A Problem Squared - 036 = Score Menu Sets and Door Etiquette

Episode Date: June 20, 2022

In this episode:  Can you create an order from a numbered menu that is always comprehensible to the server? When someone is behind you as you open a door, what is the polite distance to wait for them?  And, the cards are on the table.  As always, if you've got a problem or a solution, hit us up on our website aproblemsquared.com.    Please send in your Blue Dot problems, and we may just solve it live on stage. Just post your problem with the tag 'Blue Dot' to aproblemsquared.com - Do it now!   If you want to come and see us at Blue Dot, you can catch us on Friday, and can buy tickets here: https://tinyurl.com/BlueDotTickets You can find more about Emma Haruka Iwao's record breaking Pi calculation here: https://cloud.google.com/blog/products/compute/calculating-100-trillion-digits-of-pi-on-google-cloud  And, of course, if you want want more from A Problem Squared, come find us on Twitter and Instagram. 

In the cynical podcasting world, listeners' trivial problems are considered especially heinous. In the UK, the dedicated detectives who investigate these ridiculous queries are members of an elite squad known as a Problem Squared. These are their stories. Your hosts Thank you. Did you download Law and Order? SVU opened me. SVU, yeah, yeah, yeah. And then reworded? And then yes. Yes, I did. Good. Problem. Wow.

Well done. Thank you. Wow. You know what? You bring it up. I am one day away from retirement. But every time I think I'm out. Pull you right back in.

Pull me right back in. Yeah. I'm always late because there's just one more thing. Wow. Special problems unit. I think we're... I think that would be... I think that should be our new name.

Special problems unit. Yeah. SPU. Love it. And for any new listeners, that's not normally the intro. I just thought I'd have a little bit of fun. Matt, how are you? I'm good.

I'm very excited. So am I. You're back. I'm back. That's not normally the intro. I just thought I'd have a little bit of fun. Matt, how are you? I'm good. I'm very excited. So am I. You're back. I'm back. That's good too. Yes. Back in the UK. We are in person. We are both in the same office at the same time, which is very exciting. Lauren was going to be here. Not joined by producer Lauren. No, we've got her on a screen.

Because she's in a house full of COVID. So she's staying a long way away. Yeah, which we appreciate. But we miss you, Lauren. Currently, one in 60 people in the UK have COVID. Oof. That's a lot. More teaspoons, I bet. That's a lot.

We should redo the calculation. Yeah, but we're not going to. Nah. Nah, it's been done. It's been done. It's been done. Twice. Twice.

Yeah, no, I'm particularly happy because, and I was obviously going to chat about being in Australia and coming back and all that jazz, but everything changed this morning when I saw Breaking Maths News. Ooh. We have, we, by we I mean humankind, have now calculated pi to 100 trillion digits. That's a lot. That's a lot. It's a lot. It was done by a Google developer, Emma Haruka Awau, who actually previously held the record for most digits of pi calculated. I don't know if you remember, because you were at the recording of my humble pi stand-up

special. Yes. Which I'm very pleased that's all done in the can. Yeah. Being edited as we speak. Excellent. When I originally wrote the show, there's a joke at the beginning about Emma calculating the record number of digits of pie. Oh, yes.

Yeah. And then I think I put a clarification in the show. Were you like. That someone else has since beaten that record, but I'm refusing to update the show. Yeah. Since the recording, she's got the record back. Oh, that's amazing. Yeah.

So she's held it before, then someone else took it. Yeah. She didn't just beat her own record. No, no, no. So she got to 31 trillion digits. It was actually pi times 10 trillion digits. So it was like 31 digits, 400. Right, nice.

And 15 million, et cetera, et cetera, et cetera. Someone else then increased it to 50 trillion, which was just like a guy in a garage. Yeah. But what Emma did that was impressive was it was cloud computing. It wasn't just like a big computer in a room. It was very clever coding on cloud computing that Google have. Someone else got it to 50.

Someone else then got it to 62. Yeah. So they got tau. It feels like I'm watching an eBay bidding war. Yeah. And now Emma's got it back at 100 trillion digits of pi. Wow. So there you are.

That's amazing. It is incredible. Well done, Emma. Phenomenal effort. Are you going to put a little thing in your edited show that says, by the time this was released. Yeah. The thing is I said I wasn't going to update anything.

And then despite myself, I pointed out that. Yeah. I think it was just an example of what I'm not going to be updating. Yeah. But I know if I put a thing in, because I think I'm going to release the special in like September.

Someone else will just change again. It's like, yeah. It's definitely, given how fast it's being broken and how small the increases are, it's going to be broken again. I don't know what the next number would be.

It'll probably break by the time this episode comes out. Oh, potentially. If anyone, if you want to make my life difficult, beat the Pi calculation record again before September. Because then I can't put a clarification in my show that it's back. So anyway, I'm very excited about 100 trillion digits of pi

515 terabytes oh of storage oh my goodness they started the calculation on the 14th of october last year last year it didn't finish until the 21st of March this year. Whoa. Oh, my goodness. Why did it only just get announced now? 157 days, 23 hours, 31 minutes, 7.651 seconds. They probably had to check and verify. I suspect they're verifying. Oh, checking it.

Did they say how they used the Chugnovsky algorithm? Big fan. Okay, what does that mean? It's a, it's an equation for pi, which is optimized for running on computers. I did do work it out by hand one time. I got 14 digits.

