The Magic Math Trick That Fools Everyone

This episode is brought to you by Cancer Research UK. Imagine this. Inside all of us, billions of cells follow millions of instructions written in microscopic code. And when a new cell grows, it copies those instructions, but the smallest error can lead cancer to develop. Right, and this is the reason why there isn't a single cure for cancer, because there are more than 200 different types. Each of them have got different distinct characteristics, different challenges, different mysteries. And that means that trying to cure cancer isn't like following a single path. It's like trying to map out an entire forest. That's right. And Cancer Research UK is the world's largest charitable funder of cancer research. I mean, their work spans more than 20 countries, with over 4,000 scientists, doctors, and nurses pushing knowledge forward to save and improve lives worldwide. You know, over the last 50 years, the work that this charity has done has helped to double cancer survival in the UK. And you have to think about that is more parents at the dinner table. Right, that is more friends at their birthday parties. That is more people who are living longer, better lives. For more information about Cancer Research UK, their research breakthroughs, and how you can support them, visit cancerresearchuk.org. Forward slash rest of science. This episode is brought to you by Project Hail Mary, the new spectacular space adventure coming to cinemas. Okay, hypothetically, imagine that there's this mission to save our world. Only you can do the job. As this expert in mathematics and science, how do you think you would do? Terribly. But not because I love teaching and learning, because I'm a scaredy cat. But what about yourself, Hannah? I would like myself, Michael. I think I'd be good. I just I just be very slow. I think the point is that no one should rely on Hannah or I to save the world. But in Project Hail Mary, Ryan Gosling stars as science teacher Ryland Grace, who is sent unexpectedly on an impossible mission to space to discover why the sun and stars are dying. He teams up with an unimaginable ally to defy all odds and save the universe from extinction. See Project Hail Mary in cinemas and IMAX from Thursday, the 19th of March. You can also catch it early on Saturday, the 14th of March, Pi Day, and Sunday, the 15th of March. The world moves fast. You work day, even faster, pitching products, drafting reports, analyzing data. Microsoft 365 Copilot is your AI assistant for work built into Word, Excel, PowerPoint, and other Microsoft 365 apps you use, helping you quickly write, analyze, create, and summarize. So you can cut through clutter and clear a path to your best work. Learn more at Microsoft.com slash M365 Copilot. Welcome to the rest of science. Field Notes, this is a kind of podcast expedition diary where Michael and I trade off on our exciting objects, our exciting discoveries, big questions that have been occupying our minds. Yeah, it's kind of like show and tell, but for nerds, with a capital N. Absolutely. Every week, one of us is going to bring something strange, something quirky, something interesting, some object or some story, and yeah, we're going to chat about it together. That's right. And please send us your own weird stories, thought experiments, or questions, because we will address them on this show. What do we got today? All right. It's basically a number of wooden swords on a key chain on a key ring, and each one has six two-digit numbers on it. And some of the numbers are surrounded by a square and some by a circle. And how many swords are there? Eight swords. Eight swords, and they're all what, like how many centimeters long? Okay. So I would say that they're about 10 centimeters long. They have quite a sharp edge. Yeah, they do. That's one thing that's noticeable. They're sort of, they're engraved with these numbers along the side. Each of them has six numbers in total, two-digit numbers. And around each of these numbers is a shape, which is either a square or a circle. That's right. And they were made by Creative Craft House, a just wonderful group of people that make wooden puzzles and toys. I gave this to Hannah all the way back during our photo shoot. So we have talked about it. We know what it is, but today we're going to tell you all about it. You know what though? I think people watching will be aware that our delight of nerdy things is absolutely authentic that we do this in our own time. We did this in our own time. That's right. That's right. And we're just recreating the magic of that moment. So this one's a magic trick. So what I want you to do is look through the swords and pick one of the swords. And I actually cannot see what you're doing because of your laptop. So no trickery. Okay. Okay. Now pick a number on that sword. Don't tell me what you've picked. I'm going to pick this one here. Okay. You've got it. So now what I want you to do is to, to read the numbers, well, not the numbers, but the shapes that surround them and say the name of the shape left to right. But when you reach the number you've picked, lie and say the opposite of what its shape is. So if it's a square, say circle. If it's a circle, say square. Okay. Here we go. So we're going to go circle square, square, square, square, circle. Okay. Circle, square, square, square, square, circle. Exactly. Okay. Now