A Problem Squared - 141 = What If Peer Was More and What If Pi Was Four?

Episode Date: August 17, 2026

👬 How do you know if a work-friend is a real-friend?⭕ What would happen if Pi was 4?😴 And we have Any Other Boring-Stories…Head to our BlueSky/Twitter/Instagram to see Bec’s selfies with The Stars of Space (real and fictional), and the cute-faced Rivian Car.Why not try Hyperbolic Crochet?!https://startcrochet.com/ultimate-beginners-guide-to-hyperbolic-crochet/Why not try a checked 25x25 grid crossword from Sweden?!https://fatherben.se/wordpress/digitalt-korsord-i-sydsvenskan/ Robert Llewelyn’s YouTube channel - Everything Electric CARS If you’re at the Edinburgh Fringe and would like to see Bec’s Work In Progress show, tickets are available here: https://www.edfringe.com/tickets/whats-on/bec-hill-s-work-in-progress Matt has extended his tour - and he’s filming the show in London in October - all the dates, venues and tickets can be found here: http://standupmaths.com/shows Want to pose a problem for Bec and Matt to solve? Head over to https://www.aproblemsquared.com/ Join us on Patreon for early releases and our monthly bonus podcast I’m A Wizard!If you’re already on Patreon and have a creative Wizard offer to give Bec and Matt, please comment on our pinned post!   If you want to (we’re not forcing anyone) please do leave us a review, share the podcast with a friend, or give us a rating! Please do that. It really helps. Finally, if you want even more from A Problem Squared you can connect with us and other listeners on BlueSky, Twitter, Instagram, and on Discord.

Hello and welcome to a problem squared, the problem solving podcast that's a bit like me watching a World Cup game. Oh no. Hey, it often involves a meandering walk around all new territories. And after some dead ends, you never know what delights you'll discover. I'm Matt Parker, mathematician and performer who's a bit like watching the Australia versus Egypt game with your dog in the fox. in pub in much Wenlock, a town in Shropshire, in which regard, exciting to start with,

but then the locals get bored and play darts instead. And I'm joined by Beck Hill, comedian, writer, performer, who's a lot like watching the England versus Norway game in a women's sports bar in Brooklyn, New York. Very busy, but with a good, fun, friendly atmosphere. Thanks, Matt. By the way, our blazers in Brooklyn. Great place.

And on this episode, I finally answer the question, friend or acquaintance. Oh, wow, that could be news to me. I've explored what if pie was more square. And there'll be any other bar-ness, I guess, if you consider that Matt likes to watch football matches in bars. Bar-ness? Anyway, any other business. So, Beck, how are you? I'm very good.

Did the Latitude Festival? Oh, how was it? I was very sad to not be there. Yes, I realized at the time of this episode coming out, it's now been several weeks since the Latitude Festival. Yes. It was on the mega weekend that clashed with me being at open source that I discussed in the previous episode.

Trent from Cosmic Shambles and I were saying, you definitely need to come to a latitude at some point because it's been too long. One day. It's been too long. And I said, if we don't do like a live version of Problem Squared, We should at the very least, the two of us doing something, right? Just answering questions or whatever. And we should call it.

And I can't believe I haven't thought of this before. Oh, okay. I'm ready. Parks and Beck. How have we never thought of that before? How have we never? I realized it in the car. And then I went to go message you and producer Laura.

And then I was like, no, I'm going to say it when we're recording. I'm going to say it in the recording. I think it's such a busy time a year, but the power of the title Parks and Beck might be there. And I cut through the rest of my schedule. But it was very fun. I was hosting the Apollo stage over the Cosmic Shambles Forest. And it was great. I also got to meet Robert Hlewin, who might be better known to some as Crichton from Red Dwarf.

There's been like a lot of crossover, but I've not been. been like officially properly introduced to him before. And as someone who also gets quite excited talking about the future of solar power and electric vehicles and things like that, we had a fantastic chat about all of that for at least half an hour until I finally worked up the carriage to ask for a selfie. He's a lovely guy. Oh, and it got to meet Helen Sharman. I will say that that is arguably more impressive. as yeah, Britain's first astronaut.

Helen Shahn was fantastic. She gave a fantastic talk and it was a real treat to watch. But also just a wonderful person, really, really lovely and was very happy to have a photo taken with me, thankfully. Oh, that's nice. Yeah, it's a tough call. What's more impressive? Person who actually went to space or person who pretended to be a robot in space. Hey, they've both done a lot for the interest of space travel.

That is very true. That's very true. And The Welland does have, it was called fully charged. Now I think it's everything electric YouTube channel about electric cars and such things. Definitely worth checking out. Yeah, he did an incredible panel where he was discussing a town in the Netherlands where it's basically like a car share scheme with electric vehicles. And I may have got some of my info mixed up and I'm sure he does an episode about it. But it's all plugged into the same ground.

grid. So while some of the cars are sitting idle, they're actually helping cycle the energy around so that it's not just sitting there in an unused battery. Oh yeah. There are some aspects of that coming in on the UK grid, which is kind of cool. It was very interesting. Yeah, that's amazing stuff. When I was in San Francisco, there was a car, a Rivian electric vehicle, which I've never seen in the UK. they're a very distinctive looking and they do like it well I'd call a Ute you know like a pickup kind of thing

and an SUV they're a bit big for my liking but I do like that kind of particularly weird bold styling on a car and I'd never seen one in person and there was one in a car park and as I walk by

I watched someone walk over get in and reverse out and go to drive off and I was trying to like surreptitiously not be staring because I was quite nearby but I wanted to see this car up close. But then they stopped and they wound their window down.

