A Problem Squared - 028 = Having a Chat and Nav'ing a Sat

Episode Date: March 1, 2022

In this episode... * Could a GPS sat nav work on the moon?  * A Pudding Squared returns.   * An APS announcement. * AND format news!  If you have any memory of how 'Is This Your Card' started please (please) let us know.  As always, if you've got a problem or a solution, hit us up on our website aproblemsquared.com. And if you want want even more from A Problem Squared, find us on Twitter and Instagram.

Hello and welcome to A Problem Squared, the podcast equivalent to skydiving, in that soon you will face a problem you could have easily avoided by not getting on the plane, and will be consensually hurled into it just for fun. But don't stress, you've been equipped with a parachute in the form of Matt Parker. Not literally, of course, that would be terrifying. Correct. I mean... For everyone.

I'm talking symbolically here. You don't want to pull the cord. It's just me going, hello, I'm as concerned as you are. Or a parachute that's like a huge version of you. Like one of those Thanksgiving Day parade floats. He's not one of those guys. He's not. He will ensure your safe descent onto the firm ground of a solution.

And I am Beck Hill, the person who drives out to collect you and takes you back to civilization which doesn't sound exciting but when you're stranded in unrecognizable territory you'll be so relieved to see me you won't even care that i don't have a driver's license i mean you've you've accurately described the podcast in a nutshell yes that's that's that's the other thing that i do i'll drive out and collect you after a skydive and I'll write a very okay intro. On this episode. I solve the problem of using GPS on the moon. There's a new pudding squared.

And we've got loads of any other AOB business. Stick around. So, Matt, I do want to know how you've been. I do have questions, but before we go into that, we've got some exciting news. Oh, yeah. And no news more exciting than format news.

Not news that's format. It's format. It is for you. It is format. It's format news.'s format. It's format. Format. It is for you and for everyone. It is format. It's format, format news. We hit our Patreon goal. 500 plus.

Yeah. Thank you, everyone. Thank you so much. So we are going to be doing an episode every two weeks now. Yes. We're going to slightly more than double our output, which is terrifying. Yeah. One of the things that our listeners might not actually know is that when we record these

episodes, our problems might take about an hour each to answer. Too long. And poor Lauren has to cut everything that she can to make sure the episode doesn't go forever. But it means that she has to cut out all this really fascinating stuff. Sometimes there's really interesting facts that we can't fit in. It's all gold. So we thought, why not simplify it?

And one of us will do a big problem per episode. Yep. And that way we can keep in as much of the facts and the fun and the laughter as we know you'd like. We in no way guarantee the answers will be more exhaustive though. I don't want to set up, but now people will expect we will cover every single angle. I think there will still be as slapdash as ever, if I may, but just longer. More slaps, more dashes.

That's what I'm saying. It'll be a slip, slop, slapdash. That's what we're doing. Yes, exactly. It's very exciting. So now I can ask Matt, how have you been? What have you been up to? Well, today, as you know, and while we're peeling the curtain back on the logistics

of how this podcast works, we do record it a number of days before it goes out because it has to be edited and all those things. We're not doing this live on the day and we are recording on Tuesday, Tuesday, Boxing Day. So I am still recovering from the excitement that was yesterday, the 22nd of Feb in the year 22. 2-2-2-2-2. And it was a Tuesday. Oh, my goodness.

It's been in my diary for so long. And it finally arrived. Ever since you mentioned it on the last episode, I've been really excited about it. And then I was really disappointed when like loads of major news, like it got loads of coverage. And I was like, no. I couldn't believe it. Some of us were into Tuesday, Tuesday years ago, getting ready for this. What did you do for it, Matt?

I embarked on an overly involved YouTube project. And I realized last year. Wow, completely out of your wheelhouse. I know. I thought something new. It dawned on me last year this was on the horizon. And I thought, oh, I'll email some YouTubers and we'll come up with a plan. There's another channel called 3Blue1Brown, a guy called Grant Sanderson runs it.

So I dropped Grant an email very early on and said, hey, we should do a thing. And likewise, and Steve Malt, good mate of mine. And we're like, yeah, we should do it. But of course, did we get it all done well in advance? So it was set to go with weeks to spare? No, no, no, no, no. We were still working on it the night before Tuesday, Tuesday. On Tuesday, Tuesday Eve, we were still slotting all the bits together.

