121 = Bi-annuals and Diagonals

Speaker 1 Hello, Beck here, one half of a problem squared.

Speaker 1 Just jumping in before we start to say that we will be sending out our A Problem Squared Christmas cards, that's the digital or physical versions, to our Patreon supporters shortly.

Speaker 1 So you have until the end of November to sign up as a Patreon supporter if you would like our Christmas card either digitally or physically. Now, on with the show.

Speaker 1 Welcome to A Problem Squared, the podcast where I realized I've written the same introduction I've used before.

Speaker 1 But I'm doing it anyway.

Speaker 1 Wait, how long before? Tell you what, I'm going to do the intro and then we'll find out how long it's been. Okay.
And if how much, because I've forgotten and how much I overlap. Okay.

Speaker 1 Welcome to Problem Squared, the podcast, which is a bit like Daylight Saving Time. Oh.
Yeah.

Speaker 1 Because we're pretty sure it solves some problems. I'm not sure which ones.
Probably did a long time ago. And we keep doing it anyway in the hope it's helping someone somewhere.

Speaker 1 I'm Matt Parker, a lot like Daylight Saving Time in that I cause a lot of people to have to do extra arithmetic every now and then. Nice.
And I'm joined by Beck Hill, who is always

Speaker 1 on time plus or minus one hour. Yep, that's me.
There you go. I don't remember you doing this.
No, it's true. I just had this feeling.
I'm like, wait a minute. Have I done this before?

Speaker 1 So I messaged producer Laura this morning and I was like, have I done a daylight saving intro? And she's like, yes, you have, you dingus.

Speaker 1 And do you know what's worse about that? Because,

Speaker 1 Laura, I think, when did you start regularly producing for us? Beginning of the year.

Speaker 2 Yeah. So you did a daylight savers intro exactly six months ago.

Speaker 1 So good.

Speaker 2 At the last daylight savings.

Speaker 2 But because the clocks went the other way, it was slightly different.

Speaker 1 It was different clocks. We're going the other way.

Speaker 2 I feel like it's topical and you haven't actually repeated yourself.

Speaker 1 So what did I say last time?

Speaker 2 We were recording remotely because one of you was in Australia and one of you was in London.

Speaker 1 I think it was a lot of fun. And it was

Speaker 2 or it was just as you swapped over and we had real trouble organising records around the time difference and arranging stuff.

Speaker 2 So you said that daylight savings doesn't quite work timing-wise across all of the countries it covers.

Speaker 1 That's true.

Speaker 2 And also, when you introduced Beck, you said that she is like daylight savings because she brings a little bit of extra sunshine into everybody's life.

Speaker 1 And obviously, this time around, it's dark and cold.

Speaker 1 And you are right. I am usually off by an hour.

Speaker 1 Usually in the one direction. Normally in the one direction.
Yeah, yeah. And on this episode.
I'm going to work out which is correct. Bi-weekly or bi-weekly.
I'm going to go through some shapes.

Speaker 1 And we'll have any other

Speaker 1 brightness? Yeah.

Speaker 1 Any other business for any of the new listeners?

Speaker 1 How are you doing? I'm good. I like Daylight Savings every six months.

Speaker 1 I co-host the main stage at Brussels Comic-Con. You do? Every six months, that twice a year.
Yeah, yeah. Oh, my goodness.
With the other Matt my wife, Matt Highten. It was lovely.

Speaker 1 I do have to apologize. The lovely Denver friend of the show, who the first time I met Denver at Brussels Comic-Con, he introduced himself by holding up a plain card and saying, is this your card?

Speaker 1 And I was like, we are going to be friends forever. Denver also came sixth, I believe it was, in the World Barista Championships.
Oh, yes,

Speaker 1 we discussed Denver and their coffee making skills previously. Yeah, and he gave me some very nice coffee beans from the cafe he works at to pass to you, which I have left at home.

Speaker 1 I've about to say, I have not seen those beans back. No, no, I left them at home today because today I was, it's my birthday.
That's my excuse. Oh, wow.
I wasn't thinking about gifts format.

Speaker 1 I was wondering how long it would take before we played that card. Near immediately.
Well, I just figured it gives me an excuse.

Speaker 1 No one can get angry at me. Yep.
Were you not my gift to you for your birthday is? Not getting angry at me. No, those beans.
They're yours now.

Speaker 1 Oh, no, they're nice beans i and i plan on bringing them next time so that you can

Speaker 1 make them into coffee that you can drink okay fine they're your beans but bring them and i'll turn them into coffee

Speaker 1 but yeah it was lovely got to meet some very cool we had christopher lloyd again oh i was going to ask who the big stars were yeah christopher lloyd so that was nice as lovely as before yes we had jamie campbell bower

Speaker 1 who played Vechner in Stranger Things, the young Vechna. Young Vechner.
And he's in a bunch of other stuff. We've had him as a guest before, and he's so so easy to get along with, so easy to shout to.

Speaker 1 And so, it was really nice because it just feels like you're catching up with a mate to the point that Matt and I always forget how popular he actually is.

Speaker 1 And, like, there was already some fan accounts that have put up some footage of the interview and stuff. And we're like, oh, yeah, that's rude.
He's got like three million followers. Okay,

Speaker 1 just nice time. Nice time all around.
Oh, lovely.

Speaker 1 Also, got to catch up with Booty, who had come along to see my show in Edinburgh Fringe. Right.

Speaker 1 and had come with his friend who had heard of you. Yes.

Speaker 1 And I was like, yes, definitely go see.

Speaker 1 They went and saw you. Booty came along to the Comic-Con and I was able to ask him what he's been up to.
He's done a falconry course because he's scared of birds and wanted to overcome that.

Speaker 1 So I just love it. I love when people come up and they're like, hey.

Speaker 1 I've been listening and keeping up with what you're up to. It's nice.
It's really nice. Good, friendly folks.
Good to hear.

