A Problem Squared - 117 = Visualising Hacks and Unusual Icy Snacks

Episode Date: September 1, 2025

👁️ How do you remember things if you can’t visualisethem in your mind’s eye?🍭 What’s the best shape for a freeze pop?🪣 And there’s some Any Other Beachness  Head to our socials to see freeze pop pics, Matt(not that one)’s tooth and the AOB gifts!  Here’s a link to the University of Exeter’s The Eye’s Mind project: https://blogs.exeter.ac.uk/eyesmind/   And here’s a selection of freeze pops and anti-prisms…https://www.sainsburys.co.uk/gol-ui/product/del-monte-quality-pineapple-freeze-pop-8-x-62mlhttps://www.vimto.co.uk/vimto-range/product/vimto-pyramids/https://en.wikipedia.org/wiki/Square_antiprismhttps://en.wikipedia.org/wiki/Disphenoid  See Matt on tour! http://standupmaths.com/shows/  Here’s how to get involved with Matt’s Moon Pi Kickstarter:https://www.kickstarter.com/profile/standupmaths  And here’s how to volunteer for Calculate Pi By Hand with Matt: https://forms.gle/w44THpNJ3jWUPqHy6 If you’re 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 square, the problem solving podcast, which is a lot like a Scottish beach in summer in that. There are a lot of people there hanging out, enjoying the view, just watching and listening, but only a few brave souls kit up and swim out into the ocean. of problems to find some and solve them. How is the podcast like that? It's exactly like that. Are the listeners, the people enjoying the view? Listeners are the people just chilling on the beach and where the very few people who actually go for us swim.

Who are like we're going to go for a swim? Yeah, okay. And you've just heard Beck Hill, who's a lot like the Scottish seaside during summer in that. Actually, forget during summer, it's year-round entertainment. fun excitement and colour how diplomatic of you thank you very much and i'm matt parker a bit like the Scottish seaside in summer because well it's got the general vibe of being in Australia no one's got a tan it's just it's just a lot less active I just got back from the beach

everyone I'm in Scotland yeah and Matt said about an hour ago yeah I'm going to have a shower and write my intro thank you and I'm now saying to realize that a very little writing went on during that. That's very true. But you smell incredible. Clean. Yeah. And on this episode, I imagine I'll be helping some people with some imagery.

Oh, I'm making sure a tasty tree shapes up. And there'll be some any other beachness. Ah, there it is. Made that nice and easy for me. See, see, it writes itself. Once you get up with that first hump, smooth sailing, like at the beach. So, Beck, how are you doing? I'm all right.

We're still, as of the time of recording, in Edinburgh for the Fringe Festival. Yes. About the time of listening, we will be done. Yes, yeah. Well done us. Yeah, congrats. I like listening back to episodes because they remind me of stuff I've said. And Beck does use the podcast.

It doubles up as journaling. Yeah. Yeah, Beck, reminder, like, have you got any food in your cupboards? Maybe go to a shop today by the time you listen to this. But that goes for everyone. Yeah. If anyone there is like me, anyone listening is like, oh, that's right. I forgot to get food.

Just a little reminder, if you're on a commute, pick up that stuff that you needed to get. Solving problems people forgot they had. Before they even arrived. Yeah. I've been having a lovely time. My audiences have been fantastic. Lots of people have been sticking around afterwards to say hi, blah, blah, blah, et cetera. And I bought a tooth.

You did buy a tooth. Yeah. Yep. I've bought a tooth from another mat. I have a photo. We'll put it on socials. Great. I know you bought a tooth.

Because our shows are at the same time for people who aren't up to speak on this. We can't see each other shows. You are telepathic. No, that's also true, but I'm relevant. I was leaving my venue, finished the show, signed to calculators. I was actually rolling my bike out because I cycled in yesterday. And someone ran out to me and said, Hi, Matt, I just sold a tooth to Beck.

And it was Matt who'd sold a tooth to you and then just happened to have wandered over to where I was. I assume unrelated. And it was serendipitous. Just wanted to let you know. Yeah, update me immediately. Yes. So thank you, Matt. That was awesome.

He had the tooth extracted last year. year. They asked if you wanted to keep it. He said yes. And then he was like, oh, now I have a tooth. What do I do with it? And then he was listening to a problem squared and went, ah, I know exactly what to do with his tooth. Oh, and Beck will be in Edinburgh. He came up and asked, when would I like to purchase it from him as I was setting up the show, which is perfect. Like, that's literally, that's my kind of audience and chaos. Yeah. And it was great because it happened in front of some very confused people sitting in the front. Well, they thought they were there for a comedy show, not to watch a tooth deal go down.

Yeah, and then I explained to them, oh, I buy teeth. And they were like, oh, we look forward to hearing about it. And I was like, oh, no, I don't talk about it in the show. That doesn't make the top 10 interesting things that are in the show. No, there's loads of the things in my life happening. I don't have time to talk about teeth. Also, I don't find it funny. It's a serious commercial transaction.

Yeah, I'm not going to write jokes about it. I don't want to belittle. The serious work of the tooth fairy Yeah So I'm in a good mood Great Yeah Excellent

How about you I'm good I mean I think we're both in that kind of Obviously doing a show a day for a month That's taken as toll But there's a certain amount of giddy Enjoyment that it's all going well And we're going to make it

We're very close And my show is now finally working I did a stock take That's your show Of the show Because I would not be surprised if you just did stock take for your show. You know, we do sometimes. I have got like a tick list.

