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Hannah Fry
This episode is brought to you by Cancer Research uk.
Michael Stevens
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?
Hannah Fry
And this is the reason why there isn't a single cure for cancer. Because, you know, there are more than 200 different types. Each of them have got different distinct characteristics, you know, 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.
Michael Stevens
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.
Hannah Fry
You know, over the last 50 years, the work that this charity has done has help 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.
Michael Stevens
For more information about Cancer Research uk, their research breakthroughs and how you can support them, visit cancerresearchuk.org restoscience this podcast.
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Hannah Fry
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Hannah Fry
Welcome to the rest of science. This is 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.
Michael Stevens
Yeah, it's kind of like show and tell, but for nerds with a capital N. Absolutely.
Hannah Fry
Every week, one of us is gonna bring something strange, something quirky, something interesting, some object or some story. And yeah, we're gonna chat about it together.
Michael Stevens
That's right. And please send us your own weird stories, thought experiments, or questions, because we will address them on this show.
Hannah Fry
What do we got today?
Michael Stevens
All right, it's basically a number of wooden swords on a keychain 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?
Hannah Fry
Eight swords.
Michael Stevens
Eight swords. And they're all what, like, how many centimeters long?
Hannah Fry
Okay, so I would say that they're about 10 centimeters long. They have quite a sharp edge. That's one thing that's noticeable. 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.
Michael Stevens
That's right. And they were made by Creative Crafthouse, 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 gonna tell you all about it.
Hannah Fry
You know what, though? I think. I think people watching will be aware that our delight of nerdy things is absolutely authentic, that we did this in our own time, too. We did this in our own time.
Michael Stevens
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.
Hannah Fry
Okay?
Michael Stevens
Okay. Now pick a number on that sword. Don't tell me what you've picked.
Hannah Fry
I'm gonna pick this one here.
Michael Stevens
Okay, you've got it. So now what I want you to do is 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.
Hannah Fry
Okay, here we go. So we're gonna go circle, square, square, square, square, circle.
Michael Stevens
Okay. Circle, square, square, square, square, circle.
Hannah Fry
Exactly.
Michael Stevens
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 gonna speed this up. Cause it's gonna take me a while to do this in my head. Cause I'm out of practice, but I will come up with it. Hannah?
Hannah Fry
Yes?
Michael Stevens
Did you pick the number 36?
Hannah Fry
I did pick the number 36.
Michael Stevens
I could tell. I could feel it.
Hannah Fry
Hang on, let me just check. Is There any other 36 on here? There is not. You managed to get that exactly correct. How did you do that?
Michael Stevens
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.
Hannah Fry
How did I tell you?
Michael Stevens
In code. In binary. In binary code. So think of it this way. Imagine that the circles are actually zeros and the squares are actually ones. You gave me the digit 3 and the digit 6 because 011 is 3 in binary. Who wants to describe the rules of binary?
Hannah Fry
I think you could do it.
Michael Stevens
Okay, so we use a denary system, a decimal system, where our place values go from ones to tens to one. Hundreds. Right. A three digit number is in the hundreds.
Hannah Fry
And.
Michael Stevens
And with binary, you're only going up by 2 each time. So you'll write down 0 for 0, 1 for 1, 2. Nope, nope. We're not going to do a 2. 2 moves us to another place value. We put a 1 and then a 0. So we have 1, 2, and no ones. 10 is 2 in binary. It's 10 in hours.
Hannah Fry
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. So 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, you know, your first value, it only goes up to one. Just a zero or one, nothing else. Right. It sort of feels like very inefficient. The second value, as you're moving right to left is 2. It can be. If it's 0, it's 0. If it's 1, it's actually a 2.
Michael Stevens
Right?
Hannah Fry
Right. So 11 in binary is 2 plus 1, which is 3.
Michael Stevens
That's right.
Hannah Fry
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 1, 2, 3, 4, 5, 8, 7, 8, 9, 10. You can count to 10 on your fingers.
Michael Stevens
On two hands.