Speaker 1 How about you?

Speaker 1 Good. A small break in the tour.

Speaker 1 Well, we've got one more on the 1st of December, the big London one. Very excited about it.
Yes. Everyone, please come along.
Yes. Because the venue's 1,200 tickets.

Speaker 1 If it's sold out by the time we listen to this. Oh, there's no way.
There is no way. There's a zero percent.

Speaker 1 Maybe like on the day. Oh, and the tree's working.
There's an update. Oh,

Speaker 1 just in time for Christmas. Tree is online for Christmas.
Yep. We had a big work hang, a maker hang.
I had Seb Seb and Abby came around to the new studio. Oh yes,

Speaker 1 where we had space in the Nudio to spread out all 500 LEDs and we totally rewired the power supply for the LEDs. So we were here soldering and gluing and assembling and doing all sorts of fun stuff.

Speaker 1 Because if anyone saw my previous show, Humble Pie, Seb and Abby did the lasers in Humble Pie.

Speaker 1 And Abby is on tour taking care of the tree. And we had a wonderful day.
We had a full day just making electronics and testing LEDs and software. Then we got the hardware.
It's all now so lovely.

Speaker 1 Oh, that'd be a nice thing. Oh, it's so good.
I hacksawed down the base of the tree and I permanently attached it to a lazy Susan. So the whole tree rotates on the spot.
It's so

Speaker 1 it was a great day. Great day.
And it was wonderful use of having a bit of extra space in the Nudio. And then we've got the software.
I've updated my old software.

Speaker 1 We've got plans for better, but it's now, it's on its feet. It's just, it's taking along.
I've kind of forgotten how much fun it is to hang out with friends and build physical things.

Speaker 1 I mean, the issue I have is now already we're thinking, I was like, oh, we could do bigger, like we could get

Speaker 1 more lights on a bigger tree. That's generally how it works.
Yep, yep.

Speaker 1 Yeah, you've got to get to a point where people want you to do the Christmas tree lighting in a town, but you're running, like, it's a whole

Speaker 1 interactive thing. Yeah, yeah, yeah.
Yeah, yeah, where everyone in the town gets together, you know, like your pie stuff. Yeah.
And I've got some free time in about 2029.

Speaker 1 So we'll, we'll get, we'll get right onto that. Hey, don't say 2029 because you know for a fact you're going to get some.
Oh, someone will write that down. Don't write that down.

Speaker 1 But anyway, building physical things. The other thing I came across that reminded me how wonderful that was.
I went and spoke at a conference last week. Time has no meaning anymore.

Speaker 1 I think the one thing we've learned from this is your memory is

Speaker 1 I think I do more things than i can move into permanent memory that's the problem it's a bottleneck

Speaker 1 i was at a conference called demuxt which is for video devs people who software developers who work on video streaming services and i was the last talk of the conference and i was chatting about my adventures in coding and the like And you know what it's like when you go on to do your spot and then before you, which in this case is just a speaker at a tech conference,

Speaker 1 just like blows the gig out of the water.

Speaker 1 And then you're like, oh, why are they on right before me? I was on after someone who presented all of their slides off cartridges in a Sega Mega Drive.

Speaker 1 A Genesis, Sega Genesis for our North American friends. So he had a converter.
So he plugged in a mega drive on stage. Yeah.

Speaker 1 Had a converter because the old video out had to be converted to HDMI to go into the system.

Speaker 1 And then he had a series of numbered cartridges because you can't fit that much on a cartridge. Right.

Speaker 1 And he would put a cartridge in and turn it on and then a slide would come up and then he'd use the mega drive controller to advance through the slides

Speaker 1 on the cartridge. That's impressive.
And I was like, I've got to up my hardware game. That's incredible.
Engineer called Joey Parrish. And Joey also had a heavily modified cartridge.

Speaker 1 which he'd added some extra chips and Wi-Fi that could stream video to the mega Drive.

Speaker 1 So he could play. You have to run it through an encoder first to encode it into a format the Mega Drive can understand.
So is it like pixelated? Oh, you're so pixelated.

Speaker 1 There's a lot of interesting constrictions on color palettes on old systems because technically there's 256 colors, but you can only load so many in a palette per...

Speaker 1 Oh,

Speaker 1 it's not even per frame, per whatever.

Speaker 1 But he'd written an encoder that would pick a different color palette per scene so that the encoder has scene detection and when a scene changes that's when it would reload a new color palette that's which visually looks a lot better and obviously the sound is super compressed it is phenomenal this reminds me of when didn't michelle gondry the director helped build the software that turned footage into lego fell in love with a girl white stripes song the video for that they used a mix of genuine stop motion stuff with lego they had to like build it like physically build it based off the frames and the video and then teach the computer to understand what it had done.

Speaker 1 Right. So it could then classic machine learning to then do the rest.
Yeah, yeah, yep. Similar thing.

Speaker 1 Running it through a pointless bottleneck. Yeah.

Speaker 1 For the sake of it. Because the cartridges by default fit like 13 seconds of video on them.
Wow.

Speaker 1 So we had to have an extra thing that's what it's doing is it's constantly, there are two kind of memory chips on the cartridge that the console can be looking at, and whenever it's looking at one of them, this extra processor he's got like soldered in swaps the contents of the other one.

Speaker 1 And then by the time it looks at that one, it's swapping the first one. So as the chip's looking, the video drives looking at this one and that one, he's like, oh, this is all new.

Speaker 1 Oh, this is all new. And that's how it's constantly feeding in more of the video.
It's very, very clever. I love that.
It's like how you would distract. It's how you distract a baby.
Yeah, exactly.

Speaker 1 Yeah, yeah.

Speaker 1 It's a bit like how the angels would attack in Doctor Who. Exactly like that.
Whenever you look away, the

Speaker 1 memory content swaps.