No, I mean like the show is you doing stock take. The show is the stock take. That's what I imagine. I imagine you're just counting. Yeah. That would sell. People would show up. I would be sad for them.

Well, they wouldn't want to bring their friends. But yeah. Early in the show, I acknowledge that there are people who know who I am and there are people who have accompanied people who know who I am. And if it was only that first category, category zero, I could have advertised Matt Parker Speaksin Binary for an hour. Yeah. And they'd be there and have a great time.

Yeah. But because they bring people, I have to do a proper show. So that that's the only thing separating. It's almost like your job as a mass communicator rather than personality. Yeah. But the stock tech I have done behind the scenes, not public facing, is what tech we ended up needing to get the show running. And we're currently at projector screen and TV screen,

two Raspberry Pies, two laptops, and a phone. Okay. That's not including anything in the tech box. That's just on stage. Oh, and there's a network. So that we run our own. We had a little chat when we were setting up. We had to name the network.

Right. As we were like installing everything in the venue at the beginning of the month. I think it was Alien. I came up with Stage Lanager. Nice. So we have a stage manager. That's really good. Exactly.

Yeah. That joins all the devices together in unison. And my main laptop has, as well as the built-in keyboard, three other keyboard devices plugged into it to control it throughout the show. Although good news, no Apple script this time, everything's Python. So in that regard, we've simplified it. How could that possibly go wrong? Yeah, exactly.

Your Python codes have always been efficient. Oh, my code genuinely crashed. Like, I run it, I have to run it right before the show for reasons that would be obviously if you see the show. Because people enter data. as they're coming in, and I then use Python to analyze it and put it into the presentation. And I ran it and it crashed four minutes before the show was meant to start. And so I had to live go through, work out where it was crashing and add another little try except.

Oh, they would have loved that. The audience didn't even know. I was in the wing fixing my code. You should have a GoPro on your head for what you do is you don't have that going. going anywhere during the show. Yeah. But when you eventually, I'm sure, release a DVD special. Yeah.

They can have some behind the scenes footage of what it all looks like from your perspective. Yeah. What I'm tempted to do is there's stuff in the show that's randomly generated every night. But no one would know because you only see a show. Right. So I'm tempted to do maybe when I'm on tour a compilation of the things that change every, like just run to a supercut of the things I mess around. Yeah.

We'll see. I've got a big old feature request list. That's a lot longer before document. Yeah. Random things that change. Yeah. You know how sometimes people will film several shows and then edit together the best cuts? But they make it look like it was the one show.

I remember seeing a live recording performance of Red Hot Chili Peppers. This was dated some time ago. Yeah. And noticing that probably Flea, he was Red Hot Chili Peppers, wasn't he? He was. His Mohawk in the song. keeps going from upright, very floppy, continuously. Cutting back and forth between nights.

And at no point during the edit did someone go, oh, his hair keeps changing. Like they're wearing the same outfits. They got, is the same point as it. Didn't hire a continuity person. We always, for Spoken Nerd, would film two nights for our DVD releases. Not to cut between them, but to be able to pick the best. Yeah. And every single time, we do the first night and it would be fine.

Because we know we're being filmed, we don't want to mess it up. Yeah. And we're like, great, we have a perfectly fine recording in the can. Let's just relax and enjoy the second one because I don't really need it anymore. And every time the second one would be a million percent better. Yeah. And we'll just release the second night. Yeah.

Yeah. It's a very expensive way to trick you into relaxing while being filmed. Yeah, that's right. Speaking of doing a show. Okay. Should we do a podcast? Sure. First problem in this episode is a follow-on from an AOB.

in a previous episode, about a previous episode. So back in episode 114, Keith, Keith wrote in and talked about having a Fantasia, which is the inability to form mental images. Because Keith wanted tips on how to remember things when you can't visualize things in your mind. We put a call out at the end of that episode, and listeners have responded. They've sent in suggestions and stories, which Beck has now gone through and is going to summarize our collective findings for Keith. What do we got? Yeah, so we heard from so many of you, and it's really interesting. I'm going to talk a little bit about some of the research that one of our listeners pointed me in the direction of, who was an anonymous person who came back to us. They pointed out that

Exeter University runs the Eyes Mind Project, Professor Zeman, I hope I'm pronouncing that correctly, E-M-A-N was the original one to coin the term Amphantasia. So Professor Zeman is obviously the person behind this website. They maintain a list of volunteers with a lack of visual imagination for some studies that they do. For example, recently they had a survey testing recollection of details from excerpts of visuals, heavy fantasy stories and very bland academic writings.

Now, I don't see any results from that. I had a little look at the website. They said any listeners who want to further research might consider signing up to take part. We'll put a link in the show notes. But I did a little more research into Professor Zeman. The phenomenon of Amphantasia, the idea that some people might struggle to visualize certain images within their heads, that's been kind of noted in various different ways over time. And in fact, a psychologist in 1897, Theodoul Armand, Rebo, so that's T-H-E-O-D-U-L-E-R-M-A-N-D, and then R-I-B-O-T, reported a kind of typographic visual-type imagination consisting and mentally seeing ideas in the form of the corresponding printed words.

