A Problem Squared - 119 = Proportions by Bananas and Polygons from Lava

Episode Date: October 13, 2025

🍌 Is there a more consistent system of measuring things (and is it ‘Banana For Scale’)?🌋 Why and how do hexagons occur in nature?🔔 And there will be a whole Bec of Any Other BecnessHead to our socials to see Matt and Bec playing The Metre Game, lots of bananas for scale, and Matt sporting some very fetching headwear.Some further reading on the origins of ‘Banana For Scale’:https://knowyourmeme.com/memes/banana-for-scale Some further reading on hexagons in basalt:European Geoscience Union article:https://blogs.egu.eu/divisions/ts/2023/05/26/features-from-the-field-columnar-basalts-and-why-hexagons-are-natures-favourite-shape/Physical Review Letters: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.154301See 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/w44THpNJ3jWUPqHy6If 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.

Hey, it's me, Matt, from the podcast. You're about to listen to. I'm partway through my tour now. Next show is in Exeter. Fun fact. If you're listening to this as soon as it comes out. Anyway, come and see me at a show. It's a huge amount of fun.

I'll sign your calculators afterwards. See you there. I won't. What? Salamass.com slash shows. Hello and welcome to a problem squared, the only problem-solving podcast that claims to be the only problem-solving podcast. You know, there are more. But we're the only ones that claim...

We're the only ones that claim to be the... Yeah, yeah, yeah. I'm Matt Parker, mathematician, performer and whatnot. And I am the first ever person to finish this sentence. And I'm joined by Beck Hill, comedian. writer, performer as well and Beck Beck Hill holds

the world record for the most consecutive days being Beck Hill this specific Rebecca Hill No other Beck Hills like me exist No And on this episode

We will be doing the following things On this episode I'm on the hunt for a new measurement system I've cracked a rock mystery And I assume there'll be the first of its kind

of any other business. It's any other of the other anythings. So Beck. Hi. Have you been. I'm good. I've noticed you've made yourself a coffee. Yeah.

Do you want a coffee? If there is some. Of course. I poured a coffee. I made coffee for everyone. Oh, it's over there. For the listeners, there's a giant caraff of coffee. Listeners, take this.

I'm pouring it into Beck's thermos. I hope that you've, managed to make yourself a coffee if you're listening. If not, let this be your reminder or for whatever other beverage should you desire. So obviously you're now doing better than a moment ago, thanks to the coffee. Yes, thank you. This is very great. I split it right down the far side of your thermos. I'm very sorry. I just noticed that. The far side of my thermos is an album that I'm very proud of. How you doing? I'm good. I don't feel like I have much to report on because, as I mentioned in previous episode, I've been redecorating my flat and

my whole brain has been dedicated to that for weeks. And so I don't feel like there's anything else that's happening in my life. I think 60% of the messages you've sent me in the last couple weeks have been photos of you with various states of things spread out on the floor of your flat sorting them out. Yeah, it's a bit like that clip from Markham in the middle where Hal is asked to change a light bulb. And that's basically... I never watched Malcolm in the middle, but I know that sequence. Yeah.

Do yourself a favour if you're near an internet to look it up right now. It's very similar. I'll start doing something and then be like, oh, I think I'm going to completely change, I'm decal this old drinks cabinet and make it brightly coloured. and I'll put some, oh, I know, I'll put together this bookshelf. And while I'm doing it, why don't interlace some fairy lights around all of the, oh, that's taken me four hours. You've basically had multiple weeks of consecutive hyper-focusing on things around the house.

Yeah, yeah. And I keep forgetting how long things take. That's the classic story of me. Yeah. How about you, Matt, have you been? Yeah, as, you know, discussed, because we missed an episode a couple ago, I'm recovering from illness, gradually getting back on my feet, doing things. things. Have I talked about what I'm going to add into the show?

No. I haven't seen the show. So. No, exactly. Okay. But I've not, I've not like bounce things off you. You could add something in and I wouldn't know. You wouldn't know. Well, it would be the bit that's the least polished because I've done the rest of them 30 times each. I've decided that I, many years ago, programmed my own Christmas tree lights in that I came up with some code that could scan. and locate the 3D coordinates of all 500 LEDs on a Christmas tree and then do lighting effects based on the 3D spatial information. Yes.

So I was very proud of. And I did it two years in a row. I messed around with that tree. And then I've always wanted to do something else with it. But I'm like, what am I going to do? So I kind of packed all the lights away. And I thankfully, past Matt put everything in like neat little bags, all in the one big, really useful tub and then just kind of shoved it in a corner.

And I thought, wouldn't it be fun to get like an audience member to put all the lights on the Christmas tree on stage? And then I live scan the tree to calculate their locations and then do lighting effects on the tree as part of the show. Like make it part of the lighting on the stage. In our previous episode, Matt, we made fun of a TV show for the idea of them filming someone rolling a dice. Correct, we did. For a long time. Uh-huh. And the difference is that they can edit that down.

