A Problem Squared - 069 = Tiling Planes and Driving Planes

Episode Date: September 25, 2023

In this episode...   - What is the optimal maths based pattern to decorate a rented home?   - Is it possible to fly a plane on the autobahn?   - And some bloody brilliant Any Other Business   You can find more information about the Art Installation, or Zeitpyramide, Matt references in the catch up here: https://en.wikipedia.org/wiki/Zeitpyramide   For more amazing tile patterns, check out Ayliean's TikTok: https://www.tiktok.com/@ayliean/video/7276938427071876385   And if you'd like to read the Hat Tile original paper, you can do that here: https://arxiv.org/abs/2303.10798   Here's the APS Reddit: https://www.reddit.com/r/AProblemSquared/   We'll share our new Discord, which we don't really know how to use yet, once we've got some mods in place so watch this space...   As always, pease send your problems and solutions to our website: aproblemsquared.com.   And if you want more from A Problem Squared, find us on Twitter,  Instagram. and Patreon.

Hello and welcome to A Problem Squared, the podcast equivalent of money, in that we solve a lot of problems, but we also cause a few. And everyone always wants more of us. Your hosts are Matt Parker, who is a bit like a million dollars because he's hard to get hold of. So true. So true. And when you do, you don't want to spend me. That would defeat the purpose.

That's true. Yeah. Yeah, that's right. I want to be able to hold on to you so I can say, I've got it. Got it. You want to invest. If you get in touch with me, you want to invest that contact. You don't want to spend it immediately.

Would you say I invest you, Matt? I think so. I think so. Yeah, sure. I think you're getting returns off this friendship. I think you tend to feel quite spent after hanging out with me. Well done, yes. And the other host is me, Beck Hill, the spare cash of this duo, because I'm petty.

Hey, oh my goodness. Wow, good intro. Thanks, man. That's great. I always thought of you as fungible. Yeah, putting the jibble in fungible On this episode I've worked out the ultimate decoration pattern for your home or office I find out whether it's possible to fly a plane on the autobahn

And we have any other AOB business Ka-ching Ka-ching. Ka-ching. Ka-ching. So Matt. Beck. The last time we saw each other was in a tent. We were in a field, yes. In a field. I'm no longer in a field. No, we are recording remotely though. Remote this time. Yeah. It's a busy, busy point in my life at the moment with travel and book writing. Yeah, you're a very busy man. It's too much. I got COVID as well. That pushed a lot of things back.

Yeah, that's really squeezed my schedule now. I got better just in time, just in time to make a trip to Munich. I tell you about this. I went and saw the next part of a long-term art installation get put in. No. No. I saw some pictures of you guys with some concrete. That's exactly it.

Although, I mean, this is just in our WhatsApp group. I don't think I've shared them publicly. Alien put a TikTok out, if people want to actually go see what we were up to. There's a pyramid they're building outside a town called Wemding, which is an hour and a half drive out of Munich in Germany. And they had the 1200 year anniversary of that town in 1993. They had the 1200 year anniversary of that town in 1993. And an artist, local artist, thought, wouldn't it be fun to start an artwork now that will take another 1200 years to finish? So it'll be the same length of the town.

So the town was like first recorded in the year 793. And so 1993, 1200 years later. And you think, that's such an incredible amount of time and so they're going to build a pyramid out of blocks and it's going to be 120 blocks and they're going to put in another block every 10 years so once a decade they lift up a massive cuboid of concrete it's about 1.2 meters by 1.2 meters and then 1.6 i think meters high so it's you know big bigger than a human and they put one every 10 years so we saw the fourth block go in it's pretty exciting it also feels a bit like like there's going to be a moment where everyone looks at a half-finished pyramid and is like oh bless them for thinking we would get this far

i was wondering about this because my theory is and, bless them for thinking we would get this far. I was wondering about this, because my theory is, and by the way, for the record, I love this. I think it's a great artwork. I think it's a very good way to make us think about the passing of time, because you can see how big it's going to be, and you can see now there are four blocks put in, and that's taken 30 years. And so you can see blocks appearing on a human life scale,

and you can see how much is left to go and you're like that's an unimaginable amount of time but if they'd started it when the town was founded it'd be done by now like so it is a reasonable amount of time on the time scale of a town or a city or something so i i think it's really really nice but i was thinking 10 years is probably about the right amount of time because who's going to be the first person to break the chain when the last one just went in 10 years ago and then you don't do that? I feel like, I mean, I think it might keep going the whole way. I don't know.

I mean, who's going to break that chain? Probably just, you know, society collapsing, the overturn of capitalism, concrete being banned. Or they'll go old school and just be like a giant block of granite or something. But I really enjoyed it. So we got to see a big bit of concrete get picked up by a crane and get lowered into place. And now it's there. Was this for a video or just funsies?