Paraphrased by Jacques Hadamard, they said the words dog or animal were not accompanied by any image, but we're seeing. as being printed. And I realize that's something that I do a lot is that I spell people's names in my head to help me remember their names. It's not that I can't visualize people. Like I can visualize people, but I meet a lot of people and I really struggle to hold on to all that information at the same time. So when I meet people, I tend to spell out their names in my head or if they've got an interesting name, I ask them to spell it out, even if it doesn't sound how it's written, I can remember how it's written. I had the same thing.

When people tell me how, I'm bad at pronouncing things, and people tell me how to pronounce a word or their name, just ironically, saying the sounds as they sound, I can't really lock that in my head. But if I've got a written version, I can hang the sounds off it, even if the letters don't necessarily match. Yeah, yeah. It's interesting, isn't it? Just reading this in itself was like, huh, that's interesting, that that's a thing.

thing that I do to try and remember stuff. There's probably loads of people listening who are like, I do that too. I also want to make very clear from the get-go, no one is talking about as if they're disorders, because they're not disorders. It seems that they are part of a wide range of just how brains are wired. No two brains are the same. Exactly. So, thank goodness. None of these are ways in which anyone is deficient or lacking in something. If anything, a lot of people have pointed out how their inability to do something has actually really strengthened the way that their brains work in other ways, which means that they can do things other people can't. So I just wanted to preface everything with that.

So it was largely unstudied until 2005. So more than 100 years later. It took 108 years. I mean, there were some reports dating as early as 1880. Oh, okay. So, yeah, but it took a long time before it was actually studied. So Professor Adam Zeman of the University of, City of Exeter was approached by a man who seemed to have lost the ability to visualize after

undergoing minor surgery. So following the publication of this patient's case in 2010, a number of people approached Zeman reporting a lifelong inability to visualize. In 2015, Professor Zeman, along with Michaela D-E-W-A-R, and Sergio Della Sala, they put out a paper called Lives without imagery, congenital amphantasia. So that's what they were looking into. And Professor Zeman actually goes a bit further into the initial thing that interested him about it. It was a person with a surgery.

Yeah, it was a 65-year-old man who became unable to summon images to the mind's eye after coronary angioplasty. And that's when they were contacted by a load of people who recognize themselves in the article's account of blind imagination, which is an interesting way of discreacting. describing it. Yeah, with the important difference that it had been a lifelong thing for them. Right. So it wasn't saying that occurred to them after a surgery. They all that way. Yeah, they described the features of their condition elicited by a questionnaire, and that's how they suggested the name, Afantasia. So 21 individuals had contacted them after the paper came out. And so

they sent a questionnaire, just to probe a bit more. They found that participants typically became aware of their condition in their teens or 20s, when through conversation or reading, they realize that most people who saw things in the mind's eye, unlike our participants, enjoyed a quasi-visual experience. Our participants' rating of imagery vividness was significantly lower than that of 121 controls. Five out of 21 reported affected relatives. 10 out of 21 reported that all modalities of imagery were affected, despite their substantial or complete deficit in voluntary visual imagery. The majority of particular, participants described involuntary imagery during wakefulness and or during dreams.

I like the fact that they include the caveat of voluntary because I can recall an image of something in my head voluntarily and some people can't, but that doesn't mean that they don't dream or they don't have moments where they can see it. It's just not something they necessarily control. You can't conjure it up yourself. Yeah, in fact, some people refer to it as flashes. so occasionally they will get an image of something it's just flashed up ahead. That's an interesting distinction I hadn't realized before. Yeah, because I was wondering how dreams work.

Most participants reported difficulties with autobiographical memory. They described a varied but modest effect on mood and relationships. Now this is interesting. 14 identified compensatory strengths in verbal, mathematical and logical domains. That's two thirds of them. And I'm also thinking this might potentially be what? a lot of people really resonated with this, like this subject really resonated with our listeners. Right.

You're saying there's overlapping categories here. And quite a few of our listeners, which you'll hear from shortly, mentioned that they find that this has helped, like mathematics works really nicely for them for the very same reason. So it's interesting. We might have a higher level of people who experience some form of Amphantasia the most podcasts. Got it. Yeah. Okay.

Yep. Yeah. The successful performance in a task that would normally elicit imagery, like count how many windows there are in your house or apartment, was achieved by drawing on what participants described as knowledge, memory and sub-visual models. And I'll use this as a springboard to jump into something that someone else had said about using it for memory. like for instance we heard from Joe Thanks Joe Who said they can rarely and unreliably form very vague images But for most purposes it's easier to say they can't Yep

They pointed out that a classic question on a test for Amphantasia is how many windows are there on the front of your house Matt how do you work out how many windows are in the front of your house I picture the house and I count them Yeah same yeah But Joe I definitely picture it as if I'm standing out the front looking at it Yeah like I'm looking at a photo

Yeah Yeah For me, it's like the real thing. I'm not looking at a picture. I'm like, I imagine it flashes up me standing on the drive staring at it. So the way that Joe answers that question, because they can't visualize the house, they struggle to, is they said they think about cleaning the windows and how many I do in each room. Oh. Now, even that, I'm like, well, I visualize cleaning them.