Yes. What you're looking to do is to take the least fun thing about Christmas decorations. I don't understand. You've lost me. You know it's Christmas when you're calculating the 3D coordinates of your Christmas tree lights. Can you imagine paying tickets to go see Matt Parker and then spending the entire hour on stage, putting lights on a tree, missing the whole. whole show. Yep, yep.

Now, you haven't, now you haven't seen the show. At the beginning of the show, I point out, if it was only my fans who show up, I could literally advertise Matt Parker speaks in binary for an hour. Yeah. And they'd be very happy. Yeah. But because they insist on bringing regular humans with them, who are wonderful people, I have to do an actual show.

So I have to do this in a mildly entertaining way. Yeah. So I'm going to get, I don't always remember like before the show to put the lights on the tree. And now at the moment, my code takes like two hours. You're not making this any better. It's too slow. So my friend Abby used to be a software developer before she went into theater things. And she's helping tour my show.

And I was like, Abby, can you help me make the Christmas tree lights more efficient? So she came around. I cleared a bit of space in the new deal. And we emptied out all of. 2021 Matt's hard work. Yep. And Abby spent a day working out how on earth past Matt had wired everything together, which was not obvious. And I worked out how 2021 Matt had coded everything together. This is like some weird forensics. Yes. For something far less useful. Correct. Correct. Yeah. Yeah. So we managed to You did the crime. Now you're doing the time. Yeah. Yeah. I pay for it eventually. So we spent a whole

day working out how I got it to work in the first place. And now later this week, we're going to put some more work into improving the code so we can run way faster. Yeah. Yeah. Well, Abby's going to improve the code. Who am I kidding? Yeah.

Do you know what annoys me most about this? This will go down great. They're going to love this. People are going to talk up there. It'll be the highlight of the show for them. And the audience will get really, the audience. The audience will get really into watching someone before the show starts, put lights on a tree. Oh, yeah.

Well, they have to detangle them, I imagine. You're going to have to pack that up after each night as well. Oh, my gosh. This is the thing, though. This is the difference. Because you are at a stage in your career where you're able to hire a team. Yes. This means you can go, I'm going to do this and we'll worry about the logistics later.

Correct. Whereas. Big luxury. I'm very much. It's a case of, well, it's just me. So. I was reminiscing with Lucy, because my first tour was me in a suitcase. And I would just trundle myself, like get a train or a taxi or whatever to get to these venues.

You're saying this like, can you imagine. Can you? I don't know, Begg, if you can picture this, Beck. Imagine having a bunch of big props you got to put in a suitcase. Yeah. And then it's just you in the case. My shoulders still haven't recovered from lugging that thing around. Yeah, yeah, yeah.

But now I got the luxury of like humans in a van. Yeah. And a very tolerant, wonderful audience. I'm glad. Well, no, they're not just tolerant. Your audience are great. And you guys are all playing in the way that you want to. We're going to have a great time.

I think it's really nice. I do think it's really lovely. I'm playing the grump because there always needs to be. Yeah, yeah, yeah. You know, in a traditional double act. And it's fun to switch into the pessimist for a while. It's difficult because when I do joint shows with like with you or with Helen Arnie and Steve Mold, I've got other people who can be the pushback.

So I can go extra nerdy because other people on stage are providing the counterbalance. Whereas if it's just me, I have to do kind of both myself. You sort of vers your self against the audience. Yes. I mean, I haven't seen this show, but I know that that's your style. you kind of position yourself as their king and then ridicule them for making you their king. That's pretty much what happens.

Yeah, yeah, yeah, I'm not predictable. I think it works. It works. I admit, I have a great time. Yeah, it's nice. That's my metric. We're recording this before the first show, but this will come out during the tour.

So some folks would have seen this. Some folks will have already seen if I was successful or not, yes. And if you've seen the show and there was no. Christmas tree in it. You know it caught on fire. And if anyone wants to see the budget version, come around to my place and watch we put fairy lights on a bookshelf. That would be entertaining.

It would probably take just as long, to be honest. All right, let's do a show. Our first problem was sent in by Chris, who at a problem squared.com, aka the problem posing page, said, hi guys, love the show. been listening since episode zero zero two blah blah blah hang on sorry since episode zero two so Chris have you not listened to zero zero one that's a choice

yeah Chris has been burnt by terrible pilots before I like the idea that Chris went we brought out the second episode and they went well it wasn't a one-off yeah Chris knows the first one could be a fluke or a one-off or a that and boom two onwards I think our first episode was fine Yeah, before we found our feat with the formatting.

Oh my goodness, that was all over the place. And we knew it. Speaking of messy things, Chris says measurements are a messy thing. The US has diligently clung to the imperial system. Europe has committed to metric here in the UK. We still have no clue what we're doing and don't get me started. That's me now, not wanting to get started, not Chris.

Chris has also been started. They're like beer by the pint, petrol by the leader, fuel efficiency in miles per gallon. It's so true. It drives me up the wall. You want to double annoys me? I know we're only halfway through the problem readout. We tried to change in the 70s. The England tried, you know, the UK tried to change in the 70s.