Because like some kind of idiot, I decided a collaboration with 22 YouTubers would be an appropriate way to celebrate Tuesday, Tuesday. And then a friend of mine who does visual effects for a living. Well, actually she's moved into theme park ride design now. But in a previous life, she worked on. She's the coolest person ever. Sorry, you had to hear it this way back. She might be the coolest person I know. She did the black hole in Interstellar.

Yes. With my friend Eugénie von Tanzelmann. might be the coolest person i know she did the black hole in interstellar yes eugene yvonne tonsilman and i mean what a gross over qualification i had a collapsing hole like a singularity at the end of the video and so i got the world's black hole vfx expert to render it for my stupid tuesday tuesday video just to make it even more complicated we had to have a vfx schedule and so certain shots have to be done some had to be done in advance to be able to go into that and all this stuff so oh my goodness it was just it was totally worth it i'm glad it's done and i've got 11 years and a bit until Thursday, Thursday on the 3rd of March 33. And obviously your answer is going to be the same when I ask you how you've been, because obviously the highlight was also, I assume, Tuesday, Tuesday.

I don't know if anything else has happened. Anything else in your life other than that? I won't lie. I did sell it. I was excited about Tuesday, Tuesday. We stopped Moneyball. I had never seen Moneyball, so we were watching that. And Matt, you'll like this. My complaint about Moneyball, too much baseball, not enough maths. Too much sport, not enough numbers. I was all excited for like some whiteboard action. And there was a disappointing lack of it.

They don't even say what happened to Pete, like to, to the Jonah Hill. There's not even a, at the end, it's not like, oh, and he went on to do this. No, you don't know what the, it was his. Anyway, look, I'm getting off. I haven't seen it. I was furious. For this very reason. I didn't watch it. Cause I was like, that's too close to home. Yeah. So we, we were watching Moneyball. Yeah. And then I was annoyed because they didn't tell me what happened to all of the characters. So we paused that at 22.22, at 22 past 10 p.m. And I tweeted.

And then Gav said, okay, you have to get off your phone now. We're going to watch the rest of the film. Back to the film. So we did that. I've got some other news. Yeah. I finished the second book. Oh my goodness.

It's done. I've done the copy edit. I feel like I've said that before, but before it was like the first, like the draft that goes to the editor, but now it's all the copy edits and everything. It's done. Now live screaming. That's the name of the second horror Heights book. I'm very, very excited. Uh, did you just barricade yourself away and get it done?

Or were you picking away at this over some period of time? Both. I was picking away at it. And then the week before the deadline realized, Hey, picking away at it on a daily basis, still not enough. So then barricaded myself for a week stayed up for 36 hours straight at one point whoa still didn't get it finished had a bit of a breakdown yeah light breakdown exactly i mean i'm really i'm making light of it but i'll be honest

it was it was not nice and then took me about a day or two to vaguely recover enough, get back on my feet. And then I finished it. And I've been in a wonderful mood ever since. It's like revising for an exam. And it's good. Everything and then nothing. Yeah. Because you go through, I hate this book.

I regret every decision I ever made. Phase. Yeah. It's good. You still like it. You go to the end, you're like, hey, it's a good book. I think it's better than the first one. And now I'm all pumped. know what matt what i'm ready to hear a solution to a problem oh well are we recording the right podcast for you

this episode's main problem comes from phil th who writes, assuming the signal was strong enough, what would happen if you tried to use a GPS sat nav on the moon? Oh my goodness. I know how much you like GPSs, Matt. Big fan. Love a good GPS. And I'd never thought would a GPS unit work not on earth? earth. So obviously they work on earth and I'm taking it from Phil's question that they're talking about just a standard issue consumer GPS unit, because

obviously NASA and ESA and space agencies have specialized kit for tracking things in space. They didn't just like send Apollo 11 up to the moon and they're like, can you see us? And they're like, yep. They're like, cool. Yeah. So we've got ways to track things in space.