Exactly. But yes, then think if that room is on the front of my house. so they imagine cleaning the windows and then they can try and remember if it's yeah again it's difficult because immediately I'm like well to work out if it's the front I would visualize it yeah as far as recalling a journey that was your question map they said

I don't tend to remember landmarks while not on a journey I remember street names and streets or words on signs shortly before turns while on the journey I recognize the image of turns but I cannot recall it to describe to someone someone else. Got it. So when you see it, you're like, I remember this.

Yes. And quite a lot of people wanted to make that distinction as well. They can't bring up the images, but when they see it in real life, they go, yes, correct. I know this. The memories are there. It's just the in-head projector that's not. Well, it's funny. You should say that as well, because that relates very nicely too.

We also heard from Stephen, who also says, love the blah, blah, blah. Thanks, Steve. They think it's more down to recall. rather than storage. Yeah. So, for example, I can't remember holidays of my own accord, but if I see a photo or someone describes an event, I can unlock that experience and remember more of it.

If I then talk to someone about it, it is almost like it gets stored verbally and is easier to access in the future. The human brain. Stephen also goes on to say that a trick that they've developed for remembering names is to get people to introduce themselves with their full name and an amazing fact about themselves. The fact doesn't have to be true, just a bit unique.

Just memorable. Yeah. And then I repeat it back. This will help store it in the bit of my memory that is not linked to what they look like, but a verbal cue instead. That's great. They said many of my students say that they, so I believe they're a teacher, so they can still remember how their friends introduce themselves as they have a mental image of the amazing thing. So it can work for visualizers too, which I really like, and I'm going to try that out. And the verbal cue thing is an interesting one because you would have heard me many times say, remind me that I need to do this.

Oh yeah. And every time I say, people say, oh, I'm not going to remember. I won't remind you that. And I just say, no, I just need to say it out loud because I'm more likely to remember it now that I've said it out loud. It doesn't always work. But it is useful for me to say things aloud. And I think that's interesting in moving it into a different part of your brain. The idea of it also being down to recall rather than storage, I think is interesting.

Speaking of which, don't get to buy food. To anyone listening? No, that's for you. And me. I'll bring it up again. Yeah, yeah, yeah. We'll keep reinforcing it. If there's anything that happens from this episode, it's people will remember to buy

whatever it is they need right now. Yeah, everyone's doing their own stock take. Because a lot of our memory then gets stored into like long term, it's like a zip file. And I feel like what Stephen was describing there is like when you see a photo or someone else is recalling it or something like that, it helps you expand the zip file and access those memories. It's not that you're not storing them. This isn't the case for everyone, obviously.

but I relate to that and going back to the thing about names. So Anon, who was the anonymous person who originally told me about the Eyes Mind Project, said they also have prosopagnosia, P-R-O-S-O-P-A-G-N-O-S-I. A, which is face-blindness. Oh, yeah. It's not the same thing as Amphantasia, but I feel like it's related. I can look at someone I should easily know, like my mother, and have no idea who she is purely by her face.

This means I rely heavily on context clues as to who people are. I shamefully have to rely on a lot of sometimes unflattering facts about people that aren't visual. Don't share those with the person. No, you said it's utterly inappropriate. That's just between a you and your brain thing. Yeah, they did point out that this is why they were anonymous when they submitted. They said, it's utterly inappropriate to admit out loud. I remember you because you're the guy who brings.

reads really heavily on this floor. I remember you because you wear the same three graphic t-shirts in rotation. I'm looking at you, Matt Parker. Now I feel seen. Yeah. That's the only way I remember you. Yeah, fair enough. Otherwise, I'm like, hey, you, head above that graphic t-shirt.

Yeah, when you get a new t-shirt, it takes me a long time. A long time to go, who's this new guy? Yeah, I have to go by accent. Good luck. It's the only chance I have of not looking confused around everyone I meet every day. I can sometimes do it with nice things, like linking someone to a specific hairstyle, but that can fail fast the moment they get it cut. I thrived during the pandemic when each employee was in their own square on the video call with their name written underneath them and every chat message was labelled with a name. Yeah, that was very useful.

And I found there's a lot of people who I met in Zoom calls or meetings and things like that online or even just on Instagram or things like that. And I'm so much more inclined to remember their names. Right. Because... It was hovering next to them. Yeah, and because I could read it. I could see the name next to the face. And again, I think that's like the combination of visualizing the word along with the face.

We also heard from Lou, L-E-W, for anyone trying to remember like myself, they said that if they're trying to find their wife in a shop, they find it difficult to spot her unless they previously clocked what she's wearing. so they've made like a genuine mental note of like oh it's a blue shirt and a white skirt I'm making this up I don't I don't know what their wife looks like I mean I do that just because it's faster like if I remember what Lucy's wearing yeah I can scan as a shopping environment and find it way quicker than going face by face interestingly I often find myself going I can't remember what they're wearing today but I go by I definitely have that I go by height I remember how tall

someone is and I scan over to see if any like if I'm like in a clothing store where people are above racks and I'm like well I know they're roughly going to be this high yeah yeah no everyone looks short to me yeah I mean you're not look you're tall but I've known tall I'm not saying I'm the tallest no sorry the vast majority of people look short to me yes I notice people who are tall because I'm not used to looking up and that's very yeah and my my muscles like oh what the heck is this yeah yeah yeah whereas sometimes when people get to a certain height like over a certain height i'm like i don't know what the you can be six five or six nine and i might mentally categorize that as the same because i don't have to because the angle