I was like, oh, boy, he's doing it this way. And people who are now complaining about changing have been born since then. Yeah, right. Like, if we just did it, then, writ the Band-Aid off, all who were complaining now would have had a life. They wouldn't have to, would have been a lifetime of them. Anyway, anyway, anyway. I know.

I mean, get this. I bought a new tape measure because I needed. a longer one, doesn't have inches on it. So I don't, I don't know, like it's just got centimeters and actually it's really annoying because the amount of times I've ordered furniture and they only give me inches and then I have to convert it. I mean, I agree. I use measuring tapes to conversions.

I'm like, how many centimeters is that in inches and just. Yeah. Now, Chris is going to say some nice things. He says Imperial has the advantage of being based on something we all have access to, e.g. a foot. Nah. We've talked about... We've talked about foot size

and shoe size in itself as a whole... I mean, Chris is making the argument, you know, if it's roughly a foot, a yard is roughly a step. I'm not buying that. metric,

says Chris, has a nice numerical system. It is. But it's a lot harder to visualize. I disagree. Yeah, I disagree as well. But let's hear out the rest of the problem. You did ask me once

if I could... If I could... predict what a meter is. Yeah. And I'm pretty confident I could. Yeah. The meter game is you get someone to pull out a measuring tape upside down so they can't see the markings and see if they can pull it out to exactly a meter and they guess.

And you turn it over and see how close to a meter they were. I reckon I can do that. Do you want me to get the tape? Yeah, I do. Okay. Here's the tape. Here's how it works. You hold that end?

Oh, so I don't get to hold both ends. No. You hold that end. Well, but then I'm not looking at it from. an angle that's good. Okay, fine. I'll hold out my hands. No, you hold both ends.

Hold both ends. And then you see the, you've got the lock thing here? Yeah. It's to the end of the tape. It's the amount of yellow. Yeah. Just so there's no ambiguity about what we're measuring. No, look at it.

Okay. Okay. Yep. Pull out so you can see a meter of yellow. Beck's so confident we're going to film this and put it out on social media. Whenever you're convinced, lock it. Okay. I'm going to go over and read out the amount.

Here we go. So Beck got 128 centimetre. Shall I give it a go? I mean, you did just look at what a metre is. A little bit now, Scott, I haven't seen it now. Yeah, yeah, sure. I should have made you go first. Ready?

There. You've done slightly better than me. 108! Still too much. You've done 20 better than me. Still I thought I was going to nail it. Yeah. After all that, I'm prepared to concede.

Maybe it's difficult to visualize. yeah we were pretty confident yeah yeah okay okay so chris now wants to know i feel like we'll get to the end of the problem about the time of the end of the podcast chris wants to create a universal system of measurement where all units of measurement are based on a single standard ideally household item which everyone has access to he would like to suggest the humble banana as that single standard And for example, Chris has already worked out that they are 11 bananas tall. I assume rounded to the nearest tall banana.

And they weigh 635 bananas. They want to know, is there any unit of measurement which can't be measured using a banana? And if so, is there another household item which would offer a better source of standardization than the banana? Love you guys. Give out the word, blah, blah, blah. You added that blah, blah, blah, by the way. Beck, I'm going to give you a micro-bananas worth of time to solve this problem. Well, the first question, is there any unit of measurement which can't be measured using a banana? Yes, most.

What? Name one. I mean, anything that requires a straight line, for starters, why would you choose something curved to make a measurement? That's not a unit of measurement. First of all, like, how can you use that as a unit of measurement when it's curved? It's got a length. But where does it end? Beginning to end.

But from where? Measuring a thing with a hand. It doesn't mean your hand is a straight edge to it. It just means there's a beginning and an end in a direction. But you've already, like you've gone from your thumb to your pinky. Some people might go from the top of their middle finger to the base of the palm. That's true. You could go from the top of your index finger to the...

A banana has a very clear end. No, it's curved. I got some fruit in for the recording. Should I grab a banana? Yes, please. Oh my goodness. I'm handing over a bunch of three bananas. Yes.

So already, firstly, I'm grabbing a banana. Okay. Great. Banana. So I'm holding it up. I've got my finger at the top of the stem. You could do that. Now, I've got my other finger on the bottom of the stem.

So that is a particular length, right? But it depends which way you're holding it. That's always the same distance apart. Because that will be the same distance apart if you were doing it like that. But maybe I want to do it like this. And now I'm holding because the banana's curved. I'm doing it like at the top of the banana, but not the stem. But that's not standardization because that's going to change.

Not only that, but Matt, Matt Parker. I'm now taking a second banana. Yes. Okay. Yeah. Yeah. Look at the differences between these two bananas. They're going to be different lengths.

But does that matter? For standardization, yes. I don't know. For the longest time, we measured horses in hands. People have different hands. Yeah. And we don't do that now. Because it's not standard.

Maybe it's time we went back. Maybe we got too obsessed with things always being the same. Well, then why bananas? Why don't we go to hands for everything? Well, that's the question, literally the problem in front of us. What I'm saying is, the first part of the question was, is there any unit measurement that can't be measured using a banana? I'm saying, yeah, all of them because they're not standard.