Yeah. So the question is not, is there a way to have some kind of positioning system on the moon? The question is, could you take an Earth global positioning system set up and could you take that to the moon and would it still work? Some people may already know how GPS works. Bec, how familiar are you with the GPS? Just off the top of your head, I've not given you any warning here. Yeah. Do you know what? I'm not really. I gathered from the name, it has something to do with, you know, triangulating different satellites around the earth and using that to gauge which direction you're

facing so the system works with a minimum of 24 satellites that's a big triangle like for a triangle that's a lot of corners and um satellites come and go so they've made loads they've made like 70 or something of these things over the years since it was first put up oh i was back in the 80s i think so they come and they go, the current, the oldest satellite currently still part of the GPS network launched in 1997. So it's the oldest one up there is 25 years old and the rest are all newer than that. And when, when they get decommissioned, sometimes they get like, if they're

totally dead, they shove it way further out. Yeah, there's a bunch of junk, isn't there? A bunch of junk. They drain the batteries, all that jazz, and then they just shove it in a drawer way out in a very high orbit. Sometimes, though, the satellites get a bit old, but they're like, they still would work. And they keep them as backups. So they decommission them, but they keep them in the orbit where in an emergency, they could be powered back up again and go back into service.

So we have got a bunch of like spare ones going around. As long as there's 24 or more, it all works. And there's currently 29 of them in active service at the time of recording. And so the way they work is in a nutshell, they broadcast a clock signal, like a timestamp. All they're doing is they're constantly reading out the time and that's it. That's all they do. Oh, and they identify themselves. And to be honest, before anyone complains, there's a bunch of other metadata, things about corrections between time zones and stuff. There's a bunch of other things going on. But in terms of the actual working out where you are, all they do is they yell the time into space. And they also yell

in all directions, which is why this is a great question, because they're yelling actually, are they directional? Oh. I've just questioned myself, because I know, as previously discussed, my wife is a space scientist and I will get in trouble. Because you can have very directional satellites. So I'm going to take that back. I think they're yelling directly at the Earth. But Phil specified, assuming you can get the signal. So that's a practical concern.

Phil has conveniently hand-waved away. So they're up in space yelling the time back down at the Earth. And totally unrelated, but just something I love, they keep track of time by counting the number of weeks and the number of seconds. So as humans, we split time. Normally we do hours and minutes and seconds, and then we do days and we do years. They're like, nah, forget that. We're just going to count how many weeks it's been. And we're going to count how many seconds it's been since midnight at the end of

the 5th of January, 1980. So it's constantly just broadcasting how many weeks it's been since then, followed by how many seconds into the current week. Why that date specifically? No reason. When you set up these computer systems, they all use different dates. So, I mean, they use 1970 for a lot of things. You just need to pick an agreed point in time, and they tend to put it slightly before the system has to come online.

And so GPS was up in earnest in the 80s. And so they just picked, I don't know why the 5th of January though, they picked, maybe there's a bunch of problems with something happening right on the rollover between years. So they bumped it off by a couple of days. Yeah. Oh, so they had to pick a Monday. Maybe it was the first Monday in 1980. That feels likely. Oh, I can check that right now.

Oh. The 5th of January, 1980 was a Saturday. Okay. So their week starts. Or they wanted to start on the weekend. Between Saturday and Sunday. And then the weeks run Sunday to Saturday. Ah, one of them ones.

One of them ones. So they're constantly broadcasting out the time. And a little identifier string of arbitrary ones and zeros. But it's unique for each satellite. And they're carefully selected so they don't overlap in their heart. They're easy to distinguish. And they use a thing called a gold code, which is unrelated to this. But the reason

you can tell where you are by just things yelling the time at you is we know very accurately how long that signal takes to get to you because it goes at the speed of light which is very fast but finite so it's still the case that as something gets further away from you, it takes a bit longer for the signal to get to you. So what you can do is if you know the current time, so your GPS device knows the current time, the GPS satellites have an atomic clock in them. So they really know the current time and they're calibrated with the earth and they're updated reasonably frequently to make sure they're kept exactly in tune. And they have to compensate for general relativity because time passes at a different rate on the gps satellites than it does on the earth which is just incredible they compensate for all of that because if someone yells the time at you and by the time you hear it you're

like oh that was like three seconds ago they said that. And you know how fast the signal was traveling. You can work out how far away they were. And so if you know the distance to a bunch of other places, you can work out where you are. The question now becomes, how many do you need in terms of mathematically how many satellites your GPS has to be connected to, to be able to work out where you are. And it's always naively one more than the dimension that you're currently in. Oh. So imagine you're on like a big open sports field or grass field or something. Right.