what I need to do is I need you to think about your number. I want you to think about it very deeply. And then we're going to speed this up because it's going to take me a while to do this in my head because I'm out of practice, but I will come up with it. Hannah. Yes. Did you pick the number 36? I did pick the number 36. I could tell I could feel it. Hang on. Let me just check. Is there any other 36 on here? There is not. You, you managed to get that exactly correct. How did you do that? Thank you for asking. I was able to deduce that you had chosen 36. Is it deduce the right word? You told me. I knew you chose 36 because you told me. How did I tell you? In code, in binary. In binary codes. So think of it this way. Imagine that the circles are actually zeros and the squares are actually ones. You gave me the digit three and the digit six because zero, one, one is three in binary. But who wants to describe the rules of binary? I think you could do it. Okay. So we use a denary system, a decimal system where our place values go from ones to tens to hundreds. Right. A three digit number is in the hundreds. And with binary, you're only going up by two each time. So you'll write down zero for zero, one for one, two. Nope. Nope. We're not going to do a two. Two moves us to another place value. We put a one and then a zero. So we have one, two and no ones. One zero is two in binary. It's 10 in hours. I mean, using base 10 is for lame people who have to take their socks off when they want to count to 20, basically. I'm not interested in that. I want something much more efficient. I want something where you can cram more in. And the way that you do that with binary, it sort of seems like when you start off, your first value, it only goes up to one. It's a zero or one, nothing else. It sort of feels like very inefficient. The second value, as I'm moving right to left, is two. It can be if it's zero, it's zero. If it's one, it's actually a two. Right. So one one in binary is two plus one, which is three. That's right. It feels like, hang on a second, you've got ages to go. Counting to base 10 is so much more efficient. You can kind of cram way more in. But very, very quickly, binary numbers get you up to like extremely high levels. So for example, on your hand, if you use this as binary digits instead, right? So in our ordinary way of counting, you go one, two, three, four, five, six, seven, eight, nine, ten. You can count to 10 on your hands. On two hands. On two hands. Right. I mean, lame. Yeah. Using binary, you can do way more. It's way more efficient way of counting. And if I was doing base 10 on my hand, then I could have the tens, hundreds, thousands, 10,000s, 100,000s just on my hand. You could. You could. One thing very briefly, just to note, anytime someone flips you the double bird, right, in your mind, you can just think 132. 132. Okay. So four is one of them. Yeah. And then two of them is 132. 132. So going back to the swords then. So actually, if you just take the last three shapes, square, square, circle is the same as saying like that, which is six. It's one, four, and one, two combined. And as you can see, you can get any integer you want using this system. So you told me circle, square, square, square, square, circle. Those first three, circle, square, square is three. It's a two and a one. And then square, square, circle, one, one, zero is six. So 36. The thing that I love about these, right? So I brought them home. I showed them to my children and who are eight and six, by the way, or sorry, they are eight and six. Yeah. And they absolutely love them. I've managed to, using this, my God, I've managed to trick them into learning binary numbers. Can't get them to do, you know, normal addition in their math same work, but binary numbers using this sort of truth. It's fun and it shows them that maths is not like a who done it, where we all know the answer is already that it is a practice. It's like a fun activity. It's a craft. Quite a lot of magic tricks actually have these mathematical elements to them, right? I know a lot of like ones that use decks of cards. Yeah. I mean, there's the old like one, oh, eight, nine trick. I don't know how it works though. But if you take a three digit number, whose first and last digits are different, and then you reverse it, and you subtract the smaller from the larger, take that number, you reverse it, and you add both of those together. You will always get 1089. Okay. Yeah. So sometimes people use this to say they get a book that's got more than 100 pages, and they say, okay, you've got a four digit number. Go to the, what's your number? One, 1089. Go to the 108th page. Go to the nine word long. Is it this thing here? Yeah. Yeah. You can create, you can embellish it to make the trick really mind blowing. Yeah. And those are my favorite kind of tricks because they work all the time. There's no sleight of hand. And I don't feel bad telling people how it worked because that I'm teaching math. Yeah. Hey, any opportunity to teach math as far as I'm concerned is absolutely fine by me. The Swords of Truth, the original like design of that trick was created by an inventor named Alex Elmsley. And he came up with a way to organize all these numbers and put squares or circles around them such that