I disagree. Wait, now, for the record, you picked this problem. And I'm answering it. What's your problem? You're bananaing all over it. I'm saying it can't be measured. So I don't know why. What if we picked one banana?

Like the banana? Yeah, but then not everyone has access to the banana. Everyone gets a copy of it. Oh. I guess for ease, you could put centimeters and inches on there. You 3D print the banana at home. Everybody gets one. In the world.

The other thing is, like, not everyone has access to a banana. They will. If we send them. If we send every person in the world a banana. We'll make a cast of one banana. Now, I believe the reason that Chris has chosen a banana. Yes. Is because there is a well-known thing of...

The idea is banana for scale. And I decided to do a little bit of research to try and find out where this trend... Oh, where it came from. Came from. Okay. In my research, the earliest... I can get... Would you go on?

Go for it. Someone, it was on Reddit, and someone, were they in an attic? I want to say someone was like taking a photo of their attic and wanted to show the scale. How close is it? You're sort of close. Oh, okay. I'll take it. Reddit does come into it.

How many bananas off was there? Several. Oh, right. Six bananas of separation. Okay, I can do it. So the first one that, and I did check multiple websites to see if there was any. Any, you know, any differences. The first one that seems to come back is that in 2005...

Oh, wow, way back. So 20 years ago, more than 20 years ago, it was March 2005. Happy been on a birthday. There was a blog on Rock Dog Designs. Right. Advertising a TV for sale. Yep. It's an old-fashioned...

Well, I say old-fashioned. It's a big chunk-o television. Yeah. They're saying that the TV is for sale, they said, I don't know how big the screen is. We're moving, and I can't find the tape measure. But I do have a banana for scale. They then say, oh, wait, my husband says it's 19 inches.

Oh, well, I'll leave the banana for interest. Please be interested. There's a photo with the banana. There's a photo. We'll put this on Instagram and Twitter and whatnot. My favorite thing... The banana stuck to the screen. My favorite thing is they've positioned it by taping the banana in the corner of the screen.

They haven't even put it on the ground with the TV. It's levitating on front of the screen. It's great. Oh, that's amazing. So that was sort of the earliest that could be ascertained. I'd never seen that photo before. No. Then in, we're going to jump forward five years.

In 2010, there was a blogger called Andy Herald, who posted a photograph of a safe to Facebook. It's a very small safe Yep But a proper Safe But because it was a small safe Wanted to demonstrate How small the safe was

Yep So placed it with a banana lying next to it for scale Great More people commented on the banana Than they did the safe That is the one possible downside to the banana as a unit

Yeah Paul's focus The funny thing is Is that this host for the safe Sounds like something One of our listeners Would have sent in Right

Because they found the safe. They got it from their grandparents. They set the combo for 18 years beforehand. I had two dials that split the alphabet. So it was 13 by 13. You've got 169 possible combinations. I can hear my forgotten stuff rattling around. They asked for suggestions of combinations.

They did eventually manage to crack it. Oh, great. It was I and you with the two letters. The safe contained $5.35. change and a 20-year-old chucky cheese token. You could use it for safe. Next to the safe, pretty very popular. Two years later, there was a blog called How to Be a Dad that said the banana, a new

more forgiving unit of measurement. Oh, okay. This is very deliberate. So they do have a suggestion of how the banana should be measured. Yeah. Which is sort of just like from the actual fruit, the end of one fruit to the other. It doesn't really bother with the stem. as I do use it for estimates and loose approximations

that can be fudged as needed if desired as an example almost caught me a 2.5 banana beauty while fishing and then another example is little Johnny is seven bananas tall already don't use it for building legal language accounting medicine military purposes or any other use that requires exact standards of measure so already the internet is having a go at Chris in the past. Who is four bananas taller?

Yes, that's true. In 2013, King O Pancake submitted a photo album titled How to Win a Bet When You Lose a Bet, it contained photographs of a complicated prank lockbox containing a $15 Dunkin' Donuts card. In the two photographs, a banana is shown for scale. Then later on, two-byte Brownie posted an image gallery

containing several photographs of a hidden staircase. Just kind of behind a bookshelf. Yep. That's the one you're thinking of. That was one where they had several objects, candy wrappers and things like that, and a banana pill. And he explained that the banana pill was left there for scale. I think it's just rubbish. Now, this is my favorite.

This is where Reddit comes into it. And it really takes off after this around 2013. So later in November, there's a Rediter submitted a photograph of a large banana placed thanks to a keyboard and a smaller banana for scale. Now, I'm going to show you, because you can see the keyboard, and this is an impressively sized banana. And the banana for scale does help. We will put this. You know, that gives me a sense of how big the bigger banana is. So the large banana is almost the size of a keyboard.

And we're talking like a standard, like it's got a separate number pad, keyboard. That is an impressive banana. Of course, with that post becoming so popular. Finally, the subreddit was created bananas for scale. And then it started to really take off after that. People started posting their own banana for scale things. One of the biggest ones was a reddeter called a shark tooth of a photo of him with Tom Hanks. Tom Hanks looking perplexed and a large banana being held for scale.