I was very proud of that. Yeah. But it's not optimized for doing by hand. That's no. 14. That's not many. 14. It's not quite a hundred trillion. No, no. So anyway, Emma has written up everything she did and she's put it all together so you can read all the technical details and the results and how

they how they did it all and we'll link to that in the show notes i'm very excited but anyway how are you doing i'm great you're great i'm great i don't have any no breaking news we had the art exhibition that the five thousand pound t-shirt t-shirt five kts oh my goodness uh it did not sell oh no which is a shame i didn't think it would what was the list price for five thousand pounds that was the minimum that was the minimum bid that you could do so and i had a big, in the art exhibition as well, I did a big neon sign where it's been like cut out and someone's like just written on it in big marker. And it was like only 5,000 pounds.

For new listeners to the podcast, this was a t-shirt that Beck made a while ago. Yes, in lockdown. Yeah. Yeah, in the first lockdown where I used the same technique that the million dollar homepage used back in the early 2000s, I think it was. But you didn't sell individual pixels, you were selling blocks. I was selling 3.5 centimeter blocks.

And people paid for those? Yes. And that's where the 5,000 pounds came from. So we split the t-shirt into a grid of 500 squares. People could sponsor the squares for 10 pounds each. We raised 5 5 000 pounds for water aid but then you want to double dip and sell the t-shirt for a subsequent 5 000 pounds yeah because then it would be the 10 000 pound t-shirt and water aid would have 10 000 pounds tell you

what just like the week before the art exhibition right maradona the footballer their shirt yeah that they were wearing when the hand of god incident oh my goodness when they hit the football with their hands yeah and i think it went in the people got very emotional or it didn't go in the goal i forget yeah i'm not a football soccer person that shirt was sold in auction and it fetched 7.1 million pounds right so i thought 5 000 pounds is actually quite reasonable yeah yeah that's like point less than 0.1 percent yeah i mean it's been on television it was on johnson ross's comedy club there you go yeah people got their money's worth 10 pounds a square it was on tv yeah on tv and it was in the art exhibition yeah and i did all of the art by hand

there you go. Yeah. They're going to regret it when I'm a famous artist, which is usually after they die normally, and then everyone will be buying up all my stuff and then they'll be like, oh my gosh, and it will sell for more than 7.1 million pounds. Everyone will be like, oh, I couldn't get that for five grand.

Yeah. But I guess that's more money for WaterAid. That's true. Yeah. Swings and roundabouts. A lot of our listeners sponsored it yep so if you are one of those people or even if you're not a water aid and looking at seeing if they can create a design based off the back of the front to make into a tea towel so if anyone wants a tea towel that has their little square on it, they might be able to do that and raise money for them. You're selling people, selling it twice.

Back to people. They pay for a square. They don't have to buy it. They can, they can. You can just give money to WaterAid without that. I think I will. I think, yeah, if anything, don't create more material stuff. Just go give money to charity.

Why am I going to do this effort for everyone? Yeah, so that was it. There was the art exhibition. I had some other stuff in it. I was very nervous about doing it because it's for this documentary that has been slowly filming over the last few years about comedians who do art. Right.

And I was super nervous because it was like Vic Reeves, Simon Munnery and Spencer Jones, like all these people I really look up to and- And you. And me. And I felt a bit like, ugh. But actually, I'll tell you what, once you put something on a white plinth, it looks like art.

Give it a little label. Ah, I sold three pieces. Wow. I sold a friendship bracelet that I had made that said, is this art? Which I thought was, that sold for 30 quid, I think. Wow. Some paper mache hands around a pot with some dead time in it because it was too much time for your hands.

But there you go. But then I literally killed time. You've made a lot of pun based art. That was 50 quid. 50 quid? Went to charity from that. For killing time yep and i sold a portrait my first self-portrait that i'd done with makeup instead of paint because i use makeup more than i do paint and that there was a bidding war of two

two bids on that that's a war it sold for 150 pounds 150 And I'll tell you who won it. My mate Steph. She bought it. Which I don't know who the other person was who bid on it, but Steph was like, I don't want anyone else having this. Probably Steph's partner trying to buy it for Steph. No, although she did buy one of Spencer Jones' pieces as well and didn't realize that the bidding on the site doesn't work the same way as eBay. So when you place a bid, that is your bid.

Whereas with eBay, you can say what you're... Oh, it goes up too. Yeah, right. Yeah, it'll bid on behalf of you and you just put a cap. So I think Spencer's... Normal bidding rules. Yeah, he had a really nice painting which looked a lot like Steph, which was why she wanted it.

So, yeah, all around fun times. Free booze. I love an art exhibition. why she wanted it. So, yeah, all around fun times. Free booze. Love an art exhibition. This first problem is for you, Matt. It's from Stuart and it says, Is there a way to number a menu where giving the total will result in a correct order? Oh, so is that like if you go to a Chinese restaurant?

Yep. Sometimes it'll have like numbers next to the... Yeah. Yeah. And then you say, I'll have a three, a seven and two tens. Well, instead of doing that, you could just say, give me a 30. And then they're like, oh, well, that's two tens, a seven and a three, right? Right.

Okay. So you wouldn't be necessarily numbering it in chronological order. It would just be... Yeah, correct. Yeah, so is there a way to number a menu such that all you have to do is tell the server the total of all the dishes you want and that they can reliably reverse engineer what you were ordering? I'm guessing this mainly comes down to how many items are on the menu.

It can. Because because yes you could if you had two items on your menu yes no you're right that's good yeah you could literally do that exactly yeah yeah done so yes all right next problem what would you what would you number the two items on your menu well if it was two, I would just go one, two. What if they want two ones? Oh, bum. Yeah, you're right. Do you do negatives? Yeah. The problem now is, so what I realized very early on, I did exactly what you did, which is the first step.

You go, right, what's the simplest case of this problem? Which is a menu. Obviously, you can have a menu with nothing on it, the null menu. You can have a menu with a single item. That's still easy. And then the moment you've got two items, you're going to have ambiguity around if people are allowed to order multiples of the same dish.