A bit of both. It will be a video. Yeah, yeah. So at some point, if it happened more often than once a decade, I might have postponed going over to film it. But given it happens once every 10 years, I was like, I can't miss it. Because otherwise it's 2033 before the next one. I'm definitely going to be there in 2033. conversation between 2023 matt and 2033 matt to go out in 2043 to remind everyone that the sixth block is about to go in and i just need to i need to 10 years from now record the other half of the

conversation and then 10 years after that assuming i'm i'm still making youtube videos put out the joint conversation i and then i did a bunch of takes of just me saying things like, yeah, we did not see that coming. I'm like, oh, yeah, that makes sense. And so I can go through and edit them all. That person sure got him or herself into some sort of predicament. Yeah, exactly. Yeah.

You know the best bit? They made a mistake. Yeah. They made a mass mistake. Oh, brilliant. Is the pyramid going to be upside down or something? No, no, not quite. It's going to be upside down or something? No, not quite. It's going to finish 10 years too early because an artist.

Oh, fence post problem. Fence post problem. Yes. Classic. It's so good. For any new listeners, this is referring to the fact that if you were to make a fence, you count the poles, but if you want want the actual fences the bits that go in between the poles it's a different number yeah essentially there's always one more post everyone

forgets the zeroth post and so they the artists thought 1200 years well that's easy 1200 is 120 times 10 so we just do 120 blocks every 10 years and then they put a block in on the zeroth year so now they're not going to have the final post so they're going to finish 10 years early they're going to accidentally finish in the year 3183 instead of the actual 2400 year anniversary in the year 3193 so they're off by they'll need to like put a slide in after 10 years or something or a flag or something. I know. I tried to engage the organizers in discussion about what their plan is, and they were seemingly

quite disinterested in the problem. They had a real someone else's problem attitude, if I may. So have you been back? You've got a new background. I've been good. Yeah, it's a duvet cover. It's hiding the jackets in the cupboard i'm back in the recording cupboard no i'm good we had some nice weather recently we finally had summer

came a bit late yeah for two weeks and so i i organized you had covid so i didn't invite you because i didn't want you to get fomo when it was happening um i organized a large game of hide and seek in a park what i would have gone i i would have done that 100 yeah it was really fun yeah that's so dumb although what we it was interesting because we realized like everyone was like so what are the rules and we realized that we all had to like oh yeah remember how to play hide and seek and also like so we we did it that i stayed at the base we created a base so that went by base i mean just like somewhere where everyone could drop their bags. Right, yeah.

So as the organizer, I took the bullet and I was like, okay, I'll sit out the first round. Because we're adults now, we're stuffed. Yeah, exactly. The rules were that once you were found, you had to then seek with the seeker, but you had to always be within talking distance. You couldn't like run off and yell and be like, I found them over here. Yeah, yeah, yeah. So you would seek with them,

and then the last person to be found would be the seeker on the next round. Got it. Just been seeking, then watched the bags on the next round. And that worked out well because most people seeking found that they got really puffed out. There's a lot of moving. To sit down afterwards. Yeah. Yeah, yeah. It's like the opposite of sardinesed out. There's a lot of moving. To sit down afterwards. Yeah.

Yeah, yeah. It's like the opposite of sardines. Yes. Yeah, yeah, it is. It was fun. It was really fun. What kind of park? Yeah.

Well, I chose Caledonian Park. I think that's what it's called. It's right behind sort of the Pleasance in London, which is a venue. Yeah. And it's got a big clock tower and it's a good park because it's a reasonable size to allow enough good hiding places for a large group of adults it's surrounded by like bush and trees and everything but there is a big empty space in the middle right so in fact howard reed

who you and i both know his daughter mabel her high school was starting back the next day. So, she had that day off. So, she came with him and she spent the first round just lying on the grass reading a book in the middle of the open grass. Blending right in. She was like the second to last person to be found because no one thought to just check the people sitting on the grass. Yeah, it was great. It was good. I tried to climb up a tree.

How'd that go? Then realized halfway up the tree that I wouldn't be able to get back down. So then backed out very quickly. What I wanted to do was climb up the tree just above where the bags were. So that I would just be like above the person who was seeking. That's very funny. Yeah. Yeah.

But it was just a little bit too high for me, sadly. And who was the undisputed champion of hiding and seeking? Oh, the real winner was my sunglasses, which I lost in the second round. And no one found at all. I'd only owned them for two weeks. Yeah. That's excellent. This first problem comes from Spina, who wrote into the problem posing page,

which is at a problemsquared.com. And Spina said, I think I have a problem that would be good for both Matt and Beck to tackle. It's my favorite kind of problem. Every time my mom comes to visit, she complains about my lack of decorations and or how empty my place feels. So I'm thinking I'll decorate with things that are aesthetically pleasing, but secretly or obviously mathematics related. and or how empty my place feels. So I'm thinking I'll decorate with things that are aesthetically pleasing, but secretly or obviously mathematics related.