That posted very well. And then there started to be articles published. later in 2013 about the spread of the banana thing. There have been other items that have been used. So around the same time, extra anchovies, another Redator, submitted a photograph of his frozen pool in Phoenix, Arizona, which is strange time for the pool to freeze over.

And they wanted to show how frozen it was. So they've put an acoustic guitar sitting on a stand in the middle of the pool. How strong that ice is. Which then started the theme of banana. Banana for Scale guitar for temperature. So my favourite one that I found of something being used for scale was double bed for scale. Double bed for scale.

And this was because there was an apartment listing in 2017 where quite nice apartment. So it looks like a very large room here and they'd put double bed for scale. So you can see it's a large room. If that's a double bed. Yep. but they then proceeded to place the double bed in other rooms in the house as one in the shower one in the kitchen one in the hallway which I think so I think it only works if you're using the same item against everything right okay okay I do find it funny now I didn't know you were

going to talk about this on today's episode okay but I have also been moving everything into the new deal. And we've now got a storage room, which is very exciting. And it's already produced a measuring tape. Yeah. Do you mind if I get one more prop before we wrap up? Please. Thank you. Nice.

You didn't bring anything back. Couldn't find it. Matt has emerged from the storeroom with a banana hat. The whole banana head. Yes. I bought this for a video years ago. Mm-hmm. I just, I had a choice.

chuckle when I saw it as I was loading stuff into the storage room. And I was like, why did I keep that? I was like, oh well. And now you know. Maybe I'll need it if I want to make a concluding argument for why bananas are a good unit. We'll take a photo so viewers get a sense of how big this banana hat is. I love the fact that you've decided to put on a costume for an audio medium.

Now, two things. I don't think I've ever fully grasped the audio medium format. No, you really haven't. Secondly, like many things in life, I'm not doing this for anyone else. This is true. If anything, if it was, you wouldn't have done it. If I'd asked you, if I'd suggested it. If you brought this and asked me to put it on, there's a 0% chance I would have done it.

So, in conclusion, a banana, because I... I like how you keep concluding my problem. No, no, I'm concluding my argument within your problem. You can measure time with a banana, like how long it takes to go off. So what would four o'clock be a banana? Time to eat a banana. You've got the freezing point of a banana that will give you temperature. Sure, yep, yep, yep, yep.

The gaseous point of the banana. They will convert to plasma at some point. Uh, famously radiation, because they've got potassium in them. Uh-huh. Um, yeah. I just feel like as a strong proponent of the metric system, sometimes, like, they're different, different scales for different purposes, I think. There's a time and a place for, a home and household object. And I'm saying that time and the place is not a universal system.

By all means, use a banana for scale casually. Maybe it's because I see all. units of measurement are as arbitrary a starting point, why not? I wanted to find something that was maybe more standardized and potentially more easy to come by, depending on... I mean, bananas are pretty easy to come by, but I was trying to think of something that's a bit more universal. And I think it might be a bar of soap.

Oh! Now, I know that bars of soap can be different too, but generally, they tend to be the same size. Yep, yep, yep. You don't have to worry about it going off or anything. That's true. That does make the time thing difficult. Every time you use it, you get relatively taller. Because the soap gets smaller.

Oh, right. So you're now slightly more bars of soap. Yeah, I mean, obviously, I'm going by a bar of soap that you don't actually like. You could say that with a banana, like as you eat the banana, everything, yeah, yeah, valid point. I was thinking at some point a can of Coke, because Coke is quite universal. Yeah, not completely, but yeah, pretty good. But because it is, it does have a measurement already on it.

I don't know, I feel like soap is a... Soap is a good one. I can't think of anything more common that tends to be a standard size. Yeah, but it's got to be something. It's not like a specific... product from one manufacturer. Because you could say toilet paper, but then it depends on how many ply it is and

how big the insert is. Maybe the length of a toilet paper of like the little cardboard tube. Is that consistent? No, well, it's not because I use toilet rolls and a lot of arts and crafts and some are better than others. Right. I use a, they're not paying us,

so I'm not going to give them the venture, but I use a... Companies. One of the, if not only, subscriber-based toilet paper. And I find that their toilet rolls are much more sturdy than that of your generic supermarket toilet paper. So you're proposing the soap bar standard. That's what I can think of. Do you have any suggestions?

I mean, that's good. If you could do pressure, because pressure's already measured in bars, that's kind of fun. Oh, yeah. Yeah. how the force required to crush soap. No, I think that's, it would be hard to top that because then you've got, yeah, things like fruit and naturally occurring things that are about the same size,

but you are right. There's a lot of variation. Well, we've already seen you can have a banana that's a keyboard. If I had to pitch something, I would say a coffee mug. Generally they tend to be there. But then you're getting close to just saying a cup. Yeah. Which is already a measurement.

Yeah, but that started is just a cup and then eventually got codified to be like how many mill. Yeah. No, you're right. Yeah. But like heightwise, like the ratio of a classic coffee mug is very consistent. Ignoring novelty mugs and... Yeah. I mean, arguably a pint, but again, that is a measurement.