it's more like how much of your belly button is in line with my nose anyway lou points out that they will just go by if they can remember if they've clocked clothing clothing yep and that's what they do for other ways of recalling things. They try to make a strong mental note of sort of facts. We had several people write in and say that, you know, when they're trying to explain, how can you understand? Like I was saying, how can you know how many windows you clean if you can't visualize yourself cleaning the windows? It's possible that the answer to that has been answered by a few other people who said it's recalled in the same way that we recall facts. Like, oh, the sun is yellow, there's a rainbow. Weirdly, as I'm saying that, I am picturing

them. They're pictures. It'd be like, you know, seven is prime. Yeah, yeah. When you say that, my, I instantly visualise the numbers. And actually, someone else said, 101 is prime. Because I imagine the number. I don't imagine what it means for prime, but I, I can't hear it without the number appearing in my brain. Yeah. Yeah. And that was the other thing. someone else said that, you know, it's a fact just as much as we know that 2 plus 2 equals 4. That's text. Yeah, but if you were to give me a sum, I have to visualize the sum in my head to do it. Yeah, but that's still, you're not visualising a picture, you're visualising text.

That's true. Again, to answer your question about what it's like to navigate, they said they take mental notes of landmarks and how they relate to each other, which helps when returning to a point from a different direction. I also find it useful to combine information in order to. to aid memory. So they said, as a regular pub quizer,

when I learn a new fact, I try to find more than one way to link information together to help solidify things, such as creating acronyms for lists of interconnected items or making connections in several directions from a question I've come up against.

They said, as a somewhat poor but recent example, and I love this. So the question was, what country's flag depicts a sinking ship? The answer is Bermuda. So they said that to remember that fact moving forward,

it becomes a combination of several facts. So now we know the fact of which country has a sinking ship on its flag. Yeah. Answer, Bermuda. But it's also, Bermuda has a sinking ship on its flag. Oh. Which is, if you think more about like, oh, facts about Bermuda as opposed to facts about flags, they also said the Bermuda Triangle is famous for sinking ships.

Yep. Therefore, it connects those two bits of information together. It's a fact about Bermuda, fact about the flag. So that's how they get the answer from old. angles and I thought that was quite nice. Now you know me when I find something interesting I want to talk about it all day but I need to get back to Keith's question which was tips on how to remember things. Oh yes. So another example given to us by one of our wonderful listeners, Adistia, ADA, S-T-E-A said for me audio cues are very powerful remembering things and memories or concepts

can be triggered by hearing songs which are usually uncontrolled but on a few occasions has been useful. We've talked about that ourselves before. In fact, this is how this all came about because we were talking about using particular songs to remember certain things and remembering the lyrics to songs and things like that they said a physics exam they tapped their fingers to remind them of a tune which was playing during the studying right okay which helped them remember some of the stuff i also wonder then if smell is quite useful as well so i hope there's been enough there to help both shed a little more light on this

for anyone who was also curious and also to help you a little bit further with your aid in memorizing things Keith I just want to say one final thing because we mentioned this in 114 we were talking about how and I think Keith maybe mentioned this people who get annoyed when they see a film based on a book

because it doesn't match what they imagined when they were reading the book yeah so we also heard from Matt they said I believe that several famous cartoonists slash illustrators have Amphantasia in a way that is useful if they are illustrating a story or something similar as they don't have any preconceived ideas of what the characters should look like from reading the story with text only unlike people who do visualize things

who come in with a preconceived self-made mental image of what the character should look like interestingly when I wrote horror heights I didn't do any descriptions of the characters like physically because I always imagine myself as the main character like whenever I'm reading something that's a whole separate thing back but I don't know but but But quite often if it's about like how the characters, it kind of removes me from the story a little bit. Like I can imagine that I am someone different, but like weirdly, I don't know, it's strange. I like to leave it up to the readers as to what the characters should look like or what it feels like or something like that. And I also wonder if that's why there's quite a lot of books that I find too boring.

Like I tried to read Lord of the Rings. I just, there's too much description. And I think it's partly because I'm like, yeah, I know what it looks like. I'm picturing in my head. Like you don't have to keep going on about. Oh, cool. Right now there's that as well as well. Now, look, I enjoyed a lot of the rings, but we all skip over the songs.

So I'm forced to agree with you partly. Yeah. I really appreciate everyone writing in. And apologies if I didn't mention your names or specifically what you've written. And there's just so much information here. And I'm sure there's a bunch more who are now going, oh, I've got a new thing too. I'm sure there will be a lot more discussion on our Reddit or Discord. Go there.

Don't put them in the problem posing page because then only we can see it. Yes. Yeah. Because I think this would make for a far more interesting discussion between folks. And do we need a ding from Keith? I guess we wait for Keith to come back and see. I'd like a ding from Keith. Yeah, okay, Keith.

If you don't mind, Keith, you may use the problem posing page. Loop back around for us. Give us a ding. Our next problem comes from Mike. We went to the problem posing page at a problemsquare.com and said, Hi, Beck and Matt, thanks for the bi-weekly excitement. You are still in my life. Smiley face.