reversing any one of their shapes revealed that number's identity, which is brilliant. Yeah. It's a really cute trick. It's a really cute trick. When it comes to these Swords of Truth though, I sort of had imagined that it would been, it was an error correcting code. If you've come across these things, they are a very clever little math trick that's not used in magic, but instead is used across the board to make basically the modern world function. So if you imagine that you've got a Sudoku, okay, and I sort of pass you a Sudoku, but like a bit of the corner is rubbed out, you don't need to see the original Sudoku to know what those numbers were. It's possible for you to work it out. So now when you have a barcode, for instance, on an item, and the item gets like bashed around the supermarket, it gets to the checkout, you don't need to have a perfect reading of the entire barcode in order to be able to fill out and work out what all the numbers are. Because what it has is things called parity checks in it, so that it just needs a certain number of the numbers, and then there'll be extra rules in there, like all of these numbers must add up to 100 or every alternate digit will be even so that you can still work out what it is, even if you don't have the entire barcode itself. Okay, so you thought maybe there's a rule like, oh, there's always a pattern to the circles and squares and how it deviates tells you what the number is. Yeah, that's actually what I thought burst to. Yeah, absolutely. You know that thing about error correcting codes, by the way? So QR codes are an example of error correcting codes. You actually can cover up a third of the QR code and it will still work. Absolutely fine. Which I think for starters, gets sort of gamed by companies who put their logo in the middle of the QR. You see this, right? And then they do this, not because you don't need that bit of the QR code, they're just using up the fact that you can cover up 30% and still work. They've lost some of the error correcting ability. They've lost some of the error correcting ability. You cannot cover up a third of one which has a company logo in the middle. Right, right. It would have to be a third when you combined with the logo. Exactly. But I think quite a lot of people often get caught out by this. So the classic one is where people post photos of their boarding passes when they're like going on a trip, because even when you cover it up with your thumb or whatever, because you can recover a QR code even when you don't have the complete QR code itself. So there have been instances of people posting their boarding cards being like, oh, look, I'm flying to this place tomorrow. And then other people on the internet managing to go through logging on to the airline, changing the seat for the individual, maybe getting them to sit next to the toilet, maybe cancelling their flight, changing their flight date. Put in the middle seat. Exactly. There was one particularly viral case where someone changed the stranger's seat to have them sitting next to the toilet and posted online saying, you showed enough pixels to resurrect Jesus, let alone a QR code. Well, look, after the break, we're going to resurrect Jesus. Or will we? Probably not. But who knows what we're going to do? We'll see after the break. This episode is brought to you by NordVPN. VPNs are an incredible invention. Short for virtual private network or VPN, it works to shield your IP address. 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The link is in the podcast episode description box. This episode is brought to you by Cancer Research UK. Radiotherapy is over a century old, but it is still changing. Cancer Research UK helped lay the foundations of radiotherapy in the early 20th century and has driven progress ever since. Radiotherapy remains one of the cornerstones of cancer treatment today. Every year, millions of people worldwide benefit from Cancer Research UK's work to make it more precise. Scientists are still refining how radiotherapy is delivered. And one example is an experimental treatment called flash radiotherapy, which delivers radiation in fractions of a second up to a thousand times faster than standard radiotherapy. And early studies suggest that speed could make a real difference. Flash radiotherapy may cause up to 50% less damage to healthy cells. But scientists don't yet know why healthy cells seem to be spared. So Cancer Research UK are working to answer that. Understanding it could be key to reducing side effects in the future. For more information about Cancer Research UK, their research and breakthroughs, and how you can support them, visit cancerresearchuk.org forward slash the rest is science. This episode is brought to you by Thriver. Most of us tend to think of blood as something slightly clinical, linked to illness or bad news. But in reality, it has been quietly keeping a record of what's going on inside our bodies, almost like a biological diary. It holds clues about how everyday choices shape our health. Sleep, stress, food, movement. And without access to that information, staying healthy can feel more complicated than it needs to be. Thriver is a proactive health platform that lets you check in from home using regular at home blood testing with clear guidance to help you understand what your body is telling you. That