A Problem Squared - 023 = The Weight of Words and Graphene for Turds

Episode Date: September 30, 2021

Yes, that's right. The Weight of Words and Graphene for Turds. In this month's episode... If graphene was rolled to the size of a loo roll, how long would that roll be? What is the weight of the ink in Bec's book? Plus! The REAL answer to Earth's longest line of sight. And, Bec and Matt are reunited after two years apart. If you want want EVEN MORE from A Problem Squared, find us on Twitter, Instagram or Patreon. And as always, if you've got a problem or a solution, hit us up on our website www.aproblemsquared.com.

Welcome to A Problem Squared, the podcast which is not dissimilar to a delicious cup of coffee. You think it's going to solve all your problems and it doesn't, but you still come back to it time and time again because it's so relaxing and comforting. I'm joined by the host of A Problem Squared, Bec Hill, the espresso of the problem solving world. Oh, yeah. Yep, small, lots of energy. But people don't see the preparation and pressure going on behind the scenes to produce that final result. And it is not pronounced with an X.

Nice. Thank you. I'm very impressed with that. Don't get that wrong. And I am Matt Parker, the overly complicated cold drip. You know I say that out loud. It's more insulting than I expected. What I'm saying is a lot of people say is all that effort and detail

and unnecessary attention to detail. I can't really taste the difference. And thank you for joining us. That was an adequate intro. I lost faith when I called myself a cold drip. A cold drip. Not inaccurate, I would say. I see that very much as my role here.

I mean, I'm trying to think of a compliment to do with coffee that would up that, but I don't know enough about coffee. Like, and you're not bitter, but cold brew might be bitter. I don't know. That's true. I'm not bitter. I'm well extracted. Yes.

I don't want to show off about that. On this episode, I'll be running the numbers on graphene toilet paper. I'm going to find out how much a book would weigh without ink. And I will be dealing with the many, many of you who had opinions about my previous solution to how far you can see on Earth. Let's get to it. Yeah. So, Bec, we're here in person.

Yeah, if you're listening to this and you're like, this sounds slightly different, and why is Bec reacting so quickly to Matt's facial expressions that you can't see? Where's that lag? We've come to know and love. We're in the same room together. Well, it's like episode two was the last time we were simultaneously.

I know, right? And we're in 22 now. Isn't that? No, 23. 023, this one. Yeah. We went like 20, 21 episodes virtual. We were ahead of the curve on that.

Yeah. We went virtual early 2020. Yeah. And now here we are. Wow. What a journey. Oh, my goodness. And for what?

I'm getting back in the cupboard. So at the end of this podcast, vote on if we should send Beck back to the cupboard or if. Does it detract or enhance the podcast to have us simultaneously in the same room? All right. Get us on socials. At? At.

A problem squared. Just say cupboard or no cupboard? Yeah, don't give any context. Cupboard or nubbered. That's what we want. Cupboard or nubbered. Nubbered. Nubbered.

It's one vote for nubbered. Do you spell that cupboard but just with an N? Or do you get rid of the P? I think you keep it I think nubbid is N-U-B-B-A-R-D No, we've got the P because it's like nup That's the Oh, of course

That's the response I'm sorry, yeah I should have known That's the joke I just realised now Well done Thank you I'm impressed So anyway, other than the highlight of hanging out with me this weekend

How have you been? I don't know why I'm laughing when you said highlight. I've been good. You've been good? I've been good. So since the last episode, Makeaway Takeaway aired. You're now officially a TV star. Yeah.

And thanks to everyone who's commented on it. It's good. It's really fun. I didn't mean to say that with a tone of surprise, but like it's children's TV. I was like, okay, I'll probably like it because Beck's in there. Yeah. It's interesting how many people have said that, like I'm not surprised it's good for kids,

but they're surprised that it's quite watchable for adults. Yeah. I don't know how much I need to make it clear that the stuff that I do, I very much do as if it was for me and then make a child appropriate. Oh, 100%. Yeah, yeah. And I've seen you do both adult like stand-up sets and your kid stuff. Yeah.

It's not dissimilar. Well, that's it. Exactly. If you like my stand-up or anything that I do aimed at adults, you're going to like the stuff that I do. The secret is Beck is always 100% Beck. Yeah, that's it. Yeah.

This is it. Absolutely. And I remember someone said to me when I announced that it was coming out, you know, they were like, oh, well done, congratulations. I mean, I won't be watching because I'm too old for it. And all I could think was, oh, like how, like what a sad thing to say that you're too old. I've aged out of your.

Like I think you can be too young for something because mentally you're not prepared for stuff yeah if it's to watch or read something you're never too old if someone just shakes car keys i'm like i'm fascinated yeah you know shining movie things still i'm i'm on board yeah that's how i uh got you into the office we um because we uh lucy and was like, oh, Beck shows out. And so we brought it up on the ITV Hub player thing. Yeah. It also airs on CITV.

And we did that thing where we're like, oh, we'll have a quick skip through and just see what the show's like. And so we watched a few bits of episode three. But that came to a natural conclusion. And I went off into the kitchen to get something. And I came back. And Lucy's just still there happily watching away. Yeah. She's still watching back and she's like, no, this is great.

Yeah. It's really. She was engrossed. It crams a lot in. Even I'm surprised. It was. It was better paced than I expected from a children's TV show. Yeah.

