.

Even with the lint trap, lint 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 Saudi 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 a better job at answering it than I have.

So I appreciate 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.

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 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 see, yeah, yeah, we mispronounce people's names, just to be fair.

And this episode, we'd like to thank

Aunt Honey.

Hey, I'm Brandon.

Good old Aunt Honey.

Your favourite aunt?

Cadogan.

Car

Dugan.

I believe might be my cousin.

What?

Your cousin?

I don't know many people.

Car Dog Ann?

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.

David Nina, now this.

I know.

What this is an accidental nepo episode, a nepisode, a nepisode, the good old nepisode,

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 Erin, so it's weird for me that Eren's a Patreon supporter, even though Erin is

spending all their pocket money on supporting.

Eren is very much old enough to be a patron supporter.

And if you're not my cousin, you know, you're an honorary cousin now.

Oh, and

Christ Ian.

Christ Ian?

Chum Acre.

Oh, 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,

and that occasionally we call her old snake eyes.

And so.

She should be here for the record if she doesn't want.

Yeah, exactly.

That's what we're going to call her now.

That's what we are now.

It feels a bit mean.

It might be workplace bullying, but that's just how these things go.

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 have 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.

I'm kind of glad we didn't get it.

I really want it to happen when we're in the all all of us are in the office with the dice so we can sell it properly.

Which still won't be for a little while.

You're going to be in Australia by the time I get back.

Well, 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'm driving the main one this time.

Yeah.

So, have fun with that intro.

I haven't written it yet.

It's quite the lag, by the way.