sense of clarity changes how health feels. Instead of juggling advice, rules, and trends, you get a simpler sense of direction, what looks consistent, what's shifted a little, and what's actually worth paying attention to. Just makes health feel calmer and simpler to think about day to day. Head to Thriver.co to get started. That's T-H-R-I-V-A dot C-O. And use code TRIS for 20% off your first test. All right, we're back. I'm going to right a wrong. Okay. Because I found out that I do not follow you on YouTube. And I noticed like three weeks ago and I'm like, I'm going to wait for a field notes episode to do it. And so everyone can watch. Here I am. I've opened up YouTube. Here I am. Here's my little like channel page. I'm going to search for fry squared. Fry R squared. It's a math joke, Michael. Come on. Oh, it's fry R squared. I don't even know the name of your YouTube channel. Fry R squared is so much better than fry squared. Isn't it? I was choosing between that and E to the I fry. That's really clever. Oh my gosh. All right. Now here's the proof. Here I am logged in as Vsauce and the subscribe button is ready to be clicked. We're going to watch it all together. Boom. Is this the point that I should admit that yesterday I realized I also didn't subscribe to Vsauce? Oh, and do you now? Secretly. Just quickly press the button. I want to see how many people you follow. Hold on. Let's have a look. There's one. I don't know who it was, but someone I followed years ago, they just changed their name or someone bought the channel and it's now called like totally nude massage. Something like that. And there's this whole debate about like, why is Michael subscribed to this channel? It's because that wasn't what it was originally called. Hey, look, I think lean into it. I want to own it. I want to be like, yeah, you guys keep wondering why. Because if I unsubscribe, it's like I was embarrassed or they caught me at something. This is true. This is true. I think just, just keep teasing it. And maybe in 2035, release a video on totally nude massage. Yeah. A little collaboration. Hey, why not? Why not? You know, I was thinking during the break that people can be resurrected, but can someone be resurrected? Because to resurrect means to be resurrected. Like, oh man, I was just resurrected again. It's a bit like the one that people will talk about is well, right? Where it's like you can be underwhelmed or overwhelmed, but never wellmed. You can be under the weather, but you can't be over the weather. No. Can you be the weather? I'm going to try later today after the recording. Be the weather. I'm full of questions, but I want to hear questions from our viewers. Yeah. Okay. So we have a little mailbag, little mailbag entry here. Lucy has asked, if you couldn't live on earth, which planet would you like to live on and why? Or moon. I'm going to expand it to moon. Fair enough. There are some quite fun, fun ideas. I mean, one of them's got some reigned diamonds, isn't it? Yeah. But I'm going to say Venus, but I would want to live on like a blimp up in its atmosphere where the pressure, the atmospheric pressure is safe and gravity would be like pretty similar to earths. They're like twin planets, Venus and earth. I couldn't handle having less gravity on Mars. I think that would be, even though Mars is a fun one, even if we terraformed it, made its atmosphere breathable, it would still just not have enough gravity for the muscle strength I want to build. To be hench. Just to, yeah, just to, I don't know, I'm worried about that. I feel like even my lungs wouldn't be strong enough. And I feel like if I stayed on Mars too long, I would never be able to come back to earth. Yeah. What about the other way around? If you went somewhere with more gravity and then just did loads of weight training, you could come back to earth and be like extremely buff. Yeah. I mean, there's a limit to how strong a human could get. But yeah, I've heard from people who've done the vomit rocket thing. Have you done that? No, never. Okay. The zero G flights where you go up in a plane and then the plane just drops and you're in free fall inside the fuselage of the plane. So it's like you're in, in a free fall orbit around the earth. Your legs are one of the biggest hindrances you have. Really? Because people have a tendency to go, Oh, I want to move and they'll kick themselves to move like they're swimming. But there isn't the resistance of water around them and they fly across the room. And if you watch videos of people doing this, you'll notice that they can't control how powerful their legs are. So if you could go and live on, I mean, Jupiter's too much, but you know, in the atmosphere of Jupiter far enough away that the gravity was twice or three times earths, came back to earth, you would be like demolishing your shoes. You would, the steps would just crumble at your feet. It's a weight. I really want to understand that, that comet rocket thing. So wait, when they're pushing off from something, not just like kicking in the air, right? Yeah, kicking in the air does nothing. But if they're pushing off from something, they're suddenly extremely strong. Yeah, they'll be like, Oh, I want to move away from the wall. And they just push themselves as you might if you were in a rolly chair or if you were underwater. But that winds up