No. Well, thank you. Yeah. Yeah. I was impressed. Oh, good. I'm glad. Thank you.

I really enjoyed making it. You don't need my approval, but I enjoyed it. I'm hoping we get a second season. That would be delightful. A couple of other things. Oh, I've been doing Animator Z. Oh, yes. Which is the anime.

If anyone listening, it's not competing. You can listen to both. I can't believe you're doing another podcast. Have you seen how many podcasts I'm subscribed to? I've lost track of how many you do, let alone listen to. But if anyone, if anyone, uh, uh, listening like Sound of May or is wanting to get into one, we've just started Vinland Saga watching one episode at a time and doing deep dives. Vinland Saga is set in, well, Viking times.

Yep. We've been doing like deep dives on Vikings and stuff. So we've been talking to archaeologists and historians and all sorts. Yeah. What about you? What have you been up to this last month? I had my protractor confiscated. You know, okay.

Cause we've been catching up all weekend. Right. And I'm like, there's something I'm like, I cannot tell Beck. I had my protractor confiscated., I cannot tell Beck that I had my protractor confiscated because I want to save that as a thing for the podcast. Security took my protractor because they said it could be used as a weapon. Security where? At the Shard.

Okay. So the Shard is a very tall building in London. It's the tallest building in London. Oh, Matt, how far could you see from there? Well, yeah Okay, let's not skip ahead And I was going to go Up the Shard And I brought a protractor with me

I don't know why that sounds like such a funny I know, I know So I was going up the Shard And security's like, whoa, what are you doing? You can't take that protractor with you It could be used as a weapon And I was there with hannah fry also another mass communicator she had an inclinometer with her like a um

spirit level that measures angles and they also confiscated that wow we were doing a thing where you can calculate how big the earth is by measuring the angle to the horizon from the top of a tall building oh so this was a little bit of it's very it's it's exactly how far can you see yeah but using that experimentally to work out the radius of the earth which was done uh like a thousand years ago people were doing this we're going up the shelf showing up the shop um and the protracted what did they use thousands of years ago, people were doing this. Were going up the shaft. Going up the shaft. What did they use thousands of years ago before they had tall buildings, Matt? I can't think of any other way to be elevated above the ground than to go up a very tall building. So who knows?

I assume they were just floating. So they did have magic and stuff back in the day. Yeah, well, you know, the classic two kids in a trench coat routine. Yeah. Just that. Yeah. But four or five people and no trench coat. And a really long trench coat.

Yeah. No trench coat. This is before trench coats were invented. Okay. One guy at the top with an astrolabe measuring the angle to the horizon. And I was particularly emotional because I had handcrafted this protractor. This was not like some off-the-shelf. I just went and bought.

You whittled it? That is so close to being true. Would you like to see it? Oh, you've got it back, Ren. It's over there. So describing for the listeners, it is a large piece of perspex. Perspex, yeah. I would say, I mean, it's big enough to use as a small corner desk.

We'll post a photo of it. We'll post photos on socials, Instagram and Twitter. It's also got a plum line on it. Patreon. So when I move it around. We can see your plum. You can see my plum is just dangling at the bottom of the protractor. Can see why they come from the sky.

They're like, sir, your plum is showing. I really wish we went in person now. I don't want to see this. So anyway, yes, I made this, but I had to go through and individually notch equidistant little uh degree markings all the way around this very accurately i would argue the thing that can make it be useful as a weapon yep is that the weight that you've used it looks like a large heavy it looks like a pencil heavy pencil yeah and it's on the end of a string well you wouldn't know which if you whipped that around

your head like that would be a weapon you've basically got a small mace yeah yeah but the thing is that wasn't even on there like i had taken this off oh for portability and it was just the perspex oh chunk that they objected to that's knocking on the perspex by the way not the security on the door you guys you got plums in there So They wouldn't let you take a large Angular piece of What looks like glass With clearly That's Matt knocking on it again Oh no that is a security

He's got his plum out And when they confiscated this I was like do you want the plum as well And then they're like yep alright But they didn't actually care about the weight. It was this. That was my month. I made a protractor and had it confiscated by security.

Have you ever had anything else weird confiscated by security? I once had to get my Rubik's Cube put through a x-ray machine. To make sure you weren't hiding any. To make sure I wasn't hiding. Literally to make sure there's no contraband in it. Wow. Because I was doing maths sessions in a jail. Yeah, yeah. We don't want Andy Dufresne's spooning their way out of a wall. With a Rubik's cube. Hello, lovely A Problem Squared listeners. This is Bec.

And this is Matt. And before we jump into this episode, we just wanted to say we're aware that not everyone can be a Patreon supporter. And that angers us. No, it does not. No, sorry. Other one. Other one. That's fine. It's fine. That's fine. It's fine. We appreciate that. Totally fine. But in order for Matt and I to be able to sustain this podcast yep we will at some point need some form of income we're fussy like that well it's mainly so we can choose it over the other things so we

have time to do this yeah so uh here's the deal if you would love to be a patreon supporter but can't but for whatever reason which is fine. Which is totally fine. We're disappointed. No, we're not. We're not. Sorry, the other one. Stop trying to kill people, Matt. We're not disappointed.