But you know how far away you are from someone else. Let's say you're like 10 meters away from someone else that doesn't narrow down exactly where you are because you could be anywhere on the circle of spots 10 meters away from them right yeah you're trying to solve the problem of where you are i mean obviously you know where you are you're standing there but if all you know is you're 10 meters from someone there's a big old circle you could be anywhere on that if i was blindfolded and i wanted to know where i was on the pitch, which way I was facing or whatever.

Yeah. That doesn't help. I could be anywhere on this big circle. And then they say, oh, but you're also five meters away from this other person. Now you're like, oh, okay. So for them separately, there's a big circle around them of all the points that are five meters away from them. And you're at a point that's both 10 meters away from the first person.

So you're on their circle. That's 10 meters around them. And you're five meters away from the other person, which means the circles must overlap. But if you imagine two circles overlapping. Hang on. Just so my brain is right around this. Say it back to me. Yep.

Yep. Lauren, our producer and I are on a football pitch. Got it. Yep. And I'm blindfolded. And so I don't know where on a football pitch. Got it. Yep. And I'm blindfolded. And so I don't know where on the football pitch I am. And you say you're 10 meters away from me Beck. And I'm like,

okay, but I don't know what side of you I am. That sort of thing. The way I think about that mathematically is I imagine the big circle, 10 meters around me. And you could be anywhere on that circle. Cause they're all the points that are 10 meters away from me. Yeah. And then Lauren says, and you're five meters away from me. Well, now there's actually two places on the field, which are 10 meters from me and five meters from Lauren. Yes. Because if you imagine the circle

around Lauren of all the places that are five meters from her, and you imagine two circles overlapping, they cross at two points. And so you could like, for example, you could be to my right, 10 meters from me and five meters from Lauren, or you could be to my left, 10 meters from me, five meters from Lauren. There's then two points. So you would need a third person to come out and tell you where they are and how far away you are from them. Gotcha. Because then they're like, hey, I'm to the right of Matt and you're this far from me. Then you're like, oh, okay, now I know I must be in this place because there's now only one place that is the same, those distances from everyone. So that's the triangulation.

A football field is a 2D surface. It's a big flat surface. You can only move in two. A football field is a 2D surface. It's a big flat surface. You can only move in two directions. We're not going up or down. And it took three people before we knew where you were. Gotcha. It took one more person than the number of dimensions that you can move around in. Like in a jet pack in the football stadium, three people would no longer be enough. There's now more than one place that would match the requirements because you can now move around in 3D. You would need to know how far you are

from four people. And so when they rolled out GPS, they were like, it's fine. As long as you can connect yourself to four different satellites at once, and you know how far away you are, you can work out your position in 3D, which means you know where you are on the surface of the Earth and you know your altitude at the time, how far off the surface of the Earth compared to sea level that you may be. And I actually looked up...

Give me one second to bring this up. So I emailed Lucy and she was able to download it. You've actually got another dimension everyone's forgotten about. And that's your position in time. Because on your little GPS unit, it's trying to keep track of time. But your GPS unit hasn't got an atomic clock. It's not got some super accurate time piece.

Because it would be incredibly expensive. So there's atomic clocks on the satellites. Because we've only got, you know, 20 something of them. So your clock on your GPS device is not going to be completely accurate. It's going to be slightly off the true time and it doesn't know how inaccurate it is because if it knew how far off it was, it would just fix it. Right? So your GPS thinks it knows the time, but it knows that time is probably wrong by some amount. And so actually your GPS device doesn't know where it is in space and it doesn't know where it is in time, which means it's actually trying to locate itself in four dimensional space time for which you need five satellites to be able to

pin down your exact location and so you're you're when you use a gps it's solving a four dimensional space time problem to work out where you are it's actually looking at intersecting four dimensional cones to try and deduce your exact location in space and time. Because you don't know where you are in space if you don't know where you are in time. Are you saying a GPS is like a little TARDIS? It's a tiny TARDIS. Oh my goodness. Yep.