being 20, 30 times the force they need. And they just, and also the force doesn't die down, right? They just keep moving. And so if you kind of tap yourself to move into the middle of the plane, nope, you're going to hit the wall. Okay, but the reverse of that then is that if you did go and live on Mars, you would feel like a kangaroo. Yes, you would. That would be pretty cool. That would be very fun. I think it's more of a theme park ride than a home. And I'm looking for a home. You're going to actually live there. Yeah, I do always think when people talk about, you know, terraforming Mars, it's like, Oh, all we've got to do is is add in some atmosphere and then and then it's like, you know, guys, there are, there are inhospitable places on earth that are way more hospitable than that. Like, why don't we just go and I don't know the Sahara, for example, all it needs a little bit of water and you find, but it's got, it already checks off a lot of boxes. It's got the right amount of gravity. It's got the right kind of air. I guess a place where the wet bulb thermometer temperature gets up to a certain point. That would be a fun challenge. You know, wet bulb temperature. Go on. So this is, this is not the air temperature that a thermometer reads. It's the temperature as measured by a thermometer that's wrapped in a wet towel. So it shows you what a vapour of cooling is able to do. And if the wet bulb temperature gets above 95 Fahrenheit or 35 Celsius, that's not that high. That that's too high for your body to cool down and you will die. Hold on, hold on, hold on, hold on. Right. If you wrap a wet towel around a thermometer and then take it outside on, I mean, we can still do this on earth. Yeah. If that goes above 35 degrees, you will die. Yeah. Because your body will not be able to maintain body temperature. A vapour of cooling cannot save you. Which of course is how you, how you cool yourself down, right? Which is how you cool yourself down. And so if you have cold water, if you've got refrigeration, if you've got an air conditioner, you will be okay. But we are finding more and more places on earth that are exceeding that wet bulb temperature. Sometimes just for a day. But the longer you stay in that zone, the more people die. They have to escape. They cannot keep their bodies at a safe temperature at that level. Wow. Yeah. That's extraordinary. Yeah. What's the hottest place you've ever been? Oh, the hottest place I've ever been is Death Valley. Which by the way, it keeps setting records for highest temperature dry bulb. And I think if you went out there with enough equipment, you could detect a record high number in August. You could hold the record. Is that what you're saying? Yeah, right, right, right, right. So I've always wanted to do that as a YouTube video. I'm like, just in August, get a couple of weeks, stay out in Death Valley and you can record the hottest temperature ever recorded. They're happening out there all the time. This does feel like quite a high risk way to get a record, Michael. It's worth it though. Die doing what he loves. I wouldn't die. But if I did, think about how many views the video would give. Soul content, baby. Yeah. Tell you where I wouldn't want to live in the solar system. I think Triton is the absolute worst place imaginable. Triton is a moon of Neptune. That's far away. Super cold. It's got geysers that run on liquid nitrogen, spouting out minus 230 fountains into the sky. Also, it orbits backwards. Oh. Yeah. Just to really mess with you. I think Triton would be beautiful though. Doesn't it possibly have oceans of methane or something? Yeah, I think so. I think so. That could be cool. Oh, no, wait. Is it methane on Titan? That's the one with the methane lakes. I think there, the atmosphere is so dense that you could potentially fly. Yes. Yes, I've heard this. By flapping your arms. Because the atmosphere is very thin, but the gravity is so low that human arms they've calculated could flap and you could fly. That would be pretty cool. That would be very cool. I mean, it would stink. Okay, you're not going to take a helmet off, I think. You're just going to wear your spacesuit. And like, yeah, on the moon, gravity is very low, but there's no atmosphere. So moving your arms doesn't displace enough mass to move your mass, but on Triton, that's where you tighten. I think. On Titan. I mean, look, they all end up being the same, don't they? Really? Titan? Titan, Triton, the moon. How funny that the moon is just called the moon. Yeah. It just, it doesn't have a, does it have a name in any other languages? I don't know, you know, there must be cultures that are like, oh no, it doesn't have the general name for a satellite around a planet. It's called, you know, Jeremy or whatever. Maybe the Martians call it something different. Oh yeah. You know that thing about life on Mars, right? Which thing? I mean, just the idea of whether it's there or was there. Yeah. I got to go and see curiosity before it launched. Oh, you did. I did. It was amazing. That is so cool. I wasn't allowed in the vacuum. So you weren't able to touch it? I wasn't able to touch it. I mean, they're extremely careful about who touches it, but I got to go and see the mock-ups of it in the Mars, basically robot playground where they kind of move it around and learn how to navigate. Couple