A measurement. A pint is already a measurement. Yes, you're right, you're right, you're right. Yeah. I have strayed back to something that is a standard volume. Yeah, you're right It's like either a banana Or a bar of soap

I'm thinking of things that Or a hot dog A hot dog At least it's straight I'd be more inclined Are you happy with a hot dog I'm happy with a hot dog Than I'm a banana

And the thing is I think banana for scale Is funnier Yeah, no you're right Yeah So the comedian Hot Dog for height is not bad Hot dog for height is great Well yeah

Look the comedian in me It says, yes, shoot for banana. But this is not a comedy podcast. This is a fact-finding, serious problem-solving. I feel like we're having this argument the wrong way around. You were wearing a banana hat. Yeah, I know. It's weird.

What's happened? This nudia is cursed. This is what happens when you start off the chat with talking about something that's actually quite smart, and I decide that I'm going to be the straight man on the episode. Yeah, yes. In conclusion, banana for scale. Hot Dog Find. Soap for everything else.

Soap for everything else. Love it. Chris? I mean, I don't know. I mean, I think the answer is... Look, Chris wanted to know, is there any unit of measurement that can't be measured using a banana? I'm going to say yes. All of them.

Or, no. Like, technically you could measure anything using something else, but you've got to be creative. Yeah. As you go up, like banana for scale on. short distances and above that it's how far you can throw a banana. Oh, that's fun. For longer distances. The bananas throw away.

And what, is it your particular throw? Yes. Like, if I was to say, oh, I'm going to race you, I'm going to go 13 bananas. But you've got to go like further than me because 13 banana throws might be further. You've got longer arms. When you message me to say that you're a distance away, I already convert that from back units to real units. Now, there's an idea. Look, we've done measurements in Bex before.

We measured me and Bex beers. Oh, yes. And then we've measured places in Me's. Yes. Maybe that's it. Maybe I'm the new unit of measurement. You don't all, look, I'm not a household. It's a Betrick system.

There we go. The Bechrick system. 3D print a version of me for every household. And you're done. You're done. Ah. Case closed. I didn't think we were going to wrap this one up.

There you go. Good work. We did it, you guys. We made it. And here's a break for our sponsors. Do, do, do, do, do, do, do, do. Are you after a new unit of measurement? Do, do, do, do, do. Try the Bectric system.

Poop, poop, pooh, pooh, boop. Only 1395 plus postage per week. Per beck. Seven becks are back. Are you sick of Beck when you're back? Then Beck. You're not getting enough becks out of your back. Then try and you back.

Just three becks down. If it's not back, it's already back. I'm going to give that a Beck. Our next problem comes from Daniel, who went to the problem posing page, selected problem. Problemsquared.com and they said, why does basalt always split in those hexagons? Is it the same why honeycombs are made like that to minimize the amount of wax needed to build them? I realize I'm reading this like someone who does not know English. You're reading it like you're doing a book report in front of the class.

I'm in Iceland on vacation and here it's all over the place because of the many volcanoes. Before you answer this, Matt, yeah, yeah. What's basalt again? It's like cooled lava. Okay. Volcanic rock. I didn't even know it split into hexagons. Have you seen like the Giants Causeway?

Yeah. Is that? Okay. Okay, cool. You get these hexagonal columns. It's amazing. Like it looks so freaky because you feel like that can't be a natural. Yeah.

Well, straight lines are very rare in nature. And so to have something that feels so equal is always a bit alien. But Daniel have also pointed out that bees do the same thing. Yeah. Like it's interesting that bees make perfect hexagons. And you'll hear, other people say it's because bees know that's the most efficient use of wax to minimize the wall area while maximizing the volume within the walls. Is that true? That is true.

The statement that hexagons are the most efficient pattern is true. Yes, but do bees know that? They haven't tested them. They haven't gone, why do you do this? They have tested them. Surely it's got something just to do with the wax itself. A little bit. Okay.

So what the bees actually do, and they did a bunch of research into this, Queen Mary, University of London. There's a guy, Vincent surname, who did some research. We never spare the details on. Exactly. Problem squared. I forgot. So Vincent, I made a video and I interviewed Vincent for it years ago, and then he helped me when I was writing the book Love Triangle is a bit about Vincent and he's bees in there. Yeah.

Not enough to know his last name, but still. No, no. Everyone gets one name. That's it. Vincent Beck, I believe. Vincent Beck, exactly. That Beck is the new standard surname. Exactly.

So the way you do the research, the hypothesis is bees are good at calculating a minimum surface to save using wax. but if you give them an unusual starting shape, they won't work out the optimal angle to build the wax on. They will just split the angle in half. That's all they're doing. And the reason that happens is when a bee's making the cells and the honeycomb, they're actually kind of just making tubes. They're building a tube and just pushing out the malleable wax.