Speaker 1 Well, that's fantastic. Yeah.
So that was my highlight recently was watching someone give a presentation entirely off Mega Drive cartridges. That's a good highlight.
All right.

Speaker 1 Well, should we do a show? Let's do a show. Start doing our own highlights.
Yeah.

Speaker 1 First problem was sent in by Ahmed, who went to the problem posing page at a problemsqued.com, selected problem from the drop-down menu and typed, hi Beck and Matt.

Speaker 1 I like to consider myself fluent in English. Well, so far, so good.
I agree. Oh, even though it's not their first language, yep.

Speaker 1 However, there's one word which has been really annoying me recently, which no one seems to agree on what it means. I mean, that's not narrowing it down, Ahmed.

Speaker 1 There are so many words in the English language you could be talking about, but it turns out they are talking about bi-weekly.

Speaker 1 Bi-weekly. And Ahmed complains that some people define it as twice a week, while others define it as once every two weeks.
Ahmed then decided to check bi-monthly. Oh,

Speaker 1 I'm so sorry.

Speaker 1 Did they check like biennial? Ah, they did. They say here, out of frustration, they checked the yearly version of it.
And this is where things got a bit more interesting.

Speaker 1 At first, they found out there's biennial. and bi-yearly, which seem to be used interchangeably.

Speaker 1 And they've also got biennial, which specifically means once every two years. So seems to mean there's hope.

Speaker 1 With this bit of knowledge, Ahmed then tried to go back to monthly and weekly to see if those variants made any more sense, but they had no luck.

Speaker 1 And so their problem for Ubeck is they wonder what was the first intended meaning of these words on record. And if we know this, can we definitively and conclusively say what's the correct use?

Speaker 1 I think specifically they're talking about bi-weekly here. And Ahmed said, as an added bonus, could we come up with new words for the second meaning? Interesting.
Beck, what have you got?

Speaker 1 Well, I did some research because this also bothers me, especially as this podcast is either bi-weekly or not bi-weekly, depending on.

Speaker 1 Depending on your meaning of bi-weekly. Yeah.
So this has bothered me as well. I'm sure it bothers many of our other listeners.

Speaker 1 So I did some of my own research and couldn't really find anything definitive. Can we just quickly clarify some words here? Yes.

Speaker 1 Biannial

Speaker 1 and biennial have different meanings. Biannual can mean the same as biennial.

Speaker 1 But biennial does not mean the same as biennial. Okay, so what does so biennial has one meaning? Biennial means specifically once every two years.
Got it. And that's like an E annial.

Speaker 1 Got it. Okay, biennial

Speaker 1 should just mean the other one. Yeah.
Twice a year. Yeah.
But

Speaker 1 can sometimes be used to mean every two years. Yeah.

Speaker 1 And bi-yearly can go either way, even though we got perfectly good other words that should make this unambiguous.

Speaker 1 Okay.

Speaker 1 But then there's just bi-weekly and bi-monthly are just doing their own thing. Yeah.

Speaker 1 Okay.

Speaker 1 So after doing some research, not being entirely sure,

Speaker 1 I thought, hang on a second. I know an etymologist.

Speaker 1 He's helped us on previous episodes. Bring him up.
So I reached out to Dr. Ben Whittle, who is Schnebwittle on Instagram.
We'll link to his Instagram in the show notes. And

Speaker 1 he said that it seems, according to his research, that twice a week was the original meaning of bi-weekly. Right.
He says even the...

Speaker 1 Oxford English Dictionary and Merriam-Webster Dictionary both agree it is ambiguous and confusing.

Speaker 1 Correct.

Speaker 1 No one's confused about whether or not it's confusing. Yeah.

Speaker 1 Merriam-Webster says, to quote: the chief difficulty is that many users of BiWeekly assume that others know exactly what they mean and they do not bother to clarify. Yep, yep.

Speaker 1 Now, I thought this was a fun little bonus fact.

Speaker 1 Dr. Ben Whittle also added that random etymology that I didn't ask for: the bi bit is related to bis bis in biscuit.
What? Which means twice cooked. How great is that? That's great.

Speaker 1 I had no idea that's where the term biscuit comes from. I want to give Dr.
Ben a shout out as well. He's very funny on social media.
As I was going through my flat and reorganizing it,

Speaker 1 I found in my costumes box, as we all have,

Speaker 1 a captain's hat, you know, like a ship.

Speaker 1 Captain's hat. Yeah.
A captain's hat. And it's got an anchor on the front.
classic, but it says Scientologist. Oh, and I don't know where I got it from, don't know where it comes from.

Speaker 1 I can't believe you own that. It's one of those things where you go, okay, I've no memory of where this came from.
And I posted about that on my stories, and Dr.

Speaker 1 Ben replied to me and said, Are you sure you didn't get it on a Tom Cruise?

Speaker 1 And it was the

Speaker 1 of all the

Speaker 1 word nerds. I had so many comedians respond, and none of them were as funny.
Tom Cruise? Yeah, an etymologist.

Speaker 1 that's where the yeah yeah so give him a follow so that's that's the official answer is that apparently biweekly did a the very first recording of it meant twice a week now i think that makes sense because

Speaker 1 i would use if i meant every two weeks i would say fortnightly we have a perfectly good word for that yeah before a video game took it over

Speaker 1 Yes. Do they say fortnightly?

Speaker 1 Well, fortnight is not really used in North America. But it should.
But I'm saying we're. It should be.
100 minutes. It should be.
And Fortnite used to confuse Americans.

Speaker 1 But now it's, please do correct me if you're a North American type of person. Now it's more closely associated with a game, fork knife.

Speaker 1 Yeah, so I say... American listeners, Northern American listeners, basically anyone in a country that doesn't currently use Fortnitely, if you're

Speaker 1 speaking English, please use fortnightly. Get that

Speaker 1 friendly. Yes.
Fortnightly, I say we call it fortnightly is

Speaker 1 every two weeks.

Speaker 1 Biweekly is twice a week. We just all agree that that's the case.