Because you actually, you end up being connected to way more than the required five satellites. And there's more than one way to solve the problem because you can either do it like algebraically where you know all the distance, like, you know, the times, you know, locations and you can factor in the offset time error and then you try to cancel it all out. Or you can do what's called a numerical solution where you start with a solution that's good enough and then you just try and iterate it into the final solution. Yeah it's my kind of problem solving. In reality

you're more likely to be connected to like eight or nine satellites at a time and so you've actually got too much information and if you've got enough, you can work out where you are absolutely uniquely in 3D space and indeed time. And that works just as well if you're inside versus outside the satellites going around the Earth. Now interestingly, in the paper The Existence and Uniqueness of GPS Solutions They point out that you can sometimes still work out where you are With only four satellites If you start off by assuming that you're on Earth And when you have these iterative solutions

It starts by guessing that you're on Earth Which seems like a reasonable assumption And then just hones the answer to exactly where you are. And there's some regions in space where you're outside the earth. And if you can only connect to four satellites off the earth, because you've no longer got this safe assumption of, you know, roughly where you're starting, like on the surface of the earth, that can go wrong depending on the geometry of the satellites. So the first kind of passing answer to Phil's question is, in theory, GPS works anywhere if you've got five or more satellites

and you get a strong enough signal. If you're on four, it depends slightly on where you are. And I'm pretty sure the moon, it depends on the geometry of the satellites, is going to be arbitrary. There'll be like two possible solutions because you can't start with the assumption that you're on the earth. But there's so many satellites that this is not an issue.

The bigger problem is that your GPS device probably won't work. Is that because the satellites go around the Earth? It's not because the satellites are going around the Earth, not the moon. That should still work. Is it to do with the time being different? It's not because of the maths. No charging plugs. It's not because of a lack of charging plugs.

Is it an atmospheric thing? It's not an atmospheric thing. Nice guess. Now you've stumbled onto something else there. Because you're so far away, all the satellites relative to you look very close together. Yes. If you're on the earth, you've got like one satellite ahead of you, one directly above you, one behind you, one over there. They're all in wildly different directions, which makes it way easier to work out where you are. When you're on the moon, all the satellites are in the same direction and they're all about the same distance away.

It's like trying to pick up a pea with a spoon. It's like picking up a pea with some chopsticks. Like you've got a big surface area to get your pea onto and carry it to your mouth. Yep. Yep. But when you've got chopsticks, you got to get that right on the pea. Otherwise you're not picking up that pea. Yeah.

If you miss the pea by like even a centimeter, you're not. You know what? You're not eating a pee. That is a great analogy because you got way more margin for error with a pee on a spoon. Yeah. But if you've got like tiny chopsticks, you can bear, the margin for error is tiny. Oh, that's really good. Because I was thinking about it and people, I guess those of us who have been, if someone

was really, like if I was really close to you and you're looking straight at me, because I believe these are the social conventions for human interaction. And then I suddenly took a step, a meter to the left and you wanted to follow, to keep looking at me, you'd have to move your head a good number of degrees to still be looking at me. And that's kind of how we measure direction is like number of degrees, which way you've got to face to work out where they are. If I was like the other side of the football pitch away from you and I took a meter step

to the left, you'd barely have to move to still be looking at me. And so when the satellites are so far away, because they're all effectively, you barely got to move from one to the other, all effectively in exactly the same direction. It's way less accurate. So if you turn on the GPS, it's probably just going to say you're on the moon. And then you're like, but we're on the moon. And it'd be like the moon. Some people, when I was talking about needing three people to work out where you are on the football pitch, a few people were thinking, ah, Matt didn't mention that doesn't work if those three people are co-linear. And there are some weird exceptions where that doesn't work because of the particular arrangement of where everyone is. And it falls apart if the people line up too well yeah or i

suppose if they were bunched together yeah if they're bunched together that's not gonna it's barely gonna help 10 meters from matt and 10 meters from lauren and 10 meters from you our listener you're like well all i know is they're all together somewhere and i'm 10 meters away from them that doesn't help got the same problem with the moon you're so far away they may as well all be coplanar and they're all bunched together it's really unhelpful so in theory it works but because of the geometry you're going to have big inaccuracies. So I haven't tried to run the numbers because it gets very complicated. I suspect it wouldn't even be able to reliably place you on the moon just because it'd be so inaccurate when you get up there.