We understand. If you could pause this podcast for one moment and tell someone about it. It can either be a direct message to someone that you know who would like. A person? Yeah. Like you were listening to this and you thought, I should tell that person? Yeah. Yeah. Because this thing made me think of them. Absolutely. Someone is listening to this who previously listened to an episode and went, oh, blah, blah, would love that. And then you thought you would tell your friend and you never did, did you? You haven't. And now

we are disappointed. Yep. So go do that now. And angry. Or you were not that angry. No, I am. Matt is actually furious. He's turning bright red. This'm angry. Or you're not that angry. No, I am. Matt is actually furious. Am I right? He's turning bright red. This is as angry as I get. Steam's coming out of his ears, everything. And if you don't want that to happen, tell someone. Or you can tell your following.

I'm also disappointed. If you're on social media. I'm. Your friends and family. It's angry. Matt's just going to keep going on about his feelings, which is fine. You can put an end to this. Or leave a review on a thing or engage with an algorithm or just enjoy the podcast. That's fine.

You can do that as well. But yeah, that would be really helpful. And then we can keep doing this for you. That's the deal. I'll keep my dango bottled up. Keep your dango. Don't leave your danging. Don't leave me dangeringering and now you can listen to the rest of the podcast all right let's answer some problems this first problem comes from david from greensboro borough borough how it's been spelt and it, if you rolled up graphene into a roll the size of a toilet paper roll, how long would it be? So if you had a toilet paper's roll worth of graphene. Yeah.

It says the size of a toilet paper roll. So I'm assuming when David says that, they mean the size of like a full proper roll of toilet paper, not just the cardboard tube. Yeah. I assumed it was the paper on the tube, which just right out of the gates, there's some variation in this. I've gone with the 12-centimetre roll of paper

with a 4-centimetre tube down the centre. So you've kind of got your cylinder of paper, I guess. You can put it that way. And graphing. I've only just realised that if you say a roll of toilet paper, you're talking about the toilet paper that is on the roll. On the roll, yep. Yep.

A toilet paper roll is technically the tube. Toilet paper is the stuff that's on the tube. On the roll. On the roll. So the roll is the cardboard center. That's how I would imagine it. But I suppose, I guess the roll is a verb, isn't it? You roll it.

It's rolled around the tube. Yeah. And here in the UK, they do the you roll it it's rolling around the tube yeah and here in the uk they did their bog roll yeah roll is the now i've taken this off on a tangent very early no that's very true okay okay and so graphene the wonder substance yes explain i know vaguely what would you say is graph i would say it's a very fine mesh correct i mean that works for me It's basically a single layer of atoms That is much more specific than I thought Yeah, this is why it's the wonder material

People have been trying to make it for a very long time And they cracked it at the University of Manchester And it's basically a substance which is one atom thick Wow So you cannot get anything thinner than one layer of atoms. Wow. That's the one step up from nothing. It's thinner than a hair.

Zero atoms. Thinner than a hair. It's thinner than a human hair. The fraction of a human hair. You wouldn't be able to see it, would you? No, I can't see it. What if there's graphene in this room? It could be here.

It could be all around us. Wow. Is God graphene? Yeah. I knew it. So it's amazing because it's incredibly strong for its size it's like a hundred times stronger than steel this is an example analogy for its mass right so it's only an atom thick you could break it yeah but it's got a million applications none of which i think have actually come to market but it's got a million applications, none of which I think have actually come to market. But it's this amazing wonder substance because it's just a hexagonal grid of carbon atoms.

And they're all hanging on to the three carbon atoms nearby. And you get this hexagonal, exactly. It's an analogy for teamwork and super thin. Oh my goodness. So the first thing I had to do was find out how thick graphene is because then I can work out. Yeah, how thick is an atom? How thick is an atom?

Well, the thing is it's not just how thick is an atom because when you start putting atoms together, they do weird quantum-y interaction things. Right. So the thickness of graphene, and particularly in this case we're going to stack graphene and so the layers are interacting at like an atomic level as they're being stacked on top of each other and so i initially just thought piece of cake i will google what is the thickness of graphene i will get the answer and I'm away. Yeah, yeah. No, there's no agreed answer.

So eventually I found a scientific paper. This was published, the Institute of Physics put this out and it's literally called Accurate Thickness Measurement of Graphene. Oh, okay, yeah. And I was like, here it is. There's your answer? The answer on the plate. For free, you can read the abstract.

Okay. And the abstract is this bit at the top here this opening paragraph which does not contain the answer for how thick is graphene yeah it's the trailer sample the trailer doesn't they tell you other ones are terrible and they give the range they're like other measurements are between 0.4 and 1.7 nanometers. What is a nanometer if you were to compare it to, say, a millimeter? A millionth. Whoa! So a millimeter.

That's a tiny ruler. So a millimeter is one thousandth of a meter. A nanometer is a billionth of a meter. Oh, my gosh. It's tiny, absolutely small. Yeah. And so they're saying it's around there. That is not getting rid of any poop.

No. And we haven't even decided if this is single ply. So this paper is like, look, everyone else is not doing a good job at measuring this stuff. It's too big a range. We need to know. Now, to read the paper, I basically emailed my wife, who's a real physicist, and said, can you send me a copy of this paper? I was present. You were there.

She was in the room. Literally, Lucy, I emailed you. You were like, this is business. Yeah. We separate business from pleasure. And I'm like, if it's email, business. I'm like, hey, I started. Dear Professor Green.