And if you think this might be for a whole table of people, then there's every chance more than one person wants the same dish. Someone might want two of them. So even if you numbered them like, you know, the first one's number five, the second one's number seven. You're like, ah, excellent. But then if you multiply five and seven, you get 35. And so that would be ambiguous.

You wouldn't know if they want five rounds of dish number seven or seven rounds of dish number five so any two numbers you assign to the smallest non-trivial menu there will be an ambiguous order which is the multiple of those two oh yeah yeah so that and there's no way around that well so when i realized that i was like okay, this is just branched. There's on one hand, I'm like, okay, that proves using normal numbers, you can't do it in a way that's perfectly generalizable because there's going to be an upper limit to how many. But if you tell people you can't order more than four of the same dish,

then that system would work because that would take out the ambiguity. But I was like, okay, but it means you can't do this in general, but you could probably come up with ways of doing it if you have some reasonable bounds on what people can and cannot order. It also tells us if you want to do it perfectly in a way that will work for any size restaurant with any size order, normal numbers aren't going to cut it. We'll come back to that in a moment. So I was like, okay, okay. Let's just say you know how many dishes are on the menu and no one's going to order more than a certain number. Yep.

Then, yes, you can do it. The easiest way of doing it is you have the first item on the menu is menu item number one. The second item is menu item number 10. Okay. And then 100. And then 1. Okay. And then 100. And then 1,000. And then 10,000, right?

So then if someone wants two 10s and three 100s, they'll order 320 and you just look at it. And the number is just how many of each dish in the order they are on the menu. That's nice. But the numbers are quite big. order they are on the menu. That's nice. But the numbers are quite big. And it feels like cheating because you're literally just listing how many of each dish you want in order, but it happens to be a number.

But you've got to say zeros where you're not ordering any of a dish or anything that's less efficient than just saying, give me a number 10 and a number a thousand. What do you mean zeros? So if you like, let's say the menu's got like 20 items on it to order you're gonna need a 20 digit number for your order you're gonna be like oh yeah because you're going up by a digit so our total order is you know 17 trillion 405 million etc etc right so you know you've got this massive long number instead of just saying this one this one and this one, and this one.

Yeah, yeah, yeah, yeah. So it's inefficient. I was like, okay, could I make it more efficient? And so I think I found a way to make it more efficient. And it depends on if people can order multiples of the same item. So let's assume we've got a restaurant where you go in by yourself, you can order a couple of different dishes, but you're not allowed to order multiples.

In fact, I've got a arbitrary menu I'm going to give you. Okay. You're going to put an order together and I'm going to see if I can decode your order. Okay. Oh, this is exciting. I've typed up. Just to kind of see how it works, you know. So here.

You've done a proper menu. It's an arbitrary menu. When did you do this? I just. You've just got back from Australia. I know. I know. I typed it up very fast this morning.

All right, I'm going to read this. Don't read the copy. You've put Clipper on there as well. I put Clipper. It looks like a terrible. I tried to make it look like a diner kind of menu. You've done a proper. Is this because I keep saying we're going to put pictures of your stuff on the socials

and then you end up with these terribly drawn diagrams. We've got some lovely scripted font which says arbitrary menu thank you you're at the arbitrary restaurant yes love it i mean you've got a picture of a banana on here no banana on the menu none of the pictures match any of the items on the menu good oh and you've written descriptions for the meals as well well it didn't look like a menu when it was just a list. So I jet lagged. I generated some pointless copy, which can be largely ignored. Well, I don't think anything you generate is pointless, Matt.

Okay, I did amuse myself while I was writing it. I think what we should do, we'll pop pictures of these on Instagram and Twitter at a problem squared if you'd like to see the copy that Matt has written. Lower your expectations. For his menu. Typos and all. If any of these that I read out, you think,

I wonder what that is. A Problem Squared on Instagram or Twitter. So here I've got number one item is soup of the soup. Soup of the soup. Number three is, now do you say bruschetta or bruschetta i'll say bruschetta bruschetta there's different camps i find some people say bruschetta some people say bruschetta so a bruschetta etta yep number nine a boiled egg um number 27 is a pie and uh yeah and you spelt it pie p-i-e you haven't thank you thank you i'm impressed

and 81 which is the final fifth item on the menu which is griddled vegetable and meta tart but this one is meta the tart is made completely out of vegetables grown in compost made from pure tart very good so thank you so it's a Yeah. Do you notice what the numbers are? Are they prime numbers? No, they're powers of three. Oh, yes. Or like it's 1327. Yeah. 139.

139, sorry. 27. 81. So that means. So actually, I've got an identical copy of the same menu. Here. A different numbering system. Oh.

This is, if it was done, copy is the same. This is, for the first one, they're multiples of two. One, two, four, eight, 16, 32. But which works if you can only order a single item of each one. Yeah. And then the one that's multiples of three works if you order up to two of each one. Okay. So actually, do you want to give me an order?

Let's do the twos first. All right. So this is from the power of two menu. You add together the dishes you want. Do you want a biro? Or are you going to... No, I can do this one. Yep.

All right. Can I please have a... And I can only order one of each item on this one. One of each item. Yeah. All right. Cool. You don't have to order all of them. Cool.

May I please have a 22? Oh, you want a 22? Mm-hmm. So you've ordered the grilled vegetable meta tart. Yep. Which I actually copied that. Griddled, actually. Griddled.

It's meant to be a feta tart. I just copy and pasted and changed feta to meta. You've also gone for a number four, which is going to be, what was four? Was that the pie egg? It's the pie egg. It's the pie egg. It's the pie egg. It's a bald egg. The bald egg and the number two, which was the bruschetta.