However, still a moot point because it would not work. Your device would refuse to work. It's in a union. Well, literally, it's literally in a union. So actually, let me get up the name of the union. Hang on a second. The Coordinating Committee for Multilateral Export Controls, a union of about 17 different countries,

and this was post-Second World War through the cold war and was disbanded or at least i mean there's probably superseded by something else in the early 90s and this was a bunch of western countries agreeing what counts as like military technology and what can and can't be exported to other countries and one of the things they were worried about was GPS technology because it can be used on intercontinental ballistic missiles to steer them and guide them and do all these things. And they're like, well, we can't just make GPS available to everyone. And GPS was originally developed by the US military

and was used by them until it was eventually a certain resolution was made available for civilian use. And to this day, the US military can turn off GPS, which is terrifying. We only use it out of the goodness of the US military's heart, which- I'm so glad that I grew up knowing how to use an A to Z. I mean, it's not just that. I mean, we use the timestamping feature, like financial transactions are done using the GPS timestamp.

Trains pulling into train stations. Oh my goodness. The train knows it's in the train station because of the GPS coordinates. I know a bunch of this because Lucy works on some of the kind of business and continuity issues that would rise from a solar storm disrupting the GPS network of satellites. Oh, my goodness. It's terrifying the amount of things that depend on it. It also depends on the US military. And all of them are owned by the US.

There's not like any other countries that have been like, oh, we'll do our own version. There are some other systems kicking around. Russia has their own network that's up and running. China have their own network, which is up and running. And I assure you, if the US military decides to stop providing this, China will probably swoop in to then be the ones providing such an incredibly important bit of infrastructure nationwide. The European Union, they've been trying to get their own version

of Galileo for a long time. It's been plagued with all sorts of ridiculous problems. That's one of the biggest, biggest failings of the modern space industrial complex is getting Galileo off the ground. At the moment, though, we're very much

ancestors into the US GPS. However, they want to stop it from being used in weapons and so if you haven't got a license and you buy a standard issue consumer GPS device it's limited in two very important ways. Number one it won't work if it's moving more than a thousand knots, which is roughly 1,852 kilometers an hour, or just over 1,150 miles per hour. So if you suddenly start driving significantly faster than a thousand miles an hour, your sat nav will cease to function because they've all been designed. If they start moving too fast, they turn off. And 1,000 knots was the limit.

And they will stop working if they're more than 18 kilometers above sea level. Ah. Which is a fair way up. But the moon is definitely above that. The moon is definitely above 18 kilometers above sea level. So it turns out your GPS device will not work on the moon because it will be deliberately capped to turn off above 18 kilometers above sea level. The one final problem is these are very old regulations and there's a variation in how they're interpreted. So some manufacturers consider it to be and,

and some consider it to be or. So some devices will turn off if they're above 18 kilometers or they go faster than a thousand knots. And some only turn off if they're above 18 kilometers and traveling faster than a thousand knots. So they've gone for the much narrower definition that it has to be both those things at once. If you could find a manufacturer who's a little bit more liberal with the international multilateral export controls, as long as you could get it to the moon without going above a thousand knots, it will continue to work. But the moon moves quite fast so the moon

is 384 400 kilometers away from the earth central mass and it gets all the way around the earth every 27.32 days which means the moon is actually moving at 3832 kilometers per hour. So the moon is going faster than the GPS regulations allow. Of course, that's relative to the surface of the earth. And the surface of the earth is also moving in the same direction as the moon orbiting, but not as fast. The surface of the earth is moving 1,668 ish kilometers per hour at its maximum. So that's like on the equator, you're whipping around that fast. And because it's in the same direction as the moon orbiting, if you subtract them off your relative speed of movement compared to the surface of the Earth, if you're on the moon, is around about 1,764 kilometers per hour, which is within 100 kilometers an hour of the cutoff point of GPS.