And the driver learned over and went, Matt? I was like, oh. That's awesome. So I got a feel, they've just left work for the day. They're getting their car and they look up and there's like a YouTuber they know pretending to not be looking at their car but actually looking at their car. That's amazing. I'm looking up images of it now.

And it looks like if I were to draw a tree, truck and give it adorable cartoon eyes. Yeah, that's about right. Yeah. It's really cute. It's got anime robot eyes. You tell me that isn't a sentient truck. It's pretty cool, isn't it? You tell me it hasn't gone on exciting adventures just at night when no one's in it.

But my most recent exciting mathematical adventure, I went to the International Congress of Mathematics. Ooh la la. Which local media in Philadelphia described as the Olympics of Math. I guess it happens every four years and it moves around the world. So kind of. I mean, it was a wonderful time. A lot of fun.

My highlight was I bumped into Terence Tao, who is arguably the world's greatest living mathematician. I think he's been described that way. Top mass guy. Is Tao the number named after him? No, sadly. Different spelling. I imagine he is probably Team Tao now I think about it because he's a very good mathematician.

And I'm Team Pi because I'm a Dufus mathematician. You would not believe the city in the world where the world's current leading mathematician is from, Beck? If you say Adelaide... Well, get ready because it's Adelaide. What? Isn't that nuts? Why have neither of my math teacher father and brother both hailing from Adelaide mostly mention this to me? I mean, probably because they rightfully were like, this is of no interest to Beck.

I am very surprised. Yeah, there you go. Yeah. Old Terry. Wow. So I'd never met Terry in person. We'd emailed previously. I literally bumped into him on the street.

And we both were like, oh, hey, it's that other person. And so we went and met up for a coffee. Talked about the current state of maths and large language models solving math problems, which is all very interesting. And we thought we had picked a cafe far enough away from the convention center. but still another mathematician came in and was like hey it's you oh and you yeah and then a rivian

truck drove in yeah exactly yeah i've just seen uh terence tau described as the mozad of mathematics which is a high claim that makes sense yeah it's lovely lovely guy to hang out with in chat and it was is another case of the symmetric parasocial relationship where we had both watched videos of the other person and followed them online but had never met in person. But we both felt like we knew each other, even though we didn't. Yes. There's like a mass festival for two days, the general public and people could come in as well as everyone at the conference. Because the conference is like thousands and thousands of people.

Like it's a huge thing. And there's like a big exhibition space. There was like a two-day hands-on math fest. And so I was helping some friends run a stall there. And I'd always wanted to have a challenge. for like teenagers and just general members of the public if they could flip 10 heads in a row on a coin We give them a thousand dollars and I thought that would be a really fun way To motivate people to engage in trying to do a low likelihood activity and I always maintain you don't fully understand probability

Until you've persisted at achieving a low likelihood probability until you've done that you haven't got a benched mark for odds. Yeah, that's the story of my life. You say this, I'm immediately like, oh, I need a coin. I want to go start flipping it. See? Yeah. Yeah. Turns out though, humans, not that random at flipping a coin. So we've kind of worked out the numbers and we expected that we'd have one third of a winner per day. So it was more likely than not, we'd have at least one winner over the course of the two days. We didn't want to like never hand the prize. We're trying to tune it because we wanted to hand out a prize at least once, hopefully, but not risk handing it out too often. And on the first day, we had about what we expected, you know, 300 people or so come through.

But we had two winners. Two people flipped 10 heads in a row. In fact, the entire distribution was skewed to more in a row than you expect. And that's not the coin, because everyone could choose. we had a blue and yellow coin. People could choose which side they wanted to try and get 10 off. And people were just weirdly lucky. And at the end of the first day,

we sat down to reflect upon the lesson we just learned. Your two grand loss. $2,000. Yeah, yeah. There was a couple of different factors. And I haven't gone through the numbers yet. I'm going to analyze the numbers at some point. I might pop it up on YouTube somewhere if it's interesting.

But it was partly people are bad at flipping a coin. What do you mean by bad? at flipping a coin. Not sufficiently random. Now, I mean that partly literally, some people just don't know how to flip a coin. And so you give them a coin to flip, and they kind of put it on their hand and then just flop it

and the coin basically plonks in. And you're like, it didn't rotate in the air. Yeah. Flipping a coin is random because of the tumbling. And if people can't make it spin, it's suddenly a lot less random than you'd want. And people are pretty consistent

at starting with it the same way up, and it wasn't really flipping in the air much. And so people would pick which way up they wanted it. And there's a 50-50 chance. They're natural, if they always start the same way, whatever their terrible flipping style may be, would more consistently favour one side than the other. That's my working thing. And it was a bit hard to be really fastidious early on. Like if a family's trying to join in and a kid's trying to flip and they're not very good,

it feels disproportionate to be like, that doesn't count, that doesn't count. You can't play this game because you can't flip a coin. Yeah, yeah, yeah, yeah. You tend to turn a bit of a blind eye at the beginning sometimes. Did you introduce some rules? Yes, did introduce some rules. I got better at telling people that doesn't count. But the end of the first day, we're like, huh, what are we going to do?