Speaker 1 If you say bi-weekly meaning fortnightly, that's on you.

Speaker 1 I mean, if biennial and biennial have taught us anything, having another option does not stamp out all the ambiguity.

Speaker 1 So you're thinking maybe we just

Speaker 1 phase out bi-weekly altogether. It's too confusing.

Speaker 1 We've got fortnightly. So what should the

Speaker 1 twice a week? Yeah.

Speaker 1 Tweakly. Tweakly.

Speaker 1 Twice weekly.

Speaker 1 Yeah. Tweakly.
Because you wouldn't say

Speaker 1 twice weekly to mean... Every two weeks.
Every two weeks. No, that'd be twackly.
Yeah, exactly. Tweakly and twackly.
Twinkly and twackly. Now it.
Okay. I'm now getting rid of fortnightly.

Speaker 1 Tweakly twice a week. This podcast comes out twockly.
Yeah, twackly.

Speaker 1 I'm on it. I'm sold.
Yeah, I'm sold. I don't think we're going to be twockly.

Speaker 1 Like, the amount of fun it is to say, everyone, wherever you are right now, say twockly out loud. It's really funny.
Twockly.

Speaker 1 All right, tweakly and twackly

Speaker 1 or twuckly if you want to. Oh, yeah.
But you can't, we'll accept all pronunciations. How can we be arguing about the pronunciation of a word that was invented about 60 seconds ago?

Speaker 1 Producer Laura, can we change the description of our podcast to say that it's released twockly?

Speaker 1 Yes, we can.

Speaker 1 Okay,

Speaker 1 great.

Speaker 1 Now, but that means the description of our podcast will be forever. Like, let's say Twockly catches on.
Yeah. That would be the original citation of first use.

Speaker 1 That's the one that would get notated in all of the weekly. Yeah, yeah.
First use 2025

Speaker 1 description of a problem squared. Yeah.
So if we could get just some more people using it in an official setting. Yes.

Speaker 1 So that there are more instances. If it's just us, I'll go back to Dr.
Ben and see if he can.

Speaker 1 We'll see what Dr. Ben says about our invention.
So we've got, well, firstly, we need Ahmed to say whether he appreciates Twockly. tweakly and twackly.

Speaker 1 Now, obviously, we've got the monthly versions as well.

Speaker 1 Now, interestingly,

Speaker 1 most months are roughly four weeks long. Oh.

Speaker 1 So if you were to do something fortnightly.

Speaker 1 You're already doing it

Speaker 1 twice a month. Twonthly.

Speaker 1 I say that. There are sometimes moments.
Where we have three episodes come out. Yeah, because they're four point four and a quarter weeks long.
Yeah.

Speaker 1 Yeah.

Speaker 1 So that, so, so, twice a month is subtly different to twinkly.

Speaker 1 Yeah.

Speaker 1 So if you do have something that specifically comes out twice a month, not every two weeks, but twice a month. Yes.
Because we're not twice a month. Yeah.
We're twockly.

Speaker 1 That's right.

Speaker 1 And twice a month would be

Speaker 1 twinthly.

Speaker 1 Even you weren't confident.

Speaker 1 Tweakly and twackly. So then we need twinthly and twonthly.

Speaker 1 Officially, we should say

Speaker 1 bi-weekly means twice a week and fortnightly means every two weeks. In the same way that biannually would mean twice a year, biannually would mean every two years.

Speaker 1 However,

Speaker 1 people will still get confused.

Speaker 1 Hence, tweakly and twakly. Twiggly, twackly.

Speaker 1 So

Speaker 1 it would obviously be tweally and

Speaker 1 twale.

Speaker 1 Are there? Are there?

Speaker 1 Because we've got the word to. Twally.
We're using two for twiggly and twackly. Yep.
By,

Speaker 1 meaning to,

Speaker 1 is around. Is there anything else that means to?

Speaker 1 Duo, jewel. Duo.

Speaker 1 So maybe we could use duo so we could use that for monthly just to keep everything crisp. So you got dumprey.

Speaker 1 Which one is Dumfley? The one it sounds like.

Speaker 1 Obviously.

Speaker 1 Dawfly.

Speaker 1 They're very different words.

Speaker 1 Okay, maybe that's not going to work.

Speaker 1 What we could do

Speaker 1 while we're making sweeping reforms

Speaker 1 is

Speaker 1 make

Speaker 1 months four weeks long.

Speaker 1 Your.

Speaker 1 There's a little bit of scope creep happening here. Your answer is to completely reinvent the calendar.
Yeah, retool the calendar. It's about time.
Yeah.

Speaker 1 Sure.

Speaker 1 Why not? Thank you.

Speaker 1 13 four-week months. It's all I'm asking.

Speaker 1 I like tweakly and twakly.

Speaker 1 Yep.

Speaker 1 So twakly and twonthly.

Speaker 1 and twonthly. Are very similar periods of time.
And then tweerly

Speaker 1 and twaley.

Speaker 1 You made it worse. It's worse now.

Speaker 1 Look, that's my answer.

Speaker 1 And as far as I'm concerned, Ahmed is the person who I am trying to appease here. Now, if Ahmed turns around and says, as someone who speaks English as a second language, that is too similar.

Speaker 1 That is too confusing. Okay.
Yep. But I would say say it's still better than having one word that means both agreed agrees

Speaker 1 agreed fine i'm happy for ahmed to be the adjudicator of this what what are your i'm on board with twiggly and twarkly

Speaker 1 i feel like we've nailed that yeah

Speaker 1 i don't think i don't think anyone's gonna have any notes uh-huh i just think

Speaker 1 Biannial and biennial already exist and people get it wrong. There's not much more we can do about that.
We've got two perfectly good words. I don't know.

Speaker 1 The monthly, I think we just change the length of the month. I think that's the

Speaker 1 easiest solution here.

Speaker 1 Does that change the length of the year?