I'm open to ideas for literally any kind of decoration from scribbling raw equations on the wall, though my landlord might not be too pleased, to hanging mathsy pictures on the walls or replacing floors with interesting shapes that tile on the plane. So in short, what are some neat maths things to decorate with? And where should they put them? I have a lot of opinions about tiling things. So,

I feel like, if I'm not careful, all of my solutions are going to be tiling related. Maybe we get a few other options out of the way first, and then I can just get into the tiles. Okay, alright. I mean, Matt, i've been to your house many times and you've got lots of maths related things dotting around correct do you

have a particular favorite without mentioning tiling okay oh that's interesting because if you ignore the tiling the tiling had knock-on effects lucy correctly my wife said enough conflicting patterns yeah because it was starting to feel a bit like a show it's like a tiling showroom and so i was like okay fine so i don't know if you notice once you're in the house everything is now either rectangles which are pretty off the shelf or hexagons yes so we kind of just picked some shapes and then stuck with those to try and make things remotely systematic. But there is one thing I've always kind of wanted to do, but I haven't really got the right space for it. And that's doing a decoration that only looks like what it's meant to be from one specific angle.

And so you'll see these done occasionally online where like you stand in just the right place. Yeah, the chalk drawings on the floor. And all these seemingly disjoint shapes. Yeah, exactly. Yeah, yeah. So it's called anamorphic art. Or sometimes all the bits will line up. Like there's a bit on the staircase.

There's a bit on the wall. There's a bit over here. They all line up and oh, it's Pac-Man or something, right? Yeah. You can do that. It's pretty easy. You just get like a projector or something and you project the shape you want to have. And then you go around and wherever it hits a wall or a surface or a ceiling or whatever.

I mean, if you're in a rental, maybe you got to find a way to hang. You got to then build that shape up somehow. Yeah. Yeah, I like that. They mentioned Spina said they got a 3D printer. Ah, well, I would. Okay. If I had a 3D printer. Oh, shoot. I would. Okay, if I had a 3D printer.

And I should, I can't believe I don't have one. Yeah, I thought you did. When I was living in a share house in South London, when I first moved to the UK, I was in a shop somewhere. Might even have been Ikea. And I found a replacement set of cupboard door handles. And they were numbers. It was all 10 digits. each one was a door handle and i got so excited i came back i was like oh my goodness it's made of the shape so like those

magnets that you get for the fridge they were like in the shape of the number yeah but they're door handles for a cupboard in the kitchen great so one one would cupboard would have zero and one as the door handles that you had to use to open. The next cupboard would have like two and three and so on. I was like, this is amazing. Because then people are like, can I get a glass? And you're like, yeah, they're in cupboard four. Oh, yeah. Nice.

I was outvoted. We did not install them in the share house. I honestly, sometimes I don't think I even understand people. How did you not keep them? You know, I had them for a very long time after. Because I was like, one day. One day these will shine. That would be a lot of fun to do.

Either do digits for cupboard handles or you could do all the Archimedean solids. So you've got different shapes. Instead of having just like, you know, your classic knob, have a mathematically interesting knob for each of the sets of cupboards. Part of the episode. There you are. No one take that out of context. I think it's hard to, you know, you keep coming back to tiling, to patterns. Because I've tried several times to have interesting tiling patterns done in the house.

Wait, you didn't ask me if I've got any interesting maths decorations. Oh, sorry. Beck, what are your interesting maths decorations? I don't have any. Oh, good. I'm glad we covered that. Although your background, your zigzag triangle wave. Technically, everything is math. Correct answer. I do have math things. It's just they're not. It's just accidentally math. I do love a geometric print. Oh, yeah. Got that on my bed sheet. One year, Lucy bought me a print of the original circuit diagram

for the apple computer but it's been signed by steve wozniak and who was the designer of the circuitry and it's in my kind of pile of cool things i one day need to get framed and put up yeah i've got one which sort of counts which was that the beginning of all the Horror Heights books is an isometric map. So it's, you know, a bit like SimCity, you know, so all the buildings and everything stay the same, but you get this 3D effect of essentially a 2D map. I got that printed as a big print and framed on my wall. Spima probably has a bunch of maths related. A bunch of stuff, yeah. You know, two dimensional things that you could easily just frame with a cheap

frame and stick up with some command strips. Yeah, and if you put anything in a box frame, it's art. Yeah, that's why I got all my tiny knickknacks and then mounted them as if they're like butterflies. And then now everyone's like, wow, look at that. And I'm like, yeah, they're just tiny knickknacks but getting onto your tiling your true love so give them a tiling