And I thought mathematically would be interesting to change it. So the second day, forget the coin, we got people to roll the dice. and they had to choose odds or evens, which should be identical. Oh, yeah. And it wasn't. The distribution went straight back to where it should be for randomness. And nobody won on the second day.

We were prepared to risk a bit of money on this because I deemed it sufficiently interesting. And I need to go through the numbers now and look at, because now we've got the distribution from the day when it was the dice, and then we got the day that it was a coin. And I think it's, there's going to be some interesting maths in there. I think it's fascinating that we had a mathematical model of what we expected to happen, but our model didn't account for all aspects of human behavior.

And I think that's, if anything, the most important lesson here. That's the main problem with all maths and science communication. Like I feel like anything that they come up with, they're like, oh, this in theory should work really. In fact, that just works across the board for everything. Like there's so many systems and ideas that people have come up with where they're like, this is foolproof. What a great way to run a society or a great way to do this. And it's like, aha, but you forget, people are stupid. Yeah, yeah, exactly. It's just people are people,

you know? Because we assume that everybody does things the same as us. And then when they don't, you're like, oh, crap. Well, we took it on board and we handed out the money. So a thousand bucks was won by a mathematician and a thousand bucks was won by a child. But they were on like a summer camp. So their legal guardians weren't there. So the camp leaders had to phone. And the parents were so convinced it was a scam. Like, it sounded like such a scam. These people want to give you a kid a thousand bucks,

but you've got to come and sign a form. Because you can't just give cash to a kid. Be like, here's a thousand bucks cash kid. Off you go. Like, that's problematic for so many reasons. So we're like, we need to give it to an adult who can sign on behalf of this kid. kid to take the money. Like, no strings attached, but we need a paper trail so we're not just

peeling off money and giving it to kids. I guess because the kid didn't pay anything. But if they had, you did technically get a kid into gambling. You know what? Part of what I would like about this activity before we did it was I thought the money would motivate kids to try over and over again as a way to experience probability. I not fully appreciated. We were also encouraging a gambling addiction. So we had to make sure. And now that kid's going to go away and go, I'm lucky. Make sure we drew out the stories behind probabilities.

Well, next time you want to give away a thousand bucks, you know my details. Yeah, exactly. We'll bring you in. There's a professional thousand bucks taker. First problem was sent in on the problem posing page at a problem square.com by someone named Matt. No relation. And they say, Okay, they say a lot of things But they do at least give a headline summary of their problem

Which is, how can I find out If a business acquaintance is also a genuine friend? They say they're wrestling with this problem, thought it would be the good kind of thing your advice would be invaluable on I assume they're talking to you back, not me They say they work regularly with someone they get on very well with They think they're friends Beyond just, you know, like people who work together

Because they have a lot in common and they've been on working holidays together and they talk about non-work things and Matt says when one of them or both I guess moves on from that current employment which means they're not longer working together they would like to stay friends

but they point out that staying friends implies they're already friends and they want to work out how to find out if the other person thinks that we're friends and I think that the length of this problem is indicative of the overthinking going on here the other person's a freelancer Matt's one of their clients

I don't know if Matt changed their name for this or if I'm just giving the game away. Yeah. And so there's, here's the thing. They're already spending time together when they're getting paid. And the nature of freelance work,

and I think we'll discuss this a lot in a second back, is that you not only have to do your job, but you have to make the clients like you so you get rebooked. And so they're wondering, maybe this is just everyone being good at their jobs, which makes everyone think they're friends. And they've added this in,

I don't think this was necessary to say out loud, but an added complications that they are both neurodiverse. It's one of the things they connect about. Matt, in question here, is bad at picking up on social cues and the other person mirrors to fit in. They would like to ask up front,

but they worry, given everything said, the other person would be like, yeah, of course we're friends to keep everyone a happy customer or satisfy their neurodiversity. And so they want to know, does this problem have a solution? Or do they need to accept

that in such a transactional relationship, a true friendship can't form. Beck, I feel like I've covered that quite thoroughly. What are your thoughts? Look, dude, if you're trying to ask me, if you and I are friends, there's an easier way to go about it, then you didn't even bother changing your name. No, that's the double bluff I'm famous for.

Yeah, yeah. This is an interesting one, Matt, because you and I started as friends. and started working together so that we could actually spend more time hanging out because we both find it hard to justify social time unless it's related to work. This is true, but we were friends because we worked together. Yes, I guess we just had to create work and we'll just keep the friendship going. Yeah, but comedy's a weird one for that, I will say.

Comedy in itself, you'll end up gigging with a lot of people that you don't necessarily see that often. there's a few folks on the circuit who I get on with exceptionally well and I think in other circumstances we would be you know best friends and hang out all the time but due to the things that we do and how we want to spend our time there's just no opportunity for that so you it's interesting because you meet a lot of people where you go we would be best friends in other situations but that's not how the cards have been dealt like we just can't so we see each other and we end up having that like, I really like you kind of sort of affinity towards one another.