Speaker 1 No,

Speaker 1 it'll be what you would need to do

Speaker 1 is

Speaker 1 have 13 months, each with four weeks, and that's your 52 weeks. Which means that we need a word

Speaker 1 for

Speaker 1 26 weeks.

Speaker 1 Yes. Which would mean twice a year.
Yeah, yeah, yeah, exactly. Yeah, yeah.

Speaker 1 Which would be halfway through a month. If you were releasing, let's say this show, let's say we put out

Speaker 1 a problem squared every 26 weeks.

Speaker 1 Is there ever a chance that that means that it would be

Speaker 1 more than twice a year or less than twice a year? Got it. Yes.
Eventually, we would put out three in the same calendar year.

Speaker 1 Right. So that is an issue.
It's the same thing. So we have to change the year.

Speaker 1 We have to have a bonus day. You have another made-up day.
Or do we just say years are now 52 weeks, exactly?

Speaker 1 No, we can't do that because we're tethered to the orbit. Oh, why do we have to do that? I know.

Speaker 1 It's a bit like daylight saving in that regard. Oh, God.
The Western understanding of time. It's the worst.
It's too consumerist. Yeah.

Speaker 1 At the end of the day, everything is just going to deal with the orbit at some point. Okay.
Yeah. It's where you put the fudge factor.

Speaker 1 I love that show.

Speaker 1 You know, fudge factor. That would be a really great, like, Master Chef meets like expat.
Like, you've got to make really good fudge. Yeah.
While I'm on stage. Yeah.

Speaker 1 Yeah. I'm on board.
I would judge that.

Speaker 1 It would come out twonthly.

Speaker 1 Stop trying to make twenty a thing.

Speaker 1 I'm looking forward to all the mean girls' memes now.

Speaker 1 So, Ahmed. All of that.

Speaker 1 Let us know.

Speaker 1 Yeah.

Speaker 1 Now, look, there's going to be a lot of people writing in, suggesting. Better suggestions.
I say better using verbal quotation marks because there's no way you're going to be tweely twokly

Speaker 1 twinkly twonthly

Speaker 1 or tweally and twall twirly tweally can do better than that

Speaker 1 so

Speaker 1 don't don't bother sending your better

Speaker 1 there's not you're not gonna win you should but

Speaker 1 oh you'd have to be so sure it's better than that

Speaker 1 But if you do agree with me, just start putting it out there. Go to the problem posing page, select solution, and just tell us about the different ways in which you've used it.

Speaker 1 Put it in the problem squared Discord, put it in the problem squared Reddit. Great.

Speaker 1 Ahmed, get back to us.

Speaker 1 Let us know if it's a

Speaker 1 twing.

Speaker 1 Is that dinged twice a problem? Yes, or a ding every two problems. No, that's a twong.
Oh, sorry.

Speaker 1 This next problem is from Yoop.

Speaker 1 Y-O-U-P. I hope I'm pronouncing that correctly.
They say, my son asked me the other day what the line was called between two opposing corners of a cube.

Speaker 1 All I could come up with was that in a circle, you would call it the diameter. Yes, in Dutch, it's the same name.
Ah, it's a Dutch name.

Speaker 1 Google didn't help me out, but I'm pretty sure between the two of you, you know a lot of measures other than Bex.

Speaker 1 Yes, also Dutch. Yeah.

Speaker 1 Thanks for all the joyful hours of ear noise.

Speaker 1 Oh, you, what a wonderful

Speaker 1 that's why our description says releasing ear noise. Twockly.
Twockly.

Speaker 1 I like this question because this is the exact sort of thing I would think, hang on, what is that called? And not.

Speaker 1 Yeah. It's a real.

Speaker 1 What's the name of that thing episode? Yeah, because what would you say? Because obviously in a circle, circle it's the diameter yep would you say diameter in a sphere

Speaker 1 in a sphere yes okay

Speaker 1 anything circle sphere etc

Speaker 1 which are all part of the one big family you'll say diameter piece of cake

Speaker 1 people will sometimes uh contrive diameter to mean things for other shapes right

Speaker 1 And so it's not meaningless with other shapes, but there's less of an agreed upon that's the name. Like bi-weekly.
Like bi-weekly. Yeah.
Oh, actually, I'm going to grab. I've got a cube.

Speaker 1 It's right behind you. I'm just going to grab it now.
I 3D printed a cube, which is like

Speaker 1 the biggest misuse of the abilities of a 3D printer. Yeah.
But hold it. It's a really satisfying cube.
Like, if you ever want a really nice cube of a very specific size, look at that. That is.

Speaker 1 It's quite sharp on the corners. Real pointy corners.
It's a good cube. It's a good cube.
But the reason I printed that cube was. A tesseract.

Speaker 1 A tesseract. Oh, not quite.
A lot of cube. Lots of tesseract.
A 4D cube.

Speaker 1 So if you went up a dimension, that would be

Speaker 1 even more cube.

Speaker 1 Whoa. Yeah.
Well, you know, you're looking at that cube, and you could think about it. You're looking at six squares carefully arranged.
Yes.

Speaker 1 A tesseract is a 4D cube, which is eight 3D cubes carefully arranged. So it's...
A very similar thing, one dimension up.

Speaker 1 Sure. There you are.

Speaker 1 Every time you go into four-dimension chat, my brain's like,

Speaker 1 that's why I gave you a thing to hold. Thank you.

Speaker 1 I see what you're doing. You're distracting me on one side while you move on the other.

Speaker 1 But the reason I 3D printed that cube was

Speaker 1 people recently found a shape that can't go through itself called the NOPIT.

Speaker 1 And so I also 3D printed this cube, which if I reassemble it, here we go. This is a cube in two pieces.