so i really like tilings and we i gave up on the inside part here's the problem if you want to do a cool tiling pattern and in mathematics we use the word tiling the way a lot of people would use tessellation or repeating pattern or something like that. It just means you're fitting a bunch of shapes together. Often the same shape, sometimes combinations of shapes. It's very hard to get interesting shapes off the shelf. If you want to buy tiles or buy pavers or buy stone or whatever, your options are almost exclusively rectangles. Occasionally you'll get hexagons or something else but you're pretty limited so if

you want to do something inside you're up against a lot of custom cutting but it gets complicated so i ended up not doing it inside because the sheer number of tiles makes it prohibitively complicated or expensive outside where they're much bigger stone pavers going in i'm like oh okay this is my chance and so we got our courtyard paved a couple years ago and i spoke to the builders and i kind of tried to work out what the what the cost per cut is if i wanted to change the shape of the stone and one of my favorite tiling patterns is called a snub square pattern it's a combination of equilateral triangles and squares and because the squares off the shelf already exist, I was like, oh, brilliant.

What you can do is we'll buy a bunch of squares and use them unaltered. We'll then buy a bunch of rectangles and out of the rectangles, instead of cutting the equilateral triangles, we'll cut them out in pairs. Because if you imagine two triangles back to back, you get what we call a rhombus. Specifically a square having a rest. It's just kind of leaning over. And that wasn't too many cuts. So I worked out the exact measurements. I was like, here's what you do.

They were like, got it. And they spent a long time working out with a more straightforward pattern. It's easier to make sure they're all lining up properly because you just make sure the edges line up with a bit of string that you run across the site whereas for this they're like well how on earth do we make sure we're laying them down correctly and i was like oh if you align a bit of string to go from corner long diagonal corner to corner on the rhombi that'll give you a constant line you can work to and then they got that all to work so i was very excited so so one of my big recommendations would be lean into what shapes you can work to and then they got that all to work so i was very excited so so one of my big

recommendations would be lean into what shapes you can get off the shelf but if you can work out how to alter one shape slightly to get a much more interesting pattern then you're in business i always thought there must be a way to get rectangles do a single cut on each one to get a irregular pentagon that would then tile and i haven't looked into this properly but i feel like if you rigged up a jig and a tile saw you could churn through either one or two cuts per tile to get a very interesting either pentagonal or hexagon based tiling pattern in a bathroom. So that one day, if I ever get to do tiling again, I feel like that would be a winner. But I don't know if you remember from the Zeman Award evening where I did a talk at the Royal Society.

Yeah, yeah. And you were there. And the day before, they didn't... Yeah, we talked about the t-shirt tiles on the podcast. You were very excited about that. I would highly recommend using those to tile a surface. And you've got a lot of options because there are infinitely many tiles in that family which could tile a surface aperiodically. So you could pick your favourite one because it's like, you know, there's infinitely many rectangles

because you can just change the ratio of the two sides. Yeah. It's slightly more complicated for the hat tile but there are two lengths within it and if you change the ratio of those you can get different shapes that will still, they'll always always fit together. They'll be aperiodic but they'll be different. And so the original hat tile was a ratio of one to root three from memory. And there's another one called the turtle, which is if you do root three to one and you pick any, a bunch of other ratios, you get aperiodic tiles apart from if they're the same, if they're one, one, you get a tile which can be arranged systematically. That doesn't work and what's happened since the

last time we talked about these is i actually organized people to get a whole lot of them and put them together to make a tiling pattern what on the floor and do you remember before we started recording i went down to get a delivery because my mate alex was bringing my drone back he also brought me a box of hat tiles whoa Whoa. I'm holding up a box. It's got hat tiles written on it. The box has a picture of a lawnmower on it. It's also got a picture of a lawnmower. A hand push cylinder mower.

So repurposed box. Shall we? Yeah. Oh, look at this. It's a box of tiles. Is it foam? Foam, yeah. Foam tiles.

We found a place that would die cut foam tiles for us. That's amazing. And I got over 700 foam tiles in a variety of different colors made. And so when you're doing the tiling pattern, you have to flip some of them over to go the mirror image version. But tiling, so the people haven't heard me talk about these before what's particularly interesting is they never repeat so unlike a square pattern or something else eventually the pattern repeats again like you fall into a rhythm whereas these tiles that never happens they never fall into repeating pattern which makes laying them down a real pain in fact it's provably

mathematically difficult like you can't just start putting them down if i just get another one i'm like i'm gonna put that one there or i'll put this one here i'm probably not gonna be able to continue that pattern you need you need to be incredibly careful because they only fit together in a particular way and the way they fit together never repeats. Which I find super confusing. But amazing. So what we did. When we were tiling with these. At a conference in Newcastle.