Hannah Fry
On two hands, right? I mean, lame, yeah. Using binary, you can do way more. It's way more efficient way of counting.
Michael Stevens
And if I was doing base 10 on my hand, then I could have the tens, hundreds, thousands, ten, thousands, hundred, thousands just on my hand.
Hannah Fry
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.
Michael Stevens
Okay? So four is one of them.
Hannah Fry
Yeah.
Michael Stevens
And then two of them is 132.
Hannah Fry
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.
Michael Stevens
Is 6, it's 14 and 12 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, 1, 1, 0, is six. So 36.
Hannah Fry
The thing that I love about these, right. So I brought them home, I showed them to my children And. Who are 8 and 6, by the way. Or sorry, they are.
8, 8 and 6.
Michael Stevens
Yeah.
Hannah Fry
And they absolutely love them. I've managed to, using this, Michael, I've managed to trick them into learning binary numbers. Can't get them to do, you know, normal addition in their maths homework, but binary numbers using the schools of truth.
Michael Stevens
It'S fun and it shows them that maths is not like a whodunit where we all know the answers already. That it is a practice, it's like a fun activity, it's a craft.
Hannah Fry
Quite a lot of magic tricks actually have these mathematical elements to them. Right.
Michael Stevens
I know a lot of like ones that use decks of cards.
Hannah Fry
Yeah.
Michael Stevens
I mean, there's the old like 1089 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, you take that number, you reverse it and you add both of those together, you will always get 1,089.
Hannah Fry
Okay.
Michael Stevens
Yeah.
Hannah Fry
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? 1089. Go to the 108th page, go to the ninth word long. Is it this thing here?
Michael Stevens
Hidden. 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 then I'm teaching math.
Hannah Fry
Yeah. Hey, any opportunity to teach math as far as I'm concerned is absolutely fine by me.
Michael Stevens
The Swords of Truth, the original 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.
Hannah Fry
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 maths 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 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 that 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 a hundred 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.
Michael Stevens
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 first, too.
Hannah Fry
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.
Michael Stevens
We've seen this.
Hannah Fry
Right. And 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%.
Michael Stevens
They've lost some of the error correcting ability.
Hannah Fry
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.
Michael Stevens
Right, right. It would have to be a third when you combined with the logo.
Hannah Fry
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 post 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, you know, maybe canceling their flight, changing their. Changing their flight.
Michael Stevens
Put them in a middle seat.
Hannah Fry
Putting them in a middle seat. Exactly. There was one particularly viral case where someone changed a stranger's seat to have them sitting next to the toilet and post it online saying you showed enough pixels to resurrect Jesus, let alone a QR code.
Michael Stevens
Well, look, after the break, we're gonna resurrect Jesus.
Or will we? Probably not, but who knows what we're gonna do? We'll see you after the break.
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To get the best discount off your NordVPN plan, go to nordvpn.com restiscience and I'll link will also give you four extra months on their two year plan. There is no risk either with Norwood's 30 day money back guarantee. The link is in the Podcast Episode Description box. This episode is brought to you by Cancer Research uk. In the uk, nearly one in two people will face cancer in their lifetime. Tell you what though, I've already had it. So between us, we're fine now.
Michael Stevens
I'm safe.
Hannah Fry
That's not how statistics works.
Michael Stevens
Shoot.
Hannah Fry
The question is, could science stop cancer before it begins?
Michael Stevens
And over the past 50 years, Cancer Research UK has helped double cancer survival in the UK. And that's proof of what research can achieve. Like take cervical cancer. Almost every case is caused by hpv, the human papillomavirus. And when scientists uncovered that link, prevention became possible.
Hannah Fry
Indeed it did, by a vaccine. And it's protection that works way before the cancer itself can actually grow. After the vaccine was introduced, cervical cancer rates in England were nearly 90% lower than expected in women in their 20s.
Michael Stevens
And knowing about HPV improves screening and that's vital for diagnosing cervical cancer early.
Hannah Fry
I mean, we're now genuinely at a point where this is a disease that is disappearing in younger women in the uk. This is something that I really hope my daughters will never, never have to deal with.