Nice. I was wondering if you could download this paper for me and send it over. And I saw her roll her eyes when she read. No, don't. A noun of a. She went. So. Yes.

So in their conclusions, they say the measured height of a sheet of graphene was found to vary depending on the force used to measure it. So what they discovered is if you measure it, you squash it. So the act of classic physics, the act of measuring changes it. Is that like if you were to say that you were measuring my height and you put your hand on top of my head, but that pushes me down? Squash you, yeah, exactly, literally that. So you're making me less, yeah, yeah.

It's like I'm going to measure how big this roll of toilet paper is, but then like just crush it. Yeah. And then measure it. And is that accurate or not? And they found also in the conclusions they say if you apply a lot of force, you get close to the theoretical minimum, which is just the size of an atom. So basically they're saying if you really, really squash this stuff down,

you're getting down to just a carbon atom. So basically they're saying if you really, really squash this stuff down, you're getting down to just a carbon atom. But they almost grudgingly, I would say, do give a value of about 0.43 nanometers, give or take. So I've taken it to be roughly half a nanometer. So single ply graphene toilet paper. Now the next issue is how do you work out, like how long is it? Because you can work out how many laps. That's easy. You take the big radius, like the whole toilet paper roll. You subtract the small radius, which is the empty bit in the middle. You've got the difference between them. You divide that by the thickness of the paper and you get how many laps, right? That's a piece of cake. But now the question is, how long is it? So you've got to work out how, because it'll get longer each time,

every time it does a lap. Yeah. Each lap is bigger than the previous one. Oh my goodness. This is an insane question. Yeah. So now there's two ways you can deal with this now. You can either assume it's an Archimedean spiral, or you can just assume it's a bunch of circles. An Archimedean spiral is a spiral where it doesn't get bigger as you spiral out. It doesn't. Yeah. So the classic spiral, you get bigger and bigger and bigger. That's what you get when you wrap like rope or something around. It's spiraling out, but it's not getting thicker as you go. So the toilet paper is technically one continuous spiral coming out. I don't understand. It is getting bigger though. What are you talking about? But the rope isn't getting thicker.

No. So a lot of- But you're using more. Yes, you're using more each lap. Hang on, excuse me. At what point do you wrap something around and as you go around, the thing gets bigger? Like if you're looking at the spiral in like a-

Like a snail shell? Snail shell. Or if you're moving in a spiral action, the distance between the laps of the spiral tend to get bigger as you go. Yeah, it's like a Fibonacci. Like a Fibonacci thing. Yeah. What's happened here is mathematicians have come up with ways

to describe things that are otherwise super obvious. Yeah, yeah, yeah, yeah. For me, I'm like, oh, but it's this particular type of spiral where the thickness doesn't change. You're like, you mean it's just exactly what you expect. It's like everything you've ever, exactly. Yeah, yeah, yeah. So I've gotten unduly excited about something that's super obvious.

And is that named after Archimedes? Archimedes, yes. Oh, the bath guy. The bath guy. He may have said Eureka when he, and everyone else around him is like, why are you saying that? It's super obvious. That's just what happens when you wind something up.

He's like, but I gave it a name. Mathematicians are going to be amazed for millennia. So I didn't assume it was a spiral. I decided that was too hard. I've assumed it's just lots of concentric circles. So there's like a circle that's this big. And then there's a circle that's that big. It's bigger around it.

But that's not how it works. You're describing if you did a cross-section of a russian doll yeah but that's not how toilet paper works no yeah so i've i've i've approximated it as concentric circles because i think that's close enough within the tolerances of my estimation if anyone wants to redo this calculation as a spiral using a 12 centimeter diameter four centimeter hole through the middle half a nanometer width paper i ran the numbers on uh and then i rounded the answer to be honest so frankly and we can see whether your answer and their answer is that much different mine came out at uh 20 meters. That's a lot of meters. It's a lot of meters, 20,000 kilometers.

It is halfway around the earth. And you didn't think to go double ply? If I went double ply, you get quarter of the way around the earth. Yeah. So if you had a roll of double ply graphene toilet paper and you started unrolling it at the North Pole, it would make it to the equator pretty much exactly. Wow. Because the earth is 40 million meters around. Like by definition, a meter is one 10 millionth of the distance from the pole to the equator. It was the original

definition of a meter. Whoa. Whoa. And so a double ply roll of toilet paper is 10 million meters. And so we could have defined the meter as one 10 millionth of a roll of graphene toilet paper. Oh my goodness. Because it's the same distance as the distance, double ply, same distance as the distance from the North Pole to the equator. Something like that. Huh.

And then the next question is, how many times do we need to fold it for it to be efficient to wipe your butt with? Oh, yeah. Yeah. Like, I don't know what the strength would be. I don't want my finger going through that. I didn't look up the ratio of strength from toilet paper to graphing. It'd be pretty thin. I reckon it might be, I don't know, would it be visible?

I think it'd be visible. Would it be like wiping? I mean, it will eventually, won't it? Well, it will be eventually. But initially it's like you've got invisible toilet paper. That's disturbing. Yeah, I wouldn't trust that. No.

How would you know? How would you know? Yeah. Until it's too late, you wouldn't. Nah. Nah, no deal. Terrible idea. But anyway, there you go.