Yeah, and I think that's probably very true in general. Because I suspect there's a big percentage of the population that you could be friends with. Yeah. The potential for friendship is a very small part of the entire friendship thing. Even like in the local area where you live, there are thousands of people for whom you'd be a great friend match. And some of those people you just meet at work or in different environments in which it's not conducive nor appropriate for friendship. Comedy skews weird because you only ever really meet up in a faux social setting at a comedy gig, maybe having a drink.

But you're right, it happens so randomly distributed over time as well. Well, also a lot of comedians are neurodivergent. there is a lot of ADHD, autistic or Audi HD, that are sort of drawn to that lifestyle and that way of thinking. And it's a job that lends itself to that mindset. And so it makes sense that when you do it, you're like, oh my God, my people, because you're suddenly working with a lot of other people

whose brains work in the same way. A friend that I made, which I would also argue as a work acquaintance more than a friend. recently, but we just instantly hit it off. I was describing it to a to a neurotypical friend and I said, there are moments where you feel like it's just the ADHD talking to its, to each other. Like, we're just vessels. Right. And it actually has nothing to do with us as people. It's this condition, it's this mindset that just goes, pittu, ppoo, poup, puk, and just like bounces off each other. And you can feel it. Like, if you're someone with ADHD, you can absolutely feel when that is happening. and it's a strange situation.

And it's quite exhausting, actually. Like, it feels like unlimited source of energy because suddenly you've got all these, someone who understands and thinks along the same lines as you and you bounce off each other. And it continues like that, but it's... Feeding back as much as you're giving me. And that's why you end up overstaying at parties

and finding it hard to leave situations where most people are like, okay, I'll be on my way. Because it's just sort of pume, poup, puk, pugh. And then you'll get home and be utterly exhausted, because all of your energy has been spent. Right, yep. So I'm starting to get better at understanding that,

and it's understanding that I actually need to cut off those things, rather than letting them run themselves out, because then there's nothing left for me. Yeah. So that is something that I'm very aware of, and I absolutely mirror to fit in, which is one of the reasons why I find myself in so many, cross over industries. I'm almost 40 and I very much have started to realize that I need to stop

making new friends all the time because I don't have the time or the energy to maintain those friendships to the degree that I would like to or that feels respectful to the other person. And so I have had to start just being more honest about my limitations and things. So I'll meet people and get on with them really well. And then I'll just have to say if they're like, oh, let's hang out. And I'll be like, I'll be honest. There's a lot of things I've got on at the moment. And I would love to hang out with you.

But I wouldn't be able to give you the energy that would be worthy of this. And it's not you. It's just that I have to start limiting. That's one way to say it. The British for that sentence is, yeah, we should catch up sometime. And then that's, you never see them again. I don't know whether it's being an Aussie or whether it's the way that I'm wired. but when people are quite British about it,

I can very much often misread that into thinking that's actually what they want. Yeah, yeah, yep. Nope, they're just being polite. And it's very annoying when I later find out that that's not what they want. And I'm like, well, why would you tell me something differently? Well, actually, I'll ask you first, Matt,

because obviously you get a lot of parasocial, and you're mentioning this with Terry. Like you, that was one nice thing where you're like a parallel parosocial relationship. But are there any situations where either you've thought that your friends with someone or someone has thought their friends with you and how have you worked out whether it is a friendship or whether it's, you know, the nature of something? I mean, I think it's not a either or like it's not a case of, oh, is this a real friendship or is it fake? I think relationships in life, they are a product of the environment in which they exist. and that's not good or bad necessarily.

But as you hinted on, you can't be close friends with everyone. But I think it's a false dichotomy, is it the word I want? Like, if you're a freelancer or a client with freelancers, the best scenario there is you work with people for whom you get on well with and it's a friend-like relationship. Like, I think that's great. I don't think that's not real friends. I think that's great to have a really friendly work relationship.

I don't think you should ignore. I mean, you can't disentangle that from the fact that one person's paying the other person, but you can celebrate the joy of working with people for whom you enjoy being around, and it's fun, fun to interact. But I think these things will, you know, no, no exclusively. I've definitely got friends who I started doing work with or met them through work. But I think it's particularly complex if someone's paying someone else because then, you know, it's marketing. Yeah, yeah, there is a transactional, yeah.

Yeah, yeah. but you should celebrate the fact that you've got such wonderful work relationships rather than mourning or getting stressed about whether or not it's a quote unquote real friendship. Yeah, I also, I 100% agree with this. I'm actually going to, in order to answer your problem, Matt, as in the listener. Other Matt. This is an analogy that I often use to help myself understand friendship. and those relationships and the roles that they play in our lives.

But I think about them as seasons of a TV show. Oh. So certain friendships might be like your favorite TV show where you keep revisiting it and coming back to it again and again. And maybe you don't watch it for a while. And then you need like something just familiar and comforting and then you go back to it. And I like those ones because those friendships tend to be the ones where you might not speak or hear from each other for ages due to what's going on in your own lives,

but you'll always pick up where you left off. And there's always welcome friend to return to at a time where it's good. Then there's some friendships that are like, like a really good mini-series where like they're incredibly addictive. You spend a lot of time and you're like, oh my gosh, this is amazing. But then it comes to a conclusion. Like it moves. It moves. moves on and you've got to start, they've got to start something else, you've got to start a different show or something. And so you might just naturally end up, that sort of finishes it off, but it could be because you were working together and then that, you know, contract ends or something like that. Whenever you let go of something, something else tends to fill it,

fill that space. So it's not necessarily a case of losing something rather that something ran its course. And that doesn't make the fact that it was a short. thing, you know, just because it's short doesn't mean that it wasn't true or good. It just means that that's what it was. It was fantastic and it was short and that's it. Then sometimes you get friendships where it sort of finished ages ago and then, oh my gosh, look at that. It got a reboot years down the line, you know? Like it just, it's come back due to popular demand. And then suddenly you find yourself, you know, conversing with someone who you haven't seen. Matt, you and I met like 12 years before 10 years or something before we started working together, something like that.