Yeah. Yeah. So because I've spent too much of my life converting to and from binary, when you give me the number, so when you gave me 22, I'm like in binary that's zero one one zero and that tells me which items on the menu you've ordered where there's a one going from the bottom of the menu back up again oh so going up sorry going up the menu yeah one zero one one zero yeah huh yeah so i annoyingly i have to do it from the bottom of the menu back up again, just because of the way I do binary in my head.

But I could flip that if I practiced. Yeah. I mean, you offered me a piece of paper to make the order. But I've got a pen if I need to. Tell you what, do you want to give me an order from this one? This is the power three menu. This is the power three menu. Okay.

And I can order up to two. Up to two of any dish. Okay. All right. It does take a lot longer for people to order. All right. I am going to order. Ooh, I think I'll have a 32. Oh, a 32. Interesting order. Let me see if I can do this in my head. You've ordered a one of item number three. Wait, four.

Item number four. Yep, that's the pie. You've ordered the pie. And you've then ordered. So that leaves me five left over. So that's going to be a three and two units. So that's going to be, yeah, item number three and two of the whatever, the soup of the soup. Yeah.

Soup of the soup of the soup of the soup of the soup. That's correct. Hey, all right, all right. Cool. Okay, so this is binary and ternary, base two and base three. Okay. You work out the maximum number of dishes people might order. So in base 10, people can have up to nine of a dish before,

if you order 10 of a dish, it'd be ambiguous because that's going to roll over into the next column. So you work out the maximum number of dishes anyone human might order or table or whatever. And then you do a numbering system in the base, which is a base bigger than the maximum number of dishes you might have on a single order. So if I was going to do the next menu, I'd do powers of four

and you could order up to three. Correct. Huh. And then you can reverse how it's done. Ah. Yeah. That's very clever. So it works.

Cool. I find that very pleasing. Yeah. There are limits. The menu can be as big as you want. So there's always the next power. So you can have arbitrarily large menus, but you cannot have arbitrarily large orders. And so I was a little bit annoyed that I couldn't do that.

And I've not found a solution for how to do it. So the order can be as big as you want and the menu can be as big as you want. As we know, it's not going to be normal numbers. I tried complex numbers. Now explain what that is to me. So you've got regular old counting numbers. Yep. But in mathematics, there are so many other types of exotic things, objects that aren't numbers, let's say.

So I did complex numbers, which are where you've got a real component and an imaginary component. It's basically like having coordinates. So soup of the soup would be like 2 plus 3i. So it would be a normal part and imaginary part. So like algebra. Like algebra. Okay. And then, you know, the bruschetta etta would be like seven minus four i or something.

Right. So each one would have a two part complex number attached to it. Uh-huh. And then you can add them all up and then you can reverse it. I couldn't find a base, a basis, like a set of complex numbers that that would work for. I think there's always going to be an ambiguity. What I love about that though is that the blackboard that the menu would be written on would look like one of those, like, yeah.

Is it Good Will Hunting? Yeah. Is that the one? Yeah, where they come in and it solves the problem on the board. Yeah, I feel like that's what you're... Someone will come in and solve the menu. Yeah, that's right. There are other more exotic math objects so if anyone listening

fancies a challenge i suspect there must be some system in maths where adding the items is reversible the other way we could get around it the problem said if you need to add together all the things you're going to order if you you multiplied them, that can be solved. Because you would give each item a different prime number. And if you multiply together a bunch of primes, you can perfectly reverse that answer. Even if there's multiples of the same prime, that's perfectly reversible to go back. Prime number decomposition is a fundamental part of maths. It's unambiguous, works every time.

So if you gave prime numbers to every item on the menu and to order, you have to multiply together all the items you want. Yeah. That would work perfectly. Huh. But you get very big answers. Yes. And multiplying is a lot harder to do in a restaurant than addition.

Yeah. In my humble experience. Yeah, that's why, oh man, I remember back in the day when the receipt for your meal was like handwritten. You're adding up, easy. Yeah. Multiplying, not so much. There may be, I mean, I don't know. My intuition, I can't even say if I think it's likely or not.

be i mean i don't know my intuition i can't even say if i think it's likely or not if there's because doing part thing called partitioning where you split something apart into a sum is notoriously complicated with normal numbers but there may be some exotic system in maths where summation is reversible if you pick the right basis for how you're doing it. But I couldn't find any. But that's maybe more the limit of my knowledge than the actual limit. Before you said there are many different types of complex objects or there are more complex objects. Yeah. Yeah.

Why do you say object? That's like a general catch-all for things. Okay. Because it could be numbers. It could be like groups. It could be shapes. It could be vectors. It could be matrices.

There's all these things. And I think everything when I listed, I suspect, doesn't work. If there is an answer to this, it could be some obscure, like literally two people have done a research on this obscure offshoot of some weird branch, and they're like, oh, interestingly, decomposition of addition is perfectly defined or something like that. You know who I think could probably help with this? A better mathematician.

I was going to say Emma. Oh, yeah, yeah, yeah. I bet she's got the computing power. She's got some of the Google Cloud time on it. Yeah. That would be a practical mathematician. I was going to say Emma. Oh, yeah, yeah, yeah. I bet she's got the computing power. She's got some of the Google Cloud time on it. Yeah. That would be a practical use of the... Yeah, why not? That would be quite the pop-up though, wouldn't it?

Yeah. That cafe. Yeah. If I run a cafe, I'm going to have punch cards where you punch in your order and binary next to each item. Would you have a little computer that you stick it into? Yeah, yeah, yeah. Totally, yeah.

Yeah, like the reverse of a, well, like a time punch card. Yeah, exactly. You'd clock in your order. Oh, I'd love that. And it also worked the same as a loyalty card as well, I guess. At the same time, you only need one thing. So if anyone. What would your cafe be called?