And if you had two single roll lengths of graphene toilet paper, you could do the whole way around. You could teepee the world. The ultimate prank. One of Archimedes' famous sayings, give me two rolls of graphene toilet paper and a place to stand and I will teepee the world. He did say that.

Yeah, I think that was him. That was on a T-shirt I saw at the markets. Oh, good. Yeah, I think that was him. That was on a T-shirt I saw at the markets. Oh, good. I think I'm going to give that a tentative ding. Tentative ding? Because I want to know if anyone gets the same

or roughly the same with their other calculation. Okay. Or David from Greensboro. Greensboro. Let me know. We have a problem in from Patreon supporter Samson, who says, my brother told me that every time he reads a paper book,

he wonders how much the book would weigh without any ink. They also say if you had a totally, in their words, totally useless representation of a book, if you had a totally, in their words, totally useless representation of a book, how many pages could you save by just printing the ink without any gaps? Right. So just block pages. Block pages. So take all the ink of the book and then just move it all to the front. So all you're doing is just fully black page, black page, black page, and then just all the white spaces at the end.

Yeah. So you've sorted the book by ink. And then you get rid of all the white pages. Yeah, you don't need them anymore. Obviously, you keep the ones that you printed nothing but ink on, just like block ink. Very artistic. Yeah, exactly.

And technically, same book. Just all the ink moved to the front. So there you are. That's yet another practical everyday life problem one of our listeners has sent in. Well, I was excited about this problem because my first ever book, Horror Heights, The Slime, is being released the same time as this podcast, actually. Yeah. So if you're listening to this on September 30th.

Was that a coincidence? Or did you say put it out the same day as the podcast? I was like, wait until Problem Squared, please. So I was excited about this question because the publishers let me go to the printing press. I was so envious. Yeah. So I got to see the factory.

You got to see your own book being printed. It was so awesome, Matt. Oh, so cool. It was so, so cool. And this is a really cool moment when the cover is being glued on and all the pages are sort of being glued together and held together. It does sound like the highlight of the book printing process. It is the highlight.

It's really cool. When pages meet cover. It goes onto a conveyor belt and then it sort of gets like, you know how when you imagine a factory and you imagine all the stuff being like whizzing around. Whizzing around on conveyor belts and assembly lines. It's exactly that. It is exactly that.

They're like, look out, here comes the new edition and you all duck and another row of them comes flying down a flying fox-esque. It's not dissimilar. No, not a flying fox. They're sitting on the, they're lying on the conveyor belt. But I found out that the reason that they, because they go on the conveyor belt and they go all the way around and then they like come back to pretty much where they were for the next step of the process.

And it turns out that the reason they do that is so the glue can dry. Oh, it's like a holding pattern. Yeah. Rather than it just sitting there, they They give a little tour of the factory first Which as you can testify, good fun Good factory, yeah, I would do it I would go on a conveyor belt The other thing is that the books get printed

There's actually two in a long thing And I'll put photos up with this as well Yeah, well you showed me You stole a book from each stage of the printing process. I didn't. I was given them, Matthew. I'm sorry.

So in pairs before they've been guillotined apart. Yes, and then they whip around. They zip around the whole factory. And then cut. Books. Yeah. You get to see your own book being printed. That is amazing.

It was awesome. And the way that they print larger batches, so with batches of 5,000 or less, they do have these massive digital printers now where it works like a huge version of the way that you would at home. Print anything else. In that you send the file directly to the printer and then it works out what to do.

The way that the larger batches get printed, which is 5,000 or more. More, that's the technical one. Thank you. There's still a version of the way they did it in the sort of early stages of mass printing. Movable type. You're not quite movable type, not like little clickety-clack things that you put together. Oh, is that some guy like twisting a press?

You know, but it's sort of a version of that. So what they do is they make these big aluminium plates and then they put a large proportion of pages. Oh, they etch all the pages into one big plate? They etch all the pages. It's like immovable type. Yeah. It feels like the same thing.

Yeah, so they've skipped the moving around the little clickety-clack. They just etch them in. Stampy things. They etch them in. Wow. And then they go through a roller where the ink is applied to them. Yep. And the ink is like a mix of oil and water.

And the oil sticks to the bit that's etched. I was going to say rough, but there's something, the surface is different so the oil sticks to it. Yes. And the water's like, forget that, I'll be over here in the white space. Exactly. Exactly that. So then it gets transferred onto some paper, then transfer it again.

Oh. Because that would bleed really quickly. Yep. Yeah, like blotting. But it does mean, obviously, that you don't get a transfer of all of the ink onto the page. I haven't taken that into my calculations. I know it would affect it, but're always doing what we can yeah and it's different book i mean for my books i use a specific photographer for the photos in my books

because they will process the images in such a way to compensate for the way the ink is absorbed into the paper yeah right so the whole interaction between ink and paper is non-trivial and needs to be factored in to these processes. That's why often in books where there are photos, the paper type will suddenly change. Yeah. Yeah. My publishers don't spend that much money on my books. There's cheap paper the whole way through. Fair. Yeah. Yeah. So I actually spoke to Beth and Ollie from Clay's Printing, who are the spokespeople, and I asked them a question that Samson posed, and this is the response. It's really hard to give a definitive amount because each book is individual.