We met, yeah, 2011. We sort of met and got along. It was more like we tried a series and we're like, oh yeah. And then later, you know, got a reboot. It was like, oh, actually this has got better writers now. I just said true. I just like that you've updated Life is Like a Box of Chocolates to Life is Like a Box Set. Yay.

Nice. That's good. I will also extend this because there's others listening. might actually find use out of this, and this is how I found it quite useful as well, because it's not happened a lot in my life, but occasionally a show has to get cancelled, and a friendship needs to come to an end, and the other person might end it, you might end it. It could be circumstantial, but sometimes for whatever reason, something needs to get cancelled, it needs to end.

Again, just to reiterate, it doesn't mean that while it was running, that it was worth any less, You know, I think we focus so much on how something ends or how long it runs for that we don't necessarily consider how something is in the moment. And this comes back to what you were saying, Matt, as in my co-host slash friend. Hey, that's me. It's not really about working out whether this person, like what label to give this person, but rather just being grateful for what it is that you both have at this moment in time. And it might be that if you stop working together,

that for whatever reason you don't get to speak to each other as much. But that doesn't mean that the connection that you have at the moment is worth any less. I think we have a tendency to fear the things that we have no concern. control over. And when we can't control something, we hope that we can try and control it in order to hold on to it. So we tend to worry about and overthink, like, how do I keep this person in my life or what, where do I fit in this person's life or something? Because we know we don't really have control over what will happen next because it depends on circumstance, environment, so many other factors. And so there's this wanting to make sure this person stays in our lives

in order to, you know, feel safe or feel relaxed or something like that. But I think that could actually sometimes damage something that's quite naturally beautiful. Like it's that, you know, hold on to it and it'll crush it. Whereas, like if you love something, let it go kind of thing. It's the best way to have a friendship in this sense is to not worry about whether it's a friendship. In terms of practical advice, one thing that someone said to me was, and I think this is very good advice, and I probably said it on the show before, is that you should never

ask something of someone who you know they might not be able to say no to you. Yeah, that's good advice. This was particularly done in terms of favours. So if you know that someone tends to say yes to doing favours, even when they don't want to do them, be very wary when asking people like that because they will put themselves in situations that they shouldn't be doing those things.

And it's a grey area then because then it's like they end up doing something that they didn't really want to do. And that's not your fault because they said yes to doing it. But at the same time, if you knew that they might not be able to say no. I'm not saying that you have to be responsible for someone else's choices, but it is worth bearing in mind. Likewise, if you are the person who tends to say yes to things you don't want to do

because you're worried about letting other people down, I cannot recommend therapy enough. It's been very useful for me. Like personal boundaries are very, very important. So with that in mind, I would say, if you're nervous that they might be doing this because, you know, it's transactional and there's payment involved and that sort of thing, I would recommend not asking about the status of your friendship

while you're in that position because they are in a position where it's going to be a sort of biased result. And we had a little chat with producer Laura, who made a very good point of, it doesn't really matter until you're no longer in a transaction. relational relationship. Like if outside of a business relationship, then a friendship seems to continue naturally, you've got your answer, you know.

And if it doesn't, you've got your answer, you know. And it doesn't really affect what's happening now unless you get the feeling that right now they actually don't want to be around you. In which case, that's a different conversation, which is more about asking them what their boundaries are and how you can better recognize them. So in conclusion, Beck and I are friends. In conclusion, start a podcast with this person. Yeah, that's good advice.

There you go. Humans are complicated. But you're right. I think until you're not in a transactional relationship, you can't know because that's such a impact on, you know, the fact that if they say yes or no to are we friends, changes whether or not they earn a living, that can't be ignored. I would argue that if it looks like a friend and talks like a friend, then while that is the case, if you have to label it, that's what it is.

But just, you know, enjoy the connections and the relationships. And also it's not a black and white thing. It's not like friend and no friend. And I know we like to label things to make things easier to understand. But it is what it is. Yes, it is. And it's not worth less because of that. And yeah, I've benefited immensely from hanging out with people that I only solely knew in a work environment.

Yeah. Most of your friends, you pay, Matt. Oh, absolutely. Yeah. And I remind them every time I see them, just to keep it nice and clear. And that's what I want to remind producer Laura about whenever she invites me to her anniversary parties, which are very fun. I just realized she's not miced, so we don't get to hear her laughing. And instead, that just sounds like I'm being really rude.

we can be both I'm just silently accepting the threat that's all no I like our friendship and also Matt you were invited

but you were in Australia I feel like that too late I haven't just picked Beck over you no no no no no we know what this was Matt wrote in

because he's worried that you and I are closer than he and I are now and you're all fighting over me guys You can both be my friends and colleagues. Oh. Our next problem comes from Kath, who wrote in and said,

What would the implications be if Pi was four? What would a circle look like? What about the other places pie turns up in maths? Matt, I specifically asked you, I said, I would be interested to know the answer to this, and you have come through. Well, yeah, you sent this one straight to me. I was like, you know what? That is interesting.