Yeah. But then they push the wax one way, but the bee on the other side, making the next cell over, or even the same bee later on, making the one pushes it back. Yeah. And this back and forth, the equilibrium is just the midpoint. And so whatever starting shape you give bees, they would just subdivide all the angles with the wax walls. Yeah. And... So if you had like a bunch of straws in a sort of cube shape or something. Yeah. That's, yeah. And then you were to stretch the straws out as much

as you could in any direction. Naturally, that would probably turn them into hexagons. I'm going to say yes. The reason you get hexagons specifically with bees is because they're making tubes. If you stack cylinders, you get a row of them

then an offset row. And when you mush that back goes and fours, they become hexagons. Now, that's not totally unrelated to the fact that it's a very efficient way of doing it, but it's just the bees don't know what they're doing. They're just pushing wax around. And then stacking tubes and you end up with hexagons.

And I'm not saying that bees, this makes bees any less amazing. No, it's great. Bees are incredible. Great solution. But they don't need to be smarter than they are. No. For us to be impressed by them. Exactly.

And I get distracted with this in the book because the shape at the end of the cells is not optimal. They could do a better shape at the end and they don't. Because they're doing the shape you get when you mush things backwards and forwards, which is pretty good. But technically, there are better solutions that they're not using. So it's not even like they've ever. evolved to the optimal solution. They're just doing a good enough solution from mushing wax around.

Right. But it's not unrelated that it's just a very efficient way to do it. That's why it's hung around. Like it's a great solution to do it that way. And it happens for the hexagon ones, that is the best. Because I wasn't sure if it would be like, you know how you can make a cube out of bubbles? Yeah. By the way that you join the bubbles.

I wasn't sure if it was a bit like that. It's a little bit, there's a tiny bit like that because it's not a perfect cube because the bubbles always, it's 120 degrees around an edge and it's tetrahedral angles around a corner, which is not quite a cube, but it's close enough. Right, yeah, yeah. The bee people don't like it if you compare bee wax to bubble foam. And I've just realized, I know some of the PhD in bubbles, so yeah, that is a thing. Yeah, they don't, but I'm like, that's also how I kind of understand it. Anyway, the moral of the story is bees do make hexagons. They're not actually doing the optimal surface,

but it does happen that they stumbled across. What they do does give you the optimal slew. There's no better way to divide an area up with straight lines to make the lines as small as possible for the area in the middle than hexagons. Best case. Okay, lava. Lava cooling. You've got a big pile of hot lava.

It's cooling down. The way things cool is they cool for. from the outside in, because that's where the heat loss is. It's like when you put water in the freezer to freeze ice cubes, they freeze from the outside in, because that's where the heat's being lost first.

And when rock cools, it shrinks. So as you're cooling a massive lake of lava, and the outside's cooling first, it's pulling the middle out, because it's shrinking

around the edge and stretching the middle, which means all this tension's building up in the lava cooling or magma. I'm not using the correct terminology. But the cooling rock in the middle is under tension. And to relieve that tension, it's got a crack. Yeah. And the end point, and I read a fantastic article that we will link in the show notes from the European Geosciences Union, where Hannah Davies has written up a whole thing

about how that process of cracks forming in the stretched cooling rock. Hannah Davies. Hannah Davies. You're sure you don't mean Hannah Beck. Sorry. Beck Beckys wrote a thing about it. And the point is the optimal position for the cracks is the same solution of you want to have the shortest cracks that have the biggest area near them where they're relieving the tension. Right.

And if it's perfectly even, like any impurities change it, and the tension may not be perfectly even based on how the coolings happening around the edges. So you sometimes get perfect hexagons. A lot of the times you get close enough hexagon-ish things. There's a thing called a Voronoi diagram. If people are into the maths of that, which is all the region of all the area that's closer to one point than another point. and it's you see that kind of pattern appearing as well based on the impurities and the unevenness and the tension

but the moral story is the ultimate solution is if it cracks in a perfect hexagonal pattern that's the fewest cracks for the most tension relief got it that said if you want to go one step further in and you look up the 2015 paper y hexagonal basal columns in the physical review letters. Which I often do. Often do. A whole research paper about this.

So the surface answer is hexagons because it's the most efficient way to relieve tension. Bexagans, I think. The bexagons. Hexigans are the bexicans. That's what they say. Yeah. New t-shirts. They point out, initially, if you get one crack forming, it's relieved all the tension

that's like perpendicular to the crack because that's the direction it's separating it. just say that the amount you're talking about tension relief and cracks and perpendicular. I don't understand where you're going with this. I'm being so good right now. You're doing an excellent job. Thank you. You'll get a fruit treat at the end of this.

Oh, I hope it's a beck. It's a becknana. Yeah. It's three backs long. Wow. That's a lot of them. What is it? They point out. Because a crack relieves tension in one direction, but not the other direction.

Once you've got one crack, the next crack is most likely to be perpendicular to it to relieve all the tension that's not been relieved by the first crack. So actually what happens is the very first cracks that form on the surface are perpendicular to each other, like T-junctions. Right. But as they propagate down into the rock as it's cooling further and further down, they open up and they approach the optimal. hexagonal, 120 degree corners. Ah. So actually when you see the hexagons, it's not off, it's not the original surface because that would have been right angle cracks.