Each book will have a different content, and it's the content that will determine how much ink is used. So basically, we looked at the text data that was supplied, yn cael ei ddefnyddio. Felly, yn y bôn, roedden ni'n edrych ar y data text sydd wedi'i ddarparu ac roedden ni'n gallu gweld pa mor o'r text oedd yn gysylltiedig â phosiblion, pa mor oedd yn ysgrifennu. Felly, yn amlwg, os ydych yn defnyddio text, mae'n un cyfnod solid 100% yn ystod y cyfnod, ac yn dibynnu ar faint o brydau rydych chi'n eu cael, os oes gennych chi breisiau bennod, os oes gennych chi brydau gwbl yn ôl bennod, ond pan oes gennych chi osgoedd, er enghraifft, gallai eu gysylltu â tins. Felly, gallech chi gael rhan o'r chapter or but when you've got images for instance they could be comprised of tints so you could have some part of that image that's only at like 40% ink density and then others that are at 70 so all that sort of stuff could vary the result and the amount of ink is needed so just by looking at that and the amount of images we could give a really rough estimate and it is really rough

because there's the printing process here there's big reels it's not like little packs of ink it's it's big yeah so there's lots of ink so kind of work out 15 to 20 kilos maybe just for the whole print run for the whole print run and then per book we're looking at roughly 11.2 grams very specific I said roughly and then very specific answer. So. Yeah. That was the answer. Not quite.

Well. That is the weight of ink per book. But they want to know how much the book would weigh without the ink. Mass minus 11.2. Exactly. So I managed to find the weight of the books. Excellent. So each individual book is 157.3 grams. Right. So Matt, you do the maths

for me. I've subtracted 11.2. It's 146.1 grams. There you go. 146.1 grams is how much specifically my book would weigh without ink. And actually, you know what, 11.2 divided by the original mass, 157.3, about 7%. About 7%, there you go. The mass of the book is the ink. And obviously it's going to vary book to book. Absolutely. I could not find that out.

But using Horror Heights by Beck Hill out today. Yes, September 30, yes, today. If you're listening to this on the date of release of the podcast. 7.12% ink. Yeah. That's what you're getting for your money. That's the bit you're paying for, really, the ink. Arguably, yes.

Arguably, yeah. Yeah. Which brings us on to the second part of the question. Oh, yeah. How many pages would that be if it was block printed? And I went to you for help with this because I was like, ooh, that's gonna need harder maths well the printing people would not help i mean to be fair they they print a lot of

different books yeah and they don't care about the area of the print just the amount of yeah this is not a thing that they have to work out so why spend time on a new question for them so but you thankfully had your book in pdf form yes so i wrote a bit of python code to take all 176 pages and the the pdf you gave me is like the full print bit but i cropped it down i'm like the digital version of that machine yeah you are in the printing press yeah i cropped it down to just the bit that's in the finished book. And then I wrote a bit of software to look at every single pixel in the PDF and see if it was pure white. So it's nothing being printed or if it wasn't white, something was being printed there. And then I went through and summed them all up. Which is incredible.

And I was just going to guess. Well, I've got a page by page breakdown. Do you want to know the most colored in and the least colored in pages? I think I know which are the most colored in ones. Okay. Do you have numbers? Yeah. Okay. What do you reckon is the most colored in? I would say that the most colored in. For reference, Bec is flicking through a copy of her own book. Yeah. Can I tell you one thing I did do? No.

Occasionally, I'll tell you two then, occasionally there are greys where it would use half as much ink. I have pulled all that ink together. Oh, nice. So if there's two half bits of grey, I've just put them together

to be a solid black printing. Yeah. I'm going to say page 167. Correct. Yes, because that is the very last page before the acknowledgements. Well, not the very last. It's the second to last page before the acknowledgements. And it is pure black, which is very handy.

85.47%. Oh, I'm sorry. Black. Just, you know, roughly. And I'm going to guess that that is to do with the CMYK values. Actually, they were pretty, well, I had to convert it to RGB. Yeah. So I've just got.

Which is not the same. Not the same. But once it's, because they're all grays, once they're converted into red, green, blue, it's just the same value for all of them. So I just took the red value each time as a measure of how colored in it is as a percentage of 255, which is the scale. However, the crop marks is like an inner and outer crop mark. So the crop will be somewhere between the two.

I've split the difference. And I think for some pages, like in the very middle where the spine of the book is, there's a little, even if it's meant to be pure black, often it doesn't print all the way in. So I've done the amount of ink put down.

And so I think in the very center of like a two page spread, the bit you can't see that's glued, I'm still including that, which is why maybe you're not getting a hundred percent for some of these. Oh, yeah, yeah. Yeah, because they don't need to print that.

They're going up together. Exactly. And do you want to know the page with the least ink on it? Oh, all right. This is a good one. If you pick one, I'll be able to tell you where it ranks. I'm going to say 104. 104?

104? Okay. Page 104 is the sixth most blank page in the book. Oh, my gosh. That is good. Wow. For just flicking through it. That is impressive, Bec.

Thank you. And you're still going. You still want to beat your record. No, I'm now looking. What about 15? Where does that come? 15. Ninth.

Oh, my gosh. That's worse. You're going the wrong way. 14 is better than 15, according to my numbers here. Really? Does that check out? It's pointing to me, but no, I think you're right. I mean, I trust your maths more than...

Maybe there's more gaps. I mean, I did a few checks. Like, I never trust my code completely. I verified it, and I'm reasonably confident. No, what's the least? The page with the least ink, 32. Oh, yeah? Pretty blank?