So I thought, let's do it. What would be the implications if Pi was four? If we think about this, will the material of space and time fold in on itself? That's closer to the correct answer than I think you appreciate. Oh, God. We'll come back to that. Just put a pin in fold in on itself. So, pie, just to recap, is the ratio between the circumference around a circle,

so the distance all the way around the perimeter, and the diameter, so the distance across the middle. Or it's half of that ratio compared to the radius, so it's often phrased in terms of the radius. This is where the pi-tow debate comes in. Yeah, not Terry. Not Terry. Different spelling. Different spelling. Tao is just two pi.

So technically pi is the ratio between the diameter and the circumference and tau's ratio between the radius and the circumference. But it's all the same thing. It's just a factor of two. No one really cares. So people occasionally ask what is the equivalent of pi for other shapes that aren't circles? And so one way to answer this might be to say, hey, is there a different shape such that its pie value would be four? So something like a square where the distance across a square is a quarter of the distance around the square. But that changes based on the direction in which.

which you measure a cross for a square because the diameter, in quotes, of a square, changes based on the angle you're measuring it on. Yeah, so if you were to go from the middle of the edge, that's different from the corner to the corner. Yeah, it'd be a lot bigger from the corner, it's smaller from the edge because it's closer to the middle. And every other shape will have varying values of the diameter, depending on which way you measure it. And I can say that with reasonable confidence because the definition of a circle is that it's all the points that are a fixed distance from the centre. So it's not just a case of saying, oh, circles are interesting because they have a radius that's the same in every direction.

That's, you know, tortological. Circles are defined. They just are all the points that are at a set distance from the centre. So that's just inherently what a circle is. so there's not really a meaningful sense. I mean, there are some other interesting ways you can mess around with it, but I would say, I would argue there's not a meaningful sense to have a value of pie for other shapes, asterix.

I know I've talked before online about like the area of an oven ellipse, this kind of stuff. There are other, you know, analogous concepts for other shapes. I get that, I get that. But the classic pie, that's what we're talking about here. Are there any other shapes where the diameter is the same no matter where you measure from? No. I've come to realize that whenever I think something is an easy answer, I'm wrong. I just want to quickly deal, because people are thinking, what about shapes of constant width?

And that's a good point. What does that mean? So shape of constant width means no matter how you rotate it, it's always the same distance across. And you might think, well, hang on, that's the same. Same as a circle. It's always the same distance across. But the distances across don't always go through the same center of the shape. They go through different points through the shape.

So we're talking three-dimensional shapes there. Oh, even 2D. Even 2D shapes. Oh. Like your classic 50 or 20 peak coin in the UK is a shape of constant width. No matter how you rotate it, the distance across is always the same. But if you did that a couple different ways, like if you rotate it and draw the line across, that's the distance, they wouldn't all.

go through the same center point if you do that for a bunch of different places. So there's no like consistent center point from which you get a radius that comes out from it. So they are shapes of constant width, but not with a consistent center. Got it. Which might sound like I'm nitpicking, but that's the whole point of the radius. It's like a circle is all the points. Yes. All of that said, we can still answer the question, what would be the end?

what would be the implications if pi was four? That's a perfectly valid legitimate question with a pretty much exact answer. Because pi is pi 3.14-159, etc., etc. Assuming your circle is in Euclidean flat space, which, as far as we're aware, is the reality we live in.

So Euclid did a bunch of axioms for geometry and you could argue mass in general. And one of the things that... This is a person. This is a person. Or it's argued maybe a collection of people. We don't know. It was a long time ago. The Greeks.

Ooh. And one of the things they said was, hey, parallel lines are possible. Specifically, if you have a line, like you draw a nice straight line on a bit of paper, and then you put a dot somewhere else. They said there's only one line you can draw through that dot that's parallel to the first line. So it's a long, complicated way of saying parallel lines exist, and if you define a distance away from another line, there's a unique parallel line there. But if instead of a flat piece of paper, if I gave you a spherical piece of paper,

Like if I said do this on a balloon or do this on like a sphere, you can't do it. It's impossible. There are no parallel lines on a sphere. Because if you were to flatten it out, it would be on a curve? So if you start drawing a straight line on a sphere, it will eventually loop all the way around and come back to where it started. Yeah. If you start drawing a second line anywhere else on the sphere, it has to cross that first line. There's no way to draw a second line, straight line.

that doesn't go through the first one. If you're thinking, well, what about lines of latitude? They're not straight lines on a sphere. They're deliberately non-straight to make them work on a globe. If you wanted to get to somewhere else on the same line of latitude as you, the shortest path to get there is not to follow the line of latitude. It's to go in a different straight line that will get you there quicker. The line of latitude is not the shortest distance between two points.