Speaker 1 pieces so that actually I hand this over to you as well if you want to ever play with this one so that's a cube that's exactly the same size as the white cube so I wanted to have two identical cubes but one comes apart and one doesn't so you should be able to remove the inner section of the green cube yep and the identical sized white cube will fit through that ring section ah so what we're demonstrating is a cube is able to pass through another cube.

Speaker 1 There you are. Look at that.

Speaker 1 That's very of exactly the same size. Because a long time ago, in a very old episode for near when we're first starting out, was a Halloween episode where

Speaker 1 I carved a pumpkin

Speaker 1 pumpkin of the same size could go through it, I believe. That's the one.
I bought two as identical as I could find pumpkins to make this is called Prince Rupert's cube.

Speaker 1 And the property of going through itself is called being Rupert. That's the property of this.
Why?

Speaker 1 Because a guy called Prince Rupert came up with the question. Okay.
And, like, I think the 1600s, 1700s, ages ago.

Speaker 1 Rupert was just like, hey, I wonder if a cube can go through itself. Sure.
And the answer was yes. Prince Rupert's like, I'm just going to think about ridiculous maths and science things.
So I say.

Speaker 1 Pretty good going. Yeah, if you're going to use your privilege.
Bingo.

Speaker 1 So we call it the Prince Rupert Cube. The property of going through itself is called being Rupert.

Speaker 1 And so I made a Rupert pumpkin for Halloween 2021. He's going, Rupert!

Speaker 1 And so I made a video about a big Rupert. So a friend of mine, a guy called Tom Seven, was working on proving shapes exist that aren't Rupert.

Speaker 1 He called them the property being Nopet.

Speaker 1 Excellent name, Tom.

Speaker 1 And he's been working on it for ages. And I saw, I was in, he's in the US.
I saw him when I was in New York a little while ago. And so back then he was working on it.

Speaker 1 And since then, someone else beat him to it. No.

Speaker 1 Unbelievably, a different team of mathematicians working on the same problem he was working on with his mates. And so out of nowhere.
And they converged on almost identical methods.

Speaker 1 But he was trying to prove that a snub cube is nope it. Sorry, a snub.
No, I thought you might say that. So guess what I've got for you, fresh off the 3D printer plate? Oh,

Speaker 1 you're going to snub me. Okay, so I'm currently holding.

Speaker 1 Oh.

Speaker 1 So the best I can describe is if you could turn a cube into a

Speaker 1 constantina where you pull it out by twisting it and it creates a bunch of triangles in between. Yeah.

Speaker 1 And then, so is there a way that you can twist it and the triangles would fold into each other and go back into a cube?

Speaker 1 Could you make that with paper? Oh, you would need to have some edges not joined, and I don't.

Speaker 1 My instinct is there would be space for them all to fold up out of the way, but I couldn't guarantee that.

Speaker 1 Well, we could look into it. Someone's got a project.
Yep. So that's a famous shape called Snub Cube.
I'm a big fan of it. And what Tom Seven was trying to do is prove that

Speaker 1 the snub cube is not.

Speaker 1 We will put pictures of all of these on Instagram, Twitter, and Blue Sky.

Speaker 1 Actually, on the shelf over there behind you is Tom seven's not

Speaker 1 if you want to grab that ridiculous looking shape i wasn't expecting this to be a whole segment about nopets but given we did cover this topic 2021 this is like within the problem squared universe

Speaker 1 notepit is is you know an active

Speaker 1 thing we just we talk about oh yeah i i also i like that

Speaker 1 Sometimes because I imagine you're doing a video about this,

Speaker 1 which is why you have three. That's why I've printed them all, all back.
I like that sometimes this podcast serves as a sort of director's commentary.

Speaker 1 It's behind the scenes. I think

Speaker 1 they support each other quite well.

Speaker 1 So this is what I'm holding. Feels like it's almost got the vibe of like a cartoon diamond without a pointed bottom, but the triangular shapes that would join up are not.

Speaker 1 equilateral isosceles even they're sort of a bit odd and then one of them isn't even a triangle And then you've got a pentagon at the top and the bottom. Yeah.
Yeah. What a strange shape.
Yeah.

Speaker 1 So that's NOPAC candidate number 214. So this can't pass through itself.
We believe. No one's found a way for it to pass through itself.

Speaker 1 So I forget exactly how many on the order of six trillion attempts using Tom Seven's code. There's no way to find how that will go through itself.

Speaker 1 And when he applies the same code to shapes that can go through themselves, that finds the solutions in fractions of a second, right? So, the fact that it cannot solve this one,

Speaker 1 we're almost certain that it's NOPIT, but it's not been proven. Yeah, and the snub cube,

Speaker 1 we're almost it cannot find a solution for that, so we're pretty sure that's nope it.

Speaker 1 And Tom Seven was working on proving because you can't just check loads of times, you got to prove you haven't like you've not missed the one solution. Now, most

Speaker 1 I would argue that most things are NOPIT

Speaker 1 that's very true. we're talking specifically convex polyhedrons so shapes with flat faces and they don't have any dents in them

Speaker 1 and so classic polyhedra is this one of those examples where

Speaker 1 it's not necessarily obvious as to how

Speaker 1 this is useful

Speaker 1 oh it's very obvious that it's not useful but carry on but the

Speaker 1 processing power, I mean, not just like

Speaker 1 computational, but also just human processing, but the way you have to think about this problem

Speaker 1 does then mean it tends to play off into other ways in life. We tend to find uses for things or whatever that we're like, oh, turns out that's really useful to have worked out.
Agree.

Speaker 1 It feels very unlikely this specific knowledge about nope-pitness will have practical applications, but it cannot hurt for humans to have a better general understanding of 3D shapes.

Speaker 1 And potentially, people working on the problem could come up with new,

Speaker 1 you know, computer numerical method techniques, or then take what they learned from this and apply it to a different problem that's useful in terms of their, you know, solving problem skills, et cetera.

Speaker 1 In general, it's not like this was a problem we desperately needed the answer to.