Oh, well. We've talked about our pub. We have talked about this before. Yeah. So I don't know if I said this on the podcast. If I do a pub, I want to call it the Rose and Column. Yes. But like the roses in Rose in a spreadsheet.

Yeah. And column like, yeah, we all know what's happening here. Yeah. Anyway, if anyone can come up with something that you can add and reverse, let me know and I'll implement it at the rows and column. Well, I think that's wonderful. And I'm going to give it a half ding. I'll accept a half ding. Because with this episode, we're doing a law and order.

Just one ding. Thanks. thanks we have a problem in via the problem posing page at a problem squared.com from rowan who says when there is somebody behind you when you open the door a specific door oh yeah rowan doesn't specify what the door is but they then want to know what is the polite distance to wait for someone and what is the creepy distance to wait for someone. So Beck, I mean, we've all had this problem. Yeah.

And you're going to solve it once and for all. I'm going to solve it once and for all. Good. Well, I mean, the thing is about this. I've had this problem. And you've already come across this. This problem involves variables. Ah, big fan.

Which, what door is it that's true they just say the door yeah so let me i guess let's start with that because first of all depends where you're located in regards to the door because if you're going into a building gotcha then how are you to know if someone behind you is going to follow you into the building or just walk past oh as if you hold the door open and they just saunter straight by, that's awkward. Yeah. So already I think it's pretty,

you've got to be sure that the person is going to go into the building. I think if you go into a building, even if someone is sort of just around that corner, you know, like they're just, if it's not clear that that person is going to follow you in, they can't, they're not going to be annoyed that you didn't hold the door open for them. So if there's any ambiguity in where the person is going, just let the door close. It probably depends on their approach factor. Yes.

Because if they're walking dead towards the door, that's one thing. Totally. You can, yeah. But if they're coming orthogonal to the direction of the door opening. Yeah. Right. And they might just be coming in for a glancing blow and carry on. Yeah.

Which I've had so many times as well. I think the polite thing to do is you do the little quick rear check as if you're checking your rear view mirror. Like you just do a quick little peripherals. right yeah little peripheries check and then if it looks like they're coming towards you you might pause for a second but if they're not if they seem to be just going on course then you just go on straight in normally what will happen i think though is if you're the other person and you know that someone's going to a building you'll do the little skip the the skip

is the universal sign of i'm going to go through the door as well and i and i appreciate but this is the awkwardness right because if you hold the door open you're forcing the other person to do the skip well that's why i say that's why i think if you're going into a building you don't open the door right yeah like for someone unless it's very clear that they're coming in behind you. What you could do is get to the door. Realize the person's approaching you, but it's ambiguous. Just tie your shoe or something. Yeah.

Buy some time. Find out what they're going to do. Yeah. Act decisively. But you've got to tie your shoe like, well, either holding it open or you've gone, depending on if it's a push or pull. You're shy of the door. You let the other person overtake you.

Now it's their problem. Oh, right. You're going to let them reach the door before you. Yeah, depending on if it's a push-pull. You're shy of the door. You let the other person overtake you. Now it's their problem. Oh, right. You're going to let them reach the door before you. Yeah, they get to the door first. Oh, I think you're going to be tying your shoe laces for a very long time on a busy street. You never actually make it into the building. Good point, good point. Yeah.

That is the thing as well, is it is very much about who gets to the door first, isn't it? As to who has this problem. So I think that's in terms of if you're going into a building. Yep. Or I guess anywhere where if you're in a place with a hallway or something and there's lots of people going up and down the hallway, same rule applies, I think. If you're coming out of a room or building where there's going to be

more of a chance of other people also wanting to leave. I think it's, I'm going to say it's about like two lengths of that person if they're lying down. Two lengths of that person. Okay. That's reasonably close. That's like in the, you know. It's not though when you think about it.

Four meter range. Yeah. Yeah. That's still, but anything further than that. Okay. I'm actually thinking, I'm now just imagining four meters away from me. It's quite a distance. I think anything more than that and it then puts pressure on the other person to hurry up,

which is arguably more rude. Why is it dependent on the person's height? Because it's the same amount of steps. So children have to be a lot closer. Oh, a number of steps. Oh, okay. That makes sense. Okay.

Okay. If they can get there in four strides. Yeah. I mean, yeah. Do I stand by that? Sure. I stand by that. Why not? I mean, then you could argue that if someone,

problem with my own reasoning just then is if someone is shorter, then they might have more trouble. If it's a child, they might not have the strength to open the door on themselves. But then should you be opening the door for them? Do you want to be letting someone else's kid out of a building yeah so this comes to my next point which is the variable of the person and their ability to open the door themselves because if they're holding loads of stuff ah that would lengthen out the that length yeah so in if they're holding loads of stuff i think

that then comes down to eye contact right if you see anyone's holding, even if they're super far away, if they're coming towards the door, you make eye contact. Yeah. Because what will happen is they will either go the, oh, like the. Thanks. Yeah. Because if I'm carrying that stuff, I'll be looking ahead to lock eyes. And then I'll be like, oh, thank you.

Thank you. Like, you know, and then it's just. Yeah. Then you're away yeah i think any awkwardness from that is still preferred to the to the difficulties of that person having to deal with the door and all the stuff yeah likewise if anyone for any ability reasons can't open the door can't reach it Or they're, you know. So it's a case-by-case eye contact situation. Yeah, I think so. Can I add one complication that I struggle with?

Sure. If it's a door that's got like a security pass or something. So this was going to be my next one, which is a variable of what type of door it is. Yes. Yeah. Because when I was out in Australia, I was staying in a place where you had like a security thing on the door but then but lots of people stayed there like an apartment building thing

right so then then when you let people in if i think if it's a security one you don't open you don't hold the door open for anyone unless it is clear that they also belong in that building and they're super close to you they I think it might half the distance. I would go less than. Really? Yeah, because then anyone could just hang around and be like, oh, yeah. We were tailgating. It's a classic way to.