Michael Stevens
For more information about Cancer Research uk, their research breakthroughs and how you can support them, visit cancerresearchuk.org restiscience.
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Michael Stevens
All right, we're back. I'm gonna 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 gonna 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 gonna search for Fry Squared.
Hannah Fry
Fry R Squared. It's a maths joke, Michael. Come on.
Michael Stevens
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?
Hannah Fry
I didn't choose between that and E to the I. Fry.
Michael Stevens
That's really clever. Oh my gosh. Alright, now here's the proof. Here I am logged in as Vsauce and the subscribe button is ready to be clicked. We're gonna watch it all together. Boom.
Hannah Fry
Is this the point that I should admit that yesterday I realized I also didn't subscribe to Vsauce?
Michael Stevens
Oh, and do you now secretly just.
Hannah Fry
Quickly press the button? I want to see how many people you follow. Hold on, let's have a look.
Michael Stevens
Oh, 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.
Hannah Fry
Hey, look, I think lean into it.
Michael Stevens
I wanna own it. I wanna be like, yeah, you guys keep wondering why. Cause if I unsubscribe, it's like I was embarrassed or they caught me at something.
Hannah Fry
This is true. This is true. I think just. Just keep teasing it and maybe in 2035, release a video on Tony Nude Massage.
Michael Stevens
Y A little collaboration.
Hannah Fry
Hey, why not?
Michael Stevens
Why not? You know, I was thinking during the break that people can be resurrected, but can someone be zur ected?
Because to resurrect means to be resurrected. Like, oh man, I was just zurrected again.
Hannah Fry
It's a bit like the one that people always talk about is whelm, right? Where it's like you can be underwhelmed or overwhelmed, but never whelmed.
Michael Stevens
You can be under the weather, but you can't be over the weather.
Hannah Fry
No.
Michael Stevens
Can you be the weather? I'm gonna try later today after the recording.
Hannah Fry
Be the weather.
Michael Stevens
I'm full of questions, but I want to hear questions from our viewers.
Hannah Fry
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.
Michael Stevens
Fair enough.
Hannah Fry
There are some quite fun ideas. I mean, one of them's got rained diamonds, doesn't it?
Michael Stevens
Yeah. But I'm gonna 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 Earth's. They're like twin planets, Venus and Earth.
Hannah Fry
Yeah.
Michael Stevens
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.
Hannah Fry
I want to build to be hench.
Michael Stevens
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.
Hannah Fry
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.
Michael Stevens
Yeah. I mean, there's a limit to how strong a human can get, but. Yeah. I've heard from people who've done the vomit rocket thing. Have you done that?
Hannah Fry
No, never.
Michael Stevens
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 a free fall orbit around the Earth. Your legs are one of the biggest hindrances you have, really. 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 Earth's came back to Earth, you would be, like, demolishing your shoes. You would. The steps would just crumble at your feet.
Hannah Fry
So wait, I really wanted to understand that comet rocket thing. So wait, when they're pushing off from something, not just, like, kicking in the air, right?
Michael Stevens
Yeah. Kicking in the air does nothing.
Hannah Fry
But if they're pushing off from something, they're suddenly extremely strong.
Michael Stevens
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 a plane. Nope, you're gonna hit the wall.
Hannah Fry
Okay. But the reverse of that, then, is that if you did go and live on Mars, you would feel like a kangaroo.
Michael Stevens
Yes, you would.
Hannah Fry
That would be pretty cool.
Michael Stevens
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.
Hannah Fry
Mm. You gotta actually live there.
Michael Stevens
Yeah.
Hannah Fry
I do always think when people talk about, you know, terraforming Mars, and it's like, oh, all we've got to do is add in some atmosphere, and then. And then, da, da, da, da. It's like, you know, guys, 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 is a little bit of water, and you're fine.
Michael Stevens
But 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. So 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 evaporative cooling is able to do.
Hannah Fry
Oh.
Michael Stevens
And if the wet bulb temperature gets above 95 Fahrenheit or 35 Celsius, that's not that high. That's too high for your body to cool down, and you will die.