Speaker 1 No, but in the future, when

Speaker 1 we are under threat because AI wants to put us through ourselves.

Speaker 1 Something like that. Yeah.

Speaker 1 Yeah.

Speaker 1 And I mean, the point that Tom Seven makes is the notion of a polyhedron is pretty standard.

Speaker 1 So were there aliens who have also evolved to the point of doing mathematics, they definitely would have discovered the snub cube. Because these sorts of shapes just kind of drop out of maths.

Speaker 1 And the idea of can something go through itself is also an interesting question that humans have been wondering for centuries. This feels like a Netflix show.

Speaker 1 Is it cake? Or like that YouTube series, will it blend? Yeah, will it? Nope.

Speaker 1 Will it Rupert? Will it Rupert? But I imagine aliens have asked the same question about is something they'll have a different name for it, of course.

Speaker 1 But this concept of will a polyhedron go through itself is a sufficiently obvious. question

Speaker 1 that other intelligent species probably ask the same thing, which I think is an interesting thought experiment.

Speaker 1 Anyway, this is a very long way to say the people who beat Tom 7 to the punch, instead of Tom 6, wasn't it? Tom 6, you have to. I knew it.

Speaker 1 The higher-ranked Tom. Instead of using a pre-existing shape.
So the one you're holding, Tom ran his code and then also generated random shapes to find ones that couldn't be solved.

Speaker 1 And that's where that came from. But then he used a pre-existing shape, the snub cube, to try and prove something is definitely not.

Speaker 1 The other people who beat him, they manufactured their own notepit candidate in such a way that it would make the proof easier, which is a very clever way to go about it.

Speaker 1 And they were then able to prove the shape they generated is not.

Speaker 1 Ah, so very, very interesting maths. So I'm making a video on that.
This wired 3D printed a cube.

Speaker 1 And there you are. So that's the Rupert update.

Speaker 1 Four years later, which is a long way

Speaker 1 to talk about

Speaker 1 the actual question. Oh, yeah, I totally agree.
The problem sent in.

Speaker 1 I forgot about the question.

Speaker 1 But speaking of things we don't know the answer to, the problem sent in by you does actually also relate to an unsolved problem in mathematics. Now, it's not the name.
We have a name. Okay.

Speaker 1 So when you look at a cube, there's a couple of different diagonals you can talk about.

Speaker 1 Because you could have the diagonal that's just on a face that goes from like a corner to another corner on the same face. Yep.

Speaker 1 And we just call that a diagonal, or maybe a face diagonal, if you want to get specific. The diagonal that goes from one corner to the opposite corner

Speaker 1 is called the space diagonal,

Speaker 1 which is a great name.

Speaker 1 Or spiagonal. Or spiagonal.
It's not called that. So the space diagonal.
It is.

Speaker 1 We can't just keep cracking out new words anytime we want. Well, that's how everyone else does it.
That's so true. Can we get some reverb on this as we go? Space diagonals!

Speaker 1 Yes, we can.

Speaker 1 Diagonals in space. Yes.
So, oh, the Rupert cube follows pretty much the space diagonal when it goes through the other one. Yes.

Speaker 1 And that's why there's enough room, because if you look down the space diagonal, a cube looks like a hexagon. Yeah.

Speaker 1 And then you put the square face, the square face of a cube is smaller than the hexagonal view down the diagonal. And so the open problem about the space diagonal

Speaker 1 is people have found.

Speaker 1 Now we're going to relax the definition of cube. So we're just going to talk boxes in general, cuboids.
So it doesn't have to be the same length in every direction.

Speaker 1 You have three different lengths for different directions. People have found cuboids that have integer length edges, the three different edges, so they're all whole numbers.
Okay, yep.

Speaker 1 And all the diagonals, all the face diagonals, are whole numbers as well. It's like the 3D version of a Pythagorean triplet.
Okay.

Speaker 1 They're called Euler bricks.

Speaker 1 Right. So an Euler brick has whole number lengths and face diagonals.
No one has ever found a perfect cuboid where the space diagonal is also a whole number length.

Speaker 1 And just to double check that I'm understanding this correctly,

Speaker 1 by whole numbers, you mean

Speaker 1 like if I was to

Speaker 1 do a cuboid

Speaker 1 where it was like 3 by 7, the diagonal might be then like 4.6, and it's the decimal that makes it a non-integer. It makes it right.
Yep. So if your cube is like 1 by 1, the diagonal is 1.4.
Got it.

Speaker 1 But

Speaker 1 if instead your cube was like 3 by 4, the diagonal would be exactly 5. Nice.
Oh, that's lovely.

Speaker 1 No one's ever found a perfect cuboid where the space diagonal is also a whole number. But no one's ever managed to prove it's impossible.
So we don't know.

Speaker 1 It might exist, it might not.

Speaker 1 That's the mystery of the space diagonal.

Speaker 1 And then you put reverb on that. I loved all of that.
There you are.

Speaker 1 I mean, I could have answered it in literally two words. I could have just said space diagonal.
Oh, less fun. But I feel like, you know what?

Speaker 1 Not enough ear noise. Not enough ear noise.
Yeah. And Yoop specifically praised the ear noise.
Yeah. There you are.
So Yoop, let us know if you... I mean, I think it's pretty

Speaker 1 pretty I mean that is the name. That's the name.
I've given you the name. Do you know what?

Speaker 1 On behalf of you, I'm going to give that a space dig.

Speaker 1 Hang on. Sorry.
I'm going to give it a. Spurs dig!

Speaker 1 And now it's time for any other biannialness. Albert wrote in.

Speaker 1 When we were tackling the problem about the snake and the probability of rolling snake eyes, we referenced the snake draw, but we didn't know what it meant.

Speaker 1 Albert knows what it means, which is why Albert went to problemsquared.com and picked solution and told us a snake draw is when two captains take turns to pick teams.