That's been like worn down. But as they go down, they get closer and closer to the ideal hexagons. Wow. Again, impurities and everything else, that means it's not always perfect. Do you reckon if we go even further, it becomes like... Bexigans. Yeah. That's right.

You start to get the hat tile. You get the hat tile. So that's the answer. Now, the research paper, Y hexagonal basalt columns, is behind a publication paywall. So unless you've got academic credentials to get to it, or you've married someone who's able to do that. Yeah. It's tough to get to. But the article features from the field, columnunar basalts and why hexagons are nature's favorite shape.

the fine people at the European Geosciences Union have made that available to everyone. So we will put that in the show notes. Thank you to them. The end. And to you, Matt. I've well done. Thank you. You've explained that...

It's like the end of your book report. Inclusion, basalt, doesn't always split into hexagons, but sometimes it does. Yeah, that's it. Yeah. And it's it. It's not because of like honeycombs. It's a little bit, but not much. It's a little bit.

It's not unrelated, but it's not the same magnet. It's not because there's like once upon a time there were giant stone wasps. And they've just been fossilized. Maybe. Wait, lava and larvae. We're through the looking glass, people. This is such a silly episode. Now in Becky.

Becka, Beckness, Keith? I think you mean back. Sorry, Beck, went to the back backing back at a back, back, back, back, back, dot back. Use the top-down menu to select Beck and said, so Keith here started the Afantasia chat, thanks to a comment they left, which we then turned kind of into a full problem. Yep, which meant it was hanging dingless. And Keith is prepared to say that our work was outstanding, and we have been dinged. And Keith does sign off yours with extra blah, blah, blahs. So thank you, Keith, for dinging us.

And we know, possibly more than anything, that Fantasia chat for people who can't visualize things has caused more discussion than anything else. Yeah. So the chat is carrying on on Discord and any of our other social media platforms. I think Reddit. I think on Reddit as well. So if you want to get involved in that chat, the optimal places to do it are Discord and our subreddit. Otherwise, this does run the risk of just becoming the Afentatia podcast. Yes.

I can't even, I can imagine that happening. And as we all know, this isn't the Afentasia podcast. This is the Beckers obsessed with Tees podcast. It's a constant battle to not become that. So Tim had originally written into us asking why his baby teeth keep falling apart in episode 116. Tim has said, ding, dentist Sophie's hypothesis about my teeth being weakened by the resorption, excellent word, process seems really likely. My baby teeth took a really long time to come out as a kid and were wiggly slash loose for weeks at a time. This really frustrated my orthodontist who was a little too excited to put me in braces.

He said, I do remember it was the canines and incisors that had split, but I'm not sure about any molars. I'll root around for them next time I visit my parents. I'd be willing to contribute to the Beck Hill Tooth Fund, but I'm in the US, so shipping might be weird. I don't know. Maybe we should try it, Tim. Tim also said, it was my delight for my morning commute when groggy me slowly pieced together. Hey, cool, Tim's also my name. My teeth split too.

wait a minute a very surreal morning and signed off from split-teeth Tim which is a great pirate name and finally a third ding maybe a record number of dings in one episode

Mr. Tumnus who asked for the feminine version of Fallick back in episode 115 just to stay on theme despite my best efforts they do apologise for offering their teeth as a form of bribery.

Good. We had to draw a line somewhere. And then they point out none of them are splits. So now, great. Now listen to the self grading their teeth. Anyway, they were happy, Beck, with your solution for the feminine version of things that are phallic. And they give us the ding. Yeah, they did.

And they continued off view their teeth. So anyway. It's fine. Now, they went by, I assume the pseudonym, Mr. Tumnus, and they do sign off with yours truly, gleeful little goat man from Narnia. So, thank you, Mr. Tumnus. And I'll be in touch regarding your teeth. Yes.

Well, that's it for this episode. Thank you so much for listening along. We appreciate every listener as much as any other listener with twice as much appreciation or some ratio. For our Patreon supporters who... cough up the money to make this entire operation continue rumbling along. We exist on Patreon money and teeth. And we would, we thank three Patrions every episode by picking them at random from all our supporters, and they're mispronouncing their name, which this episode includes.

Co-Rouring. E. Rick, book. Ack, Lynn. The Wimps, Ruska. Thank you to Beck for doing the podcast. Thank you to me for doing the podcast. And thanks to our producer Laura Grimshaw.

Who? Have you noticed she's always seen in the same room as Laura Grimshaw? Oh my gosh. I know. This episode has blown my mind. Thanks for listening. Good Beck. Thank you very much

Now time for Beckle ship You've previously backed my beckleship still it's your turn to your turn to fire um i'm going to go for i'm going to go for E2 E2

hit no yes how are you are you cheating I'm not I'm just looking at the gaps. You're using strategy. Okay, well, I'm going to try and find the rest of this battleship with a shot at J-9, thanks. How dare you use strategy?

Why, I believe that is a hit and a sink. Have you still got a battleship left, right? Yes. Okay. We've been playing this for over a year now. I know, we should We should have had a party We should have celebrated

Okay, well let's see We'll be playing a year from now Ha ha ha ha Ha ha.