We had a bunch of diagrams. What you had to do. Was join a bunch of them. Into a meta tile. Made of tiles. And then you had to get those. And join them together into a bigger version of themselves and then repeat so it's like if you put you know nine squares together you get a bigger

square yeah that looks the same but bigger we found these recursive patterns like the droster hot chocolate where you put a bunch of them together and you make a shape that's the same as the original shape but bigger and then you repeat that process got it and so we did three steps in newcastle so you put a bunch together to make a shape you put a bunch of them together to make a bigger shape that looks the same but bigger and then you put a bunch of those together to make the same shape again but bigger and then part of the way they managed to prove that they're aperiodic relies on that substitution process of putting them together to make the same shape but bigger which is very very cool so and so so that's my advice not mean that the pattern

does continue at some point no if you keep growing it that way maybe the squares are a bad example because they fit in systematically when you put them, it's not like they're just like neatly side by side. They're all arranged at weird angles to each other. And the process of enlarging that, you never just end up with the same thing again. Right. Because then you're re-rotating these super tiles that are made of other tiles at weird angles. And you never get the same systematic shape repeating. At least not from one direction.

No. Yeah. It's specifically translational symmetry, which is you can't move it to the side and it lines up again. Got it. Yeah, yeah, yeah. Because I'm like, yeah, but if you're moving it, you've got to tilt it.

You've got to tessellate that mega tile to fit somewhere but then just the fact that it's tilted is what makes it non-repeatable because it's in a different angle because yeah and once once you plug it in it's not like one bit in isolation like if you pick one little patch you'll probably find that patch somewhere else but what you can't do is globally the whole thing will never repeat yeah if yeah yeah like how in pi you'll get the same number showing up but the numbers between them are different correct 100 yep that's it yeah cool all right you've nailed it so it's an it's a ridiculous tiling pattern so that's my that that's my one bit of advice was um if you want to do epiretic tilings you can get them made like I did.

I got them die cut. I wouldn't put this on the floor. They're not very hard wearing. But to bring it all the way around, I keep saying we. I helped plan this and got the shapes made from this die cutting place with my friend Katie Steckles who was organizing the conference where we did it at. Very great mathematician. Katie and I worked together to line this up. And then I was going to be there to do the big installation with members of the public in Newcastle.

And I got COVID like three days before that. So I couldn't go to the build. So my friend Aileen filled in for me. So she was there doing the build with everyone. Another brilliant mathematician. We will have a video about this at some point yeah she's great and she's the one she was also in vending in germany for the pyramid because i didn't know if i'd be better in time or not to go so she was gonna go to fill in for me if i couldn't make it and i made it just in time so

we did a joint video together nice so i couldn't go on top of that we had a person called david smith who's the person who discovered the shape was coming to the conference and i'd emailed with david but i'd never met the person who discovered the first ever monotile and so they got him to sign a tile for me. Amazing. So I've got a signed aperiodic monotile from the person who discovered it. And I'm going to get that framed. And that'll be one of my mathematical decorations that I'm going to put up around the house.

Yeah. I love that. I'll put a few together, get them all signed. And then I'll get a section of this tiled and framed. So there you are, Spina. Get some interesting bits of maths. Maybe get the person who invented them to sign it if they're still alive, which is, you know, some mathematicians.

Get them framed and put up. That's what I'm going to do. The video of Alien doing the tiling will be on my Stand Up Maths channel at some point. If you can't wait for that and you want other inspirations for mathematical decorations, I can highly recommend Aileen's TikTok and her YouTube channel. She does Numberphile videos. People may know her from Numberphile. So if you want inspiration for cool mathematical decorations,

the actual solution to your problem is to go check out Eliane's TikTok. Yeah, we probably should have just said that and saved a bunch of time, hey? Ain't that the truth. Ka-ching! No. Our next problem

that someone named Jack put into the problem posing page at problemsquad.com is, is it possible, and then they clarify, legally and or practically, to fly a plane on the German autobahn considering the lack of a speed limit? So, Beck, you've looked into this. Can you legally fly your plane down the autobahn because you're not technically breaking the non-existent speed limit? No. Oh. Oh. There you go, Jack.

Job done. Cha-ching. Yeah. Yeah. I did a bit of research and found that the rules for driving on the autobahn are that only cars, motorcycles, SUVs, and trucks are allowed on the autobahn. It's very motorcycles suvs and trucks are allowed on the autobahn it's very clear about what that was easy what vehicles because they don't want people on mopeds or bicycles or i guess tractors yep so uh someone's got a souped up tractor that can do do 100 miles an hour and then oh i mean maybe they could get away with it as an suv but uh yeah

so there's there's rules about what what vehicles you can have on there. So unfortunately, planes didn't go on there. But I did get a bit curious because I thought, how fast can you go in a plane along the autobahn before it takes off? Because eventually you take off, right? I know they did say to fly a plane on the German autobahn. And I'm guessing they mean like flying surely. At like car level.

Yeah. Like, do they mean that? Otherwise, like you're just following the Autobahn, aren't you? You're just above it. Flying over the, yeah. And then I guess you have to adhere to aviation rules. So I sort of went for, imagine if you were driving the plane along there. Got it.