Speaker 1 But to negate the advantage of picking first,

Speaker 1 instead of alternating Captain A, then B, then A, then B, then A, then B, you do Captain A picks first, and then B picks twice, and then A twice, and then B twice. Oh, interesting.

Speaker 1 So it goes A, B, B, A, A, B, B, A, A.

Speaker 1 Now.

Speaker 1 First of all, Albert, thanks. That's what a snake draw means.

Speaker 1 There's a sequence in maths called the 2A morse sequence. Ah.
And 2A morse is to solve the same problem.

Speaker 1 But it goes A, B, B, A. But then if you just keep doing that, it's still not exactly fair.
So, what you do is you then flip it. So, you do A B B A, and then you do B A A B.

Speaker 1 It's very close to what you'd call in drumming a paradiddle. Really? So, if I said right, left, you know, meaning I'm holding the sticks, okay, yep, but I'm going to change it for AB.

Speaker 1 So it'd go ABAA BABB, ABAA, B-A-B-B.

Speaker 1 I believe you.

Speaker 1 I leave you.

Speaker 1 But then you take the whole sequence again and flip it another time. Oh.

Speaker 1 So then, so it goes A, B, B, A, and then it goes B, A, A, B, and then it goes B, A, A, B, A, B, B, A, and then you take that whole sequence and flip it.

Speaker 1 And as long as you need a sequence,

Speaker 1 you just take whatever you've, the first one. And if you scale it right back, it works in the beginning because you do A, and you flip that and add it on the end, you get A, B.

Speaker 1 And you flip that and add it on the end, you get get ABBA, and then it just builds up recursively the whole way through. So,

Speaker 1 there you go.

Speaker 1 We also heard from Rob,

Speaker 1 who says, I was listening to your episode 118 about kids' names that can be grouped together, and it made me realize that my wife's and kids' names all overlap and come together into a megazord name.

Speaker 1 I love the use of megazord.

Speaker 1 I'm here for it. I love it.
So, Rob says, The wife is Lisa. The kids are Sam and Eli.
Oh, yeah. So the LI overlaps with Lisa nicely.
Yeah. So we've got...
Or Eli, Sam.

Speaker 1 That's very cool. Yeah.
It's just the two kids' names in a row has the mum's name in the middle. Yeah.
That's really nice. And I love that you realize that.
Rob, you're letting down the team.

Speaker 1 May I suggest changing your name to Amy, which would fit on the end quite nicely.

Speaker 1 Good point.

Speaker 1 Or.

Speaker 1 at the beginning, Mel. Oh, Mel would

Speaker 1 producer. Laura just mentioned Mel.

Speaker 1 And then it would be Melisam.

Speaker 1 Come on, Rob. Melisam does sound like something you would take to like up your cortisol levels or something.

Speaker 1 Take

Speaker 1 Twockly

Speaker 1 to improve.

Speaker 1 But not Tweakly.

Speaker 1 Do not take Melisam Tweakly.

Speaker 1 Cannot be held responsible for the results.

Speaker 1 Just someone running out of a bathroom, covered in hair.

Speaker 1 Rob, or Mel slash Amy, also

Speaker 1 said that they loved your show in Edinburgh, Matt. Ah, that's very kind of them.
Yeah.

Speaker 1 But you're still touring? Still touring. Come and see me.
Link in the show notes. Please come and see the London gig.

Speaker 1 Well, we've reached the end of the second ever Daylight Saving Special Edition of A Problem Squared.

Speaker 1 All that's left is to thank a few people. Thanks to you, the listeners, for listening, which by definition you are right now.
We really appreciate that.

Speaker 1 And thank you for all the five-star reviews you give us on multiple platforms. Tell your friends.
And huge thanks to our Patreon supporters who not only listen, but hand over their hard-earned money.

Speaker 1 They put their money where their ears are and they keep the whole thing ticking along.

Speaker 1 And to thank them, among other things, they do get an exclusive monthly podcast, which is not as good as this one. I would argue it's better.
Would you? I'm a Wizard, I think, is.

Speaker 1 It's something. It's definitely more something than this one.

Speaker 1 I think it's raw and unadulterated.

Speaker 1 We agree with that. And we draw different conclusions from it.
So,

Speaker 1 in addition to all of that, we pick three names of our Patreon supporters completely at random. And there's no memory, by the way.
And people say the name hasn't come up yet. It's totally random.

Speaker 1 And people come up multiple times. That's randomness.
Yeah. Them's the breaks.
The only way to get involved is to get involved. You could create multiple multiple times.
Yes.

Speaker 1 If you signed up several times. Yes.
And then you increase your chances of having your name read. Buy more tickets in the lottery.
The winners of which

Speaker 1 this time

Speaker 1 include Jay Honad

Speaker 1 Ams

Speaker 1 Yah

Speaker 1 Need Dem and

Speaker 1 Shah Lie

Speaker 1 Good Life

Speaker 1 So that's it for the episode. Thanks for listening.
I've been joined by Bekel. I'm Matt Parker and producer Laura Grimshaw is a bit like Daylight Saving in that

Speaker 1 she keeps us on time. Thanks for listening.
Bye.

Speaker 1 Hmm.

Speaker 1 F two.

Speaker 1 F

Speaker 1 two.

Speaker 1 Miss.

Speaker 1 I knew my luck would run out eventually.

Speaker 1 And I'm gonna. Ooh.
I finally completed my diagonal pass.

Speaker 1 I guess A10.

Speaker 1 Oh, my goodness.

Speaker 1 Oh, that's interesting. I don't think there is any way I can win this unless something goes horrifically wrong.
Horrifically wrong with what's about to happen. Yeah.

Speaker 1 This is where you find out that I've illegally placed one guy in the back of the bottom of the bag.

Speaker 1 One of them's sticking out of the side of the thing.

Speaker 1 Oh, Lucky, a real lucky. You have no idea how much I was hoping you would go for J1.

Speaker 1 Well, happy birthday to me.