of things that were really amazing about it. When they're checking for life on Mars, the idea is that they're, what curiosity is going to do is it's going to drill into the rock and then take these samples that can be analyzed for signs of previous microbial life. And in particular, they chose a spot on Mars, which they think isn't a really old riverbed where they think they used to be water flowing. And the idea behind that is that then when they're sampling in that space, they're not just sampling, oh, here's a patch of land. They're sampling something which has had land come in from all across the region. Which is just really, really smart, right? But the thing that is, I found so amazing about curiosity in this like process to analyze whether there's life on Mars is as they're drilling in the rock, they're not like running the analysis on the samples. They've got another mission planned to go and get those samples and then another one to get them into orbit and then another one to come back to Earth to sort of analyze them. So at the moment, what curiosity does is it drills into the rock, kind of puts these samples in these like, basically test tubes and then she chucks them on the ground. Yeah. Just litters the surface of Mars with these like scientific samples. Waiting for us to do a mission to pick them up. Yeah. And then it's like, well, have you got, do you know how you're going to do that? And then I'm like, no, no, no idea. Yeah. You know, that's sort of many billions of pounds later. That's so cool. So yeah, because I hadn't heard any results from it, but it's because we, curiosity didn't analyze the sample. Just chucked them on the ground. Chucked them on the ground. Yeah. The other thing is they're very careful about who gets to go in and touch the rover, of course. Yeah. But they're also extremely careful about the engineers who do get to work on it, not leaving their mark on it. Because I think in the early days they found people had like, you know, maybe with the Sharpie just like written their child's name on it or whatever. And they have this like blanket rule, you're not allowed to do that. But then they found that some people had started soldering or soldering if you're in the American. Soldering. Thank you. It's like our silent L's. Is that cool? Blows my mind that you call it soldering. Anyway, had like soldered in to the electrical circuits in this like microscopic way, the names of their children. But they're really like, no, this is from all of earth. Yep. This is not coming from you as the engineer. I like that. I like that. I mean, obviously you want to avoid contamination of biological agents because you touch the rover and some virus stays on there dormant until it gets to Mars. And then there could be life there, very simple life, completely unprepared for that virus. And you've literally extincted the whole planet. But then to not even put a little message, your child's name on the rover, I like, I like that. Because right, the anonymity of the individual, but the power of the species, this is from humanity. But we'll put an American flag on it. But it's from humanity. One small step for a man, one giant leap for mankind, American flag. There is no earth flag, though. And there should be and there will be, I think, soon. Yeah. And once there is, then maybe the moon will get a proper name. Mooney. Mooney McMoon face. Mooney McMoon face. If the Brits have a say, the Americans would probably call it something like freedom rock. The 51st state. Amazing. Would be pretty American. That would be pretty American. I think they would call it something like the great American Skyball. Skyball. New Texas. This episode is brought to you by Cancer Research UK. You know when the moon landing happened? There was all of this spin-off technology that made everybody's lives better, right? Nappies, cat scanners, memory phone, one big grand challenge that sparked all kinds of scientific innovation. I do. And things like that happen not just in space exploration, but even in cancer research. Like, I don't know what the analogy to a moon landing in cancer research would be, but the coolest thing I've learned recently is that the old idea that, well, cancer is what happens when there's damage to your DNA just hasn't really turned out to always be the case. The Cancer Grand Challenges team mutographs, they looked at 7,800 cancer samples and they found that there's this thing that they're calling dark carcinogens. Go on. Okay. These are molecules that cause cancer without leaving any scar on DNA at all. Right. I mean, that's completely against the previous theories. Yeah. So the new hypothesis or one new hypothesis is the promoter hypothesis, that there are other kinds of molecules that promote the expansion of mutated cells. And without those promoter molecules, mutated cells would just stay dormant. Okay. So the mutated cells are still there, but it's like they need a little friend to help them. That's right. It's like an evil friend who causes cancer. Exactly. It's not just let's pin this on DNA damage. Kind of like you can't pin a mudslide on rain. There's also other factors like deforestation and there's other causes that all combine together. So it's more than just damage to DNA because, for example, you would think, okay, well, if this damage can like randomly happen, then