Hannah Fry
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.
Michael Stevens
Yeah.
Hannah Fry
If that goes above 35 degrees, you will die.
Michael Stevens
Yeah.
Hannah Fry
Because your body will not be able to maintain body temperature.
Michael Stevens
Evaporative cooling cannot save you.
Hannah Fry
Which of course is how you, how you cool yourself down. Right.
Michael Stevens
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.
Hannah Fry
Wow.
Michael Stevens
Yeah.
Hannah Fry
That's extraordinary.
Michael Stevens
Yeah.
Hannah Fry
What's the hottest place you've ever been?
Michael Stevens
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 like equipment, you could detect a record high number in August.
Hannah Fry
You could hold the record. Is that what you're saying?
Michael Stevens
Yeah, right, right, right, right. So I've always wanted to do that as a YouTube video. I'm like, just in August, like 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.
Hannah Fry
This does feel like a quite a high risk way to get a, get a record, Michael.
Michael Stevens
It's worth it, though.
Hannah Fry
Died doing what he loves, setting records.
Michael Stevens
I wouldn't die, but if I did, think about how many views the video would give.
Hannah Fry
It's all content, baby.
Michael Stevens
Yeah. Yeah.
Hannah Fry
Tell you where. I wouldn't want to live in the solar system. I think Triton is the. Is the absolute worst place imaginable.
Michael Stevens
Triton is a moon of Neptune that's far away, super cold.
Hannah Fry
It's got geysers that run on liquid nitrogen, you know, spouting out minus 230 fountains into this, into the sky. Also it orbits backwards. Oh, yeah. Just to really mess with you.
Michael Stevens
I think Triton would be beautiful though. Doesn't it possibly have oceans of like methane or something?
Hannah Fry
Yeah, I think so. I think so.
Michael Stevens
That could be cool.
Hannah Fry
Oh, no, wait, isn't methane on Titan. That's the one with the methane lakes. I think there the atmosphere is so dense that you could potentially fly.
Michael Stevens
Yes, yes.
Hannah Fry
I've heard this by flapping your arms.
Michael Stevens
Because the atmosphere is very thin, but the gravity is so low that human arms, they've calculated, could flap and you could fly.
Hannah Fry
That would be pretty cool.
Michael Stevens
That would be very cool.
Hannah Fry
I mean, it would Stink.
Michael Stevens
Okay. You're not gonna take a helmet off. I think you're just gonna 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.
Hannah Fry
Titan. I think on Titan, I mean, look, they all end up being the same, don't they, really?
Michael Stevens
Titan, Titan, Triton, the moon.
How funny that the moon is just called the moon.
Hannah Fry
Yeah, it just.
Michael Stevens
It doesn't have a. Does it have a name in any other languages?
Hannah Fry
I don't know.
Michael Stevens
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.
Hannah Fry
Maybe the Martians call it something different.
Michael Stevens
Oh, yeah.
Hannah Fry
You know that thing about life on Mars, Right?
Michael Stevens
Which thing?
Hannah Fry
I mean, just the idea of whether.
Michael Stevens
It'S there or was there. Yeah.
Hannah Fry
I got to go and see Curiosity before it launched.
Michael Stevens
Oh, you did?
Hannah Fry
I did. It was amazing.
Michael Stevens
That is so cool.
Hannah Fry
I wasn't allowed in the vacuum lockdown.
Michael Stevens
So you weren't able to touch it?
Hannah Fry
I wasn't able to touch it. I mean, they're extremely careful about who touches it. But I gotta 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. A couple of things that were really amazing about it when they're checking for life on Mars. The idea is that 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 is 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. Which has had land come in from all across the region. Great.
Michael Stevens
Yeah.
Hannah Fry
Which is just really, really smart. Right. But the thing that is I found so amazing about Curiosity in this process to analyze whether there's life or 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 ROC kind of puts this. These samples in these like, basically test tubes and then chucks them on the ground.
Michael Stevens
Yeah.
Hannah Fry
Just litters the surface of Mars with these, like, scientific samples waiting for us.