Oh my gosh. It is so close. It's incredible. It's just on the side where it will work so in theory you'll be just you'll be way over the altitude limit you'll be just inside the speed limit but given the inaccuracies like the error bars are huge if it worked it would know it's going below the relative speed threshold but because you're so far away from would know it's going below the relative speed threshold. But because you're so far away from the satellites, like we were saying, it would be so inaccurate.

It will accidentally think it's going faster than it really is. It would trip the cutoff because now you're above the altitude and it thinks it's above the speed and it will turn itself off. And it thinks it's above the speed and it will turn itself off. So in theory, if it worked, it would work. But because it doesn't work, it won't work. Which is arguably true of a lot of things. But it's particularly true in a very specific sense in this case. Matt, I am impressed. I am.

I really am. For good reasons? Yeah. I am impressed. I am. I really am. For good reasons? I feel like, yeah, you covered, from what I believe, you covered every angle. You covered one more angle than we needed for this dimension. Hey, good work. And that's why I personally believe that that problem deserves a ding. Ding. I thought you were going to say you got slightly lost in the time dimension and that took forever, but we got there.

Now we've found our way through and out of a very big problem. We decided in our new format to have a small, a small problem, which we're currently calling the dinglet. Yeah. I don't know if that's the best working to have a small problem, which we're currently calling the dinglet. Yeah. I don't know if that's the best working title for a mini problem. Big problem. You're trying to get a ding. It's a big ding.

A little problem. It's a dinglet. Like a singlet. Like a singlet, but a dinglet. I pitched that the side ding should be called the wing ding. It's like a supporting ding, but outpoted. So anyway, Nebazuradan, I hope I got that correct, has put into the

problem posing page that there's a podcast they enjoy, excellent, which has a running joke that involves one host asking the other, is this your card? That's very familiar. I'm glad they're posing this hypothetically for us. They've lost track of why

it's a running joke, how it started, why it's funny. They're too afraid to ask the host to explain the joke, at least directly, because they think it might ruin it. Bec, can you help them out? Yep. I can't remember. Nor can I. I can't remember how it started. I think all I can say is that I would argue as our defense that it is not a joke.

You are just trying to see if you can guess a card. I am now. Yeah. But it's kind of, because as a mathematician, I've also had to work as an amateur magician. That's just how it works. It's like the classic cliche, annoying magician. Is this your card? Like it like the classic cliche, annoying magician. Is this your card? Like it's shorthand for annoying magician.

In my opinion. I'm not sure what your take is. I think it did stem from something that we were talking about. I think it did originally start from something. And then one of us did it as a callback. Like just at the end of, probably at the end of the episode, I was just like, is this your card? Oh oh it probably was because i keep cards in my study and i probably realized i could grab a pack and hold the card up to the webcam which is the perfect like when you

i don't know if anyone else here if you're listening and if you've got your own podcasts but the ultimate like the kind of best practice for podcasts is if you think of a joke that only works for the other host on the video call and is lost on every single listener, definitely put that in. And so I just, just to make you laugh, would have pulled a card out and waved it at the camera. And we've just kept doing it. I don't know why we kept doing it. Yeah. We keep doing it because you still haven't guessed my card. Are you thinking of a specific card? Yeah. Yeah. I've got one. we kept doing it. We keep doing it because you still haven't guessed my card. Are you thinking of a specific

card? Yeah, yeah, I've got one. Ah, okay, okay, okay. When I realized we were still doing it, I just got a pack of cards and started systematically working my way through them. So that's what we're doing. I'm literally going through a pack of cards, one an episode, until I get to the one

that Bec says she's thinking of. That's the whole joke. And we don't know why either. But we're finisher completers. Because there'll be someone out there, there's someone listening to this right now who's like, it's because you did the, how could you not remember? And they'll be all annoyed. Yeah.

And I apologize. We need a listener who's either binging the episodes and so it's in their recent memory or they're strategically listening to them in reverse order, which means they will later on come across it. Can you get in touch? Go to a problem squared dot com, pick solutions from the drop down menu and send it in to us. Yeah. Yeah. And now it's time for the long awaited, a pudding squared.

For any new listeners, pudding is the name of my pet hamster. And we became aware that we've got several listeners who are, uh, of the younger variety. Children. We have a lot of children listening. Yeah.