What? I know. It's ridiculous. And it's why when you look, you know when you're on a flight and you look at the map, like the in plane, like the map of where you are in the journey,

and you look at the trail behind you and you look at the city you're going to and from, the plane doesn't go, what you would consider straight between them. It goes up on this weird arc. And that's the shortest, that's the actual straight line on the spherical earth. But when we try and flatten it out onto the map,

it looks ridiculous. straight lines on a sphere are a bit weird. Okay, so the equator? Yes, is a straight line. But if you were to try and go like, oh, the Tropic of Cancer? Not a straight line. Interesting. Lines of longitude are all straight lines, but they all cross at both poles.

They're the ones, you know, they go up and down. Which is a long way to say, if you're drawing your lines in a different space, on a different type of surface, the rules change. Okay. If you draw a circle on a sphere and then you compare its radius to its circumference, you'll get a ratio smaller than normal pi. Whoa. So spherical geometry, pie isn't pi.

And it will change based on how big the circle is, which is very interesting. And triangles don't behave on a sphere. There's a bunch of weird stuff that changes once you go to spherical geometry. Yeah. I mean, I've seen you for. balls. Exactly. You see my weird balls. Why we're such good friends? Now, I would argue that we're friends despite me seeing your balls. Yeah. But this doesn't answer our question from Kath here, because spherical geometry, pie is always smaller than 3.14-159, etc. And Cath ones about if a

if our power was four, that's bigger. There is another type of geometry, which if you thought spherical was bad is even harder to imagine. It's called hyperbolic geometry. Hyperbolic geometry. I don't want to see your hyperbolics either. I'd like to acknowledge that is a very good joke. Thank you, thank you. It's very British.

It's top notch. Now, if normal geometry is, you can draw one parallel line through that dot. And spherical geometry is you can't draw any, you can draw zero parallel lines through that dot. Hyperbolic geometry is what if you can draw a number of different lines that are all parallel to the original line through that dot. Okay. And we have discussed some of these concepts in passing when we're talking about wrapping presence, about where spherical objects are. Oh, yeah. Spherical objects are, as you travel out, there's less area than you expect.

And hyperbolic is when, as you travel out, there's more area than you expect. There's like extra space per space, which is a terrible way to put it. But that's how I kind of understand it. And in hyperbolic geometry, your values for pi are always bigger than our normal value of pie. Okay. So for any hyperbolic geometry space, there will be a size circle for which pi will equal four. Well, so the implications are if you get a circle and you measure it and you're like, oh dang, pi is four, it means you're in a hyperbolic reality. And if you know how big the circle is, you can use that to deduce what level.

of hyperbolic your reality is. Whoa. So when you say what level, would you say that like, oh, this is a level for hyperbolic? Sort of. I did work out for your kind of generic negative one level hyperbolic reality. Pye is for about when you get a radius of 1.2 something on a like unit circle. That's roughly right. But there's a relationship between how hyperbolic and how fast pie changes as your circle gets bigger.

Okay. Depending on what you know, it either tells you more about the circle, how big it is, or it tells you more about the hyperbolic reality, whichever one you don't know, you can deduce it from the other one. Are there any models of a circle with the ratio is four? Yes. So, a particularly good medium for exploring a... hyperbolic surface is crocheting, which I may have mentioned before.

Crocheting, great. Yeah. You just, I'm going to use the wrong terminology here. You just cast on more loops per loop. We have some people who listen to the show while crocheting, and I really hope they're crocheting right now. And they're like, ooh. I mean, chances are they know what this is.

Yes. But if not, then my goodness, some new patterns. If you're wondering what it looks like, it looks a lot like coral in that it's very wavy and dense for want of a better word. A friend of mine, Madeline Shepard, provided, if people have seen the hyperbolic crocheting in my book, things to make and do in the fourth dimension. That was Madeline's work. And while we've been chatting, producer Laura found, and I quote here, the ultimate beginner's guide to hyperbolic crochet for non-mathematic. and it's got a pretty good explanation of what's going on there. So we'll link to that in the show notes.

But the general idea is it looks like coral because as you go out from the middle, there's more and more surface area than you expect. And depending on how much more, that's like how hyperbolic something is. And so a circle on this surface could have a pi equal to four. So that would be my proper answer.

And just for completeness, when Cass says, what about the other places, pie turns up in maths, which is something I go on about all the time. That's classic pie, I'm afraid, because if pie was four and it turns up somewhere else, that's just the number four. Whereas pie is the concept is like defined as the ratio.

It's still got a special meaning for like the flat perfect circle. That pie concept can't be. be four because it's defined to be this ridiculous number, this ratio. And the reason it pops up in other places is because it's this weird number. So, yeah. But the implications of pi being four is a meaningful sentence because it tells you that you're in this hyperbolic reality, etc. Because it can't be that normally.

The end. In conclusion, if pi was four, a circle would, look like a circle drawn on a piece of coral. Yes. And what I'm saying is, you know, let me go with a real current cultural reference point. If you're familiar with the late 90s film The Matrix. And I am. The moment when they see the same cat twice and they realize something's unusual about the reality they're in,

that's the same as seeing pie's. It tells you there's something weird going on with the reality you're in. Or is another analogy. It's like realizing that you're in a nightmare on Elm Street. As soon as Freddie turns up, you're like, oh. Oh, I'm asleep. Yeah. So if pi equals four, you're asleep.

Is that an even older cultural reference? It's like the film Train Pull. into station in that. It's terrifying the first time you see it. It's like journey to the moon. It's a bit like a zoat troop. Yeah, okay, yeah, okay. Point made.