And how fast could you go before the plane just takes off? Or more, how slow can you go? How slow can a plane go without taking off? Yeah. Yeah. How fast can you not fly a plane? How fast can you not fly a plane? So the typical takeoff air speeds for jetliners are in a range of 240 to 285 kilometers an hour.

Oh, okay. That's somewhere between 149 to 177 miles per hour that's slower than i expected well yeah yeah because the the speeds are usually over 100 miles an hour i was on the autobahn because we hired a car to get to vending to see the pyramid put in and we on the way back were on one of the autobahns because it's not like every road in Germany. It's not even every freeway or highway in Germany. It's specific autobahns. We were on one with no speed limit. And we got up to, just nonchalantly, got up to 170 kilometers an hour, which is 105 miles an hour.

And we were in the middle lane. I say nonchalantly just because that's the speed that other traffic was doing. It's not like I was like, I'm going to put my foot down and see how fast I can go. I was just keeping up with the traffic. You're just keeping up with everyone around you. And we were still being overtaken. I was doing 170k and I'm being overtaken in the fast lane by other cars going substantially faster than that. But you don't feel the speed.

It's terrifying how good the roads are that they're designed for this. They must be perfectly flat, accurately banked, all these things. It's just phenomenal. So I could imagine doing 170 and a plane overtakes me doing 240. That's conceivable. Yeah. But a light aircraft such as a cessna 150 take takes off at around 100 k's an hour oh what so that has to be in the slow lane per hour which is 62 miles per hour is like less than what people do on the freeway and just in the uk and australia yeah yeah and ultra light planes have even lower takeoff speeds. So what I'm saying is you could drive a jetliner down the autobahn,

but if you were trying to drive a Cessna or lighter along the autobahn, chances are you'll take off before you can match the speed of everyone around you. That's great. I suspect the engine, I don't know what the phrase would be, but the air being pushed out the back of a jet engine would clear the cars off the autobahn in their wake. At least slow them down. Definitely. Although that said, the amount of cars that might suck up into the engines as well. That's a good point. There's several reasons why you shouldn't fly

a commercial airliner down the autobahn. Yeah, but there you go. I thought that a commercial airliner down the autobahn. Yeah. But there you go. I thought that was a fun tip bit. I mean, I feel like you've... I guess I wonder if you could apply wings to your car, then you could... That means you could potentially,

with enough aerodynamics in place, it means maybe you could take off in your car. There's a prank. Get someone's spoiler, turn it upside down. Yeah. There you go. Well, Beck, I feel like you've answered it legally and you've answered it practically, which were the two aspects that Jack requested.

So, I think that's a cha-ching. Yeah. Cha-ching. Thank you. Cha-ching. So I think that's a cha-ching. Yeah. Cha-ching.

Thank you. Cha-ching. It's time for any other bankable business. And first up, Bec, we had several people commenting on the longest word that's one syllable. Yes. And you've got a response you're particularly pleased with. Yeah. So Christian got in contact with us via the Problem Posing page. That's at problemsquared.com and you can select solution.

And Christian got in touch because they're a linguist from Denmark. Amazing. Yes, and they said when they heard about the problem of the longest one-syllable word on episode 067, they knew they had to pitch in with an attempt at a solution. six, seven, I knew they had to pitch in with an attempt at a solution. And they provide a lot of really fascinating information about how sounds are formed in other languages. And it's very, very interesting. I don't have time to go through the entire thing on the podcast, but at some point we

will put this somewhere where other people can read it because it is very fascinating. Christian showed us the steps we would need in order to construct a long one syllable word so they said first you need to fill up the syllable so they said as you were quick to notice all combinations of three consonant sounds that can start with the syllable in english begin with an s combinations such as or are good but we can we can do better than three letters. The word... What? The word sphragistics, which is S-P-H-R-A-G-I-S-T-I-C-S, which is the study of seal emblems, starts with four consonant letters,

s-f-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r-r- which is S-T-H-R is documented in the word throne, meaning strand or beach in Yola, an extinct sibling of the English language spoken in County Wexford in Ireland until the 19th century. Oh, that counts. Yep. So he said, I'll go with through. And if that turns out to be unpronounceable, you can just say the T-H as in time or Thomas. So you could say, say, stuff. So they said a good word to start with might be thronks, which has three consonants. Thronks.

Thronks, which is S-T-H-R-A-U-R-N-X. They point out it has three consonants, one vowel and four consonants. So we've got the word thronks. Good combo. Then they said, step two, use suffixes to extend the syllable. They said, this is where mathematics may come in handy. You can attach a TH to a number to make it ordinal, even if it ends in lots of consonants, such as sixth into sixth and thousandth into thousandth. So say that our word. You're welcome, everyone else.