Yeah. Because I think even if that person is half distance but you don't recognize them. You get in, you pull the door closed. You can shut the door. Yeah, okay. Oh, wow. Yeah. Have you been in that situation where you've got a meeting or something and then i've been in a couple where i've been

invited like to a building for a meeting and then someone will use their pass to go in and you have that that weird thing where they're like they sort of go like should i offer you and i'm like no it's all right they'll buzz me in like oh you just stand outside it's all right. They'll buzz me in. There's been a few where I've been like, it's okay. Someone, yeah. I take a giddy thrill on infiltrating the building. I did do that once recently. I had an appointment and it was a woman who also had her appointment at the same time and we were both not sure what.

Turned out we were both on the same floor, but we both couldn't, the sign didn't have the names of the things that we're after. And so we buzzed and the receptionist for her appointment let both of us in and then i realized that i was half an hour early and i had to go back out again that's awkward because i'm a big fan of like physical security and all the various exploits and things around all this so i feel like i've got an extra eye on the secure option. But my goodness, it's ingrained the politeness. Like if someone's right there, it's a tough social move to close the door.

Yeah. Even though it is objectively the right thing to do in a security situation. Yeah, it comes down to social cues, doesn't it? Yeah. I mean, if anything, we're teaching people that if you want to infiltrate a security thing, as long as you look sure enough that you belong in that place. Oh, you'll roll right in. You're confident enough that someone should open the door for you.

Do you know what? If you want to sneak into a high security place, carry loads of stuff. There you are. Lots of shopping or something. And be really close by. And then lots of eye contact. And be like, oh, thank you, thank you you as you walk up to them as they go in or like pretend you're going for your pass and you can't reach it oh yeah oh it's here somewhere and they're like oh come on

so that's the security doors elevator doors oh yeah so that one i've decided that one comes down to i think as soon as anyone looks like they want to come into the elevator, if you're the only person in the elevator, you hold the doors open. That's what I was thinking. As soon as there are more people in the elevator than there are outside the elevator, then it comes down to distance versus capacity. That's a big call on behalf of everyone in the lift.

Yeah. To decide we're all going to wait. Yeah. If it's a full lift, no. You don't have to hold the door open for anyone. Is not the best option to be pretending to push the door open button, but you're not. And you're miming, you're like, I don't know, I'm trying to.

Oh, and as the doors close, you're like, sorry. Right. And then they close and you're like. I think then it does just look like you're pressing doors close good point good point and then just shrugging that sucks to be you so i think with the lift doors you don't have to technically you don't have to wait i think people are fine with it if there's other people in the lift. Yeah.

If there's a few people in the lift and you're like, again, about, you know, your height. Yeah. I've definitely been in a situation. I think Heathrow Airport, this happens. There's like, you've got to get a lift up to the car park and people come out spaced and the lifts are huge. Yes. You can be there for a long time because there's always one more jerk with a suitcase rolling and there's a long line of sight.

Yeah. You're there forever before it fills up or people start walking over. Yeah. In those situations, I think if you're coming out of the airport, you can take your time. What are you going to do? If you're going into the airport. You can't miss your flight.

In is a different story. You're pressing the close button. You're closing the doors. So that's those doors. Revolving doors. Well, I don't think you need to do anything. Yeah. It's out of your hands.

Nice and easy. Automatic doors. Same thing to do anything. Yeah, but I say it's out of your hands. Nice and easy. Automatic doors, same thing. Same deal. Yeah, in fact, because Rowan said, what is a creepy distance? I think the creepiest distance is if you just stand by rotating doors or an automatic door. And wait for someone to join you. Yeah, pretending that you're doing it for them. I like how comprehensive you've been.

What about a moat? You know, the drawbridge is down. Well been. What about a moat? You know, the drawbridge is down. Well, I mean, a moat is not a door. There's a body of water. No,

but you got like the drawbridge on the moat. The drawbridge. yeah. So how long do you wait to keep the drawbridge down? Yeah. Well, I mean,

the drawbridge is basically old, old school security. Old school security door. So that's, yeah, close it every time. Okay,

got it. So if you walk up to, if you want to, if you want to storm a castle, carry loads of shopping. You can't tailgate in. You can't wait for someone to go in. Thank you.

Thank you. Thanks. International Space Station airlock. How does the airlock work? Actually, I think it just opens up a tube and you can all come through one at a time. Yeah. But, you know, if you've got to wait're in microgravity be fun yeah you don't mind float around you don't mind i mean i think it's pretty rude if you don't let everyone in and then it is

they have to just stay in the module international incident yeah with creepy distance yeah i said this then comes down to the next variable which is what sort of person are you all right because if you're a creepy person if you're standing there with uh with like your fly undone and and a t-shirt that says female body inspector yeah and uh and and you know, a sticky hand. What you're saying is if you're a creepy individual, anything you do is creepy. Yeah, yeah.

So I would just say, do you know what? You don't need to hold any doors open. If anything, stop being creepy is my advice to you. That's great advice. I don't think anyone can look creepy unless they've been holding a door open for you and you weren't aware of it. I think all of these scenarios come down to whether someone is definitely going to go use the door

and B, if you've both sort of made that eye contact of, oh, you're holding the door open for me. I think if I was to reach a door and find that someone had been holding it for me and I realized that they were there for quite some time. Exactly. There's a point at which you're like, they're holding the door.

You're a long way away. You're like, that's weird. Why? Why do they want to wait until I get to the door? Yeah. If there's any possibility of an ulterior motive. Yeah. Other than convenience for the other human.