Well, I'm going to give it a ding. Oh, thanks. Mainly because we're friends. No, really. The more you say it, the less I believe it. I'm going to give it a ding because is you answered it. Cass, though, I'll let you properly ding this if you want.

So, Cass, if you feel like that solved it for you. If you have further questions, then please let my business acquaintance know. Now it's time for AOB, which stands for any other boring stories about watching the World Cup. And first bit of AOB, is sent in for Beck, and it was about the boat in an aqueduct question. Yes, I said that I was open to being corrected, and boy, oh boy, did people take that literally. No, it was meant to be taken literally. No, lots of people sent in some very interesting thoughts, and there were a few responses, Matt, to your thing about the dropping the stone in the lake and things like that.

But considering that wasn't the original problem, I'm going to stick to this and I wanted to give a shout out to Eric 1843 who wrote, Hi Beck, your answer to the boat crossing the canal bridge in episode 138 was correct as the boat passes over the aqueduct does not increase the load on the structure. However, some of the other details were not quite right. And I appreciate when these are said because I feel like it makes our show a lot more reliable. So Eric rightfully pointed out that a canal is not an open system because nearly all of them have locks. So between the locks, it's a closed system. And Eric, you're absolutely right.

I completely forgot about that. And it's a very obvious thing. Putting a boat into the canal would increase a total load on the canal floor, as would loading a barge already in the water. The extra weight would spread out from the boat at the speed of sound in water and be distributed over the whole of that section. The biggest difference in load on the aqueduct would be from the operation of the locks, however. If an upstream lock was opened, then the full mass of the water in the lock would be added to the next section. And if a downstream lock was filled, the entire mass of water in that section would be taken away. These water masses would far outweigh the canal boats or their loads.

A lock could easily hold 1,000 cubic metres of water and each cubic meter weighs a ton. So it doesn't change the unethysts. to the problem, but it is a very valid point that we're not necessarily working with an open system. It is a closed system, but the differences made when opening and closing locks not enough to change. Yeah, I think you were definitely right in general. If you change what's in the canal, it increases and decreases the load evenly across the entire thing at once. It doesn't matter if you start moving things around within the canal. Yes. Yeah, yeah, exactly.

So, but I appreciate that because I simplified it maybe a bit too much. And I think that was a very good clarification. So thank you, Eric. Adam's got in touch, who is the setter of the crossword problem. We had an episode 138. And they're getting back in touch to, first of all, apologize for how badly they worded the question. I don't know. I don't think that's true. I think it was fine. They're glad we got such an interesting answer. out of it. Now they're going to answer some of our questions. They are from the UK, but they were trying to make an American-style puzzle. Whoops, okay, fine. They've now gained a lot of respect for puzzle

setters who have to work within some, you know, all these constraints to keep all these long words completely checked. And they also learned that they should start with a smaller challenge, doing half-checked words for now. They do have an issue with our solution. What? When they say the number of arrangements in a 15-15 grid, it's something no one needs to know. okay, you're allowed to have that, that objection. They now want to spend the rest of their academic career running the code to solve it. Yes. And as an ending, they do have a final clue for us.

Oh, the ending of ending, four letters. Oh, very funny. Uh-huh. Thanks. I'll take it. And while speaking about crosswords, we had from Henrik, who says, Hi, Matt and Beck, love your podcast and both your respective work on YouTube and other platforms. Thank you.

All your work on YouTube. Yeah, shut up. No, I will, I will, I will, I promise. September. I only bring it up because you're really good at it. That's all. And you should do it. Carry on.

You meant to tell me I'm awful. Then I'll prove you wrong. Yeah, you couldn't make a good, funny, narrative-driven YouTube video if you're life depended on it. Yeah, I'll prove you wrong. Pay me $1,000. So I'd rather flip a coin. That's a video. Do that.

You should have a look at some Swedish crosswords where some are more than 25 by 25 grids. What? And they're all as you describe, American's style, where almost every letter overlaps in two answers. If you look at this link to a Swedish blog, there is an image of a standard Swedish newspaper crosswords. So let's take a look at that. Oh my goodness. Oh, my. A nightmare.

And the clues are like in the grid. In the grid. And there's just a picture of ghosts for no reason. Probably is a reason. I'm closing that. I like to think that the ghosts and the geist are a standard in all Swedish crosswords. We'll stick a link in the show notes anyway in case anyone is interested in seeing. Well, that's it for today's episode.

Thank you so much to everyone who listened, which by definition is you. Well done. Thanks for listening this far. We appreciate each and every single one of our listeners, and we will love to thank you all by name. Because you're all friends of ours, every single one of you, officially a friend. But we can't do that just for time constraints. So we pick three names at random from all our Patreon supporters to thank them as a representation of all of you. And as an added bonus, we mispronounce everyone's names, which this episode shall include

Bra, Dlanum, it's... Oh, demang, yo, rattle. Ghe, o'c. Well, that's it. The last thing we have to do is to thank our producer Laura Grimshaw, who's a bit like watching the England versus Argentina World Cup game on an American Airlines flight to San Francisco in that. Somehow they made everything work despite seemingly constant technical difficulties. All right. Hit us with the connecting McForo. Can I go center stage, please?

Oh. Yeah, boy.