Michael Stevens
To do a mission to pick them up.
Hannah Fry
Yeah. And then it's like, well, have you got. Do you know how you're going to do that? And they're like, no, no, no idea yet. You know, sort of many billions of pounds later.
Michael Stevens
That's so cool. So. So, yeah, because I hadn't heard any results from it. But it's because we, Curiosity didn't analyze the samples.
Hannah Fry
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, 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 a Sharpie just like written their child's name on it or whatever. And they had 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.
Michael Stevens
Soldering. We like our silent Ls.
Hannah Fry
Is that what we call it 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.
Michael Stevens
Yep.
Hannah Fry
This is not coming from you as the engineer.
Michael Stevens
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 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.
Hannah Fry
Yeah. And once there is, then maybe the moon will get a proper name.
Michael Stevens
Moony.
Hannah Fry
Moony McMoonface.
Michael Stevens
Mooney McMoonface. If the Brits have a say, the Americans would probably call it something like freedom rock the 51st state.
Hannah Fry
Amazing.
Michael Stevens
Would be pretty American.
Hannah Fry
That would Be pretty American. I think they would call it something like the great American Skyball.
Michael Stevens
Skyball New Texas.
This episode is brought to you by Cancer Research uk.
Hannah Fry
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.
Michael Stevens
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 Mutografts. They looked at 7,800 cancer samples and they found that there's this thing that they're calling dark carcinogens.
Hannah Fry
Go on.
Michael Stevens
Okay. These are molecules that cause cancer without leaving any scar on DNA at all.
Hannah Fry
Right. I mean, that's completely against the previous theories there.
Michael Stevens
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 like, stay dormant.
Hannah Fry
Okay, so the mutated cells are still there, but it's like they need a little friend to help them.
Michael Stevens
That's right.
Hannah Fry
It's just an evil friend who causes cancer.
Michael Stevens
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.
Hannah Fry
Like elephants, for example.
Michael Stevens
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.
Hannah Fry
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.
Michael Stevens
That's right, it does. And it also leads us perhaps towards better ways of preventing cancer in the first place?
Hannah Fry
Because you can target the promoters, not just the cells themselves.
Michael Stevens
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.
Hannah Fry
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 onto. 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.
Michael Stevens
That's exactly right. And for more information about Cancer Research uk, their research breakthroughs and how you can support them, visit cancerresearchuk.org restiscience.
All right, here's a question from James. He asked, I'm curious to know how we determine the age of water on Earth.
Hannah Fry
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.
Michael Stevens
How do you know?
Hannah Fry
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 the 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.
Michael Stevens
Deuterium.
Hannah Fry
Absolutely. Like two with a blocked nose.
Michael Stevens
Wait, two neutrons would be tritium, wouldn't it?
Hannah Fry
Correct. Yes.
Michael Stevens
All right, so you have one on.
Hannah Fry
Its own hydrogen atom, which is just.
Michael Stevens
A proton, just normal hydrogen.
Hannah Fry
If you have something else stuck to it, a neutron. Deuterium.
Michael Stevens
Deuterium. Two particles in the nucleus, two truia. But it's still hydrogen. Still hydrogen.
Hannah Fry
Right. Add another one in tritium.
Michael Stevens
Still chemically hydrogen.
Hannah Fry
Still chemically hydrogen.
Michael Stevens
Still tritium.
Hannah Fry
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. So it'd be like, get out of here, I'm not interested in you. And we know the rate at which it kicks them out.
Michael Stevens
And it's slow.
Hannah Fry
It's slow. Like millions of years slow.
Michael Stevens
Right. And there are a lot of hydrogen atoms in a tiny bit of water.
Hannah Fry
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 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 ratio that you found in the earliest Earth. The sort of this mixture of molten rock and. And then the big. Was it Theia that came in and sort of.
Michael Stevens
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. Theia. It was probably about the size of Mars.
Hannah Fry
Wow.
Michael Stevens
Yeah.
Hannah Fry
And the moon is just a little offshoot, a little splash.