My problem is this. I recently had a Del Monte freeze pop, and the triangular-ish shape intrigued me because it is so satisfying. Have you pronounced that correctly? Or caps. All caps. So satisfying that it has the same cross-sectional perimeter across. What is this shape or this family of shapes? called if there is a name, and why don't we see it used more often? Thanks.

Right. Back, I look into it. But before we go any further, would you like a freeze pop? Yes. All right, hang on. As Matt goes to the freezer, I'm going to point out that Matt was going to solve this problem several episodes ago, and we went to the supermarket to ensure that the freeze pops were as frozen as possible before we started recording. And there were none.

And we struggled to find these freeze pops. I noticed that this is interesting. Shall I say what you've brought out? Matt has not brought out Del Monte freeze pops. Matt has brought out Vimtoe easy-freezy pyramids. And I'm imagining this is because it is the same shape. It's the same shape. I could not find, despite promises on multiple grocery store websites,

the Del Monte freeze pops as sent in by Mike. Oh, there we goes. Yes, look at that. Okay, I didn't appreciate, I'm going to take a photo of the midway point. The property we're about to discuss is the reason why it's able to slide out of the pack by only cutting one end. That's very clever. Maybe that's why it's the shape. Now, I've got it totally loose, just sliding on a plate.

I have not thought this through. I have no mechanism by which to eat this. Like a fork? I'm going to try and reinsert it into the pattern. I think you're meant to consume it as it's coming out. Like you don't just... Yeah, it doesn't slide out. It means that you're never getting too much.

That's good. So, could you describe the shape it is? Yeah, it's like someone took a rectangle at both ends and then tried to ring it out slightly. Oh, okay, yes. Let me describe Beck describing what we're looking at. Makes sense to me. Imagine you've got a rectangle in so much as like an index card or something. And Beck is grasping the two short ends, but then holding one fixed and rotating the other

one by 90 degrees. So now it's orthogonal to the first one. And that is part of it, but it's more 3D than that. But yes, you're absolutely right. I don't think in three dimensions. I think we've mentioned this before, but I've worked very well in 2 dimensions. A3Dness. The opposite ends are at right angles to it.

each other. And then it's all joined in around it. We'll put photos of this in the show notes and on all our social medias. It's made from four triangles. So technically it's a tetrahedron. So to answer Mike's, I guess the easiest of Mike's questions, what is this shape? The easiest answer is it's a tetrahedron. Okay. Now, I did ask a WhatsApp group of mass communicators I'm in what the actual name of this shape is. Okay. Because tetrahedron just covers any triangle-based pyramid with any irregular length sides. And this feels like it's a specific type of tetrahedron.

Katie Stekles pointed out that, I mean, all the faces are the same triangle, and they're all Isosceles triangles. So Isosceles has two sides of the same. And so Katie's suggestion was it's a Isosceles tetrahedron. It's pretty good. Someone else named Richard Chippedin that it's called Richard Chippedin. Richard Contributed. Oh, right.

Someone called Richard contributed the following, that it is a dysphenoid. I've never heard of this. It's a dysphenoid tetrahedron as in it's got three acute angle isosceles faces. Okay. It's not a wide triangle. Yeah, no. All the angles. angles are under 90 degrees and they're all isosceles because I've got the two sides of the same

and they make a tetrahedron and I checked and yeah I mean I've never heard of that it's a weird thing in maths where a lot of people who aren't mathematicians are like what's the name of this shape what's the name of this shape and the answer most of the time is we haven't bothered naming that and sometimes it's we have bothered naming it but no one knows it and so only one person in the group was like, oh yeah, that's a disfantoid. The rest of us are like, never heard of it before. And we're all people, an above average amount of familiarity with the names of shapes. And I'd never heard that.

Yeah. And the thing is, it must have a name because the packaging company would have like a label or something for... I bet it's got a name where it's just the process by which it's made is described. It's a tube that's clamped into orthogonal directions to seal it. so it's basically a cylinder that's been pinched now what mike finds particularly exciting about this shape the reason mike finds it so satisfying in mike's words so satisfying

is it has the same cross-sectional perimeter across so only in one orientation but if you hold it like vertically as if you're using it as confectionery and you look along all the cross-sections of it the perimeter around the outside never changes. Right. And what dawned on me literally during the recording as we were opening it and sliding it out, that means it can slide through the tube because the packaging is flexible.

And no matter where you slide the ice lolly, it's always got the same distance around it. So the packaging can conform at any point to be a perfect snug fit. Which is why I think of the packaging, now that I've finished my ice lolly, I'm left with the empty packaging. It can be flattened. And now you're calling a tube because you're seeing it as the, you know, the fact that it can be widened. But it's still pinched to the bottom for me and I'm folding it into two dimensions, which is... It's a rectangle.

It's like the least exciting aspect. But isn't it interesting how I saw it as a rectangle before we turned it into a two-dimensional? Everything can be a rectangle if you fold hard enough. New t-shirts. I just thought Mike found that as a pleasing thing to have in general, but it turns out it's got a practical application to the way it sits in and moves around in the packaging, particularly as a confectionery that you're meant to slide out as you consume it. So I think that's deliberate now.