If I'm more than two lengths my height. Yeah. And you will measure it out. Yeah. And they've waited the whole time. I've got my measuring tape. A bit of chalk. Yeah.

I'm not carrying anything. Yeah. That is creepy. Yeah. Yeah. But like, I think that that's just inbuilt though isn't it like you're you're not gonna look creepy unless you you know that you're holding a door open for someone for the wrong reasons if you're worried that you look creepy then let the door close yeah yeah yeah

unless like someone needs help oh that's true yeah true. Yeah, yeah, yeah, yeah. Okay, yeah, yeah. I mean. I think it's more to do with why you're holding a door for someone. If you're holding it because you're being polite and you would do it regardless of who the person is, then you know. You know. You know. But if there is a person that you find attractive.

This is not the situation. Who is walking towards the door and you find yourself thinking, are they too far away? Yeah. They're too far away. The answer is yes. They're too far away. And if the other person lies down and gets some chalk out

and starts marking out how many body lengths away they are. Yeah. They're the creepy one. They're the creepy one. Get away. And if you start marking out their distance. Yeah. Of course, then the key is that if you're worried about looking creepy,

you have to measure everyone. Oh, it doesn't help. So in conclusion conclusion society is complicated just try not to be creepy yeah context context and if you're not sure twice the height twice the height that's my theory love it or just get automatic doors on everything oh that'd be great or be so rich that you have a door person. Yeah, that's the, yeah. Oh, do you know what? That's what I should have done for this.

You should have found someone who's a door person and ask them how long they wait. If it's a hotel person, because then you don't know the, you don't necessarily know everyone who lives there. Because if it closes, they're going to be there when the person gets there and they'll open it for them. Would they ever just stand there holding it open? That's what I would do. If I was a door person, I'd just do that thing where you put your foot in front of it.

You'd just wedge a doorstop. Yeah. I'm off for a break. Yeah, put a little hat on it. There you go. There's the other answer. Just get a doorstop. Yeah.

Every door you go through. Wedge it open. Wedge it open. Problem solved. Ventilation. There you go. it open problem solved ventilation there you go if you want to many other business let me hear you say i was torn between joining in and just watching how that was gonna pan out you chose correctly excellent it's any other business blue dot festival Festival is happening in July, the 21st of July until the 24th.

That's Thursday till Sunday. And we're doing our first ever live recording, as in recording in front of a live audience, of A Problem Squared. That'd be interesting. Yeah. I mean, I'm excited. I'm very excited. I'm looking forward to Blue Dot.

Great festival. Yeah. of a problem squared that'd be interesting yeah i mean i'm excited i'm very excited looking forward to blue dot great festival yeah also uh curious to see how we're gonna go doing this live on stage yeah i i'm considering how long we take to record an episode oh it's not swift oh we love chatting i don't think we're gonna get a whole episode done on stage because we've only got like an hour yeah oh yeah we might have to supplement it with backstage goodness. I think we might need to. Well, you'll find out at some point when we put out that episode. But in the meantime, if you are attending Blue Dot, or even if you're not. But particularly if you are. If you are, we're going to answer a listener problem on stage. So if you have a problem for us that you would like us to tackle

in front of a live audience, then please add it to the problem posing page. That's our problemsquared.com. And in the subject line. It's in the text box. Yeah, just put blue dot. So we can keep an eye out for it. We're just going to search. We'll search with and without the space between blue and dot. Yeah, just put blue dot. Put blue dot so we can keep an eye out for it. We're just going to search. We'll search with and without the space between blue and dot.

Yeah, we'll do either. Or if you're not sure, we'll do both. Do both. Chuck them both in. That'll be really helpful. And, you know, if time's of the essence, you are also welcome to send it to us on Twitter at problem squared. So, yeah, if you've got a problem that you would like us to solve

in front of the live audience send it to us we might just answer it while you're there we might answer one problem and run out of time oh I didn't say we were going to do all of them no also we've had a bunch of people writing in and tweeting in

about what it would feel like to fall through the earth from the previous episode 035 and on twitter murk at m-u-r-k-e-e says our physicist here oh yeah physicists i got enough physicists in my life to be honest anyway they say it would be free fall all the way so it'll be like being weightless in orbit because you're in free fall ah i was because when you slow down on the far side is that still free fall i think it might be

because everything's free fallen even though it's slowing down exactly that plays the whole way through the earth right so you're walking along. Yeah. You fall down the hole. Yeah. You just feel like you're weightless from the get go. Yeah. In the same way that skydivers I imagine feel. Yeah.

Ignoring wind resistance. Yeah. Yeah. Oh, yeah. Yeah. So you don't have wind resistance or anything. Because everything's falling at the same rate. Yeah.

So you feel. Everything's slowing down at the same rate. So it would be weightlessness the whole way through. Right through the middle. To the end. And then, but what... Then when you get to the other side, do you just step out?

Yeah. Do you just look like David Bowie at the end of Labyrinth when he comes over the step? Exactly like that. You just whoop and step and done. How you turn the world, my precious thing.

Singing is optional. Yeah, you got crystal balls. They also flag up. And I will say I did love the fact when we were reading this before, you read out R-H-O like it was an initialism. Am I supposed to pronounce it? Well, what they've done, because they're a physicist, I think they mentioned it, they wanted to say density.

And they went, oh, density is represented by the Greek letter rho. And so instead of using the word density, they couldn't be bothered pasting in the Greek letter rho. They wrote out the Greek letter rho, R-H-O, instead of writing the word density. Oh, that's super nerdy. It's ridiculous. Super nerdy and lazy?

Physicists, take a good hard look at yourself, honestly. So anyway, they've assumed, I have assumed, they've pointed out, I've assumed that the earth is the same density the whole way through, which is not true. Yeah. The density changes. Also, this has just entirely changed the nursery rhyme, row, row, row your boat for me. It does, there you go. Yeah. The density changes. Also, this is just entirely changed to the nursery rhyme, row, row, row your boat for me.