It's a page with dialogue on it. So there's a lot of gaps, not big paragraphs or anything. Well, it's not blank. It's just there's a lot of... Oh, no, it's still 2.1% ink. It's what? 2.1%. Wow, that's so small.

And if you add them all together, move all the ink to the front, 24.22 pages. Wow. That's so small. And if you add them all together. Yeah. Move all the ink to the front. Yep. 24.22 pages. Wow. Yeah. And that is 24 out of 168. Yep. Oh, 176.

Because you got some pages before the numbers start. Your book starts on page negative seven. And then counts forward. Because page one is a fair way in, right? Yeah, you're right. Yeah, yeah. There's a note from the author. I know what's going on there. That's on a blank page. Bl is a fair way in, right? Yeah, you're right. Yeah, yeah. There's a note from the author. I know what's going on there.

That's on a blank page. Blah, blah, blah, right? And so 176 actual pages, at least in the print file you sent me. So the average is actually quite high. The average amount per page is 13.8% of a page. I feel like it's a lot. But that's because you've got loads of pages with lots of slime on them. Yeah.

Yeah. And I, in fact, I've, uh, I've done that thing where, you know, when you're watching a TV show and it will be like London and it like has a

quick heading. Yeah. Yeah. And it's like, bum, bum, right in your face. You've written bum,

bum. I've written days though. So it starts on Friday and it's just a pure black page with Friday written on it in white. Yeah. And actually, this is interesting. It's a good example of why the mean is often not a good average because it can be dragged up by a few very big values. So if you just looked at the average of 13.8%, you're like, wow, that's a lot per page.

But actually, it's just the all black pages dragging it up. Yeah. like wow that's a lot per page but actually it's just the all black pages dragging it up yeah the median so that the if you if you reordered your book to be an ink order the middle page would have 4.3 ink i mean it feels like not much writing to me yeah you should put some more effort if i was like i've done a bunch of writing i I've covered this page in 4% writing. Yeah, exactly. Oh. I think you've helped with that. And, of course, if anyone has any questions about the printing process, I'm going to chuck up a video that will come up around the same time as this podcast on my YouTube channel and I'll explain.

Oh, yeah, yeah, because you've got loads more footage of the factory and everything else. Yeah, yeah, it's real fun. But given you went to the actual factory, because you asked to go and see it get printed to answer this question. Yeah. And you did the video. Yeah. And I've analysed the percentage of ink on every single page in the book.

I don't think we've ever dinged a question this hard. Oh, yeah, it is specific. Samson, if you don't give this a ding. Oh, my goodness. I'll ding you. Yeah. We want more than a 13.8% ding. We want solid ding. Solid we want more than a 13.8 percent ding we want

solid ding solid margin to margin finally as always we have some time for any other aob business that we haven't covered so far and i don't think we've got anything this time i think um the last episode was without correction. Yeah. Other than the many, many people who were dissatisfied with my how far can you see answer. And by the way, thank you to the people who congratulated me on bringing up the question of why didn't you include mountains? Yeah, I didn't include mountains. Didn't't include mountains and people were very upset yeah which i guess is fair enough arguably with the surname hill i am going to be thinking of topography yeah but for someone who did an

entire video and problem about topography and how it would change the surface area and nature the problem is as a mathematician i used just assume that the Earth is perfectly spherical. And that's the source of many of my problems in life, including forgetting about mountains. Okay, you know what? I was going to continue to stand by my policy of just looking at buildings yeah because it's how far humans can see but you're right you can go up mountains and and i was like well i need examples of people saying that mountains are superior because i think mountains the trouble is how like other mountains are going to get in the way of trying to see a long way if you're on a mountain yeah but arguably

that also helps you to see further away. Yeah. Well, okay. So anyway, people then did very kindly send in a lot of other suggestions. Yeah. So I apologize. I'm not going to name check everyone because there were so many people. So many. And in fact, since we recorded that, I remembered that when I was in Sicily in Mazzarino,

which is like, you know, sort of south, sort of central south, I could see Mount Etna from there on a clear day. And as the crow flies, that was about 86 kilometers, which I know that you were talking more about 100 kilometers. Yeah, but still. You're right. Yeah. No, I agree, Bec. It was as much your fault as it was mine.

You're right. Yeah. No, I agree, Bec. It was as much your fault as it was mine. So our eagle-eyed listeners, someone suggested Tenerife, which is the highest peak of Tenerife is 3,715 meters above sea level. And they say the other highest peak of Gran Canaria is just shy of 2,000 meters above sea level. And they reckon you can see peak to peak,

and it's over 100 kilometers apart. It's a great suggestion. Someone else said, oh, goodness, how would you pronounce that? The tallest mountain in Colombia. Pico Cristobal. Okay, that works. And they reckon you could see the ocean from that, and it's over 5,000 meters tall.