So that our word thronks is, everyone else. Say that our word strongth is a number. Matt can pick his favorite. If you divide one by strongth, you have one strongth. One strongth. That's great. You can also make the fraction plural by adding S to make two strongths. Glad I've got the pop shield in my mind two strong out of ten you can also make a verb out of an ordinal number to quarter means to split into four to tenth means just to to split into ten and a verb can be put in the past tense by adding ed. So I tenthed the cake means I split the cake into 10 pieces.

So what if you split it into throgs pieces? You throgsed it. That's already 13 letters. They've said, step three, add silent letters. Now we use Matt's strategy of adding silent letters to the word. So far, I've used the most straightforward spelling for legibility, but that won't do for the purpose of creating the longest word. The X even stands for two sounds, K and S.

So that really has to go. Here's what I've come up with. So for S, they've come up with P-S as in psychology. That works. For T, they've come up with P-H-T-H, as in tithesis. I think it's tithesis. Tithia. And tithia.

R, W-R, as in right. Yep, easy W. Easy sign W. Yep. And the A-U sound, or, they've done A-U-G-H-A, as in Vaughan, Vince Vaughan. They've done A-U-G-H-A, as in Vaughan, Vince Vaughan. So they're just, they're swapping every single letter out. Yeah.

For the longest version of that letter that teams up with a bunch of silent letters. Yeah. So R, they've got double R-H as in mer. For the N, they've got N-G as in ginko. K, they've got C-Q-U-ue as in sack the old spelling of sack i would go as far as to say as barbecue but then i guess you're pronouncing the q in that s that's really gonna be silent they've given us a different s to the opening s later on they've given us sce as in colless great uh for uh the th sound they've done uh just th I think it's a hard one to do otherwise. And for the last one, ed.

So put them together. And we've got thronkst, but it's spelt with 29 letters. It's like unpacking a zip file. That's what's happened. Yeah, that's exactly what's happened. So it's a 29-letter word with only only one syllable meaning to split something into strong pieces and you don't even have to pronounce every single sound you know what number strong is well he said you should get to choose yeah well it's a new word for 29 of course it is

of course it is duh you're right yeah so we we've shrunk the word by splitting it into 29 bits. Well, we haven't shrunk it, have we? We've done the opposite of that. We've like. We've shrunk it. We've split the word into 29 little pieces. Yeah, actually, you're right. No, you're right.

We have done that. Yeah. We have shrunk the word shrunk. Now it's split into 29 pieces. That's great. Yeah. We'll say it again. 29 letters. One word.

One syllable. Now we've got a clip that Christian sent us of the pronunciation to make sure that we're saying it right. So we'll play that now. Strongst. Thank you so much, Christian. That was an unbelievable amount of effort and such an incredible explanation. It's genuinely up

there with my favorite solutions we've received. I'm going to give them strong things. Yeah. Strong stings. Strong things. Not in strongths. We haven't strongthed it. It's just strongthed. We haven't strongthed.

It's just strongths. Strongstings. We also did, we got a few responses, but another response that I really enjoyed was from someone called Dane, which I find quite incredible considering that Christian is the Danish linguist. But not the Dane Christian. The Dane name.

The Christian name of Dane or the Dane with. The Dane name. The Christian name of Dane. Or the Dane with the Christian name of Christian. The Dane with the name of Christian. Yeah. So Dane said in the most recent word, the problem about the longest one-syllable word intrigued me. I thought I might have a go at a longer one and came up with skronksts, which is very similar.

It's the same word. It's so similar. Skronksts. Skronksts, which is very similar. It's the same word. It's so similar. Skronksts. Skronksts. What's Dane's logic? So Dane spells it S-C-H-L-R-A-U-G-H-N-S-T-S. Now, I think using Christian steps, we could probably get that pretty long as well. We could probably skronkst it. We could unpack that.

We could probably strong-st it. We could unpack that. But they've said that they think the plural of strong-st, which is a word that starting as of my writing this, means something that is as large as possible while still being considered small, e.g. the heaviest possible featherweight boxer would be strong-st, which I really like. Great work, Dane and the Dane. We also want to very quickly apologize to Olof, who I, when we were recording in a field

last time, I realized I didn't have any internet connection, so I was scrabbling through kind of old pasted notes I'd made about what I wanted to talk about, and I had incorrectly pasted the name of the person who did the incredible spreadsheet about the strawberries. What do we call them? I think I call them Eric. Yeah. That's my fault. It's Olaf.

So we got in touch with Olaf. They've sent us their incredible spreadsheet. And they're going to get themselves a commemorative bowl. Slash plate. Slash plate. In fact, that should have been our answer to the how do you decorate your house problem. Yes. Put up your commemorative plate slash bowl.