Michael Stevens
Yeah, it's made out of the guts of Earth and I guess theia too.
Hannah Fry
Absolutely. So we know that some of the water on Earth predates our moon because you know that 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 in. 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. 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. 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. 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.
Michael Stevens
So, James, there you go. If anyone else out there has questions, please send them to us. You can email us at. The rest is scienceolehanger.com or you can join our newsletter.
Hannah Fry
And we're gonna be back every Thursday with a new edition of Field Notes and on Tuesday with our normal episode.
Michael Stevens
Yeah, that's right. So we will see you then and there.
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Date: December 11, 2025
Hosts: Professor Hannah Fry & Michael Stevens (Vsauce)
This episode of The Rest Is Science explores the boundary between mathematics and magic, diving into a clever mathematical trick known as the "Swords of Truth." Hosts Hannah Fry and Michael Stevens unpick its mathematical foundation—binary code—demonstrating how math powers seemingly magical feats. Along the way, they riff about math education, magic’s role in learning, and field listener questions, blending scientific wonder, humor, and personal anecdotes throughout.
[03:30 – 06:07]
Michael introduces the "Swords of Truth," eight wooden keychain swords, each engraved with six two-digit numbers, some circled and some squared.
Michael Stevens: "Each one has six two digit numbers on it. And some of the numbers are surrounded by a square and some by a circle." [03:31]
Hannah describes the physical attributes and tactile sensation of the swords.
Hannah Fry: "They're about 10 centimeters long. They have quite a sharp edge...engraved numbers along the side." [03:49]
Michael walks Hannah (and listeners) through the magic trick: She chooses a sword, silently picks a number, and then verbally reads the sequence of shapes (saying the opposite of the actual shape at her chosen number).
Michael deduces her number (36) simply from the shapes recited, explaining that the trick works because the squares and circles encode numbers in binary.
Michael Stevens: "Imagine that the circles are actually zeros and the squares are actually ones. You gave me the digit 3 and the digit 6 because 011 is 3 in binary." [06:08]
[06:29 – 09:06]
Michael and Hannah break down how binary works, using hands and everyday examples for clarity.
Hannah Fry: “Using binary, you can do way more [than base ten]. It’s way more efficient.” [08:01] Michael Stevens: "So 11 in binary is 2 plus 1, which is 3." [07:36]
Hannah jokes about "error correcting codes" and their ubiquity in modern life.
Hannah Fry: “Anytime someone flips you the double bird…just think 132, 132.” [08:16]
Memorable Moment:
Michael and Hannah delight in how magic tricks can serve as Trojan horses for teaching math to children.
Hannah Fry: "I've managed to trick them into learning binary numbers. Can't get them to do normal addition...but binary numbers using the Swords of Truth..." [09:18]
[09:41 – 11:13]
Discussion moves to classic math-based magic tricks, like "the 1089 trick,” wherein simple arithmetic always leads to the same result, regardless of the starting number.
Michael Stevens: "If you take a three digit number whose first and last digits are different...you will always get 1,089." [09:51]
Michael emphasizes the value of these tricks—no sleight of hand, pure mathematical certainty.
Michael Stevens: "Those are my favorite kind of tricks because they work all the time...then I'm teaching math." [10:33]
The origin of the Swords of Truth is attributed to Alex Elmsley, a mathematician and magician.
Michael Stevens: "The original design was created by an inventor named Alex Elmsley..." [10:55]
[11:13 – 14:16]
Hannah likens the clues in the Swords of Truth to error-correcting codes, like those found in barcodes and QR codes that can "fill in" missing bits if part is destroyed.
Hannah Fry: "You don't need to have a perfect reading of the entire barcode...because what it has is things called parity checks." [11:43]
Michael and Hannah discuss real-world implications: you can block up to a third of a QR code and still use it—unless companies have put a logo over the important part. This has occasionally led to personal information being leaked online, like with boarding passes.