I've grown my appreciation for this shape as a frozen treat has only increased. I'm disappointed because it came in a box, which is an eight pack, but they're just sort of randomly assorted in there. They're jumble-packed. Pumble Pact, Jumble Pact. It's almost like we have a producer who is probably looking it up right now. I'm getting in Tumble Pact. That was delicious.

I don't know. I don't know much about Vimtoe, but they freeze a good pop. I think you'll find they freezey... Oh, sorry, they're easy, freezy pyramids. Yeah. Now. Ah. Ha ha ha ha ha ha.

They're calling it a pyramid. I don't know how I feel about that. I think it's technically. Okay, but if you're a little bit generous with your definition of pyramid. You can put it down on a flat surface such that there's an apex above it or joined with triangles, so just one of them is perfectly vertical. So I'm going to allow that, I think. A pyramid is a polyhedron.

Correct. Formed by connecting a polygonal base and a point called the apex. Yeah, I mean, in that regard, yes, it's a pyramid. Can't argue that. I'm going to call this face the base. Mm-hmm. Put it on my hand. There's the apex.

And it's joined to all the corners. So like a lot of things, it's got multiple names, but each name gets a bit more precise than what it means. So it's a pyramid or a tetrahedron, would be what I would say. But then within that, it's an isosceles-faced tetrahedron. And then I guess within that, you can say it's a dysfendoid tetrahedron. But what made Mike very excited was that the perimeter doesn't change. And now I'm very excited as well, Mike, because I realize the impact

of that has on the way the packaging functions. I'm very, very pleased. So now we need to work out, Mike's saying, are there other shapes that have that property? So I don't think there's a general name for the family, all shapes that have this other than shapes that have an orientation for which every horizontal cross section has the same perimeter length. But when I put this in the WhatsApp group Katie Steckles also contributed another fact

that just blew the case wide open she looked at it and said well hang on it's a bit like a straight line antiprism

so an anti-prism is so you only have a prism you have two identical faces and then you just join it up like join face to face and antiprism

is if you rotate the opposite faces so they don't quite line up and you join it with triangles instead. And so you can think about this as the beginning and the end as being lines that are rotated in different directions. Like the ends of a rectangle, maybe.

Like the ends of a rectangle. It's an anti-prism version of a rectangle. Oof, I'm going to allow that. And then I was like, yeah, I mean, Katie's absolutely correct. And it actually holds true that any antiprism has this property. too i'm going to pull up a square antiprism just a picture of one because a square prism is just a cube or a cuboid a square antiprism is what happens when you've rotated those first don't like that the base is a square the tops are square but they're rotated around so you've got

to use triangles to join them up you could freeze that and it would have the same property the cross sections are always the same all the way up and down because of the power of thinking about triangles for a while. Yeah, and what's interesting about this is that it means that the tops and the bottoms have four edges as the square, but when I'm looking at what I would imagine is, if you think of a, if you're like me, and you think very basically about three-dimensional shapes, and this is why I struggle, which is fine. I think just horizontally and vertically.

So the horizontal parts, the squares that are slightly rotated, yeah. So if you turn each side of the square as the base of a triangle, and then it goes to one corner of the opposing square, rather than your cube having four squares going around the horizontal part of it, you've got one, two, three, I'm trying to imagine the other side of it. One, two, three, four, five, six, seven, eight, nine? Right, eight. Eight. Eight, yeah. Eight makes sense, but I don't trust. No, it is right.

You counted them by picturing it. Yeah. A lot like windows on a house. It's doubling the amount that you would normally have a cube. So I hate that that's called a square antiprism. Because a monstrosity. Well, I spent a while this morning thinking about it going, yeah, every antiprism, that will work. and in fact I think any point in between will also work

and it was at that point in thinking of the logic I realized I hadn't written the intro yet and I needed to get out of the shower so that's what got us to where we are now but there's like a bunch of trivial shapes that do this if the cross-section never changes people online in the WhatsApp group pointed out if you skewed the shapes

like slid the top away from the base you still have the same property you're just like kind of moving it all over there's a bunch of other ways to do it Yeah, I'm looking at one that I find visually more pleasing. Oh, what's that? Instead of the triangles sort of coming out slightly, they go inwards. Does that make sense?

Hold on. Let me know if this is also a square antiprism. Oh, yeah. Yeah. Yeah, same thing, that everything, it's way more twisted. It's an anti-prism, but you've rotated the top even more. Instead of it coming outwards along the horizontal part, they're going inwards. Yeah.

And I find that visually far more. pleasing. I think that might still have the same perimeter all the way around. But it's not, it's non-convex, so that may break something. So in conclusion, it is a pyramid. It is a tetrahedron. It's a tetrahedron with a fancy name, a disfenoid tetrahedron. It is a shape where the cross-section always has the same perimeter that also works for any antiprism, which is kind of fun. And as I recently discovered, that's important to how you get it out of the packaging. That's an excellent question, Mike. One more thing did pop up while we were researching this.