And if you can see to the horizon, actually, you know what? I will put the height of that peak in Colombia into my spreadsheet from last time. And it will tell us how far you can see. Okay, so from the top of that, you'd be able to see, if you could see the horizon on the ocean, it would be 270 kilometers away. That's a lot of kilometers. A lot of kilometers. So, I mean, they're not saying you definitely can, but they're saying it's a big old peak

and you can probably see the ocean. Yeah. That's going to be impressive. There's a peak in Arizona where people reckon you can see Humphreys Peak and that's 187 K. If you go to Munakea, where's that? Oh, in Hawaii. Oh, of course, Hawaii is going to be a bunch of like volcanoes with plenty of space in between. Someone reckons you can get 128 K between two of those peaks. Mount Hood in Oregon. We've got a Concawaga. There's a line of sight to the

ocean again. Oh, it's even taller. Oh, you know what? They reckon that one's 6,962 meters. Let's chuck that in the spreadsheet. That's going to give us 298K. So that's pretty much 300K. We don't have visual proof of those. No. These are theories.

Well, this is it. A lot of people are just throwing theories at me saying, what about this peak? No one's bothered to go up these peaks and check. Or they have, but no one's decided to send us the proof. No one sent us the proof or they didn't make it back. We don't know. We're just, we're not getting until several, several people sent me the world record for longest distance in a photograph, like the greatest distance away from something and still taking a photograph of it.

And that is from Spain to France. Someone went up the Pyrenees in Spain, mountain range, looked at the Alps. That's a fair way away over in France. And they took a photo of the Alps from Spain. And there is a distance of 443 kilometers. Whoa. And what I love about that, because it's an actual photo, someone's done it. Yeah.

The whole time I've been ignoring the refractive index of air. So actually light will curve around the surface of the earth. So you can actually see further than is theoretically possible because you don't actually need a straight line of sight. The light will do some of the work for you and curl down so you can see even further than the theoretical maximum. Is that how that ship optical illusion, where they look like they're floating because they look like they're sitting above the waterline? Exactly that, because the light is bending in the different density air above the water. That's why when the sun sets, you actually see it set slightly later.

Like it's already set, but we can still see it. Wow. But then has it set? Like I think the sun set. Tree falling in the forest. Yeah, exactly. Yeah, yeah, yeah. So what I love about the photo is all of that's taken into account

because someone's actually taken the photo. Like light has gone from that mountain all the way across Europe is it all of that's taken into account because someone's actually taken the photo like light has gone from that mountain all the way across europe into a camera and we know they could see that mountain 443 kilometers away now it's actually says the guinness world record for longest line of sight like arguably if you googled the question in the last episode you would have been brought to this answer Okay, there are two types of people in the world, Bec People who just google the answer

This guy And people who start from first principles with a spherical earth You Yes, and one of them would have got the correct answer a lot faster But we would have less podcast content that's true you would have missed out on all of our lovely banter i honestly can't believe if i just googled like what a cliche if i just googled guinness world record longest line of sight i would have got the answer straight away you would have got it i can't but anyway i'm doing that from now on

no they'd miss all of our lovely color and flavor that's the nicest way anyone's ever put yeah me trying to do it from first principles and getting it wrong by our i mean mine yeah it's so true i wouldn't get to feel smug yeah that's my my top priority now before anyone gets emotional saying oh but there was like a zoom lens or whatever i don't care this proves that you can see it and if you want to do it by the naked eye, the mountain just has to be brighter. Like, or you put a really bright light on top of the mountain. And maybe it's so bright to be visible by the naked eye, it's not feasible. I don't care.

In theory. Make it massive. Make it massive. Exactly. Massive disco hat. You are so right. Put a massive disco hat on the mountain. You were like double right.

Yeah, I am. That I make total sense all the time. 443 kilometers is the answer. And frankly, is it my fault I didn't Google it? Or is it people sending questions into this podcast and not Googling themselves before they send them in? That's true. If you're sending us a problem.

Let's split the blame. Yeah. Yeah, I'm willing to give them that. I'm assuming if we get sent a problem, you've exhausted the just Google it option. That's true. Yeah. Why would you make us go through that? Exactly.

I slam straight into assume the earth is a sphere and work my way up. Yeah, that's fair. So there you are. Yeah. 443K. I'm going to give you a sphere and work my way up. Yeah, that's fair. So there you are. Yeah. 443K. I'm going to give you a solid ding now. Thank you. What's a solid ding sound like?

Ding! That is a solid ding. And quick, any other business? We had a bunch of you respond on Twitter to share your tips for making writing more fun. Yep. Thank you very much. My favorite was use one of those pens that vibrates. Yes.

That fits the bill. So if you want to see the suggestions that other people put, you can just check out our Twitter account and see what people replied to. Writing would be more entertaining. And we have a ding in from Positronic Girl saying that your solution to how close can the human voice get to making a real ding sound was adequate. Yay! Thank you, Beardy Man.

It's been dinged. It's a meta ding. Meta ding. For anyone who hasn't listened to that episode yet, go back and listen to it. Yeah. Right. And I think that's it. Yeah.

I have been Matt Parker, Beck Hill as always. Yes. It's been edited and produced by Lauren Armstrong Carter and supported by all you fantastic listeners and Patreon backers. So thank you very much. We love you all equally. Yeah. Yeah.

Especially you. Beck, have you got a card? What, on me? No, like in your mind. Pick a card. Okay. Oh, there's so many. You got it?

There's like 52 that I can choose from. Can I choose jokers? You cannot. Okay. You got it? Yes. Okay, next time I'll guess it. I've switched it now just in case.

No, no. All right, I've got it. In fact, I'm going to message our producer, Lauren, the card that I've thought of. That's such a good idea. So that I can't forget it. Do it. Okay. Keep that card in your mind and you'll send messages.