Bowl and a plate. Yeah. Yeah. I will say, I don't know if we're going to hit our 2 million download in November that I predicted. Oh, no. Well, not if we can help it. Yeah. We're past 1.7 million, but we've really got a exponential those downloads

to hit my predicted day i'll be close i reckon yeah if you would like if you would like to hit if you would like us to hit our goal of hitting our 2 million downloads in november then all you need to do is get someone else to listen to this. Yeah. If you told 10 people each, we'd have it done instantly. Oh. If they all listened to you. Yeah, yeah.

Please. I mean, that would be incredible. So if you could tell your friends, followers, family, anyone on social media or through other means to listen to Problem Squared, please do. Tell them what episode you think that they should start from. In fact, I think on Spotify you can specifically share a link to a specific episode, which is pretty cool. If enough people do it, I think it then says on Spotify, most shared, which is interesting. Yeah.

So eventually. I wonder what the most shared is going to be. We'll see what that is. And speaking of interacting with you guys we've had a lot of you coming back we've we're pretty much even in the amount of people saying that they want a reddit page or a discord page now just to be clear this isn't replacing the problem posing page we'll still be using that no for um at a problemsquared.com yes for all of that but uh this was more when we hear from people like Christian who sent us these incredibly detailed solutions, which are absolutely fascinating, or we want to cite specific sources or websites, it'd be nice to have someone to talk about that.

It's like being a bottleneck for listeners interacting directly to solve problems. I feel like at the moment they have to come through us. We don't want to be guarding that gate. We want to let everyone, you can workshop stuff together and without us getting in the way. Someone reached out to say they'd already created a Reddit. So by the time this goes out, hopefully Matt and I will both be moderators on there. And that is... r slash a problem squared. Yes.

Or if you're like me and very new to Reddit, it's reddit.com forward slash r forward slash a problem squared. We did have someone called hutton a hull uh or h-u-t-o-n-a-h-u-l-l who offered to help uh manage a discord said they'd like they like it when a discord isn't messy and as well set up and we'd love to take you up on your offer but um only half of the email address was filled in so maybe an auto not a great start if i may yeah so we can't email you but if you're listening to this hutton a hull uh then um yeah please uh please get in touch because we could do with some do with some help as we come to the end

of another trading day at the problem squared stock I don't know. I'm trying to go with money. That's good. I like it. Thanks. On the trading floor. Yeah. Buy. Sell. No buy. It's the end of the episode. Oh, yeah. That makes way more sense. We always like to thank our Patreon supporters who make this podcast possible.

So, in no particular order, we're going to thank three of you at random, and the people we're going to thank three of you at random. And the people we're going to thank in this episode are Lydia H. I can mispronounce that as Lydia H. Or Lydia. Oh, awful. Lydia.

Lydia. We should strongst all these names. We should strongst. Strongst. Or Arne. Arne. We should stronkst all these names. We should stronkst. Stronkst. Or Arne. Arne. Timmy Ha Man.

Hey, man. Hey, man. Yeah, if you would like us to mispronounce your name, then sign up to our Patreon. We'll pop a link in the show notes. And once a month, you'll get a bonus show show which is our I'm a Wizard show which is very silly. Sillier than this if you can imagine. Unbelievable but true.

We'd also like to thank my co-host Matt Parker. That's me. Myself, Beckel. Cash Money Parker. Cash Money Parker and our wonderful producer Lauren Armstrong Carter who isn't in the record this time and yet is somehow going to make this all sound incredible.

Bye. Bec? Yeah? How many dice are in the jar oh it's not even we're not even in the same room as the jar no no you gotta remember what the jar looked like yeah what did you guess last time i can't even remember i feel like i went in at 500 just i thought i could get like a max threshold or a. Yeah, that was incorrect. But then you didn't say whether it was up or lower.

So that's done nothing to me. I did not give you a direction. No, no. Well, it was ruled out one specific number. I've not changed the number of dice. Okay. I did have to borrow three dice from the jar and I messaged everyone on the Problem Squared WhatsApp group to say I'd borrowed three, but I've since put them back.

Oh, good. The number is still the same. Yep. Did you choose the number or is it just how many were in there? I counted them. I discovered the number. I didn't invent it. So it's not like something, it's not necessarily a hilarious mass number.

All right. I mean, this episode is a hilarious mass number and we didn't mention it once. No, because we are mature. Yeah, we're adults. All right. Well, I'm going to guess, I know that you didn't choose it, but I'm going to guess 314.

Incorrect. I think I would have struggled to have contained my excitement if it had been 314. That's true. I would have been able to read that on your face. Yeah, yeah, yeah.

Am I just guessing random? There's probably, is there a way? I mean, I don't know if I'm going higher or lower, so there's no real. Okay. Do you know what? Next time we're in the same room, I'm going to try and do it the way that I would do it if I was actually entering competition. Okay. I'll tell you what, if you do the full calculation, I'll then give you a higher or lower if you're sure you're working out. Okay. Deal. If I don't accidentally guess it, next record. Whoa.

Oh, imagine.