They might, they might not label themselves as children. They might label themselves as adults at heart. We thought we'll include some problems for them. Age is just a number. That's our policy. And we do really encourage kids to solve these. We have had grown-up listeners come back with solutions, which by all means, you know, you're welcome to. I would say the grown-up solutions have outnumbered

the children's solutions. Yeah. There was one that we had where all of the grown-ups got it slightly wrong because they didn't do the maths thoroughly enough. And the one child, the wonderful Dexter, was the only one who did it properly. Hence the phrase classic Dexter.

But we got a message from Dave Lecompte on the problem posing page, specifically asking for more of Pudding Squared questions. And I thought Dave came up with a good one. So I thought I would use this one. So this is the next Pudding Squared question. It is, if pudding can run nine kilometers a day, how long would it take Pudding to reach the edge of the solar system? That's great.

I'm not saying this is like a trick question. It's not like, oh, he never would because he'd float off or can't breathe or whatever. Let's pretend that hamsters have the unique ability to run. Run in the void of space. Yeah. Putting is on an adorable spaceship that's got a treadmill. And when you run on the treadmill, the spaceship moves at that speed.

Yeah. Very simple. And because we're releasing these every two weeks now, and we want to give enough time for people to listen to them and get back to us with our answers, we will probably come back with the answer in two episodes time so that everyone has enough time to catch up. Roughly a month from now. Standard month for a pudding squirt.

And in any other business, AOB? We have breaking ding news. A-O-B. We have breaking ding news. We've heard back from Sleepy who posed the problem about their body clock being all over the shop. Oh yes, episode 026. They have renamed themselves Awakey. Beck, you've changed someone's life and their name. They are amazed at how thoroughly you answered their question and how much time you devoted to it

they say they took your advice and instead of trying to change their sleep schedule dramatically they're changing it gradually they went and bought a sunrise alarm clock so they've taken your advice to heart and they say the most important thing is they've just stopped stressing about it they've acknowledged they can't change it at once. They're just going to gradually work on it. And they're saying, even though that they're still, you know, sleeping in sometimes more than they want, they're a lot less mad at themselves. They like the fact there are other people out there, other bee people having the same problem. And just by acknowledging it, it's made their life better. So there you are. They consider it a problem solved. So Awakey, the problem poser, previously known as Sleepy,

is giving you a big old ding. So ding. Yay! Footnote, they also want to thank you, Beck, for acknowledging that telling someone to exercise more is one of the most annoying things someone can do. Second only to is this your card? I believe. And they've, they say they've definitely heard that when talking to people about their problem and their sleep. And so they just wanted to thank you for acknowledging that, that you don't just tell someone to

get out there and exercise more. Yeah, it sucks. There you go. I thank you Awakey. You're absolutely welcome. Well done. That has made my day. And we love all of our listeners equally.

We appreciate every single one of you, but we do like to give a special mention to our Patreon supporters by choosing three at random in Matt's randomizer. Big old spreadsheet. To thank in each episode. This time we'd like

to thank Christian Hellings, Bill, and in each episode. This time we'd like to thank Christian Hellings. Bill. And Christ. How would you pronounce that back? I'll try again. What do you reckon? I don't know. It's spelt K-R-Z-Y-C-H.

We've now tried to look it up and my new best guess is Krishav. I'm still pretty convinced I got that wrong. However, we are immensely appreciative of your, and indeed all our Patreon's, support. That was episode 028 of A Problem Squared. You have been listening to myself, Bec Hill, my wonderful co-host, Matt Parker. Thank you. And this has been produced

by the fantastic Lauren Armstrong Carter. Hey, Bec. is this your card? I don't have the camera on. Hold on. No, that's not it either. Oh, this is the wrong deck. Don't even.

Oh, I'm out of system. I can see why you gave up being a magician and went into. Nailed it. Teaching. Went to math. I think it's either the wrong deck or I've just absentmindedly picked it up and shuffled it while I was doing something else. I'm nuts. We're never going to make it. In the years following this podcast, Matt Parker never did fulfill his dream of going

to the moon. He now lives in the outback of Australia, curating novelty rocks. Beck Hill went on to become famous for her invention of the hamster rocket, which she first tested with pudding. He will be forever loved. Are I pudding?