Hannah Fry: "There was one particularly viral case where someone changed a stranger's seat to have them sitting next to the toilet..." [13:59]
[20:27 – 27:25]
Michael Stevens: "Venus...on a blimp up in its atmosphere...the atmospheric pressure is safe and gravity would be, like, pretty similar to Earth's." [20:47]
Michael Stevens: "They can't control how powerful their legs are...they just keep moving." [22:49]
Hannah Fry: "If you did go and live on Mars, you would feel like a kangaroo." [23:14]
[23:45 – 25:44]
Michael and Hannah describe “wet bulb temperature” as the critical limit for human survival; above 35°C (95°F) with high humidity, humans cannot cool down and will die without artificial cooling.
Michael Stevens: "If the wet bulb temperature gets above 95 Fahrenheit or 35 Celsius...that's too high for your body to cool down, and you will die." [24:13] Hannah Fry: "That's extraordinary." [25:12]
Hottest place Michael’s experienced? Death Valley—a possible YouTube experiment is floated.
Michael Stevens: "I've always wanted to do that as a YouTube video...you can record the hottest temperature ever recorded." [25:33]
[26:03 – 27:30]
Hannah nominates Triton (Neptune’s moon) as the worst place to live: it’s cold, has nitrogen geysers, and orbits backward.
Hannah Fry: "Triton is the absolute worst place imaginable." [26:10]
Michael and Hannah switch between jovial banter and genuine wonder about planetary atmospheres, methane lakes, and whether you could fly on Titan by flapping your arms.
Hannah Fry: "I've heard this...you could potentially fly just by flapping your arms." [26:49]
[28:00 – 31:34]
Hannah recounts visiting NASA’s Curiosity rover, revealing its ingenious sample collection method: take rock samples, seal them, and drop them on Mars for future missions to collect.
Hannah Fry: "Curiosity...just litters the surface of Mars with these scientific samples waiting for us to do a mission to pick them up." [29:35]
Discussion of space ethics: stringent rules prevent engineers from marking or contaminating rovers; the mission belongs to all of humanity.
Michael Stevens: “The anonymity of the individual, but the power of the species. This is from humanity...but we'll put an American flag on it.” [30:48]
[32:18 – 34:47]
Michael Stevens: “These are molecules that cause cancer without leaving any scar on DNA at all.” [33:01]
Hannah Fry: “So the mutated cells are still there, but it’s like they need a little friend to help them. It’s just an evil friend who causes cancer.” [33:27]
[35:24 – 39:20]
Hannah Fry: “There's like a particular fraction...that can give you a good clue as to how old the water is.” [36:59]
Hannah Fry: “Zircon forms, effectively like a cage...and trap water in there.” [39:00]
Binary Magic:
"You told me. I knew you chose 36 because you told me. In code. In binary. In binary code." — Michael Stevens [06:07]
Magic’s Role in Learning:
"I've managed to trick them into learning binary numbers. Can't get them to do, you know, normal addition in their maths homework, but binary numbers using the Swords of Truth." — Hannah Fry [09:18]
Teaching with Magic:
"Those are my favorite kind of tricks because they work all the time...then I'm teaching math." — Michael Stevens [10:49]
On QR Code Security:
"You showed enough pixels to resurrect Jesus, let alone a QR code." — [Quoted anecdote, Hannah Fry] [14:08]
Space Ethics:
"The anonymity of the individual, but the power of the species. This is from humanity, but we'll put an American flag on it." — Michael Stevens [30:48]
Cancer Science Breakthrough:
"These are molecules that cause cancer without leaving any scar on DNA at all.” — Michael Stevens [33:01]
Playful, inquisitive, and deeply nerdy—Michael and Hannah blend approachable STEM explanations with wry humor and genuine delight. Quotes and stories are laced with self-deprecating jokes, spontaneous tangents, and a continual sense of scientific curiosity. Listeners are encouraged to join the fun and challenge what seems familiar, making the science feel both magical and accessible.
A quintessential Rest Is Science episode, mixing mathematical sleight of hand with everyday science, built around the infectious joy of learning and delightful intellectual digressions. Perfect for anyone curious about the subtle magic hidden within mathematics, logic, and the universe itself.