Sophie, Sophie McLean on the WhatsApp group, noticed five years ago an equivalent ice lolly was discussed on Reddit in the casual UK subreddit because they had a big conversation about what shape it is. And it's the same. This is now three different brands who have had that same shape ice lolly. so there you are it must be a very functional and fun shape what i like is i'm going to read out the top five replies that are in succession someone has just come in and said a regular tetrahedron a different person replied with you're an irregular tetrahedron new person your mum's in a regular tetrahedron your face isn't a regular tetrahedron and then it's just carried on from there yeah so anyway turns out the answer was on the packet the whole time it's a pyramid bye

And now it's time for the part of the show. We like to call any other beechness where we pick up miscellaneous bits of outstanding admin. It's my favorite bit. What are we got? Well, it's more like what has Lucy got? Oh, that's true. Because you told me some exciting news the other day. I did.

And you correctly said we should say it in the podcast. Yeah. So my wife, Lucy Green, who actually we were just chatting about between recordings because she's the one who found the frozen Fimtoe things. She said, isn't that the shape you're after? Yeah, we were walking through the supermarket, like grocery shopping. to stock the flat where you're living in at the Edinburgh Festival French and she's like

hey aren't those the shape you're trying to find and I just walk right past them so what done Lucy and it's things like that that have led to her having her own minor planet named after her there is now an asteroid Lucy Green in the solar system so it's in a similar but more eccentric orbit

to asteroid Matt Parker and it's about time Lucy got her own because she's the actual famous astronomer yeah if anything it's sort of offensive that you had one first. It really, what genuinely was. Yeah. So I'm glad that's, that's leveled out. I was present when you guys were trying to work out the maths of how, when they'll be

close to one another. And I was like, this is gross. In our lifetimes, 23rd of February, 2060, I think we got. There'll be a quarter of an astronomical unit apart. And that's the closest pass in our lifetimes. What a, what a romantic day that's going. When you make a pass at Lucy. Yeah, I do.

Yeah. And they're both visible with a. small telescope so we're going to um that's what you want to call it hey i also do want to give a quick shout out to lizzie who's written in after seeing my show i mentioned the fact that i've mentioned on the podcast before that i flooded my flat in the past and lizzie pointed out that you can get a water level alarm which is intended for like fish tanks and stuff but you can just stick it to the side of something that you want to let you want to not do with water so if i'm I put that in my kitchen sink or my bath. It will set off an alarm if I've left the tap running.

So thank you, Lizzie. I'm going to look that up. Our next bit of AOB. This is just a bit of a clearing house. People have been giving me things to give to Beck. I just want to hand them all over. Which is intriguing. Just to get them off my plate.

The first one's actual food. Someone gave me a pack of Twisties. I'm going to throw this over to you back. Oh, okay. So these Twisties are not. The Australian ones They are corn snacks with BBQ curry flavour Ah yes, I love a barbecued curry

They are from Malaysia Amazing They were given to me in Australia by I think their name was Chris Very sorry if your name's not Chris And I've misremembered that It's been a while

So there you go That's Malaysian Twisties we will eat afterwards Up next in the handover-a-thon Hazel It has made us matching key rings. I'm going to throw yours back. Here you go. What?

It's got a shrinky-dink vibe to it. It does. Hazel. A young child gave these to me after my show at the French and was already aware they were too young to come and see your show at the French back. But it's like a shrinky-dink recreation of our logo. Yeah. And then our name attached like the little metal chain thing. It's so good.

It's a really good recreation of the logo. Yeah, the logo's really good. And it's my favorite kind of bubble writing. Yeah. It's top-notch work. This is amazing. Good stuff. And finally, a piece of paper.

Now, I'm used to people giving me all sorts of things after a show. And Jack gave me a piece of paper with just binary written on it. I think people are testing if I actually am fluent in binary. So I read it. And in binary, it says, love the pod. And then the binary just spells out blood. blah, blah, blah. I was wondering what this said.

Yeah, yeah. So, Jack made me manually decode, blah, blah, blah. Great. Good work, Jack. Yeah, well done, Jack. I think we can put it. I've got a photo of Jack and I and the bit of paper that we took, so I think we can put that on socials.

I don't think Jack are mine. And that's everything people gave me. And there's been another installment of things people gave Matt to give to Beck. Thank you so much for listening. appreciate everyone who tunes in, downloads, et cetera, then listens along. You are like the tide that comes in and out at a Scottish beach in summer to keep everything ticking along. But particularly, we want to thank our Patreon supporters.

They're like the free parking I found at the Scottish beach in summer who help all the figures balance out. We like to pick three of those people from our. Patreon supporters at random every episode to thank, which this time includes. Poorly pronounced. Do minnie. Oh, nice. Kamuk.

Inley. Co. Norge. Armours. Caller. Gran. Thank you so much, everyone who supports or listens to the podcast. And that's it.

I'm Matt Parker. You've also been listening to Beck Hill. And of course, we have producer Laura Grimshaw, who is like the local council of the Scottish beach in summer. Like, without them, the bins wouldn't be emptied. They're operating. silently in the background to make everyone else's enjoyment possible, like the council. Did we vote her in? No, I think it's, I think that it's rigged.

Ah, yeah. I think Laura has her hands in a lot of people's pockets. Yeah, we should either start or stop the count. Yeah. Now, to recap last time, the two times ago Beck hit one of my battleships, but then in an exploratory nearby shot, she missed last time. Yes. So, I'm going to go for C6.

C6. miss you're narrowing it down I give you that now now I'm going to I hit last time but I don't know which way to go now

so I'm going to guess H9 hit yes the tide is turning Thank you.