It does, there you go. It's just density. That would be Reynolds' number in that situation, I suspect. Niche joke. Some people are laughing real hard right now. Someone's going to tweet that. They'll be like, this is why I love this podcast. I just go silent for a bit because I don't get it.

Love the podcast because the jokes are scale and variant. Now, so I did look at trying to work out the density, different densities in the earth, and then I couldn't be bothered. It was too complicated and, you know, geologists. I didn't. So you're right. I assumed equal density the whole way through.

I did not factor in changing density. And for someone else who wrote in, they're talking about the fact that as you go down there'd be a gradient of gravity across your body that's true but i don't think it'd be noticeable like if you're falling into a black hole i think you could care about the fact that there's the gravity on your feet which are closer is different the gravity on your head because of how the amount of mass in a black hole. I think that's the whole spaghettification thing is that.

Right. So they're saying like it would be stronger when you step in. Your feet might get pulled down more quickly than your head. When you stand on the earth, there's more gravity on your feet than your head. Yeah, but we've got earth between us and the center. Yeah. But I think by the time you get to the center, there's so little mass, I don't think it would be noticeable.

So, meh. If you're free falling through a hole, can you still hit your head? Yes. So you'd be like floating, but you can still. As in hit your head as in like the side of the wall or like. I fell in this hole again. Yeah, like stop hitting yourself. No, I mean like, yeah, hitting yourself head on the wall.

Yeah, yeah, yeah. Yeah, you can. Because it's just a hole. I think the problem is when I think of floating, like you're feeling weightless, but you're not physically floating. And that's where my brain keeps getting stuck. Yeah, right. It's like, oh, you've become a fairy.

No. It's like you've just fallen down a very long well. Going down a well. Yeah. Yeah. And you can definitely still hurt yourself. You want it to be a pretty wide hole then. You do.

So if you step off with any angular momentum and you start tumbling, the sides are far enough away you're not going to tumble into them. Yes. Because if your face hits the side, that friction would mess up my calculations. And my face. We side, that friction would mess up my calculations. And my face. We can ignore that. Yeah, actually, that's the thing.

Because if you fall off of something, you would keep going at that angle, wouldn't you? You'd want to get a real jump up and down. Yeah, you want to be like a diver. You want to be suspended above the hole. It's a long length, the earth. Yeah, it's a long old way. That's the math, isn't it? How wide does the hole have to be that you could make it through the other side without hitting the sides? I think in all of these scenarios, you'd hit yourself on the way down.

I think, yeah. Get skinned. It's a massive, what if the hole was like a kilometer across? And you're dropped in right in the middle. Yeah, well, but you're saying if you're dropped in yeah oh you think if you run and jump yeah yeah that would mess up the uh because you'd move along oh i was about to say ellipse but now i'm not i'm uncertain uh if anyone else uh has any thoughts on this keep it to yourself okay when you fall in a bottomless pit, you die of starvation.

That's my niche joke. There's going to be about three flash animation nerds out there. Oh, really? Yeah, I remember Homestar Runner. Oh, it's Homestar Runner. It's Teen Girl Squad. Oh, my goodness. The nerdy one.

Is that right? Yeah, close enough. Close enough. Nuts. And we did hear from someone who was actually responding to something that came up in our bonus podcast. I'm a wizard. Patreon only content. Yes, Patreon only content.

Because I pay for it. Yes. Where Matt and I just play a game called I Am A Wizard and pretend we're wizards. Pretend? And the question came up about whether Australia was the only country where there were different states or areas. Yeah, some states don't do daylight savings.

And some do. And then whether there was any half-hour time zones because obviously I'm from Adelaide and there's a 30-minute difference. And for the record, I'm from Perth and WA doesn't have daylight savings, but other states do. It's a nightmare. And Marcel wrote in to us on the problem posing page just to basically say that Canada.

Oh, Canada. Canada is also. Canada has the same problem. Yeah. So thank you for that, Marcel. Excellent. There's probably more out there. Canadians.

Yeah, there you go. And speaking of Patreons, we'd like to thank three of them picked entirely randomly each episode, which this time includes... Ruben Shakaturian. Brett Schofield. And Martin Lievart. Schofield. And Martin Leivart.

I looked at the names and went, I'm going to let Beck go first on this one. But thank you to all of those people and everyone else who supports us on patreon.com slash a problem squared. And also thanks to Lauren Armstrong Carter, our producer, myself, Bec Hill, and Matt Parker for bringing you this podcast. And one last thing, Bec. Oh, you've got, I've just seen you've got two cards And one last thing back. Oh. Oh. You've got, I've just seen you've got two cards with a post-it wrapped around them. I've amalgamated all the information across the various decks that I've been doing this with. Oh my goodness. And I'm just curious to know, is this your card?

Yes! Yes! No way! Oh, there it is. Four of spades. We should have recorded this Zoom. Oh, wait, wait, wait, wait, wait. Guess what I've got.

I've got a party in a bag. Matt's brought party bag twisties. Wow, there you go. That's the end of an era. You know what? We should put that in an art exhibition for 5,000 pounds. We should. I'll tell you what for 5,000 pounds. We should. I'll tell you what.

I will both sign the card. Oh, yeah. And we'll put it on eBay for WaterAid. Starting price, 5,000 pounds. I actually have a video from the original Chris Knight. Oh, yes. Where I told him what the correct card is. Because I was very tempted to get him getting the card before you.

Oh, my goodness. So seeing as he filmed it all the way out in Australia, I will pop that. We'll put that online. I'll put that on socials and tag him. Brilliant.