an animal with more cells should get more cancer. Like elephants, for example. Exactly. Elephants, giant whales, right? They've got so many more cells than us. If each cell is like a lottery ticket and some of them, unfortunately, win the cancer, well, then we should see more cancer in bigger animals, but we don't. Does that also help to explain then why you have these patterns in the way that cancer appears across human populations around the world that can't totally be explained by mutations alone? That's right. It does. And it also leads us perhaps towards better ways of preventing cancer in the first place. Because you can target the promoters, not just the cells themselves. That's right. And so, you know, there's been a lot of follow-up on this. One team prominent is now chasing down what these newly identified promoters could be. This is like a clear demonstration that even if you haven't yet cured cancer, just doing the research is giving you all of this extra, these extra kind of hooks to latch on to. The more you know about it, the more you know about how it arises, the more chances you have of being able to develop a weapon that helps defend against it. That's exactly right. And for more information about Cancer Research UK, their research, breakthroughs, and how you can support them, visit cancerresearchuk.org forward slash rest is science. All right. Here's a question from James. He asked, I'm curious to know how we determine the age of water on Earth. Because we mentioned this in our water episode, right? We said that it was older than the sun and then we gave no receipts. Yeah. How do you know? Okay. So there's a few different ways that you can tell. It works in a similar way to carbon dating effectively, which is that different atoms have different numbers of neutrons in them, right? So inside an atom, in nucleus of an atom, you have the number of protons and that tells you what type of atom it is. And in hydrogen, for example, you can just have one proton on its own, or you can have a proton and a neutron, or you can even have a proton and two neutrons. Deuterium. Absolutely. Like two with a blocked nose. Wait, two neutrons would be tritium, wouldn't it? Correct. Yes. All right. So you have one on its own hydrogen atom, which is just a proton. Just normal hydrogen. If you have something else stuck to it, a neutron, deuterium. Two particles in the nucleus. Two tritium. But it's still hydrogen. Still hydrogen, right? Add another one in, tritium. Still chemically hydrogen. But it's called tritium. Absolutely. Now the thing is, is that over time, this hydrogen atom sort of doesn't like the neutrons sticking around too much. So over time, it will like kick them out. Sort of be like, yeah, I'm not interested in you. And we know the rate at which it kicks them out. And it's slow. It's slow. Like millions of years slow. Right. And there are a lot of hydrogen atoms in a tiny bit of water. Absolutely. So the thing is, is that when water is formed, there's like a particular fraction of them that have deuterium, tritium. And then you can take a chunk of water and go in to look at how many of them are of each of, you know, normal hydrogen, deuterium and so on. And that can give you a good clue as to how old the water is. And there are a few other versions of this, right? So oxygen also has that same trick, right? You get heavier oxygen with more, more neutrons in it. And what you can do is you can, you can tell when that oxygen was formed as part of the hydrogen bond. And there's particular ratios that sort of match the, the, the ratio that you found in the earliest earth, this sort of, the, this mixture of molten rock and then, and then the big, was it Thea that came in and sort of, yeah, that's the name for the proposed, I think it's quite popular as a theory, the name of the thing that crashed into earth to create the moon Thea. It's probably about the size of Mars. Wow. Yeah. And the moon is a little offshoot, a little splash. Yeah, it's better to the guts of earth than I guess Thea too. Absolutely. So we know that some of the water on earth predates our moon because we know that from, from the oxygen isotopes. Then there's also the ancient water has dissolved noble gases in it. So things like xenon, argon, that kind of thing. And when that water has been locked inside sort of minerals in the mantle, so locked inside the rock kind of underneath the surface of earth, when you analyze that, you can see that there are xenon in there, for example, which has isotopes that you can tell how old is from that. And then finally, zircon crystals, which are by quite a long stretch, my favorite gemstone, zircon forms effectively like a cage, right, as it solidifies into crystal structure and can trap water in there. And so we know there's very, very, very old zircon crystals that have been found in Australia that tell us how old the earth is, 4.3 billion years old. And we know that that rock could only have been formed in the presence of liquid water. So James, there you go. If anyone else out there has questions, please send them to us. You can email us at therestescienceatgolehanger.com. Or you can join our newsletter. And we're going to be back every Thursday with a new edition of Field Notes. And on Tuesday with our normal episode. Yeah, that's right. So we will see you then and there.